NBS SPECIAL PUBLICATION

U.S. DEPARTMENT OF COMMERCE/National Bureau of Standards

Oil and Gas

Supply Modeling
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NATIONAL BURMAU

Of 8TANDAXDI

UBBABT

Oil and Gas Supply Modeling Sr^^-

Proceedings of a Symposium

held at the Department of Commerce,

Washington, DC

June 18-20, 1980

Edited by:

Saul I. Gass

National Engineering Laboratory

National Bureau of Standards

Washington, DC 20234

Sponsored by: Energy Information Administration

U.S. Department ol Energy Washington, DC 20461 and

Operations Research Division Center lor Applied Mathematics

National Measurement Laboratory

Washington. DC 20234

U.S. Department of Commerce, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued May 1 982
Library of Congress Catalog Card Number: 82-600508

National Bureau of Standards Special Publication 631

Nat. Bur. Stand. (U.S.), Spec. Publ. 631, 778 pages (May 1982) CODEN: XNBSAV

Papers in this volume, except those by National Bureau of

Standards authors, have not been edited or altered by the National

Bureau of Standards. Opinions expressed in non-NBS papers are those of the authors, and not necessarily those of the National

Bureau of Standards. Non-NBS authors are solely responsible for the content and quality of their submissions.

The mention of trade names in the volume is in no sense an endorsement or recommendation by the National Bureau of

Standards.

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1982
ABSTRACT

The symposium on Oil and Gas Supply Modeling, held at the Department of

Commerce, Washington, DC (June 18-20, 1980), was funded by the Energy Information Administration of the Department of Energy and co-sponsored by the

National Bureau of Standards' Operations Research Division. The symposium was organized to be a forum in which the theoretical and applied state-of-the-art

of oil and gas supply models could be presented and discussed. Speakers

addressed the following areas: the realities of oil and gas supply, prediction of oil and gas production, problems in oil and gas modeling, resource appraisal procedures, forecasting field size and production, investment and

production strategies, estimating cost and production schedules for undiscovered fields, production regulations, resource data, sensitivity analysis of

forecasts, econometric analysis of resource depletion, oil and gas finding

rates, and various models of oil and gas supply. This volume documents the

proceedings (papers and discussion) of the symposium.

Keywords: cost estimation; data collection; economic analysis; energy models;

estimation; exploration; finding rates; forecasting; gas supply models;

investment strategies; oil supply models; resource appraisal; sensitivity

analysis.

iii

CONTENTS

Goals and Purposes of the Energy Information Administration/

National Bureau of Standards Symposium on Oil and Gas Supply

Modeling — Frederic H. Murphy 1

Oil and Gas Supply: Public Perception, Modeler's

Abstraction, and Geologic Reality — John J. Schanz, Jr 7

Techniques of Prediction As Applied to the Production of

Oil and Gas — M. King Hubbert 16

Current Problems in Oil and Gas Modeling —

William C. Stitt 142

The Evolution in the Development of Petroleum Resource

Appraisal Procedures in the U.S. Geological Survey —

Betty M. Miller 171

Forecasting Future Oil Field Sizes Through Statistical

Analysis of Historical Changes in Oil Field Populations —

Michel Ducastaing and John W. Harbaugh 200

Issues Past and Present in Modeling Oil and Gas Supply —

Gordon M. Kaufman 2-57

Analysis of Investment and Production Strategies for

a Petroleum Reservoir — James W. McFarland, Anil Aggarwal,

Michael S. Parks and Leon Lasdon 272

A Methodology for Estimating Oil and Gas Production

Schedules for Undiscovered Fields — John H. Wood 295

Some Modern Notions on Oil and Gas Reservoir Production

-Regulation — John Lohrenz and Ellis A. Monash 310

Historical Growth of Estimates of Oil- and Gas-Field

Sizes — David H. Root 350

The Economic Accounts of the Resource Firm —

David Nissen 369

Gulf Coast Undiscovered Resource Data Collection System —

Richard Zaffarano 411

A Methodology for Estimating Cost of Finding, Developing,

and Producing Undiscovered Resources —

Thomas M. Garland and John H. Wood 420

The Outlook for Oil Exploration and Development —

T. R. Eck 432

Models, Understanding and Reliable Forecasts —

James B. Ramsey 445

v
The Regulatory Framework in Oil and Gas Supply Modeling —

Stephen L. McDonald 456

Firm Size and Performance in the Search for Petroleum —

L. J. Drew and E. D. Attanasi 466

Sensitivity Analysis of Forecasts for Midterm Domestic

Oil and Gas Supply — Carl M. Harris 490

Natural Resource Decisions Involving Uncertainty —

S. D. Deshmukh 535

The Depletion of U.S. Petroleum Resources:

Econometric Evidence — Dennis Epple and Lars Hansen 553

Oil and Gas Finding Rates in Projection of Future

Production — W. L. Fisher 564

Issues in Forecasting Conventional Oil and Gas Production

Richard P. O'Neill 581

Oil/Gas Supply Modeling Considerations in Long-Range

Forecasting — Ellen A. Cherniavsky 630

An Integrated Evaluation Model of Domestic Crude Oil and

Natural Gas Supply — R. Ciliano and W. J. Hery 647

An Evaluation of the Alaskan Hydrocarbon Supply Model —

Frederic Murphy and William Trapmann 661

A Prospect Specific Simulation Model of Oil and Gas

Exploration in the Outer Continental Shelf: Methodology

J. P. Brashear, F. Morra, C. Everett, F. H. Murphy,

W. Hery, and R. Ciliano 688

Concluding Session 718

Appendix: Oil and Gas Resources - Welcome to Uncertainty —

John J. Schanz, Jr 739

Symposium Program and Attendees 756

vi
Goals and Purposes of the

Energy Information Administration/

National Bureau of Standards

Symposium on Oil and Gas Suppply Modeling

Frederic H. Murphy

Energy Information Administration

Department of Energy

This conference is convened to establish the state-of-the-art in

oil and gas supply modeling: the initial step in improving the

methodology behind the Energy Information Administration (EIA)

projections. Also, to elicit critical comment on work performed

within EIA, there are presentations of the EIA models. The conference concludes with a panel discussion on the directions

needed for improving EIA forecasts

The EIA is responsible for producing forecasts of the state of

energy markets from now through the early part of the next

century. These forecasts are widely distributed to inform the

public about likely future energy costs, import levels, and

domestic production and consumption rates.

Also, EIA is of service to the executive and legislative branches

of government, providing independent analyses on the effects of

energy programs. These analyses start with the Annual Report

forecasts of energy supplies, demand, imports and prices with a

representation of current programs. Then the models are altered

to characterize the impacts of new programs within a new set of

forecasts

There have been significant advances in understanding oil and

gas markets in the past several years. The most important

advances have been in learning the right questions. When the

government entered the energy forecasting business seriously,

the questions about oil and gas were not well formed. One of

the important goals of the analysis process is to try to make

more precise the kinds of questions that the general public

and policymakers ask about oil and gas. This function is aided

by model building. Having the precise mathematical relationships of a model structures what the analyst can tell the

customer. By the same token, a better understanding of the

questions addressed comes from the debates on energy programs.

This leads to alternative model formulations.

To understand what is now the state-of-the art, it is useful

to see how perceptions of the issues evolved. The early questions were simpler than the current questions, allowing for

smaller models to be effective. After the 1973-1974 oil

embargo, the prominent questions were "Is there enough oil?"

and "When would the Organization of Petroleum Exporting

Countries (OPEC) cartel fall apart?" Except for pronouncements

about the evils and unfairness of cartel pricing, little was

1
said about the latter question except to state that all other

commodity cartels had collapsed within a few years. This conference contributes to the international discussion only

through the equation that imports equal consumption minus

domestic production.

The first question, "Is there enough oil?" is imprecise.

Efforts to turn it into a well-formulated statement led to

the first modeling efforts. Why it is not precise is that it

is a statement about supply while implicitly addressing

supply and demand. If people never consumed any oil, there

would be enough forever. What has now become abundantly

clear is that there is not enough oil at prices people are

willing to pay for the quantity they want to consume.

In a country where economic growth is matched by increased

consumption of resources, one can alter "Is there enough

oil?" to "When will oil production stop increasing?" A

decline in production has always been inevitable because

the resource base is finite. However, it was not until the

work of M. King Hubbert that the point was clear. His

remarkably accurate forecast of when production would start

to decline is an example of answering a well-formulated

question with a simple model that provided some insights.

The answers to the early questions essentially said that there

is an energy problem and there will be an inevitable transition away from oil and gas. Given that the state of knowledge

had gotten this far, the question became "How much oil is

there?" Now, this is not a very precise statement either; it

cost money to produce oil and gas, so there is a supply

response to price.

The United States Geological Survey Circular 725 addressed the

less precise question of how much oil there is while skirting

the issue of price. It essentially gave the resource parameter for the Hubbert model, which also does not consider price.

Because the bulk of the oil discovered in a region is in very

large fields, the supply response to price through new discoveries in that region, assuming uniform drilling costs, is

not very great in terms of total resources for the region.

This truth about the micro-level discovery process was extrapolated to the larger supply picture in Circular 725 by

describing the resources using the imprecise notion of current

economics. The standard diagram for representing petroleum

resource classification (Figure 1) emphasizes this viewpoint

by the sharp line dividing economic and subeconomic.

2
Figure 1. U.S. RESOURCE BASE

Identified

Demonstrated

1

inferred

Undiscovered

Economic

SubEconomic

RESERV

RES

ES

1

0 URGES

i

J

o

bio a>

«*— o

°i

CO O

o

Increasing degree of geologic assurance

Diagrammatic representation of petroleum resource

classification by the U. S. Geological Survey and

the U. S. Bureau of Mines.

3
So, the correct characterization of the supply question is:

"How much oil is economical to produce for a given range of

prices?" It is convenient to address this subject in three

parts, corresponding to this diagram. This partitioning

leads to models, or modeling systems, with three components.

For measured reserves, reservoir models can be used to

estimate what is producible and how much oil can be produced

at various prices. Next, there is the growth in reserves that

comes from people learning while they are operating in existing

fields. This constitutes the indicated and inferred reserves.

As of yet, no one has studied the supply response to price for

these reserves. The current modeling approaches use timeseries analysis.

The third price of the partition is production from undiscovered resources. This is one of the areas where it is agreed

that there is a supply response to price. The shape of the

supply curve depends on the nature of what is left to be found

and the character of the costs. If one uses the lognormal,

field-size distribution model of Kaufmann or an Arps and Roberts

model for a play, the total supply response to higher prices is

not that great because the bulk of the oil is in a few, big

pools that are found early. However, when one aggregates across

plays, the supply response to price in a region is more elastic.

This is a consequence of non-homogeneity across plays. In

addition, for drilling in frontier areas, costs are high. Consequently, there are large fields that become economic only after

prices have risen beyond what is necessary for finding the bulk

of the resource in the easily explored areas.

The partition of the problem of reestimating supply curves for

oil and gas into three prices has become more than an analytical

device. Much of Federal policy is based on the nature of the

supply repsonse to prices. If a supply curve is very steep, as

with curve A in Figure 2, Congress might not allow the price to

rise. There is not much of a supply response to price anyway,

Congress can then either pass the lower costs onto consumer or

use excise taxes to capture the profits for government. If

there is more curvature, as in curve B, then the decision to

control prices, keeping the extra profit, is more debatable

because of the foregone production. When the supply curve gets

very elastic, as in C, it does not appear to make any sense to

control prices because the supply response is large, the "excess"

profits are not as great, and the United States could achieve

import independence

So, not only is the economic quantity of oil and gas of interest,

by the supply elasticity is as well. Even further, not only is

the aggregate supply elasticity politically important, but also

the supply elasticities for differing sources. This is shown in

the legislation affecting oil and gas prices. Congress has imposed

controls on what is perceived to be the less elastic portion of the

supply curve and has allowed higher prices, or has decontrolled,

4
Figure 2 . A Range of Supply Curve Shapes
the sources of supply that are more elastic. This presents a whole new category of more complex issues to analysts and their

models. No longer are the explicit models of the anlysts, or

the mental models of the policymaker, used just to understand

the domestic supply position; they are used as an aid in determining who is paid what for their oil.

The discussion so far has emphasized the static aspect of the

problem how many resources become economic with higher prices.

The next question, first addressed by Hubbert, is "When will

the resources be produced?" The timing of the development of

these resources is important for determining when new technologies should be commercialized and how fast the country can

achieve a modicum of energy independence.

The extent to which monopoly power exists affects the timing

through the withholding of economic production. This

issue is not addressed here because oil producers outside of

OPEC are part of what is known as the competitive fringe, and

the competitiveness of natural gas producers has been explored

by the Federal Trade Commission in "The Economic Structure and

Behavior in the Natural Gas Production Industry," February

1979. There is, however, a kind of withholding of production

that could occur even if markets are competitive. With a

depletable resource, a producer may hold on to it, rather than

produce it, even if the cost of producing is less than the

price. Knowing that the resource will eventually be depleted

and its price will rise, producers can wait for the higher

prices. This kind of withholding is not an example of monopoly

power

The last, and most complex, question addressed in the conference

is "What are the impacts of all the Federal and State regulations

on the industry in distorting the behavior of the participants

by altering their incentives?" This is an important question

because of the extent to which the oil and gas industry is

regulated depends on those regulations. EIA has produced a study

called Energy Programs, Energy Markets that broadly addresses

some of these questions for all major fuels.

These last two issues of the timing of development and the effects

of regulations are treated by economics, while the earlier issues

associated with the static, ultimate recovery supply curve have

been addressed by geologists and engineers. So, there is a range

of questions that involves the work of geologist through the work

of economists. This leads to the main purpose of this conference:

to assemble the economists, operations researchers, and geologists in a room to talk about the aspect of questions on oil and

gas supply they treat most effectively.

6
OIL AND GAS STTPPLY: PUBLIC! PERCEPTION, MODELER 'S ABSTRACTION, AND GEOLOGIC REALITY

John J. Scbanz, Jr.

Senior Specialist

Congressional Research Service

Library of Congress

As some of you may recall, two years ago an article entitled "Oil and Gas

Resources - Welcome to Uncertainty" appeared in RFF's publication Resources .

That was a "plain language" effort to present: the physical character of the

search for and production of fluid hydrocarbons; the unavoidable narrowness of our approaches to examining oil and gas supply; and, the inescapable mystery of

exactly how much oil and gas nature has to offer. This reflected what we had

observed over the previous three years in trying to achieve a better public and

governmental understanding of oil and gas resources.

Since a non-modeler has little in the way of technical expertise to offer

a symposium of this type, your Chairman was kind enough to suggest that I as a consumer of vour product might open the program with a few remarks. In effect

I would like to re-examine "Welcome to Uncertainty" and comment on how much we have progressed in the past several years, and where shortcomings are still to

be found. Perhaps I can be a bit challenging and provocative in the process.

As mv title suggests, three viewpoints will be involved.

1) What is the current oublic perception of the oil and supply

situation? "ere we will regard the Dublic as anvone who is

not a professional supplv analvst.

2) How well is the modeler in his abstractions or simulations

capturing the essential ingredients in oil and gas supplv,

and, perhaps more important, how are those factors changing?

3) How much is the inescapable uncertainty about the ultimately

retrievable quantity of oil and gas still hamoering our work?

Public perception of oil and gas supplv has gone through a metamorphsis

over the past 6 years. In 1974, I arrived in Washington at the peak of concern

over "how much is there". Resource estimates based on volumetric calculations

vied against engineering projections in grabbing headlines in the Post or the

Times. Each little divergence in someone's estimate of proved reserves on a lease or in the nation's reserves fueled the fire of public interest in the

quest for who was telling the "Big Lie". The public was not yet convinced that

there wasn't a lot down there, and felt "they" iust weren't telling us how much.

1 Schanz, John J., Jr., "Oil and Gas Resource: Welcome to Uncertainty"

Resources , Resources for the Future, Washington, March 1978. This article

is reproduced in the Appendix.

7
^ventuallv this led to the transfer of the proved reserve calculations to

the federal government , and the resulting; expensive and time consuming process

of survev design, verification, and validation. It is of course somewhat

disturbing to me that we have spent so much time on ohtaining numbers that, while

needed, have limited utilitv. Now that we have a public audit of proved reserves

no one really seems too terribly interested. I doubt if a comparison of EIA

proved reserves data with the old API/AGA numbers qualifies as the latest media

sensation. Concurrently, we have waited five years for a contemporary assessment

by the U.S. Geological Survey of the undiscovered oil and gas resources of the

United States. We are akin to the driver in the desert who keeps eyeing his

gas gauge when the real question is where is the next gas station.

This early concern over "how much", next shifted to a brief period of

"they know where it is but won't drill". This involved public discussion of

how much encouragement the driller needs, if any, to drill exploratory wells.

And after oil and gas has been located, how much oil needs to be there to make

it worth while to develop. Perhaps as a result of this, some of the public

began to understand that "there are prospects- and then there are prospects".

Some properties make the drilling agenda, some don't; and some won't make it

unless the price goes up. Also, it became apparent that not every discovery

was worth producing. The big hang-up was that not everyone could agree on how

much had been found. Ouite naturally the royalty interest, in many cases this was the government, was somewhat more bullish than the working interest.

The latest episode appeared about 1978. This was the period of "thev are nroducing, but not as fast as they could", stimulated by the need for natural

gas. This led to an examination of how manv holes should vou drill, and how

fast can vou "let 'er rip" thereafter. The educational orocess of learning

about the time configuration of investments and returns, recovery efficiencies,

abandonment decisions, nav-out periods, and the flexibility or lack of flexibility

in reservoir production schemes, became essential to consideration of proper

diligence in the production of oil and gas from leases. Obviously this aspect

of improving public perception was not a head-line grabber. But it was nonethe-less an important aspect of public education. It is still going on. Adequate understanding is made difficult by the fact that an optimum development

plan for the public may not necessarily coincide with that of the lease operator.

This seems to be where we are at the moment. I think in general we have a far more sophisticated public than six years ago - particularly among those

that are close to the situation, as many public officials now have to be. I suspect that the man-on-the-street ' s perception is one of finally accepting

that what is left to be found domestically will certainly not solve our problem.

Unfortunately we may now find ourselves in the position of educational overkill.

The apparent price has gone up dramatically and extensive drilling is reported,

but we still seem to be no better off. This has led us away from the old "when

the price goes up I bet they'll know where the oil is", to the view that "no

matter how much the price goes up we won't find any more oil". As an economist

I am intrigued that both arguments continue to suggest an increase in the price

is not worthwhile.

8
This is a serious problem, because it threatens the necessary effort

reauired to find and produce the remaining oil and gas resources of the TTnited

States. Regardless of iudgments as to how much is left - 50 or 150 billion

barrels, 700 or 1200 trillion cubic feet, that is still a lot of energy. We

have left to produce more than the original endowment of many nations of the

world. If the nation persists in this "our glass if half empty" viewpoint, or making ^utile comparisons with how much Saudi Arabia has compared to the U.S.,

we could very well end up not using what we still have at our disposal. While

it is generally accepted that, short of dramatic technical change, the quantity

left at the bottom of the glass is more expensive than the first half we consumed,

oil and gas are still two of the better energy buys in town.

It appears that the next step in the continuing education of the public is

for the modelers to show what is involved in emptying the last half of the

glass. But most importantly, that the higher costs involved must be compared

to the energy alternatives of today. The ghost-of-Christmas-past must be put

to rest permanently. At issue is whether the pace of future depletion will be

determined by past, present, or future costs and prices.

Let us now turn to the state-of-the art in our attempts to portray adequately the future response of oil and gas versus price. In 1978 in "Uncertainty"

we called attention to the fundamental tunnel-vision of geologic appraisals,

engineering proiections, or econometric models. This was done in a kindly

fashion, because we recognized those efforts were constructed for certain

purposes and were limited by design. We can never ^ail to recognize that an

oil and gas supply model, as a simplification, cannot capture all of the nuances

and complexities of real world. If it did, we wouldn't need it, since we would

be right back where we started, without repeating all of the critique of

several vears ago, we said then, and can still sav, that models have design

limits. It is essential that the modeler clearly restrain the user by "redlining" the model's guages. The modeler must make certain that he, as well as the user, knows what has been ignored, assumed away, or circumnavigated in

accomplishing his purpose. I always like to be convinced that these things do

not matter in achieving that purpose so long as the machine is not pushed

beyond the red lines.

Looking back a few years ago, and comparing what I observed then with what

I expect to hear in this symposium, I think we are finally beginning to recognize the need in many of our models to separate exploration from production,

and that there are different kinds of explorers. Too many economic modelers in

the past could not unlearn their first economic lessons of bushels of wheat

versus price, or later on about manufacturing production functions. Exploration

is a percursor of production. Its behavior is not inconsistent with economic

theory, but allowing ourselves to be too quickly satisfied because the model

appears to be consistent with the economic theory of price behavior and profit

maximization can be a deception.

We have made progress in our oil and gas supply models bv including the

exploration sector and building in constraints. But I would suggest we should

not become too smug. Some may be getting good initial responses in testing

their model but not recognizing good results for the wrong reasons. While a

9
economist can always live with a "catch-all" expectation that Drice in the

Ions run captures all that is essential, T am not truly satisfied.

It is useful for everyone to occasionally go back and reread Grayson's

Decisions Under Uncertainty . 1 It was very much a part of getting our present

efforts started. Before he got involved in decision - trees and probabilities

he described how in talking with oil managers he was able to identify the key

factors in their decision process. We should remember the trio of; "goals",

"economics", and "geology". I am quite content with development models built on a foundation of economics, because that is the way development occurs. But

I continue to question a frontier exploration model that is solely profit-maximizing. If the modeler tells me that's the best he can do - so be it. I will

accept that his model may be useful, but it is not an adequate representation

of this key step in oil supply.

I focus on this because my own experience suggests that there are important

non-price, non-profit factors in the exploration decision process. Given the

fact that there is no reassuring knowledge of what is actually to be found in

completely undrilled regions, the decision cannot be as calculating as some models may suggest - even given our growing sophistication in exploration technology and subiective, probabilistic analyses. As large enterprises manage

large cash flows the decision process is not necessarily one of settling on the

best menu of profit-maximizing proiects. If this was the case, mucb of our ex- ploration should he accused of ignoring opportunity costs - which an economic

model sbould not tolerate. There is an ever present compulsion to explore be- cause it needs to be done, and the discovery of physical oil is pursued by some with a degree of disregard about its relative profitability.

I would suggest that our exploration models can not adequately reflect

governmental influence or the leverage of tax policies. Now that we are convinced that the world oil supply of the future is dependent upon the dis- > covery of giant fields, I am concerned about how well we understand the conse- quences of the cash flow from past successes being diverted away from the

companies that traditionally reinvested a maior portion of past earnings back

into frontier exploration for new fields. It now appears that much of the

future earnings will move into the hands of governments, both U.S. and foreign.

While I can see the government of an oil producing country seeking out profits

from development, I cannot foresee how they will view a quest for the deferred

profits from exploration. But more importantly, unlike multi-national companies

who sought out geologic opportunities wherever they might be, recycled oil

earnings in the hands of governments may be kept for the most part within

national boundaries. This could restrict future investment to more exploration

close to past discoveries. This is an ideal place to find a little more oil,

but the worst place to look for another giant. In addition, the shift of oil

income to non-petroleum purposes is already apparent.

1 Grayson, C. J. , Decisions Under Uncertainty , Harvard University Graduate

School of Business Administration, Boston, I960, 402 pages.

10
The modeling of recent years seems to have laid to rest the economic

expectation that raising the Drice can dramatically increase the recovery of

oil and gas from old fields. The rewards from delaving abandonment are worth

calculating but hardly of great consequence in the total picture. Also, we now recognize that an oil reservoir is not like a big factory where the production

process can be changed like retooling a new car assembly line. While a lot of

changes can be made before you develop, the economics can be very marginal if vou decide to rework the reservoir after you have been producing it for some time with a given set of wells and practices. However, there is a lot of oil

and gas left down there, and it well deserves continual economic and engineering examination of what we can do with it. Unfortunately, the evaluation and

quantification of the rewards from advanced production technology has proved

to be a frustrating exercise.

T. would suggest that our governmental managers and members of Congress and

their staffs-who have been close to this situation for nearly a decade- now

recognize that in the absence of frontier discoveries a large increase in price

will not oroduce a commensurate large increase in production. Also, they may

now be convinced that the domestic industry's economics dictate, if demand is

present, that reservoirs should be produced as rapidly as engineering prudence

and regulatory rules will permit. Which, of course, is a domestic lesson we may

now have to unlearn in that foreign governments mav not be interested in the present value of future earnings in the same context as we are. Our international

oil models will have to try to reflect a scheme of things which involves national

income management, or the present value to current leaders of future social

stabilitv. That mav prove difficult to put into a discounted cash flow model,

and does not relate to traditional economic calculations. While our economists

are now saving that foreign oil and gas may be worth more to foreign countries

in the ground, this cannot be substantiated using a traditional economic analysis

assuming conventional economic and political regimes. On purely economic grounds

the anticipated increase in real price must be very large to iustify taking a long-term risk on technical, market, and political uncertainties in preference to

taking your profits as rapidly as possible. If, however, your strategy is not

purely economic or conventional, then all signals are off.

As we view the progress we have made, we certainly must commend our modelers

on the studies of the importance of field size distribution, the variation in

the occurrence of oil and gas with depth, and the impact on exploration and production economics of investments in deep reservoirs, deep water, and hostile

environments. We are also trying to recognize how we feed on exploration

experience, with models now introducing a "play" concept.

The size of fields worth discovering in the frontiers of the world and the

lumpiness of current investments have begun to be represented more clearly.

There are lessons to be learned on how much the new game is a far cry from the

modest investments of the old onshore wildcatter. In the past, the exploration

game could turn on and off in the space of a few months, while the new world

of oil does not work in that fashion. Also, the oil industrv mav be less likely

to drill on the expectation of higher prices, so higher prices may have to be

assured. This is in conflict with some who are inclined to continue to pay

producers a low price for cheap oil ^rom the past, and onlv offer a high price

11
for more costly future oil after it has been found. Given the penchant for

governmental authorities to perhaps change their minds after the heavy front-end

billions have been sunk, there is a reluctance in some Darts to Dlay the game on

a C.O.D. basis.

Our modelers have been recognizing, but still struggling with, various

institutional restraints. In the final analysis the modeler must confess that

leasing, environmental, and regulatory policies may have been ignored, and that

Dolitical uncertainty is as difficult to deal with in the models as is geologic

uncertainty

I am concerned at the moment that there does not seem to be a public awareness of the rapidity with which oil exploratory drilling costs are going up.

Much of this trend reflects the inflationary state of the economy, but there

are also some pervasive factors relating to technology, locale, and depth that

should be reflected in our analyses. A second trend is the shift of the proportion of exploratory drilling away from new field development toward other kinds

of exploration. This must be highlighted now to defuse future public dissolutionment. Total domestric drilling has accelerated sharply and drilling rig

availabilitv may have been less restrained than we thought. As a consequence

total wells drilled is now back at the 50,000 plus of bygone decades. But

exploration in general has gone up less rapidly, and even more crucial is that new field exploration has responded least of all. The key auestion is whether

or not new field exploration behavior is a reflection of the declining availabilitv of new fielH opportunit ites , or of public policv and other institutional

restraints on new field exploration. It would seem important for our short and

intermediate term models to both examine as well as reflect this trend.

In my last set of comments, I would like to turn to our basic geologic

uncertainty. Obviously the modeler is driven to quantify, and the econometrician to place this in the context of economic theory. Unfortunately this must

be accomplished with a few crude measurements and a host of uncertain estimates

based on historical experience. When these are then coupled with a concept

such as economic rent, the old rhyme about the purple cow comes to mind - "I

have never seen an economic rent, I hope I never see one...". Perhaps my confidence in frontier leasing strategy built upon the concept of capturing the

economic rent would be bolstered if I some day would overhear a chief executive

officer brag to a colleague how he was able to keep X millions of dollars of

economic rent out of the hands of the government.

One can be quite comfortable in the classroom discussing the disposition

of surpluses earned in the market place that are over and above what is needed

to entice the proper number of investors into the exploration and development

of oil and gas resources. Yet in reality the estimates of the reserves on leases prior to drilling do not match very well with what is subsequently found.

Nor does the size of the bid or the apparent sophistication of tbe company

necessarily match up with ultimate discoveries. If our frontier leasing process

is built upon the assumption that we can estimate oil and gas resources prior

to drilling and tbus calculate the economic rent, I find that a bit wbimsical.

So I remain unconvinced that a leasing svstem can be portrayed as a finelv-tuned

exercise in tbe capture of economic rents. Tbis explicitlv suggests that we in

12
our ignorance will not alter the efficiency of our exploitation of our oil and

gas resources. One can appreciate the concept, hut that does not require the

modeler or the economist to take the quantification of economic rent too

seriously in the wrong contexture.

If we had a device that would actually detect and measure buried fluid

hydrocarbons in situ , then the players in the game would know what is there to

capture, have some idea of cost, and be able to decide what reward is needed to

make it worth trying. Even without that device, after sufficient drilling we begin to approach that condition. At some Doint in the development process a prudent government can begin to set some limits concerning acceptable lease

incomes. Prior to that, our discriminating powers about exploration targets

remain a refinement of deciding where there are distorted marine sediments of

the right age worth drilling. The process is not unlike a group of hunting

dogs moving across a field sniffing in likely places. Once an actual scent is

located, then the "play" is on and the whole pack goes charging off along a fresh trail.

To understand this process is important, because it suggests that much of our strict, new-field wild cat drilling mav tend to he a orocess where sums of

monev are simple budget allocations to the game in contrast to being calculated

investments. That does not suggest that the ante won't be increased when orice

conditions or expectations are bullish. Nor do we have to deny that the total

process through end-product sale is iustified on the basis of the eventual

profitability. It merelv suggests asking ourselves how much does bidding,

competitive or otherwise, subtract from investment in frontier exploration

drilling rather than being a simple transfer of rent which does not alter the

exploitation process. If a billion dollars in lease bids actually translates

into a reduction in exploratory drilling, then perhaps economic rents are more

effectively retrieved after initial exploration rather than before.

Our knowledge of geology constantly entices us into viewing our oil and

gas supply as a fixed inventory. But the subiective quantification of that

inventory is a reflection of the limits of our geologic imagination and conventional practices. In effect, our mental classification scheme has serai-rigid

boundaries. Over time there is a constant slippage with the appearance of oil

and gas in new geologic settings once unknown, not understood, or too complex.

Thus we now have the Overthrust Belt. A geologic opportunity not really

reflected in our resource appraisals of a decade ago. It may not be a Middle

East, but it is big enough to now show up on the charts.

A less dramatic example of this slippage is the slow evolutionary drift of

unconventional resources across the boundary from known "other occurrences"

into becoming a part of the estimate of conventional economic and sub-economic

resources. During the Inter-Agency Study of the Permian Basin, one problem was

trying to decide concerning these resources what had been counted, not counted,

or counted twice. Were we must deal with such things as heavy oils or gas in

sands and shales not previously producible, but located at the margin of opDortunitv. Wigher prices and technologv can gradually make a portion of these

quantities usable - but how much and when?

13
So I find the reality of geology is having to cope with frustrating uncertainty. However, my statistically inclined colleagues tell me that once they unlimber their Monte Carlo wheels, apply their log-normal distributions,

or introduce the nuances of Bayesian statistics, the mysteries of oil and gas resources begin to disappear. I watch with interest as they strip every bit

of statistical inference from each new bit of drilling data. They have con- vinced me, like card-counters in a one-pack Black Jack game, that they have a handle on the future odds. Once a few cards are dealt, they already know that

the Aces and high cards will be found in the top half of the deck, so we can now beat the House. Yet I have an uneasy feeling that if in estimating oil

and gas resources each deal is a different deck, with a continual variation in

the number and distribution of the cards, we still have some inadequacies in our models. We still don't know how many decks nature has left, nor is it out

of the question that there are some kinds of decks we have never seen before.

After all, the early Bradford Field drillers thought oil was distributed like

ground water, and Captain Lucas probably never had heard of a salt dome when

he drilled Spindletop. While I doubt if there are any major modes of oil and

gas occurrence still unknown, one still wonders.

As we now turn to the various papers in this symposium, I am sure we will

enjoy the magnificant display of "black boxes" and other things to fascinate

those of us who like to probe the unknowns of oil and gas supply. I think we will be impressed with how much more knowledgeable we have become, but appropriately humble about what is still left unanswered. So I close with the same old punch line—continue to strive and you will one day have a truly satisfying oil and gas supply model. Let us always hope that it will be predictive

rather than historic.

DISCUSSION

Dr. Parikh (Oak Ridge National Laboratory): Somewhere in the early part

of your presentation, you mentioned that we have passed the 50 percent mark in

oil production. I think you are referring to the Hubbert Curve. With or without a model, do you have a guess on what the cost of producing the last 10

percent is, or will be?

Dr. Schanz: Let me preface my comment that in a presentation of this

type without being able to go back and examine my exact words, I hope that I presented that point as a likelihood that we are past the mid-point as a com- monly held view.

I suspect, in my own judgment, that we are. But given the remaining inplace resources, we always can have a hope that the total presence in nature

of unexploited oil and gas resources could provide us with a pleasant surprise. We would then find that we are not past the half-way point.

Obviously as an economist, but not currently involved in trying to quantify the last 10 percent through a model, I realize that everyone would like

to identify what our energy alternative is in terms of what comes next as we

move through the various energy resources. One would have to feel, in real

costs, that the energy alternative to oil is somewhere to be found as we move

14
through the $40, $50, $60 per barrel projections now being talked about. It

would seem this kind of price level should trigger the alternative to oil,

given a little lag time for its actual appearance in the energy market.

So intuitively I suspect that we cannot go much beyond what we are now

paying for oil to start the energy replacement process for oil that all re- source economists expect eventually to take place. Thus, not far beyond the

current margin we can visualize that point where the remaining producible oil

and gas resources will become the last 10 percent in our glass. Exactly where

in the price spectrum, whether at $60 or $100 per barrel, we will cross that

point of price versus quantity that defines the final 10 percent I am hard

pressed to say. But going at the pace we now are, or expect go to, I would

think we would reach the trigger point for alternative sources that will set

the 10 percent pretty soon.

15
TECHNIQUES OF PREDICTION

AS APPLIED TO THE PRODUCTION of OIL AND GAS

M. King Hubbert*

Abstract

Techniques of prediction of future events range from the completely

irrational to the semi-rational to the highly rational . Rational techniques

of predicting the behavior of a system require first an understanding of its

mechanism and of the constraints under which it operates and evolves. This

permits the development of appropriate theoretical relations, which, when

applied to the data of the system, permit solutions of its future evolution

with varying degrees of exactitude. Such a theoretical analysis provides an

essential criterion for what data are significant and necessary for the solution.

In the case of the production of petroleum in a given region, present geologic knowledge indicates that oil and gas accumulations occur in limited volumes

of underground space, in porous rocks normally filled with water, within or

immediately adjacent to basins of sedimentary rocks. These accumulations have

resulted from plant and animal material accumulated in the sediments during the

last 600 million years, at rates so slow that no significant additions can occur

during the period of oil and gas exploitation. Therefore the exploitation of the

oil and gas accumulations in a given region represents the continuous reduction of

the amounts originally present and is a unidirectional and irreversible process,

characterized by a definite cycle of events. Oil production in a given region

begins with the first discovery at time t and ends finally at a later time t^.

Hence the cumulative production Q will have the value 0 at t - t , and a definite

finite value Q, at t = tv

. Thus, during the complete cycle of production, Q increases

Consultant, 5208 Westwood Drive, Bethesda, MD 20816.

16
monotonically during the time interval t

Q

to t^, being 0 for i < amd the

constant Qm

for t > ty. Also, during this cycle the production rate, dQ/dt,

will vary as follows:

For

Therefore

t < i' , dQ/dt = 0;

t

Q

< t < t^, dQ/dt > 0;

t

k

< t, dQ/dt = 0.

( k

{dQ/dt)dt = Q,

(1)

(2)

where

e_ = {dQ/dt) dt. (3)

Because of the definiteness of the limits of Q as compared with those of

time, it is more useful to consider the production rate, dQ/dt, as a function

/ of Q rather than of t. Then

dQ/dt = f(Q), (4)

and the integration of this equation gives the corresponding functions of time,

Q(t) and {dQ/dt) (t) . Comparable relations pertain to other variables of this

system such as the rates of discovery and cumulative discoveries, proved reserves,

and the rate of exploratory drilling and cumulative drilling. By developing the

appropriate equations among these variables, and supplying the data from petroleumindustry statistics, it becomes possible, after production in the region has

passed through about the first third of its cycle, to determine with reasonable

accuracy the principal constants of the equations: Q^, the ultimate cumulative

production; various exponential growth constants; various critical dates of the

17
cycle, such as that of the maximum rate of production.

Methods based upon this type of analysis, which have been developed and

used by the present author during the last 25 years, have consistently given

predictions of the future courses of oil and gas production in the United States

which have agreed within narrow limits with what has subsequently occurred.

****************

Techniques of Prediction

Soothsaying, while probably not the world's oldest profession, can certainly

offer a strong claim for being its second oldest. The techniques of soothsaying

may be divided roughly into those that have some rational basis, and those that

do not have; and the result of soothsaying, namely the prediction of some event,

may be expressed in language whose meaning ranges anywhere from completely indefinite to precise and unambiguous.

The nonrational techniques of prediction are well exemplified by the activities of many of the priestcrafts of the ancient world - notably those of the

famous Oracle at Delphi in Greece - and by those of the great variety of fortune

tellers of today with their tea leaves, crystal balls, or astrological interpretations of the human consequences of various planetary configurations. These

have usually been characterized by a combination of astute guesswork and ambiguous

statement, conducted behind a facade of mystical rites.

From examples of the soothsayer's art which have been handed down from

antiquity, it appears to have been learned very early in human history that a

soothsayer's life expectancy could be considerably enhanced if his professional

opinions, while appearing to convey useful information, were actually couched in

language of such ambiguity as to cover all likely contingencies. For example,

18
King Croesus of Lydia, in the sixth century B.C., was considering conducting a

war of conquest against a neighboring state, but was doubtful as to the outcome.

He decided that it would be prudent to consult the Delphian Oracle. The advice

that he received was, "If you embark upon this campaign, a great empire will be

destroyed." Thinking that to be a good omen, Croesus did embark upon the campaign and a great empire was destroyed, his own.

The technique of prediction by ambiguous statement is still by no means

obsolete and it is not unknown to the petroleum industry. During the 1950-decade,

one of the most widely quoted dicta released by the propaganda branch of the

U.S. petroleum industry was: "The United States has all the oil it will need

for the foreseeable future."

Rational techniques of prediction fall into two fairly distinct classes:

1. Techniques based upon empirical extrapolation of real data,

with little or no theoretical guidance.

2. Techniques based upon the analysis of data with the theoretical guidance provided by a prior understanding of the

mechanism of the phenomena investigated.

Prediction by trends and cycles . — Of the empirical methods, one of those

used most commonly at present is based upon the extrapolation into the future

of some variable which, during the recent past, has displayed an approximately

linear variation with time. By extending this linear trend with a straight-edge,

when the data are plotted graphically, a prediction of its future can be made.

This is the simplest semi-rational technique to apply, and it probably is the

one in widest use at present. But how reliable is it, especially when applied

to the exploitation of an exhaustible mineral resource? As an example of the

technique, the annual production of pig iron in the United States, plotted on semilogarithmic paper, for the 60-year period, 1850-^1910, is shown in Figure 1.

19
\

\

\

pig-iron

\

5n,

1850-1910.

EDICTION

A

v

\

\

V

-A rxg.

j.

ricuiLiii

productic

PRI \

m

o

in

to

CVJ

CD

o

o

to

or

<

LU

m

00

o

in

GO

GO ID

(HV3A/SN01 IdOHS)

NOdi Old jo NOiionaoad s n

20
The curve plots as an excellent straight line, corresponding to a uniform

exponential growth at an annual rate of 6.9 percent. The dashed line shows

the prediction of the growth of pig-iron production in the future. The

steel industry has been reported to have based its long-range plans on this

projection until 1925. Figure 2 shows what actually happened. Within a threeyear period from about 1907 to 1910, this curve changed abruptly from a growth

rate of 6.9 percent per year to another straight-line segment with a growth rate

of only 1.8 percent.

In other instances the quantity of interest may vary in a more or less

cyclical manner. In that case, the prediction of its future behavior consists

in an extrapolation of this type of behavior into the future. In some cases -

astronomical events within the solar system, for example - this can be done

with great precision and solar or lunar eclipses can be predicted centuries in

advance. Other cyclical or pseudo-cyclical events, such as the "business cycle,"

can be predicted by this means with much less assurance.

Necessity for knowledge of mechanism. The fundamental flaw in the use of

blind empirical methods lies in the fact that such methods take a minimal account

of the inherent constraints in the behavior of a system imposed by its mechanism

and physical properties. Thus, when dealing with cyclical events of the solar

system, the Newtonian laws of motion and of gravitation, in conjunction with

the infinitesimal rate of energy dissipation in the motions of the planets,

provides assurance that the cyclical nature of these motions will change extremely

slowly over periods of many millions of years. On the other hand, a weight-driven

pendulum clock can maintain a precise cyclical operation of its pendulum and its

hands, but the fall of the weight is noncyclical, and when the weight reaches its

lowest point, the clock stops.

21
\

o> oo h- *0 m O O O O O

(UV3A /SN01 1H0HS)

N08i old jo NOiionaoad s n

22
A similar situation prevails in the rate of consumption of natural gas in

a northern city. This curve consists of two parts, a base rate of consumption,

which is noncyclical, upon which is superposed a roughly sinusoidal variation

with a period of 1 year. This sinusoidal component is obviously related to

the annual rise and fall of climatic temperatures, and hence upon the annual

cycle of the earth's revolution. One cannot, however, predict the future of

the gas consumption by its sinusoidal component for, say, another century,

because by that time there may no longer be any natural gas.

The use of linear trends can be very reliable in cases where the mechanism

is understood and does produce a sustained linear variation with time. One of

the best known examples of this is the decay of a radioactive isotope. If

N

q

is the number of atoms of this isotope initially present in a closed system,

then, it has been found, the number N of atoms remaining after a time t is

given by

N = N e~at

, (1) o

v J

where e, equal to 2.7183, is the base of natural logarithms, and a is a

constant for the given isotope. Taking the natural logarithms of both sides

gives the linear equation

In N - In N - at, (2) o

v J

whereby In N as a function of t plots as a straight line which may be extrapolated with confidence so long as N is large as compared with its statistical

perturbations. This is the basic principle used in the radioactive dating of

past geologic events.

23
Mechanism of Petroleum Occurrence

Similarly, any rational prediction of the future of petroleum production

must depend upon a prior knowledge of the manner of origin of oil and gas, the

geological situations where these fluids now occur, the procedures of petroleum

exploration and production, and the respective time scales. As to their modes

of occurrence, oil and gas at present are found as concentrations occupying

the pore volumes of coarse-textured or fractured porous rocks in limited regions

of space within or adjacent to basins of sedimentary rocks.

In petroleum geology, if a well is drilled at any point, it commonly will

penetrate various thicknesses of porous sedimentary rocks - sandstones, shales

or mudstones, and limestones. Eventually, if drilled deep enough, the well will

reach the bottom of the sediments and will encounter the underlying older nonporous crystalline rocks which are commonly known as the basement complex, or

the '"basement." The upper surface of the basement complex is a continuous,

world-wide surface. In certain large regions - a large part of Africa, most

of the eastern half of Canada, and much of Scandinavia - the sedimentary cover

is either very thin or else absent altogether. In these regions the surface of

the basement rocks coincides with the surface of the ground. In other regions,

the top of the basement is depressed and these depressions are filled with younger

sedimentary rocks, having thicknesses ranging from zero at the edges, to a maximum

in their interiors. Commonly, this maximum thickness may not exceed 2 or 3 kilometers, but in a few cases it has been found to be as great as 10 to 15 kilometers.

Unmetamorphosed sedimentary rocks are porous, with the pore volume ranging

usually between about 10 and 30 percent of the total volume. Beneath shallow

depths of a few tens of meters from the earth's surface, the pore space of these

sedimentary rocks is filled with water which extends to depths below which the

24
porosity becomes zero. Oil and natural gas, and also coal, are found in these

sedimentary rocks. These are derived from the remains of plants and animals

which lived at the times the sediments were being deposited. They became

buried in the accumulating sedimentary sands and muds in an oxygen-deficient

environment, and have subsequently become transformed chemically into the

present fossil fuels.

Oil and gas thus occur as minority fluids immersed in an underground rockwater environment. Being fluids, oil and natural gas are mobile. Occurring

originally in a dispersed state, the separate particles have been driven by

mechanical forces or else transported in solution, into limited regions of

space, corresponding to minimum levels of potential energy with respect to the

local environment and lithologic barriers to further migration. The exploration

for petroleum consists in determining as accurately as possible from less costly

geological and geophysical data the most probable positions in three-dimensional

space at which these accumulations may occur, and then drilling exploratory wells

at the sites so selected. Most such exploratory wells are failures, but the

probability of success is considerably higher than that of random drilling.

As regards time scales, the oldest industrial-sized gas field so far discovered appears to be one in Australia which occurs in rocks of late Precambrian

geologic age - some 600 to 700 million years old. Oil and gas fields have been

found in the United States and other parts of the world in rocks ranging in age

from the Cambrian, 500 to 570 million years old, to sediments of Pleistocene age

deposited in the Mississippi Delta of coastal Louisiana during the last million

years. The exploitation of petroleum, on the other hand, did not begin on an

industrial scale until as recently as the 1850-decade. Statistics of oil production

in Romania are reported since 1857, and the initial oil discovery in the United

States, by a well drilled for that purpose, was made at Titusville, Pennsylvania,

25
in August 1859. The time required to essentially deplete the initial oil and

gas resources of the world can hardly be longer than two or three centuries

The disparity of these time scales, that for the accumulation of the

world's supply of oil and gas, and that for its depletion, is very significant.

Although the same geological processes are still operative by which the original

oil and gas were accumulated, and at about the same average rate, any additional

oil or gas that could accrue within the next few centuries would be infinitesimal as compared with that of the last 600 million years. Therefore, during

the period of oil exploitation, the production of oil and gas must consist

solely of the continuous withdrawal from a stockpile of an initially fixed and

finite magnitude, to which no additions will be made. Therefore, the amount of

oil or gas remaining can only decline monotonically as a function of time.

The So-called Geologic Methods of Petroleum Estimation

Petroleum geology and geophysics, which are fundamental to petroleum exploration, comprise the entire complex of existing knowledge regarding the origin,

migration, and entrapment of oil and gas, and their present modes of occurrence.

This involves of necessity the most detailed knowledge that can be obtained

regarding the rocks filling various sedimentary basins, their spatial distribution,

and their fluid contents, water, oil, and gas. This information is acquired

jointly by surface geological and geophysical mapping, but eventually in most

detail from the subsurface geological information provided by wells drilled into

the sediments. It is a truism of the petroleum industry that the only tool that

actually discovers oil is the drill. Hence it is the record of exploratory and

production drilling in a given region that provides the most reliable information

available regarding the occurrence of oil and gas, and the probable quantities

of these fluids that a given basin may eventually be expected to yield.

26
However, during the last twenty years, a great deal of confusion has been

introduced into the estimates of future petroleum production by the argument

that "geological" methods of estimation must somehow be more reliable than socalled statistical methods based upon the cumulative information provided by

drilling. By the advocates of this view, the scope of "geology" is seldom

defined, but it apparently excludes or minimizes the importance of the information provided by drilling. The estimates obtained by these so-called geological

methods during the 1960-decade for the ultimate amounts of crude oil and natural

gas to be produced in the Lower-48 states and adjacent continental shelves of

the United States were commonly about 600 to 650 billion barrels for crude oil

and 2,500 trillion cubic feet for natural gas.

One of the more important uses of geologic methods is in a qualitative

evaluation of the petroleum potential of an undrilled area. This is done principally by geological analogy. Suppose, for example, that two contrasting

regions, A and B, have been explored and adequately drilled. Region A has been

found to be a petroleum-rich region and Region B has been found to be barren.

Two undrilled regions, C and D, are under consideration for future exploration.

From preliminary geological and geophysical mapping, Region C is found to be

geologically similar to barren Region B, and Region D to productive Region A.

On the basis of this comparison, it would be inferred that Region D would merit

further development, and that Region C should be given a lower priority.

In this connection, the United States is the most intensively explored major

petroleum-producing region in the world. Consequently, it often has been used

as a standard in the estimation of other less-developed or undeveloped potential

petroleum-producing areas of the rest of the world. It is accordingly not

surprising that estimates of the ultimate oil potential for the world have a

strong correlation with estimates made by the same authors for the United States.

27
But how are the estimates for the primary areas to be obtained? It is

easy to show that no geological information exists, other than that provided

by drilling, that will permit an estimate to be made of the recoverable oil

obtainable from a primary area that has a range of uncertainty of less than

several orders of magnitude. To show this, consider the composite potential

of all oil-bearing sediments of a primary region.

Let A be the surface area of the potential oil-bearing region, D be the

average thickness of the sediments, and V the total volume of the sediments.

Then

V = AD

Of the total sediments, oil and gas can be produced only from coarse-textured

reservoir rocks, which are principally sandstones, and a lesser amount of porous

limestones. Let V be the volume of reservoir rocks and X the ratio between

res

V and V. Let V be the pore volume of the reservoir rocks and <j> their res P

average porosity. Finally, let S be the average oil saturation of the reservoir rocks and V the volume of the oil. Let V be the recoverable oil and

o r F the fraction of oil-in-place that can be recovered. Finally, let R be the

richness of the region, defined as the ratio of the volume of recoverable oil

to the total sedimentary volume. Then

V = XV res

is the volume of the reservoir rocks;

V = d>7 = <f>A7 p

T res

is the pore volume of the reservoir rocks;

7 = S V = s $\v

o op o

is the volume of oil in the reservoir rocks; and finally,

Vr

= (FSo $\)V

28
is the volume of recoverable oil. Also, the richness R of the region is

defined to be

r = Vr

/V = {F^X)S

o

. (8)

In equation (8), the factors F, and A are known within narrow limits.

The recovery factor F may be taken to be about 0.4, the porosity <f> of

reservoir sands has an average value of about 0.15. According to F. W. Clarke,

in his classical monograph, The Data of Geochemistry (Clarke, 1924, p. 34),

shales comprise about 80 percent of the total volume of sediments, sandstones

about 15 percent, and limestones and evaporites about 5 percent. Accordingly,

we may take about 0.15 as the average value of X. Hence the combined factor

(ityX) = 0.4 x 0.15 x 0.15

= 0.009

- 10" 2

R - 10~ 2S

q

. (9)

Then the total amount of recoverable oil that a given region will produce

would be

V

p

- (10~ 2S

o

)V. (10)

Therefore the accuracy of a geological estimate of the oil that a given region

will produce depends almost entirely upon that of the oil saturation factor S

q

.

The factor S must lie between the limits 0 and 1.0 but how, except by the data

of prior drilling can it be determined whether 10 1

, 10 4, or 10 6 is the

better value for this factor?

The cumulative results of exploratory and production drilling, on the other

hand, in petroleum-producing regions in advanced states of development, do provide

very good information as to the actual magnitudes of the richness, R, and of

S , within a range of uncertainty of 2 or less for various regions. For example,

29
consider the three following oil-rich regions, each of which is in an advanced

state of exploratory and production development:

The Los Angeles basin, California

The Lower-48 states and adjacent continental

shelves of the U.S.

The Arabian Gulf basin of the Middle East.

For the Los Angeles basin, about 97 percent of the oil discovered is found

in upper Miocene and lower Pliocene sediments, having a volume of 6.67 x 10 12 m

3

.

The cumulative discoveries amount to 7.65 x 10 9 bbl, or to 1.21 x 10 9 m

3

. (Kilkenny, 1971, p. 170-173; Gardett, 1971, p. 278). From these data, the minimum

value of the richness of this basin is

R m 1.21 x i 0 9 m

3 6.67 x io 12 m

3

and

S « 100 R = 1.8 x io-2

, o

In other words, the Los Angeles basin has about 180,000 m

3 of recoverable oil

per km 3

, or 4.7 million barrels per cubic mile, and an average oil saturation

in the reservoir rocks of nearly 2 percent.

For the Lower-48 states and continental shelves, the area of potentially

oil-producing sediments is 2.0 x 10 6 square miles, or 5.2 x 10 12 m

2 (Cram, 1971,

v. 1, p. 5). Then, with an average thickness of 2,500 meters, the total volume

would be

5.2 x io 12 x 2.5 x 10 3 = 13 x io 15 m

3

.

The cumulative oil discoveries for the Lower-48 states amount to about

155 x io 9 bbl, or to 24.6 x io 9 m

3

. From these data,

B - 24 " 6 * ?f f = 1.9 x !0-6,

13 x io 15 m 3

30
and

S = 100 R = 1.9 x ict 4

.

Thus the average oil richness for the potential oil-producing sediments

of the Lower-48 states and continental shelves is only about 1,900 cubic

meters per cubic kilometer, or 50,000 bbl per cubic mile, and the average

oil saturation is only about 2 parts in 10,000 of the total pore volume of

the reservoir rocks.

For the Arabian Gulf basin, about 460 x 10 9 bbl or 73 x 10 9 m

3 of oil

has been discovered in a sedimentary volume of 2.5 x 10 15 m

3 (Morris, 1978,

Preface; Law, 1957, p. 60). This gives for the richness

^ 73xlQ9m3 =2.9 x 10-5.

2.5 x io 15 m

3

and

S = 100 R = 2.9 x io -3

. o

Thus the Arabian Gulf basin has a richness of about 29,000 cubic meters of

recoverable oil per cubic kilometer, or about 760,000 bbl of oil per cubic mile,

and an oil saturation of the reservoir rocks of about 0.3 percent.

From these comparisons, the Los Angeles basin, the richest known basin in

the world, has a richness that is 95 times that of the entire Lower-48 states,

and 6 times that of the Arabian Gulf basin. The latter has a richness 15 times

that of the Lower-48 states.

From the foregoing discussion it should be clear that arguments over the

relative superiority of the so-called geological estimates and those arrived at

by other methods serve little useful purpose but can produce a great deal of

confusion, especially when the geological estimates are several-fold larger

than other estimates. Actually, a petroleum geologist or engineer, when studying a given region, makes use implicitly or explicitly of every kind of pertinent

31
information that may be available. A large and significant part of this information has to be the cumulative knowledge provided by prior exploratory and

production drilling.

Complete Production Cycle in Given Region

In any particular oil-bearing region, the production history of the region,

or the complete production cycle, has the following essential characteristics.

At some initial time t the first discovery well is drilled and oil production

in the region begins. The first discovery is of a single field. Additional

wells are drilled to develop the field and the rate of production increases.

Further exploration in the region is thus stimulated, and, on the basis of geological and geophysical studies, further potential oil-bearing structures are

drilled and new fields are discovered. However, since there are only a fixed

number of fields in the region, as more and more fields are discovered, progressively fewer fields remain to be discovered, and these are the more obscure

fields and commonly the smaller ones. As the undiscovered fields become scarcer,

the amount of exploratory effort, including exploratory drilling, per unit

quantity of oil discovered increases until eventually exploratory drilling becomes

prohibitively costly and ceases.

The rate of oil production, dQ/dt, in the region begins at a near-zero rate

at time t and thereafter commonly increases exponentially for a few decades.

Eventually, as the rate of discovery slows down, the rate of production follows.

It reaches one or more principal maxima, and finally goes into a slow negativeexponential decline. Then, at some definite time t^, production ceases altogether.

This sequence can be stated mathematically as follows:

32
For

t < t , dQ/dt = 0;

t

Q

< t < tkJ dQ/dt > 0;

t > t

R

, dQ/dt = 0.

The period from t

Q

when production first begins until when it ends

comprises the complete cycle of oil production in the region. During that

time, the cumulative production from time t to a later time t is given by

(11)

%

- (dQ/dt) dt

Pdt, (12)

where P = dQ/dt is the rate of production. Then for the complete cycle

Pdt. (13)

Or, since for times earlier than t and later than t^P= 0, then

+00

Pdt = Q (14)

Thus Q^ may be taken to be the ultimate amount of oil that will ever be produced

in the region during an unlimited period of time.

This complete-cycle curve has only the following essential properties:

The production rate begins at zero, increases exponentially during the early

33
period of development, and then slows down, passes one or more principal maxima,

and finally declines negative-exponentially to zero. There is no necessity

that the curve, P as a function of t, have a single maximum or that it be

symmetrical. In fact, the smaller the region, the more irregular in shape is

the curve likely to be. The crude-oil production curve for the State of Illinois,

for example, is shown in Figure 3, Here, oil was first discovered about 1900.

Until 1905, the production rate increased very slowly. It rose sharply to a

peak rate of about 35 million barrels per year during 1908 to 1910. This was

followed by a long negative-exponential decline to about 1 million barrels per

year by 1936. Then followed a new cycle of exploration and discovery based upon

the use of the reflection seismograph capable of mapping geologic structures

beneath the cover of glacial drift. With the new discoveries, the production

rate increased sharply to about 145 million barrels per year by 1940, and then

declined to 55 million barrels per year by 1953. Next followed a ten-year period

of a third production peak of about 80 million barrels per year due to water

flooding, and finally a decline to about 35 million barrels per year by 1971.

On the other hand, for large areas, such as the entire United States or the

world, the annual production curve results from the superposition of the production

from thousands of separate fields. In such cases, the irregularities of small

areas tend to cancel one another and the composite curve becomes a smooth curve

with only a single principal maximum. However, there is no theoretical necessity

that this curve be symmetrical. Whether it is or not will have to be determined

by the data themselves.

34
35
The Complete-Cycle Curve as a Function of Qm

The foregoing properties of the complete-cycle curve of production afford

a simple but powerful means of estimating the future course of the productionrate curve as a function of Q^. After the completion of the cycle, as shown

by equation (14)

,

+00

e = Pdt.

When the curve P versus t is plotted graphically with arithmetic scales, as in

Figure 4, the area between the curve and the t-axis to any given time t is a

graphical measure of cumulative production. Then, for the complete cycle, the

total area beneath the curve is a measure of Q . Also, in plotting such a

curve, scales must be chosen arbitrarily for the ordinate P, with a graphical

interval AP, and for the abscissa t, with a graphical interval At. The gridrectangle, AP x At, affords a graphical scale for cumulative production. At a

constant rate AP, the quantity of oil produced during the time At would be

LQ = AP x At. (15)

Hence each grid-rectangle beneath the curve represents hQ of cumulative production. Therefore, if Q is known, then the number of grid-rectangles beneath

the complete-cycle curve must be

n - QJLQ. (16)

This is the inverse of the usual problem of the integral calculus, where

one is given y = f(,x) , and the problem is to find

A = ydx.

Here, we are given A and the problem is to find the curve y = f(x). There are

obviously an infinite number of curves that will satisfy this condition. However,

36
i

*<

>

I

1

*—% —

if

/ uj Z//7Z

< LU > 0///A / 1- f= iz /////

'5 i I///

s y s s s s s s / / s

UJ

rH•HP

(/)

nj ~cX

<d

<+Ho

o

•H

+-> O

o

f-i

t+HO

0

i-H OX

o

<u

•

' * 4-> rH

a> rH

rH

P-i • Eo •H u tin

a>

+-> LO

CT) >—

(

H •* 13 +J

rH > 4> rHO

> X H

s

o c u

o <+H •H

+-> 13

rH •H

0) 4-1 rH •H

rH O

ct4 O

•H

•P 0)

o3 o

s rH

0) X o

+J (/) 03

rH

iP/bP = d :31Vd NOiionaodd

37
when, in the oil-production case, the further constraints imposed by the technology of oil discovery and production are taken into account, the differences

between separate solutions tend to become minor. Accordingly, although there

may be an infinite number of complete-cycle curves corresponding to a single

value for Q^, all of these curves have a strong family resemblance because the

area subtended by each is the same, namely n rectangles.

When the petroleum discovery and production in a given region reaches a

moderately mature state of development, the history of this development begins

to provide a basis for reasonably good estimates of the approximate magnitude

of Qmfor the region. Suppose that by the time t, , cumulative production has

already reached . Then the oil remaining to be produced would be

Accordingly the area beneath the curve from t to would be

rectangles, and the remaining area beneath the curve from t, to °° would be

)A« = n - «j

= n2

rectangles. Hence the future part of the curve must be consistent with the part

that has developed already, and must also be drawn subject to the constraint

that it can subtend only n2 grid-rectangles. In case the peak production rate

has not yet been reached by time t^, then the curve for the future must rise

to a maximum and then decline negative-exponentially. If the maximum production

rate has already occurred by time t*, then its future course will be principally

the negative-exponential decline.

It must be borne in mind that at time £, any figure for Qm

is only an

estimate, yet the foregoing technique provides a means of determining the

38
approximate consequences in terms of future production history of any given

estimated value for Q^. One of the most important results of such an analysis

is the determination of the approximate date at which the peak production rate

will occur. This is probably the most important event in the complete cycle

of production because it is the dividing point between the first phase of the

cycle during which the production rate steadily increases, and the second phase

during which the production rate almost as steadily declines.

Application to the United States . — As an example of this technique, consider its application to the oil production of the Lower-48 states, onshore and

continental shelves, in 1956 (Hubbert, 1956). Crude-oil production in the United

States began with the initial discovery made at Titusville, Pennsylvania, in

August 1859. By 1955 the production rate had reached 2.4 billion barrels per

year. The curve of annual rate of production from 1900 to the end of 1955 is

shown in Figure 5. By the beginning of 1956 oil had been produced in the United

States for 96 years, and cumulative production amounted to 52.4 billion barrels.

The problem was to estimate the future of the production-rate curve for the

remainder of the cycle.

By 1956, petroleum exploration and production in the United States were sufficiently advanced that reasonably good estimates could be made of the approximate

magnitude of the ultimate cumulative production Q . Published estimates for this

quantity by leaders of the petroleum industry fell principally within the range

of 150 to 200 billion barrels. I was in research with Shell Oil and Shell

Development Companies at the time, and further checking with production and

exploration managers and other well-informed petroleum geologists and engineers

showed an industry consensus that the unknown quantity Q would probably fall

within the range of 150-200 billion barrels. Using these minimum and maximum

39
40
figures for estimates of Q , in conjunction with the technique described above,

gave the results shown in Figure 6. There one APAt grid-rectangle has the

dimensions

LQ = 10 9 bbl/yr x 25 years

= 25 x io 9 bbl.

For the lower figure for Qm of 150 x io 9 bbl, the total area beneath the

curve for the complete production cycle would be 6 grid-rectangles. Of these,

2.1 corresponding to cumulative production of 52.4 x io 9 bbl had already been

developed, leaving 3.9 rectangles for future cumulative production of

97.6 x io 9 bbl. The lower dashed-line curve of Figure 6 is drawn accordingly.

To satisfy this condition in conjunction with a negative-exponential decline,

it became impossible to draw this curve very differently from the way it is

shown in Figure 6. From 1956, the curve would reach its peak rate of about

2.7 x io 9 bbl/yr about 10 years hence, and then decline negative-exponentially

back to zero.

Assuming that Q could be as large as the higher figure of- 200 x 10 9 bbl

would add another 50 x io 9 bbl to the area beneath the curve of future production, or 2 more rectangles. This curve would rise a little higher than the first,

and would reach its peak rate a little later, but the 2 extra rectangles would

be the area between the two curves, principally during their decline.

By this analysis, if Q should be as small as 150 billion barrels, the

peak in the rate of production should occur in about 10 years, or about 1966;

for the higher figure of 200 billion barrels, the date of peak production would

be delayed by about another 5 years, or to about 1971.

The curves drawn in Figure 6 were not based upon any empirical equations or

any assumptions regarding whether they should be symmetrical or asymmetrical;

they were simply drawn in accordance with the areal constraints imposed by the

41
f 1 II

1 \ 1 1 1 1 1 1

CO

_lCQ UJ CQ h-

_ o ^

co

_J

CQ ui

CQ 1-

^3 /

8 \ /

Vj1

/

/

O 3

/

/

\ /xxxx xxx>

CO / X// ///////.///

UJ / ^"*=* > CO

CC _J

LU CQ

UJ X

> o

o <*» cc z

^13 | Q_ O CQ 3 CQ O o

°- X

UJ> c\i I- ^ — <

_i y 3

3O

t H

oino

c\j

LO

CNJ oCM

o

o

oCXI

LO

CD

O <Q LO cc w ' 1.1

CXJ

CX>

O

o

cr.

in

oo

<T) CM •wsiaa jo SNOima

om

oo o *h

w • CD s~\ P iH

Ctf (N P

i/> • oo

i U > 2 lo o a> J rH E •> O +J u u

o 3

•H H

P ^

O

X> rH O 0)

rH&. rH rH•H0 c

1 o

0) -H XI rH 3 rH

rH -H O J=>

• o

CO o• Csl

. ^ <P C

O 0J

t/> o

0) LO

rH rH O

X<P

o o

<D V) +J d)

0) -H

rH fH Dh <D 6 >

O

o

CO o up tp rt O E

•rH

!/) P

<D rH P 3

E C

P &

tu X)

LO C/i rH

•H

42
estimates, and the necessity that the decline be gradual and asymptotic to

zero. The strength of this procedure lies in the insensitivity of its most

important deduction, namely the date of the peak-production rate? to errors

in the estimate of Q^. As Figure 6 shows, an increase in the lower estimate

of 150 billion barrels by one-third delays the date of peak production by only

about 5 years, or to about 1971. If the lower figure were doubled to 300

billion barrels, the date of the peak-production rate would still be delayed

only to about 1978.

Without this kind of analysis, the tendency is to extrapolate the production

curve prior to 1956 into the future by the method of linear trends which would

provide no information whatever regarding the imminence of the date of peak

production. In fact, in 1956, the estimates that two or three times as much

oil remained to be produced in the future as had been produced during the preceding century led to an attitude of complacency on the part of petroleum

geologists, engineers, and oil-company officials alike, that no oil shortages

were likely to occur in the United States before the year 2000.

The weakness of this analysis arose from the lack of an objective method

of estimating the magnitude of Q from primary petroleum- industry data. The

estimates extant in 1956 were largely intuitive judgments of people with wide

knowledge and experience, and they were reasonably unbiased because of the

comfortable prospects for the future they were thought to imply. When it was

shown, however, that if for crude oil should fall within the range of 150-

200 billion barrels the date of peak-production rate would have to occur within

about the next 10 to 15 years, this complacency was shattered. It soon became

evident that the only way this unpleasant conclusion could be voided would be

to increase the estimates of Q^, not by fractions but by multiples. Consequently,

with insignificant new information, within a year published estimates began to

be rapidly increased, and during the next 5 years, successively larger estimates

43
of 250, 300, 400, and eventually 590 billion barrels were published.

This lack of an objective means of estimating Q directly, and the 4-fold

range of such estimates, made it imperative that better methods of analysis,

based directly upon the primary objective and publicly available data of the

petroleum industry, should be derived. Such methods, which encompass the

cumulative records of discovery and production, drilling, and associated

knowledge of petroleum geology, will now be developed.

Derivation of the Complete Cycle of Oil and Gas

Exploitation from Primary Data

As we have noted heretofore, the complete production cycle of oil or gas,

or of any other exhaustible resource, has the following general characteristics:

At some initial time t production begins. Subsequently, the production rate

increases with time, passes one or more principal maxima, and finally goes into

a negative-exponential decline until at some time it ceases altogether. During this complete cycle, the cumulative production,

t

f Q

= Pdt, (18)

t

o

increases monotonicallyJ from 0 to a final value Q . The curve of cumulative OO production is a generally S-shaped curve, being asymptotic to zero initially and

to the limit Q as t increases without limit. If the curve of P versus t has

00 only a single maximum then the cumulative curve Q versus t will have but a

single inflection point, coinciding in time with the peak in the production rate.

Earlier than that, the cumulative curve will be concave upward; subsequently,

concave downward.

44
A difficulty in analyzing either P or Q as a function of time arises from

the asymptotic approaches of these quantities to their respective limits as

time increases without limit. On the other hand, Q itself has the definite

finite limits 0 and Qm

. It is convenient, therefore, to consider the production

rate dQ/dt as a function of Q, rather than of time. In this system of coordinates, dQ/dt is zero when Q = 0, and when Q = Q . Between these limits 00 dQ/dt > 0, and outside these limits, equal to zero. While it is possible that

during the production cycle dQ/dt could become zero during some interval of

time, for any large region this never happens. Hence we shall assume that for

0 < Q < Qm , dQ/dt > 0. (19)

The curve of dQ/dt versus Q between the limits 0 and Q can be represented

by the Maclaurin series,

dQ/dt = o

q + c

Y Q + a

2 Q

2 + a

3 Q

3 + (20)

Since, when Q = 0, dQ/dt = 0, it follows that c

q = 0.

Then

dQ/dt = g

x Q + o

2 Q

2 + a

3 Q

3 + 3 (21)

and, since the curve must return to zero when Q = Q , the minimum number of 00 terms that will permit this, and the simplest form of the equation, becomes

the second-degree equation,

dQ/dt = o

Y Q + a

2 Q

2

. (22)

By letting a = and -b = o

2

, this can be rewritten as

dQ/dt = aQ - bQ2

. (23)

Then, since when Q = Q dQ/dt = 0,

aQ- bQ2 = 0,

OO 00 or b = a/0 ,

45
and

dQ/dt = a(Q - Q

2 /QJ. (24)

This is the equation of the parabola shown in Figure 7 whose slope is

dm/dt)/dQ = a - (2a/QJQ, (25)

which, when Q = 0, is +a, and when Q = Q^, is -a. Also, the maximum value

of dQ/dt occurs when the slope is zero, or when

It is to be emphasized that the curve of dQ/dt versus Q does not have

to be a parabola, but that a parabola is the simplest mathematical form that

this curve can assume. We may accordingly regard the parabolic form as a sort

of idealization for all such actual data curves, just as the Gaussian error

curve is an idealization of actual probability distributions.

One further important property of equation (24) becomes apparent when we

divide it by Q. We then obtain

This is the equation of a straight line with a slope of -cl/Q^ which intersects

the vertical axis at (dQ/dt) /Q = a and the horizontal axis at Q = Q^. If the

data, dQ/dt versus Q, satisfy this equation, then the plotting of this straight

line gives the values for its constants Q and a.

oo Our problem now is to integrate equation (24) in order to determine how

dQ/dt and Q each varies as a function of time. This can be simplified by

substituting

a - (2a/QjQ = 0,

or Q = QJ2. (26)

(dQ/dt)/Q = a - (a/QJQ. (27)

or

(28)

46
LU

CO<U

i—

CO

LUI Q_

CO6

CO

ZD

CO

CXL LU>O co

•H

4-) CJ3

T>OUa

at>

•H

4J

CO iH3§

CJ

of • c CO 0 cO •H CJ

4-1 u rH c CO 3 CJ

M-l •H

4-1 cO COE

05V

CO X.

4-1 0)

4-1 CO

4-1 03 s <U 0 rH

•H e a •H 3 CO -aou o

Oh U-l

•H

+P/OP

47
Then

or

and

dQ/dt = QJduldf)

= fla(u - u

2 ),

du/dt = a[u - u

2 ),

du/ (u - u

2

) = adt.

This can be simplified by noting that

I/O - u

2

) = 1/u + 1/(1 - u)

Then the integral of equation (29) becomes

du

ft 1-u

= a dt + const,

or

and

In [(1 - u)/u] = Inc. - at.

.at

(1 - u)/u = ee~ ,

where a is the constant of integration.

Substituting Q/Q^ for u in the left-hand term of equation (30) then gives

(1 - u)lu = (G - Q)/Q = ce~at

Then, when t = ,0, Q = Q , and

c = W. --fi0 )/«0

.

equation (31) becomes

Then, letting

w.- «)/« = [w.- e0 )/y e

~at

-

= {Q - Q )/£ , o 00 o o

48
equation (33) simplifies to

-at •&> N = N e . (35)

Taking the natural logarithms of both sides of equation (35) gives

In N * In N - at, (36)

which is a linear equation between In N and t. This plots graphically as

a straight line which has the magnitude In N when t = 0, and a slope of -a.

Or, if common logarithms are used,

log N = log N

q

- (a log e)t, (37)

which has a slope of -a log e.

Solving equation (33) for Q gives

Q = QJH + N

Qe~at

). (38)

This is known as the logistic equation, which was derived originally by the

Belgian demographer, P.~F. Verhulst (1838; 1845; 1847) in his classical studies

of the growth of human populations.

In equation (38) the choice of the date for t = 0 is arbitrary so long as

it is within the range of the production cycle so that N will have a determinate

finite value. It is seen by inspection that as

t > -<*>, Q + 0,

*->+», Q + Qm

.

Also the curve of Q versus t is asymptotic to zero as t -> and is asymptotic

to Q as t -> +oo. Likewise, the curve of dQ/dt versus t is asymptotic to zero

as Q > 0 and t > and again as Q and t -> +°°.

The maximum value of dQ/dt, from equations (24), (25), and (26), is

dQ/dt = (aej/4. (39)

This coincides in time with the inflection point of the ^t-curve and occurs

when Q = Q /2.

49
In equation (24), dQ/dt is given as a function of Q. If desired, this can

be obtained as an explicit function of t by differentiating the logistic

equation (38)

,

Q = QJ(1 * N

Qe~at

),

with respect to time. This gives the result,

aN e at

dQ/dt = Q~

0

;

' (40)

(1 + N

Q

e aV

) 2

If we then note from equation (35) that

N

Q

e'

at

= N = (Qm

- Q)/Q,

and, from equation (38)

,

1/(1 + N

Q

e'

at

) 2 = tQ/QJ 2

,

and substitute these into equation (40), we obtain, as we should, our original

differential equation (24)

,

dQ/dt = a(Q - Q

2 /QJ.

Graphs of the logistic equation (38), and of its time-derivative, equation

(40), in terms of the dependent variable, u = Q/Q , as functions of time are

shown in Figure 8.

Determination of the Constants Q and a ^00

Two properties of the logistic equation are of fundamental importance. These

are represented by the linear differential equation (27),

(dQ/dt)/Q = a - ta/QJQ,

and the linear equation (36) between In N and t,

In N = In N - at.

o

50
(jXAr-OL) *P/np

Ml co

0)>

•H

+J>

•HU

0

-a

•H

s

oH

3

cr

+->

o

4-1o

c

o

•H

to0 4-1 h o

PhX W

o

i-H -H

aj +J O O H C X 3

1^4-1

fH 1/1

I 00

e

•H

4-1

bO •H

(2-0L) 00 O/O= n

51
The virtue of the first of these two equations lies in the fact that it

depends only upon the plotting of primary data, {dQ/dt) /Q, versus Q, with no

a priori assumptions whatever. Using actual data for Q and dQ/dt, it is to be

expected that there will be a considerable scatter of the plotted points as

Q 0, because in that case both Q and dQ/dt are small quantities and even small

irregularities of either quantity can produce a large variation in their ratio.

For larger values of both quantities, as the production cycle evolves, these

perturbations become progressively smaller and a comparatively smooth curve is

produced. If the data satisfy the linear equation, then a determinate straight

line results whose extrapolation to the vertical axis as Q -* 0 gives the

constant a, and whose extrapolated intercept with the Q-axis gives Q . However,

even if the data do not satisfy a linear equation, they will nevertheless produce

a definite curve whose intercept with the $-axis will still be at Q = Q^.

The use of the second linear equation,

In N = In N - at,

o

'

is somewhat less direct than the first, because in this case

N = (««,- Q)/Q = QJQ - 1.

Hence, before the linear graph can be plotted, Q must be known as a means of

determining N and N

q

. If the data satisfy the logistic equation, and if the

correct value of is used for computing N and N

q

, then the resulting graph

of In N as a function of t will continue as a straight line. If, on the other

hand, an incorrect value,

% = (41)

is assumed for Q , then CO N

b

= bQjQ - 1, (42)

52
and as

If the assumed value, is greater than the correct value of Q^, then

as t increases, the curve In versus t will approach the constant value,

{b - 1) > 0, and will deflect to the horizontal. If the assumed value, .

is less than Q , then as

and

In tf.

In this case, as t increases, the curve deflects vertically downward. This is

illustrated in Figure 9, where graphs of log 2V, versus t are plotted for the

three cases, Q. = 1.25 Q , Q» = Q , and Q. = 0.75 Q . Q 00 £P OO ^ 00

These properties provide an iteration procedure for determining the correct

value of and its associated constant a, provided the production cycle is far

enough advanced for the deflections of the linear graphs to be perceptible.

From the cumulative curve, Q versus t, a rough visual estimate of the value of

Q can be made. Then a series of assumed values Q, Q, Q-, , etc. can be used 00 D\ D2 #3

for plotting a family of curves, In versus t. For the too large values of

the curve will deflect toward the horizontal, and for the too small values,

toward the vertical. The value of for which the curve continues as a straight

line will be the correct value for Q . The slope of that line will be -a.

CO -1

A less cumbersome and more precise variation of this procedure consists in

choosing three fixed times, t , t^> and . Let Q^, regarded as a variable, be

an assumed value for Q . Then, at times t , t , and t , 00 12 3 N

1 - V«i • 1,

N

2

" 1. > V«3 '

• 1,

(43)

53

(44)

and the curve, In versus t, will consist of two line segments, one from

to t

2

, and the other from t

2 to t^. Fltom these respective line segments the

corresponding negative slopes will be

-S

12

= In {N

l /N2 )/{t2

- tj,

-S

23

= in iN2 /N

3 yit3

- t

2

).

Hence S12 an£* ~^23 each ^e a separate function of Q^. When these two

quantities are each plotted graphically as a function of , the point at

which the two curves intersect one another will correspond to

S

\2

= S

23'

for which the curve In versus t will be a straight line. The coordinates of

that point will be

~ S

12

= ~S

23

= a > (45)

% - ^

which are the desired constants of the equation.

This is illustrated in Figure 10, based upon the following data for t^ 3 t^ s

and and Q2

, and

Date (t) 1905 1945 1965

Q (10 9 bbl) 3.98 55.5 117.5

As shown in Figure 10, the values for the logistic constants corresponding to

these data are

Q = 173 x 10 9 bbl,

COa = 0.0750.

55
1 1 f 1 7

/ / \ /

zi m

zl

"cf / —j i

II / <N 1

1 j /

ezL = °°o

/

1 ! - jr 4 0i

_o

=

0.0}

•

00

o00

ix

o

_Q

_Q

O

_QO

3

00o O

O

o

CM

IXo

I

o

d

CO p

s03

+-> c

oo

<u p

c

•H C

c o

•H •H E P

03

0) p cr

<u <D T3 o

U •H o p

IH to •H O (30 o

•H

<u o p

0) p tpo

T—

03 8 o OP

•H

tJc

03U

CD

(30 •H

S3dO!S 3AI1V03N

56
An independent procedure for determining the constants Qm

and a is that

based upon equation (27)

,

{dQ/dt) Q = a - (a/QJQ.

If successive values of dQ/dt are known for successive values of Q, and if these

data correspond to the logistic equation, then the curve of equation (27) will

be a straight line intersecting the vertical axis as Q -> 0, at

(dQ/dt) /Q = a,

and the horizontal axis at

Q = Q • 00 This is illustrated in Figure 11, for the same constants as those for Figure 10.

After the best value of the constant Q has been determined, then the

00 linear graph of equation (36)

,

In N = In N - at,

o can be constructed. From this, the time at which the inflection point on the

Qt-curve , or the maximum rate of production dQ/dt, will occur can either be

read from the graph or else computed from equation (36) . According to equation

(26) , the peak production rate will occur when

Q = QJ2,

or when

N = Q /(« /2) - 1 = 1

oo do

and

In N = 0 .

Solving equation (36) for t when N = 1 then gives

t = [In (N

Q/N)]/a

= (In NJ/a.

57
1 ]«.

OL x CZL= °°0 —y~

(,-OD

0/(*P/OP)

U

U

aS

0

XI

4-> O

c

OfcoH+Jo

T3ou

a3 &

S <u

XI +J

a3

t/> i—i

+-> 3

aJ 3

•P O

1/5 C 4-1 o o

ao o h c O Uh

i—i 05

t/5 03 Of

4hO

C

o

•H

03 4^ •H \6 Q? U 'XS

<D *

> a o

i

H

IX,

58
Thus, if T be the date in years and T

q

the arbitrarily chosen date for

which t = 0, then the date of peak production rate would be

T . = T + (In N )/a. peak o

v o

(47)

Cumulative Production, Proved Reserves,

and Cumulative Discoveries

The foregoing analysis pertains to a single quantity, such as cumulative

production, and its variation with time during the complete production cycle.

Actually, there is another important variable, based upon additional information,

namely, proved reserves. Proved reserves, as defined by the Committee on Proved

Reserves of the American Petroleum Institute, represents, essentially, oil in

existing fields that has been proved by development drilling and is recoverable

by existing installed equipment and technology. Estimates of proved reserves

at the end of each year have been made annually for the United States since 1936

by the Proved Reserves Committee, and approximate figures, based upon various

earlier estimates, are available back to 1900. Because additions to proved

reserves are added annually only as new discoveries are made and older fields

are developed, the figure for proved reserves is a conservative figure and is

not intended to represent the ultimate amount of oil that the known fields will

produce. Over- and under-estimates made in previous years are adjusted as new

information becomes available by annual revisions. Proved-reserves estimates

are therefore internally consistent and probably have a reliability within a

range of a few percent

A third significant quantity is that of cumulative proved discoveries.

This does not represent independent data but is a derived quantity, defined in

terms of the primary quantities, cumulative production and proved reserves.

59
If we let Q represent cumulative production, proved reserves, and

cumulative proved discoveries, then is defined by the equation

Qd

- «p

* er

. (48)

In other words, all the oil that can be proved to have been discovered by a

given time is the sum of the oil already produced plus the proved reserves.

The manner of variation of these three quantities during the complete

production cycle, for a large region such as the United States, is indicated

in Figure 12. The cumulative production curve, Q , will be a generally S-shaped,

P

logistic-type curve, asymptotic to zero initially and to Q finally. The curve

of proved reserves, Q^, will be asymptotic to zero initially, and again at the

end of the exploitation cycle, and will reach a maximum in the midrange of

the cycle. The curve of cumulative discoveries, will also be a logistictype curve similar to that of cumulative production except that it will precede

the latter in the midrange by some time interval A£. This curve also will be

asymptotic to zero initially and to the same value of Q finally as for the

curve of cumulative production. This must be so because, as t * 00

, > 0,

and equation (48) simplifies to

Q. = Q = Q . *d *p

Taking the time derivative of equation (48) gives

dQjdt = dQJdt + dQJdt, (49)

the terms of which are the rates of proved discovery, or production, and of

increase of proved reserves. When proved reserves reach their maximum value,

dQ

r

/dt = 0,

and at that time equation (48) reduces to

dQd

/dt = dQ /dt.

60
C

ctJ

CD Sh"-H Q? OX t/) u

cd >>

fn o

0 •H

if) P

cd o

fn 13 O > Ph O

5h 0) ft P

0)

Of E

O c o

o

•H W) p C

o •H O

Of /—

\

CD CM > t/1 CN •H CD P • H

5h U>

i—

CD H

AOO

o tn CN •H

M-i T3 o> O

CD i—

c >

o •H P

•H P

P rt CD

i—i •Hu

| > o

AiiiNvno

61
This is the time at which the curve of the rate of production, which is still

ascending, crosses that of the rate of discovery, already on its descent.

The curves Q , Q , and Q, and their time derivatives, shown as functions

p r o. of t in Figures 12 and 13 provide diagnostic evidence of the approximate stage

of evolution in its complete cycle at any given time of the petroleum industry

in a large area such as the United States. Because of the geometrical similarity

between the curves of cumulative proved discoveries and of cumulative production,

and the time lag At of the production curve with respect to that of discoveries,

it follows that at any given time the discovery curve amounts to an approximate

At-preview of the curve of production. Thus, if the curve of cumulative proved

discoveries passes its inflection point, corresponding to the maximum rate of

discovery, at a time tj, then the curve of cumulative production will reach its

inflection point and maximum production rate at a later time of approximately

t^ + At. The curve of proved reserves will reach its maximum at a time about

halfway between, or at about t

1 + At/2.

Application to U.S. Petroleum Data as of 1962. On March 4, 1961, President

John F. Kennedy addressed a letter to the President of the National Academy of

Sciences asking the Academy to advise him with respect to natural -resources

policy. In response, the Academy appointed a Committee on Natural Resources to

make the requested study and prepare reports for President Kennedy. I was a

member of that Committee and directed the study and wrote the Committee's report

on Energy Resources (National Academy of Sciences-National Research Council

Publication 1000-D, 1962).

For this study, the technique used in 1956 was no longer appropriate because,

during the intervening five years, the petroleum estimates of 1956 of 150 to 200

billion barrels had been progressively increased by various authors to 250, 300,

62
0

CO •V

CD

u

CD o XJ

fS X! •H » » o

CD i—

Oo nw c

CD o

•H •H

CD

O >oo O

to fn •H ft

"0

a> P

a> >o fts

ft oo O bo

13 •H C fn

aJ T3 o to H a> +J > O

CD ^—

id to o CD (N

fHft

x) bo

CD -H

O > Uh o

to

cd ft CN M

a3 tM cn

OS

O r-H

•H

IX, WOP

63
400, and eventually 590 billion barrels for the ultimate amount of crude oil

to be produced in the Lower-48 states and adjacent continental shelves. We

thus were confronted with approximately a four- fold range in the magnitudes of

these estimates. For the lowest, the United States would reach its maximum

rate of oil production at about 1965; for the highest, this would be delayed

almost to the year 2000.

Accordingly, it became necessary to disregard the various a priori estimates

of Qm

, and instead let the historical data on discovery and production determine

the approximate stage that the petroleum industry had reached in its evolutionary

cycle. Of primary interest was the determination of such critical dates as

those of the maximum rates of discovery and production, and of the maximum of

proved reserves. From these data, as a secondary objective, an estimate of the

magnitude of the ultimate production Q could be derived.

The theoretical basis for this analysis was that shown graphically in

Figures 12 and 13. The actual data for the curves of cumulative production,

proved reserves, and cumulative proved discoveries for U.S. crude oil from 1901

to 1962 are shown graphically in Figure 14. By visual inspection, the curve of

cumulative proved discoveries had passed its inflection point at about 1957;

proved reserves appeared to be at about their maximum in 1962; and the time delay

At between the curve of production and that of discoveries was approximately 10.5

years, and had been so since 1925. Accordingly, the production rate should reach

its maximum 10-12 years after 1957, the peak in the rate of discovery, or 5 to 6

years after the proved-reserves maximum in 1962.

For more precise calculations, the three curves of Figure 15 needed to be

fitted by analytical equations so that analytical derivatives could be obtained

with which to compare the actual annual rates of production, of discovery, and

64
o

(Ti

m

C r\i nl bO

(/) •H

P-, >

CM

(0 vO

CT>

i—l

CD +-> > fH O (D U X)3

SC co

•H

+Jo cn

i—

i O i—

o

i—i i—

•Ho if>

1 o

<D •H

fn

0)

fn >

O Oo

0 to > •H

•H

-t-> 03 T3 H (1) >

e O

S-l o ft

CO >

•H

i P

i—

bO •H

(S"l3UdV8 dO SNOmiQ) 0

65
oo o O CD iD

cn

4-1 01 O -Hu

CO <U +J > c o

co o

4J 03 03 -H C T3 OO rH

•H

CD

O

A I 4J CD T3

00 3 C >-i O

OJ>H

4J

cfl 0) <H

T3 3s o a

CN C/3 >£> • ON ^ H M C O

•H 4-1co

•HU

CO3

a"

0)

<D CJ S "H

4J rH 03

CO -H

CJ 00

•H

O

a

co cu

CJJ 4-1

oo

•H

66
of increase of proved reserves. For this purpose, various forms of empirical

equations were tested, but none gave satisfactory agreement with the data until

finally the logistic equation was tried and found to fit the data with remarkable fidelity.

The curve of cumulative proved discoveries, having At more years of data

than that of cumulative production, was fitted first. This was done by the

iterative procedure of equations (41) and (42), as illustrated in Figure 9.

The results, shown graphically in Figure 15, were

Q = 170 x io 9 bbl, 00 a = 0.0687/yr.

Then the year 1901 was taken for t , and

# = W - Q )/Q = 46.8.

O 00 o o With these parameters, the equations for Q^, Q , and were

Q*

d

= (170 x 10 9 )/[1 + 46.8e" a(t' 1901)

],

Q = (170 x 10 9 )/[1 + 46.8e"a(t" 1911,5)

] A (49)

P

Q - Q, - Q . *r *d vp I' The graphs of the actual data for Q , Q^, and superposed upon the theoretical curves are shown in Figure 16. Superposition of the annual increments

of proved reserves upon the theoretical derivative curve is shown in Figure 17,

and the corresponding superposition of the rates of discovery and of production

upon their respective derivative curves are shown in Figure 18.

In the Academy report, '£ was given as 1900, but the data were as of the end

of each year. Hence the end of 1900 is actually 1901.0

67
t/5 >

u

d) bO

</) c

CD •H

fn nd T> o

CD On > Cfl O CD Ph or t3 o

C

CD •

/—

\

P

CN o tp •H o • P bO o </> •H

U, Ph O •* u CN Ph bO vO

0>

** i—

t/5 P

CD • H •\

• H £ P

fn ^

CM CD > \0 X> O CTl Xi O r—

P

to X •H o —j T3 p

V) T3 I—

C

CD •H o > O •H O P

CD 03 Ph X) P

cr

CD CD > o

•H O

+-> •H

rt CO P

t—i t/> P 13 •H

bO <P O U O i—

S"I3ayV8 JO SN0I11I9

68
1—

vO C3

C7> o

>—

H1 +-> O a3 o

<r

1—

o>o

I— H

•HO to •H

d) bO 13 O

3 rH o 0>

• e

o

h

<WO

tfl >

(L> >

o

0

V) i—

03 ^ O

•H

13 •P

0) <D > ?H • O O /—

d) Oi ftX CM

+J O 1) bO X -H

V) •M Ph P

c c - O CN e Ph\0

<D 3 C7l fn i—

O 13

0) « •H (/) +J O h

r-H Ph 0)

03 fn X Q) Xi C O, 3

3 EC

V) v—

•H

(ha/sigq jo sNomis) ip/ op

69

i
CD

tOO

P-i * fn

<D 00

P-i —

<

to • •H

Ph vO

i—

I

CM

1 O

o rH

a>

t—

i

+-> X <D > P oo

to •H to T3 PSo

T3 •H

+J >

V) ro nb

cc Ph <u EA of ic > p

13 10 PS •H

rt W)O

PS i—

(

O

•H tD •PO +-> 3

T3 4-1 O O

Ph to

tD>

O

P

O

0) +J <D

aJ >

•HP

i—

i

rt >

P •H

PS fn

<S) 3

GO

•H (HA/S199 JO SN0I~I"II9) 4P/0P

70
In Figure 17 it is seen clearly that the curve of increase of proved

reserves had already gone through its positive loop corresponding to increasing

reserves, and was crossing the zero line into its negative loop at just about

1962. This marks the date of the peak of proved reserves.

In Figure 18, the annual discoveries fluctuate widely, but their oscillations still follow the derivative curve and indicate that the peak region

had been passed at about 1957. The peak in the rate of production can accordingly be expected to occur near the end of the 1960-decade.

These were the interpretations made graphically in the Academy report of

1962. Although this was not done at the time, more precise figures can be

obtained from the equations (49) . As shown in equation (46) , the peak rate of

discoveries occurs at the time

t * t + In N /a.

o o

Hence, from equation (49), the peak discovery rate should occur at the time

t = 1901 + In 46.8/0.0687

= 1957.0.

The corresponding date for the peak in the production rate would be 10.5 years

later, or 1967.5, and the peak of proved reserves would occur at 1962.25. All

of these figures are consistent with those obtained from the graphical interpretation of the data.

An even more informative procedure consists in plotting the linear graphs

of the logistic equations of cumulative proved discoveries and cumulative production from 1901 to 1962 on semi- logarithmic graph paper. The corresponding

equations for discoveries and production are

log N

d

= log N

q

- (a log e) {t - t

Q

)

71
and

log N = log N

q

- {a log e) [t - (t

Q

+ At)],

where t = 1901, and At = 10.5 years.

In these equations, the peak discovery and production rates each occur

when 0=0/2. or when

^ = Ky^c/2 )] -i = i.

Hence the dates at which the respective linear graphs cross the line N = 1,

or log 217 = 0, are the dates of peak rates of discovery and of production. These

graphs for the cumulative discovery and production data at 5-year intervals from

1901 to 1962 are shown in Figure 19. Note that by 1962 the cumulative-discoveries

curve had already crossed the line N = 1 at 1957.0, and that the linear graph for

cumulative production had been parallel to the discoveries curve since 1925 with

the time lag of 10.5 years. Hence only a modest 6-year extrapolation of this

curve was required to reach the line N = 1, corresponding to the peak in the

rate of production at the year 1967.5.

Thus, the combined data on production, proved reserves, and proved discoveries

of crude oil in the Lower-48 states were by 1962 sufficient to establish that the

peak in the rate of production would have to occur at about the end of the 1960-

decade with a range of uncertainty of not more than about 3 years. The corresponding maximum production rate from equation (39) would be about

dCT/dt = afi/4,

p °° or

(0.0687 x 170 x 10 9 )/4 = 2.92 x io 9 bbl/yr.

The Decade of 1962-1972 . — Although the reports of the National Academy Committee were released to the public by President Kennedy in January 1963, the

influence on public policy of the Academy report on energy resources was essentially

nil. The estimate of 590 billion barrels for the ultimate crude-oil production

72
I aivH 'aotfi *xvw *xsa

o

i i i—

|—

aivH 'ao^d *xvw "isa

/

saA^asan aaAcrad *xvw

i i i—

/

S3'396T

o

00

o

o

vO

03

•H

t>/0>- °°t» = N

73
from the Lower-48 states had been given to the Academy Committee by V. E.

McKelvey, Assistant Chief Geologist of the U.S. Geological Survey, as the

official estimate of the USGS. It was cited in the Academy report but, because it could not remotely be reconciled with the petroleum- industry data,

it had to be rejected. During the next 5 years, substantially the same

figures, modified slightly from year to year, of about 600 billion barrels

of crude oil and 2,500 trillion cubic feet of natural gas, were published

repeatedly in U.S. government and other publications by McKelvey, either alone

or in collaboration with D. C. Duncan (Duncan and McKelvey, 1963; McKelvey and

Duncan, 1965; McKelvey, 1967).

In the meantime, the curve of annual crude-oil production from the Lower48 states continued on the linear upward trend that had prevailed since. 1932,

except for a distortion from 1957 to 1970 associated with the first Suez crisis

and successive Middle East disturbances and the Vietnam War. After 1957, the

production rate fell below the linear trend, but by 1970 it rose to 3.24

billion barrels per year, which was just about on the trend. During 1971 it

declined slightly to 3.18 billion barrels per year. Consequently, during the

decade 1962-1972, there was no perceptible evidence from the curve of annual

production alone of the imminence of an impending peak and subsequent decline

of the annual rate of U.S. crude-oil production.

One of the first alarms over impending trouble came in the spring of 1969

when the annual report of the Committee on Natural -Gas Reserves of the American

Gas Association was released, giving the proved reserves of natural gas as of

the end of 1968. The report showed that by the end of 1968 natural-gas proved

reserves for the Lower-48 states, which had been increasing steadily since 1947,

had dropped 7.2 trillion cubic feet from 289.3 trillion cubic feet at the end

74
of 1967 to 282.1 by the end of 1968. During the following year, the proved

reserves dropped by 12.2 trillion cubic feet, as compared with the annual

production rate of 20.7 trillion cubic feet.

By 1971, the evidences of impending declines in the rates of oil and gas

production were sufficiently clear that the U.S. Senate Committee on Interior

and Insular Affairs, under the Chairmanship of Senator Henry M. Jackson, began

a new series of hearings on National Fuels and Energy policy. As of July 23,

1971, Senator Jackson addressed a letter to the Secretary of the Interior,

Rogers C. B. Morton, requesting my assistance on statistical work for the

Committee. What I was asked to do was to bring my earlier studies on energy

resources up to date for the use of the Committee. The result was the report,

U.S. Energy Resources A Review as of 1972^ which was released as a Committee

Print in June 1974.

In Figure 20 the curves of cumulative proved discoveries, cumulative

production, and proved reserves from 1900 to 1972 are shown as solid-line

curves superposed upon the respective mathematical curves, shown as dashed lines.

The respective logistic equations are also shown in the figure.

With 10 more years of data after the Academy report of 1962, the best

value for Q was still 170 x 10 9 bbl and the growth constant a was still

0.0687/yr. The time interval At had been increased from 10.5 to 11.0 years,

and 1930 was taken for t . The corresponding value of N

q

became 6.17. By 1972,

proved reserves are plainly seen to have passed their peak about 1962, and the

curves of cumulative discoveries and of cumulative production are accurately

following their respective logistic curves. From the logistic equations the

dates for the maximum rates of discovery and of production, and of the maximum

of proved reserves are found to be:

75
00

•3-1 rH

CDo

CD

r;o

rH to

1—1 HQ •H

CD

*rjrH o

to J_| CD CD > ri

r-i CD

CO

CD

v /

f_i to T)

CD J>

;> 5_i o u o 

r-M

u

•H

4J

03 t/) *H

oij to o 0 ,—

H

J_l CD •H o

CO o H p,

T3 CO

(D T3

CDo u p 

CD

<-; j 1

rtC •H o

•H

•P •\ O (N

<T>

O rH

fH 1 o

CD> rH HP

rt tfl rH CD P 6 rt p U to 1 o

U> • H si3dava jo SNomia

76
Discoveries 1956.5,

Production 1967.5,

Proved reserves 1962.0.

The time derivatives of these three curves, with the corresponding annual

data, are shown in Figures 21 to 24, and the estimated complete cycle for crudeoil production, in Figure 25. Figure 21 shows the rate of increase of proved

reserves superposed upon the mathematical derivative. The curve completed

its positive loop and crossed the zero line in 1962, and by 1972 was approaching

the low point of its negative loop. The rates of discovery and of production

are both shown in Figure 22, and separately in Figures 23 and 24. In Figure 23,

it is unmistakable that the discovery rate passed its peak before 1960 and is

well advanced in its declining phase.

The curve of the rate of production in Figure 24 still shows no definite

evidence that its peak has been reached. Instead of reaching a maximum about

1968, the curve fell below the mathematical curve after 1957 and then rose

steeply from 1960 to 1970. Whether the slight reversal in 1971 represents the

beginning of the decline is an open question. However, the composite evidence

of all the data indicate that the reversal of the production-rate curve, if it

has not already occurred in 1971, must happen in the very near future.

The estimate of the complete production cycle as of 1972 is shown in Figure

25. Cumulative production by 1972 amounted to 96 x 10 9 bbl and proved reserves

plus additional oil in fields already discovered amounted to another 47 x 10 9

bbl, giving a total of 143 * 10 9 bbl for the ultimate amount of oil to be produced from fields already discovered. Then with 170 x 10 9 bbl for Q^, only

27 x io 9 bbl are left for future discoveries. Another informative aspect of

Figure 25 is the time span involved. The time required to produce the first

10 percent of Q , or 17 billion barrels, was from 1860 to 1932. That required

77
CD ,c

o

Ph

CD

i/l O

ft

fHH>Ph

<—

\

O

(jA/ s|qq

6 0T)»P/

J C)P

78
(jA/ s|qq

60T) »P/f)P

79
0) /—

ft (30 to

to • i

i •H

Oi

r—i1 oo

en i—

i—

P

i—

0) o

13 £ o co . H

CO 4-> • nJcr

tpo o

</)

H

0) P

•H t/) ?H •H

0) bO > o o 1—1 o

to CD •H

Tl 4-> TJ <4-l CD O >O 0)>

ft •H

-P>

•H c fH

CD

a

to

CMM

•H

aviA/siaaava jo SNomia

80
|

1

1

1

/

/

/ /

/

/

/

/ //

/

S

/

/

/

/

<\

zo

JE

OF

PRODUCT

1

J

cc\

aO"D

8

o

00

>

•H

T3

<L> A+->

4-1O

CD&

3o

c

o

0

V)O

Ph

a>a,3

•> to

r-i a> bo

t—( -H

I PL, O

O -

CT> ^

o -P

f-i

CO c

• o 3 "H

+J O 3

cr o

•H

•Po

O

ft

O

•H

4->

t/> •Ho

i-H 0) 3 +J C

5 4-1 < o

I

bO HPL,

ro cm yv3A/si3ddva jo SNomia

81
82
for the next 80 percent, computed from the logistic equation, would be the

67-year period from 1932 to 1999, and the last 10 percent would occur after

1999.

The Period from 1972 to 1980. — Until 1972, our principal concern was the

prediction of the future of the rate of U.S. crude-oil production. The mathematical curve of the rate of production passed its maximum about 1967-1968, but

the production rate continued to increase sharply until 1970, yet all the

evidence indicated that a decline was inevitable in the very near future. We

now have 7 to 8 more years of data by means of which the pre-1972 predictions

can be evaluated.

Figure 26 shows the linear graphs of the logistic equations for cumulative

discoveries and production of crude oil in the Lower-48 states for the period

1925-1973. In this case a new determination of the logistic constants was made

with the results:

Q = 170 x 10 9 bbl,

00

t = 1925,

oAt = 10.7 yr,

N = 9.05,

oa = 0.0674/yr.

Both curves by 1972 had crossed the line N = 1, corresponding to the dates of

the respective maximum rates of discovery and production. The date for the

discovery maximum rate was the year 1957.7, and that for the maximum production

rate, 1968.4.

The curves of cumulative proved discoveries, cumulative production, and of

proved reserves have been plotted to 1979 in Figure 27. These are superposed on

the logistic curves of 1972 as a means of comparing the more recent developments

83
DOo

-J

896;

AOOSTQ 'XB^

LO o o 1—

<>* E-y i o II Qo

so

a, Lo > ii < o

-3 oO

00

CTi OOo

LOoO

to

cno

rsj

to<

UJ

LO

to

CTl rH •H 1 LO

CM > CTl o i—

o

!/) •H (0 T3 0)

4-> 13 03

0) +-> > t/5 O

oo >

•H 3O

rt -J

co o pe o o

4h c i—i o •rl •H O

4-> CD s0) f-l O o

•H

+J o

t/> •H

bO o o •H

1—

PO

0) +J

OU

Ph

O 0>

•H

Ph -p

o3 03

Sh i—i bO 1

03 o

0)C X) H C

03 1 vO

CMM

•H

PL,

&/(& - d) = n

84
> < S-i o UJ

se:

LU

(- 13

si3Muva jo SNomia

85
with the 1972 predictions. It will be noted that the cumulative production is

following the logistic curve rather closely, but both the curves of proved

reserves and of cumulative discoveries have fallen significantly below their

respective mathematical curves. From this figure, it appears that cumulative

discoveries may fall short of the 170-billion-barrel asymptote for Q by as

much as 7 to 10 billion barrels. Should this be so, cumulative production will

have to do the same.

This is shown even more clearly in the derivative curves of Figures 28 and

29. Figure 28 shows that the annual rate of increase of proved reserves (which

has been negative since 1962) has been well below the mathematical curve during

the 1970-decade. The mathematical curve shows a minimum of about 0.8 billion

barrels per year occurring in 1980 for the rate of decline of proved reserves.

During the period 1973-1979 the average rate of decline was close to 1.5 billion

barrels per year, indicating that about one-half of the production during that

period was obtained by withdrawal from proved reserves.

Figure 29 shows that from 1972 to 1979 even the high points in the oscillatory

curve of annual discoveries were below the mathematical derivative curve of the

1972 logistic equation. Figure 30 shows the corresponding comparison for the

rate of production. The year 1970 was indeed the year of peak production, with

the production rate falling steeply from its maximum of 3.24 billion barrels in

1970 to 2.45 in 1979.

In view of the departures of the curves of cumulative proved discoveries

and of proved reserves during the 1970-decade, as is shown in Figure 27, from

the logistic curves of 1972, new calculations have been made with the particular

objective of obtaining a new estimate for the magnitude of Qm

. One procedure

has been to make new determinations of the constants of the logistic equation

using the data from 1900 to 1980. A second procedure was based upon the linear

86
( jA/ S|qq

6 0l)WV J6P

87
(N 13

i-H o

M-lo

e.

~> p

•H

<4H 4-> O

3


 a*

<D <u •H

fH o

•H > P

O trt O •H

tfl W)

•H O

-n i—)

<4-l 0) O

>

o <a

fH >

Ph H

P

rH

Oj >

=5 •H c in<D 13

ro cm MV3A/S13ydV8 JO snoitiis

88
89
equation (27)

,

(dQ/dt)/Q =% - ia/QJQ.

Using the method described in equations (43) to (45) , the curve of

log versus t was constructed at 5-year intervals from 1900 to 1980, using

an assumed value of 163.0 billion barrels for Q,. From this, the following

three dates and the corresponding cumulative discoveries were chosen as being

points on the smooth almost linear curve:

Dates: 1915 1960 1980

3(10 9 bbl): 8.74 92.61 136.90.

The constants obtained for the logistic equation, as shown in Figure 31, were:

t = 1915,

o N = 17.570,

oQ = 162.3 x 10 9 bbl,

a = 0.0700/year.

A second calculation was made by the same procedure except that the curve

of cumulative discoveries, versus t, was first smoothed by means of an

11-year running average except for the last 5 years. This gave the results:

Q = 161.8 x io 9 bbl, 00 a = 0.699/year.

The results of the estimate based upon the linear graph of [dQ/dt)/Q versus Q

are shown in Figure 32. In this case, the curve of cumulative discoveries versus

time from 1900 to 1980, except for the last 5 years, was smoothed by an 11-year

running average, and dQ/dt, at 5-year intervals, was based upon 5-year averages.

For the earlier figures, as was expected, there was a wide scattering of the data

points, but for the last 25 years from 1955 to 1980, the data points gave a very

good straight line. Extrapolation of this linear trend to the Q-axis and to the

90
CO

_Q

_Q OO

O

(jX/^_0L)S — adol s ^069^

3 o

00 o —io

10 o

(/> fiOo

+J

aJ 'H

cr

i a> o >

•rl •P

10 o

u

a. O >

o 3

•H O

+-> rt rH

PS -H

•H O

S i u <u +J 3

Q O

to

bfi •H

91
1

-

1 1 1 1 1 1

-

-

-

:i-q/Qoo)

iqq 60TX9 , ^79T= oo t>- —

/"

/

/

/

- -

II

p

00

00

vOO

or

•

• /

• o

II CO

1

1 / • # 1 • \V till 1

o

o

CMO

ooo

vOo

o

CMo

o

o

00

o

o

o

CN

o

CO

^3 LOOl o f—

i o

to oo

1—1

to

CD o •H

!-i tfl >

o O

•H O

4_) to >

aj •H

-d

a> i—

1 •H o o

•r-f M <L> Q?

CO •H v ' 00O O

rH O

13

4-1 <D O >

O §

c •H o a, c H+-> o

ai > CD C •H p

•H P

e aj a) i—

•p p

0) Q O 43

CNto 00 vO CO CN r-l o

o o o o o O O O o •H

•

' • • Ph o o o o o O o o o

b/(3P/bP)

92
vertical axis gave the following figures for the logistic constants:

Q = 164.6 x 10 9 bbl,

a = 0.0688/year.

Estimates Based upon Discoveries

per Unit Depth of Exploratory Drilling

Development of Theory . — Heretofore we have dealt principally with the

variations with time of cumulative proved discoveries and production, proved

reserves, and their derivatives with respect to time. One difficulty with

variations with respect to time is that such variations are sensitive to economic

influences such as fluctuations in prices. A different kind of variation, involving new data not previously used, is represented by discoveries per unit depth

of exploratory drilling as a function of cumulative depth of drilling, or of

cumulative discoveries. The rate of discovery of oil per unit depth of drilling

is determined principally by the geological situation dealt with and by the technology of exploration and production; it is highly insensitive to economic influences .

Let h be the cumulative depth of exploratory drilling in a given region, and

Q be the cumulative discoveries. Exploration in the region begins with h = 0,

and Q = 0. Then as h increases without limit, Q tends to a definite finite

limit Q^. The rate of discovery as a function of h will be dQ/dh.

Because of the indefiniteness of the upper limit of h, but not of Q, it is

convenient to consider the variation of dQ/dh as a function of Q, as we have done

previously when considering dQ/dt as a function of Q. Thus we consider the

variation with Q of dQ/dh within the limits of the complete cycle as Q increases

from 0 to Q . During this cycle, when

93
Q = 0, dQ/dh > 0;

0 < Q < Q^ dQ/dh > 0; v (50)

Q = = 0.

The variation of dQ/dh with Q, can be expressed by the Maclaurin series,

dQ/dh = a

Q

+ + c? 2 Q

2 + --- + o <f . (51)

The lowest degree and the simplest form of this equation that satisfy the

conditions of equations (50) is the first degree,

dQ/dh = o

q

+ e$. (52)

When

and from equation (52)

,

or

Q = Q, dQ/dh = 0,

a = -cQ (53)

o 1

00 Substituting this into equation (52) then gives

dQ/dh = -o

Y (Qm

- Q) ,

and letting 3 be substituted for ^e., we obtain

dQ/dh = SC^- 6). (54)

Thus dQ/dh varies linearly with respect to Q, as shown in Figure 33, having

its intercept on the vertical axis, when Q = 0, at BQ^; and on the horizontal

axis, when dQ/dh = 0. at fl . The slope of this line is -3.

oo To obtain dQ/dh as a function of 7z we separate the variables and integrate,

f dQ

Q- Q

$dh + a, (55)

or

ln(Q - Q) = -&i - o. (56)

94
0)>

o

u

0)>

E

u

+->

d) V)

CD p • H

•H ^

C CD>o

o

CD t/5 Cm H

-d

to

0) •H >

?-i •H

•P > rt O rH O

is umo

r-H -d

•HO

c

CD

CD H

£ i—

+-> i—l CD •H

,£> U

T3 c

o

•H

+J o

+-> i-i oS

<DM O

U Pm

cd 0

• HJ o

to

to

HP/OP

4j/SdU9A03S!Q

95
Then, when Q = 0, h = 0, and

-a *J ln Q (57)

Equation (56) then becomes

ln(Q -

v Q) = In Q - $h 00 y

oo (58)

or

(59)

Differentiating equation (59) with respect to h then gives

dQ/dh = Wj*'^.

The manner of variation of' both Q and dQ/dh as functions of h are shown

(60)

graphically in Figure 34.

The foregoing results, as has been shown by Arps and Roberts (1958),

Arps, Mortada, and Smith (1971), Menard and Sharman (1975), Root and Drew

(1979), and Drew, Schuenemeyer , and Root (1980), are also consistent with

the expectations of probability theory. The probability of the discovery

of a given amount of oil by a fixed amount of exploratory drilling in a

given area is roughly proportional to the undiscovered oil in the region,

Q = Q - Q. u °° Consider the idealized case of a region of exploration of total area S

which contains fields of uniform oil content A$ occurring at the constant

depth z. Let A which is small compared with S, be the total area of such

fields, and let A be the area of the fields already discovered by cumulative

depth of exploratory drilling h. Then

dQ/dh = CAS/aHCV A)/S]. (61)

Then, if

6 = Q/A (62)

is the oil per unit area in the fields,

96
o

CQ

~0

O-o -p •H

P-i rH

dlw •HH

•H

r;*1pJ M

4-* 0) d

ft

(/) ,—1 (D D . r-H •H rS M CI) CD 0

CJ *H

CO 1 > •H ctf rHHr~*

F=! Q Ri—

(j

J—

w

CO to

/1\

<L> H

H •H 0 j.j (j

f-» Ui (J

(/)

to

rrt to

•H

o3 i—

i—rH•Hu O X

rH o O

-P

03 c rH o O

•H rH

4->

ctf X

• H <D rH

4-1 > O

8

O

•H

PL,

S3U9AODs;p aAijDjnujn^

97
which, when substituted into equation (61) , gives

dQ/dh = (AQ/zS6)iQoo - Q) . (64)

This is of the same form as equation (54) , where KQ/'zSS in equation

(64) corresponds to 3 in equation (54) . Integration of equation (64) then

gives for Q versus h an equation of the form of equation (59) , and differentiation of that with respect to h gives an exponential decline of dQ/dh

versus h of the same form as equation (60)

In an actual oil-bearing region these simplified conditions do not occur.

There are commonly a small number of large fields which frequently contain

most of the oil, and a large number of small fields. Also the depths of the

fields range from a few hundred feet to as much as 20,000 feet. In addition,

in a region such as the entire United States, the technologies of discovery

and of production undergo progressive improvement during the entire cycle of

oil exploitation. This favors the discovery of the larger and shallower fields

during the earlier stages of the cycle with a rapid rate of decline of dQ/dh

versus h, followed by a slower rate of decline as the sizes of the remaining

fields decrease and their depths increase. Offsetting this somewhat is the

steady improvement of the techniques of exploration and production which tends

to increase the discoveries per foot with respect to the rates expectable by

random drilling. The net effect, however, is still roughly an exponential

decline of dQ/dh versus h.

In order to correlate the oil discoveries made in a given region with the

corresponding exploratory drilling, a different definition of the term "discoveries

from that of "proved discoveries" used previously is required. In this case all

of the oil that the fields discovered in a given year will ultimately produce

must be credited to the exploratory drilling done during that year.

98
This involves estimates of "ultimate recovery" of oil from fields discovered in a given year as estimated at a later year t .. The ultimate

recovery from fields discovered during the year t . as estimated at the later

Is year i . is defined as the sum of cumulative production from those fields to

the year of the estimate plus their proved reserves at the time of the estimate.

At the end of the year of discovery the only oil credited to the discovery year

is the item "New Field Discoveries," in the American Petroleum Institute annual

report on proved reserves. This ordinarily is only a small quantity. During

succeeding years, cumulative production from those fields steadily increases,

and the sum of cumulative production plus proved reserves gradually approaches

asymptotically the quantity SQ , which is the true ultimate amount of oil those

fields will produce.

The first study of this kind for the U.S. crude-oil production was that

made during World War II by the Petroleum Administration for War (PAW) (Frey

and Ide, 1946, Appendix 12, Table 10, p. 442; C.L. Moore, 1962, Table IV, p. 94).

In effect, what was done in the PAW study was to combine the cumulative production

to January 1, 1945, with the American Petroleum Institute estimate of proved

reserves for the same date for all the fields discovered during each successive

year from 1860 to 1944. This gave an estimate as of January 1, 1945, of the

proved oil discoveries assignable to fields by their year of discovery. Two

more such studies were made subsequently by the National Petroleum Council (1961;

1965). The first brought the PAW study up to the date of December 31, 1959, and

the second to January 1, 1964. Each of the latter studies gave a lumped increase for all the discoveries made from 1860 to 1920, and then gave separate

estimates for the fields discovered during each year from 1920 to the terminal

date of the study.

In 1966, the name of the API "Committee on Petroleum Reserves" was changed

99
to "Committee on Reserves and Productive Capacity" and the scope of its

activities was expanded. One new item in the committee's annual reports

was a table for the year of the report of estimations of ultimate recovery

for fields discovered during the pre-1920 period and for individual years

from 1920 to the year of the report. These reports are given from 1966 to

1979 in the annual publication, Reserves of Crude Oil3 Natural Gas Liquids3 and Natural Gas in the United States and Canada as of December Sl 3 [given

year], issued jointly by the American Petroleum Institute, the American Gas

Association, and the Canadian Petroleum Association, for brevity, the API,

AGA, CPA "Blue Books."

Using these data, the problem is to estimate the ultimate amount of oil

that fields discovered during successive years will eventually produce. Two

principal alternative procedures have been developed for this purpose. One,

that developed by the present author (Hubbert, 1967; 1974), consists in following the fields discovered in a given year or group of successive years, and

plotting their growth with increasing time following their year of discovery.

If we let (6Q) 1 be the initial estimate of the new oil discovered at the end

of the year of discovery, and (<5§) T be the estimate for the same fields t years

later, then we can plot a curve of

y T = C<5«) T/(6e)

1 (65)

as a function of t.

Expressed in this manner, y is dimensionless, and is independent of the

absolute magnitude of the oil discoveries in any given year, and the time-delay x

is common to the discoveries of all years. Hence the data for all discovery years

can be expressed in terms of y versus t. This will be a curve that rises steeply

initially and finally approaches the limit,

100
as x increases

This was the procedure used in 1967 (Hubbert, 1967, Figs. 4 and 5) using

the limited data then available, and again in 1972 (Hubbert, 1974, Figs. 45

and 46) with much more detailed information. In both instances, however, substantially the same growth curves were obtained, which were fitted by empirical

equations of the form,

y T = - « ]• (

The data as of 1972 are shown graphically in Figure 35, which is reproduced from my report of 1974 (Hubbert, 1974, Fig. 45). From these the constants

for equation (66) were:

By means of this equation it is possible to estimate how much more the oil

discovered in a given year will increase when its magnitude (6$) is given

after t years of production and development.

This is done by a correction factor a, defined by

Y = 0.076 per year,

o = 1.503 years.

a = yJyx

> (67)

which from equation (66) is

a = 1/[1 - e

" Y(T+c)

]. (68)

Then, since

and

yJyT = c««VC««) T

-

101
• CD ' * u LT)

CD "3" >oo bO

CO

H

•H

X)

CO "3- t3

i—i <u i—l •H

4-1 P E rH O CD

!-i XI

4-1

rH•H

v ' o

to

CD

u

CD

!hCJ

rH

4-1 CD O P X rH

rH

X > rH o 0 o >

1) •H

in 10

(0

CD CD P O

RjO 6 3

•H 10 P

r—

P

rt

0) T3 A CD p P

«s

4-1 3 O i—i

tfl >

CD CD P

Rj CD s U

•HP to

CD

to

CD rH

nJ P CDX cH

CD ,c > p •H so

rH •tH

CO

102
Hence

(6§) ro = o(6«}

t

. (69)

This first procedure is based upon the growth during successive years,

t., of the estimates of oil discovered in a given year, t.. An alternative

procedure is that described originally by Arrington (1960; 1966) and more

recently by Marsh (1971). In this case, use is made of the API estimates

for the two successive most recent years, t. and t. ,, for the oil discovered

in previous years, t^. In this case the fields considered are no longer the

same fields, but instead are the different fields discovered during successive

earlier years with an increasing value of the time-delay t.

In this manner a ratio,

r

T = C«fl) T+1 /(«fl)

T

. (70)

is obtained as a function of x for the oil discovered during each preceding

earlier year. From these successive ratios,

the growth factor y is obtained by the product

yT = ^1 r

2r

3 ••• r

T

}> (71)

which tends to y as t increases without limit.

As in the earlier procedure, the magnitude of (5$) for the discoveries

made during any given year is given by

where

In practice, instead of dealing with the discoveries made during single

years, the sum of the discoveries made during a sequence of 5 or so years may

be used. In that case, for a common value of x, the ratios must also be taken

during a corresponding sequence of successive pairs of years.

103
Three Successive Studies of U.S. Crude-Oil Discoveries

per Foot of Exploratory Drilling

The results of three successive studies of the U.S. crude-oil discoveries

in the Lower-48 states and adjacent continental shelves, as a function of cumulative depth of exploratory drilling, are shown in Figures 36, 37, and 38. The

first of these (Hubbert, 1967, Fig. 15) shows the discoveries made by the first

1.5 x 10 9 ft of drilling, which encompassed the period 1860 to 1966.7. The

second (Hubbert, 1974, Fig. 49) gives the results obtained by 1.7 x 10 9 ft of

exploratory drilling during the period from 1860 to just short of 1972. The

third, by David H. Root of the U.S. Geological Survey (Root, 1980), gives the

discoveries made by the 2.0 x 10 9 ft of exploratory drilling during the period

1860 to 1977.9. In the first two studies, the method used in estimating the

amount of oil ultimately recoverable from fields already discovered was that of

the present author, as described earlier. In the third study, Root used his

own modification of the method of Arrington and Marsh, which was applied to the

API, AGA, CPA "Blue Book" data from 1966 to 1978. For each successive study

more and better data were available than for the one preceding.

For the graphical presentation of the data, a convenient unit for hh is

10 8 ft. Hence, in the three figures, the cumulative drilling amounted to 15,

17, and 20 units respectively. For each unit of drilling, a vertical column is

shown representing the quantity of oil discovered by that unit. The lower part

of the column represents the proved cumulative discoveries as estimated at the

date of the study. The shaded area at the top of each column represents the

additional oil those fields are expected to produce as determined by the a-correction. The total amount of recoverable oil discovered by the first 15 units of

drilling in the 1967 study was estimated to be 136.04 billion barrels, of which

approximately 25 billion barrels were accounted for by the a-correction. In the

104
(M/siqq)

MP/OP 'Ad3A00Sia JO 31VH

105
siqq

6 0I x 01 / 8|BDS

U/S|qq 001

0Z6I

0961

0561

Of6

0C6I

0261

( U/ S|qq)

up/bp 'Aa3A00Sia jo 3iva

106
CO

LU

on

LU> _

o -g

to5 2

X

LU >— > °°- I— IV < to

I I— Z>

=)U

r

OZSl

IZ'LZ

VI ZZ

ZZ'Sl

6ZQI

90'6l

frC'6L

86' IG

80Zfr ^

689C

VTLZ ^1

Will

tl'ZIZ

SV6ZZ

iqq60l x59'892

I I

00

o

CO o

CO o

CN CM o 8

o

o

z

Q

>

o

oc CO O o

Q_ ^>

X

>

t—<

_l

u

(mm)

HP/OP 'JLOOd M3d S3lfJ3AODSIQ

o

rHo

cp

to

CD •HU • CD —

\

> o

o 00 o 0>

V) i—

•H P

i—l o

•H o

o Pi

CDP

O

C7> co rH

1 O

\0 <p 00 o rH p •* o

o c

D£ •H

i—

i—

H

rH T3

•H>

aS P Q O

-P

05 XI rHO

</> i—

CD P X

CD S

•H <P P O

t/5 OJ P

<P O

00 CO a> O

i—

1-1

00

to

•H

Ex.

107
1974 study, 143.44 billion barrels of recoverable oil were estimated to have

been discovered by the first 17 units of drilling. Of this, approximately

19 billion barrels were contributed by the a-correction. The total recoverable

oil estimated in the third study as having been discovered by the first 20 units

of drilling amounted to 157.87 billion barrels, of which 22.92 were due to the

a-correction

Because the results shown in Figures 36, 37, and 38 are all derived from

different suites of data, and, in the case of the last study, by a different

method of analysis, it is not to be expected that the results obtained would be

in close agreement. Nevertheless all of the studies give results of strong

similarity. All show high rates of discovery, averaging between 20 and 30 billion

barrels per 10 8 -ft unit of drilling (200 to 300 bbl/ft) for the first 4 units,

followed by a precipitous decline. In Figure 36, the discovery rate had declined

to only 3.52 (10 9 bbl/108 ft), or 35.2 bbl/ft, for the last or 15th unit; in

Figure 37 this decline had reached 30.2 bbl/ft for the 17th unit; and in Figure

38, by the 20th unit, it had declined still further to but 8.56 bbl/ft.

All of these figures show a roughly negative-exponential decline in dQ/dh

versus h during the entire cycle. In order to estimate the future, the negativeexponential curve best fitting the data needs to be determined in each instance.

To simplify notation, let dQ/dh be represented by R.

Then

R = R e~^

k

(72) o will be the desired equation of which the two parameters R and £ are to be

determined from the data. The criterion for best fit will be

h

• nRdh = Qn

, (73) o

108
where represents the total discoveries made by the units of drilling,

with the curve passing through the last point (i?^, h ) on the graph. In other

words, we wish to determine the negative-exponential curve that equalizes the

excesses and defects of the data, and passes through the last point.

Substituting the value of R from equation (72) into equation (73), we

obtain

Q = R

n o

h

e^dh

from which

g = (i? K - R )/Q . (74)

o n

J n

v J

Also, taking the logarithm of equation (72), with R = R and h = h ,

we obtain

or

In (Ron/R ) = mn

= In (RK IR )/h . . (75) o n n

J Dividing equation (75) by (74) then gives

In (i? IR ) Q

o n

J n _ f

. on n

of which the onlyJ unknown is R . -This can be solved for R by an iteration

o o procedure of substituting for R an assumed value R^ whereby the left-hand

term of equation (76) becomes f(R^). When /(i?^) has the value of 1, R = R

q

.

The decline parameter 3 is then obtained from either of equations (74) or (75).

Once R and g are known, the estimate of the ultimate cumulative discoveries,

Q, is given by

109
and that of the undiscovered oil, Q , by

%

= V3 - ( 78 ^>

The negative-exponential curves obtained in this manner from the data

of Figures 36, 37, and 38 are shown in Figures 39, 40, and 41. For the

study of 1967 (Fig. 36), the values of the parameters are:

R = 18.63 (10 9 bbl/10 8 ft),

= 186.3 bbl/ft,

3 = 0.1111 per 10 8 ft.

From these parameters and the numerical data of Figure 36,

R, c = 3.52 (10 9 bbl/108 ft),

Q = 136.04 x 10 9 bbl,

Q = 31.7 x 10 9 bbl,

u and

Q = 167.7 x io 9 bbl. oo This value of 168 billion barrels for Q obtained from the 1967 study of OO discoveries per unit depth of exploratory drilling as a function of cumulative

drilling, although based upon different data and a totally different method of

analysis, is in very close agreement with the figure of 170 billion barrels

obtained in the studies of cumulative production, proved reserves, and cumulative

proved discoveries made in 1962 and 1974.

For the negative-exponential curve for the 1974 study of dQ/dh versus h

shown in Figure 40, the values of the two parameters are:

R = 18.154 (10 9 bbl/108 ft),

= 181.54 bbl/ft,

3 = 0.1055 per 10 8 ft,

and

110
HP/DP 'A»3AODSia dO 31VH

111
m

o

to

a> to

+-> <D S ai •H P

P 75

100 00

(N I

f-t cr> <d -i So M J

•H • > CO •H •

(U to x

H O

tL, <P C to O (U 3 u

tD>

o

T3

0)

10 o

o 10 Ph-H

Ph <-i 3 -H

to O

I 0> CD >

o 3 o

OJ () W) c p -h •H u- •h e O -H *

CD P "3" T3 H N

r-{ I—

•H C - P P

<D <D <D

fS h XJ O 3 X) ftp 3

X 3 33

o•3-

•H

(«/S|qq) gp/5p

112
^3

jlMI E* n

o

CO

o

CO

O

CN

Q

>-o

I—

< **= OH 00

O o

_J '

Q_X

iO LU - >

3

o o

o

o

hpidp 'aiva AaaAODSia

4-1o

V) • P CD

rt -p E aJ H (->

4-> 10

CO

CD 00 O I 00 f-i 0> CDo

c

•H • > (/) •H •

oo 0

to X4-> bi ?h "H O

C to O CD ft *H

CD T3 >

<D O

(O O o to ft'H

CDft iH 3 'H

to O

I CD CD > T33

3 h

O O

CD CD C +-> •H CT3 -i s 0 -H

CD +J

1 3

1—1aj T3

•H £

+-> a3 c

CD CD C IH O 3

ft +J X 3

PJ <4h

•H

tu

113
R = 3.02 (109 bbl/108 ft),

q = 143.44 x 10 9 bbl,

17

Q = 28.62 x io 9 bbl, u

Q = 172.06 x io9 bbl.

00 Again, this is in very close agreement with the estimate for Qm

as of 1972

of 170 x io 9 bbl obtained by the analysis of cumulative production, proved

reserves, and cumulative proved discoveries.

The negative-exponential curve corresponding to the data of Figure 38 is

shown in Figure 41. This is of especial interest because data extending to

1978 are included, and a still different method of analysis was used. The

significant data of Figure 38 are:

R = 28.518 (10 9 bbl/10 8 ft),

= 285.18 bbl/ft,

3 = 0.1753 per 10 8 ft,

i? 2Q

= 0.8564 (10 9 bbl/108 ft),

Q = 157.81 x io 9 bbl,

Q = 4.89 x io 9 bbl,

u

Q = 162.70 x io 9 bbl.

00 Again, this value of 162.7 billion barrels for Q , as determined from data

extending to 1978, is in very close agreement with that of 162.3 billion barrels

shown in Figure 31, obtained from the logistic constants of the curve of cumulative proved discoveries to 1978. It also differs by only 1.9 billion barrels

from the figure of 164.6 shown in Figure 32, based upon the linear-decline curve

of (dQ/dt)/Q versus Q. The average of these three figures is 163.2 billion

barrels, with a range of uncertainty of only about plus or minus two billion

barrels

114
Estimation of Natural Gas

Estimations of the ultimate amount of natural gas to be produced in the

Lower-48 states, and of the future rates of production, are more difficult

than the corresponding estimates for crude oil. This is because the statistics

of natural gas are less complete than those for oil until after World War II.

Prior to that time a large amount of gas was burned (or "flared") in the fields

as gas was produced as a by-product of oil and in excess of the pipeline capacity for collection and distribution.

Since World War II, this situation has greatly improved. Large pipelines

were constructed for the transmission of gas from the producing areas to the

industrial regions of the northeast and north-central United States and to the

Pacific coast. Also, in the mid-1940s, the American Gas Association established

its Committee on Natural Gas Reserves. From 1946 to 1979, this committee has

issued annual reports on natural-gas proved reserves and production, in parallel

with those of the corresponding committee on crude oil of the American Petroleum

Institute

Another serious difficulty is that the record of cumulative production,

proved reserves, and cumulative discoveries of natural gas is much more irregular

than the corresponding record for oil, which makes mathematical analysis of the

data more difficult and of a lower level of reliability. Nevertheless, enough

information exists to permit reasonably good estimates to be made of the approximate cumulative production and of future production rates.

Earlier Estimates

Estimate of 1956. In my 1956 paper, "Nuclear Energy and the Fossil Fuels"

(Hubbert, 1956), the same technique was used for estimating the complete cycle

of U.S. natural-gas production as was used for crude oil. The best current

115
estimate for the ultimate amount of natural gas to be produced in the Lower-48

states and adjacent offshore areas was about 850 trillion cubic feet. Cumulative production by the end of 1955 amounted to about 150 and proved reserves

to 224 trillion cubic feet. This gave the figure of 374 trillion cubic feet

for cumulative proved discoveries, leaving 476 trillion cubic feet for future

discoveries

This is shown graphically in Figure 42, which is reproduced from Figure 22

of the 1956 paper. From this it was estimated that the maximum rate of gas

production of about 14 trillion cubic feet per year would occur about 1970.

As in the case of crude-oil estimates, the published estimates for the ultimate

amount of natural gas to be produced began to escalate immediately after 1956

and, by 1961, the highest estimate had reached 2,630 trillion cubic feet, a

figure three times that of 1956.

National Academy Report of 1962. In view of the lack of agreement as to

the approximate magnitude for Q , it became necessary in the National Academy of

Sciences report of 1962 to devise a new method of estimation. The statistical

data on cumulative production, proved reserves, and cumulative discoveries,

which had been available only since 1945, were insufficient for an estimate of

Q . To obtain this figure, the parallel study for crude oil was used in conjunction with the ratio of the discoveries of natural gas to those of crude

oil during a given period of time. ~ Thus,

Qa

gas = Qdgas + G[(Qm

- ^)oil], (79)

where G is the gas/oil-ratio.

At the end of 1961, cumulative proved discoveries of natural gas amounted

to 474 trillion cubic feet. Cumulative proved discoveries for crude oil were

99.1 billion barrels, and the estimate for Q for crude oil was taken as 175

billion barrels, leaving 75.9 billion barrels for the undiscovered crude oil.

116
10 M CO *

MA/ li 03 JO SNOmiBl

ooU

o

CO CM

0) bfl X "H P Uh C » H

LO C a> O »"H •HP •> O P

3 u 0 ^

ISl v—/

1 LO

>—( <7> 03 i—i 3 C P -H

o3C T3

<D

tp. +-> O o3£

0 "H

rH P

O V) o

<D 03 P

<L> <fl Ph P

E 03 O P U (/)

<N1

<3-

•H

117
For the gas/oil-ratio, two figures were used. The ratio of gas discoveries to

crude-oil discoveries during the most recent 20-year period, 1941-1961, was

6,250 ft 3 /bbl. However, the possibility was also considered that in response

to deeper drilling this ratio might increase in the future to as much as

7,500 ft 3 /bbl.

Substituting these figures into equation (79) gave, for the ultimate

amount of natural gas to be produced in the Lower-48 states, a low figure of

958 and a high figure of 1,053 trillion cubic feet, or roundly 1,000 trillion

cubic feet. Using this figure for Q in conjunction with the limited data for

Qp> Qr

> and for natural gas, gave the logistic curves of Figure 43 and their

derivatives in Figure 44. The two complete gas-production cycles, based on

both low and high estimates of 958 and 1,053 trillion cubic feet, are .shown

in Figure 45. From these figures, the time delay At between cumulative discoveries and cumulative production was estimated to be 16 years. The maximum

rate of discovery was estimated to occur at about 1961, the peak in proved

reserves in 1969, and the maximum production rate of about 18 to 20 trillion

cubic feet per year at about 1977.

Estimate of 1972. By 1972 (Hubbert, 1974), despite the fact that 10 more

years of data were available, the natural-gas data on cumulative production,

proved reserves, and cumulative proved discoveries were still so irregular as

to make the use of the logistic equation of doubtful validity. However, by

1972, the proved reserves of natural gas had already reached their maximum in

1967, two years earlier than predicted in 1962. After 1967 they declined steeply.

For estimates of Q , two methods were used, that of the gas/oil-ratio in conjunction with the oil estimate, and the gas discoveries as a function of cumulative exploratory drilling. The first method gave an estimate of about 1,000

trillion cubic feet, and the second a higher figure of 1,103 trillion cubic feet.

118
1200 T 1 r 1 r -i 1 1 r ! I

1000

Q~= iooo x io'

2 cu ft CO

1000 x 10 cu ft 0.0793U-I900)

J I

1 1

CUMULATIVE

PRODUCTION

I I I I 1900 2000 2050

Fig. 43 - Logistic equations and curves for U.S. natural gas in 1962

(Hubbert, 1962, Fig. 45).

119
CO o

t-J ti m CO o •H

bO

VI o

CD 1—1 >

<P

CD

O

CO

CD CO u ve

f-i CD 3 > O Ou <u ft >

•H

cp. P o va

CD •H

10

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CDUOC o

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T3

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CO *f o

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OS

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dA / 133 j oiano 30

120
o to cm oo <r o

CM CM

—

— ( jo sNommiv

NOiionaoad jo 3iva

121
The mean of these two figures of 1,050 trillion cubic feet was adopted as the

value for Q . This was then used, in conjunction with the statistical data

for Q , (2^, and Q^, to construct Figure 46. Although in 1972 the maximum

rate of natural -gas production had not yet been reached, all the evidence indicated that this would have to occur within the next two or three years.

This was accordingly estimated to occur about 1975, with the peak production

rate of about 24 trillion ft 3 /yr. It actually occurred in 1973, with a peak

rate of 22.6 trillion ft 3 /yr.

The difficulty of trying to fit the cumulative data for natural gas with

the logistic equation, using 1,050 * 10 12 ft 3 for Q , is evident from inspection

of Figure 47. The abrupt decline of proved reserves after 1967, and the corresponding downward deflection in the curve of cumulative discoveries combine to

suggest that the actual figure for Q may be considerably less than the value

of 1,050 x io 12 ft 3

.

Estimate of 1980. By 1980 the curve of cumulative proved discoveries is

far enough advanced beyond its inflection point, which occurred about 1961, to

permit estimates of the asymptote to which this curve is tending. For this

purpose five different procedures have been used:

1. The linear regression {dQ/dt)/Q versus Q.

2. The negative-exponential approach of the curve of versus

t to Q as t increases. 00

3. Estimate of Q for gas based upon prior estimates for oil

in conjunction with the gas/oil-ratio.

4. Estimate of the logistic constants for the curve of cumulative gas discoveries, Q^, as a function of time.

5. Estimate based upon a new analysis by Root (1980) of gas

discoveries per each 10 8 ft of exploratory drilling.

122

EE<

lp to o Pc

to <u

<D s H fto

<L> i—i >O > O

(O -a

•H

-d 0

fH -d 3P > 3 o tp ft<PO >HP p

03 Ctj .—

eHP

to

O <D -a H

nj

aj

OH

cO ft

aJ > H M bO

<D

(0

<D P U •H

T3>O

cr> ft o c o o Oi

•H 1—

po «\ to T3 03 o W> ft rH

CT3 H > 3 H P p nj

1-1 1

CO

u

•H

•H

133d oiano jo SNommi

124
Estimate based upon {dQ/dt) /Q versus Q. The first of the foregoing

procedures is based upon equation (27)

,

{dQ/dt)/Q = a{\ - Q/QJ.

This is a linear equation between {dQ/dt) /Q and Q, the graph of which intersects the Q-axis at the point Q = Q^, and the vertical axis at {dQ/dt) /Q = a.

For data, the American Gas Association (May 1980) has recently published

a table of cumulative proved discoveries of natural gas for the U.S. Lower-48

states corresponding to the end of each year from 1945 to 1979. Using these

data, mean values for dQ/dt were computed for each year from 1950 to 1974 based

upon a 10-year running average. Shorter periods of averaging were used for the

years 1975 to 1978. For Q, the actual yearly figures were used. Plotting the

data for {dQ/dt) /Q versus Q gave a very good linear graph from Q = 480 to 720

trillion cubic feet, corresponding to the period 1960 to 1979. This line, as

estimated visually, passed through the point, {dQ/dt) /Q = 0.0500; Q = 400 x

10 12 ft 3

, and intersected the #-axis at 810 * 10 12 ft 3, which is the estimated

value for Q . By backward extrapolation the line intersects the vertical axis

at the point 0.099, which gives the value of the coefficient a of the corresponding logistic equation.

Although this figure of 810 trillion cubic feet is a surprisingly low figure

for Q , the data of the graph are sufficiently linear over the interval stated

that very little latitude, possibly ±_ 10 trillion cubic feet, is allowable for

the uncertainty of the point of intersection.

Estimate by the negative-exponential approach of Q^ versus t to Q^ . The

assumption that cumulative discoveries Q approach the asymptotic value Qm

in a

negative-exponential manner during the later stages of the discovery cycle

affords another means of estimation. At a fixed date £ , let Q

q

be the magnitude

of cumulative discoveries. Then using this point as a new origin of coordinates,

let y = Q - Q be the subsequent increase in Q, and let t = £ - £ be the sub125
sequent time coordinate. Also let k be the asymptotic value ofy. We then

have the equation,

k - y = ke ^T

,

or

ln[(k - y)/k] = -bx,

in which the two parameters, k and b are to be determined. Consider two

points of the curve of y versus i, (t , y^) and (t , y^) . Introducing these

values into equation (81) then gives the two equations,

ln[(k - yj/k] = -^vl

ln[(fc - y

2 )/k] = -bT

2 J

By taking the ratio of the second to the first, b can be eliminated, and we

obtain

ln[(fc - y 2 )/k] T2

in which k is the only unknown. This can be solved by iteration if we substitute for k an assumed value k . Then the left-hand term of equation (83)

becomes fV<a

) > and when

nkj - t

2 a

/ v

k = k. a After k is known, b may be determined from equation (81) by

b = ln[(fc - yj/kl/t^

Then finally,

(80)

(81)

(82

(83

Q = G + k.

co O

The data of Q versus t and y versus t are given in Table 1 at 5-year

intervals from 1960 to 1980. Taking t, at 10 years (date 1970), and t

2 at

20 years (1980), and y and y equal to 169.05 and 267.50 trillion cubic feet,

respectively, we find that

126
a> CM to rH to LO tO Q

_ VJ

p * * OP O XJ xj LQ LO 00

e- CM o CO 00 00 00 00 00 00 00

+—1 \

fj 1

CM

1—1O CM CO CM sO 00

rH CM vO o> LO vO v ' 00 00 LO rH

LO CO C7> OiO o i i to ^1 /—\ o O o o o o 8

«-** LO 00 U)

*- *

a> o o o o o o 4-> Q cm to LO o0

Rj

Q

QQ rS

Q CM cm CM CM CM

13

a> LO to • o *fr LO to M lsT\ r* )

to Of iA cm LO to v>wo a VU KOTM J Ul o ^4. LO

COP LO CM

O CD CM to

4-1 rH o 00 LO P O 00 3 • CM Q wln\ TM / i—

00 vL*' i~H CM

O CM CM o to to

i—

r i ^ j V -/

LO CMO LO

to LO rH 00 Q? vO to LO O to 1 sQ LO C* J 00 LO vD /—\ o LO o LO o LO o X rH rH CM CM

CD o LO o LOO LO o

•p CO CO

rt o> Oi Q o

00oo<

rHom

4)o

r-t O

CO

127
when

and that

Then

HkJ - x

2 /x1 = 2

k = k = 404.78 x 10 12 ft 3

,

b = 0.054066.

Q = Q + k

= (466 + 405) x 10 12 ft 3

= 871 x io 12 ft 3

.

Estimates based upon the gas/oil-ratio

As shown in equation (79) , an

estimate of Q for gas is obtained by

Qm

gas = Qdgas + G[(Qm

- Q^oil],

where the cumulative discoveries for both gas and oil are the most recent figures

available, at present those for 1980.0, and G, the gas/oil ratio, is the ratio

of gas discoveries to oil discoveries during a recent finite period of time.

By 1980.0

Qd

oil = 136.9 x io 9 bbl,

Q oil = 163 x io 9 bbl,

00 and

{Q - Qd) oil = 26 x io 9 bbl,

Qd

gas = 734 x 10 12 ft 3.

For gas/oil -ratios during recent decades, cumulative discoveries of both

crude oil and natural gas are given for 1960.0, 1970.0, and 1980.0 in Table 2.

From these data three separate gas/oil-ratios are obtained for three different

periods of time. For the decade 1960 to 1970, the value of G was 6,789 ft 3 /bbl;

for 1970 to 1980 it had declined to 5,472 ft 3 /bbl; and for the 20-year period

128
tO • <D o J \ 00

o3 cn P rH

to 1 o

oo vO

Cn 1 i-H P

<D T3C o 03 • O

CO 00 • cn

i-H c i o

•H r^- cn

to i-H aJbo O rH

03 Cn P i—

3 i P o

03 \0 C cn

i-H -3C P

aJ o

HH

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•iH 0 P

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<P

O

O

10

to 03

a> bO

•HP

CD> o3 oo

to o

•H 00

cn

i—

CD> "3

•H

C P 03

03

i-H3 O

cn

u i-H oHP /*—\

TOH Ul CN ' 00 to

i-H "O \ CN

•rH CO o 4-> LO

fiHH

t/)

v ' o3 CJ

rrt . bOroP LO

ur\) /—\vj

'tj rH 4-1 /—\ '

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03 rH Z ^

rH /—v

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/-T\ wl

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J a; 00 00 p /—

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CD \0 t*> vO e a> Oi cn •H rH i-H i—

ft

0} i—\

bOro LO

O LO P to 00

rOl ^

rH <P

03 \Q LO to poj tO to 3h vO P O

03 rH

rH ^-N •H rH O JO rH rH o o CT> cn

(1) Ti cn 00 \D 3 O rH to P rH rH rH U x—/ /—\

rH

CD o o O p • 00

03

C cn

Q o3 rH rH rH

•-5 >—

1 MOO

0Q

(U rH

CQ

03oo

V)

to <opp

0)c

03 •H

T3

rtC

03 U

TJe

03Oo

to <

to

03

Am

O

00

cn

(D rH P3 X P 03 •HP

to In

OC. to rH to o cn < pp cn to

<u rH 03 a. vO

Am.

vOcn

rH Am.

to<uop3o

129
1960 to 1980 it had an intermediate value of 6,237 £t 3 /bbl.

For use in estimating future gas discoveries the ratio of the last 10 years

is evidently the best of the three figures, although the ratio for the last 20

years may also be considered. With the numerical data given above, the solution

of equation (79), using the gas/oil-ratio of 5,472 ft 3 /bbl, gives an estimate

for Q for natural gas of

Q = 876 x io 12 ft 3

. ^oo Using the ratio of 6,237 ft 3 /bbl of the last 20 years gives the slightly higher

estimate

Q = 896 x 10 12 ft 3

. 00

Estimate based upon the constants of the logistic equation. Despite the

fact that the curve of versus t for natural gas cannot be fitted accurately

by the logistic equation, still a good approximation can be obtained using the

data for from 1946 to 1980, during which increased from 233 to 734 trillion

cubic feet. Expressing these data in the linear form of equation (36),

In N = In N - at,

o and then using the technique described in equations (43) to (45) , approximate

values of the parameters, Qm and a can be determined. For this purpose the

following data were used:

Date (*) 19J6.0 1965.0 1980.0

Qd

(10 12 ft 3

) 233.18 553.52 733.85

The value of for which the two line segments, that from 1946.0 to 1965.0,

and that from 1965.0 to 1980.0, have the same slope was found to be 840.0 x 10 12 ft 3

,

and -S = 0.0850/yr. Hence, the estimates for the logistic constants by this

130
procedure are:

Q = 840 x io 12 ft 3 f

J CO '

a = 0.0850/yr.

Estimate based upon gas discoveries per each 10 8 ft of exploratory

drilling. David H. Root (1980) has just completed a new study of natural

gas discoveries in the Lower-48 states, based upon his own modification of the

Arrington method of estimating the additional gas that fields discovered each

year will ultimately produce. Root has estimated the ultimate amount of gas to

be produced by each of the 20 10 8 -ft units of exploratory drilling extending in

time from 1860 to 1977.9. This is a parallel study for natural gas to Root's

crude-oil study, the results of which are shown in Figures 38 and 41.

As in the case of crude oil, the discoveries made by the first 4 units of

drilling, which extended from 1860 to 1945.2, were large, averaging slightly more

than 100 trillion cubic feet each. However the discoveries per unit for the

entire 20 units declined in a roughly negative-exponential manner to a final

figure of 13.912 trillion cubic feet for the 20th unit.

Using the method developed in equations (72) to (78) , the actual data for

dQ/dh versus h can be approximated by a negative-exponential decline curve,

R = R e'

ih

, o whose integral from h = 0 to h = 20 units has the same value as the sum of the

actual discoveries, and which passes through the last data point on the curve.

The significant data for this determination are:

i? 2Q

= 13.912 (10 12 ft 3 /10 8 ft),

= 844.406 x 10 12 ft 3

.

From these,

R = 95.04118 (10 12 ft 3 /10 8 ft),

o

131
3 = 0.09608 per 10 8 ft,

Q = R /g = 989.2 x io 12 ft 3

,

« = « - Qon = 144.8 x 10 12 ft 3

.

Summary of Estimates of Natural Gas

The foregoing estimates for the ultimate quantity of natural gas to be

produced in the Lower-48 states and adjacent offshore areas are the following:

Method of estimation

Q00

/i a12 -C-t 3 *\ (10 1 ±t°)

(dQ/dt}/Q vs. Q 810

Q vs. t 871

876

Gas/oil-ratio

896

Logistic equation 840

dQ/dh vs. h 989

Mean 880

What is most impressive about these separate estimates is the range from

the lowest to the highest of 810 to 989 trillion cubic feet, or approximately

900 1. 90, with a mean value of 880 trillion cubic feet. If we omit the lowest

and the highest estimates, each of which differs by a large amount from that next

above or below, then the remaining four figures fall within the much narrower

range of 840 to 896, or 868 ± 28, with a mean value of 871 trillion cubic feet.

In this series, both the lowest figure of 810 trillion cubic feet and the

highest of 989 are anomalous, but the latter is especially suspect since it

exceeds the average of 871 trillion cubic feet of the middle four estimates by

132
118 trillion cubic feet. This analysis by Root was a companion study to

that of the crude-oil discoveries as a function of cumulative depth of exploratory drilling, the results of which are shown in Figures 38 and 41. In the

crude-oil analysis the data used were the API "Blue Book" data on "ultimate

recovery" of crude oil by year of discovery. In the natural-gas analysis the

corresponding data were the AGA "Blue Book" figures for "ultimate recovery"

by year of discovery. However, the natural-gas estimate of 989 trillion cubic

feet shows the same inconsistency with the corresponding crude-oil estimate as

it does with the other gas estimates given above.

This can be seen by using Root's data for crude-oil discoveries in conjunction with the gas/oil-ratio. In this case,

Qa

gas = Q2Q gas + GQ

u

oil. (84)

Using Root's figures of

Q2Q gas = 844.4 x 10 12 ft 3,

Q oil = 4.9 x 10 9 bbl, u

and the two values of the gas/oil-ratio from Table 1,

G = 5,472 and 6,237 ft 3 /bbl,

gives the following two estimates for Q for natural gas:

Q = 871 x 10 12 ft 3

, 00 Q = 875 x io 12 ft 3

. 00 These figures are consistent with those ranging from 840 to 896 trillion cubic

feet obtained by other methods. Combining the mean of the above two figures,

873 trillion cubic feet, with the previous estimates (omitting the low figure

of 810), gives as our present best estimate for Q for natural gas,

Qx gas = (870 1 30) x 10 12 ft 3

.

133
Conclusion

The principal thesis of the present paper has been that the successful

prediction of the future behavior of any matter-energy system must be based

upon a prior understanding of the mechanism of the system considered, and

upon a rational analysis of the data of the system in accordance with that

mechanism. Also, the final arbiter of the reliability of any prediction is

the future itself. So long as the predicted event is still in the future,

whether or not the prediction is valid must remain to some degree uncertain.

But after the time has been reached at which the predicted event was to occur,

this doubt no longer remains.

In this paper, the results of the application of this philosophical view

to the petroleum industry of the United States during the last 25 years have

been reviewed. It is now evident that by the mid-1950s the cumulative data of

the U.S. petroleum industry were sufficient to permit reasonably accurate predictions of its future development. With the passage of time, more and better

data have permitted a refinement of earlier estimates, and also provided a

verification of their degree of accuracy. By now, the peak in the rate of crudeoil production has already been passed in 1970, and that of natural gas in 1973,

and the production rates of both are now in decline.

The present cumulative .statistical evidence with regard to crude oil leads

to a figure of approximately 163 t. 2 billion barrels for the ultimate cumulative

production in the Lower-48 states. Less exact evidence for natural gas indicates

that the ultimate cumulative production from conventional sources will probably

be in the range of 870 ± 30 trillion cubic feet. However there still remain

geological uncertainties regarding the occurrences of undiscovered oil and gas

fields, yet those are being severely restricted by the extent of exploratory

134
activity. In the case of crude oil, there is also the uncertainty regarding

the magnitude of future improvements in extraction technology.

With due regard for these uncertainties, estimates for crude oil that do

not exceed that given here by more than 10 percent may still be within the

range of geological uncertainties; estimates that do not exceed this by more

than 20 percent may be within the combined range of geological and technological

uncertainties. Estimates for natural gas that do not exceed the upper limit

of the range given above by more than 10 percent may likewise be regarded as

possible although improbable. But estimates for either oil or gas, such as

those that have been published repeatedly during the last 25 years, which

exceed the present estimates by multiples of 2, 3, or more, are so completely

irreconcilable with the cumulative data of the petroleum industry as no longer

to warrant being accorded the status of scientific respectability.

135
REFERENCES

American Association of Petroleum Geologists, Committee on Exploratory Drilling,

1946 — , Annual reports on exploratory drilling, initially in the United

States but later also in Canada and Mexico: Am. Assoc. Petroleum Geologists

Bull, (various numbers, annually).

American Gas Association, Gas Supply Committee, May 1980, Summary of United States

gas supply statistics: Gas Energy Review, Supply and Production Supplement,

p. 1-4.

American Petroleum Institute, 1959, Petroleum facts and figures, Centennial Edition,

471 p.

American Petroleum Institute, American Gas Association, and Canadian Petroleum

Association, annually 1967-1980, Reserves of crude oil, natural gas liquids,

and natural gas in the United States and Canada as of December 31 (each year)

Arps, J.J., and Roberts, T.G., 1958, Economics of drilling for Cretaceous oil on east flank of Denver-Julesburg Basin: Am. Assoc. Petroleum Geologists Bull.,

v. 42, no. 11, p. 2549-2566.

Arps, J.J., Mortada, M. , and Smith, A.E., 1971, Relationship between proved reserves

and exploratory effort: Journal of Petroleum Technology, June, p. 671-675.

Arrington, J.R., 1960, Size of crude reserves is key to evaluating exploration

programs: Oil and Gas Journal, v. 58, no. 9, Feb. 29, 4 p.

1966, Estimation of future reserve revision in current fields: In Trans.

West Texas Geological Society's Symposium: Economics and the Petroleum

Geologist, p. 17-30.

Clarke, F.W., 1924, The data of geochemistry, Fifth edition: U.S. Geological Survey

Bull. 770, 841 p.

Cram, Ira H. , ed., 1971, Future petroleum provinces of the United States — their

geology and potential: Summary: Am. Assoc. Petroleum Geologists, Mem. 15,

v. 1, Preface, viii; p. 1-34.

DeGolyer and MacNaughton, 1944 — , Twentieth Century Petroleum Statistics, Dallas,

annually. —

Drew, Lawrence J., Schuenemeyer , J.H., and Root, David H. , 1980, Resource appraisal

and discovery rate forecasting in partially explored regions: Part A, An

application to the Denver Basin: U.S. Geological Survey Professional

Paper 1138, p. A1-A13.

Duncan, D.C., and McKelvey, V.E., May 1963, U.S. resources of fossil fuels, radioactive minerals, and geothermal energy: In Federal Council for Science and

Technology, Research and development on natural resources, Appendix A,

p. 43-45, table 9.

136
Frey, John W. , and Ide, H. Chandler, 1946, A history of the Petroleum Administration

for War, 1941-1945: Washington, Petroleum Administration for War.

Gardett, Peter H. , 1971, Petroleum potential of the Los Angeles Basin, California:

In Am. Assoc. Petroleum Geologists, Memoir 15, v. 1, p. 298-308.

Hubbert, M. King, 1956, Nuclear energy and the fossil fuels: Dallas, Am. Petroleum

Inst., Drilling and Production Practice (1956), p. 7-25.

1962, Energy Resources, A report to the Committee on Natural Resources:

Natl. Acad. Sci.-Natl. Research Council, Pub. 1000-D, 141 p.; Reprinted

1973 by Natl. Tech. Inf. Service, U.S. Dept. of Commerce, no. PB-222401.

1967, Degree of advancement of petroleum exploration in United States:

Am. Assoc. Petroleum Geologists Bull., v. 51, no. 11, p. 2207-2227.

1974, U.S. energy resources, a review as of 1972, Pt. 1, in A national

fuels and energy policy study: U.S. 93rd Congress, 2d Session, Senate

Committee on Interior and Insular Affairs, Serial no. 93-40 (92-75),

Washington, U.S. Govt. Printing Office, 267 p.

Kilkenny, John E., 1971, Future petroleum potential of region 2, Pacific Coastal

States and adjacent continental shelf and slope: In Am. Assoc. Petroleum

Geologists Memoir 15, v. 1, p. 170-191.

Lahee, Frederick H. , 1962, Statistics of exploratory drilling in the United States

1945-1960: Am. Assoc. Petroleum Geologists, 135 p.

Law, J., 1957, Reasons for Persian Gulf oil abundance: Am. Assoc. Petroleum Geologists Bull., v. 41, p. 51-69; Reprinted in A.A.P.G. Foreign reprint series

no. 2, 1978, p. 43-61.

Marsh, G. Rogge, 1971, How much oil are we really finding?: Oil and Gas Journal

v. 69, no. 14, April 5, p. 100-104.

McKelvey, V.E., 1967, Contradictions in energy resource estimates: The Technological

Institute, Northwestern Univ. , The Seventh Biennial Gas Dynamics Symposium,

p. 5-23.

McKelvey, V.E., and Duncan, D.C., 1965, United States and world resources of energy,

in Symposium on Fuel and Energy Economics, Joint with Division on Chemical,

Marketing and Economics: 149th Natl. Meeting, Am. Chem. Soc, Div. Fuel

Chemistry, v. 9, no. 2, p. 1-17.

Menard, H.W. , and Sharman, George, 1975, Scientific uses of random drilling models:

Science, Oct. 24, v. 190, p. 337-343.

Moore, C.L., 1962, Method for evaluating United States crude oil resources and

projecting domestic crude oil availability: Washington, Dept. Interior, Off.

of Oil and Gas, 112 p.

Morris, Anthony E.L., 1978, Preface and bibliography: Geology and productivity

of Arabian Gulf geosyncline: In Geology and productivity of Arabian Gulf

geosyncline: Am. Assoc. of Petroleum Geologists, Foreign reprint series,

no. 2, 8 p.

137
National Petroleum Council, 1961, Proved discoveries and productive capacity of

crude oil, natural gas and natural gas liquids in the United States:

Washington, Natl. Petroleum Council, 40 p., 7 tables, 6 exhibits.

1965, Proved discoveries and productive capacity of crude oil, natural gas

and natural gas liquids in the United States: Washington, Natl. Petroleum

Council, 23 p., 6 tables, 1 exhibit.

Root, David H. , 1980, Historical growth of estimates of oil and gas field size:

Paper presented on June 19, 1980, before Department of Energy and National

Bureau of Standards Symposium on Oil and Gas Supply Modeling, Washington, D.

Root, David H. , and Drew, Lawrence J., 1979, The pattern of petroleum discovery

rates: American Scientist, v. 67, no. 6, p. 648-652.

Verhulst, P. -F., 1838, Notice sur la loi que la population suit dans son accroissement : Corr. Math, et Phys., T. X, p. 113-121.

1845, Recherches mathematiques sur la loi d' accroissement de la population:

Memoires de L'Acade'mie Royale, Belgique, T. XVIII, p. 1-38.

1847, DeuxiSme Mgmoire sur la loi d

f accroissement de la population: Memoires

de L'Acade'mie Royale, Belgique, T. XX, p. 1-32.

DISCUSSION

DR. HUBBERT (in reply to question by Samuel Kao " Brookhaven): Your

statement that all of my curves are symmetric is not entirely correct. I

have stated explicitly that the complete-cycle curve of production of an

exhaustible resource in a given region has the following essential properties:

The rate of production as a function of time begins at zero. It then increases

exponentially during a period of development and later exploration and discovery.

Eventually the curve reaches one or more maxima, and finally, as the resource

is depleted, the curve goes into a negative-exponential decline back to zero.

There is no requirement that such a curve be symmetrical or that it have only

a single maximum. In small regions such a curve can be very irregular, but in

a large area such as the United States or the world these irregularities tend

to smooth out and a curve with only a single principal maximum results. If

such curves are also approximately symmetrical it is only because their data

make them so.

138
In my figure of 1956, showing two complete cycles for U.S. crude-oil

production, these curves were not derived from any mathematical equation. They

were simply tailored by hand subject to the constraints of a negative-exponential

decline and a subtended area defined by the prior estimates for the ultimate

production. Subject to these constraints, with the same data, I suggest that

anyone interested should draw the curves himself. They cannot be very different

from those I have shown.

DR. HUBBERT: As I have stated before, there is no theoretical

necessity for the complete-cycle curve to be symmetrical. When such curves

are symmetrical it is only because the data require that they be so. A

critical test of whether such a curve is symmetrical or not is the linear

equation,

In N = In N - ait - t ), o o where

N = Ww

- Q)/Q,

Q = cumulative discoveries or production,

Q = the ultimate value of Q, 00

a = the growth constant.

This is the linear form of the symmetric logistic equation. If the

quantity In N plots as a straight line as a function of time, this is evidence

that the cumulative data increase in accordance with the symmetric logistic

equation.

For cumulative discoveries and production of crude oil in the U.S.

Lower-48 states, during the period 1900-1973, the data plot as excellent

straight lines in accordance with the above equation. For discoveries, the

maximum rate occurred at about 1957. However, from 1973 to 1980, the discovery

rate has been declining faster than the equation would predict.

139
DR. HUBBERT (in response to remarks by David Nissen - DOE): Your kind

remarks with regard to my previous studies of the evolution of the U.S.

petroleum industry are greatly appreciated. However, you suggest that my

estimates of the ultimate amount of oil to be recovered is questionable for

reasons of classification and because I have not taken into account the effect

of the price of oil on ultimate recovery. You mention oil shale, coal, and the

Orinoco heavy oils of Venezuela.

With regard to classification, if unintelligibility is to be avoided,

it is essential that one define his terms and then adhere rigorously to those

definitions. In the present study I have been concerned with the techniques

of estimation as applied to conventional crude oil and natural gas in the U.S.

Lower-48 states. This excludes consideration of shale oil, coal, Orinoco

heavy oils, natural gas from unconventional sources, and also oil and gas from

Alaska.

My analyses are based upon the simple, fundamental geologic fact

that initially there was only a fixed and finite amount of oil in the ground,

and that, as exploitation proceeds, the amount of oil remaining diminishes

monotonically . We do not know how much oil was present originally or what

fraction of this will ultimately be recovered. These are among the quantities

that we are trying to estimate.

Your statement that the fraction of the original oil-in-place that

will be recovered is a function of the price of oil is correct, but the effect

may easily be exaggerated. For example, we know now how to get oil out of a

reservoir sand, but at what cost? If oil had the price of pharmaceuticals and

could be sold in unlimited quantity, we probably would get it all out except

the smell. However there is a different and more fundamental cost that is

140
independent of the monetary price. That is the energy cost of exploration

and production. So long as oil is used as a source of energy, when the

energy cost of recovering a barrel of oil becomes greater than the energy

content of the oil, production will cease no matter what the monetary price

may be. During the last decade we have had very large increases in the

monetary price of oil. This has stimulated an accelerated program of

exploratory drilling and a slightly increased rate of discovery, but the

discoveries per foot of exploratory drilling have continuously declined from

an initial rate of about 200 barrels per foot to a present rate of only

8 barrels per foot.

There is the further question of what fraction of the original

oil-in-place is now being recovered. The conventional figure most frequently

quoted is about one- third. However, a critical review of this question in a

book entitled "Determination of Residual Oil Saturation" by a panel of

nationally prominent petroleum engineers has just been published by the

Interstate Oil Compact Commission (June 1978) . In this study the average value

of the residual oil saturation in the depleted reservoir sands of a hundred

or so fields was found to be only 28 percent, as compared with previous estimates

of 38 percent. According to this study, the recovery factor at present is

evidently much higher than has been conventionally assumed, and the remaining

oil correspondingly smaller.

141
CURRENT PROBLEMS IN OIL AND GAS MODELING*

William C. Stitt

ICF Incorporated

As a starting point, I assert that those of us here today agree that

"problems" do exist in current oil and natural gas supply assessments. This

assertion, of course, relies on the assumption that these problems, their

critical importance to national policy and private sector investment, and the

search for their solution motivates our professional interest in the subject

of oil and gas supply.

I must, however, make clear at the outset the perspective which I bring to

these problems. Those engaged in oil and gas supply assessments have been

browbeaten regularly of late by our clientel and our critics. The former too

often expect certainty where none can exist. The latter too often expect

perfection, in some normative sense, where none is likely to exist until all

of our oil and gas is used up. Both too often lose sight of what is

possible, practical and feasible today; what great progress already has been

made in improving oil and gas supply assessments; and what opportunities

currently exist for intelligent use of our work. I therefore wish my comments

about "problems" to be interpreted modestly and with a sense of opportunities

for improvement rather than of condemnation of current practice.

The locus of my remarks also extend well beyond the term "modeling." The

only strictly correct and precise model of the oil and natural gas supply is

the actual resource base and myriad supply activities themselves. All practical oil and natural gas supply assessments are abstractions of this real

model. As such, they represent ideas about the real world of crude oil and

natural gas, only a small part of which set of ideas are exhibited as "formal"

models of oil and natural gas supply. Consequently, the problems of interest

here, I believe, are those related more broadly to oil and gas supply ideas, some of which are embodied in formal supply models.

In this context, oil and natural gas supply assessment is complex, difficult, and always challenging but often frustrating. Rich texture stems from

the character of the resource as well as its extraction process and its economics. From a problem- solving perspective, this character is enhanced substantially by U.S. circumstances. Our resource base resides in both mature provinces and substantial frontiers. It consists of a large quantity of discovered oil and natural gas, only a relatively small fraction of which has

been extracted. In addition, the surrounding marketplace and a highly dynamic

price, technological and policy environment provide a wealth of situations of

critical importance and intrinsic analytical interest.

*This paper also appears in the book Energy Policy Planning , edited by

B. A. Bayraktar, E. A. Cherniavsky, M. A. Laughton and L. E. Ruff,

Plenum Press, New York, N. Y. 1981. Reprinted with permission

142
Given this complexion, one point hopefully will emerge from my remarks

sound assessments proceed from a thorough understanding of the physical facts

which are unique to the oil and natural gas resource and supply process.

Another hoped for point is that facts—data and a trustworthy empirical foundation for oil and natural gas supply assessment —are scarce. A large gap

exists between elegant formulations, which pervade the literature relevant to

oil and natural gas, and empirical tests of th^ir merits. Concepts and potential techniques run far ahead of our abilities to put them to use in today's

data environment. Insufficient evidence, in my opinion, is the major obstacle

to progress in oil and natural gas supply assessment.

Nonetheless, the current oil and natural gas literature is rich. In addition, one or two dozen formal models of the U.S. oil and natural gas resource

and supply process are operable. Many have been employed extensively, along

with even more numerous informal models, throughout the U.S. domestic oil and

natural gas supply policy debate which has endured since 1970. The sheer

weight of this literature, models, and applications to policy questions defies

detailed review in an abbreviated space or timeframe. Consequently, my

approach here stands back from the details—lacking approbation and perhaps

good sense —and raises a series of questions which the literature, these

models, and the policy debate thus far suggest should be areas of emphasis and

concern in improving oil and natural gas supply assessments.

143
FRAMEWORK

Oil and natural gas supply assessments, whether or not a "formal" model is

involved, rely upon ideas about the actual resource base and supply activities. As such, all symbolize the "real model" which leads ultimately to

extraction of oil and natural gas. Figure 1 shows a highly simplified and

abstract notion of the ingredients of this supply system.

The components of the figure have the following meanings:

• Physical Description of the Resource Base ; This part consists of

a physical characterization of the resource base. For oil and

natural gas, it ideally consists of a three-dimensional description of individual deposits; their locations and depths; the

fraction of their volume which is hydrocarbons as well as the

mechanical properties of the hydrocarbons (e.g., viscosity); and

the mechanical properties of the overall reservoir (e.g., permeability, drive mechanism, pressure and temperature, etc.). Of

course, these properties of undiscovered deposits are not known

with significant certainty. And for those which have been discovered, these properties become known with a high degree of

confidence only over a drawn out period during which the deposits'

contents are exhausted through extraction.

• Physical Description of the Exploitation Process ; This part consists of a description of the physical activities and "engineering" costs which lead ultimately to production. For oil and

natural gas, three subparts of the exploitation process ideally

deserve separate identification: exploration, development, and

production. Exploration is the search for prospects, testing for

the presence of hydrocarbons by drilling, and fuller delineation

of the dimensions and mechanical properties of those which initially provide encouraging results. Exploration identifies oil- or gas-in-place and provides information relevant to deciding whether

and how to develop and produce. Development installs the capacity

to produce, initially through drilling and installation of surface

equipment and, usually later, through augmentation of reservoir

pressure and other measures which enhance the recovery of the

deposit's contents. Production operates this capacity to yield a physical flow of the hydrocarbons for use or sale.

Of special importance for oil and natural gas, a large number of

alternative development programs can be pursued in order to create

productive capacity for any deposit. Each might yield divergent

time patterns and levels of costs and production and might alter

the fraction of the hydrocarbons ultimately extracted.

144
FIGURE 1

COMPONENTS OF THE OIL AND NATURAL GAS RESOURCE ASSESSMENT PROBLEM

Physical Description of

The

Resource Base

Physical Description of

The

Exploitation Process

Behaviorial Description

Which Translates Resources Into^

Productive Capacity

Stimulus

Behaviorial Description

Which Translates Capacity

Into Production

t.

145
Finally, capacity to produce may not equate with production, even when measured in terms which envision normal downtime. For

example, certain price expectations create incentives for underutilization of existing capacity in the near term in order to

create greater returns to production later on.

• Behavioral Description Which Translates Resources Into Productive

Capacity ; An oil and natural gas assessment must describe when

and how extraction will occur over time. The idea, of course, is one of an objective function, but in the broadest sense of a description of what the agents which make extraction decisions

seek to accomplish. Importantly for oil and natural gas, the

objective(s) which motivates exploration may not be identical to

the objective(s) which stimulates development or production.

• Constraints and Stimulus ; From an assessment perspective, these

ingredients are straightforward. Limited access to portions of

the resource base may create a constraint, exemplified by leasing

practices applicable to federal lands. The stimulus usually is

price, although substantial debate surrounding U.S. oil and

natural gas policy has centered on whether price is the primary

stimulus.

• Productive Capacity ; This component emphasizes the separate

decision to actually produce. From a capacity standpoint, it

connotes a production profile over time, composed of a production

rate and a productive life . Inadequate distinction of these two

components of the supply process—rate and life—may be the

single, most important problem evidenced in existing assessments.

A prevelant description of the output of the supply process consists of reserves —the integral of the production profile over

time. Such a view of resources which provide a wealth of development alternatives, each emboding a unique production profile,

overlooks an important feature of the supply process.

• Behavioral Description Which Translates Capacity Into Production ; In a stable price environment—for example, one without an expectation of price jumps caused by either OPEC or domestic pricing

policies—excess capacity will be avoided wherever possible.* But

today, price instability and U.S. policies may make the urge to

speculatively withhold an important consideration for U.S. oil and

natural gas models.

Prior to 1970 in the U.S., numerous factors—resource finding and cost

experience, tax subsidies, and oil import quotas —combined to consistently

produce excess of oil production capacity, which was restrained artificially by market-demand prorationing.

146
A RESERVOIR LIFE CYCLE

This simple description of the supply process masks the individual activities involved over the life of a single deposit. For discussion purposes, a deposit means a generally contiguous and communicating unit within a geologic

anomaly which contains hydrocarbons, typically labelled a reservoir. The

anomaly or prospect is the micro-unit of principal interest for exploration

decisionmaking; in contrast, the reservoir is the focal point of development

and production decisionmaking. Nonetheless, exploration, development, and

production decisionmaking are linked closely because the objective of the

former is to identify concrete opportunities for the latter, through which the

actual returns for exploratory investment are realized.

For oil and natural gas assessments, the distinction between exploration,

development, and production probably should be emphasized. Exploration is

governed by a complex probability law which combines the attributes of the

natural processes which caused the deposition of hydrocarbons and of the

search process which locates them. By comparison, development is deterministic and engineering-oriented, focused mainly on making capacity decisions

which optimize in some fashion the returns available from investment in production capacity and subsequent production.

Figure 2 provides a simplified description of the lifecycle of an oil

reservoir. It does not do justice to the real character of the exploration

process. Rather it portrays an artificial situation, a play consisting of

only one prospect consisting of one reservoir. The top part of the figure

illustrates the sequence of activities which lead to the identification of

oil-in-place in the deposit.

The middle of the figure portrays a three-part development program: a primary phase of production employing only the reservoir's natural drive; a secondary phase relying on augmentation of the natural drive, for example

through the injection of water from an external source; and a tertiary phase

depending on methods which might consist of the introduction of chemicals to ease migration of oil out of the reservoir pore space. These phases may not

be distinct or sequential in practice; for example, a deposit of extremely

viscous oil, so-called heavy hydrocarbons, might require the application of

tertiary methods from the outset.

"Ultimate recovery" (shown on the middle portion of the figure) is an

economic and technological artifact—one which introduces confusion into oil

and natural gas supply assessments. In concept, ultimate recovery could equal

total oil-in-place; literally, the reservoir rock could be mined, crushed and

treated chemically to remove virtually all of the original oil contents. At

any point in time, the limits on "ultimate recovery" stem from technology and

economics.

147
FIGURE 2

Total Oil-in-Place

LIFE CYCLE OF AN ILLUSTRATIVE OIL RESERVOIR

Geological,

Geophysical

and Search

<ij Initial Discovery

Extensions

Time

Technical/Economic

Limit

Total Oil-in-Place

Ultimate Recovery

Primary

j Secondary j Tertiary

|

Technical/Economic

Limit

Annual Production

148
Importantly, my illustrative development program is silent about the

intensity with which any phase is pursued. Subject only to intensities which

would cause (economically) catastrophic reservoir damage or severely diminishing returns, development chooses the level of productive capacity to achieve

at every point in time over the reservoir's life. U.S. petroleum engineering

and conservation regulatory practices frequently evidence concern over rates

of production which might "reduce ultimate recovery." These concerns are statements about technology and economics. Extraction rates which "reduce

ultimate recovery" simply mean that more intensive development in the near term mandates new technologies and probably higher costs later in the reservoir' s life (in order to achieve a level of recovery that otherwise could be

achieved with less intense near-term development). Particularly in an environment of dynamic prices and technology, petroleum engineering jargon and

conservation thumb-rules must be inspected carefully and used cautiously for

supply assessment purposes. Fundamental doctrine of yesterday's engineering

and conservation techniques is relevant only to the extent that they are justified by current and prospective economics and technology.

The bottom of Figure 2 illustrates a production profile that assumes that

productive capacity is fully utilized. Over time the production profile consists of a super-imposition of new capacity added by each phase of development

and a subseqent production decline as continuing extraction shrinks effective

capacity.

Turning away from the illustrative and toward the "real" world, Figure 3 depicts the well classification scheme used by the American Association of

Petroleum Geologists and the American Petroleum Institute. It illustrates the

true richness of the oil and natural gas exploration and development processes. But it also provides an initial glimpse of the data problems facing

oil and natural gas supply assessments.

In the figure, unsuccessful wells are classified as "dry." "Dry" means

either that insufficient hydrocarbons were present to justify development in

the prevailing economic and technological environment or that no hydrocarbons

were present. In a dynamic price and technological environment, these two

different outcomes, hidden in the historical record of dry wells, suggest that

a backlog of previously economically_and technically submarginal identified

prospects and discovered deposits may overhang the supply process at any point

in time.

In Figure 3, development wells also are reported in a single, undifferentiated category. But the existence of development intensity alternatives

suggests that there are two types of development wells. One type adds productive capacity by drilling into previously undeveloped portions of a partially developed reservoir, thereby adding so-called proved reserves. Another

type adds productive capacity only by increasing the rate at which previously

developed or proved reserves can be extracted. Lack of this distinction in

the historical record can cause severe problems of interpretation and, in

turn, biases in oil and natural gas supply assessments.

149
FIGURE 3

AAPG AND API CLASSIFICATION OF WELLS (D

OBJECTIVE OF DRILLING

INITIAL CLASSIFICATION * WHEN DRILLING IS STARTED

FINAL CLASSIFICATION AFTER COMPLETION OR ABANDONMENT j SUCCESSFUL UNSUCCESSFUL <f

- Drilling for o ntw field on o structure or in on

environment never before productive 1. NEW-FIELD WILDCAT

NEW-FIELD DISCOVERY WIIDCAT

DRY NEW - FIELD WIIDCAT

Drilling for o new pool on o structure

or in a geological environment already

productive

NEWPOOt

TESTS

Drilling outside limit* of a proved area of pool 2. NEW-POOL (PAY) WILDCAT

NEW- POOL

DISCOVERY WEILS

ISomttimtt

intention

•elll)

NEW-POOL

DISCOVERY WILDCAT

lSommtim»i an tMttitlien will) DRY NEW- POOL

TESTS

DRY NEW- POOL

WILDCAT

Drilling inside limits of proved area

of pool

For a new pool below

deepest proven pool 3. DEEPER POOL (PAY) TEST

DEEPER POOL

DISCOVERY WELL

DRY

DEEPER- POOL

TEST

For a new pool above

deepest proven pool 4. SHALLOWER POOL (PAY) TEST

SHALLOWER POOL DISCOVERY WELL

DRY SHALLOWER POOL

TEST

Drilling for long eitension of o

portly developed pool 5. OUTPOST or EXTENSION TEST

EXTENSION WELL

(Somttimtt a nrw-poot

discover/ "II)

DRY OUTPOST

OR

Oil EXTENSION TEST

Drilling to eiploir or develop o hydrocorbon accumulation

discovered by previous drilling 6. DEVELOPMENT WELL DEVELOPMENT WELl DRY DEVELOPMENT WELL

DEEPEP '001 SNAUOWII POOL

(PAY) Tf ST BlVtlOPMINT |fA , OUTPOST I. EXTENSION TEST

..Tr-.-r*.rr..rr. ?y Jj *JK T U RE

150
THE RESOURCE STOCK

Thus far, my framework has concentrated on the flows associated with the

oil and natural gas supply process. Figure 1 connected physical knowledge,

constraints and a stimulus with the behavioral ingredients of the process.

Figure 2 portrayed the kinds of activities, time relationships, and decision

problems associated with exploration, development and production decisions.

The stock aspect of the oil and natural gas supply assessment problem

concerns the status of the resource base at each point in time. In principle, • a fully correct and complete assessment should address the full assortment of

"margins" along which the supply process can advance. Figure 4 displays the

"McKelvey Box," which is a convenient expository device for identifying the

various margins for supply activity which can exist at any point in time.

Briefly, these margins have the following meaning:

• Undiscovered Margin : this margin includes undiscovered deposits,

outside of known fields. These are the target of exploratory

tests labeled "New Field Wildcats" in the well classification

scheme shown in Figure 3. Although the McKelvey Box separates the

undiscovered margin into an economic (or recoverable) portion and

a sub-economic portion (including non-commercial deposits and

unrecoverable fractions of commercial deposits) , the preferred

assessment perspective encompass total oil- or gas-in-place

potentially residing in undiscovered deposits.

• Access Margin : this margin locates the portion of the undiscovered margin where physical access is controlled by special

institutional factors; examples include deposits on the U.S. Outer

Continental Shelf subject to federal leasing and onshore lands

owned by governments, some of which may never be accessible for reasons of environmental protection.

• Inferred/Indicated Margin : this margin encompasses deposits which

generally have been discovered or inferred by geological and

engineering work. By definition, the indicated portion resides

within deposits which literally are known; it represents the

expected results of the secondary recovery phase of development

illustrated in Figure 2. The inferred portion represents the

expected product of the kinds of exploratory drilling included in

categories two through five in Figure 3. The approach to estimating the magnitude of inferred reserves typically consists of

applying "growth curves" to measured reserves in known fields,

based upon historical experience with the occurrence of extensions

and new pays around known deposits.

151
FIGURE 4

(MODIFIED) MCKELVEY BOX (2)

CONVENTIONAL PETROLEUM RESOURCES

OF THE UNITED STATES

IDENTIFIED

DEMONSTRATED UNDISCOVERED H

MEASURED INDI CATED 1 ii

ECONOMIC

! H ^ ^ 1 i i i ii

i i ffi

SUBECONOMIC

MM

wavWAV •WAV WAV WAV

.WAV. WA'A wav! WAVV

WA'A WA'A

111

1 Undiscovered Margin

2 Access Margin

3 Indicated/Inferred Margin

4 Pure Intensive Margin

5 Uneconomic Conventional Resources Margin

6 Conventional Resources Technological Margin

7 Unconventional Resources Margin

152
• Pure Intensive Margin : this margin resides within the measured

category (equivalent to the American Petroleum Institute definition of proved reserves) . In my framework, this margin represents

the addition of productive capacity through the intensification of

development of existing proved reserves. Examples of trade terms

for this kind of activity are "infill drilling" or "drilling for

rate .

• Uneconomic Resources Margin : within the identified portion of the

McKelvey Box, this margin represents the backlog of previously

non-commercial deposits and unrecoverable portions of commercial

deposits. In the undiscovered portion, it represents resources which might suffer the same fate in today's economic and technological environment. In the modified diagram, this margin represents those resources which might become economic mainly because

of higher prices.

• Conventional Resources Technology Margin : this margin is similar

in concept to the uneconomic margin, except that it responds

mainly to improved technology. In the identified portion of the

box, certain enhanced oil recovery technologies exemplify this

margin; in the undiscovered portion, capabilities to explore and

develop in deep water exemplify the technology margin for conventional resources.

• Unconventional Resources Margin : this margin

shown as a third

dimension of the McKelvey Box—represents unconventional petroleum

liquids and natural gas resources. With respect to U.S. resources

and the historical emphasis of most previous U.S. resource appraisal work, this margin includes a long list and potentially

massive quantities of resources: most heavy hydrocarbons and tar

sands, oil shale, diatomaceous hydrocarbons, tight gas Devonian

shales, geopressured methane, methane entrained in coal seams, and

others.

IMPLICATIONS FOR OIL AND NATURAL GAS SUPPLY ASSESSMENTS

This framework suggests several things for oil and natural gas supply

assessments

• A satisfactory assessment should include physical information

about the resource base and the exploitation process, a description of constraints, and some stimulus.

• In turn, this information should be integrated in a manner which

describes how the supply process will respond to changes in the

supply environment and the technology of the process.

153
• The physical information should be organized according to all of

the "margins" which are represented in the stock of economically

and technological feasible resources relevant to the time horizon

of the model.

• At each of these margins, the model should recognize, explicitly

or implicitly , the detailed processes which occur at the level of

the micro-units of relevance to investment decisionmaking. For

exploration, a logical unit of focus is the prospect, and the

process description should recognize the complex probability laws

associated with the deposition and exploration processes, particularly for resources well outside of known fields. For development, the most logical unit of focus is the reservoir, and the

process description should recognize the flexible nature of the

optimal development investment decision problem associated with

selecting an extraction path over time for a single reservoir.

For production, the possibility of speculative withholding should

be recognized if (effective) prices may be "unstable."

• In order to appropriately accommodate the full range of relevant

margins, the focus of the model should be on productive capacity,

not reserves, and on the separate decision to operate available

capacity.

• The model should look behind current data reporting systems and

the geologic, engineering and conservation doctrine which may

muddy the historical record and the forward assessment process

with hidden economic, technical and institutional considerations.

154
CURRENT PROBLEMS WITH THE STATE OF THE ART

This framework, presented in the previous section, provides an outline for

identifying problems and opportunities for improvement with respect to oil and

natural gas assessment used for energy policy planning the U.S. My discussion

of these problems and opportunities is organized into three sections. First,

problems associated with the way models attend to the "margins" described in

the preceding framework are discussed. Then, other problems related to the

ingredient of the supply process labeled "behavior" (in Figure 1) are described. Finally, problems related to the use of resource models and reser- vations about current modeling trends are described. These three sections,

however, are preceded by a brief discussion of several recent events in the

U.S. oil and natural gas "record." Hopefully, these can illustrate the

urgency associated with the subsequent problems.

SOMETHING HAPPEND TO OIL

Figure 5 describes a simple oil supply model. The model consists of two

parts. One is an accounting representation of the stock of previously proved

reserves as they are reduced over time by production. The rate of production

for this purpose is represented by a "decline rate," in modeling practice

typically a constant ratio of production to proved reserves. The second part

is a representation of the reserves addition process, consisting of a rate of

drilling activity (measured in terms of either feet drilled or wells) and a finding rate (either per foot drilled or per successful well, often where a well success ratio is included in the formulation)

The rate of activity may be estimated exogenously or endogenously , some- times as a function of prices and even sometimes as a function of industry

cash flow. Where endogenous, the rate of drilling may be related to some expression of the costs of the drilling, the reserves added by the finding

rate as a result, and prices. Finally, remaining reserves and reserve additions are summed and multiplied by a decline rate, again often invariant with

respect to time or economic conditions, to calculate production.

To put my cards on the table immediately, many U.S. oil and natural gas

supply assessments and models, although apparently more complicated on the

surface, when stripped to their essentials, are represented reasonably

accurately by this simplified model. Further, many of those which claim to

develop the rate of drilling activity endogenously, as a practical matter, do

not; instead, they simply track overtime exogenously specified drilling

constraints. Almost all focus on reserves as the product of drilling and

subsequently employ a static decline rate to estimate production. I hasten to

add that formal models with which I have been involved heavily are not

excluded entirely from these observations.

155
FIGURE 5

A SIMPLIFIED OIL SUPPLY MODEL

Finding

Rate

t-1

Reserve

Additions

t-1

> x Decline

Rate.

(1 - Decline

Rate)

t_1

Remaining

Proved

Reserves

156
The finding rate portion of this simplified oil supply model is the primary focus of my example. A typical expression of the finding rate function

is as follows:

The relationship typically is estimated by fitting a curve, often of an exponential form, to historical series of each statistic. The fitting also

often is done to cumulative series of each, after which the first derivative

of the cumulative function is used to estimate the finding rate over time or

over successive increments of cumulative total footage drilled.

Figure 6 shows the historical behavior of the oil "finding rate" defined

in this fashion. In order to avoid an issue of how to allocate "dry holes"

between oil and natural gas, the figure displays the ratio of total reserve additions to successful oil footage drilled. In order to suppress year-toyear variations simply for discussion purposes, the figure plots cumulative

reserve additions versus cumulative drilling.

Prior to 1974, this rate appears to behave in a stable fashion, but during and afterward it appears to exhibit a downward kink. Measured crudely, a slope of 38 barrels per foot prevailed from 1960 through 1973 but was replaced

by an average of 17.5 barrels per foot in 1974. This change, alledged to

indicate abruptly declining productivity of U.S. drilling, has been a central

feature of the U.S. oil policy debate during the last five years.

The coincidence of this "kink" and three other events—the 1973-74 oil

embargo, much elevated oil prices, and imposition of price controls on crude

at the wellhead in the U.S. --is enticing. The modeling problem associated

with this simultaneity was summed-up well by Searl (3):

"There appears to be an almost complete lack of

attention to the manner in which historical data on which resource estimates are based have been conditioned by economic and institutional factors... At

the micro-level, that is the deposit, reservoir and

well level, statistics are clearly conditioned by

economic and institutional factors... As a basic

proposition, I would assert that all micro resource

data, even when stated in physical units without

economic parameters, have been tainted by economics

and that projections using such data are implicitly

projecting certain economic, institutional and

technological conditions and constraints."

157
FIGURE 6

OIL FINDING RATE

38.0 MJ 17.5 - bbl/ft. bbl/ft.

200 400 600 800 1,000 1,200

Cumulative Successful

Oil Footage

ft x 10

6

* Excludes Alaskan North Slope

158
Because the interpretation of this abrupt change in apparent drilling

productivity has profound implications for modeling and policy, its causes

have been the subject of substantial discussion. At least four hypotheses

have been offered:

• A New Geological Epoch ; This hypothesis contends that the oil

supply process encounters sequential epochs, each of which is

distinguished by an abruptly lower finding rate. This view holds

that the recent change will persist but that finding rates will

hold steady at this new, lower level for a substantial period

before descending once again.

• Changed Exploration Focus : This hypothesis resembles the geologic

epoch concept, except that the abruptness is not caused by discontinuities in nature but rather by explorationists turning to the

readily available backlog of submarginal prospects and previously

non-commercial known deposits as a first response to changed

prices and U.S. price regulations. This view holds that the low

rate is temporary; soon the rate will return to a trend slightly

below the pre-1974 level. The failure to return completely' will

be caused by the smaller-sized future discoveries which will be

commercial under higher prices.

• Changed Drilling Mix : This hypothesis adjusts the preceding one to account for the changed economics of development under higher

prices. It suggests that a short run emphasis on adding productive capacity at the pure intensive margin, without accompanying

reserve additions, caused this aggregate "finding rate" statistic

to yield misleading results. Simply, if the denominator of the

finding rate were inflated by drilling clearly not intended to add

reserves, the ratio of reserve additions to total drilling would

fall. But because the backlog of infill drilling opportunities

also is limited, the recent finding rate experience will be temporary and soon will rise to a level slightly below the earlier rate

(unless even higher future prices justify additional intensification of development). Advocates of this hypothesis also note the

peculiar incentives for drilling "stripper wells" —wells producing

10 or less barrels per day—contained in U.S. oil pricing regulations.

• The "Devil" Hypothesis : Because the historical data are provided

by the oil industry, this hypothesis claims that they are false

and are biased toward creating a case for abandonment of price

controls.

In order to test these hypotheses in a thorough and logical manner, a necessary first step would be to decompose the historical record along the

lines of the seven margins identified earlier in my framework. Unfortunately,

159
publicly-available data may be inadequate to subject these hypotheses to this

acid test. For various reasons, mostly related to a lack of detail and proper

categorization, I believe that the historical record remains unresolved and

unexplained. Somewhat catastrophically , the most fortuitous natural experiment of all time for aiding empirical understanding of the U.S. oil supply

process remains obscured by data obstacles.

A major hint, however, resides in a category of reserve additions labeled

"revisions," defined as follows by the American Petroleum Institute (4).

"Both development drilling and production history

add to the basic geological and engineering knowledge

of a petroleum reservoir and provide the basis for more accurate estimates of proved reserves in years

following discovery. Changes in earlier estimates,

either upward or downward, resulting from new information (except for an increase in proved average) are classified as 'revisions'. Revisions for a given year

also include (1) increases in proved reserves associated with the installation of improved recovery techniques; and (2) an amount which corrects the effect on proved .reserves of the difference between estimated

production for the previous year and actual production

for that year."

In the period from 1960 through 1973, revisions accounted for 55 percent of

cumulative reserve additions, averaging approximately 1.3 billion barrels

annually. Since 1973, revisions have averaged .8 billion annually. A U.S.

oil finding rate, excluding revisions, also is shown in Figure 7. Note that

this exclusion improves the regularity of this function, but does not remove the "kink" entirely. But the definition of this category itself raises

numerous, unresolved questions. Something happened. But what?

SOMETHING HAPPEND TO GAS

Figure 7 shows a similarly defined "finding rate" for non-associated gas,

which is the product of drilling identified to gas in U.S. drilling data

systems. This rate appears to evidence two "kinks," one at 1968 and another

at 1972. The coincidence in this case is that 1969 is the point in time where

U.S. interstate gas transmission systems initially became unable to obtain

contracted values of natural gas from domestic producers.

The significance of these "kinks" for modeling U.S. natural gas supply and

for domestic policy also is profound. Hypotheses identical to those put forth

for oil have been offered to explain these kinks in U.S. gas finding experience. But an additional one related specifically to natural gas revisions

also has been added to the list.

160
FIGURE 7

NON-ASSOCIATED GAS FINDING RATE

excludes revisions —

I

1 1

; 1 r

100 200 300 400 500

Cumulative Successful

Footage

6

ft x 10

161
Traditionally, revisions have accounted for a much smaller share of annual

reserve additions for natural gas than for oil. But beginning in 1969, a traditional, historical series of net positive natural gas revisions turned

negative in a magnitude equal to their former, positive level. Suppose that,

in reality, the positive side of the net revisions process remained

unchanged. Then, from 1969 through 1978 the series of net negative revisions

for natural gas (associated-dissolved and non-associated) would indicate that

30 trillion cubic feet of proved gas reserves somehow have been "written

off." One hypothesis holds that these reserves actually were not "proved" in

the first place. Rather, requirements to insure extended deliveries over long

periods of time, associated particularly with contracts to sell gas to the

interstate market, may have caused producers to include possible and even more

speculative reserves in their reserve estimates. Of course, when it became

impossible to deliver contracted volumes, it also became necessary to write

down the earlier reserve estimates. If so, the record prior to 1968 is

tainted with phantom proved reserves and the post-1968 record is tainted by

the writing-off process.

Similar to oil, the true character of these kinks cannot be determined

readily from publicly-available data. In Figure 7, however, excluding

revisions from the aggregate finding rate appears to moderate the kinkiness.

Yet, the modeling question still remains, simply because the pre-1969 record

cannot be sorted out.

PROBLEMS AT THE MARGINS

The preceding examples suggest that a lack of attention to individual

supply margins in U.S. oil and natural gas data collection systems defeat

explanations of the historical record. Assessments of the U.S. oil and

natural gas supply prospects tend to embody only the margins that the

available data reveal. In descending order, according to the amount of

emphasis they receive in existing models, as well as the literature, the

prevelant margins are:

• The Undiscovered Margin

• The Inferred/Indicated Margin

• The Access Margin

Subjectively, I judge that order-of-magnitude differences in emphasis

distinguish even these three margins in modeling and resource appraisals.

Because of attention primarily to the undiscovered margins, most assessments

focus on "proved reserves" as the controlling output of the supply process,

thereby excluding the "pure intensive margin." And as will be discussed

subsequently, development alternatives residing within the undiscovered margin

generally are treated inadequately. Also missing generally are the uneconomic

resources margin, especially in the identified portion of the resource base;

the conventional resources technology margin; and the unconventional resources

margin. Of course, there are exceptions. But I know of no model, or group of

162
models used collectively, which are uniformly complete with respect to attention to these margins. For the U.S. resource base and for short-range, midrange, and long-range estimates, this situation is less than ideal. The

forecasting result may be an overly pessimistic oil and natural gas supply

outlook, too little price responsiveness of supply, and perhaps misplaced

emphasis in the policy process. What, then are the opportunities for improvement?

Undiscovered Conventional Resources Margin

Most advances in the state-of-the art appear to be focused on this margin. This singularity of emphasis itself may be problematic. Briefly, the

trend is toward closer linkage of geostatistical models and economic models,

accompanied by the use of stochastic modeling techniques, to grapple with the

complex probabilistic laws associated with geological and search processes.

Accompanying this is a parallel effort to provide a three-dimensional picture

of deposits.

Even at this stage of advance, heroic estimating problems are encountered

immediately, especially for immature petroleum provinces. But the full range

of estimating problems goes well beyond estimating sizes, locations and depths

of deposits. On the undiscovered resources margin, economic linkage typically

is provided by an accompanying reservoir development model. In principle, to

work out an optimal development and production profile for a deposit, much

more must be known. The economics of development center around the development well. Since drilling costs dominate development investment, the commercial attractiveness of a deposit hinges on the time profile of production

associated with each well. Estimating well performance requires knowledge of

additional physical attributes of a deposit: permeability, pay thickness,

viscosity, drive mechanism and others. Suddenly, the requirements for

stochastic variables multiply, and data and estimating problems compound.

Concerns about interdependencies between these myriad variables also crop up.

Perhaps as a result, improved models of the undiscovered resources margin

tend to use a development model mainly to estimate minimum field sizes in a rough way, using some "base level" development program of static intensity.

Consequently, the effects on supply of development alternatives at the undiscovered margin may require further work. ..data permitting.

A less sophisticated but also improved method of representing the undiscovered resources margin takes the form of a marginal extraction cost curve. The curve typically consists of a function relating cumulative barrels of reserves and minimally acceptable prices required to justify extraction. I have yet to encounter one of these curves which explains its meaning. If any

deposit can be developed in different ways—the choice among which, for

example, is the one which maximizes expected profits —no unique "extraction"

cost may exist for any deposit. Further work is required to determine what

these curves imply in terms of development and how, as a result, they should

be used in models.

163
Access Margin

The access margin of major relevance to U.S. oil and natural gas centers on government-owned lands, principally in lower-48 offshore areas and in

Alaska and its offshore waters. The usual approach to this margin employs a leasing schedule; a forecast of acreage offered per lease; a fraction of

acreage sold per offering; and an estimate of the share of an aggregate

resource base underlying the leased acreage. In reality, the specific acreage

to be offered for sale seldom is known far in advance. Retrospectively, the

economic and institutional factors affecting the choice of which acreage to

offer, even at the basin level, and the fraction of the offered acreage

actually leased usually are unknown.

These shortcomings typically are resolved by a modeling procedure which

assumes that the best acreage in each offshore area is offered first and that

the share of offered acreage leased remains constant over time, regardless of

the economic and institutional environment. Review of U.S. leasing practices

contradicts the first part of the procedure, and changed economic conditions

probably contradict the latter. Consequently, there are clear opportunities

for improved knowledge and modeling techniques on the access margin.

Inferred/Indicated Margin

Where treated explicitly, most resource appraisals and most models deal

with this margin deterministically and in a highly aggregated fashion. In the

U.S., the problems with this approach is signaled by the fact that the "growth

curves" employed in U.S.G.S. 725 to estimate inferred reserves appear "shaky"

when exposed to simple statistical significance tests. Consequently, the

quantity and quality of resources residing on the inferred margin may not

deserve a deterministic treatment, either for appraising the resource base or

for modeling supply possibilities on this margin.

In addition, historically-derived "growth curves" may not be independent

of the sizes of fields and reservoirs included in a truncated sample —only

those of commercial worthiness in the past. If, as work concerning undiscovered resources suggests, larger deposits tend to be found first, a question can be raised about whether uniform growth curves estimated from experience

with large deposits are appropriate for estimating inferred reserves, especially if deposit sizes decrease over time.

Pure Intensive Margin

Most existing assessments do little more with current proved reserves than

extrapolate future production with a fixed decline rate, usually equal to an historical production to reserves ratio. Even in the most advanced, formal

supply models, it always is interesting to observe one small "box" at the tail

end of an otherwise elaborate model labeled "production from existing

reserves.

164
Yet viewed at the most aggregate level, the U.S. production to reserves

ratio for oil outside of Alaska has increased from approximately .08 to .13

since the effects of market-demand prorationing disappeared in 1971. This

suggests that the U.S. oil supply process may be changing on the pure intensive margin in a way which existing data and oil supply models do not represent. Unfortunately, the situation for gas is sufficiently confused by negative revisions that it is impossible to say whether a similar change has

occurred. Also unfortunately, the manner in which development drilling activity is reported—as a lump, undifferentiated between development purely to

produce existing reserves faster and other activity which adds both new

reserves and productive capacity—makes the importance of the pure intensive

margin difficult to evaluate. This could be a worthwhile starting point for

further work related to this margin.

Uneconomic Resources Margin

The supply assessment problems on this margin can be summed up succinctly:

virtually nothing is known. The historical record of discoveries represents a severely truncated distribution. Possibly half of the deposits actually

tested and found to contain hydrocarbons are excluded from the record because

they previously were non-commercial. Perhaps the only possible next step in

this category would be to improve the process of reporting dry holes in the

future

Conventional Resources Technology Margin

Three kinds of modeling issues exist on this margin. The one which thus

far has received most attention concerns enhanced oil recovery, mainly

achieved by tertiary recovery methods. This portion of the technology margin

has been worked over reasonably well, considering the dilemmas associated with

forecasting prospects for emerging technologies. With respect to opportunities for improvement, however, two areas may merit further work. First, a large share of today's assessments of enhanced recovery prospects consist of

extrapolations from a relatively small number of major fields to a large

universe. Because of the large role for enhanced recovery evidenced in many

current forecasts, these extrapolations need closer attention. Secondly,

current enhanced recovery estimates—even those related to the application of

reasonably well-known methods —often employ development plans whose intensity

is static. Consequently, the "pure intensive margin" within enhanced recovery

may need additional attention.

Two other issues on the conventional resources technology margin center on

drilling costs and current water-depth limits on drilling and production.

U.S. drilling costs appear to have been escalating at a rate well in excess of

the general cost of living. There are three potential explanations: costs of

traditional materials and other inputs are rising because of conventional

cost-push inflation; conversely, rising activity levels are causing inflation

of a demand-pull variety; or a qualitative change in drilling inputs has

165
occurred because of a higher oil price structure. In the past, drilling technology has exhibited substantial and continual improvement. Since drilling

costs account for the bulk of oil and natural gas supply investment, a better

understanding of what has caused costs to rise rapidly in the last decade and

a better basis for estimating future rates of cost change would prove invaluable to the modeling process. Finally, the future for drilling and production in deeper waters, accompanied by a better assessment of deeper water

prospects, could prove important and helpful.

Unconventional Resources Margin

This margin, of course, represents another dimension of technological

advance and changed economic conditions. With due respect for the difficulties accompanying technological forecasting problems, the current situation

might be improved in at least two areas. The first is a matter of emphasis,

particularly with respect to resource assessment activity. Even for unconventional resources closest to commercial practicability, the extent and quality

of the resource base largely are unknown. The resource appraisal attention

they are receiving is much too small in relation to their potential.

The second area for improvement simply may be one of semantics or communication. Typically, potentials for unconventional oil and natural gas resources are quoted in terms of recoverable reserves and in the same manner

as conventional crude oil and natural gas. What seems to be missing—and

therefore confusing to policymakers—is the much more strenuous effort

required to add an equivalent amount of productive capacity from these

resources, simply because of low densities of energy material in the

extraction streams (e.g., geopressured methane and oil shale) or low per well

production rates associated with these resources (e.g., tight gas or Devonian

shale) . It may be that a new unit of measure is required to describe the

different productive capacity potential of these resources compared to

conventional crude oil and natural gas.

PROBLEMS WITH BEHAVIOR

For purposes of policy-related energy resource modeling, the appropriate

objective for modeling behavior is to simulate the decisionmaking process of

the industry or other agents under whose control investment and production

decisionmaking reside. Hypothetical ly, the organizing principal for the

behavioral ingredient of resource models is straightforward: capital and

other inputs should be allocated to each of the individual supply margins such

that their marginal products are equal on all margins at each point in time

and at overall rates which yield extraction paths over time which satisfy some

obj ective

Three approaches toward implementation of this behavioral principal are exhibited in oil and natural gas models: econometrics, simulation, and

optimization. The appropriateness of each technique has been the subject of

166
extensive and sometimes heated debate, which will not be extended or amplified

further here. In my opinion, these techniques tend to converge in the limit.

Much criticism of econometrics appears to be focused more on an absence of

explicit process-oriented structure in previous econometric supply models and

on occasional inattention to depletion effects in some others. These are matters of physical structure rather than behavior. Similarly, simulation

often is faulted for a lack of underlying theory; I leave it to economists to

justify that current economic understanding of the behavioral aspects of the

oil and natural gas supply process deserve to be elevated above the level of

rough hypotheses. Finally, optimization is criticized for the overly normative nature of this approach. I have observed, however, that optimizing

models often are made "realistic" with the ample use of essentially behavioral

constraints, the origins of which should not leave econometricians or advocates of simulation embarrassed in their wake.

Problems on the Margins Again

Earlier, the modeling framework distinguished the decisionmaking focus

appropriate for exploration from the one appropriate for development and

production. Also, the different physical characteristics of the search

process and the more engineering-oriented development process were noted.

In contrast to these physical differences, most models do not incorporate

behavioral rules which distinguish exploration and development. The potentially special "gamblers ruin" aspect of the exploration process has been raised

by Ramsey (5). Work thus far on the different behavioral properties is sufficiently suggestive that the proposition of a difference, empirical testing,

and differentiation of behavioral tendencies between exploration and development may deserve enhanced attention on the part of oil and natural gas

modelers.

Rig Constraints

A special dilemma regarding oil and natural gas supply faces today's

optimization models. Almost without fail, models of this variety choose to

drill-up vast quantities of the remaining U.S. resource base in the first

period of their forecasts. The usual solution is to include drilling constraints in the model. The constraints usually are defined outside of the

models and, as a result, an elaborate optimizing apparatus, in fact, forecasts

simply by tracking exogenously specified drilling constraints. The constraints typically are a matter of the modeler's judgment.

If an analytical resolution of this phenomenon associated with optimization models is to be provided, there are at least three avenues for further

work. One consists of the resource base descriptions and cost data which

cause these models to see such a wealth of attractive drilling targets

immediately. Another concerns the potentially different behavioral ingredients of exploration and development decisonmaking. The third is the poten167
tial, further optimizing problem—describing the investment decisionmaking of

drilling equipment vendors and drilling contractors—which needs to be

included in these models. Among these, a better understanding of the capacity

formation process of the drilling industry would be especially helpful for

improving oil and natural gas supply models.

Investment Criteria

Measures of the decisionmaking criteria of those who control oil and

natural gas properties enter most supply models. Typically, the variable is a discount rate or an equivalent return on investment measure. In the recent

U.S. oil price decontrol debate, alternative hypotheses concerning investment

criteria were put forth. A recurring one concerns the relationship between

industry cash flow from operations and rates of activity. The suggestion is

that there is something special either about the capital markets as they apply

to oil and natural gas or about the investment criteria which guide exploration (another variant of the behavioral issue raised earlier). The validity

of this contention needs further inspection, if for no other reason than it

has played a large role in U.S. oil and natural gas pricing policy and, if

correct, would represent a new and different direction for many supply models.

For models which use an explicit discount rate, or its equivalent, much

work needs to be done. To my knowledge, no solid and current empirical basis

supports the rates used by most oil and natural gas supply models. Because of

the capital-intensive, front-end loaded nature of drilling and the drawn-out

production profile associated with oil and natural investments, supply models

are strongly sensitive to their discount rate assumptions. Consequently, more

work is required in this area.

Uncertainty, Foresight and Non-Competitive Markets

No commentary on opportunities for improving resource models would be

complete without mention of these persistent, fundamental problems. Among

these, however, the one receiving attention here is foresight, because it has

become a major analytical question surrounding U.S. energy models used at the

federal level. Also, it is of interest in the debate between econometrics,

simulation and optimization—one sometimes humorously described as the choice

between perfect hindsight and perfect foresight.

The prevailing solution to the problem appears to be "rational expectations." But from the perspective of implementing a forecasting model, what

specifically are the expectations? More work is needed here, too.

168
RESERVATIONS AND OTHER PROBLEMS

Current trends in oil and natural gas supply modeling prompt a question

about where the state-of-the-art is going and, if continued, another modeling

problem that may be encountered. I would be pleased to see both receive

serious comment and further work.

The current trends in oil and natural gas supply modeling are laden with

overtones of ever increasing model detail and, in turn, models with ever expanding computing budgets. Most supply models cannot stand alone for many

uses. Policy-relevant forecasting almost always requires linkage to other

systems which affect oil and natural gas supply: transportation, conversion,

distribution, and end-use. And because energy resources of all kinds compete

in numerous end-uses, oil and natural gas supply models often become one subpart of a comprehensive, complex and large energy market model involving

other fuels and often regional detail. If these energy market models are to

be practical, how much of their computing budget can be consumed by the representation of the oil and natural gas supply process? And if not a large

share, how are detailed, complex and large oil and natural gas supply models

to be linked effectively to them?

Finally, the prospect of more detailed, more complex and larger oil and

natural gas supply models deserves introspection by modelers and attention by

others. How much expansion of detail is productive? How much is promoted by

elaboration of modeling possibilities suggested by technique. . .without accom- panying data to justify its use? And most importantly, will the subsequent

results be an improvement from the perspective of the energy policy process?

169
REFERENCES

(1) The American Association of Petroleum Geologists, Inc., AAPG Bulletin , August 1976, p. 187.

(2) U.S. Geological Survey, Geological Estimates of Undiscoverable Recoverable Oil and Gas Resources in the United States , Geological Survey

Circular 725, 1975.

(3) Searl, M. , "Resource Assessment and Supply Curve Development: Toward

Better Methodologies," in First IIASA Conference on Energy Resources, M.

Grenin (ed. ), International Institute for Applied Systems Analysis:

Luxemburg Austria (1975), p. 71-84.

(4) API, AGA, and CPI, Reserves of Crude Oil, Natural Gas Liquids, and

Natural Gas in the United States and Canada as of December 31, 1978 , Volume 33, June 1979.

(5) James B. Ramsey, "A Preliminary Analysis of Some Aspects of Oil

Exploration," Hoover Series No. 76-136 (draft paper distributed for

purposes of soliciting critical comments).

170
THE EVOLUTION IN THE DEVELOPMENT OF PETROLEUM RESOURCE APPRAISAL

PROCEDURES IN THE U.S. GEOLOGICAL SURVEY

Betty M. Miller

U. S. Geological Survey

Reston, Virginia

INTRODUCTION

The state of the art for appraising petroleum resources has advanced

rapidly during the past decade because of the growing awareness of the

need for petroleum resource estimates for the formulation of reasonable

energy policies and long-range planning.

Events triggered by the Arab-Israeli war of 1973 focused the

attention of the world on energy problems and on the inherent uncertainty

of the estimates made for petroleum resources. Many nations will need

realistic forecasts of future petroleum supplies; these estimates of the

distribution and magnitude of oil and gas resources throughout the world

must be based upon the most reliable methods and data available. This

situation calls for a high level of domestic and international cooperation

among appraisers of petroleum resources.

Published appraisals of oil and gas resources in the United States

date back at least 70 years (Thomsen, 1979). The first published

estimates by the U.S. Geological Survey in 1909, by David T. Day, covered

the known producing areas of the conterminous United States which at that

time had a reported cumulative production of 2 billion barrels, 4 billion

barrels of proved reserves and 4 to 18 billion barrels of potential

supply. Since then, many published estimates have been made by the USGS,

industry and individual researchers. In the 20-year period after 1955,

the amounts reported from these appraisals varied widely, giving rise to

great confusion and much controversy. Attempts to compare these estimates

revealed that many of them were based upon inadequate data and were poorly

documented. Each effort had utilized different assumptions, definitions,

appraisal methods, geographic boundaries and data bases and therefore

should not be compared. Increased efforts during recent years have been

directed toward resolving some of these major problems, and there is

evidence that progress is being made. This paper discusses the efforts

made by the USGS within the last 6 years to improve upon its methods for

petroleum resource appraisal.

171
METHODS

Many methods exist for estimating petroleum-resource potential

with numerous variations in the basic techniques. Each method requires a certain level of knowledge or degree of available information on the area

to be assessed. Each method, however, has recognized limitations. Problems

arise because of misinterpretation of results and lack of recognition

of these limitations on the methods and data used. Emphasize must be made

that no single technique has universal application or appeal — nor

is there unanimity on the results. In 1974, the Oil and Gas Resource

Appraisal Group was created by the USGS to devise and study resource

appraisal methods and to apply these methods in assessing the nation's

petroleum resources as a full-time responsibility.

The first nationwide appraisal of the undiscovered oil and gas resources

for more than 100 geologic provinces was published by the Resource Appraisal

Group in 1975 as USGS Circular 725, "Geological Estimates of Undiscovered

Recoverable Oil and Gas Resources in the United States" (Miller et al. 1975).

In this study, the appraisal methodology was applied on a broad scale and

designed for the geologic basin or geologic province. The estimates of the

undiscovered resources were made: (1) by reviewing and analyzing all

available geological and geophysical information compiled on more than 100

geologic provinces; (2) by applying resource appraisal techniques, which

included extrapolations of known producibility into untested sediments of

similar geology for well-developed areas, and volumetric techniques using

geologic analogs with ranges of yield factors; (3) by using group appraisals

(in a modified Delphi procedure) determined by geologic experts applying

subjective probability procedures; and (4) by reporting final results as probability ranges rather than as single number values.

1/ Undiscovered resources are defined by the USGS as follows:

Undiscovered Resources : Quantities of a resource estimated to exist

outside of known fields on the basis of broad geologic knowledge and

theory.

Undiscovered Recoverable Resources (Potential Resources) : Those

economic resources, yet undiscovered, which are estimated to exist in

favorable geologic settings.

Original in-place Resources : Includes all discovered oil and gas reserves (produced and remaining), and the undiscovered resources believed to exist, both recoverable and nonrecoverable (Miller et al.

1975).

172
Since the organization and the first publication of the Resource

Appraisal Group's work, the evolution in petroleum resource appraisal

procedures has been significant. The methods developed and employed by the

Resource Appraisal Group are designed to emphasize the compilation and

evaluation of all available geological and geophysical data by geological

basins or provinces. Resource estimates can be made on any level of data;

however, the amount of data available will determine the method or methods

to be used for the appraisal. The method or procedure used can change as the amount and nature of the available data change within a specific basin.

In the frontier stages of exploration when some information exists on the gross interpretation of basin geology, and, when the principles of

petroleum occurrence from worldwide experience are applied, subjective

judgment may be used with minimum amounts of data as a basis for the

assumption of the presence or absence of potential hydrocarbons. As the

data base grows, because of increased exploration, and as the results of

geophysical surveys, drilling, and geochemical data become available,

methods using more objective data should become increasingly dominant.

The methods used in making estimates may evolve to the level of assessing

exploration plays and may eventually focus on making estimates of

undiscovered prospects, if this level of resource assessment is desirable.

If abundant and detailed data are available, the choice of the method to

be used may become more dependent upon the availability of the estimator's

time, the effort involved, and the purpose of the resource estimate.

The quality of the estimate is, however, dependent upon the quality of the

geologic data and studies upon which the estimate is based (Miller, 1979).

DEVELOPMENTS IN THE USGS SINCE 1975

Since the initial studies and the resource-appraisal methods

described in Circular 725, the older methods have been refined, alternate

resource appraisal techniques have evolved, and new and more detailed oil

and gas data have been compiled, particularly field and pool information,

for stratigraphic units within specifically designated pilot areas in the

United States. By using the new information increasingly available to the

Resource Appraisal Group and the refinement in resource appraisal methodology,

resource assessments can now be made for individual stratigraphic units and

by depth increments within many basins. Results of the Permian Basin study

conducted by the Resource Appraisal Group are reported in this paper to

illustrate the use of these methods. Estimates can also be made on the

probable size and number of fields in which the remaining undiscovered

resources may be found within a semi-mature or maturely explored area

and on the probable depth increments within which these fields are likely

to occur. The Gulf of Mexico studies, completed by the Resource Appraisal

Group are also used to demonstrate these methods. Additional refinements

of resource assessment methods have been completed for the application of

computerized geologic models using play analysis techniques for the appraisal

of conventional petroleum resources in the National Petroleum Reserve of

Alaska, and of unconventional natural gas resources in the Devonian black

shales of the Appalachian Basin.

173
CURRENT METHODS USED BY THE USGS

The following discussion reviews the evolution and development of each

of the basic resource appraisal methods currently being used by the Survey's

Resource Appraisal Group. Specific applications from current studies by

the Resource Appraisal Group are reviewed for each method. Although the Group

works on both oil and gas resource estimates, and the methods are often similar

for both, this paper will be directed primarily to the application of methods

and results for natural gas resources.

METHODS USING VOLUMETRIC-YIELD ANALOGS

Volumetric-yield techniques have been used in a wide variety of ways in

making petroleum-resource estimates. These techniques range from the use of

worldwide average yields expressed in barrels of oil or cubic feet of gas

per cubic mile of sedimentary rock, or per square mile of surface area (assuming constant thickness) applied uniformly over a sedimentary basin,

to more sophisticated analyses in which the yields from a geologically

analogous basin have been used to provide a basis of comparison. The

pioneer works by Weeks (1950), Zapp (1962), and Hendricks (1965) are illustrative of early techniques.

In Circular 725, wherever yield factors were used, it was done in the

context of a reasonably sound consideration of the geology of the basin or province and the selection of a geologically analogous basin or province.

The records of 75 North American basins were compiled, the oil and gas

yields being expressed per cubic mile of sediment as determined from

well-explored areas within these basins, to establish a scale of hydrocarbon

yields for geologically analogous basins. Figure 1 shows a frequency

distribution of hydrocarbon yields for these basins. The productivity of a basin may range from less than 1,000 barrels per cubic mile of sediment to more than 3 million barrels per cubic mile of sediment, as in the exceptional

case of the Los Angeles basin.

The accuracy of this method depends on the expertise of the geologist

who compares the similarity of the geology of an unexplored basin with that

of a developed basin, prior to the selection of a hydrocarbon yield used to

make a forecast for the potential of the unexplored basin or unexplored part

of a basin. A highly recommmended approach to this method is the selection

of a representative range of analogous yields to which probabilities

are assigned to determine a minimum and maximum estimate for the potential

resource. The results obtained by this method can be useful on a broad

regional basis or in a reconnaissance-type estimate of the resource potential,

particularly in evaluating frontier or unexplored geologic areas.

174
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Volumetric-yield methods have been refined recently by the Survey to

categorize hydrocarbon yields for specific stratigraphic units, which may be

characterized by lithology, environment of deposition, geologic age and basin

classification, or by relation to geologic structures and basin tectonics.

In this way, the potential of individual stratigraphic units in unexplored

or partly explored basins may be evaluated by using analogous stratigraphic

units from known basins. Hydrocarbon yields expressed as probability

distributions are used for each potential stratigraphic unit because

subjective judgments must be made on the various combinations of favorable

geologic characteristics chosen for the analogs. Estimates of the total

potential for the province are the sum of the individual stratigraphic

units aggregated by using Monte Carlo simulation. The aggregated results

of the resource estimates are reported in the form of a probability

distribution.

A recent study by the Resource Appraisal Group that applied various

aspects of this methodology has been completed on the Permian Basin of west

Texas and southeastern New Mexico (Dolton et al. 1979). In this study,

separate analyses were completed for the geologic units in the Permian, the

Carboniferous, and the older Paleozoic, with individual appraisals made for

each unit. In addition, the province was also evaluated at depth increments

of 0-10,000 feet, 10,000-20,000 feet, and deeper than 20,000 feet. Drilling

density maps penetrating each of these units as plotted from computerized

well-data systems played an important part in these assessments. Figure 2 shows an example of the individual units independently analyzed for resource assessments of natural gas in the Permian Basin. Figure 3 shows examples

of resource estimates for natural gas reported in the form of probability

distributions for the lower Paleozoic of the Permian Basin.

The volumetric-yield method is a valid procedure for resource appraisal,

providing care is taken in the selection of geologic analogs and in documenting

and qualifying the results properly. There are more sophisticated resource appraisal methods, which, when closely analyzed, reveal a key volumetric

element within their respective systems. This volumetric element usually

consists of individual variables for either stratigraphic units, or exploration plays, or reservoirs, which, when mathematically manipulated,

provide a volumetric estimate.

DISCOVERY-RATE OR BEHAVIORISTIC METHODS

Performance or behavioristic methods are based upon the extrapolation

of past experiences from historical data such as discovery-rates, drilling

rates, and productivity rates, and upon the fitting of past performances into

logistic or growth curves by various mathematical derivations that are projected for the future. These techniques are not directly applicable to

unexplored or nonproducing areas or to any area that is not a geologic and

economic analog of the historical model. Generally speaking, they are most

applicable to the later stages of exploration in a maturely explored area. Well-known examples of these models are: Hubbert's growth curve projections

(1962, 1974); Arps and Roberts (1958); Zapp (1962); and the National Petroleum

Council (1973).

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Two aspects of the performance or behavioristic methods have been

applied by the Resource Appraisal Group to resource assessment work. They

are: 1) discovery-rate or finding-rate techniques projected for undiscovered

fields, and 2) probability techniques for predicting the size of fields to

be discovered with future exploration. Both techniques are discussed

briefly below.

Discovery-Rate or Finding-Rate Methods

Since 1975, the Resource Appraisal Group has undertaken a continuing

study of regional oil and gas finding-rate methods for the United States.

The concept of finding-rate has been used at one time or another by most

researchers in assessing and projecting resource availability. Terms and

units of measurement used in defining finding-rate are variable; as a result, general finding-rate definitions have evolved. An understanding

of the applications of finding-rate procedures is required before terms can

be defined for any particular study. Regardless of the definitions used,

the ultimate purpose of determining finding-rate is to permit statistically

valid projections of resource availability based upon historical data

within a given geologic and economic frame of reference.

As pointed out by Moore (1966), the fundamental concept of continuity

of historic patterns and their validity for projecting future patterns must

be assumed. Accordingly, most historical studies begin with empirical data

and attempt to improve the projection of these data by being as quantitative

as the limits of the data permit.

Many factors must be considered when predictions of undiscovered

resources are made, but past studies indicate that the two most significant

factors are drilling-rate and finding-rate. Drilling-rate is by far the

single most important factor and the most easily controlled. Finding-rate,

on the other hand, is difficult to control and is largely dependent upon

the geologic characteristics of the area, field sizes, drilling-rate, and

economic and technological factors.

In an attempt to minimize the effect of economic and political variables

on finding-rates, some authors (principally Hubbert, 1974) have expressed

finding-rate as a unit of oil or gas discovered per unit footage of exploratory

drilling and as a function of cumulative exploratory drilling, determined

from historical data.

Most published studies to date have made projections of resources based

primarily on statistical studies of historical data and have included very

little geological information. This emphasis upon historical drilling data

rather than geologic data is due, in part, to the very large sample areas

that have generally been evaluated, such as the entire conterminous

United States, and the difficulty in assessing and quantifying the many and

varied geologic factors that ultimately contribute to the control of resource occurrences over such large areas. The lack of essential data for more detailed finding-rate studies has also been a crucial element.

179
In order to improve finding-rate methods so that they can be applied

to resource assessment work, the following procedures have been developed

in the Resource Appraisal Group:

1. Directly relate geologic information to finding-rates, and

limit the area of study to a well-defined geologic basin or

to a specific stratigraphic unit or geologic section within a basin or province.

2. Separate the oil and gas discoveries by: year of discovery,

geologic age of producing horizon and/or reservoir lithologies,

depth increments for producing reservoirs, and field-size

categories. If data are available, also identify the type of

structural or stratigraphic trap for each field discovered.

3. Analyze the discovery-rate patterns for any of the above

categories for which data are available to determine: whether

there are any significant trends; whether these trends can be

explained by the geologic data; and whether valid projections

can be made that would contribute to an understanding of the

remaining resource availability within a specified basin or province.

These finding-rate methods not only meet the requirement of being

applicable to basins or provinces, they have also attained a refinement

that will permit increased accuracy in analog comparisons between mature

areas and frontier areas.

A study by the Resource Apraisal Group in which various aspects of

the finding-rate methods have been applied has been completed on the

offshore Gulf of Mexico (Miller, et al. 1978). In this study, all the

oil- and gas-field data were compiled by size of in-place reservoir

volumes, year of discovery, age of major producing reservoirs, and depth

increments for major accumulations. Figure 4 depicts the historical

finding-rate for all natural gas fields in the Gulf of Mexico, from 0 to

200 meters water depth, that are producing from the Miocene, Pliocene,

and Pleistocene reservoirs. The discoveries, in trillions of cubic feet, are plotted with respect to the cumulative exploration effort in units of

5 million feet. The obvious decline in finding-rate from 1940, when the

first major discovery was recorded, to 1975, ranges from 29 trillion cubic

feet per 5 million feet of exploratory drilling to less than 6 trillion

cubic feet per 5 million feet. One very useful method of projecting

finding-rates consists of separating the known fields into field-size

categories and using the historical finding-rates for each category to

predict the amount of remaining resources yet to be found in each specific

field size class. The finding-rates are consistently different for each

field-size category in the Gulf of Mexico and in other areas in which these

methods have been applied. The amounts for each class can be summed to

180
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181
obtain the total estimate of resources remaining to be found in the

predictable future. Figure 5 depicts an example of the historical

finding-rates for only those gas fields in the Gulf of Mexico in the

greater-than 0.50 trillion cubic feet in-place field-size class.

Hyperbolic and exponential decline curves fit by regression analysis

to historical data show the best promise for finding-rate projections

for these investigations. The "best fit" was selected by the highest

index of determination and the F-statistic. The projected finding-rates

are usually extended another 15 million to 25 million exploratory

feet into the future, or approximately 5 to 10 years of additional

drilling. All projected finding-rates are terminated if they reach the

minimum field-size level set for the respective field-size category.

The major shortcomings of the finding-rate methods for projecting

remaining resource estimates are: They can only be applied directly to

semi-mature and maturely drilled producing areas, and they are considered

a conservative technique for estimating resources, as they do not allow

for any radical surprises in petroleum exploration, or significant

improvements in exploration technology or economics.

Finding-rate techniques are very useful for providing a means of

comparative checking on other resource-appraisal procedures used to

analyze the same basin or province. Finding-rate procedures when applied

to specific categories of geologic data often reveal some interesting

exploration trends within the basins studied. Finally, finding-rate

studies for known productive areas may be used with care as analogs

for immaturely explored or frontier areas.

Field-Size Distributions for Estimating Undiscovered Resources

New developments in projecting the estimated field sizes of the

remaining undiscovered resources hold great promise as another method of

estimating remaining resources. Several techniques have been devised to

estimate the field-size distributions for the remaining undiscovered

fields in a maturely explored area. These techniques result from detailed

studies on finding-rate methods that make use of historical field-size

distributions. Seismic data on drilled and undrilled structures in the

Gulf of Mexico are used by these methods to determine probable field size

as related to the historical field-size distributions within the same or adjacent areas. (See Table 1.) Field-size distributions can be estimated

by subjective probability procedures. The probable number of remaining

undiscovered fields may be estimated in a similar manner. The total resource potential is determined, using an aggregation of the probable

field sizes and probable numbers of fields, by means of Monte Carlo

simulation techniques. A separate procedure is used whereby the resource assessment by some other method and the probable field-size distribution

are used as input to a Monte Carlo simulation to determine the probable

number of remaining undiscovered fields in a specific area. These

techniques are still considered experimental and should be used with

caution.

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TABLE 1 ft)

Gulf of Mexico, Texas and Louisiana

Summary Table of Structure Count and Status

for

Total Shelf, 0 - 200 Meters Water Depth

Type

NUMBER OF STRUCTURES

Total Untested Tested Productive

Fault 197 112 85

Piercement 158 51 107

Domal 225 78 147

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184
EXPLORATION PLAY-ANALYSIS METHODS

Conventional Petroleum Resources

Exploration play-analysis methods have been designed for identified

or conceptual exploration plays within a basin or province for conventional

petroleum resources. The basic definition of an exploration play is: a practical, meaningful planning unit around which an integrated exploration

program can be developed. A play has geographic and stratigraphic limits

and is confined to a formation or a group of closely related formations on

the basis of lithology, depositional environment, or structural history.

There are, however, many variations to this definition and to

play concepts that have been applied by various resource estimators using

play-analysis techniques; these variations usually make the results

noncomparable for any specific area.

Play-analysis methods are usually applied to smaller areas of appraisal

than are the previously described methods, areas such as a geologic trend

consisting of a reef-play or a channel or bar sand. However, in some studies the play-analysis procedure has been applied to an entire geologic

horizon or stratigraphic unit, such as the total Cretaceous within a basin. Although the estimator may have called the procedure a "playanalysis," the basic concepts are no longer those of the original definition.

The basic technique requires more detailed data than the volumetricyield methods, utilizing all the data used in the finding-rate approach

and additional data concerning the individual fields within a play, plus

the basic information on the reservoir characteristics in these fields.

An estimate of conventional petroleum resources is usually expressed

as an equation relating a series of geologic and reservoir variables

to the amount of potential oil or gas within the reservoir. Probability

values may be assigned to the favorability of a play and usually to the

probable success of the prospects within the play. The geologic and

reservoir variables are described by subjectively derived probability

functions based upon the judgment of the estimators or by use of selected

analogs for many of the variables. The data formats are usually

designed for sophisticated computer processing, probability distributions

being assigned by the geologist for each variable. The estimates of

the resource are derived for each play by means of the equation relating

the variables to the potential resource by Monte Carlo methods. The

procedure for processing the numerous variables evaluated by the

geologist, and the accompanying probability distributions, is to use computer models that can rapidly process thousands of random samplings

of the values of the variables needed for determining the resource

appraisals which are shown as probability distributions. The total

185
resource estimate for the area or basin is determined by aggregating

the potential of all plays by using Monte Carlo simulation techniques.

The output is in the form of a probability distribution for the total resource assessment.

Figure 6 shows an example of a simplified data format being used

in a play-analysis technique currently under investigation by the U.S.

Department of the Interior, Office of Mineral Policy and Research

Analysis (OMPRA), and the USGS in a joint study to evaluate the petroleum

resources of the National Petroleum Reserve of Alaska (NPRA). Geologic

variables such as source rock, trapping mechanism, size of trap,

thickness of reservoir bed, and porosity are described by probability

distributions. A Monte Carlo technique is used to determine the size

of the prospect or field and to solve the equation relating the geologic

and reservoir variables to the resource assessments.

Table 2 shows the probability distributions for the resource

estimates, completed in September 1979, of the undiscovered oil and gas

in-place in the National Petroleum Reserve of Alaska (NPRA). The mean

value of the total resources in-place for NPRA were estimated to be

7.10 billion barrels of oil and 14.12 trillion cubic feet of gas.

These estimates were derived from the geology model in the play analysis

system developed by the U.S. Department of the Interior. The basic

geological input was provided by the USGS to OMPRA which, in turn, used

the play-analysis technique for the resource appraisal and as the basis

for the exploration, development, production, and economic evaluations

for the NPRA studies published in the "Final Report of the 105(b)

Economic and Policy Analysis" (U.S. DOI-OMPRA, 1979).

A major weakness of the play-analysis models is the assumption that

all the variables assessed in each play, as used in the Monte Carlo

simulation, are independent. Many of the geologic and reservoir

variables are not independent, and this creates some confusion in the

minds of the geologists who are to assign the values for each variable,

for the degree of risk or success for the occurrence of a favorable

play, and for a favorable prospect in that play.

One advantage of the play-analysis approach is that it simplifies,

or appears to simplify, the geologist's task in evaluating the resources

of an area by providing a fixed format for the variables he must evaluate;

the actual resource assessment is determined by statistical and mathematical

methods through the use of computer models. This method may also

reduce the amount of time necessary to evaluate an area, provided ample

data are readily available. However, such sophisticated computerized

procedures do not necessarily mean that accuracy has been increased in

the resource assessments resulting from this method over those evaluated

using other resource appraisal methods. Geologists concerned over the

results of their basic input into these programs must become increasingly

concerned over the assumptions and mathematical manipulations within

the computer system that are often designed by technical personnel who

are not familiar with the basic assumptions and concepts concerning the

geology of petroleum occurrence.

186
Oil and Gas Appraisal Data Form

Evalujtor : _______________________ Play Name

Date Evaluated:

Attribute

Probability of Favorable

or Present Comments

Play

Attributes

Hydrocarbon Source

Timing

Migration

Potential Reservoir Facies ,

Marginal Play Probability

Prospect Attributes

Trapping Mechanism

Effective Porosity (»3%)

Hydrocarbon Accumulation

Conditional Deposit

Probability

Hydrocarbon

Volume

Parameters

Reservoir Lithology Sand

Carbonate

Hydrocarbon Gas

Oil

^V,^ Fractiles

Attribute ^"V^

Probability of equal to or greater than

I00 95 75 50 25 5 0

Area of Closure

(xlO3 Acres)

Reservoir Thickness/vertical closure (Ft)

Effective Porosity

%

Trap Fill (%)

Reservoir Depth

(xlO3 Ft)

No. of drillable prospects

(a Dlav characteristic) Proved Reserves (x106 Bbl; TC F)

Figure 6 : Oil and Gas Appraisal Data Form

187
Table 2

Preliminary Distribution of Estimated

National Petroleum Reserve of Alaska Oil and Gas

Resources In-Place and Barrels of Oil Equivalent, as of September 1979

(%)

Probability

That Quantity

is at least

Given Value

95

90

50

25

10

5

1

Oil In-Place

(Billions

of Barrels)

1.04

1.35

6.03

10.01

13.72

16.45

24.80

Gas In Place

(Trillions

of cu. Ft.)

3.51

4.25

12.52

17.54

28.29

34.97

40.17

Barrels of Oil

Equivalent in Place —

(Billions of Barrels)

2.08

2.66

8.57

13.26

17.33

20.35

30.00

Mean 7.10 14.12 9.60

1/ Barrels of oil equivalent are obtained by converting the estimated gas in

place to the energy equivalent in oil and adding the resulting value to

the estimated oil in-place. The values in this table are estimated

independently, therefore, oil and gas estimates may not be added across percentiles to obtain BOE (DOI/OMPRA, 1979).

188
One of the most publicized of the play-analysis methods has been

that of the Geological Survey of Canada (Department of Energy, Mines

and Resources, 1977). Various modified versions of the Canadian approach

and some of those used by industry are currently under investigation by

the USGS. Ideally, a computerized procedure similar to that used in

the play-analysis approach could be the ultimate goal in the idealistic

world of resource appraisal. However, we have yet to achieve such a goal.

Unconventional Natural Gas Resources

The successful application of the exploration play-analysis model to

the evaluation of conventional petroleum resources led to the experimental

application of a modified play-analysis approach for an appraisal of

unconventional gas resources for a pilot study of the Devonian black shales

in the Appalachian basin.

In 1975, USGS was requested to aid the U.S. Energy Research and

Development Administration (ERDA) , now the U.S. Department of Energy (DOE),

in their investigations for appraising the energy potential of the gasproductive petroliferous black shales of Devonian age in the eastern United

States. To assist ERDA in achieving the goals of its program, the USGS was

asked to perform a series of stratigraphic , structural, geochemical, and

geophysical studies to establish a data bank and data retrieval system over a

5 year period, and to make an appraisal of the energy resources (predominantly

unconventional natural gas) of the Devonian black shales in the Appalachian

basin. The latter assignment involves the USGS Resource Appraisal Group

working with all the groups in the project to evaluate the data at hand and

then preparing an independent resource appraisal.

A review of the results of the basic stratigraphic, structural,

geochemical, source-bed, maturation, and clay mineralogy studies soon reveals the complexity of the many lithologic units that compose the

Middle and Upper Devonian black shale facies in the Applachian Basin, and

the multivariate nature of the geologic characteristics that contribute

to conditions favorable for the occurrence of producible gas from Devonian

black shales. The basic geologic characteristics and degree of uncertainty

as expressed by the geologists for explicit identification and substantial

detail for each play are very similar to the circumstances encountered in

the play-analysis approach used in appraising the petroleum resources of

NPRA. Some significant differences may also be found between the geologic

characterization for the conventional occurrence of petroleum and that of

the unconventional natural gas occurrence in the black shales.

189
These similarities and differences can be summed up as follows:

The Devonian shales can be subdivided and delineated as distinct units or plays of approximately homogeneous geological and geochemical characteristics.

The extent, geometry, and stratigraphic relations of each play can be defined

and mapped the same way that they were in NPRA. Reservoir engineering variables

such as porosity, permeability, reservoir pressures and temperatures, and

methane compressibility can be measured, and a geochemical analysis can be made

of types and amounts of organic matter within the black-shale facies.

One major difference between conventional gas and unconventional gas in

shales is that the former occurs in well defined and mappable reservoirs,

whereas the latter, when it is in commercial amounts, is usually concentrated

in areas where the shales are naturally fractured, jointed, or faulted. The

types of porosity in black shales are: 1) effective microporosity due to

matrix porosity and microfractures, and 2) porosity due to macrofractures

The Devonian shale resource appraisal includes only "movable" gas, i.e.,

gas that can leave the shale under "reservoir" conditions in response to

the disequilibrium caused by a well penetrating the shale unit. "Movable" means that the gas can leave a core sample at surface conditions without

grinding or heating. "Movable" gas is assessed only when in "black" facies,

i.e., shale having an organic-matter content greater than 2% by volume

(Schmoker, 1980).

In light of the significant differences between the geologic characteristics

that identify the conventional natural gas reservoirs and those that define the

unconventional natural gas in black shales, several changes must be made in the

geology model for assessing the natural gas resources. The most important

change is the basic equation used to calculate the amount of gas within each

play and the essential parameters required for the equation.

The basic equation as designed by members of the USGS for assessing

the amount of movable gas in the black shales is defined as follows:

Gm

= .) (Th.) (P ,) (T ) (1 ) + m e,mi B r l s <V V_«i>

Wf.ma' < Ih

f>

(P r2> <V (1 > + <V (TH0RG>

CP,) (T r2 ) (Z

2

)

where

G

m

= cubic ft of movable gas at standard conditions/square feet

of land surface

0 . = effective microporosity due to matrix porosity and

e, mi r J microfractures

0r = porosity due to macrofractures

f, ma v J

190
ft) thickness of black-shale facies (ft)

thickness of fractured interval

reservoir pressure and standard pressure, respectively

(PSI)

reservoir temperature and standard temperature,

respectively (absolute)

methane compressibility (gas-deviation factor)

cubic feet of movable gas at standard conditions /cubic

feet of organic matter

net thickness of organic matter (ft) in the black

shale facies.

The equation that calculates the amount of "movable" gas should

be evaluated for each of the geologic plays as defined for the

Appalachian Basin. The plays are defined so that within each unit

the geologic and geochemical properties represented by the equation

are relatively homogeneous. Values are determined using subjective

judgment by the geologists and geochemists for the various probability

distributions for the total "movable" gas, and the terms constituting

the equation are computed for each play. These distributions when

multiplied by the area of the play will give the expected volumes of

movable gas. The probability distributions for the resource appraisal

for the gas in each play will be aggregated statistically to give

the total assessment of gas resources within the black shales of the

basin.

In addition, the probability of each play being favorable, in

terms of the existence of "permeable pathways" (such as a fracture

system) that allow the movable gas to reach a well, is subjectively

determined. A subjective ranking of the various plays can be made.

A Pilot Study in Devonian Black Shales of the Appalachian Basin

The modified play analysis approach, incorporating the newly

formulated equation and the related assumptions and parameter values, was applied on an experimental basis to a pilot area within the

Appalachian Basin. A five-county area within West Virginia was selected for the experimental trial runs to assess the unconventional gas within the black shales. Three plays were distinguished

P P

r' r

S

T ,T

r' s

Z

Y

S =

TH

ORG

=

191
for an appraisal of the gas resources. Figure 7 is a map of the pilot area,

showing the mapped boundaries of the plays within that area. Plays IA and IB are geologically defined in part by the structural aspects of the Rome

Trough and in part by the characteristics of the organic matter within the

black shale. Play II is outside the trough area and has different organic

characteristics. Note that the county boundaries of the pilot area arbitrarily

cut out only segments of each of the naturally occurring plays for assessment;

thus, the resulting estimates do not represent a complete appraisal of any one of the three plays.

Figure 8 is an example of the data formats used to compile the essential

information for each play (Miller, 1980). A team of six geologists and one petroleum engineer met to review and interpret available information prior to

making the subjective judgments concerning the values for each of the geologic

variables shown on the format. The reservoir data were compiled whenever

available or analog data were used if specific information was not known

within the boundaries of the pilot area.

Preliminary Findings of the Resource Assessment Procedures in the Pilot Study

The play approach was used on each of the three plays for several

trial runs to remove the "bugs" from the newly modified geology model.

The assessments were reviewed and analyzed in terms of the geochemical and

technical information available in the pilot area. The following results

should be viewed as preliminary and are shown for comparative purposes for

the "gas richness" determined for the segments of each of the three plays.

Preliminary

Resource Estimates of Movable Gas

in Pilot Area, in Trillions of Cubic Feet

Probability that Quantity Probability of

is at least Given Value Favorable "Pathways"

PLAYS 95% 5% Mean Value (%)

Play 1A 1.62 4.35 2.95 100

Play IB 5.90 14.75 9.65 100

Play II .74 1.77 1.23 100

192
Devonian Black Shale Pilot Area

Plays I A & B, II

Figure 7: Average colume % Organic Content of "Black" Shales

193
Figure 8: Data format form for natural gas resource appraisal

in Devonian Black Shales

PILOT AREA: DEVONIAN BLACK SHALE

Identify Play :

PROBABILITY OF BEING

FAVORABLE ON A SCALE

PLAY FAVORABILITY OF 0 TO 1 COMMENTS

Existance of Permeable 'Pathways'*

* 'Pathways' which allow the movable gas to reach a well, whether by

fracture systems, porous lenses, etc.

GAS VOLUME PARAMETERS

PROBABILITY OF EQUAL TO

OR GREATER THAN MODE

95% 50% 5%

Effective microporosity

*E,MI (%)

Porosity due to macrofractures

^F,MA (%)

Thickness of black shale

Facies TH

fi [ft)

Reservoir Pressure

PR(PSI)

Reservoir Temperature

T

R (absolute)

Movable gas/organic matter

Y (cu.ft./cu.ft.)

Thickness of organic matter

TH = ORG* (organid content

of Black Shale) X TH

fi Estimate ORG (% vol.)

Depth of Black Shale Units

(ft.) Assume mid-point of units

Area of Play (sq. miles)

If boundaries of play are fixed,

give one value; if boundaries

are uncertain, give range

Standard Pressure P

S Standard Temperature T

g Compressibility of Gas, a factor (Tables)

194
Conclusions on the Use of the Play Analysis Approach to Black Shale Gas Appraisa

The play-analysis approach, using a modified geology model to determine

the amount of unconventional natural gas within the Devonian black shales

of the Appalachian basin, is considered by the geologists working on the

project to have high merit. Research will continue on refining the method

and the computer program and in checking out all the technical aspects

related to the basic assumptions in the geology model, in particular, the

geochemical concepts of "movable" gas and the relationships of sorbed gas

to organic content in the black shales.

The USGS plans to continue the research and development of the play

analysis approach for resource appraisal work both for conventional petroleum

resources and for the assessment of unconventional petroleum resources.

A strong interest has been expressed by other government agencies for

the Survey to use the application of the geology model to the play-analysis

approach for assessing conventional petroleum resources which would provide

input into those agencies various economic models.

A SUMMARY OF THE U.S. GEOLOGICAL SURVEY'S PETROLEUM RE SOURCE -APPRAISAL SYSTEM

The resource-appraisal system used at this time by the Resource Appraisal

Group within the U.S. Geological Survey is one that will achieve the following:

1. Resource-appraisal methods that emphasize the evaluation of all the

available geologic and geophysical data by geologic basins or provinces.

2. The compilation of a comprehensive information data base containing

all of the pertinent geologic and geophysical data, exploration

statistics, field and reservoir data, and production and reserve

data for each producing and potential petroleum province in the

United States.

3. The application of at least two or more resource-appraisal

techniques on each area to be assessed as a means of cross checking within reason the resource estimates, if time and

conditions permit.

4. The review and analysis of the basic information and appraisal

results by a team of geologists applying all the resource

appraisal procedures feasible (see Figure 9). This team provides

the final subjective probability estimates that are used as input in

the various Monte Carlo techniques to aggregate the final resource assessments by basin, region, an entire Nation, or the World.

195
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196
CURRENT ACTIVITIES IN THE RESOURCE APPRAISAL GROUP

Activities having priority in the immediate future for the Resource

Appraisal Group are: (1) A revised, expanded, and updated version of

Circular 725 which is currently in progress; this new assessment of the

Nation's petroleum resources is to be completed late in 1980; (2) current

updates on the petroleum resources of all Outer Continental Slope (OCS)

basins for the United States; (3) continuing research on resource appraisal

methods, particularly in the area of play-analysis methods; and (4) the

initial development of a world petroleum resource-appraisal system for

analyzing petroleum resources on an international basis.

CONCLUSIONS

This review of the evolution in the oil and natural gas resource

appraisal methods used by the Resource Appraisal Group in the U.S.

Geological Survey since 1975 covers the significant developments in the

appraisal procedures for assessing our Nation's resources. We recognize that some major problems related to resource assessments have arisen primarily

from a confusion in terminology and in the assumptions, qualifications and

limitations related to various resource appraisal methods. These problems

have created misunderstandings in the meaning and interpretation of resource

information and in the application of resource estimates by the media,

government and the public. Scientists making resource assessments must

strive to reach some agreement on a system of resource classification,

definitions, and basic assumptions for resource appraisal studies.

An understanding of the availability and distribution of the Nation's

resources is a fundamental requirement for the formulation of a national

energy policy. Great uncertainties are inherent in estimating undiscovered

petroleum resources and will continue to plague the geologist trying to make

these estimates. However, the limitations imposed by these uncertainties

must be recognized, understood, and dealt with realistically. Geologists

and other scientists devoting their expertise to making resource estimates

must clarify the terms used, improve upon the resource appraisal methods

applied to these studies, and keep up to date with the dynamic and

everchanging petroleum data bases. Individual scientists, government

agencies, and industry must use the best expertise available to estimate the

amounts of undiscovered petroleum resources, both domestic and worldwide,

that remain available for use, in order to plan for the rational exploration

and development of these resources in the future.

The Resource Appraisal Group, as a part of the research program of the

U.S. Geological Survey, will continue to meet its responsibilities to

develop resource appraisal methods and to apply these methods for assessing

the Nation's and the World's petroleum resources.

ACKNOWLEDGMENTS

I would like to acknowledge the work of all past and present members of

the Resource Appraisal Group of the U.S. Geological Survey, for without the

team effort provided by the Group, this paper could not have been written.

197
REFERENCES

Arps, J.J., and Roberts, T.G., 1958: "Economics of Drilling for Cretaceous

Oil on East Flank of Denver-Julesburg Basin," American Association of

Petroleum Geologists Bulletin, v. 42, no. 11, p. 2549-2566.

Day, D.T., 1909, "Petroleum Resources of the United States," in U.S.

Geological Survey Bulletin 394, p. 30-61.

Department of Energy, Mines and Resources of Canada, 1977, "Oil and

Natural Gas Resources of Canada 1976," Minister of Supply and Services

Canada, Report EP77-1, 61-73

Dolton, G. L., Coury, A. B. , Frezon, S. E . , Robinson, K. , Varnes, K. L.,

Wunder, J. M. and Allen, R. W., 1979: "Estimates of Undiscovered Oil and

Gas, Permian Basin, West Texas and Southeast New Mexico," U.S. Geological

Survey Open File Report 79-838, 72 p.

Hendricks, T. A., 1965: "Resources of Oil, Gas, and Natural-Gas Liquids

in the United States and the World," U.S. Geological Survey Circular 522,

20 p.

Hubbert, M.K. , 1962: "Energy Resources - A Report to the Committee on Natural Resources of the National Academy of Sciences - National Research

Council," National Academy of Sciences, National Research Council

Publication 1000-D, 141 p.

Hubbert, M. K. , 1974, "U.S. Energy Resources, A Review as of 1972," pt. 1 in "A National Fuels and Energy Policy Study," U.S. 93rd Congress, 2nd

session, Senate Committee Interior and Insular Affairs, Committee Print,

Serial No. 93-40 (92-75), 267 p.

Miller, B. M. , Thomson, H. L., Dolton, G. L., Coury, A. B. , Hendricks,

T. A., Lennartz, F. E., Powers, R. B. , Sable, E. G., and Varnes, K. L.,

1975, "Geological Estimates of Undiscovered Recoverable Oil and Gas

Resources in the United States," U.S. Geological Survey Circular 725, 78 p.

Miller, B. M. , Pike, R. S., Powers, R. B. , Scott, E. W., Khan, A. S.,

Carlson, K. H. , Vietti, B. T., and Lambert, G. D., 1978, "Task I Interagency

Oil and Gas Supply project, Pilot Area: Gulf of Mexico," U.S. Geological

Survey, unpublished data, 115 p.

Miller, B. M. , 1979, "The Evolution in the Development of the Petroleum Resource

Appraisal Procedures in the U.S. Geological Survey and a Summary of Current

Assessments for the United States," Proceedings SPE-AIME Symposium on Petroleum Economics and Evaluation, Dallas, Texas, Feb 11-13, 1979, SPE-7720,

p. 79-90.

Miller, Betty M., 1980, "Application of Exploration Play-Analysis Techniques

to the Assessment of Conventional and Unconventional Petroleum Resources,"

abstract, American Association of Petroleum Geologists, Bulletin 64, no. 5 and convention program, Denver, Colorado, June 8-11, 1980.

198
Moore, C. L., 1966, "Projections of U. S. Petroleum Supply to 1980," with appendix entitled "The Gompertz Curve for Analyzing and Projecting the Historical Supply Patterns of Exhaustible Natural Resources," U. S. Department of the Interior, Office of Oil and Gas, 13 p.

National Petroleum Council, 1973, "U. S. Energy Outlook, Oil and Gas Availability," National Petroleum Council, 786 p.

Schmoker, J. W. , 1980, "An Approach to Resource Appraisal in the Appalachian

Devonian Shale," U. S. Geological Survey, unpublished data, 6 p.

Thomsen, H. L., 1979, "Oil and Gas Resource Appraisal—State of the Art," abstract, American Association of Petroleum Geologists, Bulletin 63, No. 3,

p. 540.

U. S. Department of the Interior, Office of Minerals Policy and Research Analysis, 1979, "Final Report of the 105(b) Economic and Policy Analysis, Alternative Overall Procedures for the Exploration, Development, Production,

Transportation, and Distribution of the Petroleum Resources of the National Petroleum Reserve in Alaska (NPRA)," 145 p.

Weeks, L. G., 1950: "Concerning Estimates of Potential Petroleum Reserves,"

American Association of Petroleum Geologists Bulletin, V. 34, 1947-1953.

Zapp, A. D., 1962: "Future Petroleum Producing Capacity in the United

States," U. S. Geological Survey Bulletin 1142-H, 36 p.

DISCUSSION

Dr. Murphy: On the last approach, you had the probabilities assessed for

the various sets of parameters. How do you deal with the correlations across

the categories, for factors you are assessing?

Dr. Miller: What you literally are doing is sampling the values of the

parameters many times from the probability distributions that actually combine

to form the reservoir (amounts) and calculate the amount of oil or gas in the

reservoir and their distributions. The other probability values, such as the

probability of a prospect and probability of a play, literally become the marginal probabilities or conditional probabilities which modify or "risk" what

resources you have generated by the above calculations. These are used then

to risk each of the elements in the play. There is also a probability assessed (in addition to the above) as to whether or not these plays occur in areas

of fracture systems which would increase the favorability of their being within pathways of movable gas.

Most of your gas developed to date, in the shales, fall within rather

unique fracture patterns. So, this also becomes a part of the assessment.

199
FORECASTING FUTURE OIL

FIELD SIZES THROUGH STATISTICAL

ANALYSIS OF HISTORICAL CHANGES IN OIL FIELD POPULATIONS

Michel Ducastaing

and

John W. Harbaugh

Department of Applied Earth Sciences

Stanford University

Stanford, California 9^305

ABSTRACT

This study involves analysis of historical changes in oil field

sizes in Kansas, Wyoming and California. It is common knowledge that

large oil or gas fields tend to be found early in the sequence of discoveries in a region, and that the sizes of fields tend to diminish progressively as exploration proceeds. This study has found that populations

of oil (or oil and gas fields combined) tend to be more or less lognormally distributed, but in some regions or districts, the populations

of fields discovered early tend to depart more severely from an ideal

lognormal distribution than do populations discovered later. Comparisons between populations of fields discovered early, intermediate

and late were made by segregating the presently known fields in each of

the three states into intervals representing the first 20 percent to be

discovered, the second 20 percent to be discovered, and so on. This

method of segregating by discovery sequence also was employed for individual districts within each state.

The results are presented graphically and in tables, and may be

used to predict the population parameters of fields to be discovered in

the future. In most of the districts, as well as for each state, the

forecasts of new-field discoveries are pessimistic. This pessimism

stems from the general rapid decline in population parameters (median,

geometric mean, and total volume) with the progression of discoveries.

It is to be emphasized that these predictions pertain to the discovery

of new fields, and exclude increases in oil and gas that may result from

extensions of known fields, or to enhanced oil and gas recovery of

existing fields. Furthermore, the forecasts pertain to the general

regions in which fields discovered to date exist, and exclude provinces

(such as offshore central and northern California) which have been

relatively little explored.

200
In California, it is estimated that of the next 81 fields to be

discovered (within the established oil and gas producing regions of

California), the total volume of oil and gas (expressed as barrels of

oil equivalent, or BOE) will be about 0.6 percent of the total hydrocarbons that ultimately will be extracted from California's total of kOk

fields discovered from 1 86 1 through 197**. Furthermore, this forecast

population is estimated to be approximately lognormally distributed,

with a median size of only 125,000 BOE. Given the graph of this forecast distribution, probabilities attached to individual field-size

ranges (in BOE) can be estimated. Within the forecast population of 81

fields, for example, there is only a 9 percent probability that any

particular field discovered will be between 10 and 100 million BOE. The

probability of finding a field greater than 100 million BOE is only a small fraction of one percent.

In Wyoming, the forecast of the next 151 fields to be discovered is

only slightly less pessimistic. It is forecast that this population of new fields will contribute only about 1.6 percent additional BOE relative to the total BOE extractable from the 75^ fields discovered in

Wyoming from 1 884 through 1977.

The data for Kansas exclude gas and are based on cumulative production of oil through the end of 1978 for all fields discovered through

the end of 1973. Thus, the oil field size distributions for Kansas (in

contrast to Wyoming and California) are somewhat inadequate measures for

forecasting purposes because they exclude estimates of remaining re- serves. Thus, because many Kansas fields are still producing, the population parameters must be revised upward. Nevertheless, the forecast

for new-field discoveries in Kansas is pessimistic. By comparison with

the total of 2,992 oil fields discovered in Kansas from 1890 through

1973, if 598 new fields are discovered (20 percent more) they probably

will contribute only 2 or 3 percent more to the oil discovered in Kansas

through 1973.

201
INTRODUCTION

This study involves changes in the characteristics of oil field

populations with their sequence of discovery. It is common knowledge

that large oil and gas fields tend to be discovered early, and that the

sizes of fields tend to diminish progressively as exploration proceeds

in a region. If these changes are sufficiently regular, they should

permit the characteristics of future oil field populations to be predicted, based on the historical shifts observed to date.

One of the most important aspects of any mineral resource assessment is an understanding of the statistical properties of the deposits

that have been discovered. Unfortunately, inadequate effort has been

expended in preparing an inventory of the United States oil and gas

fields, and paradoxically, almost no effort has been spent in statistically analyzing the data that do exist.

This study involves a comparison of oil fields in Kansas, Wyoming

and California. The data have been derived from publically accessible

sources. We have analyzed the oil-field populations for each of these

three states as a whole, as well as for individual geographic districts

or sedimentary basins within each state. The population of oil fields

within each of the states or subdivisions thereof has been segregated

into five subpopul at ions according to sequence of discovery. The first

20 percent of fields to be discovered defines the first subpopul at ion

,

the second 20 percent discovered defines the second subpopulation, and

so on. Comparison of the differences between these subpopul at ions

provides a basis for prediction.

In California and Wyoming, data from both oil and gas fields have

been used, and the f'held sizes have been expressed in barrels of oil

equivalent (BOE) . The field sizes in these two states involve the

cumulative production per each field at the end of 1977 in Wyoming,

and the end of 1978 in California. The cumulative production figure for

each field is then combined with the estimated remaining reserves to

yield an estimate of the total recoverable BOE per field.

In Kansas, only oil production data were used, and the oil field

sizes are expressed solely as the cumulative production (to the end of

1978), data on reserves remaining in Kansas oil fields not being available.

It is important to realize that the predictions in this study are derived almost solely from historical changes and, with one exception,

do not incorporate geological data other than the field volumes themselves. The predictions apply to new fields to be discovered, and do

not pertain to increases in estimates that may arise from extension of

existing oil fields, or from enhanced oil recovery. Furthermore, the

predictions apply, more or less, to established provinces that have

undergone exploration. Offshore central and northern California, for

example, is not included in the prediction for California because this

segment of the California offshore has generally not been explored and

has not contributed to the existing resource base of proven oil and gas

fields in California.

202
PROCEDURES

The procedures employed here involved transforming the estimates of

oil and gas fields sizes as barrels of oil equivalent (BOE) for fields

in California and Wyoming. A conversion factor of 5*7 MCF (thousand

cubic feet) of gas equals one barrel of oil was used. In California the

size tabulated for each field represents the cumulative production

through the end of 1978, plus, the estimated reserves at the end of

1978. In Wyoming, the cumulative production has been tabulated through

the end of 1977 and added to estimated reserves remaining as of that

date. In Kansas, only oil production data were used (production from

gas fields and production of gas associated with oil is not included).

In Kansas, the cumulative production for each field through the end of

1978 was employed.

The oil field volumes, expressed as the total producible oil (in

BOE) in California and in Wyoming, and cumulative oil production in

Kansas, were segregated chronologically according to year of discovery

for each field. Then, for each state, as well as for selected geographic districts or basins within each state, the fields were segregated into five classes according to discovery sequence, namely (A) the

first 20 percent of the fields that were discovered relative to the

total population of fields that had been discovered by a specific date

(end of 1973 for Kansas, end of 197** for California, end of 1977 for

Wyoming), (B) the next 20 percent of fields to be discovered, (C) the

third 20 percent to be discovered, and (D) and (E) the fourth and fifth

20 percent intervals to be discovered, respectively.

The frequency distributions for each of these five intervals was

plotted, and certain population parameters were computed, namely the

median, geometric mean, and either the BOE discovered through 1978 (for

California) and 1977 (for Wyoming), or the cumulative production through

1978 (for Kansas).

The frequency distributions have been plotted on log-probability

paper, a form particularly convenient because a perfect lognormal

distribution plots as a straight line. Figure 1 provides a comparison

between a lognormal distribution plotted in conventional form, with the same distribution plotted on log-probability paper. Part a of Figure 1 shows the lognormal distribution plotted as a histogram, to which a bell-shaped curve (S) has been fitted. The same distribution plotted in

cumulative form (C) has been superimposed. The cumulative curve is

sigmoidal. Please note that the cumulative percentage scale is linear

and ranges from 0 to 100 percent.

If we now distort the cumulative percentage scale so that those

parts of the scale that lie toward both the zero-percent end and toward

the 100-percent end are progressively stretched, the cumulative percentage scale can be made to compensate for differences in the height of

the normal curve. The normal curve is, of course, asymptotic towards

its two ends, but if the cumulative percentage scale is stretched to

compensate for this, the sigmoidal curve is transformed to a straight

203
10

10

10'

10'

10*

io

3 -,

10 ' I l_J—

M 30 40 60 60 70 1 2 5 10 CUMULATIVE PERCENT

90 95 98 99

Figure 1. Diagrams illustrating forms in which a lognormal distribution

may be plotted: (a) Histograms and fitted curves representing perfect

lognormal distribution plotted in standard form(s) , and same distributee

plotted in cumulative form (c) . (b) When same distribution is plotted

on log-probability paper incorporating distorted cumulative percentage

scale, distribution plots as a straight line.

204
line. Under these circumstances, 0 and 100 percent lie at an infinite

distance, because the normal curve being asymptotic, is of infinitesimal

height at these points. If an actual distribution deviates from a straight line when plotted on log-probability paper, the deviation

provides a graphic measure of the degree to which the actual distribution differs from an ideal lognormal distribution.

The procedure for plotting a population on log-probability paper is

simple. The objects (fields in our examples) are ranked in ascending

order. A "fract? le-percentage" is assigned to each field and the

percentages are progressively accumulated. The fractile percentage is

obtained by dividing 100 percent by the number of fields plus one. Thus, if there are 2k fields, the individual fractile percentage is

100/(24+1) = k percent, and the sequence of cumulative percentage values

is 4, 8, 12, 16, . . ., 92, and 96. Thus, 0 and 100 percent are not

represented because they cannot be accomodated on log-probability plots.

By convention, the lower end of the cumulative percentage scale is

plotted so that it corresponds with the lower end of the sequence of

fields as ranked by size. The resulting plot thus extends from lower

left to upper right, provided that the cumulative percentage scale is

plotted horizontally.

Graphic Presentation of the Data

Most of the illustrations in this report, with exception of index

maps and several other figures, involve use of a standardized graphic

format. A single explanation will suffice for Figures 3 through 6, 8,

through 17» and 19 through 26, all of which employ this standard format.

Each of these figures contains four boxes labeled a, b, c, and d which

contain graphs. Box a in the upper left contains a cumulative plot for

the total population of fields within the area represented. For convenience, individual points at at 2, 5, 10, 15, 20, 30, kO, 50, 60, 70, 80,

85, 90, 95, and 98 cumulative percent) have been plotted, and a curve

then fitted manually. Since the plot is in log-probability form, the

degree to which the plot approaches a straight line is a measure of the

degree to which the overall population approaches an ideal lognormal

distribution.

Box b, in the upper right also employs log-probability plots, but

instead pertains to subpopulat ions which have been segregated according

to discovery sequence. There are five such subpopulations , labeled A, B,

C, D, and E, and which represent respectively, the first 20 percent of

fields discovered, the second 20 percent discovered and so on. These

curves are based on points plotted in a manner identical to that used

in box a, but the individual points are omitted for simplicity.

Curves F and G in box b are shown with dashed lines and represent

respectively, the forecast populations for the next 20 percent of fields

to be discovered, and the 20 percent of fields to be discovered after

that. The letters used to label these populations have been used con- sistently throughout. If we define the "present" total consisting of

205
fields that had been discovered at the end of 1973 in Kansas, the end of

197** in California, and the end of 1977 in Wyoming, as 100 percent, then

the percentage ranges and identifying letters are as follows:

Subpopulat ions

of fields that

have been

di scovered

I dent i fy ing

letter

A

B

C

D

E

Percentage range of total

fields presently discovered

0-20

20-^0

40-60

60-80

80-100

Subpopulations F 100-120

of fields forecast

to be discovered G 120-1^0

in the future

In fitting curves F and G, the medians projected for these subpopulations were employed in manually fitting smoothed curves that

conform, more or less, with the general trends observed in the progression of changes from curves A through F.

Box c in the lower left, is a plot of the medians of the subpopulations versus discovery sequence, the same letters being employed to

label the subpopulations, A being the oldest subpopulation (the first 20

percent), and E the youngest (the last 20 percent).

A curve has been manually fitted to the five points, and in some

plots, two or even three curves have been fitted, representing "optimistic" versus "realistic" projections. The extension of the fitted curve (the dashed portion) yields the projected medians for subsequent

subpopulations F and G.

Box d, in the lower right, presents the cumulative volumes in the

subpopulations, and as in box c, involves a projection (dashed part of

the fitted curve) for the subsequent populations F and G. Both boxes c and d use a log scale along the vertical axis because of the very large

ranges of volumes involved. The volumes may range as much as two

orders of magnitude, making use of a linear scale impractical.

Tabular Presentation

Standardized sets of tables have also been employed. Tables 1, 3

and 5 contain data which pertain to the standardized graphs described

206
above, plus other information. The subpopulat ion percentage ranges are arranged in rows and labeled A through G. By columns, information is

provided, including the range of years, number of fields, median, geometric mean, total quantity discovered, and percentage of present total.

The geometric mean is computed by finding the average of the logarithms of the individual field volumes in a specific population, and

then taking its antilog of this value.

Tables 2, k and 6 contain probabilities estimated for fields that

remain to be discovered (subpopulations F and G) . The number of fields

in each forecast population is presented, as well as the probabilities

attached to different field-size ranges expressed as a progression of

powers of 10. Seven columns of field-size ranges are provided, that is

>10 3 (less than 1000 barrels or BQE) , 10^ to 10 , 10 to 10 , and so on,

the highest range being 10 to 10 B0E or barrels. These probability

estimates are read from the curves F and G in box b for each population.

They represent probabilities attached to the discovery of new fields

within the specified area or district or basin. Table 7 provides a summary comparison of the three states.

CALIFORNIA

The data for California used in this study were taken largely from

a report by the California Division of Oil and Gas (1979). This report

contains information on a field-by-field basis for all fields in the

state, and provides cumulative production of oil and of gas through the

end of 1978, plus estimated reserves of oil and of gas as of that date.

By combining the cumulative production figures with the reserves, and

transforming gas to its equivalent in oil (B0E) , a single figure was obtained for each field representing its estimated size (in recoverable

oil and gas) per field.

The California Division of Oil and Gas has established six administrative districts in California (Figure 2). While these districts do

not necessarily coincide with geologic province boundaries, District 6

essentially encompasses both the Sacramento Valley and the northern part

of the San Joaquin Valley, which is a gas-producing province, whereas

Districts k and 5 combined include the central and southern San Joaquin

Valley, which is both an oil and gas-producing province. District 1 includes the Los Angeles basin as a producing province, but also includes part of the eastern extension of the Ventura basin (Newhall

area). In our work we segregated the fields into only four geographic

areas for simplicity, namely District 1, Districts 2 and 3 combined,

Districts 4 and 5 combined, and District 6.

Frequency distributions for these four areas, as well as for

California as a whole were tabulated and plotted in Tables 1 and 2 and

Figures 3 to 8. With the exception of Figure 7» the results have been

207
Figure 2. Index map of California showing six districts established by

California Division of Oil and Gas for oil-field classification purposes.

208
plotted with an identical format for each area, as well as for the whole

state, using the graphic format described in the section entitled Graphic

Presentation of the Data . The preparation of the tables is discussed in

the section entitled Tabular Presentation.

Entire State

California's overall population (Figure 3) of kOk fields approximates a lognormal distribution, although there is some skewness. The

subpopulations segregated by discovery sequence reveal a drastic de- crease in general sizes of the fields in the progression involving the

first four discovery intervals (A,B,C, and D) . As Table 1A indicates,

there is nearly a 300-fold decrease in the median size from A to D, with

corresponding large decreases in the geometric means (over 100-fold) and

in the aggregate quantity of hydrocarbons discovered (over 50-fold).

These large decreases are reversed, however, in the last 20 percent

interval (E) , which involves a dramatic rise in the median, geometric

mean, and total quantity as compared with interval D. The explanation

lies partially in a succession of discoveries of large gas fields in the

Sacramento Valley, in District 6.

Projections for California as a whole are pessimistic. Of the

population of the next 81 fields to be found in the state as a whole

(this projection excludes areas which are not part of the area of

California that had been explored as of the end of 197^), the population

is forecast to have a median size of only about 125,000 BOE, and to

yield roughly 1 85 million BOE, or about 0.6 percent of the BOE contained

in fields discovered through the end of 197^ in the state. Probabilities

attached to individual field-size ranges for this forecast population

are shown in the first row in the body of Table 2.

It is probably of marginal value to consider California as a whole

from an exploration forecasting standpoint, although the state's total

outlook for new-field discoveries has strong relevance with regard to

the nation's energy policy. Analyses of the individual districts are,

however, more revealing from an exploration standpoint.

District 1

District 1 embraces fields of the Los Angeles basin as well as the

eastern end of the Ventura basin (Newhall area). The plots (Figure A)

reveal an extremely large decline in the medians and geometric means

following interval B (which ended in 19^0). As Table 1-B details, the

medians and geometric means declined on the order of 100-fold. Such a decline reflects the early discovery of very large fields, including

Wilmington, Santa Fe Springs, Huntington Beach and Long Beach, discoveries which were not duplicated in size in later intervals.

The forecast for District 1 for new field discoveries is a guarded

one. A "realistic" versus a "pessimistic" forecast is provided In

Figure *tb and c, Table 1-A and Table 2. Two sets of curves, labeled F

209
CUMULATIVE PERCENT CUMULATIVE PERCENT

10A B

DISCOVERY c

SEQUENCE

D E F

IN 20 % INTERVALS

K) A B

DISCOVERY C

SEQUENCE

D E F

IN 20 % INTERVALS

Figure 3. Combined oil and gas field distributions for entire California. See section entitled Graphic Presentation of the Data for explan210

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Figure k. District 1, California.

214
and G, and F

1 and G' in Figure A-b, represent the "realistic" versus "pessimistic" forecasts. The "realistic" forecast distribution, however, will yield only about 0.5 percent of the present aggregate BOE if

36 new fields are actually discovered. ^

As Table 2 reveals, the probability of finding a field greater than

100 million BOE is only about li percent for any particular field among

the next 18 fields to be discovered in District 1 (assuming 18 fields

are to be discovered). On the other hand, a probability of about 21

percent is attached to a discovery of less than 10,000 BOE for each

field to be discovered among these next 18 fields. Such small sizes are absurdly uneconomic for most of District 1, and may be discounted in

advance as "non-discoveries". Nevertheless, they represent the forecast

distribution of field sizes employing the "realistic" curve, F, for

District 1

.

Districts 2 and 3

Districts 2 and 3 combined are paradoxical in that initial interval

A has a substantially smaller median (and geometric mean) than intervals

B and C (Table 1-C). Thus, the usual sequence has been reversed (Figure

5). This is explainable, in part, by the large geographic expanse of

the combined districts and their geologic diversity. Major discoveries,

such as the Ventura field, occurred in interval B, accounting for its

large median and geometric mean. Interval C, too, was blessed with

large discoveries (Santa Maria and San Ardo fields, for example),

accounting for its intermediate median and geometric mean.

Curves F and G of Figure 5~b represent the "realistic" forecast,

and seem to be in accord with overall trends.

Districts *t and 5

Districts k and 5 embrace the central and southern San Joaquin

Valley, which forms a large and diverse petroleum-producing province.

As Figure 6 reveals, the discoveries during interval A yield a population with an exceedingly large median and geometric mean. This is

readily explainable by the early discoveries of a number of giant fields

(Buena Vista, Coalinga, Elk Hills, Kern River, Kettleman Hills, MidwaySunset, and South Bel ridge). Although some major discoveries were made

in the next interval (East Coalinga Extension, for example), these

subsequent discoveries did not keep pace in size. The decrease in

field-size medians (Table 1-D) from interval A to E is impressive (more

than an 1100-fold decrease). The decline in geometric means, and in

gross BOE discovered, though less dramatic, is still very large. Based

on these trends, the forecast for Districts k and 5 is not encouraging,

as population F consisting of the next 2k fields to be discovered has a forecast median of only 52,000 BOE, with only an 8 percent probability

that any field will be larger than 10 million BOE, and a probability of

only about 1 percent that any field will be larger than 100 million BOE.

215
Figure 5. Districts 2 and 3 combined, California.

216
Figure 6. Districts k and 5 combined, California.

217
The population of 2k fields discovered during the initial interval

(A) is strongly skewed, with a predominance of large fields. This is

demonstrated by the extreme departure of the graph of this population

(Figure 6-b) from a straight line. A smoothed curve fitted to a histogram of field sizes and plotted in conventional form (Figure 7) emphasizes this departure from the log normal . Populations of fields discovered in later intervals, D and E, more closely approach the lognormal

ideal

District 6

District 6 embraces the Sacramento Valley and the central part of

the Great Valley (that is, the northern part of the San Joaquin Valley).

Virtually all of the production is gas. The overall population of 102

fields departs moderately from the lognormal (Figure 8-a) , but the

subpopulations defined by the succession of discoveries do not reveal

the abrupt decline in medians (or geometric means) observed in the other

districts. Indeed, both the medians and the geometric means decline

from A to C, (Figure 8-c and Table 1-E) but they rise again in the

succession from C to E. If we were to take a very optimistic view of

the future, we might envision a progressive rise in the field-size

parameters, as might be represented by the curve labeled "very optimistic" of Figure 8-c. However, a more realistic view is that the populations of fields to be discovered in the future will progressively

decline. An estimated median of 900,000 B0E for the next 20 fields to

be discovered (F) seem reasonable. Given the uncertainties in projection, however, we can take a view that an optimistic forecast also may

be justified. Table 2 provides probabilities attached to different

field sizes that accord with an "optimistic" projection (which coincides, more or less, with the curve labeled B in Figure 8-b) , as well as with the "realistic" projection, which yields the curves labeled F and G

in Figure 8-b.

WYOMING

The six principal sedimentary basins in Wyoming are outlined in

Figure 9. Four of the basins (Green River, Big Horn, Wind River, and

Powder River) have been analyzed in a fashion similar to that employed

in California. In addition, fields in the Powder River basin also have

been segregated according to whether they are associated with structural

traps, or with strat igraph ic traps. The two other basins (the HannaLaramie basin and the Denver basin) contain an insufficient number of

fields to be analyzed in the same manner as the other basins, although

a frequency distribution for each basin overall has been plotted.

Please note that the Denver basin is a very large basin, but only a small fraction of its total area lies within Wyoming. The Colorado and

Nebraska portions of the Denver basin are not considered here.

The data for Wyoming were obtained from an unpublished report

prepared by the firm of Barlow and Haun (1978). Segregation of the oilfield data by basins seems more desirable than by arbitrary districts,

218
BOE

Figure 7. Plot of frequency distribution in standard form of curve A

shown in Figure 6-b, representing first 20 percent of fields discovered

in Districts k and 5 combined, emphasizing strong skewness of the distribution.

219
CUMULATIVE PERCENT CUMULATIVE PERCENT

Figure 8. District 6, California.

220
particularly in Wyoming where the individual basins are geologically

segregated from each other. Our objective in this study has been to

determine whether the field-size statistics differ from basin to basin,

perhaps reflecting underlying geological controls on petroleum occurrence within individual basins.

Entire State

Statistics for entire Wyoming are presented in Figure 10, Table 3

_ A

and in Table k. The distribution of field sizes, expressed in BOE,

closely approximates an ideal lognormal distribution. When the 75*» fields incorporated in this study are segregated by discovery sequence

into 20 percent intervals, there is a general progressive decrease in

medians, geometric means, and total BOE discovered. Although there is some overlapping of the distributions (curves A through E in Figure 10-

b) , the shifts are sufficiently regular so that future discoveries can

be forecast by projection. The "realistic" projection of the medians

(Figure 10-c) accords with the curves representing forecast populations

F and G.

Green River Basin

The distribution of fields as a whole for the Green River basin

approximates the lognormal (Figure 1

1 -a ) but the subpopulat ions , A

through E, deviate considerably from the lognormal ideal (Figure 11-b).

The subpopul at ion medians, geometric means, and total BOE (Figures 11-c

and d, and Table 3"B) shift in somewhat erratic fashion. Curves F and G

(Figure 11-b) representing the populations of fields to be discovered

are based on the "realistic" projections of the medians. The probabilities attached to size ranges of fields to be discovered (Table k)

surpass those of the other basins in Wyoming, and so the Green River

basin is relatively attractive from a statistical standpoint.

Big Horn Basin

The Big Horn basin (Figure 12, Table 3~C and Table h) has an overall population that is virtually perfectly lognormal ly distributed.

There is a very sharp decrease in field-size parameters between in

tervals C and D, with some improvement from D to E. The overall fieldsize population trends are not encouraging, and populations F and G are

forecast to have small total volumes.

Wind River Basin

The populations of fields in the Wind River basin display a some- what erratic behavior. The overall population (Figure 13 -a) significantly departs from the lognormal ideal. Subpopulat ions A, B, D, and

E also depart from the ideal lognormal, although subpopulation C is

essentially lognormal (Figure 13~b). The populations to be discovered

221
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227
DISCOVERY SEQUENCE IN 20 % INTERVALS DISCOVERY SEQUENCE IN 20 % INTERVALS

Figure 11. Green River basin of Wyoming.

228
229
CUMULATIVE PERCENT CUMULATIVE PERCENT

230
(F and G) offer some encouragement, particularly in view of their projected

total volumes (Table 3-D and Figure 13"d), although the probabilities

attached to the discovery of large fields are small (Table .

Hanna-Laramie and Denver Basins

Frequency distributions for the overall populations in each of

these basins (Wyoming portion only of the Denver basin) are shown in

Figure \k. Both depart from the lognormal ideal, particularly those in

the Denver basin. Because of the small overall population (33 fields

with recorded production in Hanna-Laramie basin, and 15 in the Denver

basin), it is impractical to divide the overall populations into subpopulations.

Powder River Basin

Fields in the Powder River basin were placed in three classes,

namely, all fields (380 fields, Figure 15), fields that are structurally

controlled (13^ fields, Figure 16), and fields that are stratigraphical ly

controlled (246 fields, Figure 17). The structural field subpopulations

(except for the last interval, E) depart substantially from the lognormal ideal, there being a pronounced tendency toward early discovery

of medium-large fields (Figure 16-b). The stratigraphic fields, on the

other hand, depart less from the lognormal ideal (Figure 1 7~b )

.

Forecasts for populations of fields to be discovered in the future

differ markedly for structural versus stratigraphic fields. The decline

in field-size parameters is much less for the stratigraphic fields than

for structural fields. This relationship is not surprising, and probably reflects the fact that stratigraphic traps are much less obvious to

explorationists than structural traps and therefore the bias toward

early discovery of large fields is less for stratigraphic fields than

for structural fields.

KANSAS

Kansas has been arbitrarily divided into seven districts (Figure

18) for purposes of this study. The districts do not coincide with

officially defined districts, as in California. Districts 1 and 2

embrace much of western and northwestern Kansas. District 3 embraces

much of the intensely explored and productive Central Kansas uplift.

District 4 embraces part of the Hugoton embayment. Districts 5 and 6

incorporate much of relatively maturely explored, south-central Kansas.

District 7 incorporates the remainder of the state, and embraces many

older producing areas in southeastern Kansas.

The districts are defined in terms of townships and ranges as follows: District 1: T 1S-6S, R 16W-A2W; District 2: T 7S-15S, R 22W231
3 0 8 </> T3

3 0 8

232
CUMULATIVE PERCENT CUMULATIVE PERCENT

A B C D E F DISCOVERY SEQUENCE IN 20 % INTERVALS A B

DISCOVERY c

SEQUENCE

D E F

IN 20 % INTERVALS

Figure ,5. Powder River basin of Wyoming, ell fields.

233
CUMULATIVE PERCENT CUMULATIVE PERCENT

Figure 16. Powder River basin of Wyoming, structural fields only

234
CUMULATIVE PERCENT CUMULATIVE PERCENT

17- Powder River basin of Wyoming, stratigraphic fields only.

235
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236
42W; T. 16S-22S, R 19W-43W; District 3: T 7S-15S, R 5W-21W; T 16 S-22S,

R 5W-18W. District k: T 23S-35S, R 25W-43W. District 5: T 23S-35S, R

5W-2AW. District 6: T 1*tS-35S, R 5E-i*W. District 7: T 1S-6S, R 22E15W; T 7S-13S, R 25E-4W; T 14S-35S, R 25E-6E.

The data presented for Kansas are based on cumulative production of

oil (gas production is not incorporated, and the production statistics

are in barrels and not BOE) . The cumulative production data extend

through the end of 1978, and include all fields discovered before the

end of 1973. Reserve estimates are not included, so that the total

field sizes (in barrels of producible oil) are necessarily less than

they would be than if presented as an estimate of total recoverable oil.

Thus, the data for Kansas are not directly comparable with those for

California and Wyoming.

The data for Kansas were supplied in magnetic-tape form, but the

Kansas Geological Survey has published an equivalent compilation (Beene,

1979).

Entire State

The oil field-size distribution for Kansas as a whole closely

approximates an ideal lognormal distribution (Figure 19) » and the subpopulation parameters decline consistently when the chronologically

segregated subpopulations , A through E, are compared (Tables 5 and 6).

Recall, of course, that the more recently discovered fields have had

less time to produce, and therefore the population statistics reflect

this influence as well as the bias toward early discovery of large

fields. Note that the last 20 percent of Kansas fields included in this

study (the 578 fields which define subpopulat ion E as segregated from an overall population of 2992 fields) were discovered from 1 967 to the end

of 1973 » and it is obvious that they have had much less opportunity to

produce than fields discovered earlier, as for example, those in subpopulation A ( 1 890-1 9^*7) » many of which have been benefitted from en- hanced oil recovery operations.

Districts 1 , 2 and 3

Districts 1, 2 and 3 are somewhat similar in their statistics

(Figures 20 to 22). Because these districts have undergone extensive

exploration in recent years, the rapid drop in medians, geometric mean,

and aggregate cumulative production for the subpopulations (Table 5~B,

C, and D) may be somewhat misleading, since these statistics will necessarily increase as existing fields continue to produce. Nevertheless,

it is instructive to compare the percentages of the total production

(the last column of Table 5) with similar statistics for California and

Wyoming (where reserves remaining are incorporated). As a percentage of

the total, per each district, those for subpopulations D and E in

Kansas, although varying from district to district, do occur in the same

general range as in California and Wyoming. This may imply that the

bias toward early discovery of large fields is less in Kansas than in

237
DISCOVERY SEQUENCE IN 20 % INTERVALS DISCOVERY SEQUENCE IN 20 % INTERVALS

Figure 19. Entire Kansas. Oil field volumes are expressed in barrels

and represent cumulative production through 1978, and exclude reserves.

See section entitled Graphic Presentation of the Data for explanation.

238
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242
DISCOVERY SEQUENCE IN 20 * INTERVALS DISCOVERY SEQUENCE IN 20 % INTERVALS

Figure 20. District 1, Kansas.

243
244
245
California or Wyoming, but this possibility cannot be convincingly

determined unless reserve estimates are incorporated in the Kansas

field-size data.

Districts 4, 5, 6, and 7

Districts through 7 do not display orderly reductions in population parameters with discovery sequence. While the overall populations of each district are essentially lognormal (Figures 23 to 26)

the graphs of the chronologically segregated subpopulation cross each

other in an unpredictable manner. The medians and geometric means,

however, exhibit somewhat more orderly arrangement (Table 5~E, F, G, and

H) , and seem to permit the extrapolation of future populations (Table 6)

with some consistency.

Analysis of the Kansas data makes clear that we are dealing with

populations of fields that have much smaller parameters than those of

California or Wyoming. Table 7 presents a summary forecast new-field

discoveries for all three states, with the proviso that the estimates

for Kansas exclude gas (thus are not on a BOE basts), and must be adjusted upward to accomodate continuing production.

CONCLUSIONS AND RECOMMENDATIONS

This study was undertaken to achieve an understanding of the most

elementary of petroleum resource-base considerations, namely, the frequency distributions of oil-field volumes. Some generalized conclusions

may be drawn as follows:

(1) The lognormal distribution seems to be a very useful general

model in dealing with oil and gas fields. Unless refuted by

studies in other regions, it seems appropriate to assume that

the populations of undiscovered oil and gas fields in frontier

regions that have undergone little or no exploration will

be essentially lognormal, assuming that such populations

exi st at all.

(2) The bias toward early discovery of large fields is a major

influence, and statistically seems to be greater than many

explorationists realize. A decrease in population parameters

(median and geometric mean) of from one to as much as three

orders of magnitude (powers of ten) appears to be common

as a district or basin approaches maturity.

(3) Subpopulations of fields discovered early tend to depart

more from the lognormal ideal than later subpopulations.

However, these shifts in population characteristics vary

widely from district to district, and generalized statements

about these changes must await additional study.

(k) The "actual" distribution of oil and gas field sizes may

not be lognormal, and instead may have the general form

246
Figure 23. District 4, Kansas.

247
CUMULATIVE PERCENT CUMULATIVE PERCENT

DISCOVERV SEQUENCE IN 20 * INTERVALS DISCOVERY SEQUENCE IN 20 % INTERVALS

Figure 2k. District 5, Kansas.

248
Figure 25. District 6, Kansas.

249
Figure 26. District 7, Kansas.

250
Table 7. Summary comparison of forecasts for the three states

for the next 20 percent of fields to be discovered,

and the 20 percent after that

Next 20% 20% after that

Number

of

Fields

Millions

of . BOE—

Number

of

Fields

Mi 1 1 ions

of

1/ I B0ECal ifornia 81 185 81 118

Wyoming 151 140 151 90 i

Kansas 598 55 598 48

— Volumetric estimates for Kansas exclude gas and involve predictions

based on cumulative oil production through 1978, exclude reserves

and must necessarily be revised upwards as production continues.

251
suggested in Figure 27- The lower size limits of fields

that have actually yielded oil or gas are generally set by

either economic factors, or the ability to detect small

accumulations, or both. It is possible, and even probable,

that there is no definable lower field-size limit and that

the form of the distribution is exponential with regard to

very small accumulations. Thus, the actual distribution may

be bimodal in the sense that there are two peaks, one of

which represent the producing fields, and other (the

exponential extension) represents a virtual infinity

of accumulations, each of infinitesimal size. Obviously the

definition an "oil field" becomes meaningless when extended

to this extreme. It will suffice to say that we have almost

no knowledge of the lower limit of field-size distribution.

This shortcoming may be of minor consequence, however, since

extremely small fields are of negligible economic importance.

(5) Studies of oil field populations should be conducted regionally. Furthermore populations should be segregated geologically. The data from the Powder River Basin suggest that

the population parameters for structural versus stratigraphic

fields may differ significantly in other regions.

(6) Extrapolation of parameters of chronologically segregated

oil field populations is a useful predictive tool.

Acknowl edgements

We thank James A. Barlow, Jr., of the firm of Barlow and Haun, for

supplying information on Wyoming oil fields. Data on Kansas oil fields was made available to us by Douglas L. Beene and John C. Davis of the

Kansas Geological Survey. Clifford Hayashi of Stanford University

adapted the computer programs employed and assisted in their operation.

The report was typed by Rita Hoffmann of Stanford University.

REFERENCES

Barlow and Haun, Inc., 1978. Appendices to oil and gas production,

reserves and resources report. Report prepared for Minerals

Division, Wyoming Department of Economic Planning and Development,

108 p.

Beene, D.L., 1979. 1978 Oil and gas production in Kansas. Energy

Resources Series, 14, Kansas Geological Survey, 178 p.

California Division of Oil and Gas, 1979- California Division of Oil

and Gas 64th Annual Report, 1978. Pub. PR06, 164 p.

252
B 0 E

Figure 27. Possible alternative form of distribution of oil-field

volumes. Observed distribution is lognormal , but actual distribution

may be bimodal with long exponential tail toward lower end of individual

vol umes

253
DISCUSSION

CHAIRMAN MURPHY: Are there any questions? Yes, come up to the

mi crophone

VOICE: In the field size data that you used, were there fields

that had been discovered but which were not included in the study?

DR. HARBAUGH: This is partly a semantic problem posed by the

difficulty in defining the boundaries of fields. In general, all

relevant field-size data were included.

VOICE: The point that I am getting at is that in the curve that

you showed, you said that the left or small-field side is determined by

economic factors, whereas the right or large-field side is determined by

geologic factors. It would seem that the right side is also influenced

by economic factors?

DR. HARBAUGH: Well, indirectly it is, in that technology and

economics affect the right side to some extent. But the counter-argument

is that there are geologically inposed limits to the maximum size of

fields which strongly affect the distribution of fields toward the large

end. Whereas at the lower end, the distributions are unmeasured because

we do not know what the smallest field is. In fact, the smallest field

is incapable of being defined. It probably goes down to a teacup in size, with all possibilities in between.

VOICE: I am with the Department of Energy. I have two questions,

one of which is statistical. Have you made goodness-of-f i t tests for

the lognormal distributions, and the other question was raised by your

discussion. You were talking about the shifts in the median size of

fields over the history of a region. Have you come up with possible

predictor variables for estimating this median shift? Since you are

able to come up with geological explanations for the samples you showed,

have you found any consistent predictor variables as a result?

DR. HARBAUGH: The answer to the first question is that we have not

made goodness-of-f i t tests, but they could be made easily. However, the

data for many of these distributions are so ample that you don't need

goodness-of-f i t tests to determine whether they approximate lognormal

distributions.

The answer to the second question is also no, but it is one on which we are working. In California and Wyoming we intend to extend

these studies from more geological standpoint, in which we aggregate the

fields into geological categories such as structural versus stratigraphic and also as to whether the structures which have influenced

accumulation were perceived early or late relative to their discovery.

DR. RICHARD MAST: I am Dick Mast, with the USGS. John, is there

much depth variation in the Sacramento Valley gas fields?

DR. HARBAUGH: Yes, there are depth variations.

DR. MAST: This concept of large fields being found first has to do more with areal size of fields, and your conversion to a BOE basis turns

that around. I would rather see you employ a volumetric basis for gas fields.

254
DR. HARBAUGH: Since the Sacramento Valley fields are all gas, the

transformation to BOE is just a linear conversion, so the distributions

are not going to be changed.

DR. MAST: No, because as you get deeper, you get more gas per unit

of reservoir volume because of higher pressure.

DR. HARBAUGH: I see what you mean. The standard MCF is 1,000

cubic feet at 60 degrees F and 14.7 PS I , but at depth this amount of gas

is compressed into a much smaller volume.

DR. MAST: Yes. The resulting distributions might turn out quite

di fferently.

DR. HARBAUGH: I agree that there would be drastic differences if we tabulated gas field sizes according to actual volumes in the reservoirs,

at depth.

CHAIRMAN MURPHY: Any other questions?

VOICE: I have a question about three things. But first, do you

know of any good geological story, why the distribution of pools should

be lognormally distributed?

DR. HARBAUGH: Why it should be so geologically?

VOICE: Yes, is there a geological model that would indicate that

should be the case?

DR. HARBAUGH: Not a particularly good one. It is argued that

processes that involve progressive splitting are involved. Take an entity, cut it in half, cut those halves in half and so on in random

fashion. The result may approximate a lognormal distribution if we lose

track of many of the progressively smaller fractions. This is not a very satisfying geological rationale.

VOICE: Okay.

DR. HARBAUGH: Perhaps someone else has a view on this matter?

VOICE: The other question is, it has been argued strongly by

Kaufman that the distribution of pools within a play is lognormally

distributed. You have taken it a step somewhat to the side, and I am

not sure that it is clear to people here, that it is logically inconsistent for the distribution of plays to be lognormal, and then regard

the distribution of pools representing the distribution of fields to be

lognormally distributed within a basin.

There is a theoretical inconsistency. Do you feel uncomfortable

about it, or do you feel that this is a problem that you need not deal

wi th?

DR. HARBAUGH: I am not sure that I agree. Does your question

involve the assertion that the distribution of oil and gas field volumes

within plays is not lognormally distributed?

255
VOICE: I am claiming that some people say that the distribution of

pools within a play is lognormally distributed, and some people say that

the distribution of fields within a basin is lognormally distributed,

and then even within an aggregation of basins. The second of the two

statements that if the fields are lognormally distributed within a basin

or within an aggregation of basins is not consistent, in that the lognormal distribution does not regenerate.

CHAIRMAN MURPHY: The sum of lognormals is not lognormal; is there

an inconsistency?

DR. HARBAUGH: I agree; however, when we look at California or

Kansas as a whole, versus individual districts in these states, we are

in effect either merging or segregating sub-populations. In our experience, the lognormal model is a useful one throughout the ranges of

population sizes that we have dealt with, although there are serious

deviations from it.

VOICE: Okay. My last question is, it would be very useful to

guarantee lognormal ity very early in the exploitation of a play, so that

forecasting could be much more robust; however, examples can be found

where the lognormal model is nowhere near correct.

Have you investigated or do you have opinions on the set of con- ditions that are sufficient to guarantee lognormal i ty, and can those be

recognized early in the exploitation of a play?

DR. HARBAUGH: That is a good question, and I wish I could answer

it. I would say, the kinds of geological conditions that would most assure lognormal ity would be geological controls on accumulations that

exclude large geologic structures, and include a large number of more

subtle geologic features, such as permeability changes that form stratigraphic traps. For example, the Los Angeles basin contains very large

geological structures, which may be the principal reason why the LA

basin deviates so far from the lognormal ideal, at least in the fields

discovered early.

256
ISSUES PAST AND PRESENT IN

MODELLING OIL AND GAS SUPPLY

by

Gordon M. Kaufman

M.I.T,

1. Introduction

"For every type of animal there is a most

convenient size, and a large change in size

inevitably carries with it a change in form." — J.B.S. Haldane (1928)*

Physical principles dictate the size of animals. Haldane points out that the

human thigh bone breaks under about ten times the weight of a normal human.

The strength of bone is in proportion to its cross-sectional area, while the

weight of an animal is proportional to its volume. This lessened his respect

for Jack the Giant Killer, for the Giant, a scaled up human sixty feet tall,

would have broken his legs with his first few steps towards Jack.

If we replace the words "animal" and "size" with "policy problem" and

"model" respectively, then models of oil and gas exploration, discovery, and

production currently in vogue loosely adhere to Haldane 's observation about

the animal kingdom. At one extreme are disaggregated approaches to modelling

that focus on individual deposits as the basic unit for analysis; at the

other extreme are models that treat time series of data at the national level.

As with the Giant, a direct scaling up of models for supply from individual

petroleum plays or petroleum basins, "breaks the model's legs" in several ways

Yet there must be a logical connection between micro-models of these physical

entities and a country-wide level of aggregation, for what happens at the

national level to discovery and production of oil and gas is, after all, deter

mined by what happens in over a hundred individual petroleum basins.

The territory that lies between aggregated and unit-specific disaggregated approaches is as yet uncharted. No logically tight methodology

for aggregating projections of supply over different time frames from individual geologic units in varying stages of exploratory maturity is in sight.

Ideally, we wish to have at our disposal a system of logically inter-related

methofls and models sufficiently flexible to allow economic supply functions

to be computed for mature, partially explored, and frontier regions under a wide range of fiscal, regulatory, and technological alternatives at reasonable

cost in time, human effort, and money. The current state of the art is very

far from this ideal. *

* "Possible Worlds" by J.B.S. Haldane, Harper and Brothers, 1928.

257
An impressionistic snapshot of aspects of the current modelling environment has these salient features:

- No conceptual reconciliation of models of individual plays,

stratigraphic units, and petroleum basins that explicityly

incorporate individual deposits as components with models

that don't,

- A movement towards process-oriented models that reflect key

features of the physical processes of exploration, discovery,

and production of petroleum,

- Few publicly available data sets that allow meaningful structural

validation of highly disaggregated models,

- An increasing use of personal (or subjective) probabilities

as a vehicle for representing expert judgements about uncertain

quantities without a serious matching effort to train assessors

to avoid cognitive biases that distort assessments,

and

- Policy issues as moving targets : an often rapid change in what

policy analysts view as "important" policy problems places a heavy

burden on modellers working with models, most of which are difficult

to reconfigure rapidly.

This short list of observations about the modelling environment can be

amplified many-fold, but it does set the stage for discussion of some current

issues in probabilistic modelling of oil and gas exploration, discovery, and

production. Wood (1979) comments in depth on the energy modelling environment

and the policy research process, and Stitt (1979) gives an excellent review

of problems in resource modelling with particular attention to the linkage of

micro-economics and physical aspects of production and development of petroleum

deposits

2. Issues and Problems in Modelling Discovery

At a Disaggregated Level

Formal modelling of exploration and discovery at a disaggregated level

began with the work of Arps and Roberts (1958) and many of the issues and

problems that their work suggested are still with us:

- Taxonomy : How to classify petroleum deposits in a basin into

descriptively homogeneous sub-populations in accordance with the

idea that elements of each such sub-population will possess

statistically homogenous quantitative attributes like area, volume,

hydrocarbons in place, etc.

258
- "Size Distributions : Given that such a classification is possible,

are there particular functional forms that characteristize measurements of each of the principle quantitative attributes of individual

deposits which play a role in supply analysis?

- Measurement and Observation : The peculiar nature of exploratory

search methods and geologic interpretation of the measurements they

yield combine with economic incentives and manifold sources of

measurement error to complicate severely application of statistical

methods: testing of hypotheses about size distributions, measurements of inter-relations between quantitative attributes of deposits,

and prediction of returns to exploratory effort at a disaggregated

level.

- Stretching of Assumptions : Models of exploration and discovery

focused on individual basins and more particularly on plays within

basins ought to be designed to reflect particulars of the evolution

of discovery within such units. Attempting to "stretch" such models

and apply them uncritically to arbitrary geographic regions or larger aggregates may be an exercise in mis-specification and lead

to misleading predictions.

- Uses of Subjective Probability : When measurements are few as in

frontier provinces or in a sparsely drilled stratigraphic unit within

a partially explored or nature basin, methods currently used for

elicitation of probabilities about simply described events bearing

on occurrence or non-occurrence of petroleum and for deposit attributes conditional on the presence of hydrocarbons forces the geologistassessor to integrate mentally and boil down a large quantity of

spatially interrelated descriptive and quantitative data into a small

set of numbers. Innovative approaches to use of both quantitative

and non-quantitative data as conceptual aids to assessment are needed.

Probabilistic dependencies among uncertain quantities tend to be ignored.

- Adaptive versus Non-Adaptive Modelling : When parameters of a model

are not known with certainty a priori , learning about them from observational experience is possible. Revision of opinion about model

parameters in light of new observations and a concomitant revision of

predictions about yet to be observed quantities can in principle be

done in a logical fashion. Few energy models incorporate adaptive

learning. Should they?

That at least some of the above are contentious issues is evident in

much recent literature on modelling of exploration, discovery, and production.

2 . 1 Taxonomy, Plays, and "Size" Distributions

Each deposit is unique; each prospect is unique. Each must be modelled

in light of its particular attributes. This view leads modellers to a dead end.

Too much data and too much modelling detail are demanded. The idea that deposits can be classified into homogenous collections of descriptively similar

deposits enables us to move one rung up the ladder of aggregation; more

259
I parsimonious models of much simpler structure follow. Essential elements of

the micro-economics of individual deposit exploitation are not sacrificed at

this level of aggregation. A key concept at this level of aggregation is that

of the size distribution of such a collection of deposits.

Properties of the distribution of sizes are obviously dictated by how

membership in a particular collection is defined. It is up to the geologist

to set the rules for inclusion and exclusion. Geologists do this. They

define plays. Unfortunately, the rules for classification may vary from

geologist to geologist and very seldom so crystal clear that non-geologist

could do a meaningful classification. However, retrospective analysis of a very will explored area often leads to a classification scheme that provides

an acceptable guide for modellers.

A challenge to the geologist: Can you provide modellers with a clearer description than is presently available of how classification useful

for supply analysis should be done?

Modelling properties of collections of descriptively similar deposits

in a petroleum basin, as opposed to modelling the particulars of each deposit

and prospect greatly reduces computational cost, complexity, and amount of data

required. This idea, while rubbing against the grain of many exploration

geologists who keep detailed descriptive differences among deposits as well as descriptive similarities in focus, is behind the exploitation of the concepts

of "play" and distribution of deposit "size" - volume, area, hyrocarbons in

place, recoverable hydrocarbons - when modelling discovery, production, and

making resource projections.

Some resoundingly disagree with this modelling tactic as evinced by

the following comments by a senior geologist with a large oil company:

"...I disagree ... that the first step in making

resource projections should be to classify deposits of

a basin into homogeneous subsets. This seems to be

the essence of the current USGS-D.O.E. effort to make

regional estimates on the basis of "plays". The first

question that arises in the mind of any experienced

exploration geologist is: "Who does the classifying"?

The basis of the success of the U.S. oil and gas industry is its willingness and capability to consider

and to test a wide variety of often contradictory

geological concepts. When the D.O.E. undertakes to

classify "plays", they must use a handful of geologists

using a single concept of the geology and of the oil

and gas distribution pattern of the area under consideration. The industry on the other hand, would make

similar classifications by many different groups of

geologists operating with diverse ideas about what

the classifications should be based upon. A number

of major oil fields have been found by people who

were in fact ignorant of the accepted industry evaluation of a particular area or rock sequence.

260
"Beyond the certain inaccuracy of classification by a single group of geologists there is the fact that few

geological situations maintain any sort of uniformity

over any large region. Oil and gas accumulation is

controlled by stratigraphy, by structure, by formation

fluid physics and chemistry, and by hydrocarbon source

rock availability. Each of these factors varies independently so that the conjunction of any particular set

of circumstances rapidly changes."*

Classification of prospects in a frontier areas into play types is an exercise in judgement based on little data. The idea gains more force

when applied to partially explored and to mature provinces; plays are most

crisply delineated by a retrospective analysis of data from a region where

intensive drilling has taken place.

Much confusion arises if the concept of a "play" as a descriptive

hypothesis entertained at the outset of exploration is not viewed as distinct

from a classification of deposit types constructed from measurements provided

by intensive drilling of an area. Many such descriptive hypotheses can be

entertained at the outset of exploration of an area; one may possibly be

demonstrated to be true after extensive drilling and the understanding so acquired used by a skilled geologist to classify deposits into types.

The more descriptively divergent the set of a priori hypotheses are,

the greater one expects the "spread" of probabilistic predictions of sizes of

deposits and possibly of aggregate amounts of hydrocarbons in place to be.

This line of thought is in loose analogy with a Bayesian treatment of prediction

when a set of structurally distinct models are envisaged as possible generators

of observed data (cf. Zellner (1970) Chapter 10 of example). Figure 1 schematically displays the difference between procedures which require explicit

evaluation of probabilities for a priori hypotheses and procedures which don't.

In practice there is a difficult tradeoff to make: if a priori geologic

hypotheses are explicitly introduced, then probabilities for occurrence attributes (source, timing, migration paths, etc.) and for individual deposit

attributes must be assessed conditionally on each hypothesis. The number of

assessments required increases linearly with the number of alternative geologic

templates or hypotheses considered. Where is the balance between unwieldy

assessment and explicit consideration of key geologic concepts?

To the author's knowledge, no publicly cited resource appraisal is based

on a formal treatment of alternative descriptive geological hypotheses . It is

left up to the geologist making an appraisal to "do it in his head." As a con- sequence, when subjective probabilities are used to express judgements about

deposit attributes and resource potential, geology and probability are not as tightly coupled as they perhaps should be. I believe that a similar line of

thought motivates the following observations, again from the same experienced

petroleum geologist:

That D.O.E. "must use a handful of geologists using a single concept of the

geology ..." is challengeable. Participants in the recent government study

of NPR-A oil and gas potential will attest to the wide range of geological

hypotheses considered prior to formulating play definitions and assessing

potential resources within plays. 261
occurrence

o occurrence

(x

l' x

2' ' "' V

dry

Occurrence Attributes

(Source, Timing,

Migration Paths)

Quantitative measures of

deposit attributes

VERSUS

occurrence

no occurrence

occurrence

no occurrence

ccurrence

no occurrence

dry

dry

dry

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Descriptive

Geologic

Hypotheses

Occurrence

Attributes

(Source, Timing,

Migration Paths)

Quantitative measures

of deposit attributes

Figure 1. Trade-off between magnitude of assessments and explicit

recognition of reasoning about alternative geologic templates.

262
"I remain convinced that most economic models

attempting to describe oil and gas exploration

are seriously incomplete in their recognition of

the influence of geological concepts upon the

location and nature of exploration targets.

Alternate geological evaluations should be incorporated in the models in the same manner as cost,

price, supply, and demand alternatives. I do

not regard the probability estimates appended by

the USGS to their resource estimates as filling

this need.

2.2 Stretching Assumptions

Can predictive accuracy be maintained if the form of models designed

for plays is stretched to apply to collections of plays in a basin and possibly to even larger geographic regions? Conversely, how well can models of

arbitrary large geographic regions that do not incorporate physical and geological features of the exploration process predict? We are still fumbling

for answers, but it is clear that much work on both structural and predictive

validation of model types is warranted.

A small example illustrates the dangers in attempting to stretch the

form of a model designed for individual plays to collections of plays. Let

{A^, A^} be a collection of "sizes" (area, volume of hydrocarbons in

place or recoverable) of deposits recognized to be targets for drilling. A

parsimonious model of discovery in the absence of externalities restricting

access to them (sequestered acreage, lease blocking) follows from the assumption that discovery proceeds as sampling without replacement and proportional

to size (Kaufman, Balcer, and Kruyt (1975), Barouch and Kaufman (1978)).*

Namely the probability of discovering A.. , ... A in that order is

N

n

j=i

A./(A. V

Bloomfield et a!L (1979) propose a test of this model: in place of assuming

that the probability of discovery of a deposit is proportional to its size,

however size is defined, assume that it is proportional to a power a of size; use observed data to estimate the value of a. The model becomes

n A

a /(A

a + ... + aV

j=l J 3

This sampling process appears in the statistical literature treating a problem known as the "coupon collector's problem". There it is called

"successive sampling", a curiously uninformative name; cf. B. Rosen (1970),

(1971).

263
If the estimated value of a is close to one, then the assumption that the

probability of discovery is proportional to size is more or less reasonable,

depending on the quality of the data and the size of the sample. Using as data all oil fields found in Kansas from 1900 to 1975, they found that

"discoverability" as embodied in the parameter a was proportional to a "surprisingly low power of area", namely, a = .33, and conclude that

"... models assuming that discoverability is

proportional to either area or volume should

not be used on a regional basis without further study."

Stretching a simple probability model designed for individual plays to cover

a region in which there may be many plays apparently doesn't work well.

In a commentary on this study, Kaufman and Wang (1979) argue that the authors

findings are inconclusive and possibly misleading: the parameter a may or may

not be different from one for individual plays, but in their study "... there

is no recognition that deposits discovered in Kansas come from several descriptively distinct deposit populations and that as discovery effort grew, so did the number of deposit populations recognized as targets for drilling."

They assert that

- the analysis of the Kansas data as they have done it does no more

than confirm that a statistical model designed for data from a single population of descriptively homogeneous deposits in a petroleum basin may not be an appropriate model for discovery data

drawn from a mixture of distinguishable deposit populations.

- the surprisingly low power" of the discoverability parameter a for the Kansas data as they estimate it (a = .33) is possibly a result of use of an incorrect model: when data is generated by

sampling without replacement and exactly proportional to size

(a = 1.0) from two or more distinguishable populations, each of

which becomes a target for drilling at a different point in time,

application of a model in which deposits from all populations are regarded as targets for drilling at the outset can yield an estimate

of much less than 1.0.

- For samples of moderate size (30 observations or less) the maximum

likelihood estimator for a as proposed by Bloomfield et al.can be

very sensitive to the reported order in which fields are discovered.

A shift of a single data point can cause large changes in a maximum

likelihood estimate of a.

A value of a = 1.0 corresponds to the probability of discovery of a field

being exactly proportional to its size (area)

264
The evidence for the second assertion appears graphically in

Figures 2 and 3 which summarize results of a Monte Carlo study of the

effects of assuming that observed field sizes in a geographic region come

from a single deposit population all of whose elements are recognized as drilling targets at the outset, when in fact they don't.

In these figures is a maximum likelihood estimator (MLE) for a

if it is assumed that all observations from t two distinct populations are targets for drilling at the outset, when in fact one of the two populations is

recognized as a set of targets only after a fraction of elements of the first

population have been discovered. The function a j is a MLE for a when this

feature is explicitly taken into account.

The effects on estimation of a of sequestering acreage as opposed to

allowing unrestricted search by drilling over the full areal extent of a single play are similar. (cf. Kaufman and Wang (1979)).

2 . 3 Uses (and Abuses?) of Subjective Probability

With few exceptions, subjective probability has been used in resource

evaluation and supply projection in a very particular way: opinion is elicited,

not about model parameters, but about observables — aggregate volume of hydrocarbons in place, generic deposit attributes like net sand thickness, porosity,

etc. Said in another way, predictive distributions for deposit attributes are

assessed; no statement of an obj ective probability model describing the process

by which observables are generated is provided. As a result, when additional

data — new discoveries and measurements of their attributes, additional

measurements and revision of previous measurements of properties of previously

discovered deposits — is provided, no explicit mechanism is available for a logical revision of the original assessments. Revision of the original assess- ments must be done judgmentally by "experts". No framework for appraisal of

the coherence of a priori and a posterior assessments is in place.

Is this important? Admittedly sparse experimentation with small groups

offers evidence that, without extensive training, humans may not correctly

weight sample evidence and a priori probabilities for hypotheses about "states

of nature", (Hogarth (1975) , Tversky and Kahneman (1974) Edwards (1962)).

While, given additional data, the geologist may provide an elaborate descriptive rationale for a shift in his or her assessments in, say, the amount of

recoverable hydrocarbons in a stratigraphic unit, the correspondence between

the quantitative shift in assessed probabilities from "before the new data"

to "after the new data" is not easily fathomed.

Most practitioners of resource assessment art who use subjective

probability are aware of the cognitive biases that may distort probability

assessments. Assessment protocols for minimizing these biases have been suggested in the literature. However, in the heat of the battle to get "acceptable" assessments in a short period of time from busy geologists, selfprotection aids often are dropped. Dominant personality effects and peer

265
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by Model III*

111 11

Numbers of elements in first and second populations are N and M

respectively. The second population becomes a target after a fraction

m/N of the first population is observed.

266
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267
group pressure come into play. While it is impossible to measure the ultimate

cost of possible distortions in forecasts that this introduces, one is left

with at best an uncomfortable feeling. .

Probabilistic dependencies among uncertain quantities are almost always

ignored and mutual independence implicitly or explicitly assumed. The time

consuming nature of the assessment process and the tyranny of large numbers of

assessments that may be required combine to justify a tactical dodge away from

incorporation of dependencies among uncertain quantities. What is the character

of dependencies between reservior attributes such as porosity, net sarid thickness, etc. for a given set of deposits?

2.4 Data

Well measured data describing properties of deposits are an essential

ingredient of any recipe for cooking up evidence bearing on many of the issues

raised thus far.

For the modeller of supply it is important that the data display a recognition of the interplay between geologic features of deposition, reservoir

attributes and recovery technology. A good example is the data gathered for

the Interagency Oil and Gas Project Permian Basin study, several aspects of

which have been presented by speakers at this conference.

Another excellent illustrative example is a recent study of the Lloydminster heavy oil play in Alberta and Satchkachewan done by the Geological

Survey of Canada: the Manville section was "divided into twenty slices each

comprising a sand-shale couplet representing one cycle of trangression and

regression". Each of 1200 pools in the Alberta region of this play were

reworked and attributes remeasured by MacCallum, Stewart and Associates. That

all pools were reworked by the same group of experts using their particular

approach to measurement is important: most publically available deposit data

consists of data elements generated by more than one group of experts and different approaches to measurement of deposit characteristics may be employed

across groups. In this particular instance "between group" heterogeneity is

absent. Here are principal features of their study:

- net pay thickness, oil saturation, presence of and thickness

of overlying gas and underlying water measured or estimated for

each of twenty stratigraphic slices,

- probabilistic assessments of oil in place include "virtually all

of the oil, even in the thinnest beds, with no a priori economic

cutoff",

- individual reservoirs mapped and divided into segments according

to applicable recovery method; nine thousand reservoir segments

were processed,

268
- probabilistic assessments of recovery factors elicited for primary,

water flood, fire flood and steam soak recovery,

- a probabilistic projection of technologically feasible recoverable

oil generated for each type of recovery method.

The economics of recovery and production plays no role in this assessment; McCrossan, Proctor, and Ward probabilistically project amounts of oil

technologically feasible to recover by primary, water flood, fire flood and

steam soak methods. The amounts are large: the most likely quantity of oil

in place is about 25 billion barrels with 2.5 billion barrels technologically

recoverable, excluding unexplored areas. Of particular note for data analysts

is their observation that

"The apparent very large discrepancies between the

existing booked reserves made by the regulatory

agencies and the present study is a purely artificial one in that the booked reserves include only

those pools on production or known to be capable of

producing. The current study, on the other hand,

should be looked upon as an inventory of the total

resource with some reasonably realistic forecasts

of its producibility but without consideration of

the ultimate costs or timing, or any estimate of

when the resource might become a component of

Canada's supply."*

In addition, the authors present fractile plots on logarithmic probability

paper for oil in place and for recoverable oil. Combining a visual evaluation

of these plots with geological perspective they assert that:

"It is clear from the geological work done to date

that the oil has been pooled into discrete deposits

which appear to be closely related genetically on

the basis of the homogeneity of the pool size distributions. An examination of the distributions indicate that,

as might be expected in the logarithmically distributed

population, that there is a very large number of small pools

and only a few approaching giant class. These distributions

seem extremely orderly in spite of the fact that

these deposits lie within an extraordinarily complex

geological framework involving salt collapse, facies

variations, changing structural attitudes over short

periods of geologic time, abundant anastomosing

channels cutting various stratigraphic horizons

during various periods of time and highly variable

fluid contacts with different amounts of underlying

water and overlying gas.""!"

"Estimate of Oil Resources, Lloydminster Area, Alberta", by R.G. McCrossan,

R.M. Procter and W.J. Ward.

R.M. Procter and W.J. Ward, op_. cit .

269
Their sample is large and suited to a study of distribution shape.

In particular an examination of tail behavior along the lines suggested by

Mallows and Tukey (1979) [Section 19, p. 19] and Hoaglin (1980) recommends

itself. Both projective area and oil in place measurements are recorded

for each deposit, so the relation between area and volume of oil in individual deposits can be investigated.

The Lloydminster data exemplifies what is needed for a meaningful

retrospective study of

- size distributions

- probabilistic dependencies between reservoir attributes

- influence of volume and area on discoverability

- the impact of alternative economic scenarios on amounts of

recoverable hydrocarbons and on the portfolio of recovery

technologies that are economical to supply.

Unfortunately, the number of publicly available data bases of this type

and quality are sparse.

2 . 5 Conclus ions

There are impelling political and bureaucratic forces funneling

great effort and money into building models that can address policy problems

as currently conceived. By comparison relatively little effort is devoted

to acquisition of data in a form truly appropriate for meaningful validation

of the structure of disaggregated supply models.

Econometric and other stylized aggregate approaches to modelling

petroleum supply ride rampant over structural detail. A gradual elision of

disaggregated and aggregated approaches will probably evolve, with the former

providing a process oriented- framework for structuring the latter. In order

to speed the process up, modellers need, as they have needed from the start,

(1) Much more carefully measured data in a form that allows

meaningful structural and predictive validation of

disaggregated models of exploration, discovery, and production,

(2) To place this data in the public domain at modest cost so as to

encourage a larger component of the scientific community

to work with us

,

(3) More emphasis on a retrospective analysis of recurring problems

in resource analyses unfettered by the need to apply results

immediately to particular policy problems, and

(4) To promote a much closer liason between geologists and modellers

so that geologic ideas are more concretely represented in model

structure.

270
REFERENCES

Arps, J.J. and Roberts, R.G. (1958), "Economics of Drilling for Cretaceous

Oil Production on the East Flank of the Denver-Julesberg Basin,

Bull", AAPG, Vol. 42, No. 11, pp. 2549-2566.

Barouch, E. and Kaufman, G.M. (1976), "Oil and Gas Discovery Modelled as Sampling Proportional to Random Size", M.I.T. Sloan School of Management

Working Paper.

Edwards, W. , "Subjective Probabilities Inferred from Decisions", Pschol.

Rev . , 1962, 69, pp. 109-135.

Hoaglin, David C. and Peters, Stephen C. , "Software For Exploring Distribution

Shape", LIDS-P-909 (revised), May 28, 1979.

Hogarth, R.M. , "Cognitive processes and the assessment of subjective probability

distributions", Journal of the American Statistical Association 1975,

70, pp. 271-289.

Kaufman, G. , Balcer, Y. , Kruyt, D. , "A Probablistic Model of Oil and Gas

Discovery", Studies in Geology No. 1 , AAPG , pp. 113-142, 1975.

Kaufman, G.M. and Wang, J.W. , "Model Mis-Specification and the Princeton Study

of Volume and Area of Oil Fields and Their Impact on the Order of

Discovery", Energy Laboratory Working Paper No. MIT-EL 80-00 3WP, Jan. 1980.

Mallows, C.L. and Tukey, J.W. , "An Overview of Techniques of Data Analysis,

Emphasizing its Exploratory Aspects". Unpublished manuscript.

McCrossan, R.G., Proctor, R.M. and Ward, W.F., "Estimate of Oil Resources,

Lloydminster area, Alberta", forthcoming in Proceedings First Inter - national Conference on the Future of Heavy Crude and Tar Sands , 1980.

Stitt, William C. , "Resource Modeling: Problems in the State of the Art".

Presented to NATO Advanced Research Institute on the Applications of

Systems Science to Energy Policy Planning. Brookhaven National

Laboratory, November 12, 1979.

Tversky, Amos and Daniel Kahneman, "Judgment under Uncertainty: Heuristics

and Biases". Science , Vol. 185, Sept. 1974, pg. 1124.

Wood, David 0., "Model Assessment and the Policy Research Process: Current

Practice and Future Promise". M.I.T. Energy Laboratory and Sloan School

of Management, edited version of Workship on Validation and Assessment

of Energy Models, Gaithersburg, Maryland, 1979.

Zellner, A., An Introduction to Bayesian Inference in Econometrics , 1971,

J. Wiley & Sons, New York.

271
ANALYSIS OF INVESTMENT AND PRODUCTION

STRATEGIES FOR A PETROLEUM RESERVOIR

James W. McFarland

Anil Aggarwal

Michael S. Parks

University of Houston Central Campus

Leon Lasdon

University of Texas at Austin

I. INTRODUCTION

This paper is concerned with the optimum development planning and

management of a petroleum reservoir. Rowan and Warren [40, p. 84] describe

the problem as follows:

For any oil reservoir, newly discovered or partially

developed, the continuation of development drilling,

superimposed on the natural decline of the reservoir's

ability to produce, must eventually become unprofitable. Consequently it seems appropriate that there must

be an optimum development program, drilling schedule

and/or production rate which may be determined for a specific economic criterion when practical constraints

are imposed.

These observations are often phrased in the form of a question, "What drilling and/or production policy must

be adopted to maximize the return from a given operation

when certain practical limitations are present?"

In an offshore petroleum exploration process, one or more permanent

production platforms are installed on the seabed (Figure 1). Production

wells are drilled from the platforms into the reservoir rock. Petroleum

flows through the well bores and to the surface as a result of pressure differentials between the well bores and the reservoir. The pressure differentials may be maintained by natural forces or artificially through enhanced

recovery techniques. Production of oil or gas from a reservoir involves

displacing the oil and gas from pore spaces in the reservoir rock. The

primary mechanisms displacing the oil or gas are fluid expansion or depletion drive, fluid displacement (natural or artificial) or frontal drive,

gravitational drainage, and/or capillary expulsion. Often some combination

of drive mechanisms operate conjunctively.

The decision environment of the operator of an offshore reservoir

system is extremely complex. In making development decisions, the operator

is faced with uncertainties about almost every aspect of the problem from

the parameters describing the reservoir to future economic and political

conditions.

Several methodological approaches have been utilized to aid in reser- voir development planning. The detail and level of complexity used in

representation of the reservoir appears to be a key factor in any taxonomy.

Models of petroleum reservoirs vary in their complexity from simple

production decline curves (see Campbell [9]) ? in which it is assumed that

272
PLATFORMS

o o OqO°

o 0 • • •

yINJECTION WELLS | PRODUCTION WELLS

FIGURE is MULTIPLE PLATFORM

MULTIPLE RESERVOIR SYSTEM

273
production declines in some pre-specified way over time, for example, exponentially, to very complex three-dimensional, multiphase grid simulators of

reservoir behavior (see Richardson and Stone [38] and Crichlow [13]).

The general modeling approaches appear be of two general types:

(1) optimization formulations that have been solved with mathematical programming techniques (linear, non-linear, or mixed-integer) and (2) reservoir

simulation models of varying degrees of sophistication often combined with

an economic discounted cash flow model. The first set of models have, in

most cases, used a very simple reservoir representation. The second major

approach is the use of reservoir simulators. Most of the studies using

reservoir simulators focus on a specific part of the reservoir development

problem. A case study approach is often used where a few selected development

plans are evaluated. Some recent studies have attempted to bridge the gap

between the optimization models and reservoir simulators by generating

influence functions with the reservoir codes; these influence functions appear • in constraints in the optimization problem.

Another important consideration in the modeling process is the level of

aggregation that is assumed and the specific decisions and issues addressed;

for example, the reservoir development problem might be a component part or subsystem within a larger field or multi -reservoir development problem

(Figure 2)

A conceptual framework with which to view the reservoir development

problem is depicted in Figure 3. Given information and data on the technological, economic, regulatory and physical environment for the operator,

reservoir and economic subsystems are integrated to provide a mechanism

whereby alternative development strategies can be evaluated.

The remainder of the paper is organized as follows. A brief literature

review is given in Section II. A simple optimal control model for the

analysis of production and investment decisions for a homogeneous gas

reservoir with water drive is presented in Section III. Section 1ST contains

results for a hypothetical example in the Gulf of Mexico. Concluding remarks

are given in the last section of the paper.

274
4 INJECTION WELL |

PRODUCTION WELL

FIGURE 2: SINGLE PLATFORM-SINGLE RESERVOIR

SYSTEM

275
Physical Model

of

Gas/Oil Reservoir

INPUT

PARAMETERS:

Reservoir

Economic

Technological

Regulatory

Economic Model

of

Reservoir Operation

Production Rate Profile

Ultimate Recovery

Net Present Value Optimization

Criteria

Optimizer

Internal Rate of Return

Number and Location

of Wells & Platforms

Solution

FIGURE 3:

Schematic Representation of Management Model and Data

276
II. BRIEF LITERATURE REVIEW

In 1958, Aronofsky and Lee [3] formulated a linear programming model

for scheduling of production from a finite number of sources (reservoirs)

so as to maximize profits. Each reservoir was assumed to be homogeneous

with an infinite water drive. A Hurst-van Everdingen [45] model was used

to represent pressure behavior in the reservoir. Using basically the same model, Aronofsky and Williams [4] studied two basic problems: 1) the optimum

scheduling of production from a multi-reservoir system with no additional

drilling or a fixed drilling schedule, and 2) the scheduling of drilling

under fixed production schedules. Charnes and Cooper [10] formulated a one-reservoir, water injection model in which the objective was to minimize the cost of production, injection wells, and gathering station

facilities subject to a fixed production schedule. Attra, Wise, and Black

[6] were concerned with optimizing field operating conditions such that

a field was produced at maximum oil rate, subject to well producing capacities, gas lift and pressure maintenance requirements, sales contract

requirements, and gas compressor limitations. The production rate for

each well was determined for a given set of field conditions.

Rowan and Warren [40] state the reservoir development problem and

illustrate how the problem can be formulated in an optimal control framework. Solutions to the model are illustrated for special cases.

Bohannon [8] studies a "multi-reservoir pipeline system", that is,

a system of many reservoirs producing into one or more gathering systems.

A mixed- integer 0-1 linear programming model is specified to determine the

annual production rate for each reservoir, the number of development wells

to be drilled in each reservoir each year, and the timing of major capital

investment projects such as secondary recovery and pipeline expansion,

subject to constraints on reservoir production rates, pipeline capacities,

and capital expenditures. Well production rates are assumed to decline

exponentially with time. Odell, Steubing and Gray [37] used an optimization

model for determining optimum field development and production scheduling

from multi-reservoir gas fields. Decline curves are used to represent

reservoir behavior over time. The model is structured to determine optimum

completion times and production schedules; several optimization criteria

are investigated.

Devine and Lesso [14], Friar and Devine [17], and Babayev [7] apply

mathematical programming techniques to problems associated with offshore

petroleum operations where their analyses are primarily concerned with the

development and production of entire fields. Devine and Lesso and Friar

and Devine are concerned with decisions relating to the number, size, and

location of production platforms and the allocation of wells to platforms.

Babayev' s model focuses on the number of wells to drill in each layer of

multilayer oil and gas fields and the transfer of wells between layers.

In these studies the production rate profiles are assumed to be known or specified in terms of the number of wells (see, Babayev p. 1363). The effects

of alternative operating strategies on such variables as ultimate recovery

and reservoir pressure are subsumed within these relationships. The

production rate versus time curves are commonly represented by either

277
exponential or hyperbolic decline curves (see, e.g., Friar and Devine,

p. 1372). Extensions of these models are considered by Devine [15]

and Li lien [24]. Durrer and Slater [16] survey recent literature on the

application of operations research techniques to petroleum and natural

gas production problems.

Huppler [19] uses a single state variable dynamic programming model

to examine the optimal well and compressor horsepower investment strategies

for a homogeneous gas reservoir, given a desired gas delivery schedule

and a specified peak delivery capacity. A tank-type reservoir model with

a Hurst-van Everdingen unsteady state water influx is used. Huppler

also applies nonlinear programming to the problem of production rate scheduling for a multi -reservoir gas field.

Kuller and Cummings [21] formulate an economic model of production

and investment for petroleum reservoirs. Decision rules for the discretetime optimal control problem are derived using the Kuhn-Tucker necessary

conditions. The reservoir behavior is subsumed in the model in a maximum

production constraint in which the stock of recoverable petroleum depends

on the time paths of investment and production.

Wattenbarger [46] used a finite difference reservoir simulator to

generate well influence coefficients. A well influence coefficient

represents the pressure drop at one specific well site due to one unit of

production at another well. These coefficients formed the basis for a set

of constraints on production rates in a linear programming model to schedule

production from a gas storage reservoir. The objective was to minimize

the difference between desired and scheduled production. Rosenwald and

Green [39], using influence functions, formulated a mixed-integer programming

model to study the problem of optimum well placement. Also using the

influence function approach, Murray and Edgar [35] developed mixed-integer

algorithms to optimize the selection of well locations in a gas reservoir

and the sequential optimization of flow scheduling from a multi-well gas

reservoir.

Ali, Batchelor, Beale and Beasley [2] summarize four models that help

in the management of Kuwait Oil Company with problems ranging from day-today operations through long term planning. A reservoir development model,

based on the work of Rowan and Warren, is used to study investment policies

and production and injection rates. Nonlinear programming techniques are used

to provide optimum solutions to meet production targets given assumptions

about costs, capacities and the behavior of reservoirs and wells during

depletion.

The formulation, solution and application of grid-type reservoir

simulators are discussed by Crichlow [13]. Richardson and Stone [38] provide

a good historical perspective on the development, refinement, and use of

these models. Henderson, Dempsey, and Nelson [18] and Coats [11] present

results from applications of two-dimensional, single-phase models. Henderson,

Dempsey, and Nelson are concerned with the problem of evaluating the effect

of allocations of different flow rates among a set of wells. Coats focuses

278
on the determination of an optimum drilling schedule for developing the

remainder of a field. Coats uses complete enumeration to solve for the

development scheme that maximizes discounted cash flow.

Ashiem [5] investigates offshore petroleum development in the North

Sea using numerical simulation and optimization. A relatively detailed

simulation model of offshore development operations is formulated. In

his modular system, a two-dimensional reservoir simulator constitutes one

component. A unidimensional search procedure is used to determine the

optimum initial production processing capacity.

279
III. A SIMPLE MODEL FOR GAS RESERVOIR DEVELOPMENT

1

Production and investment decisions are Assumed to be made under the

following conditions. A single operator exploiting the reservoir is

postulated. 2 Leasing and exploration activities have been completed and

the associated costs are known. External effects such as the production

of brines are assumed to be controlled through production regulations and

the costs are reflected in the production and operation expenses. There

is no enhanced recovery.

It is assumed that the objective of the operator is to determine the

production time path { q(t), t

Q £ t <_ t, } and the investment time path

{ I(t). t

Q

<_ t <_ t, } so as to maximize a stream of discounted profits over the life of tfte reservoir. In addition, the abandonment time t,

and platform size K are decision variables. The objective function is:

(1) Maximize J J [

7r ( t )(l-e)q(t)-(f)(t)I(t)-y(t)K(t)] (l-3)e

_

",tdt^(K)

z0

where K(t) = number of producing wells at time t;

I(t) = number of wells drilled at time t;

q(t) = reservoir production rate at time t;

K = number of well slots on the production platform;

7r(t) = wellhead price of gas;

3

6 = royalty rate ;

(f)(t) = cost per well (including completion and surface

facil ity costs)

iij(K) = platform cost function;

y(t) = operating, maintenance, and overhead cost per well;

4

3 = tax rate ; and

i = discount rate.

To illustrate the methodology, a homogeneous gas reservoir with water

drive is selected for study. Several rather basic tank-type, zero-dimensional models are often used by reservoir engineers in analyzing gas

reservoirs (see, for example, Craft and Hawkins [12], Agarwal , Al-Hussainy,

and Ramey [1]. and Lutes, Chiang, Brady, and Rossen [27]). One of these

simple reservoir models, based on the Schilthuis water drive assumption,

is adopted for use in the optimal control formulation. Other reservoir

characterizations and models could be incorporated into this decision framework.

280
The reservoir model depicts a permeable region in which gas is trapped

above water from a large aquifer. Three state variables are used in describing the reservoir--the volume of the reservoir V, the pressure in the

reservoir P, and the quantity of gas in the reservoir n. The initial gas

in place is no with an initial volume Vo. Initially the gas pressure P is

at the aquifer pressure Pg. As gas is removed from the reservoir at some

rate q, the pressure drops. It is assumed that the permeability of the

reservoir is high enough that the pressure remains uniform throughout the

gaseous region. Following Schilthuis [41], the water flow rate is assumed

proportional to the pressure difference between the aquifer and gaseous

region, that is, dVw r Vo r n n\ where V,, is the volume

- t, u [Vq - Kj, W

dt PQ of water which has invaded the reservoir, and E, is the Schilthuis water

drive constant.

The following differential equation for volume can be derived from the

volume balance equation and the Schilthuis water drive equation.

(2) §- - S \

(P 0- P)

. V(t

Q

) -

V

Q

p o From the mass balance equation and the ideal equation of state, the following

equation can be derived for pressure,

0) w - _oj>

^ — + ^ -r^-j' p <V p

o.

The quantity of gas in the reservoir, n, can then be determined from the

ideal equation of state PV = nRT where R is the gas constant and T is

reservoir temperature; n(t

Q

) = n Q

.^ Equations describing the reservoir

are derived in McFarland ei al . [29] and in Monash [34]. 6 Equations (2)

and (3) describe the effect of production on the reservoir through time.'

Let K(t) denote the number of producing wells at time t, and let I(t)

denote the number of new wells drilled at t. Then dK/dt equals new investment in t, I(t) s less the rate at which wells become flooded out due

to water influx, (1 - V/Vo) K(t) . It is assumed that wells become flooded

at a rate that is proportional to the reservoir volume reduction (see

Agarwal , Al-Hussainy, and Ramey [1] and Huppler [19]). Thus,

(4) M

= 1 m

(1 - v/v

o )K > K{ h] = W

The reservoir production rate, q(t), is the sum of the individual well

flow rates. It is assumed that the flow per well is a function of reservoir

pressure squared. ° Thus, using a homogeneous reservoir model, the reservoir

flow rate is the flow per well times the number of wells,

281
(5) q(t) = a P(t)

2 K(t),

where a is the well flow constant.

A more general specification of (5) is to bound the production rate^

between zero and some maximum production rate q(t), that is, 0 q(t) <_ q(t).

In addition to the limit on production imposed by well capacities and

reservoir pressure, there are a number of possible considerations (maximum

efficient rate regulations or well allowables, pipeline capacities, etc.)

that might constrain production.

Investments in wells are constrained to be between zero and some maximum rate l(t). that is,

The upper bound I(t) could result from either physical or financial resource

limitations. Drilling equipment and support services might not be adequate

to permit drilling at a rate faster than indicated by t(t). In some applications these restrictions might be modeled using nonlinear cost functions

on I(t).

Decisions relating to the number, location, and size of production

platforms are possibly more appropriately made when considering entire fields.

In many cases the same plaftorm may be used in producing more than one reservoir. Models such as those developed by Divine and Lesso, Friar and

Divine, and Babeyev could be used to aid in making these decisions.

Given a platform with K well slots allocated to the reservoir, then

the total number of wells drilled would be constrained by K.

(6) 0 < I(t) < I(t).

(7) 1 I(t)dt < K. *0

282
IV. APPLICATION

It is assumed that a relatively shallow gas reservoir with water

drive in the Gulf of Mexico is being exploited.' 0 Leasing and exploration activities have been completed.

It is assumed that the reservoir is of intermediate size with initial

gas in place of n Q

= 100 x 109 standard cubic feet (SCF) and an initial

volume of Vq = 2.039 x 10 ft^. The depth to the reservoir is assumed

to be 2200 feet in a water depth of 200 feet, with an initial pressure

PQ

= 1000 pounds per square inch (psi). The Schilthuis water drive

constant, £, is set at 0.0025. A value for the well flow constant, a , of 0.00001 is used.

The economic parameters are based on 1977 data for the Gulf of Mexico.

The regulated price of new gas, Tr(t). is $1.42 per thousand standard

cubic feet (MSCF). The royalty rate, 0 , on Federal Outer Continental

Shelf leases is 16 2/3 percent. The cost per well, which includes

completion and surface facility costs, <j>(t), is $1 ,000,000.'' Operating,

maintenance and overhead costs, u(t), are $84,000 per well. The tax

rate, 3 , is 0.48, and theA discount rate S/j, is 0.10. Platform costs are assumed to be given by i|;(K) = 3.6 + 0.3 K.

Solutions to the model were computed using a generalized reduced

gradient code for nonlinear programming developed by Lasdon et al . ([22] ; [23]). The code was run on a CDC 6600 computer at the Los Alamos Scientific

Laboratory.

For the base case data given above, the optimal solution is to drill

10 wells^ in year one, and none thereafter. The production time path for

this investment strategy is platted in Figure 4. The reservoir is produced

for 36 years. The time paths for the state variables, pressure and volume,

are illustrated in Figure 5.

The number of wells, K, equals 10 in year one. Since no new wells

are drilled after year one, the number of wells in operation gradually

declines with time due to the water influx. Five wells remain in operation

at abandonment in year thirty-six. The net present value of the reservoir

is $8.06 million.

By examining the necessary conditions for the problem, some insights

as to the nature of the solution are obtained. The problem as stated can

be classified as a "Problem of LaGrange," and the optimal controls can be

characterized using the "Maximum Principle."

By forming the Hamiltonian and taking the appropriate derivatives,

the decision rule for investment (I > 0) is to equate the discounted marginal

cost of an additional unit of investment with the discounted marginal value

(profit) of an additional unit of investment. y

3 (t) is the adjoint variable

associated with the state equation for K(t). The adjoint variable y3(t)

equals the discounted marginal value from period t through the end of the

planning horizon for an additional well drilled in period t.

283
1.0

284
i

1 1 1 1 1 ~r'

O 6 12 18 24 30 36

TIME-YEARS

FIGURE 5: RESERVOIR PRESSURE and VOLUME

versus TIME [BASE CASE]

285
The solutions for the adjoint variables y-,(t), y2 (t), and y3 (t),

corresponding to the state variables V, P, and K, respectively, are plotted

in Figure 6. The discounted marginal value of reservoir volume, y-,(t).

is initially $20.4 million per billion ft3

. y|(t) declines exponentially

and equals zero at the end of the horizon. The discounted marginal value

of reservoir pressure, y2

(t), is initially $34.9 thousand per psi; y2t

decreases to $0 per psi. The discounted marginal value of wells, y3 (t),

is $862 thousand per well at the beginning of the decision horizon; yo(t)

declines rapidly through time and reaches $0 per well.

Investment in wells in year one is pushed to the point where the

discounted marginal cost of an additional well equals its discounted

marginal value. After year one, however, the discounted marginal cost

of an additional well exceeds its discounted marginal value. Thus, no wells are drilled after year one.

Several runs were made to test the sensitivity of the model to economic

and reservoir parameters, including price, production and investment costs,

the discount rate, the well flow constant, the initial conditions on pressure, volume, and quantity, and the Schilthuis water drive constant.

Results from selected parameter variations are given in Table 1.

Increasing price, decreasing the royalty rate, or decreasing costs

shifts the production path toward the present. The exploitation period

is shortened, the final pressure is lowered, and the net present value

and ultimate recovery for the reservoir are increased. A reduction in

the discount rate yields a longer production horizon, lower initial investment, slightly lower ultimate recovery, and increased net present value.

Varying reservoir parameters can also have a significant impact on production and investment decisions. With a stronger water drive, these

model results suggest that the reservoir should be produced at a faster

rate. However,' the net present value and ultimate recovery of the reservoir

are slightly lower than for the base case. With higher initial pressure,

the net present value and ultimate recovery from the reservoir are increased,

and the reservoir is operated for fewer years. Varying other reservoir

parameters affects model solutions as might be expected. For example,

decreasing the size of the reservoir results in fewer wells being drilled

and a lower net present value of the reservoir.

It is possible to simulate a reservoir supply response curve by varying

price. At a higher price, a larger quantity would be supplied. The

reservoir supply response function would be of the form:

(8) qQ = f (-rr(tQ)/reservoir and economic parameters)

The effect of changes in selected regulatory policies or other parameters

on supply can be investigated through sensitivity analyses.

286
Yi x 106 $

o 6 S is S 35 36

TIME-YEARS

FIGURE 6: ADJOINT VARIABLES vs. TIME[BASE CASE]
LUcc

ZD

00

oo

LUoc

Q_ 1—1 1 r»» O OO LO i—i 00 LO

00 1 to i—

CM

00 lo LO lo

D_ 1 CM CM CM CM CM LO CM

o00 uj <n t °

o<_> LU

ooo

a:

0Q

O0ooc

oo

00

LU

oc:

00

oc>-

=> o Q M O H-l DC DC

Q- O

oo

_i

_i

UJ

00

LOO

I— -OO- C_> UJ Z "3 O CO i—

O I—

c_>

LO rH lo CM i—

LO en

*zSr 00 oo Ln

LO CM

00

oo LO O o o oo o

to o o o oo oo OO CM LO LO LO CM

LO 00 CO

lo i—OO CM OO "=Cf o CM oo co cn CO CM oo LO LO oo

i—

CM t—

T—1 i—i

4-> o o LO o LO o LO i—

o LO

I—

o CM II o o O LO LU X II O OC

r-H ZD LO LO CM LU II OO CM I— oo

II <c LU UJ

1 1 CM i—l oc: > OC UJ -bO- -00- h- i—

o_ oo oo I— OC < ii ll II o Q _l

C_) C_3 zd <C

LU LU LU o OC 1—

LU CJ O O _J C_) LU h- oo t—

i—i—

_J 00 I— 1—

oc oc DC LU t—

< z: 0Q O- Q 3: i—

1-HCMoo-^-LOLor^.oo

288
IV. CONCLUDING REMARKS

The research concerned with petroleum reservoir development has

focused on providing operators with methods to aid them in reaching better

management decisions. These models also provide a framework that can be

used to analyze the potential effects of government policies and regulations on investment and production decisions.

The Secretary of Interior was charged in the "Energy Policy and

Conservation Act of 1975" [42] and "The Outer Continental Shelf Lands Act

Amendments of 1978" [43] with determining "maximum efficient rates of

production" and "maximum attainable rates of production" for oil and gas

on selected Federal lands. The responsibility of establishing diligence

requirements and setting production rates was transferred to the Department

of Energy in "The Department of Energy (DOE) Reorganization Act (PL 95-91)

Sec. 302" [44]. A methodology similar to that described in this paper has

been used in analyzing MER regulations and the effects of alternative

optimization criteria on oil and gas production rates. Some results from

this research are reported in references [20], [28] . [29], [30] and [32].

The determination of production rates is part of the larger problem of

reservoir development and management.

There are two areas of future research that appear especially deserving

of inquiry. The advantage of reservoir simulators over classical reservoir

models is the ability to consider the geometrical complexity and detailed

heterogeneity of the reservoir. In cases where heterogeneity plays a dominant role in reservoir performance, it is important that reservoir

development and management models reflect these complexities. A shortcoming

of most optimization approaches to date is that they have not, except in

limited cases, incorporated this level of sophistication. Another area especially deserving of study is the introduction of risk and the stochastic

nature of some of the underlying processes into the reservoir development

planning problem.

289
FOOTNOTES

^ Results from a similar model are given by McFarland [31].

In the case of several firms exploiting the resource, either pooling,

drilling, or unitization agreements would likely be required to avoid

"common property" problems. There are numerous legal, technical, and

administrative problems that often arise in operating a reservoir as a unit. A discussion of these is beyond the scope of this paper (see

Kuller and Cummings [21]. McDonald [33], and Lovejoy and Homan [26]).

3 Variable royalty bidding systems are also being used in some OCS lease

sales.

4 The actual tax structure for oil and gas operations is considerably

more complex than that used in this formulation. The tax rate may be

viewed as an effective tax rate, a surrogate for this more complex tax

structure. In extensions of this model, the refinement of the treatment

of taxes is one area of interest.

5

An ideal gas is assumed. For non- ideal behavior, the ideal gas law

is modified to PV = znRT, where z is the gas deviation factor (see Craft

and Hawkins). The gas deviation factor is the ratio of the volume actually

occupied by a gas at a given pressure and temperature to the volume it

would occupy if it behaved ideally.

For results of matching studies using this reservoir model, see Lohrenz

and Monash [25] and Nachtshiem and Siege! [36].

^ Ultimate recovery, tHat is, the total quantity of gas recovered from

the reservoir, is ^

_ rt-| r (-t)dt wnere

*o

15 t'1e time Proc*uction begins

i to

and t] is the time when production ceases. The relationship between ultimate

recovery and production rate for alternative model specifications is

investigated in McFarland, et al . [29].

o This function is usual ly- specified as either a linear or quadratic

function of reservoir pressure (Zaba and Doherty [47], Agarwal , Al-Hussainy,

and Ramey [1], Rowan and Warren [40]).

g The model could be extended to investigate optimal compressor horsepower

using an approach such as Huppler's. An additional state and control variable

and associated constraints would be required.

^Gas reservoirs with water drive are fairly common in the Gulf. Some

estimates suggest that approximately 15 percent of all gas reservoirs in the

Gulf are water drive.

^Well costs vary with a number Of factors (for example, well depth, water

depth, drilling time, and geological conditions); however, it is fairly

common to estimate well costs as a function of well depth or drilling time.

12The solutions for number of wells are rounded to integer values.

290
REFERENCES

[I] Agarwal , R. G., R. Al -Hussainy,and H. J. Ramey, Jr., "The Importance

of Water Influx in Gas Reservoirs," Journal of Petroleum

Technology , (November 1965), pp. 1336-1342.

[2] Ali, H. M. , A. S. J. Batchelor, E. M. L. Beale and J. F. Beasley,

"Mathematical Models to Help Manage the Oil Resources of Kuwait,"

unpublished manuscript.

[3] Aronofsky, J. S. and A. S, Lee, "A Linear Programming Model for

Scheduling Crude Oil Production," Journal of- Petrol eun

Technology , (July 1958), pp. 51-54.

[4] Aronofsky, J. S. ana A. C. Williams, "The use of Linear Programming

and Mathematical Models in Underground Oil Production," Management

Science , vol. 8, ^Juiy 1962;, pp. 3y4-407.

[5] Asheim, H. A., Offshore Petroleum Exploitation Planning by Numerical

Simulation and Optimization! Ph.D. dissertation, Department of

Petroleum Engineering, University of Texas at Austin, December,

1978.

[6] Attra, H. D. , H. B. Wise and W. M. Black, "Application of Optimizing

Techniques for Studying Field Producing Operations," Journal of

Petroleum Technology , (January 1961), pp. 82-86.

[7] Babayev, D. A., "Mathematical Models for Optimal Timing of Drilling

Multilayer Oil and Gas Fields," Management Science , Vol. 21,

No. 12, (August 1975), pp. 1361-1369.

[8] Bohannon, J. M. , "A Linear Programming Model for Optimum Development

of Multi- Reservoir Pipeline Systems," Journal of Petroleum Technology , (November 1970), pp. 1429-1436.

[9] Campbell, John M. , Oil Property Evaluation , Prentice Hall, Inc.,

Englewood Cliffs, N. J., 1959.

[10] Charnes, A. and W. W. Cooper, Management Models and Industrial Applications of Linear Programming , Vol. II, John Wiley and Sons, Inc.,

New York, 1961 , pp. 583-615.

[II] Coats, K. H., "An Approach to Locating New Wells in Heterogeneous, Gas

Producing Fields," Journal of Petroleum Technology , (May 1969)

pp. 549-558.

[12] Craft, B. C. and M. F. Hawkins, Applied Petroleum Reservoir Engineering , Prentice-Hall, Inc., Englewood Cliffs, N, J., 1959.

[13] Crichlow, H. B., Modern Reservoir Engineering: A Simulation Approach,

Prentice-Hall , Inc., Englewood Cliffs, N. J., 1977.

[14] Devine, M. D. and W. G. Lesso, "Models for Minimum Cost Development

of Offshore Oil Fields," Management Science , Vol. 18, No. 8,

(April 1972). pp. B378-B387.

291
Devine, M. D., "A Model of Minimizing the Cost of Drilling Dual

Completion Oil Wells," Management Science , Vol. 20, No. 4,

(December 1973), pp. 532-535.

Durrer, E. J. and G. E. Slater, "Optimization of Petroleum and

Natural Gas Production—A Survey," Management Science , Vol. 24,

No. 1, (September 1977), pp. 35-43.

Frair, L. and M. D. Devine, "Economic Optimization of Offshore

Petroleum Development," Management Science , Vol. 21, No. 12,

(August 1974), pp. 1370-1379.

Henderson, J. H., J. R. Dempsey, and A. D. Nelson, "Practical Application of a Two-Dimensional Numerical Model for Gas Reservoir Studies,

Journal of Petroleum Technology , (September 1967), pp. 1127-1136.

Huppler, J. D. , "Scheduling Gas Field Production for Maximum Profit,"

Society of Petroleum Engineers Journal , (June 1974), pp. 274-279.

Johnson, M. , J. W. McFarland, E. Monash and J. Lohrenz, "MER (Maximum

Efficient Rate) Using a Gas Reservoir Model with Waterflooding,"

University of California Los Alamos Scientific Laboratory, LA

6989 MS, (February 1978).

Kuller, R. G. and R. G. Cummings, "An Economic Model of Investment and

Production for Petroleum Reservoirs," American Economic Review , Vol. 64, No. 1, (March 1974), pp. 66-79.

Lasdon, L. S., A. D. Waren, A. Jain, and M. Ratner, "Design and

Testing of a Generalized Reduced Gradient Code for Nonlinear

Programming," ACM Transactions on Mathematical Software, Vol. 4,

No. 1 (March 1978), pp. 34-50.

Lasdon, L. S., A. D. Waren, and M. W. Ratner, "GRG2 User's Guide,"

October 1978.

Lilien, Gary L., "A Note on Offshore Oil Field Development Problems

and Suggested Solutions," Management Science , Vol. 20, No. 4,

(December 1973), pp. 536-539.

Lohrenz, John, and E. A. Monash, "Application of the Gas Reservoir

Per Se Model to Real Reservoirs," ARA Section Report No. 78-49,

Conservation Division, U. S. Geological Survey, September 1, 1978.

Lovejoy, W. and P. Homan, Economic Aspects of Oil Conservation Regulation , John Hopkins Press, Baltimore, 1967.

Lutes, J. L., C. P. Chiang, M. M. Brady, and R. H. Rossen, "Accelerated

Blowdown of a Strong Water Drive Gas Reservoir," Presented at the

Fall Technical Conference, Society of Petroleum Engineers, New

Orleans, October 3-6, 1979, Paper No. 6166, 19 pages.

292
McFarland, James W. "A Selected Review of Maximum Efficient Rate

(MER) and Related Resource Economics Literature," University of

California Los Alamos Scientific Laboratory, LA-6322-MS, July 1976

McFarland, J. W. , T. E. Springer, E. A. Monash and J. Lohrenz, "A

Simulation Study of MER for Gas-Water Reservoirs," University

of California Los Alamos Scientific Laboratory, LA-6866-MS, • March, 1978.

McFarland, J. W. (ed.), MER for Petroleum Reservoirs in the PCS , Symposium Proceedings, Sponsored by University of Houston Central

Campus and U. S. Department of Interior, January 29, 1979.

McFarland, J. W. , "Gas Reservoir Management: An Optimal Control Model,

CBA Working Paper No. 27, University of Houston, March 1979.

McFarland, J. W. , M. S. Parks and Anil Aggarwal , "Alternative Optimization Criteria for Production from Petroleum Reservoirs,"

University of Houston, CBA Working Paper 34, October 1979, 50 pages

McDonald, S., Petroleum Conservation in the United States , John

Hopkins Press, Baltimore, 1977.

Monash, E. A., "A Basic Mathematical Model for Determining Ultimate

Recovery vs. Rate for a Gas-Water Reservoir," SAD Section Report

No. 76-13, Conservation Division, U. S. Geological Survey,

February 1976.

Murray, J. E. Ill, and T. F. Edgar, "Optimal Scheduling of Production

and Compression in Gas Fields," Journal of Petroleum Technology , (January 1979), pp. 109-116.

Nachtshiem, C. J. and A. F. Siegel , "Modeling Hydrocarbon Reservoirs:

Parameterization, Validation and Prediction," unpublished manuscript, University of California Los Alamos Scientific Laboratory

1980, 36 pages.

O'Dell, P. M., N. W. Steubing, and J. W. Gray, "Optimization of Gas

Field Operation," Journal of Petroleum Technology , (April 1973)

pp. 419-425.

Richardson, J. G. and H. L. Stone, "A Quarter Century of Progress in

the Application of Reservoir Engineering," Journal of Petroleum

Technology , (December 1973), pp. 1371-1379.

Rosenwald, G. W. and D. W. Green, "A Method for Determining the Optimal

Location of Wells in a Reservoir Using Mixed Integer Programming,"

Society Petroleum Engineers Journal , (February 1974), pp. 44-54.

Rowan, G. and J. E. Warren, "A Systems Approach to Reservoir Engineering, Optimum Development Planning," Journal of Canadian Petroleum

Technology , (July-September 1967), pp. 84-94.

293
Schilthuis, R. J., "Active Oil and Reservoir Energy," AI ME , Vol. 18,

No. 33, (1936), pp. 25-30.

U. S. Congress, "Energy Policy and Conservation Act," Public Law

94-163, 94th Congress, S. 622, December 22, 1975.

U. S. Congress, "Outer Continental Shelf Lands Acts Amendments of

1978".

U. S. Congress, "The Department of Energy Reorganization Act

(PL 95-91) Sec. 302"

van Everdingen, A. F. and W. Hurst, "The Application of the LaPlace

Transformation to Flow Problems in Reservoirs," Transactions AIME , Vol. 186, 1949, pp. 305.

Wattenbarger, R. A., "Maximizing Seasonal Withdrawals from Gas

Storage Reservoirs, Journal of Petroleum Technology , (August 1970).

pp. 994-998.

Zaba, J. and W. T. Doherty, Practical Petroleum Engineers Handbook , Gulf Publishing Company, Houston, 5th Ed., 1970.

294
A METHODOLOGY FOR ESTIMATING OIL AND GAS PRODUCTION

SCHEDULES FOR UNDISCOVERED FIELDS

John H. Wood

Dallas Field Office

U. S. Department of Energy

Energy Information Administration

Assistant Administrator for Applied Analysis

INTRODUCTION

Oil and gas supply models disaggregated to the field level require some method of estimating the economic viability of a given size field under

various conditions. These conditions might include the price of oil and gas,

development and production costs, and regulations. Both the production costs

and income stream from a given field depend in part on the production

schedule that can be maintained. The production schedule in turn depends in

general on the size, production technique, drive mechanism, and other

physical parameters of a field. These general field parameters can be

grouped by geographic region, depth and field size.

Today, I want to concentrate on the development of production schedules for

undiscovered fields in the Permian basin. While many details are specific to

the Permian basin, many of the procedures are applicable to other regions.

This work was conducted as part of an Interagency Oil and Gas Supply Project

which, in its initial effort, performed a study of the Permian basin. More

general aspects of this study will be discussed in another paper tomorrow

morning.

BACKGROUND

Every well in every field has a unique production history and it is a difficult task to develop accurate production schedules for fields for which

reservoir parameters and drive mechanisms are reasonably well known. In this

study, the only knowledge provided by the discovery model for a field is the

depth bracket (within 5,000 feet) and the average size. Therefore, the

production schedules that were developed for future fields were based upon

the average of fields found in the past, of similar size and depth.

In the Permian basin study, field size was given in terms of barrel oil

equivalent (BOE). Gas was converted to BOE on the basis on 5.27 thousand

cubic feet of wet gas per barrel. There are 20 field size classes. The

smallest size class is from 0 to 6,000 BOE. Each class's upper limit is

double that of the previous class. The upper limit of class 20 is 3.1

billion BOE.

295
I There are four depth classes: 0-5,000, 5,000-10,000, 10,000-15,000, and

15,000-20,000 feet. However, there were no historical oil fields deeper than

15,000 feet in the Permian basin.

Three types of undiscovered fields are considered: oil fields which would

undergo secondary recovery, oil fields which would only be susceptible to

primary recovery, and non-associated gas fields. For each type of field for

each depth and class size, a production schedule was determined. Production

schedules are determined for what is considered to be the average well in

each field category. This has the advantage of ignoring the wide variations

in behavior of individual wells within a field and allowing flexibility in

the timing of field development. Field production was calculated by

multiplying well production by the number of wells in a field.

Empirically, it has been found that oil production from almost all wells

either actually declines exponentially for considerable periods of time, or that an exponential decline is a good approximation to production behavior.

It is also a very simple function to work with. Therefore, exponential

decline is used to describe the normal decline in production of all oil wells

in the Permian basin area.

To describe a production schedule for an exponentially declining oil well,

one needs to know the initial oil producing rate, QRO, the decline rate, D,

and the economic limit rate, ELR, for a well. These quantities are related

to the ultimate recovery, QWOE, by the following formula:

QWOE -. QR°

D- ELR ' (1)

where

QRO = initial oil producing rate,

ELR = economic limit rate,

D = exponential decline rate.

and

QWOE = expected ultimate oil recovery per well.

To determine the expected ultimate oil recovery per well, we first made a quick estimate of the expected ultimate recovery of every oil and gas field

in the Permian basin excluding tertiary recovery. We also estimated the

total number of wells in each field. From these data, we developed fitted

values of a nominal expected recovery per well and field for each size and

depth class. This required making estimates for 4,457 oil fields and 896 gas

fields in the Permian basin which is located in southeast New Mexico and west

Texas

The results are shown in table 1 . Note that there is a very large range in

the size classes. The expected average recovery of a class one field is

about 2,000 barrels, while a class 9 field is expected to recover about a million barrels and a class 19 field about a billion barrels.

296
Table 1. Expected Ultimate Oil

the Permian Basin

(Thousand barrels)

Recovery per Well from Primary Oil Fields in

Size Class 0-5,000 5,000-10,000 10,000-15,000

(BOE) (feet) (feet) (feet)

1 1.490 1.930 2. 160

2 4.280 4.070 4.170

3 7.580 8.670 9.590

4 11.800 15.900 18.900

5 17.300 25.900 32.400

6 24.500 39.000 50.700

7 33.800 55.100 74.100

8 45.700 74.600 103.000

9 53.300 82.900 136.000

10 54.900 118.000 198.000

11 68.900 132.000 261.000

12 95.600 140.000 333.000

13 135.000 154.000 419.000

14 188.000 189.000 526.000

15 254.000 258.000 662.000

16 334.000 374.000 834.000

17 428.000 550.000 1 ,050.000

18 536.000 802.000 1,310.000

19 658.000 1 ,140.000 1 ,630.000

20 794.000 1,580.000 2,010.000

In the 0 to 5,000-foot depth bracket, a class 20 well would be expected to

produce over 500 times as much oil as a class 1 well. A class 1 primary oil

well would be expected to produce about 1,500 barrels, a class 9 well about

53,000 barrels and a class 19 well about 658,000 barrels.

There is also a higher expected recovery per well for each class of well as the depth increases. For example, in class 9 wells the expected recovery

goes from 53,000 barrels to 83,000 barrels to 136,000 barrels respectively

for depth brackets of 0-5,000 feet, 5,000-10,000 feet and 10,000-15,000

feet. While this could be due in part to changes in the geology of fields

with depth, it is more likely that it reflects the relative economics of

drilling deep wells compared to shallow wells. It cost about two and a half

times as much to drill a well in the 5,000 to 10,000-foot depth bracket as in

the 0 to 5,000-foot depth bracket and almost six times as much in the 10,000

to 15,000-foot depth bracket. The higher costs associated with deep drilling

will always tend to push deep field development toward the minimum number of

wells necessary for complete development.

297
Decline Rates

After determining the expected ultimate oil recovery per well, QWOE, we still

have to determine the other three factors in equation one, D, ELR, and QRO.

Primary production decline rates were determined for each size and depth

category of oil fields. The decline rates are considered to be for average

wells in the average field over the life of the field. In general, decline

rates were determined from historical field production data, but there were

several factors that made this task difficult; proration of fields which

began in the late 1920's, continued drilling in old fields, changes in

production methods, changes in decline rates over the life of a field,

introduction of secondary recovery projects , wells being taken out of

production, and variations between wells in a field. In addition, variations

in the availability and quality of data led to different approaches for

determining decline rates for different categories of fields.

The smaller fields (field size classes one through three) had very short

production histories which nutde the yearly individual field data difficult to

analyze. For these three classes, the average production of all fields

discovered in a particular year was considered to be the production of an average field in that category. The decline in average production of these

fields was then calculated for several successive years. The yearly averages

were fitted to an exponential equation by the method of least squares. It was assumed that the average field was discovered at midyear and that in the

following years, the instaitaneous production rate at midyear was numerically

equal to the annual production. This procedure was followed for fields

discovered in several years and the values were averaged for each category of

field size. There was considerable scatter in the yearly results.

Exponential decline rates were calculated individually for all declining

primary fields in classes 4 through 20 for all depth brackets. The

calculations were performed by a computer program utilizing the method of

least squares on production data from 1970 through 1974. In classes 4

through 11 for the 0 to 5,000 and 5,000 to 10,000-foot depth brackets, and

for classes 4 through 20 in the 10,000 to 15,000-foot depth bracket the

average of the individual field decline rates were calculated and used. The

general result is that as fields get larger and shallower, their decline

rates get smaller. Decline rates for classes 7 through 11 in the 0 to 5,000-

foot depth bracket were averaged as were classes 7 through 9 in the 5,000 to

10,000-foot depth bracket, classes 8 through 11 and classes 12 through 20 in

the 10,000 to 15,000-foot depth bracket. This further averaging was done to

smooth the calculated decline rates for those classes.

The larger fields (classes 12 through 20) in the 0 to 5,000-foot and 5,000 to

10,000-foot depth bracket had individual estimates made on a randomly

selected sample from each category. A complete production history from 1937

or earlier, the number of wells drilled each year, number of wells producing

by artificial lift each year and the number of wells flowing each year was prepared for each field. In addition, a literature search for published

reports on these fields was made. Such factors as well top allowables,

market demand factors, reaching marginal well status, and the onset of

secondary recovery were considered. When data permitted, a number of years'

production history was fitted to an exponential decline curve by the method

of least squares.

298
The individual field rates were averaged for each field category and classes

12 through 15 in the zero foot depth bracket were averaged as were classes 12

through 14 in the 5,000 to 10,000-foot depth bracket to further smooth the

data. It was assumed that classes 16 through 20 in the 0 to 5,000-foot depth

bracket and classes 15 through 20 in the 5,000 to 10,000-foot depth bracket

would have exponential decline rates of 0.2 per year.

Considerable engineering judgment went into the selection of the years chosen

to represent the average primary production decline for a field. The larger

fields often had continuous field development, a steadily changing mix of

flowing and artifical-lift wells, a restrictive field allowable, and were

prime candidates for early secondary recovery projects. Even though there

are wide variations in decline rates among individual fields and individual

wells in a field, an exponential decline rate of 0.2 per year gives a reasonable production schedule for an average well in a large oil field.' for

example, testimony given before the Texas Railroad Commission in 1949

indicated that if the McElroy field (discovered in 1926) had been produced at

full capacity during its life, it would have been abandoned in 1953, a primary producing life of 27 years. This is in reasonable agreement with the

value of 30 years calculated for the average well in a field in that

category. Another specific example would be the Loco Hills field in New

Mexico for which a recent detailed study was available. Exponential decline

rates of four individual wells over their primary productive life had an average exponential decline rate of .204 per year.

The exponential decline rates used for the Permian basin fields are shown in

table 2. It should be noted that an exponential decline rate of one per year means that the annual production declines to 36.8 percent of the previous

year's production or a production decline of 63.2 percent per year.

Nominal Economic Limit Rate

Nominal economic limit rates were calculated and used only for determining

what the initial oil producing rate would be for a well. Once the initial

producing rate has been determined , and annual oil production is being

computed, the actual economic limit rate is computed for the well, depending

upon the price of oil and gas, and when income is equal to out-of-pocket

expenses. Table 3 shows the nominal economic limit rate for wells in the

Permian basin. These rates were calculated for each depth bracket by using

the estimated 1976 direct operating expenses for wells in each depth bracket

and assuming an oil price of $14.00 per barrel.

Initial Producing Rate for Permian Basin Wells

An initial producing rate is calculated for wells in each depth bracket and

B0E class by substituting the appropriate QWOE, D, and noninal economic limit

rate, ELRN, into the following equation:

QRO = (D) (QWOE) + ELRN. (2)

This is just equation one solved for QRO.

299
Table 2. Exponential Decline Rate per Year for Oil Wells in the Permian Basin

(Thousand barrels)

oize Class U—D , UUU D , UUU— I U , UUU 1 f\ r\r\r\ a tz nnn 1 U, UUU—

0 , UUU

( RDF ^ / -poof ^

k i ee x>

)

1 1 .50 1 .50 1 .50

2 1 .00 1.10 1.10

3 0.90 1 .00 1 .00

4 0.35 0.51 0.61

5 0.29 0.38 0.40

6 0.24 0. 34 0. 35

7

oo

n. dd U. jd n do

y

n dd n do U . id n oo U . dy

1 U (J . U.^4 c\ on U .dy

1 1

I I n do n Oil n oo U . dy

1 oI d n on U.*:U n o 1 U.^l n on U .dV

1 0 nu • d\J on n o 1 U • d I nU • d\J on

1 U n on Ui£ 1 nU . C?nv

15 0.20 0.20 0.20

16 UtCv 0 20

17 0.20 0.20 0.20

18 0.20 0.20 0.20

19 0.20 0.20 0.20

20 0.20 0.20 0.20

iaDie 3. Nominal Economic Limit Rates for Wells by Depth in tne rermian nasin

Oil Depth Bracket, Feet

Production 0-5,000 5,000-10,000 10,000-15,000

bbl/day 1.18 1.63 2. 16

bbl/year 431 594 790

In this study, it is assumed that the initial oil producing rate of a well in

a newly discovered oil field will not be allowed to exceed the Texas Railroad

Commission 1965 yardstick allowable schedule. This allowable rate takes into

consideration the depths of wells and spacing between wells. This schedule,

in effect, established the maximum rate of oil production for an oil well.

In most cases, the initial oil producing rate will be less than the maximum

allowed. The maximum rates of oil production allowed for this study for

wells in the Permian basin for the three depth brackets are shown in table 4.

300
Table 4. Maximum Oil Production, by Depth Brackets, for the Permian Basin

Oil

Production

Depth Bracket, Feet

0-5,000 5,000-10,000 10,000-15,000

bbl/day

bbl/year

84

30,660

121

44,165

365

133,225

It was assumed that these rates would represent good field production

practice or would be mandated by regulation. The rates are based on 40-acre

spacing in the 0 to 5,000 and 5,000 to 10,000-foot depth brackets and on 80-

acre spacing for the 10,000 to 15,000-foot depth bracket.

Those field size classes where wells would have initial producing rates that

exceeded the 1965 Texas yardstick allowable production rate will be held to

that rate until they have produced a sufficient quantity of oil so that they

could no longer maintain the yardstick allowable. From this time on, they

are allowed to decline at the calculated decline rate until their ELR is

reached

Example of Oil Production Schedules

Shown in figure 1 are the oil production curves for classes 10, 15, and 17,

calculated for wells in the 5,000 to 10,000-foot bracket. Note that wells of

classes 10 and 15 did not have an initial producing rate that exceeded the

Texas Railroad Commission yardstick allowable and began to decline

immediately. However, the initial producing rate for the class 17 well did

exceed the yardstick allowable and, therefore, production was constant at the

allowable rate for 7.5 years before the production decline started.

There are numerous factors that affect the production of associated and

dissolved gas from a reservoir and it is impractical to attempt to take each,

individually, into consideration. For the Permian basin, it was assumed that

the associated gas will be produced as dissolved gas, thereby resulting in a higher overall gas production per oil well. Also, because no attempt was made to predict the drive mechanisms of reservoirs to be discovered in the

future, it is assumed that dissolved gas production will be related to a depletion-type drive mechanism.

The methodology for a gas production schedule is based upon a relationship

between cumulative gas produced and cumulative oil produced. This

relationship was derived from a calculation of the Schilthius' form of the

material balance equation for depletion drive reservoirs as shown in

"Elements of Oil Reservoir Engineering" by Pirson. The production of oil and

gas for a depletion drive mechanism, as reported by Pirson, was converted to

percents of ultimate recovery and an equation relating the percent of

cumulative dissolved gas production to the cumulative oil production was developed by the method of least squares. The theoretical gas-oil ratio and

Associated Dissolved Gas Production

301
60 r10 15 20

TIME (years)

25 30

Figure 1. Oil Production Decline Curve for Primary Recovery

at 7,200 feet in the Permian Basin

gas production curves resulting from the use of this relationship were compared to actual field performance curves and the curves are similar though

not identical. Of necessity, this relationship will be used to represent

composite oil reservoirs with a wide variety of drive mechanisms in the

Permian basin. For a different basin, different assumptions would probably

be made. In an area where water drives predominate, a nearly constant gasoil ratio would be assumed.

Figure 2 shows the behavior of percent cumulative dissolved gas production as

a function of percent of cumulative oil production. As you can see, about 20

percent of the expected gas is produced when 60 percent of the oil is

produced leading to relatively low gas-oil ratios. From the 60 percent point

on, the curve increases rapidly leading to higher gas-oil ratios. This is

the type of behavior typically observed in the Permian basin.

In computing the annual gas production from oil reservoirs, the expected

ultimate gas recovery per oil well, as shown in table 5, and the expected

ultimate oil recovery per well are utilized. The percent cumulative gas

produced to the end of a year is calculated as a function of the percent

cumulative oil production, as was shown in figure 2. That is, for each year,

the cumulative oil production is determined and the percent of expected

ultimate recovery is computed. The. percent ultimate gas recovery is

determined and multiplied by the expected ultimate recovery shown in table

5. The cumulative gas production at the end of the preceding year is then

subtracted from the resulting cumulative gas production at the end of the

year under consideration. This difference will give the annual gas

production

302
PERCENT OF EXPECTED ULTIMATE OIL RECOVERY

Figure 2. Percent of Expected Ultimate Gas Recovery as a Function of

Percent of Expected Ultimate Oil Recovery in the Permian Basin

Production Schedule for Secondary Recovery Fields

Primary Phase Oil Production

Fields that are assumed to undergo secondary recovery have two distinct

production phases. They first go through a primary phase which is basically

the same as the production schedule for primary oil fields with the exception

of expected ultimate recovery per well. The expected ultimate recovery for

secondary and pressure maintenance fields per oil well that had ever produced

oil was calculated. It was assumed that 60 percent of the expected ultimate

field recovery could be produced by primary means.

In the 0 to 5, 000- foot depth bracket, only 70 percent of the total oil wells

were assumed to be drilled during the primary production phase. In the 5,000

to 10,000-foot depth bracket, the expected ultimate primary recovery per well

was 60 percent of the expected ultimate recovery because it was assumed that

all producing oil wells would be drilled during the primary development

phase. The primary phase oil production schedule was then calculated with

the same decline rates, nominal economic limit rates, and maximum oil

production rates as for primary production.

303
Table 5. Expected Ultimate Associated-Dissolved Gas Recovery per Oil Well

from Primary Fields in the Permian Basin

(Million Cubic Feet at 14.73 psia and 60° F)

Size Class

(BOE)

0-5 , 000

(feet)

5,000-10,000

(feet)

10,000-15,000

(feet)

1 1.490 4.320 7.470

2 4.740 9.210 14.400

3 9.050 20.100 32.000

4 15.200 38.400 63.000

5 24.100 65.700 110.000

6 36.500 103.000 175.000

7 53.200 153.000 261 .000

8 75. 100 216.000 371 .000

9 81 .900 266.000 506.000

10 1 1 7 . 000 327.000 657.000

11 164.000 389.000 806.000

12 223.000 453.000 1,070.000

13 293.000 518.000 1,460.000

14 374.000 584.000 1 ,960.000

15 467.000 652.000 2,580.000

16 572.000 721.000 3,320.000

17 688.000 1,080.000 4,170.000

18 816.000 1 ,570.000 5,150.000

19 955.000 2,240.000 6,240.000

20 1,110.000 3,100.000 7,450.000

Secondary Recovery Phase Oil Production

Primary oil production will continue until the annual oil production per well

is less than the stripper stage (10 barrels of oil per day). It was assumed

that a waterflood project will be initiated at the beginning of the following

year. In general, each well that produces during the waterflood will be

assigned an expected ultimate waterflood recovery, a variable fraction of

which will be produced each year during the life of the waterflood. The

specific production schedule depends on the size and depth of the field.

When the waterflood is initiated, some new oil wells may be drilled, some primary wells continue to produce, some primary wells are converted to

injectors and some new injectors may be drilled. During the first year of

the waterflood, all producing wells produce both primary production and a small amount of production that is due to the waterflood. After the first

year, the production from each well is determined entirely by the waterflood

production schedule.

It was assumed that for secondary recovery fields, 40 percent of the expected

ultimate recovery for a field would be due to a waterflood. This oil plus

the unrecovered expected ultimate primary production was divided by the

number of oil wells that produce during the waterflood stage to determine the

expected ultimate waterflood production per well.

304
The relationship between waterflood oil recovery and time is based on the

extensive work of J. D. Walters of Sun Oil Company. His empirically derived

curves were utilized to derive an equation representing the fraction of

ultimate waterflood oil recovery as a function of the fraction of expected

waterflood life. This equation was good only for fractions of expected

waterflood life less than or equal to one. However, the expected ultimate

waterflood recovery may not be reached or may be exceeded, depending on how

each assumed oil price affects the economic limit rate per well. Therefore,

the limits for life expectancy have been extended to values up to 1.5 times

the expected waterflood life. The resulting curve is shown in figure 3. The

expected waterflood life was assumed to be 10 years.

Primary Phase Associated-Dissolved Gas Production

The gas production procedure was basically the same as that for primary oil

fields. It is assumed that all the expected ultimate associated-dissolved

gas for a field would be produced if the oil wells that produce during the

primary phase were produced down to their nominal economic limit rate.

Secondary Phase Gas Production

During the secondary phase, associated-dissolved gas that is not recovered

under primary production schedules is recovered. It was assumed that wells

producing under the secondary production schedule would have a constant gasoil ratio. This ratio was determined by dividing expected ultimate

associated-dissolved gas unrecovered under primary production schedules by

the expected ultimate waterflood production of oil for each category of

field. The annual gas production per producing oil well under the secondary

production schedule was found by multiplying the annual waterflood oil

production by this gas-oil ratio. The first year that the waterflood is

initiated, gas is assumed to be produced by both the continuation of the

primary production schedule and a small increment due to the waterflood.

After the first year, gas production is assumed to result only from the

waterflood production schedule.

Economic Limit Rate

In all cases, production is assumed to cease when an economic limit rate for

production is reached. This occurs in the year in which annual operator

income equals the sum of direct annual waterflood operating expenses and the

operator's severence and ad valorem taxes. The operator is assumed to have a 7/8 working interest.

Pressure Maintenance Oil Fields

Oil Production

For depths greater than 10,000 feet, it was assumed that those fields which

undergo a production process other than primary would have a pressure

305
306
maintenance program carried out from the initial stage of development. The

oil production schedule for these pressure maintenance fields is basically

the same as the production schedule for primary fields with the exception of

the expected ultimate recovery per well. Wells in a large field would have a period of constant production and then decline to their ELR.

Associated Dissolved Gas Production

Due to the nature of pressure maintenance, it was assumed that there would be

a constant gas-oil ratio during the life of these fields. The gas-oil ratio

was found by dividing the expected ultimate associated-dissolved gas

production per well by the expected ultimate oil recovery per well. The

cumulative gas production at the end of each year was then found by

multiplying the cumulative oil production by the gas-oil ratio. Annual gas

production was found by subtracting successive cumulative gas productions.

Non-Associated Gas Production Schedule Per Well

Non-associated gas production schedules were calculated for the combined BOE

classes 1 through 4 and BOE classes 5 through 18 for each of 4 depth

brackets. The schedules were based on the average reservoir and gas

characteristics of fields in southeast New Mexico and Texas Railroad

Commission Districts 7B, 7C, 8, 8A, and part of District 1. The gas

production schedules look similar to the oil production schedules, but they

are calculated in a different manner. The oil fields made use of empirically

determined decline rates while the gas field production schedules were based

on equations which relate the average physical parameters of the fields. As

with oil fields, the expected recovery per field, and number of wells per

field for each size class and depth bracket along with gas in place were estimated

A gas deliverability schedule was then calculated for each category of field

by utilizing a computer program, which made use of the material balance

equation with zero water influx and the back-pressure equation. The computer

program required as input data the field gas in place, number of wells, gas

gravity, absolute open flow rates, back-pressure equation slope, reservoir

pressures, and gas production. Most of these data weie obtained from a purchased computer tape which contained data obtained from state files that

had already been manipulated into a suitable format.

The gas deliverability schedule for the representative well in a field was

found by dividing the field gas deliverability by the number of wells in the

field. It was assumed that the initial production rate for each of the

larger fields would be limited to a daily contract quantity (DCQ) of

approximately one million standard cubic feet/day for every 3 billion

standard cubic feet of reserves.

The representative well for each category of field would than produce at this

initial production rate until the breaking point (the time at which the well

could no longer maintain the initial production rate) was reached. In

classes 1 through 9, the well production capacity was extremely large for the

amount of gas in place. For this reason, the representative wells in these

307
classes were scheduled at a greater initial production rate which was obtained from a curve of BOE class size versus the initial producing rate for

the larger classes.

After the annual breaking point was reached, the annual production predicted

by the deliverability program was fit by an exponential decline curve. This was done to provide a convenient analytical form for production schedules.

Figure 4 shows a production schedule for a well in BOE class 13 in the 0 to

5,000-foot depth bracket. The gas production from a well in this category

was assumed to remain constant for about 6 years at a rate of 254 million

standard cubic feet per year and then decline exponentially with a decline

rate of 0.305 per year until it reached an economic limit rate (the

production rate where the operator's income is equal to operating expenses).

As with oil field production schedules, the initial production rates and

recovery per well increased for larger and deeper fields.

500 rFigure 4,

15

TIME (years)

Non-associated Gas Well Production Curve for a Class 13

Field in the 0-5,000 foot Depth Bracket for the

Permian Basin

DISCUSSION

Question: Have you looked at "any data in terms of the economics of

different gathering line pressures?

Dr. Wood: There was an assumed cut-off pressure. The pressure was built

into the analysis for gas production curves.

308
Question: Can you tell me how you derived your equation one?

Dr. Wood:

equation

That is an intergral of an exponential production decline

Q (QRO)e-Dt

where

Q production rate.

The integral of Q with respect to time yeilds equation one.

Question: Wouldn't you get another exponential?

Dr. Wood: Yes, but you recall that the economic limit rate is, in fact,

an exponential equation. You know it is a function which declines with time

and what we did there was pick a production rate which was non-economical.

You know that is the rate at which the operator income was equal to operating

expenses, at an oil price of $14.00 per barrel. And then as the model was

run, different prices were put into the model, and a different set of

economic limit rates was calculated.

So, again, back to your question, that economic limit rate is in general

an exponential function, but it declines each year, and when you talk about

the expected recovery, you have to pick a point at which production will

terminate. And the point we picked was the point where production will just

meet the operating expenses.

Mr. Brashear (Lewin & Associates): John, I appreciate your work and we have used it a number of times, that and your offshore stuff too. You

assumed that the gas-oil ratio, in the primary period of production was essentially a depletion type drive. Some of those then go on into a waterflood, and you get a standard gas-oil ratio. That all makes sense to me.

The fields that don't have a secondary flood, though, I am wondering if

there is not an inconsistency there for those fields that never are slated to

go to secondary, if that shouldn't be a standard gas-oil ratio, as the most

likely case.

Dr. Wood: That is something one well might want to consider doing. There

are other reasons why a waterflood is not put in. Well, I might just drop it

at that. If one had, that those fields which were always eliminated or eliminated primarily because they had a water drive, then one might want to

use a constant gas-oil ratio.

Mr. Brashear: I guess that is kind of my question. Do you have any feel

for whether they are just too tight, too fractured, whatever?

Dr. Wood: In the deeper categories, they might have started tending more

toward water drive fields. In the others, there was a variety of reasons why

it wasn't done.

309
SOME MODERN NOTIONS ON OIL AND GAS RESERVOIR PRODUCTION REGULATION

John Lohrenz and Ellis A. Monash *

ABSTRACT

The historic rhetoric of oil and gas reservoir production regulations

has been burdened with misconceptions. One was that most reservoirs are rate insensitive. Another was that a reservoir's decline is primarily a function of reservoir mechanism rather than a choice unconstrained by the

laws of physics. Relieved of old notions like these, we introduce some modern notions, the most basic being that production regulation should

have the purpose of obtaining the highest value from production per irreversible diminution of thermodynamically available energy. The laws of

thermodynamics determine the available energy. What then is value? Value

may include contributions other than production per se and purely monetary

economic outcomes.

"The Fable of the Jones-Smith Apple Orchard"

Jones and Smith got some land as equal partners for the purposes of

developing an apple orchard. However, before starting to develop the apple

orchard, they learned they had a difference of opinion as to how to proceed.

Jones said he loved to eat apples, his family loved to eat apples, and

all his friends just loved apples. Jones wanted to keep his family, friends,

and himself well-supplied with apples. And Jones felt the more apples he got

from the apple orchard for his family and friends and for himself, the more

successful the apple orchard would be.

Smith said that was hogwash. If he wanted an apple for himself or family or friends, he would buy one. All Smith said he wanted out of the

apple orchard was some money to take home after all the apples were sold.

And then he could use that money to buy apples or anything else that pleased

him. And Smith felt that the more money he got to take home from the apple

orchard, the more successful the apple orchard would be.

So Jones and Smith argued and argued until, since this is a fable, they

agreed on a precise definition of how to count being successful with their

apple orchard. And they proceeded with the development of their apple orchard

only to learn they had yet another difference of opinion.

Jones preferred a special kind of little, red apple which was very tangy

and tasty. And in that part of their definition how to count being successful

that involved bushels of apples, he was going to include only those little,

red apples which were tangy and tasty. Smith said to wait just a damn minute!

An apple was an apple, Smith averred, regardless of how tasty or tangy it was,

whether someone ate it or baked it, or if it was red or yellow. But, an apple

was good only if someone bought it. And Smith said that under their definition

of how to count being successful with their apple orchard, all other things

being equal, they should grow apples which make more bushels.

Now Jones became livid at Smith and his position. Jones recalled that

Smith intended to give the unsaleable apples from the orchard to Smith's

*Geological Survey, U. S. Department of Interior, Denver, Colorado

310
brother who ran a hog farm. Smith's brother would feed these rotten apples to

his hogs because, according to Smith, they had no value and would have to be

gotten rid of anyhow. Jones said that if those rotten apples have a use, and

your brother does wish to use them, then they have value and should be counted

as money to take home—and included in our definition of how successful we are

whether you get actual money for them or not.

So Jones and Smith argued and argued some more until, since this is a fable

they agreed on the details of what should and should not be included in their

definition of how success in the apple orchard should be counted. And they proceeded with the development of their apple orchard only to learn they had yet

another difference of opinion.

Jones wanted to purchase an expensive species of apple tree for their

orchard because this species was hardy and could withstand the occasional plagues

of diseases and insects and very severe frosts. Jones said that way the apple

orchard would still be there for his children, grandchildren, great great-grandchildren, etc.

Smith was aghast at that notion. Smith said neither he nor Jones would be

around when their great- and greater-grandchildren were about and that it was unreasonable to worry about them now. Maybe they wouldn't even want apples or money from apples. So, Smith said, let them fend for themselves in their time

as we must in our time. Smith said they should get some decent, less expensive

trees while taking some reasonable chances with the diseases, insects, and frosts

the next few years. And let our succeeding generations take care of themselves

as it is presumptuous for us to even think we can.

So again Jones and Smith argued and argued until, since this is a fable, they

agreed on what species of tree to buy. And they proceeded with the development of

their apple orchard only to learn they had yet another difference of opinion.

Smith wanted to plant the apple trees very close together and fertilize them

heavily. In this way, they would get a lot more apples and money to take home

and, thus, be even more successful according to their previously agreed upon

definition of how to count success.

Jones was pained at this notion. He said that it would be exceedingly

troublesome to work around those closely planted trees and hauling all that

fertilizer. Jones said it just wasn't worth all that trouble they would have

to be that little bit more successful.

So again Jones and Smith argued and argued until, since this is a fable, they

agreed precisely on the spacing of the trees and amount of fertilization that made

the trouble balance out with the success. And they proceeded with the development

of their apple orchard.

Now, during the development and life of the apple orchard, Smith and Jones

had many other differences of opinion just as these four. But, since this is a fable, Jones and Smith quickly resolved all their differences of opinion with an agreement on the policy to apply to their apple orchard. Therefore, they always

agreed on and had defined the quantitative objectives of their apple orchard

business and did not deviate from those objectives—as this is a fable.

Thus, Smith, Jones, and the apple orchard lived most amicably and happily

not ever after—but throughout the planning horizon of this fable and because this

is a fable. *****

311
To put that fable in perspective, given our subject, the production

regulation of oil and gas reservoirs, we consider a hypothetical situation

and some questions:

Suppose we discovered a huge oil and gas reservoir in this nation

so huge that it's production could free us of worries about oil and

gas shortages for, at least, a generation or longer. What should we do with that reservoir? How should we produce it? How fast?

Should we produce it at all?

It is a safe prediction that if_ that huge oil and gas reservoir did exist

today, there would be arguments regarding how to answer the question. Some

would be pleased with the existence of such a reservoir; among this group

there would be arguments about how fast and exactly how to produce the

reservoir. Some among this group might even argue that the best way to

"produce" the reservoir is not to produce it at all, to "save" the reservoir

for some future purposes. Yet others might be displeased with the existence

of the reservoir at all. Perhaps, the reservoir's production would interfere

with goals and purposes they believe of greater importance. Just like the

bickering of Smith and Jones regarding the development of their apple orchard,

there would be bickering regarding the development of this huge hypothetical

reservoir. In fact, the only reason the story of the apple orchard is a fable

is that Smith and Jones quickly and neatly arbitrated their arguments. The

arguments regarding the apple orchard have the exact analogy in the plethora

of arguments that would rage regarding the huge oil and "gas reservoir. But,

in the real world, the rapid and neat resolution of all these arguments yielding

a decision for action is not so realistic an expectation.

The reason seems clear. In these arguments, basic cultural value judgments are exposed to harsh lights. To the extent that we disagree in these

basic, even moral, judgments, we will likely disagree about what to do with

a huge oil and gas reservoir. We might even disagree whether such a reservoir

is good or bad. And we will continue to disagree as long as we do not share

a common cultural value assessment regarding what, for example, we do and do

not owe succeeding generations. Given disagreement over such fundamental

judgments, true agreement is impossible and, even, rational bargaining to some concensus position is slow and difficult.

While the huge oil and gas reservoir is hypothetical, the thousands of

smaller oil and gas reservoirs of the past, present, and likely future are

not. For each of the past reservoirs, somehow the questions regarding

whether and how the reservoir should be produced were answered. For each

of the current reservoirs the questions are being answered and, no doubt,

will be for reservoirs yet to be discovered. The business of oil and gas

production regulation is answering these questions for the thousands of real

oil and gas reservoirs.

We have already noted that for the non-existent huge oil and gas reservoir,

the arguments involved in answering the questions regarding its production

would center on fundamental cultural values and, therefore, would not be prone

to quick resolution. Yet, these same arguments portend for the thousands of

real, smaller reservoirs. The answers, right or wrong, to the questions

regarding how to produce these reservoirs have been and are being made. The

questions are answered for real oil and gas reservoirs one way or another.

312
No doubt, the difficulty or, even, impossibility reasonably conjectured about

the difficulty of getting the production regulation questions answered for

the imaginary huge oil and gas reservoir are also imaginary. If we had a real, huge oil and gas reservoir, as with ^smaller reservoirs, the production

regulation questions would be answered with reasonable dispatch just as with

all other reservoirs. As these questions are answered, we do have production

regulation whether we want to or not. We cannot avoid having production regulation. Somehow, we answer the questions regarding how oil and gas reservoirs

should be produced. Let no one be misled into thinking that answering the

production regulation questions can be avoided. One can transfer the responsibility for the answers to some other place, but the answers are and will be

made. The answers are and will be made either articulately or not, either

with knowledge of choices or not, either with informed judgment or fiat.

The next Section, OIL AND GAS RESERVOIR PRODUCTION: PAST AND PRESENT,

briefly reviews the past history. In effect, to address the modem notions

of production regulations, we find we must dismiss some of the past and

present and return to first principles. This we do in the Section, THE PRODUCTION RATE DECISION IN THE MOST SIMPLE FORM. Here, we consider the problem

of what rate to produce an oil and gas reservoir in the most simple form we

could contrive and yet show the basic technical issues. Thereby, we unmask

some issues in the past history which do not turn out to be meaningful. Real

reservoirs need not and, indeed, do not follow the simple form reservoir.

The Section, PRODUCTION RATE DECISIONS FOR REAL OIL AND GAS RESERVOIRS, shows

how, for real reservoirs, the problem can become much more complex than for

the simple form reservoir; nonetheless, the underlying heuristics of the

production regulation and rate decisions are exactly the same. Where previously we have adhered to the old notions of production regulations and

rates which implicitly assume only recovery and economic outcomes can be

involved in the decision, we expand the potential decision algebra in the

Section, THE THERMODYNAMIC NOTION OF OIL AND GAS RESERVOIR PRODUCTION. Here, we show that how we define value obtained from oil and gas reservoir production may be defined considering not only production and economic contributions to value, but any other contributions such as strategic and intergenerational values. We conclude that the real purpose of production regulations is to obtain the highest value, however defined, per expenditure of

the only irreversible quantity that is expended when producing a reservoir.

That expenditure is thermodynamically available energy. The final Section,

CONCLUDING REMARKS, summarizes to what extent we attained our purposes.

Throughout, our purposes are to delineate the arguments regarding production control based upon what we "know" about the laws of physics unburdened

by past traditions and even myths. We shall not make choices, but we shall

point to alternatives as clearly as we can. We hope to make the answers that

will be made regarding the production regulations more articulate, more the

result of knowledgeable choices and informed judgments.

OIL AND GAS RESERVOIR PRODUCTION REGULATION: PAST AND PRESENT

The history of oil and gas reservoir production regulation is long and

so is the literature treating the subject^*. Unresolved controversies permeate

the literature. There is controversy over the inclusion of economics in the

public policy production regulations. Some have said it has not been included.

*Numerical superscripts refer to notes following the main body.

313
Others agree, but are aghast at the omission. Those who would include

economics argue about how it should properly be considered. The objective

that production regulation policies should restrict avoidable waste triggered long-standing controversies regarding what constitutes waste. Is

waste physical or economic or both? The one thing we do know about that

question is that it has been the wellspring of much rhetoric.

The extant Federal laws relating to oil and gas reservoir production

regulation are the Energy Policy and Conservation Act of 1975 (Public Law

94-163, Dec. 22, 1975) which invoked a Maximum Efficient Rate (MER) and the

Outer Continental Shelf Lands Act of 1978 (Public Law 95-372, Sept. 18, 1978)

which defines a Maximum Attainable Rate (MAR) . The definition in the Act of

the MER is:

" the maximum rate of production of crude oil or natural gas, or both, which may be sustained without loss of ultimate' recovery

of crude oil and natural gas, or both, under sound engineering and

economic principles."

The MAR is defined in its Act as:

" the maximum rate of production of crude oil and natural gas

which may be produced under actual operating conditions without

loss of ultimate recovery of crude oil and natural gas."

The definitions of these Acts leave some rather horrendous concepts undefined.

Does a sustained maximum rate of production imply a constant rate? How

ultimate is the ultimate in ultimate recovery? What are "sound engineering

and economic principles?" What are their opposites? What are actual operating conditions? Certainly, there is enough vagueness, enough ambivalency

in those definitions so that no equally expert practitioners in reservoir

management will necessarily arrive at the same MER or MAR rate (or rates)

or even nearly so. That is true even if the practitioners agree on all

pertinent reservoir properties and economic parameters. There is no quantitative stipulation of what, exactly, is maximized by operating at the

MER or MAR and no indication of what is lost or not. What McFarland (1976)

concluded with regard to MER is still true and applies to MAR as well.

He wrote: —"It appears that MER has actually been utilized to mean different

things to different people. The use of MER as a regulatory tool

also appears to have been very imprecise with considerable variability

in its implementation." (p. 19)

Our title presages some modern notions of oil and gas reservoir production

regulation. Given the vague and non-quantitative nature of the past and current

production regulations, one is, we think, well disposed to forget, at least for

the moment, the past and what is current in the "arts" and return to first and

basic questions, those being the questions already phrased in the introductory

Section. Given one has a reservoir, of all of the ways and rates it could be

produced, how should it be produced? How fast? Those are the basic questions

314
of the business of production regulation and we shall endeavor to treat them

directly paying only a modest, as seems fitting, obeisance to the past history

of production regulation in this Section.

THE PRODUCTION RATE DECISION IN THE MOST SIMPLE FORM

Given an oil and gas reservoir, how does the decision with regard to

what rates shall be produced proceed? Subject to any enforced production

regulations how does the reservoir operator decide at what rates to produce?

We consider, here, a most simple form of this production rate decision problem.

Suppose we have a known producible reserve of Q°° that will be produced

at an exponentially declining rate. Thus, the rate, q, at any time, t, is

given by Eq. (1)

-Dt

q

=

q

ie (1)

where q^ is the rate at t=0 and D is the rate of decline in reciprocal time.

Q°° is the integral of q from t»0 to °°:

00 I qdt = I q

4 Q = | qdt = | q.ee "dt« = —± (2)

0 0

Note the meaning of Eq. (2) which is depicted on Figure 1. If we produce to

infinite time, we will obtain the entire producible reserve, Q

00

. The only

choice we have with regard to producing this reservoir is the rate of decline,

D. Figure 1 shows three possible choices for D or, more specifically, l/D of

10, 20, and 50 years. Consistent with Eq. (2), the areas under all three curves of q versus t extended to infinite time are equal. But, if q-^ is

higher, then D must also be higher and l/D lower, i.e., by setting q i} we

set the rate of decline, D.

Assume the development costs we incur to start production, V-p, are directly

proportional to the production rate at time t=0 such that:

Here, p is the unit selling price of the producible reserve, say in dollars

per barrel, Cp is a constant of proportionality, and is an adjustment

factor for payments and credits resulting from direct development costs.

These may be due to taxes and leasing contracts which, for example, involve

profit sharing. If there are no taxes or other payments or credits affecting

direct development costs, then XD

=1. Substituting Eq. (2) into Eq. (3):

V

D

= VPDX

D

< 4 >

Further, in this most simple problem, assume that all development costs are incurred as a lump sum when t=0 at which time production starts. (This is a simplifying assumption, but not a limiting one for any costs incurred over a period of time can be lumped to an effective cost incurred at a specific time.)

315
3

Q

o

a.

^

z W UJ

w >

O uj

OC DC

O

D

= 50

I 0 10 20 30

YEARS

40 50

Figure 1

Three Exponentially Declining Production

Rate Profiles with the Same Producible

Reserves, (f

30

316
Having considered the development costs, we now consider the net revenue

being produced per unit time, vr, which is:

vR

= [(1 - r - c

Q

) qp - C

Q

] ^ (5)

Here, r is the fractional rate at which royalty is assessed on the gross value

of production, cq is a constant of proportionality relating operating costs

that depend on the amount of value of production, Cq represents the fixed

operating costs that do not depend on the amount of production, but would

cease only if there were no production, and Xr (analagously to XD ) adjusts

for payments and credits that result from the direct net revenue. Substituting

Eqs. (1) and (2) into Eq. (5) yields:

oo —T)t vR

= [(1 - r - co

) Q P e - C

Q

] X

R (6)

00 The aggregated potential net revenue from the production of Q of

producible reserves in the period from t=0 through t=°° is the integral of

vr over the same time period. However, let us assume an operator averse to

losing money out of pocket, i.e., operating with a negative vr, and not

constrained to continue production beyond that point. At that point the

so called "economic limit" where the marginal rate of return becomes negative

occurs. At that time, A : e

(1 - r - c

0

)Q°°Dpe"

DA

e = C

Q

(7)

Solving Eq. (7) for A , yields:

e

1 , I c

o A

e " " t l» (i- (1 - r -\) Q*- 1 (8 >

Figure 2 graphs Ae versus 1/D with [CQ/(l-r-C0)Q°°p] as a parameter. Note

that when there are no fixed operating costs (Cq=0) , Ae = °°. Figure 2 also

shows that Ae increases with 1/D until some maximum is reached after which

Ae decreases with 1/D until some point where 1/D is equal to the reciprocal

of the parameter, [Cq/ (l-r-co)Q°°p] , and Ae=0 again, where the project would

just break even considering operating costs, but not "pay back" any development costs.

00 Of course, if Ae < 00

, then the actual reserves produced, Q < Q . Substituting Eq. (2) into Eq. (1) and integrating from 0 to Ae as defined by Eq. (8), one finds:

°J. (l-r-c

0

)Q°° P ^ }

Eq. (9) defines the fraction of actua} reserves produced of^the reserves that

would be produced if production were maintained to t=°°, Q/Q , as a function of

the rate of decline, D, and the parameter, [Cq/ (l-r-CQ)Q°°p] . Figure 3 graphs

Eq. (9) showing Q/Q°° is a straight line function of 1/D with [C

Q

/ (l-r-c 0

)Q°°p] as a parameter. Note that Q/Q°° = 1 only when there are no fixed operating costs,

317
100

1/D, YEARS

Figure 2

The Time After Production Starts When the Economic Limit

Occurs as a Function of the Rate of Exponential

Decline with the Fixed Operating Cost

Parameter

318
0

.005

Co

(1-r-c o

)Q~p=:01

J L I I

I L

100

1/D, YEARS

Figure 3

The Ratio of the Reserves Recovered at Economic Limit to Infinite

Time as a Function of the Rate of Exponential Decline with the

Fixed Operating Cost Parameter

319
i.e., Cq=0. Otherwise, the difference between the amount of reserves which

could have been produced until t=°° and would be produced until t=Ae increases

as the parameter, [Cq/ (l-r-CQ)Q°°p] increases and as 1/D increases. The higher

the initial rate of production, qi} the higher t$at decline rate, D (according

to Eq. (2)), but the greater the proportion of reserves, Q°°, that will be produced before t=Ae

. As a specific example, if the parameter, [CQ/(l-r-CQ) Q°°p] = 0.01 and the decline rate, D=0.10, then according to Eq. (9) and Figure 3,

Q/Q°° - 0.9. Only 10 percent of the reserves that could have been produced

until t=°° were lost by ceasing production where the economic limit is reached

when t=Ae with Ae = 23 years from Eq. (8) and Figure 3. Where the "loss" of

10 percent of the possible production may be acceptable, consider what happens

with a slower decline rate, say D=0.02 and the same parameter, [Cq/ (l-r-CQ)Q°°p]

Here, Ae =35 years; the time to reach economic limit has increased. However,

Q/Q00 = 0.5; the amount of production that would actually be obtained from the same source, Q

00

, if produced until t=Ae , has decreased. In other words, in

the latter case with the lower rate of decline, production would be maintained

over a longer period of time, but, overall, less production would be obtained

over the longer production period compared to the former case with a higher

rate of decline. And, where a 10 percent "loss" might be acceptable, a 50

percent "loss" is certainly less so. All this impinges on a technical point,

frequently misunderstood, about the relationship between rates of production

and ultimate recoveries from oil and gas reservoirs which we shall return to

again.

The total potential present value of future profit, V^, of producing the reserves Q of the producible reserves that could be produced until t=°°, Q°°, is

the difference between the development cost, Vp, (Eq. (4)) and the net revenues,

v^, integrated from t»0 to Ae

: /eA

[(1 - r - c 0

) (fDpe

" Dt

- C

0 ]XR

e _lt

dt. (10)

0

Note in Eq. (10), the term e

^ t has been added in the integral of vR

. Here, i

is the investor's discount factor, i.e., that fractional rate at which the

investor discounts a present dollar compared to a future dollar. When i=0,

the investor has the luxury of not caring when a dollar is spent or received

while, of course, still preferring to receive rather than spend. Since development costs are, in this most simple problem, all deemed to occur when t=0 where

e-lt=l, discounting of development costs is moot. The total potential profit,

includes the superscript, d, to indicate Eq. (10) yields a value discounted

at the rate, i, such that when i=0, V^=V where V is the undiscounted total

potential profit.

Substituting Eq. (8) into Eq. (10) and integrating yields:

oo - (D+i) A . „ (1 " r - c Q

) Q p DX

R

(1-e e)

V = - C Q p DX +

D y F D D+i

C

0

X

R

( 1 ~e_1Ae ) (ID

320
Figure 4 shows characteristic curves described by Eq. (11) of Vd versus 1/D

with the discount factor, i, as a parameter. Note the locus of the maxima

of V"d with respect to i. Maxima exist for positive in the range from i=0

to some i= imax at which the maximum in the V" versus l/D curve occurs just

where V

d=0; imax is generally called the internal rate of return.

An investor who can and who does select the initial rate of production,

q-^, and, therefore, D, in such a way as to maximize V

d is a present value of

future profit maximizer. In other words, such an investor would, either

explicitly or implicitly according to an unseen hand posited by Adam Smith,

look at a curve like that on Figure 4 for the economic parameters and discount

rate deemed appropriate and choose that decline rate which maximizes V

d . If

the investor's discount rate is greater than imax> this investor will forgo

the project. This investor's present value of future profit maximizing choices

can be found by differentiating Eq. (11) to find (dV^/dD), setting the derivative equal to zero, yielding a relation defining this investor's optimum

selection of D which we will call D°:

dyf " C

D

X

D dD

(Du + i) In

(1 "

r "

C 0 )X

R

( ?) ((l-r-c A7

(D° + i)

2 + i

Q P

D°+i

(12)

Note that Eq. (12) really describes a function, 4>> in 4 parameters as follows:

0 = <}> (D , i

,

C

D

X

D

(1 - r " C o )XR

' O-r-c

0 ) Q-p

(13)

Eq. (13) simply states that D° is completely defined given the discount factor

i and the dimensionless parameters, [C^Xp/ (l-r-CQ)XR ] and [Co/(l-r-co)Q°°p]

Consider these dimensionless parameters. The first is a ratio of the development costs with adjustments for taxes and other affected payments and credits

required to get an annual dollar of revenue net of royalty and productionproportional operating costs similarly adjusted^. The second is the ratio of

the annual fixed operating costs that are not production-dependent and would

cease if production stopped to the revenue net of royalty and productionproportional operating costs that would be obtained if Q

00 were produced.

We call [CDXD

/ (l-r-CQ)XR] the development-revenue ratio and [Cq/ (l-r-c0

)Q°°p]

the fixed operating cost-revenue ratio. The analogy of these dimensionless

numbers to those used in engineering like the Reynolds number for the ratio

of inertial to viscous forces if fluid flow is entirely apt. These are dimensionless numbers ratioing economic forces. For notational brevity, we will set [CDXD /(l-r-c0 )XR ] = N

dr and [C0 / (l-r-c0 )Q°°P ] = N

Qr .

Past and current values based on prevailing policies of N^ have been

estimated to be around 2^. Figure 5 presents solutions for D° versus i with

N(j r=2 and Nor at parametric values of 0, 0.01, and 0.02. Figure 5 shows

that a present value of future profit maximizer with a discount factor in

321
Characteristic Curves of the Present Value of Future

Profits Versus the Reciprocal Rate of Decline

with the Discount Factor as a Parameter

322
20

CO

<

111

>

a* 10 Q

N„r=0 r 'max;Nor"-0 1

N or=.02

Nor =.02

0

.2 .3 .4 .5

i, FRACTION

Figure 5

A Present Value of Profit Maximizing Operator's Selections of

the Decline Rate as a Function of the Discount Fadtor

with the Fixed Operating Cost Parameter

323
the range between about 0.10 and 0.25 would select a value of 1/D° from

about 7 to 10 varying only slightly with Nor . This is equivalent to a D°

,

the selected decline rate, of .10 to .14. Actual decline rates on aggregated

Federal offshore oil and gas production have been calculated as 0.13 for

liquid and 0.09 for gas (Lohrenz, Dunham, and Tomlinson, 1979) in good

agreement. Certainly, the agreement is within the range of uncertainties

about the exact economic parameters and the simplifications introduced by

this most simple model.

Does this agreement mean that the actual production regulation policy

however stated and implemented—was to produce at those rates which maximized

the present value of future profits? There can be no definitive answer;

however, the results using this most simple problem are consistent with such

a conjecture.

What the results from analyzing this most simple problem show is the

speciousness of two notions sometimes adduced in the matter of production

regulation. The first specious notion is that the decline rate of an oil and

gas reservoir is determined by the mechanisms of the reservoir. Obviously,

as we have just shown, this is not so. How fast the reservoir declines, how

fast it produces are selections, realized or not, made by the operator within

any prior production regulations enforced. The laws of physics do not constrain

the operator's decision. The laws of physics would allow any selection of rates

up to those approaching infinity. The particular mechanism of the reservoir

affects the economics of the particular reservoir or, in the format of this

most simple problem, the values of Cd, cq» and Cq. But, these do not determine

the decline rate, but merely influence its magnitude given some optimum objective

such as the maximization of the present value of future profits.

A second specious notion is implicit in the assertion that there are reservoirs, some say many, which are rate insensitive, i.e., the ultimate

recoveries from these reservoirs are invariant with the rates at which they

are produced. For these reservoirs, the assertion continues, production

regulation is moot since one will obtain the same ultimate recovery regardless

of what rate that production is obtained. Analysis of the most simple problem

and, particularly, Eq. (9) and Figure 3 show what is wrong with that assertion.

Here we are dealing with a source that is truly rate insensitive when produced

to infinite time and thermodynamic exhaustion. The most simple kinds of

reservoirs, those involving only an expansion in-place mechanism sometimes

called a solution-gas or depletion drive, actually are rate insensitive when

produced to thermodynamic exhaustion. But, reservoirs which are rate insensitive when produced to thermodynamic exhaustion are not rate insensitive when

production ceases at some time prior to thermodynamic exhaustion, prior to

infinite time. All reservoirs produced to some state less than thermodynamic

exhaustion are rate sensitive . Of course, the production of a reservoir to

thermodynamic exhaustion is a hypothetical notion; real reservoirs are always

produced only to some prior state. Therefore, all real reservoirs are rate

sensitive . Thus, the realm of production regulation is not the least limited

by being constrained only to reservoirs which are rate-sensitive.

We see, then, that production regulation would be an issue even for any

reservoir which actually followed every assumption inherent in the most simple

form problem with which we have just dealt. What happens when the assumptions

are challenged by real reservoirs? This is the question considered in the next

Section in which we show that real reservoirs and their development decisions

are essentially variations, albeit with added complexities, of the theme

provided by this most simple form problem.

324
PRODUCTION RATE DECISIONS FOR REAL OIL AND GAS RESERVOIRS

Let us enumerate the differences between the oil and gas reservoir development-production scenario treated in the most simple form of the production rate

decisions problem of the previous Section and real reservoirs.

First, real reservoirs are rate sensitive. The ultimate recovery of real

reservoirs when produced to thermodynamic exhaustion, as well as to some prior

limit such as an economic limit, may depend on the rates at which the production

is obtained. From a reservoir viewpoint, there are two mechanisms^ which make

a reservoir rate-sensitive:

(1) Influx of water from an adjacent aquifer with entrapment of

hydrocarbons behind the invading water. The effect is that,

ceteris paribus , ultimate recovery is increased by producing

faster. Faster production prevents the invading wafer from

occluding more hydrocarbons.

(2) A time-dependent segregation between the liquid and gas in

the reservoir whereby gas evolved migrates to a gas cap.

The effect is that, ceteris paribus , ultimate recovery is

increased by producing slower. The slower production gives

more time for the gas to migrate into the gas cap.

When both effects are present, water influx with ^ultimate recovery increased

by faster withdrawals of hydrocarbons and time-dependent segregation with the

opposite effect on ultimate recovery, then a physical maximum of ultimate

recovery obtained at thermodynamic exhaustion occurs with respect to rates.

The two mechanisms cited are overall reservoir mechanisms prevailing in

reservoirs which are homogeneous with respect to pressure as well as heterogeneous. The potential mechanisms which affect ultimate recovery because of

pressure heterogeneities in reservoirs are profuse and preponderantly occupy

the lore of reservoir engineering. These heterogeneities occur because

reservoir withdrawals must be made, of course, through wells, i.e., discrete

apertures in the reservoir rock matrix. The fluid flow patterns through the

rock, which has heterogeneous properties itself, to the apertures can only

be maintained with a pressure difference thereby invoking the rule, no producing reservoir is pressure homogeneous. In effect, by assuming a reservoir is pressure homogeneous, the assumption is that all wells are "perfectly" drilled, i.e., drilled and operated in such a way as not to

disturb the assumption that the reservoir can be considered homogeneous

with respect to pressure. The point is that wells and the pressure heterogeneities they cause, while adding complexity to the mechanisms in a real

reservoir, simply perturb the overall reservoir mechanisms. These complicating perturbations can be modeled by the more complex models commonly

available and usually are. Of course, to be cost-effective, one should

justify that the cost of a more complex form of a model is really justified

by the reservoir data at hand. The production rate decision can proceed

either by assuming pressure homogeneity/ and that all wells can be drilled

"perfectly" or considering pressure heterogeneity which is, after all, only

a more complicated variant of the pressure homogeneous assumption.

325
Either way, for each detailed development scheme, ultimate recovery to

thermodynamic exhaustion versus rate parameter functions exist. The rate

parameters may take various forms such as initial or peak production rates

,

well density, or, for enhanced recovery schemes, amounts or proportions of

fluids injected. These functions can be developed given the appropriate

physical reservoir data and model. Similar functions can be developed for

ultimate recovery to cutoffs prior to thermodynamic exhaustion; these ultimate

recoveries will necessarily be less than or, as a limit, equal to the recoveries

to thermodynamic exhaustion.

What are the forms of these functions? The literature of production regulation is full of hypothesized forms almost entirely without quantitative analysis

in support. Figure 6 shows some that have been given. All these forms of the

function of the ultimate recovery, presumed to be Q rather than Q°°, versus the

rate or, more properly, a rate parameter have been advanced as a basis upon

which to assess production regulations. Of these, only the one given by Carlson

(1975) has some quantitative analysis in support^.

What are ultimate recovery versus rate functions really like? Figures 7 through 10 show some^. Here we consider the case of an oil and gas reservoir

which is drilled up in order to attain some initial rate of production, q-^.

After production starts, no further drilling is done. Production declines

proportional to the reservoir pressure. If production is allowed to continue

until the reservoir pressure in the reservoir is zero (or all of the hydrocarbons in the reservoir not occluded by invading water disappear) , the ultimate

recovery is Q°° depicted by the top curve on Figures 7 through 10. Below the curve for Q

00 versus q^ on each of Figures 7 through 10, lie the curves of Q versu; q^ parametric in the cutoff production rate. The cutoff rate is that q^

for which Q=0. Figures 7 through 10 show Q°° and Q through two orders of magniture of q^ on a logarithmic abscissa.

Figure 7 depicts a reservoir solely under a hydrocarbon fluid expansiontype drive with no water drive and no time-dependent segregation. Q

00 is constant

for all q^; yet Q varies with q^. Figure 7 graphically reinforces what we have

concluded earlier—that reservoirs which are insensitive to rate with respect

to Q°° are rate sensitive with respect to Q.

A reservoir with a water drive with entrapment behind invading water is

shown on Figure 8. Note that faster production uniformly increases Q , the

faster the more so. Faster production "gets" reserves before they are entrapped

behind invading water.

The effect of a reservoir with a time-dependent segregation effect superimposed on the expansion-type drive that all reservoirs have is shown on Figure

9. Here, opposite to the water drive reservoir of Figure 8, Q uniformly

increases as q^ decreases. Slower production increases Q ; the mechanism being

that slower production allows more time for the beneficial effects of the segregation to occur.

Figure 9 shows maxima occurring with respect to Q versus q^. These maxima

occur at some point where the ultimate recovery, Q, is optimum between high

rates of production that allow little time for the segregation effect to act

and low initial rates of production that leave little time for production before

the cutoff rate is reached. Actually, maxima in curves of Q versus q^ can also

326
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occur for reservoirs with a water drive depicted on Figure 8. Depending on

the range of q^ considered, maxima in Q versus curves may or may not occur

for reservoirs with a water drive and/or a time-dependent segregation mechanism.

Figure 10 shows a reservoir with both a water drive and time-dependent

segregation superimposed upon the expansion-type drive. Here, the curve of

Q versus q^ exhibits a maximum as do the curves for Q versus q^

.

Returning our attention to Figure 6 , there appears little

value in indulging in the exercise of judging the hypothesized curves compared

to those that occur. The truth is that each reservoir has not only a curve,

but a host of curves of Q versus q^ and all other rate parameters involved in

the development plan. Any error of the hypothesized curves of Figure 6 is not

so much in the curves, but that they were hypothesized without quantitative

analysis of any reservoir.

A second group of differences between the simple form production rate

decision problem of the previous Section and the "real world" are the mathematical assumptions imbedded in its formulation.

The simple form assumes that drilling occurs after which production

immediately initiates. This is an assumption of mathematical convenience

which likely does not approximate most actual cases. If there is an anticipated delay between when development costs are incurred and production

proceeds, that will effect the economic outcomes and the operator's decision

regarding rates of production'.

No economies of scale are considered; the simple form assumes development

costs are exactly proportional to the initial production rate. Some reduction

in the unit development costs to obtain a unit of production rate as the rate

increases would be expected8.

The simple form mathematics may be considered as including inflation either

by considering all costs and revenues adjusted to a constant-dollar adjusted

for inflation or using a discount factor which is the same as the inflation

rate and the inflation-free discount factor. Either way, the simple form

assumption still is that unit costs and prices inflate equally. The simple

form would have to be modified to include unequal inflation rates between

costs and prices.

As long as the simple form inflation assumption holds , a given oil and

gas reservoir either is an attractive investment at a given discount factor,

i.e., has a greater than 0 at the investor's i, or is an unattractive

investment and will always be so unless there are technological, policy, or unit selling price changing affecting Ndr , or Nor making the formerly un- attractive investment attractive. This raises the issue of speculations

affecting the operator's decision regarding what rates to produce at^ or whether to delay the start of production.

* We have already mentioned the simple form assumption of a lump sum development cost. The simple form also considers no limitations on the external

supplies in the development scenario. Sufficient drilling rigs, platforms, and

other equipment are presumed available without physical constraint, at the cost

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332
imputed, to implement the desired development plan. (One would expect any

such constraint to be a temporary one.) The simple form considers no enhanced

recovery schemes.

All or some of these assumptions and limitations of the simple form which,

make it simple can, however, be removed. The "real world" can be more closely

approximated by perturbing the simple form without changing what is required

to arrive at the quantitative production rate decision by the operator or assessing the quantitative effects of any production regulations on those

decisions-'-^.

A third and, perhaps, most burdening assumption inherent in the simple

form development-production scenario is that no development drilling subsequent

to the initial development is considered. The simple form boldly presumes an initial production "surge" followed by an exponential decline. An exponential

decline is merely a mathematical form of a decline that has been empirically

successful—possibly because practitioners have and use semi-logarithmic graph

paper—in tracking declining production rates when they occur. There is no law

of reservoirs requiring declines be exponential; other forms occur (such as the

hyperbolic) and are used. Further, there is no reason why a decline must occur

at all; additional drilling can, not only, arrest a decline, but yield a production rate increase. Admittedly, it is a severe restriction of the simple

form to take the exponential decline following initial production as the only

production rate profile available to the operator; this is clearly not so.

Yet, removing this assumption is another perturbation, albeit adding

complexities, to the simple form. Bradley (1967) considered the case where

individual wells decline exponentially^ . McFarland (1979b) has implemented

a linear programming model considering a gas reservoir with and without a natural water drive where as many wells are drilled to start and continue

production as indicated by the operator's economic criterion. A similar

model considering an oil and gas reservoir which may have a water drive and/or

time-dependent segregation is under development (McFarland, 1980).

In summary, the simple form of the previous Section, where Q°° was independent of q^, yielded relationships between V^, Q, and q^, the only rate parameter.

If the simple form were the "real world", the operator should select q^ to

optimize whatever he or she chose, maximization of being a reasonable

presumption. The business of production regulation made as a matter of public

policy would be to guide, influence, or, even, set those operator choices in

conformance with the public policy, whatever it is. And that is still true

in the more complicated case where the simple form does not occur. Here,

Q is dependent upon q^ and all rate parameters involved in the development

plan. One needs to consider, implicity at least, the function of Q with all

these rate parameters. Further, one needs to consider this function for each

and every technically feasible development plan, all types of form of enhanced

recovery, for example. No doubt, the problem is not of the magnitude that may,

at first reading, imply because reservoir engineering practitioners, given a reservoir and prevailing economics and policies, quickly hone in on those development plans which are technically feasible and also amenable economically and

policy-wise.

THE THERMODYNAMIC NOTION OF OIL AND GAS RESERVOIR PRODUCTION REGULATION

In the production rate and regulation analyses of the previous Sections, we considered the trade-offs between ultimate recovery, Q, the rates of recovery,

333
q, and the economic outcome measured as the present value of future profit, V^.

In so doing, without stating it, we have made an implicit assumption of rather

startling magnitude. We have assumed that the only values that can possibly

be obtained (and, of course, that can be \fiasted) are physical values, i.e.,

the oil and gas themselves, that could be produced from a reservoir and/or

economic values that could be obtained from production of oil and gas from a reservoir. Once that assumption is exposed, it is then obvious why one has

the arguments about physical versus economic waste in the rhetoric of production

regulation. We need only to recall, once again, the rational arguments between

Jones and Smith about their apple orchard to entertain the notion that values

other than just the production of oil and gas themselves and profit in so doing

are involved. Even if one does not agree, one could not dismiss those who believe

other values are involved as irrational.

The thermodynamic notion of production regulation allows a completely

general specification of the values one obtains from an oil and gas reservoir.

The thermodynamic approach to assessing energy processes and policies can be

broadly applied-^, but, here, we shall discuss the application to oil and gas

reservoirs

The immutable laws of thermodynamics which have no basis in mathematical

logic!3 are the foundation of the thermodynamic notion. The laws of thermodynamics are "proved" because no one has been able to "by-pass" these laws.

The laws are not positive laws; they do not state what can be done. The laws are negative laws; they state what can never be done. Compared to the laws of

thermodynamics, other physical and economic laws are flimsy, i.e., these other

laws can be overturned without affecting the laws of thermodynamics. For example, one could develop a society with a culture that abhors what is rare and prizes

what is available in profusion. That society would certainly differ from our current, developed societies. That society would have revised economic laws of

supply and demand. But, that society would still be constrained to the same

laws of thermodynamics.

If we proceed from the laws of thermodynamics to the questions of how oil

and gas reservoirs should be produced and regulated, we start with the recognition that there is only one- real kind of waste that can occur. We can incur

thermodynamic waste. In the course of incurring thermodynamic waste, we can incur wastes that others may call physical waste and/or economic waste (and,

likely, will argue about which). But, these are secondary names for effects seen when thermodynamic waste occurs. One cannot have physical, economic, or any other kind of waste without the occurrence of thermodynamic waste.

What, then, is thermodynamic waste? Thermodynamic waste occurs when

thermodynamically available energy is spent and value that could have been

obtained was not obtained. Note, the laws of thermodynamics do not settle

any argument between Jones and Smith or between operators and production

regulators of oil and gas reservoirs regarding what value is, what comprises

value. A mathematical statement of thermodynamic waste follows from the definition of the ratio, $, as follows:

(14)

334
Here, and t2 are the times, t, at the extremes of a planning horizon and

rvis the rate at which values, however defined, are produced in the planning

horizon. The thermodynamically available energy that is expended to obtain

those values is -w. (We continue thermodynamic sign conventions where a system that can do work on the surroundings has a negative available energy.)

The denominator of Eq. (14) is the difference between the thermodynamically

available energy of the reservoir at time, t]_, and at time t£. We know from

the second laws of physics that any withdrawal from the reservoir will occur only at the expense of a diminution of the thermodynamically available energy

in the reservoir^. We know this because of the second law of thermodynamics

(and failure to be able to build the perpetual motion machine we could build

if there were no diminution). An oil and gas reservoir is, first of all, a source of thermodynamically available energy and irreversibly so. Once we

have spent any or all of that available energy, we cannot get it back. We

could, at best, only reconstruct the past conditions in the reservoir by

spending more available energy than what we are replacing. The fundamental

thing we "spend" when producing a reservoir, however it is done, is the available energy in the reservoir. It is this expenditure which is our choice to use well or waste-^.

The thermodynamically available energy is a state function, i.e., its

magnitude depends only upon the contents of the reservoir. That is why the

denominator of Eq. (14) is not an integral. On the other hand, rv in Eq. (14)

depends on the path of the production process and the numerator must be an integral.

Note that the numerator of Eq. (14) is the arena of the arguments about

what value is produced by oil and gas reservoirs. Whoever is winning the

arguments decides what rv is. When the former winner loses, the new winner

decides what rv

is and, most likely, will want to change the decision regarding

what rv

is. This can be done. But, what neither can do is change the way the

thermodynamic accounting is done in the denominator. Old winners and new winners

(indeed, all of us) feed at a thermodynamic trough and the most fundamental

measure of efficiency is whether we get value enough for what we irreversibly

take from that trough. The best we can do is get the highest §, however rv

is

defined, in Eq. (14). We avoid thermodynamic waste by maximizing $; thermodynamic waste occurs when $ is not maximized.

The theoretical "gadget" conceived which would regulate the rate of production according to Eq. (14) would be a ^-maximizing machine. Here, the production

regulations policy maker would program the quantitative definitions and con- straints by and within which ry may be defined and these locked in. Then, the

operator would program his or her objective function for which maximization is

sought (if there are any options left). The ^-maximizing machine then simply

does what it's name implies and produces the reservoir so that $ is maximized

between times, t^ and t£. During this period, the production regulation policy

maker can be satisfied that the reservoir is being produced to obtain the highest

values per expenditure of thermodynamically available energy according to definitions and constraints deemed appropriate. During this same period, the operator

can be satisfied that, subject to the constraints of the production regulation

policies—regardless of whether the operator agrees with them or not, the

reservoir is being produced in such a way to optimize what he or she has

335
decided to optimize. Of course, when a time, t2, occurs, another production

regulations policy maker can program new quantitative definitions and con- straints, but the ^-maximizing machine adjusts!6 and, again, the policy maker

and the operator can be assured that, given their definitions of value, the

reservoir is producing such that the greatest value is being obtained per unit

diminution of thermodynamically available energy.

The ^-maximizing machine will, in the current planning horizon, remain a theoretical device, we project. We do not expect one to be build in some erstwhile inventor's garage or full-equipped modern laboratory. For one thing, the

machine would have to be able to decide when and how to drill and continually

operate wells in oil and gas reservoirs^? . Machines, even the most highly

automated, just cannot do that. The reason is that , even when we have a good

information "fix" on the extent and nature of a reservoir, we truly know little

compared to the vagaries of Mother Nature when the reservoir was constructed.

Those who would like a ^-maximizing machine built out of hardware will be disappointed and those who do not like the notion need not worry.

As a concept, the "^-maximizing machine leads us to an interesting recognition. Arguments over how and how fast to produce a reservoir should and, eventually, will revolve around assertions like, "I get more value per diminution

of available energy than you do", where value is defined by the production

regulation and operator policies.

To make the notion of. production regulation according to Eq. (14) and

^-maximization more understandable, we consider an oil and gas reservoir as a buried tank with valves given choices with regard to whether we want oil or

gas brought to the surface^. Figure 11 depicts the situation schematically.

We will proceed under the constraint that the buried tank cannot be exhumedl9.

To make our illustration more meaningful, let us consider a specific buried

tank which has a volume of 2000 cm^ made up half of an ideal gas and half of an incompressible liquid. We shall consider the gas and the incompressible

liquid mutually insolvent. Let the temperature of the buried tank be 300°

Kelvin and let us consider there is so much thermal inertia that any process

involving the tank proceeds isothermally . We shall take the original pressure

inside the tank as 2 atm. ; the pressure at the surface of 1 atm. , so that when

the pressure in the tank is 1 atm. , the tank is thermodynamically exhausted.

One can see the basic similarities between this buried tank and oil and gas

reservoirs. One has choice of producing either gas or liquid from the buried

tank of Figure 11; one does not have that either-or choice for reservoir, but

one does have a constrained choice between producing more or less gas compared

to liquid.

How shall we produce from this buried tank? That's the key question.

Shall we produce liquid? Or, shall we produce gas? If we prize the liquid, we can produce all of the liquid after which the pressure in the tank will fall

to 1 atm. and we will be able to produce none of the gas. If we prize only

the gas^O, we could produce the gas only with no liquid until the pressure falls

to 1 atm. Thereby, we will have produced half of the gas, but will be unable

to produce any of the liquid. What should we do? The answer, of course, depends

upon which we value, gas or liquid. Regardless of which of the ways we produce

the tank, we expend the tank's available energy. We decide to open either the

336
H2h

/////////

Figure 11

A Schematic Depiction of the Buried Tank

337
liquid or gas valve in order to make that expenditure to maximize the value,

however defined, we get for that expenditure. Eq. (14) operates and $ is

maximized even in this simple case.

I Suppose now, we define t^ and t2 as the times between which one who

values liquid only can withdraw exactly half of the liquid from the buried

tank. In so doing, the pressure in the tank will decrease to 1.33 atm.

Now, let the policy change and let some one who values only gas at the controls

of the apparatus on Figure 11. Gas will be withdrawn until the tank pressure

is 1 atm. ; 25 percent of the gas will be withdrawn. The liquid valuator will

get half of the liquid; the gas valuator will get one quarter of the gas.

But, now, let us change the order and give the gas valuator the first

change at the controls to withdraw half of the gas. This will lower the

pressure in the tank to 1 atm., and, when the liquid valuator gets a chance,

he or she will get skunked I Here, the gas valuator will get half of the liquid;

the liquid valuator gets nothing.

How can we preserve more equity in a situation like this? How can we prevent one set of production regulation and operator policies from closing

out options to subsequent policies? Or, more precisely, how can we keep a score, an accounting of the effects of any production regulation and operator

policies, whatever they are? The answer is, of course, to keep track of the

expenditure of the thermodynamically available energy, -w.

Suppose now, we measure how much has been withdrawn from the buried tank

by measuring -w. Let us assume that only the gas in the tank contributed available energy, -w, because without gas we could not even get any of the incompressible liquid^l. The amount of gas originally in the buried tank is:

3 (2 atm.) (1000 cm ) n nQinK , = 0.08125 gm - moles

_ 3

(82.05 - attn ~ cm

ov) (300°K)

gm - mole - K

where 82.05 atm-cm3/gm-mole-°K. is the universal ideal gas constant, R. If we were to expand that gas or any ideal gas through a fractionless turbine

under reversible conditions, i.e., maximum production of work by the turbine,

the energy available would be:

-w = n

G

RT In |- (15)

s

for isothermal operation. Here, ng is the amount of gas in the tank, T is

the absolute temperature, P is the pressure in the tank, and P

g is the pressure

at the surface. The available energy in the buried tank originally is:

3 - w = (0.08125 gm-moles) (82.05

*^"e _oK

) ( 30 ° K) ln

3 = 1386 atm - cm

338
Now, let us see what happens if we let the gas and liquid valuators at the

controls of the buried tank of Figure 11 in sequence, but who ever gets

first chance at the controls can only withdraw half of the available energy,

-w. The other valuator takes over the controls when -w=693 atm-cm^.

If the liquid valuator is at the controls first, he or she will withdraw

liquid until -w=693 atm-cm^ withdrawing 41.42 percent of the liquid and reaching a pressure of 1.414 atm22. Now, the gas valuator can thermodynamically

exhaust the tank by withdrawing gas until P=Pg = 1 atm. The gas remaining

in the tank after the gas valuator makes the withdrawal he or she can is:

(1 atm.) (1414.2 cm

3

) 3 = 0.05745 gm-moles

(82.05

atm -°m

0K ) (300 °K)

gm - mole - U K

The gas valuator will get 0.02380 gm-moles (0.08125-0.05745) or 29.29 percent

of the gas originally in the tank. Note that the gas valuator did somewhat

better when given the second chance at the controls here than with second

chance after the liquid valuator took half the liquid.

Suppose the gas valuator got first chance at the controls and could withdraw gas, but only until -w=693 atm-cm^. The gas valuator would withdraw

0.01787 gm-moles of gas reaching a pressure of 1.560 atm^3. Now, the liquid

valuator can withdraw liquid until P=Ps=l atm. Thereby, the liquid valuator

will withdraw 56.01 percent of the liquid originally in' the tank24. Here,

unlike the case where the gas valuator took half the gas when given first

chance at the controls and canceled the liquid valuator's opportunity for

any production, the liquid valuator was guaranteed production and, indeed,

could get more than 50 percent.

The reservoir's available energy, -w, is the fundamental thermodynamic

measure of what a reservoir has originally or has left after production. The

buried tank problem merely illustrates, in a grossly simplified way, the sense

and equity of accounting reservoir production using -w.

Now, consider what decisions with respect to Eq. (14) are hidden in our treatment of the simple form reservoir production rate problem of an earlier

Section. Effectively, we set t^=0 and t2=°° clearly implying that production

regulation and operator policies once implemented are forever frozen admitting

no subsequent changes in operating plans not previously anticipated. Further,

the only possible contributors to rv

we considered were the ultimate recovery,

Q or Q°°, the rates of production, q, and the economic outcome, V^. Even further,

when we considered operators' maximization of V^, applied to Eq. (14), we

"decided" the policy was that the integrated numerator of Eq. (14) was equal

to V^. In that case, the ^-maximizing solution to Eq. (14) is trivial, of course. We have defined a reservoir and an rv

which makes it so.

Solutions which maximize $ in Eq. (14) are also trivial if we define

rv=cl> even if we allow the constraint that production ceases when vr, as defined by Eq. (5) goes to zero. Then the integrated numerator of Eq. (14)

simply becomes either Q°° or Q. The trivial solution to Eq. (14) yields the

edict: You will maximize $ in Eq. (14) by producing as much stuff as possible

before exhaustion of the reservoir.

339
Solutions to Eq. (14) are not generally trivial, however. There are two

generic reasons. One reason is the consideration of other contributions to

the values obtained from production from a reservoir, rv

. The other reason is

that real reservoira depart from the assumpfeLons of the simple form reservoir

as already noted in the previous Section and in other ways as well.

As an example of the first reason, suppose we wish to consider the policy

of counting earlier production of greater value because of current pressing

exigencies presuming upcoming solutions from other sources. Then one might

define r =3©"^ where I is a positive value expressing how much more we would

prefer a unit of production per se today rather than a year from now. (If I is negative, I indicates how much more we prefer a unit today than a year

from now.) If Eq. (1) applies, then r^q^e^1-0 )

11 which basically defines

decision algebra of a speculator who may be an operator or policy-maker. If

(I-D)>0, then the speculator believes the future values, which may include

non-economic contributions, are increasing so fast they over-ride any decline

rate of production. Therefore, the speculator concludes not to produce, but

hold the potential of producing. This ^-maximizing solution implies that there

is a definite contribution to rv

by having a reservoir capable of production

and not producing from it. The contribution might be deemed appropriate for reasons of security and/or strategy. Or, the contribution to values of a reservoir conserved might be what economists call an intergenerational value

a gift we hand to succeeding generations. Such gifts require an overt policy

decision. Certainly, the only things we spontaneously conserve for the future

are things we do not know are there and things which are presently deemed grossly

uneconomic. Eq. (14) and its use provides the quantitative policy flexibility

of considering values from oil and gas reservoir production other than those

having only to do with the production from the reservoir and/or profits made

from that production.

A second generic reason why Eq. (14) ^-maximization solutions are not

trivial are departures of reservoir behavior from the assumptions of the simple

form of Eq. (1). In the previous Section, two departures from an overall reser- voir performance covered were: —Reservoirs having a natural gas water influx which entraps oil and/or

gas behind the invading water such that entrapped hydrocarbons are no longer recoverable". —reservoirs having a time-dependent segregation with respect to the

overall movement of reservoir liquid and gas relative to each other.

Note that optimization solutions of Eq. (14) using definitions of rv

that would

be trivial for simple form reservoirs are not trivial for reservoirs with a water influx and/or time—dependent segregation. Likewise, solutions are not

trivial for reservoirs with enhanced recovery schemes. And in cases where the

reservoir mechanisms must consider local effects due to wells and their operations and other substantive reservoir homogeneities, then, most certainly, the

^-maximization solution of Eq. (14) is non-trivial and becomes more complex.

Yet, throughout, the objective function, $, is the same.

The thermodynamic approach to production regulation and rate decisions

embodied in Eq. (14) recognizes that every oil and gas reservoir exists only

once and irreversibly so. Once produced, any oil and gas reservoir is gone

340
forever; no recipe exists for reconstructing that oil and gas reservoir.

As far as the reservoir in situ is concerned, it is a source of available

energy and the "score" of what we do with any reservoir is really kept in

whether we husband or how well we expend the available energy of a reservoir.

How would the thermodynamic approach be adapted to production regulation?

We have already invented an imaginary ^-maximization machine, but concluded it

will remain imaginary. But it need remain imaginary only as a piece of hardware; the machine can function in a dialogue between production regulation

policy makers, operators, and the "people-ware" between. We have pointed to

the advantage of policy flexibility and equity of the ^-maximization machine

to produce regulation and rate decisions. Another advantage, it appears to

us, is the administrative simplicity with which the ^-maximization non-hardware machine could be run. Basically, the policy makers' job would be to

define quantitative rules, ways, and constraints for defining rv . Presuming

the policy makers do not completely define rv

, the operator can then make his

or her own detailed specification within what the production regulation policies

allow, i The operator's obligation to the production regulations is fulfilled

with a statement like the following:

You have told me a way or rules that I must use to define rv , the value of production from my reservoir (which I may or may not

agree with). Where you did not already specify everything, I completed a definition of rv within your specifications. But after

all that, I can now certify that the reservoir is being produced

properly because it is being produced so that we are getting the

greatest value the way you (and maybe I) defined it per unit of

available energy being expended .

Once the production regulation policy definition and constraints affecting

rv

are made, then the only challenges to an operator's reservoir operations

and rates can be (1) that the rules, definitions, or constraints are not

being adhered to or (2) that there is disagreement with the operator's

technical assessments and analyses regarding the reservoir. Here, of course,

the arena for potential argument has been much delimited including only

whether the rules are being followed and the technical area. The argument

about what are true values that should be obtained from a reservoir have been

resolved after, at least possibly, considering the full gamut of potential

contributions to those values. Perhaps the arguments regarding value will

not have been correctly resolved in the view of subsequent history, but,

then, even historians are flawed. But, just as Jones and Smith disagreed

while proceeding with the apple orchard, one can do whatever it is we do with

oil and gas reservoirs in the same way.

CONCLUDING REMARKS

The title promised some modern notions about oil and gas reservoir

production regulations. We note that no promise of the answer to how oil

and gas reservoirs should be regulated was implied. Rather, we hoped to make

the process of deciding production regulations more articulate with the issues

better delineated.

341
We have delineated the issue of reservoir sensitivity and insensitivity

to rates of production. We hope we have put to rest the myth that there are any reservoirs insensitive to rate such that production regulation is not an

issue.

We have pointed out that the rate at which an oil and gas reservoir

declines in production is most directly a choice that can be made by the operator and only indirectly influenced by the inter-relationship between economics

and reservoir mechanisms. One can, as a matter of policy, choose to impose

production regulations requiring certain decline rates or a certain recovery

reserves to production rate ratio, but then the choice is made by the production

regulations policy instead of the operator. It is still a choice made, not

something defined by the laws of physics and reservoirs.

We have shown that concerns involving specific kinds of wastes such as physical or economic and the arguments that ensue about these kinds are really

semantic chatterings about secondary effects. There is only one waste. That

waste is thermodynamic. Waste occurs when we do not get the value we could

have for what we expend thermodynamically

Finally, and most importantly, we have pointed out that the definition of

what we call value is a public policy perogative and necessity. And the definition of value is not restricted, necessarily, to considering only contributions

of oil and gas per se from reservoir production or profit or only these two.

Rather, the components of value used to define production regulations may include

any of the entire array of. what our society should value. As consumers, we are often counseled to get the most value for our money. As a society, we would

seek the most value for the thermodynamically available energy we expend.

All these value decisions need to be made quantitatively to define production regulations. Jones and Smith did it so they could run their apple

orchard. Whether we realize it or not, we are doing the same thing to run

oil and gas reservoirs.

ACKNOWLEDGMENTS

The support of the Conservation Division of the U.S. Geological Survey

and its management for this work is gratefully acknowledged. This is not,

however, an official expression of the Survey, but a technical expression

for which the authors are responsible. Of the many colleagues with the

Survey who helped us, we want particularly to acknowledge Dr. R.G. Wayland,

former Chief of the Division, who recognized the continuing importance of

the technical issues of oil and gas production regulations early.

We want to express a special gratitude to the many colleagues with whom

we discussed these matters. Many had or were employed by organizations who

had definite policy views regarding oil and gas production regulations. We

asked them to set aside their policy views and address only the technical

issues with us which they did.

342
NOTES

1. We cite only some of the more recent treatments of the background

of oil and gas reservoir production regulations as follows: Bishop, 1979;

McDonald, 1971, 1979a, 1979b; McFarland, 1976, 1979; Schanz , 1976.

2. Lohrenz, Burzlaff, and Dougherty (1980) discuss the technological,

economic, and policy matters that effect the parameter, [CDXD / (l-r-cg)XR]

.

Note that when Xr=Xj), the choice of D° is not affected; however, is proportionately affected.

3. Lohrnez, Burzlaff, and Dougherty (1980) present results for D° for

different values of N(j r

.

4. These two mechanisms have been quantified for oil and gas reservoirs

using a reservoir per se model by Lohrenz and Monash (1979). The special case

of a gas (only) reservoir has also been treated. For a gas reservoir, segregation is moot and only the water influx mechanism is important from an overall

reservoir point of view. Gas reservoir ultimate recovery is, ceteris paribus , always increased by faster production. Once production has started, one might

as well produce the gas lest the water invade and occlude the gas. This special

case has been treated extensively by Monash and Lohrenz (1979) who used a gas

reservoir per se model to match data for real gas reservoirs including storage

reservoirs for which the fluctuating pressure history puts models in severe

jeopardy. (One side effect of these results is a challenge to the frequently

used, more complicated reservoir models. Overkill in reservoir modeling, the

substitution of complex mechanisms without examination to see if the data available actually justify the addition of a complexity, appears more prevalent than one might have supposed. The arguments about modeling seem many times to be

decided upon the issue, "My model is more sophisticated and handles more mechanisms than yours", rather than, "My model efficiently handles the data that

Mother Nature and her flawed helpers make available." This should not be so,

but is is.) The case of waterflooding a reservoir has also been treated

(Johnson, Monash, and Waterman, 1979). It turns out that, ceteris paribus , to increase ultimate recovery, one should initiate waterflooding after prior

depletion of a gas reservoir to as low a pressure as possible. This result is

entirely consistent with the natural water influx result.

5. The quantitative support is that due to Thachuk (1974) who studied

reservoir cases using a sophisticated grid model. The curves were parametric

with the density of the wells drilled.

6. The curves of Figures 7 through 10 were taken from Lohrenz and

Monash (1979). Only the curves for oil are shown on Figures 7 through 10; curves for gas are depicted in the reference cited.

7. Lohrenz, Burzlaff, and Dougherty (1980) show that an anticipated

delay causes a present value of future profits maximizing operator to decrease

production rates.

8. Lohrenz, Burzlaff, and Dougherty (1980) treat economies of scale

using the power scale-up law.

9. Under the constraint that the operator must start production,

Lohrenz, Burzlaff, and Dougherty (1980) treat the case of the present value

343
of future profits maximizing operator's decision speculating on a price jump

some years after production starts. Payoff matrices (2x2) are given showing

the present values obtained by an operator making the production rate decision

ignoring and considering the price jump and, then, if the price jump actually

occurred and if it did not. The result is a break-even frequency such that the

operator should believe the probability of the possible price jump is greater

than the break-even frequency in order to base the production rate decision on

the presumed price jump.

10. We cite three examples. McFarland, Springer, Monash, and Lohrenz

(1978) treated gas reservoirs with and without a natural water drive drilled

up then declining with the reservoir pressure and examined the relationship

between Q, V^, and in^. Johnson, McFarland, Monash, and Lohrenz (1978),

considering waterflooding of gas reservoirs, found that with current practices,

economics, and policies, no region where V

d>0, a persuasive explanation why

one finds waterflooded natural gas reservoir absent in the real world.

McFarland, Parks, and Aggarwal (1979) have implemented a model treating an oil and gas reservoir which may have a natural water drive and/or time-dependent

segregation examining the relationships between Q, V^, and imax .

11. Actually, the thrust of the work by Bradley (1967) was to track

the required selling prices of the aggregation of reservoirs being developed in

a geological region.

12. Georgescu-Roegen (1971, 1976, 1979) has written most articulately

and ardently on this subject. Others we select to cite are Keenan, Gyftopoulos,

and Hatsopoulos (1974), Ross (1978), Rotty and Van Artsdalen (1978) and an interesting Ph.D. thesis by Hertzmark (1978).

13. It is interesting to note that laws based on mathematical logic

are vulnerable to fallibilities G6*del's Theorem finds cannot be avoided. The

laws of thermodynamics are free of the burden of Godel's Theorem.

14. This is true just as well for reservoirs with any kind of enhanced

recovery where the reservoir system must include the reservoir and the enhanced

recovery facilities. It is true that the thermodynamically available energy

in the reservoir per se may increase with withdrawals, but, most assuredly,

the available energy of the system including the enhanced recovery facilities

will not.

15. In these times when the private and public worry is energy

shortages and the high costs of energy, it may be, nonetheless, instructive

to ponder what would happen in the "fortunate" happenstance that the energy

problem would be solved by some surprising or miraculous discovery of inew sources or processes. In other words, we have available energy, -w, without

limits as far as we can see. Therefore, we can make withdrawals on that

available energy to obtain our values, however defined, at any rate, rv , without limit. This "fortunate" happenstance would, however, not just be moderated,

but, essentially, be incinerated along with us because al] use of energy, no matter how efficient, involves the dumping as energy in its lowest form, heat.

If we used energy without limit, we would also create a limitless garbage dump

for our heat. Thus, even if energy were freely available without limits and

costs, constraints on its use would be necessary for survival if nothing else.

(We will leave to non- technical disciplines, say ethics and theology, the

considerations of the moral Issues that may be involved if energy were "free".)

344
If that is true with unlimited available energy, then is it not reasonable

that constraints also arise when energy is limited? The laws of thermodynamics tell us we cannot escape even when available energy is limitless.

We still could only afford to use available energy within limits.

16. Any adjustment of a reservoir's operating strategy responding

to a change in the definition of rv would have to, of course, consider the

cost of implementing the changed strategy. In real reservoirs, an operating

strategy cannot likely be changed by re-programming a computerized algorithm

or twiddling a few dials, of course, like our hypothetical ^-maximizing machine.

17. Actually, one of the easier things that the ^-maximizing machine

would need done is the measurement of the available energy, -w, in the reservoir.

Recall that -w is a state function defined only by the contents, pressure, and

temperature of the reservoir and not dependent on any historical past by which

those contents, pressure, and temperature were obtained. Admittedly, reservoir

engineers only have uncertain estimates of the data needed to define -w, but

they do make and do have those estimates in current technology.

18. The buried tank problem has been previously treated by Lohrenz

and Monash (1979b) who treated a case where both the oil and gas had the same molal available energy.

19. This would amount to mining an oil and gas reservoir—something

under active consideration (Maugh, 1980). The entire system including the

reservoir itself and the mining process and apparatus would still fall under

the tenets of Eq. (14) just as would any other enhanced recovery process.

20. Even the consideration of the possibility of prizing only the

gas and assigning no value to potential liquid production may be anathema,

at least at first, when considering oil and gas reservoirs. This means assigning no value to the condensate of gas condensate reservoir, for example.

One of the authors was present at discussions regarding the large Prudhoe Bay

reservoir where the alternative of producing gas only and eschewing oil

production was listed. Umbrage was immediate and loudly offered only to be

informed that the situation could develop that gas has by far the overwhelming

value compared to oil. (The search for diamonds in the dung changes when the

relative value of diamonds to dung becomes fractional.) Properly and not un- reasonably chastened, the author recognized the thesis herein propounded, that

how you should run an oil and gas reservoir depends on what you value in its

production. We should note that the alternative of producing only gas from

this Prudhoe Bay or any other oil reservoir is not being seriously considered,

as far as we know. But, that is only because the policy decision is that gas

values do not overwhelm oil values.

21. Here, we ignore effects on -w such as the potential, surface,

and chemical contributions to available energy. In assuming these can be

ignored, we are adding no new burden to our analyses beyond what is already

in standard reservoir engineering which assumes thermodynamic equilibrium

of the in situ reservoir fluids. Complex reservoir engineering models which

consider reservoir heterogeneities do_ consider how potential and surface

energy effects are determinants of how fluids flow within the reservoir. But,

that is another matter. In a broader sense, one should consider the surface,

345
mechanical, and other available energies used in drilling, equipping, and

operating wells. One might also consider the available energy used in

the drilling rigs and other physical equipment between the time they are used on the reservoir and their use on subsequent reservoirs or salvage.

22.

693.14 = (0.08125) (82.05) (300)£n P

Solving P = 1.414 atm

rru i * *u (0.08125) (82.05) (300) .... _ 3 , . , 1 The volume of gas then is

j — = 1414.2 cirr from the ideal

gas law. The volume of liquid is 1000 cm^ less than the volume of gas remaining,

23. From the ideal gas law, nRT is the product of the pressure and

gas volume, 1000 cm^. Substituting into Eq. (15):

693.14 = P(1000) In P

Solving P = 1.560 atm.

The amount of gas left is (32^05) (300)

= °' 063 38 gm-moles. The gas produced

is 0.08125-0.06338 = 0.01787 gm-moles.

24. The volume of gas remaining in the tank when P = 1 atm is:

3

1 - en gm-

(0.06338) (82.05

atm

, Cm

Qv ) (300 "K) Rm-mole-uK

= 1560.1 cm

3

1 atm

Therefore, 1560.1 - 1000.0 = 560.1 cm3 of liquid will be withdrawn.

25. Even a reservoir that is shut-in after production may not be

preserved thermodynamically , but actually decline in available energy when

water invades and entraps hydrocarbons. Whether a shut-in reservoir increases

or decreases in available energy with water influx depends on the relative

amounts of entrapment to water invasion. In terms of Eq. (14), this means

that one can shut-in a reservoir (which is the thermodynamic equivalent of

producing at a reversibly slow rate) and still obtain a diminution of -w. Obviously, the only time one would rationally do this is if there were values

perceived in shutting in the reservoir that over-ride the thermodynamic expenditure of available energy in doing so.

346
REFERENCES CITED

Bishop, K.E. "Maximum Efficient Rate—A Changing Game." Symp. Proc . , Maximum

Efficient Rate (MER) for Petroleum Reservoirs in the Outer Continental

Shelf , J.W. McFarland, ed., Univ. of Houston, Jan. 29, 1979.

Bradley, P.G. The Economics of Crude Petroleum Production . North-Holland,

Amsterdam, 1967.

Brooks, D.B. "Mineral Supply as a Stock." Economics of the Mineral Industries , 3rd ed., Chap. 2.5A, William A. Volgely, ed., AIME, New York, 1976.

Carlson, J.W. Statement to the Senate Subcomm. Antitrust and Monopoly, Comm.

on Judiciary, Sept. 23, 1975.

Davidson, P. "Public Policy Problems of the Domestic Crude Oil Industry." Amer . Econ. Rev., 53, 85-108 (March, 1963).

Georgescu-Roegen, N. The Entropy Law and the Economic Process . Harvard University,

Cambridge, 1971.

Georgescu-Roegen, N. Energy and Economic Myths , Institutional and Analytical

Economic Essays . Pergamon , New York, 1976.

Georgescu-Roegen, N. "Energy Analysis and Economic Evaluation." South . Econ. . , 45, 102 3-1058 (1979).

Hertzmark, D.I. Economics , Thermodynamics , and the Allocation of Energy . Ph.D.

Thesis (Agric. Econ.), Univ. of Wisconsin, Madison, 1978.

Johnson, M.E., J.W. McFarland, E.A. Monash, and J. Lohrenz. "MER (Maximum Efficient

Rate) Using a Gas Reservoir Model with Waterf looding. " Informal Report

LA-6989-MS, Los Alamos Scientific Laboratory, Feb., 1978.

Johnson, M.E., E.A. Monash, and M.S. Waterman. "Modeling and Optimizing a Gas-Water

Reservoir: Enhanced Recovery with Waterf looding. " J. Inter . Assoc . Math . Geol . , 11, no. 1, 63-74 (1979).

Keenan, J. H. , E. P. Gyftopoulos, and G.N. Hatsopoulos. "The Fuel Shortage and

Thermodynamics—The Entropy Crisis." Energy : Demand , Conservation , and

Institutional Problems , M.S. Macrakis, ed. , pp. 455-466. MIT Press,

Cambridge, 1974.

Lohrenz, J., B.H. Burzlaff, and E.L. Dougherty. "How Policies Affect the Rates of

Recovery from Mineral Sources." Report MER-10.4A (P-5), App. Res. Anal.

Sect., Cons. Div. , U.S. Geol. Surv., Denver, Apr. 28, 1980.

Lohrenz, J., D.A. Dunham, and H. Tomlinson. "A study of Factors Affecting Profit

for Different Federal Offshore Oil and Gas Lease Bidders." SPE 7714, Proc .

,

SPE-AIME Symp . Petrol . Econ . Eval . , pp. 43-52, Dallas, Feb. 11-13, 1979.

347
Lohrenz, J., and E.A. Monash. "Ultimate Recovery, Rate of Withdrawal, and Maximum || Efficient Rate (MER) for Oil Reservoirs." Symp . Proc . , Maximum Efficient

Rate (MER) for Petroleum Reservoirs in the Outer Continental Shelf , J.W.

McFarland, ed., 20-66, Univ. of Houston, Jan. 29, 1979a.

Lohrenz, J., and E.A. Monash. "The Thermodynamic Approach to Production Regulation | of Oil and Gas Reservoirs." Symp . Proc . , Maximum Efficient Rate ( MER) for

Petroleum Reservoirs in the Outer Continental Shelf , 127-147, Univ. of

Houston, Jan. 29, 1979b. ~

I Maugh, T.H., II. "Mining Could Increase Petroleum Reserves." Science , 207 , 1334- ! 1335 (Mar. 21, 1980).

McDonald, S.L. Petroleum Conservation in the United States : An Economic Analysis . Johns Hopkins, Baltimore, 1971.

McDonald, S.L. "MER: Three Definitions." Symp . Proc., Maximum Efficient Rate

(MER) for Petroleum Reservoirs in the Outer Continental Shelf , J.W. McFarland,

ed., 7-19, Univ. of Houston, Jan. 29, 1979.

McDonald, S.L. The Leasing of Federal Land s for Fossil Fuels Production . Johns

Hopkins, Baltimore, 1979.

McFarland, J.W. "A Selected Review of Maximum Efficient Rate (MER) and Related

Resource Economics Literature." Informal Report LA-6322-MS, Los Alamos

Scientific Laboratory, Jul., 1976.

McFarland, J.W. "Introduction and Overview" for the Symp. Proc, Maximum Efficient

Rate (MER) for Petroleum Reservoirs in the Outer Continental Shelf , 1-6,

University of Houston, Jan. 29, 1979a.

McFarland, J.W. "Gas Reservoir Management: An Optimal Control Model." CBA

Working Paper 27, Univ. of Houston, 1979b.

McFarland, J.W. Personal Communication , 1980.

McFarland, J.W., M.S. Parks, A. Aggarwal. "Alternative Optimization Criteria for

Production from Petroleum Reservoirs." CBA Working Paper 34, Univ. of

Houston, Oct., 1979

McFarland, J.W., T.E. Springer, E.A. Monash, and J. Lohrenz. "A Simulation Study

of MER for Gas-Water Reservoirs." Informal Report LA-6866-MS, Los Alamos

Scientific Laboratory, MAR., 1978.

Monash, E.A. , and J. Lohrenz. "Real Natural Gas Reservoir Data vs. Natural Gas

Reservoir Models." Clemson Univ . Rev . Indust . Man . Textile Sci . , 18 , no. 2,

49-69 (Fall, 1979)

Pirson, S.J. Elements of Oil Reservoir Engineering , 391-394. McGraw-Hill, New York,

1950.

Pirson, S.J. Oil Reservoir Engineering , 708-710. McGraw-Hill, New York, 1958.

348
Ross, M. "Second Law Efficiencies and Public Policy." Energy Analysis : A New

Public Policy Tool , M.W. Gilliland, ed., pp. 43-52. Westview Press, Boulder

Co, 1978.

Rotty, R.M. , and E.R. Van Artsdalen. "Thermodynamics and Its Value as an Energy

Policy Tool." Energy, 3, 111-117, (1978).

Schanz, J.J., Jr. "The Use of Maximum Efficient Rate (MER) as a Regulatory Tool."

Report prepared by Resources for the Future for the U.S. Dept. of Interior,

Jan., 1976.

Thachuk, A.R. "MER: Ultimate Recovery vs. Rate—A Reservoir Simulation Study, Vol

1 and 2." Report prepared for the Cons. Div., U.S. Geol. Surv. , by Sclent if

Software Corp., Englewood, CO, June 7, 1974, Contract No. 14-08-0001-13238.

DISCUSSION

Q. How would you minimize the entropy in terms of the initial rates, based

on what you said? Have you developed a formulation that would enable

you to minimize entropy as a function of the initial rate?

A. No, that's not whdt I like to do.

Q. You statement implied, at least to me, that you wanted to minimize

entropy. Maybe I misunderstood you. That is what I though you were driving at.

A. What we measure is the reversible maximum available energy.

Q. But you haven't formulated the entropy, as part of the determination of initial rates?

A. No.

Q. What about the Soviets? As you well know, they have said very often

(that they) maximize short-term ultimate recovery.

A. That could be done. (Comment added post-session: For example, in the

numerator of Eq. (14) , one would simply define t^ and t_ consistent with the shortterm value judgments or weight r such that earlier production is preferred in

computing values.)

349
Historical Growth of Estimates of Oil- and Gas-Field Sizes

David H- Root

U.S. Geological Survey

Reston, VA 22092

Estimates of proved reserves of crude oil, natural gas, and naturalgas liquids in the United States have been published annually by the American

Petroleum Institute (API) and the American Gas Association (AGA) since 1966.

These estimates are updated periodically as the fields are developed and

produced. The usual experience is that the estimated ultimate recovery

(past production plus proved reserves) of all fields discovered in a given

year tends to increase from one estimate to the next. Such an increase is

to be expected from the conservative nature of the definition of proved

reserves. The increases are proportionately larger for younger discoveries

than for older. The purpose of this paper is to estimate how much this

"growth of reserves" will add to the proved reserves of oil and gas fields

that were discovered prior to 1979. Crude oil, including both recoverable

oil and original oil in place, will be considered first, and then recoverable

natural gas will be considered.

The estimate of the ultimately recoverable oil in fields discovered in

a given year can change for several reasons. (a) Drilling could show that

the field was physically larger or smaller than had been thought. (b) Production experience could show that the assumed recovery factor was too high

or too low. (c) The application of water flooding or another improved

recovery technique could change the anticipated recovery. (d) A field could

be reported to the reserves committees for the first time several years after

its discovery. (e) The discovery year assigned to a field could be changed,

and this date change would shift the estimate of the field's recoverable oil

from one discovery year to another. (f) New producing zones could be found

in an old field. The available data are not sufficiently detailed to allow

the estimation of the relative importance of these several factors, though by

studying the changes in estimates of original oil in place, one can estimate

how much growth in estimates of recoverable oil is due to improved recovery.

The phenomenon of growth in estimates of the sizes of oil and gas fields has

been studied by many authors (Arrington, 1960; Hubbert, 1974; Marsh, 1971;

Pelto, 1973; White and others, 1975). These studies were usually carried out

as a subsidiary part of an effort to estimate future discovery rates by

extrapolating past discovery rates. In order to avoid serious underestimation

of what the future discovery rate will be, the extrapolator must take account

of the fact that estimates of proved reserves are conservatively made,

especially for fields discovered near the end of the discovery series. The

methods used by the different authors for estimating future growth are similar

to that described here.

Figure 1 shows estimates made since 1966 through 1978 of the amount of

recoverable oil discovered in the conterminous United States in each decade

from 1920 to 1969. Except the curve for the decade 1920-1929, each of the

350
curves shows an increasing trend, the most recent decade showing the largest

percentage increase.

The future growth of estimates of ultimate recovery from fields discovered

before 1979 is estimated under the assumptions a) that when a field has been

known for 59 years, its estimated ultimate recovery will no longer change and

b) that estimates of recoverable oil in recently discovered fields will show

the same percentage growth year by year, as estimates of recoverable oil in

fields that were discovered years ago have shown in recent years. Annual data

go back only to 1920; hence, the choice of 59 years. Several estimates of

ultimate recovery are available for fields discovered in the years 1966 through

1977; they include estimates made at the end of the year of their discovery and

estimates made 1 year after that. From these estimates, one can calculate the

expected percentage increase between the first and second estimate. Let w(i, j)

be the estimate as of the end of year j of recoverable oil in all fields discovered during year i. The estimated 1-year growth factor from the first to

the second estimate is then given by the ratio

1977

£ w(i, i+1)

i = 1966

1977 = r (D (1)

£ w(i, i)

i = 1966

In general, the estimated 1-year growth factor from the n-1 year estimate

to the nth year estimate is given by

1978-n

£ w(i, i+n)

i = max of 1967-n, 1919

1978-n = r(n)

( 2 ) £ w(i, i+n-1)

i = max of 1967-n, 1919

For the purposes of these calculations, all fields discovered before 1920 were

credited to 1919.

Figure 2 is a graph of the average 1-year percentage growth of estimates

made during 1971-78 of the amount of ultimately recoverable crude oil in fields

of the conterminous United States versus years since discovery of the fields.

Notice that positive changes are much more common than negative changes. The

amount to which the estimates of ultimate recovery from fields discovered in

a given year are expected to increase is obtained by multiplying the 1978

estimated ultimate recovery estimate by all of the r(n) from equation (2) where

n is greater than the difference between 1978 and the discovery year and is

less than 60. Define the growth factor for an estimate of recoverable oil in a field discovered n-1 years ago as of 12/31/78 to be

59

R(n) = 7Tr(i) (3)

i=n

351
This method of calculating growth factors could be carried out equally

well if the API had begun publishing annual data series either before or after

1966. The only requirement is that data be Available for at least 2 years.

Table 1 shows the 12/31/78 estimated ultimate recovery from oil fields

discovered in the conterminous United States by year of discovery as well as the growth factors (from equation 3) for each discovery year. The growth

factors were computed by using only a part of the available data series.

The estimates of ultimate recovery from 12/31/71 through 12/31/78 were used,

and those as of 12/31/66 through 12/31/70 were not used. The estimate of

expected future growth of estimates of oil in fields discovered before 1979

is affected by the arbitrary choice of which part of the data series is used.

Figure 3 shows how the anticipated growth during the 10-year period 1979-1989

varies as the length of the data series is reduced from 13 years (1966-1978)

to 2 years (1977-1978). Figure 4 shows how the total anticipated growth of

ultimately recoverable oil varies as length of the data series decreases from

13 years (1966-1978) to 2 years (1977-1978).

The same calculations for growth of estimates of ultimately recoverable

oil can be carried out for original oil in place. The analogous table and

figures (table 2, figs. 5-8) are presented; however, no accompanying text

explains the calculations because the explanation would be completely redundant. The principal result is that the total growth projected for estimates

of original oil in place is, proportionate to the 1978 estimate, smaller than

that for recoverable oil, i.e., 6.9 percent versus 17.3 percent. This difference is to be expected because in estimating original oil in place, engineers need not consider the uncertainties of reservoir and fluid properties

that affect recoverability

Because the growth factors for estimates of original oil in place are smaller than those for estimates of ultimately recoverable oil, the fraction

of oil in known fields that can be recovered is projected to increase. However,

the increase is not large. Applying the growth factors for original oil in

place and for recoverable oil shows the recovery factor for fields discovered

before 1979 increasing from 0.3172 in 1978 to 0.3290 in 1990, or an average

increase of one-tenth of a percentage point each year. Applying the growth

factors out to the limit of 59 years shows the recovery factor increasing to

0.3480. These results indicate that about half the anticipated increase in

estimates of recoverable oil from fields discovered before 1979 comes from

improved recovery and about half comes from an increase in the estimates of

original oil in place.

Estimates of recoverable natural gas in fields in the conterminous

United States have been published annually by the American Gas Association.

The recoverable natural gas figures are broken down by year of discovery,

and associated gas and non-associated gas are tabulated separately. Figure

9 shows the estimates made at the ends of the years 1966 through 1978 of the

total recoverable natural gas discovered in the conterminous United States

in each decade from 1920 to 1969.

Growth factors for estimates of recoverable natural gas, like growth

factors for estimates of recoverable oil and original oil in place, can be

352
estimated by use of equations 1 , 2, and 3. Figure 10 shows the 1-year

growth factors for estimates of natural gas and is analogous to figure 2.

However, frequent negative revisions are shown in figure 10, whereas only

a few negative revisions are shown in figures 2 and 6; these negative

revisions shown in figure 10 indicate that successive estimates of the

amount of recoverable natural gas discovered in a given year approach the

true value in a more erratic fashion than do successive estimates of crude

oil. The erratic behavior of past estimates makes the forecasting of

future estimates difficult and uncertain. The results of the growth factor

calculations for natural-gas estimates are shown in table 3. The growth

of estimates of non-associated gas and the growth of estimates of associated

gas were calculated both separately and together. Those three calculations

are only roughly consistent in that the growths of non-associated and

associated gas do not sum to the calculated growth of all gas. The results

in table 3 were based upon the use of a data series nine years long (1970-

1978). The values of the total growth and the growth for ten years based

upon data series of varying lengths are shown in figures 11 and 12. These

figures are analogous to figures 3 and 4 and figures 7 and 8.

Conclusions

In the past, successive estimates of the amount of oil and gas discovered

in any given year in the conterminous United States have tended to increase.

This trend is a result of several factors including: late reporting of discoveries, the conservative nature of the definition of proved reserves,

the application of improved recovery techniques, and the discovery of new reservoirs in old fields. Because there is available a series of estimates

of the original oil in place and the ultimate recovery (past production plus

proved reserves) from oil and gas fields in the conterminous United States

by year of discovery, one can quantify this trend in growth of estimates.

For both oil and gas fields, estimates of their contents grow each year by

larger percentages for recently discovered fields than for older fields.

Estimates of the amount of crude oil and natural gas discovered continue

to increase for many years after the field's discovery. At what year the

growth ceases, of course, depends upon the particular field in question;

however, for the purpose of analysis, growth was assumed to cease when a field became 59 years old. By using that assumption and the assumption that

growth proceeds in the future as it has in the past, one can estimate that

the quantity of recoverable crude oil discovered in the conterminous United

States before 1979, which was estimated as of December 31, 1978, to be 135

x 10 9 bbl, will ultimately increase by 23.4 x 10 9 bbl to 158.4 x 109 bbl.

Natural gas is projected to increase from 721 x 10^ c f to 853 x 10^ cf

Implicit in these projections is the idea that the realization of the

increases will require 59 years from the end of 1978. The amount of the

increase that will appear in the first 10 years is 11.0 x 109 bbl for

recoverable oil, 14.3 x 109 bbl for original oil in place, and 41 x lO-^ cf

natural gas. The long time span during which estimates increase means that

the calculations were significantly affected by the growth of estimates of resources in the large fields discovered before 1950. Oil and gas fields

353
discovered in recent years are smaller than the fields found in the 1920' s, 30' s, and 40' s and they are developed more rapidly, so the prolonged

growth (59 years) herein projected may never take place. For this reason,

the estimated additions to reserves from fields discovered before 1979,

that is 23.4 x 10^ bbl recoverable crude oil and 132 x 10^-2 c f natural gas, are more likely to be overestimates than to be underestimates.

References

American Petroleum Institute American Gas Association, and Canadian

Petroleum Association, 1966-1978, Reserves of Crude Oil, Natural Gas

Liquids and Natural Gas in the United States and Canada as of Dec.

31: v. 21-33.

Arrington, J. R., 1960, Size of crude reserves is key to evaluating

exploration programs: Oil and Gas Journal, v. 58, no. 9, Feb. 29,

p. 130-134.

Hubbert, M. K. , 1974, 'U.S. energy resources, a review as of 1972,' pt.

1, A National Fuels and Energy Policy Study: U.S. 93rd Congress,

second session, Senate Committee on Interior and Insular Affairs,

Comm. Print, Serial No. 93-40(92-75), 267 p.

Marsh, Rogge G. , 1971, How much oil are we really finding: Oil and Gas

Journal, v. 68, no. 14, April 5, p. 100-104.

Pelto, Chester, 1973, Forecasting ultimate oil recovery, JLn Petroleum

Economics and Evaluation Symposium, Dallas, Tex., 1973: Am. Inst.

Mining, Metallurgical and Petroleum Engineers, Society of Petroleum

Engineers, p. 45-52.

White, D. A., Garrett, R. W., Jr., Marsh, G. R., Baker, R. A., and Gehman,

H. M. , 1975, Assessing regional oil and gas potential, in Haun, J. D. , ed, Methods of estimating the volume of undiscovered oil and gas

resources: American Association of Petroleum Geologists, studies in

Geology, no. 1, p. 143-159.

354
o

40

1930's

30

•

1 940'

20 /

. lOSfl'c

10

. 1 960's

0 i i i i i i i i i i 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 ESTIMATE YEAR

Figure 1. —Estimates made each year have 1966 through 1978 of the amount

of ultimately recoverable crude oil discovered in the conterminous

United States in each decade from 1920 to 1969. Estimates from

American Petroleum Institute, American Gas Association, and

Canadian Petroleum Association (1967-1979, v. 22-34).

YEARS SINCE DISCOVERY

Figure 2. —Average 1-year percentage growth of estimates made during 1971-1978

of the amount of ultimately recoverable crude oil in fields of the

conterminous United States versus years since discovery of the fields.

Estimates were published by American Petroleum Institute, American Gas

Association, and Canadian Petroleum Association, 1972-1979 (v. 27-34).

355
16

CD

eoO

o

o

13 12 10 9 8 7 6 5 NUMBER OF YEARS OF DATA

Figure 3. —Projected 10-year (1979-1989) growth of estimates of the amount of

ultimately recoverable crude oil in fields discovered before 1979

in the conterminous United States versus the number of years of data

used. Thirteen years of data are from 1966 to 1978; two years of

data are from 1977 to 1978.

13 12 11 10 9 8 7 6 5 NUMBER OF YEARS OF DATA

Figure 4. —Projected total growth of estimates of the amount of ultimately recoverable

crude oil in fields discovered before 1979 in the conterminous United States versus the number of years of data used. Thirteen years of data are from

1966 to 1978; two years of data are from 1977 to 1978.

356
1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 ESTIMATE YEAR

Figure 5. —Estimates made at the ends of the years 1966 through 1978 of the amount

of original oil in place discovered in the conterminous United States

in each decade from 1920 to 1969.

Figure 6. —Average 1-year percentage growth of estimates made during 1971-1978 of

the amount of original oil in place in fields of the conterminous

United States versus years since discovery of the fields.

357
10 9 8 7 6 5 NUMBER OF YEARS OF DATA

Figure 7. —Projected 10-year (1979-1989) growth of estimates of the amount of original

oil in place in fields discovered before 1979 in the conterminous United States versus the number of years of data used. Thirteen years of data are from 1966

to 1978; two years of data are from 1977 to 1978.

70 i60 -

50 -

^ 30 - I — , COCQ 20- |

1

| X

10 " I—£ o O I 1 ee. O -io -

| -20 -

-30 - I I

-40 -

_ so

I I I I J 1 1

1 ' 1 ' ' L 13 12 11 10 9 8 7 6 5 4 3 2 NUMBER OF YEARS OF DATA

Figure 8. —Projected total growth of estimates of the amount of original oil in place in

fields discovered before 1979 in the conterminous United States versus the

number of years of data used. Thirteen years of data are from 1966 to 1978;

two years of data are from 1977 to 1978.

358
150

1 1 1 1 1 I I 1 I I I i 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 ESTIMATE YEAR

igure 9. —Estimates made at the ends of the years 1966 through 1978 of the amount of

ultimately recoverable natural gas discovered in the conterminous United States

in each decade from 1920 to 1969.

81 r

_l I I I I 1 I 20 25 30 35 40 45 50 YEARS SINCE DISCOVERY

Figure 10. —Average 1-year percentage growth

amount of ultimately recoverable

United States versus years since

of estimates made during 1970-1978 of the

natural gas in fields of the conterminous

discovery of the field.

359
60

50

10

10 9 8 7 6 5 NUMBER OF YEARS OF DATA

Figure 11. —Projected 10-year (1979-1989) growth of estimates of the amount of ultimately

recoverable natural gas in fields discovered before 1979 in the conterminous

United States versus the number of years of data used. Thirteen years of data are from 1966 to 1978, two years of data are from 1977 to 1978.

160

10 9 8 7 6 5 NUMBER OF YEARS OF DATA

Figure 12. —Projected total growth in estimates of the amount of ultimately recoverable

natural gas in fields discovered before 1979 in the conterminous United State versus the number of years of data used. Thirteen years of data are from

1966 to 1978; two years of data are from 1977 to 1978.

360
Table 1. —Discoveries of recoverable crude oil in the conterminous

United States by year of discovery estimated as of 12/31/78

and multiplied by the growth factors. [Discovery estimates

were published by American Petroleum Institute, American Gas

Association, and Canadian Petroleum Association, 1979, v. 33]

Discoveries

times

Discoveries growth factor

Year 106 bbl 106 bbl Growth factor

1978 63 480 7.581

1977 136 494 3.624

1976 172 451 2.610

1975 344 763 2.216

1974 351 663 1.888

1973 513 876 1.708

1972 313 534 1.704

1971 595 978 1.643

1970 706 1126 1. 595

1969 577 903 1.564

1968 967 1460 1. 509

1967 X J \J 1 700 1051 1.499

1966 X J \J \J 502 739 1.471

1965 721 1059 1.468

1 9 64 R4R 1230 1 . 450

1963 x j yj _» 475 675 1.422

1962 962 1337 1.390

1961 J- J \J _L 498 686 1.377

1 960 1005 X \J \J -J 1363 1.356

1959 740 1009 1.363

19X J 58\J X1174 X / *T 1597 1. 360

1957 2062 2791 1.353

1956 1923 2601 1.352

1955 1524 2037 1.335

1954 2148 2851 1.327

1953 2155 2819 1.308

1 9 5? J.1105 J U J 1682 1.288

1951 1733 2213 1.277

1950 2742 3451 1.258

1949 3425 4268 1.246

1948 3463 4327 1.249

1947 1569 1967 1.253

1946 1488 1825 1.226

1945 2098 2567 1.223

1944 2720 3291 1.209

1943 1339 1620 1.209

1942 1443 1734 1.201

1941 2247 2752 1.224

1940 3813 4520 1.185

1939 1963 2290 1.166

1938 4030 4678 1.160

361
Table 1. —Discoveries of recoverable crude oil in the conterminous

United States by year of discovery estimated as of 12/31/78

and multiplied by the growth factors (continued).

Discoveries

times

Year

Discoveries

106 bbl

growth factor

106 bbl Growth factor

1937 3425 3973 1.159

1936 6681 7678 1.149

1935 2493 2814 1.128

1934 3858 4322 1.120

1933 1578 1762 1.116

1932 579 644 1 .112

1931 2477 2747 1.108

1930 7673 8471 1.103

1929 3770 4127 1.094

1928 2915 3237 1.110

1927 1770 1919 1.084

1926 4726 5083 1.075

1925 1062 1183 1.113

1924 896 988 1.103

1923 1082 1127 1.042

1922 1366 1404 1.027

1921 1934 1974 1.020

1920 2238 2252 1.006

Pre-1920 26857 26857 1.000

TOTALS 134962 158352 Growth 23390 x 10 6 bbl

362
Table 2. —Discoveries of original oil in place in the conterminous

United States by year of discovery estimated as of 12/31/78

and multiplied by the growth fafctors. [Discovery estimates

were published by American Petroleum Institute, American Gas

Association, and Canadian Petroleum Association, 1979, v. 33]

Discoveries

times

Discoveries growth factor

Year 10 6 bbl 10 6 bbl Growth factor

1978 255 1267 4.967

1977 613 1603 2.611

1976 786 1531 1.947

1975 1361 2333 1.714

1974 1312 2060 1.570

1973 1860 2608 1.401

1972 1334 1845 1.382

1971 1798 2422 1.347

1970 2375 3187 1.341

1969 2496 3296 1.320

1968 3146 4070 1.293

1967 2628 3376 1.284

1966 2161 2747 1.270

1965 2586 3295 1.273

1964 3050 3827 1.254

1963 1688 2088 1.237

1962 2700 3300 1.222

1961 210.0 2543 1.210

1960 3436 4044 1.176

1959 2828 3297 1.165

1958 4072 4735 1.162

1957 6356 7333 1.153

1956 6368 7356 1.155

1955 5701 6515 1.142

1954 7330 8267 1.127

1953 8154 9036 1.108

1952 4670 5069 1.085

1951 6331 6884 1.087

1950 7624 8242 1.081

1949 18537 19890 1.072

1948 8122 8752 1.077

1947 5633 6065 1.076

1946 4227 4497 1.063

1945 6678 7153 1.071

1944 8051 8457 1.050

1943 4071 4283 1.052

1942 4433 4655 1.050

1941 6963 7421 1.065

1940 9568 9995 1.044

1939 5799 6035 1.040

1938 10374 10795 1.040

363
Table 2. —Discoveries of original oil in place in the conterminous

United States by year of discovery estimated as of 12/31/78

and multiplied by the growth factors (continued).

Year

Discoveries

10 6 bbl

Discoveries

times

growth factor

106 bbl Growth factor

1937 8557 8880 1.037

1936 19646 20352 1.035

1935 7015 7223 1.029

1934 9317 9529 1.022

1933 4229 4302 1.017

1932 1984 2012 1.014

1931 5930 6000 1.011

1930 13731 13885 1.011

1929 10657 10778 1.011

1928 8093 8382 1.035

1927 4901 4968 1.013

1926 13326 13428 1.012

1925 4069 4298 1.056

1924 3165 3358 1.060

1923 3617 3640 1.006

1922 4215 4148 0.984

1921 6176 6331 1. 025

1920 9020 9017 0.999

Pre-1920 98277 98277 1.000

TOTALS 425527 455068 Growth 29541 x 10 6 bbl
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365
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366
DISCUSSION

MR HERRON: Potter Herron from Drury Federal.

Dave, your gas numbers were 900 trillion cubic feet, and the oil

numbers 154 billion barrels and that compares almost exactly with

the ultimate recovery reserve Dr. Hubbert gave us yesterday. It's

all over? Is that what you're saying?

DR. ROOT: Well, we all work from the same series of data, yes, I got the same answers.

MR. MOORE: Frank Moore of Lewin and Associates.

We've just completed an analysis of the blue book series for Canada,

and we found similar general trends. I was wondering, in your

various graphs that showed, there was wide variability in recovery

as a function of the number of data sources (figs. 3, 4, 7, 8, 11,

and 12). In view of the fact that the standard variable is a variance in sample means as a function of samples size, have you tried

some procedure for using — for every estimate you get of the growth

ratio, there are different numbers that I take it you're averaging.

Have you tried to incorporate a variability in that, perhaps using

some sort of Monte Carlo, the selector growth factor, and using a large number of trials in some way, to incorporate variability and

to give limit to uncertainty?

DR. ROOT: No, I really haven't. I don't know what causes the variation, but

it doesn't seem to me that it's really a random error. I think it

might be a change of personnel on the committees who put together

the data. It really doesn't seem like the kind of thing I can compensate for, so I haven't tried. I'd be happy to get rid of the

variability but I haven't seen any way to do it.

MR. MOORE: In our 1977 analysis, for ERDA, we did a Monte Carlo analysis, and

the limits were fairly tight. The second question I had: Have you

tried to, in any way, arrive at a behavioral explanation of the

characteristic shape of the growth curve, tried to find any reasons

or deterministic factors for the five-year precipitous drop in gas

and the four-year drop for oil?

DR. ROOT: No, I don't know where it comes from. It might be that it just takes

that long, once you find a field, to develop it to get it all reported.

And by the time six years is up, if the field is worth anything, then

that's been done. And thereafter it's just minor improvements in

recovery. But I don't have any detailed explanation for the shape of

the growth curves for oil and gas fields.

367
MR. BEPEK- John Bepek from Standard Oil.

The blue books show that some amount of oil is added from discoveries before 1920' s. Did you take into account in your estimate of future recoveries, and if so, how do you do that?

DR. ROOT: Well, it is true that they do record oil discovered before 1920,

and I did use it in my calculations, certainly for the totals.

I assumed that growth would persist only for 60 years, which is

admittedly a conservative assumption in that there are very large,

very old fields that will probably still grow some. On the other

hand, there are fields being discovered recently, which won't grow

for anywhere near 60 years, because they'll be abandoned before

they're 60 years old. So 60 years seemed like a compromise number.

It was obviously to small for some and too large for others but I couldn't see any way to refine the choice more than that.

CHAIRMAN KEENE: Thank you very much.

I get a more uncomfortable feeling as people go through their

analysis with the blue book, because we just published our first reserves report and probably in five years we'll have

a total of eight white or yellow or however they're going to come out books, so save all your models and your charts,

because you'll be able to redo them with different numbers —

and perhaps it'll explain some of the anomalies that you

picked up.

Our variances from API and AGA are like in the state of

California off by about 30 percent. So there are some differences

368
The Economic Accounts of the Resource Firm

David Nissen*

I. SUMMARY AND ABSTRACT

This paper develops the economic accounts of the resource firm.

The economic valuation of the firm's net cash flow, computed as

the sum of the discounted cash flow (DCF) , is analyzed in the

format of conventional financial analysis. This permits consistent comparison of the economic valuation and the conventional

financial analysis of the resource firm or resource project.

Economic net worth is defined as the DCF value of net cash

payments to equity (dividends). The remainder of the economic

balance sheet is completed with the economic valuation of the

resource firm's assets: proven reserves, developing resources,

and undeveloped resources.

The DCF valuation method is shown to contain implicitly a

natural definition of economic income. Identification of income

as the change in net worth (retained earnings 1

) plus dividends

(distributed earnings) allows construction of the economic

income statement that is consistent with the economic balance

sheet. The key feature of the economic income statement, in

general, is that it properly organizes and evaluates the

imputed components of income: holding gains, allowance for

finance during construction, tax expense discounting due to tax

payment deferral (not treated here) , and replacement cost

expensing of depreciation, depletion, and amortization.

In this first report on research in progress, a highly simplified characterization of the resource production process is

analyzed. In particular the tax regime, alternative production

strategies, technical change, and uncertainty are assumed away. 2

II. FINANCIAL AND ECONOMIC ACCOUNTING

A firm's management evaluates and chooses among investment

projects. The financial community, viewing the firm as a

managed portfolio of investment projects, evaluates and chooses

among firms. These evaluations are accomplished using different,

and more or less inconsistent, methods.

369
Discussion

The firm evaluates investment projects by the discounted cash

flow method (DCF) , summing the discounted net cash inflow and

outflow of the project over time to develop a single "figure of

merit" for the project. This figure can be interpreted as the

excess or deficit present value of the project compared to a

project yielding (and reinvesting) income at the discount rate

used. 3

The DCF evaluation of a firm's project is essentially forwardlooking, evaluating the investment's prospects . By design,

this method aggregates over the time intervals between cash

outflows and inflows which embody much of the risk that is of

interest to financial analysts.

The conventional financial accounts of the firm as a whole

the income statement, balance sheet, and f low-of-funds statement—also organize and present information about the cash

flow of the firm. These statements are constructed with labels

which evoke valuation: income, expense, assets, liabilities,

and net worth; in fact, when the firm's activities occur

entirely on current account, the entries beside these labels

represent what economic intuition suggests. However, when

production entails capital expenditures—when there are

substantial lags between costs and consequent revenues

conventional accounting and economic valuation measures

diverge. 4 In times of inflation in particular, the conservative bias of "generally accepted accounting practice" usually

leads to undervaluation of income and assets.

The guiding principle of conventional financial accounting is

to be "conservative" and "objective." Because the accounting

profession regards its primary responsibility to be to present

and potential stockholders rather than to managers and entrepreneurs, accounting practice is controlled by the goal of

limiting the opportunity for dubious, self-serving, or fraudulent inflation of income and assets. As a consequence, the

conventional accounting valuation of assets and liabilities is

based on original cost rather than imputed market or replacement value, and the valuation of income is based on realized

revenue net of the expiration (expensing) of original costs. 5

Revenue realization and original cost expensing to some degree

separate what is known from what is speculative about the firm.

Thus, trends in cash flow and income realization implicitly

embody the development of information about the firm's investments, as well as the development of the investments themselves.

This, in turn, is implicitly recognized in the panoply of

ratios between balance sheet, income, and funds statement items

which financial analysts use to assess risk and performance of

firms

370
Thus the format of conventional fij^ancial accounts furnishes

types of information, not directly available from the DCF

analysis, which find widespread use for the analysis of risk

and performance in the business community. Of course, because

of differing measurement conventions, the content of conventional accounts differs from that of the DCF analysis as well.

Evaluation of the balance sheet at original cost (rather than

replacement cost or market value) is consistent with the

realization test and original cost treatment of the income

statement. This treatment excludes four classes of imputed

income and expense items which are central to the economic

valuation of income and of balance sheet entries. 6

These are:

o unrealized holding gains on tangible or financial

assets and fixed-interest-rate liabilities, 7

o imputed income allowance for finance during

construction (AFDC)

,

o imputed tax expense discount due to tax payment

deferral, and

o replacement cost recognition in depreciation,

depletion, and amortization (DD&A) expense.

The production process of the resource firm, which comprises

the ownership, discovery, development, and production of natural

resources, is among the most capital-intensive economic

activities. Although these processes employ large, durable

facilities and equipment, as is true in heavy manufacturing,

more important are the long lead times required to find and

develop resources before production begins , and the long period

required to complete production of developed reserves. Purchases of labor, materials, services, and property rights during

the exploration and development phases are just as much capital

expenditure as the purchase of tangible assets (though these

purchases may be expensed for tax purposes) . Valuation of these

assets in economic rather than financial terms requires recognition of holding gains on marketable assets, increases in

asset cost due to finance required during construction, reduced

tax expense due to tax relief 8 and discounting of deferred tax

payments, and recognition of replacement costs in depreciation,

cost depletion, and amortization expense.

As assets change in economic value over time, consistent

accounting requires that the economic measure of net worth

change in step. Since the change in net worth flows from the

retained earnings portion of income, the imputed income and expense items must be recognized in the determination of economic

income.

371
This discussion suggests that the results of a DCF investment

evaluation can be analyzed in the format of conventional

financial analysis, thus constituting the economic accounts

of the firm. This is true, and the purpose of this paper is

to present a basic version of the analysis for a highly simplified depiction of the resource firm—that which is used in

the optimal resource extraction (or Hotelling) literature.

This is the first step in developing these accounts for the

general case, with accurate representation of project investment timing, service life, technical change, and tax regime.

Motivation

The economic accounts, when developed for the general case,

serve several purposes. They provide for cross-fertilization

between financial and economic analysis. Economic information

is made available to financial analysts in a familiar format.

Economic valuations of balance sheet items are consistently

presented. A consistent economic interpretation of income

statement items—particularly imputed income and expenses

is provided.

Collaterally, the conventional financial accounting format

the allocation of value and income—becomes available to sharpen

and refine the economic evaluation of the DCF method. The conventional analyses of cash flow, liquidity, coverage, and exposure can be carried out with economically meaningful values.

At a time when the structure and terms of investment in resource

industries, especially energy industries, are being resolved by

the analysis and debate of operating business, financial business, government policy makers, and academics, this rationalization of measurement systems should sharpen understanding of

costs, gains, and incentives.

An important and inflammatory issue in this debate is the

question of "undue profits" in the resource industries, particularly the petroleum industry, where levels of profit,

profits share of sales, and profitability are usually compared

to manufacturing. Construction of the appropriate economic

accounts can resolve this issue with regard to the comparative

levels of economic profits and profitability.

In anticipation of this, two qualitative observations can be

made. First, profits' competitive share of sales should probably be relatively higher in petroleum compared to manufacturing due to greater capital intensity. Since much of this

capital accrues over the life of the resource project as

holding gains, AFDC, and deferred tax discounting, the bias in

conventional accounting measures of income, assets, and equity

is to underestimate the petroleum figures relatively more than

those of manufacturing. 9

372
Second, since both the numerator and denominator of the returnon-assets and return-on-equity probably suffer relatively

greater underestimation in the petroleum industry, the effects

of the conventional accounting bias on the measurement of the

absolute level of profitability in petroleum and profitability

relative to manufacturing are unclear. In any case, measures

of relative profitability taken from conventional accounts

should be viewed with caution. I believe construction of the

economic accounts with adequate representation of the investment timing, project service life, and tax regime in each

industry is required to resolve this issue.

Further, the economic accounts directly provide a tool for use

by and evaluation of management. Such a tool can be an important ingredient in the response to a pervasive theme in today's

business press—that U.S. management, guided and evaluated by

conventional accounting systems, behaves short-sightedly

Certainly, a manager must be especially articulate to prosper

in the eyes of his board of directors, while following an

investment strategy whose returns accrue economically but not

financially during his tenure.

Finally, in these times of general inflation and the further

relative escalation of resource and capital goods prices, the

divergence -between economic reality and accounting practice

has induced a sense of unease in the accounting financial

community, leading to a variety of proposed reforms: inflation

accounting, replacement cost accounting, and the like. Neither

the purposes nor the consequences of the proposals are well

understood. Laying the economic accounts of the firm beside

the conventional accounts in a common format should go a long

way toward clarifying the relation of these measures to

economic valuation.

III. FUNDAMENTALS OF THE ECONOMIC ACCOUNTS

The basis of the economic accounts of a firm (or project) is

the definition of economic net worth as the DCF value (present

value) of the firm's net cash payout stream, here defined as

dividends. 10 Then, defining the change in net worth as

retained earnings, it is natural to define economic income

as equal to dividends plus retained earnings^ that is, income

distributed plus income retained.

The balance sheet is completed by allocating to each asset

(liability) the present value of the net cash flow it generates

(requires) . In vertically integrated production processes this

is accomplished by determining the appropriate transfer price

for evaluating the flows between asset classes. In the

373
integrated resource production process, for example, there are

four prices characterizing transactions with external markets:

the price of acquisition of property rights to undeveloped

resources (the lease bonus plus royalty commitment) , the prices

of capital goods inputs, the prices of operating inputs, and

the prices of finished products. The acts of exploration and

finding, and development create intermediate assets, here distinguished as the developing resource and the proven reserve.

Prices of these assets are constructed to reflect the resource

acquisition cost, capital outlays, and the allowance for

financing the required inventory of developing resources

With income defined as the change in net worth plus dividends,

and net worth equal to assets minus liabilities, the income

statement is generated by classifying the components of changes

in assets and liabilities.

The net cash flow generated by a class of assets can be separated into the value of the capital services generated (implicitly, the rental imputed to the capital service) minus

capital expenditures. For intangible assets, those whose

value cannot be decomposed into a measure of quantity and

price, the change in the value of assets can be allocated to

capital expenditure plus an allowance for finance required for

holding the asset minus amortization of the capital services

expired (expensed). For tangible assets, those whose value can

be decomposed into measurements of price and quantity, 11 a

sharper allocation of the change in asset value is available.

Changes in the price of tangible assets generate holding gains,

and changes in the quantity of assets held (or more generally,

expiration of the value of remaining future services) generate

depreciation plus depletion expense. Hence changes in the

value of tangible assets held can be allocated to capital

expenditures plus holding gains minus depreciation and depletion.

The whole point of the economic valuation of firms or investment projects or individual assets is that there is an intimate connection between their value as assets and the value

of the capital services they furnish over time. Here we show

that the economic value of an asset's capital services will

cover depreciation and depletion plus a finance allowance net

of capital gain while holding. Equivalently , the price of an

asset equals the discounted, depreciated value of its capital

services

12

To demonstrate these propositions we introduce the present

value operator PV[ ] . Let X and r on [t,°°) represent cash

flow and the discount rate between now (time t) and the indefinite future. Define the present value of X with discount

rate r, say V, as:

374
V

t

= PV

t

[X;r] = F(t,x;r) X dx (3-1)

t

T

where the discount factor is

rT

F(t,r;r) = e

r dz

t

z

The change in V

fc is given by

^t = ar *Vx ' rj = r

t

v

t

" x

t-

(3 " 2)

When there is no ambiguity, PVt [X;r] will be written, PV[X] , and

F(t,T;r) will be written F(r). 13

One technical note: throughout this paper, in all expressions

of the form of equation (3-1) assume a boundedness condition , that the growth rate of X is bounded below r so that the improper integral in (3-1) exists and

lim F(t,x;r) X =0.

Relation of Net Worth and Income

If we define net worth (NW) of a firm or project as the present

value of its dividend stream, DIV,

NW = PV[DIV] , (3-3)

and define income to be equal to dividends plus the change in

net worth (retained earnings)

,

INC = DIV + NW, (3-4)

then, since (from (3-2))

NW = r NW - DIV, (3-5)

income must equal the discount rate times net worth,

INC = r NW. (3-6)

Note that this intuitively desirable result is not imposed but

is derived from the natural definition of economic net worth

and the inescapable accounting definition of income as income

375
distributed (DIV) plus income retained (NW) . This is because

the DCF valuation method implicitly compares the investment

yielding DIV to an investment yielding r (both reinvesting at

r) and, in effect, reinvests its excess value, NW, at r.

Asset Valuation and Balance Sheet

To permit an intellible discussion of the core results of the

analysis, assume debt and interest, new equity, taxes, and

working capital are all zero (generalization to accommodate

these phenomena will be offered in subsequent papers) . The

only source of cash is operating income (OY) and the only uses

for cash are capital expenditure (CE) and dividends (DIV) . Thus

the simple cash account might appear as in Figure 1. This can

be expressed as:

Suppose capital expenditure is divided between tangible and

intangible assets,

DIV = OY - CE. (3-7)

" T I CE = CE X + CE , (3-8)

and operating income is allocated between the services of

tangible and intangible assets,

At I OY = CS + CS . (3-9)

SIMPLE CASH ACCOUNT

Sources Symbol

Operating income

= Total sources,

OY

I Uses

Dividends

+ Capital expenditure

= Total uses

DIV

+CE

Figure 1. Simple cash account

376
(The determination of the value of capital services from tangible

assets, CST , is listed below; given CS^, the residual from operating income, OY, is the imputed value of capital services from

intangible assets, CS 1

.) Defining tangible and intangible asset

values:

TA = PV[CST

- CET

] , (3-10)

IA = PVfCS 1 - CE 1

] , (3-11)

we have (from Equations 3-3, 3-7, 3-8, 3-9, 3-10, and 3-11) the

balance sheet identity,

NW = TA + IA, (3-12)

net worth equals tangible assets plus intangible assets (recall

there is no debt or taxes)

Income Statement

To construct the income statement, we must allocate the changes

in assets. Define the allowance for finance on intangible

assets

,

AF = rIA, (3-13)

and amortization of intangible assets equal to capital services

expired,

AM = CS 1

. (3-14)

Then given (from Equation 3-11)

IA = PVtCS 1 - CE 1

] ,

we have (from Equations 3-2, 3-13, and 3-14)

IA = rIA - (CS

1 - CE1

), (3-15)

= AF - AM + CE1

.

377
Suppose the value of tangible assets can be written as price

times net capital stock, say,

A

TA = pK, (3-16)

and capital expenditure can be written as the value of net

investment plus depreciation,

CE

T

= pK + DP. (3-17)

Define holding gains as the capital stocks times price change,

HG ^ pK. (3-18)

Then

• • • IA = pK + pK, (3-19)

and (from Equations 3-17 and 3-18)

IA = HG + CET

- DP. (3-20)

Recall (from Equation 3-4)

INC = DIV + NW,

so (from Equation 3-12)

• • INC = DIV + TA + IA

and (from Equations 3-15 and 3-19)

INC = OY - CE + HG + CET

- DP + AF - AM + CE1

, (3-21)

so

INC = OY + (AF + HG) - (DP + AM). (3-22)

378
(Economic income equals operating income plus imputed income

items (allowance for finance plus holding gains) minus imputed

expenses (depreciation and depletion plus amortization of

intangible assets)).

This proves the income statement shown in Figure 2.

INCOME STATEMENT

Operating Income OY

-4- T ^

^ Uilvj/-\ X

1 /ILI Xt ncr I ly «aLjdlllD 1 no XT x I ur x

Allowance for finance on intangibles) AF)

- (Depreciation and Depletion + - (DP + Amortization) AM) = Income = INC

Figure 2 . Development of the income statement

We can understand the difference between economic accounting and

conventional accounting by considering the three equations:

NW = PV[DIV] , (I)

INC = DIV + NW, (II)

INC = OY + (AF + HG) - (DP + AM) . (Ill)

Economic accounting takes I as the definition of net worth and

II as the definition of income. Then III is derived as a consequence of the definitions. Conventional financial accounting

takes III as the definition of income, given special rules

about the determination of the non-cash items: finance allowance, holding gain, depreciation and amortization. Then II is

taken as the definition of the change in net worth given conventions about initial and on-going capitalization. Of course

in conventional financial accounts, Equation I is irrelevant. 11*

379
Capital Asset and Capital Service Pricing

To develop the relationship between the value of an asset and

the value of its services, first note (from Equations 3-10 and

3-15)

TA = PV[CST - CET

] = pK.

Then

TA + rTA - CST+ CET = pK + pK. (3-23)

Recall (from Equations 3-17 and 3-18)

HG = pK,

T A CE = pK + DP,

and define

T A AF = rTA. (3-24)

Then, combining the last four equations,

CST

= AFT

+ DP - HG. (3-25)

This relation says the value of capital services from an asset

equals the allowance for finance on the asset minus holding

gains. It may be alternatively written to show that gains

equal losses in this accounting system;

CST

+ HG = DP + AFT

,

which says current account yield (CS ) plus capital gains (HG)

equals depreciation and depletion expense (DP) plus carrying

charges (AFT

) . This result is at the heart of Jorgenson's

development of capital theory [6]

380
Special Case; The Constant Rate of Depreciation of Net Capital

Jorgenson's treatment can be exploited to provide a computationally simple set of accounts in the case that the rate of

depreciation of net capital is constant. Define economic

depreciation as the replacement value of Dhysical depreciation

(6K),

DP = 6pK. (.3-26)

Now the value of services from a unit of capital, called the

capital charge factor or the user cost of capital services, c,

is,

C — AF + DP - HG, (3-27)

c = rp + 6p - p.

This may be immediately integrated (given the boundedness

condition) to give,

rT

Pt

(r + 6)dz

e

#t

c dx (3-28)

t

= PV[c; r + 6] .

Thus, the asset price equals the discounted and depreciated sum

of its service values.

A similar relation between the value of tangible assets and the

value of their services holds. Given:

TA = PV[CST - CET

]

,

and

CST = cK = (rp + 6p - p)K,

CET

= pK + 6pK,

381
we have

TA = PV[rp + <5p - p)K-(pK + 6pK) ]

= PV[rpK - pK - pK]

,

T r dz

z

t

S- (e

fc " p K ) dx

dl V T T

'

-e

rT r dz „

. Z | oo t PT

K

T

J t

.

= P-(- K

t (9^ven ^he boundedness condition) . (3-29)

This says the balance sheet valuation of tangible assets equals

the market value of the net tangible capital stock.

In fact, with these assumptions we may now develop the balance

sheet and income statement for the constant rate of depreciation case with complete computational operationality . Given

time paths for,

OY - operating income (revenue, RV, minus operating

cost, OC)

K - net tangible capital stock,

CE

1 - capital expenditure on intangible assets,

r - the discount rate,

p - the price of the tangkble asset,

6 - the (constant) rate of physical depreciation

of tangible capital,

define

382
NW = PV[DIV] = PV[OY - CE]

,

= PV[OY - CE

1 - CK] + PV[cK

= IA + pK, (3-30)

where

IA = PV[OY - CE1 - cK] . (3-31)

Thus the intangible asset valuation is revealed as the present

value of operating income minus intangible capital expenditure

minus the appropriate charge for services of tangible capital.

This information may be calculated and presented in the balance

sheet and income statement shown in Figures 3 and 4.

BALANCE SHEET

Assets Notation Calculation

Tangible assets TA pK (=PV[cK - CET

]

)

+ Intangible assets IA + PV[OY - CE

1 - cK]

Net Worth

NW = PV[DIV]

= PV[OY - CE]

Figure 3

The economic balance

constant depreciation

sheet —

rate case

- p(K + 6K)],

383
INCOME STATEMENT

Notation Calculation

Revenue RV RV

— Operating cost OC - or

= Operating income OY = OY

+ Holding gain on tangible assets HG + pK

+ Allowance for finance on

intangible assets

AF + rIA

- Depreciation and depletion DP -6pk

- Amortization AM - (OY - cK) = Income INC = rIA+(c + p - Sp) K

= r(IA + pK)

= rNW

Figure 4. Economic income statement--

the constant depreciation rate case

Finally the cash statement (more properly, the flow of funds

statement or the statement of changes in financial position) in

the traditional financial form, showing adjustments to income,

is presented in Figure 5. (Net change in cash equals zero

because there is no working capital and thus no changes in

working capital)

To recapitulate, for the special case of a constant rate of

depreciation for net capital stock (which allows analytic evaluation of the appropriate integrals) , a computationally complete

specification of the economic balance sheet, income statement,

and cash statement is given in Figures 3, 4, and 5.

384
LAbH statement

Sources Notation Calculation

Income INC rNW (=rIA + rpK)

Non-cash income - (HG+AF)

• - (pK + rIA)

+ Non-cash expense + (DP + AM) + (6pK + rIA)

Total sources Z = rpK - pK + 6pK + OY - CK

— OY

Uses

Dividends DIV OY - CE

+ Capital expenditure + CE + CE

Total uses = OY

Figure 5. Cash statement--constant

rate of depreciation case

IV. ECONOMIC ACCOUNTS FOR THE RESOURCE PROCESS

We now address the main problem of this paper, construction of

the economic accounts for the resource production process . The

structure of the resource process is described in the next section. In the following section, the value of each asset which is

distinguished in the process is analyzed. An asset's economic

value is shown to have simultaneously a retrospective and prospective interpretation. Retrospectively, it represents replacement cost; prospectively it represents the present value of the

operating income stream which the asset generates.

The accounts for the resource process are developed in the final

section of this chapter. These accounts for developed by

assuming optimizing competitive behavior for the process as

whole and using the shadow prices on the constraints relating

activities as the appropriate transfer prices between the

activities. 15 Shadow prices on inventory requirement constraints

are the unit production allowances for financing these inventories net of holding gains.

385
The Resource Production Process

The resource production process for which we develop economic

accounts is depicted in Figure 6 and a glossary of the notation

is in Figure 7. Figure 6 shows three aspects of the process.

The diagram on the left shows value flows between the activities

in the process and between the process as a whole and the outside

world (generally, quantities are on the left and actual or imputed prices are on the right of an arc representing value flow)

The center column gives the dividend flow from each activity and

from the entire process. These flows are implied by the conservation of value (and the absence of cash accumulation) in each

activity.

The constraints characterizing each activity and the (imputed)

prices measuring the value-added they induce are given on the

right of Figure 6.

The process is divided into three vertically integrated activities: Production of the final resource product (say crude oil)

,

Development (finding proven reserves from a pool of resources

under development) , and Ownership and Exploration (selling and

exploring property rights to undiscovered resources for exploration) . There is a- slightly unnatural aspect of this description. Capital

expenditure is shown as an input to Ownership and Exploration.

This is done to internalize the relationship between capital

requirements and resource exhaustion. On the other hand,

Development shows no inputs but developing resources and adds

value only by holding them in inventory. But since Ownership

and Exploration requires no inventory, this is equivalent to

showing capital expenditures occurring at the beginning of the

development activity. 16

In the Production activity, proven reserves, R, are added to by

finding, f, and are depleted by production, q, so

R = f - q.

Production is constrained by the level of reserves divided by i , which is the reserve inventory required to produce one unit per

period (the reserve-production ratio) , thus

q = R/iR

. p This inventory constraint adds value a to production as an

allowance for financing the required inventory of proven reserves

(net of holding gains) . Thus the dividend flow from Production is

386
STRUCTURE

Q

p q

DIVIDENDS CONSTRAINTS

Production

(R)

v

R

(wq)

Development

(D)

7fi

x

Exploration

* 7K

u v x

Ownership

(U)

K

DIVR

= p

Q

q - wq - VR

f

= Q R£

y q - v f

DIVD = v

R

f - v

Dx

nTT.U D K DIV = v x - p z

k(U)

(wq)

DIV =yQ

q - p

Kk(U)x

(VR

) R = f - q

(aR

) q=R/iR

(v

D

) D = x - f

(aD

) f 2 D/iR

(v

U

) U =-x

z = k (U) x, k = 0

U(-U =x)

Figure 6. The resource production process

387
Physical flows

q - production (bbl/yr)

f - finding proven reserves (bbl/hr)

z - investment in undiscovered

resources (units/yr)

x - acquisition and exploration of

undiscovered resources (bbl/yr)

Flow prices

y^ operating income ($/bbl)

proven reserve value ($/bbl)

capital goods price ($/unit)

Q

p w

v - K

P

"

Uv - undeveloped resource value

($/bbl)

Physical assets

R - proven reserves (bbl)

D - developing resources (bbl)

U - undiscovered resources (bbl)

Asset prices

v - proven reserve value ($/bbl) v

D - developing resource value

($/bbl)

v

U - undeveloped resource value3

($/bbl)

Technical ratios

i - required inventory of reserves

unit of production (yr)

iD

- required inventory of developed

reserves/unit of reserves

produced

k(U)-unit capital requirement for

developing the marginal

undeveloped resource (unit/bbl)

Finance allowances

a - finance allowance for proven

reserve13 ($/bbl)

a - finance allowance for developing resource*3 ($/bbl)

a. lease bonus plus royalty commitments

b. net of holding gain

Figure 7. Structured glossary of quantities and prices

388
DIVR

= p

Q

q - wq - v

R

f

,

= y

Q

q - v

R

f,

where y^ is operating income. 18

There is a symmetric though slightly less familiar characterization of Development. Resources under development, D, are added

to by exploration of new resources, x, and "depleted" by finding

proven reserves, f, so

D = x - f.

Finding is constrained by the level of developing resources and

the required per-unit inventory i D , so

f = D/iD

.

The inventory constraint adds value to proveg reserves through an

allowance for finance during construction, a . Thus the cash flow

to Development is

DIVD

= v

R

f - v

D

x.

Finally Exploration, x, depletes undiscovered resources,

U = -x,

and as the graph in Figure 6 shows, this depletion increases the

required capital per unit of resources explored as the stock of

undeveloped resources declines.

In summary, the resource production as a whole faces external

prices for product, or operating factors for Production (normalized per-unit output) and for capital factors of Ownership and

Exploration. The product of one activity within the process

adds to the asset base of the next.

Exploration depletes Ownership's stock of undeveloped resources

and adds to Development's developing resources. In addition to

the exhaustion premium (the lease bonus) it adds value through

the purchase of capital factors. Development adds value through

389
the allowance for financing the required inventory of developing

resources. Development's product, the finding of proven reserves adds to Production's inventory of proven reserves. The

requirement for Production to hold inventory at at least a minimum reserve-Production ratio adds value through the allowance for financing the reserve inventory. The relationship

among flows, stocks, constraints, and prices is illustrated in

the layout of the glossary.

Resource Process Valuation

The task before us now is to derive the asset transfer prices and

inventory holding costs for the activities in the resource process. Then with these prices we can evaluate the net worth of

each activity in the resource process and construct the balance

sheet and income statement recognizing the assets distinguished

in the process description.

The analysis strategy is to derive the optimum behavior of the

resource firm with the structure described. Characterization

of this behavior provides shadow prices on the constraints

describing interactivity transactions (asset transfer prices)

and activity inventory requirements (finance allowances) . (Note

that the focus here is on prices —necessary relations between

values when an optimum exists —rather than on quantities, the

usual objects of attention in this kind of derivation.)

Figure 8 presents this derivation. In Equation 4-1 net worth is

defined as the present value of the dividend stream qiven

optimal behavior. Equations 4-2 through 4-4 represent the asset

acquisition/depletion process, and Equations 4-5 and 4-6 represent

the inventory requirements of the process depicted in Figure 6.

Constructing the Hamiltonian, we find the conditions which

obtain if optimum behavior exists (see e.g., Arrow [1]).

Equations 4-7 through 4-9 establish the necessary relations between

product prices and input prices. Equations 4-10 and 4-11 quantify

the inventory costs and Equation 4-12 quantifies the price of

property rights to the marginal unit of undiscovered resources

(the lease bonus) . Equation 4-13 imposes the boundedness conditions which are required to make the present value calcualtion

meaningful. 19

Asset Prices

We now examine these pricing relationships in detail. 20 There

are two main results characterizing asset prices. The first is

that the prices of the products of an activity must cover replacement costs, including depletion and depreciation plus the

v 390
NW = max PV[p^ - w)q

f ,q,x

- p

K k(u)x] (4-1)

Subject to:

(vR

) R = f - q , q = 0, (4-2)

(vD

) D = x - f , f = o, (4-3)

(v°) U = -x , x ^ 0, (4-4)

(a

R

) q 1 R/iR

, (4-5)

(a

D

) f S D/iD

, (4-6)

given initial R, D, andI U > 0.

fl = F(r) [ (pQ - w)q - p

Kk(U)x + v

R

(f - q) +vD (x-f) - v°x

+ a

R

(R/i R - q) +aDD/iD -f)] .

|| < 0=>yQ = (pQ -w) ^ v

R +aR

, "<" => q = 0, (4-7)

* v

D

+ a

D

, »<» => f = 0, (4-8)

I I=o=> ^ v

U

+ p

K

k, "<" => x = 0, (4-9)

-|| = v^_ rvR = -a

R

/iR

and a

R

> 0 => q = R/iR

, (4-10)

d% *D D D / . D

"3D V " rV =

" a A and a

D

> 0 => f =D/iR

, (4-11)

8?i *U U K, • ~ 3U = v -rv = pkx =

K, • ,_ K,

-p k U = -p k

(4-12)

F(r)vR

R -» F(r)vD

D -»• F(r)vU

U > 0 as t -* oo

• (4-13)

Figure 8. Optimal behavior - the derivation of the

value of assets and inventories

391
inventory finance allowance. This is essentially a retrospective view of prices. The second result is prospective. It is

that an asset's value is the present value of the operating

income stream it generates.

The characterization of asset prices as replacement costs is

presented in Figure 9. There are three activity products in

the system: final product, proven reserves, and developing

resources. For each product, its price (or unit operating

income) must cover depletion cost (the "v" terms) plus the

capital cost of production. For the first two products, capital

costs take the form on inventory allowances (the "a" terms)

These allowances equal the required inventory level (per unit of

production) times the finance charge minus holding gain.

Asset/product prices

y

Q = v

R

+ a

R

, if q > 0, (4- 14)

v

R

= v

D + aD

, if f > 0, (4- 15)

(operating income) = (depletion) + (inventory allowance)

V —— tt^ V

_lT pr>^Vis., _L_L -i f Ji. y s> H\J i

( 4_ 1 fi}

(price) = (depletion) + (unit depreciation of capital)

Inventory allowance

a = i (rv - v )

,

(4- 17)

D -D , D *D X a = i (rv - v )

,

(5- 18)

(inventory allowance) = (inventory requirement) x

(unit finance allowance - holding gain)

Figure 9. Product prices at replacement cost

392
The second result is the forward valuation of assets. There are

three assets in the resource production system: proven reserves,

developing resources, and undeveloped resources. Each is worth

the present value of the operating income it produces (or the

cost it avoids). These results are presented in Figure 10.

For example, the first (equation (4-19) says that if future production is positive, 21 the value of a unit of proven reserves

(v ) equals the present value of its operating income (y^) times

the decline rate (dR , the level of initial production) discounted

by the discount rate plus the decline rate. The derivation in

Figure 10a shows this to be equal to the present value of the

production stream from a unit of reserves times unit operating

income. The second equation of Figure 10 (4-20) is a similar

statement about the value of a unit of developing resources.

The evaluation of undeveloped resources (Equation 4-21) is in terms

of opportunity cost rather than replacement cost (exhaustability

implies uniqueness) . When an additional unit of undeveloped

resources is exploited, the world must make do with inferior

remaining deposits. A time path of increased unit capital costs,

p£k

t

dt = p*(dk/dt)dt = p*dk=p*k'dUt

,

is imposed on reproducible capital by the exhaustion of an incremental unit of undeveloped resources. Thus the value of the

marginal undeveloped resource is the present value of the profile of these costs. 22

Balance Sheet

The economic balance sheet for the resource process is displayed

in Figure 11. We partition the dividend stream for the process

as a whole into the dividends (operating income minus capital

expenditures) for each activity (from Figure 6). Then the net

worth of each activity (the present value of the dividend stream

equals the market value of the asset it possesses) . Specifically, the net worth of the Production activity equals the value

of the proven reserve inventory (this is proven in Figure 11a)

the net worth of the Development activity equals the value of

the inventory of developing resources; and the net worth of

Ownership and Exploration equals the present value of the future

stream of lease bonuses generated by exploration.

(The proof in Figure 11a collects the four necessary conditions

for price and quantity behavior and shows they imply that the

dividend stream can be integrated to give the initial asset

value. Jorgenson's development of neoclassical capital theory

[6] entails such a step.)

393
Given: y

Q = v

R

+ a

R

, if q > (4-7)

a

R

= (rvR -vR

)/dR

, (4-8)

then: v

R

= PV[yQdR

; r + dR

] if q > 0, a.e.

a (4-19)

Given: v

R

= r

D

+ a

D

, if f > 0, (4-9)

a

D

= (rvD- v

D )/dD

, (4-10)

then: v

D

= PV[vR

d

D

; r +

D

] , if f > 0, a.e.

a (4-20)

So: (asset value) = unit production discounted at the

interest rate plus decline rate.

* U U K

* Given: v - rv = -p k,

then: v

U

= PV[pK

k] . (4-21)

So: (undeveloped resource value) = (value of induced

exhaustion)

a. This condition is discussed in Footnote 19.

Figure 10. Forward valuation of assets

394
Recall

Q R R

y = v + a , R .R, R *R,

a =1 (rv - v )

,

if q > 0, (from 4-14)

(from 4-18)

hence,

v

R = rv

R = -dR

(yQ - v

R

)

,

v

R

= (r +dR

) = -dR

y

Q

,

R

so: v = PVty^d ;r+d] if q > 0, a.e.,

t

v,R

(r

z + d

R

)dz

0 ytd dt,

^

y^dV^^^O^dt,

= PV[yQ

q]

,

where

,R -dR

(t - t n ) ^ = d e 0' , t/t

0

is the production at time t from a unit of reserves put into production at time zero.

Figure 10a. Derivation of proven reserve values

395
DIV ^ pQq

= P kx

,

= DIVR

+ DIVD

+ DIV0

,

where

DIVR

= p

Q

q

- v f,

DIV0 i v

R

f - DV X,

DIV - v x - P kx,

then:

NWR ^ PV[p Q

g - v

R

f] = v

R

R, (4- 2)

NW° £ (v

R

f _ D i D^

v x] = v D

,

(4- 3)

NWU

= PV[v°x - p

K

k] = PV[vUx]

BALANCE SHEET

Assets Liab. & NW

v

R

R

v

D

D

PV[vU

x] NW

Figure 11. Balance Sheet

396
Recall

R = q - f, (4-2)

q = R/iR

, "<" => aR = 0, (4-5)

yQ = V

R

+ a

R

, "<" =>q = 0, (4-7)

a

R = iR

(v

R

- rv

R

) . (4-10)

Then:

DIVU

= y

Q

q - v

R

f,

= (v

R

+ a

R

)q - v

R

f, (from 4-7)

= a

R R/iR

= v

R

(q - f ) , (from 4-5)

= (vR

- rv

R

) R - v

R

R, (from 4-10 & 4-2)

F(r)DIVU

= -^[F(r)vR

R] .

Integrating both sides and imposing the convergence conditions

gives,

so,

00 NW = -F(r)vR

R] = v

R

R . o

t

0

t

0

t

0

Figure 11a. Proof of the balance sheet for production

397
Income Statement

The evaluation of income for each activity is given in Figure 12.

Given activity dividends (from Figure 6) and net worth (from

Figure 6) and net worth (from Figure 11) , income is defined as

dividends plus the change in net worth. Income can be equivalently expressed as

INC = operating income - depletion + holding gains,

or

INC = inventory allowance + holding gains,

or

INC = allowance for finance on net worth.

These relationships are derived for the Production activity in

Figure 12a and are assembled in Figure 13. These activity income

statements contain interactivity transactions which net out in

the consolidated income statement or the resource process as a

whole.

The consolidated income statement is described in Figure 14. There,

income comprises [operating income minus depletion on production] plus [the inventory allowance on finding new reserves

and the finance allowance on future lease bonuses] plus [holding

gains on inventories of proven reserves and developing resources]

The associated cash statement is presented in Figure 15, revealing that the consolidated resource production process takes in

operating income on production and pays out dividends plus capital

expenditure. This is consistent with the process specification

in Figure 6.

To recapitulate, this Section derives economic accounts and asset

pricing for the resource process designated in Figure 6. The

derivation depends on the imputation of the competitive value of

the assets and asset inventories found in the resource process.

This imputation of value is accomplished through the device of

imputing optimality to observed behavior deriving the necessarily

implied valuation (in Figure 8)

Once asset values and inventory allowances are in hand, the

balance sheet and income statement follow from the valuation

of assets and the principle that total income equals income

distributed plus income retained.

398
Given

INC = INCR

+ INCD

+ INC0

,

we have:

Production

INCR= DIVR

+ NWR

* y

Q

q - V

R

f + (v

R

R)

,

=yq-vq+vf Q R * R

(= operating income - depletion

+ holding gain)

,

R * R = a q + v R (= inventory allowance + holding gain)

,

R R = rv R = rNW = (allowance for finance on net worth;

Development

INC

D

= DIVD

+ NWD

= v

R

f - v°x + (v

DD),

= v

R

f - v

D

f + v°D,

*D = a f + v D,

= rv

D

D = rNWD

;

Ownership and Exploration

INCU

= DIVU

+ NWR

= v

D

x - p

Kkx + PV[vU

x]

,

= rPV[vU

x] = rNWU

.

Figure 12. Evaluation of income by activity

399
Given:

INCR

= DIVR

+ NWR

= y

Q

q - v

R

f + (v^F) ,

the first condensation nets out net investment, i.e.,

(v

R

R - v

R

f) = v

RR + vR

R - v

R

f

,

= v

RR + v

R

(q - f) - v

R

f, (from 4-2)

= v

R

R - v

R

q,

leaving holding gains minus depletion as the "non-cash" change

in capital stock.

So:

INCR

= y

Qq - v

R

q + v

R

R.

Then since

y

Q - v

R

= a

R

or q = 0, (from 4-7)

we have INCR= a

R

q + v

R

R.

Finally since

a

R

= i R

(rvR

- v

R

) , (from 4-10)

iR

q = R or a

R

= 0, (from 4-10 & 4-5)

we have INCR = rv

R

R.

Figure 12a. Proof of income evaluation for production

400
Gross income statement Production E&F Ownership Total

Operating income Q

y q

i R, +v f +v

D

x

- Depletion & depreciation R

-v q -v

D

f -p kx

+ Holding gain +vR

R +;d

d

* U +NWU

= Income INCR INCD INCU =INC

Capital charges income statement

Inventory charges against

production

+a

R

q +a

D

f

. u

+v X

+ Holding gains +v

R

R +;

d

d

* U +NW

= Income INCR +INCD

+ INCU = INC

Allowance for finance on assets

= AFDC rv

R

R +rv

D

D +rNWU

= rNW

Memo: Balance sheet

Assets = v

R

R +v

D

D +PV[vU

x]

NW NWR +NWD +NWU

= NW

Figure 13. Activity income statement and balance sheet

401
Recall

NW = PV[DIV] = PV[yQ

q - p

K

kx] = v

R

R + v

D

D + PV[vU

x]

,

INC = DIV + NW.

It can be shown that

INC = y

Q

q - v

R

q + a

D

f + rPV[v°x]

' Tt * n

+ v R + v D,

so that we can form the:

CONSOLIDATED INCOME STATEMENT

Operating income o

y q

- Depletion R - v q

+ AFDC + aDf + rPV[vU

x]

+ Holding gain ••P "D + v

r

'R + v D

= Income

< = INC

Figure 14. Derivation of the consolidated income statement

402
CONSOLIDATED

Source

Income

- Non-cash income

+ Non-cash expenses

= Total sources

Uses

Dividends

+ capital expenditure

= Total uses

Figure 15. The consolidated cash statement

V. CONCLUSION

Section iv presents a detailed development of the economic

accounts of the resource process. The derivation clarifies the

role of non-cash income items (financial allowances and holding

gains) and non-cash expenses (depletion and amortization) which

are so prominent a part of valuation in this process. The

method of Section iv, expanded to include the "intangible

assets" treatment of Section III can be used to provide an

economic accounting for any behavior associated with the management of any production process.

CASH STATEMENT

y

Q

q - vR

q + AF + HG

- (AF + HG)

+ v q

QY q

Q K. y q - p kx

p

Kkx

0

y q

403
FOOTNOTES

*I am grateful to Vince Calarco, Ed Cazalet, Harvey Greenberg,

Bill Hogan, Dale Jorgenson, Pat Keenan, George Lady, Rao

Mangipudi, Fred Murphy, and Bob Pendley for discussions. The

material developed here is an extension of the theory of capital

developed by Jorgenson, described in [6] . In fact the basis of

the balance sheet presented here is Equations 12 and ff . of [6]

I regard the contribution here to be the discovery of the appropriate definition of income and the exploitation of Jorgenson 's

"user cost of capital services" in elaborating the income statement. Errors and ambiguities are mine.

1. Retained earnings as used here include new equity financing.

Negative dividends represent the investment of equity capital

by owners

2. An empirically applicable analysis admitting general treatment project investment lead structure, service life, and

tax regime is being developed and programmed and will be

reported later (see [8]).

3. This certainty-equivalent valuation may be an ingredient of

a general analysis of risk and yield through a decision tree

analysis, which is the formal economic version of risk

analysis

4. Leveraged by the long lead times involved, special tax

treatment for resource firms, especially tax expensing of

intangible drilling costs, enhances the divergence between

economic and conventional accounting measures

5. The "cost" and "realization" principles not only adhere to

the principle of conservatism, they also follow the maxim:

"Anticipate no gains; provide for all losses." The

historical-cost approach, as modified (by the lower-of-costor-market rule) , also is believed to result in objective

figures free from personal, subjective bias. A consequence

of this approach is that the accounting literature is filled

with admonitions to refrain from connecting accounting measures with valuations:

The auditor 1 s ... report expresses an opinion that the

balance sheet presents fairly the financial position

of a company in conformity with generally accepted

accounting principles. It is incorrect to conclude

404
from this, however, that a balance sheet is a

statement of financial position in the sense of

showing the value of a business (see [3, 23-24]).

Nor, it is fair to add, does the balance sheet, in general,

show the value of anything the business owns or owes which

is in the nature of a long-lived entity.

6. There is some recognition of these items in public utilities

accounting where asset valuation is central to cost-ofservice or rate-base/rate-of-return pricing.

7. Recognition of gains and losses is asymmetric in conventional accounting. Recognition of losses is encouraged

by the " lower-of-cost-or market" valuation rule.

8. Tax relief includes investment tax credits and the excess

of percentage depletion over cost depletion.

9. If you consider the oil production process to begin with the

geological and geophysical evaluation of provinces and structures, and to end with the closing of the last stripper well,

a process that can take 50 years or more, the average value

of goods-in-process may amount to five to twenty years of

production, where manufacturing typically has substantially

less than a year's production of goods in process. (Reserveproduction ratios for petroleum projects start at seven years

and go up, and reserves are declared to be proven on average

toward the end of the exploration and development process,

so this measure excludes resources in prior stages of development. On the other hand reserves are worth less than production, so the quantity ratio overstates the value ratio.)

The difference in the goods-in-process/production ratio

between the petroleum and manufacturing industries is partly

due to a classification difference and is partly intrinsic.

The exploration and production of oil are considered as a vertically integrated activity, while the construction of,

say, shoe factories and the production of shoes are not. On

the other hand both the "construction" and production phase

take longer in the oil business.

The importance of the classification differences is that in

the integrated petroleum industry, AFDC in the construction

phase is never realized in the conventional account books.

Similarly, in the longer-lived petroleum industry, imputed

holding costs on the requisite reserve inventory are not

capitalized.

405
10. We won't distinguish new equity as sources of funds, so negative

dividends imply a capital levy on owners.

11. The nomenclature of the conventional accounting classification of assets as tangible and intangible is, I believe,

misleading. Corbin [3, 28-29] says:

Whether these things differ from property, plant, and equipment in their tactile properties is not the point. What

matters is the commensurability or fungibility of their

quantity --can the concept of usage or capital service

expiration be made sufficiently and acceptably concrete so

that a depreciation schedule for financial expensing can be

published and adhered to. Intangible assets are those which

by convention cannot be depreciated. The only measurement of

quantity is value, and thus intangible assets are amortized,

often on an admittedly arbitrary basis. Of course in the

economic treatment, the measurement of depreciation and amortization is based on the expiration of the value of capital

services (cf . Hotelling [1] and Jorgenson [7]), so from an

economic point of view the difference between depreciation

and amortization is unimportant.

12. This argument follows Jorgenson [6].

13. The demonstrations here are carried through in continuous

time because differentiating is easier than differencing.

For implementation as an accounting system a discrete time

formulation is required. The following accomplished this

conversion. (The machinations in what follows are required

to get the dating in the change equation to be contemporaneous .

)

Define the (t-1) closing balance,

The main types of intangible assets are: patents,

copyrights, trademarks, tradenames, secret processes, leaseholds, licenses, franchises, corporate

organization costs, stock promotion costs, and goodwill .

oo V.t-1 = I T =t F(t,T)X

T

where

F(t, t + 1) =

T (The product over the null range

is defined as unity.) F ( t , t ) = n. t (1-r.)

406
Then m

CO Vfl = X

t

+ (1 - r

t' l Tmt+1 F(t + 1 ' T)X

T'

or

AV

t

= r

t Vt

-X

t

.

Thus the difference equation and its "integral" above can

replace the differential equations and present value integrals of the text. The discount factor (1-r. ) is not

usually encountered in present value calculations; rather

one sees (l+rf)"f as the one-period discount factor, where

r might be called the coupon discount rate. That is, an

instrument yielding a coupon r* , and so worth 1+r, at the

end of one period, discounted by (1+r*)" 1 to the present is

worth 1 today. If r is the contemporaneous discount rate

so that

(1-r) = (1 +r )

then

r = r*/(l + r*)

,

the contemporaneous discount rate is the discounted value of

the coupon discount rate.

14. My friend Patrick Keenan, a financial analyst, holds to the

view that, "Income is what Price-Waterhouse says it is!"

15. The extent to which institutions and behavior differ from

these assumptions can be captured in a residual "intangible

assets" account as in Section III of this paper.

16. An empirically usable implementation would distinguish many

stages of development and might show capital (pre-inventory

constraint) outlays and operating (post-inventory constraint)

outlays at any level.

17. This formulation finesses the "vintaging" that is required

in more general treatment and suffices for our expositional

purposes. The resource-finding constraint, like the reserveproduction constraint, can be regarded as a simple

407
approximation to a deterministic time profile for extraction

or for development. In fact the reserve decline rate

dR = l/iR

can be interpreted as the probability that a given unit of

reserves will be produced in the period; similarly, the

developing resource-finding decline rate (discussed below)

d

D

= l/iD

is the probability that a unit of resources under development will be proven in the period.

18. The price of operating factors, w, is per unit of production,

subsuming the technical coefficient. The assumption here of

independent operating costs, w, means that depletion is concentrated entirely in the quality decline of unexplored

resources, not reserves. In reality, after discovery,

reserves are declared proven (bankable is the operative

word amongst independent producers) only if the production

operating revenue covers development and operating costs.

To represent this generally, depletion would degrade

resource quality at all stages of production.

19. This is not strictly a necessary condition without further

restrictions, which eliminate mathematical pathologies.

20. This is something of a diversion from the treatment of the

accounts of an enterprise, but it shows that each unit of

an asset can be considered an enterprise in itself (tax

treatment, however , generates externalities) and justifies

the use of these prices in the enterprise accounting of the

next section.

21. If the future contains intervals where production, finding,

or exploration are zero, the problem is more complex. The

analysis would follow Arrow's treatment of irreversible

investment [2] where, during "blocked periods," for speculative reasons the producers would wish to pump produced resources back into the ground. This happens when capital

gains (plus "repletion") exceed the interest rate.

408
In the regulated natural gas industry of the U.S., this

behavior is pejoratively called "withholding," an abrogation of service commitments. It was alleged that this

behavior was rife when deregulation was in prospect.

Though assiduously searched for, little evidence to support

this claim surfaced. This implies either that American gas

producers lack effective initiative or possess effective

discretion.

The equation for resource value can be integrated to obtain

an interesting equation for the value of a developing

resource. That is,

U T*iT t r K»,

v = PV[p k]

integrates to

v =PV[k(rp -pk-p],

which says that the value of a unit of developing resources

equals the present value of the finance allowance net of

holding gain on its acquistion cost through the future.

409
REFERENCES

[1] Arrow, K. J. , "Applications of Control Theory to Economic

Growth," in Mathematics of the Decision Sciences , Part 2,

ed. by G.B. Dantzig and A.F. Veinott, Providence, R.I.,

American Mathematical Society, 1968.

[2] , "Optimal Capital Policy with Irreversible

Investment," in Value, Capital, and Growth, Papers in

Honour of Sir John Hicks , ed. by H.N. Wolfe, Edinburgh,

Edinburgh University Press, 1968.

[3] Corbin, D.A., "Financial Statements —Income Statements and

Balances Sheets," chapter 2 in [4].

[4] Davidson, S., and R.L. Weil, Handbook of Modern Accounting , 2nd Edition, McGraw-Hill Book Company, New York, 1977.

[5] Hotelling, H., "A General Mathematical Theory of Depreciation,"

Journal of the American Statistical Association , 20 (1925)

340-353.

[6] Jorgenson, D.W., "The Theory of Investment Behavior," in

Determinants of Investment Behavior , ed. by R. Ferber,

National Bureau of Economic Research, New York, 1967.

[7] , D.W., "The Economic Theory of Replacement and

Depreciation," in Econometrics and Economic Theory , ed. by

W. Sellekaerts, MacMillan, London, 1974.

[8] Nissen, D., "The Economic Accounts of the Firm," 1978,

unpublished.

410
Gulf Coast Undiscovered Resource

Data Collection System

Richard Zaffarano

Department of Energy

INTRODUCTION

In the midst of the World's deteriorating energy supply, the Nation is

increasingly relying upon conventional domestic offshore oil and gas

resources to offset import dependency,. Investment in synthetic fuel

projects are becoming more intimidating, with discouraging lead-times

and escalating capital costs. A key element in federal energy policy

analysis is the ability to estimate the conversion rate from petroleum

resources to reserves.

The Energy Information Administration (EIA) within the Department of

Energy (DOE) with Lewin and Associates, Inc. have been developing a model to analyze the impacts of policy changes on the rate of

exploration, development and production of hydrocarbons from offshore

regions.

This paper describes the data collection system applicable to 700

undeveloped prospects that provides model inputs concerning

uncertainty in resources development. The model simulates the rate

of exploration, development and production. A data collection

protocol was devised to collect hard core and subjective estimates of

undiscovered resource data for computer processing with probability

distributions assigned key parameters. Objective resource element

estimates were obtained on a prospect basis by means of standard

engineering equations relating parameters to potential resources using

Monte Carlo methods. Collection methodology and documentation are presented, stressing quantifying uncertainty inherent in the

estimating process.

411
Use of conventional regional resource appraisals, distributional data,

analogs and simulations have been inadequate to capture real-world

site specific prospects containing exploratory and developmental

criteria to estimate hydrocarbon potential and economic

attractiveness. Purpose of the data collection project was to test

the feasibility of constructing a disaggregated undiscovered resource prospect-specific data base for Gulf Coast to improve the validity of

projections. The study is devoted to prospect geologic and

engineering data developed from leasing tracts in water depths from

surfline to ]000 meters or less. (Figure 1)

Company confidential files, records and maps of the Conservation

Division of the U.S. Geological Survey (USGS) in Metairie, Louisiana

provided the highly sensitive source data. Stringent security

precautions were taken concerning data access, extraction and

processing to maintain the integrity of the information. A team of

experienced Gulf Coast geologists and consultants collected,

transformed, interpreted and prepared subjective estimates for the

Gulf Coast undiscovered resources. On site geological, geophysical,

engineering and lease data were reviewed and used. In addition,

consultations were held with USGS stratigraphic specialists regarding

interpretation of data in deep water areas.

The data protocol is shown in Table 1, source of data

element in Table 2, and the cover sheet used to bind fifty randomly

numbered data sheet to maintain confidentiality in Table 3. The cover

sheet and detached upper stub of data sheet remained with the USGS to

protect against disclosure and to facilitate future data updating.

The prospect is the basic study unit. It is an exploration

opportunity that would be evaluated as a single entity by an operator

deciding to bid^ explore or develop resources. It may consist of one

or more potential closures, if more than one closure was considered,

the relationships among respective closures was made explicit. That

is to say, the prospect could be developed from a common platform and

have common source rocks and/or were created by a common geologic

phenomenom

Data sources in the order appearing in Table 2 were as follows:

412
MAPS

Seismic:

(1) USGS prepared, evaluated for leasing areas adjacent to

evaluated areas.

(2) Commercially prepared, of some leasing areas.

Evaluation:

Status map showing USGS sale number and leasing area.

Overall

Large scale leasing area map of entire Gulf of Mexico.

Trend:

USGS prepared - depiciting aerial extent of recognized geologic

age producing trends.

Status

Section map for each of 26 official identified leasing areas commencing from the shoreline and extending to 1000 meters water

depth. Tract data were superimposed showing if evaluated and noting

lease sale number. Status of each tract was determined as to proved

or dry, leased and drilled, leased and undrilled, or unleased.

Hazard

USGS prepared indicating areas subsea stability of sediments

regarding developmental hazards i.e., mudlumps, gas seeps, mudflows

and deep seated faults that cut the shelf surface.

Bathymetr ic:

Bureau of Land Management, Department of the Interior prepared

map indicating water depth distribution in Gulf of Mexico.

Interpretation/Calculations

Data for tracts that had been evaluated by USGS, were

transcribed from appropriate files. For areas adjacent to evaluated

areas and those classed as other mapped areas, an appropriate

evaluated analog was selected. These analogs were either near the

prospect, of the same geologic age or at approximately the same vertical depth.

413
The following three columns in Table 2 refer to standard USGS forms in

their evaluation files that contain engineering and physical

parameters used as base data for the evaluated tracts and others

estimated by analog.

In the interest of purposely modeling degrees of uncertainity the USGS

leasing information (excluding lease sales 58 and 58-A, held in 1979) were assigned within four classes: (1) evaluated, (2) adjacent, (3)

other mapped and (4) unmapped. Commencing with the most recent

evaluated data, applicable relevant files and records were accessed

for each tract. If a tract was considered a drainage or a downstructure tract of a proved oil or gas field, it was eliminated.

These tracts are treated in a separate statistical analysis of

inferred reserves and are not part of the undiscovered resources.

In adjacent tracts, USGS seismic maps were evaluated and tract

data used as analogs for reservoir data. Closure areas were estimated from these maps using templates. For areas classed as other

mapped, commercial seismic maps were used. The maps were covered with

transparent paper; closures were identified; most likely areas drawn,

and trap type assigned. The process was repeated for all horizons

within the prospect. TP determine the maximum reach of conventional

platforms based on directional drilling to each horizon, a mathematical formula was derived. The radius of maximum reach was

equated to the tangent of 55 degrees times the difference in average

vertical depth and water depth. Number of platforms were determined

on the basis of trap type and maximum drilling reach.

In the unmapped areas, interpretative data were assembled using

analogs from evaluated or other mapped identified prospects.

Pipeline districts were established upon the assumption that each

platform is equipped with 10 miles of gathering line.

Districts were assigned as follows:

1. A strip 10 miles wide from shore was defined and named minus

one. If a platform is less than 10 miles from shore, it is assumed

the pipeline will be built to shore.

2. The area demarcated by a 10 mile strip along both sides of

existing trunklines was drawn. At the terminus of existing lines, a circle of 10 mile radius was drawn. This area was termed pipeline

district "zero" (area served by existing trunk pipelines)

3. Areas not covered in (1) or (2) were divided into circles of

about 20 miles radius or less, depending on the density of prospects.

These designated areas were randomly numbered to prevent

identification.

All pipeline district boundaries were made to conform to discrete

tracts with each tract in one and only one pipeline district.

414
The data collection system described was applicable to approximately

60 percent of the Gulf offshore because of limitations in project time

and resource availability. The remaining data were developed using a play-prospect analog method. For this approach, sub geographic

areas are assumed to contain sufficient geologic similar

counterparts. The geographic areas are termed "plays" of common

geologic history. Analogs were assigned to these areas from

evaluations and judgments of geologic trends designations and

comparable exploration prognosis. These representative analogs were

used in systemic sampling of the ratio of unproved areas of donor

(leasing area for which data were available or could be estimated) and

recipient (areas of common geographic and geologic composition for

which no data are available) areas. Plans are to complete the Gulf

sampling in fiscal year 1980.

The CCS Model concepts and implementation will be presented later in

the symposium and also was presented at the 11th Annual Offshore

Technology Conference in Houston, Texas on May 3, 1979. 1/ The

approach uses these disaggregated resource data in a novel prospect byprospect evaluation of costs with explicit treatment of risk.

REFERENCES

H »l

aSh^' 3 ' ?" mrra ' F " ^PhY' F.H., Ciliano, R. , and Hery,

w.J., A Model for Evaluating the Impact of Federal Policy on Offshore

Oil and Gas Recovery," Offshore Technology Conference May 3. 1979

Houston, Texas. ~ '

415
416
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419
A METHODOLOGY FOR ESTIMATING COST OF

FINDING, DEVELOPING, AND PRODUCING UNDISCOVERED RESOURCES

Thomas M. Garland

John H. Wood

Dallas Field Office

U.S. Department of Energy

Energy Information Administration

Assistant Administrator for Applied Analysis

It's a pleasure to be here this morning, and I welcome the opportunity to

give a brief explanation of the rationale utilized in developing the

methodology in the Permian basin study. As most of you know, the Permian

basin study was an interagency study by the Energy Information

Administration (EIA) and the United States Geological Survey (USGS) with a primary objective of turning "resource" estimates into "recoverable resource"

estimates with the cost required. The USGS was to develop the methodology

for the resource estimates, and EIA was to develop the engineering and cost

methodologies

Before I get into the methodology details, I would like to quote Mr. Charles

Masters of the USGS from a paper presented in the March 19, 1979, Oil and Gas

Journal concerning resource estimates. He stated, "The reliability depends

on (1) the estimator's ability to adequately organize and express the

conventional wisdom and (2) the former assuming that, indeed, the

conventional wisdom does reflect the factors that control petroleum

occurrence. Its credibility depends on (1) the critic's perception as to the

adequacy of the systematics of data manipulation in the assessment process

and (2) the confidence in the data set."

This quote also truly applies in the development of a model for the

engineering and cost factors related to undiscovered recoverable oil and gas resources. In the Permian basin study, our conventional wisdom for the

engineering and cost model was that: (1) the production characteristics of

undiscovered oil and gas fields of a given size would be similar to those of

fields of comparable size , and (2) depth of all undiscovered resources was critical in estimating the cost of exploration, development, and production.

Therefore, with this as our conventional wisdom, we set about to develop both

a data set that we had confidence in and a credible methodology for

systematically manipulating the data set. The data set was developed by the

Dallas Field Office by estimating the recoverable oil and gas from some 9t400

active and inactive oil and gas reservoirs in the Permian basin area. This

data set was initially developed for the USGS for their resource appraisal

study conducted in Denver and the field size distribution by depth study

conducted in Reston. It was also utilized in our engineering and cost

methodology. Basically, for each reservoir, this data set consisted of:

420
1. original oil in place or original gas in place,

2. recoverable oil and/or gas,

3. lithology,

4. depth,

5. number of wells,

6. seven years of production, and

7. secondary recovery process.

Using these data, a systematic data manipulation process evolved that was combined with engineering judgment and assumptions to develop the methodology

for the Permian basin study.

With this as a background, let's now get into the methodology. The depth

brackets used in the study were less than 5,000 feet, 5,000 to 10,000 feet,

10,000 to 15,000 feet, and 15,000 to 20,000 feet.

There were 20 barrel oil equivalent (BOE) size classes of oil and gas fields,

with the smallest size class of 0 to 6,000 BOE and the upper limit of the

largest class of 3.1 billion BOE.

As Bill Stitt mentioned yesterday, there's always one courageous individual

in the study. In this Permian basin study I personally believe that the most

courageous individual is my good friend Larry Drew, with the USGS. He is the

one who had to come up with the finding rate for the whole study. He

developed the discovery model which predicted the number of BOE fields by

size class and depth for each 1,000 well increment in exploratory drilling.

Knowing the number of BOE fields of each size class in each of the depth

brackets, the logic of the study was then to develop an exploration model, a development and production model , and an economic model as shown in figure

1. Today we will be concerned only with the first two.

BOE field size distribution

for each depth bracket

vs each 1000 exploratory wells drilled

Exploration Cost

Model

Total

Cost

Development and

Production Cost Model

Economic

Model

Recoverable

Resources at

Selected Rate of

Return and Price

Figure 1. Logic of Study

421
However, figure 2 shows the overall schematic of the economic model as developed by John Wood in the Dallas Field Office and Emil Attanasi of the

USGS in Reston, utilizing the price, rate of return (ROR), and cost. I would

like to discuss briefly this economic model to show how the cost data that was developed fit into the economic model. As you can see, when you get the

number of fields by size and depth, the first thing that has to be done is to

determine whether they are non-associated gas fields, oil fields that only go

through primary recovery, or oil fields that go through primary and secondary

recovery.

Then the model generates a production schedule, as discussed yesterday by

John Wood. It determines the cash flow using assumed wellhead prices in

determining the present value for the assumed rate of return that was required, and if the present value was greater than or equal to zero, the

deposit was developed and its reserves added to the total reserves. The

process was repeated for each type of deposit for each size and each depth.

The model then adds up the net present values of economic deposits of oil and

gas and determines the cost of exploratory wells. For the last 1,000

exploratory wells, if exploration cost is greater than the net present value

of the resources found, then the model stopped exploration and subtracted the

last calculated reserves from the total reserves. If there was a profit made

from the last 1,000 exploratory wells, then it continued on.

The exploration model was developed in a separate study in the Dallas Field

Office. It related the total exploration cost less lease bonus to the total

cost of drilling exploratory wells. Therefore, for each 1,000 exploratory

wells drilled, an average depth and average cost per well drilled at that

depth was determined to calculate the total exploration costs.

Figure 3 shows the relationship between the average depth of future

exploratory wells and the cumulative number of exploratory wells. This was determined by an extrapolation of a fitted function of average exploratory

well depth versus the cumulative number of exploratory wells drilled since

1956. In this model, for each 1,000 well increment of additional exploratory

wells, an average depth per exploratory well was calculated. For a value of

33.000 exploratory wells drilled the average depth was approaching 8,000 feet.

The average cost for drilling and equipping exploratory wells were expressed

as a fitted function of average depth as shown in figure 4. Data used for

estimating this function were found in Joint Association of Survey of the Oil

and Gas Producing Industry (JAS) for 1975 published by the American Petroleum

Institute (API). These costs were inflated to 1977 values for use in the

model. For an 8,000-foot exploratory well the calculated average drilling

and equipping cost per well was roughly $200,000 in the Permian basin.

To obtain total exploration cost per well, exclusive of costs of acquiring

undeveloped acreage (lease bonus), a function of total exploration cost per

well versus the cost of drilling and equipping exploratory wells was developed using data published in the JAS and in the Annual Summary of the

Quarterly Review of Drilling Statistics for the United States published by

API from 1966 through 1975. For our 8, 000-foot exploratory well which had

drilling and equipping costs of around $200,000, the total exploration

expenditures would be roughly $400,000 as shown in figure 5. The exploration cost

422
FOR EACH .WELLHEAD PRICE

.RATE OF RETURN

NEXT SUCCESSIVE INCREMENT

OF 1000 EXPLORATORY WELLS

DISCOVERIES

GENERATED

WITH DISCOVERY

PROCESS MODEL

DETERMINE

DEPOSIT

TYPE

^NON-ASSOCIATED GAS

-OIL; PRIMARY RECOVERY

"-OIL; PRIMARY & SECONDARY RECOVERY

GENERATE

PRODUCTION

SCHEDULE

X

DETERMINE

CASH FLOW AND

WELL-LIFE

T

DETERMINE

PRESENT VALUE (PV)

FOR ASSUMED

RATE OF RETURN

IF PV>0

DEPOSIT DEVELOPED

& RESERVES

ADDED TO TOTAL RESERVES

X

REPEAT PROCESS

FOR EACH DEPOSIT

TYPE, FOR EACH

SIZE AND DEPTH

CLASS

SUMMATION : NET

PRESENT VALUES OF

ECONOMIC DEPOSITS

(OIL AND GAS)

DETERMINE COSTS

OF LAST INCREMENT

OF EXPLORATORY WELLS

HZ

FOR LAST 1000 EXPLORATORY WELLS IF EXPLORATION

COST IS GREATER THAN NET PRESENT VALUE OF

RESOURCES FOUND STOP EXPLORATION AND SUBTRACT

RESERVES FOUND FROM TOTAL RESERVES] OTHERWISE

CONTINUE EXPLORATION

Figure 2. - Schematic of Costing Algorithm

423
10 20 30 40 50 60

CUMULATIVE EXPLORATORY WELLS (thousand)

Figure 3. Average Exploratory Well Depth as a Function of Cumulative

Exploratory Wells

0 5 10 15 20

WELL DEPTH (thousand feet)

Figure 4. Exploratory Well Drilling and Equipping Costs as a Function of Well Depths

424
1000

0

' 1 1 1 1 J

0 100 200 300 400 500

DRILLING AND EQUIPPING COST (thousand dollars/well)

Figure 5. Total Exploratory Well Cost as a Function of Drilling

and Equipping Cost

for each increment of 1,000 exploratory wells was then determined by simply

multiplying the per well cost by 1,000.

Figure 6 is a schematic of the exploration cost model. Briefly, the

procedure was to take the number of exploratory wells from the USGS discovery

model, get the average depth and the cost for that depth, and determine the

exploration cost less lease bonus.

For the benefit of those who are concerned about the lease bonus cost being

excluded, it was excluded only in the exploration model. It was picked up in

the economic model . In the economic model we assumed $50 per acre and 640

acres per exploratory well. We excluded the lease bonus cost from the

exploration cost model because the data were very erratic. If you subtracted

the lease bonuses that you knew were paid for offshore leases during any

particular year from the U.S. total, then that would give you a negative

lease bonus in that year from the onshore total for several years. The lease

bonus data for the onshore United States were very poor. We couldn't find

any data at all that would suit our needs so we just had to make reasonable

assumptions for those costs. The lease bonus cost was brought into the

economic model after the number of reserves (barrels of oil or thousand cubic

feet of gas) had been calculated.

Note that we did make an allocation of the total exploration cost between the

expenditures for oil and expenditures for gas. This has long been a controversial subject but we felt it was needed for proper determination of

cost per barrel or per thousand cubic feet. Based upon a study of JAS cost

data and API drilling statistics, we did develop a rationale that led us to

make the assumption that 60 percent of the total exploration cost would be

for gas and 40 percent for oil.

425
Number of Exploratory Wells

(from USGS)

Cost Per Exploratory Well

Average depth vs cumulative

exploratory wells

Cost of exploratory well vs average depth

Total Exploration Cost (Less

Lease Bonus) Per Well

Total exploratory cost per

well vs exploratory

well cost

Allocation of Exploration Cost

Oil = .4 Gas = .6

Adjustment of Cost For

Successful Oil Wells

Adjustment of Cost For

Successful Nonassociated Gas Wells

Exploration Cost

For Oil

Exploration Cost

For Gas

To Total Cost

of Gas

To Total Cost

of Oil

Figure 6. - Exploration Cost Model

426
Note, also, that an adjustment was made to the total cost for the successful

exploratory wells. Because exploration costs are not included in the

discounted cash flow calculations for successful oil and gas fields, an adjustment to exploration cost was made before exploration costs were brought

into the picture for determining total cost per barrel or per thousand cubic

feet. Otherwise, the cost of successful exploratory wells would be included

in both the exploratory cost and development cost. This adjustment consisted

of deducting from exploration costs, before combining with development costs,

the cost of one exploratory oil or gas well for each oil and gas field

found. The cost of these wells were included in the development cost.

In designing the "Development and Production" model, we first made an allocation of the BOE fields predicted by the discovery model as shown in

figure 7. A further allocation of the oil fields was made between those that

would undergo only primary recovery and those that would have both primary

and secondary recovery or pressure maintenance.

Table 1 shows the ratio of oil fields to total fields based upon a fitted

function of the time series of historical ratios developed from the data set

discussed earlier. Note that a ratio was determined for each size class by

depth bracket. It can be seen that the gas fields become more prominent with

depth, especially below 10,000 feet. For size class 1 7 * 100 percent of the

fields shallower than 5,000 feet were considered to be oil. In the 5,000 to

10,000-foot bracket, only 89 percent were oil, and in the 10,000 to 15,000-

foot bracket, 35 percent were oil. Below 15 f 000 feet there were no

Allocation of BOE Fields between

Oil and Non-associated Gas

Number of Non- associated Gas. Fields

by Depth and BOE Class

Number of Oil Fields by Depth

and BOE Class

Allocation of Total Oil Fields

Between Those Undergoing Secondary Recovery and Pressure Maintenance & Those Under Primary

Production Only

Number of

Primary

Fields

Number of Secondary &

Pressure Maintenance

Fields

Figure 7. Development and Production Cost Model

427
Table 1. Ratio of Oil Fields to Total Fields in the Permian Basin

Size Class 0-5 , 000 5,000-10,000 10,000-15,000 Greater than 1 (BOE) feet feet feet

(depth

(depth) (depth; I A onepci~ V»a l)

1 0.86 0.84 0.54 0.00

2 0.78 0.78 0.51 0.00

3 0.72 0.73 0.49 0.00

4 0.68 0.69 0.47 0.00

5 0.65 0.67 0.45 0.00

6 0.65 0.66 0.43 0.00

7 0.65 0.66 0.41 0.00

8 0.67 0.67 0.40 0.00

9 0.70 0.69 0.39 0.00

10 0.73 0.71 0.37 0.00

1

0.77 0.73 0.36 0.00

12 0.81 0.76 0.36 0.00

13 0.86 0.79 0.35 0.00

14 0.90 0.82 0.35 0.00

15 0.94 0.85 0.35 0.00

16 0.97 0.87 0.34 0.00

17 1.00 0.89 0.35 0.00

18 1.00 0.90 0.35 0.00

19 1.00 0.91 0.35 0.00

20 1.00 0.90 0.36 0.00

historical oil fields in the Permian basin, therefore, in the model none are predicted

Table 2 shows the ratio of primary oil fields to total oil fields for each

size class by depth bracket. These were also computed from historical trends

developed from the data set. Note that as the size class increases, more

fields will have secondary recovery and/or pressure maintenance processes

installed. However, for a given size class, the number of secondary recovery

and pressure maintenance fields decreased with depth.

In determining the cost of developing oil and gas fields, the field design

was determined by dividing the expected ultimate field recovery by the

expected reserves per well to give the total number of wells to be drilled.

These nominal values were discussed yesterday by John Wood, so I will not

repeat them. In addition, the following field design data for each field

size class and depth bracket were utilized:

1. expected ultimate oil recovery per field,

2. expected ultimate oil recovery per well for primary fields,

3. expected ultimate oil recovery per well for secondary recovery and

pressure maintenance fields,

4. expected ultimate associated-dissolved gas recovery per oil well from

primary fields,

428
5. expected ultimate associated-dissolved gas recovery per oil well from

secondary recovery and pressure maintenance fields,

6. expected ultimate non-associated gas recovery per gas field, and

7. expected ultimate non-associated gas recovery per well.

Table 2. Ratio of Primary Oil Fields to Total Oil Fields in the Permian Basin

Size Class 0-5,000 5,000-10,000 10,000-15,000

(BOE) feet feet feet

(depth) (depth) (depth)

1 1 .000 1 .000 1.000

2 1 .000 1 .000 1.000

3 1 .000 1 .000 1 .000

4 1 .000 1 .000 1 .000

5 1 .000 1 .000 1 .000

6 0.984 0.986 1 .000

7 0.958 0.983 1 .000

8 0.891 0.972 1.000

9 0.781 0.940 0.981

10 0.636 0.881 0.962

11 0.474 0.792 0.938

12 0.318 0.679 0.895

13 0.188 0.554 0.818

14 0.097 0.429 0.693

15 0.048 0.315 0.515

16 0.030 0.213 0.307

17 0.025 0.119 0.116

18 0.013 0.032 0.001

19 0.000 0.000 0.000

20 0.000 0.000 0.000

Of course, the cost of drilling and equipping the wells in all size classes

is dependent upon the depth. Within each depth bracket, an average depth was determined from the historical data set. For oil fields in the Permian

basin, the average depths were 3,400 feet for the 0 to 5,000-foot bracket,

7,200 feet for the 5,000 to 10,000-foot bracket, and 11,400 feet for the

10,000 to 15,000-foot bracket. As perviously mentioned, there were no historical oil fields below 15,000 feet in the Permian basin. The average

depths of gas fields were 3,400, 7, M00, 12,000, and 17,700 feet in the 15,000

to 20,000-foot bracket. The cost per well versus depth was determined by

using JAS cost data. Using these data, the total drilling and equipping cost

was calculated by multiplying the total number of wells by the cost per well.

We all know that development wells drilled are not always successful.. A study

of drilling data from 1970 through 1975 indicated that for every 100

producing wells drilled, 19 dry holes were drilled. Therefore, we added 19

percent of the cost of a dry development well to the cost of each producing

well to obtain the total development drilling costs.

429
I

To obtain total development cost, we then added the cost of the lease

equipment per well. The lease equipment cost data were also developed on the

basis of well depth for primary operations, and for secondary recovery and

pressure maintenance operations. For oil fields assumed to be susceptible to

secondary recovery or pressure maintenance, additional assumptions were made:

1. For fields less than 5,000 feet below the surface, the number of

producing wells during the primary stage was assumed to constitute 70

percent of all wells that produced oil. At the outset of the

secondary recovery program, the remaining 30 percent of the wells

that produce oil were drilled. Then, sufficient wells are assumed to

be converted to injection wells so that one injection well existed

for each producing well during secondary operations. This provides a means of allocating well cost to secondary recovery operations.

2. For fields in the interval from 5,000 to 10,000 feet, the number of

newly drilled injection wells was given by calculating the number of

wells needed to infill drill the centers of a square array of the

wells that produced during the primary stage. Some primary producing

wells are converted to injection wells so that the ratio of producing

wells to injection wells would be 1:1 at the beginning of the

secondary recovery program.

3. For depth intervals greater than 10,000 feet, a pressure maintenance

program was assumed to be carried out from the initial stage of

development. One injection well was drilled for every four producing

oil wells.

Annual oil and gas operating costs were also determined on a producing well

basis for each depth. These costs included the direct operating cost (or so- called lifting cost) and the indirect operating costs which included the

general and administrative overhead costs, and severance and property taxes.

Using these development and operating costs for each size class oil or gas

field and the production schedule from each size class field, as discussed by

John Wood yesterday, the economic model was used to calculate the recoverable

resources that could be developed at varying prices and discounted cash flow

rates of return.

In summary, I have attempted to illustrate the rationale, in detail, that can

be developed for modeling, when your data set is complete and properly

designed to fulfill the requirements of the final product. As in most

modeling situations, the data set is critical with respect to both model

design and credibility.

430
Discussion

Mr. Brashear (Lewin & Associates): Tom, I greatly appreciate that

methodology, as you well know. One question that occured to me as you were

talking is on the development dry hole rate. Some of those, if we use historical data, were just lousy wells that weren't completely dry. It's more economic to write them off in taxes than to produce them. As prices

come up real fast, though, some of those might be keepers. Did you attempt

to plow that back into your developmental dry hole rate? We haven't figured

out a good way of doing that.

Mr. Garland: No, we didn't look at it that way, Jerry. We looked at

just the number of dry holes from our experience in the development of the

wells at the time the secondary recovery went in. At that same time the

price was probably constant and therefore, if the price had been higher, they

may or may not have been completed

I don't know of operators that would have plugged marginal wells when

they could go ahead and complete them, and at least get some of the cost

back. Whereas if they went ahead and abandoned them, all they get is just

their dry hole charge-off.

Mr. Brashear: So you wouldn't think it was a major factor, then?

Mr. Garland: Beg pardon?

Mr. Brashear: You wouldn't think the historical data would have much

effect?

Mr. Garland: I don't think so. I don't think we looked at it that way,

but I don't think it would make a change.

Mr. Brashear: Thank you.

Chairman Keene: Thank you. You might be interested to know that data

that the Dallas Field Office put together on this study are publicly

available, and if anybody's interested in that, they should see Tom after the

symposium.

You might also be interested in knowing that the case of the Permian

basin is an on-going item of review, and we're matching data that we've

received from individual companies by reservoir against the other results

that were found earlier. Hopefully, we'll be able to use this to test

theories that we've been unable to test previously.

431
THE OUTLOOK FOR OIL EXPLORATION AND DEVELOPMENT

By T. R. Eck*

I greatly appreciate this opportunity to be with you, and to share with you

some of Standard Oil Company's thinking with respect to the energy challenges

facing our nation. It is my conviction that through opinion interchanges

such as this—involving representatives of the industry, government, and

academia—we can begin to dispel many of the myths that have too long

surrounded the entire spectrum of energy supply and demand.

Within the context of my comments, I hope to develop some coherent thoughts

of the magnitude of our energy problems, my company's perception of their

derivation, and the approaches we believe requisite to their solution.

Within limits imposed by normal proprietary considerations, I should like

also to discuss some of the approaches my company takes to oil-finding and

the methodology we employ in predicting petroleum accumulations.

Should you be predisposed to predictions of imminent doom, I fear that I shall disappoint you. On balance, my company is reasonably optimistic about

the prospect of providing adequate energy supplies, both for the immediate

future and over the longer term. Our outlook applies pre-eminently to the

U.S. energy base, but extends also to world supply.

To find solutions, one obviously must first define the problems. Our

contemporary problems with respect to energy involve, in fact, a single

energy source: crude oil. More specifically, our problems revolve about the

availability of this commodity at prices we can afford to pay. The

unprecedented drain on U.S. financial resources occasioned by a ten-fold

increase in world oil prices over the past seven years has created a broad-based awareness of our dependence on this single energy source. Under

free-market conditions, an escalating price pattern of this magnitude would

have signalled sharply reduced consumption, increased production, and a scramble to develop alternative sources. Our unique problem here in the U.S.

derives from the fact that, unlike other industrial nations, we have aborted

this normal response by imposing price controls and complex regulations.

The consequences of our national predilection for substituting political

decisions for economic reality have been as numerous as they have been

disastrous. With respect to energy, these consequences have included the

emergence of "conservation" as the favorite tool of government policy, and

efforts to dampen demand without—at the same time—seeking to increase

production or practicalize alternative fuels. Only in recent months have we, as a nation, arrived at the belated realization that mandated conservation

would be necessary if oil and its products were allowed to seek their natural

levels in the marketplace. Had this economic truism been recognized several

years ago, our economy would quite likely have avoided much of its present

disarray.

Chief Economist, Standard Oil Company (Indiana)

432
It is perhaps axiomatic that nations, like men, must reach their nadir before

invoking some higher power to set their affairs in order. Having indulged

ourselves in political palliatives, we now se^m better prepared to allow a somewhat higher order of economic reason to prevail. Herein lies a significant, if somewhat nebulous, cause for my company's optimism vis-a-vis

U.S. oil supply.

As this chart (fig. 1) shows, there is little cause to believe that the world

petroleum base, proved and prospective, will prove inadequate to meet any

predictable demands that may be placed upon it. Proved world reserves currently approximate 600 billion barrels, while those in the United States

now total about 27 billion barrels. Prospective world reserves, including

U.S., are roughly twice the 600 billion number.

Translating these reserves into years of supply at current production rates

(fig. 2), we see that the U.S. has almost 9 years of proved reserves and more

than 30 years of prospective reserves. OPEC reserves, proved and

prospective, will sustain current production rates for another 40 years,

while other free world reserves could conceivably last well into the

Twenty-Second Century at today's production rates. I would caution that

these numbers represent merely the energy base upon which we can base our predictions of future supply. Given today's international tensions,

availability of supply is quite another matter.

For a somewhat different view of how the world petroleum base equates in

terms of availability, let us look now at the CIA's interpretation of

current OPEC capacity (fig. 3). Here we see that the maximum sustainable

production rate is about 34.9 million barrels per day, while the politically

available production rate is some 3.5 million barrels per day lower. At

present, the "politically available" figure used for Iran is overstated by

some 3 million barrels per day, as that unhappy nation struggles to regain a semblance of economic order. Even so, it is apparent that surplus OPEC

capacity exists today, and we expect that situation to prevail for the

balance of this century. Obviously, we must anticipate temporary supply

interruptions in the future much as we have experienced them in the past, but

these are more related to world politics than to reserves or productive

capacity.

Because political instability is the norm rather than the exception in much

of the Middle East, we see an infinite marketability for all non-OPEC crude

oil, whether in the U.S. or offshore. We see a somewhat different picture

emerging for natural gas, however, where we forecast a ready market for North

American gas, but a surplus situation offshore. Particularly will this be

true if the OPEC countries, and gas exporters in general, insist on anything

approaching oil-equivalent parity for natural gas at the wellhead. The cost

of liquefying and transporting gas is simply too great, even for peak-shaving

purposes, to sustain export markets based on wellhead parity*

A secondary but important factor with respect to the U.S. gas market is the

increased availability of this commodity from domestic sources at the higher

prices permitted under provisions of the Natural Gas Policy Act. Simply put,

America is unwilling to pay any price asked for natural gas; it must compete

with other fuels including oil, coal, and nuclear power. We feel confident

that the U.S. natural-gas resource base will be adequate to serve all

residential demands for the balance of this century and, given the continued

use of coal as replacement fuel, most industrial demand as well. Looking

433
further ahead, we do not dismiss the possibility that passive energy sources will ultimately back out some fraction of residential gas demand.

I should like to turn now to the effect that realistic prices for crude oil

and natural gas are having on exploration and production expenditures in the

U.S. (fig. 4) , and use that as a springboard for our relatively optimistic

outlook for U.S. energy supplies. As you can see, the domestic petroleum

industry invested $20 billion in E&P activities in 1978 and $28 billion in

1979. This year, the industry is expected to spend about $33 billion on

finding and developing U.S. reserves, and we expect the six-year average—now

through 1985 —to be about $50 billion a year in current dollars. Total

spending for the six-year period will be about $300 billion.

You will note, also, that we expect drilling activity to increase about 7 per

cent through 1985, with a gradual decline—on the order of 2 per cent a year—in crude oil and natural-gas equivalents discovered per foot of hole

drilled.

There is no legerdemain in these numbers. They are mathematical

extrapolations of trends that have existed for some years, plus our interpretation of results that can reasonably be expected from advancements

in oil-finding technology, completions from thinner and tighter pays, deeper

drilling, and—of course—improved economic incentives. These are factors

that I will develop in somewhat greater detail a little later.

I want to put another table (fig. 5) on the screen while I indulge in a bit

of philosophical ruminating. For several years it has been popular to

predict severe energy shortages looming just over the horizon, and some of

today's predictions continue to reflect this view. My company tends to

believe, however, that the parameters of the energy situation in the U.S. are undergoing profound and dramatic change, and that yesterday's thinking

does not necessarily apply to today's realities. For several reasons, we reject the validity of the perennial shortage syndrome that has found its

quintessential embodiment in a government-mandated conservation ethic.

Two things of far-reaching consequence have occurred. First, U.S. and world

consumption forecasts have been scaled down radically; we are now looking at

annual increases in world oil demand on the order of 1 or possibly 2 per

cent, compared with predicted increases of 5 to 6 per cent only a few years

ago. Second, we have developed a much improved definition of availability,

of the magnitude of our resource base. We at Standard—and I hope others as well—are increasingly confident that our postulated reserve numbers are realistic, and that technology does indeed exist that will permit us to

convert prospective reserves into proved reserves. This growing confidence

is reflected to some extent in the API and AGA reserve estimates published

last month. The upward revisions of previous estimates reflect two factors

pre-eminently: increased price incentives, and the industry's rapidly

accelerating efforts to improve recovery from existing fields through the

application of higher technology and more intensive development practices.

I assume that as I have been talking you have been studying our predictions

of U.S. reserve additions and withdrawals. Our assumption is that during the

1980-1985 period an average of 5 billion barrels of crude oil and natural-gas

equivalents will be added to our reserve base, divided about equally between

new discoveries and upward revisions in recoverability from existing

reservoirs. Hence, with respect to reserves, we anticipate that higher

434
activity levels on all fronts will allow the domestic industry to do at least

as well as it did last year.

The other side of the coin, of course, is the rate at which we expect

reserves to be depleted through production. Here we expect withdrawals in

line with reduced demand, or at the average annual rate of about 6.5 billion

barrels a year. Based on these assumptions, we expect our combined crude oil

and natural-gas equivalent reserves at the end of 1985 to be some 9 billion

barrels below current levels.

One area in which we may depart slightly from conventional wisdom is in

lumping together domestic crude oil and natural gas and considering them, in

effect, part of the same energy pie. We believe we are on a firm ground in

doing this, however, because of the interchangeability of these two fuels for

many—notably industrial—purposes. Moreover, as permitted by federal law,

domestic gas already is being sold at or near parity with crude—a fact which

greatly increases its desirability as a target for North American

exploration.

As I observed earlier, we do not find it realistic to view the

interchangeabilty of offshore crude oil and natural gas in the same light as we do domestic production. The notable exception is North Sea production,

where markets for natural gas comparable to the U.S. are being developed.

For the exporting nations, we are looking almost exclusively at crude-oil

production when we consider the impact on world-energy supply.

I should like now to turn briefly to what we believe to be a realistic

outlook for world oil production through 1985. This table (fig. 6) compares

our production estimates with those prepared by the Central Intelligence

Agency. As you can see, our numbers differ rather markedly from the CIA's

and are considerably optimistic.

The CIA forecasts OPEC production declining by 2.9 to 5.4 million barrels a day by 1985, while we predict a decline of only 1.3 million barrels a day.

They see production in the OECD nations remaining essentially static, while

we anticipate an increase of 1.3 million barrels daily. Our outlook for

production increases in other free-world countries exceeds the CIA's high

case by 2 million barrels a day. And while they believe China and the Soviet

block will experience a production decline of 2.3 million barrels a day by

1985, we forecast a relatively modest drop of some 800,000 barrels daily.

We possess no great insight as to how the CIA and some of our competitors

have developed their numbers. We can only assume that they are making

assumptions that exploratory activity will be significantly less than we postulate, or that their projected discovery rate is much lower than we

predict. We have made what we believe to be conservative assumptions, yet we

find ourselves on the high side as compared with government and some other

company predictions.

Standard makes a conscientious effort to insulate its industry-wide

predictions from internal biases. Still, it is conceivable that our outlook

for U.S. oil supply is colored by our exploratory successes of recent years.

To the extent that a large measure of our success can be attributed to our

435
role as the nation's most aggressive wildcatter, and to our employment of

increasingly sophisticated exploration and production technology, we believe

it probable that other major companies will be similarly rewarded as they

turn their attention to the U.S.

Due largely to the expectation of higher prices for domestic production, the

upswing in U.S. exploratory activity is significantly higher than in the

remainder of the non-OPEC free world. Despite our problems with the so- called "windfall profits" tax and multitudinous regulations, the U.S.

environment is one of the best in the world at this time. Not the least of our domestic advantages is the fact that U.S. taxes—burdensome though they are—are generally assessed on a percentage basis, rather than the ad valorem

basis favored by several foreign governments. There appears to be a lack of

rationality in the governments that favor 95 per cent of nothing rather than

50 or even 70 per cent of whatever production can be established under less

confiscatory taxing policies.

I question whether anyone outside the petroleum industry—and quite possibly

many within it—are fully cognizant of the technological advances that have

characterized oil finding and development in recent years. We are today

finding, with near routine regularity, petroleum accumulations that eluded

our best efforts half a dozen years ago. Rather than being characterized by

isolated revolutionary breakthroughs, our progress has been of an evolutionary nature, requiring the honing of interdisciplinary skills in

concert with advancements in computer technology and oil-finding tools. The

nation's universities have been unable to keep pace with this technological

explosion, much of which is still proprietary, and most if not all of the

major companies are conducting intensive and extensive training programs of

their own.

Quite obviously, the front-end costs for developing and applying petroleum

technology must be factored into the replacement value of crude oil.

Enhanced recovery, as but one example, is proving more difficult and

expensive than anything yet envisioned within or without the petroleum

industry. Yet the payoff, assuming successful efforts, will be billions of

barrels of additional oil from secure domestic sources. The truly selfdefeating thing about so much of our government policy, implicitly including

the "windfall profits" tax, is the assumption that tomorrow's oil will be

found and produced at yesterday's prices. Such is not the case.

Because of the high order of technology and front-end costs associated with

current and future oil-finding and production, I am persuaded that the

competitive edge will increasingly belong to the larger companies possessing

requisite funding and cash-generating capabilities. Tax-law revisions and

regulatory red-tape are factors, of course, but cold hard cash is the main

reason why drilling funds and small independent operators are apt to find

extremely rough sledding in the years ahead. Major field development now

costs a billion dollars, minimum, and only the large, technologically

oriented companies can be expected to undertake such ventures—particularly

with respect to hostile and frontier environments such as found in the

arctic, deep-water offshore, and onshore plays below 20,000 feet.

In closing, I should like to recite one example of complementary,

interdisciplinary technology that I don't believe has been widely discussed

outside my own company.

436
As perhaps you know, exploratory efforts off our Eastern seaboard in geologic

province known as the Baltimore Canyon have not met with overwhelming

success. So far, 19 exploration wells have been drilled. One rather modest

gas field has been discovered and two other w&Lls have tested what may prove

to be commercial shows of gas. No oil has been found. Drilling costs

incurred to date exceed $217 million, excluding acquisition costs of

$1.13 billion paid to the Federal Government.

As perhaps you also know, Standard was one of the few major companies that

declined to enter into the spirited and high-cost bidding that characterized

the Federal Government's lease sale in the Baltimore Canyon. Instead, we were beaver ing away out in the Rocky Mountains, leasing every scrap of

acreage we could find along the geologic trend that has since become well

known as the Western Overthrust Belt. Before the Pineview discovery, on Amoco acreage in late 1974-early 1975, more than 500 dry holes had been

drilled along the U.S. portion of the Belt. Since the Pineview discovery, 14

other commercial fields have been found. Some of the fields have multiple

pays, and at least 10 separate formations have been proved productive.

Many months before drilling began in the Baltimore Canyon or along the

Overthrust Belt, Amoco earth scientists had predicted that the latter

province would be productive of both oil and gas, but that the former held

far less probability of success. We based our predictions largely on source- bed evaluations having to do with the richness or content of organic matter

in the rocks, the type of hydrocarbons this organic matter had probably

generated, and the thermal maturity of the two provinces. Our application of

this sphere of earth science, known as geochemistry, led to our conclusion

that source beds in the Baltimore Canyon had been heated only to a marginal

level and had just barely started the main phase of gas generation. We found

that source beds in the Overthrust Belt, to the contrary, were well along in

their maturity, and had been heated sufficiently to produce both oil and gas.

It was largely on the basis of our geochemical findings that we eschewed the

Baltimore Canyon leases and concentrated our efforts in the Overthrust Belt.

But having done so, we were still far from home. The geological complexity

of the Overthrust Belt, consisting essentially of repeated thrust sheets and

multiple trapping mechanisms, stymied exploration success until geophysical

research developed new technology that enabled us to decipher the structural

configuration of the reservoir beds.

I have several reasons for citing this example, none of which are intended to

imply that Amoco is the only company in America that can find oil. Indeed, we are not. Rather, the observations I hope to leave with you are these:

My first observation obviously relates to the financial and technological resources that are being brought to bear throughout the entire spectrum of

energy development. I have concentrated today on petroleum exploration and

development. But my company and many others also are devoting increasingly

large amounts of time and effort to developing technology associated with

alternative fuels. Unless stifled by regressive taxing policies or regulatory harrassment, the job of supplying adequate energy can and will be

done.

The second thought I should like to leave with you is the substantial amount

of time and expense that precedes the finding and development of oil and gas

437
resources. A review of my company's exploratory activities over the past 20

years reveals the average lead times of five to eight years , but sometimes as great as 13 years, are required between lease acquisition and initial

discovery. Another four to six years are typically required for field

development.

The obvious implication is the absolute and overriding need for access to

public lands if the exploratory momentum now begun is to be sustained

throughout this decade. A cloud of uncertainty surrounds the amount of

Federal acreage that will be made available—and when. It is essential that

governmental processes be speeded up.

My third and final observation has to do with the potentially massive

petroleum resource base that remains to be developed in the United States.

We see the oil and gas in place, we see the drilling, and developmental

activity occurring, we see new technology coming on stream, and we see the

impressive results being reported by our company and others. We simply do

not share the pessimistic outlook that seems so much in vogue today.

I thank you for being a kind and attentive audience. If you have questions

and time remains, I will be pleased to respond to any questions you may have.

438
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444
MODELS, UNDERSTANDING AND RELIABLE FORECASTS

James B. Ramsey

New York University,

New York, N.Y.

INTRODUCTION

While the interest of the Department of Energy, not to mention the

general public, is strongly focused on the central question of how much oil

and gas we can obtain at what price and how scon, the answers will

inevitably depend on various models of supply and of discovery. It is also

inevitable that the various models which purport to make such forecasts

will all differ in their predictions and that the more models are consulted, the greater the number of differing opinions. The intent of the

discussion in this paper is to indicate how one may reduce the plethora of

alternatives to a manageable number and to give guidelines to models in

which some modest reliance can be placed. Policies will be implemented;

let us at least attempt to base these decision on model results in which

some reasonable confidence can be placed.

There are five major sections to this paper. The first introduces the

intuitively pleasing notion of "reliability of a forecast" and in the

process indicates why black-box forecasting is dangerous. The second

section extends the analysis in the first section by contrasting the

concept of data fits with that of specification error analysis and the

"maximization of residual entropy". The third section briefly discusses an often mentioned, but seldom analyzed, problem, that of "sampling" and the

effects of different ways of obtaining samples on inferences about

reservoir distributions, and so on. The fourth and fifth sections indicate

the role that theory must play in trying to obtain reliable forecasts and

in delineating the characteristics of reliable forecasts.

BLACK-BOX FORECASTING VS. "UNDERSTANDING"

The motivation for the main idea introduced in this section can be

provided by performing the following hypothetical experiment; better still,

the reader is requested to cover up the graph in Figure 1 from the right up

to the line marked "a". Make a forecast based on the observed data up to

point "a" only , recognizing that a near-perfect fit of an appropriate line can be obtained . Now move the covering card to "b" , recognize your

"forecast error", and forecast again; move the card to "c", discover your

error, and then move to "d" to make your last forecast, and then evaluate

your forecast record, even though at each stage you obtained a perfect fit

to the historical data.

This simple exercise provides a number of important insights and

several useful lessons.

Before beginning the discussion we need to recognize that the problems

to be discussed have nothing to do with "random errors" and their unknown

distribution since in the example above, there is a negligible amount of

residual error. Secondly, the problems have nothing to do with the fitting

procedure; the problems are as severe no matter whether one uses simple

regression, Box-Jenkins, spectral analysis, or whatever. The fit to "the

445
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446
historical time path" in each case a,b,c, and d is perfect; but each

forecast is less than perfect, it is in truth irrelevant.

Reasonable forecasts which the reader might well have made at each

point are: At "a" , a straight line upward trend;

At "b", a curve which rises to a maximum and then approaches a lower

bound (maybe zero) asymptotically;

At "c" ; an oscillating curve;

At "d"; you may be convinced you now have it right, only to discover

how wrong your latest forecast is.

The above curve and the series of forecasts from the observed

historical time paths illustrate two basic but related lessons.

Fitting historical data in an economic time series without benefit of

any theory inevitably leads to unreliable forecasts, a phrase to be defined

below. "Good fits" to historical data, even perfect fits give no guarantee

of reliability.

The question now arises - what is meant by the term "reliability"?

This is a fundamental concept of importance in the inferential process

prior to estimation and the choice of statistical methods as usually

defined. Intuitively stated, the reliability of a forecast is the

"confidence" one has in the maintained hypothesis or in the basic

estimation model together with its required distributional assumptions.

Essentially, reliability is the confidence one has that the model used to

analyze the data is applicable to the situation being estimated and that

the assumed model will continue to be relevant over the period of the

forecast. Reliability, in short, is what is always assumed by a researcher

whenever he begins to talk about standard errors of forecasts and setting

probability limits on forecast values.

Indeed, the whole concept of probability statements attached to

forecasts assumes implicity that the model used to generate these estimates

is in truth relevant to the observed phenomena and that the researcher

knows this with certainty. For if one entertains any doubts as to the

validity of the model itself, then that doubt, expressed probabilistically,

should be used to modify one's "estimated" probability statements based on

the model.

Reliability, then, is pre-statistics, both in time and in that it is a concept which is essentially "discipline determined". This is to say, one gains confidence in a model in so far as the model provides an explanation

for the phenomenon under examination and in so far as that explanation is

consistent with other related theoretical ideas in which one has a high

level of confidence.

Clearly, an "explanation" which is not in consonance with the observed

facts is no explanation at all so that statistical rejection of a model

itself, not just particular parameter values, is sufficient to reject the

model and to state that the corresponding theory provides no explanation

for the class of phenomena under examination. But in contrast the

obtaining of a good fit to a set of historical data by some statistical

447
expression not generated by a theory only reflects on the ingenuity of the

data fitter and says nothing else.

To see the difference most clearly imagine we have a set of data on the

time path of the volume of oil discovered within a year by year. Suppose

further two sub-cases. In one, we have an interaction of economic and

geological theories of discovery and market interaction which "explains" in

terms of these theories why the observed time pattern is as it is. Further,

suppose that the historical circumstances are such that the theoretical

analysis reduces to a fairly simple model relating oil discoveries and time.

Now, in contrast, suppose someone tries a number of simple statistical

models and finds one which seems to fit well; let this model so serendipitously

discovered be exactly the same model as that generated by economic and

geological theory. The striking fact in these two situations is that the

results are not the same; the former model is "reliable", the latter is not.

Standard errors of forecast and forecast probabilities can be quoted in the

former case, but not in the latter. It is this paradox, if you will, which

requires some explanation.

In the latter case our colleague's sum total of knowledge is that he

obtained a good fit between a particular form of a model and the given

historical data, but given some regularity in any data series, that can always

be done. What has one learnt? Nothing, other than that a particularly

convenient way to summarize or represent the existing data series is provided

by the fitted model. It is true that there are a lot of matters our colleague

wishes to know, such as, that the model does represent the data in an essential

way and that this representation will apply in the future, that forecast

probabilities can be assigned and are to be believed. But if wishes were truth,

we would all be rich.

As opposed to our colleague, what do we know? At least something. First,

if not most importantly, our theory will delimit those conditions and circumstances under which the historically determined simple relationship can be

suspected to hold. This is important, especially in the subject matter of

economics, wherein enormous bureaucracies, not to mention the rest of us, are dedicated to trying to change the existing economic structure.

This then is the real need for forecasting the outcome of human behavior,

we are almost always having to extrapolate beyond our current experience and

more importantly beyond the conditions under which our models were fitted.

Unless we have some insight into when and when not extrapolations of the

existing experience are useful and valid, we can never rely on our historical

data fits. In the case with oil and gas there have been a number of large

scale changes.

For example, the current U.S. situation reflects the joint facts that at

approximately the same time that the availability of the very large low cost

discovery and easily accessible fields was drying up, much greener exploration

pastures were being discovered elsewhere, notably in Latin America, the

Middle East, and even Canada. As a direct consequence seismic crew days in

the U.S. fell dramatically during the mid to late '50's and remained at low

levels until recently. We are now reaping our previous lack of effort.

448
Over the decades of this century, there has been a substantial shift

in the overall orientation of the bureaucracy dealing with the oil industry

from the encouragement and subsidy of exploration during the early period . to the discouragement and indirect taxation of it today. Both the natural

and governmentally induced shifts in demand which translate into pressures

on supply are also neglected by mechanistic models. If oil had not been

discovered to be an incredibly suitable fuel for locomotion, the time path

of oil discovery would have had a vastly different shape. Similarly, a change in the technology of discovery and extraction (so far the technology

of discovery and extraction has advanced relatively little) would have a significant effect on the time path of discoveries. All of this is "ignored"

by mechanistic models, or rather, the assumption is that whatever determined

optimal rates of effort, type and quality of inputs, and the relative payoff in the past will remain constant in the future. But, if there is one

thing we can know in an uncertain world, it is that whatever determined the

course of events in the past, it will not be the same in the future. With

certainty one can predict that mechanistic models will have to be

"adjusted" to account for the change in the time path of discovery.

In contrast, theoretically based models gain evidence in so far as they constitute specific applications of generally accepted theories.

Moreover, a theory which has already been subjected to a most extensive and

intensive series of empirical tests outside of the particular situation in

hand implies that one can have more assurance in relying on these

particular results; in short, the testing of the general theory lends

substantial evidence for the credibility of the results of any part.

Moreover, unless we are willing to act on faith alone, the fact that

we can spin a plausible story which not only "explains" the path of our

particular series, but more importantly relates that experience to more

general events, then this fact in itself provides further evidence about

the reliability of our forecasts.

Finally, if one reviews black-box forecasts (i.e. non-theoretically

449
based, purely empirical forecasts) over any reasonable length of time f what scon becomes clear is that the forecasting model changes

constantly over time as data accumulates and as new observations

continually belie the guesses based on the old. Simply put, black-box

forecasts do exactly what the reader did in making his forecast

experiment at the beginning of this paper. Since we can see our errors

in retrospect so easily, it should take little imagination to recognize

that a retrospective view "in years hence" will also show how badly we went wrong. If then, we know with high probability that our

retrospective view will show that we will have been wrong and likely to

have been spectacularly wrong, we should view our mechanistic

forecasts-without-understanding with considerable suspicion; i.e.

black-box models do not provide reliable forecasts.

While mechanistic black-box forecasts are inevitably doomed to

constant failure and revision by their proponents, this observation

does not mean that even sound theoretically based models are perfectly

reliable; clearly, they are not. But what we can say is that with

theoretically based models, models wherein one understands why events were as they were, we can achieve our highest levels of reliability.

And in this game, something is far better than nothing.

GOOD HISTORICAL FIT VERSUS ERROR ANALYSIS

We have already seen that if a data series has any observed

regularities to it at all, it is no difficult matter to obtain a very

"good fit" between some model and the observed data. Indeed, the

objective of most data fitting procedures is precisely that, to produce

a good fit, so that it is not surprising that good fits are obtained.

But as we have now seen, producing a good fit does not reveal the truth

whatever it might be. For the more statistically knowledgeable good

fits are represented in terms of concepts like high R2 , or even high

R2

, large t-ratios, big F's, and so on. Impressive language, but

without the reliability provided by the knowledge that the model is

relevant in the first place, these statistics are basically

irrelevant.

Let us now suppose we have available to us a potentially reliable

theory with valid and useful applications to our problem, but we do not

know the precise form of our model. We are not too sure which

variables we can safely ignore; we are not too sure of how far the

model can be simplified without producing ,serious and inferentially

significant errors.

In order to handle this perennial problem and aid us in our search

for more reliable forecasts, I am going lk> make another apparently

heretical statement. The analyst's objective should not be produce good

fits, his objective should be to produce a set of residuals whose

distribution is pure white noise; put more colorfully, his objective is

to maximize the entropy of the residuals.

A less striking, but more cogent statement is that what we want for

reliable forecasts are valid maintained hypotheses. And the empirical

path to such a happy state is through specification error analysis. One

may obtain R2 values of 0.99 and higher and still have a seriously

450
misspecified model; a model which has omitted an essential variable, uses

the wrong functional form, is heteroskedastic, or has disturbances which

are not independently and identically distributed. In order to begin the

process of trying to detect these errors, one must engage in a series of

careful analyses of the model, its properties, and its relationship to the

data as exhibited in the observed distribution of the model's residuals.

In this respect specification error analysis of one type or another is a vital, but unfortunately, much neglected, tool; see, for example, Ramsey

(1969), (1974), Hausman (1978), Learner (1978), and Hale et al,(1980).

Fortunately, the realization of the importance of specification error

analysis is now beginning to grow at an ever faster pace. Inferences

based on simple fits of data, while acceptable in the past, will no longer

provide a suitable basis for policy in the future.

THE SAMPLING PROBLEM IN OIL SUPPLY FORECASTS

This is a topic to which much lip service is given, but little real

analysis. The crucial issue is that the non-independent, non-random,

truncated distribution of pools, reservoirs, and oil fields obtained by

systematic sequential search is used to make inferences about distributions

of reservior and pool sizes as if the data were a simple independently and

identically distributed (i.i.d) sample. Nothing could be further from the

truth. At least some researchers, Kaufman most notably, have taken into

explicit account that the sampling within a basin is without replacement

and is affected by the relationship between surface area of reservoir and

volume discovered as well as the search process used to discover oil.

To give some idea of the effect of the search process on the

characteristics of an observed sample and inferences to be drawn from it,

imagine trying to determine the distribution of consumption of various

goods without understanding the role of income and relative prices and

where one's sampling procedure is to track down only people with gold

American Express cards. Further, imagine that you only record credit-card

expenditures and you throw out anyone who spends less than $100 per month

on the card. The distribution of consumption obtained from this procedure

makes as much sense as our current procedures in trying to determine the

distribution of oil reservoirs.

SEARCH AND IMPLICATIONS FOR SUPPLY FORECAST MODELLING

Until very recently in economics the theory of search and exploration

was an almost totally ignored subject. Consequently, it is not at all

surprising that most so-called "econometric models" were based on very

simple comparative static models with little recognition of the economic

role of exploration and the crucial importance of understanding the nature,

type, and degree of constraints imposed by geological factors.

Consequently, such models in that they lacked an appropriately developed

theoretical base were as unreliable as any other ad hoc modelling attempt.

Economists still have not mastered the relevant economic theory in this

branch of applications, but progress, albeit slowly, is being made.

In order to illustrate the importance of developing an economic theory

of exploration consider some of the following examples. These examples

illustrate the limitations of simple conventional models and point out that

the use of such conventional models will produce significant specification

451
errors and thereby lead to extremely unreliable forecasts.

First, one cannot usefully ignore the role of expected marginal

information costs in determining the timing, location, and rate of oil

exploration sampling. Essentially, we "search" where the anticipated

marginal cost of information is low relative to the expected discovery

gains. This type of procedure leads not only to a "success breeds

success" view of exploration, but more importantly to a view that"

non-success breeds neglect"; an area unsearched is guaranteed to produce

no new discoveries.

Next, the economics of exploration theory developed by Ramsey (1980)

indicates that mean (or log mean) size of fields discovered and success rates are in fact endogenous variables, not geologically predetermined

exogenous variables. Mean field size discovered and drilling success rates are in fact a function of the distribution of firm sizes and degree

of exploratory specialization as well as a function of conditions

determined by geological factors. The distribution of field size and success rate can both change with economic conditions and with the rate of

exploration.

The role of non-market forces in affecting the type, nature,

distribution, and rate of exploration is usually ignored in "models of oil

supply". Consider briefly the effects of government restrictions and

sometimes subsidies on where, when, how, and by whom search is performed.

Differential taxation between large and small firms will dramatically shift

the distribution of type of exploration and the distribution of areas searched

The analysis of the economics of exploration indicates that the

distribution of exploratory effort and the role of exploratory

specialization are far more important characteristics than a simple measure of the rate of exploration. Changes in the distributions of firms by size

will change the distribution of fields (or reservoirs) discovered by size, see for example, Ramsey (1980).

For the economist trying to analyze exploration, ignoring the role of

geological constraints is a serious lack in trying to build a model to

produce reliable forecasts. The lack of an acceptable and unified

geological theory in itself is a difficulty in trying to build a useful

model of exploration. The uncertainty generated by a lack of a clear

understanding of geological processes leads to a search behavior dominated,

but not exclusively however, by searching in those types of areas which

provided success before. Progress in exploration procedure is

serendipitously made by the odd maverick who looks where every fool

geologist knows one should never look.

These are merely some of the characteristics of the exploratory

process which help to distinguish it from simple standard economic models

of static equilibrium. Most attempts at building even a dynamic analysis

of exploration have in the main ignored many of the above ideas.

Economists have a long way to go before being able to claim we have

sufficient understanding of the discovery process to be able to provide

useful and reliable forecasts. Progress will be made in this respect, but

452
only if a sufficient number of economists become interested and only then

if the necessary funds for research are available.

SOME CHARACTERISTICS OF A RELIABLE FORECAST MODEL

My scattered comments can be most usefully summarized by making some

recommendations for obtaining and recognizing a reliable forecast model for

discovery.

A reliable model will be one which explains the empirically estimated

relationships between the various observed values of the theoretically

determined relevant variables. The conditions under which the simplified

version of the theory generating the specific model is useful will be

carefully delineated. The model will incorporate economic theory in

explaining firm behavior and decision-making and geological ideas to

determine the constraints on firm behavior.

A reliable model will not be a black-box of the simple mechanistic

kind nor an ad hoc regression fit as characterized so many early

"econometric" models. The relationship between the predicted behavior in

the model under consideration and the rest of economic theory should be

clear.

In the development of the model the economics of exploration as modified by governmental intervention should be recognized. The outcome

will be a model which not only fits the historically observed data, but

enables one to understand how the exploration market works and how it is

affected by both governmental action and geological conditions.

Sample values of reservoir sizes or even geographic distributions of

reservoirs will be recognized as the outcome of purposive search.

The estimation procedures should leave no doubt that the model in its

basic form is not only relevant, but that the maintained hypothesis

generated by it is acceptable with high confidence. The actual fitting of

the model should give no indication of specification error and the

estimated residuals should appear to be pure white noise.

If all of the above has been followed, one may claim to have a

"reliable" model with which policy prognoses can be made with some confidence of success.

But, be humble in your forecasts, for nevertheless, you may still be

wrong.

REFERENCES

Hale, C, Mariano, R. S., and Ramage, J. G. (1980) "Finite Sample Analysis

of Misspecification in Simultaneous Equation Models", JASA, vol.75,

p. 418-427.

Hausman, J., (1978) "Specification Error Tests in Econometrics",

Econometrica , vol. 46, p. 1251-1271.

Learner, Edward E., (1978) Specification Searches , Wiley, New York.

453
Ramsey, James B., (1969), "Tests for Specification Errors in Classical

Linear Least Squares Regression Analysis," JRSS , Series B, vol.31,

p. 359-371.

, (1974), Classical Model Selection Through Specification

Error Tests", in Frontiers in Econometrics , edt. P. Zarembka, New

York, Academic Press, p. 13-47.

and Schmidt, P., (1976), "Some Further Results in the Use of

OLS and BLUS Residuals in Specification Error Tests," JASA, vol.71,

p. 389-390.

Ramsey, James B., (1980), "The Economics of Oil Exploration: A Probability

of Ruin Approach", Energy Economics , vol. 2, p. 14-30.

DISCUSSION

QUESTION: I would only ask how close do you see us as being to this

sort of, admittedly, optimal model which explains the features. It just

seems to me that in the absence of good understanding of all these complicated processes, we are sort of like Galileo who dropped the two rocks

and finds, consistently, that they land.

He may not understand the theory of gravity, but still may be willing

to accept, on the basis of observations, a certain kind of prediction can

be made. So, while I would agree with you that it is optimal to have this

kind of theoretical model, I think we are more or less forced into less

than optimal models. Would you agree with that assessment or not?

DR. RAMSEY: Clearly, we always have a compromise with reality, so that a fairly reliable forecast is possible, as I said.

The point is that given where we are, what is the degree of confidence

that we place in what we do. If you are fully aware of the difficulties,

you will be very sure of not engaging in a very sensitive and rash policy

when you know that the outcome is very unsettled.

There is a big difference between getting a computer output, which is so common these days, and say here are the numbers; this tells me what I

should do. Go ahead and let's implement it; then you may discover that you

made a ghastly mistake.

It would be far better to be aware that you can make a ghastly mistake

and be very cautious before moving. So, my point is to exercise caution

and also to indicate what one can do to improve the situation. How does one

improve it?

One, insure that more and more theory is utilized in the development

of these models, to insure that the theory is consistent and that one recognizes that it is carefully and properly formulated; to insure that the estimation process is such as to meet the extraordinary demands on the use of

the procedure, and to insure that the maintained hypothesis is a reasonable

and useful approximation to the ideal.

454
On that basis, there are a whole battery of tests, or procedures,

which can be utilized to achieve this result. There is very little evidence

that this, in fact, is going on.

If you start looking under these logs, you will be horrified to discover the incredible number, degree, extent, and intensiveness of problems

of all sorts, from simple computational arithmetic difficulties all the way

through to the complete erroneous formulation of the hypothesis.

PHIL GLASNER (Standard Oil of California) : Can you elaborate on how

the process of search affects the distribution of reservoirs? You mentioned

it; you did not go into it.

DR. RAMSEY: I think it would take longer than I have here. I will

give you a copy of my paper on this and that will help to elaborate.

JOHN WOOD (EIA) : Would you care to comment on what types of theory

you think are ones that you should fundamentally understand? For example,

whether econometric models are ever reliable and, let's say, resource estimate

or supply, as opposed to certain underlying geological principles?

DR. RAMSEY: Let's put it this way. With the current models which I

have seen to date, I would be extremely cautious in making any extrapolations

from the historic data.

455
The Regulatory Framework in Oil and Gas Supply Modeling

Stephen L. McDonald

The University of Texas

Ordinarily, supply modeling assumes that producers are free to

respond to price and other economic incentives in both the short and

the long run. This assumption cannot be made without qualification

with respect to the oil and gas industry in the United States. Although gas production is relatively free, oil production is regulated in the name of conservation, and this regulation, anticipated

by operators, significantly affects investment in exploration and

development in the long run. Gas production in the long run is affected indirectly by oil regulation, due to the fact that oil and gas are joint products in the exploration phase and often in the development phase as well. In addition to production regulation proper,

administratively determined leasing schedules on the Outer Continental

Shelf and on some state lands influence the short- and long-run supply

responses to economic incentives. This paper will be concerned with

these regulatory restraints on supply.

Two systems of production regulation

There are two systems of oil production regulation in use today

in the United States. The first of these is based on the concept of

MER, or maximum efficient rate of recovery. MER is the basis of production regulation by the federal government on the OCS and by a number

of states in their respective jurisdictions. In California MERs are estimated by the Conservation Committee of California Oil Producers

for all reservoirs in which they are applicable and are recommended

to operators for voluntary use as the basis of production restraint.

Regulators in the Rocky Mountain states do not routinely estimate

MERs in new reservoirs, but they do intervene to restrict production

to something like MER when there is evidence of physical waste in

the form of loss of ultimate recovery. In the Southwestern states,

best known for market-demand prorationing in the 1950s and 1960s,

MER is the basis of production restraint in a relatively few selected

problem reservoirs.

The second system of oil production regulation, generally employed

in Texas, New Mexico, Oklahoma, Kansas and Louisiana, is based on an instrument of market-demand prorationing, the depth-acreage allowable

schedule. The schedules differ among the states named, but they have

in common a table of maximum allowables per well per day, the allowables

increasing exponentially with well depth and more nearly proportionately

with the number of acres per well. They are designed so that the allowable per well increases with increasing drilling and production costs,

as with increasing depth, so that all operators can "make a living"

under production restraint. The schedules provide an administratively

feasible method of restricting statewide output and allocating the total

456
among wells in states where there are thousands of separate reservoirs.

The allowables have little or no relation to MERs where such have been

estimated.

The optimum rate of production

It will help to bring out the significance of production res- triction if we have in mind the conditions under which the optimum

rate of production would continually be sought by profit-motivated

operators

It is well known that the basic problem of unregulated oil production stems from (1) the rule of capture as the law of property in

produced oil, (2) the fluid nature of oil in the reservoir, and (3)

the inverse dependence of ultimate recovery on the rate of production.

The first two of these mean that the operator who produces at a faster

rate than his neighbors can drain oil (or gas) from beneath his neighbor's land. Every operator, then, has a motivation to drill wells

densely and to produce at capacity. This is turn means that, given

the third factor mentioned, competitive exploitation of an oil reser- voir results in loss of ultimate recovery. Hence conservation regulation.

As indicated, the response to the conservation problem has been

to restrict oroduction (and incidentally to restrict the number of

wells drilled on a given acreage) . Another possible response is to

require the unitization of reservoirs, so that the element of competition within reservoirs is removed. Under unitization, separate

leases are pooled, costs and revenues are shared equitably, and the

reservoir is operated as a unit by a single management. What benefits

the operators as a whole benefits each individual lease-holder. On

behalf of the operators as a whole, the unit manager would select the

pattern of well spacing and the rate of production which promised to

maximize the present value of the reservoir. As changes occurred in

the rate of interest or the relation of present to expected future

prices and costs, he would change the rate of production (and perhaps

the number of operating wells) so as to track continually the rate

that promised to maximize present value. The rate would not necessarily

be that which maximized ultimate recovery, but any prospective loss

would be taken into account in the present value calculation and weighed

against the interest saving of speedier recovery.

Although it can be argued, as I have elsewhere done,* that unitization of oil reservoirs is a fundamental solution of the conservation

problem and is in the social interest, that is not our primary concern

here. Here we are concerned simply with the response of output to

economic incentives, in the short and the long run, when unit operators

are free to pursue the rate of output that maximizes present value—

the optimum rate of output in an economic sense.

457
We note first that under unitization short-run supply would have

some price elasticity. Given expected future prices, a fall in present

prices would induce a reduction in current output (and perhaps a re- duction in the number of operating wells per reservoir) , while a rise

in present prices would induce an increase in current output (and

perhaps an increase in the number of operating wells r>er reservoir),

even though ultimate recovery might suffer somewhat. This result

would follow simply from the continuous effort to maximize present

value. Note that since capacity depends in part on the number of

wells in a reservoir, the optimum rate of output and the optimum

number of wells are jointly determined.

Second, if unit operators were free to maximize present value of

reservoirs, investment in exploration and development would tend to

be optimal also. If explorer-developers could anticipate that new

reservoirs would be unitized and operated so as to maximize present

value continuously, they would extend the margin of exploration to

the maximum extent feasible under given expected price and cost conditions. Only some sort of subsidy would yield a more extended margin. Although the relative response of output to a change in price

need not be affected, the absolute response to a level of price would

be maximized, absent a subsidy, under a regime of unitized operation

of reservoirs.

Before considering short- and long-run output response to incentives under different regimes, it is necessary to examine the economics

of MER and depth-acreage allowable schedules.

MER: Definitions and implications

Among state regulators of oil production MER is typically defined

as the rate of production from a reservoir which if exceeded will result

in significant loss of ultimate recovery. It is an engineering concept

which, as a tool of conservation, fits with the view that conservation

consists of the prevention of physical waste. It is not an economic

concept, although at least one authority admits that economics may have

to be considered in estimating MER in cases where extremely low2rates

of recovery are indicated on grounds of engineering efficiency. In any

case, except by coincidence MER so defined does not correspond to the

rate of production which maximizes the present value of the reservoir.

For purposes of oil production regulation on the OCS, current

regulations define MER as:

The maximum sustainable daily oil or gas withdrawal rate

from a reservoir which will permit economic development

and depletion of that reservoir without detriment to

ultimate recovery."^

The Outer Continental Shelf Lands Act Amendments of 1978 appear to

define MER in a consistent way as:

458
The maximum rate of production which may be sustained without

loss of ultimate recovery of oil or gas, or both, under sound

engineering and economic principles.

Both definitions refer to economics, but neither explains just how

economics is to be used in estimating MER.

One possibility has been suggested authoritatively by a then

official of the Department of the Interior. According to his suggestion, MER is the rate of production which results in the highest

ultimate recovery consistent with a just-acceptable rate of return

on the overall operation. This definition implicitly takes into

account the fact that in many instances maximizing ultimate recovery

may be uneconomic and prevent the development of otherwise viable

reservoirs. However, MER so defined does not necessarily correspond

to the rate of production which maximizes present value. This may

be shown by means of an illustration.

Suppose that a tentative rate of production has been adopted in

a unitized reservoir which promises to maximize ultimate recovery;

and suppose that at that rate of production the operators earn an acceptable rate of return on the overall investment. Now suppose

that the unit operator calculates that if he drilled additional wells

and sped up production he would reduce ultimate recovery but would

earn a satisfactory rate of return on the incremental investment by

virtue of speeding up receipts. If he were free to maximize value,

the unit operator would take this step; the value of the reservoir to

him and his associates would be increased. On the other hand, if the

regulators used the indicated definition of MER as the basis of production restriction, he would not be permitted to take this step and

the present value of the reservoir to him and his associates would be

less than it might be.

There are two implications of the use of these definitions of MER

in production regulation: (1) effectively zero short-run elasticity

of supply, and (2) restrained investment in exploration and development

at any given level of present and expected price.

As for the first, outside the Southwestern market -demand prorationing states operators have always been permitted to produce at the

MER, or at an equivalent non -wasteful rate, even in the worst days of

national over-capacity. The same is true, for the period since 1970,

in the Federal OCS jurisdiction. In reservoirs with multiple operators

the MER has also tended to be the minimum rate of production. This is

because of the adverse drainage problem: the individual operator who

restricts production below MER suffers drainage to any of his neighbors

who do not similarly restrict the rate of output. Without cooperation,

all operators are thus induced to produce continuously at the maximum

allowable rate. Therefore, only in single-operator reservoirs would

459
we expect to find any short -run supply elasticity. On the OCS, since

1973, even this source of elasticity is missing as pressure is put on

all operators to produce at the maximum allowable rate so as to minimize imports.

It should be emphasized that this short-run supply inelasticity

does not have to be; it is not in the nature of the industry as such.

It is in the nature of an approach to conservation regulation that

emphasizes prevention of physical waste, regardless of opportunity

cost, and that fails to do anything directly about the problem of

adverse drainage. As we have seen, operator freedom under a regime

of unitized reservoirs would result in significant short-run elasticity

of supply.

As for the second implication, production restriction based on MER causes all reservoirs, except by coincidence, to be less valuable

to operators than they could be. Such restriction thus contracts the

margin of exploration and development at any level of present and ex- pected price. Long-run supply elasticity, the proportionate response

of output to a proportionate increase in price, may be about the same

as under unitization; but the entire long-run supply curve is farther

to the left on the quantity axis. MER-based regulation thus keeps us from making the most of our national resources and increases our dependence on imports, with all that implies.

Again, it does not have to be. Under a regime of unitized reservoirs, the prospective value of reservoirs is maximized and the level

of unsubsidized investment in exploration and development is corres- pondingly maximized. (I shall not go into the merits of subsidizing

domestic exploration and development so as to reduce imports.)

Production restriction based on depth-acreage allowable schedules

As earlier noted, the predominant basis of production restriction

in the Southwestern states is the depth-acreage allowable schedule,

according to which maximum oil allowables are prescribed as functions

of depth of wells and acreage per well. The general nature of the

schedules, which differ from state to state, can be illustrated by means

of the following excerpt from the 1965 Texas Yardstick, as it is called.

460
From the 1965 Texas Yardstick

Maximum Oil Allowable

in barrels per day

Depth

(000 ft)

10

Acreage per well

20 40 80 160

0.0-2.0 21 39 74 129 238

8.0-8.5 34 68 133 215 380

14.0-14.5 200 400 600 1000

It is readily seen that the allowables increase not quite proportionately to the acreage per well and exponentially with depth. (Drilling

and operating costs per well tend to increase exponentially with depth.)

These are maximum allowables per well; that is, the allowables when

the market-demand factor is 100%, as it is now and has been for a number

of years. Subject to capacity, they also tend to be minimum rates of

output per well, due to the adverse drainage problem; if any operator

unilaterally restrains production below the allowable, he will suffer

drainage to his neighbors 1 wells. The allowables have no systematic

relation to MERs where the latter have been estimated. MERs may tend

to increase with depth, due to increasing pressure and temperature in

the reservoir, but every reservoir is unique and no one would suppose

that every reservoir at 14,000 feet, for instance, would have an MER

of exactly 1,000 barrels per day if developed at one well per 160

acres, etc.

A most important feature of the schedule is that the allowable

depends on the acreage per well. By choosing a spacing pattern, which

usually is uniform within a reservoir, the operators choose a maximum

allowable. The present value of the reservoir depends on both of these,

tending to increase with the total allowable (at least until loss of

ultimate recovery becomes a significant factor) and to decrease with

the number of wells. These relationships suggest that there^is an optimum acreage per well at every depth, as indeed there is. This

optimum decreases with price of oil and increases with cost per well.

But whatever the acreage chosen, there is only one effective rate of

output. This means that in the joint selection of acreage per well

and output per well operators are severely constrained, so that it

would be a coincidence if the present value of any reservoir could be

maximized

461
Again, we have two implications: (1) short-run inelasticity of

supply and (2) a contracted margin of exploration and development.

With regard to the first, we have seen that the maximum allowable

also tends to be the minimum rate of output, so that in response to

a change in price there can be no change in output in the short run. There is conceivably an intermediate-run responsiveness. If there

is sufficient rise in price it may pay the operators in a reservoir

to secure permission from the regulators and drill additional wells

and thereby increase the total reservoir allowable. Using the 1965

Texas Yardstick as an example, if one well 14,500 feet deep was drilled

per 160 acres the allowable per 160 acres would be 1000 barrels per

day; but if an additional well is now drilled on 160 acres the tract

allowable would be 1200 barrels per day. The additional present value

from speeding up recovery would, of course, have to be weighed against

the additional cost of wells, cost of production and loss of ultimate

recovery.

With regard to the second implication, the argument is essentially

the same as that in regard to MER-based regulation. However, the

arbitrariness of the depth- acreage allowable schedule suggests that

regulation of production based on it has a more adverse effect on the

margin of exploration and development than regulation based on MER.

It may be observed that most wells in the Southwest are now

producing at capacity and that capacity, not the depth-acreage allowables, is limiting output in the region. This may be correct, but

it does not alter our conclusion about short-run inelasticity of

supply. As for contraction of the margin of exploration and development, capacity is not independent of the number of wells originally

drilled in a reservoir, which depends in part on the allowable schedule. Also capacity output suggests the possibility of significant

loss of ultimate recovery which operators cannot effectively do anything about since capacity tends to be the minimum as well as the

maximum rate of output. In either case, our conclusion stands that

production regulation based on allowable schedules tends to contract

the margin of exploration and development.

A word on natural gas

The production of natural gas in the United States is not systematically regulated on the basis of MER or depth-acreage allowable schedules. Occasionally an MER may be applied, or reservoir output may be

restricted to pipeline demand and allocated among lessees as a means of

assuring ratable take and protecting correlative rights. So most of

what we have said about oil production does not apply to natural gas.

However, in many situations natural gas is a joint product with

oil, particularly at the exploration stage. If regulation of oil production tends to contract the margin of exploration for oil, it does

likewise for gas. A rise in the expected price of gas stimulates oil/

gas exploration, but due to the pattern of oil production regulation

462
anticipated, the response is not as gfbat as it would be if oil production were under a regime of unitization with operator freedom.

Thus in the long run gas production is constrained by regulations

that apply only indirectly to it.

The rate of leasing on the PCS

When the expected price of oil or gas rises, exploration is of course increased. But in the short run the industry's results are constrained by the inventory of prospects. These prospects vary in

quality, and the industry's response to a price stimulus is to "dig

deeper" into the bag of prospects, lowering the marginal and average

quality of the prospects actually explored. Consequently, subsequent

discoveries do not increase in proportion to exploration effort. If

it were not possible to subject new land to pre-drilling exploration,

and to secure new leases, the decline in the quality of prospects

would severely limit the long-run response of supply to a price stimulus .

In general, leases are freely available to be bid for in the

continental United States (onshore) . The main limiting factor is the

restricted stock of continental lands that have not already been thoroughly explored. But on the OCS, where perhaps the bulk of the oil

and gas of the United States remaining to be found is located, the

availability of leases is restrained by policy; and the leasing authorities cannot quickly react to a price stimulus. As present law is

officially interpreted, the leasing authorities are required "(1) to assure orderly and timely resource development; (2) to protect the

environment; (3) to insure the public a fair market value return on

the disposition of its resources."^ All of these requirements, but

especially the second and third, stand in the way of a sudden marked

increase in the rate of leasing in response to a price stimulus.

This in turn restrains the oil and gas supply response to such a stimulus, particularly in the short and intermediate run.

Part of the problem is coordinating oil company preleasing ex- ploration with the rate of leasing. If the industry was certain of

the number and general location of leases to be granted in a given

period of time, it could do the preliminary exploration essential to

assuring "fair market value" bidding. Thus the leasing authorities

could, with sufficient notice to the oil companies, raise the rate of

leasing and sustain it for many years. But they still could not res- pond adequately to sudden and unexpected increases in prospective prices.

The problem of protecting the environment alone, with all of the required

impact studies, hearings and perhaps litigation, would seriously interfere with quick and flexible reaction. OCS leasing policy will probably continue to be a short- and intermediate -run restraint on oil

and gas supply as the industry responds to price incentives.

463
Conclusion

I conclude that the continued regulation of oil production i; the United States significantly constrains the oil and gas supply

response to price stimuli, in both the short and the long run. Successful supply modeling must take into account the constraints

we have discussed.

FOOTNOTES

1. Stephen L. McDonald, Petroleum Conservation in the United States:

An Economic Analysis (Baltimore: The Johns Hopkins University

Press for Resources for the Future, 1971).

2. Stuart E. Buckley, ed., Petroleum Conservation (Dallas: American

Institute of Mining and Metallurgical Engineers, 1951), pp.

151-52.

3. U. S. Geological Survey, Conservation Division, Gulf of Mexico

Area, PCS Order No. 11 , p. 2.

4. The Outer Continental Shelf Lands Act Amendments of 1978 , U. S. Congress, Conference Report No. 95-1474, August 10, 1978,

Sec. 204(g).

5. Statement of Jack W. Carlson, Assistant Secretary, Energy and

Minerals, Department of the Interior, before the Subcommittee on Antitrust and Monopoly, Senate Committee on the Judiciary,

Sept. 23, 1975, (mimeo) p. 20.

6. McDonald, op. cit . , pp. 173-80.

7. Statement of Harrison Loesch, Federal Leasing and Disposal

Policies, Hearings before the Committee on Interior and Insular

Affairs, U. S. Senate (Washington, D. C. , June 19, 1972), p. 38.

464
DISCUSSION

LARRY BUSH: My name is Larry Bush, and I am with the Texas

Counsel of Public Accounts.

I have heard the concern expressed by two separate independent

producers that there are occasions where large producers, primarily

major producers, will over produce a field even beyond the state

conservation rate in order to satisfy short-term cash flow needs.

Does that appear to be maximizing social value of the natural

resource?

DR. McDONALD : Maximizing cash flow is not necessarily consistent

with conservation as such. I define, as you know, Larry, conservation

as action designed to maximize present value of the resource. Maximizing current cash flow will not necessarily do that.

Whether there are cases such as you mention, I don't know. I think it might well be more likely for a small independent who had a heavy bank debt and had to make payments on it to do that than a large company with good access to the capital market.

DR. HUBBERT: How do you maximize my present value? What is the

technique?

DR. McDONALD: The technique is to rearrange the flow of your

cash in such a way that when you discount it, it achieves the maximum

present value. In the case of oil and gas production, what you would

rearrange would be the time schedule of your production, that depending,

of course, upon what the trend in expected prices is.

As I indicated, if you expect future prices to rise relative to

present prices, you would shift production toward the future, and vice

versa. But it is simply a matter of equating discounted marginal net revenues in all periods. That is the technique.

465
Firm Size and Performance in the Search for Petroleum

L. J- Drew and E. D. Attanasi

U.S. Geological Survey, Reston, VA 22090

Introduction

Crude-oil production in the conterminous 48 States of the United States

peaked in 1970. At that time, few were concerned with the consequences of

the rapidly increasing consumption of imported oil by the United States.

Because of the oil embargo of 1973, by means of which OPEC (Organization of

Petroleum Exporting Countries) became a functioning world oil cartel, attention was focused upon the structure of the domestic oil industry. Allegations

have been made that the large integrated firms were engaged in monopolistic

pricing within the United States. These allegations were based upon the fact

that these firms spent a large part of their funds for exploratory drilling

in foreign countries during the 1960's and early 1970's while at the same

time they held vast amounts of undeveloped acreage favorable for the occurrence

of petroleum within the United States. Industry critics (Blair, 1976) have

pointed to this allocation of exploration as evidence that the large integrated

oil firms were restricting potential domestic supplies by not exploring in the

United States in order to drive up the price. Some critics (Engler, 1977)

advocated that divestiture of the exploration and production units of the large

integrated firms into regional units would increase domestic exploratory

drilling and thereby increase the supply.

Before a major restructuring of the industry is attempted, the policymakers must face the dilemma of predicting how the performance of the industry

might be changed as a result of the suggested divestiture and regionalization

of the exploration and production units of the major integrated firms. However,

466
very few analyses have been made of the history of the efficiency of the performance of different sizes of oil firms in exploring for and discovering

crude petroleum; two examples of such analysis were prepared by McKie (1961)

and West (1977). In order to expand on the conclusions reached in these two

studies, we undertook a detailed examination of the relative roles played by

firms of different sizes in the exploration of a significant petroleum-producing

province (the Denver basin) • The exploration and production history of the

firms operating in the Denver basin was examined (1) to compare the relative

search performances of firms of different sizes and (2) to determine whether

physical variables can explain the exploration strategies of firms of different

sizes*

The exploration behavior observed in the Denver basin, we believe, is

representative of how onshore exploration progressed in the United States.

For example, in the United States from 1946 to 1953, the major firms drilled

19 percent of the wildcat wells (29 percent if those financed by them are

included). Alternatively, from 1970 to 1976, the majors accounted for less

than 10 percent of the wildcat wells drilled (West, 1977, p. 86). In the

Denver basin during 1955, the major firms accounted for about 20 percent of

the wildcat wells drilled, and by the mid-1960' s, they had almost completely

shut down their wildcat drilling in this area, thus, for the period 1949 to

1974, independent firms accounted for 88 percent of the wildcat wells drilled.

Drilling costs in the Denver basin were cheap, and mineral rights were easily

and regularly transferred. Consequently, the independent and small firms seem

to have had a better chance here than elsewhere to play a significant role in

the area's exploration.

Because our purpose is to demonstrate how physical characteristics of

467
petroleum discoveries and the results of past exploration affected industry

behavior the first part of the paper discusses physical characteristics of

oil and gas fields that produce regularity in the petroleum-discovery process.

This discussion is followed by a brief description of the exploration history

of the Denver basin. A summary of the results is presented along with their

implications in the concluding section.

Physical Characteristics Affecting the Petroleum-Discovery Process

Petroleum fields occur in sedimentary rocks in geologic basins or provinces that extend over millions of acres. Figure 1 shows the size distribution of discoveries in the Permian basin, in western Texas and southeastern

New Mexico. This field-size distribution is typical of other basins or

petroleum provinces in that fields occur in a wide range of sizes, most fields

are small, and most of the basin's reserves are contained in just a few large

fields. The largest 38 fields, or less than 1 percent of the total fields,

contain more than half the hydrocarbons whereas the 3,789 fields in the smallest

class size account for only 16 percent of the hydrocarbons discovered. Figure

2 presents the same data as figure 1 but is drawn to scale without breaks in

the y-axis in order to emphasize that small fields are much more common than

large fields in the same basin- At the scale used in figure 2, the large

deposits are too few to be graphed. The disparity in sizes between the smallest

and largest size class is six orders of magnitude. Table 1, which lists pairs

of items whose sizes differ by six orders of magnitude, is presented so that

a vivid impression might be gained about the disparity in field sizes.

A major consequence of the wide disparity in field sizes is that the rate of

discovery (volume of oil and gas discovered per unit exploration effort) declines

as cumulative exploration increases. Because large fields generally have large

468
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Table 1. —Comparisons illustrating a difference of six orders of magnitude.

Category suia x x lc em Large item

groups of people

(number)

K-ac UdocUdll o r\ oil t- q otti Lcdili lNcw lUIK tjlty

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time half minute year

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areas Liechtenstein Pacific Ocean

beight 1/3 inch Mt - Everest

foot race 4- cm. sprint marathon

volume 1 drop 1 barrel of oil

From Root and Drew, 1979.

471
surface areas and are contained in large easily detected geologic structures,

they are more easily discovered than small fields. In the Permian hasin, the

Yates field, which contains more than 2 billion barrels of recoverable oil

equivalent has a surface area of about 50 square miles. The distribution in

field sizes and the fact that large fields typically are more easily detected

than small fields causes the rate of discovery to decline after the few large

fields are found. Figure 3 presents the average field sizes for 14 drilling

increments of approximately 2,000 wells each in the Permian basin. The rate

of discovery in this region appears to have gone through three stages. These

include (1) a short initial phase when the discovery rate was high, (2) a

second stage when the discovery rate declined rapidly, and (3) the third stage

when a low but stable discovery rate was maintained. These stages are also

characteristic of the discovery rate for the conterminous United States as

seen in figure 4 (modified from Hubbert, 1967). After World War II, the

discovery rate dropped rapidly, and since 1953, the discovery rate has been

fairly stable (Root and Drew, 1979). The rapid drop in the U.S. discovery

rate was not immediately recognized at that time because generally, several

years are needed to determine the size of a large oil field. However, the

dramatic reduction in wildcat drilling in the United States and the shift of

exploration by the major firms toward foreign areas of operation that began

in the late 1950' s clearly was induced by the precipitous drop in the U.S.

discovery rate shortly after World War II. Major oil firms that had attractive prospects or opportunities in foreign areas because discovery rates were

higher in these regions than U.S. discovery rates moved their exploration

efforts to these areas. The regularity in the petroleum-discovery process for

nearly all domestic areas, including the Denver basin, is the result of the

physical characteristics of petroleum fields.

472
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The Study Area

The Denver basin consists of approximately 40,000 square miles in eastern

Colorado, southwestern Nebraska, and southeastern Wyoming. Data pertaining to

the exploration history of the Denver basin were obtained from the Well History

Control File of Petroleum Information, Inc. , Denver, Colo. From 1949 to 1974,

11,577 exploratory wells were drilled in the basin, resulting in the discovery

of 909 petroleum fields, which range in size from the Adena field (63.4 million

barrels of oil) down to numerous one-well fields that produce only a few thousand

barrels. The estimated amount of oil found In the 909 fields discovered between

1949 to 1974 was 742 million barrels of oil.

The skewed size distribution of fields present in the Permian basin also

typifies the Denver basin. The largest of the 909 fields contains 8.5 percent

of the oil found during the 1949-1974 period, and the smallest 659 fields

accounted for only 7 percent of the oil found. Furthermore, the largest 31

fields accounted for 45 percent of the oil found. As a result of the wide range

in field sizes, the discovery rate for the Denver basin (fig. 5) shows the same

behavior as the discovery rates for the Permian basin (fig. 3) and the conterminous United States (fig. 4). The slight increase in the discovery rate in

1970 is accounted for by several significant discoveries made on acreage that

was formerly withheld from exploration by the Union Pacific Railroad.

Firm Size and Search Performance in the Denver Basin

Firms operating in the Denver basin were classified into four groups. The

first group consists of the major firms that are vertically integrated and are

active in all stages of the petroleum industry from exploration and production

on through transportation, refining, and product marketing. Table 2 presents

a list of the major operators. The second group consists of large independent

475
476
Table 2- —Numbers of wildcat and development wells drilled by the

major integrated operators in the Denver basin 1949-1974.

[Data are from Petroleum Information, Inc- , Denver, Colo-, 1975.]

Firm

Unsuccessful

wildcat wells

Successful

wildcat wells

Producible crude

oil discovered-*-

Successful

development wells

Unsuccessful

development wells

AMERADA 24 1 1.4 18 16

AMOCO 232 14 12.3 598 176

BRITISH AM. 241 28 58.2 333 180

CHAMPLIN 49 4 9.8 72 41

CHEVRON 11 3 6.7 37 6

CHICAGO 9 3 8.0 18 12

CONTINENTAL 45 4 9.3 67 44

GULF 32 2 0.5 40 29

KOCH 27 2 5.7 44 3

MOBIL 7 2 0.2 86 39

MONSANTO 37 3 1.3 117 34

OHIO 91 27 41.5 211 104

SHELL 276 25 17.4 250 113

SINCLAIR 54 4 7.2 99 46

SKELLY 47 10 7.8 107 63

SOHIO 37 0 0.0 24 13

SUN 20 1 1.8 35 15

SUNRAY 19 2 2.3 19 17

SUPERIOR 40 5 8.7 67 25

TEXACO 33 4 6.8 84 31

TOTAL 1331 144 206.9 2326 1007

In millions of barrels.

477
firms that are principally involved in exploration and production. Drilling

contractors are classified as the third group <*f operators; this group includes

only firms whose principal business is the sale of contract drilling services

to the petroleum industry. The fourth group, "small independents," consists

of more than 3,000 individuals and small firmsThe performance of each group of operators is measured in terms of the

wildcat success rates, development-well success ratios, oil discovered per

exploratory well and the quantity of reserves owned. Because oil fields

commonly encompass several leases, the firm that discovers a field generally

does not own all the field's reserves. An estimate of ultimate oil recovery

was assigned on a production-well basis in order to allocate reserve ownership

to a specific class of operator. The method for apportioning expected field

recovery to individual wells was based upon the assumption that a well's

ultimate productivity is directly proportional to the initial producing rate

of that well. For example, if a two-well field is estimated to have an

ultimate recovery of 69,800 barrels and one well had an initial producing

rate of 180 barrels per day and the other well has an initial rate of 120

barrels per day, the first well is assigned an ultimate recovery of 41,880

barrels, and the second well is assigned 27,920 barrels of reserves.

In table 3, the drilling records of the four groups of operators are

presented. During the period considered, as a class, the major integrated

firms discovered 206.9 million barrels of oil (28 percent of the total) by

drilling 1,475 wildcat wells, of which 144 were successful. Per wildcat well,

they discovered 140.3 thousand barrels, more than twice the amount discovered

per well by any other group. Their wildcat success ratio was also the highest

at 0.098.

478
Table 3- —Discovery success and volumes of petroleum discovered

by operator class from 1949 to 1974 in the Denver basin.

[Data are from Petroleum Information, Inc., Denver, Colo., 1975.]

Large Large Drilling Small

majors independents contractors independents TOTAL

Number of

successful

wildcats 144 275 84 406 909

Number of

unsuccessful

wildcats 1,331 3,484 1,228 4,614 10,657

Wildcat-well

success ratio .098 .073 .064 -081 .079

Petroleum

discovered 206.9 185.6 80.8 268.7 742.0

Petroleum discovered

per wildcat well

drilled2 140.3 49.4 61.6 53.5 64-2

In millions of barrels of producible oil.

In thousands of barrels of producible oil479
Figure 6 presents the time profile of discoveries and wildcat drilling

for the four classes of operators- The figure shows that the major integrated

firms had essentially stopped drilling wildcat wells in the basin in the late

1950's. The reason why the major integrated firms left in the late 1950's is

that the rate of discovery had fallen off sharply after 1955 and they moved on

into other regions where high rates of discovery could be obtained, that is,

offshore areas and foreign countries. The number of wildcat wells drilled by

the majors closely tracks the total volume of discoveries per year when wildcats are lagged by 2 years- Attanasi and Drew (1977) modeled this effect by a

distributed lag function. Drilling rates for each of the other three classes

of operators show to a lesser degree the same lag effect- However, these other

operators (combined) still drilled more than 200 wildcat wells each year

throughout the 1960's and 1970's. This record of exploratory drilling obviously

indicates that. the major firms could not have been actively excluding smaller

firms from exploring the basin.

The strategy that seems to have been followed by the majors was to assemble

and hold large blocks of acreage during the long term- As a result of this strategy, the major firms can systematically evaluate and select for drilling what

they regard as the higher quality acreage and then, in turn, farm out the poorer

quality acreage to independent firms- In these arrangements, the major firm

(usually holding a dominant acreage position on a particular prospect) provides

the smaller operator with a parcel of its own lease or working interest in a

parcel of acreage in exchange for information on the results of a specified

number of exploratory wells that the smaller firm is committed to drill. This

kind of exchange agreement may also be used when potential development acreage

is farmed out, usually on the fringes of the field.

480
=3 1 1 1 I | 1950 1955 1960 1965 1970 1975

Graphs showing the time profile from 1949 to 1974 of oil discoveries and

wildcat drilling for the four classes of operators. Data are from Petroleum

Information, Inc., Denver, Colo. (1975).

FIGURE 6.

481
Figure 7 indicates the location of the discovery and development wells

drilled by type of firm in the Sloss field., one of the largest fields in the

Denver basin. First, the disc overy of the field was credited to an independent

at a site that ultimately proved to be on the edge of the productive limit of

the field. Second, the major firms also drilled most of the normally more

productive areas in the central part of the field, whereas areas drilled by the

independent firms were generally on the margins of the field where petroleum

yields are almost always inferior. Of the 31 largest fields in the basin

(representing 45 percent of reserves found between 1949 and 1974), at most 13

were discovered by major operators. Field maps for the largest 20 fields show

that these fields have the same pattern of discovery- and development-well

ownership as the Sloss field (fig. 7). Apparently, even though the majors had

identified the area as favorable to the occurrence of oil, they regarded it as

marginal in terms of committing cash for exploratory drilling that could have

been used elsewhere, and they were willing to farm out acreage to facilitate

timely evaluation of the prospect.

Results of development drilling and reserve ownership by class of operator

are compared in table 4. The major's development-well success ratio was substantially higher than those of any of the other classes of firms. Additional

evidence that the major firms were able to retain the highest quality production

acreage is that their reserves per development well were 46 percent higher than

those for the large independent firms, almost twice as high as those for the

drilling contractors, and almost four times the reserves per well of the small

independent firms. Although the major firms were credited with the discovery

of only 28 percent of the total value of oil discovered, they are expected to

develop 47.3 percent of the reserves represented by these discoveries. Conse482
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Table 4. —Development-well success and volumes of petroleum reserves credited i by operator class from fields discovered from 1949 to 1974 In the

Denver basin-

[Data from Petroleum Information, Inc., Denver, Colo., 1975]

Large

majors

Large

independents

Drilling

contractors

Small

independents

$n * i TOTAL

Number of successful

development wells 2,326 1,106 309 1,926 5,667

Number of unsuccessful

development wells 1,007 1,342 533 2,462 5,344

Development-well

success ratio .698 .452 .367 .439 .515

Reserves owned^- 351.2 176.6 47.0 167.2 742.0

Reserves per

development

well drilled2 105.4 72.1 55.8 26.6 67.4

In millions of barrels of producible oil.

In thousands of barrels of producible oil.

484
quently, the major firm's strategy of acquiring and holding large blocks of

undeveloped acreage for the long term permitted them to gain production rights

to oil that was not discovered by their own wildcat wells. The strategy of

farming-out exploration and marginal production acreage is consistent with

the precipitous decline in the discovery rate in the mid-1950' s and their

subsequent movement of their own exploration activities to offshore and

foreign areas where discovery rates were still high. Moreover, major firms

typically like to use their large cash assets for exploratory activities in

high-cost frontier and international areas where both the expected returns and

contingency risks are likely to be very large.

What seems to be more difficult to explain is why the independent firms

drilled so many poor-quality development acreage locations. In their attempt

to develop reserves that represent just over half the oil in the Denver basin,

the large and small independent firms and the drilling contractors drilled

4,337 (81 percent) of the 5,344 total dry development wells drilled. By definition, these wells were drilled in locations directly offsetting productive

wells. However, they were just beyond the productive limits of the field.

The behavior of the independents, particularly, the smaller ones is due in

part to complex promotional devices used by the independent firms to finance

both exploration and development drilling. These firms typically have few

fixed resources; small or non-existent geologic staffs, few leases, and little

if any drilling or production equipment. An important source of funds for

these firms are individuals' speculative funds that would normally be taken

as income taxes- A promoter for an independent may even get individuals to

subscribe to the drilling of a well in a specific location. It is well known

within the petroleum industry that certain independent firms can and do make a

485
profit for themselves on a dry hole. The Independent who has individuals

subscribe to individual holes does not usually consider the opportunity cost

of using these funds on other prospects. In contrast, major firms finance

drilling from retained earnings generated by production or selling additional

equity and they evaluate the opportunity cost of using capital in a whole

range of areas and prospects. This explanation of the results leads to the

suggestion that the major's principal objective is to develop production,

perhaps because of the profit it can make on oil in its downstream (refining,

retailing, and transporting) activities, whereas the independent firm who

makes a profit on the act of drilling, has the objective of drilling as many

wells as possible.

Conclusions

Industry critics argue .for divestiture and perhaps regionalization of

major oil firms by pointing to the facts that (1) during the last 30 years,

the largest 20 integrated (or major) oil companies have owned more than 50

percent of the undeveloped favorable acreage in the United States and (2)

starting in the mid-1950' s and continuing for more than a decade, these same

oil companies steadily decreased their level of exploratory drilling within

the United States (Blair, 1976) • These advocates claim that such evidence

can mean only that the major integrated firms acted together to restrict

exploratory drilling which, in turn, resulted in the restricting of the supply

of domestic crude oil and ultimately forced up the price.

In this analysis of exploration of the Denver basin, which we think is

representative of exploration of the onshore conterminous 48 States, no evidence was found to support the assertion that the major integrated firms had

restricted supply of crude petroleum by restricting access to favorable acreage.

486
As long as major firms continue to evaluate prospects by using farm-out

agreements they cannot restrict supply of oil and gas in an area. If a

small firm discovers oil or gas on acreage obtained from a farm-out agreement,

the owners of adjacent tracts (that also contain part of the new field) must

immediately begin production on their property or risk losing these resources

by a neighbor draining their tracts. The symbiotic relationship between large

and small firms may accelerate exploration but will probably not significantly

affect the region's or nation's petroleum supply. The willingness of the large

firms to enter into such agreements implies that the prospect has been evaluated

sufficiently to determine that the likely size of the discovery will be marginal

when compared to the firm's other opportunities. The major firms reduced their

own exploratory drilling in response to the sharp declines in the discovery

rates in the United States and the Denver basin.

The practice of holding large amounts of undeveloped acreage is only one

element in the overall exploration strategy used by the major integrated

companies. Briefly, this land-holding practice gives these firms (1) a

superior chance at obtaining significant parts of the larger, more profitable

oil fields, which are for the most part, discovered early in the exploration

of a region, and (2) an additional source of income to them, after the discovery rates have fallen below an acceptable level, from farming out parcels

of acreage for continued exploration and development by the independent firms.

These independent firms use a complex set of promotional devices to raise taxsheltered and other types of speculative funds to finance their drilling

activities. They normally deal with the major firms for acreage contributions,

dry-hole money, and other assets* The essential idea is that an independent

firm could make a profit on the act of drilling a well. Whether the well pro487
duces a net profit for its production may be only a secondary concern. In

fact, the independents serve as instruments to divert speculative and taxsheltered funds into the exploration industry, and because they can make a

profit on the drilling of a hole itself, they can continue to drill even when

the average rate of return from the petroleum produced does not justify such

drilling- This behavior contrasts sharply with the major firm's primary

objective in carrying out exploration; that is, to develop production for

downstream activities.

488
References

Attanasi, E. D- and Drew, L. J- , 1977, "Field Expectations and the Determinants of Wildcat Drilling," Southern Economic Journal , vol. 44, no. 1,

pp. 53-67.

Blair, J. M. , 1976, The Control of Oil , Pantheon Press, New York, N.Y. , 441 p.

Engler, R. , 1977, The Brotherhood of Oil , University of Chicago Press, Chicago,

111. , 337 p.

Hubbert, M. K. , 1967, "Degree of Advancement of Petroleum Exploration in the

United States," American Association of Petroleum Geologists Bulletin ,

vol. 51, no. 11, p. 2207-2227.

McKie, J. W., 1961, "Market Structure and Uncertainty in Oil and Gas Exploration," Quarterly Journal of Economics , pp. 543-571.

Root, D. H. , and Drew, L- J., 1979, "The Patterns of Petroleum Discovery

Rates," American Scientist , vol. 67, no. 6, pp. 648-652.

West, J., 1977, "Independents Vital to U. S. Petroleum Supply," Oil and Gas

Journal , vol. 75. no. 44, pp. 85-92.

489
SENSITIVITY ANALYSIS OF FORECASTS FOR

MIDTERM DOMESTIC OIL AND GAS SUPPLY

Carl M. Harris

Center for Management ^nd Policy Research

Washington, D.C.

1. EXECUTIVE SUMMARY

This report describes a quantitative sensitivity analysis of midterm

projections of United States crude oil and natural gas production for

the Department of Energy's (DOE) EIA Annual Report to Congress, 1979

( 1979 ARC).

1 . 1 The Project's Objectives

The specific target of this study is a set of projections of midterm

oil and gas production generated by the 1979 version of the DOE

analysis system MOGSMS (the Midterm Oil and Gas Supply Modeling

System) , in conjunction with the 1979 ARC . These forecasts apply to

conventional oil and gas, on-shore and off-shore, in the lower 48

states, for the years 1985 to 1995, inclusive. The specific objective

of this work was to employ analytic procedures to examine the

sensitivity of the 1979 midterm oil and gas projections to some of its

key elements.

« The sensitivity analysis employed to achieve this objective draws

heavily upon procedures and insights developed in model validation

efforts recently carried out by the National Bureau of Standards

of the United States Department of Commerce, for the Office of

Analysis Oversight and Access of EIA.

1.2 Overview of the Study Design

The primary emphasis in this current study was the analysis of

the sensitivity of the target projections to uncertainties in: (1)

the (exogenous) estimates of regional finding rates and the original

resource bases; and (2) various other significant data elements

underlying the projections. Accordingly, three distinct statistical

experiments served as the vehicles for the sensitivity analysis:

o Experiment 1 : A Monte Carlo analysis of

the USGS Circular 725 estimates of

regional undiscovered (oil and gas) resources and their impact on MOGSMS

finding rates and ultimate outputs.

o Experiment 2 : A Monte Carlo analysis

of other selected key elements (namely,

recovery factors and decline rates) and

their impacts on MOGSMS output.

o Experiment 3 : A response surface analysis

of various MOGSMS input data elements,

including both physical and economic

elements, to identify those in which

uncertainty has the greatest effect

on MOGSMS results.

490
Each of these experiments involved exercising MOGSMS in tests to

determine the effects of input uncertainty or variations on the MOGSMS

forecasts of conventional oil and gas production. We measured these

effects primarily through computed product measures , which were time

averages of production for crude oil, gas and NGL.

1.3 Key Results Obtained

The three experiments each yielded significant results, which can be

summarized as follows. In Experiment 1, explicit treatment of this

uncertainty via a Monte-Carlo analysis leads to higher production

forecasts than the deterministic approach yielded for the 1979 ARC , especially for natural gas. The increment in gas production, as measured by the mean values of the Monte Carlo results, is 2.10 TCF in

1990 (17 percent higher than the 1979 ARC projection), increasing to

3.68 TCF in 1995. The average gas production increment is 1 .91

TCF/year (16 percent) for the period 1985-1990-1995. AcrossaTl

products, the Monte-Carlo analysis leads to the significant average

production increment of 1 .0 million barrels of oil equivalent per day, over the same period.

As anticipated at the start of the study, the probablistic treatment

of resources keeps the spread between the "optimistic" and

"pessimistic" projections of production relatively tight:

Monte-Carlo Ranges of MOGSMS Production Forecasts

Percent of

Time-Average Mean Value

Crude Oil (MM Bbl/day) 0.40 8%

Natural Gas (TCF/yr) .1.10 8%

NGL (MM Bbl/day) 0.06 6%

(Interquartile Ranges:

25th-75th Percentiles)

Thus, in this experiment, explicit recognition and treatment of

uncertainty in a key input data element leads to: (Da fairly small

estimate for the dispersion resulting from that random element; and

(2) a small (but possibly significant) increase in the production

forecast

From Experiment 2 (the second Monte-Carlo analysis), we see that

variability in either decline rates or recovery factors has a very

major impact on ultimate production. The average interquartile

widths here have been computed as a percentage of the base case totals

to be:

Decline Rate Experiment

Crude oil average range = 13.8 percent

Natural gas average range = 29.4 percent

Recovery Factor Experiment

Crude oil average range = 12.9 percent

491
Experiment 3 - Response Surface Analysis - the response surface

analysis - comprised a sequence of three sub-experiments, each

relating MOGSMS oil and gas production projections to systematic

variation in specific sets of input elements subject to uncertainty.

Each sub-experiment led (via regression analysis) to a linear equation

relating changes in the oil and gas product measures to changes in the

values of the input data elements.

The experiments revealed broadly that the seven data elements

originally suspected as vital were quite important. The only

exception was the apparent minimal effect on natural gas production to

be credited to the discount rate and drilling costs. Some key

examples of the results are that:

a 25 percent increase in the assumed discount rate

induces about a 123,000 Bbl/day decrease in

average oil production over the midterm;

a 10 percent increase in the total-to-exploratory

drilling ratio reduces production by an estimated

159,000 Bbl/day;

a 1-year increase in the capital planning horizon

leads to a decrease of approximately 92,000 Bbl/

day .

2. BACKGROUND AND MOTIVATION FOR THE SENSITIVITY EXPERIMENTS

The detailed discussion of this study's analytical issues,

experiments, and results begins in this section and continues for the

remaining four sections. By way of background and orientation

to this report, we begin by offering a brief summary of the objectives

and context of the study.

The Energy Information Administration (EIA) has sponsored numerous

activities to improve the inherent quality of EIA's Applied Analysis

products. In that connection, its Office of Analysis Oversight and

Access (OAOA) recently commissioned a set of reports evaluating

various energy system projections and analyses published in the ETA

Annual Report to Congress 1978, Volume 3 (referred to here as the

1978 ARCTI A major element in this set is a study by Harris and

Associates, and Hirshfeld and Associates (see Harris and Hirshfeld,

1980) for the National Bureau of Standards (NBS), U.S. Department of

Commerce. That study's objective was to apply analytic procedures

to determine and communicate the quality and usefulness of the EIA

1978 midterm oil and gas production projections. More specifically,

the contract under which the study was performed (NBS No. NB80SBCA035)

called for a "sensitivity analysis of DOE forecasts of midterm oil and

gas supply for the 1978 Annual Report to Congress".

492
Since late 1978, the National Bureau of Standards has been one of the agencies conducting projects sponsored by OAOA to develop

energy model assessment procedures and guidelines. The NBS work has

focused on EIA's Midterm Oil and Gas Supply Modeling System (MOGSMS)

as the vehicle for development of a sound assessment methodology.

OAOA assigned to NBS the investigation of the 1978 ARC midterm

projections of oil and gas production because they rest in large measure upon certain results generated by the 1978 version of MOGSMS.

Through their work to date, NBS staff and consultants have developed a considerable store of knowledge on MOGSMS' s data, analytical structure

and content, and performance (see Harris, 1979a; Harris, 1979b;

Harris 1979c; Hirshfeld, 1979; Hoffman and Joel, 1979 , Gass and Joel,

1980; Gass, et al., 1979; and Gass, et al., 1980). The present study

draws heavily on this knowledge and its documentation and especially

on the methodologies established in Harris and Hirshfeld (1980). A

major purpose thus is to extend the NBS and related efforts to a similar sensitivity study of the 1979 ARC forecasts of midterm oil and

gas supply.

To clarify we repeat the following four basic groundrules for the

current study:

(1) MOGSMS Results are the Object of the Analysis : Our study

explicitly addresses only the MOGSMS output that leads to annual

supply possibility functions for conventional oil and gas (excluding

the Alaskan North Slope and other sources)

(2) Analysis Restricted to One Set of Price Increments : The

supply possibility functions produced by MOGSMS are sorted tabulations

(by year) of computed oil and gas production levels corresponding to numerous (exogenous) price trajectories (or "increments"). To reduce

the size of our analysis without altering its relevance, we chose to

work with just one set of those price increments:

o Oil - Price Increment 9 (in 1979$)

$32.00/Bbl in 1985, then increasing to

$41.00/Bbl by 2008

o Gas - Price Increment 1 (in 1979$)

$2.42/MCF

These are the standard, user-supplied price increments (the others are internally generated by the addition or subtraction of various price

increments uniformly over the planning horizon).

(3) Analysis Restricted to the Midprice Projection : The

1979 ARC contains a number of different midterm oil and gas supply

projections, corresponding to various scenarios (see its Appendix B

for a listing of assumptions) . To further reduce the size of the

sensitivity analysis, we deal exclusively with those MOGSMS results

that entered the midprice, standard projection of the 1979 ARC . Applying our sensitivity analysis to the one central ARC projection

yields findings that appear relevant to all the ARC'S midterm oil and

gas supply forecasts. The last basic ground rule is:

493
i m I

I (*0 Input Data Changes Are Permitted; Model Changes are Not : The issue here is an investigation of the sensitivity of MOGSMS output

to changes in the input data, not to changes in the model structure.

But the difference is not as clear as it may at first seem. For

example, two of MOGSMS' s key input data elements are the decline

rates and the exploratory dry hole ratio for crude oil. One might

wish to determine the effects of varying these data elements as a function of time over the model's planning horizon. However, MOGSMS'

internal structure treats these elements as constants over the

planning horizon. So, varying them as a function of time would

require modification of the model's design philosophy and of the

programs embodying MOGSMS' s model structure. Such modifications can be very time-consuming and may unneccessarily complicate the

sensitivity analysis.

Therefore this study deals only with systematic changes in MOGSMS

input data items. Operationally, this means that: (1) we were free

to vary any element in MOGSMS 's input data sets; but (2) we did not

touch the programs that implement the MOGSMS model.

Thus, in our example, we could indeed have varied the decline rates

and the exploratory dry hole ratio, but only in their current form as constraints over the MOGSMS planning horizon.

This report is rather long, so some brief comments regarding its

organization and content may be appropriate. *

This section deals primarily with the study's objective and basis, and

specifically cites that portion of the 1979 ARC containing the

projections analyzed in the study. In addition, we introduce the main

analytical features of our work and specify the major categories of

uncertainty. Section 3 then discusses the nature of the sensitivity

analysis experiments that the study comprised.

Sections 4, 5, and 6, respectively, describe the three sensitivity

analysis experiments performed in the study. Each section treats the

design, implementation, and results of a particular experiment.

2. 1 Technical Issues

Explicit treatment of the uncertainty associated with energy supply

and demand projections clearly enhances their usefulness for policy

analysis. This study is part of an unfolding effort to develop and

apply methods for the quantitative treatment of the uncertainty

associated with the results generated by the energy models and

analysis systems of the EIA.

In this context, we define "uncertainty" broadly, to include:

(1) true randomness in input data and parameters; (2) errors in

measurement of these exogenous factors; and (3) potential errors residing in model logic, model structure, or computational

procedures. Sensitivity analysis, in turn, is the examination of the

494
quantitative and qualitative effects of results of perturbations

(random or deterministic) in a model's (or analysis system's) input

data elements, parameters, or mathematical structure. Consistent with

this definition, the present study is a sensitivity analysis of the

oil and gas supply forecasts generated by EIA's MOGSMS analysis system.

This study is a direct outgrowth of the aforementioned NBS project

for energy model assessment procedure development, sponsored by DOE's

Office of Analysis Oversight and Access. We apply some of the major

results of the NBS project to enhance the quality and usefulness of

those MOGSMS results that are a part of the 1979 ARC 'S midterm

forecasts of oil and gas supply. Specifically, our work is in the

form of a sensitivity analysis (as defined above) of these MOSGMS

results, with respect to uncertainty (or possible errors) in: o input data, and

o logical structure.

Our sensitivity analysis does not address three other areas of

uncertainty or possible error:

o statistical methods,

o mathematical formulations, and

o computational procedures.

The first two of these three would have required a much larger effort

than this study and the latter does not appear to be a critical aspect

of MOGSMS.

Sensitivity analysis is especially pertinent for MOGSMS because its

results are widely distributed, and these results appear to be

sensitive to key input data elements, parameters, and assumptions.

The 1979 ARC makes frequent reference to the effects of alternative

input scenarios, uncertainties in parameters and variables, and even alternative procedures for making the forecasts.

This sensitivity is not surprising, because MOGSMS is a static model

generating deterministic results that are to be forecasts of timedynamic, highly uncertain phenomena. EIA has contracted for the

development of a new family of oil and gas supply models that will

capture more of the time dynamics and randomness in the target

physical system. The present sensitivity analysis may provide some additional guidance for those modeling efforts, as well as improving

the usefulness of the current MOGSMS results.

495
Many issues suggested themselves to be addressed in this sensitivity

analysis. Our choice was influenced by a number of factors: the

usual constraints on time and resources, a direct charge to address

oil and gas resource estimates and finding rates, and the recognition

that this study would be followed by others, perhaps broader in

scope. These factors impelled us to concentrate on the impact of the

estimation of the underlying resource base on MOGSMS results and on the explicit treatment and assessment of uncertainty in (at least) some of MOGSMS' s input data elements. In particular, our quantitative

sensitivity analysis comprises the following three distinct

experiments, each addressing a specific issue affecting MOGSMS

results:

o Issue 1: The effects on MOGSMS 's oil and gas supply

forecasts of the intrinsic uncertainty in the estimates

of regional oil and gas resources (undiscovered

recoverables)

o Issue 2: Likewise for other pre- identified key variables.

o Issue 3: The identification of the (relatively few)

input data elements "critical" to MOGSMS - that is,

those elements which are uncertain or random in nature

and whose values strongly affect MOGSMS results.

Analytical considerations associated with these issues are discussed

in this section. We introduce that discussion with a few remarks.

A primary source of uncertainty in MOGSMS results is the inherent

uncertainty in estimates of the regional oil and gas resource bases

(reserves plus undiscovered recoverable resources). USGS Circular

725, source of the resource based estimates used in MOGSMS, sets

forth individual probability distribution functions for the oil and

gas resource base estimates in each NPC region. In an effort to

delineate the effects of this particular source of uncertainty, the

1978 ARC, Vol. 3 showed (on pages 176 and 199) MOGSMS-generated

responses to "optimistic" and "pessimistic" resource base

assumptions. (See Figure 1, taken from page 199 of that ARC.) For

crude oil, the difference between the extremes reached 5.0 million

barrels per day by 1995.

The regional oil and gas resource base estimates are a particularly

good target for a statistical treatment of uncertainty because: (1)

they are of fundamental importance to the MOGSMS methodology (and, in

particular, to the estimation of MOGSMS' s finding rates); (2) they are inherently uncertain; and (3) widely accepted probability distribution

functions exist for them (in USGS 725 ) Consequently, a Monte-Carlo

analysis of the effects of resource base uncertainty of MOGSMS 's oil

and gas supply forecasts became the first element in this sensitivity

analysis.

The second element of our study is a pair of Monte-Carlo experiments

on two additional sets of input elements felt to be vital. These are the recovery factors and the decline rates .

496
Fiaure 1 1978 ARC Estimates of the Effect of Resource Base

Uncertainty on U.S. Crude Oil Production

(1977-1995)

in Bbl/day

10

1976 1980 1984 1988

Year

High Geology

^"optimistic"

)

Medium Geology

Low Geology

("pessimistic"

)

1992 1996

497
I f

More generally, many (if not virtually all) of MOGSMS' s input data

elements are uncertain - because of their fundamental randomness

(e.g., the resource base estimates), because they pertain to future

conditions (e.g., prices, costs, drillng distributions, etc.), or because they describe imperfectly understood phenomena (e.g., regional

recovery factors, total-to-exploratory drilling ratios, etc.).

Conceivably, explicit treatment of uncertainty in some MCGSMS data

elements (in addition to the resource base estimates) would expose

significant corresponding uncertainty in MOGSMS results. Conversely,

MOGSMS oil and gas forecasts may be (relatively) insensitive to

uncertainty in other input data elements. Thus a systematic effort

to:

o identify those input data elements in which

uncertainty has an important effect on MOGSMS

results, and

o determine the magnitude of their effects

on MOGSMS oil and gas supply forecasts

becomes the other key element in the sensitivity analysis.

The three issues addressed in our sensitivity analysis form a progression of increasing generality. The first issue is quite

narrow: it deals strictly with a known set of data characterized by

uncertainty and illustrating the application of Monte-Carlo methods

for sensitivity analysis. The second does likewise, but for a broader

class of elements. The third is more general yet, involving a search

for the significant areas of uncertainty via a generally applicable

analytical method.

2.2 Treating Estimates of Regional Oil and Gas Resource Bases

To motivate properly the discussion in this section and those to

follow, we must recall a few definitions pertaining to the regional

finding rates in MOGSMS. The finding-rate function employed in

MOGSMS (for both oil and gas) follows from the assumption that

undiscovered resource deposits (in an entire region) have a log-normal

size distribution. This assumption leads to an exponential decline

relationship (by virtue of the constant percentage depletion

associated with log-normality) between cumulative oil (gas)in-place

discovered and cumulative exploratory drilling, of the general form:

coiPk

I or ( = ^ M-exp^ . CMFTk

)] (1)

CGIpJ

where

COIPk

= Cumulative oil-in-place dicovered in NPC

498
region k up to a reference year;

Qk

= Oil (gas) resource base, defined (for MOGSMS

purposes) as discoveries from 1956 on plus

the resources remaining to be discovered as of the start of MOGSMS' s planning horizon

(1 January 1979 for this ARC);

CMFTk

= Cumulative exploratory (total) drilling

assignable to oil (gas) in NPC region k

from 1956 until the appropriate reference year

(as described in Hoffman and Joel, 1980, MOGSMS

relates oil discoveries to exploratory drilling

assignable to oil, but relates gas discoveries

to total drilling assignable to gas).

b^ = A finding-rate parameter that is region

specific for oil and gas.

The regional finding rate, F^, is then the incremental quantity of

oil (gas) discovered per unit exploratory (total) drilling. Its

formula can be obtained by differentiating Equation (1) with respect

to CMFT :

Oil: F = afoOIP) = h . Q. . exp(-b. . CMFT.) oil (2)

' ci( cmft ) k k k k

Gas: F = a(CGlP)

= b n exp(-b. . CMFT. ) gas (3)

a(CMFT) k k k k

Thus F^is in units of:

o Barrels discovered/Ft . of drilling (oil)

o MCF discovered/Ft. of drilling (gas)

(This functional form asserts that the oil and gas finding rates must

decline exponentially with increasing drilling.) Taking the natural

logarithm of both sides yields the convenient form

in Fk

= In [ (t^. )]- \ . CMFTk

(4)

499
Another log-linear version of this relationship is very useful in the

subsequent data analysis:

In [Qk

- COIP

k

]= In 0^ - b

R

. CMFT

k

(5)

MOGSMS contains relationships similar to Equations (2) and (3) to

calculate reserve discoveries year by year for oil and for gas in each

NPC region as drilling proceeds through the planning horizon. Cbserve

that the finding rate, F

k

, depends upon uniquely specified values of

Q

k

(the resource base) and b

k (the slope). So MOGSMS runs require external determination of the values of each Q and b. . The 1978 procedure for MOGSMS employed a (log-linear) regression

analysis of historical data since 1956 (drilling and reserve

additions, by region) on the functional form of Equation (5) to

estimate bk for each mature region. In this procedure, the for

each region was taken as a constant, equal to the mean resource value

presented in USGS Circular 725 for the given region. Both the b

k

and Q. values then become MOGSMS input. In 1979, direct nonlinear

regessions where done on Equation (5), assuming the Q values to be at

USGS levels and then finding the resultant {b^}. V

1/ For the immature regions, namely, 1A, 2A, and 1 1 A, MOGSMS utilizes

the exploration experience (annual drilling footage and discoveries)

as a direct estimate of the finding rate ( A discovery/ A footage) in

the vicinity of the origin (i.e., near zero cumulative drilling

footage)

500
Consequently, one aspect of the issue at hand is to determine if a sound statistical strategy can be employed to provide a meaningful

assessment of the range of uncertainty fh MOGSMS' s oil and gas supply

forecasts given the probabilistic information available from USGS

725 . Note that the treatment by MOGSMS of USGS 725 ' s log-normal

probability distributions on regional resource bases also affects the

expected values (or central tendency) of future oil and gas supply.

Recall that log-normal distribution functions have two parameters, the

mean (y) and the standard deviation (a) of the originating normal

population. If the log-normal variable is designated as Y and its

logarithm (i.e., the parent normal) by X, then the following

relationships obtain:

P = E[X] = 1n/(Y

>g5

)(Y

>Q5

) (6)

o = S.D.CX] = [1n Y.95 - y 3/1.645 (7)

E[Y] = exp( p ~o2 /2) (8)

Mode [Y] = exp(y-a2

) (9)

Median [Y] = exp(y) (10)

Also note that the mulitplication of Y by a constant does not affect

the underlying normal's standard deviation since the addition of the

logarithm of such a constant to X yields another normal with the same

standard deviation.

Considerable confusion has existed in the MOGSMS literature regarding

means and medians . Most notably, page 195 of Volume 3 of the 1978

ARC contained a statement that "the projections in Series C are based

on the median (statistical mean ) assessment of undiscovered

recoverable resources provided by the USGS in 1975 (see Table 11.11)"

The USGS 725 values in question are, in fact, estimates of the

expected or mean remaining recoverables- totally different from the

median (and the mode for that matter). The median value is the 50thpercentile value, or that level both above and below which lies one- half of the probability distribution. The mode , the third major

measure of central tendency, is merely the point (or points) with the

highest probability (discrete case ) or the variable value giving the

largest value to the probability density function (continuous case)

.

A footnote to these statements on page 195 adds that the "statistical

mean" of the undiscovered recoverable resource in any NPC region is

the sum of the 5th percentile value, the 95th percentile value, and

the modal value, divided by three. This is a correct interpretation

of the manner in which USGS derived the mean values for its log-normal

distributions. However, this formula is only an approximation, and it

creates some possible errors in MOGSMS results (though generally of a minor nature).

501
I The first formal part of this study then deals with the relationship

between the (probabilistic) regional resource base estimates offered

in USGS 725 and the (deterministic) analysis to which these estimates

have historically been applied in MOGSMS. This issue has two facets:

o the potential extreme values of U.S. oil and gas

production, as delineated for example in the

"optimistic" and "pessimistic" geology cases cases (Series A and E, respectively) of the

1978 ARC , and

o the verification of nominal values of U.S.

oil and gas production, as provided by the

nominal midprice case in the 1979 ARC .

Clearly, the nominal, midprice ARC supply forecasts alone do not

offer a meaningful assessment of the effects of underlying resource

uncertainty on possible levels of future oil and gas production.

USGS Circular 725 sets forth estimated (log-normal) distributions of

the undiscovered recoverable oil and gas resources in each NPC

region. These distributions reflect the intrinsic uncertainty in any

estimation of future oil and gas discovery prospects or of total

resource- in-place. However , the MOGSMS-based analysis of oil and gas

supply prospects has treated these resource estimates

deterministically, and thus does not come to grips with the underlying

uncertainty.

In particular, the 1978 ARC 'S optimistic geology case (Series A) assumes that the resource base of oil and gas in each of the NPC

regions corresponds to the high values set forth for that region in

USGS Circular 725 (properly adjusted for exploration experience

subsequent to 197*0. The USGS high values are the 95th percentile

points for the assumed statistical distributions (all taken as lognormals). On the other hand, the pessimistic geology case (Series E) assumes that regional resource bases corresond to the USGS 5th

percentile points. The estimated resource bases employed for the 1978

Series C projection are the expected values (according to the

appropriate log-normals) for each region in USGS 725 .

If we assume that the USGS 725 frequency distributions are valid, it

is extremely unlikely that all regions simultaneously exhibit either

the upper or the lower level of resource base. In fact, we can compute the probability that all regions are on the pessimistic side

(that is, have recoverable resources wi^in the lower 5 percent

probability tail) as (0.05) = 3 X 10~ , essentially zero.

(All of this assumes that the resource base estimates are purely

that and incorporate no other issues in their calculation. That is to

say, no systematic factors, such as price responses, new technologies,

etc., affect the independence of these probability functions.)

502
In summary then, the first element of our sensitivity analysis

assesses the effects of uncertainty (or randomness) in resource base

estimates (specifically as embodied in USGS 725 ' s log-normal

probability distributions) on MOGSMS-based oil and gas supply

forecasts

2.3 Additional Key Random Elements

For Experiment 2 we have carried out a Monte-Carlo analysis much like

that of Experiment 1 on two sets of variables deemed to be of

significant import to the model results. These are recovery factors

(primary and secondary) and the decline rates .

In each case, subjective probability distributions were established

and random draws carried out by computer. For the recovery factors,

both primary and secondary factors were assumed to be uniformly

distributed on a range from 80 percent of their nominal or base values

up to 120 percent of nominal. For the decline rates, uniform

distributions were also specified, but they ranged from 75 percent

to 125 percent of nominal.

2.4 The Notion of Critical Data Elements and Its Application to

MOGSMS

As we have noted, other MOGSMS data elements in addition to the

resource base estimates are subject to uncertainty, for a variety of

reasons. The nature and extent of the inherent uncertainty in MOGSMS

has only recently come under any close scrutiny (see Harris and

Hirshfeld, 1980).

Experience and judgement provide some guidelines in this regard. For

example, MOGSMS' s developers have indicated (EIA, 1978) a relatively

small number of input elements. However, this assessment did not

quantify the notion of "high sensitivity" or estimate the potential

uncertainty in any of the indicated data elements.

Clearly an exhaustive analysis of the effects on MOGSMS results of

uncertainty or change in each input data element is infeasible, as well as unwarranted. (The input data set for MOGSMS contains about

2,000 distinct numerical values.) What is feasible - and valuable -

is an analysis to identify the "critical" input data elements in the

current version of MOGSMS.

In this context, we define "critical" input elements to be those

having two properties:

503
o Their values are highly uncertain (or random); and

o MOGSMS* s results appear to be highly sensitive to

variations in their values.

The first of these is related to inherent properties of the input data

(sources, transformations applied, etc.) and the phenomena they are to

describe. The second is related to the logical and mathematical

structure of MOGSMS itself.

The nature of this study dictated the approach to identifying critical

input elements. First, we specified candidate elements on the basis

of judgement and experience. Second, we subjected these elements to

quantitative analysis to determine the relationship between changes

in the values and changes in MOGSMS results. Such an analysis is the

object of the third element in our sensitivity analysis.

3. OVERVIEW OF THE STUDY

As indicated in Section 2, this study consisted mainly of a series of

statistical experiments, focusing on the general nature and effects of

uncertainty on MOGSMS results, and the individual analytical issues

identified there. This section offers a brief overview of the study,

in terms of these elements.

3. 1 Statistical Experiments

The three statistical experiments addressed, in order, the analytical

issues raised in Sections 2.2, 2.3 and 2.4.

o Experiment 1: A Monte Carlo analysis of the USGS

Circular 725 estimates of regional undiscovered (oil

and gas) resources and their impact on MOGSMS finding

rates and ultimate outputs.

o Experiment 2 : A Monte Carlo analysis of the impact

on MOGSMS output of subjective probability structures

postulated for recovery factors and decline rates.

o Experiment 3: A response surface analysis of various

MOGSMS input data elements, including both physical

and economic elements, to identify those in which

uncertainty has the greatest effect on MOGSMS

results

Each of these experiments involved exercising MOGSMS in tests to

determine the effects of input variations on the MOGSMS forecasts of

conventional oil and gas production. We observed these effects

primarily through computed product measures (defined in Section 3.2)

for crude oil, gas, and NGL.

504
The Monte-Carlo resource experiment treats the uncertainty inherent in

the USGS Circular 725 estimates, through a two-stage procedure:

o Generating one hundred vectors of estimates of

of regional oil and gas resource bases, where each

vector is made up of elements, each of which is an estimate of a region's undiscovered reserve of oil

or gas. These resource realization vectors are randomly constructed according to a Latin Hypercube

design.

o Running one MOGSMS test for each of the one hundred

resource realization vectors, with all other model

inputs unchanged , to obtain the corresponding set of

one hundred oil and gas production forecasts.

The second Monte-Carlo experiment assesses the effects on MCGSMS

output of possible stochastic variability in recovery factors and

decline rates. Forty runs of MCGSMS were performed for each set

here. In each case, the values of the random variables were predetermined by sampling. For both the recovery factors and decline

rates, the individual elements were combined as a Latin Hypercube as

in Experiment 1. Finally, the response surface experiment seeks to

identify the critical input data element for MOGSMS, through a threestage procedure:

o Creating a series of factorial experiments,

involving systematic variations of MOGSMS input

data elements, in each of two (arbitrary)

categories: economics and drilling.

o Running one MOGSMS test for each factorial

combination of input values, to obtain the

corresponding sets of oil and gas production

forecasts.

o Applying linear regression analysis to each set

of forecasts to identify those input elements

whose values (and changes therein) have the

greatest influence on MOGSMS results.

Thus, all of the experiments involved repeated full executions of

MOGSMS (always involving both the oil and gas routines). To drive

these experiments, we developed simple computer routines to (1) create

the modified input data sets, as needed for each experiment and (2)

summarize and tabulate the test results for subsequent statistical

analysis.

505
3.2 Product Measures

The output of any given MOGSMS run is physically voluminous and

logically complex (embodying as it does the dimensions of region,

time, product, and process), and the experiments involved many MOGSMS

runs. Therefore, to facilitate (if not simply to permit) analysis of

the experimental results, we chose specific element (s) of MOGSMS

output to serve as descriptors of the full set of MOGSMS results.

That is, we focused our analysis of the sensitivity of results to the

specified measures associated with each MOGSMS run, rather than work

with the entire set of output values. One might think of the output

measures as the defined dependent variables of interest to us in each

test (here, a test is simply a MOGSMS execution with a distinct input

data set)

The primary measures that we established for this purpose correspond

to six MOGSMS-computed production levels:

o Oil [Crude Oil Supply]

[Associated-Dissolved Gas Supply]

[Associated Natural Gas Liquids Supply]

o Gas [Non-Associated Gas Supply]

[Non-Associated Natural Gas Liquids Supply]

[Non-Associated Lease Condensate Supply]

Each of these is an element of MOGSMS output reported by the MOGSMS

post-processors, OREPORT, and GREPORT, respectively. The brackets

above - [ ] - denote that our defined measure corresponding to each of

these elements is the average of the total U.S. value (taken over all

regions) reported for four target years: 1985 , 1990 , 1995 , and

2000 .

The ultimate or product measures that we established are the three

product aggregates of the primary measures:

(OIL MODEL) (GAS MODEL)

o [Crude Oil] = [Crude Oil Supply] + [Non-Associated Lease

Condensate Supply]

o [Natural Gas] = [Associated Dissolved Gas Supply] +

[Non-Associated Gas Supply]

o [NGL] = [Assoicated Natural Gas Liquids Supply] + [Non-Assoicated Natural Gas Liquids Supply]

These three product measures (dependent variables) are, collectively,

close indicators of the cumulative oil and gas supply over the entire

planning horizon forecast by MOGSMS in response to a given input data

set.

506
n. EXPERIMENT 1: MONTE CARLO ANALYSIS *

Experiment 1 was a Monte-Carlo analysis of the effects on MOGSMS

results of uncertainty in the USGS Circular 725 estimates of

regional undiscovered (oil and gas) resources. In particular, it was aimed at the "establishment" of "High Geology" (optimistic) and "Low

Geology" (pessimistic) forecasts of oil and gas supply for the 1979

ARC .

4. 1 Design Considerations

Broadly speaking, the overall range of uncertainty in MOGSMS results

is generated from the joint probability law governing the endogenous

parameters (call them U) , and exogenous input data elements (sayV),

together represented by the vector ( jj, V) . Experiment 1 explores the

underlying stochastic character of part of the V set, namely, the

regional resource base estimates. More preciseTy, we worked with the

subset of input data elements corresponding to the (random) amount of

original crude oil and natural gas still remaining to be discovered,

by region, at the outset of the model's 1979 ARC planning horizon

(January 1, 1979). Our specification of the distribution functions of

these stochastic variables is that described in USGS Circular 725 , with means adjusted according to subsequent revisions made since .1975

by USGS. As we have seen in Section 2, that document offered lognormal distributions for the undiscovered resource bases in each of

the NPC oil and gas regions, assuming complete statistical

independence between regions.

The properties of the resulting probability distributions on MOGSMS output (call it 1 with CDF F(z)) cannot be obtained by any

closed-form analytic operations because of MOGSMS' s complexity. To

obtain such a distribution as the one measure of uncertainty in MOGSMS

results we turned to Monte-Carlo methods.

In our experiment then: (1) values of the vector V were drawn

randomly according to its distribution (here equal~to the product of

the marginals in light of independence) according to a specific

sampling plan; and (2) values of 1 were obtained by running MOGSMS

tests with X i° the input set. When this procedure is carried out n times, it generated a sample of size n for Z.' This sample permitted a detailed analysis of measures of central tendency, dispersion, and the

distribution function itself. The generation of a complete Monte

Carlo sample would have been rather expensive because of the

complexity of the subject model and the relatively large number of

regions (components of $ . Therefore we employed a modified sampling

procedure which reduced the cost and time required for the experiment,

without sacrificing any statistical precision. The approach we chose

uses a multi-dimensional version of the classifical Latin Square - called the Latin Hypercube - as described by McKay et al. (1979).

Results presented by those authors indicated an approximate reduction

in sampling of 75 percent vs. conventional methods, at comparable

levels of precision.

507
The Monte-Carlo experiment thus comprised two main steps:

1 . Generating one hundred vectors of estimates of regional oil

and gas resource bases, where each vector is made up of elements, each

of which is an estimate of a region's Q value, for oil and for

gas. ( We call such vectors resource realization vectors . ) The

vectors were randomly constructed according to a Latin Hypercube

design, described shortly in Section M.2.

2. Running one MOGSMS test for each of the one hundred resource realization vectors, with all other model inputs unchanged, to obtain

the corresponding oil and gas production forecasts. The end result of

this effort was one set of three product measures (see Section 3) for

each of the one hundred resource realization vectors.

The results of the total set of runs can be summarized via a number of

empirical statistical measures. We focus on: a) the mean, together

with the interquartile range; and b) the empirical frequency function.

The key step in the experiment is the generation of the resource realization vectors. To be more specific on the starting points of

this process, we begin with the assumption of log-normal

distributions on the estimated sizes of the regional (oil and gas)

resource bases. This assumption is the basis for the regional finding

rates currently used in MOGSMS. Recall that a log-normal random

variable is one whose logarithm - called the parent or underlying

normal - is normally distributed. As a result of this defining

variable transformation, a log-normal random variable thus is

characterized by two parameters, the mean and the standard deviation

(or variance) of the parent normal. With the means and variances of

these normal distributions, one can derive random log-normal deviates

of the estimated resource bases upon suitable transformation of the

percentage points of the standard unit normal distribution.

A fundamental property of the log-normal distribution plays a key role

in the subsequent interpretation of our results. The expected value

of a log-normal random variable (say Y) is greater than or equal to the

exponentiation of the mean of the parent normal ( say X) T* In more

precise notation,

This is easily proved by a direct argument involving Jensen's

inequality for the expectation of a convex function of a random

variable (see, for example, Feller, 1966). Of course, when we replace

the expectation operator by the median, equality is obtained; that is,

E[Y] = E[eX

] leE[X]

(11)

Median (Y) - e Median (X).

508
A log-normal distribution always exhibits the property that

Mode <_ Median <_ Mean (12)

and thus the means and medians of log-normal samples are higher than

one expects intuitively. This relationship is important to the

results obtained in this experiment. (A typical log-normal density

function is displayed in Figure 2)

Getting back to the derivation of the log-normal deviates for our experiment, let P. denote the undiscovered resource base (for oil or

gas, as the case may be) in the kth (NPC) region as of January 1,

1979 > as estimated in USGS Circular 725 (adjusted for reserve

additions reported after 1974). Also, let Q denote the cumulative

resource base remaining as of January 1 , 1956 . Then P. is a standard log-normal variable, while Q^is a shifted one with

Q

k

= p

k

+ [Cumulative oil (gas) -in-piace found during 1956-1977

inclusive]

(13)

= Pk

+ Rk

To proceed , we must next find the appropriate parameters of the

log-normal distributions of the undiscovered resources: the means

( y) and standard deviations ( o) associated with the respective

parent normals. To get these, we have proceeded in the following

way. For a we have used the 5th and 95th percentage points

estimated for each region by the USGS. Since percentage points are preserved by any monotonic transformation,

X = 3n(Y ) .05 .05

(14)

and

X = ln(Y ) .95 .95(15)

But (as is well known), the 5th and 95th percentage points of the

standard unit normal are separated by approximately 3.29 0 • So

= ^

Y

.95 /Y .05 ) 3-29

(16)

By similar argument, we can find the mean as

v = In Y Q, - (1.645) a .

• 95

(17)

509
Figure 2 Typical Log-Normal Density

510
However , as noted earlier , USGS erred in its computation of the mean

and instead used an approximation formula. We decided to stay with

the USGS (log-normal) means, despite the small errors so incurred.

Accordingly, we find the parameter in the following way. Any lognormal variable Y has mean

2

y + a /2

E(Y) = e (18)

Therefore

2

y = In E(Y) -a /2 (19)

Now, with y . and o in hand , it follows that

Pkj = «cp[ak

rjk + yk ] (20)

where Pj. is the jth random yariate of Pk

, for the unit normal

deviate r^j . Likewise,

0. is the jth random variate of Q , corresponding to

Table 1 shows mean regional resource levels used in^tl

where

r. .. Tible 1 shows mean regional resource levels used in ' the non- froniier regions for both the 1978 and 1980 reports to Congress.

Table 2 then shows the mean Q for each region in addition to the

standard deviations.

4.2 Implementation Considerations

In accordance with the foregoing reasoning, the procedure for Step 1 of our experiment, generating a set of (random) regional resource

realization vectors for oil and gas,{Q. }, is as follows:

(i) Divide the range of each random resource variable into 50

intervals, j, of equal probability (0.02) (j = 1, 2, 50).

(ii) Let the probabilistic midpoint of each interval be Q ., when the corresponding r

fc .is the j th odd percentage point"'of the

standard unit normal. J

(iii) Generate the order in which the 50 percentage points of each

region are to be used in each of 50 MCGSMS runs by creating a sequence

of 25 (for the 12 oil and then 13 gas regions) unique random

permutations of the integers 1 to 50.

511
(iv) Form the required {Q,} vector for the first run by taking

the leading percentage point from each of the 25 random permutations.

Continue to do this by similarly matching the ith elements of each

permutation to the ith resource realization vector, until all 50 are formed

(v) Repeat Steps (i) and (iv) to obtain a total of 100 random resource realization vectors, to drive 100 test runs. Each of these vectors then is a probabilistic estimate of the U.S. oil

and gas resource base for the provinces covered in USGS Circular 725 .

Table 1. Mean Regional Resource Base (Q Values)

1978 ARC VALUES 1979 ARC VALUES

REGION MCGSMS (1) MOGSMS (2)

Oil (10

u Bb)

2 32,864 36,540

3 24,139 47,132

4 32,436 37,641

5 54,153 52,618

6 31,026 54,163

6A 28,924 27,567

7 19,734 34,290

8-10 13,834 19,515

TOTAL 237,110 289,466

GAS (109 Ft 3

)

2 13,922 13,798

3 19,184 47,870

4 30,244 30,244

5 66,638 46,710

6 275,494 261,936

6A 182,625 170,156

7 114,090 93,112

10 20,739 30,742

TOTAL 722,936 694,570

NOTES: (1) From USGS Circular 725 adjusted accordingly.

(2) New values obtained from the EIA Office of Oil and Gas

Analysis.

512
Table 2. Parameters of Log-Normal Resource Distributions

<10

6Bb> 9 3

(1°9ft3)

(10 Bb) standard (10 ft ) standard

Oil Mean deviation Gas Mean deviation

Region Q for Q (1) Region Q for Q

1A 24,806 30,481

2 36,540 8,198

2A 19,198 5,564

3 47,132 8,685

4 37,641 6,278

5 52,618 11,762

6 54,163 4,592

6A 27,567 5,471

7 34,290 6,208

8-10 19,515 5,288

11 2,827 2,034

11A 7,500 3,196

1A 30,741 29,092

2 13,798 3,473

2A 4,440 1,316

3 47,870 3,092

4 30,244 6,047

5 46,710 14,473

6 261,936 40,774

6A 170,156 30,751

7 93,112 35,891

8-9 3,231 1,198

10 30,742 7,688

11 120 179

11A 10,080 1,619

(1) Note that the standard deviation for a Q is given in terms of

the a of its parent normal as

E[Q]^yea2-i

j

513
Step 2 in the Monte Carlo experiment is the generation of a vector

of regional finding rate slopes , {b^} (for oil and for gas),

corresponding to each resource realization vector, {Q^}.

Recall from Section 2 that the regional parameters, b, , were

estimated for oil by DOE for input to MOGSMS via an off-line nonlineai

regression program for each region with the corresponding Q value at

the USGS number. For gas, each Q was again fixed and b then found by

using the most recent exploration experience.

For any oil Q specified as input via the first step in our experimental aesign, a (nonlinear) least-squares estimate b can be

found. But, of course, we are treating the {Q, } as random variables

in this experiment. By applying this process to the historical

exploration and discovery data in each region, for each randomly

selected value Q ., we can compute the corresponding b, .. Hence we can reaaily construct the 100 vectors {b, } corresponding to

gas except for the fitting process, as indicated in the prior

paragraph.

Finally, we produce the numerical values of the elements in the 100

vectors {b. } in MOGSMS input format, and use each vector as the

driving input for a MOGSMS test run. Each MOGSMS test generates

output defining an oil and gas production forecast (over time)

,

corresponding to the particular resource realization vector tQ^}*

The experimental procedure described here is, of course, not

restricted to 100 or any other number of MOGSMS tests. We specified

100 runs for our experiment, because it appeared to offer the most

reasonable tradeoff between statistical precision and resource

expenditure.

4.3 Results of Experiment s

To facilitate our analysis of experimental results, we developed a small computer program to compute statistical measures and to plot

these results. The accompanying graphs (Figures 3-7) are adapted from our computer-produced plots.

The results of this experiment are set forth in the following:

o Table 3 - showing the mean production figures for

the three key forecast years produced by both

Experiment 1 and the ARC itself.

our 100 vectors {Q, }. natural

514
o Figures 3-5 - showing the relative frequency

functions (histograms) of the three product

measures over the 100 tests in the experiment.

o Figures 6-7 - showing the interquartile range

(25th to 75th - percentiles) of production

profiles for crude oil and natural gas obtained

in the experiment - in comparison with the

1979 ARC base projections.

The most important aspects of these results can be summarized as

follows

o The frequency distributions of the product measures

(Figures 3-5) are generally smooth and slightly skewed

right, as might be expected from the log-normality of

the regional resource distributions (the Q values). The

bimodal distribution of the NGL results simply reflects

the separate modes for crude oil and natural gas, both

of which contribute to the total NGL. This suggests

that, because of the Latin Square design, the 100 tests

provide an adequate level of precision, in the sense

that the primary statistical measures of the results

of the experiments closely approximate their anticipated

(theoretical) values. More generally this result suggests

that FJA can achieve significant economies through the use of properly designed sampling techniques in its computerbased statistical analyses.

o Explicit treatment of the uncertainty in the USGS 725

estimates via the Monte Carlo analysis leads to higher

mean production forecasts than the deterministic

approach yielded directly for the 1979 ARC . As Table 3

indicates, the production increments are measured by the

mean values of the Monte Carlo results are largest for

natural gas, and smallest for crude oil (NGL, naturally

shows an intermediate response). In general, the

production increment is largest for 1985 and decreases

uniformly with time.

o In particular, the Monte Carlo mean value of gas

production is 1.85 TCF (11$) higher than the 1979 ARC

value for 1985. The increment drops to 0.25 TCF (2%)

for 1995. The average gas production increment is

1.12 TCF/year (7%) for the period 1985-1990-1995.

Across all products, the Monte Carlo analysis leads to an average production increment of 0.62 MM BOE/day , over the

same period.

515
o As anticipated at the start of the study, the Monte

Carlo analysis leads to a fairly limited spread

between the "optimistic" and "pessimistic" projections

of production (Figures 6 and 7). We selected the 25th - 75th percentile (interquartile) range as the most

meaningful measure of dispersion in the results of

the Monte Carlo analysis. (The 5th and 95th ranges of

the Monte Carlo results are not significantly wider than

the interquartile ranges.) For crude oil, the maximum

interquartile range of projections from MOGSMS is 0.8

MM Bb//day with an average of 0.4 MM Bbl/day , or only 8 percent of the mean value. The comparisons

for natural gas and NGL are of roughly equal

magnitudes.

Figure 3 distribution of crude oil product measure

Experiment 1 : Monte-Carlo Resource Analysis

1

4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0

Crude Oil Production Measure

(MM Bbl/day)

516
Figure 4 distribution of natural gas product measure

Experiment 1 : Monte-Carlo Analysis of Resources

I 12.0 12.2 12.4 12.6 12.8 13.0 13.2 13.4 13.6 * 13.8 14.0

Natural Gas Product Measure

(TCF/Yr)

Figure 5 natural gas liquids product measure

Experiment 1 : Monte-Carlo Analysis of Resources

0.40

0.30

0.20

0.10

0

89.0 91.0 93.0 95.0 97.0 99.0 101.0 103.0

(10* Bbl/day)

517
Figure 6

10 1-

Effects of Resource Uncertainty

on U.S. Crude Oil Production,

1978-1995

>»

CO Q

i_0>Q.

tn

a>

k_k_(0 CDc

o

8 -

6 - _ High Geology — Medium Geology

~" Low Geology

2 -

1975 1980 1985 1990 1995

3

m

c

o

"O

(0

20 i16 -

12 -

8 -

Figure 7

Effects of Resource Uncertainty

on U.S. Natural Gas Production,

1978-1995

High Geology

^ Medium Geology

^

Low Geology

1975 1980 1985 1990 1995

518
Table 3. MOGSMS Mean Production Forecasts

Experiment 1: Monte Carlo

Analysis of Resource Base Estimates

(Lower-48 States Ex. South Alaska)

MOGSMS Values For Mean Values

ARC Base Series Experiment 1

Crude (In MM Bb/day)

1965 5.742 5.663

1990 5.248 5.313

1995 4.922 5.016

Natural Gas (In TCF/Year)

1985 15.755 15.699

1990 12.093 14.190

1995 8.751 12.429

NGL (In MM Bbl/day)

T955 1.155 1.112

1990 0.93^ 0.985

1995 0.763 0.877

519
5. EXPERIMENT

The second major element of this study was a pair of Monte-Carlo

experiments on two additional sets of input elements. These were the

crude oil recovery factors (both primary and secondary) and the oil

and gas decline rates. The issue here was to assess the effect on MOGSMS output of possible stochastic variability in these two variable

sets

Forty runs of MOGSMS were performed for each variable, as a distinct

experiment. In each case, the values of the random variables were predetermined by sampling and then the individual elements combined as a Latin Hypercube as in Experiment 1. For the recovery factors,

both primary and secondary factors were assumed to be uniformly

distributed on a range from 80 percent of the nominal or base values

up to 120 percent of nominal. For the decline rates, uniform

distributions were also specified, but they ranged from 75 percent to

125 percent of nominal.

520
5. 1 Results of Experiment 2

The results here will be presented in a form very much like those of

Experiment 1. They are set forth in the following:

o Table 4 - showing the interquartile range (25 th and

75th percentiles) and the extreme (5th and 95th

percentiles) production profiles obtained from the decline

rate experiment, all expressed as percent changes from the

base case.

o Table 5 - showing likewise for the recovery factor

experiment.

o Figures 8-10 - showing the frequency histograms of the

three product measures over the 40 tests in the decline rate

experiment.

o Figures 11 - showing the crude oil histogram for the

recovery factor experiment.

The most important aspects of these results can be summarized as follows: ' °S

o The frequency distributions of the crude oil product measure

for each sub-experiment are generally uniform over a relatively tight range, as might be expected from the

uniform nature of the input random variation. For crude

oil, the interquartile range has widths ranging from 10.8

percent of the base case in 1985, to 15.5 percent in 1995,

finally reaching 16.8 percent by 2000. The interquartile

results for crude are a little different in the recovery

factor experiment: they start from a width of 5.4 percent

in 1985, hitting 16.5 percent in 1995, and then 18.7 percent

in 2000.

o For natural gas however, the results appear somewhat mixed.

In the decline rate experiment, there is an apparent

(increasing) monotonicity. Here, the interquartile width

starts at 31.9 percent of the base case for 1985, peaking at

38.6 percent in 1990, and finally receding to 18.1 percent

by 2000. Thus we see the particular importance of decline

in gas production.

o The natural gas liquids results fully reflect the fact that

they come from the combination of oil and gas production.

521
Table 4. Results of Sensitivity Run on Decline Rates

(Percent Changes from Base Case)

5th 25th 75th 95th

Percentile Percentile Percentile Percentile

1985

Oil

Gas

1990

Oil

Gas

1995

Oil

Gas

2000

Oil

Gas

-12.3%

-29.456

•12.9%

-34.6%

•15.5%

•33.0%

•17.3%

•28.1%

-5.1%

-16.2%

-5.9%

-17.9%

-8.1%

-13.6%

-8.4%

-8.4%

+5.7%

+15.7%

+6.4%

+20.7%

+7.4%

+15.4%

+8.4%

+9.7%

+9.8%

+30.3%

+11.2%

+27.4%

+14.4%

+17.4%

+15.7%

+11.2%

Table 5. Results of Sensitivity Run on Oil Recovery Factors

(Primary and Secondary)

5th 25th 75th 95th

Percentile Percentile Percentile Percentile

1985 -5.7% -2.8% +2.6% +7.4%

1990 -10.4% -6.0% +5.2% +13-1%

1995 -13.5% -8.7% +7.7% +17.0%

2000 -17.3% -9.5% +9.2% +19.7%

522
Figure 8

Experiment 2: Monte-Carlo Analysis of Decline Rates

0.16 -

0.12 -

0.08

0.04 -

Mean = 5.16

0.28

0.24

0.20

0.16

0.12

0.08

0.04

0

4.3 4.5 4.7 4.9 5.1 5.3 5.5 5.7 5.9

(MM Bbl/day)

Figure 9

Experiment 2: Monte-Carlo Analysis of Decline Rates

Mean = 13.17

7.9 8.9 9.9 10.9 11.9 12.9 13.9 14.9 15.9

(TCF/ Year

523
0.20

0.16

0.12

0.08

0.04

Figure 10

Experiment 2: Monte-Carlo Analysis of Decline Rates

Mean=.933

0.20

0.16

0.12

0.08

0.04

.65 .70 .75 .80 .85 .90 .95 1.00 1.05 1.10

(MM Bbl/day)

Figure 11

Experiment 3: Monte-Carlo Analysis of Recovery Factors

Means.518

4.00 4.25 4.45 4.65 4.85 5.05 5.25 5.45 5.65 5.85 6.05

(MM Bbl/day)

524
6. EXPERIMENT 3: RESPONSE SURFACE ANALYSIS

Experiment 3 was a first-order response surface experiment. It was aimed at identifying those MOGSMS input data elements whose values

most strongly impact MOGSMS output values and at estimating the

magnitude of these effects.

6. 1 Design Considerations

The selection of the response surface approach draws upon an earlier

survey of sensitivity analysis methodology (Harris, 1979c) and the

earlier mentioned work of Harris and Hirshfeld (1980). That survey

suggested that response surface analysis would be a powerful and

economic method of screening MOGSMS input elements (independent

variable) to identify the critical ones: those whose values have the

largest effect on the MOGSMS output measures (dependent variables).

The term response surface refers to a formal mathematical relationship

expressing the anticipated value of the dependent variable in an experiment as a function of the experiment's independent variables.

The relationship is derived by statistical analysis of the results of

designed factorial experiments.

More specifically, for a dependent variable, Y, say the crude oil

production measure, we will assume a response surface having linear

form:

Y = B

o + iIlBi

X

i (22)

where the {X^} are the set of independent variables in a particualr

test, corresponding to a subset of the MOGSMS input data elements. A

"test" in this context, as before, is simply an execution of MOGSMS

for a given input data set, containing some systematic variations in

X^ from the base (Midprice, Standard Projection) data set.

In general, each of the elments X

i

in Equation (22) may be either a direct value of a data element or a transformed value.

Transformations (i.e., logarithmic, exponential, etc.) maybe

necessary to preserve the validity of the linearity form.

In the response surface context, the effect on the MOGSMS output

measure , Y, of a given input element , X. , is measured by the

magnitude of its coefficient B

i

in Equation (22) as derived by a step-wise linear regression analysis. The larger the coefficient

B^, the more important is the variable X^ to the level of the

product measure, Y. (This is true unless there are such wide

variations possible in X. , that the product (X-.B.) can be

"large" even for "small" B. . Of course, the usual analysis of

variance provides some additional clues in the search for the

important input elements.)

525
i

For a reason that will become clear as the discussion proceeds, we have run not one, but three response surface experiments. Each subexperiment addressed a specific subset of input data elements (as the

independent variables in the experiment), and the first two

experiments have no data elements in common. The third experiment

(called the integrating experiment) is built up from the results of

the first two.

With few minor exceptions (discussed in Section 6.2), the subexperiments followed standard procedure, involving these steps:

(i) Define three response surface equations for the

experiment, one for each of the product measures (as dependent

variables:

Y = B + 8 B X

OIL k1 i=1 ki1 i

Y = B + § B X.

Gas k2 i=1 ki2

Y = B Y + B

NGL k3 OIL k4

where the Y's are the product measures, the X. 's denote the same MOGSMS input data elements (independent variables) in each equation,

and K denotes the sub-experiment.

(ii) Specify three numerical values for each independent

variable: an upper value, a lower value, and a midpoint

value. These three numbers were chosen purely for parsimony

in the experimental design. They do not represent any

assumption whatsoever of the stochastic behavior of the

independent variables, inside or outside the stated range.

The upper and lower values constitute our estimates of the range of

variation likely to occur or exist in nature for the given input data

element. The corresponding midpoint value is either an (arithmetic)

average or a "most likely" value for that element.

The upper and lower values need not be construed as absolute bounds on the corresponding independent variables. The response surface

analysis seeks an approximation (linear, in this experiment) to the

real functional from over some domain, defined here by the ranges of

all the upper and lower values. If a close linear approximation

within that domain can be found, one can resonably assume that the

approximation would remain useful for some distance outside of the

domain

526
(iii) Define a factorial set of MOGSMS tests by assigning the

extreme (or perhaps some midpoint) values to each independent variable

inperiment, in all possible combinations. The MOGSMS run corresponding to the 1979 midprice forecast may be thought of as the

"base case" test in each sub-experiment.

Since we have n independent variables in each sub-experiment and we work with the extreme values only, we have thus defined 2

11 + 1 MOGSMS tests. We split the overall experiment into sub-experiments

simply to keep the total number of tests within reason.

(v) For each test run in Step (iv), record the values of the

three product measures and the values of the subject input data

elements

(vi) Perform step-wise linear regression analyses on the

experimental data recorded in Step (v) either "as is" or transformed,

to obtain the coefficients in the response surface equations.

(vii) Sharpen the fit of the response surface equations by

executing additional MOGSMS tests involving some of the (unused)

midpoint values defined in Step (ii) above.

We ran a final, integrating sub-experiment , following the same

procedure. The integrating sub-experiment had as its independent

variables those input data elements revealed as most "significant" in

the initial round of four sub-experiments. This final set of

independent variables is thus the set of critical input data elements

delineated by the response surface experiment.

o Table 6 sets forth the input data elements that we selected

for the first round of two response surface sub-experiments

described above. Several comments regarding Table 6 are in

order

o The selected elements are arranged in two broad

categories, corresponding to the first two response

surface sub-experiments.

o Three types of input data elements are indicated:

Scalars are single numerical values

in the oil or gas input data set;

Vectors are sets of numerical values

in the input data, one per region;

Functions are more complex sets of

values in the input data, varying

both by region and by some independent

parameter (total exploratory drilling

footage or year)

527
o The input data elements pertaining to drilling were included

in the analysis to produce systematic variation in the

exploratory drilling trajectories (a key input element).

Our selection of input data elements for the response surface

experiment was based on the judgement of various model reviewers

(including the authors) and the experience of MOGSMS's developers and users (EIA 1978). An element's appearance in Table 6 is not an assertion that we consider the underlying MOGSMS data specious.

Rather, it is a reflection of our prior belief that MOGSMS results

were likely to be sensitive to the stipulated input data element,

and that some uncertainty is connected with the values of these

elements.

Table 6. Input Data Elements (Independent Variables)

for the Response Surface Experiments

Data Submodel Type

Category Element Col Gas Scalar Vector Function

Economics

(SE-1)

Drilling

(SE-2)

Discount rate X

Drilling costs, X

producing wells

Drilling costs, X

dry wells

Total-to-exploratoryX

drilling ratio

Lease acreage foot- X

age offshore

Years of foresight, X

rig .mgrs.

Rig and plant life X

X

X

X

X

6.2 Implementation Considerations

As we have seen, Experiment 3 comprises three sub-experiments (SE-1,

SE-2 and SE-3), each a response surface analysis of a specified

subset of MOGSMS input data elements:

o SE-1 Economics data elements

o SE-2 Drilling data elements

o SE-3 Critical elements identified

in the first round of SE's

528
SE-1 and SE-2 involved the same experimental procedure, just

described in Section 6.1. The essence of each sub-experiment was the

specification of the numerical values of the X

i

data elements for

each test. Collectively, the set of tests in each sub-experiment

define a modified "Latin Hypercube" in n-dimensional space, where n is the number of target data elements. Normally each test (but one)

corresponds to a unique vertex in that hypercube. There are two types

of exceptions to this: the first corresponds to the center point of

the hypercube, while the second type is any edge point not completely

out at a vertex. Table 7 and 8 define the tests comprising SE's 1 and 2, respectively. The definitions are in terms of the values

(high, medium high, medium low, low, or center) assigned to each X.

in each test. J

Tables 9 and 10 further define SE's 1 and 2, respectively. These

exhibits set forth the rules we used for calculating the values for

each of the X.'s in the corresponding SE. In most instances, the

experimental values were calculated as a multiplicative factor times

the corresponding values in the base projection run for the 1979 ARC , reflecting our (subjective) estimates of the potential ranges for the

values of the various data elements..

Inspection of the results of SE-1 and SE-2 led us to combine all of

their input data elements for the integrating response surface

analysis (SE-3). SE-3 involved one modification to the standard

experimental procedures. Specifically, in lieu of executing steps

(ii), (iii), and (iv) of the procedure, we defined SE-3's test set to

be the union of all of the tests originally defined and run in SE-1

and SE-2. That is, we did not define run a new set of MOGSMS tests to

drive the subsequent regression analysis. Instead, we used the test

results we already had and simply redefined the set of independent

variables (X.) to be union of those included in SE-1 and SE-2.

%J This tactic created a set of 251 tests, all having the same independent variables. We performed the usual regression analysis on

this (derived) set of tests to obtain SE-3's response surface

equation. Thus we were able to carry out sub-experiment 3 without

executing any new MOGSMS tests.

529
Table 7. Tests for Sub-Experiment 1

Economics 9 Tests

Independent Variables (Xj)

^ DiR DC

OIL: X X

Test GAS: X X

1 Hi Ce

2 Med Hi Ce

3 Med Lo Ce

H Lo Ce

5 Lo Hi

6 Ce Med Hi

7 Base Case Base Case

8 Ce Med Lo

9 Ce Lo

DC: Drilling Costs, producing Wells & Dry Wells

Table 9 defines the high, low, and center (base

values) for each of the X j's and specifies the

the precise location (by card image) of the

Xj's in the MOGSMS input data set.

Table 8. Tests for Sub-Experiment 2

Drilling 243 Tests

Independent Variables (Xj) TER DRC YF RPL

OIL: X X X X Test Gl5~; X X

Hi Hi Hi Hi 2 Hi Hi Hi Hi

3 Hi Hi Hi Hi Hi Hi Hi Lo

5 Hi Hi Hi Lo

6 Hi Hi Hi Lo

7 Hi Hi Hi Hi 8 Hi Hi Hi Hi

9 Hi Hi Hi Hi

10 Hi Hi Lo Lo

11 Hi Hi Lo Lo

12 Hi Hi Lo Lo

13 Hi Hi Lo Hi

11 Hi Hi Lo Hi

15 Hi Hi Hi Hi

16 Hi Hi Lo Lo

17 Hi Hi Lo Lo

18 Hi Hi Lo Lo

etc

Key to the Xj's

TER: Total-to Exploratory Drilling Ratio

DRC: Oil Drilling Constraints

YF: Years of Foresight, Rig Mfgrs.

RPL: Rig and Plant Life

CAPL: Planning Horizon

Table 10 defines the high, low, and center (base)

values for each of the Xj's and specifies the precise location (by card image) of the Xj's

in the MOGSMS input data set.

530
Table 9. Specification of Numerical Values in Sub-Experiment 1 Category: Economics

Data

Element OIL GAS Input Data Set/Cards Type Vertex Values

OFRIS OTAIL GFRIS GTAIL HIGH LOW BASE

Discount

Rate

(DiR) X 227-229 Scalar .15 .05 .10

X 211-212 .15 .05 .10

Drilling

Costs , X X 176-199 Function 1.5 0.5 Mid

Producing X X Price

Wells (Base) (Base) Input

Drilling

Cost , X X 18-73

Dry Wells

(DC)

Table 10. Specification of Numerical Values in Sub-Experiment 2

Category: Drilling

DATA OIL GAS Input Data Set/ Cards Type Vertex Values

ELEMENT OFRIS OTAIL GFRIS GTAIL HIGH LOW BASE

Total to Exploratory

Drilling Ratio

(TER) X 55-66

Oil Drilling

Constraints

(DRC)

Years of

foresight

rig manufacturers

(YF)

Rig and

Plant

Lift

(RPL)

Planning

Horizon

(CAPL)

Function 0.8x 1.2x Mid

(Base) (Base) Price

Input

Scalar

Scalar

1.5x 0.5x

(Base) (Base)

Mid

Price

Input

Scalar

Scalar

Mid

Price

Input

Scalar

Scalar

15

7.5

5

2.5

Scalar

Scalar

15

7.5

5

2.5

10

5

531
6.3 Results

The primary results of Experiment 3 appear in Tables 11-1 3. The most

important aspects of these results can be summarized as follows:

o Sub-experiments 1 and 2 deal with those input data elements that

we deemed to be potentially the critical ones. Table 12 (oil

and 13 (gas) summarize the results of these experiments and

highlight the key explanatory variables or critical elements

identified by this (screening) around of sub-experiments. The

tables show the change in oil and gas production (dependent

variables) for a given change in each of the data elements

(independent variables), as specified by the coefficients in

the derived response surface equation (Table 11).

o All response surface equations emerging from the sub-experiments

show high R values ( >0.82 in all cases). This result implies

that the true response surfaces are well-approximated by a (nontransformed) linear form. By way of verification, the equations

all closely fit the corresponding center points (which were not

used in deriving the equations, but reserved for calibration

purposes)

Table 11. Response Surface Equations: Sub-Experiments 1, 2, and 3

SUB-EXPERIMENT

Indendent 1: Economics 2: Drilling 3: Integrating

Variables Oil Gas Oil Gas Oil Gas

Dir

DC

-4930.35

- 772.08

-4930.35

- 772.08

TER

DRC

YR

RPL

CAPL

„2

•317.59

107.18

102.58

-440.84

-230.97

-114.30

54.40

543.58

-1252.86

-425.75

-'317.59

107.18

102.58

-440.84

-230.97

0.9402 0.8515 0.9513 0.8242

-114.30

54.40

-1252.86

-425.75

0.9337

532
Table 12. Sensitivity of (Average) Oil Production to Changes in

Key Input Variables

For This This Amount Leads To This Change

Input Element Of Change (In MBl/Day)

Total-to-Exploratory

Drilling Ratio 10% (2) -159

Drilling ) Regional: 10% (2)

Constraints /Total: 7% (2) +107

Years of

Foresight 1 Year (1) +34

Rig and Plant

Life 1 Year (1) -176

Cap. Planning

Horizon 1 Year (1) -92

Discount Rate 25% (2) -123

Drilling Costs 25% (2) -193

2 Changes in numerical values.

These are percent changes from nominal or base values.

Table 13. Sensitivity of (Average) Gas Production To Changes in Key

Input Variables

For This This Amount Leads to This Change

Input Element Of Change (In MCF/Day)

Total-to-Exploratory

Drilling Ratio 10% (2) -57

Drilling t Regional:

Constraints/Total

10% (2)

7% (2)

+54

Years of Foresight 1 Year (1) +181

Righ and Plant Life 1 Year (1) -501

Cap. Planning Horizon 1 Year (1) -170

Discount Rate 25% (2) Infinitesimal

Drilling Costs 25% (2) Infinitesimal

Changes in numerical values.

These are percent changes from nominal or base values.

533
REFERENCES

EIA Division of Oil and Gas Analysis, Office of Energy Source Analysis (1978)

Medium Run Oil and Gas Supply Model 1977 Data Update , Research Memorandum

78/015, U.S. Department of Energy, Washington, D.C.

Energy Information Administration (1979) . Annual Report to Congress, 1978 , Volume 3, U.S. Department of Energy, Washington, D.C.

Energy Information Administration (1980) . Annual Report to Congress, 1979 , Volume 3, U.S. Department of Energy, Washington, D.C.

Feller, W.G. (1966) . Introduction to Probability Theory , John Wiley and Sons,

New York.

Gass, S.I. and Joel, L.S. (1980). Concepts of Model Confidence , Project

Report, Center for Applied Mathematics, National Bureau of Standards,

Washington, D.C. 20234.

Gass, S., Hoffman, K.L., Jackson, R.H.F.; Joel, L.S., and Saunders, P.B. (1980).

Interim Report on Model Assessment Methodology; Documentation Assessment , NBSIR 80-1971, National Bureau of Standards, Washington, D.C. 20234.

Harris, CM. and Hirshfeld, D.S. (1979). Sensitivity Analysis of DOE Forecasts

of Midterm Oil and Gas Supply for the 1978 Annual Report to Congress ; Final

Project Report to National Bureau of Standards.

Harris, CM. (1979a) . Data Extrapolation and Statistical Forecasting , Project

Report CMHl-NBS-DOE to National Bureau of Standards.

Harris CM. (1979b) . Model Validation, Simulation, and Sensitivity Analysis , Project Report CMH2-NBS-DOE to National Bureau of Standards.

Harris CM. (1979c) . Statistical Methods for the Assessment of Model

Sensitivity to Input Variables , Project Report CMH3-NBS-DOE to National

Bureau of Standards.

Hirshfeld, D.S. (1979). Investigation of Underlying Data: Midterm Oil and

Gas Supply Modeling System, Final Report to National Bureau of Standards.

Hoffman, K.L. and Joel, L.S. (1979). Midterm Oil and Gas Supply Modeling

System: Mathematical Descriptions , Project Report, Center for Applied

Mathematics, National Bureau of Standards, Washington, D.C. 20234.

McKay, M.D., Beckman, R.J. and Conover, W.J. (1979). "A Comparison of Three

Methods for Selecting Values of Input Variables in the Analysis of Output

From a Computer Code," Technometries 21 , pp. 239-245.

U.S. Geological Survey Circular 725 (1975). Geological Estimates of

Undiscovered Recoverable Oil and Gas Resources" in the United States , prepared

for the Federal Energy Administration.

534
NATURAL RESOURCE DECISIONS

INVOLVING UNCERTAINTY

by

S.D. Deshmukh1

1. INTRODUCTION

With the increasing scarcity of natural resources in recent years there

has been a growing interest in problems of optimal management of these resource stocks. Starting with the classic paper by Hotelling (1931), the more recent extensive literature on the economics of exhaustible resources is

represented by Solow1 s (1974) exposition of the basic theory, essays in the

1974 Symposium of the Review of Economic Studies and the monograph by Dasgupta

and Heal (1978).

In general, however, only a few of the studies have explicitly

incorporated the crucial element of uncertainty in their analysis. These

studies may be broadly classified into three categories. Models in the first

category are concerned with optimal resource extraction decisions when the

total resource stock is unknown and may be suddenly exhausted, as in Kemp

(1976, 77) Cropper (1976), Loury (1978) and Gilbert (1979), or it may be

expropriated as in Long (1975). The second category of models involves

uncertainty regarding the time at which a perfect producible substitute

becomes available so as to eliminate the dependence of the economy on the

natural resource. Dasgupta and Heal (1974) and Dasgupta and Stiglitz (1976)

analyze optimal extraction decisions when the probability distribution of the

uncertain timing of innovation of a substitute is specified exogenously, while

Dasgupta, Heal and Majumdar (1977) and Kamien and Schwartz (1978) also permit

1. Department of Managerial Economics and Decision Sciences,

J.L. Kellogg Graduate School of Management, Northwestern

University, Evanston, Illinois 60201. Research supported by

Kellogg Research Grant and the J.L. Kellogg Center for Advanced

Study in Managerial Economics and Decision Sciences.

535
1

the innovation process to be controlled through R&D expenditures. In a I

related model Hoel (1978) assumes that the time of innovation is known but the

cost of producing the substitute is uncertain. In the third category of

models the uncertainty is regarding the discovery of additional resource

stocks through search and exploration. Arrow and Chang (1980) and Deshmukh

and Pliska (1980) have studied optimal consumption and exploration decisions

that control the uncertain timings and magnitudes of discoveries; see also

MacQueen (1961, 64) and Heal (1978) for related models involving stochastic

discoveries and Pindyck (1978) for the certainty case.

In this paper we present a general model of natural resource decisions in

the presence of uncertainty regarding the time of occurrence of some significant event. The decisions involve selection of extraction

(consumption) and exploration (search or R & D expenditure) rates and the

uncertain event corresponds to resource exhaustion or discovery of additional

stock or invention of a substitute. In addition to characterizing optimal

decisions under uncertainty, we also consider the behavior of the resource

price over time. The general model is presented in Section 2 and its special

cases are studied in the subsequent sections in light of the related

literature outlined above.

2. THE MODEL

The distinguishing characteristic of a natural energy resource (such as oil or natural gas) is that it is nonproducible and nonrenewable.

Consequently, the future supply of the resource cannot be controlled or determined with certainty. In an extreme event, the resource may be

exhausted, thereby imposing a severe hardship on the economy. At the other

extreme, a perfect producible substitute may become available, rendering the

natural resource inessential. Between these possibilities of extremely

unfavorable and favorable events, an interesting intermediate case is the one in which an additional stock of the same resource is discovered. In this

section, by an "event" we mean exhaustion of the resource stock or discovery

of an additional stock or development of a producible substitute. We assume,

for simplicity and consistency, that only one type of event may occur and that

it can occur only once. The time at which the event takes place is a random

536
variable, and its probability distribution can be controlled through the

extraction and exploration rate decisions. Resource extraction (consumption)

yields social utility but depletes the stock, on hand and hastens exhaustion.

On the other hand, exploration involves (search or R & D) expenditures but

also expedites the occurrence of a desirable event (i.e. discovery of an

additional stock or development of a producible substitute). The problem then

is to determine optimal extraction and exploration policies in face of the

uncertain timing of occurrence of the event of interest.

Let the nonnegative random variable X

t denote the state of the natural

resource in the economy at time t > 0. For instance, X

t may be the size of

proven reserves on hand at time t or it may be the cumulative amount extracted

and consumed by t. Suppose the central planner's decision variable

c

t e[0,c] denotes the consumption (extraction) rate at which the resource

stock is depleted at time t. This yields a social utility (net of extraction

costs) to the economy at rate U(c

t

), which is assumed to be increasing and

concave in c

t

. Denote by a > 0 the rate at which future utilities and costs

are discounted.

In addition to the resource state X

t

, let the binary valued random

variable Y. denote the occurrence or nonoccurrence of the event of interest

(i.e. exhaustion, discovery or innovation) by time t. Suppose Y

t - 0 means

the event has not occurred by time t and Y = 1 corresponds to the occurrence

of the event prior to t (so that Y

t = 1 implies Y

g = 1 for all s > t).

Equivalently, we let the nonnegative random variable T denote the (Markov)

time of occurrence of the event, i.e. T = min {t > 0; Y = l}. While c

t advances the date of exhaustion, the exploration expenditure rate

e

fc e [0, e] expedites the discovery of an additional stock or a substitute

through search or R & D activities. In general, let X(x, c, e) denote the

hazard rate (success or failure rate) associated with the event time T, i.e.

X(x, c, e) is the probabilistic rate of occurrence of the event at t, given

that T > t, X

t = x, ct= c and e

t = e. Roughly, X(x, c, e) dt is the

probability that the event will occur during (t, t+dt), given that it has not

occurred by time t, the resource state is X

t

- = x and the consumption and

exploration decisions are c

t = c and e

t = e. We assume that X is increasing

in (c,e) in order to reflect the advancing of exhaustion through c or of

discovery through e.

537
Once the uncertain event occurs at time T, the planner's problem then

becomes a relatively easy one of determining optimal consumption pattern under

certainty. Let W(x) denote the maximum attainable total discounted utility

over [T, 00 ) , given Xj, = x and Yrj, = 1. For instance, in the event of

exhaustion, W = 0; in the case of discovery of size z, W(x + z) is the total

utility from consuming the stock x + z optimally, as in Hotelling (1931); in

the case of substitute discovery, W(x) is the optimal value of the program as in Dasgupta and Heal (1974).

The planner's problem is then to determine {(c

t> et

); 0 < t < T} so as to

maximize E{ /

T

exp(-at) [U(c ) - e ] + exp(-aT) W(X )|X = x}

0

Let V(x) denote the optimal value of this program starting in the resource

state Xq = x andYQ = 0. Selection of decisions (c, e) in [0,t] yields net

utility [U(c) - e]t and the resource state changes to X

t = x - ct (if X is the

stock on hand) or X

t = x +ct (if X is the cumulative consumption). Also, the

uncertain event occurs in (0,t) with probability X(x, c, e)t (so that the

optimal value is determined by W(X

fc )) and with probability

[1 - X(x, c, e)t] the event does not occur (so that the optimal value

is V(Xt )). The dynamic programming argument then yields

V(x) = Max {[U(c) - e]t + exp (-at) [X(x,c,e)t W(X

t

) + (l-X(x,c,e)t)V(X

t )]}

Using exp(-at) = 1-at + o(t), and the Taylor's expansion of V(*) and W(')

around x, dividing by t and letting t 4- 0 yields the optimality equation

(1) a V(x) = Max {U(c) - e - c V'(x) + X(x,c,e) [W(x)-V(x)] }

, x > 0

c , e

prior to the occurrence of the event, if X

t=x represents the stock on hand

t i (with V (x) replaced by -V (x) if X

fc is the cumulative consumption). Upon

occurrence of the event, exploration is unnecessary (i.e. e^. = 0), and the

optimal value function W(') satisfies the optimality equation

(2) a W(x) = Max {u(c) - cW'(x)}, x > 0.

Optimal decision policies specify, as functions of the resource state X =x at

538
any time t<T those consumption and exploration rates c*(x) and e*(x) that

attain the maximum in (1). Similarly, given X = x at any time t > T, c*(x)

attains the maximum in (2) and e*(x) = 0.

The optimality equations (1) and (2), which characterize the optimal

policies c*(*) and e*(*), may be written in a comprehensive fashion in terms

of a more general optimal value function as follows. Let V(x,y) denote the

optimal value function starting in Xq = x and Yq = ye { 0,1} so that

V(x,0) = V(x) and V(x,l) = W(x). Consider the infinitesimal generator A

c of the Markov process {(X , Y ) ; t > 0} defined by

which is the expected rate of change in the value of V starting in

Xq = x, Yq= 0 and selecting (c,e) decisions. Similarly

A V(x,l) = A W(x) = - c W*(x). With this additional notation, (1) and

c,e c (2) may be rewritten compactly as

Recall that, given t < T and X

t = x, V(x) is the maximum long-run

expected net utility over [t,»). Therefore, V*(x), the marginal improvement

from an incremental unit of the resource stock, corresponds to the imputed

(shadow) price P of the resource prior to the occurrence of the event.

(Similarly, if X

fc = x and t > T, W'(x) is the resource price after the event

occurs.) The rate of change in the resource price without taking into account

the possibility of occurrence of the event is then the time derivative

P = ~c V'XX^). However, the expected rate of change in the resource

price, allowing for the possibility of occurrence of the event (and the

consequent change in the price from V to W

1 ), is obtained by considering the

infinitesimal generator A evaluated at V'(x). Therefore,

A

c eV(x,0) = lim {E[V(X

t

, Y

fc ) |XQ= x, Y=0, c

Q= c, e( = e] - V(x, 0)}/t

t+0

= - c V'(x) + X(x,c,e) [W(x) - V(x)],

(3)

(4) V'(x) = -c*(x) V"(x) +X(x,c*(x),e*(x))[W , (x) -V'(x)]

539
is the expected rate of change in the resource price prior to the event and

(5) A W'(x) = -c*(x) W"(x)

c*

is the corresponding price dynamics after the occurrence of the event.

In the rest of the paper we shall study the optimal policies c*(x) and

e*(x) and the dynamics of prices V'(x) and W'(x) in a number of special

cases. In Section 3 we first consider the benchmark case of certainty, while

in the three subsequent sections we consider the uncertain events of

exhaustion, discovery of new stock, and development of a substitute

respectively. We shall also discuss in each section the related literature.

3. KNOWN, FIXED RESOURCE STOCK

In this classic case studied by .Hotellihg (1931), Heal (1973) and Solow

(1974), the given initial stock Xq is to be consumed optimally over [0, » ) when no additional stock or a substitute is anticipated. If the resource is

essential, its exhaustion occurs only asymptotically (under the typical

i assumption of U (0) = °°). While the usual approach to analysis of this case employs variational calculus, our optimality equation (1) with X = e = 0

specializes to

(6) a V(x) = Max {u(c) - cV'(x) }, x > 0.

It can be shown that its unique solution V is concave and increasing in resource stock size x. Thus, the shadow price of the resource, V'(x), is

positive and decreasing in the amount on hand. As to the optimal consumption

rate c*(x), an interior optimum in (6) requires U'(c*(x)) = V'(x). Thus, the

marginal utility of consumption is equated with the marginal worth of unit

consumption postponed. Since, by concavity, U'(') and V'(') are decreasing,

optimal consumption rate c*(x) is increasing in the stock size.

Also note that U'(c*(x)) is the shadow price of consumption and V'(x) is

the shadow price of holding reserves. Thus, X =x and t < T yields the price

P = U'(c*(x)) = V'(x). The rate of change in the price is then

540
P = - c*(x) V"(x). Now optimality of c*(x) in (6) implies

a V(x) = U(c*(x)) - c*(x) V'(x).

Differentiating and using the optimality condition yields

a V'(x) = [U f (c*(x)) - V

f (x)]c* f (x) - c*(x) V"(x)

= - c*(x) V"(x)

i.e. aP = P , so that we have

t t

(7) P

t - P

Q

.<".

Thus, the resource price (net of extraction costs) rises at the rate of

discount, which is the fundamental theorem of economics of exhaustible

resources (Hotelling (1931), Solow (1974)). In the competitive resource market this may be interpreted as the arbitrage condition as follows. In the

flow equilibrium, in order for the resource holders to be indifferent between

supplying at different points in time, the discounted prices must be the same

—(x(t~f"S) —OtS

* at each point in time, i.e. e P = e P , so that P = a P otherwise

U i S S L L j it would be preferable to change the supply pattern. Alternatively, the

suppliers hold the resource stock as an asset and the stock equilibrium in the

assets market requires that all assets yield the same rate of return

(dividends plus capital gain) equal to a. Since the resource stock in ground

yields no dividends, its value (price) must grow at rate a. If it grows

slower, more will be supplied earlier and the resource will be exhausted too

quickly. If the price grows at a rate faster than a, then it is better for

the resource holders to hold the stock as an investment that yields a rate of

return higher than a. The welfare economics implication of the above theorem

is that, in a socially managed economy, the imputed price (net of extraction

costs) of the resource rises at the social rate of discount. Finally, if the resource is owned by a monopolist, the corresponding statement is that his

marginal profit must rise at the rate of interest.

Given the above price dynamics, the optimal consumption pattern over time can be derived. Since c*(") is decreasing in the stock size which is

depleting over time (in absence of new discoveries), the optimal consumption

rate declines through time. More precisely, we have P

t = U'(c*

t

) so that

P = c* U" (c*), which together with P

t

/ p

t = <* yields

c* I c* = o/[c* IT (c*)/U'(c*)]

541
i.e.

(8) c*/c* = -a/n(c*), where n(c) = -c U" (c) /U'(c)

is the elasticity of marginal utility. For. example, if

U(c) = c

* £ ^for 0 < e < 1, then n(c) = e and hence c* = c* e at ^ e i.e.

optimal consumption decreases exponentially. The initial rate of c*q is then

chosen so that qJ c* dt = Xq i.e. c* = a X^/e.

4. EXTRACTION OF FIXED UNCERTAIN STOCK SIZE

This is the case of optimally "eating a cake of unknown size" studied by

Kemp (1976, 77), Cropper (1976), Loury (1978) and Gilbert (1979). The total

stock size is a random variable S with the distribution function F(") and the

density function f('), and no additional discoveries of the resource or a substitute are expected. The resource state Xt is the cumulative amount

consumed by time t, the "event" corresponds to exhaustion (so that Y = 0 if

X

t < S and Yt = 1 if Xt = S) and the post-event return is W(x) = 0. Given

X

t = x and Y = 0 (i.e. S > x), the conditional density function of S is

X(x) = f(x)/[l - F(x)]. It can be seen that, if the consumption rate is

c

t=c, the hazard rate of the time of exhaustion is X(x,c) = c \(x) . Thus

the optimality equation (1) specializes to

(9) a V(x) = Max {U(c) + cV*(x) - cX(x) V(x) }, x > 0.

Note that the certainty case of the previous section is obtained by taking

X(x) = 0 for all x < S, the known resource stock, and X(S) = «». Note also

that V(x) is the optimal value over [t, 00 ) given that X

fc - x and that the

exhaustion has not occurred by t. Equivalently, using

X(x) = f (x)/[l-F(x)] and multiplying both sides of (8) by [1 - F(x)] we get

(10) a v(x) = max {u(c) [1 - F(x)] + c v»(x)}

where

(11) v(x) = V(x) [1 - F(x)]

is the expected optimal value over [t, °°) if the cumulative consumption over

[0, t] is X

t = x (but it is not known whether the exhaustion has occurred by

542
t), Optimality of c*(x) in (10) requires

(12) U'(c*(x)) [1 - F(x)] = - v'(x),

which is the resource price ? r. The expected rate of change in the resource

price is then P = A^v(x) = - c*(x) v"(x). Also, since c*(x) is the

maximizer in (10), we have a v(x) = U(c*(x)) [1 - F(x) ] + c*(x) v'(x), which

upon differentiating with respect to x and using (12) yields

(13) a v'(x) = - U'(c*(x)) f(x) + c*(x) v"(x).

Hence, from (12) and (13), we have

(14) P

t /Pt = a - X(x) U(c*(x))/U'(c*(x))

i.e. the price is expected to rise at a rate slower than the rate of

discount. In fact, if X(x) or c*(x) is very high, the price may even fall

through time.

As to the consumption pattern, note from (12) that

so that

yielding

P = U»(c* ) [1 - F(x )] t t t

P = - U'(c* ) f(x ) c* + U"(c* ) c* [1 - F(xJ]

t t t t t t t

(15) P

t /Pt = U"(c*

t

) c*

t /U'(c*t

) - X(x) c*

t

.

Equating the right hand sides of (14) and (15) and rearranging we get

(16) c*

t /c*t = {- a + X(x) c* [U(c*)/c* - U'(c* )]/U'(c* )}/n(c* ),

where again n(c) = - cU"(c)/U'(c) is the elasticity of marginal utility. To

interpret (16) note that deferring a unit consumption at time t is like an investment that costs U'(c

t

) but delays the exhaustion instant (which is t with probability X(x) c

t

) by l/c

t during which additional utility can be

earned at rate U(c

t ). Thus X(x)c

t [U(ct )/ct - U' (cfc ) ] /U 1 (c

fc ) is the expected

net rate of return per unit investment at t (which is positive, due to the

543
concavity of U). It is the conservation motive in favor of delaying

consumption; consumption tends to rise over time (or is postponed to reduce

the probability of exhaustion) due to this factor. On the other hand,

-a represents the time preference in favor of current consumption. As a combined effect of these two conflicting factors, the consumption may be

rising or falling through time, in constrast with the certainty case of

Section 3 wherein (X(x) = 0 and hence) the consumption falls over time. For

example, if the exhaustion probability X(x) is very high, the consumption may

rise; if X(x) is increasing in x, the consumption may fall or first fall and

then rise through time; if the discount rate a is small (i.e. if the plan is more future-oriented), then the consumption rises (it is postponed); see Kemp

(1976), Cropper (1976) and Loury (1978) for details.

We close this section by considering a special case in which X(x) is a constant X or, equivalently, when the distribution of the resource stock size

is exponential, i.e. F(x) = 1 - e . From the memorylessness property of

the exponential distribution it is clear that, given no exhaustion yet, the

optimal value V(x) is independent of the cumulative consumption x. Hence, (9)

becomes a V = Max {u(c) - cXV} and the optimal consumption rate is a constant

c* which satisfies U'(c*) = XV. Also V = U(c*)/(a + Xc*), which is the

expected discounted utility from the constant consumption rate c* until the

moment of exhaustion. The resource uncertainty may thus be viewed as raising

the discount rate from a to a + Xc*.

5. EXPLORATION AND UNCERTAIN -DISCOVERY OF NEW STOCK

In the previous section, learning about the uncertain stock size was accomplished through extraction alone; the probability distribution of the

stock size was then updated over time merely using the fact that the true

stock has to be at least as large as the cumulative amount already

extracted. In this section, exploration is considered as a distinct activity

of learning that involves expenditures to search for and discover the

existence of additional stocks. Pindyck (1978) has considered the exploration

activity under certainty, MacQueen (1961, 64) and Heal (1978) have studied

related models involving uncontrolled stochastic discoveries, while Arrow and

544
Chang ( 1980),.- and Deshmukh and Pliska (1980)>have analyzed optimal consumption

and exploration decisions when the latter controls the uncertainty about

timings and/or magnitudes of discoveries.

In this section, Xt denotes the size of proven reserves on hand at time t and the "event" refers to the discovery of a new stock. We assume that only

one discovery is possible and it occurs at a random time T which can be

controlled through the exploration expenditure rate e e [0,e]. The

probabilistic rate of discovery X(e) is assumed to be increasing in e, with X(0) = 0. Let the nonnegative random variable Z denote the size of the

stock discovered at T and suppose G( * ) is the probability distribution of Z.

If the resource stock just before the discovery is = x and if the

discovery is of size Z=z then the post discovery problem is that of optimally

consuming the total resource stock X^, = (x + z) on [T, »). This problem was analyzed in Section 3 to yield the maximum discounted utility V(x + z), where

V(') is the concave increasing function that is the solution of (6).

Consequently, the terminal reward at T for the problem in the present section

is

(17) W(x) = /°° V(x + z) dG(z),

0

which is also concave and increasing in x > 0. With this W( * )

, the optimality

equation (1) now becomes

(18) ctV(x) = Max {U(c) - cV'(x)} + Max {-e + X(e) [W(x) - V(x)]}, x > 0, c e with the boundary condition

(19) a V(0) = Max {- e + X(e) [W(0) - V(0)]}.

e

It can be shown that (18) and (19) have the unique solution V(") which is concave and increasing in the stock size; V(x) is the optimal value of the

stock size x prior to the occurrence of the favorable event of discovery of a new stock. From (17) and monotonicity of V it follows that W(x) > V(x).

Also concavity of V(') implies that [W(x) - V(x)] is decreasing in x, i.e.

W' (x) < V'(x) , so that the marginal value of the original resource stock

falls after the discovery of an additional stock. (Strictly speaking, these

conclusions hold when an infinite sequence of discoveries is permitted). Note

545
that A(e) = 0 (i.e. impossibility of new discoveries) yields the case of

Section 3.

The optimal consumption rate c*(x) is a maximizer of the first term on

the RHS of (18). By concavity of U(') and V( # ), it can be seen, as before,

that c*(x) is increasing in x. Consequently, as the resource stock depletes

on [0,T), the consumption rate decreases and the shadow price of consumption

U'(c*(x)) rises through time. When the stock level jumps by amount Z at T,

the consumption rate increases and the price falls, depending on the discovery

size z.

Prior to the discovery, the optimal exploration cost rate e*(x) maximizes

the second term on the RHS of (18), namely,

(20) f(x, e) = -e + A(e) [W(x) - V(x)J.

Since X(e) is increasing in e and [W(x) - V(x)] is decreasing in x, it

follows that e*(x) is decreasing in x. To see this suppose x^ > x^ but that

e*(x2) > e*(xj). Now

[f(x

2

, e) - f(x

2 e)] = X(e) {[W(x

2

) - V(x

2

)] - [W^) - V^)]}

is positive and increasing in e. Hence

[f(x

2 , e*(x2

)) - f( X]L , e*(x

2 ))] > [f(x

2 , e*^)) - fU^ e*^))]

i.e. [f(x

x

, e*( Xl )) + f(x

2 , e*(x2 ))] > [f

^, e*(x

2

» + f(x2> e*(xr))].

But this contradicts the fact that e*(x^) maximizes f(x^, *) and e*(x2

) maximizes f(x2,*). Hence we must have e*(x2

) < e*(x^), i.e. the exploration

effort rate should be higher when the resource level is lower. Thus,

initially very little investment is made in exploration (and more stock is

consumed); as the resource stock depletes, more search effort is expended (and

less stock is consumed), until new stock is discovered, at which point the

exploration effort drops (to zero if no more discoveries are anticipated).

To determine the expected rate of change in the shadow price prior to T

546
note that

A * *V(x) = - c*(x) V"(x) + X(e*(x))[W»(x) - V'(x)]

c , e while

a V(x) = U(c*(x)) - c*(x) V»(x) - e*(x) + X(e*(x)) [W(x) -V(x)]

so that

a V*(x) = c**(x) [U'(c*(x)) - V'(x)] - c*(x) V"(x)

- e*»(x) {1 - X

f (e*(x))[W(x) - V(x)]} + X(e*(x) ) [W (x) - V'(x)]

= A V'(x), c*,e*

where the last equality follows from optimality of c*(x) and e*(x) and the

definition of A

c

* V'(x).Thus, we have

(21) A^ ^ V'(x)/V»(x) = a

i.e. given that a discovery has not occurred by t and that X

t = x, the price

is expected to rise at the rate of discount. This is a stochastic analog of

the Hotelling's (1931) result discussed in Section 3, wherein no additional

discoveries were possible. At the instant T of discovery if X^,_ = x and if

the discovery is of size z, the. stock price decreases from V'(x) to V'(x + z)

and then it increases again at the rate of discount, as before. For the

analysis involving multiple discoveries see Deshmukh and Pliska (1980).

6. R&D AND UNCERTAIN DEVELOPMENT OF A SUBSTITUTE

In the previous section, the occurrence of the favorable event of

discovery of new stock relaxed the resource constraint temporarily. In this

section we consider the possibility of an extremely favorable event

(technological change) that permanently eliminates the resource constraint as

a result of the development of a producible perfect substitute. The

substitute development process may be expedited by allocating higher R&D

expenditures. The special case of uncontrolled development was analyzed by

Dasgupta and Heal (1974), Dasgupta and Stiglitz (1976) and Hoel (1978), while

Dasgupta, Heal and Majumdar (1977) and Kamien and Schwartz (1978) have

547
permitted the development process to be controlled endogenously.

Let Xt be the size of the natural resource stock on hand at time t and

suppose T corresponds to the random time at which the perfect substitute

becomes available. If the substitute can be produced then on at a unit cost

of k and if = x, the planner's problem on [T, 00 ) is to determine the

substitute production rate s^ e[0,s] and the resource consumption rate

c

t e[0,cj, t > T , so as to

00 00 maximize / e a

[U(c + s ) - k s ] subject to / c dt = x. 0

t t t - 0t

Let W(x) be the optimal value of this program, given X^, = x. Then, as in (2),

the dynamic programming argument yields the following optimality equation

(22) a W(x) = Max {U(c + s) - ks - cW'(x)}, x > 0

with

a W(0) = Max {u(s) - ks}.

It can be shown that the optimal value function W(x) is concave increasing in

x. Optimal consumption and production rates c*(x) and s*(x) are then obtained

as the maximizers in (22) and can be characterized as follows. If W'(x) < k

(i.e. the imputed price of the resource is less than the cost of producing the

substitute) then s*(x) = 0 and U'(c*(x)) = W'(x), so that c*(*) is

increasing. As the resource stock depletes over time, consumption rate

decreases and shadow price rises at rate a (as in Section 3) until

U'(c*(x)) = W'(x) = k. At that time the resource stock is just exhausted and

the optimal production rate s* then on is determined by

U'(s*) = k with W(0) = [U(s*) - ks*]/«.

Prior to the development instant T, the control variables are c (the resource consumption rate ) and e (the R&D expenditure rate), the former

depletes the resource and the latter increases the rate X(e) of discovery of

the substitute. The resulting optimal value function V then satisfies the

following specialization of the optimality equation (1).

(23) ctV(x) = Max{u(c) - c V'(x)} + Max{-e + X(e) [W(x) - V(x)]}

c e

548
Given that W(') is concave increasing in x, it can be shown that V(*) also has

the properties. Moreover, since the event of a substitute discovery is a beneficial one, we have W(x) > V(x); otherwise it is clear from (23) that

e*(x) = 0. Moreover, it turns out that W'(x) < V'(x), so that the marginal

value of the resource falls after the discovery of the substitute.

Prior to the substitute development, c*(x) satisfies U'(c*(x)) = V'(x),

while after T we have U'(c*(x)) =W'(x). Concavity of U, V and W implies that

c*(x) is increasing in x, before as well as after the development. Moreover,

since W'(x) < V'(x), it follows that, given the same stock, size x, c*(x) prior

to the discovery is smaller than after the discovery, i.e. the conservation

motive is stronger prior to the discovery, as to be expected.

The optimal R&D expenditure rate e*(x) is a maximizer of the second

term on RHS of (23), which is similar to (20) of the previous section. Since

X(*) is increasing and W'(x) < V'(x), as in the previous section, it follows

that e*(x) is decreasing in x.

Similarly, one can show that

< 24 > A * 0 *v '(x)/V'(x) = a

c , e

i.e. given that the substitute has not been discovered by t and that X

t = x, the price is expected to rise at the rate of discount, as before. At the time

of invention of the substitute if Xj, = x, the price falls from V (x) to

W'(x). Then it rises again at rate a until it becomes k = W'(0) and stays at

that level from then on.

Thus, as the resource level falls over time, the stock price rises, the

consumption rate is reduced and the intensity of the R&D activity is

increased until a substitute is discovered. At that time the stock price

drops, consumption rate is increased and R&D expendutures become unnecessary. From then on the price rises, only the resource is consumed until it

is exhausted, at which point the price equals the cost of producing the

substitute. In the final phase, the constant rate of consumption is sustained

only through the substitute production.

549
7. REMARKS

We have presented a general model of natural resource decisions that

involves uncertainty regarding the occurrence of some significant event of

interest. The consumption rate decision depletes the resource stock and the

exploration rate decision expedites the occurrence of a favorable event.

Dynamic programming was employed to characterize the optimal value function,

optimal decision policies and the behavior of prices. The model was then

specilized to the analysis of three cases involving the events that are most

unfavorable (exhaustion), somewhat favorable (discovery of a new stock) and

most favorable (development of a substitute). The analysis was mostly

heuristic and the emphasis was on intuitive arguments and interpretations

rather than on the technical details involved. The related literature was also reviewed within the context of the general model and its three special

cases.

The model could be extended along two significant directions. It may be

important to allow for the possibility of occurrence of multiple random

events, such as a sequence of discoveries of new stocks or a sequence of

partial substitutes developed. Secondly, the probabilistic rate of occurrence

of the events should depend not only on current decisions but also on some aspect of the past history (such as the time elapsed, the cumulative amount of

stock discovered or the cumulative R&D expenditures), which may expedite or delay the occurrence of the event.

REFERENCES

Arrow, K.J. and S. Chang (1980), "Optimal Pricing, Use and Exploration of

Uncertain Natural Resource Stocks" in Pan-Tai Liu (ed.), Dynamic

Optimization and Mathematical Economics , Plenum, New York.

Cropper, M. L. (1976), "Regulating Activities with Catastrophic Environmental

Effects", Journal of Environmental Economics and Managment , Vol. 3, 1-15.

Dasgupta, P. and G.M. Heal (1974) "The Optimal Depletion of Exhaustible

Resources", Review of Economic Studies , Vol. 41, 3-29.

550
Dasgupta, P. and G.M. Heal (1978), Economics of Exhaustible Resources , Cambridge University Press.

Dasgupta, P., G.M. Heal and M. Majumdar (1977), "Resource Depletion and

Research and Development," in M. Intriligator (ed.), Frontiers of

Quantitative Economics , Vol. 3, 483-506.

Dasgupta, P. and J.E. Stiglitz (1976), "Uncertainty and the Rate of Extraction

under Alternative Institutional Arrangements", Technical Report No. 179,

IMSSS, Stanford University.

Deshmukh, S.D. and S.R. Pliska (1980), "Optimal Consumption and Exploration of

Nonrenewable Resources Uncer Uncertainty," Econometrica , Vol.48, 177-200.

Gilbert, R. (1979), Optimal Depletion of an Uncertain Stock", Review of

Economic Studies , Vol 46, 47-57.

Heal, G.M. (1978), "Uncertainty and the Optimal Supply Policy for an Exhaustible Resource", in R.S. Pindyck (ed.) Advances in the Economics of

Energy and Resources , JAI Press.

Hoel, M. (1978), "Resource Extraction when Future Substitute has an Uncertain

Cost", Review of Economic Studies , Vol. 45, 637-644.

Hotelling, H. (1931), "The Economics and Exhaustible Resources", Journal of

Political Economy , Vol. 39, 137-175.

Kamien, M.I. and N.L. Schwartz (1978), "Optimal Exhaustible Resource Depletion

with Endogenous Technical Change", Review of Economic Studies, Vol. 45,

179-196.

Kemp, M.C. (1976), "How to Eat a Cake of Unknown Size" in M.C. Kemp (ed.),

Three Topics in the Theory of International Trade , North Holland.

Kemp., M.C. (1977), "Further Generalizations of the Cake-Eating Problem under

Uncertainty", Theory and Decision , Vol. 8, 363-367.

Long, N.V. (1975), "Resource Extraction under the Uncertainty about Possible

Nationalization", Journal of Economic Theory , Vol. 10, 42-53.

Loury, G.C. (1978), "The Optimum Exploitation of an Unknown Reserve," Review

of Economic Studies , Vol. 45, 621-636.

MacQueen, J.B. (1961), "A Problem in Survival", Annals of Mathematical

Statistics , Vol. 32, 605-609.

MacQueen, J.B. (1964), "A Problem in Making Resources Last," Management

Science , Vol. 11, 341-347.

551
Pindyck, R.S., "The Optimum Exploration and Production of Nonrenewable

Resources," Journal of Political Economy , Vol. 86, 841-862.

Solow,R.M. (1974), "The Economics of Resources or the Resources of Economics"

American Economic Review , Vol. 64, 1-14.

552
The Depletion of U. S. Petroleum Resources:

Econometric Evidence

Dennis Epple and Lars Hansen

Carnegie-Mellon University

Introduction

Econometric models of exhaustible resource supply have tended

to focus on characterizing the near term path of supply of the

resource. Depletion, if it is captured at all, has been impounded

in a time trend. This leads inevitably to unsatisfactory long term

forecasts? no credible estimate of ultimate resource recovery is

available from such models. By contrast, geological resource base

assessments result in estimates of ultimate recovery without a

characterization of the time path by which this ultimate recovery

will be realized.

We have developed an econometric modeling strategy capable of

integrating the problem of estimating ultimate recovery and the

problem of forecasting the time path of recovery. The dependence of

both ultimate recovery and the time path of recovery on economic

variables is captured by the model. Results of applying this methodology to exploration and development of U.S. oil and natural gas

reserves are discussed in this paper.

Overview of Modeling Approach

In this section we provide a brief summary description of the

derivation of our model. More detailed discussion of our modeling

strategy and its application to oil and natural gas supply may be found

in Epple and Hansen (1980a, 1980b).

We view the producer of exhaustible resources as choosing the time

path of exploitation of the resource to maximize the expected after-tax

* net present discounted value of the resource. The cost function for

553
the resource is assumed to depend on both current and cumulative

exploitation. A quadratic specification for this cost function is

adopted to permit formal derivation of the econometric equations from

the producer's objective function. Uncertainty enters this problem

in two ways. Uncertainty about extraction cost is represented by a

random shock to the cost function. Future prices are also assumed

to be uncertain, and the producer is assumed to use past and present

data to forecast future prices. Forecasting equations for prices are

thus a part of the model.

Application of this approach to oil and natural gas exploration

and development is accomplished as follows. New discoveries result

from exploration decisions made by oil and natural gas producers.

Price forecasts and exploration costs affect the exploration 'decision.

The producer is assumed to form expectations of future oil and natural

gas prices based on past and present information including past and

present oil and natural gas prices. Exploration costs are assumed to

depend on current and cumulative discoveries as well as random shocks.

The resource exhaustion feature of the model derives from the appearance

of cumulative discoveries in the exploration cost function which is

expressed as follows:

1.

+

554
In equation (1), Ay and Ay are current oil and natural gas

o, t g , t discoveries while y and y are cumulative discoveries. Hence o,t y g,t

Ay = y - y , . Random components are (i and M- . There

•'Ojt o,t o,t-l oo,t ggjt

are nine parameters in equation (1). The off-diagonal terms ® Qg» n

0g>

and tt permit interaction between oil and gas in the determination of

go

r

exploration costs. This gives rise to the potential for "directionality"

in the exploration process. The producer determines the amount of exploration to undertake to maximize discounted expected after tax profits

using the price forecast and exploration cost equations.

Exploration adds to the inventory of known reservoirs. These

increases in the cumulative amounts discovered feed back via the cost

function in (1) causing an upward shift in the exploration cost function

for subsequent periods. The inventory of known reservoirs serves

as the input to the development process. As with exploration, development decisions are affected by price forecasts and the costs of development. The cost functions for oil and gas reserve additions are:

a) A a I o o o,t,T _o o,t,T o,t,T

2.

10+9 Aa + tt a + ?

~1

o> L >

' A,. A,. -1

Note that current oil reserve additions Aa _ and cumulative oil reserve g,t,r

additions a affect the cost of oil development. Subscript t denotes

g,t,T

the current date while T denotes the date of reservoir discovery. The

random component of oil development cost is § T

. The cost of development

o , t , -

555
per unit of reserve additions is an inverse function of the amount

discovered in a particular year, Ay Thus, the appearance of

o, t

Ay^ ^ in (2) links development cost to the output of the exploration

process. The development cost function for natural gas (2b) has

exactly the same form as for oil. Note too that equations (1) and

(2) are quite similar in form. The difference in the functional

forms of the exploration and development cost expressions is the

absence of interaction terms between oil and gas in the cost functions

for development. The output of the development process is proved

reserves. The amount of proved reserve additions feed back to affect

future development costs via the cumulative component of cost in (2a)

and (2b).

The remainder of the model is relatively mechanical. Production

is presumed to be proportional to proved reserves, and the unit cost

of production is assumed to be constant in real terms.

Parameters in the econometric model arise from two sources. First,

there are parameters in the cost functions (1) and (2). The other

source of parameters are the equation by which producers forecasts future

oil and natural gas prices. In implementation of the model thus far,

we have assumed that producers employ static price expectations. As a

result, no additional parameters are introduced from the price forecasting

equations.

It is useful to discuss the development model first. Maximization

of expected discounted profits leads to the following equation for reserve

additions:

556
3. Aa (h . \

, (1 -p)A

y_T r (i-c) [ P i -ct ;

o a,

The form of the development equations for oil and gas are the same.

Therefore, only a single equation is presented in (3) to avoid the

redundancy of presenting two equations differing only in subscripts.

Parameters i|r , f^, and 0 are functions of the cost function parameters

in (2). The discount factor is P, and tax parameters are T^

fc , T^

and T, . Unit production cost is c and the ratio of production to

d,t p

reserve additions is (1-e).

The exploration model derived from producers optimization problem

is:

4 - Av i

1 - m ] yt -i

+ (1- P) T

xt

(I - ^ *'i )_1

-i -i

T

x,t ~o x,t t

. (q - 0 T ) +

*~ T

A

M< ^x,t

In equation (4), Ay. is a vector, Ay = [Ay , Ay ], as is y . t|r and i|r 71 ^ t t o,t g , t , t ~ ~ l are two-dimensional square matrices of parameters and 0 is a two-dimensional

parameter vector. A (~) beneath the parameter matrices and vectors is used

to distinguish the parameters of the exploration model from the scalar

parameters in the development model, jjr and

J; are functions of the

parameters in equation (1). In this equation, q is the after tax

x, t

discounted present value of revenues per unit discovered net of production

and development costs.

557
The econometric equations are (3) and (4). Equation (3) is

estimated separately for oil and natural gas reserve additions.

The equations for oil and natural gas discoveries in (4) are interdependent and are estimated jointly. The results of estimating these

equations are presented in Epple and Hansen (1980). Work on estimation

of the model is continuing and results available to date are still

somewhat tentative.

Equations (3) and (4) can be used to simulate future time paths

of reserve discovery and development. When a

fc ^ ?

is added to both sides

equation (3), the equation is converted into a linear difference

equation in cumulative reserve additions. Similarly, when y ^ is

added to both sides of (4) , it is converted into a linear difference

equation in cumulative discoveries. By solving these difference

equations and taking the limit as t — we obtain equations for forecasting ultimate resource recovery.

While the obvious use of these equations is to forecast ultimate recovery, they also have a second and perhaps more interesting application.

Estimates of ultimate recovery are available from a variety of sources.

Rather than simply comparing our forecasts to those made by others, we

can formally test whether forecasts made by others are significantly

different from those resulting from our model. To accomplish this, we

impose the restriction that the parameters estimated by our model be

consistent with the ultimate recovery predictions to which comparison

is being made. We do this by setting our expression for ultimate

recovery equal to the estimates of interest.

558
In the case of oil and natural gas, two restrictions result

because there are two resources. Imposition of these restrictions

reduces by two the number of free parameters to be estimated. By

estimating our model with and without the resource base constraints,

we obtain separate likelihood function values. A likelihood ratio test

can then be employed to determine whether the constraints significantly

reduce the quality of fit of the model.

Results

The procedure outlined above has been applied using the resource

base estimates provided by the U.S. Geological Survey. U.S. Geological

Survey Circular #725 contains resource base estimates for the United

States for 1974. We have estimated our model subject to the restriction

that ultimate recovery be consistent with mean values estimated by the

USGS. In addition, we consider a high estimate in which the mean USGS

values are doubled and a low estimate equal to one half of the mean USGS

estimates.

Resulting likelihood and chi-square values are presented in Table 1.

Both the high and mean estimates are rejected at a high level of

significance. The low oil-low gas case is not rejected at the 5 percent

level but is rejected at the 10 percent level. The final result in the

table tests the low oil-mean gas case. This proves to yield a likelihood

function value quite close to the unrestricted case.

These results suggest that the low oil and mean natural gas

values of the U.S. Geological Survey are quite close to those estimated

by our econometric model. We emphasize that these results should be

559
TABLE 1

TESTS OF RESOURCE BASE RESTRICTIONS

FOR CRUDE OIL AND NATURAL GAS IN THE U.S.

Resource Base Assumption Likelihood Function Value Chi-Square Value

Unrestricted .18

High Oil, High Gas -11.49 23.34

Mean Oil, Mean Gas -7.02 14.40

Low Oil, Low Gas -2.24 4.85

Low Oil, Mean Gas -0.06 .48

High is double the mean USGS value.

Low is half the mean USGS value.

The x statistic with two degrees of freedom at the .05 significance

level has the following percentile values:

Percentile Value

10 4.61

5 5.99

1 9.21

.5 10.60

560
considered somewhat tentative as we are continuing work on estimation

of our model. However, the results demonstrate that our approach is

operational. We believe that it provides a promising avenue for

integrating econometric analyses and geological resource bas estimation.

References

Epple, Dennis and Lars Peter Hansen, "An Econometric Framework for

Modeling Exhaustible Resource Supply," in The Economics of

Exploration for Energy Resources (J. Ramsey, ed.), forthcoming,

1980a.

, "An Econometric Model of U.S. Petroleum

Supply with Optimal Endogenous Depletion", Carnegie-Mellon

University, Working Paper, September 1980b.

DISCUSSION

DR. KAUFMAN: Dennis, in particular with respect to gas, the

recent change in world price structure and following change on the

domestic market has instigated a rather enormous burst of drilling

activity to leak gas, because of a rent window that this affords

within our tax structure, so you have enormous rates of drilling in

the Tuscalossa trend, in the overthrust belt, and elsewhere, which

looks as if it's going to discovery very, very significant amount of

gas that will be brought on line. There are typical sections which

have 37 trillion cubic feet in place, reminding that you consume 20

trillion cubic feet a year, currently — 18 to 20.

561
Where does that appear in the context of this kind of model? One

would expect that what's going to happen is you'll get bumps or peaks as

a result of that impetus, and then if the time rate of production of gas

how do you get that into the model?

It's certainly not this kind of phenomenon, which is an interaction

of economics and geology. Certainly it's not in the Geological Survey

estimates. Circular 725 came out circa 1975-1976.

MR. EPPLE: In our model the amounts of oil and natural gas

ultimately recovered depend upon their prices. We are thus estimating

equations which can be used to generate schedules of oil and natural

gas recovery as functions of prices. When we impose restrictions during

estimation, those restrictions require that the price-ultimate recovery

schedules go through specified points. For example, in one case, we

impose the U.S. Geological Survey mean estimates of oil and gas

recovery as restrictions during estimation. Those restrictions assure

that our model will predict mean oil and gas recovery as specified by

the USGS at the prices assumed by the USGS. The USGS estimates are

based on prices prevailing in 1974. Hence, for this particular case,

our price-ultimate recovery schedules yield mean USGS ultimate recovery

estimates at 1974 prices. If higher prices are substituted into our

model, then ultimate recovery values predicted by our model will be

higher as well.

Our model does not simply predict ultimate recovery. It also

predicts the time rate of discovery of new reservoirs, the. time rate

of development of proved reserves in those reservoirs, and the rate of

production from proved reserves. If a jump in price occurs, then a

bulge in discoveries will be predicted by the model. That bulge will

work its way through the development and production components of the

model in subsequent years.

562
In my presentation, I have emphasized the ultimate recovery predictions of the model. However, our model provides an integrated

treatment of the time path of recovery and the problem of predicting

ultimate recovery. Both the time path of recovery and ultimate recovery

depend on prices. The link between geology and economics that we

attempt to make is, as I've indicated above, the use of USGS estimates

in fixing particular points on the ultimate recovery schedule generated

by our model.

-MR. COMER: I'm Dan Comer from EPA. I'd like to suggest that

you look at the financing, as well as the other scenarios. And why

don't you get bigger bumps?

MR. EPPLE: Well, I'm not quite sure in what sense we're missing

them. I've shown you what the historical data are that we used for

estimation. The model has been fitted to that data, and it fits quite

well the large bumps in the historical senses.

MR. COMER: You alluded to a steady state solution for the model.

MR. EPPLE: Ultimate recovery predictions from our model depend on

the values to which ultimately converge as the limit is taken with

respect to time. Hence, the transient characteristics of the model do

not matter for purposes of determining ultimate recovery. The time

path of recovery is, of course, dependent on the actual path of prices.

Simulations of the model to generate paths of discovery, reserve

development, and production, are based on specific price paths, and

those simulations do reflect any transient responses that result from

price changes.

563
OIL AND GAS FINDING RATES IN PROJECTION OF

FUTURE PRODUCTION

1

W. L. Fisher

Future levels of production of crude oil, natural gas,

and natural gas liquids are critical elements in domestic

energy supply forecasts. These domestically produced commodities constitute more than 50 percent of our total energy

supply and some 65 percent of our total domestic production

of energy. The U.S. currently produces about 19.4 mmboed of

oil, gas, and NGL.

Oil production amounts to 8.5 mmbd, or 44 percent of the

total; NGL, 1.6 mmbd, or 8 percent; and natural gas, 19.7 TCF,

or 48 percent. This production comes from a year-end, proven

reserve base of 27.1 billion barrels of oil and 195 TCF of

natural gas. At the current level of contribution, slight

percentage changes in future levels of production translate

into significant supply volumes. Production of these commodities is so much a part of our total supply that a difference of one percentage point in average annual decline

rate amounts to 2.0 mmboed by' 1990, or a total of some 4

billion barrels of oil and oil equivalent.

Yet despite the critical importance of future production

levels, there is a significant range in forecasted production

over the next decade. If one surveys some 14 separate projections made over the past 2 years, including 7 projections

made by oil companies and 7 made by government, academic,

and other non-industry entities, one sees the following range

in 1990 levels of projected production: Crude oil and liquid

levels range from 7.2 to 11.5 mmbd, or from 29 percent less

than last year to 14 percent more. Average of the forecasts

was 9.6 mmbd for 1990. The range of estimates, as well as

averages , was exactly the same for industry and non-industry

projections

,

The ranges in natural gas forecasted production by 1990

are 14.3 to 17.9 TCF, or a decline of 9 to 27 percent from

last year's production; average of the various forecasts was

16.3 TCF. Industry forecasts ranged from 14.3 to 17.6 TCF,

with an average of 15,9 TCF; non-industry forecasts were 16.3

to 17.9 TCF, with an average of 16.7. The average of the variou:

oil and liquid production forecasts indicates an average annual

Director, Bureau of Economic Geology, The University of Texa.s

at Austin.

564
decline through 1990 of about 0.5 percent; this compares with

the actual average annual decline from 1973 through 1979 of

1.8 percent, or 3.7 percent if North Slope Alaska production

is excluded. The average annual decline of natural gas production, as shown by the average of the several forecasts, is

1.5 percent; this compares with the 1977-79 average annual

decline of 2.3 percent.

One may note that the range between low and high estimates for oil and liquids is a rather wide 6 0 percent. The

range in forecasted natural gas production is significantly

tighter, about 25 percent.

Nearly all the forecasts assume continued increases in

total drilling activity with an average annual increase (AAI)

of 6 to 7 percent through the 1980 's; most assume pricing and

taxing policy to be essentially the same as that now in place;

and nearly all assume that North Slope Alaska gas production

will be on stream in 1990. But beyond these assumptions,

variations in forecasts hinge on three main variables: (1)

degree of optimism relative to potential major discoveries

in the frontier areas, notably onshore and offshore Alaska,

as well as availability of the lands to exploration and development and necessary lead times; (2) assumptions relative

to unconventional oil and gas production—be it synthetics,

tertiary recovery, or unconventional infill drilling; and

(3) assumptions as to future rate of finding and its behavior.

Variations in projected unconventional recovery, including synthetics, were not very great nor significant in the

forecasts. The higher forecasts, especially for oil production by 1990, generally assume significant additional production from frontier areas. If the volumes based on these

assumptions are backed out, the spread in range of oil forecasts becomes about 30 percent, approximately that shown for

ranges in natural gas production. Accordingly, one may infer

that the range in forecasts from low to high of 25 to 30 percent is largely attributable to assumptions relative to oil

and gas finding rates over the next decade.

With more than 50 years of statistical record of finding

in most of the U.S. non-frontier basins, and with a reasonably

sophisticated understanding of the geology and hydrocarbon

occurrence of these basins, one might assume a bit more precision in our ability to calculate reserve additions as a

function of the level of future drilling. Unfortunately,

this appears not to be the case, and although several efforts

in calculating and projecting oil and gas finding rates have

been made, we can certainly say that no consistent methodology

has been obtained.

565
Variations mainly include: (1) how finding rate is calculated, that is, what kind of drilling should be related to what kind

of reserve additions; (2) how the calculated values are interpreted, such as, are changes related to changes in the resource

base or are they a function of changes in drilling mix and

exploratory targets; and (3) finally, of course, how finding

rates are projected into the future.

Basically, finding rate is nothing more than hydrocarbons

discovered as a function of drilling. But what drilling and

what reserves added? Drilling, as classed by The American

Association of Petroleum Geologists (AAPG), consists of exploratory drilling, including highest risk drilling new field

wildcats (NFW) along with outposts, new-pool wildcats, deeppool tests, and shallow-pool tests, and developmental drilling.

Additional minor classes of drilling include service wells and

stratigraphic tests. The other half of the equation: reserve

additions are subdivided into revisions, extensions, new field

discoveries, and new reservoir discoveries in old fields.

A common simple calculation of finding rate involves dividing footage into volumes of oil and gas added as reserves.

In some cases, this involves dividing total footage of all

drilling into total reserve additions, including revisions,

extensions, and discoveries. In other cases, barrels per foot

have been calculated, leaving out revisions. Other calculations have considered total annual reserve additions, with or

without revisions, as a function of total annual exploratory

and/or new field wildcats drilling. Still other calculations

consider only new field discoveries as a function of new field

wildcats drilling. Obviously any combination of drilling and

reserve additions will give a statistical value expressed in

barrels per foot, and when plotted give historical trends in

the values. It is important to relate appropriate classes of

reserve additions to appropriate classes of drilling, to

appreciate growth factors in new discoveries and the time lag

in additions as a function of development drilling.

What is obvious in even casual observation and calculations

is that decrease in discovery per unit of drilling began as

early as the early 1950 's, was subsequently followed by a decline in drilling in the late 1950' s, followed by a decline in

reserve additions, then a decline in proven reserves, and in

the early 1970's, a decline in production.

Since about 1950, drilling additions of oil have been

steadily declining (Fig. 1) ; this trend has been due to both

declines in drilling and declines in reserve additions per

increment of drilling. Only in the past 7 years, with a

steady upsurge in drilling, have total drilling additions

begun to level off. One component of reserve additions —that

attributable directly to wildcat drilling—has remained relatively stable since the early 1950's (Fig. 2). Reserve additions from other exploratory drilling stayed reasonably stable

566
from the early 1950' s to the early 1970 »s. Since 1972, additions from that component of drilling, as measured on a per

well or per foot basis, have declined sharply. Additions as

a direct function of development drilling have likewise declined, and, although for years much higher than for wildcat

drilling, have now dropped below new field wildcat drilling

on a per well or per foot basis. Oil revisions have played a

changing historical role in contribution to reserve additions

(Fig. 1). From the late 1940's until about 1960, revisions

represented about one-third of total reserve additions. Since

1960, oil revisions have contributed between 50 and. 6 5 percent

of total additions. In the early 1960's, significant increases

in revisions, due in my judgment to active development in the

offshore Gulf of Mexico and certain secondary recovery projects

on land, actually raised total additions. Since the middle

1960's, revisions have been in decline and in particularly

sharp decline since 1970.

Associated gas has behaved, as expected, in much the

same fashion as oil. The situation with non-associated gas

has been somewhat different (Fig. 3) . Sharp declines in

total additions as well as exploratory additions occurred in

the late 1960's. Since then exploratory additions have remained relatively stable, with sharply increased drilling

since 1972 generally sufficient to offset declines on a per

well or per foot basis. Development drilling additions have

declined, and revisions have fluctuated widely.

If one calculates new field discoveries of total hydrocarbons as a function of new field wildcats, one sees a relatively stable rate of finding over the past 15 to 20 years

(Fig. 4) . By contrast, if one considers non-wildcat drilling

and additions other than new discoveries, one sees a steady

deterioration in rate of finding.

With increased prices for domestic oil and gas that began

in the early 1970' s, there has been a strong upsurge in total

drilling effort. Nationwide that increase has been greater

for development and non-wildcat drilling than for wildcat

drilling. This has led some to argue that the reduced finding rate experienced during most of this decade is attributable

to the relatively greater increase in lower yielding, but less

risky, non-wildcat drilling, and further that a significant

number of previously known small prospects, uneconomic at

lower prices, have been appropriate targets, at the expense

of true high-risk wildcat drilling. Certainly the increased

success ratio of both oil and gas wells in all areas of

drilling, in the face of declining finding rates, would support this point. But do the shifts tell the whole story?

The crux of the situation is this: (1) Are we facing a

lower quality resource base and will recent trends in finding

persist into the future?, or (2) Are recent trends anomalously

low, and if used as a basis for formal projecting, do they

understate future reserve additions? How one interprets and

judges these data becomes significant in projecting future oil

and gas additions as a function of drilling.

567
While the recent shift in drilling mix has had some effect

on overall finding rate, I doubt that it has been that significant. For one, the rate of finding for non-wildcat drilling,

while declining rapidly, has been on the average only about 1

barrel per foot lower than wildcat drilling over the past few

years. Further, in areas of the country where intrastate

demand has been high and where intrastate prices for gas were

at market rates during the 1970' s, the percentage of wildcat

drilling of total drilling has increased over a comparable

period of time preceding increased prices. Previously known

small prospects may have indeed been drilled, but these were

wildcats and previously untested nonetheless.

Statistics on average field size are difficult to develop

for fields discovered over the past 6 years. But, longer term

trends, established long before the price increases of the

early 1970' s, do indicate that the average size of fields and

drillable prospects is decreasing. Accordingly, the quality

of the resource base is declining as measured by rate of

finding, even though the total volume of estimated and

discovered oil and gas is still substantial.

Another aspect pertinent to finding rate calculation and

interpretation is that of reserves growth, that is, the ultimate reserves of a field compared with reserves based on initial

discovery. A number of statistical calculations have been made,

and while the calculated volumes of reserves growth vary, these

data indicate that the growth potential of larger fields,

through subsequent non-wildcat drilling, was , and is, significantly greater than for smaller fields, and that the growth

factor for fields older than 48 years (i.e., larger fields)

is greater than for more recent smaller fields.

A recent analysis by Professor John Haun, Colorado School

of Mines, is worth note. Professor Haun made an extensive

calculation of reserves growth, calculating ultimate growth of

fields discovered this century. He then calculated rate of

finding by crediting calculated ultimate reserve to discovery

wildcat drilling. His plot of finding rates for oil, gas, and

total hydrocarbon shows steady declines since the late 1940 's

(Figs. 5-10). As calculated, total ultimate barrels of oil and

oil equivalent per foot of wildcat drilling steadily declined

from 352 barrels per foot in the late 1940 's to 53 barrels per

foot in the late 1970' s. His projections put finding rate of

23.5 barrels per foot in 1990. His method of calculation tends

to rule out such effects as changes in drilling mix in that all

ultimate reserve is credited to original discovery.

Conclusions

1. The business of oil and gas projection is something

less than an exact science even when reduced to the

statistical components.

568
2. Variation in assumption of future rates of finding

has significant impact on projected volumes of

reserve additions and production per unit volume of

drilling.

3. Nevertheless, in my judgment, the facts are sufficient to indicate that recent rates of finding are

valid for future projection in that they are consistent with long-term declines, basically the

result of decrease in size of prospect targets, and

a decrease in growth potential through subsequent

drilling. This is shown basically by the fact that

while wildcat finding rate has remained stable, longterm finding rates of non-wildcat drilling are declining sharply.

4. If these trends in finding of different kinds of drilling are valid and relate primarily to a universe of

smaller prospects and fields, we should pay particular

attention to prospect- and field-sized populations.

The distribution of size could have significant bearing on the behavior of finding rates through time.

Decline through time may not be a continuous function,

but rather periods of relatively stable, but progressively lower plateaus. This could be a positive

aspect to the overall decline in oil and gas finding

in mature basins.

References

Comptroller General (1979) Analysis of Current Trends in

U.S. Petroleum and Natural Gas Production: U.S.

General Accounting Office, EMD-80-24, 56 p.

Haun, J.D. (1979) Future of Petroleum Exploration in United

States: Manuscript, 13 p. , with Tables and Figures.

Various Statistical Sources: American Association of Petroleum

Geologists, American Gas Association, American Petroleum

Institute, and Energy Information Agency, U.S. Department of Energy.

569
DISCUSSION

DR. GORDON EVERETT: One of the things I wanted to

ask you about was the fact that you concentrated on the statistics that Haun had on a per foot basis. But if you take a look at some of those finding rates on a per well basis, because we're tackling the situation of having to continually

look at deeper and deeper strata; therefore, that footage has

got to increase on new finds. So you've got a factor in this

per footage basis that tends to give some of these curves a somewhat increased downward trend versus plotting on the per

well basis, and as an example, for instance, when we take a look at the drilling in the west side of the Williston Basin,

several years ago, at 8,000 feet, the success ratio per well

was fairly low—it was a fairly mature horizon, and we were

largely drilling on the flanks of known fields.

When that shifted to 11,000 feet the first year, it was

a 100-percent success ratio for wildcats, because it was a different horizon that hadn't been explored with a successful

exploration model we had a high number of hits.

So I wonder if perhaps we shouldn't be taking a look at

some of these things on a per well effort basis; rather than

a footage basis, because of the effect that this footage basis

is going to have on forcing this thing down continually.

DR. FISHER: Gordon, I think that is a very good

point. At this point the trends are quite similar irrespective of whether plotted on a per well or per foot basis.

I suspect though, particularly with the stimulus for

deeper drilling, which we are seeing in a number of areas for

gas, that there will be over the next 10 years more disparity

in the trends on a per foot and a per well basis than there

has been up to now.

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580
ISSDES IN FORECASTING CONVENTIONAL OIL AND GAS PRODUCTION

RICHARD P. O'NEILL

ENERGY INFORMATION R%MIHISTR ATION

DEPARTMENT OF EHERGY

"AN IDEALIST IS ONE WHO ON NOTICING THAT A ROSE SMELLS

BETTER THAN CABBAGE CONCLUDES THAT IT WILL MAKE BETTER

SOUP." - H.L. HENCKEH

1. INTRODUCTION

In the United States, petroleum (crude oil and natural gas)

is being produced and used at a faster rate than it is being

found. Since 1970, proven petroleum reserves, which include

crude oil, natural gas, and liguids, have been consulted at

an annual rate 4 percent higher than the rate at which thev

have been expanded. The most important guestion is: Will

this trend continue, and if not, when and how will it

change?

This paper addresses the issues in and approaches to

forecasting conventional supply in the onshore Lower-48

states. These projections are critical since Lower-48,

production is the "pivot point" for Government policy. After

conventional Lower-48 production, the remaining supply from

imports, unconventional sources, and frontier areas is

strongly affected by Government policy. Further, the issues

and approach to Lower-*»8 conventional production are

basically different from those regarding other sources.

2. THE EXPLORITION-DISCOVERY-PRODUCTION PROCESS

Formation, Migration, and Entrapment of Petroleum

No one knows for sure how petroleum is originally formed.

The petroleum formation process, like other occurrences of

eons ago, rests on theory. Basically, two different

theories attempt to explain the origins of crude oil and

natural gas: the inorganic theory and the organic theory.

The inorganic theory — not widely accepted outside the

Soviet Union — holds that methane was inorganically formed

deep in the Earth , s crust, migrated upward, and accumulated

in traps (reservoirs) . The organic theory, for which a preponderance of evidence exists, is that living organisms

were the starting point in petroleum's formation. As these

organisms died, their remains were carried to and deposited

581
in the sediment beds of ancient rivers and seas. Gradually

over lonq periods of time and tinder appropriate temperature

and pressure conditions, bacterial, chemical, and physical

processes transformed these renains into petroleum (for more

detail, see [661, chapter 11).

Rarely, however, is the concentration of petroleum in the

source beds of rivers and seas sufficient for commercial

viability. Large accumulations are. believed to be the result

of migration. Since petroleum is insoluble and not as dense

as water, gravity causes it to partially separate from water

and draws it from the source rocks through permeable

sedimentary rocks toward the Earth's surface. This migration

ends when the petroleum encounters impermeable rock, forming

a trap, or when the petroleum reaches the surface, at which

point the lighter fractions evaporate and the heavier

fractions form a natural tar desposit called a seep.

There are two distinct types of geological traps, although

most traps are a combination of the two. The first type,

structural traps, are formed by abrupt changes in geology,

caused by faulting, the intrusion of salt domes, or wore

gradual deformations, such as anticlines. The second type,

stratigraphic traps, on the other hand, result from more

subtle changes in rock permeability. In summary, the four

necessary factors for commercial petroleum accumulation are:

(1) Source sediments containing once living organisms, (2)

Appropriate subsurface environaental conditions, (3)

Migration opportunity, and (*l) Existence of a trap formed

prior to the migration.

Search for Petroleum Prospects

That petroleum occurs at surface seeps has been known since

early recorded history. Petroleum seeps were often an

important part of the religious, medical, and economic life

of societies in many parts of the world. In the United

States, E. I. Drake drilled the first intentional oil well

in 1859 (the Chinese had been drilling them for centuries)

near an oil seep, discovering an oil bearing anticline (a

structural trap) at Oil Creek, Pa. He was offered $20 per

barrel (in 1859 dollars)

For many years thereafter, decisions to drill were based on

intuition and even dowsing rods were used. Eventually,

surface geology was studied to assess subsurface potential.

Geophysical methods — indirect measurements of subsurface

rocks — were introduced around 1920. Today sophisticated

eguipment, including satellites and high speed conputers,

are used to gather and process huge quantities of

information to aid exploration. These methods demand high

582
levels of technical skills and substantial financial

investment.

Even with all this highly developed exploration technology,

two classical problems remain. The first is the

identification of promising geological conditions, and the

second is the determination of the presence of petroleum in

a prospective trap. The detection of stratigraphic traps is

especially difficult because there are only subtle changes

in the subsurface geology. Moreover, the presence of a trap

is only one of four necessary conditions for the existence

of a petroleum reservoir. Drilling is the only conclusive

test to determine if petroleum is available underground in

commercial guantities. Once a prospect is identified the

right to drill must be obtained through a lease.

The Leasing Process

The leasing process, beyond the standard legal rituals, is

probably the facet of the mineral extraction industry that

is least understood by energy analysts. Obtaining the

rights to explore and drill for oil and gas is the job of a landman. This activity has developed to the point that a professional organization, the American Association of

Petroleum Landmen, has been formed.

Since reservoirs and fields often extend over large areas

with many landowners involved, a firm usually attempts to

acguire a "position" by leasing as much land as possible in

a specific area. A typical private lease contract specifies

bonus and rental payments, reguirements for exploration and

production activity, and a royalty payment, if commercial

production is established.

In "hot" areas (where activity is brisk) , bonus and rental

payments usually rise dramatically — an indication that

some of the "economic rent" is captured by the landowner.

Otherwise, such fees are usually nominal. A standard royalty

payment is one-eighth of the production, but can be

negotiated. The contractual reguirements concern the term of

lease, which is automatically extended as long as the

property is producing, and the obligation to drill and

continue drilling to maintain the lease. In leases

contracted recently, drilling usually must commence within a year and continue, with periods of inactivity of less than a year, until a producing well is found or the lease expires.

The O.S. Government has its own system of leasing onshore

Federal lands. If the property is on a "known geologic

structure (KGS)" it is leased by sealed bids, just as with

offshore areas. If it is not on a KGS, only a $10 reguest to

583
explore is filed, and when 2 or sore requests are filed, a lottery is held to grant rights. (This process has been

suspended recently because of suspected irregularities.)

These leases are harder for oil and gas producers to acquire

mostly because absentee leaseholders (who also do not live

near the leased land) hold a large portion of the property

leased in this manner. The United States Geological Survey

(USGS) estimates that approximately 50 percent of the

undiscovered petroleum remaining in the United States is on

government land.

Exploration and Development

after surface exploration and lease acquisition, a well may

be drilled. The drill bit resolves the most uncertainty in

the process of exploration, discovery, and production. If

drilling finds no petroleum, the well and the formation is

declared dry. (Petroleum may have been present at one time,

but it may have migrated through the area before the

structural trapping conditions were formed.) If petroleum is

discovered, commercial viability must be determined which

involves determination of product guality and the capacity

of the reservoir to produce. If the petroleum is not

considered commercially producible, the well also is

declared dry. Otherwise, , it is declared successful.

Hells are classified initially according to the intentions

of the driller into one of several categories (see

Appendices B and C) . Most risky of these is the new field

wildcat, which historically has had about a 10 percent

success rate. & field is a geographically distinct area

consisting of one or more reservoirs, each characterized by

its own pressure system. Next in level of risk are

exploratory wells for new reservoirs and boundary extensions

to existing reservoirs in already discovered fields. These

have an historical success rate of about 25 percent. The

last category is development wells; these are drilled within

the existing boundaries of the reservoir, and have a success

rate of more than 90 percent.

Development and production

Once a new field has been discovered, development and

production operations begin. Development wells are drilled

and there is additional exploration to confirm and enlarge

the proved area and discover new pools. Development wells

(using the Lahee definition; see Appendices B and C)

"exploit or develop a hydrocarbon accumulation discovered by

previous drilling,TM and are successful more than 90 percent

of the time. Production from newly discovered fields is

often shut-in (i.e., not producing) initally, waiting for

584
the installation of the equipment and facilities necessary

for continuous production, including storage facilities and

gathering pipelines. Initially, some oil wells produce

because of nataral forces (for example, gas pressure and

water drive) in the reservoir. However, about 90 percent of

producing oil wells eventually reguire artificial lift

supplied by pumping. Hsually less than 25 percent of the oil

in the reservoir can be recovered in this primary stage. By

contrast, gas wells have primary recovery rates of 60 to 80

percent or higher and do not require application of

artificial production methods.

Secondary recovery techniques, applicable only to oil

reservoirs, augment the drive mechanism of the reservoir by

iniecting water or reinjecting natural gas. About 460

billion barrels of oil have been discovered in the ffnited

States to date, but only about 33 percent is currently

recoverable by primary and secondary methods. Tertiary, or

enhanced, recovery processes seek to overcome natural forcas

trapping the remaining oil. These techniques include steam

injection, in situ combustion, gas injection (other than

natural gas), and surfactant/polymer and caustic flooding.

It is estimated that between 8 billion and 50 billion

barrels of the remaining 310 billion barrels of discovered

oil could be recovered with tertiary techniques.

Regulation and Taxes

Regulation and taxes in the oil and gas industry have a long

history dating from the early 1900* s. Since the turn of the

century, pipeline operations, imports, and prices have been

regulated by the Federal Government. Since then. States have

imposed conservation regulations and severance taxes on

production, and both State and Federal Governments have

imposed excise taxes on petroleum products.

Crude Oil Regulations, Price Controls, and the

Windfall Profit Tax

When government originally intervened in oil and gas

markets, it was to the benefit of the producer. Eventually,

the regulatory environment worked to reduce returns to

producers. Since 1906, oil pipelines have been subject to

regulation. Passage of the depletion allowance, and

well-spacing and prorationing regulations in the 1920»s and

the Connally Hot Oil Act of 1935, which nationalized

prorationing, gave producers higher prices and lower costs.

In 1959, the Mandatory Oil Imports Program limited imports.

However, in the late 1960*s and early 1970*s, the regulation

and tax milieu that had been beneficial to the producers

started to turn against them. Price controls were

585
established and fees were imposed on imports. Since the

early 1970* s oil prices have been controlled under the

Economic Stabilization Act, the Emergency Petroleum

allocation Act of 1973, and the Energy Policy and

Conservation Act (EPCA) of t975.

In September 1973, the Cost of Living Council (CLC)

established a two-tiered pricing system. Old oil was price

controlled and new oil was not. The essential distinction

between old oil and new oil was based on a base production

control level (BPCL) for a "property". Onder CLC*s

definition of "property," oil discovered on a producing

property was considered old oil if the BPCL was not being

maintained. Such old oil was released to market prices on a barrel- for-barrel basis with new oil produced. This created

an incentive greater than the market price (i.e., adding the

difference between the old oil price and the market) for new

oil up to the BPCL. Once the base level was reached, the

incentive price was the market price alone. Stripper oil

(oil from a property averaging 10 barrels or less per well

per day) was also raised to the market price. From 1973 to

1975, numerous adjustments were made in the regulations (for

more details, see T83")).

In 1976, the property and base level definition changed in a significant way and a three-tier system was created. The

definition of property was changed, allowing for more newly

discovered oil to be classified in the middle ("upper")

tier. For the remainder of the 1970*s, many adjustments

continued to be made. When price controls expired, there

were at least 11 categories of oil. Price controls were

followed by the Windfall Profit Tax.

The Windfall Profit Tax (WPT) of 1980 allows crude oil to be

sold at the market price, but taxes the producer on a portion of the difference between the market price and a base price. The first two tiers under controls constitute

Tier 1 of the WPT. Tier 2 is stripper oil and oil from

national petroleum reserves. Tier 3 is newly discovered,

heavy, and incremental tertiary oil. The tax varies for each

tier (30 to 70 percent) and gives a lower rate to oil

companies classified as "independents" in Tiers 1 and 2.

Mso, there is a provision that one may not be taxed on more

than 90 percent of his profits. The tax phases out when the

O.S. Treasury has collected $227.3 billion or in December

19 87, whichever comes latest, but no later than December

1990. 1

Natural Gas Price fiegulations

Federal regulations for natural gas were initiated for the

586
benefit of the producers. Federal regulation of interstate

natural gas pipelines began with the Natural Gas Act of

19 38. In 1954, the United States Supreme Court decision in

P hillips vs . Wisconsin created wellhead price controls. This

decision immediately created separate markets in each

producing state for intrastate ana interstate gas. In the

1970»s, the interstate system had low wellhead prices and

supply shortages, while the intrastate system had almost the

opposite higher market clearing prices and no shortages.

After several regulatory adjustments, the natural Gas Policy

Act (HGPA) of 1978 was passed as the legislative response to

the problem.

The NGPA created no fewer than 12 price ceilings for the

wellhead price of natural gas. These categories include new

(on and offshore) gas, gas dedicated to interstate commerce

before 1978, gas under existing interstate contracts, gas

under rollovers of existing contracts, high cost gas,

stripper gas, gas dedicated to intrastate commerce, Prudhoe

Bay area (north Alaska) gas and miscellaneous gas categories

(for more details see T29]).

3. HODFXIHG THE FUTtTCE

Objectives in Modeling the Future

The approach to modeling the future is highly dependent on

the purpose of modeling. Since very few analysis groups can

afford the luxury of maintaining more than one modeling

system, a choice must be made. The choice should be based on

the main purpose of the analysis; for example, forecast

accuracy, the ability to perform "what if" analysis, or

general understanding.

Forecast accuracy may be defined or measured in several

ways. One way is the mean sguare error, a retrospective

statistic, composed of the sum of the sguared deviations of

the forecasted values from the actual historical values. A

second way is to count how often the actual values fall into

some constructed confidence band around the- forecast,

rewarding the capture of the actual value. The pitfall in

the second statistic is understanding the penalty for

constructing intervals that are too large. One way of

identifying this type of forecasting is when the independent

variable is time. The examples of this type of forecasting

are Box-Jenkins time series forecasting and other

extrapolations based on time. The theory behind these

methods is analogous to Rewton»s first lair of motion: Things

in motion tend to stay in motion. That is, large inertial

forces exist in the system that will not deter it from its

inertially ordained future. These methods often perform

587
reasonably well in short-term forecasting where seasonal and

secular trends must be sorted out. Sensitivity or "what if"

analysis is not possible.

Models that have a theoretical premise capable of doing

"what if" analysis constitute a second class of models.

Besides giving forecasts based on some theoretical

foundation, these models are often used to examine first

differences in the forecast. In cases where there appears to

be a systematic bias, such models can perform poorly at

absolute forecasting and do well at examining differences.

Econometric models often fall into this class. This approach

is closer to Newton* s second law of motion: Each action has

an egual and opposite reaction. This approach may sacrifice

absolute accuracy to obtain levers with which to analyze the

effects of certain "driving" variables. In oil and gas

forecasting these variables are typically prices, costs, rig

availability and funds availability.

A vaguer but often more important objective is modeling for

understanding. The hard measures of accuracy almost

disappear. An example of this approach is exploratory data

analysis where the objective is to play in a statistical

"sandbox" until the analyst is satisfied with some

statistical relationship that improves his or her

understanding or insight.

In most situations the luxury of having all of the above

systems is not feasible. The last system should always be

available. The choice is usually between the first and

second. The rigor that is produced by forcing the analyst to

produce consistent numbers cannot be overemphasized. Numbers

can return to haunt an analyst, but numbers force the

analyst to look deeper, examine definitions, and understand

the input data. Also, reproducibility allows for future

improvement of the process.

Theories of Behavior and the

Politics of Forecasting

Forecasting by its very nature involves many assumptions and

simplifications. It encompasses everything from

prognostication by informed and less well-informed analysts

to the output of complicated hierarchical modeling systems.

Much debate has been devoted to the minimum threshold of

"tests" the model must pass before it can be used for

forecasting. Creating an arbitrary absolute threshold does

not address the issue properly. Forecasts will be produced.

The issue is whether one method improves on the other and

whether the addition of another forecast illuminates the

discussion about the future. Further, it is difficult to

588
determine where the modeler stops and the model starts. In

most analyses they are inseparable. Modelers and the

sponsor should be part of the model assessment process.

Perhaps the most important questions that must be addressed

in buildinq a model are: What are the critical aspects of

the problems being modeled and how should they be modeled?

Several theories are presented below that demonstrate

different points of view about what is or is not important

in modeling the discovery/production process. There is a high correlation between the background of the group and

what the group considers important.

Geologists tend to focus on remaining resources and finding

rates. Finding rates are measured in terms of

resource-in- place or reserves found as a function of

drilling, usually wells or footage. Geologists prefer to

work with new field discoveries and new field wildcat wells.

Many believe that sheer system inertia will determine the

production level for about 10 to 15 years. Also, most prefer

to work on a disaggregate basis.

Economists, on the other extreme, are more comfortable

working at more aggregate abstract levels. They believe that

profitability is the determining factor in any market, and

for finite resources, they add some concepts about eventual

exhaustion or "backstop" technology. Economists also tend to

be concerned about the industry structure, both vertical and

horizontal. Bankers and financial analysts, a special breed

of economist, place a strong emphasis on investment or cash

flow as a determinant of production. They usually give less

attention to the technological, since the capital markets

and cash flow are considered to be the critical aspects.

Many oil and gas companies believed that if they were just

"left alone," they would supply the United States with

energy. "Left alone" must be gualified. They would like to

be free of what they view as poorly devised and implemented

environmental regulations and have more government land

available for exploration. additionally, some tax incentives

and subsidies for risky capital intensive ventures are

considered desirable. The independent (non-integrated)

operators are often behavorially characterized as "macho,"

"high rollers," or brinksmen who love high risk ventures and

pay less attention than the majors to scientific information

and economic analysis. By definition, they must dispose of

the oil and gas they find. On the other hand, the drilling

fund investor is said to invest for tax shelters and

cocktail conversation.

Policymakers believe that rules can be written to change the

589
behavior of the agents in the process and protect the public

interest. The general theme of policy as contained in the

HPT and NGPA is to extract all the "economic rent" above

some nominal level and create income transfers.

Nevertheless, the public's collective characterization of

the petroleum industry has been one of distrust of the

majors.

None of these characterizations are necessarily right or

vrong. The question is which are more important to model?

A Simple Hodel

The next step is to build a simple conceptual model of the

discovery/production process. The model ia Figure 1 contains

several parts. (The annotation on the arcs refers to the

organization that collects information on the process.) The

figure will be used as a scheme to organize the presentation

that follows. The next step in the modeling process is to

examine the data.

H. THE DATA

There are basically four sources of petroleum data: The

Federal Government, the State governments, the petroleum

industry, and private data collection firms. Within the

Federal Government, the O.S. Geological Survey (TISGS) , the

Energy Information Administration (EI A) , and the Bureau of

the Census collect most of the available data. Each State

has its own unigue system to collect information mainly for

taxation and "conservation" purposes. Within the industry,

the two principal sources of data are the American Petroleum

Institute (API) and the American Gas Association (AG A) . Both

are industry trade groups. In the remaining group, there

are a number of private firms - for example, the Petroleum

Data System of North America (PDS) and the Petroleum

Information Corporation (PI) (both are partially funded by

Federal agencies) - that supply information primarily to

explorers.

Much of the available data is a transcript of some primary

source, but it is often very difficult to determine the

primary source. Additionally, some of the data are

intelligence data, since various types of information give a competitive advantage to an explorer. Consequently, accuracy

often is compromised for timeliness. Often data collected

for one purpose has guestionable value for another activity.

For example, data that are collected for regulatory purposes

often becomes rosy "museum" data for use by lawyers. To

follow H.L. Mencken* s reasoning, it is sniffed but never

used in the analytic soup. Models need cabbage not roses.

590
591
What are primary, basic (i.e., raw) data and what are not is

a difficult question. What many consider to be basic

physical data (e.g., reserves or drilling) has already been

through the human judgment process (as opposed to basic

physical measurement) . In this paper, the arbitrary

distinction will be that historical information is raw, or

primary, data.

Financial Data

Financial data can be divided into four groups: costs,

prices, taxes, and financing. Host of the costs of finding

and producing petroleum are associated with drilling. The

basic and most complete source of drilling cost data is the

Joint Association Survey on Drilling Costs This

information is reported by region and depth interval. Until

1978, this survey also contained other expenditures for

finding, developing, and producing oil and gas. However, it

has been discontinued because similar data are collected by

the Census Bureau's annua l Survey of Oil and Gas.

Additional cost data are collected and published by EIA's

Dallas Field Office {see HQ]).

The IRS Income Tax Return publications (f58], ("59]) present

information on revenues, taxes, and profitability of

proprietorships, partnerships, and corporations. Host

industry statistics are reported on a regional basis. The

Census and IRS report by company size and type.

Seismic Activity and Lease Data

Data are collected at various points in the exploration

process. The exploration process begins with the leasing of

property and seismic activity. There is little or no central

collection of lease activity, although each lease is

recorded in the local (county or parish) court house.

Seismic activity is collected by the Society of Exploration

Geophysicists [95 1 and measured by number of active seismic

crews and line miles of seismic activity. Seismic activity

is considered a leading indicator of the discovery process,

but has been used very little in quantititive analysis.

Rigs and Drilling Data

After the analysis of seismic and other geologic

information, the decision to drill must be considered. The

leading indicators for drilling are the average number of

rotary rigs in use, which is collected by the Hughes Tool

Company T55], and the rig count, which is collected by the

592
1 

Reed Tool Company £87]). Unfortunately, these two series are

not coapatible since the regional boundaries for the rig

counts are Heed sales districts are different from the sore

standard API subdivisions used by Hughes.

Before drilling can commence, state agencies must issue a drilling permit. These agencies also reguire well tickets to

be filed when the well is completed. The American Petroleum

Institute (API) and the American Association of Petroleum

Geologists (AAPG) collect a well ticket that contains

reguests for information such as the depth, location,

success status, and Lahee class of the well (see Appendices

B and C) . Since this information is supplied voluntarily, it

is often not complete. Space for two volumetric guantities

is provided on the well ticket for the estimated ultimate

yield for oil and gas. Por some reason, they are reguested

only for new field wildcats and deeper pool tests. The

yield information is based on the "judgment of the AAPG

Committeemen" and it is not stated explicitly whether it is

for the well or the entire reservoir being discovered.

Currently, there are foar sources that collect drilling data

for the entire United States: the Energy Information

Administration (EIA) , Petroleum Information Corporation

(PIC), API, and the Bureau of Census. PIC»s Well History

Control File is probably the most comprehensive and detailed

source with information on more than one million wells. The

Census Bureau collects drilling information as part of its

Annua l Survey of Oil and Gas f 25]. Table I illustrates a basic problem between the data collected by the Census

Bureau's survey and that collected by API as presented in

EIA's Annua l Report to Congress 1979. Volume 2.

593
Table 1. Wells

(In

Drilled

Thousands)

in

Exploration

Total

Oil

Gas

Dry

Success Ratio

1977 *

Census API

8.95

2. 15

1.73

5.07

0.43

9.96

1.21

1.H8

7.28

0.27

1977-1978

1978

Census API

9.77

2. 12

2.07

5.58

0.43

10.68

1.13

1.60

7.95

0.26

Development Patio

Total 21.68 35.02 23.16 36.38

Oil 11.12 17.70 11.45 16.65

Gas 6.65 9.70 7.48 47.06

Dry 3.91 7.42 4.23 8.27

Success Ratio 0.82 0.79 0.82 0.77

All Wells

Total 30.63 44.98 32.93 97.06

Oil 13.27 18.91 13.57 17.78

Gas 8.38 11.38 9.55 13.06

Dry 8.98 14.70 9.81 16.52

Success Ratio 0.71 0.61 0.70 0.65

Sources: Bureau of Census, Annua l Survey of Oil and Gas,

1 977 , 1978 : Energy Information Administration,

Annual Report to Congress 1979 , Volume 2, Table 17,

Tables 13 and ia.

As shown in Table 1, the most striking difference is

summarized in the exploration success ratio. Any time trencl

is completely blurred by the marked difference between these

series. In both years, the Census reports about 30 percent

fewer wells drilled, and reports more successful exploratory

wells than API. Moreover, successful exploratory oil wells

differ by a factor close to 2. Wells are classified as dry

if they are not capable of commercial production. Often,

wells will produce for a short time and then become

uneconomical because of a high water/oil production ratio,

for example. How these wells are classified presents a problem.

An additional complicating factor can be seen in Table 2.

EI A collects "net successful (in finding) natural gas

footage" as a part of its Annual Survey of Domestic Oil and

Gas Reserves* In the Lahee classification taxonomy (see

Appendix C) the first five classes of wells are exploratory

594
and they are the only wells (by definition) that can

discover new reserves. Therefore, the amount of "net

successful" footage from the ETA A nnual Sur vey should be the

same as exploratory drilling reported by API and the Census.

One conclusion that can be drawn from this data is that

development well drilling must be producing reserves.

Another conclusion is that no one pays attention to

def init ions.

Table 2. Natural Gas Footage

(in millions of feet)

1978 1977

Census EIA API Census EIA API

Exploratory 11.4 NA 9.7 13.7 NA 10.8

"Net Successful" NA 30.6 NA NA 32.8 NA

Total 47.3 NA 59.5 66.0 NA 70.2

NA= Not Available.

There are several possible reasons for the discrepancies

shown in Table 2. First, since API reports 50 percent more

wells, the sampling frame for the Census is probably biased

and not complete. Second, the determination of an

exploratory well in the API/AAPG series is determined by the

AAPG. The Census data is from the company. Companies keep

separate records for external reporting (e.g., annual

reports), tax purposes, internal decisionmaking, and

possibly one or more for non-IFS Government reports. The

external financial reporting process is governed by the

statement of Financial Accounting Standards No. 19 [401 and

has vague definitions for classification of wells. In some

companies exploratory wells are defined as those wells

drilled by the exploration department and the development

wells are drilled by the production department. Further, the

companies may never know how the well was classified by

AAPG, which appears to be more stringent in its

classification of exploratory wells. A third reason may be

the treatment of the well for tax or regulatory purposes.

There is no difference in the intangible drilling expense

for exploration vs. development, but there is a difference

in the pricing if a well finds a new reservoir. The

definition of new oil prices includes oil from new

reservoirs, creating a strong economic incentive to classify

a well as exploratory whenever possible. A well that to the

595
&&PG looked like infill drilling may be classified by the

company and the regulatory authority as finding "virgin"

pressure and hence a new reservoir.

Reserves and Resource- In-Place

Once a successful exploratory well has been completed, the

guestion is how much petroleum did it find? This is a difficult guestion to answer. Since 1946, API/AGA/CPI have

been reporting information on reserves in an annual

publication called the Blue Book i%% Recently, API/AGA

announced that in 1979 they would discontinue the publishing

of the Blue Book since EIA-Form 23 was now collecting and

publishing the same reserve information. Reserves are the

volumes of crude oil and natural gas that are currently

economical to bring to the surface. But it is not reserves

that are found; rather, what is found is a reservoir

containing fluid. This fluid (or fluids for multiple phase

reservoirs) consists of hydrocarbons, water, and various

other compounds and molecules. Along with other physical

properties of the reservoirs, each discovery is unigue.

The amount of petroleum that can be economically produced is

a function of reservoir energy, technology, guality of the

product, prices, and costs of production. With no change in

what is physically in the reservoir, its reserves can

change. One guantity that cannot change is the amount of

petroleum initially in the reservoir — original

resource-in-place. The ratio of reserves to

resource-in-place is called the recovery factor

(historically 33 percent) for crude oil. Reserves are more

important to the economics of the operation since, for

example, banks will loan money on reserves.

Resource-in-place by date-of-discovery has more modeling

importance. At this point ETA's reserves survey has not

addressed resource-in-place and date-of-discovery

information which many modelers, analysts, and engineers

consider more useful and critical information.

Resource-in-place can be measured by an estimate of the

reservoir size and data on porosity and water saturation.

Reserves are measured using methods ranging from rules of

thumb or analogy to complex reservoir simulation models.

Since engineers, accountants, and bankers are taught to be

conservative when dealing with reserves, the announced

reserves after a discovery tend to underestimate the amount

actually discovered (although in small reservoirs this bias

is usually less) . To accommodate this approach the API/AGA

reserve additions are reported in four categories:

revisions, extensions, new reservoirs in old fields, and new

field discoveries.

596
Reporting of Discoveries

The reporting of new field discoveries is something like a strip tease - after a new field is fonnd (which at some

later date aay even be declared not to have been a new field

due to results of further drilling and testing) only part of

what was found is revealed (reported) to the public. But as

tiae goes on, more and more is revealed. This "dance"

includes the drilling of confirmation and extension wells,

discovery of new reservoirs, analysis of data, and

principles of engineering and accounting conservatism. The

revelation seguence may take five years or more.

The problem of determining when discoveries are made is

illustrated by the discovery and reporting of reserves for

Prudhoe Bay. In T970, the B lue Book 's Table II reported

reserve additions in Alaska of 9.85 billion barrels. From

the information, one aay assume that Prudhoe Bay was

discovered in 1969 or 1970. Upon turning to Table III-2,

which contains original resource- in-place and ultimate

recovery by year of discovery, one finds 9.4 billion barrels

(ultimate recovery) discovered in 1968 and 320 million in

1969, but nothing in 1970. One must conclude that it took 2

years to report the discovery of Prudhoe Bay as reserves. Is

this a standard operating practice? Do all new fields take

this long to report? Will the date of discovery be lost

forever, when EIA is the only organization reporting?

Extensions are used to report additions to proved areas.

Revisions are a catch-all category that includes positive

and negative revisions due to errors in calculation, changes

in economics, new data often froa infill drilling, and

installation of secondary or tertiary recovery technigues.

Revisions always create serious problems for three reasons.

First, they are a category for reporting anything that does

not fit nicely into other categories. Second, excluding

secondary and tertiary recovery, revision should be

attributed to estimates made in the past, but currently only

ad hoc aethods exist for Batching these data to the data

they correct. Third, development drilling can produce new

reserves. New pools- can be discovered, better information on

the reservoir characterisitics is obtained, or better flow

is established in a poorly connected reservoir. Ho one has

attempted to estiaate the magnitude of these phenomena

separately.

From 1968 through 1978, revisions in natural gas reserves

have been mostly negative. This problem was so serious that

the resulting total associa ted -dissolved natural gas

reserves were negative. Without being able to assign these

597
revisions to past data, extrapolating trends becomes

difficult.

i The Ideal Data Base

In order to properly understand the domestic exploration and

production industry, a good data base must be constructed

(cabbage for the soup) . The first step in building that data

base is to define the reasonable micro units of the process.

For the physical discovery process, these units are the

reservoir and the well. The reservoir is important because

it characterizes the target of exploration drilling and the

natural unit of oil and gas occurrence, Reservoirs

aggregate into plays, and fields aggregate into basins, and

then provinces and regions. Re lis are important because

wells are the final determinant of discovery and production.

Without complete and compatible data for wells and

reservoirs, any analysis of the past starts with a severe

handicap. The data needed for this data base differs only

slightly from that currently being collected.

The ideal data base would have three parts linked by common

identifiers. The first part would be the well data file.

This part would contain information very similar to a current API/AAPG well ticket with the addition of a reservoir code. The second part would contain geologic,

resource, and production data by reservoir, and would

include information on the discovery well and number of

wells and well months of operation in the reservoir. Part

of the reservoir identifier would be the field, basin, and

region of which it is a member, additionally, production

would be reported by regulatory category. The third part

would contain financial information reported on a gross

operator basis for each field and would include a breakdown

of ownership of production and profit distribution.

Additionally, companies could be asked for financial

information, including land acguisition, lease inventory,

and geological and geophysical costs. This information could

serve as a crosscheck on the gross operator data and the

sampling frame.

5. RESOURCES AND WITHHOLDING

Resource Distribution

Many authors have made estimates of remaining petroleum

resources using a number of different approaches (!"^61r

f521, T531, f 51»]» F76], r60"!K. Recently, the most visible

and detailed assessment is the USGS Circular 725 T781. The

critical dimensions for the resource distribution are depth

(both water and actual) , the size of the reservoirs or

598
fields, the cost of discovery, and availability of the

potential resource. The size distribution is generally

accepted to be lognornal. This conclusion has resulted from

empirical analysis and deductive inference using geologic

theories ([95% Additionally, the AAPG

classification scheme (see Appendix B) reflects this

assumption.

The cost dimension covers many facets. Among them: the

depth of deposit, the above and below ground environment,

characteristics of the reservoir and the amount and type of

petroleum in it, and the trap detection mechanism. The trap

detection mechanism includes the geology and geophysics used

to discover the trap, and the geochemistry used to

contribute to the estimation of the presence of petroleum.

After all predrilling information is assembled, the number

of holes necessary to explore the geologic prospect becomes

a very important determinant of the costs. For example, to

detect and discover stratigraphic traps usually reguires

more drilling than structural traps.

Leasing, Withholding, and Intertemporal Rent

In 1931, Hotelling demonstrated the existence of

intertemporal "economic rent" that, if not paid to the

owners of exhaustible resources, would encourage the owner

to withhold the resource from production [18]. The U.S.

Government withholds land for a variety of economic and

non -economic reasons.

Oil and gas leases transfer the mineral ownership rights.

There is no doubt that some speculative withholding exists

in the production process. Whether it is massive or minor is

a guestion that has not been fully answered. Today, leases

are harder to acguire because the owners are smarter and

more knowledgeable. Conseguent ly , landowners are demanding

and getting more "upfront" or bonus money and higher rent.

The bonus money is extracting some of the "economic rent."

In general, the term of the lease is getting shorter. The

old "sample" leases were for 10 years or longer and were

usually renewed by a rent payment and with no reguirement to

drill. Today, leases are being written for 1 to 5 years. In

"hot" areas, leases also contain a provision to drill within

6 months. In addition, lease bonuses have gone from $3 to $5

per acre to $75 to $100 per acre. In a 1980 Permian Basin

lease sale by the University of Texas, up to $11,000 per

acre was paid in bonus money in addition to a 25 percent

royalty.

Also, lease terms are much more variable today than in the

past, an indication that owners of expected marginal

599
properties are not getting much, if any, intertemporal

"economic rent." Whether anyone actually undei stands what

they are withholding, or that they are allocating their

resources where the expected marginal cost is lower, is

difficult to assess. ^

6. INVESTMENT, BIGS AND DRILLING

Investment and Funds Flow

Drilling for oil and gas reguires investment. There are

three general groups of agents that operate in the petroleum

exploration business: (1) the majors, (2) the independents,

and (3) the fund investor. Each has separate motivations. As

a general policy, banks have refused to loan money for

exploration. Nevertheless, when a large bank loans a large

oil company money, no specific collateral is regnired. Even

if the money is borrowed for a new refinery plant and

eguipment, it frees other funds for possible use in the

exploratory program. The majors are vertically integrated

with massive investments in refining and in the distribution

and retailing systems. To make their operations profitable,

they a need large flow of crude. They can either find it or

buy it. For example, in 1979 Shell purchased Belridge Oil

Company for $3.6 billion, increasing its reserves by

percent.

The independents are in the business of finding petroleum.

The motivation behind this group is conjectured to be a complex combination of the high-stakes gambler, who goes

broke at least twice in his career, and the small

businessman trying to make a fortune. To remain solvent this

group must find oil in profitable guantities, but usually

its only use for the oil, once it is found, is to sell it.

another source of funds is from the private investor or a drilling fund. This activity is very attractive to those in

high tax brackets because the tax laws allow a large portion

of the investment to be expensed by the investor. Private

investment is a function of the general well-being of the

high-tax brackets and the commodity markets. The major

companies, who have a large share of the oil and gas leases,

contract with an independent financed by a drilling fund to

drill its poorer prospects on the property leased by the

major. The major retains the right to the crude. The

independent receives cash and the drilling fund gets a tax

write-off. This type of operation is called Mf armout.

According to the IRS, proprietorships and partnerships in

oil and gas exploration have been operating collectively at

a loss at least since the early seventies ([58], f 59 "J) .

600
The timing of cash realization for the various

explorationists differs drastically. An integrated oil

company receives cash resulting from a discovery only after

the refined product is sold, although there are transfer

payments for bookkeeping purposes. On the other hand, the

independent can borrow on the reserves found as soon as they

are proved. In the middle is an operator who sells the crude

as it is produced. In the extreme cases the timing of the

actual final cash realization from a discovery differs by 20

years or more. Further, the tax structures of the majors and

independents differ substantially. For example, the majors

have foreign tax credits (credits to their United States

income tax) in the billions of dollars. The independents

have lower excise taxes and still have a depletion

allowance.

The above description of the industry is obviously

oversimplified, but serves to highlight the complexity of

the funds-flow problems. Some models use a "top-down"

finding approach and are driven by the industry "exploration

budget." After the "budget" is determined, the number of

exploratory wells drilled is the budget divided by the

average well cost. A projected budget for each year would

need to address the reallocation of the major's internal

budgets, the reinvestment of the independent's profits, and

the size of private investments. S simple recycling of the

previous period's profits may seriously understate the

budget. Unless surrogates are found for the various

components of the "exploration budget," it is very difficult

to forecast.

The "bottom-up" approach is to use the micro technique of

discounted cash flow analysis. Using project costs, finding

rates, price, and production profiles, each region is then

treated as a project. With this approach alone production

forecasts would be very high because it could over- state the

funds available to the projects.

Figs

Projecting the amount of exploratory or developmental

drilling is a perplexing task. The drilling industry can be

viewed as two separate industries - the rig builders and the

drilling contractors. There are about 20 rig building

companies in the United States. Several are subsidiaries of

steel companies. The market for rigs is international and no

hard data exists on the number of rigs that are shipped

abroad or returned each year. The raw material for building

rigs is mainly tubular steel. In periods of high demand for

steel, this market can become tight. The price of a rig

varies according to its depth rating. For example, a rig

601
rated for 5,000 feet costs about $500,000; for 10,000 feet

it costs about $2 Billion; and for 20,000 feet it costs

about $5 million. The well costs increase at a highly

nonlinear rate as a function of depth.

The composition and size of the rig fleet has changed

dramatically since 1973. From 1973 to 1979 the number of

rigs (as reported in the Beed Census) grew at an annual rate

of 10 percent. Bigs rated below 10,000 feet grew only at a rate of 7 percent while those rated at or above 10,000 feet

qrew at a rate of 13 percent, indicating a shift to deeper

drilling potential. Nevertheless, at the same time, the

average depth of wells was less in 1979 than in 1973.

The drilling industry has changed its basic composition over

the last HO years. In 1939, about half of the drilling was

done by the oil companies. Since then oil companies have

gradually divested their drilling operations and currently

they account for only 1 percent of drilling. The other 99

percent is done by 680 contractors, none of whom is large

enough to dominate the market. The majors now contract for

most of their drilling. Drilling contractors occasionally

drill holes for themselves.

One of the conjectured reasons for the majors* divestiture

is the inability to move crews as fast as their prospect

analysis and corporate strategy dictate. This raises the

guestion of rig mobility. That is, in a model that is

regionally disaggregated, how should the migration of rigs

be represented? Certainly, premiums must be paid to move rig

crews long distances from their homes. Further, in periods

of high demand, it is probably more difficult to move rigs

and their crews. Two simplifying approaches exist. One

approach disregards mobility and allows drilling increases

only by the introduction of new rigs in each region. The

other approach allows a percentage of the rigs to migrate to

other areas based on relative regional profitability. After

the number of rigs has been determined, the next guestion is

what type of hole will be drilled.

Drilling

Althouqh developmental well drilling has been increasing at

an annual rate of 13 percent since 1973, exploratory well

drilling has only increased at a rate of 6 percent, and it

declined in 1979. These changes have been taking place

under a changing and complicated series of price controls.

In addition, the proper decisionmaking unit for drilling

should be the reservoir. However, regulations, taxes, and

controls are based on a legal property definition, which

often contains many reservoirs or subdivides a reservoir,

602
and distort optimal economic decisions. How should these

trends be extrapolated over the next 10 years?

The fraction of successful exploratory wells increased

steadily from 16 percent in 1972 to 29 percent in 1979. The

significance of this increase is difficult to assess since a combination of factors could account for this change. First,

due to price increases, the minimum prospect size (dry hola

threshold) is lowered; therefore, more wells are successful.

Second, better exploration technigues help avoid the

drilling of dry holes. Third, some "exploration" is simply

the redrilling of geologic structures that were drilled,

plugged, and abandoned as dry holes in previous years.

Fourth, there has been a general conservative shift in the

broad category of exploratory drilling (e.g., from new field

wildcats to extension wells)

Whether, when, and how current trends will change are

critical issues. For example, if the recent increase in the

proportion of exploratory wells declared successful were to

continue, by 1990 60 percent of exploratory wells would be

successful, a dramatic historical change.

Producers, adjusting to the higher prices, soon may have

drilled the inventory of prospects in existing fields. If

the prices continue to rise, the infield inventory of new

viable prospects will increase, allowing current trends to

continue. If prices do not rise, the infield prospects soon

decline. As infield drilling declines, rigs are idled,

reducing rig demand and shortage rents (currently, there is

at least a 1 year wait to drill a well) which may provide a further incentive to drill the riskier wildcat wells.

Intentional Drilling

Does the driller have prior intentions of finding oil or gas

or is the search simply for petroleum? Most people in the

industry believe that a large part of exploratory drilling

is "intentional." That is, before drilling a well the

driller has specific intentions of finding either oil or

gas. When a successful hole is drilled, it usually produces

a mixture of liguids and gases. The decision whether it is

declared an oil or gas well is based on the gas to liguid

ratio.

From a modeling viewpoint, it is often convenient to treat

discoveries of oil and gas as independent events (except for

the coproducts, associated natural gas, and natural gas

liguids) . There are several reasons why this choice is made

by most modelers. Natural gas and crude oil differ in the

way they are processed and distributed. Further, the prices

603
on a heat value basi.s have never been the sane and they are

substitutes in the market place on a limited basis.

Additionally, the constituencies of each product are

different and the sponsor of the model usually wants more

attention paid to one of the products.

An important question regarding intentional drilling is how

to allocate dry holes. Since there can be no information on

what was not there, the easy choice and the one pursued by

many modelers is to allocate dry holes (or footage) in

proportion to successful oil and gas wells (footage). I second choice is to allocate them in a more sophisticated

way, for example, by historical regression of successful oil

well and successful gas wells on dry holes. The results are

presented in the table below.

Table 3. Dry Hole Allocation

All Exploratory Drilling New Field Hildcat

Wells Feet Wells Feet

(Thousand) (Hill ions) (Thousand) (Millions)

Oil 1. 1U 7.50 0.49 3.31

Gas 1.78 1 1.77 0.67 4.71

Dry 7.i»6 43.22 5. 16 32.50

Ratio

(Oil/Gas) 0.6 4 0.64 0.73 0.70

Dry Oil 2.916.86 2.17 13.38

Dry Gas 4.55 26.36 2.98 1 9.12

Regression

Ratio 3.65 2.90 NE m

Dry Oil 5.85 32. 14 NE NE

Dry Gas 1.6 0 11.08 m NE

NE = Not Estimated.

The difference between these two approaches is significant.

Almost twice as many dry holes are allocated to oil and less

than half are allocated to gas if the regression analysis is

used. But the regression masks two important historical

trends. While the ratio of successful oil to gas wells

changed from approximately 3 in the 1950*s to .67 in the

late 1970* s, the average depth of all holes steadily

increased by more than 50 percent. An additional confounding

factor is that advances in technology were made concurrently

with these trends.

In 1978, about 1 in 3 exploratory wells drilled deeper than

7,500 feet were successful, while approximately 1 in 4 of

those drilled less than 7,500 feet were successful. Since

deeper wells cost more to drill, good economics dictates

604
that more care and analysis be exercised in drilling deeper,

and hence, fewer dry holes. Gas wells have historically been

deeper than oil wells.

If the intentional drilling approach is abandoned, the

statistical problem of allocating dry holes vanishes, but in

its place is the problem of modeling the economic and

regulatory incentives that change relative profitability of

liguids and gas.

7. DISCOVERY AND FINDING HATES

{fhat is a finding rate? In a broad sense a finding rate for

petroleum is the amount of petroleum found measured against

some unit of activity or factor input needed to find it.

This section will examine several approaches to modeling the

discovery process. The choice of numerator and denominator

of the finding rate has been the subject of much debate,

political and scientific.

For example, on November 4, 1977, the Governor of Texas,

Dolph Briscoe, sent a letter to James Schlesinger, Secretary

of Energy, stating that finding rates were a "critical

issue" and suggested that "about 15 barrels per foot" would

be appropriate for Lower-48 onshore production. In his

response, Schlesinger stated that finding rates are "the

paramount determinant of future supply" and the data must be

"meticulously studied." He stated that Briscoe's definition

of finding rate was not "clear." In a second letter.

Governor Briscoe stated that "I concur with your observation

that forecasting of finding rates is a paramount determinant

of future supply." He went on to address the question of

finding rate definitions and the use of recent vs. longer

term trends.

The range of possible choices for the numerator includes new

fields or discoveries measured as reserves or

resource-in -place of crude oil, natural gas, or the net

eguivalent amount of crude oil. The choices for the

denominator include time, total footage (or wells) drilled,

total exploratory footage (or wells), total successful

exploratory footage for oil (or gas), total footage (or

wells) for oil (or gas) , new field wildcat footage (or

wells) rank, wildcat footage (or wells), dollars invested,

or cash flow.

The Hatching Problem

Depending on the numerator of the finding rate calculation,

an appropriate denominator must be chosen. For example, if

new field discoveries are to be used in the numerator, new

wildcats (wells or footage) must be used in the denominator.

A very serious problem arises when an attempt is made to

determine what was found in a new field wildcat. When

reserves are reported (in the past by the API and AGA; now

on EIA Form 23) , there is no mention of tie wells that

discovered them. Further, reserves are not reported by date

of discovery, but often up to 4 years later. To estimate

finding rates, drilling must be matched with the amount

found by that drilling. Currently, although the reporting of

605
reserves lags behind the reporting of the discovery wells,

only anecdotal evidence exists for any estimate of this lag.

The problem is what reserves or resources-in-place are found

by which wells — the matching problem. In addition to the

timeliness of reporting, the relationship between drilling

categories and reserve addition categories is worrisome.

Table H presents drilling and reserve reporting categories

and several different finding rates.

Table H. Reserve/Drilling Finding Bates

Drilling

1. New-field Wildcat

2. New-pool Wildcat

3. Deeper-pool test

4. Shallower pool test

5. Outpost (extension) test

6. Development

Reserves

ft. New field discoveries

B. New reservoir discoveries

in oil fields.

C. Extensions

D. Revisions

Name

Possible Finding Rates

Calculation

New Fields

New Reserviors

New Discoveries

Reserve additions

All Drilling

f (M I/HI) 1 r <MMB) 3/T <1)M2)M3)*(*) 1

c m*m *icr*(D) yr in*m*o)*m*m i

t (A) + (B) (H (D) ]/r (1) (2) (3) + (H) + (5) + (6) ]

There are several basic approaches to modeling the discovery

process. One approach estimates a finding rate for new

fields, a measure of long-term, high-risk exploration.

Subseguent to finding a field, the extensions, revisions,

and new pool discoveries must be estimated. This approach

has two drawbacks. First, the data reported as new field

discoveries freguently underestimates the amount found.

Second, the remainder of the discovery sequence and the

staging of production must be estimated adding a second

complicated estimation process. The finding rate for new

reservoirs is a more conservative measure of discoveries,

but suffers from the same problems as the finding rate for

new fields.

The finding rate for new discoveries has appeal since all

discoveries and exploratory drilling are included, but any

revisions must be estimated separately. When the finding

rate for new dicoveries is calculated on a yearly basis and

plotted against time, its behavior is a reasonably snooth

606
decline. When the sane plot is generated using finding rate

for reserve additions (i.e., including revisions) the

behavior exhibits considerably more variation Figure 2.

The reserve additions and all drilling finding rates differ

by the inclusion of developmental drilling. They are not

theoretically pleasing, but allow the modeler to neglect

many of the staging and data definition problems since they

are all inclusive.

Finding Rate Categorizations

It has been proposed that finding rates be differentiated by

depth of holes, trapping mechanism, search type (e.g.,

surface and subsurface geology and geophysics) , company type

(e.g., majors vs. independent), regulatory category, and

geographical region. Additionally, guestions of using

long-term (e.g., from 1940's), midterm, or short-term (from

1974) trends in performing the analysis are debated

religiously.

Even though information to categorize finding rates is

available only on a limited basis and is not done on a national level, the research into and arguments for the

additional stratification are interesting. For example,

depth stratification allows for three additional

refinements. First, the success ratio increases with depth.

Secondly, the well costs increase nonlinearly with depth.

Third, depth can be considered a "third dimension" of

discovery process.

There are two basic types of trapping mechanisms for

petroleum: structural and stratigraphic. Structural traps

are easier to find and usually present very definitive

targets. On the other hand, stratigraphic traps are harder

to detect and are often detected accidently or as the result

of a more random type drilling. Success rates and amount

found, it is hypothesized, could be markedly different for

reservoirs with different trapping mechanisms.

Categorization by the field or reservoir size is also

desirable, since for example, the costs of finding and

developing 100 million barrel fields is different from a 100

million barrel field.

The Arps-Roberts flodel

In 1958, Arps and Roberts published a paper on the economics

of drilling in the Denver-Julesburg basin which contained

finding rates differentiated by the size of discovery [7}.

The paper proposed the following model of discovery:

607
608
F(W,A) = F0(A)*(1-exp(C(A)*W))

where W is the cumulative number of wildcat wells drilled, A is the area size of a field, FU (A) is the ultimate number

of fields of size A , C(A) is an "efficiency of drilling 1* parameter, and F(W,A) is the number of fields of size A

discovered after W wildcats.

FtT (A) and C (A) need to be estimated from data on F(W,A) and

W. Arps and Roberts describe three different cases for

deducing C(A): (1) For random drilling, C(*)=A/B where 8 is

the basin or search area; (2) For pattern drilling, C (A) = infinity or C(A) = A/B depending on the well spacing; and

(3) For drilling based on geological or geophysical

analysis, C {A) = 2*A/B. That is, geology and geophysics in

effect increase the search efficiency or decrease the search

area by a factor of two. Since more than two decades have

passed since the initial work, it would be worthwhile to

reexamine this model and its predictive ability.

Play Analysis

A play is a series of discoveries resulting from one

geologic idea or concept usually geographically confined.

For more than 20 years, Kaufman and his collegues have been

modeling plays (f12% T13], [ 1Q1, 115% [60], [61], r 631) . The discovery model is based on four postulates:

1. The size distribution (in barrels or million cubic

feet) of petroleum deposits in pools within a subpopulation is lognormal.

2. Within a subpopulation, the probability that the

"next" discovery will be of a given size (in barrels

or million cubic feet) is egual to the ratio of

that size to the sum of sizes of as-yet-undiscovered

pools within the subpopulation.

3. The probability that an exploratory well will discover

a new pool is a function of the number of non-dry

and dry drilling targets.

4. Interarrival times between successive plays are

uncertain guantities. The mean time between two

successive plays, measured on a scale of cumulative

exploratory wells drilled, (a) increases with

an increase in the proportion of wells drilled

extensively subseguent to the beginning of the

first of these two plays, and (b) increases as

the volume of unexplored sediment in the province

decreases.

609
The most successful part of these studies has been the

ability to verify the lcgnormal assumption (Postulate 1) and

the sequencing of discovery size (Postulate 2) . Two

significant aspects that these studies do not address are

the tine sequencing and the aggregation of plays, nnited

States data in general are not available in a form in which

the above postulates can be tested. Only in a few instances

are data available in a form amenable to proper analysis.

Further, whether the analogy between the United States and

other countries can be made is questionable. Plays in the

United States compared to other countries normally involve

more drilling and smaller, hence more, leases. Consequently,

subplays could be created based on lease holdinqs. Further,

the rules for sharing of exploration information differ

among countries.

The question of aqqregation of plays was addressed

inadvertently by Benjamini et al. when attempting to test

the Kaufman model on Kansas discovery data f 181. Although

aware that the data contained the aqgregation of 3 to 5

plays, Benjamini et al. set out to test Kaufman's single

play model and found that it did not fit the data. Kaufman

and Vang then showed that by the aggregation of 3 to 5 plays

using the Kaufman model, the results of Benjamini et al

could be obtained T621. Although not the original purpose

of the research, these results demonstrated that the

aggregation of plays cannot be modeled as a play.

Permian Basin Study

In mid- 1976, the Interagency Oil and Gas Supply Project was

established to extend the work of USGS Circular 725 by

taking a closer look at several basins: the Permian in west

Texas and southeast New Mexico; the Gulf of Mexico; and the

Atlantic's Baltimore Canyon. The Permian Basin study has

been completed [57]. The report contains detailed

assessments of what has been found, what is yet to be founl

and the costs of extraction. The Arps-Eoberts model was

chosen as the discovery process model and enhanced by adding

depth categories. Detailed cost estimates were made for

drilling and operating in the basin and cost curves were

developed terminating at $40 (in 1977 dollars) . Methods and

potential of enhanced recovery were also examined. As a result, the USGS estimate of recoverable resources in the

Permian Basin was reduced by more than half. Since this is

the only onshore region that was or is planned for study,

several caveats should be issued. First, the Permian Basin

is only part of the United States, and is not necessarily

representative of other geologic regions. Second,

alternative methodologies and new data could change the

610
assessments.

Long-Terra vs. Short-Term Finding Rates

In the early 1960* s, the domestic petroleum production

industry started to "close up shop." In 1970, the average

number of seismic crews hit an over 20- year low of 195.

Levels three times higher were sustained in the fifties. In

1971, the average number of rotary rigs in use, the number

of exploratory wells, and total wells drilled hit record

lows. Levels two or more times higher were sustained in the

fifties. In real terms the price of crude oil had been

dropping from more than $4.50 (1972 dollars) in the fifties

to about $3.50 in the early seventies. The domestic industry

was depressed. In 1973, the embargo hit. By 1974 the real

price of upper tier crude oil had more than doubled. New

price controls were instituted.

Throughout the 1970* s, the seismic crew and rotary rigs in

use grew at more than 8 percent per year. Total drilling

footage grew at more than 6 percent per year. Exploratory

footage grew at less than 4 percent per year. The real cost

of drilling a well grew by more than 6 percent per year. The

real price of a barrel of crude oil grew at more than 8

percent per year, but after the 1974 jump, the growth was

less than 2 percent per year. What will happen in the

1980 f s? In September 1980, rotary rigs hit a record high of

3,138. Total drilling in 1980 was 40 percent higher than for

the same period in 1979.

The post embargo finding rate (measured in reserves

additions per total exploratory footage) for crude oil has

been in the twenties. In 1979, the rate was up to 35. There

is virtual unanimous agreement among analysts that due to

the depletion effect, the finding rate should decrease as

exploratory drilling increases (with appropriate caveats)

over the long run, but in the short run, there are hills and

valleys. One of the most hotly debated guestions of the past

several years is: should the 1975-1978 low finding rates be

used as a basis of a long-run trend, or should they be

considered a temporal anomaly? When a simple model such as

R = RO* (1-exp (-b*CEFT) ) (where RU is the ultimate amount of resource, CEFT is the

cumulative exploratory footage, b is a coefficient

representing the depletion effect, and R is the cumulative

resource discovered as a function of RO and CEET) , is use<3

to estimate finding rates, the residuals are almost always

serially correlated. The recent finding rates are well below

the long-term trend estimated by a nonlinear least sguares

611
fit of the equation. The next section will present several

reasons why the post-embargo trends could be a temporal

anomaly.

Risk. Aversion, Prices, and Success Rates

In 1975, Drew hypothesized the existence of two components

of wildcat drilling: ambient and cyclical T321. Using data

from the Powder River Basin, ambient drilling was defined as

the lonq-term systematic exploration program and was found

to be characterized by low success rates and high finding

rates (measured in reserves of crude oil per wildcat well)

Cyclical or transient drilling was associated with the

initiation of plays (e.g., the Hinnelusa Sandstone play of

the late 1950's and early 1960's, and the Muddy Sandstone

play a decade later) . This type of exploratory drilling is

initiated by a large discovery, is transient in nature, and

usually lasts about 3 to 5 years. It was found to be

characterized by a surge in activity close to the time of

discovery, higher success rates (34 percent higher) and

lower finding rates (about 1/3 of ambient) . This is evidence

of strong risk aversion and/or the "herd" instinct. With

some modifications this theory can be adapted to exploratory

drilling for the entire country.

When a play is initiated by a discovery, almost immediately

an inventory of prospects associated with the play is

upgraded and becomes less risky. Similarly, when the price

(net of tax) of crude oil is increased, the inventory of

prospects that are considered economic (in a probabilistic

sense) grows. This inventory addition is lower risk since it

is usually associated with known fields and geologic

horizons. But it results in low reserve additions, that is,

this inventory consists of the small pools and extensions to

the thin sands of the reservoir. Analogously this risk

aversion process would be characterized by high success

rates and low finding rates, exactly what has occurred since

1973. This theory argues that finding rates in the short

term fall as the price rises. Dnder this hypothesis, this

trend will continue as long as the price continues to rise

and rigs are in short supply. With the phaseout of price

controls, the eventual phaseout of the windfall profit tax

and the recent forecasts of imported oil prices, the price

should rise through the remainder of the century.

Hajors and Independents

Exploration strategies differ depending on the motivation

and oblectives behind the search. Perhaps the most discussed

difference is between the majors and the independents.

Depending, on how a major is defined, there are 8 to 50

612
companies. The independents are a collection of everyone

else. The labors need crude to keep their downstream

activities operating at high levels. Further, the majors,

because of size and personnel, are in a better position to

undertake high-risk and high-technology ventures, a successful venture that could dotfcle the company size of an independent may be insignificant to a malor. Tax

differences, risk aversion, and the utility of the smaller

payoffs, therefore, differentiate the independents from the

malors.

If the above hypothesis is true, the majors would be

drilling high-cost, high-risk (low success rates) prospects

and finding at high rates when compared to the independents.

Data presented in Table 5 support this hypothesis

(neglecting the difference of opinion between the Census

Bureau and the API/AAPG on well classification) . These

statistics are basically the same as those of the 1977

Census survey. The larger companies drill the deeper and

more costly wells and have lower success rates. To fully

test this hypothesis, it is necessary to know the amount

found. Unfortunately, this information is not easily

obtained. The majors assess risk and profitability on an

international basis and have in the past turned their

operations away from the United States when the opportunity

presented itself. As a caveat, however, the same data also

could lead to the conclusion that the large companies are

not as efficient or as cost effective as the smaller

independents.

Table 5. Companies Banked By Sales of Crude Oil,

Condensate!, and Natural Gas

Number of Companies

First First Ninth thru nTs~

Eiaht Fifty Smallest Total

Exploration Wells 676 1,725 9,095 9,771

Success Hate 0.30 0. 36 Q.47 0.44

Average Depth

(feet) 9,750 8,920 6,490 6,723

Average Cost

(Thousands of

Dollars) 1,837 1,225 379 452

Source: Annual Survev of Oil and Gas, 1978 , Bureau

of the Census, Tables 4B and 17.

8. PBODHCTTON

613
Once a field has been discovered and initial operations are

established, the operator must manage the property with

sound engineering, economic judgment, and according to State

(or other government) regulations. One objective is to

establish a level of production that fully utilizes the

capacity of the lease eguipment. That is, the decision to

drill additional development wells during the mid-life of a field is usually taken when existing well production is

declining. The proper decision is to examine the discounted

cash flow of each additional well. Further, the operator

must decide whether and when to drill for new pools and

extensions that are riskier, or whether to simply increase

the production rate by infill drilling.

Once a "find" occurs on a property, the strategy changes to

delineation and development. There are two court rulings

that apply. They are the "rule of capture" and the

reguirement to produce "in paying guantities." Unless the

mineral rights to the entire reservoir are clearly in

possession of a single owner, there is a great incentive to

drill (and produce guickly) due to the "rule of capture."

Unitization and production regulation can control

overproduction, but there are numerous State regulations

about unitization that tend to deter withholding of

production (see, for example, McDonald [731).

Production from a well is usually modeled using a exponential, hyperbolic, or harmonic decline function. The

most common is the exponential that is represented by a constant production to reserves (P/R) ratio. For the

Lower-48 the P/R ratio has been climbing from .08 in the

early 1960' s at a rate of about 4 percent a year. If this

trend were to continue the P/R ratio would be about .21 by

1990. This statistic has been largely taken for granted by

modelers, but needs careful study. Aggregate models usually

do not address the P/R ratio as a function of price, but on

a micro basis the discounted cash flow is an important

determinant in infill drilling. Ideally, this process should

be modeled at the reservoir level and aggregated, but would

reguire significant attention to detail.

Secondary recovery technigues such as waterflood and natural

gas reinjection are now standard practice. The guestion

arises whether post- 1973 environmental and technological

advances have changed the timestaging of these methods.

Wells are reguired for injection. Hence, the demand for

wells comes from several sources and the operator must

choose properly between the various opportunities based on discounted cash flow. The reporting of reserve additions and

production by recovery method would be helpful in analyzing

614
this problem.

Double Counting and Underconnt ing

The various approaches to projections reguire estimation of

the potential resource base. This information can often

subtly appear twice when production from different sources

is estimated independently. For example, the resource

potential for gas from tight sands may be counted in the

resource base for conventional gas. In another example, the

reserves from steam drive may be included in proved reserves

and at the same time projected by an enhanced recovery

methodology.

There are two basic approaches to enhanced oil recovery

(EOR) forecasting, a siiple, but not very appealing,

approach is simply to increase the recovery factors in the

conventional model and call the resulting increase enhanced

oil recovery. A second, but more complex, approach is to

develop a separate data base and model for enhanced

recovery. This model would allow for analysis of the recent

enormous change in incentives created bv the WPT and the

front-end incentives program. Care must be taken not to

include proved reserves from successful EOR projects (e.g.,

steam drive) in the conventional model and the EOR model.

Currently, it is difficult to determine which portion of the

revisions are due to the EOR methods, although EI A will

collect this information beginning with its 1980 survey.

The reporting of natural gas statistics has similar

definitional difficulties, natural gas is reported on a "wet" (before liguids extraction) and a dry basis. Liguids

include crude oil, natural gas liguids, and condensate, but

the latter two are not always counted. The difference

between natural gas liguids and condensate is now defined by

regulations. It is often difficult to compare forecasts due

to these definitional problems.

Secton 107 of the Natural Gas policy Act (NGPft) contains a provision for deregulating gas from wells deeper than 15,000

feet, and from geopressured brine, coal seams, or Devonian

shale high-cost gas. There are estimated large guantities of

natural gas in tight sand reservoirs, coal seams, shale, and

geopressured brines. Since technological and financial

problems have inhibited high-cost gas production there is

little historic precedence for production. These sources are

referred to as unconventional. Studies of these categories

are being undertaken to assess resource and production

potential. Whenever the results of a specially focused study

are combined with a more general forecasting technigue, the

risk of double counting becomes great. For example, there

615
may already be reserves or drilling from these sources

embedded in the data series used to forecast conventional

production.

Co-Product Effects

Natural gas and liguid petroleum emerge from the ground

together. The costs of producing gas and oil are joint until

the two products reach the surface. At the surface, the two

receive different treatment, natural gas can be flared,

reinjected for pressure maintenance, or marketed via

pipeline. Petroleum liguids generally are shipped to

refineries via pipeline, water, or ground transportation.

Due to regulatory, physical, and safety restrictions,

liguids and natural gas are only partial substitutes.

Natural gas has always been cheaper than any of the liguids

on a heat value basis because natural gas does not compete

with liguids in many markets — for example, for

transportation fuel and for residential and commerical

heating outside the proximity of natural gas pipelines. When

liguid prices are high, the joint cost effect lowers natural

gas prices. Care must be taken to include the price of

liguids in the price of products emerging from a gas well

and vice versa.

Regulatory Crosswalks

How should regulatory impacts be assessed? Since data series

giving historical evidence of. behavior under new or proposed

regulations and taxes do not exist, impacts must be assessed

by postulating models of behavior on a priori grounds.

To project impacts, a matrix of "sharing" coefficients (same

properties as a Markov matrix) is often constructed so that

forecasted guantities can be converted into regulated

guantities (using historical data) . More importantly, the

incentives are almost always changed by regulations and

taxes.

9. SOFTWARE AND MODELING

Different supply models and model structures have been

compared in several studies [231, f"2«l, T56]. There has

been much debate over the technigue and categorization of

the models (i.e., linear programming, econometric,

structural, probabilistic) and how they perform. The

arguments at the overall model level generate a good deal of

heated discussion, but miss the point. The proper

perspective is to look at which technigues are better for

what components of the model. Almost all models for oil and

gas forecasting are implemented in Fortran on digital

616
computers. Often these models are reviewed as black boxes.

That is, the modeler or analyst, unless participating in

codinq the model, seldom examines the code to discover

exactly what the model does. Usually reading the code is

considered a long and arduous task or virtually impossible,

since much of the coding and design is behind the

state-of-the-art in programming. Further, when the analyst

wants to make a change to the model, the change often

requires a coding modification. In order to test various

hypotheses and examine alternative model structures, a modular hierarchical software system needs to be designed

where, for example, changing the form of the finding rate or the production function is only slightly more difficult than

changing input parameters such as the discount rate. In this

way many theories can be quickly examined and evaluated.

BIBLIOGR APHY

1. Adelman, M.A. World Petroleum Market, John Hopkins

University, Press, Baltimore Md. 1972.

2. Aguilera R . and VanPollen, "How to Determine Primary

Reserves in a Reservoir," Oil and Gas Journal, pp.

98-102.

3. Anderson, T C, Depth and Producing Rate Classification of

Domestic Oil Reservoirs, 1974, EIA/DOE, Dallas, Texas,

October 1978.

4. American Petroleum Institute, "Joint Association Survey

of Drilling Costs," Annual, Washington, D.C. , February

1980.

5. American Petroleum Institute, American Gas Association,

and Candian Petroleum Association, "Reserves of Crude

Oil, Natural Gas liquids, and Natural Gas in the United

States and Canada as of December 3 1, 1979", Volume 34,

Washington, D.C, June 1980, annual.

6. Ariri-Garoussi, K. and Hayer, I. S., "A Survey of

Approaches to World Petroleum Resource Estimation,"

Department of Statistics, Princeton University, Januarv,

1980.

7. Arps, J. J. and Roberts, T. G. , "Economics of Drilling

for Cretaceous Oil on East Flank of Denver- Julesburq

Basin," Bul let in of American A ssociation of Petroleum

Geologists, Volume 4 2, No. If, November, 195 8.

8. Arps, J. J., fi. Mortada and A.E. Smith, "Relationship

Between Proved Reserves and Exploratory Effort," Journal

617
of Petroleum Technology. June 1971.

9. Attanasi, E. D., Bietzman, W. D. , Garland, T. and Woods,

H. J. , "Economics and Resource Appraisal: The Case of the

Permian Basin," Proceedings of the SPE- AIME Symposium on

Petroleum Economics and Evaluation , Dallas, Texas,

Feburary 1979.

10. Attanasi, E. D. , and Drew, L.J. "Field Expectations and

the Determinants of Wildcat Drilling," Southern Economic

Journal . Volume ftft. Ho. 1, July, 1977.

11. Balcer, Y . , Kaufman, G. H. and Kruyt, D. "A

Probabilistic Model of Oil and Gas Discovery", Studies

iS Geology No. 1, AAPG, 1975, pp. 113-142.

12. Barouch, E. D. and Kaufman, G. M. , "Detection of

Geologic Anomalies by Grid Line Search," Massachusetts

Institute Technology, Energy Laboratory Working Paper

Ho. MIT-E1-79-008WP, Cambrigde, Mass., February 1979.

13. Barouch, E. D. and Kaufman, G. H., "The Interface

between Geostatistical Modeling of Oil and Gas Discovery

and Economics," Proceed ings of the Symposium Geologj,

Volume 10, Ho. 5, 1978.

1ft. Barouch, E. D. and Kaufman, G. H. , "The Structure of

Probabilistic Discovery Process Models," MIT Sloan

School, Unpublished Paper.

15. Barouch, E. , and Kaufman, G.M. "The Structure of

Probabilistic Modeling of Oil and Gas Discovery,"

Energy: Mathematics and Models, edited by F. S. Roberts.

Society for Industrial and Applied Mathematics,

Philadelphia, 1967, pp. 133-152.

16. Bawiec, W. J., Drew D. J. and Root, D. H. , "Estimating

Future Rates of Petroleum Discoveries in the Permian

Basin," Proceedings of the S PE-AIHE Symposium on

Petroleum Economics and Evaluation, Dallas, Texas,

February 11-13, 1979.

17. Bell, K. L. , Meyer, L. S. and Perwin, E. S. , "On the Use

of Cru<1e oil Initial Production statistics to Estimate

Ultimate Production," Department of Statistics,

Princeton University, Feburary 1979.

18. Benjamini, Y. , Benjamini, P., Deffeyes, K. S.,

Silverman, B. , Stine, R. A. and Watson, G. S., "Volume

and Area of Oil Fields and Validation Prolect",

Departments of Statistics and Geology, Princeton

618
University, January 1980.

19. Bureau of the Census, Annual Survey of Oil and Gas,

MA: 13K (78) -1 , Department of Commerce.

20. Chapman, R. E. , Petroleum G eology. Elsevier, New York,

1976.

21. Cherniavsky, E. A., "Long-Bange Oil and Gas Forecasting

Methodologies: literature Survey," Department of Energy

and Enivironment, Brookhaven National Laboratory, Upton,

N.Y. May 1980.

22. Committee on Energy Taxation, National Research Council,

"Energy Taxation: An Analysis of Selected Taxes,"

EIA/DOE, Septeaber, 1980.

23. Ciliano, R. , Limaye, D. and Hu, S.D., "A Comparative

State-of-the- &rt Assessment of Gas Supply Modeling,"

Palo Alto, California, Electric Power Research

Institute, EPRI-EA-201, February 1977.

24. Ciliano, R. , Fallah, M.H. and Limaye, D. , "Comparative

State-of-the- Art-Assesment of Oil Supply Modeling," Palo

Alto, California, Electric Power Research Institute,

EPRT EA-609, June 1978.

25. Cook, E. , "Economic Uncertainties in Assessing Oil and

Gas Resources." Presented to the Annual Meeting,

American Association for the Advancement of Science,

Houston, Texas, January 5, 1979.

26. Deffeyes, K.S. and HacGregor, T.D., "Slorld Uranium

Resources," Scientific Ame rican , 242, 1, (1980), pp.

66-76.

27. DeGeoffroy, J., and Wu, S.M., "A Statistical Study of

Ore Occurrences in the Greenstone Belts of the Canadian

Shield," Economic Geology, 65 (1970), pp. 496-504.

28. Dickens, Paul F., Effects of Oil Regulation on Prices

and Quantit ies: A Qualitative Analysis, Energy Policy

Study , Volume I, DOE/EJ.A-0201/1 , December 1979.

29. Dickens, Paul F., and Thrasher, Richard, Pricing

Provisions of the Natural Gas Policy Act of J97 8, Energy

Policy Stud y Volume 3, DOE/FIA-0201/3, 0ctober~1979.

30. Dietzman, W.D., Pearce, H.F., Anderson, T.C., and Funk,

V.T., Cost and I ndexes for Oilfield Equipment and

Production Operations in the United States, EIA/DOE,

619
Dallas, Texas, October 1978.

31. Drew, L. J., "Analysis of the Bate of Wildcat Drilling

and Deposit Discovery," Mathematical Geology, Volume 7,

(1975).

32. Drew, L. J., "Linkage Effects Between Deposit Discovery

and Post-Discovery Exploratory Drilling, "Journal

Research 0. s. Geological Survey, Volume 3, March- Apr il

,

1975, Reston, 7a., pp. 169-179.

33. Drew, L. J., "Pattern Drilling Exploration: Optimum

Pattern Types and Hole Spacings When Searching for

Elliptical Shaped Targets," M athematical Seolocj^, Volume

11, No. 2, 1979.

34. Drew L. J., Root, D. H. and Schuenemeyer, "The TTse of a Discovery Process Model Based on the Concept of Area of

Influence of a Drill Hole to Predict Discovery Rates in

the Denver Basin," Rockv Mountain Association of

Geologist, 1978 Symposium.

35. Drew, L. J., Rttanasi, E. D. , and Poot, D. H.

,

"Importance of Physical Parameters in Petroleum

Petroleum Supply Model, " Proceedings of the Mineral

Economics , Symposium _AIME, Volume 3, pp. 16 3-174,

November 8, 1977.

36. Eckbo, P.L. , Jacoby, H.D. and Smith, J. I., "Oil Supply

Forecasting: A Disaggregated Process Approach," The Bell

Journal of Economics, 9, 1, (1978), pp. 218-235.

37. Energy Information Administration, Annual Report to

Congress, V olume s 1, 2, 3, DOE/EIH-0173 (1979)

38. Epple, D.N., " Petroleum Discoveries and Government

Policy." Ballinger Publishing Company, Cambridge, Mass.,

1975.

39. Everett C. , Mahn, N. and Jones, K. , Mid term Oi l and Gas

Supply Modeling S ystem Description, EI A/DOE, Washington,

D.C., November 1978, TM/ES/79-05.

40. Financial Accounting Standards Board, Statement of

Financial Accounting Standards, No. 19, Financial

Accounting and Reporting by oil and Gas Producing

Companies, Stanford, Connecticut, December 1977.

41. Feller, W. , Introduction to Probability Theory and Its

Applications Volume II. John Wiley and Sons, Inc. , New

York, 1966.

620
42. Frederiksen, fl. J. , An A nalysis of the Productivity of

Domestic Petroleu m Expl oration Activities. Energy

Information Administration, AH/EI/78-14, (1978) .

43. Griffiths, J.C. , "Exploration for Natural Besonrces,"

Operations Besearch 2 (1966), pp. 189-209.

44 . Harris, C. M. A Statistical Method for the Assessment

of Model Sensitivity to Injgut Variables, Report to

National Bureau of Standards, August, 1979.

45. Harris, CM., and Hirshfield, D. , "Sensitivity Analysis

of DOE Forecasts of Midterm Oil and Gas Supply for the

1978 Annual R eport to Congress, " Draft National Bureau

of Standards technical report, March 1980.

46. Halbounty, M.T., "The Future of Giant Oil Fields,"

Offshore. June 20, 1980.

47. Heal, G . , "The Relationship Between Price and Extraction

Cost for A Resource With A Backstop Technology," The

Bell Journal of Eco nomic s, 7, 2, (1976) , pp. 371-378.

48. Hotelling H., "The Economics of Exhaustible Resouces,"

Jou rnal of Economics, Volume 39, No. 2, April 1931.

49. Hayes, J. H . , "Petroleum — A Prediction Hade in 1950,"

Rand Corp.i December 1973.

50. Herron, H. E., Humar, R. M. and Kurta, B., "Lower-48

Natural Gas Supply Potential From Conventional Sources,"

Proceedings of the SPE-AIME Symposium on Petroleum

Economics and Eva luation, Dallas, Texas, February 13-15,

1979." 0184/29, February, 1980.

51. Hoffman, K. H. and Joel, 1. S. , An Annotated Restatement

of the Midterm Oil and Gas Supply Modeling Sy_stem

Methodology

,

National Bureau of Standards, Washington,

D.C., June, 1980.

52. Hubbert, M.K., Energy Resources: A Report to the

Committee on Natural Resources of the National Academy

Sciences National Research Council, Washington, D.C.,

U.S. Government Printing Office, 1962. Publication

1000-D.

53. Hubbert, M.K. , "National Academy of Sciences Report on

Energy Resources: Reply," American Associa t ion of

Petroleum Geologists, 49, 10 (1965), pp. 1720-1727.

621
54. Hubbert, H.K., U T S. Energ; Resources. A Review as of

1972. Part 1 of k National Fuels and Energy Policy

Study. Washington, D.C., U.S. Government Printing

Office, 1974. Serial No. 93-40 (92-75) , pp. 1-267.

55. Hughes Tool Company, "Average Number of Rigs in Use,"

Weekly, Houston, Texas.

56. ICF, Incorporated, n h Review of the Methodology of

Selected U.S. Oil and Gas Supply Models," June 1980,

Washington, D.C.

57. United States. Interagency Oil and Gas Supply Project,

"Future Supply of Oil and Gas from the Permian Basin of

West Texas and Southeastern New Mexico," Geological

Survey Circular 828.

58. Internal Revenue Service, Busines s Income Tax Returns^

A nnual. Department of Treasury.

59. Internal Revenue Service, Corporation I ncome Tax

Returns. Annual. Department of Treasury.

60. Kaufman, G. H. , "Models and Methods for Estimating

Undiscovered Oil and Gas—What They Do and Do Not Do,"

First IIASA, M. Grenon, Editor, Hay, 1975.

61. Kaufman, G. M. , Livne, Z. and Ruggaldier, W. "Predicting

the Time Rate of Supply from a Petroleum Play," Energy

Laboratory Working Paper, No. NIT-EL-79-001WP, January,

1979.

62. Kaufman, G. M. and Wang, J. W., "Model Mis-Specification

and the Princeton Study of Volume and Area of Oil Fields

and Their Impact on the Order of Discovery," Sloan

School of Management, Energy Laboratory Working Paper,

No. HIT-EL-80-3WP, January, 1980.

63. Kaufman, G.M. , Statist ica l Decisi on and Related

Techniques in Oil . and Gas Exploration . Englewood Cliffs,

N.J., Prentice-Hall, Inc., 1963.

64. Khazzoom, J.D., "The Federal Power Commission Staff's

Econometric Model of Natural Gas Supply in the TTnited

States," The Bell Journal of Economics and Management

S ciences. 2, 1 (1971), pp. 51-93.

65. Macftvoy, P. W. and Pindyck, R.S., "Alternative Regulatory

Policies for Dealing with the Natural Gas Shortage," The

Bell J ournal of Economics and Man aqeme nt Science, 4, 2

(1973), pp. 454-498.

622
66. Levorsen, A.I., Geology of Petrolenm , Second Edition,

w". H. Freeman, San Francisco, California, 1967.

67. Marshall, E., "Energy Forecasts: Sinking to New Lows,"

Science , Volume 208, June, 1980.

68. Master, C. D. , "U.S. Oil Resources: The Critical

Years," Pet ro leg

E ngineer Internationa l, December,

1977.

69. Maugh T. H. , "Mining Could Increase Petroleum Reserves,"

Science , Volume 207, March, 1980.

70. Mayer, L.S. , Silverman, B. , Zeger, S. L. , and Bruce,

A.G., "Assessing the Hubbert Approach to Modeling Rate

of Domestic Crude Oil Production," Department of

Statistics and Geology, Princeton University, September

1979.

71. McKelvey, V.E., M ineral Resources Estimates an d Public

Policy in United States Mineral R esources, edited by

D.A., Brobst and S.P., Pratt U.S. Geological Survey

Prof. Paper 820 pp. 9-19.

7 2. Mead, H. N. , "Modifications to Decline Curve Analysis,"

Transactions of AIME, Volume 207, pp. 11-15, Venezuelan

Atlantic Refining Company, Caracas, Venezuela, 1956.

73. McDonald, S.L., Petroleum Conservation in t h e United

States , John Hopkins University Press, Baltimore, Md.

1971.

74. McDonald, S.L., The leasing of Federal Lands for Fossil

Fuels Production , John Hopkins Univ. Press, Baltimore

Md, 1979.

75. Menard, H. W. and Sharman, G. , "Scientific Uses of

Random Drilling Models," Science , Volume 190, No. 4214,

October, 1975.

76. Mendershausen, H. and Nehring, R. , "Protecting the U.S

Petroleum Market Against Future Denials of Imports,"

Rand Corp., ARPft Order No. 189-1, October, 1974.

77. Miller, B. M. , "The Evolution in the Development of the

Petroleum Resource Appraisal Procedures in the U.S.

Geological Survey and a Summary of Current Assessments

for the United States," Proceedings of the SPE-RIME

S ym posium on Petroleum Economics and Evaluation , Dallas,

Texas, 1979.

623
78. Hiller, B.H., Thomsen, H.L., DoIton , G.L., Coury, A.B.

,

Hendricks, T. A. , Lennartz, F. E. , Powers, R. B. , Sable,

E.G. and Varnes, K.L. , Geological Estimates of

Undiscovered Recoverable Oil and Gas Resources in the

United States . Eeston. Va. , U.S. Geological Survey,

1975. Circular 725.

79. Homper, J. A., "Domestic Oil Reserves Forecasting," Oil

and Gas Journal, 77, 33 (August 13, 1979), pp. 144-149.

80. Murphy, F. H. , Sanders, R. C. , Shaw, S. H. and Thrasher,

R. 1., Modeling Natnral Gas Regulatory. Proposals rising

the Project Independence E valuation System, Energy

Information Administration, Department of Energy,

TR/AOA/79-, 1978.

81. Hehring, Richard, "Giant Oil Fields and World Oil

Resources," Rand Corporation, Santa Monica, Calif., June

1978.

82. Nordhaus, W. D., "The Allocation of Energy Resources,"

Brookings Papers on Economics Activity, Harch, 1973,

Brookings Institution, Washington, D. C.

83. Ody Nancy, "A Chronology of Oil and Gas Regulations,"

[DOE/EIA1 Draft Techncial Report.

84. Pindyck, R.S., "The Optimal Exploration and Production

of Nonrenewable Resources", Journal oj Poli tical

Economy . 86, 5 (1978), pp. 841-861.

85. Ramsey, J. B., "The Economics of Oil Exploration, A

Probability of Ruin Approach," Energy Economics

,

January, 1980.

86. Rapoport, L. A., "Methodology for Development of

Normalize Exploration Functions and of Related Data

Base," Lorendas Project, Virginia Polytechnic Institute

and State University, June 1978.

87. Reed Tool Company, Annual Rotary Rig Census,

Drilling-DCW, October 1980.

88. Root, D.H. , and Drew, L.J. "The Pattern of the Petroleum

Discovery Rates," American Scientist. Volume 67, No. 6,

November-December, 1979.

89. Ryan, J.M. , "National Academy of Sciences Report on Energy Resources: Discussion of Limitations of Logistic

Projections," Bu lle tin of th e American Association of

I

624
P etrole

Geo log ists* 49, 10 (1965).

90. Byan, J.N. , "Limitations of Statistical Methods for

Predicting Petroleum and Natural Gas Reserves and

Availability, B Journal of Petroleum Technology. 18, 3

(1966) , pp 281-284.

91. Ryckborst, "Determining Probable Maximum Size of Oil,

Gas Pools, Oil in Place Volumes," Oil and Gas Journal,

78, 6 (Feb. 1 1, 1980)

92. Sather, C. J., "A Capital Budgeting Model for Petroleum

Exploration," Department of Mineral Economics, Colorado

School of Mines, No. T-1760, (1975).

93. Searl, M.F. , "Resource Assessment and Supply Curve

Development," in First IIASA Conference on Energy

Resources, edited by M. Grenon, Laxenburg, Austria,

International Institute for Applied Systems Analvsis,

May 1975, pp. 71-84, CP-76-4.

94. Seidl, R.F., Implications cf Changing 0^1 Prices on

Resource Eval uation in The Future Supply of Nature-made

Petroleum and Gas, edited by R.F. , Meyer. New York,

Pergamon Press, 1977, pp. 113-138.

95. Singer, D.A., and Drew, I.J. and "The Area of Influence

of an Exploratory Hole," Economics Geology. Volume 71,

Ho. 3, May 1976, pp. 642-647.

96. Society of Exploration Geophysicists, "Average Number of

Seismic Crews and Lines Miles of Seismic Surveys," SEG

New Release, Monthly, Tulsa, Oklahoma.

97. Tukey, J., presentation to EI A on Den ver-Julesburg Basin

data. Autumn 1979.

625
appendix R Definitions

This appendix is provided to establish definitions for terns

that are often ambiguous.

Barrel

Oil or <jas

in-Place

Oil or gas

2221

(reservoir)

Oil or

gas field

Province

Standard barrel of 42 U.S. gallons, used as an

oil measure, abbreviated as Bbl.

The total amount of oil or gas contained

in a reservoir, a portion of which

will remain in the reservoir upon abandonment

for economic or technological reasons.

A discrete unit of porous, permeable

rock containing oil and or gas and

distinguished by a single pressure system so

that withdrawal of fluids from any part of the

reservoir affects the pressure in all other

parts. The terms "reservoir" and "pool" are

synonymous and are used interchangeably.

Any area underlain by one or more oil

and/or gas pools (reservoirs) that are

recognized as being part of a common geologic

or production unit. Where only one reservoir

is involved, the terms "field" and "pool" (or

"reservoir") may be used interchangeably to

designate the same unit.

A large, bowl-shaped subsurface geologic

feature formed by downwarping of the

underlying basement rock and filled with

sedimentary rocks. Large basins such as the

Permian Basin may be divided after initial

formation by uplifts and platforms which in

effect create other basins (such as the

Midland and Delaware Basins) within the

original structure.

A rather loosely defined term implying a region of common geologic character that

contains one or more basins.

Resource A concentration of naturally occurring solid

or liquid petroleum or petroleum-like

626
material, or natural gas, in or on the Earth's

crust in such form that economic extraction is

currently or potentially feasible. The

resource includes all tfee material in-place in

a deposit.

Discovered

resources Resources, and reasonable extensions

thereof, whose location, quality, and guantity

are known from drilling and geologic evidence

supported by engineering measurements.

fl n disco vered

resources Resources surmised to exist on the basis

of broad geologic knowledge and theory.

Reserve That portion of the resource base from which a usable mineral and energy commodity can be

economically extracted at the time of

estimation. Such commodities include but are

not necessarily restricted to petroleum,

condensate, natural gas, tar sands, and

naturally occurring asphalt, without regard to

mode of occurrence. In terms of the resource

classification nomenclature, this includes

proved, indicated, and inferred categories.

Prove d

reserve Material for which estimates of the

guality and guantity have been computed from

analyses and measurements from closely spaced

and geologically well-known sample sites.

627
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628
Appendix C

AAPG (CSD) WELL CLASSIFICATIONS

CODE

NO.

1 — NEW-FIELD WILDCAT - A new-field wildcat is a well located on a structural feature or other type of trap which has not previously produced oil or gas. In regions where local geological conditions have little or no control over

accumulations, these wells are generally at least two miles from the nearest productive area. Distance, however, is not the determining factor. Of greater importance is the degree of risk assumed by the operator, and his intention to

test a structure or stratigraphic condition not previously proved productive.

2 — NEW-POOL WILDCAT - A new-pool wildcat is a well located to explore for a new pool on a structural feature or other type of trap already producing oil or gas, but outside the known limits of the presently producing area. In some

regions where local geological conditions exert an almost negligible control, exploratory holes of this type may be

called "near wildcats." Such wells will usually be less than two miles from the nearest productive area.

3 — DEEFER-POOL TEST - A deeper-pool test is an exploratory hole located within the productive area of a pool, or pools, already partly or wholly developed. It is drilled below the deepest productive pool in order to explore for deeper

unknown prospects.

4 — SHALLOWER-POOL TEST - A shallower-pool test is an exploratory well drilled in search of a new productive reservoir, unknown but possibly suspected from data secured from other wells, and shallower than known productive pools. The test is located within the productive area of a pool or pools, previously developed.

5 — OUTPOST (EXTENSION) TEST - An outpost is a well located and drilled with the expectation of extending for a

considerable distance the productive area of a partly developed pool. It is usually two or more locations distant from

the nearest productive site. 6 — DEVELOPMENT WELL - in general, a development well is a well drilled within the proved area of an oil or gas

reservoir to the depth of a stratigraphic horizon known to be productive. If the well is completed for production, it is classified as an oil or gas development well. If the well is not completed for production, it is classified as a dry

development hole.

7 — STRATIGRAPHIC TEST - A stratigraphic test is a drilling effort, geologically directed, to obtain information pertaining

to a specific geological condition that might lead toward the discovery of an accumulation of hydrocarbons. Such

wells are customarily drilled without the intention of being completed for hydrocarbon production. This classification also includes tests identified as core tests and oil types of expendable holes related to hydrocarbon exploration.

8 — SERVICE WELL - A service well is a well drilled or completed for the purpose of supporting production in an existing

field. Wells of this class are drilled for the following specific purposes.

Gas injection (natural gas, propane, butane, or flue gas) Water injection Steam injection Air injection

Salt water disposal Water supply for injection Observation

Injection for in-situ combustion

OWDD- An old well drilled deeper is a previously drilled hole which is reentered and deepened by additional drilling. Such wells are reported as either oil or gas wells if completed for the production of oil or gas; or as dry holes if sufficient quantities of oil or gas are not found to justify completion of the greater depth.

ESTIAAATED ULTIMATE YIELD

This item must be filled in for all New Field Wildcat discoveries and successful Deeper Pool Tests. The yield indicated should

reflect the possible overall significance of the discovery, based upon the best professional judgement of the CSD

committeemen. Letter values are: A— over 50 million barrels cr 300 billion cubic feet; 8=25 to 50 miijion barrels or 150 to 300 billion cubic feet; C= iO to 25 million barrels or 60 to !50 BCF, D= 1 to 10 million barrels or 6 to 60 BCF; E=less than 1 million barrels or less than 6 BCF; F= abandoned as non-profitable.

629
OIL/GAS SUPPLY MODELING CONSIDERATIONS IN

LONG-RANGE FORECASTING

Ellen A. Chernlavsky

Brookhaven National Laboratory

National Center for Analysis of Energy Systems

Building 475

Upton, New York 11973

Oil and gas supply modeling may not only generate forecasts on a "stand-alone" basis, but may provide input data and assumptions to large

scale, long-range integrated energy -economy models. In such a framework,

parameters that may not have seemed especially crucial in the stand-alone

formulation may be found to have an unexpectedly great influence on the

results. Additionally, it may become necessary to incorporate considerations that are usually omitted from conventional oil and gas supply

models. This paper discusses two examples of this: the decline rate, or more generally the production profile, and the treatment of resource exhaustion.

This investigation arose in connection with a project for the Energy

Information Administration (EIA) . One part of the project was to incorporate the assumptions and input data of EIA's Midterm Oil and Gas Modeling

System (MOGSMS), which has already been discussed in this symposium, into

EIA's Long-Term Energy Analysis Program (LEAP).

LEAP is a large scale general equilibrium model of energy economy

interactions. Its time horizon spans 50 years. In each time period, the

energy -economy system is represented by a network of process nodes. At the

"bottom" of the network are the resource process nodes. They accept quantities as inputs, and output the prices required to bring forth those

quantities. (Fuller description of the basic general equilibrium model

structure may be found in (1) while more detail on the resource submodels

appears in(2)X The prices and quantities are then passed up the network. At

the "top" of the network are demand process nodes which take prices as inputs and output quantities. The new quantities are passed back down

through the network. If they are the same as those previously input to the resource process, convergence has been achieved, and the general equilibrium sought has been found. In the course of incorporating MOGSMS oil and

gas assumptions and input data into the LEAP oil and gas resource processes, it became apparent that the decline rate plays a major role.

630
It is typically assumed, in oil and gas supply models, and also in

LEAP, that the production from proved reserves will follow an exponentially

declining pattern. Equivalently , a fixed fraction of reserves is produced

each year. This fixed fraction, or production to reserves ratio, is called

the decline rate. In LEAP, the decline rate, by determining production,

implies levels of commitments (i.e., reserves that must be discovered and

proved) that must be achieved. The cumulative commitment level is related

to the capital investment required by an increasing function, reflecting

the assumption that costs of discovery will increase as the resource base

is depleted. Finally, the price is computed using discounted cash flow

techniques and adding a bonus for scarcity rent; the decline rate determines the behavior of the revenue stream. Figure 1 depicts the role of the

decline rate on the production schedule.

The importance of the decline rate can be illustrated by considering

its impacts on commitment levels and the differential between minimum

acceptable price and operating cost. First, the commitment levels vary as the inverse of the decline rate, which is a relatively small number, on the

order of ten percent, so that small absolute differences in estimates of

its value cause required commitments to vary widely. Suppose d is the

decline rate, and R is initial reserves. Then production in year n is

R*d*(l-d) n "1.

If q is the quantity required in a given year, then C, the commitment level

required, is given by

C = q/d.

Comparing commitment level C when d = 0.11 with commitment levels C when

d = 0.08, one finds

c< - c

= vdin: - m = £ - 1 = 0.375.

C q/d d

1

This is a substantial difference, which is even more important when one considers the implications for oil-in -place discovered; normally only a third of oil-in-place is ultimately recovered. The potential difficulty is

somewhat alleviated by the fact that the LEAP time frame is five years.

Given q, one must determine the commitment level required to produce at an average quantity q over five years:

5

1/5 * C * £ d*(l-d) n -i = q

n=l

631
QUANTITIES DEMANDED

i

Decline rate determines resource commitment levels In

each time period needed to produce these quantities

I

Commitments determine capital cost in each time period

i

Using discounted cash flow techniques, capital cost

(a function of the decline rate) is set equal to

net present revenue (also a functon of the decline

rate) to find minimum acceptable price

I

Output price is minimum acceptable price plus

a bonus for scarcity rent

i

PRICES

REST OF LEAP

Figure 1 Functions of the Decline Rate in LEAP

632
or

C = 5q/[l-(l-d) 5

].

Again comparing the commitment levels,

C - C = [l-Cl-d') 5 ]-1 r [l-(l-d) 5 ]"1

C [l-(l-d)'5 ]-1

,

l-(l-«)5 ml , q.295

l-(l-d') 5

Given this potential sensitivity, two questions arise: first, is

there that much variation in the data, and second, does it matter in the

long-run.

The answer to the first question is that the decline rate has not

remained constant over time, as is seen in Table 1. These data are taken

from the Energy Information Administration (EIA) Annual Report to Congress

(Ref. 5, pp. 32 and 39). The behavior of this parameter has been erratic:

it has not been monotonically increasing, as one might expect due to technological progress, and even between two consecutive years the difference

in decline rates can be as much as 34 percent. Of course, the discontinuity in 1970-1971 is due to the Prudhoe Bay discovery, production from which

could not begin until completion of the Alaskan pipeline. Cumulative

production from Prudhoe Bay up to the beginning of 1978 was only 129.4

million barrels (Ref. 6, p. 216). When Prudhoe Bay reserves are removed

from the calculation, the decline rate continues to rise (although not

monotonically) to nearly 14 percent.

When one looks at regional data, for south Alaska and the Lower-48,

the picture is even worse. Data collected for the 1977 update of the

Midterm Oil and Gas Supply Modeling System(4)and listed in Table 2 show

regional decline rates ranging from 9.9 to 19.1 percent. The weighted

average is 13.4 percent. (These are the National Petroleum Council Oil and

Gas regions, shown in Figure 2.) The differences in regional characteristics could greatly affect the future behavior of the average decline rate,

since some regions have far better prospects than others. The conclusion

is that decline rate data show a significant amount of variation, both

regionally and over time.

The next question is, what effects does this uncertainty have over an extended time horizon? Will it all even out in the end?

633
I

U.S. Production to

Table 1 Reserves Ratios, 1949-1978

Year

Reserves

10 9 bbl

Production

10 6 bbl/day Ratio

1949 23.3 5.05 0.0791

1950 24.6 5.41 0.0803

1951 25.3 6.16 0.0889

1 Q CO liOZ 0"7 C Z/ .J 0 . ZD U . UoJl

1953 28.0 6.46 0.0842

1954 28.9 6.34 0.0801

1955 29.6 6.81 0.0840

1956 30.0 7.15 0.0870

1957 30.4 7.17 0.0861

1958 30.3 6.71 0.0808

1959 30.5 7.05 0.0844

1960 31.7 7.04 0.0811

1961 31.6 1.18 0.0829

1 CiC o 19oZ 1.55 U.Uo41

1963 31.4 7.54 0.0876

1964 31.0 7.61 0.0896

1965 31.0 7.80 0.0918

1966 31.4 8.30 0.0965

1967 31.5 8.81 0.1021

1968 31.4 8.66 0.1007

1969 30.7 8.78 0.1044

1970 29.6 9.18 0.1132

1971 39.0 9.03 0.0845

1972 38.1 9.00 0.0862

1973 36.3 8.78 0.0883

1974 35.3 8.38 0.0866

1975 34.2 8.01 0.0855

1976 32.7 7.78 0.0868

1977 30.9 7.88 0.0931

1978 29.5 8.67 0.1073

634
Table 2

Regional Decline Rates

Region Reserves Decline Rate

1 386 0.154

2 2,728 0.099

2A 862 0.099

3 356 0.178

4 1,259 0.150

5 5,948 0.130

6 5,719 0.138

7 1,700 0.138

8-10 571 0.154

11 40 0.191

11A 0 0.155

21,537

635
636
Consider cumulative production over a 30 year well life for different

decline rates, as shown in Table 3. The differences are especially marked

in the early years, e.g., a 50 percent difference after five years between

cumulative production given decline rates of eight and 15 percent. One can

see that production levels each year will be higher for some years given a higher initial decline rate. For the first nine years, yearly production

with d = 0.13 exceeds that at d = 0.08. One can calculate the "break -even"

year n at which production at the lower rate, d]_, equals or exceeds

production at the higher decline rate, d2 •

di (l-d!) 11 "1

>_ d2 (l-d2 ) n "1

when

n > 1 + ln(di/d2 )/ln[(l-d2)/(l-d 1 )], for di < d2

.

Comparing rates of 0.10 and 0.13, one finds n ^ 8 years; this holds even

for di = 0.12, d 2 = 0.13.

The immediate implication is that for normal discount rates, the minimum acceptable price, using discounted cash flow techniques, will be higher

for the project with the lower decline rate. (In M0GSMS, total yearly

discoveries in a region are treated as a single project.) How much higher

can be estimated by looking at the expression for present value of discounted cash flow as a function of discount and decline rates, PV(d,<5),

assuming constant prices and operating costs or a constant differential.

L

PV(d,5) = £ (p-^)d(l - d)*-l 5k-l

k=l

where

p = minimum acceptable price,

it = operating cost,

d = decline rate,

6 = discount factor,

L = lifetime.

This can be rewritten as

xx ,

v L (1 - [1 - d)6] L

) PV(d,6) = (p - 77) d* 1 . (1 , jU

637
Table 3

Cumulative Production, 1 - (1 - d) n

N d=.08 d=.10 d=.ll d=.13 d=.15

1 0.08 0.10 0.11 0.13 0.15

2 0.1536 0.19 0.2079 0.2431 0.2775

3 0.2213 0.271 0.2950 0.3415 0.3859

4 0.2836 0.3439 0.3726 0.4271 0.4780

5 0.3409 0.4095 0.4416 0.5016 0.5563

10 0.5656 0.6513 0.6882 0.7516 0.8031

15 0.7137 0.7941 0.8259 0.8762 0.9126

20 0.8113 0.9284 0.9028 0.9383 0.9612

25 0.8756 0.9282 0.9457 0.9692 0.9828

30 0.9180 0.9576 0..9597 0.9847 0.9924

The term in brackets is the present value of production,

PVP(d,6) = d*[l-((l-d)6)L]/[l-(l-d)6].

Values of this present value of production for different decline rates are shown in Table 4 with a lifetime L=30. For 6 = 0.10, the present value of

production when d = 0.13 is about 1.3 times the present value of production

when d = 0.10. In general, at the same discount rate the present value of

production is proportional to the decline rate, while for the same decline

rate the percentage difference in present value of production is proportional to the percentage difference in discount rate (e.g. increasing

<5 from 0.05 to 0.10 causes roughly a five percent increase in present value

of production).

Table 4

Present Value of Production

Decline Rate 6 = 0.05 6 = 0.10 6 = 0.15

0.08 0.0839 0.0881 0.0928

0.09 0.0943 0.0990 0.1042

0.10 0.1047 0.1099 0.1156

0.11 0.1151 0.1207 0.1269

0.12 0.1255 0.1316 0.1382

0.13 0.1359 0.1424 0.1495

0.14 0.1463 0.1532 0.1607

0.15 0.1567 0.1639 0.1719

0.16 0.1670 0.1747 0.1831

0.17 0.1774 0.1854 0.1942

0.18 0.1877 0.1961 0.2052

0.19 0.1980 0.2067 0.2163

0.20 0.2083 0.2174 0.2273

638
The proper value to use for the discount rate has often been debated,

so one might wonder whether uncertainties in the decline rate are over- shadowed by uncertainties in this parameter. This seems not to be true.

For example, if the decline rate is 13 percent and the discount rate

changes from 10 to 15 percent, the decline rate that would yield the same present value of production as before is 12.4 percent (L = 30). There does

not exist a positive discount factor which equalizes present value of production with a 10 percent discount factor and 10 percent decline rate to

present value of production with a 13 percent decline rate.

In some energy models, what happens in future periods is discounted:

for example in linear programming models where the objective is to minimize

total discounted cost over the time horizon. But in LEAP, although prices

are partly computed using discounted cash flow techniques, each time period

is equally important. Within the LEAP resource submodel framework, the

decline rate has a more profound effect than the discount rate, though the

latter, being thought a more judgemental and political parameter, tends to

be exposed and discussed to a far greater extent.

Pursuing the investigation of the effect of the decline rate on minimum acceptable price, if one equates the present value of cash flow for two

different decline rates, one finds that the inverse of the ratio of present

values of production equals the ratio of differentials between minimum

acceptable price and operating cost.

(Pi ) * PVP(dlf « ) - (P2

- *) * PVP(d2 , 6 )

Pl-TT

Pl

pi : ^2

pi

>

Ratio of present

values of

production

percentage

change in

present value

of production

ratio of

profit

to price

percentage

change

in price

639
so if the decline rate is 10 percent instead of 13 percent, the differential between price and operating cost must rime by about 30 percent. Even

a change from 13 to 12 percent involves an increase in the differential of

8 percent.

The decline rate affects the minimum acceptable price in another way.

Within the LEAP methodology, it is assumed that an input curve relates

capital investment to cumulative commitments. This capital investment then

enters the minimum acceptable price computation (adjustments for technological change over time may be made). Suppose quantities qi,q2»»«« are demanded, and the decline rate is d. One can calculate commitment levels

I&1 » ]&2 * * * * assuming, without loss of generality, no initial reserves.

In the first year, one must have

qi = Rxd.

In the second year, R^(l-d) of those reserves remain, so

q2 = Ri(l - d)d + R2 d.

In general,

«r = Zk=l *k (1 "

By induction,

Rl = qi/d

Rn = [qn

- (1 - d) qn -i]/d,

so cumulative commitments at year n are

I? R

j " ZJT

1

<lj +

In any year n, the difference in commitment levels with decline rates d'

and d is

qn

*(l/d' - 1/d).

With d' = 0.10, d = 0.13, the factor multiplying qn is 2.3. In LEAP, the

time period is five years, so the aggregation magnifies differences by a factor of five. Depending on the steepness of the capital cost curve,

small changes in the decline rate mean large changes in commitment levels;

for conventional oil and gas this curve becomes steep in the LEAP time

because these resources are nearing exhaustion.

640
The preceeding discussion of the impacts of the decline rate may be

generalized by considering production schedules which need not be exponentially declining. In practice, production from an oil well does not

strictly follow this pattern, because of secondary recovery efforts -and

developmental drilling. The question is whether it is necessary to represent the production schedule explicitly. An alternative is to find a decline rate which yields the same present value of production. It is easy

to see that this can be done, since

f(x) = PVP(x,6)

= (l-[(l - x) 6]

L

) * x/[l-(l - x) 6 ]

is the product of two non-negative functions increasing in x for x in [0,1]

and is therefore increasing for x in [0,1]. f(0) = 0, f(l) = 1 and f is

continuous in [0,1], therefore if

0 < X£=i \ - Q < l >

where is fraction of ultimate production in year k (E q^ = 1) then some

(unique) value of x exists such that f(x) = Q. In fact, under not very

stringent conditions, it is possible to find a decline rate which, given

future prices and operating costs, will yield the same present value of net revenue as an arbitrary production schedule. One might anticipate that as long as the equalizing decline rate value is near the first year's production fraction, meaning that first year commitment levels will be about the same in either case, the approximation will suffice.

First, consider the case where production is constant over a 30 year

life. Then d = 1/30 = 0.0333. The equivalent decline rate, at a 10

percent discount rate, is d' = 0.0334. If the time periods are aggregated

to five years, the LEAP time step, d = 0.167 and d' = 0.17. The equivalent

decline rate does turn out to be near the first period's production fraction. The resulting production patterns are shown in Table 5. Although

cumulative production levels are reasonably close for the first two to

three time periods, the ultimate production using the equivalent decline

rate is only two thirds of the true value. This Implies that commitment

levels will be higher than if the actual production schedule was used.

Prices will be higher and production lower than the "true" values. So

while the decline rate formulation is mathematically tractable, it appears

to yield a poor approximation in these cases.

641
Table 5

Production Patterns

Cumulative Production - 30 year life

Year

Constant

Production

Equivalent

Decline Rate

1 .0333 .0334

2 .0667 .0658

3 .1000 .0970

5 .1667 .1564

10 .3333 .2884

20 .6667 .4936

30 1.0000 .6396

Cumulative Production - 6 period life

Time

Period Years

Constant

Production

Equivalent

Decline Rate

1 5 .167 .170

2 10 .333 .310

3 15 .500 .428

4 20 .667 .525

5 25 .833 .606

6 30 1.000 .673

642
Although a constant production level pattern is more characteristic of

coal mines than oil and gas reservoirs, the investigation above is relevant

because enhanced oil recovery (EOR) projects follow a pattern similar to

that of coal. A typical EOR schedule (Ref. 3, p. 31) is given below.

EOR Production Schedule

Steam Drive

Percent of

Year Incremental Recovery

1 12

2 22

3 22

4 20

5 14

6 10

In conclusion, the outputs of the LEAP resource submodel are quite

sensitive to variations in the decline rate. The evidence is that this

parameter's influence in the LEAP framework, outweighs that of the discount

rate, which is usually assumed to play a major role in long-term models.

Quantifying the decline rate is not a straight -forward matter. The

national data show significant variation over time; regionally the dispersion is even greater. To some extent reservoir production schedules can be

altered by drilling additional wells; one can expect this to happen if the

economics provide appropriate incentives. An important future direction

for oil and gas supply model development is investigation and representation of the regional and economic factors affecting oil and gas production

schedules.

Another modeling consideration that deserves more attention is the

effects of depleting the resource base. It is expected that conventional

sources of oil and gas will be exhausted in the long-term time frame. What

happens in the model when resources run out?

643
In a linear programming formulation, one can always impose con- straints. Then no matter how high the marginal, or shadow, prices rise, no more of the resource will be forthcoming. Economists criticize this sort

of result on the grounds that in the real world higher prices will in fact

lead to reserve additions.

Another approach is to use a supply curve that rises very sharply as the resource nears depletion, with the hope that increasing prices will

dampen demand. This mechanism is used within LEAP; when the resource is

exhausted, the price is set to a level that represents some multiple (the

actual value is an input parameter) of the last price on the supply curve.

There are two possible problems here, first, one ends up with artificially high prices being passed through the network, perhaps impeding

convergence; second, if the ultimate price is not high enough, the model

will behave as though an infinite quantity of the resource is available at

this fixed price. On the other hand, the supply curves are probably higher

than they should be because the sub-economic resource base is not considered. Data are lacking on how extensive it is now; in most oil and gas

models, drilling results either in success or failure. There's no inbetween. Either the discovery is economically exploitable or it is classified as completely dry. This is not realistic. In the long-term, with

greater depletion and higher prices wells that were previously sub -economic

will be brought into production. For this reason, current models probably

overstate exploratory drilling requirements.

Like subeconomic deposits, enhanced recovery will become increasingly

attractive. This option should be integrated into oil and gas supply

submodel of a large scale energy -economy framework in order to maintain

consistency between price and quantity available for resources extracted in

primary, secondary, or tertiary phases of reservoir development. For oil,

imposing a constraint on ultimate recovery that is lower than oil-in-place

is open to question. After all, the resource is known to be present.

Here, the economics set the limitations.

To summarize, two important areas for oil and gas supply model development and data collection are representation of the decline rate or production schedule from reserves, and the treatment of resource depletion

including the subeconomic resource base and enhanced recovery. Both aspects receive relatively little attention in oil and gas supply models, but

play key roles when the assumptions of these models are integrated into a long-term model such as LEAP.

644
REFERENCES

1. Adler, R.J., Cazalet, E.G., Haas, S.M. , Marshalla,R.A. , Nesbitt, D.M.

,

and Phillips, R.L., The DFI Generalized Equilibrium Modeling System , Decision Focus Incorporated, Palo Alto, CA, Dec. 1979.

2. Cherniavsky, E.A. and Juang, L.L., Resource Submodels of the LongRange Energy Analysis Program; Documentation . Report to the Division

of Long-range Analysis, Energy Information Administration, Department

of Energy, Washington, D.C., Oct. 1979.

3. Division of Oil and Gas Analysis, Office of Energy Source Analysis,

Assistant Administrator for Applied Analysis, EIA, Enhanced Oil

Recovery Model; Methodology and Model Description , Department of

Energy, Washington, D.C., MDR/ES/79 (prepublication draft), 1979.

4. , Medium -Run Oil and Gas Supply Model 1977 Data Update , Department of Energy, Research memo No. 78-015, Dec. 1977.

5. Energy Information Administration, Annual Report to Congress 1978,

Vol. II; Data . DOE/EIA-0173/2 , Department of Energy, Washington,

D.C., 1978.

6. International Petroleum Encyclopedia , Vol. 12 , John C. McCaslin, Ed.,

The Petroleum Publishing Co., Tulsa, OK, 1979.

DISCUSSION

MR WOOD: John Wood, EIA. There are two things I'd like to ask.

The first one would follow some of the remarks made yesterday. Am I right

in assuming you're applying that analysis to the entire United States on a supply curve, or a major subdivision of the United States?

MS. CHERNIAVKSY: Yes. Usually the analysis is done regionally,

using the National Petroleum Council regions, because the data are available for those regions. At other times, the data have been aggregated to a national supply curve.

MR WOOD: Okay. Well, I would suggest to you that you'd better

look at that with extreme care because it looks like a case of badly

stretching the assumptions that were mentioned yesterday. You looked at a discounted cash flow type analysis which is applied to an individual well,

sometimes to a lease, perhaps with care to a field, and you applied it to a reigon, which isn't allowable.

My second question is, in the model, you use what you call the

decline rate, which is really a production to reserve ratio. You know,

that doesn't correspond to the actual production decline rate in any of

those regions, necessarily, which may be higher or lower, depending on how

new discoveries come into the production strain. So, it seems like you're

ignoring an awful lot if you make assumptions that apply to a well — and

then extend them to an entire region of the United States.

645
MS. CHERNIAVSKY: Yes. This is a problem that has been mentioned, as you say, yesterday, that when you go from the smaller to the

larger, it does tend to stretch the assumptions. [However these are the

assumptions in the Midterm Oil and Gas Supply Modeling System, which were

to be incorporated into LEAP]

MR. ALEXANDER: Alexander , DOE. You said you were concerned about

the assumption of infinite resources [When using a high price to depress

demand]. Well, it's possible that we might have infinite resources in the

form of hydrogen. In time we'll be able to get hydrogen down to a competitive price. Why would you assume infinite resource availability is an unreasonable assumption?

MS. CHERNIAVSKY: It might be an unreasonable assumption for

hydrogen; but for oil and gas, as I say, the coventional wisdom is that

these are finite and unrenewable.

646
AN INTEGRATED EVALUATION MODEL OF

DOMESTIC CRUDE OIL AND NATURAL GAS SUPPLY

R. Ciliano and W. J. Hery

Energy Studies Group, MATHTECH, Inc.

BACKGROUND

This paper describes a system designed, developed and implemented

by MATHTECH, Inc., for the Electric Power Research. Institute (EPRI)

to evaluate factors influencing future supplies of crude oil and

natural gas in the Lower 4 8 onshore and offshore provinces. The

models and associated data bases described were installed during

the past year on the Boeing Computer Services (BCS) time-sharing

network and are currently being exercised and maintained by the

Supply Program staff of EPRI * s Energy and Environmental Analysis

Division.

Over the past four years, MATHTECH had conducted for EPRI comprehensive state-of-the-art assessments of both natural gas and crude oil

supply models and modeling techniques.* In these two assessments a

combined total of twenty-two models and methodologies were thoroughly

analyzed with respect to technical, data and policy-related evaluation

criteria.

Based on this assessment, it was concluded that major new model

development appeared unwarranted either on methodological or informational grounds inasmuch as (i) no innovative theoretical approaches

could be identified which had not as yet been applied to this problem,

but which might offer the potential for fruitful application in the

future; and (ii) no major data sources were identified which had been

untapped by previous research in this area.

Rather, it was recommended that the most cost-effective way to

proceed would be to adapt, integrate and synthesize existent methodologies into a single comprehensive evaluation system of oil and gas

supply. It was on this premise that MATHTECH embarked upon the development and implementation of the integrated supply model discussed

below.

It is our belief that the model finally delivered to EPRI in this

effort does incorporate what we perceived to be the most refined techniques available at the time for handling each of the various aspects

of supply forecasting and evaluation.

See References (1) and (2)

647
SYSTEMS OVERVIEW

I I The effort resulted in the installation of a fully integrated,

systems-oriented process model consisting of the following three

principal component modules

• The Onshore Module models future exploration,

discovery and production of oil and gas in the

onshore portion of the Lower 48.

• The Offshore Module performs the same task for the

offshore regions.

• The GAS NET2 Module is a detailed model of the domestic natural gas transmission system.

Among the modeling techniques used are:

• Geostatistical analysis - expected discoveries as

a function of exploratory activity is based on statistically derived "finding rate functions."

• Engineering cost analysis - costs of exploration,

development and production were derived from a

variety of sources.

• Econometrics - onshore exploratory activity is

modeled as an econometrically derived function of

a "profitability index."

• Economic decision analysis - regional and directional

(oil vs. gas) allocation of exploratory activity is

based on economic decision analysis.

• Nonlinear optimization - offshore exploratory activity

is modeled using nonlinear optimization with a "short

term" finding rate function.

• Linear optimization - the "GASNET2" component is a generalized network model which is solved by a

special linear programming procedure.

• Deterministic simulation - both the onshore and offshore components simulate oil and gas industry

behavior over time.

The model is accessed via a series of interactive rountines

(controlled by a single master control program) which leads the user

through a series of questions to allow him to create, store and use

sets of control and data variables (prices, expected total reserves

,

648
tax rates, report options, etc.) which run the model. CSee Exhibit 1«)

Each of the three components can be run independently, or all three

can be run together, with the onshore and offshore components providing

input to GASNET2.

Each module is structured in "breadboard" fashion from a series

of smaller components (i.e., programs, subroutines and data files)

which can easily be replaced in future revisions. Thus, for example,

if a new costing model for exploratory wells is developed, only minor

program changes would be needed to incorporate it in the existing

model structure.

ONSHORE EXPLORATION AND DISCOVERY MODULE

The Onshore Module forecasts exploratory effort, reserve additions and production of onshore oil and natural gas in each of the

ten NPC Petroleum Provinces in the contiguous Lower 48 United States.

Production includes both output from new discoveries forecast by the

model as well as from existing proven reserves previously booked.

Two key concepts drive the model: (i) a "profitability index"

is used to determine the total level of exploratory effort and its

allocation to oil and gas exploration in each province; and (ii) a province-specific "discovery curve" that is used to estimate the new

reserves found by a given level of exploration.

A typical discovery curve is derived from empirical data relating

to cumulative reserve additions and cumulative exploratory footage

drilled as well as estimates of total discoverable, recoverable resource-in-place. A set of actual data for sixty (60) such curves

(oil and gas in ten (10) provinces for each of three (3) total resource

level scenarios) was compiled and a logistic -type curve fitted to the data

so as to asymptotically approach the hypothetical total reserves

Using this sort of curve, new reserves discovered can be estimated as

a function of new future drilling and cumulative prior drilling. Appropriate corrections are made- for the fact that the last actual data

points probably do not fall on the fitted curve.

The three scenarios correspond to the low, mid and high total

resource level estimates published in U.S.G.S. Circular 72 5. In any

run of the onshore or offshore models, the user selects the desired

scenario.

The profitability index (PI) is defined as the expected net

present value of future post-tax cash inflows as a fraction of the

expected net present value of all future cash outflows associated with

649
BATCH

650
a given incremental level of exploratory drilling effort. Each, year,

the PI is computed for the prior year's total exploration and discovery

effort. A preliminary estimate of the total number of exploratory wells

in the current year is made using the actual (or computed) profitability

indices for the prior two years. In order to simulate the effect of

capital and materiel limitations, the annual growth rate of total

exploratory wells may also be constrained to a maximum pre-set by the

user.

The user may specify a preliminary allocation to each region of a

certain percentage of its prior year's exploratory effort, with additional exploratory wells allocated to oil and gas in each region based

on the expected PI for each hydrocarbon in each region.

Exploratory wells are allocated in sets of a predetermined size

of "N" wells (e.g., 10 or 100, but modifiable at the user's option),

as follows: For each of the 20 (region, hydrocarbon) pairs, an expected PI is computed for the case where all N exploratory wells

are drilled for that pair; the expected discoveries for the N wells

are estimated from the discovery curves. The N wells are then allocated to (in proportion to the Pi's) those pairs whose Pi's are

positive. This process continues until all expected exploratory wells

for the year have been allocated, or other constraints halt further

exploratory effort. (In order to simulate regional materiel limitations, the growth rate of exploratory wells for each region is

constrained to the maximum pre-set by the user or the largest compound

annual growth rate observed in that region for any three-year period

since 19 50.)

The new reserves discovered each year are then translated into

annual production by applying typical wellhead deliverability profiles

for oil and gas.

Optionally, the gas production for a given year can be allocated

to the 144 GASNET2 "nodes" for analysis in the GASNET2 model. The

significance of these nodes is described later.

Exhibit 2 displays the sequence of interrelated steps that are

employed in this module.

OFFSHORE EXPLORATION AND DISCOVERY MODULE

In the Offshore Module, aggregate offshore drilling decisions

are simulated in the context of a user-designated scenario defined

on various policy, economic and physical factors. Based upon these

assumed conditions, the model projects expected future exploratory

drilling, developmental drilling, gas and oil discoveries, reserve

additions, and production for each U.S. Outer Continental Shelf (OCS)

region.

651
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652
The user has control over a wide variety of factors in the

design of a scenario to be simulated by the model. The model is

formulated to consider policy, economic and technologic/geophysical

variables and constraints such as

• wellhead oil and gas prices

• acreage leasing schedules

• acreage bid and acceptance rates

• in-place resource base and ultimate discovery potential

• resource finding rates

• production and deliverability profiles

• royalty and income tax rates

• drilling, well completion and O&M costs for exploration

delineation and development

• investment credits and intangible tax treatment

• capital depreciation rates

• rig fleet and materiel constraints

• density of drilling constraints

• lease-discovery-production phased time lags

• minimum acceptable rate of return on capital investment

• estimated maximum and minimum feasible bonus payments

The intended purpose of the Offshore Module is to determine additions to reserves and production levels under various alternative

policy sets and geological states of nature. The general framework

developed is adaptable to the Gulf of Mexico, Atlantic, Pacific Coast

and Alaskan Gulf OCS areas provided the specification of the required

geologic parameters can be made. Except for the Gulf of Mexico, these

regions are largely unexplored. Thus, assumptions regarding the

resource levels and ultimate recovery in each area are of critical

importance.

The basic structure of the model entails the determination of the

optimum level of exploratory drilling activity for any lease offering.

This requires an analysis of the expected revenue and cost streams,

with the bonus level determined by the minimum required rate of return

on the investment.

653
The discounted revenue stream is functionally related to the

finding rates for oil and gas, ultimate recovery , deliverability

profiles and the time trajectory of oif and gas prices. The discounted expected cost stream is determined by the royalty rate,

income tax and intangibles rates, and unit exploration, delineation,

development and production costs net of bonus payments. The bonus

range is then determined as the difference between the expected

revenues and expected costs including the entrepreneurial return.

Major activity-influencing factors in the model are the leasing

schedule, the prices of oil and gas, finding rates (related to ultimate recovery) and rig fleet and materiel constraints.

The model simulates aggregate offshore drilling decisions annually

for each outer continental shelf by optimizing expected net' present

value after taxes through an algorithm which structurally simulates

established industry accounting and decision-making practices. For

each year in each region, the model selects a number of trial drilling

levels. Given a trial drilling level and the set of user-specified

conditions, the time-series of expected costs is computed and discounted to net present value, the time-series of expected revenues is

computed and discounted, aid their net difference calculated. The

optimum drilling level in each region is determined by comparison

of net present values of the alternative drilling levels.

The goal was to develop a general formulation whose applicability

would be equally valid to as yet largely unexplored areas (e.g., the

Atlantic OCS) as to maturing areas (e.g., the Gulf of Mexico). Thus,

the main effort was directed at developing a formulation which considers in a detailed and logical fashion, the relationships among the

host of policy variables which influence the decision to bid on,

acquire, explore and develop offshore acreage given postulated states

of economics, geology and technology. The result of the exploration

activity undertaken offshore is subject to a much greater degree of

uncertainty than corresponding activity onshore because the regions

considered are, for the most part, "frontier areas."

Thus, the model strives to reliably emulate the decisions which

will most likely be made by those who will actually undertake these

ventures and to forecast exploratory and development effort based on

a rationale which roughly corresponds to the manner in which the

industry itself views these risks and benefits. However, in translating this effort into actual reserve additions and production levels,

one can expect to encounter a much greater degree of uncertainty and

corresponding margin of error.

In describing the detailed workings of the module, it is convenieni

to segment the computational process into four distinct phases:

654
(1) the specification of physical parameters;

(2) the specification of economic parameters;

(3) the optimization process; and

(4) the feedback, recycle and adjustment process.

Exhibit 3 contains a highly simplified diagrammatic overview of

the model structure which illustrates the four-stage computational

sequence discussed above.

GASNET2 TRANSMISSION MODULE

GASNET 2 consists of programs and data which together define a

detailed model of the U.S. natural gas delivery system. This model

consists of three fundamental parts: a regionalized supply (production) file, a regionalized and sectoralized demand (requirements)

file, and a network model of the system used to deliver the gas from

producers to consumers.

Regionalization of production is defined by a breakdown of the

U.S. into 144 substate areas. These substate areas have been carefully chosen to reflect the various franchise areas of natural gas

distributors and the sales areas of natural gas pipelines. In this

disaggregation, for instance, Texas has thirteen different areas,

New Mexico, Wyoming, Ohio and New York have four, many have three or

two and a few states are not subdivided at all. In addition, Canada

and Mexico are included because of their current and future roles in

natural gas imports into the U.S.

Natural gas consumption is divided regionally and by end-use

category in GASNET2. Each production area in GASNET 2 is also a

potential demand area. Each demand area is an existing or potential

production area. Thus great flexibility in modeling new sources of

alternative gaseous energy production on a local level is possible

with GASNET.

The end-use categories defined in the GASNET2 base model include

"residential," "commercial," firm industrial," "public authorities,"

interruptible industrial and/or commercial," "miscellaneous other,"

"electric utilities and interdepartmental," and "undifferentiated."

The last category is necessary for some companies for whom historical

sales data is not separated by end-use class.

The GASNET2 network model is a highly disaggregated generalized

network model of nearly all of the major interstate natural gas pipelines and most of the major natural gas distributors in the country

today. Over 100 pipelines and 240 distributors are explicitly represented in the model.

655
656
Each pipeline is modeled as a subnetwork of nodes and arcs.

Each node corresponds to one of the GASlsygT2 substate areas which is

served by the pipeline either through purchases from producers of

other pipelines, sales to distributors, end-users, or other pipelines

or simply delivery of gas through the area. All of the pipeline's

transmission and/or distribution plant located in this area is included

in this node. Each arc in the submodel represents either (i) a connection between two areas (nodes) by natural gas transmission lines

crossing the boundary between them, or (ii) a transaction between

producers, pipelines or distributors. Each node is parameterized by

a "loss factor" which represents gas lost in transmission, distribution, storage, or unaccounted for, as well as gas used by the pipeline

to power transmission or distribution line compressor stations. Each

transmission arc is parameterized by a capacity which defines an upper

limit to the quantity of gas deliverable over an inter-area boundary

on the pipeline's transmission lines in a given time period and a unit

cost of transmission between "centroids" in two connected areas.

These centroids are defined individually for each pipeline in a particular region and are based on the location of its transmission lines

rather than on some "average" centroid for all the pipelines. Each

transaction arc is parameterized by a cost which represents the average

unit "markup" by the seller on that transaction.

Each distributor in the model is defined by the areas and demand

sectors it serves. A distributor is allowed to receive gas from interstate pipelines, intrastate producers, and its own manufacturing plants.

A distributor which operates in more than one area cannot communicate

directly between these areas. This defines the logical difference

between a "distributor" and a "pipeline": a "pipeline" can sell gas

to other companies for resale, a "distributor" cannot. This does not

pose a real problem to the modeler, however, since companies which

both transport and distribute gas can be modeled as two separate

company divisions with the transmission division delivering gas to

the distribution division for resale.

In the network model there are six basic "transactions":

(1) deliveries by producers to pipelines (XS)

(2) deliveries by producers to distributors (XI)

(3) deliveries by pipelines to distributors (XD)

(4) deliveries by pipelines to other pipelines (XX)

(5) deliveries by pipelines by transmission line

between contiguous areas (XT) ; and

(6) deliveries by distributors to consumers (XC)

Each of these deliveries is represented as a flow on an arc in

the model. These flows are constrained by upper and lower bounds

representing capacities and/or contractual arrangements between

657
seller and buyer. These flows are also subject to reduction due to

losses and use of gas as pipeline fuel in compressor stations. As

discussed previously, these losses are considered to occur in the

nodes . In the computerized implementation of GASNET2, however, it

is more convenient (and standard) to define losses as occurring on

arcs . Thus in GASNET2 , each node's loss factor is applied to all

arc flows leading into that node. Thus each arc's flow corresponds

to the amount delivered after losses have been accounted for in the

"upstream" node and prior to losses in the "downstream" node.

GASNET2 is essentially a linear network model and can be solved

by linear programming routines. It is fairly large in its complete

form (2,200 equations and 5,300 variables), however, and rather expensive to solve using standard general purpose LP codes. Tests

were run using IBM's MPS360 general purpose LP routine and a new

state-of-the-art special purpose network code in order to establish

the savings in costs which such a code could achieve for the model.

The results indicate a savings on the order of about 30/1 using the

special purpose solution algorithm.

SUMMARY

Recall that the EPRI model was developed by adapting and (where

necessary) extending "preferred" concepts and techniques found in

other oil and gas models to form an integrated system. As such, the

resultant model has several important strengths, as well as remaining

limitations, which indicate the need and directions for future model

improvements

Among the noteworthy strengths are:

• An integrated evaluation framework which allows a nonprogrammer to easily run the model to see the effect of

different price scenarios, tax policies, cost estimates,

etc

• A modular structure which provides for easily installed

improvements in model modules and input data, as well

as integration with other supply evaluation systems.

• Explicitly considered relationships among public policy,

economic, geological, technological and institutional

factors which impact on oil and gas supply.

• An attempt to utilize the methodological procedures

best suited to the behavioral and physical phenomena

being modeled.

Some of the model limitations

• Finding rate curve parameter estimates are based on

(among other things) the resource base estimates in

658
U.S.G.S. Circular 725; these should be recomputed

when better data is available.

• Technology representation and costing can and should

be improved; e.g., exploration costs might be estimated as a function of region and average drilling

depth instead of the overall "per hole" average now

used.

• Constraints need to be more directly linked to models

of public policy planning and macro/micro economic

activity with corresponding feedback.

• Structural changes in the industry (caused by OPEC

and U.S. government policy as well as macroeconomic

conditions) not embedded in the historic on which

the model is based are methodologically well represented, but poorly measured:

- directionality of drilling (oil vs. gas)

- regional allocation of effort

- drilling success rates and prospect

inventories

During the period of performance, three other major efforts were

undertaken in the area of oil and gas supply which, due to their concurrent development, could not, except for some minor features, be

adapted into the EPRI model. These were:

• DOE-EIA OCS Oil and Gas Supply Model (Lewin-MATHTECH)

• Inter-Agency Task Force on Resource Base Reappraisal

(USGS-RAG)

• Nehring Geostatistical Assessment of Major Lower 48

Reservoirs (RAND)

The EIA effort is especially noteworthy because, for the first

time, structure-specific data permitted a level of disaggregated

analysis heretofore impractical to consider. Even at this date,

however, EIA is still testing and evaluating the output of this model.

The RAND effort is really a retrospective rather than a prospective view of oil and gas supply, but with some very interesting and

potentially quite transferable application of geostatistical techniques.

Similar work along these lines is also being pursued at U.S.G.S .-Res ton.

In summary, except for the three efforts just described, we

believe the model developed for EPRI does, in fact, incorporate those

state-of-the-art features uncovered in MATHTECH's extensive. examination of previous oil and gas supply modeling. However, current \> prospects for its use by EPRI as a forecasting and evaluation tool

659
remain clouded in the context of the changing role of the Supply

Program as a "producer of forecasts and supply projections" to a sponsor of information systems and planning models which can be

adapted by the utility industry to assist in securing adequate

supplies of fuel in an uncertain decision-making environment.

REFERENCES

1. "Comparative State-of-the-Art Assessment of Gas Supply

Modeling," EA-201, Project 436-1, Final Report, February 1977.

2. "Comparative State-of-the-Art Assessment of Oil Supply

Modeling," EA-609, Project 665, Final Report, June 1978.

3. "EPRI Oil and Gas Supply Model: An Integrated Forecasting

and Evaluation System, " "Volume 1 - Onshore and Offshore

Supply Models," Final Report, June 19 80.

4. , "Volume 2 - GASNET2 Natural Gas Transmission, Distribution and Pricing Model," Final Report, June 1980.

5. , "Volume 3 - User's Guide," Final Report, June 1980.

660
AN EVALUATION OF THE ALASKAN HYDROCARBON SUPPLY MODEL

Frederic Murphy and William Trapmann

Energy Information Administration

Department of Energy

Introduction

Alaskan oil and gas supply forecasts are a key component of

the forecasting of energy markets by the Energy Information

Administration (EIA) of the Department of Energy. Earlier EIA

efforts to forecast Alaskan oil and gas supplies were generally

inadequate. The forecasts were simple aggregates based almost

entirely on the expectations of the industry. While this

approach is not without merit, it is too rigid and cannot be

adjusted to reflect responses to varying economic stimuli. The

Alaskan Hydrocarbon Supply Model (AHSM) was developed to enhance

EIA's capability for estimating future supplies from this

region. The model incorporates engineering and economic factors

that affect both resource extraction and transportation.

The approach to estimating future supply consists of segmenting

the model into components. The first part describes the extent

and quality of the resource base of crude oil and associated

and dissolved natural gas. The next part focuses on the nonassociated natural gas resource base. The third piece of the

model deals with the transportation possibilities for all

hydrocarbons within Alaska. These three components are combined

to provide a forecast of supply in future years using

trajectories of domestic hydrocarbon prices.

In estimating the resource base for both oil and gas, the model

samples possible geological outcomes and produces tables that

classify potential reserve additions by the exploratory drilling

needed to prove them and by the average total cost of finding,

developing and producing the reserves. These tables reflect

the results of the resource evaluation and contain, in effect,

regional families of supply curves. Each curve represents the

expected volume of reserves distinguished by the level of

exploratory effort; in other words, the drilling required to

discover the supply of reserves.

These supply tables become part of the data base for the

"integrating" model —the portion^of the AHSM that uses linear

programming to maximize the present values of profits from

production and transportation investments over time, linking the

individual sources of supply. Market and policy parameters

661
that affect the solution are prevailing market prices for oil

and gas, leasing constraints, and limitations on the potential

for pipeline network expansion.

The AHSM in its current form represents a significant

improvement in the forecasting of Alaskan oil and gas

production. It is a dynamic modeling system which

incorporates a large degree of flexibility while still

retaining a reasonable level of computational efficiency.

Nonetheless, AHSM contains certain shortcomings in its

structure. The major problems within AHSM include the

inability to deal directly with the nonlinear relations

that affect pipeline design and the conceptual difficulties

associated with the handling of uncertainty in the current

model design.

This paper is organized as follows. The next section describes

the linear programming system of the model. The description is

brief but provides sufficient detail to aid in the evaluation of

the model. The resource submodel in AHSM is not described in

this paper with any detail because it is not germane to this

evaluation. The problems associated with pipeline costing in

the linear program are presented, followed by a description

of the conceptual problem of dealing with uncertainty.

Mathematical Formulation of the Integrating Model

This section describes the linear programming submodel. The

integrating model chooses the timing and extent of

exploration, development and transportation activities to

maximize the present value of profits in light of expected

selling prices of oil and natural gas at the Alaskan border.

The model that represents this choice process consists of a time-staged, linear program that depicts five activities:

exploration, development, transportation, transportation

network expansion, and sales. The specification of the

equation system is presented next, followed by discussion of

the activities and relations.

In addition to the objective function, there are five basic

relations in the linear program: a reserves inventory

equation, a material balance equation, a pipeline capacity

equation, and convexity constraints on both exploration

activity and pipeline expansion. The entire set of

equations can be found in Table 1 of Appendix A. Before

presenting the entire system, each relation of the system is

presented in turn.

662
Reserves Inventory Balance

The first class of equations is the reserves inventory

balance. Relation (1) transfers unproduced inventory of a given fuel to the succeeding time period. The inequality

simply ensures that beginning stocks plus new reserve

additions must be at least as great as the production plus

remaining stock; that is, hydrocarbons may be "wasted," but

they cannot be "created" in the solution process.

Mathematically,

-I (f ,s,p,t) e(f ,s,k,p) *E(f ,s,k,t)

+D(f,s,p,t) + I(f,s,p,t+1) < 0 (1)

where

f = fuel type

s = supply region

p = supply price

t = time period

k = unit of exploratory drilling

E(f,s,k,t): exploration unit k in region s for

fuel f in time t.

e(f,s,k,p): yield of fuel f from exploratory unit

k in region s at supply price p.

D(f ,s,p,t) : development activity for fuel f at

price p in region s at time t.

I(f,s,p,t): unproduced inventory of fuel f with

supply price p in region s at time t.

The entire system of equations along with subscript and

variable definitions appear in Table 1 of Appendix A.

The I(f,s,p,t) variable represents the inventory of fuel f in

supply region s with a supply price p that has not been developed

by time t. The supply price p does not refer to the exogenously

entered market price that is received for all sales. It measures

instead the average total costs for producing that component of

the total regional reserves. For reserves with p exceeding the

product price in every time period, there is no established

production plan. These reserves are retained from one time

period to the next until the market price exceeds p. Thus p may

663
be interpreted as a minimum acceptable price. In the

implementation of the model, p is not continuous. The values for

p constitute a set of discrete price categories. The

predetermination of possible cost or price levels serves to

limit the size of the overall equation system and the

corresponding computational burden.

The D(f,s,p,t) term represents the development activity for

fuel f in supply region s. The development plan differs for

different supply prices p and is initiated at time t. Each D

activity "develops" the found reserves leading to a production

schedule for future time periods. The representation of actual

production appears in the next equation, and so discussion is

deferred until then.

The last element of Relation (1) measures the reserves additions

from units of exploratory activity. Total exploratory drilling

for a region is the accumulation of successive blocks of drilling

feet. Yields of reserves decrease with increasing drilling. As

the k-th unit of exploratory activity occurs, reserves from all

supply price categories are both possible and likely to result.

The E variable represents the particular unit of exploratory

activity and ranges from zero to one where a value of one

indicates the exhaustion of the entire exploratory unit. The e coefficient marks the yield from the given exploration unit for a particular supply price level. Thus, for the total reserves

discovered in a particular cost category, the product of these

two values must be summed across all k exploratory units. In

other words, j^e ( f , s , k ,p) *E (f , s , k , t ) measures the reserves of

fuel f with a supply price of p from region s in time t.

The value of e is determined through the resource simulation

model. The resource evaluation is modeled by successive sampling

of the geology base in a Monte Carlo framework. Each particular

realization of the geology base is evaluated to determine the

amount of exploratory drilling and the production costs to

develop the deposits within that realization. Then the complete

set of results for all realizations are used to determine

expected values for reserves yielded at each level of exploratory

drilling within all cost categories. A unit of exploratory

drilling typically yields reserves across all price categories.

The e coefficient is the expected value for reserves of a given

fuel in a given supply region differentiated by drilling effort

required and the unit costs of production. The reserves

inventory balance must be imposed on both fuel categories (f) in

all supply regions (s) , for each time period (t)

664
Material Balance

The next set of inequalities, material balance relations,

accounts for sources and uses of fuel at all activity points.

All sources and uses of fuel are traced, precluding the

occurrence of artificial gains or losses within the system. The

accounting occurs for all fuels in all time periods at all

geographic entities within the model: supply regions, demand

regions, and transshipment points.

Within the context of the current model, only certain activities

may occur at any activity point. For example, sales do not occur

at supply regions. The three representative forms of the

inequality appear below. However, for conciseness, the entire

relationship is provided in Table 1. The intent of the

inequality is quite straightforward: the amount of fuel used for

sales or further shipments must not exceed the total receipts

from production and shipments received (less transportation

loss) . Receipts consist of production at and shipments to the node.

Production is a flow of product over time, a consequence of

earlier development activity. Production of fuel f from region s in time period- t is denoted by :| , D(f ,s ,p,t) *d (f ,s ,p, t-z)

The coefficient d(f,s,p,t-z) measures the amount of fuel f at a supply price p yielded from region s in time t given the initial

development of the field in time z. Note that in the development

of an oil deposit, associated-dissolved gas is possible. In such

a case the yield variable, d (f ,s ,p, t-z) , reflects both oil and

natural gas. In the supply region inequality, supply region s is

linked to transportation node n. Shipments of product occur at all points in the network. The

amount of shipment of fuel f from point m to point n in time t is

measured by T (f , (m,n) , t) . As a notational convention, the

summation over the first (second) link parameter indicates the

summation of all upstream (downstream) flows into (out of) the

activity point (e.g., £ T(f,(n,q),t) represents the total

shipments from point n)? The summation over a link parameter is

designed so that this occurs only for links recognized as flowing

to or from the transshipment point. Shipments received must be

adjusted for transportation losses. The proportionate

transmission loss is represented by L(f,(m,n)).

Sales of fuel f at demand region j in time t are represented by

S(f,j,t). In the demand region inequality, demand region j is

linked to transportation node n. The three inqualities

accounting for the above activities follow.

665
Supply regions:

P^1 D(f/S,p,z)*d(f ,s,p,t-z)-ZT(f ,(n,q) ,t) > 0

Transshipment points:

^T(f, (m,n) ,t)*(l-L(f, (m,n) )

) -|T(f , (n,qj ,t) > 0

Demand regions:

m T(f,(m,n)t)*(l-L(f,(m,n)))-S(f,j,t) > 0

Where

f: fuel type

t: time period

p: supply price (or equivalently , average total

costs of production)

s: supply region

j: demand region

(m,n) : shipment link from point m to point n

z: for development only, z represents the

initiation year for development

D(f ,s,p,t) : development activity for fuel f at price

p in region s at time t

d (f ,s ,p, t-z) : proportion of fuel f at price p in region s produced in time t given the initiation of development in

time z

T (f , (m,n) ,t) : transportation of fuel f from point m to

point n in time t

S(f,j,t): sales of fuel f at demand region j in time t

L(f,(m,n)): proportionate loss incurred in transmission

of fuel f from point m to point n

Pipeline Capacity

Each of the major pipeline links connecting transshipment

points in the system has an explicit capacity that imposes an

upper limit on the volume of product that may travel along the

route at any instant. The capacity, location and cost data

concerning these projects are exogenously fed into the system.

The occurrence and timing of the projects, however, are

determined as part of the LP solution.

666
The concern here is only for the links between transshipment

points. These links constitute the major pipeline system

bringing the product to market. Between the supply regions and

the major pipeline network are the gathering systems for the

producing fields within a region. Gathering systems are

represented within the model by "spurs." Spurs are similar to

the major links in that they move products. The construction

schedule and capacity are assumed, however, to accommodate the

field development schedule and requirements. The essential

feature in this discussion is that only the major pipeline

links have a capacity constraint.

The capacity of a pipeline link for fuel f from point m to

pgint n existing in time t is given as

Z . X (f , (m,n) , i ,y) *K (f , (m,n) , i ) . The K parameter is the

capacity of the given(m,n) link from project i. The X variable

measures the degree of completeness for the particular

project. In the mixed integer formulation for the model

the X variables are constrained to equal zero or one. As a continuous variable LP, the X variables are bounded by zero and

one. The summation over i is required to account for multiple

projects being possible between two given points. The i subscript serves as an identifier for each project. The

summation over all earlier time periods is required since a pipeline once constructed is available for all future time

periods

The pipeline capacity constraint is imposed at each link for

all fuels in every time period. It requires the capacity to be

at least as great as the flow. The specific inequality is:

|M X(f , (m,n) ,i,y)*K(f , (m,n) ,i)-T(f , (m,n) ,t) > 0 (3)

where

f: fuel

y,t: time

i: project identifer for pipeline expansion

(m,n) : shipment link from point m to point n

T (f , (m,n) ,t) : transportation of fuel f from point m to

point n in time t

X (f , (m ,n) i , t) : pipeline expansion for fuel f, project i,

from point m to point n in time t

K(f , (m,n) ,i) : pipeline capacity for fuel f from point

m to point n, project i

667
Convexity Constraints

There are variables that measure bounded activities within the

system: pipeline expansion, X(f , (m,n) , i ,t) and exploration,

E(f,s,k,t). By definition of each variable, the associated event

can be allowed to occur only once even though segments, of the

activity may occur in different time periods. To ensure this

result, the sum of these activities over time has an upper bound

of one as represented in the following relations.

^X(f , (m,n) ,i,t) < 1 (4)

|l(f,s,k,t) < 1 (5)

f: fuel

t: time

s: supply region

(m,n) : shipment link from point m to point n

k: exploratory drilling unit

i: project identifier for pipeline expansion

X(f , (m,n) ,i ,t) : pipeline expansion for fuel f,

project i, from point m to point n in time t

E(f,s,k,t): exploration unit k in region s for fuel f in time t

The Objective Function

The objective of the linear program is to maximize the

present value of profits by optimally timing the

occurrence and extent of exploration, development,

transportation, network expansion, and sales.

The objective function is statement (6) in Table 1 of the

Appendix. All activities present in (6) have been

discussed earlier. The additional variables are either

product prices for sales, or costs of the other

activities. An additional feature is that all value

figures are discounted over time. Thus, the optimization

is over net present value.

668
Summary of the Linear Programming Integrating Structure

In the linear program, exploration activities yield

additions to reserves in each development cost class.

The additions are joint; that is, each increment of

exploratory activity leads to discoveries potentially

distributed across all cost categories. The yields from

exploration activities appear in Relation 1. The

convexity constraint ensures that each unit of exploratory

activity is conducted only once, regardless of the

relative profitability.

In turn, development activities "consume" the reserves

included within a particular cost category and yield production over time of both primary products (crude oil and

non-associated gas) and associated-dissolved gas. The

shapes of the "production profiles" conform to the baselevel plan used in the resource model to calculate minimumacceptable supply prices and thus to grade potential

reserves into cost categories. Consequently, these

profiles and cost categories serve as the critical linkage

between the stand-alone resource model and the integrating

model

Downstream from production, liquids and gas are

transported to terminals located at the Alaskan boundary.

The transportation network consists of three kinds of

activities. Network expansion adds capacity to the links

of the network. These expansion activities are

"comprehensive" projects in the sense that capacity is

added jointly to any number of links in the network.

Each transportation activity moves a product between

pairs of regions. The transportation activity consumes

capacity of a link. A spur also moves products from

supply regions to transshipment points but does not

consume capacity. Spurs connect supply regions to the

network at a unit cost based upon an exogenously estimated

pipeline size.

All of the production and transportation activities

involve cash expenditures discounted in relation to the

time of their initiation. Sales activities at the Alaskan

terminals provide the discounted revenues driving the

system. These activities are simply variables that

"consume" the delivered product at an exogenously supplied

price

669
One additional note is warranted here. The subscript for

time is presented in the above equations without

qualification. However, in the actual implementation

of the model, all of the exploratory activities are

provided with early start dates. Early start dates are

also provided for some network expansion projects. These

dates are provided in the latter case to prevent

unreasonably early initiation periods and in the former

case to reflect the anticipated leasing schedule.

This completes the presentation of the mathematical

formulation of the model. The entire specification is

provided in Table 1. The discussion now turns to the

treatment of transportation charges in the system and the

possible distortion resulting from this treatment.

Pipeline Design

The following discussion focuses upon certain formulation

issues embedded within the Alaskan Hydrocarbon Supply

Model (AHSM) . The specific problem concerns the effects

of linear approximations on the nonlinear pipeline design

relationships. As a general conclusion, the costs of

transportation within the postulated pipeline network are

understated. This statement is valid for both the major

pipeline links and the spurs, even though the computation

for them differs substantially.

Pipeline design relations are nonlinear with respect to

the planned flow rate. Specifically, pipeline diameter

increases at a decreasing rate with respect to increases

in the planned flow rate, other things being equal. (This

statement is made with extreme caution. For a good

treatment of the subject see Petroleum Transportation

Handbook , Harold S. Bell, ed . , McGraw-Hill Book Company,

Inc., 1963; or Pipeline Design for Hydrocarbon Gases and

Liquids , American Society of Civil Engineers , 1975.)

This nonlinearity in design is propagated in the equations

used to calculate the pipeline costs for both oil and

gas. The equations used in AHSM to scale the pipeline

cost estimates are provided in Table 2 of the Appendix.

The approach to cost determination relies on initial

estimates for total pipeline costs, less overhead, for a link of a given capacity. (2 million barrels per day is

the reference size for oil, 2.4 billion cubic feet per day

for gas.) These reference cost estimates are then divided

670
by the reference sizes to provide cost estimates per unit

of volume for the new link. It is sufficient to evaluate

the scale equations alone since the reference cost

estimates are constant for a particular link transporting

a given fuel. The scale equations are referred to as the

cost equations from now on for convenience.

The decision to expand the pipeline network to a given

supply region is made on the basis of the region's

production potential. The chief determinant of this

potential is the level of the region's reserves. One may

therefore say that the decision to construct the new

pipeline link is based on the expected reserves that may

be tapped for production. The cost equations are clearly

nonlinear in the flow rate. Nevertheless, the methodology

treats the cost of new capacity as a given, based on an a priori estimate of the flow rate. The linear program

accepts this information, then computes the optimal

expansion strategy based on these costs as one part of the

overall profit maximization problem.

The evaluation of the error due to linear approximations

of pipeline costs requires a more detailed look, at the

equations listed in Table 2. Table 2 contains the

normalized equations based on a flow rate of 2

million barels per day- and 2.4 billion cubic feet per day

for oil or gas, respectively. These reference capacities

were not chosen arbitrarily. They are the respective

capacities of the Trans-Alaska Pipeline System (TAPS) and

the Alaskan Natural Gas Transportation System (ANGTS)

TAPS and ANGTS have been studied in depth and constitute

the only knowledge the industry has relevant to large

scale transportation of oil and gas in this area.

The cost equations in Table 2 are both nonlinear in Q,

the flow rate. The first derivative of the equation,

denoted by S' , is strictly positive throughout, indicating

increasing costs with higher flows. The second

derivative, S

n

, is strictly negative for natural gas for

all positive values of Q. The second derivative for the

oil equation is negative with Q less than 1 million

barrels per day and positive where Q exceeds this figure.

(The actual inflection point occurs at roughly 1.006, but

the conclusion will be the same.) Coincidentally

,

1 million barrels per day is the largest pipeline capacity

proposed for any of the new pipeline links. With the

relevant range for new oil pipeline capacity confined to

flows between zero and 1 million barrels per day, each of

the cost equations can be characterized as concave over

the relevant range of flows.

671
A representative graph of the scale, or cost, function

appears in Figure 1 of Appendix A as curve S. OA measures

a hypothetical design capacity for a new pipeline link.

The value of the cost function for flow OA is represented

by segment AB. As a mixed integer program, total costs

are either zero with no flow, or AB with flow OA. When

AHSM is run as a linear program, the entire project need

not be undertaken, and the actual cost is approximated by

OB in Figure 1. How closely the linear approximation

compares to the nonlinear estimates is considered next.

The comparison of the two functions requires some

preliminary discussion. Obviously, the total costs for a new pipeline link as computed by either function will be

close to AB only as the flow value approaches OA.

However, by varying the value of Q and comparing the

results, it is possible to approximate the difference

between the two estimators. Table 3 contains a listing of

the results of the comparison. The equations for both oil

and gas are used to derive the values in the SCALE

column. In the case of oil, the SCALE values must be

normalized. The 0.737 value of the normalized SCALE for

Q=0 . 2 means that a pipeline designed for a flow of

0.2 million barrels per day would cost 73.7 percent of the

cost for a 1 million barrels per day pipeline. (The

implicit working assumption of this paper is that the

costing equations are valid. The quality of these

relations is the subject of a future paper. The current

study is focused upon the merits of the linear

approximations in AHSM.) With the linear function, a line

carrying 20 percent of 1 million barrels per day would

cost only 20 percent of the total for the larger flow.

Thus the figures from the nonlinear equation is 368

percent of the figure from the linear function. If oil

flowed at 50 percent of the 1 million barrels per day

design capacity, the incurred cost in the linear case is

not even 60 percent of the nonlinear estimate.

In the case of natural gas,. the table is slightly

different. For gas, the SCALE equation yields normalized

values. That is, the nonlinear SCALE equation yields

figures from zero to one. However, the SCALE values for

the linear equation require normalization. The balance of

the Tables remains the same in character and intent. The

ratios of nonlinear to linear estimates are slightly less

severe. However, the gas comparison uses a pipeline

capacity of 2.4 billion cubic feet per day. With larger

capacity values, the linear approximation is better. The

proposed values in AHSM for expansion of new gas pipeline

links are only 0.8 or 1.0 billion cubic feet per day. So

672
the test results listed in Table 3 do not reflect the

degree of distortion actually encountered in the

implementation of AHSM.

The results of the comparison listed in Table 3

demonstrate that the linear approximation employed within

AHSM performs well only within a limited neighborhood of

the design capacity. Unfortunately there is no method to

control the value of the flow variable within its range

without sacrificing the flexibility embodied within the

LP. In fact, a survey of results used in the 1979 edition

of the Energy Information Administration's Annual Report

to Congress shows that most expansion projects are well

below their design capacities. It appears as though AHSM

may be grossly understating transportation costs along the

major pipeline links in its system.

Unfortunately, underestimation of transportation charges

also occurs in the case of the spurs linking supply

regions to the major pipeline links. The underestimation

arises for a different reason, however, as the costs of

the spurs are handled differently within AHSM.

Spurs in AHSM are proxy variables for the network that is

required to transport products from the supply region

fields to the major pipeline links. The intrafield

gathering system is included as a part of the production

process, and so that cost is incorporated into the total

costs of production. The spurs represent the connecting

lines between the intrafield gathering systems and the

major transportation network. Since one spur generally

represents multiple pipelines, detailed specifications

such as capacity are omitted for spurs. The costs for

this transportation segment, however, must still be

recovered. AHSM charges a single per unit cost for all

transportation along spurs for one supply region. The

computation of the unit cost is based on postulated flow

rates along the spur for both oil and gas. The scale

equation of Table 2 employs these rates to adjust the

reference cost estimates. The reference cost estimates

are $7 million/mile and $8.35 million/mile for a 2 million

barrels per day oil line and 2.4 billion cubic feet per

day natural gas line, respectively. The postulated flows

are 100 thousand barrels per day for oil and 1.3 billion

cubic feet per day for natural gas. The derived cost

estimates are $3.58 million/mile and $6.4 million/mile for

oil and gas lines, respectively. These figures would then

be increased by computing the product of the unit cost and

an estimate for mean distance. The 1.3 billion cubic feet

per day figure is not documented; it is the figure that

most closely yields the $6.4 million total cost per mile

for gas pipelines.

673
The above procedure incurs inaccuracies due to the very

large flows postulated for the spurs. Proposed flows of

100 thousand barrels per day and 1.3 billion cubic feet

per day are quite optimistic. The survey of

representative AHSM runs generated for the 1979 Annual

Report to Congress demonstrated that these estimates are

entirely unrealistic. The largest gas flow along a spur

in the 15 year forecast horizon is 0.15 billion cubic feet

per day. This figure is not even 12 percent of the 1.3

billion cubic feet per day as postulated. Oil fares

somewhat better. Flows along spurs range as high as 333

thousand barrels per day in one instance. However, each

region consists of large tracts, covering hundreds of

square miles. Given such a vast area, it would seem

unreasonable to assume the existence of centralized groups

of deposits to support the massive spur lines. In fact, a 100 thousand barrels per day flow of crude implies a reserve of 730 million barrels. (Maximum production from

reserves is 5 percent per year.) It is likely that there

would be multiple spurs, each less than 100 thousand

barrels per day. If this is so, transportation charges

along these spurs are underestimated. In addition, the

other figures were generally not even one-half the 333

thousand barrels per day recorded for the single instance

cited above.

The above problem can be ameliorated to some degree by

simply choosing a smaller flow value for the

calculations. A strong candidate for selection is the

expected value for the flow. Two problems work against

this choice however. First, computing the expected value

for production constitutes an extremely complex, if not

intractable, problem. The expected production depends

upon the entire set of interrelations within the model.

These parameters, of course, include the transportation

costs. Altering that set of parameters changes the

initial equation system. Thus, the expected production

as calculated initially would not necessarily match the

expected production values of the respecified system.

The problem could be formulated as a mixed integer program

(MIP) . The MIP imposes integer values of zero or one on

the pipeline expansion activities [the X(f , (m,n) ,i , t) of

Table 1] . This approach is intuitively appealing since

pipeline expansion occurs as a discrete event: one either

constructs a line or not. Multiple projects may be

possible, each one of a different size. The range of

sizes would then allow for the selection of a possible

size most appropriate for its use. In the current

context, "most appropriate" is the lowest cost alternative

for the proposed flow over all possibilities.

674
Even if the system were guaranteed to converge, the

advantages of repeatedly solving such % massive problem

may not justify the cost. Because the cost structure is

nonconvex, there is no easy solution to the resulting

mathematical program.

The Problem Of Representing Uncertainty

Even if the MIP could be made to work, problems arise with

the uncertainties in the resource estimates. The resource

evaluation model employs stochastic variables within a Monte Carlo framework to compute expected volumes of

reserves for increasing drilling effort and costs of

production (i.e., the e(f,s,k,p,) of Table 1). The effect

of this uncertainty is contingent upon whether the model

has been run as a continuous variable linear program (LP)

or as a mixed integer problem.

If the MIP approach is used, the expected, or average,

outcome of the final decision may differ markedly from the

final decision based upon expected input data. A simple

example, valid for both oil and natural gas, clarifies the

point. Consider a model with a supply region containing

one potentially productive site. The probability of

hydrocarbon occurrence is discrete; one out of three

times, a reserves level of R will be present, zero the

other times. Assume that production is proportional to

the level of reserves. If R is the level of reserves,

then production flows at a rate of X units per time

period. Assume the associated economics of the problem

are such that the transportation costs can be recovered

only with a flow of at least 0.5X. The problem is to

determine the expected flow rate, if any, from this supply

region

The final answer depends upon the approach used to solve

the problem. The AHSM methodology first computes expected

reserves and then forms its decision based on that data.

The expected level of reserves is 0.33R. The resulting

production would be 0.33X, which would be inadequate to

recover all transportation costs, while a production rate

of 0.5X provides a sufficient return for production to be

profitable. The level of production determined by

using the AHSM approach is therefore zero, whereas

expected production should be .33X.

The above argument demonstrates that there is a clear

potential for distortion when AHSM is solved as a MIP.

Activity levels are underestimated whenever the expected

675
level of reserves is inadequate to support production yet

the range of possible values for reserves includes levels

sufficient to support profitable production. As a practical matter, however, the equation system is so

massive that it is quite a burden to solve as an MIP. In

providing forecasts to the Annual Report to Congress AHSM

has been solved as a continuous variable LP.

Presented so far have been an example of overestimating

supply due to underestimating costs, and an example where

supply would be underestimated if a MIP formulation were

used. The following example shows supply would be

underestimated if the correct pipeline cost function is

combined with expected flow.

The problem is presented graphically in Figure 2. Suppose

for a given spur, the production flow based upon the

expected reserves equals OZ . The OZ flow incurs a spur

cost of ZC. The OZ flow is based upon a given level of

expected reserves treated as a certain value. However,

the conceptually correct procedure to derive the expected

total cost would be to employ an iterative process to

realize successive possible geologic states and compute

the expected value of total costs based on the complete

set of outcomes. (This agrees with the earlier argument

concerning the execution of AHSM as a MIP.) Suppose that

successive runs based on single realizations of the

geology yield positive points ranging from OX to OY. Zero

values are likely, but they are ignored in the present

discussion. The argument deals only with the flow values,

conditional upon the presence of petroleum. The total

cost figures from each iteration would lie along arc ACB.

If the event space were defined as the set of iterations

yielding positive flows, the probability of any of these

flows occurring would be 1/N, where N equals the number of

iterations when the flow is positive. The expected value

for total cost conditional upon the presence of a positive

flow equals the simple average of all positive total cost

values. Since the expected value function is a convex

combination of the points along arc ACB, its value would

lie in the region bounded by arc ACB and line AB. The

value would lie below arc ACB and be less than ZC. Thus,

computing total cost based on the expected flow would

overstate the expected total cost based on the presence of

a positive flow. Naturally, this difference is greater if

one were to compute the expected total cost over all

676
iterations, including those when the flow and total cost

are zero. Thus, within the current structure of AHSM,

correctly calculating spur costs for the average flow

values may well lead to overestimates of costs, the

opposite problem of the underestimates previously

discussed

Concl us ions

The Alaskan Hydrocarbon Supply Model (AHSM) is a useful

forecasting tool. For most of the midterm forecast

period, having the accounting structure of the model and a leasing schedule is sufficient to produce a credible

forecast. However, the model is not without its faults.

AHSM's major deficiency is in the treatment of

transportation costs. This area is critical due to the

extremely high costs for all phases of industry operations

in the harsh conditions of Alaska. Accurate computation

of transportation costs is necessary to evaluate fields

that are on the margin of prof itablity. As Alaska enters

a more mature state of exploration, any existing giant

field such as Prudhoe Bay will have been discovered. As

exploration proceeds, the smaller, less profitable fields

will serve increasingly as the source of production.

Reliable estimates of Alaska's productive potential depend

as much on accurate estimates of transportation costs as

they do on precise estimates of production costs and the

geology base itself.

The cumulative effect of the AHSM treatment is probably to

understate transportation costs. The unit transportation

charges imposed on shipments from supply regions to major

pipeline links are calculated as if these activities may

enjoy the economies of scale afforded by an unreasonably

large pipeline. The shipments along the major pipeline

links similarly enjoy the economies of scale inherent in a large diameter line regardless of whether the entire

project is constructed. This understating of pipeline

costs along major pipeline links occurs when AHSM is

executed and solved as a continuous variable LP. If AHSM

is treated as a MIP, this understatement of costs is

avoided, but the activity levels in the solution may then

be underestimated.

Estimating the exact measure of distortion within the

activity levels in the AHSM solution is computationally

burdensome. Some insight into the degree of

677
error in the cost calculations is provided in the figures

listed in Table 3. The large divergence between the

estimates of the nonlinear equations and the associated

linear approximations is cause for concern. Although the

resulting degree of distortion in the LP solution is

uncertain, it has the potential to be significant.

These conclusions are based on an argument that implicitly

assumes the correctness of the two pipeline cost

equations. This assumption allowed the study to focus on

the conceptual issues in the AHSM system. The equations

themselves might require corrections to specific parameter

values, but the nonlinear properties of the relations

would be the same in all likelihood. Thus, the conceptual

argument and its conclusions would still apply; only the

intensity of the problems would vary.

Alternatives to the Current Version of AHSM

In light of the preceding statements, the last issue to

address concerns the direction of future work. There are

two alternative paths to be considered. One path involves

an overhaul to the existing AHSM framework. The conceptual difficulties would be eliminated by incorporating

the linear programming equation system into the iterative

Monte Carlo procedure that evaluates the resource

potential and then solving the constrained optimization

problem as a MIP. This would avoid the conceptual

difficulty inherent in basing the LP solution on expected

values of resources. The user could compute the expected

activity levels correctly. Solving the equation system as

a MIP would correctly estimate the total pipeline costs

for the major links. However, transportation charges for

spurs would continue to be estimated incorrectly. Also,

the computational burden of numerous executions of such a large LP is impractical. In fairness to the developers of

AHSM, it is noted in the model documentation that the LP

should be incorporated into the Monte Carlo procedure.

They, too, noted the computational considerations and

dismissed it as impractical.

678
The second alternative is the option being pursued

currently at the Department of Energy. That alternative

is to retain the best features of AHSM while developing an

alternate methodology that avoids the problems inherent in

AHSM. The AHSM work includes valuable data on costs of

operation at all stages of operation: exploration,

development, and transportation. There is a complete set

of stochastic variables that depicts the geology base of

northern Alaska. These data represent the product of a many hours of research. Perhaps the most valuable feature

of AHSM is the insight gained from the total experience.

This insight will provide a useful foundation for the new

model. The new model is currently under development.

The rough framework for a single iteration of the new

model appears in Appendix B. The model also employs a Monte Carlo framework that iteratively determines possible

geologic states. Within the geologic state present in any

iteration, all decisions are represented explicitly. The

explicit representation of decisions has a dual advantage.

First, the nonlinear pipeline relations can be incorporated directly into the simulation of the decision process.

Second, the data available for decisionmaking can be controlled. The true state of geology, for example, is

unknown to the exploration decision, and becomes known

only through exploratory drilling.

The process depicted in Appendix B is oversimplified but

conveys some of the model's flavor. Each iteration begins

with the initialization of a state of geology and expected

values for exploration and development costs and product

prices. The former constitutes the true state of

geology. The latter set of data is used in the decisionmaking of the operators. Since virtually any decision

concerns the determination of activity through "future"

years, the operators need to have economic expectations to

calculate the expected profitability of a proposed

project. As presented here, the operators acquire a set

of economic expectations for all years in the

initialization. An alternate choice is to develop a dynamic adjustment process that would occur at the start

of each time period.

679
After initialization, the model proceeds with successive

time periods. In each time period, three major activities

are conducted —exploration, development and

transportation. Exploration activities are modeled as a search process based on limited, uncertain information.

Development activities convert the known reserves into

flows of production over time. Development requires the

drilling of wells and the construction of surface

equipment. Transportation activities include the shipping

of petroleum along the existing system and the

construction of both new links and expansion to existing

capacity. Any decisions result in implementation only if

the project is expected to be profitable. The decisions

are made on the basis of available information. Thus,

although the operators work to attain the best possible

outcome, the lack of perfect knowledge may result in

losses on projects undertaken. The uncertainty resulting

from the lack of foresight is exacerbated in the

exploration process since the true geologic state is

unknown.

A complete description of the model will be available when

it becomes operational, currently expected in the summer

of 1981. The model will avoid the omniscient character of

the decision process inherent in the linear programming

framework of AHSM and rely on decisionmaking under

uncertainty. The model can accommodate the nonlinear

relations required for the calculations of pipeline

links. Also, the output from the numerous iterations

lends itself to statistical analyses of the results. Each

of the three advantages is considered to be a significant

improvement over the modeling characteristics of AHSM.

Bibliography

1 . Alaskan Hydrocarbon Supply Model: Methodology Description , EIA #TM/ES/79-09; January 1979.

2 . Alaskan Hydrocarbon Supply Model: Methodology Description . Appendix I. Data Documentation , EIA #MDR/ES/79-02; October,

1979.

3. Alaskan Hydrocarbon Supply Model: User's Guide , unpublished

draft

680
APPENDIX A

ID

Table 1. Mathematical Formulation Used in the Alaskan

Hydrocarbon Supply Model

Equations : Reserves Inventory Balance

for all f,s,p,t:

-I(f ,s,p,t)-£e(f ,s,k,p)*E(f ,s,k,t)

+D(f ,s,p,t,)+I(f ,s,p,t+l) < 0 (1)

Material Balance

for all f ,t,s, j , (m,n)

l=lpD(f ' s ' p rZ)*d(f,s,p,t-z)+

m

T(f, (m,n) ,t)*(l-L(f, (m,n))

-q

T(f,(m,q) ,t)-S(f,j,t) > 0 (2)

Pipeline Capacity

for all f , (m,n) ,t

?ii5x(f*(m,n,),i,y)*K(f,(m,n),i)-T(f,(m,n),t) > 0 ' (3)

Convexity Constraints

-Pipeline Expansion

for all f , (m,n) , i

|X(1, (m,n) ,i,t) < 1 (4)

-Exploration

for all f f s,k,:

|E(f ,s,k,t) < 1 (5)

Objective Function

yyy Maximize £^ t S{t n ,t)*a{t ,i ,t)

681
(6)

7777 TTY'T

tksf CE(f,s,k,t)*E(f,s,k,t)-J^D(f,s r p,t)*CD(f,s f p,t)

"f (m^n)

T(f ' (m ' n) ' t )* CT ( f ' ( m ' n )

"tf (m*n) i c Mf , (m,n) ,i,t)*X(f , (m,n) ,i,t)

Subscripts :

f: fuel type

t: time period

p: supply price (or equi valently , average

total cost of production)

s: supply region

j: demand region

(m,n) : shipment link from point m to point n

k: exploratory drilling unit

i: project identifier for pipeline expansion

z: for developement only, z represents the

initiation year for development

Variables ;

E ( f , s , k , t ) : exploration unit k in region s for

fuel f in time t

e(f,s,k,p): yield of fuel f from exploratory

unit k in region s at supply price p

CE(f ,s,k,t) : present value (PV) of the k-th

unit of exploration for fuel f in region s at

time t

D(f,s,p,t): development activity for fuel f at price p

in region s at time t

d (f , s ,p, t-z) : proportion of fuel f at price p in region

s produced in time t given the initiation of development

in time z CD(f,s,p,t): PV of the development cost for fuel f in

region s at time t with suppy price p

T(f , (m,n) ,t) : transportation of fuel f from point m to

point n in time t

682
CT(f , (m,n) ,t) : PV of transportation charge for fuel

f from point m to point n in time t

X (f , (m,n) , i , t) : pipeline expansion for fuel f, project

i, from point m to point n in time t

K(f , (m,n) ,i) : pipeline capacity for fuel f from point

m to point n, project i CK(f , (m, n) , i ,t) : PV of constructing pipeline project

i for fuel f from point m to point n in time t

S (f , j , t) : sales of fuel f at demand region j in time t

a(frj y t): PV of selling price for fuel f at demand region

j in time t

I(f,s,p,t): unproduced inventory of fuel f with supply

price p in region s at time t

L(f,(m,n)): proportionate loss incurred in transmission

of fuel f from point m to point n

683
Table 2. AHSM Pipeline Cost Equations For Oil and Gas

Oil

S=0 . 149+0 . 58Q**0. 2+0 . 046Q**2

S'=0.116Q**(-0.8)+0.092Q

S"=-0 . 093Q** (-1 . 8) +0 . 092

Natural Gas ;

S=0. 17+0. 416Q**0. 4+0. 1Q

S'=0.166Q**(-0.6)+0.1

S

n =-0.10Q**(-1.6)

Variables: S: scale factor for total costs for new pipeline

links

Q: flow rate; MMB/D (oil), or BCF/D (gas)

Notation: ** denotes exponentiation

S' and S" represent the first and second derivatives

of the original equation, respectively.

684
Table 3. Comparison of Cost Factors for the Linear and

Nonlinear Functions

Oil : SCALE=0 . 149+0 . 58Q**0 . 2+0 . 046Q**2

Normalized Linear Ratio

Q SCALE SCALE SCALE (Normalized: Linear)

.2 .571 .737 .2 3.68

.4 .639 .825 .4 2.06

.5 .665 .859 .5 1.72

.6 .689 .889 .6 1.48

.8 .733 .946 .8 1.18

1.0 .775 1.0 1.0 1.0

Natural Gas ; SCALE=0 . 17+0 . 416 Q**0.4+0.1Q

Normal i zed

Linear Ratio

Q SCALE SCALE (Nonlinear; Linear)

.4 .498 .167 2.98

.8 .630 .333 1.89

1.0 .686 .417 1.65

1.6 .832 .667 1.25

2.0 .919 .833 1.10

2.4 1.0 1.0 1.0

685
Figure 1. Total Cost Function: Major pipeline Links

TC

C

B

r TC

A

/ !

i

i 0 X Z Y Q

Quantity

Figure 2. Total Cost Function: Spurs

686
Appendix B

Program Flow for Proposed Model; Single Interation

1. Initialization:

A. Establish a state of geology - number

of structures and their associated

area

B. Generate the expected value for

exploration and development costs

to be used for reference.

2. Exploration:

A. Calculate the expected unit costs for

selected sites in a given region.

B. 'Drill' successive sites until limit

on exploratory drilling is met or the

portfolio of profitable projects is

exhausted

3. Development:

A. Drill wells for field development.

B. Construct:

1. Surface equipment.

2. Larger pad(s) or island (s).

3. Flowlines.

C. Determine the total reserves and

production rates.

4. Transportation:

A. For existing lines: transportation

activities will use up available capacity.

B. Construct new pipelines for known reserves

lacking transportation facilities, if

profitable

687
A PROSPECT SPECIFIC SIMULATION MODEL OF OIL AND GAS EXPLORATION

IN THE OUTER CONTINENTAL SHELF: METHODOLOGY*

J. P. Brashear,** F. Morra **, C. Everett***, F.H. Murphy***

W. Hery,  and R. Ciliano** **

Hydrocarbon resources in the Outer Continental Shelf (OCS) regions

are an important but uncertain component of the nation's energy

future. This paper describes the methodology used in constructing a model and database to forecast reserve additions and production from

the OCS as a function of price and Federal policy in the context of

explicit geologic drilling prospects and engineering costs.

The model is based on microeconomic analysis of individual

exploration prospects as identified from seismic maps. A prospect was defined as one or more traps that, if productive, would be developed

as a new field. A resource distribution is built for each prospect by

including uncertainty concerning geological and engineering properties

of the prospect. Exploration and development decisions are based on deterministic cost and engineering information for each phase of the

project. Bidding and exploration decisions are based on expected net

present value incorporating full costs and resource uncertainty.

Development decisions occurring after successful exploration and

delineation drilling, are based on present value given known field

size with lease acquisition and exploration costs sunk. The model

incorporates Federal leasing schedules and leasing policy (variations

on bonus, royalty, and profit share bidding), user-specified, market

price tracks and constraints on rigs, platforms and pipelines.

* Opinions stated reflect the views of the authors and not necessarily

the positions of their organizations. This research was supported

by Contract No. EM-77-C-01-8597 between DOE and Lewin and Associates.

** Lewin and Associates, Inc. *** Energy Information Administration, U.S. Department of Energy. **** Mathtech, Inc.

688
1. Introduction and Summary

Domestic offshore oil and gas production, especially from the deep

water frontier areas, offers the possibility of reducing America's

near-term dependence on imports. The rate at which these resources

are explored is highly sensitive to the policies of the Federal

Government, especially leasing schedules, leasing system (bidding on bonus, royalty, profit-share, or mixed systems), oil and gas prices,

and tax policies. The rate at which the resource is developed is

influenced, however, by the number and size of hydrocarbon deposits

actually found, and costs of development, and the available market

price.

The Energy Information Administration of the U.S. Department of

Energy sought to model these relationships as the basis for improved

production forecasting and analyses of Federal policy options. To

take advantage of valuable data sources with a minimum of data preparation or interpretation, a disaggregate analytic strategy was adopted. The resulting model simulates the behavior of the individual

oil and gas explorationi st who must make two discrete decisions: (1)

whether to acquire and explore the prospect given full geologic uncer- tainty and full engineering costs and (2) whether to develop and

produce the prospect given the marginal costs of platforms, developmental drilling, operations, and transportation for a field whose size

has become known through prior exploration, and delineation. A

prospect, as used in this study, consists of one or more potentially

productive traps (as shown on seismic interpretation maps) that, if

productive, would be developed as a new field. The data available to

the model were obtained by inspection of the records of the USGS

Conservation Division at Metarie, Louisiana which approximate the type

of geological information that would be available to the individual

explorationi st.

This paper describes both the methodology and the supporting database required for this analytic strategy. The goal of the effort was

to implement the strategy in a computer model with the capacity to

simulate future exploration, development and production from Outer

Continental Shelf (OCS) regions of the lower 48 states. The model

produces estimates of oil and gas supply from 1980 to 2000. Projections are made individually for the Gulf, Atlantic and Pacific OCS

from the surf line to 1000 meters water depth and are subdivided into

estimates of proved reserves, extensions (and revisions) to proved

reserves, and undiscovered resources.

The supporting database contains information collected by geologic

interpretation of seismic and engineering data. Approximately 65% of

the undeveloped prospects in the Gulf were believed to be covered by

this process; for the remaining 35%, sampling based on geographic

proximity and common geologic trend was used to complete the working

database. "Prospects" in the Atlantic and Pacific were arbitral* ly

689
created by sampling of field sizes from assumed distributions to match

the total regional resource estimates published in USGS Circular 725

[2] and its updates. Consistent with the analytic approach of the

model described here, these synthetic data should eventually be

replaced with data developed in a manner similar to that used in the

Gulf.

The supply of oil and gas from undiscovered resources is the major

emphasis of the model; it is evaluated by means of four serially

executed submodels:

o Geology : The uncertainty expressed by the geologist in specifying the value of specific reservoir parameters is estimated

through Monte Carlo* simulation to produce a prospectspecific resource distribution.

o Technology : Engineering options, production profiles, and

costs associated with the exploration, delineation, and

development phases are evaluated for selected points on the resource distribution of each prospect.

o Field Sampling : The prospect-specific resource distributions

are sampled to supply a set of field-size Values that represent

a potential geologic outcome of exploration, for each Monte

Carlo trial of the analysis submodel.

o Analysis : Given a time series of assumed market prices, leasing schedules, and leasing policy specifications, the phases of

exploration, delineation, development and operations are simulated for each prospect, based on the geologic outcomes. A

number of Monte Carlo trials are run to incorporate uncertainty

in the resource base.

Production from currently proved reserves and their likely future

extensions and revisions are estimated by constant ratio of reserves

to production which is calculated from historical trends. Additions

to proved reserves through extension drilling in existing fields

(inferred reserves) are computed by methods similar to Hubbert [3].

The model is depicted in Figure 1. The technology, geology and

discovered reserves models are used only to initialize the model, as data is updated. The field locator (sampling) and policy analysis

models are used whenever new policies are considered.

*Pseudo-random sampling over a large number of trials.

690
Figure 1:

OVERALL SYSTEM FLOW

GEOLOGICAL, RESERVOIR

AND PRODUCTION DATA

GEOLOGY

COMPONENT

COST AND

ENGINEERING DATA

TECHNOLOGY/

COSTING

COMPONENT

I "

I POLICY ANALY

I FEDERAL POLICY I SPECIFICATIONS ,

PRODUCTION

FROM RESERVES

SIS SIMULATION

FIELD

SAMPLING

COMPONENT

POLICY

ANALYSIS

COMPONENT

MEAN AND CONFIDENCE LIMIT ESTIMATES OF:

Q RESERVE ADDITIONS • PRODUCTION

O RESOURCES NOT DEVELOPED

691
2. Model Approach in Contrast with Previous Studies

i

The model forecasts production from discovered fields as a constant percentage of reserves. A Hubbert-type analysis is used to

model reserves additions through extension drilling (the "inferred

reserves" of USGS Circular 725). The analysis of inferred reserves is

based on the prior work of Hubbert [3], Root [8], and Mast and Dingier

[6];and achieves notably closer precision in "backcasting" existing

data series than preceding studies. See [10] for the comparison.

For undiscovered resources, the model represents a departure from

earlier studies (see Kalter, [4]; Mansvelt-Beck, [5]; EIA Midterm

Energy Forecasting System, [11]). In general, previous models had

been forced to employ aggregate data which may suffer from internal

confounding of technology, policy and economic factors.

The disaggregate approach of the present work is aimed at improving prediction by eliminating the use of aggregate resource estimates,

historical "finding rates," and assumed field-size distributions. For

example, all prior studies referenced above use area-wide resource

estimates derived from a process of group-decision making that

considers geological evidence only in an indirect fashion. All three

previous models yield forecasts of economically recoverable reserves

only. The use of these models to forecast the quantities of resource

foregone resulting from Federal policy variations or from technical,

geological or logistical constraints is virtually impossible, requiring a large number of subjective assumptions. The EIA Midterm model

[11] is based on the use of "finding rates" which represent historical

trends in the marginal quantity of discovered resource attributable to

yearly increments of drilling activity. The data series upon which

finding rates are based does not permit the unraveling of the tangled

effects of changed Federal policy, improved technology or economics.

The Kalter [4] and Mansvelt-Beck [5] models represent a further

refinement by explicitly representing Federal policy effects by use of

decisionmaking based on microeconomic analysis of "prospects" (sampled

from the Circular 725 resource distributions). However, neither model

makes a separate assessment of oil and gas production. Further, since

costs are assessed on a "per BOE" basis derived from historical

averages, these two models cannot represent the specific engineering

decisions which must be faced in the development of oil versus gas

prospects.

This model provides an improvement over the previous work in five

areas:

o Uncertainty in the resource base is a function of the interpretation of individual of prospect specific seismic and

engineering data. -

692
o Exploration and development costs are based on actual engineering studies applied to prospects of known extent in known water

depths.

o The detailed geologic data base enables the model to make

specific estimates of the production of oil, associated gas,

nonassociated gas, and natural gas liquids.

o Because the model begins with a prospect-specific resource

distribution, it is possible to provide a full accounting of

the undiscovered resource including that which is not produced

due to economics, constraints and leasing schedule. (The full

accounting is shown in attached Figure 2).

o The model may be easily updated as new geologic and engineering

information is acquired. As more seismic exploration is

conducted, additional prospects (especially smaller and deeper)

will be identified. Other prospects will be drilled, thereby

becoming fields or abandoned leases — no longer prospects.

Finally, offshore technology is rapidly changing. Updated

geology and technology requires only minor modifications or additions to the database. Other models require costly, time

consuming area-wide resource estimates which cannot be readily

updated as experience accumulates.

In sum, through the detailed engineering and geologic database

this model represents a significant advancement over previous effort

by reducing the need for "empirical generalization".

3. Production from Identified Reserves

While the primary emphasis is on production from undiscovered

resources, production from proved and inferred reserves (which sum to

the "identified reserves" of Circular 725) is included in order to

provide a complete estimate of OCS production. Proved reserves are the portion of the resource in known fields that can be produced under

current technology and economics. (Circular 725 refers to these as the sum of "measured" and "indicated" reserves). Inferred reserves represent future additions to proved reserves due to extension

drilling, revisions of estimates, and the discovery of pools in known

fields (too small to be considered significant new finds). Production

from "identified" reserves is assumed to be insensitive to Federal

policies affecting the undiscovered portion resource; estimates of

this production are based on projections of the separate time series

of (a) production from proved reserves, (b) additions to inferred

reserves, and (c) production from inferred reserves.

693
THE MODEL CAN PROVIDE A FULL ACCOUNTING

OF THE UNDISCOVERED RESOURCE BASE

BECAUSE IT IS BASED ON MICROECONOMIC ANALYSIS

OF INDIVIDUAL PROSPECTS

HYDROCARBON RESOURCE

IDENTIFIED UNDISCOVERED

Proved Inferred

Evaluated

&

Adjacent

Other

Mapped

Unmapped

ECONOMIC BASE

ANAL

LINE

YSIS

MODEL

SUBECONOMIC HPH

777

UNDISCOVERED

TOTAL

RESOURCE

BASE

Recoverable Resource

LU Economic and developedfuture reserves and

production

Uneconomic due

to economic limit

< *- AC c

UJ %

Economic but undeveloped

due to constraints

(Operating costs'

marginal revenue)

ECHNICALLY

UNRECO'

(Residual

at

Abandon

Explored but uneconomic to develop

(marginal costs)

Apparently explorable but

unexplored due to constraints

Uneconomic to explore (full costs)

r—

UNDISCOVERED

RESOURCE

BASE

LUO

<

-I

Q.

I Z

ill o

oc

z>o

CO

LU

cc

694
Proved reserves are assumed to be produced at a constant fraction

of the stock of remaining reserves; the rate of production was based

on recent reserve decline trends. Inferred reserves are added by a Hubbert-type model [3] which uses the time series data of the American

Petroleum In sti tut ion /American Gas Association (API/AGA) [1]; calculations are based on the year of discovery of the reservoirs that

constitute proved reserves.

Each year, API/AGA [1] report both estimates of ultimate recovery

by year of discovery of the reservoir and estimates of new reserves

added during the year. According to API/AGA definitions, this change

cannot come from "new" discoveries -- these would be recognized as discovered in the subject year. Hence, the change implies additional reserves added by means of additions, revisions, extensions and discovery of new pools within existing fields - i.e., inferred reserves. Subsequent production from inferred reserves employs the same decline

rate used for proved reserves.

The approach used for estimating additions to reserves from

revisions, extentions, and new pools is as follows:

Let

u = the number of years since the resource was added to reserves,

f(u) = the yearly percentage change in ultimate recovery from

reserves discovered "u" years previous to the current

year.

For example, f(10) would be found by averaging the change in

estimates of ultimate recovery detected between their ninth and tenth

years; f(20) would be the change in estimate for fields between 19 and

20 years and so-on. Since the API/AGA data is available for the

period 1967-1979, there are 13 estimates for values of f(u) for

l<u<48. The value of f(u) used by the model is determined by averaging the percentage changes in ultimate recovery at age "u".

It is possible to use f(u) in combination with the most recent

API/AGA estimates to forecast yearly changes in reserves by the

fol lowing:

Let

Q(t,d) Represent the ultimate recovery of nonassociated gas from

fields discovered in year "t" (e.g., 1947) as reported in

year "d" (e.g., the API/AGA time series for 1978)

A(t,d) = Age of reserves discovered in year "t" at time "d"

= d-t

Then Q(t, d+1) = (f(A(t, d+1)) + l)*Q(t,d)

695
Production data for offshore areas are reported by the API/AGA,

USGS, DOE, and a variety of state and private sources. Reserves data,

however, are reported separately only by API/AGA [1] and these only

for the Gulf of Mexico. Production estimates for the Atlantic and

Pacific OCS regions are made by using ratios keyed to Gulf of Mexico

figures

Proved and inferred reserves and production of natural gas liquids

are proportional to natural gas reserves and production; similarly,

associated/dissolved gas production is proportional to crude oil

production. In all cases, gaseous and liquid hydrocarbons are reported separately.

This component of the model provides base supply estimates,

representing the likely future contribution to production from

measured, indicated, and inferred reserves using current technology

and economics.

4. Geological Data Base

The data used to forecast production from undiscovered reserves

are derived by four basic processes:

Class A: Data are taken directly from the files of the Conservation

Division of the United States Geological Survey, which

evaluates each tract nominated for sale. This evaluation

includes seismic interpretation, engineering analysis, and

economic evaluation. In addition, all structures in tracts

adjacent to nominated tracts have been seismically interpreted. In the Western Gulf of Mexico, virtually all tracts

with prospects of trapped hydrocarbons to a water depth of

200 meters have been mapped seismically and the majority

have been evaluated.

Class B: Commercially prepared low-resolution seismic data for areas

not covered by "Class A" methods -- essentially between 200

and 1,000 m in water depth -- were examined by USGS geologists and other geologists under contract to DOE. These

reviews identified the existence of prospective traps and

outlined three potential areas of closure depending on estimates of the location of the hydrocarbon -water contact.

Engineering parameters were taken from an analogue prospect

selected from the "Class A" data group based on geographic

proximity and common geologic characteristics.

Figure 3 shows the data collection form used in this activity.

The form was designed to protect the confidentiality of the USGS data

by detaching all explicit references to location. Note that the

evaluating geologists estimated a number of engineering, logistical,

and geological factors as point-estimates. Geological uncertainty was

696
FIGURE 3

FORM USED IN COLLECTING

PROSPECT-SPECIFIC DATA

697
introduced by estimates of the "minimum" (defined as the 0.95

probability), "maximum" (defined as the 0.05 probability), and "most

likely" (or 0.50 probability) for parameters controlling resource

in-place and technically recoverable resource, as discussed below.

The intention is to eventually employ methods of Class A and B for

all lower-48-state 0CS waters. Resource limitations in the study

restricted coverage to about 65 percent of the Gulf of Mexico area. Accordingly, two additional techniques were used to approximate the

remaining prospects in the Gulf, and in the Atlantic and Pacific Ocean.

Class C: Within the remaining portions of the Gulf, geographic areas of similar geological history, near to areas with Class "A" or "B" data, are designated as "recipients." The sampling

frame for "donors" (i.e., prospects having detailed data)

was the "play" defined by common geologic trends and water

depth. Individual prospects were sampled from donors in

proportion to the area of the recipient zone. Details of

this approach may be found in [12].

Class D: For the Atlantic and Pacific, only broad, basin analogues

from USGS Circular 725 are available. Prospects were

sampled from the lognormal distributions, aggregating to the

basin-wide resource estimates of Circular 725. A map of the

Atlantic and Pacific areas under consideration was ruled

into blocks approximately 20 miles square. Sampled prospects were randomly assigned to blocks with probability

proportional to the number of nominated tracts in the block;

water depth and depth of pay were estimated from bathymetric

maps and regional geologic maps, respectively. This procedure helps insure that the prospects have a close analogue

relationship to existing physical properties, field sizes

and total resource estimates. Appropriate correlations

(c.f., Standing [9]) and known relationships based on depth were used to assign reservoir engineering parameters to the

sampled prospects. All of the specific data elements and

methods are described in detail in [12].

For the Class A and B data collection activities, many of the data

elements were simply read from seismic or other maps (e.g., true

vertical depth, trap type, water depth, distances from shore, to

nearest pipeline). Estimates of reservoir properties were made by

using the following techniques:

Reservoir Area : Based on seismic structure maps, the geologists measured the area of apparent traps based on the assumption of an oil - or gas-water contact at the point where the

trap was 5%, 50%, and 95% percent "full." Multiple traps could

be included in the prospect if they had a common seismic occurrence and common source rock. When multiple traps were

included, their respective areas were added for the three

estimates because they were assumed to vary together due to common geologic history.

698
Reservoir Thickness : The net reservoir thickness was estimated

based on nearby producing fields in the same geologic trend and

the shape of the trap.

Fraction of Reservoir Volume Containing Oil (Gas) : Assigned by

analogue from the nearest field with similar geologic history.

Oil -proved and gas-proved areas are relatively well established

in the Gulf.

Oil (Gas) In-Place per Acre-Foot : These values were calculated

volumetrical ly based on" engineering parameters, using the

following equations:

Oil in Place = 7758 0 (1-Sw)

per acre-foot B0

Gas in Place = 43.56 0 (1-Sw)

per acre -foot g.

Where: 7758 = Barrels per Acre foot

0 = Bulk porosity (%)

Sw

= Connate water saturation

B0

= Oil formation volume factor (ratio of

reservoir volume to volume of surface

conditions

43.56 = Thousands of cubic feet per acre-foot

Bg = Gas formation volume factor

Nearby analogue fields of common geologic history and depth

provided estimates of porosity, connate water saturation, and

oil formation volume factor. Gas formation volume factor was calculated from the pressure, temperature and gas compressibility based on the actual prospect depth using engineering

correlations (See Standing [9]).

Recoverable Oil (Gas) : Based on nearby analogue fields, both

the expected drive type (natural water drive or pressure

depletion) and its efficiency were considered. Based on this,

three percentage "recovery factors" (representing min, max and

most likely values for oil (gas), respectively) were multipled

by the oil (gas) in place to estimate the portion recoverable.

Recovery of Associated Products : Producing gas-oil ratio (GOR)

and natural gas liquids yield (NGL) were assigned on the basis

of the nearest analogue field, as corrected for pressure,

temperature and compressibility as a function of measured depth.

699
Number of Platforms : Platforms were assigned by estimating the

radius of a circle that could be drained by directional drilling at 55° after the first 1,000 feet of hole. The number of

circles of this radius necessary to cover the full prospect was estimated based on the size and shape of the prospect. The

number of these circles is the number of platforms required.

Percentage of Resource Under Each Platform : Was assigned by

estimating the relative volume of traps under each platform

tempi ate.

Probability of Hydrocarbons : Was defined as the likelihood of

hydrocarbons in any quantity being in the trap, and was assigned by the geologist as a subjective function of his own experience and drilling success in nearby fields.

5. Geology Model

The purpose of the Geology Model is to combine individual distributions of separate uncertain reservoir parameters using Monte Carlo

sampling, into an overall resource distribution. As described above,

the input data reflect uncertainty about specific geologic and reservoir parameters that determine the type and amount of hydrocarbon

resource which is "in-place" and which may be produced from a given

prospect. For each prospect, the geologists made three point

estimates for the following:

o Fraction of bulk sediment occupied by oil;

o Recovery of oil (bbl/Ac-ft);

o Recovery of nonassociated gas (Mcf/Ac-ft);

o Yield of natural gas liquids (bbl/MMcf);

o Productive area (Ac);

o Net pay, or effective thickness (ft);

o Producing gas-oil ratio (Mcf/bbl);

The minimum, maximum, and most likely estimates are used to

determine a triangular distribution for each parameter; 1000 psuedorandom sample trials are used to combine these individual distributions (in conjunction with basic engineering relationships) into

overall distributions.

700
The calculation sequence for each pseudo-random sample trial is:

1. Bulk sediments = productive area x net pay

2. Oil producing volume = bulk sediments x fraction occupied by oil

3. Gas producing volume = bulk sediments x (1 minus fraction occupied

by oil

)

4. Oil-in-place = oil producing volume x unit volume oil-in-place

5. Associated-dissolved gas in place = oil in place x gas-oil ratio

6. Recoverable oil = oil producing volume x oil recovery factor

7. Recoverable gas = gas producing volume x gas recovery factor

8. Recoverable associated/dissolved gas = recoverable oil x gas-oil

ratio

9. Recoverable NGL = recoverable gas x NGL yield ratio

The distributions for items 4 through 9 are saved for later combinations into total liquids and total gases, in-place and recoverable, to

complete the accounting for resources and reserves.

By combining over 1,000 pseudo-random samples trials, a continuous

distribution is formed as shown in Figure 4. The distribution is

summarized for later use by six points corresponding to the expected

values of outcomes lying within the 0th and 5th, 5th and 25th, 25th

and 50th, 50th and 75th, 75th and 95th, and 95th and 100th percentiles.

FIGURE 4

Statistical Low

OVER A LARGE NUMBER OF TRIALS (1000-2000) A QUASICONTINUOUS DISTRIBUTION IS FORMED

Statistical

High

Extreme

Maximum

PERCENTILES

i<fc

5th 25th bOth 7>th 9bth

> RECOVERABLE OIL —

RECOVERABLE GAS

701
The full operation of the geology model, including a detailed

statement of the data and equations may be found in [14].

6. Technology and Costing Model

The purpose of the Technology/Costing Model is to evaluate the

cost of exploraton, delineation and development for each prospect in

the data file. For each of the six field sizes derived from the oil

and gas resource distributions and for the condition "dry," (i.e., no hydrocarbons at all in the trap) for each prospect, the Technology/

Costing Model estimates the investment costs and discounts them to

their net present values. Thus, in general seven cases are costestimated for each prospect. When more than one platform is required

for some field sizes, the costs of alternative development schemes are also estimated for later optimization, as described below. The model

is based on an extensive study of the costs and availability of offshore technology.

The development of a typical offshore project is conducted

according to the following schedule:

Phase Acti vity/Deci sions

Exploration First year that a prospect becomes available for

exploration; time of decision whether to explore.

Delineation End of exploration phase; dry prospects are abandoned

and delineation drilling begins in "non-dry"

prospects to determine field size.

Development Delineation drilling completed, defining field size;

time of decision on whether to develop; development

begins in fields that are economic at the margin

viewing exploration costs as "sunk".

Production Development completed; production operations commence.

Economic Limit* Economic limit is reached; production ceases.

Abandonment Platform is abandoned and removed.

Cost data were developed in conjunction with the Dallas Field Office

of EIA and through independent engineering analyses.

* Because the economic limit is a function of price, this phase of

each prospect's development is treated in the policy analysis model.

702
The exploration costs are those expenditures required to determine

whether the prospect is "Dry" or "Not Dry". Exploration is generally

conducted from a mobile drilling rig. Exploration costs are based

entirely on the external physical parameters of the prospect; the size

of the field which may be contained in the prospect does not influence

exploration costs. The following costs are estimated:

o Geological and geophysical costs (function of surface area);

o Number of exploration wells (function of surface area and type

of trap);

o Cost per well (function of water depth and drilled depth);

o Drilling rate per year (function of total drilled depth,

allowing for movement of rigs); and

o Business factors (overhead, rate of return).

Where exploratory wells fail to find hydrocarbons, the sequence is

ended. Given the field has been determined to contain hydrocarbons in

the exploration phase, however, delineation costs are expendited for

additional exploratory wells to determine the size of field contained

in the prospect. Delineation drilling commences with the termination

of exploration. Delineation wells are drilled using the same technology (and per well cost) as exploratory wells. All exploratory and

delineation wells are assumed to be plugged and abandoned due to lack

of production facilities. When delineation drilling determines the

field is too small for commercial development, the prospect is

abandoned. When the field size is sufficient to justify further

investment, development costs are estimated.

Some development costs depend only on the physical properties of

the prospect and not the field-sizes including:

o Per-Well Development Drilling Costs : Including the cost of a single successful production well and a single developmental

dry-hole. (Function of water depth and average drilled depth).

o Expected Fraction of Developmental Dry Holes : A function of

trap-type, recognizing that various traps require inherently

different patterns (and risks) of development.

703
o Pipeline Costs : If the prospect is within 10 miles of a pipeline trunk or the shoreline, the actual amount of connect line

needed for each product (oil and/or gas) is costed. If the

prospect is not within 10 miles of a trunk, only 10 miles of 2

inch connect line are built for each product. (A separate

algorithm "builds" trunk pipelines).

o Distance to Shore : A regression equation is used to yield

distance to shore as a function of water-depth. This equation

is made possible by the gently sloping bottom of the shelf; it

is made necessary by the requirement that the confidentiality

of the data be preserved, and that actual distances could not

be included in the database.

Once these costs are calculated, development costs that depend on field extent and size are estimated. In the data collection process,

the geologists estimated the number of platforms required to drain the

entire prospect based on the "reach" of a directional ly drilled well

(to a maximum of 56° from vertical from each platform). For

prospects requiring more than one platform, the proportion of the resource under each platform was estimated based on the estimates of

the area of closure. This procedure allowed large and/or unusually

shaped prospects to be incorporated into the analysis, with a pattern

of development which would approximate that which would be followed in

actual exploration.

For prospects requiring only one platform , estimation of the

remaining development costs is straightforward.

Number of wells in prospect : a function of field size and flow

rate.

Platform Cost : a function of water depth, and number of wells . Overal 1 total wells are assigned to platforms according to an apportionment of resource to platforms. The platform count was obtained by laying circular templates representing radius of

drilling on the volume of closure on the seismic map (as interpreted by the staff geologist). The number of platforms is determined by the number of "circles" required to cover the prospect.

Percent of resource attributable to each platform is based on the

per cent of volume drained by the platform.

Platform Construction Time : a function of water-depth and number

of platforms.

Peak Production : a function of product (i.e., oil or gas) and

field size.

Equipment Costs : a function of peak production, product, and

distance to shore.

704
Yearly Drilling Costs : a functiofr of number of wells, dry hole

rate, rate of drilling and per-well costs.

Yearly Platform Development Costs : a function of platform cost

and platform construction rate.

When more than one platform is required , optimization is

necessary. The model estimates the costs of a number of development

options, including additional platforms and use of subsea satellite

wells, and mixes of these. The shape of the prospect may be such that

a portion of the prospect lies too far from the platform to be reached

by directional drilling but is too small in itself to justify an additional platform. In such cases, subsea satellite wells can be

used to obtain production from portions of the prospect that might be

uneconomic if each portion had to bear the full cost of platform

development. This development system requires at least one permanent

platform, but, production from the satellite wells uses a subsea wellhead with remote control metering and safety devices. Maintenance is

accomplished by a "through flowline" system requiring one dedicated

2-inch flowline to transport special tools; production is transported

to the platform by a second 2-inch flowline for metering and eventual

sales to a trunk pipeline.

All conventional technology costs are discounted to the time at

which platform construction starts. The development sequence, is as

fol lows:

When more than one platform is needed, the model calculates the

investment cost of all relevant permutations of additional platforms

and subsea completions.

Subsea satellites are used when the marginal cost of a subsea well

is less than the prorata share of platform costs attributable to each

platform-based we FT TRe marginal cost of a subsea or satellite well

is:

o The difference in drilling costs between wells drilled from an exploration-type temporary rig and those drilled from a platform (including dry hole costs), plus

o The costs of the subsea or satellite wellhead completion system

(installed) plus

o The costs of flowlines to the platform.

The costs of the satellite completions vary with the water depth.

For water depth less than 60 feet, caisson completions are used. At

greater depths, full subsea completions with "through flowline

maintenance" are used, requiring two 2-inch flowlines. The length of

the flowlines is set at two times the maximum drilling radius from the

fixed platform

705
The net present value of all relevant development options is

calculated and passed to the Analysis Model. In that model, the pet

present value of the revenues from each option is compared with the

costs, permitting selection of the optimal development option on the

basis of marginal revenues and marginal costs.

All equations, and coefficients, and procedures used in this

section may be found in [13].

7. Field Sampling Component

The Geology Model and Technology Costing Model need be run only

after updating because they create large datasets for the remaining

two modules. The Field Sampling Routine and analysis model are the

two portions of the OCS model that are run routinely for forecasting

and policy analysis. The purpose of the Field Sampler is to provide a particular field-size assignment to each prospect in the data-base for

each Monte Carlo trial (see Figure 5). This serves the role of linking uncertainty in the resource base with the deterministic engineering and business decisions in the Analysis Model. As shown in

Figure 6, the unit interval is first partitioned into "dry" (i.e., no measurable hydrocarbons in the prospect) and "not dry" on the basis of

the geologist's estimate in the data collection phase. The "not dry"

portion is further subdivided according to the percentiles of the six

key points used to characterize the prospect's resource distribution.

This creates a seven-fold partition of the unit interval; sampling

from this interval is accomplished by selecting a random fraction on

(0, 1].

706
Figure 5:

POLICY ANALYSIS MODEL (RESOURCE UNCERTAINTY)

A SPECIALIZED PROGRAM CALLED THE FIELD LOCATOR ASSIGNS FIELDS

(OR 'DRY') TO EACH STRUCTURE BASED ON THEIR LIKELIHOOD

(i.e.. P(Dry), P(EV1) ... P(EV6))

START -3-

I FIELD LOCATOR

YES

OPERATE POLICY

ANALYSIS COMPONENT

OVER ALL PROSPECTS

(See Figure 7 for remaining analysis)

STORE

RESULTS

TRIALS

NOT

FINISHED

MONTE

CARLO

COUNTER

TRIALS

FINISHED

DISPLAY

RESULTS

OVER A NUMBER OF MONTE CARLO TRIALS,

THE UNCERTAINTY IN THE RESOURCE IS INTRODUCED

TO THE DETERMINISTIC ECONOMIC ANALYSIS

707
Figure 6 Sample Outcomes and Their Probabilities

Dry Not Dry

Possible

Outcome

Class Size

1 2 3 4 5 6

Probability P (1-P).05 (1-P). 20 (1-P). 25 (1-P) .25 (1-P). 20 (1-P). 05

The sampling of all prospects is repeated for each Monte Carlo

iteration of the analysis submodel.

Each Monte Carlo trial requires an assignment for each of approximately 1800 prospects. For a 'suite' of 100 Monte Carlo trials of the

analysis model some 180,000 assignments would be made. These assignments are kept in a computer file, for access by the Analysis Model

as the costs of exploration are paid, the model "discovers" whether

hydrocarbons are present; as costs of delineation are paid, field size

is "determined".

8. Analysis Model

The Analysis Model is designed to account for the disposition of

the undiscovered resource as a function of (1) geologic, engineering,

and economic factors and (2) specific Federal policies. The Federal

policies which may be specified by the user are:

o Assumed market prices for oil and gas at the wellhead for the

period 1980-2000.

o Leasing schedules in acres per year by the USGS leasing

districts (e.g., Georges Bank, Western Gulf).

708
o Bidding rules, including (a) lease bonus -- fixed or variable;

(b) royalty system—fixed or declining for the life of the

prospect; (c) profit share —fixed or variable.

o Corporate tax rates, investment tax credits, etc.; and

o Institutional delay (in yr.) between delineation and development to provide for permitting.

The Analysis Model simulates decision-making under uncertainty for

the industry as a whole annually from the present through the planning

horizon (e.g., 1990, 2000). Figure 7 presents a general flowchart of

this model

The simulation of exploration, development and production for each

prospect is the core of the model including:

o Prospect evaluation and ranking;

o Bid determination;

o The "go," "no-go" and "defer" decisions associated with — bidding, — exploration,

-- development; and

o Production to the economic limit.

All decisions in the model are made using a discounted cash flow

analysis. Economic attractiveness is determined only on the basis of

expected net present value, as opposed to other motives such as secure supply or other issues ancillary to the venture itself, such as denying access to competitors.

Given the availability of prospects expected to be profitable,

exploratory drilling activity is determined by both the leasing

schedule and rig capacity. The model can be set to constrain the rate

of growth of capacity to drill after it is initialized at the current

capacity.

The model recalculates expected present value for each prospect in

each time period to accommodate (a) changing prices and (b) evidence

obtained from exploratory drilling in prior periods. The expected

present value is the statistically weighted combination of the net

present value (NPV) of each of the possible outcomes that can be

selected in the field sampling component. The NPV for each outcome is

based on:

709
Figure 7:

POLICY ANALYSIS MODEL (ECONOMICS)

FLOW OF ONE MONTE CARLO TRIAL

START

TIME REMAINS

RANK ALL

PROSPECTS BY

OVERALL EXPECTED

PRESENT VALUE

DONE

GO TO

NEXT

TIME

PERIOD

BAYESIAN

UPDATE

ALL PROSPECT

EXHAUSTED

SELECT NEXT PROSPECT

FROM ORDERED LIST

YES

DRY? EXPLORE

NEXT PROSPECT

YES

NO

DELINEATE

(LEARN TRUE

FIELD SIZE)

m

I

COMPUTE MARGINAL

PV OF DEVELOPMENT

WITH EXPLORATION AND

DELINEATION 'SUNK'

NO IS PV EVER

GREATER THAN

0?

NO

YES

MARK FOR

DEVELOPMENT

IN FUTURE

TIME PERIOD

PRODUCE

UNTIL

ABANDONMENT

DEVELOP

WAIT LIST

PLATFORM & PIPELINE

AVAILABLE IN LATER TIMES

710
o A cost stream representing exploration, delineation,

development, and abandonment (generated by the Technology/-

Costing Model) and is discounted appropriately.

o A revenue stream composed of production multiplied by price and

adjusted to reflect the effects of taxation and operating costs

up to the economic limit.

o Appropriate relations between cost and revenue suggested by the

bidding strategy.

The net present values representing all possible outcomes are combined to form an overall expected present value by using probabilities based on two cojoint factors:

o The relative likelihood of each field size for each prospect

given an estimate of the probability of a "dry" structure.

o Four states of nature representing various possibilities for

the dry structure rate with a priori likelihood for each state.

The a priori likelihood of each state of nature is a function of

initial geologic uncertainty and accumulated experience. These are specific to a "play" (a confined geologic and geographic area) defined

as all prospects of a given trend within the east-west width of the

USGS nominclature districts (e.g., Galveston, Eugene Island). These

probabilities are updated in part by a Bayesian process at the end of

each time period. This process was adopted to simulate "play"

behavior often observed -- i.e., a few discoveries tend to revise the

explorationist ' s probabilities upwards, whereas disappointing

exploration results tends to discourage further exploration. These

adjustments often appear to be larger than simply a Bayesian reconsideration of earlier data.

In establishing bid values, the Analysis Model treats the industry

as a unitary entity, not attempting to model intercompany competitive

bidding. Of the various bidding options (lease bonus, royalty, profit

share, etc.) it is assumed that (1) the Federal Government fixes the

rates for all components except for one and (2) the maximum, economic

bid (the one which would produce an expected net present value of

zero) is then calculated. This bid is not necessarily the bid that

would happen in practice. Depending on assumptions about risk

aversion and distributions of expectations in firms, the actual bids

in an auction could be higher or lower. Once the bids are calculated,

they are compared against a minimum bid, if the model is run with this

option. The prospects with positive bids that (a) exceed the minimum

bid (if specified); and (b) are available for lease, are ranked

according to expected profitability.

711
The unexplored prospects are rank -ordered according to the overall

expected net present value. All profitable prospects are scheduled

for exploration, subject to acreage and rig availability. To maintain

close correspondence with current leasing practice, the model assumes that the number of prospects that can "be drawn" from undrilled

structures in any time interval is constrained by (1) lease schedules;

(2) remaining exploration "commitments" carried over from earlier

decision points; (3) remaining delineation "commitments" generated by

successful exploration efforts in earlier periods; and (4) rig availability after these prior commitments are satisfied. This ensures compliance with the acreage and drilling industry capacity restrictions imposed upon the system.

A user-specified lease schedule is defined in terms of acres per

year by leasing area. Before exploration is simulated, the amount of

drilling capacity not previously committed is calculated. Based on this and total rig capacity, the uncommitted rigs are assigned to each

structure to be drilled and an accounting of rigs is kept by type

(i.e., appropriate to water depth ranges) and "ocean" location (Gulf,

Atlantic and Pacific). Rig assignment is made in three passes:

o Wherever possible, the economically most attractive prospects

are assigned available rigs of an appropriate type currently in

the same ocean as the prospect.

o Next, rigs capable of drilling in deeper water, in the

appropriate ocean, are assigned prospects in shallower water.

This rig is then committed to shallower water for the duration

of the exploration and delineation of this prospect.

o Finally, a limited number of rigs may be transferred from other

oceans. This transfer is permanent unless conditions warrant a return

Prospects are then explored and delineated according to their

ordering on expected net present value within the constraints upon the

availability of rigs. Structures that cannot be explored during the

present time period due to rig constraints are deferred until future

periods.

As the costs of exploration and delineation are paid, the Model

simulates "discovery" by referencing the Field Sampler file to

determine the "true contents" of the prospect for that Monte Carlo

trial (i.e., both presence of hydrocarbons and the field size).

Prospects that have been determined to contain hydrocarbons are then evaluated for development on the basis of the marginal costs of

development. The present value given known field size governs the

decision to initiate development or to continue production and is

based solely on incremental costs. Lease acquisition and exploration

costs, for example, are sunk and do not influence the development

decision.

712
Given that exploration yields hydrocarbons, a prospect need not be

developed immediately. A "prospect inventory" is kept, where development that is currently uneconomic may be deferred to some later

period. For example, development may be postponed until there is a sufficient future increase in real oil and gas market prices (as

specified in terms of an input growth in the real price trajectory for

each) or if other nearby prospects justify the construction of a pipeline to that region. The marginal venture would be developed when net

present value, using development and operating costs only, is

positive. The "prospect inventory" is re-evaluated on each cycle, and

deferred prospects must compete with prospects newly discovered in the

cycle. The model does not allow for the speculative withholding of

currently profitable structures.

The prospects that pass the marginal cost evaluation are scheduled

for development in conjunction with constraints on:

o Pipeline availability . Each structure is assigned to a pipeline district. If a trunk line serves the district, there is no pipeline constraint for that structure. Each district without a pipeline is assigned a list of "nearby" pipeline

districts (including the shore) along with the minimum

reserves* required in that district to justify construction of

a trunk pipeline into that district from a neighbor.

Unproduced but proved reserves available in each district are summed each year; when they reach the minimum level, a pipeline

is assumed to be built, and all economic reserves in that

district then become eligible for development. The cost and

benefits of building the trunk pipeline are assumed to be borne

by an external pipeline service company and do not directly

enter exploration or development decisions.

o Development platform availability . A maximum number of

development platforms is specified for each year as an input

variable. Structures with the highest dollar value of reserves

are given the available platforms. Since platform building

constraints are not currently expected to materialize, the

constraints have been set to be inoperative. Those prospects

that cannot be developed due to constraints during the current

time period remain available for development in future years.

* A separate subprogram computes the investment costs of a main trunk

pipeline based on water depth, pipeline length and pipe diameter.

Operating revenues are assumed to be derived from a tariff on the

flow of oil and gas. Minimum reserves are calculated as the amount

needed to provide a flow sufficient to repay the investment costs

plus rate of return and operating costs of the pipeline over a 20

year period.

713
The model schedules production from each developed prospect

according to the capacity that was estimated in the Technology/Costing

Model associated with the field size that resulted. Year-by-year

production, is aggregated across prospects and resource-accounting

bookkeeping is kept over the period 1980-2050. Results are saved for

each Monte Carlo iteration. The volume of recoverable resource for

each of several categories (developed, unexplored due to economics,

unexplored due to constraints, undeveloped due to economics,

undeveloped due to constraints), is recorded by ocean. Cumulative reserve additions, cumulative reserve adjustments, cumulative and

incremental production by year and ocean are also tallied.

Total production is derived by. adding production levels associated

with currently identified reserves (see Section 2) to those from

undiscovered reserves evaluated in the Analysis Model. The final resource and production accounting is performed at the conclusion of

the complete simulation. Variability across Monte Carlo trials is

reported.

9. Limitations of the Present PCS Data Base and Model

As with any model, the OCS model can be improved with several

enhancements. First, the database needs to be completed for the

missing portions of the Gulf and for the Atlantic and Pacific. In addition, systematic procedures should be developed to maintain and

update the files as new seismic prospects are identified, interpretations change, and as real exploratory drilling either "condemns" as dry or "proves" as reserves the prospects in the file. Moreover,

routine updating of the technology specifications and costs as these

evolve should occur. However, the existing database is sufficient for

sensitivity analysis and experimentation with policy variables. As a forecasting tool, the missing data are a handicap, but even with this

limitation, the treatment of Class D data (Atlantic and Pacific)

represents a more precise analysis of the subjective resource estimates and is well structured for updating as new prospects are included, "old" prospects are explored, and/or technology or costs

change.

As data for the remaining identified seismic anomalies are entered

as prospects, a further limitation must be noted. Maximum precision

and validity of the OCS analytic strategy lies in explicitly limiting

the forecasts to production from seismically identified prospects.

Certainly for the near term, and very probably for the intermediate

term (through 1995), this poses no difficulty. When completed, the

database will, in fact, represent exploration targets for this time

horizon. For the longer term, however, current limitations of seismic

technology require acknowledgement that additional, future prospects

will be identified over time as pre-drilling exploration technology

improves. The OCS analytic approach will always understate the

ultimate potential of the offshore regions by the amount of the

714
prospects not yet identified. For very deep prospects and very large,

stratigraphic prospects, this future cannot be estimated. Two

possible solutions to this limitation appear feasible. First, limit

the forecast period to, say, twenty years or so, without attempting to

represent the "all-time" ultimate resources or reserves. Alternatively, acquire subjective resource assessments of these unidentified

prospects and simulate them using the methods employed for "Class D"

data described in Section 4. This latter approach would permit reconciliation with the "overall" estimates of USGS and others while incorporating some of the precision of this approach: if one knows where

the identified prospects are , by deduction, one also knows where the

unindentif ied are not. Thus, they must be in unmapped areas (generally in deeper water or further from existing pipelines) or at

greater total water depth. This knowledge alone permits insightful

economic calculations. If this second approach is used, it is

recommended that the resulting estimates be segregated according to

the class of source data so that the user of the analysis will

recognize the distinction.

A model of rig capacity and rig movement needs to be developed to

eliminate arbitrary constraints as well as provide more realistic

estimates of cost changes in drilling activity. Reduced form, econo- metric models may be sufficient.

The method of revising the a priori probability of hydrocarbon

occurrence should be reconsidered^ A straightforward approach would

be to take each of the prospects and group them by the geologists'

evaluations of the probability of success within geologic trends.

Each group could have its associated prior distribution updated whenever a member of the group is chosen for exploration. Establishing

the prior distribution for the initial year would require, however,

further data gathering and analysis which tends to be very expensive.

Grouping all prospects in a region together and applying a pure

Bayesian update on the aggregate is unsatisfactory because the best

(i.e., highest ENPV) opportunities tend to have higher probabilities

of success. This approach would bias the model to drilling beyond the

point at which it is economic to continue exploration. Finally, there

is the theoretic question of what the update means since the initial

geologic assessment is what is used to sample the states of nature.

It would appear that the notion of "learning" from exploratory

experience is necessary to the realism of the model — vis, "play"

behavior in industry -- but the specific theory and calculation

deserve further development.

As currently structured, the model requires over 6 CPU minutes (on

an IBM 3033 MP system under MVS) to prepare a forecast. However, substantial efficiencies might be achieved through elimination of repetitious calculations through judicious assumptions and restructing of

the simulation accordingly.

715
10. Conclusions

The OCS model provides a rigorous tool to analyze many important,

sometimes subtle, questions of Federal policy on the basis of geophysical and other disaggregate data. In this, the experimental

analytic approach adopted by the OCS study is very promising.

The majority of the data exists in readily accessible form in USGS

files. Both the database and models are readily updated in modular

form, obviating massive new studies as conditions change or new, more precise policy questions are raised.

Forecasts and analyses from this model can serve the needs of many

users. Such users would include leasing-policy officials in DOE and

the Department of Interior, market planners for offshore technology in

private industry, policy-makers attempting to provide special offshore

incentives, public and private decision-makers seeking to relax logistical constraints, and others. In particular, this modeling approach

serves to bridge the gap between overall subjective appraisals of

undiscovered resources and detailed accounting for proved reserves,

permitting the monitoring of the flow from highly speculative undiscovered resources to cumulative production. Models requiring more assumptions and less data than this approach can produce widely

differing conclusions with reasonable choices for aggregate parameter

settings, thereby confusing the policy analysis process.

716
References

1. API/AGA/CPA, Reserves of Crude Oil, Natural Gas Liquids and

Natural Gas in the United States and Canada . Published yearly by

the API, AGA, and the Canadian Petroleum Association.

2. Geological Survey Circular 725, "Geological Estimates of

Undiscovered Recoverable Oil and Gas Resources in the United

States", USGS 1975.

3. Hubbert, M.K., "Degree of Advancement of Petroleum Exploration in

the United States", American Association of Petroleum Geologists

Bulletin , Vol. 51, No. 11, pp 2207-2227. I9P

4. Kalter, R.J., Tyner, W.E., and Stevens, T.H., "Atlantic Outer

Continental Shelf Resources: An Economic Analysis", Ithaca, New

York: Cornel University Document, AE RES 74-17, November 1974.

5. Man sve It -Beck, K.W., et. al ., "Outer Continental Shelf Oil and Gas

Costs and Production Volume", Washington, D.C.: U.S. Department

of Commerce, July 1976, Publication Number PB-262-533 (NTIS).

6. Mast, R.F., and Dingier, J., "Estimates of Inferred and Indicated

Reserves for the United States by State", USGS Circular 725, pp.

73-18.

7. Mineral Resources Conservation Board", Theory and Practice of the

Testing of Gas Wells", Alberta, Canada: 1975, #ERCD-75-34.

8. Root, D.M., "Inferred Reserves of Oil and Gas", unpublished

memorandum 3-29-77.

9. Standing, M.B., "A Pressure Volume Temperature Correlation for

Mixtures of California Oils and Gases", Drilling and Production

Practice , API, 1947.

10. Energy Information Administration, Enhanced Recovery of

Unconventional Gas: The Methodology , VcTT III. , February 1979

ACP/T2705-03. pp 2-9-2-25. 1980

11. Energy Information Administration: "Oil and Gas Modeling at FEA".

1980

12. Energy Information Administration: PCS Oil and Gas Model

Documentation Volume III: Data Description . 1980

13. Energy Information Administration: PCS Oil and Gas Model

Documentations Volume VI: Software Description . 198P

14. Newendorp, P. Decision Analysis for Petroleum Exploration , (Tulsa: Petroleum Publishing Company: 1975), pp. 47P-473.

717
CCKCLUDIHG SESSICN

DR. GASS: Good afternoon: the panel will be run by Dick

O'Neill and Fred Murphy from EIA. Charles Everett and Hall?

Keene will be joining then. We^ould like to have an

interchange between the panelists, the audience, and try to

develop some ideas and raise seme guestions from the point

of view of DOE's future activities in the development of oil

and gas supply models.

DR. MURPHY: We spent two and a half days with people

presenting their work; showing us what they perceive to be

the state of the art and what they are doing.

This morning, we spent time locking at models that are built

to provide complete oil and gas forecasts. It is useless to

have complete knowledge about a single aspect of oil, and gas

supply if you can't bring that knowledge to bear on national

oil and gas supply issues. Most of the models being

presented this morning are models that are used by EIA to

develop national forecasts.

What we hope to achieve from this panel discussion is advice

from the participants in the audience as to where the Energy

Information Administration ought to use its resources to

improve the state of the art in oil and gas supply

forecasts.

Dick, dc you want to say something?

DR. O'NEILL: Yes, I'd just like to continue and possibly be

a little more specific, with seme guestions to the audience.

We've been telling you how we do our modeling, this morning.

One guestion that should be addressed is: What kind of data

should we collect?

The Energy Information Administration has the opportunity to

collect energy data that it can justify as being important

in this area. It has to consider costs and the burden on

the respondent. One of the biggest problems that I mentioned in my presentation this morning, is that people

want to talk about finding rates; but, in fact, the way the

data are gathered and put together, you are almost

hopelessly lost from the beginning, in obtaining good data

for the estimation of finding rates.

Another guestion is: What level of aggregation should our

models take?

Something that has been mentioned infreguently in this

718
discussion, bat that has been causing headaches for the Oil

and Gas Division, Fred and a y self is the use of models for

policy studies, which leads to the question: How do you get

the physical model correct, and then on top of it, do policy

analysis? If you model new discoveries, new field

discoveries, extensions, or revisions in one way. Congress

and the various regulatory agencies create legislation and

regulations that often dc not nap well onto the data

collection categories.

If you look at the original definitions of leases and

properties for old oil, lower tier oil, upper tier oil or the three tiers oil for windfall profit tax you find that

they don't map conveniently into physical quantities that

have been discussed in a modeling framework here.

DE. HCFABLAND: I'm James McFarland, University of Houston.

It appears to me that people have not been asking the

questions that need to be answered, and that should be

what's driving the data collection and model building

phases. There seems to be a let of concern for large models

without that driving mechanism, and it's not at all clear to me that very simple models could be be used to give you much

better insights to some very basic policy issues.

But it would appear that you should

state what the policy guestion is, and then ask what data

and what models might be used to try to gain insights into

that.

It's not at all clear to me that the very complex models buy

you that much; especially, when you're not putting the

questions to be answered at the top.

DS. O'HEILL: I agree with you. Could you be more specific?

Remember, you don't always have the time to build a model

from scratch to answer a guestion. On occassion, you have

less than 24 hours.

DR. MCFABLAND: Bell, I think it has to start at the front

end. You don't build a general purpose model to answer all

questions.

There's no general policy model. It just doesn't exist, and

it doesn't appear to be that DOE is going to be making

decisions about where Exxon is going to explore, or how are

they goinq to develop, except through certain policies and

regulations. That will control it to some extent, but Exxon

will be building models to make these decisions, or they

will have decisionmakers making these decisions, as long as

we have the free enterprise systen.

719
And so I think there's a real question about what DOE should

be modeling. I would think that you primarily should be

developing models to assist the government policymakers in

reaching better decisions; and hopefully, providing insights

into what some of the regulations that are being formulated

will have—from the producer up.

DR. MUREHY: Could you also give us your idea of what you

think a large model is?

DR. HCFARLAND: Sell, several have been described.

For example, the work that's been dene at Brookhaven

involving process-type models that are driven by final

demands, and I assume that what was being discussed was some

type of exhaustible resource model that acts as a constraint

on that model. I consider that a very large model. The

model that was discussed as being developed at EPRI; I would

consider that a large model. I would consider some of the

models at FEA large models, whether they're linear

programing or whatever.

I guestion whether or net some of the policy issues that

need to be answered can't be answered with simpler models.

Before beginning model building phases, questions should be

asked such as. How much do I really need to know about this*

Do I want to be specific enought to know to drill a well, a 100 miles off Houston, or am I just looking for

general—broader insights into some of these policy issues*

I don't have the answers. The model building seems to be

evolving before some of the key questions are asked.

MR. EVERETT: Let me take a shot. I'm somewhat sympathetic

to some of the things you're iiplying and stating.

EIA has a model simplification program of sorts. It is

directed towards the simplification of existing EIA models.

It is hoped that as a result of the program some models will

be more directly updatable and will consume less resources

to operate and document. In the process we will have to

choose public policy issues that are most important and the

models that apply.

I think one of the ma jor problems with many models currently

is the lack of clear documentation and precision in

definitions at the data element level. (A data element

being crude oil production or-natural gas liquids

production, gas/oil ratios, etc.) A second problem which is

related involves a clear classification of what information

is reguired to discuss policy issues.

720
I think a lot of people in this room, certainly the speakers

and a great majority of the audience, know what issues

they •re interested in--can speak and communicate on oil and

qas supply aodeling in particular.

But you'd be surprised how many times the saae people really

say something where they don't mean exactly that. They're

talking about crude oil and you have to beg the question,

"Do you mean total petroleum liquids? Are natural gas

liquids to be included?"

When they say, "Gas" you have to beg the question, "Is it

non-associated gas only, or are you talking about total gas

production; from all sources, or simply conventional

sources?"

One of the programs in EIA, which is not resident in the

Office of Applied Analysis, but is very closely aligned, is

a top-down approach to data requirements analysis. It is

being dene by the Office of the National Enerqy Information

Systea.

Step Number 1 is to answer the question: What issues and

what public policy areas need information? This information

might be provided by a simple data collection mechanism—

survey, the development of an indicator or an index from

existing data or, a model; but, a couple of things have to

happen. Step Number 2, a vocabulary has to be established.

Step Nuaber 3, the information holdinqs of the EIA must be

described with this vocabulary. These holdinqs include

models, survey forms, publications (tables in publications),

and frequently used data not generated by EIA. Finally all

of this has to be indexed and classified, and to be blunt,

put into some kind of form like yellow pages.

When we have the yellow pages there won't be nearly as much

of a problem in tryinq to qet to the root cause of certain

definitional problems. The yellow pages ought to be indexed

by aajor issue-area, as well as by a simple energy source

and function scheme (e.g., crude oil transportation, or oil

refining)

Currently the yellow pages are aissinq, but it is beinq

developed. The Department of Enerqy and the EIA have only

existed for a reasonably short period of time with respect

to the time that aqencies like Census, or BIS, or BEA, or

other qroups have been approachinq their subject area.

DR. MCFaELAND: I would be concerned that people develop

information systems for the sake of developing information

systems. I can understand why you need data for various

uses, but I'd really be concerned about large information

721
systems just for the sake of having large information

systems.

I've worked on very few projects where you could get the

data that you needed to use in trying to address some issue

exactly in the form you wanted.

I think people dreai about having data bases and some great

computer program where you push a button and it's going

to give you all sorts of answers to guestions as you ask

them. I'm just afraid that's not likely to happen. In

fact, I'd be very surprised if that ever happens.

MS. EVERETT: Well, people don't dream of the yellow pages,

and it's a useful device. I'm working on it at the present

and would be glad to take into account any suggestions you

might have.

DR. MCFSRLAND: let me give one example. Let's suppose

you're looking at the offshore development problem in the

Gulf Coast. You're concerned with petroleum reservoir,

development. You can take one company's data, just on one

reservoir that has a fairly long lifetime, and you're going

to find that they have a tremendous amount of data of

various kinds.

If you look at what's reported to federal agencies, it's

really a small percentage of data that the company has, and

most of the time it's net in a very useable form if you're

really concerned about the problem of petroleum reservoir

development.

In fact, as best I can determine, companies seldom report

pressure data, which is probably the most critical variable

in terms of the reservoir behavior. You can have volumes

and volumes of data that's totally irrelevant for

managing a petroleum reservior.

So I really guestion whether or not we are ever going to get

to the point where DOE can have data to answer some of these

basic guestions. There's no way you can collect enough data

to answer some of these guestions, and that's the reason I

say I think you've got to start with the basic guestion that

you're trying to look at, if it's a policy issue or whatever, you take the best models you can get, the best

data you can get, and ycu try to provide policymakers with

the best answers that you can provide them.

MR. EVERETT: I'm being more modest than that. Once you

define your issues, and I think that you would agree they're

fairly straightforward (as is petroleum development off the

Gulf Coast) , I just simply would like to index the

722
information that we (the people at this conference, for

example) currently feel comfortable with. I'm not for

annexing private property without due process. We don't

want all the oil company information, as near as T can tell.

(Moreover, pressure data oay currently be reported to the

OSGS.y

DR. HARBA0GH: John W. Harbaugh, Stanford University. I'd

like to comment on geological resource base data. I touched on data sources when I gave my presentation, and one of my recommendations involve the creation of a national

inventory of oil aad gas fields within the United States.

Such an inventory could be created at very small cost

relative to its value. Many of the data are already

available, such as oil and gas field cumulative production,

and in some states, estiiates of remaining reserves are

available. The cumulative production data and the reserve

estimates could be updated annually and maintained in a computer file. It could be made available on computer tape,

and printouts, which would probably aggregate about the size

of the D.C. phone book, could be produced for convenient

manual reference.

MR. EVERETT: I agree, and I think—Sally Keene, who's our

Director of Oil and Gas Information, has a program that's

moving in that direction quickly.

DR. O'NEILL: Well, there is a problem with that. Wally's

main thrust is to reproduce the reserve estimates. The

future of oil (gas) -in-place ultimate recovery and date of

discovery information is not clear at this time.

VOICE: Well, that night be work that could go on for

years—estimated reserves in place is an enormous

undertaking.

DR. O'NEILL: Elft is only collecting reserve estimates, not

producing the estimates.

MR. FEENE: Let me lust address a piece of that. First off,

we sample in our survey, so that has a certain amount of

problems with it as it stands. In the next cycle—between

now and January 1981, I guess, it would safe to say our goal

is to come up with a composite list (of fields) . We started

with the old FPC field code list, if you're familiar with

it. We want to come up with a composite list from several

sources, including the Oniversity of Oklahoma's Petroleum

Data System, and the information submitted to us by

operators on fields.

The field level data, which we've already received from our

•77 and '78 surveys, probably hits around between 92 and 95

723
percent of domestic crude oil and natural gas production in

the Dnited States. So, while we can't say we have totally

complete information on all fields, between the information

which we currently have in other systems, I think it's

probably achievable that between now and January of next

year we would have a pretty gocd index: One, of all of the

fields in the United States; and^twc, probably relatively

complete information by field for those reported.

DR. HARBAUGH: What information will be contained by fields?

MR. KEEFE: I don't know that we would publish reserve

information by field. 8e would probably publish information

that is accessible to the public, if you had enough time and

money to dig it up, like production information, or cumulative production, or perhaps if we have other sources

we're integrating—maybe original hydrocarbon in place, I'm

not sure.

we have the sources I mentioned, plus we also have

information from API and AGA that underlie the Blue Book,

which they have published for »77. We have to get their

permission to be able to release it. So there are some

proprietary data guestions and some data-access guestions.

However, I think some general information and certainly an

index of the fields is achievable probably by January.

DR. HARBAUGH: It would be desirable, as a longer term

effort, to incorporate certain basic geological data in the

information base, as for example, the names and ages* of the

reservoir horizons. In California, which has less than 500

fields (although many of them are very large) , relatively

thorough descriptions of the geology of most of the fields

are available through the reports of the California Division

of Oil and Gas. Equivalent agencies in other states,

however, have not documented the oil and gas fields within

their boundaries in such detail. To do so nationally would

be desirable albeit a large undertaking. Information that

could be treated systematically in such a descriptive

inventory could include volume of structural closure and the

type of trap present. Such information would be useful for

statistical classification purposes, and would permit

various kinds of Bayesian relationship to be extracted which

would bear strongly on resource forecasts.

MB. KEENE: I'm a little reticent to go into how much we

might be able to achieve in integrating ail that. I mean

you can go to Bartlesville and they can tell you the amount

of carbon residue involved in various oil samples. What

we're planning to do is use the Permian Basin Study, as we

mentioned several times, and try to see if we can integrate

into an engineering framework, by reservoir and field,

724
enough information so that yon would get a feel for what

might be achievable.

But we're only goinq to do a soall piece of it. We may even

only wind up doing a piece of the Permian Basin; but,

there's information available from Eartlesville, there's

other information—a ton of publicly available

information—it's just never been integrated.

DR. HAREAUGH: Yes, I have a few comments on data. One of

the ironies is that the OSGS's Conservation Division has

accumulated an immense mass of geological, geophysical, and

production information for all OCS regions. This

information could be used for statistical forecasting

purposes. The data repose in four locations: here in

Washington for the Atlantic OCS, Betairie for the Gulf

Coasts, Los Angeles for the Pacific Coast except Alaska, and

Anchorage for Alaska. The information includes seismic

data, borehole logs, well-engineering data, and production

data. So, within the Federal government, there is a very

large file of data useful for post mortem analysis and for

resource forecasting. Unfortunately , most of this

information has a high security classification and is

relatively inaccessible. For example, in the Louisiana and

Texas OCS, there are a number of tracts that have not been

nominated for leasing and do not form part of the proven

resource base. Some of these tracts, however, have

potential which could be estimated on the basis of the

available seismic data and other data.

For example, in the Louisiana OCS and Texas OCS regions,

there are a number of tracts that have not been

nominated—come up for testing, in other words, which do

form part of the resource base. How the resource assessment

people could most effectively estimate potential for these

untested tracts on the basis of the available seismic data.

DR. HORPHY: That Metairie data is the basis for the Outer

Continental Shelf model.

Remember the discussion on the data for that model,

yesterday. What was done was to gather all of the pre-lease

evaluations that were done—a tract has to be evaluated if

it's going to be leased or if it's adjacent to something

that's going to be leased. This means there's almost

complete coverage of the Gulf, to 200 meters, for a tract-by-tract evaluation. The OSGS evaluations formed the

core of the data for the OCS model.

DR. BRASHEAB: What we did was to look at estimates of

undiscovered resources. In order to define a specific point

in the process so that our data collection did not overlap

725
with inferred reserves or proved reserves, we -Just asked

whether a tract entered the peeved reserves stream yet. T

think what Dr. Harbaugh is suggesting, and I would certainly

endorse it, is that there is also the proved reserve data

files.

If someone took the effort and felt it were useful, it would

be possible to start with something that's a gross regional

resource appraisal, such as DSGS Circular 725, in truly

frontier areas, where we don't know anything. As seismic

data begin to build, the eguivalent of the OCS data could be

collected, so that you can begin to say, "Here are real

prospects. This is what their economics look like.

The next step is to stay on top of information on prospects

that were drilled, tracking into the reserve system. At

that point you would have a coaplete inventory of the

onshore and offshore prospects, right to the point of

abandonment. It's a matter of integrating it. It's not a matter of magic. It's all there.

DR. MORPHY: There is, however, the problem of how best to

update the prior estimates for the prospects that remain to

be drilled.

DR. BR fiSBEAR : Yes. Update with real data.

The interesting point is that DSGS gets logs on every well

that's drilled. So, by watching those logs, you literally

could keep .that data up to speed where things that are

currently estimated could suddenly be made clear, such as

thickness of the reservoir and hydrocarbon content.

DR. LOHREHZ: May I make a brief observation about what

HcFarland said and tie something together with what you're

saying cow.

Is there anyone saying here there's an inconsistency in what

Dr. HcFarland said and what Dr. Brashear is saying: "Boy,

there's all kinds of data." Dr. HcFarland said, "Lousy

data.

He are talking undiscovered oil—future undiscovered oil.

You say there's a lot of that. Bat you are also talking

about something that's intangible. I can't touch

undiscovered oil.

Dr. HcFarland said the data's lousy. But he was talking

about pressure data. You have some in the ground, and know

how much is there. What can you do with xt? This is where

pressure data is important. What these gentlemen are saying

is not inconsistent. There is a consistency, isn't it true?

726
VOICE: It's always harder to get good data on real things,

than it is on imaginary things.

DR. BRASHEAR: Just for clarity, in the offshore, there are

periodic pressure tests that are public and in the USGS

files. Those files are confidential, but they can be made

available, with proper safe-guards, for legitimate purposes

of DOE. Pressure data are not a problem in the offshore.

Where pressure data and other reservoir data becomes very

problematic is in those states that have not put together

data collection systems. California is a superb example

that it can be done. They have an excellent data set

without being a major burden to the operators. Oklahoma is

the opposite extreme. They don't bother the operators for

anything. They, in fact, buy their production data, or it's

given to them by Dwight Service. Between those two

extremes, major producing states are everywhere along the

line.

So, the answer is the data are terrible, in some places.

The data are very good in other places. There are some data

on existing reservoirs. It does need to be swept up and put

together, and there are a lot cf people looking at that.

Intercoup is looking at it. PDS is constantly updating it.

Tom Garland's office has constantly got a sweep going on to

clean up these data and update those files. Several private

data bases are around. Already the government has bought

into Petroleum Information Corporation (PIC) , and Well

History Control System (WHCS) . It's there. It's

a big job to integrate it.

DR. HCFARLAWD: The point is though, so what if you have a few pressure observations? What are you going to do with

those few pressure observations?

DR. L0H8ENZ : I think that's the point, What are you going

to do with it? Can you estimate reserves with it?

VOICE: He* re talking about reservoir pressure data, not

pressure build-up, data. The people that you have, have a lot of pressure build-up, but not reservoir pressure data.

VOICE: Ch, Okay.

(JR. KEEHE: When we described--when I described the kind of

data that we're pulling together, I* didn't want to lead you

into saying—"that's great," and "Gee, shouldn't we have

more geologic data?" We can go in that direction, or we could even go to the direction, where you say, "We're -oing

to get rid of the AAPG and API well ticket, and we're going

727
to come oat with a Federal well ticket; everytime somebody

even steps on land, they're going to log it in."

DR. HAREAUGH: We should be cautioned that mere collection

of raw data will not provide much information that is

directly usable for resource forecasting. For example, you

can buy Pi's (Petroleum Information Incorporated) file of

about 1.2 million wells, which consists principally of scout

ticket information placed in machinable form. Pi's well

data must still be interpreted geologically before they are

useful for resource forecasting purposes.

MR. KEEHE: Now, we just can't--we have to draw a line

someplace to the kind of information we're going to capture,

the cost of that data, and the burden that it imposes on the

industry. And I'll tell you one thing further, if you have

some specific ideas about how data could specifically be

used in analysis and the benefit to the American public, if

you'd write it down, I'll make sure that we get it into some

kind of system or palled together, if the trade-off is to

the benefit is to the Aaerican public.

That's a battle we have to fight every time we go to the

Office of Management and Budget, and it's a battle, both

from a forms clearance standpoint and also to collect money.

So we could probably use your insight as to why you would

need an additional data element. Just to collect API

gravity is a nightmare. To get the approval of Office of

Management and Budget to do that, is a nightmare.

DR. MORPHY: Let me say something about the problems of

using small models. Everyone knows the problems of large

models. They have a 100 percent probability of coding error

or operating error for any run. They consume vast amounts

of resources to maintain and they do not necessarily have

increased information because of increased size.

By the same token, small models have problems.

The smallest model of oil and gas would be to specify the

elasticity of cumulative supply as a function of price.

Reasonable choices would be .1 or .2.

I have seen this kind of small model used with the

elasticity of . 1 when a person wanted to show that a piece

of legislation was bad. I saw the same person use an

elasticity of .2 when we wanted to improve the merits of

another piece of legislation. The problem with small models

is that they use aggregate parameters with a wide range of

reasonable estimates. They have the problem of calibration.

So the guestion is, how do you get from the large masses of

728
data to a form that you can operate a small model? One

alternative that I've been locking at is building a big

model but treat it as something that creates pseudo data,

from which you can estimate a small, usable policy analysis

model.

But that task is hard. I do not know of a truly successful

one, although several attempts have been made.

MR. EVERETT: Before the next question is asked, let me just

point out one of the themes that I think has run pretty

strongly through this conference.

The models are a way for organizing the data collection, or

as I like to call it the "mining" of existing data. (I am

not for collecting more information until we're down to a point where we really can't satisfy a lot of our analytic

reguirements with existing EIA data.) This also includes

data in state regulatory agencies, and data from other

agencies of the Federal Government like OSGS. I just think

there's an awful lot of guidance that can be derived from

reviewing these supply models.

If somebody wants to use a straightforward elasticity

computation to predict supply in some future year, let that

person go out and measure elasticities. That's impossible

or, at best very hard to do.

DR. MCFABLAHD: I want to make my position clear on the

large versus small model thing. I'm not opposed to large

models. I don't particularly favor small models, unless

they will do the job. I don't see it as a large versus

small model issue, necessarily.

I do think that if you're doing policy analysis where a decision is going to be made, there may not be time to

implement a large model. So if response time is critical,

and you're looking for just qualitative answers to policy

questions, the small model may be the only approach that's

available, if you're going to ase a modeling approach. So

I'm not arguing small versus large in terms of models. You

do what it takes to adeguately represent the problem.

Let me say something about supply response that is the topic

of the symposium. If we think about an econometric model, a supply model, suppose we are trying tc estimate a supply

curve for oil, where we have price and guantity data,

historical price and guantity data. There's a classic

identification problem in that we would like to be able to

say how much supply is going to change as a result of a change in pr ice.

729
Unfortunately, we do not have data so that we can identify

the supply curve, because what we have got is a series of

points that would be considered equilibrium points. So we really don't have the data necessary to identify that curve.

So if we collect all the data we wanted, we cannot—it's not

possible to have the economic experiment that generates the

data points to estimate the function. I think that's

another kind of classic example where—regardless of how

much data we have, we cannot —we don't have an experiment

that we can replicate to give the data that we would

actually need to estimate that function and get the simple

elasticity coefficient.

MR. EVERETT: Your position is that it's hard.

DR. HCFABLAND: That's right.

DR. IOHRENZ: What you're talking about is a very difficult

problem.

I want to identify one general caution with regard to, I

guess, energy supply modeling, but actually all kinds of

modeling and then give one specific example.

It must have been about ten years ago when I first heard the

phrase—Latin phrase. Had to look it up, what it meant, and

subsquently found out that it means "assuming all other

things stay equal,'' but at least I only use it when

I know that they aren't going to.

Now, case in point, right now the Department of Energy is

talking about different bidding alternatives for the

offshore, like profit sharing. Higher royalty rates are

already in effect, either set at a third, or due to royality

bidding, or to sliding royalties, they're higher royalty

rates. Their work commitment is allowed under the law, but

they are proceeding with this.

All I'm saying is that all of the work and all the data that

you have on previous energy supply is based on historical,

traditional royalties of an eighth, and a sixth, and

something like that. And the models show that if they're

rational—people, deciding how fast to produce what you've

got, it's going to change it immensely.

Hubbert's difference between discovery and subseguent

production was ten and a half years. That's ten and a half

years, because of traditional, past royalty rates in general

overall economic principle.

When we play with the bidding alternatives, that whole thing

can be upset. The ceteris paribus assumption goes down the

730
drain. I'll cite that only as a specific, but I'm sure

there are many others.

DR. BRASHEAR: I just want to make a couple of general

comments. Things that I found missing in our discussions,

or they were alluded to in passing.

One of the things, because we have done a fair amount of our

work in unconventional resources, example of unconventional

resources are tight gas sands or enhanced oil recovery,

things like that—we are very sensitive to the notion of

technology change within a finite foreseeable period, and it

doesn't just have to happen in the "unconventional

resources. w We're seeing a significant increase in drilling

speed, for example. Whether it's reflected in reduced costs

over time, we have yet to see that. But drilling speed is

going way up.

Some of the things—certainly in frontier areas—deeper

water, and the miserable cold environment of Alaska—we're

going to see are new technology ideas. Some of them are on the drawing boards new, some are in tests. It'll change a lot of the economics and timing.

It's awfully difficult fcr me to see how one can incorporate

technology change into a finding rate supply curve kind of

an approach.

One of the reasons that He have always found a more disaggregated approach to be helpful is that our other

objective is to assist in R and D planning, so we had a separate issue.

Second general point: by the way this town works and the

kind of laws that Congress writes and the kind of demands

that come up within the Administration, models very guickly

get put into use in policies. We're all happy to see that

happen, and that makes us feel good that we're making a contribution and we believe very much in our results; but,

we all know that we have some limitations in our results.

I think it's incumbent cn us as modelers, when there is a policy decision--policy issue at stake, is to look at the

implications, maybe just in terms of what's the opportunity

cost of the wrong decision. Cur models might be able to

help us there through some sensitivity anaLyses. They might

not. They might just be able to say we should do this. On

the other hand, if that's wrong, what fallbacks have we got?

How will we know we've made a mistake, whether it's data, or further analysis, or restructuring of a model. I don't

know—the answer would be different in each case.

731
But we do very often get to the point of debating one model

against another lodel, bcth of which have limitations and

probably use enough difference in definitions and standards,

that they're really not comaprable at all.

And somehow the impact of models hasn't been brought to the

surface in the sympcsiuo. I think we're all aware of it.

It's sort of like walking around with a loaded gun; you have

to be careful with it. find I suspect all of us are

insufficiently aware of that in the heat of the discussion

or the press of a deadline.

DR. O'NEILL: Most of the people who are modelers, believe

that the key result of aodeling is insight into the process

that is being modeled.

We've gotten into the habit of publishing hard numbers which

imposes rigor on the modeling system, but the people who

aren't modelers have a tendency to take them more seriously

than we do. We're not really sure how to put proper

confidence limits on forecasts. The standard 95 and 90

percent confidence ranges, are the result of one man's

(Fisher) thinking about agricultural problems a long time

ago. Another very well-known statistician in time series

analysis, James Durbin, has stated that 50 percent

confidence intervals are good enough, and when asked why, he

said he didn't have to explain because after all. Fisher

didn't.

MR. PARKER i. I'm Jerry Parker from DOE's Office of Oil and

Gas, and at the outset of the panel discussion, you framed a few guestions, Dick. And one of them dealt with enhanced

oil recovery. And as you are aware, my office has been

involved with prosoting the sort of framework in which we can optimize and maximize enhanced oil recovery.

I have not been able to attend oany of the sessions, but in

looking over the symposium schedule and program, I didn't

notice any specific topics on ICR and I was wondering if

during the symposium, or at this time, you might summarize

what you're doing. Because, in our view, we're in a whole

new ballgame, and your using historical data on finding

rates and ultimate recovery rates and the like does not

acknowledge that we're looking for a big payoff from

enhanced oil recovery.

DR. O'NEILL: I think enhanced oil recovery has all the

classic problems of a new technology. By changing the rate

of penetration of a new technology, you can make projections

look very good, or very bad.

VOICE: It would be nice to have a data base that

732

i
highlighted, on a f ield-by-f ield basis, including abandoned

fields, what was originally found or expected to have been

in place, what was ultimately recovered, and what some final

estimate of residual oil in place is.

That kind of a well-organized, well-documented data base

would be something that could be useful to policy—a set of

scholarly analyses that have very little to do with

economics, or to a specific regulatory program in DOE. I

think that's what's happening in that area, that , s all.

Maybe not guickly enough.

MR. PARKER: As you* re probably aware, we have set in place

a regulatory framework from a financial incentive

standpoint, and we are dealing with the environmental

problems. In our recent meetings with the majors, they seem

to have firm—as firm as they can be —mid and long-range

plans for their enhanced oil recovery production, and

perhaps the time is here to get that kind of information and

try to crank it into your forecasting.

DR. C NULL; Given the problem of data collection, we'll

probably have the data base constructed properly when EOR

starts to decline after a peak.

MR. EVERETT: Whether it's the Resource Applications Office

within DOE, or the Economic Regulatory Administration (ERA)

,

the people with the carrots,' or the people with the sticks

in DOE, both groups should think about what information they

require. A very simple question usually lays waste to

anyone who thinks he or she wants all the data in the world

about everything, and that is, "What do you want to do with

it?"

I think if you're going to operate a regulatory program you

will want to track its performance—how much money-- (public

money) was pushed in and how much oil came out. That is a straightforward information requirement. EIA services the

regulatory functions of DOE, and that kind of data

collection should fit in.

This year there's a burden budqet, just like there's a dollar budget for the Federal Government. And I'm not sure

how adequately or fairly it's going to be divided up with

regard to oil and gas supply. I would hope a major portion

of it gets directed to that end, but it's encumbent upon the

program offices within DCE to identify and defend data

requirements to run their programs. If they can't do that,

they probably don't have to defend their programs in the

first place. This strikes me as an unreal situation. And

as Wally pointed out, everything should fit in its place.

733
ERA has proposed a fori, I forget the number of it, that

collects soie information on prospective EOR projects (from

operating companies). I doubt if it' s particularly oriented

to be plugged into a supply modeling framework; certainly

none of those we heard about during this conference. This

conference mainly addressed conventional oil and gas supply,

except for the resource classification and resource

appraisal discussion earlier.

MR. KEEKE: Perhaps on a little more straightforward

engineering approach, on the principal data collection form

which we use. Form 23, for an annual survey, we received

information on about 10,000 oil reservoir units, and we didn't get as much data as we'd like. We have a letter from

Bartlesville that lists the additional data elements they'd

like to see tacked on to such a form going back to

operators. We're currently in the process of working on a task jointly with Bartlesville that would identify the

burden —the best place to take that information, whether

it's from an operator, or refinery, or wherever, the burden

associated with doing that—do we want a point estimate or point value or can we ccme up with a range, which would

certainly be a lot less burden, and what would the EOR

program do to individual data elements?

Now in theory, we could wind up at the end of this year

going back out with a form to anybody that operates an oil

field in the United States, and collect ail the information

they need for EOR.

Probably somewhere between that and collecting no reservoir

data is where we'll wind up. And it's a function of the

kind of engineering input Bartlesville puts into the job

that we're looking at right now.

So it's not that it's not being given any thought. There's

money being spent right new with petroleum engineers putting

together the information that we need. Whether it's timely

I don't know, whether or not CHB will buy a budget —a burden

budget and allow us to collect it, that's not really clear.

There are some issues that have to be resolved, but it's not

something that's being ignored.

VOICE: I'd like to ask about—well, while we're talking

about data, I think there are two basic distinctions in data

that we've tried to draw out. There are two kinds of

information that's needed.

One is, what regulatory information is needed to see whether

a law is being implemented as planned, and the other kind of

data are the research type data. The

kind of data that have an error component. Regulatory- based

734
data are generally affirmed and generally, you know, the

respondent assures that data are correct under some penalty.

That's one type of data that's collected for a very specific

purpose.

Then there's another kind of data base. The kind of data

base where for some reason or another you're willing to

tolerate a little epsilon on the end.

Because regulatory infomation servesa legal purpose, it

tends to dominate. And I think if you look at the corpus of

data that EIA maintains, a lot of it is regulatory based,

and it's concerned with a certain number of small issues.

It's like the Eskimos that have essentially one word for the

whole non-white spectrum of colors and a thousand different

words for white.

It's the same sort of thing within the Government. The

regulatory information draws you to make finer and finer

distinctions, until you get to the end where there are vast whole

areas that don't even have data points.

There's a need for some sort of pro-active data collection.

For example, if you want to characterize the geologic

resource of the United States, probably the best possible

study would be to drill one core on every square mile. Mow

you can't do that, because of constraints.

and so to move away from the simple solution, you apply soae

heuristics. You apply seme theoty and soae values that lead

you to just put wells where there is sedimentary deposits or something else like that.

In the data planning, is there not a need to specify in some

way, to maybe convene a blue ribbon panel of experts, or

some technique, to specify the heuristics that you would use

to either put an item in your data base or take it out and

to look at the relative driving or regulatory function

versus pro-active anticipatory functions, or evaluate a function sort of to keep the machine on keel, to see if

there's not a need to go outside the boundaries of the

system?

It seems that every time I go through a data series, either

the API ,AGA, or EIA's own data series, the good stuff, the

stuff that you're locking at to answer today's guestions,

isn't there. There needs to be a new categorization. Or

you'd say, "Gee, I'd like to have this cross-categorized by

this."

The existing data base is based on today's questions, and

what I get is, "How can we possibly anticipate tomorrow's

735
questions in a Federal framework where you have all the

lags?"

MR- EVERETT: All right. Seriously, that's right. The

first job is to try to identify what we have in this "EI

Data Base," and try to put it in perspective with what

others have. Like what, for example, the current industrial

reports cut of the Department cf Commerce, Bureau of the

Census, mean with regard to Rally's survey on oil and gas

reserves.

Cost data are sort of another open area where a lot of people

have done important work, but it hasn't been tied

together—no concordances have been drannbetween certain

prominent series. Various things still have to be done.

To summarize to this pcint I can say that the models are the

vanguard of helping one organize information in a useful

way. One of the things that is also necessary is access to

information (this conference helps to some degree) . As many

people in as many classes of endeavor as possible deserve

access. I think that in the next several years major

inroads will probably be achieved in these areas, with just

the emphasis that you mentioned.

HE. EVEEETT: One other brief point on this. Then we'll

take the next question.

For the economists in the room, remember the Unemployment

Insurance Statute's and IRS have a great deal to do with

economic information that currently is in place in other

agencies in town. Census is a special case, in which

Congress decided a long time ago that it was necessary to

count heads. Begulations are the best way in the world to

ensure that data collection satisfies some minimum degree of

verification and validation.

DR. HAREAUGH: I'd like to ccmaent again on the data

acguisition policies. Geophysical data are of great

importance in assessing the potential of frontier regions.

If we appraise the Atlantic OCS at the moment, much of the

useful information ccnsists of seismic data. These data

reside with the USGS's Conservation Division here in

Washington, but they are inaccessible to the public, and

only with difficulty accessible to ether Government

aqencies. A change in policy might be considered by the

Federal Government, whereby permits for seismic and other

qeophysical surveys in OCS regions would be qranted with the

provision that the data later become accessible to other

aqencies for purposes of analysis and forecasting.

MR. EVERETT: Tou're talking mainly about the tJSGS. The

736
Conservation Division holds most of the seismic information

on public lands. Several of the papers delivered here dealt

with EIA's attempt to loin with the Conservation Division to

interpret these data, and put them. into a data base. Now,

whether or not the data can be manipulated so that the ' Office of Primary Control (the Conservation Division) is

happy with the release of that data to the public, is

another question. I think that it is possible with careful

aggregation and masking.

DR. HAREAUGH: The Conservation Division probably won't be

very happy because of agreements with the oil companies

regarding security of the data. What has been lacking,

however, is appropriate policy with regard to subsequent

utilization of these data by various Federal agencies as a condition for qranting of permits to obtain the data in the

first place.

PR. O'NEILL: You've made a very important point. The

United States, as a property owner, probably has one of the

poorest information systems concerning the resources it

manages. If you were to look at the majors and the value they

place on information {for example, seismic and well data)

,

the Federal Government, by comparison, has a very poor

assessment of what it owns.

The Department of Agriculture has recently realized that

forestry may not be as important as oil and gas and other

minerals on the lands it manages. There is no central point

in the United States Government where the management of its

total resource is considered. I'm sure that oil -companies

has much better information on property they have leased.

DR. HftREAUGH: Release of information is obviously a very

controversial issue, and one that would provoke anguish

within the oil industry simply by raising the question.

However, it is appropriate to review existing policies

regarding the acquisition and release of oil and gas data

that involve Federal lands, both onshore and offshore.

MR. KEENE; We've been attempting, for well over two years,

to establish a policy—I say we, the Energy Information

Administration—to establish a policy just for the Energy

Information Administration, on the handling of proprietary

data —if that helps give you an idea of how difficult that

issue is. We've been in court battles. We've been in

Congressional hearings, and it's a very, very, difficult

problem.

I don't know —even if we started today, my best guess is

before you could even get a preliminary opinion, it would

probably take two years—another two years.

737
DR. MUBFHY: Let ae present a straw man, to get at some of

the modeling issues. The first statement that was made is

that it's important to have models that deal with policy

questions. You have to know your question first, before you

build your model.

Let me pose a question, and I'd like to ask the audience

what the right way is to deal with the question.

The Natural Gas Policy Set has aany categories of gas that

are controlled at various price levels. How do you deal

with a supply response tc all of these different price

levels?

He make the bold assumption that for any of the tiers that

are controlled, there is no increased supply at higher

prices beyond the control prices. For oil say that the

supply elasticity is entirely in new discoveries and EOR.

DR. O'NEILL: Let ae add that, if you say that you can't

address an issue because you cannot apply all the proper • methods of science someone else in this town will. The

process of the scientific method, as explained in the

freshman textbooks, does not exist anywhere and has never

existed.

DR. LOHBENZ: That's a fundamental conundrum. You can

initially say, "Hell, let's assume the guy will behave

rationally." But then the question is how rational is

rational. I want to talk about the Hindfall Profit Tax

where the saae thinq cooes. Now here's a guy—let's say I'm

a major, I have a producing property, but the tax, you see,

is higher on me than on the other guy. So when I model,

shall I say that "Okay, this is a major, and he's going to

maximise the present value of future profits, t>ased on that

tax." Or, the other thing I can do is say, "Hi, buddy, you

non-major. I got this property that I can sell you at an incremental difference and let's split the pie." Shall we crank that in too?

The question I'm qetting at, hew—where does rationality

stop? I'm not answering here how to do it, I'm just saying

I don't know how. You don't either, do you?

DR. HORPHY: No

DR. GASS: The rational decision right now would be to

adjourn. Is that correct?

{Whereupon, at 3:30 p.m., the symposium was concluded.

738
APPENDIX

OIL AND GAS RESOURCES -

WELCOME TO UNCERTAINTY

by

John J. Schanz, Jr.

This article was originally published by

Resources for the Future (RFF) in March

1978 as isuue No. 58 of the RFF newsletter

Resources . Reprinted with permission.

739
GLOSSARY

A number of oil and gas terms are used differently by different people.

Below are some short, nontechnical

definitions that may be helpful in read- ing this issue as well as other reports about oil and gas resources. Commercial accumulation an occur- rence of oil and gas that meets the minimum requirement for size and

accessibility to be of commercial

interest to a company. The term commercial is frequently synony- mous with economic.

Dellverabllity the amount of natural gas that a well, field, pipeline, or system can supply in a given period of time. Only valid for that period.

Discovered resources that portion of

the oil and gas in the earth whose

presence has been physically con- firmed through actual exploration

drilling. Indicated reserves known oil and gas

that is currently producible but can- not be estimated accurately enough

to qualify as proved.

Inferred reserves reserves that are pro- ducible but the assumption of their presence is based upon limited physical evidence and considerable geologic extrapolation. This places them on the borderline of being undiscovered. The accuracy of the estimate

is very poor. Inplace all of the oil and gas in the

reservoir, combining both the recoverable and nonrecoverable portions.

Maximum efficient rate (MER) when

used in a practical or operational

sense, it is the optimum rate, as of a

specific time, at which oil and gas should be drawn from a developed

field in order to balance cost, percent- age recovery, and speed of with- drawal. To exceed this rate for the

reservoir or td produce individual wells too rapidly can lead to loss of

oil and gas recovery from the reservoir. Occurrence a physical accumulation of

oil or gas or related hydrocarbons in the earth regardless of size and physical or economic characteristics.

Resources NO. 68 RESOURCES FOR THE FUTURE, MARCH, 1976 SPECIAL ISSUE

From time to time, RFF will publish a special issue of Resources that focuses on a single, timely topic. This, the first such issue, written by RFF Fellow John J. Schanz, Jr., embodies the results of a series of workshops.

Oil and Gas Resources —

Welcome to Uncertainty

Until 1973, the American public was accustomed to glad tidings about

U.S. oil and gas resources. If you read the business sections of newspapers or followed the trade and professional publications, you were aware

that the forecasts became increasingly optimistic over the years (see table 1 )

There were some less sanguine estimates from those who looked at the

ever-declining curves of oil field production and projected rising costs through time. But these more cautious projections appeared to be over- shadowed by the upward path of U.S. oil production. As the world's leading oil producer, the nation passed the 1 billion-barrel level in 1939, 2 billion in 1948, 3 billion in 1966, and reached the 3 and one-half billion level in 1970. The perennial optimism of the wildcatter—"Give us an

incentive and we'll go find you some oil and gas"—was well supported

by over 100 years of production history. The United States seemed a permanent fixture as the world's number one producer of oil and gas. The -undercurrent of concern during the 1960s over declining exploratory activity in the United States elicited little real attention outside of

the oil and gas industry itself and a small circle of petroleum specialists.

It was easy for others to treat these worries as merely the customary

background noises that accompany an industry's efforts to encourage

favorable treatment by Congress on taxation, incentives, or protection

from foreign competition. However, the major disturbance caused by the Organization of Petroleum Exporting Countries (OPEC) oil embargo in 1973 brought an immediate end to this lack of public attention. In 1975, a report by the Committee on Resources and the Environment

(COMRATE) of the National Academy of Sciences, based on a review of contemporary estimates, stated that, of the original stock of crude oil and

natural gas liquids (249 billion barrels), only 113 remained to be dis- covered. For natural gas 530 trillion cubic feet (of an original 1,227 tril- lion) remained.1 This marked the end of general optimism both in industry

and government about the future U.S. oil and gas resource position. For the public and Congress, whose ears are normally more receptive to good news,

it was a shocking revelation to learn that instead of over 400 billion barrels of liquid hydrocarbons there might be much less. To have this unwelcome

news appear in the midst of the oil and gas industries' post-embargo

clamoring for high prices resulted in both public confusion and distrust. With respect to natural gas, the winter crisis of 1976-77 caused renewed

1 M. King Hubbert, whose work received considerable attention in the press, was among the COMRATE participants. His estimate was reported as 72 billion barrels of oil and 540 trillion cubic feet of gas.

740
Table 1. CHANGING PERSPECTIVES OF U.S. OIL AND GAS RESOURCES

Original supply of recoverable reserves"

Forecast Oil Natural gas

in Year (billion barrels) (trillion cubic feet)

1948 110 1952 400

300 856

1965 400 2,000 1969 1,859

1970 432

1972 458 1,980 1975 249 1,227

11 Unfortunately, any sampling of estimates encounters variations in the treatment

of past production, recoverability, and the inclusion of natural gas liquids. These

have been chosen, or adjusted when possible, to make the totals roughly comparable

regardless of year of estimate.

Oil basin a large basin-like geologic

structure in which oil and gas fields will be found.

Oil field a geologic unit in which one

or more individual, structurally and

geologically related, reservoirs are found.

Oil region a large oil-bearing area, often encompassing several states, in which oil basins and fields are found

in close proximity.

Production or decline curve (S curve)

the annual production of an oil or gas

reservoir through time is a domeshaped profile with its peak usually to the left of center. The progress of

the production from its peak toward

depletion is called the "decline curve."

If this is plotted as cumulative pro- duction it follows a gradual S-shape

as it approaches the total, or ultimate, production of the reservoir. Productive capacity the amount of oil that can be withdrawn each day from

existing wells with available production facilities. Only valid at one point

in time. Proved reserves an estimate of oil and

gas reserves contained primarily in the drilled portion of fields. The data

to be employed and the method of

estimation are specified so that the average error will normally be less than 20 percent. May also be called measured reserves. Recoverable that portion of oil and

gas resources that can be brought to the surface, as distinct from the oil and gas found in place in the reservoir. Reserves oil and gas that has been

discovered and is producible at the

prices and technology that existed when the estimate was made.

Reservoir a continuous, interconnected volume of rock containing oil and gas as a hydraulic unit. Resource base the total amount of oil and gas that physically exists in a

specified volume of the earth's crust. Resources the total amount of oil and

gas, including reserves, that is ex- pected to be produced in the future. S-curve. See production or decline

curve. Subeconomic resources oil and gas

in the ground that are not producible

under present prices and technology

but may become producible at some

future date under higher prices or improved technology.

Undiscovered resources resources which are estimated totally by geologic speculation with no physical evidence through drilling available.

doubts and confusion among the public, the media, and members of government.

In the three years since the COMRATE report, several staff members at Resources for the Future have been

looking into questions about oil and gas

reserves and resources. It, therefore, seems appropriate at this time to distill from these recent RFF efforts as much

understanding about oil and gas re- sources as possible. We have no intention of producing a new set of resource

estimates; there are more than enough

of these. Rather, we hope to show why

we keep getting different signals about

the status of our oil and gas resources.

If we can reduce some of the confusion, our efforts will be well rewarded.

Obviously, it will not be possible to explore in these few pages all of the problems in the collection and use of oil and gas statistics. Our attention is directed toward the different methodologies and perspectives employed by the various analysts who produce conflicting estimates. The following discussion draws heavily upon a number of recent RFF activities, including: a workshop on oil and

gas resources sponsored by the National

Science Foundation, a study on resource terminology sponsored by the Electric Power Research Institute, a workshop

on Maximum Efficient Rate (MER) of

oil and gas production sponsored by the U.S. Department of the Interior, and a workshop which reviewed the Federal Energy Administration's National Energy Outlook, 1976 sponsored by the National Science Foundation. In addition, members of the RFF staff have

participated on a regular basis in the work of the committees and boards of

the National Academy of Sciences, the Gas Policy Advisory Council of the Federal Power Commission, and the oil 741

and gas resource appraisal groups of the American Association of Petroleum Geologists and the U.S. Geological Survey.

The contribution to this summary report of Dr. John C. Calhoun, Jr., Vice- Chancellor of Texas A&M University,

who directed the oil and gas resources workshop, is especially acknowledged.

A Matter of Definition and

Classification

An oil or gas reservoir is not a subter- ranean cavern filled with oil and gas, which we empty like a huge storage

tank. During geological time, various mixtures of crude oil, natural gas, and

salt water were formed and moved

about in the interconnected minute pores

of certain kinds of rock where they have remained trapped. When the

driller's bit penetrates the rock, natural

pressures cause a slow migration of the

fluids toward the well bore. The well operator may decide initially, or eventually, to give the flow of oil and gas an

assist through the application of the sucking action of a pump, or by frac- turing the rock around the well, or by

injecting water, chemicals, heat, or gases

into the rock. To understand this pro- duction process, three things must be

kept in mind: 1, the flow of fluids through rock pores is a function of the physical forces at work; 2, the quantity

resulting from additional effort gradually diminishes, just as wringing a wet

rag produces less and less water; and,

3, the only actual measurement that can

be made is of the oil and gas produced

at the surface—all other information about the reservoir is estimated. An oil and gas reservoir or pool is basically a hydraulic unit where all the interconnected pores holding the oil and
Figure 1 . Diagram of Reserves and Resources

gas in the rock behave as a single fluid system. Theoretically, a well drilled at precisely the right place would be all that would be needed to produce all of

the oil or gas the reservoir will ever produce, given sufficient time for the

fluids to move through the rock to this one point. In one geographic area, en- compassing a few or thousands of acres, there may be a series of reservoirs or

individual traps containing oil and gas

that are geologically related but not

physically interconnected. To find and

produce all of the oil and gas requires additional wells, dispersed either verti- cally or horizontally. A single isolated reservoir or a group of reservoirs related by physical proximity and geological

origin are identified as an oil or gas

field. Once the oil and gas exploration teams have found a specific bed of rock

that contains oil and gas accumulations,

they will tend to follow this "play" by

drilling down to that bed or zone over an extended area. A discrete geological

environment having a large number of

oil and gas fields is known as a basin or

province. In the United States, there

are over 100 basins found clustered in

five major regions. Within the basins

there are thousands of fields and many

thousands of individual reservoirs. Over

2 million wells have penetrated the earth

in the vicinity of these oil and gas traps, and more than 500,000 successful ones

are still producing oil and gas. Approximately 10,000 wells are abandoned each

year. Once the physical characteristics of an oil and gas resource system is appreciated, the complexity of the question

"how much oil and gas do we have?" becomes more apparent. Any response can be no more than a judgmental esti- mate. Intelligent communication about

oil and gas resources becomes exceedingly difficult unless both the questioner

and respondent understand what kind of data they are using. A start in this direction is to use a diagram becoming common in governmental circles (see

figure 1). A complete oil and gas resource dia- gram is a pictorial representation of all unproduced natural oil and gas hydrocarbons that may exist. We can also

visualize a valve attached to the diagram

representing the oil and gas wells through

which oil and gas is removed from the

reservoirs that have already been penetrated by the drill. Beyond this valve

there is a conduit which represents the

pipelines, tankers, barges, railroad cars, and trucks used to move the oil and gas through processing and on to the final user. It is worth repeating that past production, that is, the quantity already

delivered by this system, is our only

actual measurement. That quantity of

oil and gas is gone forever. References

to original oil and gas in place mean the sum of both the remaining oil and gas

plus all that has ever been produced.

The productivity capacity of the United States is the amount of oil and

gas that can be produced from existing wells during a specified period of time under specified operating conditions. The totality of physical oil and gas in the earth but not yet produced from the

continental crust to a depth of perhaps

50,000 feet is sometimes called the oil and gas resource base. There are four

kinds of oil and gas found in this resource base. The first kind (segment

A in figure 1) consists of oil and gas which has already been found and is considered producible under present

prices using current technology. These

quantities are customarily known as

reserves. The immediately producible

portion of these reserves—the oil and

gas that will flow from wells in devel- oped reservoirs, the quantity of which

can be estimated with considerable accu- racy—is classified as proved reserves. The balance, or unproved reserves, has been discovered but cannot be estimated with as great accuracy and may require

additional drilling and development (see

figure 2). In segment B we find oil and gas that has been discovered but in the judgment

of the operators cannot be produced

under current prices with existing tech- nology. These quantities are known as subeconomic resources. There are two

kinds of subeconomic resources. First, the unrecoverable, high-cost portion of

oil and gas currently left behind in pro- ducing reservoirs. Second, oil and gas

in other reservoirs that have been found

but are not now producing or have been abandoned because they would cost too much to produce due to size or other problems.

Segment C of the resources diagram encompasses the oil and gas that re- mains to be discovered. Exploratory

drilling has not proceeded to a point

where there is physical evidence of the

actual presence of this oil and gas. There

is only expectation, and estimates of undiscovered oil and gas are based

solely upon geologic and engineering

extrapolation. This requires the use of

geological and geophysical data rather than using physical data based upon the

actual existence of the oil and gas. It is possible to subdivide undiscovered re- sources into economic and subeconomic

quantities, but to do so requires the

analyst to make some sort of assumption

about prices and technology conditions. Present prices and technology are fre- quently assumed despite the fact that the

oil and gas, when actually discovered,

will be produced under future conditions of price and technology.

The final portion is segment D

other

occurrences. This includes any oil and

gas left behind that is not expected under any future circumstances to be worth the effort or cost of production,

as well as deposits which are considered

too small to either find or produce if found. Finally, this category is a convenient place to account for other forms

of oil and gas hydrocarbons about which either little is known, or production technology is so immature that economic and technologic judgments

cannot be made, even though large quantities may be involved.

Estimation of Reserves As the drill bit penetrates a rock reser- voir for the first time and finds oil and

gas, the first questions asked are how

much has been found and can it be produced economically. The initial well provides limited information about the rock strata that have been penetrated

and nothing about strata that are below

the bottom of the well. Once a layer of rock containing oil and gas has been

found, the approximate thickness of the bed at that point—anything from a few

to hundreds of feet—is known. A core

of rock is usually taken from the bed. 742
New-field

wildcat New-pool

wildcat p,y O O

Deeper Shallow pool Development pool

test well producer test

Shallower pool Extension

test

4>

Figure 2. The Classification of Wells by Geologists

Note: Proved reserves are established by the producing wells (P). Unproved reserves in the field will require additional drilling by wells

3, 4, 5, and 6. Wildcat exploratory drilling can find undiscovered resources in adjacent pools or in separate fields (1 and 2).

Electrical and other measurements are taken inside the hole. All of these data provide information about the porosity

and permeability of the rock and the amounts and kinds of fluids it contains.

If the reservoir seems to justify production on the basis of this preliminary

information, then the drilling equipment

is removed, production pipe is put in place, and the well prepared for production. The initial flow of a new well provides information about the production rate, pressure, and other physical

data. At this point, a preliminary judgment on how much oil and gas have been found can be made based on: the flow from a single well; a rock sample a few

inches in diameter of a multiacre reservoir; a map of the surface geology; and

a seismic "shadow picture" of the struc- ture holding the oil and gas thousands

of feet below the surface. Obviously,

this first estimate cannot be very precise. Yet based on this one well and past experience with the kind of reservoir

that appears to have been found, the engineer makes a judgment. This esti- mate may range from the least amount

of oil and gas that appears to have been found to the outer limit of what the

reservoir might ultimately produce if the buried structure is entirely filled with

oil and gas. The scientific guesswork about a res- ervoir hundreds of acres in size is useful but extremely crude. It is akin to going

to an unfamiliar supermarket on a foggy

night and trying to estimate the total amount of asphalt used in paving the parking lot, with no other data than a

cubic inch sample of the blacktop used. How uncertain these judgments about

reserves can be was illustrated in a study

published by the National Academy of

Sciences in 1976. The study concerned the amount of

gas reserves under lease in certain . fields in the Gulf of Mexico. Previous esti- mates had been made by the technical

staff of the Federal Power Commission

(FPC), but there was disagreement about

their accuracy. The Academy suggested

that two consulting firms, experienced

in the Gulf fields, should make inde- pendent estimates using the same geological survey data that was used by the FPC. This was done for a random sample of nineteen (out of a total 168)

leases. All the estimates by these firms proved to be lower than those of the FPC staff, but a comparison between

the estimates made by the two firms was more interesting. For one lease, the

difference between their estimates was

only 10 percent. But for nine of the

leases, the upper estimate was from two

to eleven times higher than the lower

estimate. Even before a well is drilled, companies will appraise the potential of a new region to help them determine whether or not exploratory wells are worth drilling (see figure 3). Once a

well has been successful in finding oil and gas, two new estimates can be made: first, an estimate of the minimum

amount (the proved reserve) that seems

to be producible by that well and, sec- ond, a less certain estimate of what

might be the ultimate potential of the

entire field. As more wells are drilled and additional production data are gathered, the proved reserve estimate may be revised up or down. The expectation of ultimate production can also change upward or downward, usually over a much wider range than that of

the proved reserve figure—several multiples are common. For a typical field

it takes approximately five or six years before the proved reserve estimate of remaining oil plus past production begins

to approach a true estimate of ultimate production. In other words, it takes a number of years before there emerges a reasonably accurate estimate of what

has been discovered in toto in a reservoir. The exact amount of producible

oil or gas is not known until the field 743

is permanently abandoned and that oil or gas has been measured as past production. In addition to a company's estimates of proved and ultimate, other appraisals

may be made by a producing company

during the life of a field for various

purposes. Estimates based on well logs

and other data are commonly used by

banks for making loans. Information is also released to the press about the importance of new discoveries. The

Securities and Exchange Commission

expects that companies will release in- formation to stockholders about their holdings and expectations. And, finally, the many kinds of information required

by government agencies lead to a number of estimates being provided by a

variety of federal offices. Considering

the array of purposes for which reserve estimates are made and the constant

revision of most of these through time,

it is not surprising that various reserve

reports may appear to be in conflict. The proved reserves of oil and gas represent only a small portion of the

total oil and gas resource base that re- mains unrecovered in the United States. Yet, these proved reserve data sometimes receive more attention, and in recent years have prompted more controversy, than the more significant re- source estimates of undiscovered oil and

gas. 2 For crude oil, proved reserves represent the stock of immediately pro- ducible oil from existing wells. The oil

2 Despite the apparent clarity of the

generalized concept of proved reserves the

actual estimation requires certain judg- ments to be made concerning the amount

of extrapolation to be used, whether to include oil and gas from known reservoirs not actually being produced, or how to account for oil resulting from secondary

stimulation. As a consequence, there are

.at least nine "official" definitions from

various professional, industrial, or govern- ment agencies. Each one leads to some

variation in the estimates made.
3tfO Pro-discovery

Years

Figure 3. Life Cycle of Oil Reservoir Estimates

(adapted from G. C. Bankston, API Reserves Seminar).

producer knows that the amount of oil or gas that can flow in a given year from

producing wells is physically linked to the number of wells available and the quantity of oil and gas still remaining in the reservoir. Thus, proved reserves for many years have been the industry's

empirical indicator of current capability, not a measure of the total supply of oil and gas left for the future. Equating

proved reserves with "years of supply"

is particularly misleading. Since proved reserves plus past pro- duction are normally less than we might

reasonably expect to produce from

known oil and gas fields, do we have any estimates of this undeveloped and

less certain, part of our discovered oil and gas reserves? Unfortunately, there are no regular government or industrywide efforts to report on what is known

as indicated or inferred oil and gas. 3 The American Petroleum Institute (API)

does report on additional reserves of oil that could be produced from secondary

recovery projects but that are not yet

fully evaluated at the time of the proved

reserve estimations. An industry-spon- sored effort, called the Potential Gas

Committee, has included this portion of

the gas reserves in its occasional reports on gas resources. The Federal Energy

Administration in its 1975 survey of

operators had hoped to go beyond merely

proved reserves, but its final report only

included oil from secondary and tertiary projects not the less certain oil and gas

quantities. Currently, the new Depart- ment of Energy is again considering how

to define and request data on oil and gas

reserves that are not reported as proved.

The U.S. Geological Survey in its 1975 Circular 725 relied upon the use

of a statistical ratio devised by M. King

Hubbert to account for indicated re- serves. This ratio is based on the his- torical relationship of the amount of oil and gas that has been added through

extensions and revisions to proved re- serves during the typical life of reservoirs. The relationship shows that ap- proximately 80 percent more oil and gas

will be produced from known fields than

is currently being reported as proved.

Although proved reserves data are considered to be accurate within plus or minus 20 percent, this refers to the oil and gas expected to flow from existing

wells. On the average, almost twice as much oil and gas will ultimately be found in these fields once their true size or limits become fully identified. This

is not an intentional understating or

"hiding" of reserves, but merely a reflec- tion that the definition of "proved"

8 The terms probable and possible are

also used to describe discovered reserves

that cannot qualify as proved or measured.

limits the estimators to the drilled portion of the field. One must be aware that when esti- mates go beyond proved, accuracy deteriorates rapidly, with errors of perhaps

50 percent or more for indicated reserves (mostly oil and gas resulting from fur- ther development of the reservoir) and

amounting to perhaps several multiples

for inferred reserves (oil and gas result- ing from the discovery of additional

reservoirs within the same field). Many

U.S. professionals and Canadian govern- ment specialists would prefer, because

of the uncertainty, to consider inferred

oil and gas as not actually discovered. To obtain more information on what

lies beyond proved reserves in known

fields involves a reservoir-by-reservoir

examination of considerable magnitude.

Considering the range of judgment in- volved and the unavoidable approximations, the added information obtained may not be worth the cost of acquiring

it. In addition, there are problems of handling proprietary data, which, in any

event, would be diverse, constantly

changing, and of unknown quality and

usefulness. It would require combining

the personal judgment of the ultimate

potential for field A<nade by a geologist

from Company X with estimates for

field B from Company Y's geologist,

through all of the thousands of fields in the United States. In the final analysis, to know that indicated and inferred U.S. reserves are considered to be 2.4 times our proved reserves instead of

1 .8 times has little significance in deter- mining our policies with respect to oil and gas. The more important questions

are found in the categories of subeco- nomic and undiscovered oil and gas

resources. It is upon these quantities

744

that our energy future depends most

heavily in the medium term.

Estimation of Subeconomic

Resources

Subeconomic resources include all of

the oil and gas in known reservoirs that

is not producible by present technology

at present prices, but may become pro- ducible in the future with improved

technology or higher prices. It should be noted that a simple downward move- ment in prices or other incentives can

cause some reserves to be reclassified, at least temporarily, as subeconomic

resources. As a field is developed, following the

drilling of a discovery well, the producer

adopts a plan which he hopes will extract

all of the oil from the reservoir that can

be produced. He then hopes to sell the

oil at an anticipated price that will return

as much or more than the additional

cost of producing it. He hopes that the aggregate return from all wells, over and above the direct costs of production, will pay him not only for production costs but also for the costs of

exploration, dry holes, and abandoned

wells. To minimize the duration of his exposure to uncertainty, he hopes the pace of production will permit a quick

return of his initial investment. The investment decision in oil pro- duction is a balancing of the total quantity to be recovered, the various costs,

•the rate at which the oil will be re- covered, and the price at which it can

be sold. Once the decision is made on how many wells to drill and what recov- ery technology to use, that is, natural

flow, pumping, water flooding, injection
of steam, or other methods, the amount

of oil that will be recovered and the

rate at which it will reach the surface

are limited within a fairly narrow range. To change that plan, additional invest- ments must be made in drilling additional wells or in altering the production

methodology being used. Such a change

in the production scheme will be adopted

only if the faster production or greater recovery can justify the extra cost. Thus, an increase in the price of oil or gas may not be adequate to change

the plan for the operation of a field already being developed. The only effect of higher prices in that event may be to permit the reservoir to decline to a lower

level of daily output per well before it is abandoned because of low oil flow or

gas pressure. This additional quantity of oil and gas produced in the later life of a reservoir may only involve a 1 or 2

percent increase in the ultimate recovery because most of the oil or gas left behind

is entrapped in the reservoir and could

only be recovered by the use of a differ- ent technology. However, higher prices

which occur before a production plan

is fully implemented in a new field can

lead not only to later abandonment but

to higher recoveries because the prices can be reflected in a timely investment

in a modified development scheme. The appearance of significant im- provements in production technology or markedly higher prices can justify modifying the way new reservoirs as well as

fully developed fields are being operated. Even an abandoned reservoir can be

reopened, although this is less likely because of the expense. It should be

noted, however, that new methods of enhancing the recovery of oil and gas should not be viewed as applicable to

all kinds of reservoirs. How successfully a new technology can be employed is determined by the kind of structure and

natural energies in the reservoir, as well

as the kind of rock that is found in it. There has not been much experience

in estimating the size of the national subeconomic resources of oil and gas because in the past the opportunity to discover new and plentiful oil and gas resources has always seemed more at- tractive to industry. Even for known

fields, the estimation of subeconomic

resources is complex. First, the estimator must face uncertainty about new

and perhaps untested technology. Sec- ond, there is need to deal with the effect of price on production using established technology, as well as what price is required to make new technology commercially feasible. Third, there is a lack of information on exactly how much oil or gas is left in the reservoir to be

recovered by new technology. Finally,

if the data are to have meaning, there

is need to deal with the problem of the time over which these prices and tech- nology can be assumed to occur.

It is perhaps surprising that the amount of oil left behind in a reservoir

is uncertain. Depending upon the kind

of reservoir and the years during which

it was exploited, oil recovery from the

initial development plan used can vary anywhere from 10 percent to 80 percent of the oil estimated to have been in place originally.4 In some cases, reser- voirs have been reworked with a secondary production technology long after primary methods were begun. More

recently, developed fields tend to be

exploited by several integrated methods.

Since oil in place, recoverable reserves, and a reservoir's recovery factor are all parts of the same equation, it is apparent that estimates for two of them allows

the derivation of the third. Thus, if greater production from a reservoir is achieved than originally expected, one

is never sure whether the cause is more

oil in place, more reserves, or a higher recovery factor. There is some indication that the

overall recovery factor for oil in the United States did not improve very much during the 1960-75 period for

several reasons. U.S. production shifted from regions with naturally higher re- covery potential to areas with poorer

recovery potential. Early estimates of

the quantity of oil to be recovered by

primary recovery techniques were probably overstated or, conversely, the oil in place may have been understated.

Finally, there is a tendency to use a standard recovery factor in relating future production expectations to oil in the reservoir. Each of these tendencies could contribute to the assumption that the U.S. recovery factor has remained

near 30 percent for many years. Realistically, it must be concluded that the

true national recovery of oil is an un- known percentage. The current interest in enhancing

petroleum recovery by injecting heat, C02, or chemicals has led to more

vigorous examination of subeconomic

resources than ever before. Our major

oil regions have been examined in terms

of the amenability of the various kinds

of reservoirs to newer methods for in- creasing recovery. Although some opti- mistic suggestions have been made that U.S. recovery could be increased from

an assumed 32 percent to ultimately 60

* Natural gas, because of its physical

characteristics, normally has a high re- covery factor—on the order of 75 percent. Subeconomic resources and opportunities

for enhanced recovery of gas are thus

limited for the most part to the fracturing of dense, low-permeability reservoir rock. 745

percent, more modest near-term goals are now being set for the upgrading of some of our subeconomic resources to

reserves. These suggest an overall in- crease of perhaps 5 to 8 percentage

points in the U.S. recovery factor may

be possible.

The uncertainty of how much sub- economic oil and gas may be produced

is illustrated by the recent report of the National Petroleum Council (NPC).

The additional oil from enhanced recovery, according to the NPC, could be as

little as 7 billion barrels, under a price

assumption of $10 per barrel (1976),

but this would increase to 24 billion barrels at $25 per barrel. The effect on

the rate of annual production would also vary. At the higher price level, U.S.

oil production could be 3.5 million bar- • rels per day greater in 1995. The

uncertainty in the estimates is reflected in the judgment that the higher 24

billion barrel amount is merely the

central value of an estimate ranging

from as little as 12 or as much as 33

billion barrels. In contrast, another

study viewed the outer limit of enhanced

recovery at 76 billion barrels at $15 per

barrel (1974). Despite the fact that en- hanced recovery deals with "discovered"

oil in known fields, this does not narrow

the range of uncertainty. Technological

and economic forecasting of recovery is a

source of frustration equal to that of

estimating the undiscovered (table 2).

Estimation of Undiscovered Resources

If the United States would suddenly

cease drilling its customary 25 to 50

thousand new wells each year and would

be content with merely producing what

it could from existing wells, production

would decline progressively by approximately 12 percent per year. After some

forty years, production would fall to approximately 1 percent of present production. Since reservoirs do not cease production abruptly, some wells might

still be producing a few barrels per day

after one hundred years. Unlike manufacturing, or some kinds

of mining operations, the capacity to produce petroleum is not a constant. To avoid a decline in national production, there must be continuous drilling and development. The process of continual annual replacement of what we

have produced is heavily dependent

upon the magnitude of our undiscovered

oil and gas resources. The potential size of these resources

is usually evaluated in one of three ways. There is the geologic or volumetric approach, which attempts to make

a direct estimate of the quantity of oil
Table 2. NATIONAL PETROLEUM COUNCIL REPORT ON ESTIMATES OF

U.S. ENHANCED OIL RECOVERY POTENTIAL

Potential Production in 1985

Source of estimate recovery (millions of and price assumption ^billions of barrels ) barrels/ day

)

National Petroleum Council Report

$ 5 ) 2.2 0.3 7.2 0.4 (1976 dollars) 13.2 0.9 20.5 1.5

GURC»

$10

$15 (1974 dollars)

24.0 1.7

18-36 1.1 51-76 —

FEA/PIR"

business as usual, $11 — 1.8 accelerated development, $11 — 2.3 EPA°

llllll | '""dollars)

J. =

FEA/ Energy Outlookd $12 — 0.9 FEAe$11.28 (1975 dollars) 15.6-30.5 1-2

a Gulf Universities Research Consortium Reports, Number 130, November 1973, and Number 148, February 28, 1976. i b Project Independence Report, Federal Energy Administration, November 1974.

c The Estimated Recovery Potential of Conventional Source Domestic Crude Oil, Mathematica, Inc., for the U.S. Environmental Protection Agency, May 1975.

<i 1976 National Energy Outlook, Federal Energy Administration.

e The Potential and Economics of Enhanced Oil Recovery, Lewin & Associates, Inc., for the Federal Energy Administration, April 1976.

and gas remaining to be discovered and

recovered. No attempt is made to show

when or if these resources will be pro- duced. The second approach is that of

the engineer-manager who makes projections of the drilling, discovery, and

production process. These future pro- duction profiles implicitly suggest the amount of recoverable oil and gas that

is left in the ground. The third methodology is that of the economist who uses the equations in his model to suggest what future supply can be achieved by

the oil and gas producers as they re- spond to price changes. Like the engineer-manager, the econometrician may indicate the quantity of remaining

oil and gas resources in his model

Implicitly rather than explicitly.

The volumetric approach. The geologist's volumetric estimate is essentially

what the name suggests. The total volume of sedimentary rock suspected

to contain petroleum and natural gas

is calculated for the entire United

States, region by region. Based upon

past geological knowledge, an estimate

is made as to the total oil and gas that may exist in these rock volumes. It is quite apparent that this is a subjective

judgment linked to past experience.

Underestimates are possible since past experience does not readily account for unknown types of occurrences or future improvement in the ability to detect and

produce oil. In contrast, since there is evidence that better areas and larger

pools are found first, unexplored regions

may prove to be less prolific. The volumetric determination of the

oil and gas that exists in the ground

may not be the only calculation. The

quantity of oil and gas in place in the rock strata only has economic meaning

in terms of the proportion that is both

discoverable and producible. The quantity of oil and gas eventually captured

depends upon future effort, the effective- ness of the search, the size and depth of

the reservoirs, and the economic and

technical capacity for producing it. Considering the many judgmental ele- ments, volumetric estimates, not unexpectedly, have varied widely over the

years. Part of this variation reflects the fact that some estimates are the product of extensive study by large groups while others may be the work

of a single expert using a relatively simplistic approach to obtain a quick

approximation. Moreover, subjective

judgments about unknown resources change as more geological information becomes available. These normal diver- gences are further accentuated by the

fact that different analysts have used

different assumptions and have estimated

different resource elements.

A careful examination of past geologic estimates reveals that it is rare for the same type of resource concept to be

involved. Total oil and gas originally

in place, oil and gas remaining in place, discoverable oil and gas in place, undis- covered commercial accumulations of

oil and gas, or recoverable oil and gas under given economic and technologic

conditions are markedly different quantitative concepts. Unfortunately, the authors of petroleum resource reports

all too frequently are obscure about what they have estimated, their methodology, and their assumptions. Yet all of these numbers are generally identified as estimates of "the oil and gas re- sources" of the United States. The

unsuspecting recipients of this information must then puzzle over how one

expert can say that the oil resources of the United States are 50 billion barrels and another, with seemingly equal confidence, provides an estimate of 1,000

billion barrels.

If one reduces all of these various

estimates as best he can to a common

base, such as the quantity of undis- covered oil that is discoverable and

producible at prices as of a certain date with an assumed 30 percent recovery

factor, then the wide differences begin

to shrink drastically. An estimate that appeared to be twenty times as large as another sudenly is only twice as large. Once reduced to a common base, there remain understandable differences in judgment between two analysts who

possess varying degrees of optimism

about what is still to be discovered. But

this kind of comparison is not available

to the casual reader who cannot know

that one geologist has estimated all of

the oil in the ground, another has assumed an optimistic 60 percent recov- ery factor, and another uses the current 30 percent recovery factor.

Geological resource analysis took on

a new dimension with the 1975 publication by the U.S. Geological Survey of Circular 725, Geological Estimates of Undiscovered Recoverable Oil and Gas

Resources of the United States. This 746
was a major scale-up in the Survey's

effort and involved a whole team of

geologists working for a number of months. It entailed not only the use of

traditional volumetric information, but

incorporated sophisticated statistical in- tegration of subjective judgments about each of 102 oil and gas provinces. The

end product was a probabilistic appraisal of undiscovered, recoverable oil and gas. Experimentation with this type of

delphic approach has been going on for a number of years. Companies and

various research groups have searched

for a way to combine the various judg- ments of experienced individuals into a numerical expression of the probability of finding oil and gas. Circular 725 was

the first attempt by the federal govern- ment to try this approach (see figure 4).

Single number estimates that suggested

a precision that does not exist have been abandoned. The public and Congress

may now have to become used to re- source estimates that indicate there is a 95 percent chance there may be a mini- mal quantity of oil resources but also a 5 percent chance that there could be

quite a bit more. For example, the Survey

estimates that there is a 95 percent probability that the remaining undiscovered

recoverable oil reserves will be at least 50

billion barrels, but only a 5 percent probability that they will be as large as 127

billion barrels. Outside of these ranges

there still remain low-level possibilities that a new province may have no oil or gas at all, or that it may contain an

undetected Middle East. Only the drill can tell. Some cautious individuals still prefer not to try to attach numbers

to what they consider immeasurable

quantities.

The Geological Survey recognizes that Circular 725, while a major advancement, was a first effort and must be used

with considerable care. Only the portion of the report concerning "undis- covered, economic" resources of crude

oil and natural gas are totally new esti- mates. All other numbers presented

were based on other sources of statistics or were derived by simple ratios. Thus

the measured and indicated additional

reserves are taken from the reports of

the American Petroleum Institute and

the American Gas Association. The in- ferred reserves of oil and gas are based

not on an evaluation of fields and basins but on the historical trend of extensions and revisions of proved reserves through

time. The subeconomic resources are based on simple ratios using two as- sumptions—that the average U.S. crude

oil recovery might reach 60 percent and

natural gas 90 percent at some unspecified time in the future. The additional data provided by Cir- cular 725 has been useful, but it presents problems for many of its users. If the undiscovered oil and gas resources are shown as a probability range. " what

does one use if one needs a single number? Unfortunately, many seemed to prefer to use the lower limit. In using

these data, it has been common to over- look the fact that the subjective judg- ments behind the estimates were based upon price and technological conditions

that prevailed prior to the Arab embargo

and the quadrupling of the world price of oil. This leads to the question of how

much current prices might alter the esti- mates. It is believed by many that a recalculation would not make a large difference because the estimates are dominated by large fields which were economic before 1973. The Survey is now searching out the answers to a number of questions. Can

the reserves portion of the estimate,

which received modest attention in the

first effort, be improved? In estimating

subeconomic resources, there is the important question concerning the realism of ever reaching an overall 60 percent

5 The Survey does provide an average of the most likely and upper and lower esti- mates. However, the statistical usefulness of this average is uncertain and it only appears in the tables.

recovery. This may now be better understood because of the extensive work just completed in examining enhanced re- covery. Since the availability of actual experience by Survey geologists for every oil and gas "play" was naturally

somewhat limited, there is an interest

in how to tap a broader spectrum of judgment. There is a need to have

future appraisals encompass more data

on: size distribution of undiscovered

fields, depths, reservoir types, and basins found in deep water offshore. These

data may be the key to determining

actually how "price sensitive" are oil and gas resource estimates. Until these answers are forthcoming, the user of the Survey's Circular 725 must remain fully aware that these are subjective views by

a group of government geologists concerning the recoverable amount of pre- 1973 "commercial" oil left in the unexplored portions of U.S. basins onshore

or to a depth of 200 meters offshore. This recoverable amount is only a portion of the total physical quantity of

oil and gas in place remaining beneath

the surface in the United States.

Engineering projections. The fact that

oil production is a process in which

production declines and costs increase became apparent to engineer-managers soon after Colonel Drake, a retired rail- road conductor, drilled the first well in Pennsylvania in 1859. Fortunately, many

wells do better than Drake's, but a ruler placed on the graph of past production

and the cost per barrel of any well or field always provides a dismal picture of a downward trend in the absence of new

discoveries and technology. In contrast, projections made by individual companies or industry groups showing in- creasing future production are illustra- tions of how additional investment in exploration, drilling, or applications of new technology can cause the aggregate

production of oil or gas to increase in the

future despite the fact that the older wells are declining and future efforts will face

nut

production

106

CRUDE OIL RESOURCES (billion barrels)

IDENTIFIED I UNDISCOVERED

Demonstrated \lnferred\

1

ECONOMIC

SUBECONOMIC

Maesurad Indicated, RESERVES

34.250 \4.636\ 23.1

120-140

I

50-127

44-111

NATURAL GAS RESOURCES (trillion cubic foot)

IDENTIFIED 1 UNDISCOVERED

Demonstrated Inferred

J Past

Msasured

1 production 1 RESERVES

481 ECONOMIC 237. 132 201.6 j 322-655

1

1

1

SUBECONOMIC 90-115 40-82

i Increasing geological assurance Increasing geological assurance

Figure 4. USGS Estimates of Crude Oil and Natural Gas Resources of the United States, December 31, 1974. 747
greater costs per barrel produced per

foot drilled. The best illustrations of this kind of

analysis are found in the extensive series of reports by the National Petroleum

Council (NPC) to the U.S. Department

of the Interior. They contain many

examples of how a given number of

dollars invested, assuming a specified

rate of return to the investor, could

generate a required level of geologicalgeophysical work, leading to the drilling of wildcat wells, and finally the develop- ment effort needed to produce the new

oil found. Figure 5 from the 1972 NPC

study demonstrates how this can lead to various perceptions of the future. By their very nature, these projections of future production, based on a

specified amount of additional effort or

investment, are expansive. These speculative futures may or may not incor- porate a judgment as to whether the remaining oil and gas resources in the ground are sufficient to provide for these annual flows. In the NPC's extensive study of U.S. energy from 1970 to 1973, projections were coupled to a geologic study of the U.S. petroleum

provinces. Since most of the NPC's

projections were only to the year 1985,

the possibility of a production decline

after 1985 due to dwindling resources was not shown. Many government or industry projections of future production are not

primarily designed to deal with the ulti- mate size of our oil and gas resources. Nonetheless, they still may foster a

public belief that resources are adequate

in size to meet the projected goals. In

addition, there may be only minimal

attention paid to the price required to

elicit the necessary investment. And

whatever that price may be, the accompanying alterations in the demand for

oil and gas, given that price, may not be

addressed at all. One specialized form of engineering

projection that has been employed by

many authors over the years has been

to use a production-history profile that

will follow the standard pattern ob- served when minerals or fuels are pro- duced from a finite deposit. The classical configuration is a bell-shaped curve showing an upward sweep, a peaking of production, followed by a decline to

final depletion. Not only a specific deposit, but a state, a region, or a

nation, as an aggregate of many deposits, often appears to follow this pathway.

If one assumes that this is the general behavior of production, then it becomes

possible to estimate when the peak will occur, the quantity that iwill be pro- duced, and how it will be distributed over time. Customarily this is done by

rather simple curve-fitting techniques

Million b»rr»l* p«r <J»y

Figure 5. Estimated U.S. Production

of Petroleum Liquids at Three Levels

of Future Drilling Activity

(from National Petroleum Council, U.S. Energy Outlook, 1972)

using an appropriate mathematical for- mula. One of the most popular production-history curves has been the logistic growth curve, since it is both bell-shaped

and symmetrical when fitted to annual

data. It can also be used as a long

attenuated "S" showing how cumulative

production will approach asymptotically

a line representing the maximum recoverable resources. In reviewing forecasts between 1948 and the mid-1950s, RFF's Sam Schurr and Bruce Netschert found

at least six authors using this kind of approach who expected U.S. petroleum

production to peak by 1970. Among this group, perhaps the greatest amount of attention in recent years has been directed toward the work of M. King Hubbert. Relying heavily on

the logistic curve and a family of various

statistical series to track the behavior of U.S. oil production, his analysis is both

extensive and detailed. Among the family of interrelated curves that he uses

are: cumulative proved discoveries, cumulative production, proved reserves, annual production, annual increases and

decreases in proved reserves, and dis- coveries of oil per foot drilled versus

total footage drilled. The first three of

these, with the appropriate fitted curves, are shown in figure 6. The logistic curve provides a particularly good fit to any historical series that

is approaching or has already reached

a plateau. But one must be careful not

to assume that the fitting of the curve

to the several variations of the same

historical series in some way confirms

the validity of its use. Despite the vigor with which Hubbert examines past be- havior and projects the various patterns of U.S. oil discovery and production

into the future, this does not necessarily

indicate that the logistic curve is a more

reliable predictor of the future than any

other curve that might have been chosen. The use of mathematical formulas to

project trends forward provides an aura

of precision and objectivity. However,

the process of fitting and projecting is a more subjective process than it might

appear. The choice of the type of curve

to be used preordains in a general way

what the future will look like. Then the

analyst must exercise further judgment

as to the time period to be used and how

the curve is fitted to the data. Judgments

at this stage of the analysis are particularly critical, because the manner in which the final years are fitted affects the steepness of the expected production decline. In addition to his decision to use the

logistic curve rather than another, Hubbert's case for future decline is bolstered by his assumption that a declining amount of oil will be found per foot

drilled. This is a persuasive position to take if one expects that the largest and

near-surface fields have been found first. Hubbert supports this hypothesis by

another projection involving again the choice of proper data and a mathematical formula0 to project the trend

of oil found per foot drilled. In this extrapolation he shows that despite extensive drilling the quantity of oil found

in the future becomes relatively insig- nificant and his gloomy expectations for the future are further substantiated. In mature, densely drilled areas, such

as the onshore areas of the lower 48

states, one might be persuaded that it is unlikely that there are many "surprises"

left. It does appear unlikely that there

are a number of Prudhoe Bays cleverly hidden by nature along the Gulf Coast

or in the Rocky Mountains. For these

areas it seems to be a question not of new peaks in production but of the duration of the current level of production and the nature of the subsequent

decline. But in those areas where drill- ing has been infrequent—natural gas at greater depths along the Gulf or oil and

gas in the Arctic or farther offshore

the future is not as clearly defined. For

these regions, most analysts, including

Hubbert, do not trust unalterable for- mulas but turn back to more traditional geologic speculation about the quality of

the targets that may be found in these unexplored volumes of rock. Production-history profiles provide for many a sense of "rightness" because

they follow the classical pattern of mineral production. Yet they leave a number of questions unanswered. Is it fair to assume that the historical inter- relations between the many factors that

affect oil exploration and production

°In this case a line representing a constant percentage of decrease each year is used. 748
tarn*

[ J

' UK mat WWy

; • / i —

if pr ami/A

<//«< M_L 1 on Cumutat

product) ~T~

1

1 J

L

•60 '80 2000 ?0. «J »

Figure 6. Application of Logistic Curve

to U.S. Petroleum Data

(from M. King Hubbert; see References).

will continue unchanged into the future?

If our production of oil and gas has peaked, has that fact been induced by

external institutional factors rather than by a limitation in our hydrocarbon

endowment? Might not our technical ingenuity or the new frontiers of ex- ploration once again produce a major

surprise? If secondary peaks have been

observed in the past for states and

nations, why not for the United States? There are no certain answers to these

questions. But for the United States, M. King Hubbert has reminded us of one unavoidable truth—we are not de- bating whether there will be decline, merely when and how. This does not

deter the exploration optimist from re- minding us how we drilled for many

years in Texas, Saudi Arabia, and the Arctic with little or no success.

Econometric models. The third group

to deal with the future supply of oil and

gas has been the economists. By professional instinct and training, they ini- tially turn to the marketplace as the

starting point for their analysis. Their

facility for portraying relationships by

mathematical equations, combined with

the ability of modern computers to pro- vide rapid and complex calculations, has

led to the use of econometric models. Normally found within these models are equations that relate the supply of oil and gas to exploratory and development

efforts prompted by changes in price. Perhaps over the decades more general attention has been directed toward

oil rather than gas resources. But more

recently, gas supply has demanded considerable attention from the econometrician. This reflects the fact that gas

prices have been regulated and there are questions about what would happen

if the regulated price were increased or

if regulation were to be removed entirely. Interest has intensified with the recent, rapid decline in proved gas reserves. The

occurrence of gas and the search for

it are not necessarily linked to oil, so gas supply can be disengaged for separate study. The task is also simplified

by the fact that gas supply models are

essentially domestic, that is, they need

not incorporate, as in the case of oil, the impact of large imports from abroad. A number of models for gas supply have appeared over the last two decades. Some provide projections and forecasts and a number deal with the supplyprice relationships. However, like the engineer-manager projections, the econ- ometric models are not designed to pro- vide estimates of the remaining oil and

gas resources of the United States. Nonetheless, in addressing the supplyprice question they unavoidably give an

impression of resource availability. An examination of the better-known

gas supply models reveals that the in- clusion of total U.S. gas resources, or any limit to discoverable and producible

resources, tends to be implicit rather than explicit. This is intentional and is not a serious flaw for the intended use of the models. For the most part, econometric equations are not considered particularly reliable beyond short periods of time—of the order of five or ten

years. Given these limits, to introduce

total resource quantities is an unneeded

refinement. However, many models are designed

to indicate that price will trigger an

exploration response and the resulting greater production suggests that oil and

gas resources are adequate to support

higher levels of production than now

prevail. The MacAvoy-Pindyck model,

developed in the early 1970s to analyze

the effects of deregulation policy, sug- gested the possibility that 34 trillion cubic feet of natural gas could be pro- duced in 1980 at an average wholesale

price of 88.3 cents per thousand cubic

feet (MCF) with a newly-discoveredfield price of 100.3 cents per MCF

(see table 3). This result did not hinge upon the total quantity of undiscovered

resources required for the United States to achieve that level of production. Nor

was the model constructed to deal with

the mechanics of annual investment,

the number of wells to be drilled, or the physical ability of the productive system

to achieve the required level of effort. The MacAvoy-Pindyck model shares with most of its econometric companions

a necessity to simplify the national en- ergy economy. It was designed to an- swer a specific question—in that process

it ignored others. - Econometric models have their own

special link to the past. The response, or elasticity, of oil and gas supply to price must be judged in large measure

in terms of historical data, despite the

realization that in each future year we

will deal with a different segment of the

original resource. Future resources may

very well differ in character and, as a consequence, in cost from those dis- covered in the past. Economic behavior

patterns of operations conducted on

vast federal leases in 1 ,000 feet of water

are not the same as those encountered

in the private farmlands of Kansas. Nor

will the response of gas supply to a doubling in price (in constant dollars) be the same when it starts at 10 cents per MCF as when it starts at $1. A

reason to question further the future

validity of past experience is to recall that much of the past was characterized by smaller movements in the price of oil and gas relative to other prices, and that for the most part this was downward not upward.

Current efforts. In making resource es- timates geologists, engineers, and economists are all to some degree projecting

past experience into the future. Insofar

as the past does not adequately represent the future, their estimates are likely to be in error. In addition, each profession, starting from its own particular

analytical framework, is the victim of

a certain amount of tunnel vision. The

geologist prefers to perform his task in a price-free, time-free fashion. The

engineer may ignore resource constraints and economic reactions in his production model. The econometrician may demonstrate what market price is necessary

to reach an equilibrium point but in so doing may violate the time sequence or engineering requirements needed for the

process to be accomplished, given the magnitude of the remaining resources and national capabilities.

It is not suggested that the various

analysts are totally unaware of the

limits of their work. More often than

not the problem is the difficulty of trying

to link all dimensions of the resource system into one model or into one forecast. Moreover, the purposes being

served may not demand a complexity

that exceeds available time and financial resources. The Federal Energy Administration (FEA), in projecting the needs of the nation by 1985 for Project Independence, initially employed the committee

approach to the problem; so, too, did

the National Petroleum Council. However, subsequent in-house work by the FEA staff on the 7976 National Energy

Outlook (NEO) led to the development

of a complex computer model (PIES).

This effort has been an excellent illustra- tion of the long and difficult task of

attempting to introduce the many dimensions of energy into one integrated

analysis. The many scenarios developed

749
Table 3. ECONOMETRIC SIMULATIONS OF PHASED DEREGULATION

OF NATURAL GAS

New

contract Total field price reserves Production Demand (cents per

(trillion (trillion (trillion thousand Year cubic ft) cubic ft) cubic ft) cubic ft)

1972 233.4 23.3 23.5 31.7 1973 227.8 23.6 24.3 34.7 1974 222.9 24.3 26.3 39.7 1975 222.3 26.4 28.7 64.7 1976 226.1 27.6 30.4 71.7 1977 233.9 28.6 31.9 78.8 1978 245.8 30.2 32.9 85.9 1979 258.6 32.1 33.7 93.1 1980 271.2 34.1 34.2 100.3 From MacAvoy and Pindyck, Price Controls and the Natural Gas Shortage, 1975

Table 4. PIES MODEL NATURAL GAS PRODUCTION REFERENCE SCENARIO

1985 domestic production 1985 average Assumed (trillion cubic ft) city gate price world oil Nonassoc. Assoc. (dollars per

prices $/bbl gas gas Total thousand cubic ft)

8 16.3 4.1 20.4 1.79 13 17.4 4.9 22.3 2.03 16 17.4 5.1 22.5 2.07

Note: The Reference Scenario is a market clearing price at which supply and demand

are at equilibrium in an uncontrolled market or deregulated condition. From FEA's National Energy Outlook, 1976.

for the National Energy Outlook re- quired an analysis of demand, supply,

finance, the environment, the national economy, and international aspects. This should not be construed as suggesting that the ultimate model is now

available to the new Department of Energy. A close examination of PIES

reveals that the tie between energy and

the national economy tends to be one

directional. In the 1976 report, envi- ronmental and international aspects were

not introduced as specifically as one

might desire. The model reflects the many imperfections in our understanding of the behavior of energy demand

in the marketplace. The resource component of the model is still the familiar 1973 data from the USGS Circular 725. Perhaps most important to the user is the fact that the PIES model does not

generate a single forecast, but rather

as many forecasts as there are policy combinations that an administration wishes to test (see table 4). It is easy

to overlook, in the copious statistics and

discussions of the model and its sce- narios, that much reliance has been

placed on a few key sources of data or

relationships. Thus, to whatever extent Circular 725 is limited in its perspective of U.S. oil and gas resources, the National Energy Outlook series is equally

limited. Since so many analyses have come

to depend upon it, the further work of

the USGS has become extremely critical. Currently, the Survey is hoping to refine

its presentation of probability data on

undiscovered oil and gas resources so

that the full range of potential resources within the hypothetical and speculative

categories is more apparent. This will allow for an appreciation that beyond

the 5 and 95 percent probability boundaries there still remain possibilities for

either zero finds or major discoveries for which past experience has not prepared

us. Recent interest on the part of the National Petroleum Council and other groups in enhanced recovery will now

permit the Survey to be somewhat more

specific about the magnitude of sub- economic, discovered resources. In addition, the presentation of data on indi- cated and inferred reserves (reserves beyond proved) in known fields may be expanded by the Survey.

A number of agencies have joined

forces with the Survey in this effort to determine how additional information

in economics and technology could be combined with the essentially geological data from the Survey's Resource Appraisal Group. This Inter-Agency Study

Group on Oil and Gas Supply is examining not only the amount of the oil and

gas resources present but their distribu- tion with respect to size, geography, and

depth. An attempt will then be made

to define the level of exploratory drilling activity required to find these deposits. This can then be followed with studies that deal with drilling, production, and

finding costs, which incorporate considerations of reservoir depth, water

depth, and other geological characteristics. Currently the group is in a testing

phase, using three pilot areas to deter- mine the feasibility of performing these various tasks. It is not expected that the current effort will attempt to deal immediately with the time distribution of future oil and gas supplies. But it is hoped that a better appreciation of the magnitude of oil and gas resources at various costs will be obtained, as well

as an understanding of the exploratory

effort that will be involved.

Other Occurrences

Other occurrences are frequently the source of possible deception about the

size of the nation's usable oil and gas

supplies. Billions of barrels of oil in low-quality shale, gas locked in impervious shales and sandstones, methane

found in coal beds or dissolved in brines under great pressure at depths of 1 5,000

feet are all a part of our physical re- source base. They can and should be accounted for in any total resource

inventory, but they cannot and should

not be considered comparable to re- serves or subeconomic resources. The

likelihood of their soon becoming pro- ducible under present or near-future

prices and technology is small enough

that their importance for present generations is uncertain. Thus considerable caution must be taken to avoid giving

them too much leverage in current

decisions. After fifty years of effort and

anticipation, the first commercial barrel of U.S. shale oil has not yet been pro- duced. To be deceived by a too hasty

reliance on methane dissolved in the waters of the Gulf of Mexico would be

foolish indeed. Although the oil shales of the West

have become the classic example of

a "just-around-the-corner" resource, we

must somehow account for such a vast quantity of hydrocarbons. Many oil and

gas resource appraisals do not include 750
the oil shales because they are restricted to conventional crude oil, natural gas, and natural gas liquids produced from

wells. Other analysts do not include them because they are not economically

producible at the present time. If, however, a complete accounting is desired, then it is appropriate to at least identify these as other occurrences or non- economic resources which are currently not produced and are likely to be sig- nificantly more costly than other forms

of energy now being used. Whether

quantification is attempted depends upon

the purposes of the inventory.

Hydrocarbons occur in many forms

in nature. Just as there are many types of coal (anthracite, bituminous, or lig- nite) there are heavy oils, tar sands, and

kerogens which will not flow to drilled

wells. This requires the extraction of

the material either through the use of heat and chemicals or physically mining

the rock so that it can be processed above ground. Since these are sedimentary deposits, they can be vast in extent but highly variable in recoverable energy

content. In effect, they are low-grade

deposits requiring expensive processing.

As such they must be considered as

either subeconomic or probably nonexploitable in any period of time that

is of significance to present generations.

A number of largely unexploited

sources of methane, the most abundant

of the natural gases, have also attracted considerable attention. Among these are natural gas in dense sandstones of

the West and the Devonian shales of

the East where the rock is relatively impermeable and does not allow the gas

to flow freely to a well. As a conse- quence, the drilling of a well in these formations is not often rewarded with

a great quantity of producible gas or a high daily rate of production. Methane

in coal is well known as a hazard to mining and is actually recoverable by

drilling holes in the coal bed in advance

of mining. Another recent discovery has been of the presence of methane in underground salt water found at considerable depth in the Gulf Coast area. The gas is held in the water by the

great pressures that exist at the depth.

Relatively simple calculations of the volume of oil shale in the Piceance

basin, tarlike substances in Utah, and

methane in coal beds or other geological

settings yield vast quantities of energy

that physically exist. However, like exotic rocks on the moon, the fact of

their existence should not be confused

with economic and technological accessibility. In the other occurrence classification, there is also that portion of conventional oil and gas that we do not expect

to recover. Similar to low-grade oil

shale, it would be physically possible

to produce this oil and gas at great

cost. One could literally mine an oil reservoir and produce all of the oil, or

let a gas well produce until there was

no more pressure left. Obviously, long

before this, it would be far more sensible to use some other source of energy. Thus, those portions of our oil and gas

resources unlikely to ever be recoverable can be accounted for among the other

occurrences.

Productive Capacity

It is virtually impossible to determine how much oil and gas can be produced

in any given year solely on the basis of knowing the quantity of proved re- serves of oil and gas. If the nation finds

itself lining up at gas stations or shutting

down factories because adequate pres- sure cannot be maintained in all the

utility mains during cold weather, the immediate supply problem is the pro- ductive capability of the delivery system, not proved reserves or undiscovered

resources. 7 Over the years little study has been

directed toward understanding the limits of the delivery system upon which we

depend to move energy from the well

to the burner tip. For the fossil fuel group, we have only the American

Petroleum Institute's (API) estimate of

productive capacity. This is the maximum daily rate of production which

could be attained under specific condition on March 3 1 of any given year. It would require ninety days to reach,

starting January 1, and is based upon

existing wells, well equipment, and

surface facilities. The estimate provides

for no reduction in ultimate recovery, and environmental damage or other hazards are not accepted.

Obviously, it is useful to have such

a measure of our capability. It is important, however, to be aware that the API definition of national productive

capacity does not imply anything about

the sustainability of this capacity over any specified period of time beyond

the ninety days. Beyond March 31 of

the year of estimate, the productive

capability would begin to decline. This

particular measure of productive capacity does not encompass our capability, or lack of it, for storage, transportation,

and processing facilities to handle the

oil once produced.

The gas shortage of the winter of

t Productive capacity is the more com- mon expression in the oil industry. The

gas utility industry's immediate capability

is referred to as the "deliverability" of the

gas. 751

1976-77 was a combination of system

limits and the declining deliverability of

gas from existing wells. Through emergency measures, such as denying some

customers gas and shifting gas between

systems on an ad hoc basis, the nation coped with the situation. This does not

alter the fact that the gas deliverability

from wells in 1977-78 will be different from what it was in the past winter. It

is not generally appreciated that ad

hoc plans that worked once may not work as well in another heating season. The fact remains that our oil and gas systems involve thousands of enterprises

delivering fuel to millions of households and commercial customers. Exactly how

that system works and what its capability might be, given the declining pro- duction curves of oil and gas, is only

partially understood. As of midwinter,

the weather and the amount of natural gas in storage did provide some opti- mism for the 1977-78 heating season. The inability to discriminate between

reserves and deliverability is the source

of considerable confusion in the re- porting on the oil and gas situation in the United States. References to the estimated total reserves in a field or

resources in a new region are equated

with annual production or requirements.

Since only approximately 10 to 15 per- cent of the reserves of a field can be produced in a single year, if connected

to a delivery system, billions of barrels of oil reserves or trillions of cubic feet of gas translate into a much smaller amount of oil and gas available even

in the early peak years. To understand oil and gas supply

requires more than a realization that estimating reserves is an inexact process;

it also involves an appreciation of the

limited capability of a well to produce

oil and gas upon demand. The time

required to explore, find, drill develop- ment wells, lay pipe, and provide process facilities is a further restraint on

translating reserves into production. To

this year's energy consumer the only

supply that counts is deliverable oil and

gas, not reserves or resources. If that flow is inadequate, periods of five to ten years or more and considerable in- vestment will be required to alter it in any significant way. Considerably more

attention to the limits of this process, and perhaps less to reserves, seems

warranted.

It is understandable that the productive capacity of the vast oil and gas producing industry and its downstream

facilities presents problems in terms of measurement. One would expect, in contrast, that the capability of a known

producing reservoir would be a reason- ably precise number. This has taken on a new importance in recent years, as
questions have been asked about whether

or not producers holding federal leases have been producing oil and gas as

diligently as they might if the price for

oil and gas were higher. This particular question has revived

interest ijka measurement that appeared

during World War II called maximum

efficient rate (MER). In concept, MER

can mean the theoretical physical capability of a reservoir to produce oil and

gas over time as a hydraulic unit. To ex- ceed this rate may reduce the amount of

oil and gas recovered. In practice, MER

has come to mean the maximum rate, in terms of barrels or cubic feet per day,

a reservoir can produce "efficiently" and "economically" from a fixed number

of wells under actual operating and

market conditions. In effect, this is the design capacity of the reservoir develop- ment plan, and reflects what the operator feels is economically justifiable. Producing the existing wells too rapidly could cause oil and gas to be lost in the reservoirs. Drilling additional wells could increase the flow from a reservoir without harm and might even increase the amount ultimately produced, but

the decision then rests on whether the extra expense of the well can be justified by the economic advantage to be gained

by producing more oil or gas or pro- ducing it faster. That particular judg- ment may depend on whether you are the producer or the federal government

leaseholder. Even the term efficiency provides its own share of problems. To the economist, efficiency will tend to be inter- preted as determining how recovery should be distributed over time to arrive

at a maximum value for the oil and

gas produced regardless of the physical recovery. The reservoir engineer's technical efficiency will be to achieve maxi- mum physical recovery at the lowest cost under current market cenditions. The

government administrator may be inter- ested in a production rate that provides a maximum quantity of oil and gas to the

public when it needs it, commensurate

with a reasonable return to the pro- ducer and acceptable payments to the Treasury of bonuses and royalties. For

a given reservoir, the annual production under these three criteria will not necessarily be the same. A difficult aspect of using MER is that it is not a constant. Since production of a well or reservoir is from a declining reserve, the producible quantity actually decreases from day to day. In practice, MER is determined periodically for most federal leases. It should be remembered that a reservoir may include a large number of wells, and that the maximum efficient rate of production applies to the whole reservoir and not to any individual well. In

the past, MER was considered a conservation technique to prevent wasting

the natural energies of the reservoir by

moving the various fluids so rapidly

that oil or gas is left behind entrapped

in the reservoir. Even so, in emergencies such as World War II, it is sometimes considered in the nation's

best interest to produce oil or gas at a

rate that actually causes some loss in ultimate production. Offshore operations from costly plat- forms have introduced new dimensions

to production and transport that have

increased the difficulty of determining

what is both physically and economically possible to accomplish. As a result, MER, which in the past has been pri- marily a state conservation regulatory

tool, creates a number of problems

When it is used as a measure of diligence

in exploiting federal leases. The federal government continues to look for a means whereby it can properly monitor

operator performance in terms of the

national interest without harming the entitlement of the leaseholder to serve and to protect his own interests as a private enterprise.

Conclusions

i

• The RFF staff has now engaged in over two years of studying, discussing and

explaining the uncertainties of oil and

resource estimation. That has led not

to better numbers but to perhaps a better understanding of what the existing data can or cannot do for us. By and

large, we find that most examinations

of oil and gas resources reflect in part the professional background of the esti- mator but most importantly the purpose

for which the work is designed. Many

estimates that have been published pro- vide total future quantities of oil and

gas that may be produced rather than

supply in the economic sense or rates of production over future time. All too

frequently, these totals may be trans- lated into years of remaining oil and

gas by dividing them by the current or some other assumed rate of production. This leads to the too-simple conclusion

that we may be out of oil and gas at the end of that number of years. Published estimates of total future producible hydrocarbon fluids provide

the public with a narrow view of future

oil and gas supply. This is compounded

by the fact that the public does not know how to interpret the figures. As

one RFF workshop participant noted, "the difficulty [in publishing estimates] was the problem and confusion in the

public's mind of what all these numbers

mean. It has just been an absolute

mess. They [the public] have taken undiscovered resources and related them

to reserves, and this was not really our

intent at all. Suddenly, we find ourselves quoted in the most peculiar ways. And much to our embarrassment." To the economist, it is important to know how much and for what period of time oil and gas production rates might be increased by a change in the economic structure of the industry or

in the cost-price ratios. Or how sensitive future oil and gas production rates are to changes in technology. Answers

to these kinds of questions are not contained in the usual published estimates

of future oil and gas reserves. As a participant in one RFF workshop said, "Not a single technique, approach, publication, or anything, has yet adequately

dealt with what the economists would

call the supply schedule. Somehow we

have got to get some indication of what

different levels of future supply would

be available at different cost-price re- lationships." In any given year the production of U.S. crude oil encompasses production

from a reservoir that has been newly

discovered, along with the production

from reservoirs ten to fifty years of age. The important point to note is that the

future rate of supply will be a composite of the rates from both old and new reservoirs. The experts who have appeared in the RFF workshops are agreed that the

rates of oil and gas production cannot

be increased indefinitely. At some point, the rates must inevitably peak and then

continue to decline until the hydro- carbon resources of the earth are ex- hausted. What the experts cannot agree upon is whether the annual rates of oil and gas supply can still be increased,

and over what period of time, before

the final decline begins. The extremes

are illustrated by proposing different extensions into the future of the past

oil production rate curve (see figure 7). The conservative view states that most of our giant fields have been

found; the maximum annual rate has

already been reached; and that, henceforth, there will be nothing but decline

(see Curve A). An optimistic view

might be that the annual oil production

rate may still rise in response to exploration and new technology to some future maximum from whence it would decline

until all reservoirs were exhausted (see Curve B). A moderate view would be

a future annual production rate curve somewhat between these two extremes

(see Curve C).

Whatever extension is predicted for the future rate of oil supply, the area under the resulting profile of the future can be no greater than the total amount 752
of oil which one estimates can ultimately be recovered. Thus, the estimator of

the conservative situation (Curve A)

not only envisions a declining rate of production but also a limited amount

of total production yet to be achieved. The optimistic estimator (Curve B)

sees not only an increased annual rate of supply but also a larger volume of

oil yet to be produced. Whether the estimator approaches the problem in terms of rates or total future production, the results of the estimate must

be internally consistent with respect to the relationship between rates and cumulative production.

Many of the published estimates of

future oil and gas supplies have pro- vided a value for the total supply

through use of the traditional "volu- metric" method. No matter how pol- ished and sophisticated the details may

be, the volumetric method still contains two basic perceptions: (1) that the occurrence of hydrocarbons in an unexplored geological region and the pa- rameters that are associated with its occurrence will probably bear a relation- ship to previously explored regions, and

(2) that the searching efficiency for finding oil in new areas will likely resemble what it has been in the past

in older regions.

Any resources estimate for future oil and gas production in an unknown

region may convey a misleading impression to the nonprofessional. The

only thing an estimator can say with

absolute accuracy is that he does not know whether there is oil or gas in a given region until wells are drilled to

find out. The history of past estimates

is rife with situations in which either

little oil was found in areas where there was a high expectancy or much oi! was

found in areas where there was a low

expectancy. Thus the U.S. Geological

Survey's probabilistic 2 to 4 billion barrels of undiscovered recoverable oil off the eastern U.S. Atlantic shore may

be used by many as a "guaranteed" number. It may become the basis of

a political decision either to explore or

ignore the area. An individual particularly concerned about environmental

protection might be inclined to conclude

that this amount of oil does not justify taking the risk of polluting the environ- ment to go after it. The fact is that there may be no oil at all off the Atlantic shore or there may be many times the estimated USGS figure.

If one prefers to approach the future by considering the production rate curve

rather than total future production, then

the immediate problem is the lack of an established theoretical basis for pre- dicting the future shape of that curve.

It appears to be somewhat unwarranted

to assume that the curve would be symmetrical. On the contrary, there is reason to suggest that the rising leg of

the curve is dominated by one physical

and economic process, that is, the dis- covery of new reservoirs, while the

decline will be dominated by a different physical and economic process, that is, the depletion of discovered reservoirs. The nature of oil and gas reservoirs

is such that the highest rates of pro- duction occur in the early life of the

reservoir. The flow factors of a reser- voir taken together generally mean that more than half the production from a particular reservoir will occur after the maximum rate of production is reached.

If it is possible to supplement the natural producing energy of the reser- voir or to apply technology that will make more of the reservoir oil accessible

to production, the history of the reser- voir may show additional productionrate peaks after the first one has been

reached. This was the case in Pennsyl- vania and in Illinois. The best current estimate is that, with

present technology and prices, an aver- age of between 30 and 40 percent of

the oil known to exist in discovered

reservoirs will have been produced at the time the reservoir is considered commercially exhausted. This is an

average to be interpreted as we understand expectancy, that is, some people

die younger and some live longer. The

amount that can be taken from a particular reservoir is dependent upon the nature of the oil itself and the nature

of the reservoir. There are known oil reservoirs from which the ultimate pro- duction will be as much as 80 percent

of the oil contained in the reservoir. In other instances, the amount of oil that can be produced with present tech- nology and prices may be as low as 10 or 15 percent of the oil in the

reservoir. If technology improvement

or a price rise permitted an abrupt

change in recovery factors, a late pro- 753

duction rate peak might show in the

oil supply curve. Another approach to examining the

future of oil and gas is an examination

of the rate at which exploratory drilling finds new oil and gas reservoirs. This approach does not necessarily depend

upon prior estimate of whether oil or

gas is present. It assumes that, if oil and

gas are present, they will be found. The approach requires, however, an

estimate of the efficiency for finding in the future. The published graphs which

show the manner in which the amount

of new oil found in the past related to the total exploratory footage drilled indicate that the finding rate has been

decreasing. The reasons generally given

for why less oil is being found per

foot of exploratory hole drilled include

1. We have already found the big

reservoirs and those near the surface. Future reservoirs will be found at deeper

horizons.

2. The most desirable geological re- gions have been explored and drilled.

3. The geological areas remaining to be drilled are more inaccessible and more expensive; for example, on the

continental shelf. Whatever the reasons may be for an

expected decline in search efficiency, it

is relatively easy to see that if one

extrapolates this decline into the future, the contribution to production rates due

to finding new reservoirs will diminish. Consequently, one would conclude that the maximum production rate probably

has been reached, but not all the experts agree that the search efficiency must decline. Both technology and

economics could affect the trend. Disagreement resulting from various methods of estimating future oil and

gas supply revolves around whether the volume of oil and gas remaining to be

fpund, or our productive capability, is the primary limiting factor on the domestic production rate in the immediate years ahead. The National Pe-
troleum Council concluded from its inquiry that at least until 1985 the amount remaining to be found is not

the limiting factor. NPC visualizes that annual production can increase with

appropriate attention to the drilling

rates, finding rates, improvements in recovery factor, and economic adjust- ments. The straightforward production-his- tory approach of M. King Hubbert and

others, which is appealing to many,

does appear to be very useful in telling us what is likely to happen in the near

future, if we continue doing things more or less the way we have been. It implies that production, drilling, and

so on are insensitive to economics and

policies. Barring an almost total inter- ruption in exploration, such curves do

seem to provide us with what should be our minimum expectation for future U.S. oil and gas output. However, this

is not to suggest that any of the other kinds of appraisals are totally free of

ties to past reserve and in-place figures

and historical, economic, and technological factors. There is greater satisfaction with

recent estimates of future oil and gas

supplies because the numbers appear

to be converging. Instead of difference

in orders of magnitude, two estimates may be within 10 or 25 percent of one

another. In part, this merely reflects a greater consistency in methodology

and assumptions than previously. Any

comfort derived from this apparent consensus can be false. Although two esti- mators may now agree, even if they have used different methods, this does

not necessarily mean that they are both

right. Finally, it is important to emphasize

that all oil and gas resource estimates by the many analyses both public and

private are dependent upon the same

sets of numbers as starting points. Be- yond this, there is no right methodology,

and estimates are sophisticated guesses

at best. All experts are agreed that the usable oil and gas hydrocarbon re- sources are probably sufficiently limited

that the maximum annual rate of pro- duction and the decline until reserves are exhausted are events that will fall within a few decades, not much beyond

that. The peak in the United States may have already been reached. Yet

one must not minimize the importance

of capturing the remaining one-half or

one-third of our oil and gas. So basically we are dealing with forecasts of annual production rates for two

or three decades, and we must get an

idea of the impacts of economic and

technological changes on these rates. Cost data should be assembled so that

it will be possible to analyze better the

responses to economic change. Attention must be directed to the effect of

technological change on increasing the recovery factor of existing reservoirs and the lead times needed to accomplish

this.This work will be aided if we can

eliminate some of the past disagree- ments of estimators that stemmed from

a lack of consistency in defining re- covery factors and other concepts employed. If estimators are agreed on

anything, it is that the definitions of terms must be examined closely and more standard definitions accepted for future resolution, if not of the supply

question, then at least of why the esti- mators disagree in fact. Such a resolution would be an important step toward

substantive agreement.

This is not as easy as it may seem. Even a seemingly simple term "total

oil and gas in place" changes in meaning due to changes in information and

the economic or technological perception of the analyst. Gas in tight sands

or heavy oils would not have been encompassed within the definition of

that term a few years ago. Yet some

output from these sources has now

joined the production stream. The realization that there are no

measurements in oil and gas resource

appraisals is important to impress upon

everyone. Even in discovered reservoirs we do not measure the oil in place—it

is estimated. Reserves are an estimated

value derived from a prior estimate of

the oil in place, taking into account economics and technology. If the oil- in-place estimate changes, so will that of the reserves. Reserves and resources

are equal to the estimated oil in place

multiplied by an assumed recovery

factor, substantially less than 100 per- cent for oil, less the amount of cumulative production. Nothing could be simpler yet so uncertain. There are no

hidden formulas for predicting the end

of the finite supply of oil and gas in the United States or the world. The

definitive study of future oil and gas supply and how it may be altered by

economic and technological parameters

that have not yet emerged still remains

to be done. It is of little comfort that the final, reliable, appraisal of the oil and gas resources of the United States

will prove to be historic rather than

predictive.

REFERENCES

American Petroleum Institute, Seminar on

Reserves and Productive Capacity

(Washington, D.C., April 1, 1975). American Petroleum Institute, Standard

Definitions for Petroleum Statistics Technical Report No. 1, 2nd edition (Washington, D.C., 1976).

American Gas Association and American

Petroleum Institute, Reserves of Crude

Oil, Natural Gas Liquids, and Natural Gas in the United States and Canada

(Washington, D.C.) annual. Eugene Ayres and Charles A. Scarlott, Energy Sources—The Wealth of the World (McGraw-Hill, New York,

1952). Federal Energy Administration, National Energy Outlook (Government Printing

Office, 1976). M. King Hubbert, UJS. Energy Resources: Review as of 1972. Committee Print: Senate Committee on Interior and In- sular Affairs, 93 Cong. 2nd sess. Hans H. Landsberg, "Review of Federal Energy Administration National Energy

Outlook (Report to NSF under pro- posal No. 7680248) (mimeo, Resources

for the Future, March 1977). Mathematica, Inc., A Comparative State- of-the-Art Assessment of Gas Supply

Modeling (Research Project #436-1)

(Electric Power Research Institute, Palo

Alto, California, February 1977).

P. W. MacAvoy and R. S. Pindyck, The

Economics of the Natural Gas Short- age (1960-1980) (North-Holland, Amsterdam and New York, 1975). James W. McFarland, MER [Maximum

Efficient Rate) Definitions and Calculations Using a Gas-Water Reservoir Model (LA-6533-MS) (Los Alamos

Scientific Laboratory, Los Alamos, New

Mexico, October 1976). National Academy of Sciences, Gas Reserve Estimation 'of Offshore Producible

Shut-in Leases in the Gulf of Mexico

(Washington, D.C, March 1976). National Academy of Sciences, Natural Gas from Unconventional Geologic

Sources (Washington, D.C. 1976). National Academy of Sciences, Committee on Mineral Resources and the Environment, Mineral Resources and the Environment (Washington, D.C, February 1975). National Petroleum Council, U.S. Energy

Outlook (Washington, D.C, December

1972).

Potential Gas Committee, Colorado School

of Mines, Potential Supply of Natural Gas in the United States (Golden,

Colorado, November 1973). John J. Schanz, Jr., Resource Terminology:

An Examination of Concepts and Terms and Recommendations for Improvement (Springfield, Va., National Technical Information Service, 1975), PB 244-433. Sam H. Schurr and Bruce C. Netschert, Energy in the American Economy:

1850-1975 (Baltimore, Johns Hopkins

University Press for Resources for the Future, 1960). Richard P. Sheldon, "Estimates of Undis- covered Petroleum Resources—A Perspective," United States Geological Sur- vey Annual Report, Fiscal Year 1975,

p. llff. United States Geological Survey, Geological Estimates of Undiscovered Recoverable Oil and Gas Resources in the United States, Geological Survey Circular 725 (1975). 754
RFF WORKSHOP PARTICIPANTS

Resources for the Future wishes to ac- knowledge the contributions made by participants in the series of workshops held

in recent years. These were: the Workshop on Oil and Gas Resources chaired by John C. Calhoun, Texas A&M, and

Earl Cook, Texas A&M, rapporteur; the Workshop on Maximum Efficient Rate

chaired by John J. Schanz, Jr., Resources

for the Future, and Hans H. Landsberg, Resources for the Future, rapporteur; and

the Workshop which reviewed the FEA's

1976 National Energy Outlook, chaired by

William A. Vogely, Penn State, and Hel- mut Frank, University of Arizona, rapporteur. The participants, some of whom participated in more than one workshop, are

listed alphabetically below with their affil- iation at the time of the workshop.

Philip H. Abelson, Carnegie Institution M. A. Adelman, Massachusetts Institute of Technology

Ralph E. Bailey, Consolidated Coal Company

Daniel Bass, Colorado School of Mines

B. Warren Beebe, Energy Consultant Harold W. Bertholf, Resources Agency of

California Richard C. Byrd, Interstate Oil Compact

Commission

John C. Calhoun, Jr., Texas A&M University Monte Canfield, Jr., General Accounting

Office Earl Cook, Texas A&M University

Benjamin S. Cooper, Senate Interior Committee Gordon R. Corey, Commonwealth Edison Company

Ronald G. Cummings, University of New

Mexico

Joel Darmstadter, Resources for the Future John Davidson, Council on Environmental Quality W. Kenneth Davis, Bechtel Power Corporation

Nicholas G. Dumbros (ret.), Marathon Oil Company

Lloyd D. Elkins, AMOCO Production Company

Herman Enzer, Department of the Interior Edward W. Erickson, North Carolina State University

Helmut Frank, The University of Arizona Herman T. Franssen, Congressional Research Service John H. Gibbons, University of Tennessee Edwin D. Goebel, Federal Power Commission Richard L. Gordon, Pennsylvania State University Bernardo Grossling, U.S. Geological Sur- vey Marcel Grunspan, Energy Research and Development Administration Mariano Gurfinkel, International Monetary Fund

DeVerle Harris, University of Arizona John D. Haun, Colorado School of Mines

Hollis Hedberg, Princeton University Claude Hocott, University of Texas Kenneth Hoffman, Brookhaven National

Laboratories William Hogan, Federal Energy Administration M. King Hubbert, U.S. Geological Survey Richard L. Jodry, Sun Oil Company

John C. Joers, Continental Oil Company

John M. Kelly, Consultant Hans H. Landsberg, Resources for the Future

Milton Lipton, W. J. Levy, Inc. Paul W. MacAvoy, Massachusetts Institute of Technology

Charles S. Matthews, Shell Oil Company

R. G. McCrossan, Institute of Sedimentary

& Petroleum Geology

Stephen L. McDonald, The University of Texas

Vincent E. McKelvey, U.S.. Geological

Survey

Charles Mankin, Oklahoma Geological

Survey

Horst Mendershausen, The RAND Corporation Betty Miller, U.S. Geological Survey John D. Moody, Petroleum Consultant Bruce C. Netschert, National Economic

Research Associates David Nissen, Federal Energy Administration Peter R. Odell, Erasmus University John F. O'Leary, The MITRE Corporation

Joseph D. Parent, Institute of Gas Technology

Harry Perry, Resources for the Future James Plummer, National Science Foundation A. L. Porter (ret.), New Mexico Conservation Commission

William Prast, Continental Oil Company

R. A. Purvis, Energy Resources Conservation George W. Rathjens, Massachusetts Insti- tute of Technology

Steve Rattien, National Science Foundation

Larry Ruff, The Ford Foundation

Milton Russell, Resources for the Future W. K. Savage, Scientific Software John J. Schanz, Jr., Resources for the Future

Walter W. Schroeder, House Subcommittee on Energy and Power Sam H. Schurr, Resources for the Future David Schwartz, Michigan State University Milton F. Searl, Electric Power Research

Institute Mark Sharefkin, Resources for the Future

Marshall B. Standing, Stanford University

Henry B. Steele, University of Houston

James L. Sweeney, Federal Energy Administration Edward Symonds, Consultant

Philip Verleger, Council of Economic Advisors William A. Vogely, Pennsylvania State University Leonard Waverman, Stanford University Robert Whiting, Texas A&M University Mason Willrich, University of Virginia

Law School

Please let us know if you change your address, since Resources cannot be forwarded. RESOURCES IS PUBLISHED THREE TIMES A YEAR. REPUBLICATION WITH CREDIT IS PERMITTED

Resources for the Future, Inc. is a nonprofit organization

for research and education, established in 1952 with the cooperation of the Ford Foundation to advance the development, conservation, and use of natural resources, and

the improvement of the quality of the environment. Board of Directors: Gilbert F. White, Chairman, Irving Bluestone, Harrison Brown, Roberto de O. Campos, William T. Coleman, Jr., Luther H. Foster, F. Kenneth Hare, Charles J. Hitch, Charles F. Luce, George C. McGhee, Ian MacGregor,

Laurence I. Moss, Frank Pace, Jr., Emanuel R. Piore, Stanley H. Ruttenberg, Lauren Soth, Janez Stanovnik,

Julia D. Stuart, Robert D. Stuart, Jr., Russell E. Train,

P. F. Watzek

Honorary Directors: Horace M. Albright, Erwin D. Canham,

Edward J. Cleary, Hugh L. Keenleyside, Edward S. Mason,

William S. Paley, John W. Vanderwilt

Officers: President: Charles J. Hitch

Vice President: Emery N. Castle Secretary-Treasurer: John E. Herbert

RESOURCES FOR THE FUTURE

1755 Massachusetts Avenue, N.W.

Washington, D.C. 20036

755
SYMPOSIUM ON

OIL AND GAS SUPPLY MODELING

Sponsored by

The Department of Energy and The National Bureau of Standards

June 18, 19, 20, 1980

Main Auditorium

Department of Commerce

14th & E Streets, NW

Washington, DC

Wednesday, June 18, 1980

9:00 a.m. - 9:20 a.m.

Welcome Saul I. Gass, U. of MD/NBS

Symposium Chairman

Lincoln E. Moses

Administrator, EIA/DOE

H. William Menard

Director, USGS

9:20 a.m. - 9:30 a.m.

Symposium Objectives Frederic H. Murphy

DOE/EI

9:30 a.m. - 10:15 a.m.:

Oil and Gas Supply: Public Perception, Modelers'

Abstraction, and Geologic Reality John J. Schanz, Jr.

CRS/LOC

10:15 a.m. - 10:30 a.m.: Coffee

10:30 a.m. - 11:15 a.m.:

Techniques of Prediction as Applied to the

Production of Oil and Gas M. King Hubbert

756
11:15 a.m. - 12:00 p.m.:

Current Problems in Oil and Gas Modeling William Stitt

ICF

12:00 p.m. - 1:30 p.m.: Lunch

Session Chairman: Frederic H. Murphy , DOE

1:30 p.m. - 2:00 p.m.:

The Evolution in the Development of Petroleum

Resource Appraisal Procedures in the U. S.

Geological Survey Betty Miller

USGS

2:00 p.m. - 2:30 p.m.:

Review and Recommendations Concerning Statistical Procedures in Oil and Gas Resource

Forecasting John W. Harbaugh

Stanford

2:30 p.m. - 3:00 p.m.:

Probabilistic Approaches to Projecting Oil

and Gas Supply In Our Time Gordon M. Kaufman

MIT

3:00 p.m. - 3:15 p.m.: Coffee

3:15 p.m. - 3:45 p.m.:

Analysis of Production and Investment Strategies

for Petroleum Reserves James W. McFarland

U. of Houston

3:45 p.m. - 4:15 p.m.:

A Methodology for Estimating Oil and Gas Production Schedules for Undiscovered Fields John H. Wood

DOE

4:15 p.m. - 4:45 p.m.:

Some Modern Notions on Oil and Gas Reservoir

Production Regulation John Lohrenz and

Ellis A. Monash

USGS

757
Thursday, June 19, 1980

Session Chairman; Wallace 0. Keene, DOE

9:00 a.m. - 9:30 a.m.

Historical Growth of Estimates of Oil

and Gas Field Size David Root

USGS

9:30 a.m. - 10:00 a.m.:

Results in Successive Sampling in Oil and

Gas Exploration Models Louis Gordon

DOE

10:00 a.m. - 10:30 a.m. :

Technology Specification and Economic Accounts

for Resource Exploration and Production David Nissen

Chase Manhattan

10:30 a.m. - 10:45 a.m.: Coffee

10:45 a.m. - 1 1 :*15 a.m.?

Gulf Coast Resource Model Data Collection

Process Richard Zaffarano

DOE

11:15 a.m. - 11:45 a.m.:

A Methodology for Estimating Cost of Finding,

Developing, and Producing Undiscovered

Resources Thomas Garland and

John H. Wood

DOE

11:45 a.m. - 1:00 p.m.: Lunch

Session Chairman: David S. Hirshfeld, DSH Assoc.

1 : 00 p.m. - 1 : 30 p.m.

Petroleum Industry Exploration and Production

Decision Methodologies Ted Eck

Standard Oil of IN

1:30 p.m. - 2:00 p.m.:

The Economics of Exploration: Some Further

Results in Empirical Implications James B. Ramsey

NYU

758
2:00 p.m. - 2: 30 p.m.

The Regulatory Framework in Oil and Gas

Supply Modeling Stephen L. McDonald

U. of TX at Austin

2:30 p.m. - 3:00 p.m.:

Firm Size and Performance in the Search

for Petroleum Lawrence J. Drew

USGS

3:00 p.m. - 3:15 p.m.: Coffee

3:15 p.m. - 3:45 p.m.:

Sensitivity and Statistical Analysis of Oil

and Gas Supply Models Carl M. Harris

Ctr. for Mgmt. and

Policy Research

3:45 p.m. - 4:15 p.m.:

Natural Resource Exploration, Extraction,

and Pricing Under Uncertainty Sudhakar D. Deshmukh

Northwestern U.

4:15 p.m. - 4:45 p.m.:

The Depletion of U. S. Petroleum Reserves:

Econometric Evidence Dennis Epple and

Lars Hansen

Carnegi e-'Me 1 Ion

Friday, June 20 t 1980

Session Chairman: Charles Everett, DOE

9:00 a.m. - 9:30 a.m.:

Finding Rates as a Factor in Oil and Gas

Economic Projections William K. Fisher

U. of TX at Austin

9:30 a.m. - 10:00 a.m.

Modeling Future Onshore Domestic Production. > Steve Muzzo, ICF and

Richard O'Neill, DOE

759
10:0U a.m. - 10:30 a.m.

Long-Range Forecasting Methodologies for

Conventional Oil and Gas Ellen Cherniavsky

Brookhaven

10:30 a.m. - 10:45 a.m.: Coffee

10:45 a.m. - 11:15 a.m.:

An Integrated Evaluation Model of Domestic

Crude Oil and Natural Gas Supply Robert Ciliano

Mathtech

11:15 a.m. - 11:45 a.m.:

Modeling Alaska Oil and Gas Supply Frederic H. Murphy and

William Trapmann

DOE

11:45 a.m. - 12:15 p.m.:

Oil and Gas Production Potential from

the Lower 48 Outer Continental Shelf Jerry Brashear and

Frank Morra

Lewin & Assoc.

12:15 p.m. - 1:30 p.m.: Lunch

1:30 p.m. - 3:30 p.m.: PANEL

Suggestions for Future Directions in Oil and Gas

Supply Data Collection and Model Development. .. .Frederic H. Murphy and

Richard O'Neill

DOE

The panel will give the speakers and audience an opportunity to present their

views on oil and gas supply model research, development, and related needs.

Note: There is no registration fee . Coffee is available in the main cafeteria situated one floor below the auditorium. The cafeteria is open

from 7:30 a.m. to 3:30 p.m. Conference Room 1851 (behind the front of

the auditorium) is available each day for informal discussions.

760
OIL AND GAS SUPPLY MODELING SYMPOSIUM

PARTICIPANTS

Mark A. Alexander

U. S. Department of Energy

Room GA-257, Forrestal Bldg.

Washington, D. C.

H. J. Allison

National Science Foundation

1800 G Street, N. W.

Washington, D. C. 20530

William C. Anderson

Department of Energy/FERC

Room 7010F

825 N. Capital Street

Washington, D. C.

Giovanni Andreatta

Massachusetts Inst, of Technology

Sloan School of Management

50 Memorial Drive

Cambridge, Massachusetts 02178

David Andres

David Andress Associates

7813 Garland Ave.

Takoma Park, Maryland 20013

Anthony Apostolides

Jack Faucett Associates

5454 Wisconsin Ave., N. W.

Chevy Chase, Maryland 20015

Gary L. Ardell

Stanford University

336 Swett Rd.

Woodside, California 94062

Paul S. Basile

Energy and Power Subcommittee

U. S. House of Representatives

HOB Annex No. 2 Washington, D. C. 20515

M. S. Becker

Department of Energy

2849 LaFora Ct.

Vienna, Virginia 22180

Edward J. Bentz, Jr.

E. J. Bentz & Associates, Inc.

7915 Richfield Rd.

Springfield, Virginia 22153

Javier Bernal

National Bureau of Standards

Center for Applied Mathematics

Operations Research Division

Washington, D. C. 20234

Harry J. Bialek

American Petroleum Institute

2101 L Street, N. W.

Washington, D. C. 20037

Charles L. Blake

Federal Aviation Administration

AEM-201

800 Independence Ave., S. W.

Washington, D. C. 20591

Peter S. Blau

Petroleum Institute

1299 National Press Bldg.

Washington, D. C. 20045

James B. Borden

E . I . DuPont de Nemours Co .

, Inc

Wilmington, Delaware 19898

Ellis R. Boyd, Jr.

Dept. of Energy, EIA

12th & Pennsylvania Ave., N. W.

Mail Stop 5302

Washington, D. C. 20461

Monica Bradley

Department of Energy, Mail Stop 4530

12th & Pennsylvania Ave., N. W.

Washington, D. C. 20461

J. P. Brashear

Lewin & Associates

470 L' Enfant Plaza

Washington, D. C. 20002

761
John W. Broderick

Department of Energy

Resource Applic. Leasing Policy

Room 2334

12th & Pennsylvania Ave., N. W.

Washington, D. C. 20461

Larry Buch

Texas Comptroller of Public Accounts

111 E. 17th Street, #304

Austin, Texas 78774

Tom Buckmeyer

Congressional Research Service

Library of Congress

Environment & Natural Resource Div.

423 James Madison Bldg.

Washington, D. C. 20540

Paul Bugg

U. S. Dept. of the Interior

Office of Minerals Policy

and Research Analysis

Main Interior Bldg.

18th & C Streets, N. W.

Washington, D. C. 20240

Anthony E. Burris

Los Alamos Scientific Laboratory

Mail Stop #605

P. 0. Box 1663

Los Alamos, N. Mexico 87544

B. H. Burzlaff

Kentron International, Inc.

11317 Smallwood Drive

Burleson, Texas 76028

Joan Burzlaff

Kentron International, Inc.

11317 Smallwood Drive

Burleson, Texas 76028

E. Ann Butler

Atlantic Richfield Co.

AP 4037

515 S. Flower Street

Los Angeles, California 90071

William Butler

Office oft* Natural Gas

Department of Energy

1000 Independence Ave., S. W.

Washington, D. C.

Van R. Cammack

Atlantic Richfield Co.

P. 0. Box 2819

Dallas, Texas 75221

Frank Capece

Department of Energy/EIA

Room 8443

12th & Pennsylvania Ave., N. W.

Washington, D. C. 20461

Mary E. Carlson

Department of Energy

EI-522, Room 4522

12th & Pennsylvania Ave., N. W.

Washington, D. C. 20461

John Scott Carter

Boeing Computer Services

7890 Gallows Court

Vienna, Virginia 22180

Armando Cervi, Jr.

Rohm and Haas Co.

Independence Mall West

Philadelphia, Pennsylvania 19105

Robert E. Chapman

National Bureau of Standards

Center for Applied Mathematics

Operations Research Division

Washington, D. C. 20234

Federick E. Chemay

Louisiana Dept. of Natural Resources

P. 0. Box 44156

Baton Rouge, Louisiana 70804

Ellen A. Cherniavsky

Brookhaven National Laboratory

Upton, New York 11973

762
Leland M. Cheskis

OGS, ESA, EIA

Dept. of Energy

Mail Stop 4530, EI-522

12th & Pennsylvania Ave., N. W.

Washington, D. C. 20461

Kunmo Chung

National Science Foundation

Room 1240

1800 G Street

Washington, D. C. 20550

Robert Ciliano

Mathtech, Inc.

P. 0. Box 2392

Princeton, New Jersey 08540

Mark Cimino

Lewin & Associates

470 L' Enfant East, S. W.

Suite 4100

Washington, D. C. 20024

John J. Coleman

EPA

401 M Street, S. W.

RD-681

Washington, D. C.

Jerry P. Conner

Los Alamos Scientific Laboratories

Department of Energy

Office of Intl. Security Affairs

Forrestal Bldg., MS-SF-066

Washington, D. C. 20525

William G. Cook

Department of Energy/EIA/FRS

Federal Bldg.

12th & Pennsylvania Ave., N. W.

Washington, D. C. 20461

Colleen M. Cornett

EIA/ DOE

12th & Pennsylvania Ave., N. W.

Mail Stop #5317

Washington, D. C. 20461

Charles M. Cowles

FERC/Room 5007

825 N. Capitol Street, N. W.

Washington, D. C. 20426

Robert 0. Crockett

Department of Energy/EIA

Room 5315

12th & Pennsylvania Ave., N. W.

Washington, D. C. 20461

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772
NBS-114A (rev. 2-bo) U.S. DEPT. OF COMM. 2. Pforming Organ. Report No. BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBS SP 631

3. Publication Date May 1982

4. TITLE AND SUBTITLE

Oil and Gas Supply Modeling

Proceedings of a Symposium held at the Department of COnmerce,

Washington, DC, June 18-20, 1980

Saul I. Gass, Editor

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

Operations Research Division Energy Information Administration

Center for Applied Mathematics U.S. Department of Energy

National Bureau of Standards Washington, DC 2 OA 61

Washington, DC 20231* 10. SUPPLEMENTARY NOTES

Library of Congress Catalog Number: 82-600508

| | Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

The symposium on Oil and Gas Supply Modeling, held at the Department of Commerce,

Washington, DC (June 18-20, 1980), was funded "by the Energy Information Administration

of the Department of Energy and co-sponsored by the National Bureau of Standards'

Operations Research Division. The symposium was organized to he a forum in which the

theoretical and applied state-of-the-art of oil and gas supply models could he presented and discussed. Speakers addressed the following areas: the realities of oil and

gas supply, prediction of oil and gas production, problems in oil and gas modeling,

resource appraisal procedures, forecasting field size and production, investment and

production strategies, estimating cost and production schedules for undiscovered fields

production regulations, resource data, sensitivity analysis of forecasts, econometric

analysis of resource depletion, oil and gas finding rates, and various models of oil

and gas supply. This volume documents the proceedings (papers and discussion) of the

symposium.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

cost estimation; data collection; economic analysis; energy models; estimation;

exploration; finding rates; forecasting; gas supply models; investment strategies;

oil supply models; resource appraisal; sensitivity analysis.

13. AVAILABILITY

1X1 Unlimited

I I For Official Distribution. Do Not Release to NTIS

I I Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D C

20402. y Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

778

15. Price

USCOMM-OC 8043-P80

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