Reserve Growth of Oil and Gas Fields—Investigations and 

Applications

Scientific Investigations Report 2013–5063

U.S. Department of the Interior

U.S. Geological Survey
COVER. Outcrop of Tensleep Sandstone in Sinks Canyon, Wyoming, showing the complex 

compartmentalization commonly observed in this important eolian oil and gas reservoir (photo taken 

by Christopher J. Schenk, U.S, Geological Survey, in 2004).
Reserve Growth of Oil and Gas Fields—

Investigations and Applications

By Troy A. Cook

Scientific Investigations Report 2013–5063

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2013

For more information on the USGS—the Federal source for science about the Earth, its natural and living 

resources, natural hazards, and the environment, visit http://www.usgs.gov or call 1–888–ASK–USGS.

For an overview of USGS information products, including maps, imagery, and publications, 

visit http://www.usgs.gov/pubprod

To order this and other USGS information products, visit http://store.usgs.gov

Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the 

U.S. Government.

Although this information product, for the most part, is in the public domain, it also may contain copyrighted materials 

as noted in the text. Permission to reproduce copyrighted items must be secured from the copyright owner.

Suggested citation:

Cook, T.A., 2013, Reserve growth of oil and gas fields—Investigations and applications: U.S. Geological Survey 

Scientific Investigations Report 2013–5063, 29 p., http://pubs.usgs.gov/sir/2013/5063/.
iii

Contents

Abstract...........................................................................................................................................................1

Introduction.....................................................................................................................................................1

Statement of Problem....................................................................................................................................2

Reserve-Growth Profile ................................................................................................................................3

Production Replacement Ratio....................................................................................................................4

Data and Analysis..........................................................................................................................................6

Disaggregating a Single Age-Group Pair .........................................................................................6

Disaggregating All Age-Group Pairs .................................................................................................8

Natural Tendencies of the Arrington-Style Assembly..................................................................16

Conventional Versus Continuous Accumulations .........................................................................19

Discussion.....................................................................................................................................................22

General Behavior of Arrington-Style Assemblies .........................................................................22

Reserve-Growth Outliers...................................................................................................................24

Commonness of Reserve Growth.....................................................................................................25

Age Correlation of Reserve Growth.................................................................................................25

The Lifespan of Reserve Growth......................................................................................................25

Implications..........................................................................................................................................26

Summary........................................................................................................................................................27

Acknowledgments.......................................................................................................................................28

References Cited..........................................................................................................................................28

Figures

1 Coalinga oil field cumulative production, estimated ultimate recovery, and 

production-replacement ratio (PRR) with respect to time.....................................................4

2 Mount Poso oil field cumulative production, estimated ultimate recovery, and 

production replacement ratio (PRR) with respect to time.....................................................5

3 Estimated known recoverable oil for conventional oil fields 61 years after 

discovery year...............................................................................................................................8

4 Average conventional oil field size, volume changes, and field counts for all age 

 groups.............................................................................................................................................9

5 Average reserve growth in conventional oil fields per field per age-group pair 

including percentage of fields where cumulative production equals estimated 

known recovery ............................................................................................................................9

6 Number and size of oil fields required to generate 75 percent of gross field 

growth in each age-group pair.................................................................................................10

7 Volumetric contribution of gross reserve growth for major and nonmajor 

conventional oil fields in each age group...............................................................................11

8 Percentage of gross reserve growth and total known recovery of the single largest 

growing oil field in each age-group pair.................................................................................11

9. Gross reserve growth of five largest growing oil fields in each age group......................12

10. Field counts and gross reserve growth of major oil fields...................................................12

11. Field counts and net reserve growth of nonmajor oil fields ................................................13
iv

12. Net reserve growth from San Joaquin Basin oil fields and volumetrically weighted 

reserve growth by American Petroleum Institute (API) oil gravity ....................................14

13. Field counts and gross reserve growth of major gas fields ................................................14

14. Field counts and net reserve growth of nonmajor gas fields..............................................15

15. Gross reserve growth of oil from a few fields across multiple age-group pairs. ............15

16. Example of the interaction of nine nonlinear declines.........................................................18

17. Annual fractional change of nine nonlinear declines and dependency of that 

answer on smallest decline ......................................................................................................18

18. Fractional effect on group behavior caused by the difference between 

group behavior and the single smallest decline within the group .....................................19

19. Discovery-year groups with early histories of estimated ultimate recovery through 

time................................................................................................................................................20

20. Annual growth factors for top five oil fields in each age-group pair versus all 

others............................................................................................................................................20

21. Annual growth factors for top five gas fields in each age-group pair versus all 

others............................................................................................................................................21

22. Example of consistent reserve growth in an actual billion-barrel oil field in Texas .......21

23. Differences in cumulative growth curve results based on a single annual growth 

factor change ..............................................................................................................................23

24. Differences in cumulative growth curve results based on the removal of all fields 

with no changes in reserve growth in that age-group pair.................................................24

Tables

1. Mount Poso oil field production replacement ratio (PRR) calculation over two 

different time spans......................................................................................................................6

2. Known petroleum volumes (KPVs) for conterminous United States, excluding Federal 

offshore and continuous fields......................................................................................................7

3. Single age-group sequence of known recovery change and related calculations ........17

4. Example of an annual growth factor calculation that includes all fields ..........................22

5. Example of an annual growth factor with a single field removed from the 

calculation ...................................................................................................................................23

Initialisms

AGF annual growth factor

API American Petroleum Institute

CGF cumulative growth function

EIA Energy Information Agency

EPCA Environmental Policy and Conservation Act

GOR gas to oil ratio

OGIFF Oil and Gas Integrated Field File

PRR production replacement ratio
Abstract 

The reserve growth of fields has been a topic for ongoing

discussion for over half a century and will continue to be 

studied well into the future. This is due to the expected size 

of the volumetric contribution of reserve growth to the future 

supply of oil and natural gas. Understanding past methods of 

estimating future volumes based on the data assembly methods that have been used can lead to a better understanding of 

their applicability. The statistical nature of past methods and 

the (1) possible high level of dependency on a limited number 

of fields, (2) assumption of an age-based correlation with 

effective reserve growth, and (3) assumption of long-lived and 

more common than not reserve growth, may be improved by 

employing a more geologically based approach. 

Introduction

Reserve growth, inferred reserves, field appreciation, 

ultimate recovery appreciation, and field growth are all terms 

that have been used to refer to changes in the estimated ultimate size of an oil and gas field or an aggregation of fields. 

The term “reserve growth” will be used in this study. The term 

“field” will be used to refer to an oil and gas producing entity 

based on a collection of oil and gas pools of varying depths, 

sizes, and geologic characteristics. The estimated ultimate size 

of a field’s recoverable volume changes with respect to time, 

additions and extensions of the field, new pools discovered 

within the field, improvements in recovery technology, and the 

level of development of a field. It should be noted that fields 

can also have their estimated ultimate size revised downward 

as well.

Comments on reserve growth have been made at the field, 

play, basin, country, and world level, and various individuals 

and organizations have recognized, described, and estimated 

reserve growth for nearly 50 years. The importance of understanding and estimating reserve growth is critical to future 

reserve and resource appraisals because its magnitude can 

equal or exceed the volumes of future discoveries. If reserve 

growth of existing fields is not taken into account, the result 

would be a continual underestimation of the current inventory 

of oil and natural gas resources available for development.

This study of reserve growth was completed as part of an 

ongoing U.S. Geological Survey (USGS) project to investigate 

the causes and behavior of reserve growth that lead to better 

estimates of future petroleum potential. As part of this analysis 

of reserve growth, an additional component—the production 

replacement ratio (PRR) of reserve growth—was created. 

The PRR focuses on a profile of reserve growth that is independent of volume or percentage measures and is capable of 

identifying fields displaying the reserve-growth profile at any 

particular point in time or across the entire history of a field. 

Once the PRR was conceptually formulated, it was tested 

using field-level reserve-growth information of the United 

States contained within the Nehring Associates (NRG) database (NRG Associates, 2008). 

In addition to identifying this profile of reserve growth, 

an analysis of the Arrington-style age-based methods 

(Arrington, 1960; hereafter referred to as Arrington-style 

methods) was undertaken to better understand the consequences of temporal aggregations and to determine if the 

implications from these aggregations are valid. This analysis 

uncovered a high level of volumetric dependency on a small 

number of fields revealing a bimodal population within the 

field growth data. Initially a field’s estimated known recovery 

can grow (or shrink) as well performance establishes reservoir 

behavior, new pools are tested, and the delineation of the field 

continues with early field development. This early reservegrowth (or shrink) effect then combines with a separate and 

near-linear growth mechanism in a minority of fields. These 

two effects, early and late, are generally combined to provide 

an overall impression of reserve growth. 

Understanding how these mechanisms interact is important when constructing a method to estimate future reserve 

growth. Field reserve growth in the past has been a significant 

and consistent volumetric contributor to the total volume 

inventory in the United States and is expected to have the 

same effect at the international level. 

No systematic attempt was made in this study to explain 

or find definitive geological or engineering significance 

that is causally related to reserve growth at the field level, 

although general comments on these topics are discussed. 

This study utilizes the information from approximately 

Reserve Growth of Oil and Gas Fields—Investigations 

and Applications

By Troy A. Cook
2 Reserve Growth of Oil and Gas Fields—Investigations and Applications

15,000 conventional oil and gas fields spanning 24 years of 

known recovery estimates within the NRG Associates (2008) 

database to draw conclusions. These conclusions may not be 

valid beyond the bounds of this particular dataset; however, a 

review of other reserve-growth studies shows similar patterns, 

and the work demonstrated here might be appropriate for a 

similar analysis in other groups of fields.

Statement of Problem

It has been widely recognized that Arrington (1960) was 

the first to use an age-based “running rate of growth with time 

with a constantly changing group of fields” method to estimate 

reserve growth, which he applied to the oil fields of Carter Oil 

Co. in the 1940s. Of note in Arrington’s examples is that his 

“running rate of growth” calculation covered 27 years, and 

he stated “This is a valuable tool for management in helping 

them learn new facts which might not otherwise be available 

for 5 or 10 years” (Arrington, 1960, p. 134). He also listed the 

limitations of the method and cautioned that studies of this 

type can be used improperly, further writing that (1) the results 

could not be used on any group of fields except those from 

which they were derived; (2) the results could not be applied 

to a smaller number of statistics than the group from which 

they were derived (never to a single field); and (3) the entire 

construction was a probability concept.

This “running rate of growth” method can be described 

as the volume changes between sequential sums being quantified as a percentage change between sums. When the percent 

changes in ultimate field recovery are plotted with respect to 

time, this manner of assembling the data leads to a decline that 

resembles a natural decay function. 

Hubbert (1967) used a slightly different method to 

calculate reserve growth while still maintaining the age relation to the size of the reserve growth. This method involved 

average cumulative growth curves derived from past changes 

in estimates of American Petroleum Institute (API)-American 

Gas Association ultimate oil and gas recovery with respect to 

the time since the fields were discovered. Unlike Arrington’s 

(1960) concept, Hubbert fit his function to the cumulative 

growth through time and incorporated an asymptote into this 

equation to calculate the growth from initial discovery size 

at any point in time. This distinction, to limit both the total 

length of growth and any ultimate sizes derived from 

it, becomes more critical as reserve-growth estimates are 

made over long time frames. The USGS incorporated this 

method into its domestic assessments starting in 1975 (Mast 

and Dingler, 1975) and used it with slight modifications 

afterwards.

A variation of the age-based growth concept was 

described by Attanasi and Root (1994) through the use of 

a monotone growth function. This method is similar to the 

Arrington-style of assembling the data but utilizes a custom 

algorithm to fit the running rate of growth data. Attanasi and 

Root (1994) also identified subgroups within the data labeled 

as “outliers.” These outliers were characterized as large heavyoil fields and old low-permeability gas fields whose reserve 

growth was six times faster than the common fields. These 

fields were located by comparing an individual field to an 

initial regression of all the data and labeling those outside that 

average regression “outliers.” This average initial regression 

was based on field ultimate-recovery-size data from 1977 

to 1991.

The monotone function became the method for 

calculating reserve-growth projections for USGS domestic 

assessments in 1995 (Gautier and others, 1996) and international assessments (Schmoker and Klett, 2000). Schmoker 

and Klett (2000) enumerated “formidable” difficulties in 

estimating potential future reserve growth. Included in their 

analysis was documentation of their reasoning for how this 

method may overestimate or underestimate the actual reserve 

growth. Based on the potential size of this growth, as well as 

the uncertainty in its volumetric size, their conclusion was that 

no world-level assessment could be complete without providing a reserve-growth estimate.

Two other age-based methods have also been used to 

project potential growth after the publication of the USGS 

world energy assessment results (U.S. Geological Survey 

World Energy Assessment Team, 2000). One is the modified 

Arrington approach utilized by Verma (2005) for the United 

States, Verma and Henry (2004) for Saskatchewan, Verma and 

Ulmishek (2003) for the West Siberian Basin, and Verma and 

others (2001) for the Volga-Ural Province. This method differs 

from the original Arrington method primarily by making a 

best-fit to the cumulative of the running rate of growth rather 

than the running rate itself. It is similar to Hubbert’s (1967) 

method in that growth has been captured in a single equation 

best-fit to the cumulative growth curve. It is dissimilar in that 

it does not incorporate an asymptote in the equation. This bestfit to the cumulative curve is also similar to the hyperbolic fit 

used to estimate potential growth on onshore Federal lands by 

the Environmental Policy and Conservation Act report (EPCA) 

(U.S. Departments of Interior, Agriculture, and Energy, 2008). 

It was used on relatively small groups of data when compared 

to some of the national-scale studies completed previously and 

explicitly extends reserve-growth estimates to three centuries. 

The combination of this timespan and a hyperbolic fit also 

implies that reserve growth is seemingly endless and may even 

be projected beyond the three centuries already used.

After the Attanasi and Root (1994) results were published, concerns were raised about the information and 

conclusions, as well as suggestions that additional study was 

warranted. The best example available of these concerns 

within a single study was given by Morehouse (1997) of the 

Energy Information Agency (EIA) who posed questions and 

presented comments that directly influenced the direction of 

the present investigation. Following Morehouse (1997) these 

concerns are as follows:
Reserve-Growth Profile 3

1. Multiple types of differently formulated but similar curves 

could be fit to the existing data with “little objective 

assurance that the results are either significantly unique or 

even appropriate.” 

2. Due to inherent data limitations, including a high variance

among what was considered “good” data, statistical 

smoothing was required to render the data suitable for 

analytical use.

3. Causal relations, particularly those of interest to a geologist, were “deeply buried” within the datasets with no 

apparent ability to subset the data appropriately.

4. Only a single study had been done that included both the 

time component of reserve growth and drilling activity 

assumed necessary to create that growth.

5. There are questions related to data applicability because 

of the perceived differences between large and small 

fields. This comment appears to extend beyond the outliers noticed in the work of Attanasi and Root (1994) to the 

size of fields in general.

Field groups of the North Sea were analyzed in a study 

completed by Sem and Ellerman (1999) that was designed 

to examine reserve growth with respect to location, size, and 

discovery date in different sectors of the North Sea. This 

study is also one of the few to include an estimate of the total 

production generated from that reserve growth. As part of their 

conclusions, Sem and Ellerman (1999) expressed surprise that 

growth did not appear as expected in certain sizes of fields.

Klett (2003) in an investigation of reserve-growth 

models, observed that a list of assumptions was made during 

nearly all projections of reserve growth. He also (1) summarized models of reserve growth linked to closely related 

factors, such as economic conditions, geologic characteristics, 

and engineering practices and (2) suggested that reservegrowth models might be improved, stating “The relative 

importance of reservoir properties, trapping mechanisms, oil 

and gas characteristics, and other geological factors, oil and 

gas recoverability, commodity price, drilling activity, development of new technologies, and development of infrastructure, 

such as platforms and pipelines, must be identified to fully 

characterize and quantify the controls on reserve growth. Such 

studies can best be done in those few areas of the world where 

development is advanced and fields, resources, technology, 

and data are abundant.”

Tennyson (2005) studied some of the California oil 

fields originally labeled as outliers by Attanasi and Root 

(1994) and appeared to have concerns similar to item 

number 1 listed above, stating that “Without at least a qualitative understanding of the factors responsible for the late 

growth in these old fields, future assessments risk continued 

imprecise prediction of additions to reserves in this important 

region, along with perhaps undue influence on other regions 

stemming from failure to isolate factors peculiar to California” 

(Tennyson, 2005, p. 1). Although the comment itself is specific 

to the California oil field outliers, it is possible that the same 

concept might apply to other areas as well.

The most common assumption in studies of reserve 

growth is that there is an overall age dependency allowing 

sequential projections of the aggregate data. This assumption, 

which could also be referred to as “the future will look like 

the past,” influences not only how reserve growth is thought 

about, studied, and tested, but how its effects are extrapolated.

A more recent concept is that of reserve-growth “outliers,” a term used to describe fields that do not behave in an 

expected manner. Reasonable questions have been raised as 

to the nature and effect of these “outliers” and their relation 

to the majority of fields. A study of these outliers has led to 

comments questioning the very methods used to identify these 

particular field groups in the first place. The present study was 

designed to investigate these types of questions and to determine what, if any, implications or guidance could be derived 

from the results, including (1) defining a new profile-based 

definition of reserve growth, (2) providing individual fieldlevel examples, and (3) an in-depth examination of the way 

reserve-growth information is aggregated.

Reserve-Growth Profile

Reserve growth is generally measured in terms of volume 

or percentages. To some extent the Arrington-style calculation of “running rate of growth” is a combination of both. 

The problem with these types of comparisons is that they are 

frame-of-reference specific and make it difficult to compare 

results relative to one another. A volumetric comparison or 

ranking will not yield the same result as a percentage comparison or ranking. For example, assume that (1) there are two oil 

fields, one with an estimated ultimate recovery of 100 million 

barrels and the other with 1 million barrels; and (2) the larger 

field grows by 1 million barrels over a 10-year time span 

(1-percent growth) and the other by 0.1 million barrels over 

the same time span (10-percent growth). Either field can now 

demonstrate larger reserve growth than the other.

In order to minimize this type of comparative confusion, 

a signature or profile of reserve growth was created and is 

referred to in this study as the production replacement ratio 

(PRR). Sem and Ellerman (1999) touched briefly on the basis 

for this type of reserve-growth signature by stating “When 

reserves are appreciating at 2–3% of total reserves and depletion is occurring at similar rates, production is being replaced. 

The result is a more or less constant level of inventory.” This 

concept of Sem and Ellerman (1999) is referred to in this 

study as the stable-inventory profile of reserve growth. 

The understanding of reserve growth can be improved by 

incorporating this type of age- and size-independent profile. 

The profile can be used to locate fields displaying present-day 

or past reserve-growth behavior and compare those fields with 
4 Reserve Growth of Oil and Gas Fields—Investigations and Applications

other growing or nongrowing fields regardless of field size and 

age. The comparison between consistently growing fields with 

all others will allow a detailed examination and quantification 

of the actual causes of reserve growth.

Production Replacement Ratio

Production replacement ratio is the means by which the 

stable-inventory profile can be identified and the strength of 

the profile quantified. It can be described as the difference in 

estimated ultimate field size between any two points in time 

divided by the cumulative production over that same period of 

time. If P1 equals cumulative production at time 1, P2 equals 

cumulative production at time 2, KR1 equals the estimated 

ultimate field size at time 1, and KR2 equals the estimated 

ultimate field size at time 2, then the PRR = (KR2–KR1)/

(P2–P1). The PRR is dimensionless with respect to absolute 

barrels and equal to 1 when a field has achieved the stableinventory-profile condition described by Sem and Ellerman 

(1999). This profile of PRR=1, although sustainable over long 

periods of time, cannot be infinitely maintained, because all 

fields have an upper limit bounded by their geology. As the 

PRR decreases toward 0, progressively smaller amounts of 

production are being replaced by growth in estimated ultimate 

field size. A PRR of 0 means that reserve growth of the field is 

zero. When PRR is negative, the field is actually shrinking in 

ultimate size for every unit of oil or gas produced. The PRR 

can be calculated over the entire history of a field or for just 

a portion of it. This subdividing of the field’s lifespan can be 

used to determine the time frame when changes in reservegrowth behavior took place or if reserve growth for a field has 

ceased.

Described another way, a strong reserve-growth profile 

exists when the known recoverable size of a field remains 

stable with respect to gains in cumulative production over 

the same period of time. A field’s known recoverable size is 

the sum of its cumulative production and estimated remaining recoverable volumes over the entire life of the field. 

This change in known recoverable size with respect to time 

is the most common measure of reserve growth. Figure 1 is 

an example of this effect. The Coalinga oil field in the San 

Joaquin Basin of California had produced approximately 

406,059,000 barrels by 1945 and 906,373,000 barrels by 

2005. During that same period of time, estimates of its known 

recovery had grown from 510,009,000 barrels to 969,890,000 

barrels. The PRR for this oilfield spanning the referenced 

time frame is (969,890,000–510,009,000)/(906,373,000–

406,059,000) = 0.92. For each barrel of oil produced across 

Figure 1. Coalinga oil field cumulative production, estimated ultimate recovery, and production replacement ratio (PRR) with 

respect to time. Unpublished data courtesy of M.E. Tennyson, U.S. Geological Survey.

Cumulative production

EXPLANATION

Estimated ultimate field size

1 Year PRR

5 Year PRR

Thousand barrels of oil

2005

Production replacement ratio

1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000

Year

1,000,000

800,000

600,000

400,000

200,000

0

12

10

8

6

4

2

0

−2
Reserve-Growth Profile 5

this time frame, 0.92 barrel was “discovered” in the field and 

added to its known recovery. Coalinga is therefore a relatively 

strong example of reserve growth at the field level by this 

measure. PRRs are included in figure 1 for single-year changes 

as well as 5-year changes for reference.

Figure 2 shows the Mount Poso oil field in the San 

Joaquin Basin of California in the same format as figure 1. 

Table 1 demonstrates how using the PRR over intermediate 

periods of time can be used to identify growth periods during 

the life of a given field. PRRs for this field are also included in 

figure 2 for single-year changes as well as 5-year changes.

Using these two fields as examples, it would be reasonable to state that both fields have demonstrated strong reserve 

growth in the past. However, Coalinga was able to maintain 

that growth consistently through the year 1990, but Mount 

Poso did not. Since 1985 Mount Poso has shown a profile 

related to reserve shrinkage rather than growth, whereas 

Coalinga has shown a reduction in its reserve-growth profile 

since 1990. The current PRR profile does not preclude either 

field from going through another growth period, but based on 

their PRR profiles, both fields appear to be tapering off from 

past high-growth periods. Factors that might activate another 

round of growth are the same factors that are assumed to drive 

reserve growth in the first place, such as better economics, 

new production technologies, or revisions and extensions 

(field size or new pools) of the field. These possible futuregrowth scenarios are unlikely to be predictable in a statistical manner at the field level without substantial geologic or 

engineering insight.

One characteristic of note is that the PRR is 0 for all 

fields prior to the onset of production. Unlike an Arringtonstyle of assembly based on discovery date, the PRR cannot 

identify growth until initial production and field-size estimates 

are established. As has been noted by other authors (for example, Forbes and Zampelli, 2009; Verma and Ulmishek, 2003), 

the results of an Arrington-style of assembly are different and 

are sensitive to the starting position of the data assembly. 

The advantages of including this profile of reserve 

growth with other measures of volume and percentage can be 

substantial. The PRR identifies the historical profile of growth 

irrespective of field percentage or volume growth, overall field 

size, or age. It can be tailored to the length and specificity of 

the production and known recoverability information and can 

be used to identify anomalous fields for a more detailed investigation of why reserve growth did, or did not, happen.

Figure 2. Mount Poso oil field cumulative production, estimated ultimate recovery, and production replacement ratio (PRR) 

with respect to time. Unpublished data courtesy of M.E. Tennyson, U.S. Geological Survey.

Cumulative production

Estimated ultimate field size

1 Year PRR

5 Year PRR

EXPLANATION

Production replacement ratio

Thousand barrels of oil

1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Year

400,000

350,000

300,000

150,000

50,000

0

12

10

8

6

4

2

0

−2

250,000

200,000

100,000
6 Reserve Growth of Oil and Gas Fields—Investigations and Applications

Data and Analysis

Disaggregating a Single Age-Group Pair

An integral part of this study was an examination of 

the Arrington-style of assembly and the data within it. This 

included examining the combinations of fields used to calculate annual growth factors (AGF) across large datasets and 

looking for common elements. AGFs are the fractional change 

in known recovery size from the same group of fields between 

one year and the next. To demonstrate this technique, the NRG 

Associates (2008) database was used to assemble the data 

in a similar fashion to Verma’s (2005) example; table 2 is a 

reproduction of Verma’s table for use as a reference for this 

form of assembly. These types of sum and percentage calculations are common to the Arrington-style of data assembly and 

are explained in detail by Attanasi and Root (1994) and Verma 

(2005). Continuous accumulations as assessed by the USGS 

were excluded from this dataset to the extent it was possible to 

accurately identify them. Determination of an oil field versus a 

gas field was done on the basis of gas to oil ratios (GOR); that 

is, a field having a cumulative GOR of less than 20,000 standard cubic feet of gas per barrel of oil was designated an oil 

field, whereas a field with a GOR greater than 20,000 standard 

cubic feet of gas per barrel of oil was considered a gas field.

Two measures of aggregate reserve growth will be used 

when discussing the reserve growth of a group of fields: (1) 

gross reserve growth is the sum of only increasing growth for 

a group of fields and (2) net reserve growth is the sum of all 

growth, increasing or decreasing. This distinction is necessary 

because it is possible to have large volumetric reserve growth 

yet have zero, or less, net reserve growth. Gross reserve 

growth is therefore the most useful to calculate the percentage 

contribution of the total growth from individual fields without shrinking fields masking or exaggerating these types of 

comparisons.

For the purposes of illustration, we are going to start 

by examining all the data used to calculate the AGF for a 

single age-group pair of the Arrington-style assembly. As an 

example, table 2 contains (1) a single age-group pair contained 

in the sums of the diagonally highlighted and dashed boxes 

or (2) nineteen age-group pairs if you consider the difference 

between each highlighted and dashed box individually. In 

either case, the percentage difference is calculated between the 

pairs (be it one or 19) and then an algorithm is used to fit the 

results. This process is repeated for the next age-group pair(s) 

with a slightly different combination of fields and continues 

until there is insufficient data to continue.

For an initial examination, we are going to keep all field 

information disaggregated and examine all fields within one 

of these age-group pairs at a known distance in time from the 

date of discovery, or start of production, and calculate some 

basic information on that pair. The age-group pair selected 

is for conventional oil fields in the United States, utilizes the 

normalized timeframe of 60 and 61 years since discovery, and 

uses the data at the field level from the NRG Associates (2008) 

database. The discovery years in this group range from 1922 

to 1945 and consist of 1,739 oil fields. Figure 3 is a histogram 

of the estimated known recovery sizes at year 61. The total 

known recovery volume contained in the 61-year age-group 

pair is 73,074,732,000 barrels and the total known recovery 

volume in the year 61 age group total is 73,254,973,000 barrels. The AGF for this change is 1.0025. Of the 1,739 fields 

in the group, 884 increased their estimated ultimate size by 

351,803,000 barrels, 353 decreased by 171,562,000 barrels

and 502 had no change; the net volumetric change was 

180,241,000 barrels. The top ten growing fields contained 

33.3 percent of the gross field growth and 65.1 percent of the 

net growth for the entire age-group pair. These ten fields contained 6.2 percent of the total estimated known recovery in the 

fields contained within this age-group-pair example.

This heavy concentration of growth (33.3-percent gross 

or 65.1-percent net) in a fraction of the number of fields 

available (0.57 percent) shows that the possibility exists for 

a small number of fields to dominate individual AGFs within 

the Arrington-style of data assembly. Grace (2006) noted that 

field-growth results in his study appeared lognormally distributed (without describing any parameters for this lognormal 

distribution). Attanasi and Root (1994) noted the presence of 

outliers within the U.S. oil field data using the Oil and Gas 

Integrated Field File (OGIFF) from the EIA. Further attention on the implications of skewed reserve-growth results is 

warranted if the final result appears overly dependent on such 

a small number of fields. The Arrington-style of assembly uses 

the data from a single field across as many age-group pairs 

as the data permit. It is therefore possible that a single field 

in one age-group pair can heavily influence other age-group 

pairs. This can be described as a stretching effect in the sense 

that a single field’s estimated recoverable changes can be used 

in a large number of age-group pairs, effectively stretching its 

reserve growth influence across a wide swath of an Arringtonstyle assembly. This stretching effect has the potential for a 

single influential field, or small group of influential fields, to 

have a corresponding influential effect across a large number 

of AGF calculations. To determine if this type of behavior 

exists across the entire spectrum of age-group pairs, it is necessary to expand the analysis to all fields in all age-group pairs 

and examine them in relation to each other. 

Year

Cumulative oil 

production

Ultimate oil 

recovery estimate PRR

 1955 113,430,000 140,000,000 ----

 1980 203,242,000 296,015,000 1.74

 2005 297,613,000 313,777,000 0.19

Table 1. Mount Poso oil field production replacement ratio (PRR) 

calculation over two different time spans.
Table 2. Known petroleum volumes (KPVs) for conterminous United States, excluding Federal offshore and continuous fields. From Verma (2005.)[KPVs in million barrels. Data source: 1977–1996 Oil and Gas Integrated Field File. AGF, annual growth factor; D. Year, discovery year]
8 Reserve Growth of Oil and Gas Fields—Investigations and Applications

Disaggregating All Age-Group Pairs

Figure 4 is a breakdown of all conventional oil fields 

meeting the same criteria as listed previously except for all 

age-group pairs rather than just one. Figure 5 uses the same 

criteria and shows the average net reserve growth per field per 

age-group pair since discovery and the dead-field ratio. The 

dead-field ratio is the percentage of fields in which the cumulative production is equal to or nearly equals the estimated 

ultimate field size. This was calculated to determine at what 

point fields become uneconomic and are shut down.

Figures 4 and 5 demonstrate that the average size of 

older fields is larger than the newer oil fields. The dead-field 

ratio has an inflection point as data transitions between older 

and newer oil fields. Average volumetric field growth in the 

older discovered fields is anomalously large compared to the 

younger oil fields. These differences justify a further investigation into what appears to be different distributions of results 

contained within the same dataset. 

The discovery of large fields early in the discovery 

history of a particular area has been documented previously 

by Arps and Roberts (1958). Of note is that fields in the 85- 

to 105-year age groups show higher growth per field than 

younger age groups, as much as two orders of magnitude. 

The dead-field ratio climbs steadily until the maximum field 

discovery age group is reached, at which point it declines to 

reflect that these larger and higher growth fields remain in 

production at higher percentages than smaller fields. After the 

105-year age group, the dead-field ratio grows rapidly as the 

overall average age-group growth drops. The ratio dropping 

to zero at approximately the 130-year age group is caused by 

data scarcity; a single producing field remaining in a dataset 

comprised of one field signifies a zero-percent dead-field ratio. 

Also note that the placement of this above-average reserve 

growth correlates with the age range of the outliers noted by 

Attanasi and Root (1994), given an additional 15 years of 

data. These outliers were referenced as being California fields 

with relatively low API gravities, fitting into the data stream at 

approximately the 70- to 80-year age group. The OGIFF data 

used by Attanasi and Root (1994) was vintage 1991, and the 

data used in this study was vintage 2006, placing those outliers 

in the 85- to 95-year age group.

To determine the approximate number of fields required 

to reach some arbitrary amount of gross reserve growth in 

each age-group pair, all fields were arranged from highest to 

lowest reserve growth. These fields, from largest to smallest, 

were then counted and their reserve growth summed until 

75 percent of the total growth in each age-group pair was 

accounted for. The estimated ultimate recoverable size of these 

fields was also summed, and this information is displayed in 

figure 6. Two things affect the percent of gross growth line 

in figure 6: data density and a shrinking absolute number 

of fields with large effects on age-group pairs past year 85. 

Except for early and late age-group pairs, less than 10 percent 

of the fields (and commonly less than 5 percent) in any given 

age-group pair are required to achieve 75 percent of the gross 

Figure 3. Estimated known recoverable oil for conventional oil fields 61 years after discovery year.

Estimated recoverable oil field sizes (thousand barrels of oil)

Frequency-number of fields

300

250

200

150

100

50

0

250

500

1,000

2,000

4,000

8,000

16,000

32,000

64,000

128,000

512,000

1,024,000

2,048,000

4,096,000

8,192,000

More

256,000
Data and Analysis 9

reserve growth. The size of their aggregate estimated known 

recovery within the age-group pair is approximately 25 percent. Stated another way, less than 10 percent of the fields in 

every age-group pair, encompassing 25 percent of the known 

recoverable size of the age-group pair, are responsible for 

75 percent of the gross volumetric reserve growth. 

Based on the contribution of this limited number of fields 

generating a majority of the reserve growth in each age-group 

pair, a definition for “major” reserve-growth field was constructed. A “major” field is one generating 2 percent or more 

of the gross reserve growth in any age-group pair. If the gross 

reserve growth of the major fields was subtracted out of the 

total gross growth, it would reveal what contribution toward 

net reserve growth the remainder of the nonmajor fields would 

generate.

Figure 4. Average conventional oil field size, volume changes, and field counts for all age groups.

Figure 5. Average reserve growth in conventional oil fields per field per age-group pair including percentage of 

fields where cumulative production equals estimated known recovery.

Growth per field

Dead-field ratio

EXPLANATION

Thousand barrels of oil

Dead-field ratio

Age group (years since discovery)

3,500

3,000

2,500

2,000

1,500

1,000

500

0

−500

−1,000

−1,500

100%

90%

80%

70%

60%

50%

40%

30%

20%

10%

0%

0 20 40 60 80 100 120 140

Average net field size

Volume change

Field count

EXPLANATION

Thousand barrels of oil

Field count

Age group (years since discovery)

900,000

800,000

700,000

600,000

500,000

400,000

300,000

200,000

100,000

–100,000

0

0 20 40 60 80 100 120 140

5,000

4,500

4,000

3,500

3,000

2,500

2,000

1,500

1,000

500

0
10 Reserve Growth of Oil and Gas Fields—Investigations and Applications

Figure 7 shows that if the major fields are removed from 

the data, the contribution of the remaining fields falls to nearly 

zero, and in many cases the result is a decrease in overall net 

growth. Reserve growth effectively disappears for all but a 

minority of fields shortly after discovery. By comparing figure 

7 to figure 6, it becomes obvious that (1) the reserve growth 

built into an Arrington-style assembly is created by less than 

10 percent of the fields in most cases, and (2) with the removal 

of this 10 percent, there is little or no growth left in the 

remainder.

To better determine how only a few fields might have a 

substantial impact on gross reserve growth in each age-group 

pair, the largest growing field for each age-group pair was 

used to generate figure 8. As the data density thins toward 

age-group pair 100, it is reasonable to expect that a single, old 

producing field might dominate the age-group pair. As demonstrated in figure 8, nearly 20 percent of the gross reserve 

growth is dependent on a single oil field after age-group pair 

65 and tends to grow through the end of the period for which 

data are available. Until age-group pair 85, the percentage 

of the estimated recoverable sum upon which this growth is 

based is less than 5 percent. 

Figure 9 is constructed in a manner similar to figure 8, 

except that the top five growing oil fields are ordered sequentially. By age-group pair 100, nearly all the gross growth 

can be attributed to the top five fields. By age-group pair 50, 

these top five fields are accounting for a consistent 35 percent 

of gross reserve growth. Figure 4 shows that age-group pair 

50 has approximately 3,500 fields contained within it. This 

calculates to approximately 0.14 percent of the fields generating 35 percent or more of the gross volumetric growth in the 

later years of this particular Arrington-style assembly.

Figure 10 was constructed to examine the dependency 

of total reserve growth on all major reserve growth fields 

across all age-group pairs. The number of oil fields meeting 

this criterion rarely exceeds ten; yet starting at age-group pair 

50, the volumetric contribution of this group grows quickly. 

The effect of data density on the higher age groups is also 

more obvious as the major field count drops to a few, at which 

point nearly all reserve growth is based in that age-group pair. 

Figure 11 is the same chart assembled from all fields that did 

not qualify as major contributors and shows the net remaining 

growth. By age-group 65, the reserve growth of all remaining 

fields is diminishing, and by age-group 95, there are still 120 

fields that are consistently acting as a counterbalance on the 

growing reserve growth in the 3 or 4 major-contributor fields. 

For a majority of the 100-year oil fields, reserve growth has 

ceased.

It is apparent that a relatively small number or small percentage of oil fields are capable of providing reserve-growth 

volumes out of proportion to what their size or numbers might 

indicate. Attanasi and Root (1994) mentioned California 

heavy-oil fields as providing a late-growth spurt to reserve 

growth, and Tennyson (2005) specifically dealt with some of 

these California oil fields in the San Joaquin Basin. It would 

be reasonable to speculate that if these fields were outliers, 

their imprint would be revealed in the appropriate age-group 

pairs. 

Figure 6. Number and size of oil fields required to generate 75 percent of gross field growth in each 

age-group pair.

Age group (years since discovery)

Major field percent of total fields

Percent of gross growth

Major field percent of known estimated recoverable in age group

EXPLANATION

100

90

80

70

60

50

40

30

20

10

0

Percent

0 10 20 30 40 50 60 70 80 90 100 110 120
Data and Analysis 11

Figure 7. Volumetric contribution of gross reserve growth for major and nonmajor conventional oil fields in 

each age group. Major fields are those that contribute more than two percent of the gross reserve growth in 

an age-group pair.

Figure 8. Percentage of gross reserve growth and total known recovery of the single largest growing oil 

field in each age-group pair.

Nonmajor field reserve growth

Major field growth

EXPLANATION

500,000

400,000

300,000

200,000

100,000

0

–100,000

–200,000

0 20 40 60 80 100 120

Thousand barrels of oil

Age group (years since discovery)

100

90

80

70

60

50

40

30

20

10

0

0 10 20 30 40 50 60 70 80 90 100 110 120

Percentage of known recovery of total

Percentage of gross reserve growth

EXPLANATION

Age group (years since discovery)

Percent gross reserve growth

and estimated known recovery
12 Reserve Growth of Oil and Gas Fields—Investigations and Applications

Figure 10. Field counts and gross reserve growth of major oil fields. A major field is any field that contains 

more than two percent of the gross growth in a single age group.

Figure 9. Gross reserve growth of five largest growing oil fields in each age group.

Top 1 field

Top 2 fields

Top 3 fields

Top 4 fields

Top 5 fields

EXPLANATION

100

90

80

70

60

50

40

30

20

10

0

0 10 20 30 40 50 60 70 80 90 100 110 120

Age group (years since discovery)

Percent gross reserve growth Field count

Gross growth

Field count

EXPLANATION

Percent of gross growth from major oil fields

50

45

40

35

30

25

20

15

10

5

0

100

90

80

70

60

50

40

30

20

10

0

0 10 20 30 40 50 60 70 80 90 100 110 120

Age group (years since discovery)
Data and Analysis 13

Figure 12 shows the amount of net reserve growth of 

each age-group pair for all fields in the San Joaquin Basin. 

Starting at about the 70-year age group, the effect of the 

San Joaquin oil fields begins at 20 to 40 percent of the net 

growth, and by year 85 it increases to 80 percent or more 

through age-group pair 110. Net reserve growth larger than 

100 percent indicates that the sum of the growth of all other 

fields is negative (shrinkage) and is counterbalancing the 

growth shown. At approximately the same point where the 

San Joaquin reserve growth begins to increase, the volumeweighted API gravity of all reserve growth in the United 

States begins to decrease reflecting the nature of the heavier 

API-gravity oils in this basin.

The examples presented in foregoing discussions have all 

focused on conventional oil fields. The possibility exists that 

conventional gas fields have a completely different profile of 

growth or shrinkage, or have different dependencies on differing numbers of fields. Figures 13 and 14 are similar to figures 

10 and 11 in that they are both based on the concept of major 

contributors to reserve growth (fields producing greater than 

two percent of the gross growth within any given age-group 

pair), except that figures 13 and 14 are based on all conventional natural gas fields in the NRG Associates (2008) database. Reserve growth in natural gas fields becomes dependent 

on fewer fields within each age-group pair in less time than oil 

fields. Also net reserve growth for the nonmajor contributors 

reaches zero and becomes negative more consistently and 

quickly, so that by age-group 70, reserve growth on all but 

the major contributors has effectively ceased. At that time, 

the major contributors are supplying at least 75 percent of the 

gross growth and are increasing rapidly afterwards.

So far this analysis has concentrated on quantifying the 

effect that a limited number of fields has within each agegroup pair. However, any one field within an Arrington-style 

assembly has the potential to affect each age-group pair that 

it resides within. Potentially a single field could have enough 

reserve growth within an age-group pair to make any function

derived from the Arrington-style of assembly completely 

dependent on that field. Figure 15 is a plot of 13 fields, ranging through age-group pairs 48 to 126, and their individual and 

combined contributions to the gross reserve growth in each 

pair. The overall field count in each age group is also included 

because there are less data for the older age groups. 

This disaggregation of the age-group pairs reveals that 

gross reserve growth in many age-group pairs is dependent on 

a small number of fields, regardless of the exact field combinations composing any particular age-group pair. The older 

the field discovery date the more the age-group pairs become 

dependent on relatively smaller numbers of fields for the gross 

reserve growth in any age-group pair because other fields 

cease growing. Further, the Arrington-style of assembly allows 

this effect to continue across other age-group pairs, so any 

Figure 11. Field counts and net reserve growth of nonmajor oil fields. Nonmajor oil fields are all of those 

not included in figure 10.

Age group (years since discovery)

Field count

Percent of net growth from nonmajor oil fields

5,000

4,500

4,000

3,500

3,000

2,500

2,000

1,500

1,000

500

0

100

90

80

70

60

50

40

30

20

10

0

–10

–20

–30

–40

–50

–60

–70

–80

–90

–100

Net reserve growth Field count

EXPLANATION

0 10 20 30 40 50 60 70 80 90 100 110 120
14 Reserve Growth of Oil and Gas Fields—Investigations and Applications

Figure 12. Net reserve growth from San Joaquin Basin oil fields and volumetrically weighted reserve 

growth by American Petroleum Institute (API) oil gravity. Net reserve growth above 100 percent indicates 

offsetting reserve shrinks in the same age-group pair.

Figure 13. Field counts and gross reserve growth of major gas fields. A major gas field is any field that 

contains more than two percent of the gross growth in a single age group.

Age group (years since discovery)

Net reserve growth

0

0 10 20 30 40 50 60 70 80 90 100 110 120 130

10

20

30

40

50

60

70

80

90

100

–20

–10

–30

–40

–50

–60

–70

–80

–90

–100

Net reserve growth

API gravity weighted by reserve volume

EXPLANATION

45

50

55

60

65

70

75

80

85

90

95

100

40

35

30

25

20

15

10

5

0

Volume weighted API gravity

Age group (years since discovery)

Field count

Gross reservoir growth

Field count

EXPLANATION

0 10 20 30 40 50 60 70 80 90 100

40

35

30

25

20

15

10

5

0

100

90

80

70

60

50

40

30

20

10

0

Percent of gross growth from major gas fields
Data and Analysis 15

Figure 14. Field counts and net reserve growth of nonmajor gas fields. Nonmajor gas fields are all of those not 

included in figure 13. 

Figure 15. Gross reserve growth of oil from a few fields across multiple age-group pairs.

Age group (years since discovery)

Field count

1,000

900

800

700

600

500

400

300

200

100

0

Wasson area

Oil fields

Slaughter-Levelland

Sho-Vel-Tum

Seminole

Midway-Sunset

Lost Hills

Kern River

Field count

Hobbs

Elk Hills

Coalinga

Cymric

Brea-Olinda

Belridge South

EXPLANATION

100

90

80

70

60

50

40

30

20

10

0

45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130

Percentage gross growth

Age group (years since discovery)

Field count

Percent of net growth from nonmajor gas fields

Net reserve growth

Field count

EXPLANATION

3,000

2,500

2,000

1,500

1,000

500

0

100

90

80

70

60

50

40

30

20

10

–10

–20

–30

–40

–50

–60

–70

–80

–90

–100

0

0 10 20 30 40 50 60 70 80 90 100
16 Reserve Growth of Oil and Gas Fields—Investigations and Applications

one field can actually dominate as many age-group pairs as 

are represented in the data for that field. In this study, the data 

strings are for 24 years, so that number minus one would be 

the maximum number of age-group pairs (23) any single field 

could affect.

Natural Tendencies of the Arrington-Style 

Assembly

The Arrington-style assembly for reserve growth is a 

specific combination of (1) volumetric weighting, (2) conversion to a percentage change for a particular group, and (3) 

some type of best fit to the resulting percentage changes across 

the entire timespan. This construction uses data of different 

time periods from a discovery date to assemble a long string 

of AGFs from shorter data strings. Arrington’s method can be 

used to construct these AGFs for a single long string of data 

providing the same sort of “running rate of growth” configuration without best-fitting multiple data pairs at every age step in 

the calculation.

Table 3 consists of the discovery-year age groups for 

the first 23 years of an actual age-group sequence of oil fields 

from the NRG Associates (2008) database. Starting with year 

24, the values listed are extrapolations based on a 2-percent 

exponential decline in the changes in known recovery. This 

extrapolation is illustrative of some hypothetical measure of 

future growth for this group of fields used in this example. The 

data from the NRG Associates (2008) database are used for 

calculations of the AGFs (column 5) and cumulative growth 

functions (CGFs) (column 6). Column 7 is based on the 

assumption that a field beginning from the year of discovery 

has a stable-inventory profile that accounts for 0.6 percent 

of the first-year growth in known recoverable volumes. The 

difference between this field and all the others in the group 

is that it will consistently grow this amount year by year in 

the manner of a stable-inventory profile. Table 3 shows the 

increasing relative value of this type of growth profile extrapolated over 100 years. A single field maintaining steady growth 

can increase from 0.6 percent of the growth in a given age 

group to more than 40 percent in 100 years.

Though this simulated stable inventory field has a small 

initial starting point and minor but consistent growth year after 

year, it should be noted that this type of profile (1) establishes 

an ever-increasing denominator in an Arrington-style assembly and (2) creates a natural decay function such that even a 

small amount of static growth can dominate a given group in 

a reasonable amount of time. This effect can best be explained 

by the following statement: The sum of change in multiple, 

nonlinearly declining datasets can become dominated by 

an individual string given enough time and a slightly lower 

decline rate between it and the others. Thought of another way, 

this is an example of negative compounding interest. Figure 16

is a graphical representation of this basic idea. Given nine 

exponential declines of varying rates (in black) and one with 

a smaller decline (in red), the one with the smaller decline 

can dominate the changes of the entire group given adequate 

time. The speed required for this domination to present itself 

depends on the smallest decline’s relative starting position and 

the difference in decline rate between itself and the next 

closest decline. If all declines are similar, as they might be 

with a small group of fields all operated in the same manner by 

the same operator, this effect may never manifest itself. Given 

sufficient time, the dependency of the sum of the change on 

the single anomaly will be complete. Figure 17 shows the rate 

at which the smallest decline in the example dominates the 

sum of the changes in the group. In the case presented, the 

decline rate difference between the smallest decline and the 

rest of the group is two-thirds less than the mean of the others. 

Even much smaller differences in decline rate between the 

smallest decline and the main group can make a difference.

The best way to display the rapidity with which the 

dependency develops is to create a simple sensitivity analysis. 

An example, illustrated in figure 16, is for a group of declines 

varying from 10 to 20 percent per unit of time and with starting points ranging from 1,500- to 2,500-rate units at time zero. 

A rate unit in this case represents a rate in any consistent units. 

An additional hypothetical decline will vary from the mean 

decline of all others downward to one-eighth of its original 

value, and its initial starting point will be at least two-thirds 

lower than all others. Five simulations for decline rates of 

15.0, 10.0, 7.5, 5.0, and 2.5 percent were run at six different 

time points starting at time zero and continuing through 

100 time units. When the additional hypothetical decline is 

the same size as the mean of all other declines, there is no 

anomalous dependency on this hypothetical decline. As the 

difference between the hypothetical decline and the mean 

decline of the rest of the group widens, however, the hypothetical decline begins to dominate any sum of changes 

calculation. In the most extreme case, the hypothetical decline 

already represents a majority of the change somewhere 

between 25 and 50 time units. However, even a decline rate 

that is half of the mean of the rest of the group is enough for 

the single hypothetical decline to dominate the behavior of the 

group. 

The simulation results in figure 18 show how quickly 

an anomalous decline dominates a group based on differences in time and decline rates. The answers for each scenario 

are expressed as an envelope of probability to describe the 

uncertainty associated with how this particular Monte Carlo 

simulation was designed. Use of this type of presentation 

readily demonstrates that the size and effect of an anomalous 

decline is nonlinear in nature and has reasonable, but not 

extreme, uncertainty associated with each particular scenario. 

A summary statement for figure 18 might best be described as 

“He who declines the least wins.”

There is a related side effect to this issue as well. The 

sum of change in multiple nonlinear declines will tend to be 

hyperbolic until the smallest decline is responsible for all 

of the volumetric growth. As each decline asymptotically 

approaches zero, the absolute value of the change it provides 

to the total also approaches zero. Various individual declines 
Data and Analysis 17

approaching zero at different rates and times has the group 

appearance of an ever flattening decline, closely similar to a 

hyperbolic decline. If the final decline was to change its behavior at this point in time, the group behavior will mimic it.

This example is not meant to be directly representative 

of reserve growth but to be more of an illustration of how a 

particular nonlinear decline can come to dominate a particular 

group if given the time and difference in decline rate. Total 

growth in known recovery for a group ultimately declines with 

time, but the question of what that growth is predicated on 

within a particular type of data assembly is critical to building 

a more accurate means of estimating future reserve growth.

Figure 19 shows how a large number of these single 

discovery-year age groups grow from their discovery year 

to varying time periods based on the length of time of the 

data available. Growth during the first five years is relatively 

pronounced, and then there is a profile of slow but steady 

increases. Also noticeable is a trend toward smaller initial 

discovered volumes year after year. The fields represented in 

figure 19 are important because an Arrington-style of assembly 

would use this group to generate the early growth AGFs upon 

which all later AGFs would multiply against.

Once it becomes apparent that a small number of fields 

are actually the drivers of reserve growth within any particular 

age group, it is reasonable to explore how the removal of those 

fields would affect an Arrington-style assembly. Figure 20 is 

a plot showing changes in the AGFs for the top five oil fields 

in each age-group pair versus all other fields; it demonstrates 

how rapidly AGFs fall below 1 percent per annum without the 

inclusion of this particular minority of fields. Similar to what 

has been shown in figures 13 and 14, once the actual growing fields have been located and removed there is only minor 

growth in the remaining majority of fields. Figure 21 depicts 

Table 3. Single age-group sequence of known recovery change and related calculations.

Bold numbers are real data from NRG and Associates (2008) database; italic numbers are hypothetical extrapolations; MBBL, thousand barrels. 

(1) (2) (3) (4) (5) (6) (7) (8)

AGF

annual

growth factor

CGF

cumulative

growth factor

(MBBL) (MBBL) (MBBL) (MBBL) (Percent)

1 23,455 67,735 44,280 2.8879 2.8879 250 0.6

2 69,325 95,640 26,315 1.3796 3.9841 250 1.0

3 96,240 121,535 25,295 1.2628 5.0312 250 1.0

4 142,351 150,156 7,805 1.0548 5.3071 250 3.2

5 150,156 152,679 2,523 1.0168 5.3962 250 9.9

6 152,679 157,155 4,476 1.0293 5.5544 250 5.6

7 157,155 163,090 5,935 1.0378 5.7642 250 4.2

8 163,090 175,340 12,250 1.0751 6.1972 250 2.0

9 175,340 186,928 11,588 1.0661 6.6067 250 2.2

10 186,928 180,567 –6,361 0.9660 6.3819 250 –3.9

11 180,567 178,710 –1,857 0.9897 6.3163 250 –13.5

12 178,710 182,468 3,758 1.0210 6.4491 250 6.7

13 182,468 182,690 222 1.0012 6.4569 250 112.6

14 182,690 184,608 1,918 1.0105 6.5247 250 13.0

15 184,608 186,801 2,193 1.0119 6.6022 250 11.4

16 186,801 189,107 2,306 1.0123 6.6838 250 10.8

17 189,107 194,704 5,597 1.0296 6.8816 250 4.5

18 194,704 199,043 4,339 1.0223 7.0349 250 5.8

19 199,043 203,487 4,444 1.0223 7.1920 250 5.6

20 203,487 206,665 3,178 1.0156 7.3043 250 7.9

21 206,665 208,829 2,164 1.0105 7.3808 250 11.6

22 208,829 212,574 3,745 1.0179 7.5132 250 6.7

23 212,574 215,403 2,829 1.0133 7.6131 250 8.8

30 231,228 233,684 2,456 1.0106 8.2593 250 10.2

35 243,026 245,246 2,220 1.0091 8.6679 250 11.3

40 253,690 255,697 2,007 1.0079 9.0373 250 12.5

45 263,330 265,144 1,814 1.0069 9.3712 250 13.8

50 272,044 273,684 1,640 1.0060 9.6730 250 15.2

55 279,921 281,403 1,482 1.0053 9.9458 250 16.9

60 287,041 288,380 1,340 1.0047 10.1924 250 18.7

65 293,476 294,687 1,211 1.0041 10.4154 250 20.6

70 299,294 300,388 1,095 1.0037 10.6168 250 22.8

75 304,552 305,542 989 1.0032 10.7990 250 25.3

80 309,305 310,200 894 1.0029 10.9636 250 28.0

85 313,602 314,410 808 1.0026 11.1124 250 30.9

90 317,486 318,216 731 1.0023 11.2470 250 34.2

95 320,996 321,657 661 1.0021 11.3686 250 37.8

100 324,169 324,767 597 1.0018 11.4785 250 41.9

Percentage of growth

from stable inventory 

Age

group 

Known recoverable

year start 

Known recoverable

year end 

Change in known

recoverable 

Known recovery from

stable inventory 
18 Reserve Growth of Oil and Gas Fields—Investigations and Applications

Figure 16. Example of the interaction of nine nonlinear declines.

Figure 17. Annual fractional change of nine nonlinear declines and dependency of that answer on 

smallest decline.

3,000

2,500

2,000

1,500

1,000

500

0

0 4 8 12 16 20 26

Time change

Rate

Decline 1

Decline 2

Decline 3

Decline 4

Decline 5

Decline 6

Decline 7

Decline 8

Anomaly

EXPLANATION

Annual time change

Fractional change

Fractional change attributed to smallest decline

EXPLANATION

1.00

0.90

0.80

0.70

0.60

0.50

0.40

0.30

0.20

0.10

0.00

0 10 20 30 40 50 60 70 80 90 100

Fractional change
Data and Analysis 19

a similar relation when the top five gas fields are withdrawn 

from the overall data and are calculated separately versus 

all other fields, except that the early precipitous drop-off in 

initial growth is less pronounced. A cumulative growth curve 

(created by sequential multiplication of AGFs) constructed 

from either of these sets of AGFs for oil and gas (figs. 20 

and 21) tends to give a final cumulative answer of 4 to 7 for 

the smaller contributing fields and a multiplier of 10,000 to 

100,000 for the top five fields in both cases. It is not assumed 

that cumulative curves constructed from either of these AGFs 

are representative or comparative.

Conventional Versus Continuous Accumulations

If the potential exists for a type of growth profile to 

induce high levels of dependency into the Arrington-style 

of assembly, then the possibility must be considered that the 

same profile, generated through another means, could do the 

same. A key difference between conventional and continuous 

accumulations is the type of growth available. Conventional 

accumulations are discrete, and it is generally assumed that, 

once delineated, the field outlines do not substantially change. 

Continuous accumulations can be areally extensive and have 

varying well productivities. This situation can lead to sweet 

spots being developed over small areas, upon which the initial 

problems can be solved with respect to the best well-drilling, 

completion, and production design. Once refined, these techniques allow for development of less productive areas within 

the continuous accumulation and lead to a growth in the 

overall areal extent of the accumulation. Reserves then grow 

in proportion to the expanding size of the developed acreage, 

and there is the potential for extensive growth for long periods 

of time. Although the mechanism is different from how a 

conventional field grows, the reserve-growth profile displayed 

by these two different types of fields will be similar. Figure 22 

is an example of a continuous oil field in Texas displaying the 

sort of reserve-growth profile in conventional fields following 

the stable-inventory profile. The primary difference between 

this area and a conventional accumulation, such as South Belridge field in the San Joaquin Basin of California, is that the 

area of the continuous Texas oil field continues to grow in step 

with its cumulative production. South-Belridge, in contrast, 

has been relatively static in terms of the field’s areal extent.

Figure 18. Fractional effect on group behavior caused by the difference between group behavior and the single 

smallest decline within the group. Std. dev., standard deviation. Fractional effect Time 0/for given decline Time 10/for given decline Time 25/for given decline Time 50/for given decline Time 75/for given decline Time 10/for given decline Time 25/for given decline Time 50/for given decline Time 75/for given decline Time 100/for given decline Time 100/for given decline Time 0/for given decline Time 10/for given decline Time 25/for given decline Time 50/for given decline

Time 75/for given decline

Time 100/for given decline

Time 0/for given decline

Time 10/for given declineTime 25/for given declineTime 50/for given declineTime 75/for given decline

Time 100/for given decline

Time 0/for given decline

Time 10/for given declineTime 25/for given declineTime 50/for given declineTime 75/for given decline

Time 100/for given decline

Time 0/for given decline

Decline=0.15 Decline=0.10 Decline=0.075 Decline=0.05 Decline=0.025

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

−0.1

+/–1 std. dev.

1%–99%

Mean

EXPLANATION
20 Reserve Growth of Oil and Gas Fields—Investigations and Applications

Figure 19. Discovery-year groups with early histories of estimated ultimate recovery through time in U.S. conventional onshore 

and State waters.

Figure 20. Annual growth factors for top five oil fields in each age-group pair versus all others.

Year of estimate

Estimated known recoverable

(thousand barrels of oil)

10,000,000

1,000,000

100,000

10,000

1,000

100

1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006

EXPLANATION

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

40

38

36

34

32

30

28

26

24

22

20

18

16

14

12

10

 8

 6

 4

 2

 0

−2

0 10 20 30 40 50 60 70 80 90 100 110 120

Age group (years since discovery)

Annual growth factor as percent change per year

Annual growth factors for five top oil fields

Annual growth factors for all others

EXPLANATION
Data and Analysis 21

Figure 21. Annual growth factors for top five gas fields in each age-group pair versus all others.

Figure 22. Example of consistent reserve growth in an actual billion-barrel oil field in Texas. Annual growth factor as percent change per year

40

38

36

34

32

30

28

26

24

22

20

18

16

14

12

10

 8

 6

 4

 2

 0

−2

0 10 20 30 40 50 60 70 80 90

Age group (years since discovery)

Annual growth factors for five top oil fields

Annual growth factors for all others

EXPLANATION

Years since discovery

Known recovery and

cumulative production

30 35 40 45 50 55 60

EXPLANATION

Cumulative production

Estimated ultimate recovery
22 Reserve Growth of Oil and Gas Fields—Investigations and Applications

Continuous accumulations are recognized as being 

geologically distinct from conventional accumulations and are 

removed from the field-level data prior to the construction of 

discovery tables or any other reserve-growth calculations. If 

not removed they would induce the same dependency effects 

that a stable-inventory conventional field does.

Discussion

To a large extent, analysis of reserve growth is dependent 

on the timing of the analysis, for example, (1) the status of 

existing data, (2) when the fields were discovered in relation to 

when a key technology was invented and applied, and (3) the 

effect of the upward trend in real oil prices that began at the 

end of the 1960s on the economics of exploration and development. Snapshots of reserve growth across decades could lead 

to varying conclusions and assumptions.

Questions about the basic assumptions of reserve growth 

were already being discussed in the literature within a few 

years of the Attanasi and Root (1994) study; the best overall 

summary was by Morehouse (1997). Other concerns included 

the lack of age correlation of certain fields (Tennyson, 2005), 

the skewed distribution of reserve growth results (Grace, 

2006), a single-sentence description of the stable-inventory 

profile (Sem and Ellerman, 1999), and a proposal to concentrate on the geologic characteristics of the fields involved 

(Stanley, 2001). Individually these concerns were insufficient 

to justify fundamental modifications of what appears to be 

a reasonable and time-tested statistical method to estimate 

reserve growth. Woven into a greater context and tested 

against a dataset of similar scope and more recent data than 

that used in the Attanasi and Root (1994) study, these assumptions of reasonableness may not apply.

General Behavior of Arrington-Style Assemblies

Attanasi and Root (1994) recognized several important 

components of reserve growth such as the outliers within the 

data and the idea that growth was now continuing substantially beyond what once was a perceived limit on the time 

span available for growth. Attanasi and Root (1994) also used 

the results of the cumulative growth curve from two different datasets (one including outliers and the other excluding 

them) as a measure of difference between groups, which was 

apparently accepted by Morehouse (1997) as a way to measure 

difference in growth between groups and was continued by 

Verma and others (2001).

Because Arrington (1960) placed limitations on the 

statistical nature of his type of assembly, particularly in relation to the application of the resulting function, a few logical 

questions could be raised. For example, a reasonable assumption about any function designed to quantify reserve growth is 

that a reduction in volumetric reserve growth should correspond with a reduction in any resulting function’s results. The 

Arrington-style methods, as a combination of volumetric and 

percentage change, might not react as expected to changes 

within the data.

Table 4 is an example of an Arrington-style assembly 

utilizing five hypothetical fields, labeled A through E. The 

AGF resulting from this combination of five fields is 1.0426. 

Table 5 is the same example with field A, which is the third 

largest percentage growing field and the largest growing field 

volumetrically, removed from the calculation. The AGF for 

this combination of four fields is 1.0969; thus 66 percent of 

the gross volumetric growth is removed from this hypothetical age-group pair, and the resulting AGF becomes 5 percent 

higher. This is not necessarily a common result, but with the 

high level of dependency on a single field or small number of 

fields, it is a reasonable and possible outcome. A plot using 

table 2 as a hypothetical AGF string for an Arrington-style 

assembly and the resulting 5-percent increase to the AGF in 

year-slice 16 results in the cumulative curve for the entire 

string as demonstrated in figure 23. The effect of a single 

5-percent increase to the AGF in age-group 16, as shown in 

figure 23, illustrates how such an increase in a single AGF 

affects the cumulative curve from that point in time onward. 

For the same amount of change, the effect will be larger or 

smaller based on its distance from the start of the cumulative 

Field name Known recovery

year 5

Known recovery

year 6

Percent 

change

Volume

change

Percent

of gross growth

A 3,000,000 3,100,000 3.33% 100,000 66.49%

B 5,000 5,100 2.00% 100 0.07%

C 500,000 550,000 10.00% 50,000 33.24%

D 10,000 9,500 –5.00% –500

E 200 500 150.00% 300 0.20%

Totals 3,515,200 3,665,100 4.26% 149,900 100.00%

Table 4. Example of an annual growth factor calculation that includes all fields.
Discussion 23

Field name Known recovery

year 5

Known recovery

year 6

Percent 

change

Volume

change

 Percent

 of gross growth

A

B 5,000 5,100 2.00% 100 0.07%

C 500,000 550,000 10.00% 50,000 33.24%

D 10,000 9,500 –5.00% –500

E 200 500 150.00% 300 0.20%

Totals 515,200 565,100 9.69% 49,900 33.51%

Table 5. Example of an annual growth factor with a single field removed from the calculation.

Figure 23. Differences in cumulative growth curve results based on a 

single annual growth factor change.

Years since discovery

Cumulative multiplier

14

12

10

8

6

4

2

0

0 10 20 30 40 50 60 70 80 90 100

12.05

11.47

EXPLANATION

Original cumulative curve

Modified cumulative curve
24 Reserve Growth of Oil and Gas Fields—Investigations and Applications

curve; for this example, the resulting change is a 0.58 increase. 

If this field had the same dominating effect on other age-group 

pairs under the same conditions, it would be reasonable to 

speculate that by removing this high-dependency and highvolume reserve-growth field from the data the AGF could 

possibly increase across a number of age-group pairs, and the 

cumulative result might increase even more.

The Arrington-style of assembly has other possible 

dependencies within it. One of Arrington’s (1960) stated 

limitations is that no resulting rate of growth could be applied 

to other datasets or to an individual field. This may also apply 

to exactly the same growth and shrinkage if the static fields, 

those within each age-group pair that neither grow nor shrink 

and are therefore net neutral to any reserve growth volume 

changes, are removed and a growth function calculated. Their 

estimated known recoverable is included in the denominator of each age-group pair. Excluding this group of fields 

would therefore not change the numerator but would certainly 

decrease the denominator and by extension increase AGFs 

in all age-group pairs. Figure 24 is a real discovery group 

example of this type of effect. Any and all fields that did not 

change in a given year were excluded from the AGF calculation, and these AGFs were then multiplied together to form 

a cumulative curve to compare with the other examples. The 

cumulative result in this case reaches an expected value of 

11.02 within 24 years.

The uncertain behavior of these derivative products of the 

Arrington-style assembly warrants caution in their use. The 

function is not only limited to the fields in any aggregation 

of data but is dependent on the exact and unique combination 

only for that dataset. The same amount of growth in any 

aggregation, identical in volumetric measure, can lead to 

completely different results in either a positive or negative 

direction based solely on the inclusion or exclusion of fields 

that show no growth or shrinkage whatsoever. 

Arrington (1960) categorized his method as a running 

rate of growth for an exact combination of fields and issued 

some general warnings on its use for good reason. One of his 

assumptions—more fields would yield a better result—might 

not be reasonable if the addition or subtraction of a single field 

can change the results randomly.

Reserve-Growth Outliers

Attanasi and Root (1994) used a cumulative curve to 

demonstrate differences between common and outlier fields 

and also noted their respective contributions to the overall 

growth in the United States. These outliers were characterized 

as large heavy-oil fields and old low-permeability gas fields 

whose reserve growth was six times faster than the common 

fields; the common fields were all of those remaining after the 

outliers were removed. Attanasi and Root’s (1994) analysis 

was based on the Oil and Gas Integrated Field File (OGIFF) 

provided by the EIA, and the information in this study relies 

on the NRG Associates (2008) database. The term “outlier” 

in this study is used to describe oil or gas fields that have an 

effect on the overall reserve growth out of proportion to their 

known recoverable size. The count of outliers in the Attanasi 

and Root (1994) study numbered 7,492 of 18,529 oilfields 

(40 percent) and 4,784 of 14,851 gas fields (32 percent). The 

results of this study indicate that the concentration of outliers 

might be much smaller than that envisioned by Attanasi and 

Root (1994).

To calculate the outliers for the present study, the NRG 

Associates (2008) database was divided into two groups. All 

oil and gas fields discovered after 1982 were separated from 

the older fields to quantify growth of the newer fields separately from the older fields.

Oil fields discovered from 1982 to 2006 totaled 974 with 

1.7 billion barrels of known recoverable oil, and the 8,300 oil 

fields discovered prior to 1982 grew 22.5 billion barrels in 

known recoverable oil between 1982 and 2006. A total of 887 

gas fields were discovered from 1982 to 2006 with a known 

recoverable gas of 21.7 trillion cubic feet of gas (TCFG) in 

2006, and the 4,032 fields discovered prior to 1982 grew 

166.0 TCFG between 1982 and 2006. The newer oil fields 

are approximately 7 percent of the total known recoverable in 

2006, and the newer gas fields are approximately 11.5 percent 

of the total known recoverable in 2006.

Of all oil fields discovered prior to 1982, 256 (3.1 

percent) accounted for 75 percent of gross oil reserve growth 

between 1982 and 2006. Of those fields, 191 also had a PRR 

>0.75 and contained 63 percent of all gross oil reserve growth 

discovered between 1982 and 2006.

Of all gas fields discovered prior to 1982, 228 (5.6 

percent) accounted for 75 percent of gross gas reserve growth 

Figure 24. Differences in cumulative growth curve results 

based on the removal of all fields with no changes in reserve 

growth in that age-group pair. Excluded cumulative growth line 

terminated early for reasons of scale.

Years since discovery

Cumulative multiplier

11.02

12.05

11.47

14

12

10

8

6

4

2

0

0 10 20 30 40 50 60 70 80 90 100

EXPLANATION

Original cumulative curve

Modified cumulative curve

Static fields excluded
Discussion 25

between 1982 and 2006. Of those fields, 132 also had a PRR 

>0.75 and contained 42 percent of all gross reserve growth 

discovered between 1982 and 2006.

The Attanasi and Root (1994) outliers were determined 

by comparing a field’s growth performance against the behavior of the group. The outlier fields in the summary above were 

determined by the size of their volumetric contribution to 

overall reserve growth contained within the NRG Associates 

(2008) dataset. The difference between these two methods of 

calculating outliers indicates that volumetric reserve growth is 

a much more stringent criterion than measuring variation from 

group behavior. Understanding this concentration of effective 

reserve growth in so few fields is critical to understanding 

reserve growth in general.

Commonness of Reserve Growth

Another assumption of reserve growth is that it is a common phenomenon that involves oil and gas fields of all types 

over extended periods of time. However, based on the near 

volumetric balance between growing fields and shrinking

fields in any particular age-group pair, the reality is that 

reserve growth relies on a minority of fields to sustain the 

growth for the entire group. This is readily apparent from an 

examination of figure 19, which shows that there is growth 

for a short period of time after discovery; in a relatively few 

years there is already a reliance on a minority of the fields 

for continued growth of the entire group. A small number of 

fields, many clearly displaying the stable-inventory profile, 

have been responsible for the large amounts of reserve growth 

seen in the United States over the past 25 years. Rather than 

a common characteristic, effective reserve growth in terms of 

substantial volumetric change is actually the minority effect of 

a few fields. Once these types of fields are excluded from the 

data, the true time span of common reserve growth becomes 

more obvious; hence, it could be argued that newly discovered 

fields are more likely to follow that general time span and to 

more accurately represent the size of reserve growth than one 

predicated on high dependency on a small minority of fields.

It would be reasonable to suggest that the profile of stable 

inventory is not only the signature of reserve growth but has 

single handedly created the assumption of long-term and common reserve growth. Following from this reasoning is the idea 

that a better understanding of reserve growth would involve 

localizing attention on the fields displaying a stable-inventory 

profile. An examination of these fields would reveal not only 

how they acquired this particular profile but how long they can 

maintain it. If an assessment of reserve growth is based on the 

infinite “tail” of an Arrington-style assembly, it leads to the 

conclusion that reserve growth is a process that could continue 

for centuries. In fact, when the final field upon which this 

infinite-appearing function is built achieves its geologic limit, 

the ability to project infinite-appearing growth in that group 

ends with it. Some fields can maintain this stable-inventory 

profile for multiple decades but many more are shrinking and 

in danger of becoming economically challenged within 70 

years for oil fields and 50 years for gas fields.

Age Correlation of Reserve Growth

Another common assumption is that reserve growth is 

age-based, with significant increases more common early in 

a field’s life than as the field ages. Although this assumption 

does appear to operate in a general sense early in a field’s life, 

it does not appear to extend beyond approximately a decade 

after the start of production. At that point, the field-level 

growth of the majority of fields has decreased significantly, 

leaving behind only a small minority of fields exhibiting the 

stable-inventory profile. Part of this assumption relates to the 

volumetric/percentage form of measure used while a particular 

field or combination of fields grows, or shrinks, when compared to others. The PRR is age-independent and created in 

part to deal with exactly this type of ambiguity. The PRR also 

has the capacity to find the timing of the change of the reservegrowth profile from a stable inventory to a field that no longer 

replaces its production. This is a critical difference because it 

signals the possible beginning of the end for reserve growth 

in a particular field, and the factors causing it may not be age 

dependent.

The Lifespan of Reserve Growth

The concept of reserve growth in fields has been well 

established in various individual field-level analysis and 

field-grouping studies at both the domestic and international 

levels. For purposes of discussion and convenience, the study 

of reserve growth prior to Attanasi and Root (1994) will be 

referred to as the early era of the study of reserve growth and 

everything after the publication of their study will be considered the modern era. This division is important because of the 

changing nature of reserve-growth concepts with respect to 

time. The Attanasi and Root (1994) study is used as the dividing line because within it are questions that continue to this 

day.

Upon examining the modern literature, it becomes 

apparent that reserve growth is accepted as a common and 

long-lived phenomenon. Functions formulated from various 

datasets are used to project growth as far into the future as 

their creators might wish. It is noteworthy that some studies

have applied functions over three centuries of growth in 

an expectation of near-infinite growth. However, studies in 

the early era estimated reserve growth in more finite terms. 

Arrington’s (1960) original example terminated AGFs within 

30 years, and Hubbert’s (1967) method had an assigned 

asymptote that approached a given CGF within 50 years. This 

same type of limit was used by Mast and Dingler (1975) of the 

USGS for inferred reserves calculations. Reserve-growth 

functions were terminated by design.

The difference between short-term reserve growth 

(approximated at 50 years) and long-term growth dominated 
26 Reserve Growth of Oil and Gas Fields—Investigations and Applications

by fields displaying the stable-inventory profile is evident 

from the breakdowns of age-group pairs previously discussed 

in the Reserve-Growth Outliers section of this study. It is 

also reasonable to infer that a stable profile might not exist 

in other groups because of the “too early for the technology” 

nature of these particular fields. If the fields in question had 

been developed initially using the same technology they are 

subjected to today, their stable-inventory profile might not survive a 50-year lifespan any better than other fields. Because of 

this delayed development and the resulting outsized reservegrowth effect, any method to assess their potential must be 

more detailed than a general statistical study. 

Other studies have noted the uneven nature of reserve 

growth within their area of interest. If reserve growth in these 

areas is driven by a small number of fields creating a substantial part or a majority of the reserve growth, it would not 

be unexpected. Key indicators are (1) fields discovered prior 

to modern technology in general and a technology specifically necessary for that field’s development, (2) fields with a 

delayed access to modern technology, (3) improper or early 

application of a technology later corrected or improved, (4) 

extensive secondary pools available after primary reservoir 

depletion, and (5) lack of a governing or regulatory environment conducive to oil and gas development.

Early methods of estimating reserve growth had time and 

growth limitations as part of their design. Arrington (1960), 

for example, could use a French curve to create an AGF of 1.0 

at a specific point, and Hubbert (1967) constructed equations 

with built-in asymptotes. The fields used in their studies were 

younger, and in some cases the stable-inventory profiles had 

not been established in advance of the widespread use of a 

particular technology. Without a study of individual field data 

at this early stage, the early indicators of anomalous fields 

would not necessarily have revealed themselves as many 

modern technologies were not common industry practice in 

this approximate time frame.

By the time the Attanasi and Root (1994) study was 

published, the accumulated oil and gas field information had 

grown substantially in length and scope, covering all fieldlevel data available to the EIA in the OGIFF file. This added 

substantial amounts of detailed data to any Arrington-style 

assembly, and based on Arrington’s (1960) own statement, “it 

follows that the greater number of statistics used, the greater 

is the probability of final accuracy,” should lead to better 

estimates. However, the additional data in Attanasi and Root 

(1994) also began to reveal a higher performing subgroup 

within the overall data. A cumulative curve was constructed 

and used to compare this subgroup to the data as a whole, thus 

creating both a comparative metric and the perception that 

reserve growth did not have the natural limitations as practiced by Arrington (1960) and Hubbert (1967). These ideas 

propagated within the general literature from that point in time 

forward.

Beliveau and Baker (2003), for example, stated “Reserve 

growth occurs in all fields, but it is more pronounced in lower 

quality reservoirs such as heavy oil, tight gas, or other marginal resources,” which implied that if reserve growth occurs 

in all fields, it is therefore significant on a general basis. They 

also incorporated the idea of a cumulative curve growth function as a means of comparison between the U.S. fields and the 

Western Canadian Sedimentary Basin fields.

Verma (2007) used seven different cumulative growth 

curves on a single chart to compare growth among widely 

different areas. Baker and Jong (2004) stated that “A particularly significant finding from Attanasi and Root’s study is that 

the multiple of initial reserves estimate does not plateau after 

time but continues to gradually increase...” A natural extension 

of these assumptions arrived in the form of the “Inventory of 

Federal Onshore Oil and Natural Gas Resources and Restrictions to Their Development,” appendix 7 of the EPCA Phase 

III inventory (U.S. Departments of Interior, Agriculture, and 

Energy, 2008). Appendix 7 of EPCA dealt with the initial estimates of remaining proved ultimate recovery growth included 

in the report, and several examples of the previously mentioned issues are demonstrated such as (1) there is no mention of reservoir differentiation with respect to continuous or 

conventional accumulations, (2) a type of cumulative growth 

graph forecasts reserve growth across three centuries from 

initial discovery and was the primary means of comparison

and calculation, and (3) data anomalies (outliers) were 

accepted “as-is.” This report is the perfectly logical extension of what was implied from the prior 15 years in concepts 

related to reserve growth.

Implications 

The generally assumed pattern of reserve growth when 

quantified using an Arrington-style of assembly is strongly 

influenced by outliers included in the data. Outliers, for the 

purposes of this discussion, are fields that produce reserve 

growth of sufficient volumes to not only offset the cumulative reserve shrinkage from all other fields of similar age 

but create enough additional growth to create the impression 

that the entire group is growing. These outliers, a majority 

of which display the stable-inventory profile, have a much 

greater impact on the aggregate data than expected. As the 

dependence on fewer fields (or even one) dominates the 

resulting AGF calculation, the likelihood of that calculation no longer behaving in a predictable manner increases. 

A single change in a single AGF calculation resulting from a 

single field is more than enough to change the outcome of the 

entire cumulative growth curve as demonstrated in figure 23. 

As the stable-inventory profile ceases in one field, the growth 

displayed by the group will become more dependent upon the 

stable-inventory fields remaining. This cascading effect will 

continue down to the final field displaying a stable-inventory 

profile, and group reserve growth will terminate abruptly with 

that field.

Based on the volumetric influence of these outliers and 

their minority presence within the data, it is reasonable to 
Summary 27

ask if these outliers are in fact the only reserve growth that 

needs to be studied. This would appear to be a reasonable 

approach considering that only 3.1 percent of the oil fields 

and 5.6 percent of the gas fields account for 75 percent of the 

gross reserve growth in the United States for the past quarter 

century. 

Once the perspective of reserve growth as a profile rather 

than a volumetric or percentage calculation has been established, other assumptions about reserve growth such as an 

age correlation for growth and its overall commonality may 

not hold up to further scrutiny. The stable-inventory profile of 

growth is tied to not just development over a field’s lifetime 

but the ability to maintain a steady pace of development. In the 

examples of Midway Sunset and Mount Poso oil fields, this 

development has continued for several decades. The technological improvements upon which that growth was based will 

not occur in future oil fields at the same temporal distance 

from discovery but will be applied earlier and over shorter 

timeframes. This precludes two assumptions from being 

applied to future estimates of reserve growth: (1) the future 

will look like the past and (2) the application of this development to smaller fields (based on the assumption that larger 

fields tend to be found first) will not yield the same volumetric 

gains as their larger and older precursors. The large field size 

of the early discoveries allows large-scale applications of costlier technologies and the economies of scale that come with it. 

Applying that same technology on an oil field 1/1,000 the size 

would be volumetrically insignificant.

The concept of reserve growth is that it is pervasive 

for all fields, basins, provinces, or countries. The concept of 

“effective reserve growth” (demonstrated by the outliers), on 

the other hand, may not be so broadly applicable. The data 

indicate that most fields grow to their recoverable size early in 

their lives, as shown in figure 19. As development continues, 

uncertainties with respect to continued growth are minimized 

as well as estimates of ultimate field size. Within this overall 

growth pattern, and providing the main volumetric basis for 

reserve growth, are the effective reserve-growth fields. It is 

expected that these fields, small in number, will drive the 

growth profile of any group within which they are included. 

Exploration within the data using a field-size measure and the 

PRR could find effective reserve-growth fields and allow them 

to be extracted for further study upon which a more accurate 

forecast of reserve growth could be built.

The presumption of how long reserve growth could 

continue has changed since Arrington published his running 

rate of growth method (Arrington, 1960). Early methods like 

his and that of Hubbert (1967) were limited by design, and 

the effect of technological advancement was not discernible 

within the available data. There was no presumption at that 

point in time of seemingly endless growth.

The perspective of generally short-term reserve growth 

changed with the publication of the Attanasi and Root (1994) 

study. The primary effect was that the sequential length of 

AGFs greater than 1.0 were extended as far as the available 

data would permit and could now be configured into a cumulative growth curve. This cumulative curve (1) did not appear 

to have a natural asymptote, and successive users of this 

technique arrived at the previously mentioned (and logically 

expected) three centuries of expected reserve growth and (2) 

seemed like a reasonable comparative measure at the time.

The precursor to the “effective reserve growth” fields in 

this study were identified as “outliers” (old, large California 

oil fields and low-permeability gas fields) and quantified. 

Identified in this study as a much smaller subset, these stableinventory-profile fields creating “effective reserve growth” 

were already dominating any Arrington-style method of data 

assembly. These fields, producing reserve-growth oil and 

natural gas at rates equal to their actual production, out of 

sequence with their actual age when compared to other fields, 

were creating an effect far larger than their numbers would 

otherwise suggest.

Long-term reserve growth is completely dependent on 

the mix of stable-inventory fields included in a group and will 

continue as long as there are fields maintaining the stableinventory profile. Reserve growth ultimately ceases when the 

final field within any given group changes from having an 

inventory profile to a PRR approaching 0. Based on oil and 

gas fields in the United States, this is the most common result 

for a majority of the fields producing approximately five to 

seven decades. It should be noted that the stable-inventory 

profile also resembles the profile of continuous accumulations 

as they expand in area during development. Without careful 

examination of the applicable geologic considerations, the 

unconventional fields could also cause the illusion of nearinfinite growth if included in any conventional field-growth 

analysis.

This study has shown that calculations of the AGF that 

compose the cumulative growth curve have the ability, under 

certain conditions, to fluctuate results arbitrarily. Whether 

the problem is the reduction in growth causing increases in 

Arrington-style functions or no changes in growth causing 

increases or decreases in Arrington-style functions, the level 

and unpredictability of these fluctuations is substantial enough 

to call into question not only the value of the AGF calculation 

but also that of any derivative product. This study does not 

discount the possibility that the AGF calculation used strictly 

as a nonlinear, best-fit regression of Arrington’s (1960) original “running rates of decline” problem might have some value 

if the underlying data and limitations of the method are well 

understood. 

Summary 

Reserve growth has been and will continue to be a critical 

component of conventional resource assessments. Since the 

release of the USGS 2000 world assessment (U.S. Geological 

Survey World Energy Assessment Team, 2000) and through 

2009, volumetric conventional oil and natural gas field reserve 
28 Reserve Growth of Oil and Gas Fields—Investigations and Applications

growth has outpaced new oil and gas discoveries by approximately 3:1 and 2:1, respectively.

Based on this examination of reserve growth in the NRG 

Associates (2008) database, this study shows that though 

many fields grow, far fewer than suspected are providing 

effective reserve growth. These fields are of a specific type of 

production and growth profile and are of such size that they 

can generate impressions of overall and long-lasting growth 

even when combined with tens, hundreds, or thousands of 

others. The nature of the Arrington-style assembly and its 

derivative products only reinforce these impressions and 

provide no comparative measures among groups of fields.

These implications indicate that including a focused 

geologic and engineering examination at the field level will 

improve assessments of future reserve growth. The large volumetric contribution of reserve growth from a small number of 

fields makes this time- and labor-intensive examination possible. Statistical aggregation methods based on the Arringtonstyle of assembly should be used with great care and a high 

level of understanding of the follow-on effects when dealing 

with the highly skewed distribution of volumetric reserve 

growth in fields.

Acknowledgments

I would like to thank Lauri Burke and Ronald Charpentier 

for their review of this manuscript. I wish to thank Mahendra 

Verma for engineering-centric conversations on past mechanisms and processes of reserve growth, Lynn Tennyson for 

never forgetting to mention that the San Joaquin Basin really 

was different and having the information to prove it, and 

James Schmoker and Tim Klett for demonstrating how interesting this topic was in the first place.

References Cited

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.

Arrington, J.R., 1960, Predicting the size of crude reserves is 

key to evaluating exploration programs: Oil & Gas Journal, 

v. 58, no. 9 (19 February), p. 130–134.

Attanasi, E.D., and Root, D.H., 1994, The enigma of oil 

and gas field growth: American Association of Petroleum 

Geologists Bulletin, v. 78, no. 3, p. 321–332.

Baker, R.O., and Jong, E.W.S., 2004, Understanding the 

enigma of reserves growth: The whys: Canadian International Petroleum Conference Paper 2004-272.

Beliveau, D., and Baker, R., 2003, Reserves growth: Enigma, 

expectation or fact?: Society of Petroleum Engineers Paper 

SPE 84144, SPE Annual Technical Conference and Exhibition, Denver, Colorado, 5–8 October, 10 p.

Forbes, K.F., and Zampelli, E.M., 2009, Modeling the growth 

in gas reserves from known fields: The Energy Journal, 

Special Issue, World Natural Gas Markets and Trade: A 

Multi-Modeling Perspective, p. 201–213.

Gautier, D.L., Dolton, G.L., Takahashi, K.I., and Varnes, K.L., 

eds., 1996, 1995 National assessment of United States oil 

and gas resources—Results, methodology, and supporting 

data: U.S. Geological Survey Digital Data Series DDS–30, 

release 2, one CD-ROM.

Grace, J.D., 2006, A closer look at field reserve growth: 

Science, engineering, or just money: Reservoir characterization: Integrating technology and business practices: 26th 

Annual, p. 1–22, DOI: 10.5724/gcs.06.26.0001.

Hubbert, M.K., 1967, Degree of advancement of petroleum 

exploration in United States: American Association of 

Petroleum Geologists Bulletin, v. 51, no. 11, p. 2207–2227.

Klett, T.R., 2003, Graphical comparison of reserve-growth 

models for conventional oil and gas accumulations, in

Dyman, T.S., Schmoker, J.W., and Verma, M.K., eds., 

Geologic, engineering, and assessment studies of reserve 

growth: U.S. Geological Survey Bulletin 2172–F, 63 p., 

http://geology.cr.usgs.gov/pub/bulletins/b2172-f/.

Mast, R.F., and Dingler, J., 1975, Estimates of inferred and 

indicated reserves for the United States by States, in

Miller, B.M., Thomson, H.L., Dolton, G.L., Coury, A.B., 

Hendricks, T.A., Lennartz, F.A., Powers, R.B., Sable, E.G., 

and Varnes, K.L., eds., Geological estimates of undiscovered recoverable oil and gas resources in the United States: 

U.S. Geological Survey Circular 725, p. 73–78.

Morehouse, D.F., 1997, The intricate puzzle of oil and gas 

“reserve growth”: Energy Information Administration, 

Natural Gas Monthly, July 1997, 20 p.

NRG Associates, 2008 [includes data current as of December 2006], The significant oil and gas fields of the United 

States: NRG Associates, Inc.; database available from NRG 

Associates, Inc., P.O. Box 1655, Colorado Springs, CO 

80901, U.S.A.
References Cited 29

Schmoker, J.W., and Klett, T.R., 2000, Estimating potential 

reserve growth of known (discovered) fields: A component 

of the USGS world petroleum assessment 2000, in U.S. 

Geological Survey World Energy Assessment Team, eds., 

U.S. Geological Survey world petroleum assessment 2000: 

U.S. Geological Survey Digital Data Series DDS-60, 

4 CD-ROMs, 20 p.

Sem, T., and Ellerman, A.D., 1999, North Sea oil reserve 

appreciation, production and depletion: Cambridge, 

Massachusetts Institute of Technology, Center for Energy 

and Environmental Policy Research Paper MIT-CEEPR 

99-011 WP, 39 p.

Stanley, R.G, 2001, Geologic constraints on the upper limits of 

reserve growth: U.S. Geological Survey Open-File Report 

01–265, 7 p.

Tennyson, M.E., 2005, Growth history of oil reserves in 

major California oil fields during the twentieth century, 

in Dyman, T.S., Schmoker, J.W., and Verma, M.K., eds., 

Geologic, engineering, and assessment studies of reserve 

growth: U.S. Geological Survey Bulletin 2172–H, 15 p., 

http://geology.cr.usgs.gov/pub/bulletins/b2172-h/.

U.S. Departments of Interior, Agriculture, and Energy, 2008, 

Inventory of onshore Federal oil and natural gas resources 

and restrictions to their development, Phase III inventory—

Onshore United States: Bureau of Land Management Web 

site, appendix 7, p. 329–340, http://www.blm.gov/wo/st/en/

prog/energy/oil_and_gas/EPCA_III.html.

U.S. Geological Survey World Energy Assessment Team, 

2000, U.S. Geological Survey world petroleum assessment 

2000: U.S. Geological Survey Digital Data Series DDS–60, 

4 CD-ROMs.

Verma, M.K., 2005, A new reserve growth model for United 

States oil and gas fields: Natural Resources Research, v. 14, 

no. 2, p. 77–89.

Verma, M.K., 2007, The reality of reserve growth: Geo ExPro, 

October 2007, p. 34–35.

Verma, M.K., and Henry, M.E., 2004, Historical and potential 

reserve growth in oil and gas pools in Saskatchewan, in

Summary of investigations 2004, v. I: Saskatchewan 

Geological Survey, Saskatchewan Industry Resources, 

Miscellaneous Report 2004-4.1, CD-ROM, Paper A-1, 20 p.

Verma, M.K., and Ulmishek, G.F., 2003, Reserve growth in 

oil fields of West Siberian Basin, Russia: Natural Resources 

Research, v. 12, no. 2, p. 105–119.

Verma, M.K., Ulmishek, G.F., and Gilbershtein, A.P., 2001, 

Slower reserve growth rates observed in Volga-Ural 

Province, Russia: Oil & Gas Journal, v. 99, no. 9 

(26 February), p. 34–44.

Publishing support provided by: 

Denver Publishing Service Center

For more information concerning this publication, contact: 

Center Director, USGS Central Energy Resources Science Center 

Box 25046, Mail Stop 939 

Denver, CO 80225 

(303) 236-1647 

Or visit the Central Energy Resources Science Center Web site at: 

http://energy.usgs.gov/ 
Cook— Reserve Growth of Oil and Gas Fields—Investigations and Applications—Scientific Investigations Report 2013–5063