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Resources and Energy 3 (1981) 297-335. North-Holland Publishing Company
A COMPARISON OF TEN U.S. OIL AND GAS SUPPLY MODELS*
Peter CLARK Federal Reserve System, Washington, DC 20551, USA
Patrick COENE Stanford University, Stanford, CA 94305, USA
National Fund for Scientific Research, Brussels, Belgium
Douglas LOGAN Stun~ord University, StanJord, CA 94305, USA
Ten recent forecasting models of the US. domestic supply of crude oil and natural gas are analyzed and compared. The actual supply process is divided up into its main stages, being exploration, development and production. For each of these stages, major ways of modeling them are distinguished. These methodologies are analyzed in detail and we discuss the ways m which the models implement them. Particular attention is paid towards how prices, taxes, government regulations and offshore leasing schedules are incorporated into the models.
1. Introduction
Domestic production of crude oil and natural gas satisfies an important fraction of the U.S. energy needs. Future energy prices, as well as the U.S. dependence on foreign oil, will partially be determined by the extent to which these production levels can be maintained or increased.
Therefore, forecasts of these levels are important in evaluating and choosing among various options for national energy policy. This has led to the construction of many models of the petroleum sector. These models provide quantitative forecasts of domestic oil and gas production levels under alternative scenarios. Several of these models are currently used in both private and public decision making. Given this role, a review of their structure and an assessment of their strengths and weaknesses is appropriate.
*This paper is part of the tifth study (U.S. Oil and Gas Supply) of the Energy Modeling Forum at Stanford Universtty. The Electric Power Research Institute sponsors the Energy Modeling Forum. The Gas Research Institute sponsors the EMF-5 study jointly with the Electric Power Research Institute. We thank James Sweeney and John Weyant for valuable comments, Richard Forberg for his participation in the initial stages of the research, and each of the modelers for their cooperation in providing information and for comments on a previous draft of thts paper. Of course, all errors remam the sole r~pons~bility of the authors.
0165-0572/81/0000-0000/$02.75 0 1981 North-Holland
298 P. Clark et al., Ten U.S. oil and gas supp1.v models
In this paper, we compare ten forecasting models’ of U.S. domestic oil and gas supply. As will be described in section 2, one can distinguish three major stages in the supply process of oil and natural gas: exploration, development and production. For each of these stages we will discuss the different modeling approaches and indicate the specific implementation of these approaches in each model. We will pay special attention to the description of the resource base, as well as to how prices, taxes, and government leasing schedules affect the results of the models.
The paper is organized as follows: First, we identify the main components of the supply process, and describe them briefly. Then we give a short overview of the models using a table. In the next sections (4 through 8) the modeling methodologies used and their implementation in each of the models is discussed for each stage of the supply process separately. Next, we describe the way prices (section 9), taxation, regulation, and government leasing policy (section 10) are introduced and how they influence the forecasts.
2. The supply process and the major modeling approaches
The ten models considered in this paper span a wide range of approaches to modeling oil and gas supply. While the methodologies employed are widely divergent, each model is trying to explain the same process of petroleum supply. In order to understand and evaluate the models, one must first understand how pools of oil and gas are found and how production facilities are subsequently installed to supply crude oil to refineries and natural gas to pipelines. This process is like a production line, moving the resources from an undiscovered state through delivery to final demand, as shown schematically in fig. 1.
Fig. 1. Oil and gas supply process.
Initially, crude oil and natural gas are undiscovered pools of various sizes situated at various depths in the earth’s crust. .Geological and geophysical surveys yield some clues about their position and size, but the only way to determine whether oil or gas is present is to drill exploratory wells. When an exploratory well is successful, and a new pool is discovered, it still must be
‘The ten models described here took part in the fifth study of the Energy Modeling Forum (U.S. Oil and Gas Supply). The modelers ran their models for a set of scenarios designed by the working group of EMF 5. The results of this simulation are not described in this paper, but will appear in the report of the study.
P. Clnrk et al., Ten U.S. oil and gas supply models 299
developed by drilling additional wells, and in the case of gas, installing a feeder pipeline. Once the production capacity is installed, oil and gas is produced over a number of years, usually at a declining rate as the initial stock of resource in the pool is depleted.
A majority of the models considered have structures that are closely related to the actual process of production. They start with an estimate of resources yet to be found. In one model this description is a very detailed geological description, while in the other models an aggregate resource base is given. Levels of exploratory activity are then determined, usually with some consideration of the costs and benefits of drilling, and the outcome of this exploration (additions to the stock of discovered resources) is estimated. The models then estimate the extent to which these resources will be developed, produced, and ultimately depleted. Not all of these decisions in the supply process (exploration, installation of productive capacity, and production) are modeled behaviorally in each case, but almost all of the models allow for some behavioral response in the supply process.
A minority of the models do not take the ‘process-oriented’ approach described above, but instead try to represent the supply process implicitly, by estimating how supplies respond to variations in prices. In this case, the amount of undiscovered resources may be inferred by the model as a result of the statistical relationships between prices, exploration, and production. The end result for all of the models, however, is a forecast of oil and gas supply, conditional on prices, regulation, taxes, and in some cases, assumptions about eventual resource availability and the short-run supply of drilling rigs.
At each stage in the supply process, there is a substantial amount of uncertainty: the extent of undiscovered resources is unknown, future amounts of exploratory effort cannot be predicted with much confidence, and the relationship between exploratory effort and eventual discoveries might deviate substantially from historical experience. Even after an oil or gas pool has been discovered, and its size accurately measured, the extent of development and rate of production from it is harder to predict than in the past, given the current environment of rapidly rising prices. As the different submodels of each stage of the supply process are discussed below, the reader should keep in mind that the estimates being generated by the models are only the mean value of or ‘best guess’ at levels of supply activity and production in the future.
3. An overview of the models
Table 1 contains a catalog of the ten oil and gas supply models considered in this paper. Although the meaning of most of the columns is clear, some further explanation may be necessary, The third column gives the dates over
Mod
el
Bui
lder
s
Tab
le
1
A c
atal
og
of o
il an
d ga
s su
pply
mod
els.
_-
U
sers
M
ode
of
g
(fun
ders
) D
ates
A
nces
tors
R
esou
rces
G
eogr
aphy
M
etho
dolo
gy
oper
atio
n In
tegr
ated
-
AG
A-T
ER
A
onsh
ore
offs
hore
DFI
-GE
MS
EIA
-IC
F O
GM
AH
M
E-M
-S
Epp
le-H
anse
n
FOSS
IL2
Kim
- T
hom
pson
LO
RE
ND
AS
MIT
-WO
P
Ric
e
L. T
ucke
r (A
GA
)
R.
Mar
shal
la
(DFI
) E
IA/D
FI
77-7
8 SR
I/G
ulf
oil,
gas
all
U.S
. D
. N
esbi
tt (D
FI)
and
othe
rs
W. S
titt
(IC
F)
E. E
rick
son
(NC
SU)
R. S
pann
(U
PI)
S. M
illsa
ps (
ASU
)
D.
Epp
le,
L. H
anse
n (C
arne
gie-
Mel
lon)
R. N
ail1
(D
artm
outh
-DO
E)
AG
A
71-7
9 -
oil
and
gas
low
er 4
8 on
shor
e lo
wer
48
offs
hore
NPC
/FE
A
oil
and
gas
low
er 4
8 on
an
d of
fsho
re
DO
E
1619
Bro
okin
gs
74
- In
stitu
tion
- 15
-79
--
DO
E
Ye-
79
-
Y.
Kim
(U
. of
Hou
ston
) T
EA
C
77-7
8 N
PC
R. T
hom
pson
(U
. of
H
oust
on)
L.
Rap
opor
t @
PI)
VPI
/NSF
75
-79
-
M.A
. A
delm
an (
MIT
) J.
Pad
dock
(M
IT)
H.D
. Ja
cobi
(M
IT)
P. R
ice
(OR
NL
)
MIT
/NS
F
76-7
9 -
75-7
9 -
oil
and
gas
Ala
ska
oil
low
er 4
8 on
and
off
shor
e
oil
and
gas
low
er 4
8 on
and
off
shor
e
oil,
gas
all
U.S
. an
d ot
hers
oii
and
gas
low
er 4
8 on
shor
e
oil,
gas
all
US
and
othe
rs
oil
wor
ld
oil
and
gas
low
er 4
8 on
and
off
shor
e
econ
omet
ric
engi
neer
ing
proc
ess
engi
neer
ing
proc
ess
engi
neer
ing
proc
ess
econ
omet
ric
econ
omet
ric
engi
neer
ing
proc
ess
engi
neer
ing
proc
ess
engi
neer
ing
proc
ess
engi
neer
ing
proc
ess
sim
ulat
ion
no
optim
izat
ion
no
sim
ulat
ion
yes
sim
ulat
ion
yes
inte
rtem
pora
l op
t~is
atio
n
sim
ulat
ion
no
sim
ulat
ion
no
sim
ulat
ion
yes
optim
izat
ion
no
inte
rtem
pora
l ye
s op
timiz
atio
n
sim
ulat
ion
no
econ
omet
ric
sim
ulat
ion
yes
P. Clark ei al., Ten U.S. oil and gas supply models 301
which the model was developed. A date of 1979 indicates that current work may be in progress. The fourth column identifies antecedent models to the ones discussed. Column 8 classifies model methodology into two types: econometric or engineering process.
An econometric model of production is a model which relies extensively on statistical analysis of historical data pertaining to the oil and gas industry. Models of this type are usually formulated in two stages. First, an economic theory is developed as to what variables are thought to have primary impact on the various aspects of oil and gas supply. Second, historical data are collected and statistical methods are employed to estimate the linkages between the dependent and independent variables in the model.
Engineering-process models differ in a fundamental way from the econometric models. While econometric models concentrate on the statistical relationships between prices and production, engineering-process models concentrate on simulating the process itself. Typically, each stage of the supply process (exploration, development, and production) is represented by a separate submodel that functions according to an optimization principle. While some of the parameters in a submodel may be statistically estimated, others are determined judgmentally from engineering considerations.
The ninth column in table 1 indicates the procedures used to generate forecasts with the models. Three of these procedures or ‘modes of operation’ are distinguished:
(1) Simulation: In this case, the set of equations that constitute the model is solved for the endogenous variables, given a set of values for the exogenous variables. While the solution of the model may be complicated by simultaneity between sets of equations, each equation is anaiytical in nature and does not require the calculation of a maximum or minimum value.
(2) One-period optimization: For each time period, values of the endogenous variables are found which not only satisfy the equations of the model, but also maximize or minimize an objective function. For example, given current prices and costs, the discounted present value of future revenue flows may be maximized.
(3) ln~er~ernpo~~~ op~imizu~ion~ The model solves simultaneously for an optimal set of values for all endogenous variables for all time periods in order to optimize an objective function. The operational difference between the intertemporal optimization and one-period optimization is one of foresight: an intertemporal model can ‘look ahead’ into future periods and adjust current decisions to make them optimal with respect to information available about the future. With oil and gas models, future prices (or expectations about future prices) can be very important in determining the time profile of production; intertemporal optimization models can react to future price rises by lowering current production, while one-period optimization models do not have this feature.
302 P Clark et al., Ten U.S. oil and gas supply models
4. Undiscovered resources
In the exploration process, the industry drills down into geological formations, which have unknown quantities and grades of crude oil and natural gas, thus obtaining information about the true extent of petroleum deposiis in the formation. If a sufficient volume of oil or gas is found, a ‘discovery’ is reported, If no oil or gas is found, or if something is found but the quantity is insurgent to be profitable to develop, a ‘dry hole’ is reported. The total amount of oil and gas discoveries reported in a single year includes only what was found in deposits large enough to be profitable. The rest is ignored. Current technology and economic conditions determine whether a given deposit is a discovery or a dry hole. What was a ‘dry hole’ in one year may be called a ‘discovery’ in a later year when prices are higher and recovery techniques have improved. Thus, the total amount of discoveries in a single year, and an estimate of total remaining undiscovered resources requires explicit economic and technological assumptions to be meaningful.
In representing the undiscovered resources, the models in this study took one of two broad approaches:
(a) The undiscovered resources in a region may be modeled as a finite collection of individual deposits, with probability distributions for certain relevant characteristics of the deposits - volume, porosity of the rock, grade of crude oil present, etc. See fig. 2.
frequency distribution
rlcutoff
Deposita smaller than *toff are not profitable for given
economic and technologicfd assumptions. With improved technology,
ioww operating costs, OI increased prices for crude oil. this
boundary nloves left.
Fig. 2. Hypothetical distribution of oil deposits by volume.
P. Clark et al., Ten U.S. oil and gas supply models 303
C-9 Alternatively, a region’s undiscovered resources may be modeled by a ‘finding function’, relating discoveries to some measure of exploratory effort. Some models use a ‘cost function’ or variant thereof, which can be shown to be equivalent to a finding function under certain assumptions regarding costs. See fig. 3.
diswvcwies
finding rate
- This asymptote represents the total volume of d,rcovemble resources
cwnuiiitive exptoratory effort
The shapes of these CUWBS depend On tbs size distribution of deposits, on the amount of effort required to
The wea undar the curve mprasents the volume of discovarabls re~Ourcc+s
cumulatwe explontory effort
marginal cost of sxplordtion The rhap of this cuwe
depends on the a&s of exploration as well as the factors indicated for the other culMI
cumulative?iiscoverier
Fig. 3. Hypothetical finding curves and cost curves.
The first approach allows the pro~tabi~ity of each prospect to be determined at the time the model is run, while in the second approach, economic and technological prejudgments are embedded in the finding or cost function. Also, certain assumptions regarding the exploration process - most obviously, that there is a tendency for the larger and easier to find deposits to be found first - are embedded in the finding or cost function approach. The asymptote of the cumulative discoveries curve, the limit of the integral of the finding rate curve, and the asymptote of the marginal cost curve are the total quantities of discoverable resources implicit in these functions, when the limits or asymptotes exist. The shape of the curves
304 P. Clark et al., Ten U.S. oil and gas supply models
depends upon the size distribution of deposits and the assumptions regarding the exploration process mentioned above. Section 6 below analyzes the implementation of finding curves in some detail.
The parameters of the probability distributions or the finding or cost functions used in a particular model may be obtained by geological judgement or by estimation from historical data. In most cases, both are used. Many of the finding or cost curves were estimated from historical data on exploration and discoveries with the constraint that the total amount of discoverable resources is equal to a predetermined value. This specific value is usually a widely recognized estimate of discoverable resources. The most widely used estimates of discoverable oil and gas resources for the United States are those of the U.S. Geological Survey (published in USGS Circular 725), the National Petroleum Council, and the Potential Gas Committee. Different assumptions regarding technoIogy and prices underlie each of these estimates, and the area covered by offshore estimates differs. The estimates for U.S. lower 48 onshore are summarized in table 2.
Table 2
U.S. undiscovered and inferred petroleum resources onshore and offshore.
Crude oil {b~~~~offs of barrels)
Natural gas (trillion cubic feet)
USGS” 95th percentile 13 524 Mean 105 686 5th percentile 150 857
NPCb 103 1178
PGC” - 1146
‘U.S. Geologicaf Survey, Oil and Gas Branch Resource AppraisaI Group (1975); includes offshore resources to water depth of 200m.
bNational Petroleum Council, ‘U.S. energy outlook - Oil and gas availability’ (1973); includes offshore resourrxs to water depth of 2500m.
‘Potential Gas Committee, ‘Potentiai supply of natural gas in the United States’ (1973); includes offshore resources to water depth of 46Om.
The probability distributions representing size and other characteristics of petroleum deposits may be adjusted so that total volume of discoverable resources for a given technology and prices equals some chosen estimate.
When a resource base model is calibrated to a particular estimate, care must be taken in running that model with a different estimate. For example, the shape parameters of a finding curve which have been estimated from historical data under the constraint that total resources equal some value will, in general, be different from those estimated with a different constraint. Et is incorrect to merely adjust the parameter indicating the quantity of total
P. Clark et al., Ten U.S. 011 and gas supply models 305
Table 3
Model
Representatton of undiscovered resources
Source of parameters Calibrated to
Can total quantity of resources be characterized by one number?
AGA-TERA
onshore
offshore
DFI-GEMS
EIA-ICF
OGM
AHM
EOR
E-M-S
Epple-Hansen
FOSSIL2
Kim-Thompson
LORENDAS
MIT-WOP
Ri#
success ratto and discovery stze function
finding function
cost function
finding function
distribution of characteristics of deposits
distribution of charateristics of deposits”
exogenous cost coefficient
cost function
estimated from historical data
estimated from historical data
judgmental
USGS PCG (preferred) NPC
USGS PGC (preferred) _s
estimated from historical data
judgmental
USGS
USGS
Lewin & ASSOC. data base
-
judgmental _b
estimated from historical data
USGS
capital productivity judgmental function
finding function estimated from historical data
finding function estimated from historical data
finding function judgmental
cost function estimated from historical data
USGS
_c
USGS (oil) NPC (gas)
yes
Yes
yes
no
no
no
yes
yes
no
yes
yes
no
“The EOR model deals with resources in known fields, which are added to reserves through tertiary development. Thus, the starting point is not, strictly speaking, undiscovered resources.
bCalibrated only for EMF 5. ‘Functional form does not permit calibration of total resources; finite limit does not exist.
resources to accommodate different resource base assumptions without adjusting the shape parameters as well.
Table 3 indicates for each of the models the approach taken to represent undiscovered resources, and the method by which the requisite parameters were obtained. The last column indicates whether or not the total quantity of
306 P. Clark et al., Ten U.S. oil and gas supply models
the resources is characterized by a single number. A ‘yes’ in this column indicates that this number has been used as the asymptote of the cumulative discoveries curve, the marginal cost curve, or the limit of the integral of the finding rate curve. A ‘no’ in this column indicates that either the asymptote or limit does not exist for the functional form used, or that the resource base is represented by probability distributions on deposit characteristics.
5. Exploratory drilling effort
As pointed out in the introduction, exploration involves much more than just exploratory drilling. Geological and geophysical research precede actual drilling. Five different kinds of exploratory drilling can be distinguished: new field wildcats, new pool wildcats, shallower pool tests, deeper pool tests and outpost or extension tests (AAPG and API drilling classification). In this section, we will identify the kinds of exploratory effort each model takes into account, and the types of drilling included. Furthermore, we will describe how these variables are determined in each of the models, and in what units they are measured.
In several models, exogenously specified or endogenously generated constraints determine to a great extent exploratory effort. In such cases, those constraints will be identified and explained. How aggregate exploratory effort is allocated to different resources and to different regions is also important. The way costs of exploratory effort are included will be discussed as well. The major elements of this section are summarized in table 4.
5.1. Definition of exploratory effort
Different definitions for exploratory effort are used in the models, as can be seen in the first column of table 4. These subcategories of exploratory effort differ in their economic properties (cost, probability of success, size of discovery). It is likely that prices affect these subcategories differently. However, it is not clear how - if at all - these differences in the definitions affect the behavior and the results of the models. Similarly, the use of different units for exploratory effort (as described in column 2 of table 4) may or may not affect the results of the models. Indeed, the three measures used are equivalent only under very stringent assumptions, since there is no one- to-one relationship between them. The number of wells cannot be translated directly into feet drilled, since the depth of the fields varies. If the discoveries of oil are closely related to the number of attempts made to find it, then the number of wells drilled might be a more appropriate unit to use. The MIT- WOP model uses rig years. ‘Rig years’ includes the idle time while a rig is being moved or repaired. It seems therefore less directly linked to discoveries than the other definitions used, and therefore less appropriate for forecasting
P. Cfark et al., Ten U.S. ail and gas supply models 307
discoveries. Rig years is more a measure of the capital stock available for exploration. The MIT-WOP model is therefore similar to FOSSIL2, where ‘physical assets’ (i.e., rigs, casings, etc.) are used as a representation of both exploration and development effort lumped together.
5.2. Determination of exploratory effort
The submodel determining the amount of exploratory effort is the central part of many of the models. Exploratory effort is crucial in determining the future supply of oil and gas, since without exploration, no new resources are found, and depletion of already discovered resources limits future production. The decision to explore depends essentially on the economic, technical, and institutional environment. The exploration process is represented in substantially different ways by the models in this study. Because of its importance, the procedures used to determine exploratory effort in each of the models will be discussed in detail. In the following subsections the basic methodologies will be distinguished.
5.2.1. Exploratory effort is modeled only implicitly (Epple-Hansen, E-M-S, DFI-GEMS, FOSSILZ, MIT-WOP)
These models do not have an explicit representation of exploratory drilling. The process of looking for resources, the decision about how intensely to look, and the results of this searching is not explicitly modeled, although some properties of the exploration process are implicitly assumed. The E-M-S and DFI/GEMS model determine additions to production capacity, i.e., the amount of resources that can be recovered in any time period, thereby collapsing exploration and development into one variable: the cost of adding another unit of production capacity. In addition, DFI- GEMS assumes that this cost is monotonically increasing, as more resources are made producible (in their language: ‘committed’). This is equivalent to assuming that the cheapest and easiest-to-reach resources are discovered and developed first.
In FOSSIL5 physical assets (drilling rigs, casings, etc.) are used to represent the exploration and development effort, lumped together. This can be considered as a capacity to drill rather than drilling per se. Since capacity may not be fully utilized, there is no direct link between effort and ‘physical assets’. Investment in and retirement of the capital stock determine the level of the capital stock for every period. It is not clear from the available documentation how investment is determined. In the MIT-WOP model, as in FOSSIL2, exploratory and development effort are approximated by a capital stock variable (rig years). However, this variable is an exogenous input to the model, and is therefore determined by the modeler (or user). The
Tab
le 4
Mod
el
Typ
e of
ex
plor
ator
y ef
fort
U
nit
Geo
logi
cal
and
geop
hysi
cal
rese
arch
D
eter
min
atio
n of
T
ype
of c
onst
rain
t D
irec
tiona
hty
incl
uded
ex
plor
ator
y ef
fort
us
ed
in d
rilli
ng
b
AG
A-T
ER
A
onsh
ore
offs
hore
DFI
-GE
MS
EIA
-IC
F O
GM
AH
M
EO
R
E-M
-S
new
fie
ld a
nd
new
poo
l w
ildca
ts
No.
of
wel
ls
new
fie
ld a
nd
feet
dri
lled
new
poo
l w
ildca
ts,
deep
er a
nd s
hallo
wer
po
ol t
ests
idem
not
mod
eled
new
fie
ld
wild
cats
(oi
l)
- -
feet
dri
lled
idem
new
fie
ld
wild
cats
NA
not
expl
icitl
y m
odel
ed
MA
NA
in t
he c
ost
mod
el
prop
ortio
nal
to
expl
orat
ory
effo
rt
depe
nds
on a
vera
ge
of p
rofi
tabi
lity
inde
x of
4 p
rior
ye
ars
(est
imat
ed
rela
tions
hip)
fixe
d ra
tio t
o th
e ar
ea e
xplo
red,
th
e la
tter
bein
g de
term
ined
by
opt
imiz
atio
n
-
idem
expl
ores
al
l ec
onom
ic
reso
urce
s up
to
limits
ca
used
by
drill
ing
cons
trai
nts
dete
rmin
ed
by
inte
rtem
pora
l op
timiz
atio
n (L
P)
NA
NA
NA
NA
feet
dri
lled
drilh
ng
rig
cons
trai
nt
impl
icit
in
endo
geno
usly
th
e di
scov
ery
dete
rmin
ed
equa
tions
max
. ex
plor
ator
y no
ne
drill
ing
feet
ava
ilabl
e in
any
tim
e pe
riod
; en
doge
nous
ly
dete
rmin
ed
- oi
l m
odel
onl
y
max
. ex
plor
ator
y fe
et
oil
and
gas
avai
labl
e in
eac
h m
odel
ed
regi
on e
ndog
enou
sly
mde
pend
ently
de
term
ined
none
NA
NA
sepa
rate
ex
plor
ator
y ef
fort
for
oil
and
gas
NA
oil
mod
el o
nly
P. Clark et ai., Ten U.S. ail and gas supply models
310 P. Clark et al., Ten U.S. 011 and gas supply models
Epple-Hansen model determines annual discoveries as a function of a set of exogenous variables, without explicitly specifying how much drilling must be done to result in these discoveries.
5.2.2. Exploratory activity is specijed as an estimated function of prices and costs (TERA-onshore, Rice)
In the TERA-onshore model, exploratory effort depends exclusively on a weighted average of profitability indices of four prior years. However, if the resulting amount is larger than the drilling capacity, then the latter determines exploratory effort. The profitability index equals the ratio of the expected net present value to expected net capitalized costs associated with the decision to drill an exploratory wildcat. The costs considered include five categories of exploratory costs (drilling equipment, acreage acquisition, lease rental, scouting and surveying, administration overhead), in addition to development, production and royalty costs. Those costs are split over expensed and capitalized costs for tax purposes.
In the Rice model, two equations for exploratory effort are estimated by econometric methods. First, the number of new field wildcats depends positively on the price of ‘new-new’ crude and the number of successful new field wildcats of the previous period (as a proxy for the expected value for this variable), and negatively on a measure of the replacement cost of a barrel of crude. Second, the number of extensions and other exploratory wells depends positively on a weighted average of the price of new and old oil, on the expected number of successful extension and other exploratory wells, and negatively on the average cost of drilling a well. The structural form of these equations, and the choice of the exogenous variables was not explicitly derived from any economic model of the exploration decision. The measure of the replacement cost in the first equation is the so-called ‘user cost of capital’, as derived in the neoclassical investment theory, with a unit of reserve of the resource being considered as capital.
5.2.3. Marginal costs are considered in connection with a set of drilling constraints (EIA-OGM, Kim-Thompson)
These models determine a threshold in cumulative exploratory effort on the basis of the resource, cost and price data. When more exploration is done, the present value (PV) of costs exceeds the PV of revenues. As long as current cumulative drilling is less than the threshold, more exploration is done up to the constraint caused by the drilling model. This threshold is a way to state the first-order necessary conditions of a maximization problem, which is to maximize the net present value to the industry. The procedure to calculate this threshold and the way it is used to determine the actual level of
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drilling are rather involved, but interesting. We will therefore discuss them in somewhat greater detail.
EZA-OGM. The EIA lower-48 oil and gas model (OGM) determines the level of exploratory effort in two steps. First, the model is used to determine the economic properties of the as yet undiscovered resources by calculating a minimum acceptable price for obtaining different amounts of oil and gas from each region. This is done in the following way: First, the ‘latent drilling demand curves’ are generated. A hypothetical large drilling level is projected for a period of 15 years for example. For each year, each region and each resource, a minimum acceptable price is calculated. This is the price that, if held constant over future years, would yield a satisfactory return on investment: it is the sum of discounted cost projections (including a rate of return on investment, and taking into account current tax provisions) divided by the sum of discounted production projections. This calculation yields for each region and resource a set of points in the cumulative-drilling-versus- price space. These are then considered as time-independent demand curves for cumulative exploratory drilling. The curves indicate the drilling effort which would be economical to do in each region, at a given expected price.
In the second step, the levels of exploratory effort are forecasted. The wellhead price of the resource determines for each region the total amount of drilling that is economical to do, using the latent drilling demand curves determined in the first step. The actual level of drilling is the minimum of this amount and the available drilling capacity. The drilling capacity is determined in a separate drilling capacity model for each region (see below). For the offshore regions, drilling is further restricted by the availability of leases. Each newly leased acreage will be explored over five consecutive years according to a fixed schedule. Acreage explored is translated into feet drilled by the following calculation: the number of wells drilled is proportional to acreage explored, and this number times the average depth of a well, which is also determined in the model, yields footage.
Kim-Thompson. The Kim-Thompson model uses profitability considerations to determine both exploratory drilling and the optimal depletion rate. For a given set of exogenous parameters (prices, costs, taxes, etc.) the model determines on a period-by-period basis ‘terminal finding rates’ for both oil and gas. These are essentially break-even finding rates; they give the amount of resources to be found in one more unit of exploratory effort in order for that exploratory venture to be profitable in present value terms. The ‘terminal finding rate’ is the point on the finding rate curve where the marginal value of the production from the newly-found reserves just equals the marginal costs of exploratory drilling, development, and production.
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The differences between the cumulative drilling corresponding to the terminal finding rate and current cumulative feet drilled (these differences added up for oil and gas) give the total drilling capacity needed to explore the economically recoverable resources. A drilling model then determines the annual dritling capacity in such a way as to maximize drilling industry profits, Three major constraints are imposed on drilIing capacity: (i) drilling capacity cannot expand faster than by a given fraction of current capacity, (ii) capacity is always fully utilized, and (iii) constraints involving the retirement of obsolete rigs.
In fact, due to the particular formulation of this drilling submodel (constant expected costs and prices), the drilling capacity expands as fast as permitted by constraint (i) until further expansion would cause overcapacity in later periods. Exploratory drilling in any particular year then is equal to total available drilling capacity in that year.
Both the calculation of the ‘terminal finding rate’ in the Kim-Thompson model, and the amount of exploratory effort that is economical in the EIA- OGM model, assume constant future prices. If prices rise, then the level of cumulative drilling that is economic to do will be adjusted upward in subsequent periods. However, if prices were to decline, it might very well occur that too much drilling capacity had been built and that constraint (ii) of the Kim-Thompson drilling submodel is not satisfied. Given that drilling in both models under current actual price conditions is restricted by the drilling capacity, the incorporation of perfect foresight under rising prices wouid not affect the forecast of the models. However, this would not necessarily be true if prices were expected to decline.
5.2.4. Explicit one-period optimization (TER A-offsshare)
The models of the previous category use marginal cost and marginal return considerations to determine the level of drilling. These models can be considered as using the first-order conditions of a maximization problem, whereby the exploring firm maximizes net present value, subject to drilling capacity constraints. In the TERA-offshore model and in the models discussed in section 52.5, such an optimization is performed explicitly. In the TERA model, the number of feet drilled in a region is determined in fixed proportion to the acreage that is going to be explored. For every period (bid- year) the model determines the percentage of the total amount of acreage leased in that year that will be explored, in such a way as to maximize the net present value of that acreage. This determines the exploratory drilling done on that acreage. The total amount of exploratory drilling is then allocated over five calendar years, using an exogenously fixed drilling profile. For every calendar year, the exploratory drilling done in areas leased currently and that implied by leases in four previous years is aggregated to
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the total amount of exploratory drilling performed in that calendar year. This total is constrained by the drilling capacity available. When capacity is not sufficient, drilling rigs are allocated first to acreage leased in previous years. Drilling capacity is specified by the number of exploratory feet that can be drilled in any calendar year. It is worthwhile to note that the total amount of acreage leased each year and exogenously specified leasing schedules play a crucial role in the determination of exploratory effort.
Central in this one period optimization is the notion of short-run finding rate curves: for a particular acreage leased, some of the oil in that acreage may be easier to find. It is likely that this easy-to-find oil is discovered first. This phenomenon is represented by a short-run marginal cost curve, with the marginal cost of a discovery increasing as more drilling is done on a particular lease. Under these assumptions, there is a point where the marginal gain from exploring more on a lease is less than the cost, i.e., there exists an optimal point to stop drilling. However, the model only considers this optimization once. If prices suddenly jump in a future period, the decisions of previous periods are not reconsidered, thereby probably underestimating price effects on oil and gas supply.
52.5. ~ntertemporffl optimization (LORENDAS, EIA-AH&f)
In both models, exploratory effort for all periods under consideration is determined at the beginning of the planning period. The exploratory effort that maximizes the present value of (pre-tax) profits for the industry is chosen. Both models are formulated as linear programming models, but their structure is sufficiently different to make a separate discussion worthwhile.
EIA-AHM. As in the ETA-OGM system, the AHM model works in two steps. First, the economic properties of the resources in each region are generated on the basis of a Monte Carlo simulation, using the stochastic description of the resource base. The following exploratory process is assumed: prior to exploratory drilling, explorers can identify the depth and area of each structure. Then they drill into the structures with the largest areas first. The geologic properties of each region are generated several times, as well as the exploratory process associated with it. The results of this simulation are the average drilling effort necessary to discover an amount of resources and the minimum acceptable price associated with it. In other words, the simulation gives for each level of cumulative drilling a vector of discovered resources. The vector contains for each price range the additional resources that could be economically recovered from the reservoirs discovered due to the additional drilling, if wellhead prices were within that range.
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In a second step, these economic descriptions of the resources for each region are input into a large linear programming model which incorporates both the development process and transportation possibilities. This model then determines the timing and level of exploration, development and expansion of transport lines in each region, to maximize the present value of pre-tax profits in light of expected selling prices of oil and gas at the Alaskan border. This model currently does not include drihing constraints, but leasing schedules impose constraints on exploratory activity.
LORENDAS. In LORENDAS, exploration, development, and production are allocated over time and space (i.e., regions) in such a way as to maximize the present vaiue of profits to the industry (another criterion function is available in the model: minimization of costs). Two major sets of constraints limit exploratory drilling: First, total drilling in each region cannot expand faster than at a prespecified rate. This yields a set of endogenous constraints on total exploratory drilling. Second, exploratory drilling may further be restricted by exogenous constraints, specified on a regional or national basis.
It should be clear from the discussion of exploratory effort that drilling constraints play an important role in most of the models. In the models where long-run marginal costs (LRMC) are compared with long-run marginal returns, high returns generate optimal drilling levels that are much higher than those currently observed. This is probably because most models do not capture increasing short-run marginal costs very well. Limited capacity to produce new drilling equipment, or a limited supply of managerial expertise might slow the expansion of exploratory activity. In addition, the currently prevailing expectation that the relative price of petroleum will continue to rise may have generated a much more leisurely attitude toward the immediate exploitation of current drilling rights. Whatever the true cause of the slow increase in domestic drilling, many of the models use drilling constraints as a means to smooth the path of exploratory effort. These constraints are analyzed below.
The DFI-GEMS, EIA-AHM, E-M-S, Epple-Hansen and Rice models do not contain drilling constraints. As mentioned above, the MIT-WOP and the FOSSIL2 models measure ‘exploratory effort’ by the capital stock available for exploration and development. This can correctly be considered as a form of a drilling constraint. In MIT-WOP, the time path of the capital stock is specified exogenously, while in FOSSIL2, investment and depreciation determine the capital stock endogenously.
AGA-TERA (both models), LORENDAS, EIA-OGM, and Kim- Thompson contain drilling constraints. A small drilling capacity submodel determines how the drilling constraint evolves over time. In AGA-TERA
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(both models), drilling capacity is a function of last year’s capacity capacity utilization. If capacity utilization is higher than a certain threshold level (75%) then capacity is increased in proportion to the difference between the utilization and the threshold. In LORENDAS, the drilling capacity expansion is determined endogenously, as part of the output of the optimization. However, exogenous growth rate restrictions (maximum levels of growth) for each region and possibly other aggregate constraints may limit the possible expansion paths. In the EIA-OGM and the Kim-Thompson models, the submodel for drilling capacity is more detailed: it specifies the origin of the drilling rigs, and makes assumptions about their depreciation.
In all of these cases, the behavior of the model is fundamentally affected by the exogenous specification of drilling capacity, or the assumptions embodied in the drilling capacity submodel. When the output of these models is analyzed, the drilling assumptions should be kept in mind because they are fundamental to understanding how these models work.
5.4. Levels of aggregation
So far, very little attention has been paid to the level of aggregation of exploratory effort. Two different forms of aggregation can be distinguished: by region and by resource (oil or gas). About half the models determine exploratory effort on an aggregate (nationwide) basis. AGA-TERA (onshore), MIT-WOP, FOSSIL2, Rice, and Kim-Thompson fall into this category. In AGA-TERA (offshore), LORENDAS, and EIA-AHM, drilling levels are determined separately for each region of the model. This is - as far as we can determine - also the case for EIA-OGM. This last approach allows for a greater flexibility in the model, i.e., different economic characteristics of the resource base in each region can cause different expansion paths of the drilling capacity.
Disaggregation by resource is usually called ‘directionality’. Some models assume that one drills essentially to find a hydrocarbon deposit, without knowing if the deposit is going to be gas or oil. Then only one level of drilling is specified per geographical unit (Rice, AGA-TERA (on and offshore), LORENDAS). If no reallocation of drilling capacity over regions is possible, then changes in the relative price of oil versus gas will not affect discoveries of oil versus gas, i.e., there is no directionality of drilling in these models. However, if such a reallocation of drilling capacity is possible, then relative prices of oil/gas may change the relative expansion path of drilling, and, therefore, alter the relative amount of gas discoveries versus those of oil. This is the case in LORENDAS and in AGA-TERA (offshore). The directionality effect is incorporated in AGA-TERA (onshore) in an indirect way; the ratio of oil and gas prices appears in the ‘success ratio’ and ‘average discovery size’ equations. These are described below.
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The other models (EIA-OCM, EIA-AHS, Kim-Thompson~ FOSSIL2) determine a separate exploratory effort variable for oil and gas, thereby assuming that wildcatters have some idea whether a given structure will yield gas or oil. In Kim-Thompson, an estimated relationship between the ratio of drilling for oil to total exploratory drilling and a relative profitability index of oil versus gas is used to determine the national split of aggregate exploratory drilling. Constant regional adjustment factors are then applied to get the regional split. In the EIA-AHM model, exploratory effort for each resource and region is determined directly by the optimization procedure. In the EIA-UGM model, the drilling variables for oil and gas in each region are presumably determined in such a way that the minimum acceptable price for BTU equivalent oil and gas is the same in each region. Of the models that consider both resources, the Rice model is the only one not to include a directionality effect in discoveries, This, however, does not imply that the supply of oil and gas will appear in fixed proportions, independent of refative prices, since these prices may still influence the development and production decisions differently (as they actually do in the Rice model),
All of the models {except MIT-WOP) use economic considerations to determine the level of exploratory effort, i.e., exploration costs, current and expected future prices, expected development and production costs are somehow considered in order to determine if an exploratory venture is profitabie. Even models that do not explicitly describe exploratory effort incorporate some exploratory costs as part of the costs of adding oil producing capacity. The cost aspect wifl be discussed below, while the ex~ctations aspect will be covered in the next section.
In the engineering process models that include an explicit representation of exploratory effort, all costs of exploration are proportional to this effort, i.e., the cost to drill one well (or foot) is constant, and scouting cost, overhead, etc., are proportional ta the same drilling variable. This is the case for AGA- TERA (on and offshore), EIA-OGM, EIA-AHM, LORENDAS, and Kim- Thompson. In each of these models, some provision is made for tax rules with regard to expensing and capitalizing of exploratory expenditures. The detailed structure of each of these is rather complex, and would require a lengthy description, We refer the interested reader to the respective model documentation.
The Epple-Hansen model is a special case. Their theoretical model, from which the estimated model is derived, specifies a joint quadratic cost function for the discovery of oil and gas. This function relates the costs of discovering oil and gas to the cumulative amount discovered of each of the resources, and the amount discovered in this period. This formulation allows for both
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short-term and long-term increasing marginal costs of exploration. The parameters of this cost function are estimated by econometric techniques. Since discoveries are not deterministically related to exploratory effort, it is impossible to determine the exact relationship between these estimated cost coefficients, and the technological per unit costs of drilling used in the models discussed above. The DFI-GEMS model uses an input-output approach to determine costs of adding a unit of committed capacity; the per unit inputs of different factors are specified. Several adjustment factors (one for the depletion effect, and one for a learning effect) are used to alter these costs as more resources are ‘committed’. Multiplying these adjusted input- output coefficients by the prices of inputs yields the exploration and development costs.
In the Rice model, total costs of exploration and development in any time period are an estimated function of total wells drilled (both exploratory and non-exploratory), the average depth of a well and Texas shutdown days. The average depth of wells drilled is specified exogenously. We cannot find a reasonable justification for the inclusion of a production restriction variable (the Texas shutdown days) in this equation. The E-M-S model includes one cost parameter. In the specification and the estimation, this cost of adding one unit to the producible resources (i.e., both exploration and development costs are incorporated in this one parameter) is assumed constant. However, when the model was used for the EMF experiments, this parameter was increased exponentially over time, as an ad hoc way of representing the depletion effect and the different resource base assumptions. Finally, FOSSIL2 calculates operating and maintenance costs related to the capital assets used for exploration. These costs rise as resources are depleted.
5.6. Expectations
Most of the models incorporate a net present value calculation, or consider in another way future prices and costs when determining exploratory effort. There are important differences among the models in the way expectations are modeled.
One set of models assumes perfect foresight. This means that whenever a decision is made, the decision-maker has perfect knowledge of future prices. In the DFI-GEMS model, this future price path is endogenous (as a result of supply and demand balancing), while in AGA-TERA, LORENDAS, and EIA-AHM, it is exogenously given.
The other models use static expectations, i.e., future prices are assumed to be equal to current prices. This does not mean that prices cannot change. Prices are allowed to change in time, but at any point in time, decisions for that period are made using constant future prices equal to the prices in the period under consideration. This is the case for the EIA-OGM, Kim-
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Thompson, Epple-Hansen, E-M-S, Rice, and BIT-WOP models. It should be noted, however, that while the Kim-Thompson and EIA-OGM model calculate a threshold, thereby assuming constant future prices, this threshold usually requires substantially more exploratory effort than possible, given the drilling constraints. Therefore, if the expected future price path were higher, or only slightly lower, the predicted amount of exploratory effort would remain the same. While the current version of the Epple-Hansen model was estimated using static expectations, the underlying theoretical model allows for any kind of expectation; plans for incorporating other expectations have been made. Rather than using the current price, the Rice model uses last period’s prices as the current expectation of future prices.
6. Relation between exploratory effort and discoveries
We explained in section 2 how exploratory effort transforms undiscovered resources into discovered resources. The modelers use many different ways to describe the results of exploratory effort.
Some models assume a deterministic relationship between cumulative exploratory effort and the cumulative amount of resources discovered. This relationship is represented by the cumulative discoveries curve. The derivative of this curve with respect to exploratory effort is the finding rate curve which gives the relation between cumulative exploratory effort and discoveries per unit of exploratory effort. Both curves are depicted in fig. 3. The meaning of ‘discovered resources’ is somewhat ambiguous. Ideally, one would expect the term to mean ‘resources in place’, independent of their cost to recover. In many models ‘discovered resources’ refer to just those resources that are recoverable under current economic conditions. Therefore, this representation of the relation between exploratory drilling and discoveries is not independent of the economic environment.
Another appraoch is used in most econometric models. The total amount of resources discovered in a particular year equals the number of wells drilled times the average success ratio times the average size of a discovery. Both the success ratio and the discovery size may depend on the cumulative amount of drilling done, on prices, and on other variables. Cumulative drilling represents the depletion effect, while prices explain the effect of recovery cost on total resources recoverable. Statistical estimates of equations to explain the number of wells drilled, the success ratio, and average discovery size were first made by Franklin Fisher in 1964. We therefore call this approach the ‘Fisher approach’.
‘Extensions’ (increases in the estimated size of previously discovered pools generated by extension wells) are also the result of exploratory effort. Some models treat this category separately. Although revisions (re-estimates of pool
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size) are not really related to exploratory effort, they are often modeled together with extensions, and we will therefore discuss them together.
In the remainder of this section, we discuss the issue of defining ‘discovered resources’, the way discoveries are related to exploratory effort, and the way extensions and revisions are incorporated in each of the models. We also discuss the estimation of the parameters of these equations, and we conclude with a short discussion of the depletion effect.
Whenever a new field is discovered as a result of exploratory effort, large uncertainties remain with respect to the precise extent of that field. An original estimate of the size of the deposit is made. This estimate is commonly associated with discoveries. However, as more drilling in that field is done (exploration, development, production) new information about the deposit becomes available, and the original estimates are revised. These changes appear in the data series as ‘extensions and revisions’. There is considerable doubt concerning the value and consistency of this series. Furthermore, as with the estimates of the total resource base, they are not independent of economic conditions: one price schedule might lead to one trajectory of revisions and extensions, while a substantially higher price trajectory might cause higher extensions and revisions. Most of the models use the same API data series as a basis for estimating discoveries (or reserve additions). For a few models (FOSSIL2, DFI-GEMS, and LORENDAS), the documentation does not specify precisely what data are used. However, various models still use different elements of these API series.
One group of models (AGA-TERA and Rice) only uses the discovery data from newly discovered fields, defined as the original estimate of ultimate recoverable resources from those fields. The Kim-Thompson model adjusts current discovery estimates by ‘Hubbert factors’ which are estimates of the future revisions and extensions that will be allocated to newly discovered fields. In the case of oil the adjusted estimate is more than nine times the original estimate at the time of discovery.
The LORENDAS and the EIA-OGM models use ‘oil-in-place’, which they obtain by multiplying discovery estimate by the inverse of the average recovery rate. The MIT-WOP and E-M-S models use the annual ‘reserve additions’ series of the API data. Hence, they do not distinguish between discoveries and extensions and revisions, and they do not relate these extensions and revisions to the discoveries from which they follow. The Epple-Hansen model uses its own constructed measure of discoveries, which is proportional to the total ultimate recoverable resources (including adjustments through extensions and revisions) of a discovered reservoir. It is therefore similar to the Kim-Thompson model.
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6.2. Relation between exploratory effort and discoveries
As mentioned above, there are two basic approaches: models using the finding rate concept (TERA offshore, Kim-Thompson, LORENDAS, EIA- OGM, MIT-WOP), and the ‘Fisher approach’ (TERA-onshore, Rice). The other models use very different approaches, and will be collected in a category ‘other’. Finally, some models (E-M-S, DFI-GEMS) do not consider discoveries nor exploratory effort, and will therefore not be discussed here.
6.2.1. Models using the ‘jindiqg rate’ concept
The finding rate curves express the idea that when more drilling is done, the average result of that effort decreases. This would be the case if big deposits are found first, or if areas with the highest ‘probabilities of containing hydrocarbon deposits are explored first. The integral of the finding rate curve is the cumulative discoveries curve. Two different specifications for this curve are used.
Negative exponential (EIA-OGM, LORENDAS, TERA-offshore):
Y=Q[l -eeax],
Double exponential (Kim-Thompson):
where
(log Y - b,J2 = b, + b, log X,
Y = cumulative discoveries, Q =an estimate of total discoverable resources in this region, X = cumulative exploratory effort, a, bO, b,, b2 = parameters, estimated from historical drilling results.
The negative exponential has an easy interpretation. We define the remaining undiscovered discoverable resources as
and
Q- Y=QeeaX,
d Y/dX = aQemaX = a(Q - Y).
It follows that in the exponential case, exploratory efficiency (finding rate) is assumed proportional to the remaining undiscovered resources. The double exponential does not have such a straightforward interpretation. However,
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one can derive the following expression:
Therefore, if b2 ~0, the relative change of cumulative discoveries due to a relative increase in cumulative exploratory effort decreases as more resources are found.
The actual implementation of these cumulative finding curves in each of the models is different. The TERA-offshore and the EIA-OGM model have a cumulative finding curve for each resource (oil and gas) and for each region of the model. TERA-offshore makes a distinction between long-term finding rate curves (LTFR) as described above, and short-term finding rate curves (STFR). The LTFR is assumed to represent the expectations of the explorers before the lease, i.e., with limited geologic information. The STFR is assumed to represent the relationship between feet drilled on that lease and discovered resources, after more information has been gathered. The total amount of resources implied by both curves is the same, but more resources will be found in early stages of exploration on a lease than is projected by the LTFR. This short-run finding rate function is also used in the calculations of net present value and therefore in the determination of exploratory effort.
The LORENDAS model has cumulative discoveries curves for each region for six resource types (including non-associated gas). Cumulative drilling in a region will result in cumulative resource discoveries for each type of crude. However, the way these curves are specified constrains all discoveries of different resources for every level of cumulative drilling to assume the same proportion. A negative exponential relationship is used, and then linearized in order to make it tit in the linear programming structure of the model.
The Kim-Thompson model estimates an aggregate cumulative discoveries curve for oil and one for gas. The derivative of these curves gives the aggregate finding rates for both resources. In order to get regional finding rates, the national aggregates are multiplied by regional multiplication factors.
Although the MIT-WOP model constructs its ‘finding rate’ concept in a different way, it implicitly uses a negative exponential finding curve, since its finding rate is proportional to the remaining undiscovered resources. Some easy transformations on their formula for reserve additions will make that clear,
dY= m.RACl- Y/QI/Cl- Y7JQx1, where
RA =a constant,
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Y,, =cumulative reserve additions up to 1975, Q5 =estimate of Q in 1975, A = the difference operator, i.e., dY= Y;- Y;_1, and the other symbols are
defined above (with the appropriate adjustment for different units used).
This is equivalent to
AY/‘AX=RA-(l- Y,,,‘Q7J1.(1/Q)[Q- Y]=a[Q- I’].
As in the negative exponential case, drilling efficiency is proportional to remaining undiscovered resources.
6.2.2. Fisher ~p~r~u~h
The basic equation for this approach is
Oil discoveries = (Number of wildcats drilled) * (Success ratio) * (Oil wells/Successful wells) * (Average size of oil discovery).
The same equation also holds for gas, after replacing oil by gas whenever appropriate. The success ratio is the ratio of successful wells to total wells drilled. In the TERA model, the success ratio is determined by an estimated relationship as a function of the average oil and gas wellhead prices and the proportion of the initial resources already discovered. The proportion of successful wells that are oil wells depends on the ratio of oil and gas prices adjusted for their heat content. The model implies that when relative price of oil versus gas rises, more of the successful wells will contain oil. This is meant to represent the directionality effect, i.e., that relative price changes cause the exploratory effort to be directed to one particuIar resource (see above). The average size of an oil (gas) discovery depends negatively on the wellhead price of oil (gas) and on the proportion of resources already discovered. Discoveries of associated gas are proportional to discoveries of oil.
The Rice model uses the same approach for wildcat drilling, as well as for extension and development drilling. The success ratios in this model are specific for each type of drilling and for each resource. For example, the ratio of successful wildcats that contain oil to total wildcats (= definition of success ratio in the Rice model) equals [success ratio *(oil wells/successful wells)] as defined above. The success ratios in the Rice model (six in total) as well as the average discoveries (extensions, revisions) per well are specified
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exogenously. Success ratios are based on five-year averages of actual data from 1972 through 1976 and assumed constant over the forecast period. Average discovery size is determined in the same way, but allowed to increase or decline over time according to their performance between 1946 and 1976.
6.2.3. Other approaches
The Epple-Hansen model uses an econometrically estimated equation to determine discoveries of oil and gas as a function of cumulative discoveries of oil and gas, and of prices of both resources. This equation was derived explicitly as the first-order necessary condition for optimality of a dynamic model for the oil and gas supply sector. Taxes and production costs are included as variables in the equations. The EIA-AHM model does not report nor calculate discoveries. The result of a level of cumulative exploration in a region is a set of ‘resources groups’ recoverable for a particular ‘minimum acceptable price’, i.e., the model produces an economic description of the resources discovered during the exploration process.
6.3. Extensions and revisions
The Kim-Thompson, LORENDAS, and EIA-OGM models do not consider extensions and revisions explicitly. Instead, all ultimately recoverable resources, or in some cases oil in place, are allocated to the discovery at the time of discovery. Of the models that do include annual forecasts of extensions and revisions, there are two major groups. AGA- TERA, Epple-Hansen, and FOSSIL2 might be labeled ‘vintage models’ in which extensions and revisions are traced back to the original discovery. In FOSSIL2 and the two AGA-TERA models, this is done by specifying a fixed time schedule of extensions and revisions, i.e., extensions and revisions related to a discovery made T years ago is a given percentage of the size of that discovery. The Epple-Hansen model has an estimated equation that relates ‘reserve additions’ from a particular vintage of discoveries to the size of those discoveries and to the price of the resource. The equation is derived as the first-order condition for optimality for the development model (cf. below) and then estimated econometrically.
In the other major group (E-M-S, Rice, DFI-GEMS, MIT-WOP), extensions and revisions are not traced back to the original discovery. Of these, only the Rice model determines the extensions and revisions explicitly. Extensions are the result of extension wells drilled, while revisions depend upon non-exploratory wells drilled in each period. These relationships are very similar to the equations that relate discoveries to exploratory effort in the Fisher approach.
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The other three models forecast ‘reserve additions’, which are the sum of discoveries, extensions and revisions.
6.4. Depletion efSect
The amount of gas and oil in the ground is finite. Therefore, the more of these resources were discovered in the past, the less likely that further exploratory effort will be successful. This effect, called ‘depletion’, governs the relationship between exploratory effort and discoveries in all the EMF-5 models. Many of the models use a concave cumulative discoveries curve (EIA-OGM, TERA-offshore, Kim-Thompson, MIT-WOP, LORENDAS). However, there are other possibilities. The DFI-GEMS and Epple-Hansen models include a depletion effect by increasing the marginal cost of finding one more unit of resource as cumulative exploratory effort rises; in DFI-GEMS, a set of input-output coefficients determine the input require- ments necessary to install one unit of capacity. As more capacity is built, more inputs of each of these factors are needed (according to the model). Two cost multipliers - one for capital and one for variable inputs - of the following form are used:
where 1 + a(N)b,
N = cumulative committed resources, a, b = parameters where a > 0, b > 1.
These cost multipliers increase geometrically, causing rather sharp rises in costs of adding more capacity.
The Epple-Hansen model uses a quadratic cost function of the form
where
TC=z’Az+z’By+z’c,
TC= total finding cost per period, 2 = (z,, zg) = vector of current oil and gas discoveries, y = (ye, y,) = vector of cumulative oil and gas discoveries, A =positive definite symmetric matrix, B =positive definite matrix, C = vector parameter.
A, B, and c are estimated from historical data. The z’By term represents the manner in which long-term finding costs increase with cumulative discoveries. The z’Az term represents an increasing short-run marginal cost effect. The equation implies an interaction between the costs of discovering oil and those of discovering gas.
P. Clark et at., Ten U.S. 011 and gas supply models 325
Other means of modeling the depletion effect include the use of success ratio and discovery size variables, which are negatively related to the cumulative amount of drilling done, as in the TERA-onshore model; and the construction of an explicit probabilistic model of the resource base with assumptions about how each of the simulated reservoirs might be discovered (EIA-AHM). The Rice and E-M-S models do not incorporate an endogenous depletion effect. In the Rice model, two exogenous variables, the average discovery size and average depth of a well, are linear extrapolations of the recent past. Since average discovery size goes down and average depth of a well increases, it becomes more expensive over time to find one unit of resources. However, this is not at all related to the cumulative exploration, and can therefore not really be labeled a depletion effect. Similarly, the E-M-S model specifies exogenously a trajectory for the cost of adding one unit to the reserves.
The marginal cost representatidn is closely related to the concept of a finding rate curve. If the costs of exploratory effort are known, then the marginal cost curve can be derived from the finding rate curve by a simple transformation (i.e., take the inverse of the finding rate curve, and multiply exploratory effort by the relevant cost data). However, the finding rate curve does not depend on economic factors (ideally), and can therefore safely be used over the whole time period of the model, whereas costs might change over time and thereby alter the marginal cost curve. In other words, the finding rate curve is a more stable representation of the depletion effect. On the other hand, most models do use constant cost projections over time, which makes the two approaches equivalent.
7. Development
In the development stage, production capacity is installed. This is the point at which capital investments are made for production. In some of the models, development activity is lumped together with exploration activity, so that discoveries and additions to productive capacity are generated-in themodels by a single process. The DFI-GEMS, E-M-S, and MIT-WOP models are in this category. In most of the remaining models, development is automatic; that is, once the resources are discovered, they are developed and produced according to an exogenous profile. EIA-OGM, FOSSIL5 and both AGA- TERA models fall into this category. However, in a few of the models the decision to install productive capacity is modeled explicitly; these models are discussed in more detail below.
7.1. Optimization of development drilling over time
Two models, the LORENDAS model and the EIA-AHM model determine the level of development drilling for all time periods simultaneously in an explicit comprehensive optimization problem. In the LORENDAS model,
326 P. Clurk et al., Ten U.S. oil and gas supply models
primary, secondary, and tertiary development activity for each time period for ail regions on resources of each type and vintage are separate instruments in the profit maximization formulation. Development costs are linear and are included in the objective function. The cost coefficients are derived from FEA Project Independence estimates and the only constraints on development activity are on the fraction of additional recoverable reserves available from secondary development. The Alaska Hydrocarbon model also includes the costs of transportation.
The DFI-GEMS model does not purport to be an optimization model. But its method of calculating economic rents in the generalized equilibrium setting with perfect foresight has the same effect as explicit optimization. In the GEMS model, the exploration and development decision are lumped together in a single decision to increment ‘cumulative committed production’ through ‘capacity additions’. The marginal cost of this incremental commitment is obtained from a marginal cost curve whose abscissa is the level of cumulative commitments to date. The long-run price of the incremental production is then calculated as the sum of this marginal cost and the maximum over a11 future dates of discounted economic rents, where rent is the difference between price and marginaf costs. In equilibrium, the market price equals the long-run price thus calculated. This procedure implements the first-order necessary condition for an intertemporal optimization.
Drilling constraints in the GEMS model are represented by supply curves of ‘secondary materials’. Secondary materials requirements are proportional to capacity additions, and their cost is subtracted from the market price of the resource, before economic rents are calculated. The supply of secondary materials is ailowed to grow at a fixed exogenous rate. When capacity additions are high, secondary material requirements are high, the cost of secondary materiafs is high, and consequently the net profit (rent) of current capacity additions relative to later additions is reduced, tending to delay development to a later date when drilling constraints are not so tight. The solution is the same as if the model were explicitly maximizing profits, given the same marginal resource costs, secondary materials constraints, and market demand.
The EIA-EOR model, which has not been discussed so far, selects tertiary recovery projects using the internal rate of return as a criterion. Each reservoir is screened and the tertiary recovery technology is assigned to it which would be profitable at the lowest crude oil price. Then, for given price trajectories, the set of tertiary recovery projects is selected which maximizes industry-wide rate of return.
7.2. O~ti~~zati~~ ~~co~sta~t ~e~~eti~~ rate
The Kim-Thompson model assumes that resources discovered in a given
P Chk et al., Ten U.S. oii and gas supply models 327
year will be depleted exponentially at a constant rate over the life of those reserves. But that depletion rate is optimized for each individual discovery year, assuming that future prices will be the same as current prices. Secondary and/or tertiary recovery from resources in a given region and discovered in a given year is undertaken whenever the net present value of the incremental secondary or tertiary investment is positive. The quantity of incremental reserves is the product of primary discoveries and a coefficient expressing the historical relation between secondary or tertiary and primary reserves in that region, Costs are taken from FEA estimates. Secondary and tertiary depletion rates are presumed to be the same as for primary reserves. But it is not clear whether the optimum depletion rate is calculated with or without the additional reserves. The MIT-WOP model also calculates an optimal depletion rate for primary and secondary reserves along these lines, but since historical depletion is different from the indicated optimum, it then uses a projection of historical rates to calculate future production.
7.3. econometric modeling of ~eve~oprne~~
Two models take an econometric approach. The Rice model obtains the number of development wells (both oil and gas, together) as a function of the price of ‘old’ oil, expected gas revenues, drilling costs, and expected number of successful wildcats and extensions,
+0.064 * log R,
where
D =number of development wells, P = wellhead price of ‘old’ oil, A =average cost of drilling a well, W = expected number of successful wildcats and extension wells, R =expected revenues from natural gas.
Development occurs in part in fields that are already discovered but for which price regulation holds wellhead prices below the prices obtained for new discoveries. So the ‘old’ oil price and a value for gas revenues which reflects ‘old’ and ‘new’ gas prices is used. The Rice model is the only model which explicitly uses current prices for old oil or gas in the calculation of current development drilling.
In the Epple-Hansen model, discovered resources are vintaged by year of discovery and total amount of developed resources for a year is the sum over
328 P Clark et al.. Ten U.S. 011 and gas supply models
all vintages of the developed resources of each vintage,
where
Rt,i=aoR,-,,i+ziCa,P,+ll+u,,,,
and where
R =proved reserves of oil plus cumulative production, R,,i =proved reserves of oil plus cumulative production at time t, in fields
discovered at time i,
P = wellhead price for upper tier oil, 11 = random disturbance term, a,, a,, zi = econometrically estimated parameters.
A similar equation holds for gas. Note that this model does not provide the levels of development drilling, but does give the results thereof. The equations are derived assuming that producers maximize expected discounted profits subject to a quadratic development cost function. Expectations are assumed to be formed rationally. But estimation of the model under the rational expectations assumption is not yet completed; the parameter estimates used in the EMF scenarios are based on static expectations.
8. Production
Production is the last step in oil and gas supply with which this comparison is concerned. Beyond this step are transportation, relining (for oil), distribution, and marketing. In most of the models, the level of production is the consequence of decisions made at previous steps. In the E- M-S, MIT-WOP, and Epple-Hansen models, and for the EIA-OGM model onshore, production is a constant fraction of ‘proved reserves’.
In the EIA-OGM (offshore), Kim-Thompson, and AGA-TERA models, production from each vintage of discoveries follows a fixed profile. For the Kim-Thompson model, the production profile is a constant rate exponential decline, but the depletion rate may vary from one vintage to the next; this is not the same as a constant aggregate production to reserves ratio. For the TERA model and for offshore regions of EIA-OGM, the fixed profile exhibits some buildup of production up to peak production, and a gradual decline of production thereafter.
In two models, LORENDAS and FOSSIL2, a separate production decision is made each period. Production from each of primary, secondary, or tertiary reserves of each resource in each vintage, time, and region is again a separate control variable in the LORENDAS model. There are no
P Clark et ai., Ten U.S. oil and gas supply models 329
constraints other than productive capacity here. This constraint is always binding unless prices are rising rapidly, because production costs are linear. In the FOSSIL2 model, a capacity utilization factor may be adjusted in case demand slacks off, so production may be adjusted in response to demand. But, it is likely that in the case of U.S. oil and gas, demand outstrips supply, with the result that production equals capacity, which is a constant fraction of reserves.
In the Rice model, production of oil and gas are expressed separately as functions of a ‘user cost’ and the respective proved reserves and prices or revenues,
Q, = -498.7 + 0.085 * R, - 0.05 * U f 109.89 * P,,
log Q, = 0.826 * log R, - 0.022 * log U + 0.005 * log S,,
where
Q. =production of crude oil, Q, =production of gas, R, ---proved reserves of oil, R, =proved reserves of gas, P, =average price of crude oil, S, =expected revenues from natural gas, V = ‘user cost’ of oil and gas reserves.
No explanation is given for the use of the logarithmic form in one relation and a non-logarithmic form in the other.
“User cost’ is a concept originating from neoclassical capital theory.2 It is an implicit rental price for a unit of capital services. Since a piece of capital equipment is renewable, it seems to us that the use of this user cost concept for a depletable resource is theoretically inappropriate. It is also interesting to note that the equations do not guarantee that production is zero when the resource is depleted.
Finally, in the remaining model, GEMS, the production decision is so closely related to the development decision as to be inseparable.
9. Price ‘levers’ in the models
The preceding detailed discussions of the various steps in the process of discovering and producing oil and gas resources may have obscured the original purpose of EMF 5: to understand the relationship between prices paid for petroleum and the quantities produced. In theory, output price should affect each decision in the supply process.
‘See D.W. Jorgenson, ‘Capttal theory and investment behavior’, American Economic Review 53 (1963) pp. 247-259.
R&--B
330 P. Ciark et al., Ten U.S. otl and gas supply models
in areas would not attractive at prices. Second, an oil gas pool been found, current and future level prices should determine the of development Since later are discounted than earlier with static expectations (future
of oil gas equal their present early development be limited by the costs associated accelerated completion the development Oil or prices should only the of initial (not its and revisions development when turn out be different those that expected when original decisions made. If are expected rise over this early picture might dramatically, but
price increases not likely be an consideration except oil or prices are Finally, once development process been completed, can again the process the decision produce is
The dependence each of three decisions price is in table For almost of the prices have most important
on oil gas supply the exploratory In nine the ten studied (the model is exception) price
generate additional effort. In of the process models Kim-Thompson, LORENDAS, TERA-offshore), the of exploratory is determined comparing the present value oil or that may found with cost of it. In
Table 5
The role of prices in the EMF-5 models.
Prices enter the model at the following stages:
Model Exploration Production
DFI-GEMS E-M-S Epple-Hansen FOSSIL2 Kim-Thompson LORENDAS MIT-WOP EIA-ICF
OGM AHM
Rice AGA-TERA
onshore oNshore
Prices affect reserve additions Prices affect reserve additions Yes Yes Yes No Yes Yes Yes Yes No No
Yes No Yes Yes Yes Yes
Yes No Yes No
No No No No No Yes No
No NO Yes
No No
P. Clnrk et al, Ten U.S. oil and gas supply models 331
the three econometric models (E-M-S, Epple-Hansen, and Rice), this calculation is implicit, with new discoveries embedded in one or more equations relating discoveries to price.
While almost all models emphasize the role of exploration and make it central to the reIationship between price and quantity supplied, there is much less agreement on the relationship between discoveries and price. In the econometric models, which try to estimate this relationship explicitly, price variables are often statistically insigni~cant, and frequently influence the dependent variable in an unexpected way. In such cases, the numerical relationships eventually used in the model are largely the modeler’s choice, given his latitude for experimentation with the model specification. Non- econometric models are less explicit about this difficulty; the parameters are often jud~entally chosen by the modeler. Given the statistical problems with the econometric formulations, one suspects that many of the parameters in the engineering process models may also be subject to substantial error.
Once a new field is discovered, price can determine the extent to which it is developed. At higher prices, it will pay to drill extension wells outside the expected boundary of the original pool, in the hope that it extends further than originally estimated. Even given the size of a pool, additional wells may be able to increase the amount of oil or gas recovered. Some of the models (TERA, FOSSIL’?, E-M-S, MIT-WOP, and EIA-OGM) either implicitly or explicitly assume that the relationship between development and discoveries follows historical trends, and does not respond to price. Others (EIA-AHM, Epple-Hansen, Kim-Thompson, LORENDAS and Rice) allow for more intensive development of previously discovered fields when prices rise. In some of these models, however, the possibilities for increasing eventual recovery from an individual pool are largely ignored. Most of the models are explicit about part of this; ‘enhanced’ or ‘tertiary’ recovery is not included. However, even for primary and secondary recovery methods, the possibility of more extensive development at higher prices might significantly add to total supplies.
After oil and gas has been discovered and developed, with production facilities put in place, prices coufd conceivably affect the rate at which oil and gas flows out of the ground. However, in most cases, the deliberate reduction of production below developed capacity is a viable option for Saudi Arabia or Iran, but not for price-taking producers in the United States. The one exception to the general rule of production at full capacity is encountered with price controls. Only when prices are expected to rise faster than the discount rate (which is conceivable when sudden decontrol of prices is expected), may it be profitable for the oil producer to reduce production temporarily.
Almost all the models in the current study reflect the historical observation that production follows expenditures on development by locking the two
332 P. Clark et al., Ten U.S. oil and gas supply models
together. Only the LORENDAS model allows endogenous production cutbacks to take advantage of a rapidly rising price profile. Thus, in the high-price scenarios for natural gas, LORENDAS predicts a reduction of output until the end of controls, and then a dramatic rebound when the gas price jumps. The absence of this sort of behavior in the other models is a handicap if scenarios with pre-announced changes in regulated prices are to be analyzed.
There seem to be three general conclusions that can be drawn about the price response of the ten models of oil and gas supply in this study. First, increases in exploratory activity may be the most important way in which the rising price of oil and gas will influence future domestic supply. Most of the models take this linkage into account, but there is reason to believe that their projections of new discoveries are subject to a substantial amount of error. The historical relationship between exploratory effort and new discoveries has varied widely; this results in a substantial amount of uncertainty about future discoveries, particularly when drilling activity is expected to be outside the historicai range. Additional uncertainty is introduced by the range of possibilities for future exploratory effort.
Second, although the intensity of development of previously discovered pools of oif and gas is responsive to price in some of the models, it is likely that the much higher prices we are experiencing today will result in a higher fraction of ultimate recovery from a given pool of oil or gas. By and large, the models ignore this possibility; consequently, they probably underestimate the long-run price elasticity of supply.
Finally, expected steep price increases generated by price controls may generate substantial delays in development and production. Most of the models do not treat this possibility correctly.
10. Regulation, taxation and leasing
One of the primary uses of the models under consideration in this study is the analysis of federal energy policy. Direct manipulation of domestic prices can be analyzed by most of the models, although some of the effects of price controls are ignored. Taxes are used in making net present value calculations in most of the models that employ optimization and are included in prices in some of the econometric ones, so that the effects of tax changes can be analyzed in many cases. Leasing is included in only the largest models; more aggregated models cannot analyze the effect of changes in leasing schedules.
While government health, safety, and environmental regulations have probably changed the supply of petroleum in the U.S., none of these is
P. Clark et al., Ten U.S. oil and gas supply models 333
explicitly analyzed in any of the models in this study. Instead, attention has been (correctly) focused on the regulation of oil and gas prices, which have played a major role in petroleum industry decisions over the past 25 years. The standard answer, supplied by the economists’ doctrine that the price equals marginal cost, is that if new supplies command the market price, decontrol of ‘old’ oil or renegotiation of ‘old’ natural gas contracts would not change the incentive to produce. Many of the models in the study (EIA- OGM, Epple-Hansen, E-M-S and TERA) take this point of view, and therefore attribute no additional supply to price increases for ‘old’ oil and gas. FOSSIL2 allows for a small increase in supply through the cost of capital; decontrol of ‘old’ oil or gas increases internal funds and lowers the need for more costly external borrowing. The LORENDAS and EIA-AHM models allow for some decontrol effects by allowing more extensive exploration and more intensive development of known fields at higher prices.
It may be that decontrol of old oil or renegotiation of existing natural gas contracts would generate a supply response larger than that envisioned by any of the models in this study. Existence of controls on the price of resources discovered in the past must naturally limit expectations of future price rises for newly discovered oil or gas. And criticism of ‘obscene’ profits can only reduce the expected rate of return on investments in the discovery and production of petroleum. While it is hard to make the case that increased revenues from resources that have already been developed can be as powerful an incentive as revenues from new exploration, these old revenues should create some incentive for new supplies. It seems likely that the ‘marginal price’ approach taken by the models in this study understates the supply response to decontrol of oil prices or deregulation of natural gas. On the other hand, a satisfactory numerical estimate of the ‘expectation’ effect of decontrolling old oil of renegotiating old gas contracts is far beyond the capability of current modeling techniques. The most that can be said is that it should have a positive effect on quantities supplied.
10.2. Taxation
All the models in this study include tax parameters in their formulation, making direct analysis of tax policy initiatives possible. Ad valorem taxes on output (royalties, severance taxes, etc.) are subtracted from oil and gas prices to obtain the prices received by producers. Thus, the models’ responses to ad valorem tax changes are the same as the response to changes in price.
The other taxes or tax features included in the models (percentage depletion investment tax credit, and corporate income tax) are all features of the tax treatment of income from capital. The incorporation of these tax features is straightforward in all of the models which use them: Taxes are subtracted from gross revenue in cash flow and net present value
334 P Clark et al, Ten U.S. 011 and gas s~~~~y models
calculations, Implicit in this formulation is the assumption that there is no substitution of capital for labor in the production of oil and gas. To the extent that this assumption is incorrect, the cost reduction associated with tax breaks will be understated, but the econometric evidence on this issue in other areas of the economy indicates that the bias may be small.
Another positive aspect of the treatment of business taxes in most of the models is that the discount rate is not varied with the corporate tax rate; this amounts to the assumption that the after-tax rate of return is constant. Given the wide variety of investment opportunities available, this assumption is much more appropriate than assuming that the before-tax rate of return is constant, and that the discount rate varies inversely with the rate of tax on income from capital.
Of course, the treatment of taxes in some of the models is less than perfect: The Epple model approximates percentage depletion by including it in the ad valorem tax term and ignores the investment tax credit; the MIT-WOP model ignores taxes for all practical purposes. For reasons that are not clear, the TERA model seems to overestimate the effect of taxes, especially when such tax changes are compared to price changes that should result in about the same reaction in quantity supplied. In general, taxes are entered in simple ways that are appropriate for models designed to focus on the interaction between quantity and price.
Although it is clear that the federal leasing schedules for lands under its control should have some impact on oil and gas production, only two models are disaggregated enough to take this factor into account: TERA and EIA-OGM. Even in these models, the estimated availability of drilling rigs may make accelerated leasing ineffective in expanding supply, although sharp leasing cutbacks could reduce supply, particularly in 1990 or 2000.
References
AGA-TERA
American Gas Association. I977 and 1979. TERA: Total energy resoutCe analysis model. Technical documentation: Vol. I, Offshore gas and oif supply model, AGA F30078, and Vol. II, Onshore gas and oil supply model, AGA F30178.
DFI-GEMS3
Adler. R.J. et al., 1978, The DFI energy-economy modeling system, Final report (Decision Focus, inc., Palo Alto, CA).
HA-ICF
U.S. Department of Energy, 1978, Midterm oil and gas supply modeling system: Methodology description, Technical memorandum T~/ES/79~5, Nov. (DOE, Washington, DC).
‘For these models, there does not exist - as far as we know - published documentation of the model version used for the EMF model runs.
P Clark et al., Ten U.S. oil and gas supply models 335
lJ.S Department of Energy, 1979a, Alaskan hydrocarbon supply model: Methodology descriptton, Technical memorandum TM/ES/79-09. Jan. (DOE, Washington, DC).
US. Department of Energy, 1979b, Enhanced oil recovery model: Methodology description, Technical memorandum TM/ES/79-7 (DOE, Washington, DC).
E-M-S
Erickson, E.W., S.W. Millsaps and R.M. Spann, 1974, 011 supply and tax incentives, Brookings Papers on Economic Activity 2, 449478.
Epple-Hansen
Epple, D. and L. Hansen, 1979, An econometric model of U.S. petroleum supply with optimal endogenous depletion, Working paper no. 53-78-79, April (Carnegie-Mellon University, Pittsburgh, PA).
FOSSIL2’
Masevtce, A., 1978, A review and assessment of the FOSSIL1 supply structure, DSD no. 125, Sept. (Thayer School of Engineering, Dartmouth College, Hanover, NH).
Kim-Thompson
Kim, Y.Y. and R.G. Thompson, 1978, New oil and gas supplies in the lower 48 states (Gulf Publ. Co., Houston, TX).
LORENDAS
Rapoport, L.A. (principal investigator), 1977, LORENDAS model documentation: Vol. I, Mathematical concepts and formulation, May (Virginia Polytechnic Institute and State University, Blacksburg, VA).
MIT-WOP
Adelman, M.A. and J.L. Paddock, 1978, An aggregate model of petroleum production capacity and supply forecasting, MIT World Oil Project Working Paper, Aug. (Massachusetts Institute of Technology, Cambridge, MA).
RICE3
Rice, P. and V.K. Smith, 1977, An econometric model of the petroleum industry, Journal of Econometrics 6,263-287.
