U.S. DEPARTMENT OF THE INTERIOR 

U.S. GEOLOGICAL SURVEY

Description of a Discovery Process Modeling System

To Forecast Future Oil and Gas Incorporating Field GrowthARDS Ver. 5.01

By 

John H. Schuenemeyer

and 

Lawrence J. Drew

Open-File Report 98-111

This report is preliminary and has not been reviewed for conformity with U.S. Geological 

Survey editorial standards (or North American Stratigraphic Code).
Table of Contents:

1. Purpose

2. Model

3. Data Requirements, Options and Output

4. System Description

5. Operating Procedures

6. Program Descriptions

7. Description of Example

8. Future Work

List of Figures:

1. Example of Arps-Roberts Model Fit

2. Example of Piecewise Linear-Arps-Roberts Model Fit

3. Example of Ill-Fitting Data

4. Input (Nehring) Field File Format

5. Wildcat Wells by Year, File p653.wel

6. System Flow Chart

7. Input and Output Files by Program

8. Cumulative Discoveries verses Cumulative Wildcat Wells

9. Onshore Growth Tables

10. Report of Parameters and Constants

List of Exhibits:

Exhibit File Name Generating Program

1

2

3

4

5

6

7

8

9

p653.tcw

p653.dt

p653.dp

p653.stb

p653.dtr

p653.pem

p653.rem

p653.fsd

p653.ult

amerg.for

adtable.for

adtable.for

asarea.for

agrow.for

aest.for

aresult.for

aresult.for

aresult.for

10 p653.con all previous Fortran programs

References

Appendix A. Example
1. PURPOSE

The purpose of this report is to describe an oil and gas supply forecasting system, called 

ARDS (Arps-Roberts Discovery System), which incorporates field growth, and is based upon the 

Arps-Roberts discovery process model (Schuenemeyer and Drew, 1983). The specific version to 

be discussed in this report is called ARDS 5.01. Discovery process models are statistical models 

that have a basis in geology. ARDS uses historical drilling and discovery data to forecast the 

number and size distribution of fields remaining to be found. It is to be applied in partially 

explored areas that have seen some discoveries. A certain amount of structure or regularity in the 

historical data is required. This structure includes the fact that, on average, the larger fields are 

found early in the discovery sequence. ARDS works best when used in geologically 

homogeneous areas called a play, however, with proper care it can be applied to regions where 

less stringent requirements exist. For example, in the 1995 national assessment of United States 

oil and gas resources (U.S. Geological Survey National Oil and Gas Resource Assessment Team, 

1995), ARDS was used in larger regions.

The forecasting system described in this report allows for growth of individual fields before 

making a forecast, so that the discovery process model will be operating with more accurate data 

(see Drew and Schuenemeyer, 1992). Onshore and offshore growth models are available. It also 

has the ability to forecast the number of small fields remaining to be discovered. Recent changes 

to the model also permit estimation in certain instances when data sets are small and not well 

behaved.

The organization of this report is to first describe the model (section 2). Following this, the 

input data and major results are presented (section 3). The system is described in section 4 and

1
operating procedures are given in section 5. The individual computer programs, which constitute 

the system, are explained in section 6, and section 7 describes an example, which is given in 

Appendix A. In section 8 we outline plans for future work. Output data files are presented in 

exhibits 1 through 10.

The user of this model should be generally familiar with oil and gas exploration data and 

have a basic understanding of the concepts of statistical variability and modeling. The user will 

need to install and execute a series of Fortran programs and should have the facility to graph 

computer output.

2. THE MODEL 

2.1 Description

The model used in this system is actually a class of models with various options. The basic 

model, however, is a modified Arps-Roberts (AR) model which estimates the number of 

undiscovered fields within size class using historical drilling and discovery data. The size class is 

typically expressed as a range of values in logarithms of barrels of oil equivalent (BOE). The 

functional form of this model is:

= Fi(*>)(l - exp (-CiAP/B)) + s

where

i is the i th size class,
Fj(w) are the number of fields found by w cumulative wildcat wells,

FI(OO) are the total number of fields in the play,

q is the discovery efficiency,

Ai is the mean surface projection area of fields,

B is the play size, and

e's are identically, independently distributed errors with mean 0 and constant variance. 

Fi(oo) and Cj are model parameters estimated from the discovery data (Fj(w), w). The (assumed) 

known constants are Aj and B. An example of a reasonable fit to an AR model is shown in figure 

1.

Sometimes a change in the historical discovery data results in a significant lack of fit of the 

AR model. This is often observed near the start of exploration and might be attributable to 

learning where to site wells or it might be caused by multiple plays. One approach to modeling 

this type of data is a piecewise linear-Arps Roberts model (called LAR). When this option is 

chosen, ARDS will attempt to fit the following model:

w + e,

where kj = cjAj/B. An example of a data set that is best fit by this model is given in figure 2. The 

parameters to be estimated in the LAR model are: Ft (*>), Ct, Fu, a and y. Those of most interest 

are Fi(*>) and a- In ARDS, the user is given the choice of running the AR, the LAR, or the best
fit between the two.

2.2 Restrictions and Limitations

The model parameters are estimated in program AEST.FOR using a non-linear least square 

estimation procedure. Occasionally such procedures converge but give unrealistic values for 

parameter estimates. To mitigate such problems, the ARDS 5.01 restricts the estimate of 

discovery efficiency ci to be less than or equal to 99. Also the estimate of the ultimate

/\

number of fields in a given size class Ft (oo)is restricted to be less than or equal to four times the

number of discoveries in size class i. These restrictions can be changed by simple modifications to 

program AEST.FOR.

The ARDS 5.01 model provides reasonable estimates of parameters for the data shown in 

figures 1 and 2 and even functions well when data is moderately ill conditioned. However, it will 

not provide meaningful estimates when given the data shown in figure 3. The second upturn in 

the discovery curve shown in figure 3 might be the result of a second play offset in time from the 

first play, or it may have resulted from the introduction of new technology, access to a previously 

restricted area or a significant increase in price. When this phenomenon is observed, the 

investigator should make every effort to determine the cause and disaggregate the data. Even 

when ARDS converges in this situation, the resultant estimate of Cj will be too low and the 

resultant estimate of Fi (o>) too high.

3. DATA REQUIREMENTS, OPTIONS AND PRINCIPAL OUTPUT

3.1 Data Requirements and Conventions

4
Ideally the input to this system would be discovered fields on a scale of wildcat wells, i.e., 

each field would be identified by its discovery well, where the discovery wells in an exploration 

play are ordered by date. Thus a data set consisting of n fields ideally would be of the form 

{(Wj,Vj),j = !, ..,#}, where Wj is the cumulative wildcat well (number) that discovered field Vj.

The field size V must be a unit of volume of oil or gas. Often these "connected" data sets are not 

available but the investigator knows the number of wildcat wells drilled by year and the dates of 

discoveries. The input requirements for ARDS are setup to handle this latter case, namely that 

there is a field file containing discovery information, and a well file. Note that a "connected" data 

set should be used when available. How this is accomplished will be addressed later.

The field file must contain the discovery date, estimates of the ultimate oil, natural gas, and 

natural gas liquid or BOE, and the spatial area of each field. In addition, the field name and its 

geographic location, if present, are also read from the field file. The field file (figure 4) used in 

this report was derived from Nehring data (NRG Associates, Inc., 1986). The field file must be 

sorted in ascending order by discovery year. (It is not necessary for the file to be sorted by month 

and day.) The well file (figure 5) contains years and wildcat wells per year. The field file and the 

well file are merged so that sizes of discoveries will be placed on a scale of wildcat wells. A more 

complete description of the merge is given in section 6.2.

A question that is frequently asked concerns the minimum size of the data set needed to run 

ARDS. Unfortunately there is no simple answer to this question. We have successfully run 

ARDS with a data set containing only 30 discoveries and have failed to produce reasonable results 

with data sets containing several hundred observations. Basically if data is well behaved, i.e., a 

decline in the number of discoveries with respect to cumulative wildcat wells has been observed,
there is consistency among class sizes, namely the degree of decline is proportional to size class 

and, the variability with size class is small, relatively few observations will be required. Often 

large data sets can be disaggregated using exogenous information when problems with 

convergence occur. We have observed, however, that the ARDS model is relatively robust to 

minor inconsistencies in the data.

The units of oil in the input file, fh.fld can be either millions or billions of barrels of oil and 

the units of gas can be millions or trillions of cubic feet, however, internally and on ARDS 

generated reports the units are in millions of barrels of oil equivalent (BOE). For the area of 

fields the user may select among acres, square kilometers and square miles, however internally 

and on ARDS generated reports the units are in square kilometers.

The file designator convention used in ARDS is to have the user assign a name to a play, 

such as p653. This will be referred to generically as fh and must be at most 10 alpha-numeric 

characters. The field file used by this system must be named "fh.fld" (i.e., the suffix must be fid). 

The well file used by this system must be named "fh.wel".

3.2 Options

The following options are available in ARDS. Some have been discussed in the previous 

section; others will be explained later in this report.

1. User specified units of the volume and area of field size.

2. An option to process oil, gas, or oil and gas fields.

3. Pre-specified or user-defined field-size classes.

4. User specified well increments, which are used to summarize historical data.
5. Length of data series (number of wells or dates) used for estimation.

6. Growth or no growth for fields~an onshore and an offshore growth model are 

available.

7. Negative exponential or piecewise-linear negative exponential models.

8. Estimation of small fields.

3.3 Output

Data files created by ARDS will be labeled fh. suffix, where the suffix is a two or a threecharacter designator for the type of file created. An example of each file (except for files that only 

transfer information between ARDS programs) is given in exhibits 1 through 10 at the end of this 

report. The content of these files will be discussed later. In addition, most programs produce 

print files designated by the program name followed by the suffix PRN. These are log files that 

contain intermediate results and information about possible program or data errors. They should 

be viewed before proceeding to the next program in sequence.

The major output of this system is estimates of the remaining volume and numbers of oil and 

gas to be discovered by size class. Estimates are also disaggregated into small fields and large 

sized fields. In addition, when a growth option is chosen, estimates of uncertainty associated with 

growth are provided. File "fh.dt" (exhibit 2) is a discovery table, which contains cumulative 

wildcat wells and the corresponding cumulative number of discoveries by field size class. It can 

be used to analyze ungrown fields. File "fn.dp" (exhibit 3) is the merged field and well file. The 

basic statistics file "fn.stb" (exhibit 4) contains information on actual discoveries by class and 

BOE discovered. In file "fh.con" (exhibit 10) are the constants and other input data necessary to
recreate a run. These and other files are discussed in detail in section 6.

4. SYSTEM DESCRIPTION

The system consists of a series of Fortran programs, which perform the basic calculations. 

We illustrate the output at various stages in the modeling process using Systat DOS version 5.02 

(SYSTAT, Inc., 1990) macros. The user is also strongly encouraged to do the same. The data is 

written to files in ASCII format and almost any commercially available plotting program can be 

used. A brief description of each program shown in figure 6 follows. The input and output files 

are listed by program in figure 7. A more detailed description of the programs is given in section 

6.

Program AFORMAT.FOR

reformats the field file and estimates missing discovery dates. 

Program AMERG.FOR

merges the field and well files and estimates missing areas. 

Program ADTABLE.FOR

generates summary statistics and prepares a file to be used as input to the growth

program AGROW.FOR. Note that if fields are on a scale of wildcat wells.

ADTABLE.FOR will be the initial program. The input well-field file is fh.dtw.

Note: At this point the user should plot the cumulative discoveries versus 

cumulative wildcat well as given in file fh.dt. This can be accomplished by using

8
program APPPLOT.FOR and Systat or with another commercial plptting package 

figure 8). (See section 6.4 for a description of program APPPLOT.FOR.)

Program ASAREA.FOR

estimates the missing average areas and smooths those present. The resultant 

smoothed basic statistics file "fh.stb" and the field file "fh.dp" produced by 

ADTABLE.FOR serve as input to AGROW.FOR.

Systat macro ASAREA.CMD

plots the average surface projection area versus average volume for each size class.

Program AGROW.FOR

grows fields from a given year to a given year. Four growth options are available. 

One is for no growth. A second, estimates the year of mortality and grows fields 

according to a model fit to offshore data. The third is an onshore model that 

consists of two-growth rate tables (figure 9). The fourth (not yet implement) is for 

a user specified world oil growth model. These models are described in section 6. 

The output from AGROW.FOR is a set of a 101 discovery tables (file "fh.dtr"). 

Each table within this set contains a replication number, cumulative wildcat well 

numbers, and cumulative discoveries by class sizes. (The 101 replication number 

was chosen to provide reasonably consistent estimates of ultimate resources.) This 

data together with file "fh.stb" serves as input to program AEST.FOR. When 

fields are grown, the estimated growth for each replication is produced (file 

"fh.gro").

Program AEST.FOR
is a nonlinear estimation program. It estimates the parameters of the AR and/or 

LAR models for each replication generated by AGROW.FOR.

Program ARESULT.FOR

produces estimates (when growth is specified) of the remaining BOE for each 

replication and then computes quantile estimates (at 10, 50, and 90 percent) of the 

remaining BOE. Also produced are quantile estimates of growth, and estimates of 

the mean and trimmed mean. These reflect estimates of uncertainty due to field 

growth. When the no-growth option is chosen, only a single suite of estimates is 

generated. The major output information is in files fh.fsd and fh.ult.

Program ACON.FOR

prints information (figure 10) from the fn.con file and the fh.stb file that provides 

the user with the suite of parameters and constants used to generate the final 

output. With this information and files fn.fld and fn.wel the user can regenerate all 

of the output.

5. OPERATING PROCEDURES 

5.1 General Information

The total time to run ARDS for p653, a play with 646 fields, is less than one hour on a 90 

MHz Pentium personal computer (play p653 has 646 fields). The user can stop the system after 

completing any Fortran run and resume processing ARDS later.

Two programs (AMERG.FOR and AGROW.FOR) require continuous (0 to 1) uniform 

random numbers. A random number seed can be entered from the keyboard or the program will

10
choose one by accessing the tenths and hundredths of seconds from the system clock. The random 

numbers are obtained by calling Microsoft subroutines SEED (once) and RANDOM (as needed). 

Note that Microsoft uniform random numbers will differ between a 16 and 32-bit machine, even 

when the same seed is used. Another uniform random generator could be easily substituted.

The Fortran programs have been dimensioned for a maximum of 25 class sizes in all of the 

programs using a Fortran PARAMETER statement. If there are more than 25 classes, these 

statements will need to be changed and the programs recompiled. A maximum of 62,999 

cumulative wildcat wells is allowed and is represented in the PARAMETER statement of programs 

ADTABLE.FOR, AGROW.FOR, AEST.FOR, and ARESULT.FOR as 629, for six hundred and 

twenty-nine, 100 well increments. In addition, a maximum of 101 replications is allowed. The 

PARAMETER statements in AEST.FOR and ARESULT.FOR would need to be modified to 

increase the number of replications.

ARDS is interactive and typical information requested by the computer is found in the 

example presented in Appendix A. We suggest that the user review this example and the remainder 

of this report before running the system. Only supplemental information needed to run the 

programs will be presented here.

5.2 Installation, Loading and Compiling Programs for DOS

Store the Fortran programs, the data, and Systat macros (if you choose to use this system for 

plotting) in the directories as follows: 

a. Make a directory called ARDS. 

b. Copy the Fortran programs into it. All of the Fortran source programs have the extension FOR.

11
c. Make a subdirectory called DATA. 

d. Copy the Systat macros (having extensions CMD) into it.

e. Copy the data sets "fh.fld" and "fn.wel" into subdirectory DATA. Note that the field file and the 

well file must have extensions fld and wel respectively. Note also that file "fn.fld" must be 

sorted by discovery year (columns 186-189\ 

f. If the U.S. onshore growth model is to be used, file "GRONS.DAT" must be copied into the

DATA subdirectory.

g. All programs were compiled by the authors in Fortran 90 (Microsoft Fortran PowerStation, 

Version 4.0, 1995). Subroutines are compiled in the ARDS5A.LIB, which should be copied into 

directory ARDS. To compile a program, specify the program name with the FOR suffix and 

ARDS5A.LIB. For example, to compile AFORMAT.FOR, type:

FL32 AFORMAT.FOR ARDS5A.LIB

Note that this compile is for a 32-bit system (usually a Windows 95 operating system). You 

may use either upper or lowercase letters when typing Microsoft compile commands. For a 16 

bit Microsoft compile you will need to use the command FL AFORMAT.FOR ARDS5.LIB, 

where ARDS5.LIB is the 16-bit version of the ARDS subroutine library.

5.3 Running the System 

5.3.1 General Instructions

A system flow chart is given in figure 6 and an example, which includes the dialogue between 

terminal and user, is presented in Appendix A. An introduction to the example is found in section 

7.

12
5.3.2 Fortran Programs

All Fortran programs must be run from the ARDSMDATA directory. Entering the name 

(without extension) of the main program runs them. For example, to execute AFORMAT from 

subdirectory DATA (ARDS\DATA), enter AFORMAT.

Note: A yes or no ("y" or "n") reply to a question asked by a program must be entered in 

lowercase. Program and macro names can be entered in upper or lowercase. The user must follow 

a consistent convention (upper or lowercase) for entering file names. In the instructions that 

follow, bold letters denote the information to be entered (except for directory names).

5.3.3 Data

All files created by either Fortran programs or Systat macros will be written to the 

ARDSVDATA directory. A list of input and output files generated by program is given in figure 7. 

The user will be informed of any file to be overwritten by a program except for the print (PRN) 

files and can stop and rename that file if desired. The user will be prompted for any information 

requested from the terminal.

5.3.4 Running ARDS

Make sure that you are in the ARDS\DATA directory. To run ARDS begin by typing the 

name of the first program, namely AFORMAT. Each program, upon successful completion will 

identify the subsequent program to be run. A systems flow chart is given in figure 6. All programs 

operate interactively and will request needed information from the user.

13
6. PROGRAM DESCRIPTIONS

A description for each of the Fortran programs and plot routines (Systat macros) used in this 

system follows. It is presented in the order in which they would normally be run. Programs are 

available from the authors on a 3-!4 inch diskette. The user should refer to figure 6 to follow the 

run sequence. The connecting arrows in figure 6 are for a growth option run. The order of 

program execution is the same when the no-growth option is chosen (in AGROW.FOR) but the 

file transfer of information is somewhat different. Parameters and constants used by the Fortran 

programs are written to a file called "fh.con" (see exhibit 10 for an example). For simplicity, file 

"fh.con" outputs are not shown in figure 6. They are, however, listed in figure 7.

6 1 AFORMAT.FOR

Program AFORMAT.FOR estimates missing discovery months and days, as necessary, 

computes BOE, sorts fields by discovery month and day within year, and reformats the data for 

program AMERG.FOR. This output is contained in file "fh.ytw". A missing month is estimated 

by randomly selecting an integer 1 through 12. Records containing missing discovery years are 

discarded. Output file "fh.tcw" (exhibit 1) establishes a date-to-cumulative well correspondence, 

which can be used to help interpret graphs plotted on a scale of cumulative wildcat wells.

6.2 AMERG.FOR

Program AMERG.FOR merges the Nehring field file output from program 

AFORMAT.FOR (file "fn.ytw") and the well file "fh.wel". The well file (figure 5) contains the

14
year and number of wells by year. Column two contains total exploratory wells per year (Lahee 

classes 2 through 5). Column four, if present, contains new field wildcats per year (Lahee class 5). 

Either column can be selected.

A cumulative well number is assigned to each discovery by dividing the Julian day of 

discovery by 366 and multiplying by the number of wildcat wells in the year of discovery. If the 

well file contains fewer discovery wells in a given year than there are discoveries, the minimum 

required number of wells is added. An output of this program (file "fh.dtw") serves as input for 

ADTABLE.FOR. If discoveries are available on a scale of wells, those data should be used. 

Program AMERG.FOR also estimates the area of a field, if missing, from the corresponding 

volume (in BOE) using the following model specified in function AREST:

area=exp(bO)*BOEbl

If the volume (BOE) is missing, the record is discarded. Parameters bO and bl are estimated using 

ordinary least squares fit to the log of the above model. A table "fh.tcw" that lists years and 

cumulative wells is also generated.

63 ADTABLE FOR

Program ADTABLE.FOR generates a discovery table ("fh.dt"; see exhibit 2, a discovery file 

("fn.dp"; see exhibit 3) and a table of basic statistics using the merged well-field file "fn.dtw" as 

input. The user is asked to supply the play size and choose a log-based class size that is needed by 

the Arps-Roberts discovery process model. In class sizes where no discoveries are present, the 

expected volume of oil is computed as geometric mean of the class size (in BOE) boundaries. 

Volumes and areas in other size classes are the arithmetic average of the observations. Output of

15
ADTABLE.FOR (written to print file ADTABLE.PRN) links cumulative wildcat wells with 

calendar dates and provides running sums of BOE. Also, the user can hide a portion of the 

field/well data and use it to evaluate the model. When this option is chosen additional files 

("fh.dpf', "fh.dtf' and "fh.stf) are created to store the forecasted interval data.

6.4 APPPLOT FOR

APPPLOT.FOR is a pre-processor for plotting cumulative discoveries versus cumulative 

wells using Systat. (It should be omitted if another graphic package is used.) We strongly 

encourage users to make this plot because it can reveal possible shifts in the data or other factors 

that would bear further investigation. Program APPPLOT requires a data file, APPPLOT.DAT to 

be loaded in the DATA subdirectory. The data that can be plotted are in files fh.dt and fh.dtr. 

Program APPPLOT.FOR generates a Systat macro plt.cmd. To run this macro, type macro and 

then submit plt.cmd.

6.5 ASAREA.FOR

AS ARE A estimates surface projection areas for classes that do not contain data. It also 

smoothes the areas across size classes. The model used is:

log(ave area) = const+bi*log(ave BOE)+b2 *log(ave BOE)**2

It is fit by a Tukey bi-weight robust regression procedure because this fitting procedure is less 

sensitive to outliers (points far from the regression line) than is ordinary least squares. The user 

should view the residuals and change the model as needed, since this equation may not be the best

16
model for all situations. In addition, it may be necessary to down-weight or delete areas associated 

with small class sizes that contain few fields. This program creates a file called fn.stb reproduces 

the information in fh.sta and adds smoothed areas (see exhibit 4).

6.5.1 SystatMacroASAREA.CMD

ASAREA.CMD plots the smoothed and raw average BOE versus average surface projection 

area (using file "fh.stb" as input) and the log(ave BOE) versus log(ave area).

6.6 AGROW FOR

Program AGROW.FOR grows the original fields (in BOE), as given in file "fn.dp" (exhibit 

3), and produces cumulative discovery tables. The process of growing fields is repeated 101 times. 

A representative sample of the output file "fh.dtr" is given in exhibit 5. The default number of 

replications (101) gives reasonably stable estimates of remaining BOE (which will be estimated by 

program AEST.FOR). Two growth models, an onshore and an offshore, are available. Fields can 

be grown from a base year, usually the year the field file was last updated, to a specified year in the 

future. For the onshore model, the user can choose either field or reservoir growth. When the 

offshore model is chosen, an estimate of the year when production will cease is made for each field. 

Fields are then grown to the minimum of the year of mortality or the year specified to end growth. 

A brief description of the mortality and growth modules follows. Additional details are given in 

Schuenemeyer and Drew (1996).

17
The mortality model is implemented as subroutine EXPPF. The probability of a field of size 

S surviving to age A is estimated using loglinear regression and the Western Gulf of Mexico data to 

be:

Ps(A,S) = b/(l+b),

where b = exp(-4.491 - 0.213*A + 0.813*8) and S = log2(X/0.00593) + 2.5. X is the field size at 

expiration in millions of BOE. The following algorithm is used to estimate the year of expiration 

of afield: 

a: Let nc d nfb - ny + 1, where nfb is the year the forecast is to begin and ny is the year of

discovery,

b: d <= ps(nc-l,x), the probability of a field of size x surviving at least nc-1 years, 

c: u <= u(0,l), a uniform random number, 

d: my <= nfe - ny, where nfe is the year the forecast is to end, 

e: if (u < ps(my,x)/d) then the field will not expire in the forecast period, else 

f: for i = nc to my: if (u > ps(i,x)/d) then go to step h; note that ps(i,x)/d is the conditional

probability of survival of a field of size x. 

g: field does not expire in the specified time, 

h: field will expire in year nye <= ny + i.

18
The onshore growth model is given in subroutine GRONSH. It computes yearly growth for 

either fields or reservoirs based upon a table (in data set "GRONS.DAT") supplied by Emil 

Attanasi of the U.S. Geological Survey and included in the ARDS 5.01 packet of programs. See 

Attanasi and Root, 1994 for a discussion of the U.S. domestic oil and gas growth models. For 

growth purposes, a field is classified as an oil field if the fraction of oil is greater than 0.23 on a 

BOE basis (ignoring liquid natural gas) and is classified as a gas field otherwise. This is equivalent 

to a classification of a field as gas if the gas to oil ratio is greater than 20,000 cu. ft to 1 bbl oil, 

assuming 6,000 cu. ft. of gas to one barrel of oil. We assume that the growth error is normally 

distributed with mean 0 and standard deviation 0.045781 (the standard deviation estimated for the 

offshore model).

The offshore growth model is given in subroutine GRMODR. The incremental average field 

growth data for the Miocene-Pliocene trend in the western Gulf of Mexico (Drew and Lore, 1992 

and Drew and Schuenemeyer, 1992) was fit to the following model:

\ogfG(A, S;

where G is the ratio (averaged over n^s] observations) of fields of age A to fields of age A-l of 

size S (in BOE). In the Miocene-Pliocene data used to fit this model, S={9,10,...,17}, 

A={ 1,2,3, ...,41} and n^s] is the number of fields (observations) of size S (size class i[S]) at age A. 

The n's vary between 1 and 66. Weighted (by the n's) least squares and robust procedures were 

used to fit the model. Since the results were similar, the weighted least squares estimates are 

reported. The estimates for the model parameters are:

19
PQ = 0.177980 (0.005305) 

/?, -=-.007165 (0.000425) 

f}2 =-. 002063 (0.000098)

The standard errors are given in parenthesis. The F ratio at 2 and 4273 degrees of freedom was 

699. The estimated standard deviation (the square root of the mean square error) of the yearly 

growth for a field of size Sis a = 0.04578. The error for the growth model was assumed to be 

normally distributed. An analysis of residuals and other diagnostics indicates that model 

assumptions have been met. Thus, G = exp(0.177980-0.007165S-0.002063 A), G>J and

Gr = G + r,where r~N(0,<j2).

In both the onshore and the offshore growth models, the growth multiplying factor Gr is 

restricted to be greater than 0.001. Note, that because of the presence of a random deviate r, 

shrinkage (Gr<l) can occur. The growth multiplying factor Gr is bounded away from zero because 

this would indicate that a field disappeared through a merger. While possible, this feature has not 

been incorporated into the model. The estimated field size at age A+l is the size at age A, times 

the growth-multiplying factor Gr.

Note that the user has the option of choosing no growth. In this case the fields are essentially 

passed through AGROW.FOR and the model only runs for replication.

6.7 AEST.FOR.

This program estimates parameters for either the modified Arps-Roberts (AR) model or the 

piecewise linear Arps-Roberts (LAR) model using cumulative discoveries versus cumulative

20
wildcat wells in a specified range of size classes. When the field growth option is specified, 

estimation is attempted for each replication. The models are described in detail in section 2 of this 

report. The fitting procedure is nonlinear least squares using the Gauss-Newton method. The key 

input data to this program are the discovery tables generated by AGROW.FOR (see exhibit 5). 

Prior to fitting the cumulative wells versus cumulative discovery data, the data will be shifted (if 

necessary) so that there is no more than one zero cumulative discovery at the beginning of the 

series. For example, if (for a given class) the cumulative discoveries for the first three, hundred 

well increments were 0, 0, and 3, the AR or LAR fit would begin at 200 wells. In AEST.FOR the 

user can select an AR fit (option 1), a LAR fit (option 2), or allow the model to choosing the best 

fit (according to a regression significance test) between the two (option 3).

AEST.FOR requires three major subroutines. They are NLLSLM1 .FOR, which is the GaussNewton algorithm, and Linpack routines DQRDC.FOR and DQRSL.FOR. These latter routines 

are called by NLLSLM1.FOR to solve the Gauss-Newton algorithm via a Householder 

transformation. In NLLSLM1, subroutines FCODE1 and PCODE1 contain the AR model and first 

derivatives with respect to the parameters, respectively. The model for LAR is given in FCODE2. 

LAR estimation uses numerical derivatives. The output (file "fh.pem") contains estimates of the 

ultimate number of fields, discovery efficiencies, the number of discoveries (as determined by 

growth model), and the sum of squares error of the fits (see exhibit 6).

We suggest using the class size of the average modal class (supplied by the program) as the 

minimum size class for estimation in AEST.FOR. Smaller class sizes are subject to economic 

truncation and, in addition, it may not be possible to obtain convergence. An error message will be 

printed should this occur and the user should examine graphs of the data. Convergence of model

21
mil be difficult to obtain when the relationship between cumulative discoveries (on the vertical 

axis) versus cumulative wildcat wells (on the horizontal axis) is straight or concave up (each 

successive well finds more discoveries). The relationship between discoveries and wells may be 

concave up for a short period due to random chance. The cause of a concave up trend that exists 

over a long time period may be due to structural changes such as an advance in technology or 

access to a new area. When this occurs, the user should try to pinpoint the source of the problem 

and, where possible, disaggregate the data. If the discovery efficiency in a given class is less than 

one and the discoveries appear to be found at approximately equal increments of exploration (i.e., a 

plot of cumulative discoveries versus cumulative wildcats is linear), the play (basin) size may be too 

small. The user should try increasing the play size. Finally, the largest size class used for 

estimation should contain at least three discovered fields.

For the no-growth option (specified in AGROW) only one replication will have been 

generated. When growth is specified, 101 data sets containing grown fields will have been 

generated. An estimate of the remaining BOE for each replication is computed. Note that for very 

small or extremely ill-behaved data sets, some replications may not contain enough classes for the 

model to produce a reliable estimate of the remaining BOE. At least four classes in a given 

replication must converge. When this does not happen, the replication is omitted.

6.8 ARESULT.FOR

Program ARESULT.FOR computes estimates of the volume of BOE remaining to be 

discovered. If requested by the user during input, this program also estimates the number of small 

fields remaining to be discovered using a geometric ratio procedure (see Schuenemeyer and Drew,

22
1983). Estimation of the geometric ratio begins in one class size larger than that used as the 

beginning class size in AEST.FOR. The right-hand end of the class size distribution is truncated 

when four or fewer fields have been discovered in a given class since size classes containing fewer 

fields are judged to be too erratic to be used in the estimation of the geometric ratio. Alternatively, 

the user can supply a geometric ratio.

The estimate of the remaining BOE is divided between small and large field sized class 

estimates. (Large field size classes are defined to be those that can be estimated directly from the 

model as opposed to being estimated from the geometric ratio.) From the distributions of the 

volume of BOE remaining to be found in the large field size classes (growth option only), the 10, 

50 and 90 percent quantile estimates are obtained. The mean and 80 percent-trimmed mean are 

also computed. Quantiles for growth are estimated independently of remaining BOE using growth 

data transferred from AGROW.FOR. The remaining BOE, growth and geometric ratio for each 

replication are given in file "fh.rem" (see exhibit 7). The mean and trimmed mean are also 

computed for growth. The summary output is in file "fn.fsd" (see exhibit 8). The ultimate number 

of fields and volume of BOE remaining to be discovered is given in file fh.ult (see exhibit 9). The 

small field size class estimates are indicated with an asterisk in exhibit 9. Efficiency estimates are 

not used when making small field size class estimates, only the geometric ratio. When growth is 

specified, these results are given for the 10, 50 and 90 quantiles based on the volume of BOE 

remaining to be discovered in the large field size classes. Finally, all of the parameters and 

constants used in a run of ARDS are given in file p653.con (exhibit 10). These can be printed out 

(written to file ACON.PRN) using program ACON.FOR.

23
7. DESCRIPTION OF EXAMPLE

An example from an onshore play denoted as p653 in East Texas is given in Appendix A. It 

consists of the screen dialogue (input and output) for each of the Fortran programs. Section 5 

discuss the procedures to use to run ARDS.

8. FUTURE WORK

The following product improvements are planned for future versions of ARDS:

 Implementation of a sequential procedure to detect when an upward shift begins to occur 

in the discovery profile (cumulative discoveries versus cumulative wildcat wells).

 Estimate the uncertainty associated with model lack of fit and forecasting error for large 

field size class forecasts.

 Estimate the uncertainty associated with projections of the estimated remaining number of 

fields and BOE in small fields.

24
REFERENCES CITED

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.

Drew, L.J. and Lore, G.L., 1992, Field growth in the Gulf of Mexico - a progress report, in U.S. 

Geological Survey Research on Energy Resources, 1992, U.S.G.S. Circular 1074, p. 22-23.

Drew, L.J. and Schuenemeyer, J.H., 1992, A petroleum discovery-rate forecast revisited-the 

problem of field growth: Nonrenewable Resources, v. 1, p. 51-60.

Microsoft, 1995, Microsoft Fortran PowerStation, Version 4.0, Microsoft Corporation, Redmond, 

WA.

NRG Associates, Inc., 1986, The significant oil and gas fields of the United States (through 

December 31, 1985): Available from Nehring Associates, Inc., P.O. Box 1655, Colorado Springs, 

CO 80901.

Root, D.H., 1982, Historical growth of estimates of oil- and gas-field sizes: Oil and Gas Supply 

Modeling, NBS Special Pub. 631, p.350-368.

Schuenemeyer, J.H. and Drew, L.J., 1983, A procedure to estimate the parent population of size of 

oil and gas fields as revealed by a study of economic truncation, Jour. Math. Geol., v. 15, p. 145- 

161.

Schuenemeyer, J.H. and Drew, L.J., 1996, Description of a discovery process modeling procedure 

to forecast future oil and gas using field growth (ARDS 4.01): U.S. Geological Survey Digital Data 

Series DDS-3 6.

SYSTAT, 1990, SYSTAT, Inc., Evanston, IL.

U.S. Geological Survey National Oil and Gas Resource Assessment Team, 1995, 1995 national 

assessment of United States oil and gas resources, U.S. Geological Survey Circular 1118, 20 p.

25
Discoveries of Number Cumulative 

O

c

c

0

Q. 

O

= 

0)

X

O 

O

Ol

o

o 

o

CO

N) 

G)

CO 

CD

Ol 

N)

G) 

00 Ol

Ol

o

T3

CD

Ol

CO

Jb

CO

o

O

CO

_JL

O

3

orq

w

 5

o 

cr

2

O 

G-
2<FQ*

Discoveries Cumulative 

o b

CO

pi 

fo CD

o

P 

bo

CD O

Oc

CD

Q. O* 

(Dr-h I

CO XoO

01 O

o o

Ol o

T3

GO

Ol

CO

iD

Ol Oo

CO

P3 X&a 3"5L 

STe

S 

fft 

&a

 Oo

Q.
c 

- o 

o

01 = 

~ o 3 

o

g

a 

o

- 8 1 

0)

- 01 

o

Discoveries Cumulative 

DOOOOOOOC

1 1 1 1 II 

B ' . 

 \

 .

\

I

* 

°\

\

\

\

»

D

31 (E*

c

(D

CO

m

X

3

73

<D

^

1

^^ ^ 

^^ ^

5"

(Q 

O

5T
Figure 4. Input (Nehring) Field File Format

POSITION DESCRIPTION

1-10 NEHRING ID CODE

12-36 FIELD NAME 25 CHARACTERS

38-45 LATITUDE F8.5

47-55 LONGITUDE F9 . 5

57-59 UGSG PROVINCE CODE 13

61-62 YEAR $\quad$ 12

64-73 GAS ANNUAL (MILLIONS CF)

75-84 GAS CUMULATIVE PROD. (MILLIONS CF)

86-95 GAS KNOWN REG. (MILLIONS CF)

97-106 GAS LIQU. ANNUAL (THOUSAND BBL)

108-117 GAS LIQU. CUM. PROD. (THOUSAND BBL)

119-128 GAS LIQU. KNOWN REG (THOUSAND BBL)

130-139 OIL ANN. PROD (THOUSAND BBL)

141-150 OIL CUM. PROD (THOUSAND BBL)

152-161 OIL KNOWN REG (THOUSAND BBL)

163-166 STATE CODE (2 DIGS ST CD, NEXT 2 SUB AREA, MOSTLY 00

168-171 STATE CODE (2 DIGS ST CD, NEXT 2 SUB AREA, MOSTLY 00)

173-176 STATE CODE (2 DIGS ST CD,NEXT 2 SUB AREA, MOSTLY 00)

177-182 MAXACRE 16

186-195 COMPLETION DATE OF DISCOVERY WELL YYYY/MM/DD

198-202 TOTAL DEPTH $=$ TOTAL DEPTH

204-208 TOPINT1 $=$ DEPTH TO PRODUCING INTERVAL 1

210-214 TOPINT2 $=$ DEPTH .TO PRODUCING INTERVAL 2
Figure 5. Wildcat Wells by Year, File p653.wel

Year Wildcat 

wells

1902

1903

1904

1905

1906

1907

1908

1909

1910

1911

1912

1913

1914

1915

1916

1917

1918

1919

1920

1921

1922

1923

1924

1925

 

1971

1972

1973

1974

1975

1976

1977

1978

1979

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

0

0

0

0

0

0

0

1

0

0

0

0

0

1

1

1

1

1

3

7

4

4

5

8

 

189

188

167

212

240

218

232

289

268

281

318

270

245

302

232

103

60

56

40

6
ARDS 5.01 Flow Chart

1 r

aformat.for

asarea.for

adtable.for

^ r fh.pem

^ r

aresult.for

fh.dtq,fn.pe,fn.rem 

,fn.fsd,fn.ult

0
Figure 7. Input and Output Files by Program

Program Input Files Output Files

AFORMAT.FOR fn.fld fn.con

fn.ytw

AMERG.FOR fn.wel fn.dtw

fn.con fatcw

fn.ytw fn.con

ADTABLE.FOR fn.dtw fn.dp

facon fn.dt

fn.sta 

fn.con fn.dpf4 

fh.dtf4 

fastf4

ASAREA.FOR fn.sta fn.stb 

AGROW.FOR

AEST.FOR

ARESULT.FOR

fn.stb

fn.dp 

grons.dat 

facon

fn.stb 

fadtr

fn.con

fn.gro 

fn.stb 

fa pern 

fh.dtr

fn.con

fh.dtr

fn.gro 

fn.con 

fadpr2

fn.pem 

facon

fn.rem fh.dtq3 

fh.pe 

fn.con

fh.ult

'if forecast option interval chosen.

2One replication only.

3Not generated for no growth model.

fafsd
<J

8

CO

0~L_

0

O

(D

p653

40

6 30 -

O 

CO

Q

20 -

-§ 10 -

13

13

O

0

0 1300 2600 3900 5200 6500

Cumulative Wildcat Wells
Figure 9. Onshore Growth Tables

Cumulative Growth (in percent)

ear

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

 riciuOil

1.000

3.075

4.339

5.204

5.893

6.285

6.703

6.929

7.162

7.403

7.653

7.910

8.127

8.313

8.503

8.592

8.683

8.774

8.866

8.960

9.054

13.402

13.474

13.547

13.620

13.694

13.768

13.842

13.917

13.992

14.068

14.144

14.220

14.297

14.374

14.452

14.530

14.609

14.688

14.767

14.847

 n

Gas

1.000

2.854

4.522

5.175

5.921

6.553

7.252

7.719

8.090

8.478

8.740

8.932

9.126

9.314

9.507

9.704

9.904

10.109

10.318

10.531

10.646

16.342

16.372

16.401

16.401

16.401

16.401

16.401

16.401

16.401

16.401

16.401

16.401

16.401

16.401

16.401

16.401

1 6.401

16.401

16.401

16.401

tCdCI VUII 

Oil

1.000

2.788

3.786

4.554

5.062

5.335

5.622

5.781

5.944

6.111

6.284

6.461

6.643

6.814

6.989

7.057

7.125

7.194

7.264

7.334

7.406

11.107

11.165

1 1 .223

1 1 .282

11.341

1 1 .400

1 1 .460

11.520

11.580

11.641

11.701

1 1 .763

1 1 .824

11.886

1 1 .948

12.011

12.073

12.136

1 2.200

12.264

Gas

1.000

2.790

4.163

4.944

5.677

6.103

6.561

6.749

6.942

7.141

7.346

7.557

7.774

7.902

7.989

8.076

8.165

8.254

8.345

8.436

8.508

10.285

10.286

10.287

10.288

10.289

10.289

10.290

10.291

10.292

10.293

10.293

10.294

10.294

10.294

10.294

10.294

10.294

10.294

10.294

10.294
Figure 10. Report of Parameters and Constants

ARDS V5.01 Date: 11/10/1997 Time: 11:45

File: ACON.PRN, report of parameters and constants

PLAY 653

Model option: Best AR or LAR 

BOE Scale: log 2 (6=1 mmBOE) 

Well increment for model: 100

Growth from year 1990 to 2010 

Growth model:Onshore - Field 

Largest size class-data present in all reps 16

Random num seed in aformat 4627 

Random num seed in agrow 9034

Wells - total exploratory

Cumulative well num of last discovery 11665

Number of fields used 646 

Type of fields: Oil & Gas 

Unit of input data: 

Oil thousand bbl Gas millions cu ft 

Area acres

NOTE-in the ARDS files the unit of oil and gas is mm BOE 

Unit of area is sq. km.

Play/basin size (sq. km.) - 42362. 

Ave modal class size 7 

Beg class size-non linear est. 7 

End class size-non linear est. 16

Beginning size class for small field estimation 5 

Replication numbers in p653.dtr for:

qlO 14

q50 42

q90 61 

Mean 65

Size class Right hand end (Millions BOE)

1 .063

2 .125

3 .250

14 512.000

15 1024.000

16 2048.000

17 4096.000

18 8192.000
LIST OF EXHIBITS (SAMPLE OUTPUT FILES)

Exh. File Name Generating Program

1 p653.tcw amerg.for

2 p653.dt adtable.for

3 p653.dp adtable.for

4 p653.stb asarea.for

5 p653.dtr agrow.for

6 p653.pem aest.for

7 p653.rem aresult.for

8 p653.fsd aresult.for

9 p653.ult aresult.for

10 p653.con all previous Fortran programs
Exhibit 1. Year End vs. Cumulative Wildcat Number, File p653.tcw

Cumulative 

Year Wildcat

1902 0

1903 0

1904 0

1905 0

1906 0

1907 1

1908 2

1909 3

1910 3

1911 3

1912 3

1913 3

1914 3

1915 4

1969 7568

1970 7762

1971 7951

1972 8139

1973 8306

1974 8518

1975 8758

1976 8976

1977 9208

1978 9497

1979 9765

1980 10046

1981 10364

1982 10634

1983 10879

1984 11181

1985 11413

1986 11516

1987 11576

1988 11632

1989 11672

1990 11678
Exhibit 2. Discovery Table, File p653.dt

Cum. Cumulative number of

wildcat

well

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700

1800

1900

2000

 *

9900

10000

10100

10200

10300

10400

10500

10600

10700

10800

10900

11000

11100

11200

11300

11400

11500

11600

11700

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

2

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

3

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

4

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Size class

5678

0021

0221

0221

0242

0662

0664

0767

0 8 8 10

0 8 9 10

0 9 9 13

0 10 11 13

0 11 13 14

0 12 14 15

0 15 17 18

0 17 18 21

0 21 21 25

0 23 24 25

0 25 24 28

0 27 27 29

0 28 31 36

0 138 121 117

0 140 121 117

0 140 121 117

0 141 121 117

0 142 122 117

0 143 122 118

0 144 122 119

0 147 122 119

0 147 123 119

0 149 126 119

0 151 127 120

0 153 127 121

0 153 127 122

0 153 127 122

0 153 127 122

0 153 128 123

0 153 129 123

0 156 129 123

0 158 130 124

discoveries

9

0

2

3

4

7

12

14

15

18

19

22

26

27

29

31

33

37

38

39

41

78

78

78

79

79

79

79

81

81

81

81

82

82

82

82

82

82

82

82

10

2

4

7

13

16

20

27

28

28

31

31

32

35

37

40

45

45

45

45

46

73

73

73

73

73

73

73

73

73

73

73

74

74

74

74

74

74

74

74

11

0

1

2

3

5

8

10

12

13

16

16

17

18

18

20

20

21

21

22

22

36

36

36

36

36

36

36

36

36

36

36

36

36

36"

36

36

36

36

36

12

0

1

1

1

3

5

7

9

9

9

9

9

9

10

10

10

12

13

13

13

16

16

16

16

16

16

16

16

16

16

16

16

16

16

16

16

16

16

16

13

3

3

5

7

8

11

11

11

12

12

12

12

12

12

12

12

12

12

12

13

14

14

14

14

14

14

14

14

14

14

14

14

14

14

14

14

14

14

14

14

0

0

0

2

2

3

4

4

4

4

4

4

4

4

4

4

4

4

4

4

7

7

7

7

7

7

7

7

7

7

7

7

7

7

7

7

7

7

7

15

0

0

1

1

1

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

16

1

2

2

2

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

 *

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3
Exhibit 3. Field File, File p653.dp (headings added)

Discovery 

number Discovery

^wxj.at;«a 

well)

1

2

8

9

18

23

44

68

97

108

121

140

145

153

163

181

184

186

203

225

252

281

282

11577

11582

11620

11634

11651

11665

t voj.urae oxze /vtrfc 

MBOE class km

220.

18.

205.

3.

5.

235.

23.

1332.

2.

15.

126.

1.

19.

43.

1.

12.

1494.

22.

18.

564.

8.

139.

53.

1.

1.

1.

2.

1.

4.

710

910

080

347

448

210

295

100

Oil

895

440

260

835

200

848

564

460

900

965

690

979

140

985

060

360

570

005

680

020

13

10

13

7

8

13

10

16

7

9

12

6

10

11

6

9

16

10

10

15

9

13

11

6

6

6

7

6

8

24.

9.

61.

4.

9.

45.

17.

217.

7.

5.

15.

5.

6.

17.

3.

84.

7.

8.

31.

8.

16.

17.

1.

1.

2.

2.

2.

3.

id

sq

80

10

00

20

40

50

50

40

00

90

43

00

53

80

60

00

50

00

30

70

40

13

50

68

88

01

26

08

12

adte 

.YYYYMMDD

19070128

19080606

19190918

19200216

19211218

19230118

19260602

19280815

19291120

19300621

19310215

19311201

19320130

19320506

19320831

19330402

19330505

19330523

19331214

19340508

19341028

19350413

19350419

19880101

19880202

19881013

19890112

19890615

19891024

 x 

Gas

47

4

47

16

99

55

50

68

97

37

70

33

48

42

47

53

34

32

40

30

11

52

82

24

62

89

87

65

93

.12

.79

.18

.43

.58

.69

.01

.88

.27

.43

.78

.73

.65

.13

.08

.72

.53

.31

.86

.11

.36

.82

.43

 

.53

.50

.17

.28

.48

.28

'eircents 

NGL

5

4

1

7

2

19

1

1

5

6

3

4

2

4

4

8

10

12

1

6

.03

.02

.84

.40

.42

.89

.51

.88

.59

.98

.27

.00

.93

.90

.49

.03

.24

.00

.82

.16

.00

.84

.56

 

.00

.09

.83

.72

.79

.72

Oil

47.85

95.19

47.98

82.16

.00

36.41

47.48

11.25

1.14

60.59

28.95

66.27

50.42

51.97

46.43

46.24

62.23

67.69

54.31

67.74

88.64

42.33

13.01

 

75.47

29.41

.00

.00

32.74

.00
Exhibit 4. Basic Statistics (Area Smoothed), File p653.stb

Average 

Size volume 

class nun BOE

1 .3125000E-01

2 .8838835E-01

3 .1767767

4 .3535534

5 .7071068

6 1.427490

7 2.859417

8 5.602127

9 11.49754

10 22.67801

11 46.72191

12 94.17100

13 178.1572

14 300.1193

15 578.0200

16 1559.720

17 2896.309

18 5792.619

Number Total 

of fids volume 

found mm BOE

0 .0000000

0 .0000000

0 .0000000

0 .0000000

0 .0000000

158 225.5433

130 371.7242

124 694.6638

82 942.7979

74 1678.173

36 1681.989

16 1506.736

14 2494.200

7 2100.835

2 1156.040

3 4679.160

0 .0000000

0 .0000000

Smoothed 

areas 

(km.sq.)

1.761554

1.931527

2.130603

2.420192

2.831019

3.419463

4.245590

5.384124

7.156324

9.639074

13.64950

19.71755

28.27948

38.69027

58.73806

116.2056

183.3194

314.0461

Right end Unsmoothed

size class areas

mm BOE (km.sq.)

.6250000E

.1250000

.2500000

.5000000

1.000000

2.000000

4.000000

8.000000

16.00000

32.00000

64.00000

128.0000

256.0000

512.0000

1024.000

2048.000

4096.000

8192.000

-01 .0000000

.0000000

.0000000

.0000000

.0000000

3.398725

3.979058

5.552815

6.959765

10.65404

13.07518

22.15187

34.89410

39.96001

28.73280

165.3822

.0000000

.0000000

1+0
Exhibit 5. Grown Discovery Table Replications, File p653.dtr

Cumulative number of discoveries

Rep CWW

num 100

1 1

1 2

1 3

1 4

1 5

1 6

1 7

1 8

1 9

1 10

1 11

1 12

1 13

1 14

1 15

1 16

1 17

1 18

1 19

1 20

.1 21

1 22

1 23

1 24

101 97

101 98

101 99

101100

101101

101102

101103

101104

101105

101106

101107

101108

101109

101110

101111

101112

101113

101114

101115

101116

101117

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

2

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

3

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

4

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Size class

5 6 7 8 9 10

002102

013105

013118

0 1 5 2 3 12

0 4 8 2 5 16

0 4 8 5 8 18

0 5 8 6 12 25

0 7 10 8 13 26

0 7 10 9 14 28

0 8 10 12 15 30

0 9 11 13 17 31

0 10 12 14 21 33

0 10 13 15 23 36

1 11 17 16 26 37

1 12 19 18 29 40

2 14 23 20 31 45

2 15 26 21 34 46

2 17 26 24 35 46

2 17 31 25 36 46

2 18 34 29 41 47

2 19 35 34 41 48

2 20 36 35 44 49

3 20 36 38 45 49

3 20 39 39 46 49

* 

9 73120127 99 70

9 73120127 99 70

9 74121128 99 70

9 74123128 99 70

9 74123128 99 70

9 74123129 99 70

9 74124129100 70

9 74125129101 70

9 75125130101 70

9 75127130103 71

9 75127131103 71

9 75130133103 71

9 76131134104 71

9 76132135104 73

9 76132136104 73

9 76132136104 73

9 76132136104 73

9 76133136105 73

9 76133136106 73

9 76135137106 73

9 77135139106 74

11 12

0 0

2 0

3 0

4 2

6 3

11 5

13 7

15 8

16 8

18 10

18 10

18 11

18 12

20 13

20 15

22 15

23 17

23 17

24 17

25 17

25 18

26 19

26 19

28 19

50 24

50 24

50 24

50 24

50 24

51 24

51 24

51 24

51 24

51 24

51 24

51 24

51 24

51 25

51 25

51 25

51 25

51 25

51 25

51 25

51 25

13

2

3

5

6

8

11

11

12

13

13

13

13

13

13

13

13

13

14

14

14

15

15

15

15

17

17

17

17

17

17

17

17

17

17

17

17

17

17

17

17

17

17

17

17

17

14

1

1

1

3

3

6

7

7

7

7

7

7

7

7

7

7

7

7

7

8

9

9

9

9

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

.8

8

15

0

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

16

1

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

17

0

0

0

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1
Exhibit 6. Unsmoothed Parameter Estimates, File p653.pem

(1)(2) (3)(4)(5)(6)(7)(8) (9) (10) (11) (12) (13) (14) (15)

1 7

1 8

1 9

1 10

1 11

1 12

1 13

1 14

1 15

1 16

101 7

101 8

101 9

101 10

101 11

101 12

101 13

101 14

101 15

101 16

138

136

96

62

49

20

14

10

2

3

140

136

89

74

43

23

18

4

4

2

2 0

2 0

1 0

1 0

1 0

1 0

1 0

1 0

1 0

1 0

2 0

2 0

1 0

1 0

1 0

1 0

1 0

1 0

1 0

1 0

1

1

1

1

1

1

1

1

2

1

1

1

1

1

1

2

1

1

2

1

117

117

117

117

117

117

117

117

116

117

117

117

117

117

117

116

117

117

116

117

4

4

2

2

2

2

2

2

2

2

4

4

2

2

2

2

2

2

2

2

446.

540.

527.

403.

153.

79.

17.

44.

1.

1.

374.

196.

502.

635.

117.

50.

-61.

21.

21.

0.

173.70

145.73

100.17

62.34

49.00

20.09

14.04

10.00

2.01

3.00

172.05

140.52

90.42

74.07

43.46

23.00

18.00

4.00

4.00

2.00

1.

1.

1.

1.

1.

1.

1.

.

2.

1.

1.

2.

1.

1.

1.

1.

2.

1.

.

3.

397

676

502

801

818

243

835

709

270

608

424

131

531

539

627

231

039

310

978

600

542.

785.

0.

0.

0.

0.

0.

0.

0.

0.

738.

893.

0.

0.

0.

0.

0.

0.

0.

0.

1078.

1209.

0.

0.

0.

0.

0.

0.

0.

0.

1123.

1525.

0.

0.

0.

0.

0.

0.

0.

0.

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

Field Description:

(1) Replication number

(2) Class size

(3) Number of simulated fields found

(4) Model, 1=AR, 2=LAR (piecewise)

(5) Error code (0 & 1 imply convergence)

(6) Shift of number of cumulative wildcat well increments

(7) Number of well increments used by model

(8) Number of model parameters estimated

(9) Sum of squares error

(10) Unsmoothed estimate of ultimate number of fields

(11) Unsmoothed estimate of discovery efficiency

(12) Estimate of AR shift (gamma in LAR model)

(13) Estimate of joint (or cut) point (alpha in LAR model) 

(14-15) Currently not used
Exhibit 7. Remaining BOE, Growth and Geometric Ratio by 

Replication, File p653.rem

Rep Remaining Growth 

num BOE BOE

1

2

3

4

5

6

7

8

9

10

11

12

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

101

131.55

100.63

96.00

125.27

100.05

87.03

107.80

91.10

91.08

78.46

35.53

213.54

87.67

113.32

74.81

89.51

148.90

134.64

145.23

71.89

152.73

160.13

78.44

71.24

113.58

117.71

48.33

64.73

1060.77

822.09

979.14

1020.10

1083.06

1014.13

946.60

1077.60

965.16

1032.06

828.00

1202.99

1051.86

844.68

956.76

937.79

979.77

1024.55

1014.23

792.21

1099.29

892.73

928.36

936.43

1081.51

886.35

845.37

874.89

Growth Geometric ratio 

class 8-11 mean s.d. n

2501.8

3973.0

3087.2

2664.6

3167.1

3550.9

3681.0

4247.9

2755.4

2433.7

2957.8

2236.4

2968.2

2840.4

2266.8

3231.8

2665.5

1821.6

3016.1

2489.9

3809.5

1924.3

2115.6

2885.9

1834.8

2069.1

2779.7

2598.6

1.565

1.515

1.541

1.548

1.573

1.544

1.541

1.562

1.536

1.566

1.512

1.587

1.553

1.508

1.542

1.539

1.541

1.545

1.565

1.499

1.569

1.508

1.530

1.535

1.567

1.533

1.519

1.507

.174

.124

.110

.192

.448

.122

.111

.101

.206

.265

.167

.292

.248

.297

.111

.138

.194

.221

.168

.169

.213

.249

.367

.198

.251

.313

.245

.127

7

7

7

7

7

7

7

7

7

7

7

7

7

7

7

7

7

7

7

7

7

7

7

7

7

7

7

6

Estimated ultimate 

numbers of fields

Classes 567

580.6 371.0 237.1

482.4 318.4 210.2

540.8 350.9 227.7

552.1 356.8 230.5

589.9 375.1 238.5

548.1 355.1 230.0

531.4 344.9 223.8

578.5 370.3 237.1

533.4 347.3 226.2

569.9 364.0 232.4

480.0 317.4 209.8

629.7 396.8 250.1

564.0 363.2 234.0

481.7 319.5 211.9

533.9 346.3 224.6

528.2 343.3 223.1

539.6 350.2 227.3

554.8 359.1 232.5

568.2 363.0 231.9

465.7 310.6 207.2

586.7 373.9 238.3

494.9 328.2 217.6

518.0 338.5 221.2

523.9 341.2 222.3

583.1 372.2 237.6

510.9 333.3 217.4

488.3 321.4 211.6

490.7 325.6 216.0
Exhibit 8. Remaining and Growth BOE Summary Statistics, File 

p653.fsd

ARDS V5.01 Date: 10/30/1997 Time: 15:39

FILE p653.fsd

Growth from year 1990 to 2010 

Growth model:Onshore - Field 

Model option: Best AR or LAR 

BOE Scale: log 2 (6=1 MBOE) 

Well increment: 100

Expected remaining field sizes-class by class averaged 

over 101 replications. 

WARNING results may be affected by unusual reps.

Class Ave Num of Fids Ave MBOE

5

6

7

8

9

10

11

12

13

14

15

16

539.64

241.85

89.49

5.89

2.97

.41

.04

.14

.01

.03

.01

.00

.71

1.43

2.86

5.60

11.50

22.68

46.72

94.17

178.16

300.12

578.02

1559.72

Rep

Q.10 14 

Q.50 42 

Q.90 61

Mean 65 

80% T-mean

Growth

Rep

Q.10 82 

Q.50 79 

Q.90 71

Mean 97 

80% T-mean

Remaining mm BOE

Class Sizes

8- 16 5- 7

59.602 1032.062

107.796 902.748

153.687 1024.548

107.950

106.558

mm BOE 

All Fields 

1989.580 

2826.610 

3952.820

2888.518

2866.539

982.716

For means, replication is one closest to mean

For quantiles, replication based upon large size class estimates
Exhibit 9. Estimated Ultimates, File p653.ult

ARDS vS.Ol Date: 10/30/1997 Time: 15:39

PLAY p653

Model option: Best AR or LAR 

BOE Scale: log 2 (6=1 MBOE) 

Well increment: 100 

Type of fields: Oil & Gas 

Growth from year 1990 to 2010 

Growth model: Onshore - Field

yueui

tile

10

10

10

10

10

10

10

10

10

10

10

10

Total

*

50

50

50

50

50

50

50

50

50

50

50

50

Total

*

90

90

90

90

90

90

90

90

90

90

90

90

Total

*

Class Eff

5 .000

6 .000

7 1.554

8 2.013

9 1.531

10 1.959

11 1.334

12 1.564

13 1.767

14 .684

15 2.270

16 3.600

Geometric

5 .000

6 .000

7 1.528

8 1.709

9 1.573

10 1.812

11 1.713

12 1.364

13 2.152

14 .583

15 .807

16 1.608

Geometric

5 .000

6 .000

7 2.069

8 1.350

9 1.570

10 1.898

11 1.494

12 1.131

13 2.643

14 1.052

15 .970

16 2.338

Geometric

<j.cown ACUlleU. DU£j X. J.WCJO

Ult Fids Fids Fnd Fids Fnd Remaining Ultimate

517.3*

337.7*

220.4*

131.4

102.9

71.0

38.0

24.1

17.0

9.0

2.0

2.0

1472.9

ratio = 1.53

525.7*

341.8*

222.2*

134.3

93.9

75.0

45.0

19.2

18.0

7.0

3.0

3.0

1488.1

ratio = 1.54

598.3*

380.7*

242.2*

150.7

97.0

69.0

42.0

22.2

15.0

10.0

4.0

1.0

1632.0

ratio = 1.57

0.

0.

139.

128.

101.

71.

38.

24.

17.

9.

2.

2.

531.

0.

0.

153.

126.

91.

75.

45.

19.

18.

7.

3.

3.

540.

0.

0.

131.

130.

95.

69.

42.

22.

15.

10.

4.

1.

519.

0

158

130

124

82

74

36

16

14

7

2

3

646

0

158

130

124

82

74

36

16

14

7

2

3

1292

0

158

130

124

82

- 74

36

16

14

7

2

3

1938

365.8

482.1

232.8

19.2

22.4

.0

.0

12.2

.0

.0

5.8

.0

1140.2

371.7

487.9

197.9

46.7

33.0

.0

.0

17.0

5.3

.0

5.8

.0

1165.3

423.1

543.4

318.0

115.7

22.9

.0

.0

15.1

.0

.0

.0

.0

1438.2

365.8

482.1

630.2

736.2

1183.7

1610.1

1775.4

2272.3

3028.7

2701.1

1161.8

3119.4

19066.9

371.7

487.9

635.4

752.6

1079.3

1700.9

2102.5

1806.2

3212.2

2100.8

1739.8

4679.2

20668.4

423.1

543.4

692.6

844.0

1115.1

1564.8

1962.3

2086.8

2672.4

3001.2

2312.1

1559.7

18777.5
Exhibit 10. Constant File p653.con and Descriptors (file grcon.dat)

File p653.con follows:

p653 1110 4627 646 1 11665 11700 42362. 100 2 9034 16 

1 1 1990 2010 7 7 16 3 1 5 14 42 61 65

Description of the elements in file p653.con.

grcon.doc documents the fn.con file used by all Fortran programs

in ARDS 5.00.

Cols. Format Description Program

1-10 alO play name aformat.for 

11-12 i2 oil/gas code (1=O&G, 2=O, 3=G)

13-14 i2 input units of oil code (l=thous bbl, 2=mill bbl) 

15-16 i2 input units of gas code

(l=millions cu ft, 2=billions cu ft) 

17-18 i2 input units of area code

(0=acre, l=sq km, 3=sq mi)

19-24 i6 random number seed-missing dates 

25-30 i6 number of fields 

31-32 i2 wells l=total exploratory (Lahee 2-5) amerg.for

2-new field wildcats (Lahee 5) 

33-38 i6 cumulative wildcat-last 

39-44 i6 number of wells processed-rounded adtable.for

up to next well increment 

45-54 flO.O play size (sq.km.) 

55-60 i6 well increment 

61-62 i2 scale for size classes

l=log base (2) scale=0.0593

2=log base (2) Class 6=1 MBOE, usual

3=log base (4) Class 6=1 MBOE

4=user defined size classes

63-68 i6 random number seed-growth model agrow.for 

69-72 i4 largest size class-grown fields

all data present

73-74 i2 onshore(l), offshore(2),no growth(0) 

75-76 i2 field(l), reservoir(2) growth 

77-81 i5 year-grow fields from 

82-86 i5 year-grow fields to 

87-90 i4 average modal class 

91-94 i4 beginning class size for nonlinear aest.for

estimation

95-98 i4 ending class size for nonlinear est 

99-100 i2 model option, AR(1), LAR(2), best(3) 

101-102 i2 estimate small fields (l=y,0=n) 

103-105 i3 beginning class size, small field est 

106-109 i4 replication for qlO remaining BOE aresult.for 

110-113 i4 replication for qSO remaining BOE 

114-117 i4 replication for q90 remaining BOE 

118-121 i4 replication closest to mean rem BOE
APPENDIX A. EXAMPLE FROM SUPERPLAY 653

aformat

ARDS vS.Ol

Date: 09/09/1997 Time: 20:27

Program AFORMAT.FOR reformats the field file and 

estimates missing month, day

Enter play name - no extensions, i.e., p653 (9 char max) 

p653

Field file data:

3-digit year, i.e. 938, in ID

Field name

Gas (if used)

Natural gas liquid (if used)

Oil (if used)

Area

Date of discovery yyyy/mm/dd

The format is: (4x,i3,4x,a25, 49x, ilO, 23x, ilO, 23x, 

ilO,15x,f6.0,3x,i4,Ix,i2,Ix,i2)

It is assumed the field file is named p653.fld 

The reformated output file is p653.ytw 

If OK, hit Enter/ else Break, Rename, and Restart

The current year in this computer is: 1997

Type of fields to include:

1-Oil & Gas

2-Oil only (Non assoc gas:oil < 20mcf:l bbl)

3-Gas only

Natural Gas Liquid (NGL) is coverted to bbl and counted as oil 

1

Enter units 

Oil, t=thousands of barrel, m=millions of barrel

Note: Units of NGL assumed to be same as oil 

t

Gas/ m=millions cu. ft./ b=billions cu. ft. 

m

To estimate missing month/day (if necessary),

enter random seed [1 to 32767] or 0 (to have computer choose) 

4627

Field AREA in Acres (Nehring convention)? y/n

y

646 fields written to output file p653.ytw

Output file is p653.ytw 

It contains:

Discovery YR, MON, DAY, BOE (thousands bbl), Area (sq km), 

% Ultimate Gas, NGL, Oil & Field Name

The next program AMERG. FOR, merges fields with wells:

To run/ enter AMERG 

Stop - Program terminated.
[W] C:\My Documents\ards\data>amerg

ARDS vS.Ol

Date: 09/09/1997 Time: 20:28

Program AMERG.FOR-Merge well & field files,

estimate missing areas-function AREST 

Enter name of play - no extensions, i.e. p653 

p653

It is assumed that the reformated Nehring file is named p653.ytw

The input well file is p653.wel

The merged field-well output file is p653.dtw

The year-cumulative wildcat well table is p653.tcw

The constant (input/output) file is p653.con

** If OK, hit Enter, else Break, Rename, and Restart

Pause - Please enter a blank line (to continue) or a DOS command.

Type of Wells to be Processed

1 = Total Exploratory Wells (Lahee classes 2-5)

2 = New Field Wildcats (Lahee class 5) 

Enter 1 or 2

1

There are 71 missing areas

Model used is: In area= .4911 + .4639 In BOE 

R2= .49 Std Dev= .6599 n= 575

Use these calculated values? y/n

y

Merged field-well file is p653.dtw It has 646 fields 

File contains: Cumulative wildcat well

BOE (millions of barrels)

Area (sq. km.)

Year, month, day of discovery

% Gas, NGL, Oil of ultimate recovery

Field name

First discovery at 1 wells, on 1907/02/14 

Last discovery at 11665 wells, on 1989/10/24

Next program ADTABLE.FOR generates discovery table & basic stats 

To run enter ADTABLE 

Stop - Program terminated.
[W] C:\My Documents\ards\data>adtable

ARDS vS.Ol

Date: 09/09/1997 Time: 20:28

Program ADTABLE.FOR creates discovery table, file & basic stats

Enter name of data, i.e. p653 (No extension) 

p653

It is assumed the well/field file is named p653.dtw 

and data (separated by spaces or ,) are: 

Wells, boe, area, year, mon, day of discovery

Discovery table, disc, file, basic stats, and constants 

will be named p653 with extensions: 

.dt 

.dp

.sta, and 

.con respectively. 

A print file is adtable.prn.

** Existing files with these names will be destroyed ** 

If OK, hit Enter, else Break, Rename, and Restart

Pause - 1

Enter play (or basin) size (sq. km.) 

42362.

ENTER well increment - 100 is usual 

100

ENTER a,m, or d

a - to use all wells

m - to specify maximum well number

d - to specify maximum date

Specify scale (size class):

l=log base 2(0.005930)

2=log base 2 (usual)

3=log base 4

4=user defined 

2

Next program is ASAREA.FOR

which yields regression smoothed Average Area by Class. 

To plot this smoothed area (& raw area) vs BOE, run Systat 

macro: ASAREA.CMD. Type macro, then submit asarea

Stop - Program terminated.
[W]C:\My Documents\ards\data>asarea

ARDS vS.Ol

Date: 09/09/1997 Time: 20:36

Program ASAREA.FOR

Creates smoothed areas using the model: 

log(area)=bO+bl*log(ave boe)+b2*log(ave boe)^2 

Enter name of data, i.e. p653 (No extension)

p653 

Convergence : SSE= 6.873863743064701E-001 Iterations

Plot smoothed areas using Systat Macro ASAREA.CMD 

To run ASAREA, type macro, then submit asarea 

Next Fortran program is AGROW.FOR 

Stop - Program terminated.

S'O
p653

ARDS vS.Ol Date: 10/30/1997 Time: 12:33

FILE p653.fsd

Growth from year 1990 to 2010 

Growth model:Onshore - Field 

Model option: Best AR or LAR 

BOE Scale: log 2 (6=1 MBOE) 

Well increment: 100

Expected remaining field sizes-class by class averaged 

over 101 replications. 

WARNING results may be affected by unusual reps.

Class Ave Num of Fids Ave MBOE

5

6

7

8

9

10

11

12

13

14

15

16

539.64 .71

241.85 1.43

89.49 2.86

5.89 5.60

2.97 11.50

.41 22.68

.04 46.72

.14 94.17

.01 178.16

.03 300.12

.01 578.02

.00 1559.72

Remaining MBOE

Q.10 

Q.50 

Q.90

Rep 

14 

42 

61

Class Sizes

8- 16 5- 7

59.602 1032.062

107.796 902.748

153.687 1024.548

Mean 65 

80% T-mean

Growth MBOE

Rep

Q.10 82 

Q.50 79 

Q.90 71

Mean 97 

80% T-mean

107.950

106.558

All Fields 

1989.580 

2826.610 

3952.820

2888.518

2866.539

982.716

For means, replication is one closest to mean

For quantiles, replication based upon large size class estimates

Page 1
p653

90 16 2.338 1.0 1. 3 .0 1559.7 

Total 1632.0 519. 1938 1438.2 18777.5 

* Geometric ratio = 1.57

Page 2 5*1
[W]C:\My Documents\ards\data>agrow

ARDS V5.01

Date: 10/30/1997 Time: 20:47

Program AGROW.FOR grows fields

Program produces 101 discovery tables (replications)

Enter name of data, i.e. p653 

p653

Input files must be named p653 with extensions: 

.con, constants (input/output file) 

.dp, well/field 

.stb, basic stats file

Output files will be named p653 with extensions 

.dpr, grown fields for 1st replication 

.dtr, discovery table files; 1 per replication 

.gro, simulated growth for each replication 

IF OK PRESS ENTER

Pause - 1

Play size= 42362. Max wells= 11700 Scale code= 2 

Growth option, y/n?

Enter random seed [1 to 32767] or 0 (to have computer choose)

9034

Growth model (enter):

1-US onshore

2-W.Gulf Mexico offshore

3-World Oil 

1

Field (1) or Reservoir (2) growth? 

1

Grow fields to enter 4 digit year 

2010

Enter year (4 digits) to begin growth 

Normally this is year of last update 

1990

Largest Size Class Containing at Least One Field: 17 

Largest Size Class with Data Present in All-Classes 16

The next program is AEST.FOR 

Stop - Program terminated.
[W] C:\My Documents\ards\data>aest

ARDS vS.Ol

Date: 10/30/1997 Time: 20:48

Program AEST.FOR estimates A-R or linear AR model parameters

Enter name of data, i.e., p653 

p653

Model: AR(1), Linear-AR(2), Best model(3) 

3

Enter beginning and ending class size for estimates.

Beginning is typically the modal class size M or M+l of grown distn

Ave modal class = 7

Largest size class with data present in all reps = 16 

7,16

Last replication used 101 

Next program is ARESULT.FOR 

Stop - Program terminated.

Slf-
[W] C:\My Documents\ards\data>aresult

ARDS vS.Ol

Date: 10/30/1997 Time: 20:49

Program ARESULT.FOR estimates remaining BOE for each rep.

Enter name of data, i.e. p653 

p653 

Estimate remaining small fields? y/n

y

Enter geometric ratio or 0 to have it computed

Computed geometric ratio bounded between 1 and 2 

0 

Enter minimum size class for small field estimation

Note, this is usually 1 to 3 class sizes below the mode. 

5

Last replication used 101

See file p653.fsd for field size distn & quantile est 

See file p653.ult for ultimates on quantile est

Stop - Program terminated.