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Year 2008 UCD- ITS- RR- 08- 26
Modeling of Energy Production Decisions:
An Alaska Oil Case Study
September 8, 2008
Author
Wayne Leighty
wwleighty@ ucdavis. edu
Advisors
Cynthia Lin
Joan Ogden
James Wilen
Institute of Transportation Studies * University of California, Davis
One Shields Avenue * Davis, California 95616
PHONE: ( 530) 752- 6548 * FAX: ( 530) 752- 6572
WEB: http:// its. ucdavis. edu/
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Table of Contents
GLOSSARY AND ABBREVIATIONS...................................................................................................... V
1 INTRODUCTION ............................................................................................................................... 1
1.1 ORGANIZATION OF THE REPORT.................................................................................................... 1
1.2 THREE PRIMARY OBJECTIVES ....................................................................................................... 2
1.3 MODELING OVERVIEW.................................................................................................................. 3
1.4 RESEARCH IMPORTANCE............................................................................................................... 3
1.5 RELEVANCE TO FUTURE TRANSPORTATION ENERGY.................................................................... 4
2 BACKGROUND..................................................................................................................... ............ 5
2.1 RELATED LITERATURE.................................................................................................................. 5
2.2 THE ALASKA OIL AND GAS INDUSTRY........................................................................................ 10
2.2.1 History of Oil Production...................................................................................................... 10
2.2.2 Future Oil and Natural Gas Production ............................................................................... 12
2.3 A DYNAMIC MODEL OF UNIT PRODUCTION .................................................................................. 14
2.3.1 The Multi- Stage Investment Timing Game ............................................................................ 16
3 DATA, COST ESTIMATION, PRICE ESTIMATION................................................................. 18
3.1 DATA ............................................................................................................................... .......... 18
3.1.1 Resource Data ....................................................................................................................... 20
3.1.2 Production Data .................................................................................................................... 21
3.1.3 Price Data ............................................................................................................................. 22
3.1.4 Production Cost Data............................................................................................................ 22
3.1.5 Well Data........................................................................................................................... ... 23
3.1.6 Drilling Cost Data................................................................................................................. 23
3.2 COST ESTIMATION ...................................................................................................................... 23
3.2.1 Base ( Average) Cost .............................................................................................................. 27
3.2.2 Drilling Cost Scalar .............................................................................................................. 30
3.2.3 Decreasing Returns to Scale.................................................................................................. 34
3.2.4 The Composite Cost Function ............................................................................................... 40
3.2.5 Discussion of Methods for Cost Estimation, part I................................................................ 42
3.2.6 Discussion of Methods for Cost Estimation, part II .............................................................. 43
3.3 PRICE ESTIMATION..................................................................................................................... 44
4 MODELING ALASKA OIL PRODUCTION................................................................................. 49
4.1 OBJECTIVE FUNCTION AND OPTIMAL CONTROL PROBLEM ......................................................... 49
4.2 SOLVING THE OPTIMAL CONTROL PROBLEM .............................................................................. 51
4.3 SENSITIVITY ANALYSES.............................................................................................................. 52
4.4 MODEL CALIBRATION................................................................................................................. 53
4.5 TAX SCENARIOS...................................................................................................................... ... 56
5 RESULTS AND DISCUSSION........................................................................................................ 59
5.1 OUR ORIGINAL THREE RESEARCH TASKS ..................................................................................... 59
5.2 HOW TAXES CAN AFFECT PRODUCTION PATHS, PROFITS, AND TAX REVENUE .............................. 61
5.3 OBSERVATIONS AND NOTES ABOUT INTERPRETATION OF RESULTS ............................................. 62
5.4 SIGNIFICANCE OF WORK............................................................................................................. 73
6 EXTENSIONS AND FUTURE WORK........................................................................................... 74
6.1 ENDOGENOUS PIPELINE SIZING.................................................................................................... 74
6.2 THE IMPACT OF TAX CHANGES .................................................................................................... 75
6.3 THE IMPACT OF IMPERFECT FORESIGHT....................................................................................... 75
6.4 THE IMPACT OF CARBON VALUE AND ENHANCED OIL RECOVERY................................................ 76
6.5 OIL SUBSTITUTES AND BACKSTOP ENERGY TECHNOLOGIES ........................................................ 76
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6.6 HEDGING BEHAVIOR IN OILFIELD DEVELOPMENT........................................................................ 77
6.7 A VARIABLE DISCOUNT RATE FOR CAPITAL INVESTMENT RECOVERY.......................................... 77
6.8 AN INTEGRATED MODEL OF EXPLORATION, DEVELOPMENT, AND PRODUCTION .......................... 78
6.9 GREATER ATTENTION TO ENGINEERING AND RESERVOIR GEOLOGY............................................ 78
6.10 APPLICATIONS TO OTHER ENERGY INDUSTRIES ........................................................................... 79
6.11 MONTE CARLO FOR CONFIDENCE INTERVALS ............................................................................ 79
6.12 MYOPIC DECISION- MAKERS AND HISTORICAL DISCOUNT RATES .............................................. 79
6.13 SOCIAL OPTIMALITY WITH ENVIRONMENTAL COSTS.................................................................. 80
6.14 ALASKA’S OPTIMAL PRODUCTION.............................................................................................. 80
6.15 A STRATEGIC MODEL OF DYNAMIC PRODUCTION DECISIONS .................................................... 81
REFERENCES..................................................................................................................... ...................... 83
APPENDIX A: NORTH SLOPE PRODUCTION UNITS ...................................................................... 90
APPENDIX B: DATA PLOTS BY FIELD: WELLS, PRODUCTION, RESERVES REMAINING..... 92
APPENDIX C: CONSTANT RETURNS TO SCALE PLANES ............................................................ 95
APPENDIX D: SPECIFICATION OF UNIT- SPECIFIC DECREASING- RETURNS WELL FUNCTIONS .98
APPENDIX E: DECREASING RETURNS TO SCALE SURFACES................................................. 102
APPENDIX F: COMPOSITE COST FUNCTIONS.............................................................................. 105
APPENDIX G: MODELING WITH THE ORDINARY DIFFERENTIAL BOUNDARY VALUE
PROBLEM APPROACH....................................................................................................................... . 108
APPENDIX H: DERIVATIONS OF ELF............................................................................................... 122
APPENDIX I: DERIVATION OF STEP 1 OF BOUNDARY VALUE PROBLEM FOR MODEL
SPECIFICATIONS INCLUDING ROYALTY AND SEVERANCE TAX.......................................... 127
APPENDIX J: SUMMARY STATISTICS FOR MODEL RESULTS BY UNIT ............................... 131
APPENDIX K: PRESENT DISCOUNTED VALUES AND CORRELATION COEFFICIENTS FOR
MODEL RESULTS AND HISTORICAL PRODUCTION BY UNIT AND NORTH SLOPE TOTAL,
5% FIXED DISCOUNT RATE................................................................................................................. 134
APPENDIX L: PRESENT DISCOUNTED VALUES AND CORRELATION COEFFICIENTS FOR
MODEL RESULTS AND HISTORICAL PRODUCTION BY UNIT AND NORTH SLOPE TOTAL,
VARIABLE DISCOUNT RATE AS DEFINED IN EACH SCENARIO............................................. 142
APPENDIX M: DERIVATION OF MODEL STRUCTURE FOR VARIABLE DISCOUNT RATE ... 150
APPENDIX N: MODEL RESULTS PLOTS BY FIELD ...................................................................... 155
PRUDHOE BAY: UNCALIBRATED MODEL RESULTS ................................................................................... 155
PRUDHOE BAY: CALIBRATED MODEL RESULTS........................................................................................ 158
PRUDHOE BAY: TAX SCENARIO MODEL RESULTS..................................................................................... 161
KUPARUK RIVER: UNCALIBRATED MODEL RESULTS................................................................................ 164
KUPARUK RIVER: CALIBRATED MODEL RESULTS .................................................................................... 166
KUPARUK RIVER: TAX SCENARIO MODEL RESULTS ................................................................................. 169
MILNE POINT: UNCALIBRATED MODEL RESULTS ..................................................................................... 172
MILNE POINT: CALIBRATED MODEL RESULTS.......................................................................................... 174
MILNE POINT: TAX SCENARIO MODEL RESULTS....................................................................................... 177
COLVILLE RIVER: UNCALIBRATED MODEL RESULTS................................................................................ 180
COLVILLE RIVER: CALIBRATED MODEL RESULTS .................................................................................... 182
COLVILLE RIVER: TAX SCENARIO MODEL RESULTS ................................................................................. 185
ENDICOTT: UNCALIBRATED MODEL RESULTS .......................................................................................... 188
ENDICOTT: CALIBRATED MODEL RESULTS............................................................................................... 190
ENDICOTT: TAX SCENARIO MODEL RESULTS............................................................................................ 193
NORTHSTAR: UNCALIBRATED MODEL RESULTS ....................................................................................... 196
NORTHSTAR: CALIBRATED MODEL RESULTS............................................................................................ 198
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NORTHSTAR: TAX SCENARIO MODEL RESULTS......................................................................................... 201
NORTH SLOPE TOTAL: UNCALIBRATED MODEL RESULTS......................................................................... 204
NORTH SLOPE TOTAL: CALIBRATED MODEL RESULTS ............................................................................. 206
NORTH SLOPE TOTAL: TAX SCENARIO MODEL RESULTS .......................................................................... 209
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Glossary and Abbreviations
Adjustment cost: the cost of increasing or
decreasing ( adjusting) production rate.
Generally, a company cannot instantly
change its rate of production without
incurring some costs of adjustment, which
may include fixed costs that are the same
for any change and variable costs that
depend on the magnitude or rate of change.
Oil producers generally face a tradeoff
between project timeline and cost since
fixing unforeseen events quickly costs more
than slower response. This implies a
variable adjustment cost since making an
adjustment more rapidly ( i. e., with project
timeline the binding constraint) increases
the project’s cost. Other costs of oil
production adjustment, like labor time and
equipment replacement, may be fixed or
variable costs. See the sidebar in section 4.4
for further discussion.
Cooperative ( and non- cooperative)
models: Models of non- cooperative
behavior use game theory to account for
strategic interactions. For example, two
competing oil producers may impact each
other’s profits if they are large enough to
influence market price or if they are
producing from the same oil reservoir.
Consequently, they each consider what the
other may do in deciding on their own
course of action. Models of cooperative
behavior do not include such game theory.
See the sidebar in section 2.1 for further
discussion.
Economic Limit Factor ( ELF): used to
adjust severance taxes in Alaska from 1977
to 2006, the ELF was a fraction between
zero and one. The nominal severance tax
rate ( 12.5 or 15 percent) was multiplied by
the ELF calculated for each field to
determine the tax rate actually paid. For
marginal fields near the “ economic limit”
Abbreviations
AC Adjustment Cost
ADR Alaska Dept. of
Revenue
ANWR Arctic National Wildlife
Refuge
AOGCC Alaska Oil and Gas
Conservation
Commission
API American Petroleum
Institute
AS Alaska Statute
BC Base Cost
CEO Chief Executive Officer
CCF Composite Cost
Function
CRWells Constant Returns Wells
plane
DCS Drilling Cost Scalar
DDCS Dampened Drilling Cost
Scalar
Dmp Dampener for the
Drilling Cost Scalar
OLS Ordinary Least Squares
DR Discount Rate
DRTS_ M Decreasing Returns to
Scale Margin, a factor
that shifts the slope of
the composite cost
function
DRWells Decreasing Returns
Wells surface
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of viable production, the ELF reduced the
severance tax rate to encourage continued
production. Calculation of the ELF was
based on the number of wells and total
production rate ( see footnote 46). In 2006,
when the ELF was eliminated as part of
comprehensive revision to severance tax
policy in Alaska, no field was paying 100
percent of the nominal severance tax ( ELF
factors by field in March, 2006 were
0.82415 for Prudhoe Bay, 0.00032 for
Kuparuk, 0.0000 for Endicott, and 0.6856
for Northstar; personal communication,
Dick Tremaine and Jenny Duval, Alaska
Department of Revenue, July, 2007).
Economically recoverable oil: oil that can
be produced at a profit given the production
cost and market price. Only a fraction of the
oil in a reservoir is technically recoverable,
and only a fraction of the technically
recoverable oil is economically recoverable.
As technology improves, the fraction that is
technically recoverable increases and the
fraction that is economically recoverable
also increases because production cost
decreases. Higher market price also
increases the fraction that is economically
recoverable.
Extraction externality: the effect of one
leaseholder’s oil production reducing the
reserves available for neighboring
leaseholders to produce if the oil reservoir
is common among them. See the sidebar in section 2.1 for further discussion.
FOB ( free on board): another way of saying the value ( price) of oil at the point of
production ( i. e., the well where it comes out of the ground) rather than at the point of sale
( e. g., an oil refinery). Free on board ( FOB) price is equivalent to wellhead value since the
buyer pays the transportation cost from origin to final destination.
Information externality: the improvement in knowledge about the likelihood of finding
oil gleaned by one leaseholder from observing the results of a neighboring lease holder’s
exploration. See the sidebar in section 2.1 for further discussion.
Net Social Benefit: generally defined as the social benefits of an action minus the social
costs of the action, where “ social” implies a broad summation of benefits and costs that
includes externalities. Net social benefit can be thought of as the size of the pie available
ELF Economic Limit Factor,
an adjustment to
severance tax eliminated
from Alaska statute in
2006
FOB Free On Board
NGL Natural Gas Liquid
OIP Oil In Place
OPEC Organization of the
Petroleum Exporting
Countries
PC Production Cost, dollars
per barrel
Q Oil Production Rate,
millions of barrels per
month
S Technically Recoverable
Reserves Remaining,
millions of barrels
TAPS Trans- Alaska Pipeline
System
TCF Trillion Cubic Feet
USGS United States Geological
Survey
WHV Wellhead Value
WS Wells Scalar
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for distribution. In the case of our research, we define the net social benefit of oil
production as the sum of producer profit and tax revenue.
Oil in Place: the amount of oil originally present in reservoir rock. Only a fraction of oil
in place is technically recoverable with current production methods, and only a fraction
of technically recoverable oil is economically recoverable ( i. e., can be produced at a
profit).
Production cost: the cost of producing output from known fields. Generally, oil
production cost includes the costs of exploration to find and evaluate oil reserves,
development costs to build the infrastructure for producing the reserve, and the variable
costs of actually producing output from existing wells. Since we model the production
decisions of unit operators for known oil fields, “ production cost” as we defined and
estimated it does not include exploration costs because rational economic agents should
make production decisions for known fields without regard to past exploration
investments. This distinction requires care in interpreting our results for “ producer
profit,” which are profits from oil production from which exploration and overhead costs
should be deducted to approximate net corporate profits.
Severance tax: imposed on the extraction of a natural resource to compensate for the
removal of the resource from the area in which it originated. In Alaska, the severance tax
rate was 12.25 percent of the gross value of production prior to July, 1981, changed to 15
percent, and then changed to a tax on the net value of production in 2006. See the sidebar
in section 2.2.2 for further discussion.
Structural economics: the use of economic theory to define the structure for statistical
modeling. Economic theory is the basis for defining mathematical relationships between
observable “ endogenous” variables and “ explanatory” variables. The use of economic
theory to define the structure often enables estimation of parameter values with
meaningful interpretation, like elasticities. See Reiss and Wolak ( 2007) for further
discussion.
Technically recoverable oil: the quantity of oil that can possibly be recovered,
regardless of cost or time, from a particular reservoir. The technically recoverable oil for
a given reservoir changes as oil production technology improves.
Unitization: the process by which an agreement is reached among leaseholders to
cooperate in the production from an oil reservoir that is common among them.
Unitization is legally required in Alaska prior to production, to mitigate extraction
externalities.
Unit operating agreement: the result of unitization, the unit operating agreement
specifies the share ( percentage) of oil and gas production each leaseholder receives and
specifies one unit operator. The unit operator makes all operating decisions for the field,
subject to approval from the other leaseholders.
Wellhead value: the value ( price) of oil at the point of production ( i. e., the well where it
comes out of the ground) rather than at the point of sale ( e. g., an oil refinery). The
wellhead value is generally the market price less transportation cost from the production
well to market.
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Acknowledgements
The author would like to thank the Sponsors of the Sustainable Transportation Energy
Pathways ( STEPS) Program, the Chevron Graduate Fellowship at UC Davis, and the
Graduate Automotive Technology Education ( GATE) fellowship program for financial
support of this work. Several Alaska state agencies were kind in providing data,
especially Stephen McMains with the Alaska Oil and Gas Conservation Commission.
The author also thanks Cynthia Lin for guidance and mentoring throughout this project
and Joan Ogden and James Wilen for valuable comments and reviews of this report. The
views and opinions expressed in this report are those of the author alone and do not
necessarily represent those of any sponsoring organization or outside reviewer.
1
1 Introduction
Understanding the dynamics of optimal oil production has been a major
application in economics of theories regarding finite resource extraction and dynamic
programming for many decades. Recent high oil prices have caused oil- holding nations
and states to revise their tax policies. Many of these revisions have tipped the tax slope
( i. e., more share of both upside potential and downside risk via higher tax rate) and have
introduced a variety of credits and deductions for oil company investments in the area. 1
This report seeks to inform such policymaking by investigating the effect of
government tax policy on dynamic firm behavior in oil production in Alaska. The main
novelty of our paper is modeling the effects of a wide variety of tax structures ( not just
tax rates) on dynamically optimal oil production paths. We also develop a method for
estimating field- specific cost functions without direct observations of production cost.
Our research addresses questions like the following:
• Have oil producers approximated dynamically optimal production despite
imperfect information ( e. g., inability to predict future oil price) and stochastic
production processes ( e. g., equipment failures)?
• Can tax policy encourage more rapid or gradual energy production in the future?
• Does government policy create inefficiency in the oil industry?
• Are there tradeoffs between maximizing the net social benefit from energy
production and achieving a desired allocation of producer profit and tax revenue?
We find that changing the tax rate alone does not change the oil production path
except for marginal fields that cease production. Introducing credits or deductions into
the tax policy, however, can change the oil production path, but at the expense of net
social benefit, meaning either oil companies or the government will be made worse off
( i. e., lower profits or lower tax revenue). Analyses of Alaska’s oil production industry are
particularly valuable now because of Alaska’s potential role in the next several decades
of US energy supply.
1.1 Organization of the Report
This report is organized into several distinct sections, with subsections in each. In
the remainder of the introduction, we describe the objectives of our research, outline our
modeling approach in general terms, and describe the research importance and relevance
to future transportation energy supply. The purpose is to establish the motivation for this
research with broad understanding of the context, methods, and potential application of
results.
Section 2 provides background information on related literature, the Alaska oil
and gas industry, and the concept of a dynamic model of oil production. The information
in this section will be helpful for understanding the remainder of the paper, particularly
the data described in section 3 and the modeling methods described in section 4.
1 The author participated in one such policy revision as staff for an Alaska state senator. In that debate, the
oil company response to tax credits and deductions for investment was assumed to be increased investment,
which was assumed to improve the government tax revenue. Yet these assumptions were not supported by
research. In fact, some research that did exist at the time ( but was not cited in the debate) suggested that
such policy changes would have negligible effect on oil company behavior ( Kunce, 2003).
2
Section 3 provides description of the data used in this research, the estimation of
an exogenous price function, and our novel method of building field- specific cost
functions from relatively little cost data. Although the motivation for needing the data
presented in section 3 may not be clear without understanding of the modeling methods
presented in section 4, we decided to present the data – and particularly the estimation of
cost and price functions – first to obviate confusion regarding modeling methods in
section 4.
Section 4 presents our dynamic model of Alaska oil production, including a
simple model formulation without taxes, the complete model with taxes included,
sensitivity analysis, model calibration to historical production data, and the tax scenarios
we evaluated with the calibrated model.
Finally, Section 5 presents results pertaining to the ability to do such modeling
with limited data, evaluation of dynamic optimality in historical production decisions,
and how taxes can affect production paths, profits, and tax revenue. We offer
recommendations for interpretation of these results. Section 6 concludes with discussion
of possible extensions of this research and recommendations for future work.
There is a glossary at the beginning of the report for clarification of terminology
that is either technical or unique to this paper. The glossary also includes a list of
abbreviations. Sidebars in the text, shaded grey, provide additional explanation of key
concepts.
1.2 Three Primary Objectives
We have three primary objectives for this research. First, we evaluate the ability
to do such modeling, with both analytic and empiric approaches, given data constraints.
To address this topic, we test the limits to complexity in dynamic modeling while
considering what features need to be added to the model to bring economic theory close
to observed behavior ( i. e., minimize discrepancy between modeled optimal production
paths and actual production histories for each of the seven North Slope production units).
We find that adjustment costs with fixed initial production rate are key components, as
well as discount rate.
Second, we evaluate whether producers have been dynamically optimal in their
production decisions by comparing the discount rates that best fit the model to historical
production with the discount rate range that is considered “ reasonable” for the oil
industry. 2
Third, we simulate the effect of alternative tax policies on production paths and
present discounted values of producer profits and state tax revenue. We present results for
a range of tax policies, including the actual historical policies and an approximation of
the new policy enacted in 2006 ( revised in 2007) by the Alaska legislature, with
2 Interpretation is complicated by two competing explanations. On one hand, theory could be inadequate.
Producers are successful dynamic optimizers and historical production data show the optimal path, with
perturbation for stochastic events ( accidents, etc.). The path computed based on theory deviates from the
historical path because the theory is not adequate for predicting the optimal path. On the other hand,
economic theory might accurately predict the dynamically optimal path, with the benefit of perfect
hindsight, and the deviation from this path in historical data is the degree to which producers failed to be
dynamically optimal in their production decisions.
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implications for designing policy to maximize net social benefit ( defined as the sum of
producer profit and tax revenue).
1.3 Modeling Overview
We propose a simple dynamic model of oil production for seven production units
( fields) on Alaska’s North Slope, add taxes to the model structure, use adjustment cost
and discount rate to calibrate the model against historical production data, and use the
calibrated model to simulate the impact of tax policy on production rate. In Alaska, the
efficiency of petroleum production may be influenced by tax and leasing policies and
contract structures. Our research approach is to simulate the optimal production path and
compare it to actual production data to evaluate differences. We present empirical
estimates for wellhead price, drilling cost, an inverse production function for producing
wells, and production cost functions. A variety of modeling frameworks are discussed
and the potential benefits of such modeling are proposed.
1.4 Research Importance
Our research in Alaska seeks better understanding of oil production decision-making
and how to model these decisions. By improving upon a simple dynamic model
of oil production to incorporate more realism in producer decision- making, cost
functions, and the policy context in which decisions are made, we examine whether
producers have been successful dynamic optimizers. The resulting insights are useful for
the design of efficient policies that will be important for future petroleum development
and may be relevant for other energy industries as well.
• The degree to which actual production history deviates from the modeled optimal
path may represent an unclaimed profit opportunity for producers as well as lost
tax revenue for government.
• With the methodological question of what features need to be added to bring
theory close to reality answered, simulation of production paths and resulting
revenue streams can indicate which tax policies are likely to yield higher producer
profit and/ or government revenue.
• For Alaska, the state legislature made major changes to the oil and gas tax system
in 2006 and 2007. The government should consider what impact those changes
may have on production decisions since tax revenue is determined by the
combination of tax policy and production decisions.
Alaska has 37.5 trillion cubic feet ( TCF) of proven natural gas reserves and over
100 TCF of likely resources ( USGS, 2005). This quantity is sufficient for supplying
approximately six percent of total United States demand for 30 years, but the gas is
stranded without construction of a $ 25 billion pipeline ( Alaska Gas Pipeline website,
2007). As the state develops policy for the commercialization of this resource, lessons
about pipeline sizing and the influence of policy on production paths in the oil industry
may apply.
For other energy supplies, like wind power or biofuels, lessons from the oil
industry may help to inform what policy levers would be effective stimulus for faster
development and production. The models of dynamic behavior that emerge from our
research are models of firm- level decision- making and of the effects of policies and
institutions on these decisions. As such, similar models may be used in the future to
4
examine firm behavior and decisions under many pending policies, like the low carbon
fuels standard in California and, more broadly, all types of policies that employ
incentives or penalties to encourage developing alternative sources of energy.
Implications of this research include the following. For oil producers, evaluation
of the dynamic optimality of past production may inform future production decisions. For
policy makers, evaluation of the effects of policy tools on producer behavior may provide
insight into means for encouraging more rapid or gradual energy production in the future,
and tradeoffs between maximizing net social benefit and achieving a desired allocation of
producer profit and tax revenue.
1.5 Relevance to Future Transportation Energy
The question of how policy effects oil production is important for our
transportation future for several reasons. In the short- term, our current transportation
systems depend on oil for more than 95 percent of their energy supply ( EIA, 2008) and
Alaska accounts for 13 percent of total US oil production and supplies five percent of
total US oil consumption ( EIA, 2008b). Understanding Alaska oil production is important
for understanding our transportation energy supply in the short term.
In the long term, understanding past energy production decisions and how policy
can impact these decisions will help us understand how future energy development and
production may occur and be guided. It is increasingly clear that new, low carbon
transportation fuels will emerge over the next several decades for several reasons. Public
policy is beginning to internalize the costs of global climate change, which will re- shuffle
the relative costs of energy alternatives by adding cost for CO2 and other GHG
( California Assembly Bills 32 and 1493; Leighty et al., 2007). The world will reach peak
oil production rates, at which point supply will begin to diverge from demand and
alternative primary energy sources will become more competitive ( Campbell and
Laherrere, 1998; Rogner, 1997). New technologies and energy conversion devices will
change the value proposition of energy forms ( Williams, 2006).
Many researchers have focused on the systems optimization for emerging energy
markets, from engineering economic optimization of hydrogen pipeline systems ( Johnson
et al., 2005) to biomass feedstock gathering and plant location ( Parker, 2007) to impacts
of new transportation fuels on the electric grid ( McCarthy et al., 2007 and 2008).
Economics- based research is also needed to explore the potential effect of policy on
industry behavior in these emerging energy markets. Our research takes a step toward this
goal by developing a flexible dynamic framework that may be adapted to other energy
industries.
Our development of a model for understanding dynamic production behavior in
the Alaska oil industry may provide a foundation for similar modeling of the potential
Alaska natural gas industry, which may be an important component of the future
domestic energy supply, and other low- carbon energy sources.
5
2 Background
This section provides background information on related literature, the Alaska oil
and gas industry, and the concept of a dynamic model of oil production that may be
useful for understanding the remainder of the paper, particularly the data described in
section 3 and the modeling methods described in section 4.
2.1 Related Literature
The oil crises of 1973 and 1979/ 1980 motivated modeling designed to forecast
future supply and demand for US crude oil resources. A dichotomy formed between
models based on economic theory describing supply and demand interactions ( Dasgupta
and Heal, 1979; Pindyck, 1982; Horwich and Wimer, 1984; Griffin, 1985) and
engineering- process models that simulate the exploration, development, and production
processes ( Davidsen et al., 1990). The former generally exclude physical and engineering
factors that influence the supply of oil while the latter generally exclude economic forces
( e. g., prices) that influence supply and demand. Neither approach accurately forecast
future supply and demand ( Kaufmann, 1991).
What is “ optimal” and why is oil production a “ path”?
Many disciplines seek to optimize a situation by maximizing or minimizing
an “ objective function.” In economics, the objective function is often assumed to be
either cost or profit. For example, the plant manager’s optimization problem is to
minimize cost for a particular level of output while the CEO’s optimization problem
is to maximize profit. Since profit is generally defined as revenue less cost, the
CEO is taking the plant manager’s cost minimization as given and is trying to
maximize revenue.
To find the profit- maximizing production plan, a method is needed for
adding up profit that is earned over time in a consistent manner. The notion of
discount rate is used for this purpose. One way to understand the discount rate is to
realize that a dollar in your pocket today is worth more to you than a dollar next
year because you can put the dollar to work earning interest in a bank. In the case of
oil production, this means the CEO is trying to maximize the “ net present value” or
“ present discounted value” of the entire stream of future profits, where profits
earned next year are worth slightly less than profits earned today. Consequently,
unless specified otherwise, the “ optimal” oil production path is the one that
maximizes the present discounted value of profits.
However, in some cases it may also be important to recognize objectives
other than profit maximization as well. For example, investing in exploration to
increase the quantity of oil a company can access for production ( known as
“ bookable reserves”) can increase stock value by improving the prospects for future
production. Increasing the size of a company can improve the CEO’s cache. If the
oil producer is a national oil company, it may have social goals like delivering
short- term revenue for building infrastructure to help diversify the economy.
6
Ruth and Cleveland ( 1993) extended this literature by using a nonlinear dynamic
model of oil exploration, development, and production coded in STELLA3 to simulate
optimal depletion paths for the 48 contiguous United States in the period 1985 to 2020.
They used the theoretical model of optimal depletion developed by Pindyck ( 1978),
which considers supply and demand, with their own econometric estimation of supply
and demand parameters. The authors model demand and all three phases in oil supply –
exploration, development and production – to “ derive optimal time paths for drilling
rates, discoveries, production, costs, and prices of crude oil.” Similarly, Rao ( 2000, 2002)
used a dynamic model to examine the “ joint production- investment decision for the entire
supply process from drilling through production” for petroleum resources in India.
These integrated modeling efforts for oil industries produced interest in more
detailed consideration of producer- level decision making. A series of papers on the Gulf
of Mexico oil industry is perhaps the best example of structural econometric modeling of
decision- making in an oil industry. Papers by Hendricks and Kovenock ( 1989) and
Hendricks and Porter ( 1993, 1996) analyzed the learning and strategic delay caused by
information externality associated with exploratory drilling and found that plausible non-cooperative
models generated reasonably accurate and more descriptive equilibrium
predictions than cooperative models. However, these papers were based on theoretical
models and reduced- form empirical analyses. The subsequent work by Lin ( 2007)
improved upon these models by using a structural model to estimate the effects of a
neighbor’s actions on firm profits and by adding real options theory in the structural
econometric context to model the multi- stage investment timing game of exploration and
development.
3 STELLA is systems modeling software that uses an icon- based graphical user interface rather than the
command- line coding common in other software packages. STELLA is well suited for modeling system
evolution over time with stocks and flows for discrete or continuous processes.
Consequently, the profit- maximizing objective function is an assumption, albeit a
standard one, underlying most oil production modeling exercises.
Finally, the optimal oil production plan is called a path because the plan is
specified for all periods into the future ( tracing a path on a production vs. time
graph). Oil production is an inherently dynamic optimization problem, meaning
current- period decisions impact future- period opportunities, because each reservoir
contains a finite quantity of oil. Thus, production today impacts future period
profits by reducing the reserves that remain. Consequently, the production plan that
optimizes the present discounted value of profits will specify the production in
every period into the future – an entire production path. See Figure 20 for an
example of this “ path.”
7
The work by Lin ( 2007) documented the potential impact of government leasing
policy on multi- stage investment timing decisions in oil exploration and development in
the Gulf of Mexico. The focus in Lin’s work was on the potential for lease tract size, set
by government leasing policy, to induce wasteful non- cooperative strategic behavior due
to competing information and extraction externalities. The modeling we develop for the
Alaska oil industry is different in methodology and specific research questions, but
addresses the same fundamental question of whether government policy creates
inefficiency in the oil industry. Our model of Alaska unit production decisions4
incorporates the impact of government policy on the dynamic optimal control problem
inherent in these decisions, but focuses on the production phase rather than exploration
and development investments.
4 The concepts of unitization and unit production are described in section 2.2.
What are cooperative versus non- cooperative models?
Modeling behavior in an industry like oil production requires some
knowledge or assumption about the industry structure ( sometimes testing for
elements of industry structure is a research objective). Intuitively, we would
expect behavior to be different for monopolies ( one company), oligopolies ( a few
companies), and situations of perfect competition ( many homogenous
companies). These structural differences require differences in model construction
as well. For example, the ability of monopolies ( and to some extend oligopolies)
to influence both supply quantity and price means price is an endogenous part of
the model ( via the market- clearing equilibrium of supply and demand).
Conversely, perfect competition is modeled with exogenous price.
In an oligopoly situation, which is often the case for oil production where
there are relatively few large producing companies, the dichotomy of cooperative
vs. non- cooperative modeling becomes important. If companies are coordinating
their production plans ( i. e., cooperating, like OPEC has done in the past), then one
should model optimization of oil production for the whole region. It’s as if there
is a single CEO of a single company making production decisions, with
production then allocated among the several actual companies ( in fact, this is
essentially how OPEC has operated in the past).
If companies are not cooperating, but rather are making production
decisions independently and in competition with one another, then one should
include strategic interactions in modeling each company’s optimization. Modeling
with strategic interactions implies game theory and the fundamental concept of
best responses – each company considers the likely response of other companies
to its actions and formulates a best response given the others’ likely responses.
Thus, the distinction between cooperative and non- cooperative modeling
is essentially a distinction between including game theory in the model or not,
which is determined by whether the industry structure implies strategic
interactions are important. Non- cooperative models incorporate game theory to
account for strategic interactions.
8
Externalities in Oil Production
One way to define the term “ externality” is an impact on one party that is
not considered by the actor causing the impact. For example, you may benefit
from seeing and smelling my flower garden, but I may plant it for my own
reasons without considering its impact on you. The flower garden provides a
positive externality. Untaxed pollution from industry is often cited as a negative
externality because the industry does not consider the costs associated with health
effects and environmental damage in its financial decision to pollute.
For oil production, two forms of externality have been well documented
( see Lin, 2007, for further discussion of both). Both stem from the fact that oil
occurs in particular locations around the world in geologic formations that trap the
oil ( i. e., reservoirs) and the general practice of leasing tracts of land to confer the
right to explore for and produce oil vertically beneath these leases.
Information externality relates to the exploration stage of oil production. If
oil is found one leased tract, there may also be oil beneath neighboring leases if
the leases are close in proximity because they may share the same geologic
structure and same oil reservoir or may share similar geologic features that
contain multiple oil reservoirs. Thus, if one lease holder can observe her
neighbor’s success in finding oil, an information externality is conferred since the
neighbor’s action in finding oil impacts our hypothetical lease holder’s
assessment of her own likelihood of finding oil. Technically, this is referred to as
Bayesian Updating wherein the prior assessment of the probability of finding oil
is updated with new information. In fact, observing a neighbor’s discovery of oil
is quite easy if she acts on it because a production rig is visually distinguishable
from an exploration drilling rig. The result is a positive externality – like the
flower garden – where one leaseholder’s exploration investments confer a benefit
to neighbors who can observe the results and get a better idea of whether they
should invest in exploration. The incentive in this case is to delay one’s own
exploration in hopes of benefiting from this positive externality.
Extraction externality relates to the extraction stage of oil production. If
neighboring leases share a common oil reservoir, several leaseholders will be
producing from the same resource and the production decisions of one will impact
the others’ ability to produce. Actor Daniel Day- Lewis explained this notion of
“ drainage” in the 2007 film “ There Will Be Blood” as follows,
If you have a milkshake, and I have a milkshake, and I have a straw… my
straw reaches across, and starts to drink your milkshake. I drink your
milkshake! { slurp} I drink it up!
The result is a negative externality – like pollution – where one leaseholder’s oil
production can effectively reduce the reserves available for neighboring
leaseholders to produce. The incentive in this case is to produce faster than one’s
neighbors to mitigate the negative externality by getting more of the common oil
resource.
9
The study by Kunce ( 2003) is directly related to our consideration of the impact
of severance tax policy on oil production industries. It extended previous research by
Deacon et al. ( 1990) and Moroney ( 1997) by generalizing the analysis to all U. S. states
with a dynamic profit- maximizing framework. 5 Kunce continued in the vein of integrated
modeling of exploration, development and production by embedding tax policy into
Pindyck’s ( 1978) theoretical model of exhaustible resource supply. 6
In this paper, we model producer behavior at the field level, taking known fields
as given ( i. e., the exploration stage is complete) and modeling production decisions only.
That is, we do not model the exploration stage of oil production but rather model the
profit maximizing extraction of a known reserve. Consequently, our model is not
intended to forecast future production but rather to simulate the effect of tax policy on
field- level production decisions. Despite the difference in methods, we produce results
similar to those found by Helmi- Oskoui et al. ( 1992) and Kunce ( 2003), namely that tax
policy has relatively little affect on the optimal time path of production but does change
the allocation of surplus between producer profit and government revenue. 7 However, we
offer the additional insight that tax policy can affect the production path if distortionary
components like credits and deductions are introduced. Future work may expand our
Alaska case study with one or more of the integrated dynamic empirical frameworks
discussed above, to examine the impact of tax policy on exploration and development
activities and the impact of modeling method on results. Case studies of the Alaska oil
industry are particularly relevant now since the state revised its severance tax system in
2007, is considering a pipeline contract and policy structure under which 37.5 TCF of
natural gas will be commercialized, and likely holds oil reserves that may be produced in
the future ( see section 2.2).
5 Deacon et al. focused on California; Moroney focused on Texas. Another example of previous work
considering the impact of tax policy on oil production industries is Pesaran’s ( 1990) econometric model of
offshore oil production in the UK which was extended to include taxes by Favero ( 1992). However, the
shadow value of oil in these analyses is not always positive, suggesting overestimation of the impact of
taxation on profit ( Kunce, 2003).
6 Other “ Pindyck- based simulation studies” that consider the effects of taxation on exploration and
production include Yucel ( 1989) and Deacon ( 1993). These studies were focused on “ assessing the
generality of theoretical results obtained in more limited settings” rather than empirical case study of a
particular oil industry or change in state tax policy ( Kunce, 2003).
7 Helmi- Oskoui et al. ( 1992) added the interesting twist of using reservoir pressure ( based on actual well
data and reservoir characteristics) as a control variable in their dynamic model of joint oil and natural gas
production. They argue that, “ controlling the reservoir pressure and bottom well- hole flowing pressure of
the producing well are key elements in petroleum production from a given reservoir” ( Helmi- Oskoui et al.,
1992). We do not include reservoir pressure explicitly in our modeling, but proxy for it with the
diminishing returns to production rate built into our cost function. Helmi- Oskoui et al. also included the
effect of tax policy on production in their modeling, but found that “ production and severance taxes, federal
corporation income taxes, and depletion allowances do not affect the optimal time path of oil and gas
production… because the tax deductions and depletion allowances only affect the net revenue but not the
production and energy requirement,” which is also consistent with Uhler ( 1979). However, Helmi- Oskoui
et al. did find that, “ the imposition of taxes increases the present value of the revenues of the state and
federal governments and decreases the revenues of the firms for all discount rates” and the “ discount rate is
an important factor in the determination of joint production rates and the length of production periods.” Our
findings are quite similar, with the added insight that tax policy can impact the production path if
distortionary components like credits and deductions are introduced.
10
2.2 The Alaska Oil and Gas Industry
The oil and gas industry in the state of Alaska presents a unique “ laboratory” for
the study of primary energy production for several reasons. The state is isolated, with
only one export point for oil at the port of Valdez. Oil from Alaska’s North Slope is
delivered to market via 800 miles of Trans- Alaska Pipeline System ( TAPS) and
approximately 3,000 miles of tanker travel ( Alyeska Pipeline Service Company, 2007;
Kumins, 2005). As such, the physical boundaries of the market are well defined.
2.2.1 History of Oil Production
The history of oil production in Alaska runs from the late 1950s to the present.
The first oil leases were sold in the Cook Inlet area near Anchorage in 1959. But the
discovery of the Prudhoe Bay oil field on Alaska’s North Slope in 1968 signaled the start
of what we now consider Alaska’s oil and gas industry. The Prudhoe Bay field contained
nearly 20 billion barrels when discovered, making it more than double the size of the
second largest oil field in the United States, the East Texas oil field ( personal
communication, Vincent Monico, BP- Alaska, 2 July 2007). Completion of the Trans-
Alaska pipeline in 1977 created a means for delivering this oil to market. The pipe carried
peak flow of 2 million barrels per day in 1988 and currently carries just under 1 million
barrels per day ( Alyeska Pipeline Service Company, 2007). Structural breaks define the
following three distinct periods. 8, 9
• 1957 to 1977 was a period of oil discovery, exploration, and limited development
that occurred before completion of the 800- mile Trans- Alaska Pipeline
connecting the North Slope oil fields to the port of Valdez. These events occurred
under Alaska’s initial tax laws, including the corporate income tax, property tax,
royalty, and severance tax.
• 1977 to 2006 was a period of oil production after revision of Alaska’s severance
tax system to include the Economic Limit Factor ( ELF), that was intended to spur
new exploration and development investment. 10
• 1987 to 2006 was a period of oil production after significant revision of Alaska’s
corporate income tax.
The composition of firms active in oil exploration and development in Alaska has
changed over time, leading to the present situation of only three primary oil producers
active in the state: BP, ConocoPhillips, and ExxonMobil. The small number of players
presents a situation where economic theory would suggest the possibility of strong
strategic considerations and the potential for collusive actions. The questions of whether
8 These structural breaks afford the opportunity to evaluate the impact of changing conditions – especially
the construction of infrastructure for delivering oil to market and several changes to the tax landscape – on
producer investment decisions, and provide valuable reference points for modeling strategic behavior.
However, much of the potential for use of these structural breaks in modeling strategic behavior is left to
future work.
9 Note, the requirement for unitization was passed in 1955 ( amended in 1978 and 1980; AS 31.05.110),
which was before production on the North Slope began, so it is not a structural break that is relevant for our
modeling.
10 The petroleum production tax ( PPT), passed in 2006, replaced the gross- profits- based ELF system with a
net profits tax, thereby creating another structural break and defining the start of a new period in Alaska’s
oil industry ( Petroleum Production Tax website, 2007; Alaska Department of Revenue website, 2007;
Alaska State Legislature website, 2007).
11
strategic considerations and collusion are substantial in Alaska are important to policy
makers in the state.
However, the legal requirement for unitization prior to production in Alaska likely
mitigates the potential for strategic interactions in oil production. This requirement
( described below) is somewhat unique to Alaska and impacts our modeling of production
decisions.
Oil leases are two- dimensional polygons on the earth’s surface, many of which
may be located vertically above the same oil resource. If multiple different lease- holders
are producing from the same common resource, strategic considerations may lead to
inefficient results ( e. g., a race to pump faster than optimal since some oil is lost to the
other lease holders as a consequence of waiting to pump) ( Lin, 2007). The policy of
mandatory unitization is intended to mitigate this extraction externality. When a new oil
field is found in Alaska, its extent is carefully mapped and all lease- holders with a claim
on the reserve must agree on a unit operating agreement prior to any production ( AS
31.05.110). The primary components of this agreement are the production shares
( percentages of total production) for oil and gas and designation of a unit operator ( the
company that will make all operating decisions, subject to approval from all the other
What are structural breaks?
Modeling behavior in an industry like oil production requires some
knowledge or assumption about the industry “ structure” – how many companies
are in business and under what rules do they interact. To help identify the
appropriate structure to use in modeling, economists ask whether companies in
the industry are similar in their production methods and products, whether there
are barriers to entry of new companies, whether the companies have good
information about the marketplace, and whether any one company is large relative
to the market size. Sometimes testing for elements of industry structure is a
research objective in itself.
The results from a model built on one particular industry structure ( e. g.,
perfect competition with exogenous price) are only valid for that particular
industry structure. If something in the underlying structure changes, the model
forecasts may no longer hold. For example, a nice paper by Moschini and Meilke
( 1989) identified a structural break in the demand for red meat and poultry when
the health effects of cholesterol were documented and publicized. There was a
shift in demand that market models predicated on no- cholesterol- knowledge
demand structure could not have predicted.
In oil production, tax and regulatory policy changes are common sources
of structural change. An oil producer makes production plans based on the current
tax regime but likely cannot predict what future policymakers will enact. A
change in the tax policy, however, may change the rules of the game in a way that
would change the producers’ optimal production plan. This kind of structural
break is one of the main topics of our research.
12
companies involved). Production shares are based on geologic assessment of the
percentage of the reserve beneath each lease and are extremely contentious and
valuable. 11 Some companies want to be unit operators to gain experience with technology
and operations while others do not ( personal communication, Vincent Monico, BP-Alaska,
July, 2007). For this research, the salient point is that these required unit
agreements eliminate the strategic interactions present in other places during the
production phase since the unit operator makes production decisions for the entire field.
Thus, we can consider the decisions of the unit operator as the single owner of the
resource, optimizing production without strategic consideration with regard to the other
owners of the common resource. Hence, we model oil production for the seven individual
units on Alaska’s North Slope: Prudhoe Bay, Kuparuk River, Milne Point, Endicott,
Badami, Colville River, and Northstar ( Appendix A). 12
In practice, however, it is not as simple as we have described and some strategic
interactions persist. For example, the production shares for oil and gas are usually quite
different since some leases are located above the oil reserve while others are above the
gas cap. For example, the production shares for Prudhoe Bay are the following: 51% oil
and 14% gas for BP; 22% oil and 42% gas for Exxon; 22% oil and 42% gas for
ConocoPhillips ( Libecap and Smith, 1999). Since natural gas on the North Slope is
stranded without a pipeline to deliver it to market, the unit operator may wish to process
associated gas into natural gas liquids ( NGL) for shipment down TAPS or for re- injection
to boost oil recovery ( flaring is not permitted), depending on its relative oil and gas
shares of production ( ibid). For example, when BP took over as unit operator of Prudhoe
Bay in 2000, it was clear that BP would benefit from re- injection while the other
companies would benefit from NGL processing, and litigation over unit management
decisions ensued ( ibid). 13 Although such strategic interactions are largely resolved in
negotiation and court rooms rather than by non- cooperative strategic behavior in the
marketplace, future work may include consideration of the impact of unit agreement
contract structures on production decisions.
2.2.2 Future Oil and Natural Gas Production
High oil prices are prompting major new policy development and infrastructure
investment in Alaska. The Alaska Legislature adopted an entirely new severance tax
system in August 2006 and then again in November 2007.10 The state is also currently
negotiating the contractual context for construction of a $ 25 billion, 3,000- mile natural
gas pipeline to bring 37.5 trillion cubic feet ( TCF) of known natural gas reserves on the
North Slope to market. 14 Analyses of Alaska’s oil production industry are particularly
11 Production shares are carried out to the tenth decimal and revision of the fifth decimal for the Prudhoe
Bay field equates to tens of millions of dollars ( personal communication, Vincent Monico, BP- Alaska, 2
July 2007).
12 We will use the terms “ unit” and “ field” interchangeably hence forth.
13 Prudhoe Bay was comprised of the East Operating Area ( operated by ARCO) and the West Operating
Area ( operated by BP) prior to 2000 ( BP, 2006). We abstract from this complexity by treating Prudhoe Bay
as a single field in our modeling.
14 USGS, 2005; Petroleum Production Tax website, 2007; Alaska Gasline Inducement Act website, 2007.
In fact, the former governor of Alaska, Frank Murkowski, negotiated a contract for the construction of this
natural gas pipeline, but the legislature did not approve the contract before the end of his term of office
( Alaska Gas Pipeline website, 2007).
13
valuable now because of Alaska’s potential role in the next several decades of US energy
supply.
A Primer on Oil Taxes
Oil production in the United States is taxed in four ways - royalty,
severance, property, and income taxes. The relative magnitudes of these four
types of taxation differ greatly among oil producing states ( see Deacon et al.,
1990 for comparison of Alaska, California, Louisiana, Oklahoma, Texas, and
Wyoming).
Royalty refers to payments made to a landowner for the rights to produce
oil. If the landowner is the federal government, these royalty payments are 12.5 to
16.7 percent of the value of the oil and gas actually produced ( 12.5% for onshore,
16.7% for offshore). In Alaska, most oil production occurs on state- owned land.
Lease terms for these state lands have varied over time for different lease sales
and areas, but the most common royalty rates are 12.5% and 16.7% as well.
Finally, royalties can often be paid in value or in kind, with the former payment
made in dollars based on market price ( less downstream costs incurred) and the
latter payment made in barrels of oil, which the recipient must then market and
sell. The option for royalty in kind is often used infrequently only as a check on
producer- reported market sales revenue because establishing their own oil sales
capability is difficult for royalty recipients.
Severance tax is imposed on the extraction of a natural resource, for its
severance from the state in which it originated. This tax is generally levied by the
state regardless of the landowner as recompense for the general population for the
removal of a natural resource from their state. In Alaska, the severance tax rate
was 12.25 percent of the gross value of production prior to July, 1981, when it
was changed to 15 percent, and then was changed to a tax on the net value of
production in 2006. Since at least 25 percent of severance tax receipts are
deposited in the Alaska Permanent Fund, which now has a balance of more than
$ 35 billion and pays annual dividends to all Alaska residents based on a rolling
average of earnings on the principal, the conversion of natural resource wealth
into financial wealth implied by the concept of severance tax is literal and for all
Alaska residents.
Property tax for oil production is generally very similar to other types of
property tax. The tax is based on a small percentage of the value of all capital
assets owned in a particular area. In the case of oil production, these assets are
often pipelines, drilling rigs, production platforms, and the like. The property tax
is often collected for use by local government.
Similarly, corporate income tax for oil production is similar to other
corporate income taxes, levied as a percentage of net profit from operations in a
particular jurisdiction.
14
Natural gas is often cited as a clean fossil energy source for future energy
systems. 15 If climate change becomes a more significant motivation in energy decisions,
demand for low- carbon natural gas will grow. Thus, understanding future natural gas
supply in the United States is relevant to a wide range of future scenarios, from business
as usual to hydrogen- fueled vehicles. Alaska’s proven reserves of 37.5 TCF of natural
gas is projected to provide 6.5 percent of United States supply for the period 2016 to
2030 ( Alaska Gas Pipeline, 2007). But infrastructure for delivering this gas to market has
not been built for a variety of reasons, including strategic considerations ( Leighty, 2007).
Similarly, the potential for additional oil exploration and development in Alaska
( e. g. in the Arctic National Wildlife Refuge, ANWR) will likely be a perennial topic of
interest as oil becomes more scarce, and will require development of new institutional
and regulatory frameworks.
Consequently, studying the effects of institutions and policies on production
decisions in Alaska to find policy parameters that lead to socially desirable outcomes is
especially important. By analyzing dynamic behavior under existing policies and
institutions, we can improve national energy planning and policy for the future.
2.3 A dynamic model of unit production
We focus on production decisions rather than exploration and development
investment decisions because the conditions in Alaska are not conducive to econometric
analysis of the first two stages. In the Gulf of Mexico, Lin modeled exploration and
development investment timing decisions in a situation where many producers compete
and make these decisions independently ( Lin 2007). In Alaska, there are few oil
producers and cooperation is required by law ( in the form of unit operating agreements)
prior to oil production. The mandate for eventual cooperation would likely complicate
modeling of the exploration and development stages leading up to production. We avoid
such complication by starting our modeling after unitization and by not including
exploration or development investment timing decisions. This separation of the
production phase from preceding exploration and development phases is justified by the
notion of forward- looking rational economic agents who make production decisions
based on future revenue without regard to past activities.
15 For example, ongoing research suggests on- site reformation of natural gas will be the low cost hydrogen
production method for vehicle fuel until significant market penetration ( perhaps 10 percent) of hydrogen
vehicles is achieved ( Personal Communication, Nils Johnson, presentation in STEPS seminar at UC Davis,
2007). Understanding future natural gas supply in the United States is relevant to scenarios for hydrogen-fueled
vehicles.
15
We use economic theory and empirical data to model both the physical
component and behavioral component of oil production. The physical component is the
extraction of a finite resource ( i. e., reserves remaining equal original reserves less
cumulative extraction) and the behavioral component is the maximization of an objective
function ( we assume profit maximization). A dynamic model is appropriate for oil
production modeling since production today impacts reserves quantity tomorrow,
meaning current period decisions will impact future period profits.
The theory for dynamic modeling of non- renewable resource extraction dates
back to the work of Harold Hotelling ( Hotelling, 1931). As Lin has carefully documented
( Lin 2008), many researchers have subsequently used and built on this basic theory. We
continue this approach, combining the Hotelling model with optimal control theory to
compare simulated optimal oil production with historic actual oil production in Alaska.
The general approach is to develop an understanding of the physical processes and
economic conditions that characterize an industry, define these processes and conditions
in the equations of a dynamic optimization model, and then estimate parameters in the
equations via matching the model to real- world data. The motivation for comparing
model results to historical production is to better understand how well producers have
optimized production, how economic theory differs from reality, and how policy may
affect production decisions.
Three Stages of Oil Production
The production of crude oil can generally be divided into three stages –
exploration, development, and extraction ( or production). The exploration stage
involves seismic geologic and geophysical mapping of the reservoir rock to
identify likely reservoirs and “ wildcat” drilling to confirm the presence of oil.
The development stage involves drilling the production and injection wells
necessary to recover oil in large quantities and building the surface infrastructure
to process the oil and send it to market. Surface facilities generally include roads,
well pads, equipment and maintenance facilities, employee housing and facilities,
and collector pipelines to bring oil together from several wells. In Alaska, surface
facilities also included the $ 8 billion Trans- Alaska Pipeline system to bring oil
800 miles to the tanker terminal in Valdez and, since flaring of associated gas is
not permitted, a $ 2 billion central gas processing facility to separate natural gas
liquids for shipment down TAPS and natural gas for re- injection into the oil
reservoirs.
The extraction stage is where actual oil production occurs. In addition to
the variable costs of extraction like labor, energy for equipment and pumping, and
equipment depreciation and replacement, extraction may also require some well
drilling. This is because initial producing wells are often drilled “ downdip” of the
reservoir “ crest” ( i. e., below the highest point) and injection wells are often
drilled below the oil/ water contact in a reservoir. As oil is produced and water
injected, the oil/ water contact rises, causing initial wells to “ water out” and
requiring new wells to be drilled “ updip.”
16
The result of this research is a model for estimating the optimal oil production
path and how that path may change under different government tax policies and unit
contract structures, and for evaluating how closely Alaskan oil producers have
approximated the optimal rate of production. The model will also enable evaluation of
whether tax and leasing policies and contract structures have introduced inefficiencies in
Alaska petroleum production, thereby informing the design of policies and institutions
that lead to more socially efficient and desirable outcomes.
2.3.1 The Multi- Stage Investment Timing Game
Firms producing petroleum in Alaska make the following decisions: 1) whether to
bid on a lease; 2) whether to invest in a seismic study of a particular area; 3) whether to
apply for exploratory ( or any) well drilling; 4) whether to proceed with exploratory well
drilling; 5) whether to initiate, participate in and/ or complete a unit agreement; 6)
whether to invest in infill drilling in a producing unit to maintain or boost production; 7)
whether to invest in production infrastructure; 8) whether to invest in major infrastructure
such as TAPS, a gas treatment facility, or collector pipes; and 9) production rates.
Unit operators' production decisions are dynamic because current period decisions
will impact next period profits. 16 Current- period production impacts next- period reserves
quantity, exploration investment decisions impact future reserves quantity through new
finds, and sequential investment decisions necessary prior to production impact the future
ability to produce. Taken together, the sequential nature of decisions and investments
causes the situation to be dynamic, making it a multi- stage game. That is, for example,
unitization must come before production in Alaska, so the decisions leading up to
unitization comprise one stage and production decisions after unitization comprise a
second stage.
There are several sources of strategic behavior in Alaska. In the leasing process,
the game is a closed- bid auction, where each company uses its private information ( and
public information) to assess the value of lease tracts and determine their bids. Each
company's optimal bid will be the lowest possible such that it is larger than all other bids,
but still lower than their valuation of the tract. Thus, the bidding is a game with each
player's strategy contingent on the play of the others.
In the exploration phase after leasing, each company proceeds with the knowledge
that a unit agreement must be negotiated before production. Thus, the goal of exploration
is both to find oil and to document that a large share of the oil exists under the leases a
particular company owns. Since exploration is costly, there is an optimal amount of
exploration, which is related to the amount done by other companies. On the one hand, a
company would save money by letting other companies explore to find the oil and then
getting a share during the unit negotiations. However, the unit negotiation will require
enough information to credibly argue for a large share of the production. This could be
accomplished by having skilled geologists to review the information provided from the
other companies' exploratory activities and/ or independent exploration by the particular
company in question. In addition, there is the issue of whether other companies will do
exploration quickly enough and in the locations most advantageous to the company in
16 Kunce ( 2003) also makes the argument that since “ firms extracting nonrenewable resources are tied to an
immobile reserve base that represents the key component of their capital stock, [ they] view time, rather
than space, as the most important dimension over which to substitute in response to changes in tax policy.”
17
question. Thus, it would seem that the companies most intent on finding new resources
due to their firm- specific business model would do more exploration rather than wait for
others, whereas the companies least intent on finding new resources would do less
exploration. Similarly, it would seem that companies with large tracts of leases and/ or no
nearby leases would be more prone to invest in exploration ( since no one else is going to
find the oil under their leases) than in cases with mixed lease ownership all in close
proximity.
As mentioned previously, our research focuses on the production stage only, in
which strategic considerations are mitigated by the requirement for unitization.
Consequently, we develop a dynamic model without strategic components that is an
isolated model of the unit operator’s production decision ( i. e., not integrated with
exploration and development activities that would increase reserves). Thus, we model
each field with an initial stock that does not increase over time. 17 Each unit operator is
treated as an independent decision- maker, not influenced by other unit operating
decisions.
17 See section 6 for several ways to relax this assumption, by adding satellite fields incrementally as they
were discovered or by using an integrated modeling framework like those used by Kunce ( 2003) and
others.
18
3 Data, Cost Estimation, Price Estimation
3.1 Data
In developing a dynamic model for oil production, we needed data for a number
of variables. These are listed in Table 1 below. Data for this research came from a variety
of federal and Alaska state government agencies, industry reports, research documents,
and personal communication with personnel active in the Alaska oil industry ( Table 1).
More detailed explanation of these data follow; summary statistics are shown in Table 4.
For all monetary data, we used the urban consumer price index to adjust to 1982- 84
constant US dollars. 18
18 We chose to use 1982- 1984 constant dollars for monetary units rather than a different reference year
( e. g., 2006 or 2008) for two reasons. First, the period 1982- 84 is used by the US Department of Labor as
the reference for calculating the consumer price index. This makes the reader’s own scaling of our results
to alternative reference years relatively easy via simple multiplication by the consumer price index for her
preferred reference year. Second, we are both hindcasting historical production and forecasting future
production in our modeling, which raises the potential for misinterpretation of our results. For the
hindcasting, using a reference in the historical period mitigates the risk of interpreting current- dollar profits
as actual profits earned in past years. For the forecasting, using a future- year reference would avoid similar
misinterpretation, but would require some prediction of future inflation, which would be unwise.
Consequently, we chose to use a reference year during the historical period of production. We
acknowledge, however, that some readers may find interpretation of current dollars more intuitive than
constant 1982- 84 dollars.
19
Variable Units Definition of Original Data Source Sample
Mean
OIPi Billion
barrel
Original Oil in Place for unit i ( billions
barrels) AOGCC1 5.5
Sit Billion
barrel
Reserves remaining for unit i in month t,
where S( 0) = 50% of OIP ( billions barrels) calculated 2.4
Qit Million
bbl/ mo.
Quantity oil produced from unit i in month
t ( millions barrels per month) AOGCC2 10.6
AKWHVt $/ barrel
Alaska wellhead value, weighted average
for all destinations, annual 1978– 2006
($/ bbl, 1982- 84 US dollars)
ADR3 $ 12.19
USWHVt $/ barrel
USA spot price, FOB, average weighted
by volume, weekly, 1997– 2004 ($/ bbl,
1982- 84 US dollars)
EIA4 $ 13.46
FWHVt $/ barrel
Forecast USA wellhead value, 2004– 2030,
reference, low- and high- price cases
( annual, $/ bbl, 1982- 84 US dollars).
EIA4
$ 24.42
$ 17.91
$ 36.57
Cs $/ barrel
Total facilities investment cost of
production ( capital cost) in 2003 by field
size, ( 13 categories, $/ bbl, 1982- 84 US
dollars)
USGS5 $ 1.64i
$ 1.35ii
WELLSit Count Number of active wells by field for each
month of production AOGCC2 270
DCt $ mil./ well
$/ ft.
Well drilling cost data for Alaska ($
millions per well and $ per foot, 1982- 84
US dollars)
API6 $ 3.6
$ 341
Table 1: Variable definitions, data sources, and sample means. Free on board ( FOB) price
is equivalent to wellhead value since the buyer pays the transportation cost from origin to
the final destination. Data sources are: 1) Alaska Oil and Gas Conservation Commission
( AOGCC), 2008; 2) Personal communication, Stephen McMains, Alaska Oil and Gas
Conservation Commission, June, 2007; 3) Alaska Department of Revenue ( ADR), 2007;
4) Energy Information Administration ( EIA), 2007; 5) Attanasi and Freeman, 2005; 6)
American Petroleum Institute ( API), 1969- 2004. i average of the 13 categories defined by
Attanasi and Freeman ( 2005). ii average of facilities investment cost of production for all monthly
production observations for all seven fields on the Alaska North Slope.
20
3.1.1 Resource Data
To understand how producers make decisions about production, we need to know
how much oil was originally in place in each unit area in Alaska. Data on original oil in
place ( OIP) are estimates from a variety of published sources compiled by the Alaska Oil
and Gas Conservation Commission in “ pool statistics” documents for each field. The OIP
data were aggregated into units as follows ( see appendix A). These seven units account
for more than 90 percent of the OIP in Alaska.
• Prudhoe Unit = Prudhoe + Aurora + Borealis + Midnight Sun + Orion + Polaris
+ Lisburne + Niakuk + North Prudhoe + Point McIntyre + West Beach + Raven
• Kuparuk Unit = Kuparuk + Meltwater + Tabasco + Tarn19
• Milne Unit = Milne + Sag River + Schrader Bluff
• Badami Unit = Badami ( no associated fields)
• Colville Unit = Alpine + Fiord + Nanuq + Nankup + Qannik
• Endicott Unit = Endicott + Eider + Ivishak
• Northstar Unit = Northstar ( no associated fields)
Published estimates for original OIP were not available for the Lisburne ( est. 400 million
bbl), Raven ( est. 10 million bbl), Nankup ( est. 20 million bbl), and Qannik ( est. 20
million bbl) fields, which account for 1.5% of the Prudhoe unit and 4.3% of the Colville
unit. The estimate for original OIP for Kuparuk was revised to exclude the heavy/ viscous
oil in West Sak ( approx. 15 billion barrels) which is not yet technically recoverable,
making the estimate for Kuparuk 5 billion barrels. See Table 4 for OIP data by unit.
It is evident from this list that most of the seven production units on the North
Slope have many associated satellite fields. We decided to include these fields in the
initial estimate of OIP for each unit since this total is the best representation of the
quantity of oil actually present initially in each unit. However, many of the satellite fields
were discovered some time after the original discovery in each unit. Thus, we have
inherently assumed perfect information regarding total resources that the producers did
not have when developing each unit. The dilemma for how to include imperfect
information in modeling producer behavior will appear elsewhere in this paper and is left
to future work. For example, future model revisions could add the reserves of satellite
fields incrementally as each one came online.
Only a fraction of OIP is technologically recoverable, and only a fraction of
technologically recoverable oil is economically recoverable. The technologically
recoverable fraction has been between 20% and 50% of original OIP ( personal
communication, Emil Attanasi, USGS, August, 2007), but this fraction has been
increasing over time as technology improves. For this research, the original OIP data
were scaled by 50% to estimate initial technologically recoverable reserves ( see Table
4). 20
19 West Sak was not included because its heavy oil is not currently technically recoverable.
20 Note, scaling by 20% and 35% result in historical production greater than initial reserves, a nonsensical
result. Thus, it appears that estimates of original OIP were conservative or a higher fraction of original OIP
has been technologically recoverable in Alaska.
21
3.1.2 Production Data
To validate our model, we need to compare actual production data to model
predictions. For the modeling of production decisions described in this paper, the unit is
taken as the level of production decision- making and thus production data are aggregated
at the unit level. Thus, we use the quantity of production from each unit by month and
year. Production data were obtained from the Alaska Oil and Gas Conservation
Commission. 21 These data are summarized by year in Table 2.
Year Prudhoe Kuparuk Milne Badami Colville Endicott Northstar
N. Slope
Total
1978 34.41 34.41
1979 39.82 39.82
1980 46.25 46.25
1981 46.35 1.80 48.15
1982 46.62 2.76 49.37
1983 46.75 3.39 50.14
1984 46.50 3.97 50.46
1985 47.86 6.76 0.41 55.03
1986 47.35 8.02 0.35 0.00 55.72
1987 48.72 8.51 0.00 1.03 58.26
1988 47.74 9.32 0.00 3.07 60.13
1989 43.09 9.09 0.36 3.03 55.57
1990 40.33 8.91 0.55 3.16 52.95
1991 39.61 9.59 0.62 3.44 53.26
1992 36.78 9.84 0.57 3.48 50.67
1993 33.66 9.57 0.57 3.23 47.02
1994 33.20 9.29 0.56 2.84 45.89
1995 31.15 8.87 0.74 2.75 43.50
1996 29.53 8.26 1.24 2.17 41.21
1997 26.69 8.00 1.59 1.74 38.02
1998 23.40 8.03 1.70 0.14 1.43 34.69
1999 19.92 7.86 1.63 0.09 1.16 30.67
2000 18.47 7.14 1.59 0.08 1.44 1.00 29.70
2001 16.60 6.63 1.62 0.05 2.75 0.86 0.59 29.10
2002 15.66 6.44 1.55 0.05 2.92 0.75 1.53 28.88
2003 15.04 6.40 1.56 0.02 2.98 0.79 1.99 28.78
2004 13.64 5.96 1.56 0.00 3.05 0.62 2.06 26.88
2005 12.63 5.49 1.31 0.02 3.67 0.53 1.82 25.47
2006 9.87 5.20 1.08 0.04 3.69 0.43 1.57 21.87
Table 2: Average annual production for each unit in millions of barrels per month. Note,
maximum TAPS throughput is approximately 2.033 million barrels per day, or 60.99
million barrels per month. Source: personal communication, Stephen McMains, Alaska
Oil and Gas Conservation Commission, June, 2007.
21 The AOGCC is an independent quasi- judicial state agency charged with preventing the “ physical waste
of hydrocarbon resources, promot[ ing] greater ultimate recovery, protect[ ing] underground supplies of
drinking water, and afford[ ing] all owners of oil and gas rights an equal opportunity to recover their fair
share of the resource.”
22
3.1.3 Price Data
The price of oil is a key factor in production decisions. A combination of three
sources of price data were used to estimate a price function for Alaska oil. These data are
for the wellhead value of oil, or the market price less shipping costs. Historical data for
Alaska North Slope wellhead value were calculated annually by the Alaska Department
of Revenue for the Alaska fiscal year spanning from July 1 to June 30 ( ADR, 2007).
There is also a one- month lag between production data and tax data because taxes are
filed monthly and revenue from production in one month is taxed in the next month.
These details become important when estimating the price function. Historical data for
average United States wellhead value ( reported as price, FOB and weighted by volume)
were compiled by the Energy Information Administration weekly for the period 1997 to
2006 ( EIA, 2007). Finally, the Energy Information Administration has also developed
price forecasts ( also reported as price, FOB) for reference-, low-, and high- price cases
through the year 2030 ( EIA, 2007).
3.1.4 Production Cost Data
Data for estimating production cost are often the
crux of econometric modeling since most production cost
data are proprietary and not available. Our research is no
exception and future refinement of our models will
benefit from improved cost data.
The total “ facilities investment cost” of oil
production on the Alaska North Slope was estimated by
the United States Geological Survey ( Attanasi and
Freeman, 2005). These costs, expressed in dollars per
barrel of oil produced, include the cost of drill pads, flow
lines from drilling sites, central processing units, and
infrastructure required for housing workers ( including
amenities). In other words, these are the capital costs of
oil production. The costs were estimated for a generic oil
field on the Alaska North Slope, specifically in ANWR,
in the year 2003. Attanasi and Freeman developed a “ cost
relationship that specified investment cost per barrel as a
function of peak fluid flow rates…” and expressed their
cost estimates by discreet accumulation size class, where
field size is technically recoverable resource ( Table 3).
The facilities investment cost estimates provide a
reasonable approximation of total production costs since
the Alaska oil industry is capital dominated, meaning
labor and other costs of production are small relative to
the facilities investment cost ( personal communication,
Neal Fried, Alaska Department of Labor, July, 2007).
Field Size
( MMBO)
Cost
($/ bbl)
32 4.51
48 3.39
64 2.77
96 2.09
128 1.73
192 1.41
256 1.22
384 1.00
512 0.86
768 0.71
1,024 0.61
1,536 0.50
2,048 0.43
Table 3: Facilities
investment ( capital) cost
for the Alaska North
Slope, in 1982- 84
dollars, by initial field
size in millions of
barrels of technically
recoverable oil ( Attanasi
and Freeman, 2005)
23
3.1.5 Well Data
Data on the number of producing wells and the well- days of production by field
for each month of operation were provided by the Alaska Oil and Gas Conservation
Commission ( personal communication, Stephen McMains, AOGCC, 2007).
3.1.6 Drilling Cost Data
Data on the drilling cost per well and per foot were compiled from the American
Petroleum Institute’s Joint Association Survey of the U. S. Oil and Gas Industry from the
years 1969 through 2004 ( API, 1969- 2004). These costs are Alaska- specific, based on
industry responses to the annual API survey. The survey has been used extensively for
cost data in previous studies of oil production ( e. g., Kunce, 2003 and Lin, 2007). For our
modeling of oil production, we used the cost of onshore oil wells and dry holes ( i. e., we
did not use cost data for offshore or gas wells).
Prudhoe Kuparuk Milne Endicott Badami Colville Northstar
Start Date Jan. 1978* Nov. 1981 Oct. 1985 Jun. 1986 Jul. 1998 Oct. 2000 Sept. 2001
Initial OIP 28,764 5,351 1,747 1,127 240 920 247
Initial Technically Recoverable Reserves
14,382 2,675 874 564 120 460 124
Technically Recoverable Reserves Remaining in 2006
2,902 478 624 114 115 231 15
Historical Production
Mean 33.02 7.29 0.98 1.82 0.05 3.11 1.72
Max. 51.85 10.52 1.83 3.70 0.22 4.18 2.44
Min. 6.00 1.09 0.00 0.00 0.00 0.53 0.00
Std. Dev. 13.03 2.04 0.59 1.19 0.04 0.65 0.45
Wellhead Value ($/ bbl, 1982- 84 dollars)
Mean 12.19 11.95 10.69 10.59 13.66 15.86 16.47
Max. 27.90 27.90 27.90 27.90 27.90 27.90 27.90
Min. 5.05 5.05 5.05 5.05 5.05 9.43 9.43
Std. Dev. 5.61 5.52 4.99 5.04 6.45 5.97 6.26
Wells
Mean 701 378 86 50 5 37 13
Max. 961 552 142 64 7 59 19
Min. 113 1 1 1 2 13 1
Std. Dev. 264 138 45 14 1 13 5
Table 4: Summary statistics for historical data by unit. All quantities are in millions of
barrels ( production is millions barrels per month). * The first well at Prudhoe Bay
produced oil on March 12, 1968, but the first oil flowed down TAPS in January, 1978.
3.2 Cost Estimation
We assume maximization of the discounted stream of future profits as the
producers’ objective function. Consequently, a function to define the cost of oil
production is necessary. Information on the cost of oil production, however, is guarded as
24
proprietary and there is a paucity of publicly available data. Chakravorty et al. ( 1997)
used cost data compiled by the East- West Center Energy Program to estimate extraction
cost functions econometrically. Dismukes et al. ( 2003) compiled information on per- unit
costs for oil and gas activities by water depth in the Gulf of Mexico to develop an
industry- specific expenditure profile. But the distinct environment ( arctic) and location
( remote on- shore) of Alaska’s North Slope suggest production costs very different from
other oil production operations. Consequently, we needed to develop an estimation of
Alaska- specific costs. Furthermore, to model seven unique fields, we needed field-specific
cost functions. To accomplish this task, we developed a novel method for
estimating cost functions from available data that may be applicable to other modeling
exercises as well.
We estimate the cost function from available data by scaling an average Alaska
North Slope cost function ( Attanasi and Freeman, 2005) by a constructed Alaska- specific
drilling cost scalar and field- specific wells scalar. The result is a production cost surface
with marginal cost increasing as reserves are depleted and as production rate exceeds
limits to reservoir flow rates. Lack of original cost data ( i. e., observations of production
cost and other variables like production rate and reserves quantity) necessitated our
development of this novel approach rather than a more standard econometric approach of
estimating the parameters of the cost function from data using an econometric model of
the cost function.
Economic theory and reservoir geology suggest a production cost function should
incorporate the following three effects:
1) Economies of scale for increasing field size as captured in the USGS facilities
investment cost estimates ( Attanasi and Freeman, 2005; Figure 1). The assumption that
production cost is a decreasing function of stock size is common in the economic
literature ( e. g., Farrow, 1985; Hartwick, 1982; Pindyck, 1978; Ruth and Cleveland,
1993).
2) A time trend as the North Slope industry developed, technology improved and
adapted to the arctic environment, rigs and labor became less limiting, and learning
occurred for arctic operations, as indicated by well drilling costs from the American
Petroleum Institute ( API, 1969- 2004; Figure 2).
3) Diseconomies of scale for very high production due to physical constraints on
oil flow rate, as indicated by State of Alaska data on the number of wells producing on
each field across time and production rate ( personal communication, Stephen McMains,
AOGCC, 2007; Figure 3).
25
Figure 1: A generic ( not from
data) average production cost
curve showing economies of scale
for increasing field size.
Figure 2: A generic ( not from data)
time trend in production cost
indicated by Alaska well drilling
costs ($/ well).
Figure 3: A generic ( not from data)
wells function showing diseconomy
of scale for high production rate,
indicated by the number of wells
required. Historical maximum
production rates tend to be below
the range of significant
diseconomies of scale.
26
There are three variables in a cost function that combine these three effects:
production rate ( Q), reserves remaining ( S), and time ( T). Allowing only one to vary at a
time, the desired result in a composite cost function is as follows:
1) For a given field size and year, there are economies of scale as production
increases up to some point where geology becomes limiting and excessive pumping
causes diseconomies of scale ( Figure 4).
2) For a given quantity of production and year, marginal, average, and total costs
are lower for larger fields ( Figure 5).
3) For a given quantity of production and field size, costs generally peaked around
completion of TAPS, declined for a decade, and then began a steep climb in the late
1990s ( Figure 6).
Figure 4: Behavior of a theoretical production cost function. For a given field
size and year, marginal production cost initially decreases as production rate
increases, but then begins to increase when production rate exceeds the
reservoir’s natural flow rate.
Figure 5: Behavior of a theoretical production cost function. For a given
production rate and year, production cost is lower for larger quantity of
reserves remaining.
27
Figure 6: Behavior of a theoretical cost
function. For a given production rate
and quantity of reserves, production
cost peaked around the completion of
TAPS ( 1977), declined for a decade,
and then climbed in the late 1990s.
Finally, it is important to note that each field is unique in its geology, oil
properties, and context of development. Consequently, it is logical to estimate field-specific
cost functions, as we do in this paper.
Our general approach for estimating a “ composite” cost function with the
attributes just described was as follows. The USGS data ( Attanasi and Freeman, 2005)
were used to estimate a “ base” cost function that describes the fundamental facilities
investment cost of production ( capital cost, which approximates total cost) for a
particular field size on the Alaska North Slope in 2003. Next, the field- specific wells data
were used to construct a scalar for production rate, multiplying the base cost function.
Then, the Alaska- specific API well- drilling- cost data ( API, 1969- 2004) were used as a
proxy for the time trend in production cost to construct a second scalar for the base cost
function. Finally, the composite cost function was defined as the product of the base cost
function and one or more of the scalars, depending on conditions in the modeling. We
now describe the estimation of the composite cost function in detail, taking each of the
three effects described above in turn.
3.2.1 Base ( Average) Cost
We began by estimating a continuous function for average cost ($/ bbl) for oil
production by fitting a function to the total facilities investment cost ( capital cost) of oil
production estimated by the USGS ( Attanasi and Freeman, 2005). The results are shown
in Figure 7.
28
Facilities Cost of Production ($/ bbl)
y = 49.608x- 0.5488
R2 = 0.9942
0
2
4
6
8
10
0 500 1,000 1,500 2,000 2,500
Field Size ( millions bbl)
$ per barrel ( 2003 US dollars)
Figure 7: Average facilities investment cost ( capital cost) of production ($/ bbl)
function fit to data from Attanasi and Freeman ( 2005).
For dynamic modeling of oil production decisions, however, marginal cost is
necessary. In other words, we needed the cost per barrel for any particular combination of
production rate ( Q) and reserves remaining under the ground ( S) at any moment in time
since this is the relevant cost for production decisions. The field size categories in
facilities investment cost estimates from Attanasi and Freeman ( 2005) were based on the
original field size, so their cost estimates were for average cost rather than marginal cost
( i. e., an estimated single average cost for a field’s entire life based on the initial field
size). This made estimation of a stock effect in the marginal cost of production from these
data impossible. 22, 23
Consequently, the next step for estimating the “ base” cost function required the
following assumption. Consider an oil field. When first discovered, the situation matches
what Attanasi and Freeman quantified— namely, a field of that particular size may be
expected to have an average cost per barrel for production over its lifetime equal to what
22 Estimation of the facilities cost of production ($/ bbl) was motivated by the question of what the cost of
production would be for the field sizes that might be found in ANWR. The facilities cost is a reasonable
approximation of total production cost since labor cost is a relatively small portion ( personal
communication, Neal Fried, Alaska Department of Labor, July, 2007).
23 The term “ stock effect” refers to the increase in production cost that generally occurs as reserves are
depleted. Average cost data for the entire production life of a field do not contain information on such
changes in production cost.
29
Attanasi and Freeman estimated. Now, imagine the same field 10 years later from the
dual perspective of a potential buyer. There is less oil in the ground because some of the
initial reserve has been produced. The average facilities investment cost of production,
however, could be estimated for the future of that field and, in fact, would be the same as
a newly- found field of the same size since the cost of facilities are amortized over their
useful life and the remaining life is included in the purchase price. Thus, the average
production cost by field size estimated by Attanasi and Freeman should apply equally to
newly- discovered fields and producing fields, at any particular moment in time.
With an estimate of the initial reserves for each field, and monthly data on the
production rate ( bbl/ mo), we calculated the reserves remaining in each field for each
month and used the facilities investment cost function shown in Figure 7 to associate this
with an average cost of production ($/ bbl) for that month. Multiplying by the quantity of
production in that particular month yields the total cost of production. Thus, we
constructed data on production rate ( Q), reserves remaining ( S), and total cost of
production ( C) for each field in each month. These calculations were made for the 12
months of 2003 for each field since the facilities investment cost of production data were
estimated for 2003. Costs are deflated to 1982- 84 dollars for consistent constant- dollars
units used throughout our modeling.
These data enabled estimation of a total cost function of the form
costi 2 3
1
c
i
c
i = c Q S , which is similar in form to previous studies of oil production and
incorporates both production and stock effects ( Lin & Wagner 2007; Lin 2007). 24 A log-linear
form was used to estimate parameters by ordinary lease squares ( OLS), where S is
reserves remaining measured in millions of barrels, Q is production rate measured in
millions of barrels per month, and cost is measured in constant 1982- 84 US dollars ( eq. 1,
Figure 8).
1 Base total cost of production: TC = c1Qc2Sc3 = 91495468( Q1.00065)( S- 0.549262)
Standard error: 25 ( 0.0037146) ( 0.000474736) ( 0.000651287)
Adjusted R2: 0.999985
All coefficients are statistically significant at the 0.1% level. 26
24 Production and stock effects relate to the conceptual figures at the beginning of this section in the
following ways. Production rate affects production cost if economies of scale exist ( see Figure 4).
Decreasing stock of reserves remaining as production occurs generally causes increased production cost as
reserves are depleted ( see Figure 5).
25 The standard error reported for c1 is for the estimate of ln( c1) calculated by linear regression rather than
for c1 itself.
26 The estimated magnitude of c2 is interesting because it indicates the elasticity of total cost with respect to
production rate. The estimated magnitude suggests slightly more than unitary elasticity, meaning total cost
increases more than one percent for a one percent increase in production rate.
30
0%
78%
156%
234%
5%
20%
35%
50%
65%
80%
95%
0
50000000
100000000
150000000
200000000
250000000
300000000
350000000
400000000
Total Cost ($, 1982- 84)
Production ( Q)
Reserves
Remaining ( S)
Base Total Cost of Production
Prudhoe Bay
Figure 8: The base total cost of production for any
combination of reserves remaining and production
rate is plotted in three dimensions. The axes for
production and reserves are in percentage terms, in
this case for Prudhoe Bay, from zero to 100 percent
of original reserves in the field and from 0 to 300
percent of historical maximum production rate. The
vertical axis is in dollars, normalized to 1982- 84
dollars.
3.2.2 Drilling Cost Scalar
With the base cost function defined, our next task was to incorporate the evolution
of capital costs over time into the cost function. The majority of oil production costs in
Alaska are facilities and equipment costs ( i. e., labor is relatively small). Furthermore,
changes in drilling cost may be a reasonable indicator for changes in total facilities and
equipment costs due to use of similar inputs. Consequently, since drilling costs have
fluctuated over time ( Figure 9), it may be logical to scale the cost function in any
particular year based on the drilling cost in that year ( or a prior year for lagged effect on
production cost) by multiplying by the ratio of drilling cost in that year relative to the
reference cost in 2003. We made this assumption, but included a dampening parameter
for use in sensitivity analysis.
31
Well Drilling Costs
Alaska onshore oil wells and dry holes
$-
$ 2,000
$ 4,000
$ 6,000
$ 8,000
$ 10,000
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
Year
Cost per well ( M $ 1982- 84)
$-
$ 100
$ 200
$ 300
$ 400
$ 500
$ 600
$ 700
$ 800
Cost per Foot ($ 1982- 84)
Cost per Well, Real ( M $ 1982- 84)
Cost per Foot, Real ($/ ft., 1982- 84)
Third- order polynomial ( cost per well)
Fourth- order polynomial ( cost per well)
Sixth- order polynomial ( cost per well)
Figure 9: Well drilling costs in Alaska over time, per well and per foot,
with third-, fourth-, and six- order polynomial regressions shown ( API,
1969- 2004).
Drilling costs in Alaska have fluctuated over time ( Figure 9). One explanation is
quasi- rents from drilling equipment scarcity, materials costs, technological change, and
improvement in operational knowledge. A boom in exploration and development
followed the discovery of Prudhoe Bay in 1968, which included the construction of
TAPS ( completed in 1977). The shortage of skilled labor, materials, and equipment
associated with this boom coincides with the first peak in drilling costs from 1970 to
1980. With TAPS and the initial rush of exploration and development completed, labor
and equipment became readily available. Since Alaska’s North Slope was one of the first
arctic oil developments, the technological and operational learning curves for arctic oil
production were steep. These events coincide with the decline and trough in drilling costs
from 1980 to the late 1990s. In recent years, global demand for materials and skilled
labor may have pushed drilling costs upward again. In this light, it is reasonable to think
of a scalar for oil production cost based on drilling cost that is an approximation of
similar fluctuations in the cost of oil production factors. 27
27 An alternative explanation, however, is changes in the quality of drilling sites in response to oil price. If
more marginal sites are given the green light for drilling when oil price is high, then the first peak in
drilling cost may correspond to the high prices caused by the oil crises of 1973 and 1979, the decline and
trough in drilling cost from 1980 to the late 1990s may correspond to the relatively low oil prices of this
32
The API data ( API, 1969- 2004) were deflated to 1982- 84 dollars and scaled so the
value is approximately equal to one in 2003, thereby creating a multiplier that will scale
the cost function in other years appropriately for changes in oil production costs ( as
proxied by drilling costs).
Third, fourth, and sixth order polynomial functions were evaluated for regressing
the cost of well drilling on time using a time index ( 1969 = 1) rather than the actual year
to avoid overflow errors ( e. g. when 1970 is raised to the sixth power). A user- defined lag
parameter ( Lag) was added to account for the delay between an increase in drilling costs
translating into an increase in oil production cost. The sixth order polynomial regression
best fit historical data on well drilling costs by accurately mapping five inflection points
( Figure 10). Consequently, we defined the Drilling Cost Scalar ( DCS) as a sixth- order
polynomial function of the indexed and lagged year ( YrIL). 28
2 Drilling Cost Scalar:
DCS = c4 + c5YrIL + c6YrIL2 + c7YrIL3 + c8YrIL4 + c9YrIL5 + c10YrIL6
C4 C5 C6 C7 C8 C9 C10
Coeff. 1.413501 - 0.5839932 0.161024 - 0.0175783 0.0008877 - 0.0000211 1.92E- 07
Std. Error .156303 .1086034 .0242834 .0023998 .0001165 2.72e- 06 2.44e- 08
Adjusted R2 = 0.9233; all coefficients are statistically significant at the 0.1% level.
period, and the recent increase in drilling cost may correspond to recent increases in oil prices. In this case,
a scalar based on drilling cost may have less relationship with oil production cost.
28 For example, with year equal to 1985 and a lag of 2 years between drilling costs and production costs, the
variable YrIL equals 1985 - 1968 - 2 = 15.
33
Driling Cost Scalar for Adjusting Base Cost Function
( scalar = 1 in 2003)
0.00
0.50
1.00
1.50
2.00
2.50
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
Year
Scalar
Cost per Well, SCALAR (= 1 in 2003)
3rd order regression
4th order regression
6th order regression
y = 0.0002481x^ 3 - 0.0121255x^ 2 + 0.1248137x + 0.5586948 ( R^ 2 = 0.7893)
y = 0.00000431x^ 4 - 0.0000706x^ 3 - 0.0044746x^ 2 + 0.0698522x + 0.6936254 ( R^ 2 = 0.80)
y = 0.000000192x^ 6 - 0.0000211x^ 5 + 0.0008877x^ 4 - 0.0175783x^ 3 + 0.161024x^ 2 - 0.5839932x + 1.413501 ( R^ 2 = 0.9364)
Figure 10: Drilling cost scalar ( DCS) for multiplication of the base cost function to
account for the evolution of drilling costs – which proxies for changes in oil
production costs – due to quasi- rents from scarcity in drilling equipment, material
and labor supplies and to improving knowledge of oil production in the arctic
environment. A dampener was included to allow sensitivity analysis since an
alternative explanation for drilling cost may be changes in the quality of drilling
sites in response to oil price, in which case the DCS may have less correlation with
oil production cost.
We used the DCS to scale the base cost function to adjust for changes in
production cost over time. However, the validity of drilling cost as a proxy for production
cost is weakened if the evolution of drilling cost was due to changes in the quality of
drilling sites in response to oil price rather than to changes in quasi- rents and the cost of
inputs like materials, equipment, and labor. Consequently, the scalar range from 0.28 to
1.6 may cause overly large changes in the cost of production. To account for this
possibility and to examine the impact on results with sensitivity analysis, we added a
“ dampener” ( Dmp) to the drilling cost scalar that can be used to restrict its range. The
dampened drilling cost scalar ( DDCS) is defined as follows,
3 Dampened Drilling Cost Scalar: DDCS = 1+( DCS- 1)/ Dmp
34
where DCS is the drilling cost scalar defined by equation 2 and Dmp is a user- defined
dampening factor.
Finally, it is evident from Figure 10 that well drilling costs were increasing
rapidly in the period 2000 to 2004 and that this trend is incorporated into the DCS and
DDCS. Consequently, we applied the DDCS in the composite cost function for the
historical period for which we have data only ( i. e., 1969 to 2004), implicitly assuming
drilling costs remain constant ( other than inflationary change) at 2004 levels into the
future.
3.2.3 Decreasing Returns to Scale
The last piece of reality to incorporate in the composite cost function is the notion
of decreasing returns to scale as production rate exceeds the geologic limit to flow rate
for each particular field ( Bedrikovetsky, 1993; Allain, 1979). In other words, more wells
are needed to produce at a faster rate and at some point the number of additional wells
needed per additional increment of production rate increases rapidly as producers try to
draw oil out of the ground faster than the rock is willing to yield it.
Data from the North Slope fields show this pattern ( Figure 11). In this graph, the
number of wells increases in order to maintain a certain production rate while reserves
remaining declines. In fact, the increased number of wells is often insufficient to maintain
a production rate, causing the typical tailing- off of production for the field. The tailing-off
of production is typically not due to a decrease in the number of operating wells until
very near the end of the field’s life. Thus, it appears producers have made the rational
decision to produce below the point of diminishing returns to additional wells. That is,
they do not devote resources to using many wells to pump oil faster than the geology is
willing to yield it.
When a field is discovered, it is generally characterized by how much oil there is
( OIP), how much is technically recoverable ( typically 30% - 50% of OIP), and the
anticipated maximum production rate ( and thus lifetime of the field). This information
comes largely from geologists. Thus, the geology sets maximum production rate, not
economics, and we are faced with the task of reflecting this physical reality in our cost
function for economic modeling. We used estimation of functional relationships between
wells and the rate of oil production to tackle this challenge. 29 The resulting inverse
production functions give the number of wells needed in each field for any particular
combination of production rate and level of reserves remaining.
29 We anticipated finding a non- linear increasing trend for the number of wells needed for production as the
production rate became exceedingly high, since such extreme production would require extra inducement
for oil to flow faster than the predominant geology would dictate. However, changing well technology
could also influence the number of wells needed to produce oil at a certain rate, ceteris paribus, so our
regressions may suffer from omitted variable bias. Lacking data on well technology in use on the North
Slope, we considered adding a time regressor to account for evolutionary change. But development of well
technology may have been lumpy ( personal communication, Frank Kareeny, BP- Alaska, July, 2007) and
including time in our wells scalar made the derivations used in solving the boundary value problem for
optimization prohibitively complex. Thus, including well technology is left to future work.
35
Wells, Production, Reserves Remaining for Prudhoe Bay
0
20
40
60
80
100
120
140
160
Jun 1968 Feb 1982 Oct 1995 Jul 2009
Time ( month, year)
Oil Quantity
0
200
400
600
800
1000
1200
Wells Count
Oil Production
( million bbl/ mo)
Reserves
Remaining
( 10^ 8 bbl)
Producing
Wells
Figure 11: The number of producing wells, production rate, and reserves
remaining for Prudhoe Bay. Similar plots for other units are shown in appendix B.
To establish the relationship between wells and oil production, we regressed the
number of producing wells on oil production rate and reserves remaining ( to control for
the influence of field size on the number of wells necessary for a given rate of oil
production). 30 We estimated two well functions, one presuming constant returns to scale
( i. e., a plane, eq. 4) and a second presuming decreasing returns to scale ( i. e., a convex
surface, eq.
5). Since the number of wells required for oil production is highly reservoir
specific, we allowed the functional specification for the latter estimation to vary among
fields. 31
4 Constant returns wells plane: CRWells = c11 + c12Q + c13S
5 Decreasing returns wells surfaces:
Prudhoe Bay: DRWells = c14P+ c15PQ+ c16PQ2+ c17PQ3+ c18PS + c19PS2+ c20PS3
Kuparuk River: DRWells = c14K + c15KQ + c16KQ2 + c17KQ3 + c18KS
Milne Point: DRWells = c14M + c15MQS + c16MQ2S + c17MQ3
Endicott: DRWells = c14E+ c15EQS+ c16EQS2+ c17EQ+ c18EQ2+ c19EQ3+ c20ES
Colville: DRWells = c14C + c15CQ + c16CQ2 + c17CQ3 + c18CS + c19CS2
Northstar: DRWells = c14N + c15NQ + c16NQ2 + c17NQ3 + c18NQS
30 One would expect a smaller field to require more wells to achieve a given rate of production since
production at a given rate from a small field will require encouragement of faster flow rates via more wells.
31 We recognize that well technology may differ between fields due to reservoir differences as well as
across time. We do not include this complexity in the current work.
36
where CRWells and DRWells are the number of wells, for the constant returns and
decreasing returns cases respectively, S is reserves remaining measured in millions of
barrels, and Q is production rate measured in millions of barrels per month.
We used a stepwise variable selection technique for model specification based on
significance at the 5 percent level. The stepwise technique combines forward and
backward variable selection by starting with the zero model, using the forward selection
technique to add variables, and the backward selection technique to evaluate the result. 32
However, this technique failed to produce acceptable forms ( i. e., erratic forms and/ or
non- decreasing returns to scale) for the Kuparuk and Prudhoe Bay fields. Consequently,
we used iterative model specification to define the decreasing returns model specification
for these fields. Due to this heavy- handed approach, we withheld 10% of observations
( selected randomly) for model validation. The results of these regressions are presented
in Table 5 and Table 6, and example plots for the Colville River field are shown in Figure
12 ( see appendix C and E for other fields). The Durbin- Watson statistics presented
include a correction for first order serial autocorrelation using a Cochrane- Orcutt
procedure ( Ramanathan, 2002). 33
Constant Q_ index S_ index Adj. R2 DW stat.
Colville 88.7405*** 0.402406 - 0.155815*** 0.97882 2.06323
Std. error 3.33065 0.540647 0.00645563
Endicott 63.341*** 3.68028*** - 0.0677256*** 0.963985 2.55515
Std. error 4.19891 0.665917 0.0148555
Kuparuk 567.158*** 2.75862** - 0.118193*** 0.996603 2.00689
Std. error 32.3279 0.937735 0.0214271
Milne 341.272*** 18.7964*** - 0.354895*** 0.990938 2.64668
Std. error 42.4184 2.01307 0.0556701
Northstar 16.87012*** 2.481977*** - 0.1251358*** 0.9468 1.356
Std. error 0.5410759 0.2916317 0.003565918
Prudhoe 1066.89*** 1.09976** - 0.0616073** 0.998266 2.61257
Std. error 147.569 0.337912 0.0202845
32 The forward selection technique adds variables to the regression model one at a time with the sequence
based on choosing the variable that minimizes the residual sum of squares provided the variable is
significant at our chosen 5 percent level. The backward selection technique eliminates statistically
insignificant variables ( F- statistic below the critical value for our chosen 5 percent level) from the
regression model one at a time with the sequence based on choosing the least significant. The stepwise
procedure offers an improvement over the forward selection and backward elimination procedures on their
own because it guards against any variables becoming statistically insignificant with the addition of the
next variable to the model.
33 The Durbin- Watson is a statistical test for the presence of first- order serial correlation ( i. e., first- order
autoregressive or AR( 1)) that is centered around the value two. Failure to correct for serial correlation in
OLS regression produces unbiased, consistent, but inefficient estimates because the standard assumption of
independence of errors across observations is violated. Although not important for our research since we do
not perform formal hypothesis tests, the inefficiency of OLS estimates in the presence of serial correlation
will cause bias and inconsistency in test statistics because standard errors are biased and inconsistent.
Consequently and to conform with best practices, we used the Cochrane- Orcutt method for correcting for
serial correlation, which is an iterative procedure that begins with OLS to obtain residuals, calculation of an
estimated serial correlation coefficient from these residuals, transformation of the data with the estimated
serial correlation coefficient, and generalized least squares ( GLS) on the transformed data.
37
Table 5: Parameter estimates for the constant returns wells plane, for Q, S in millions
barrels. Statistical significance for coefficient estimates is indicated at the 5% level (*),
1% level (**), and 0.1% level (***).
38
Colville Constant Q Q2 Q3 S S2 Adj. R2 DW Stat
Coeff. Est. 68.2945*** 8.07675 - 2.95748 0.35801 - 0.0631439 - 0.00014196 0.978864 2.0309
std. error 12.4577 7.73784 2.82791 0.335916 0.0552247 8.3671E- 05
Endicott Constant QS QS2 Q Q2 Q3 S Adj. R2 DW Stat
Coeff. Est. 65.1632*** 0.171746*** - 0.000207604*** - 7.46746 - 8.06115*** 0.854042** - 0.111207*** 0.971796 2.2
std. error 2.31291 0.0175386 0.0000213501 4.03617 1.96804 0.322885 0.00575513
Kuparuk Constant Q Q2 Q3 S Adj. R2 DW Stat
Coeff. Est. 513.389*** 18.2461** - 1.62634 0.0503533 - 0.106936*** 0.996686 2.10729
std. error 42.9937 6.2585 1.0215 0.0538752 0.0298598
Milne Constant QS Q2S Q3 Adj. R2 DW Stat
Coeff. Est. 144.02** 0.0729054*** - 0.0396082** 5.55127 0.992833 2.35932
std. error 48.005 0.00990767 0.0132308 3.33221
Northstar Constant Q Q2 Q3 QS Adj. R2 DW Stat
Coeff. Est. 0.844783 21.46647*** - 7.329782* 1.265286 - 0.08179707*** 0.8904 0.771358
std. error 1.568916 4.062971 3.455657 0.8765398 0.003815506
Prudhoe Constant Q Q2 Q3 S S2 S3 Adj. R2 DW Stat
Coeff. Est. 68.0352 10.7607*** - 0.304704*** 0.00288675*** 0.343354*** - 4.5943E- 05*** 1.51203E- 09*** 0.998519 2.38227
std. error 40.9523 1.49721 0.0647278 0.000738853 0.01654 2.1625E- 06 8.71092E- 11
Table 6: Parameter estimates for the decreasing returns wells surface. Statistical significance for coefficient estimates is indicated at
the 5% level (*), 1% level (**), and 0.1% level (***).
39
0%
42%
84%
126%
168%
210%
252%
294%
0%
20%
40%
60%
80%
100%
0
50
100
150
200
250
300
Number of Operating Wells
Production ( Q)
Reserves
Remaining ( S)
Constant Returns Wells Plane, Colville River
0%
48%
96%
144%
192%
240%
288%
0%
20%
40%
60%
80%
100%
0
50
100
150
200
250
300
Number of Operating wells
Production ( Q)
Reserves
Remaining ( S)
Decreasing Returns Wells Surface, Colville River
Figure 12: The constant returns wells plane ( left panel) and decreasing returns wells
surface ( right panel) for Colville River. The axis for reserves remaining extends from the
original quantity of technically recoverable oil to zero. The production axis ranges from
zero to three times the maximum historical rate of production. The vertical axis is the
number of operating wells.
In both the constant returns and diminishing returns plots, more wells are required
to maintain a given rate of production as the reserves remaining declines and more wells
are required to produce faster, given a level of reserves remaining. However, the rates of
change for these well requirements are greater for the decreasing returns graph.
The type or size of well and/ or well capacity influences the number of wells
needed to produce oil at a given rate. If such specifications for wells on the North Slope
changed over time, adding a time regressor would pick up the impact of this change. But
if the change occurred in one brief period of time, it would confound our regression
attempts. Coil tube drilling was developed in Alaska in the early 1990s and has enabled
development of some smaller fields and drilling multiple wells from the same pad
( personal communication, Frank Kareeny, BP- Alaska, July, 2007). 34 This technology
may have changed the capacity of a well for production. There are also two basic
categories of prospects. Infrastructure led exploration ( ILX) is for satellite fields where
the field size is small but it is close to existing infrastructure. Industry generally pursues
these only if there is better than a one in three chance of finding oil. The other type is
34 Water injection began in 1984 at Prudhoe Bay and miscible gas injection ( ethane, propane, butanes)
began in 1987 with construction of the Central Gas Facility ( CGF) and Central Compressor Project ( CCP)
( ibid).
40
wildcat or corex, where the field is far from existing infrastructure but the size is large
enough to cover the cost of new infrastructure and large enough to justify further
investigation even if the chance of oil is as small as 1 in 10 ( personal communication,
Vincent Monico, BP- Alaska, July, 2007). There may be systematic differences in the
production capacity for wells drilled at satellite fields versus wildcat tracts due to
differences in the equipment that can be brought in to each location. Finally, there is a
possibility for larger- capacity wells to be drilled in larger, easy- to- extract pools. We have
abstracted away from these complexities in the current modeling by assuming all the
wells in a particular field are about the same capacity and estimating unique wells
functions for each field. Future work may examine this assumption more carefully.
Having defined well functions for each unit, the remaining task is to incorporate
this information regarding the increasing number of wells needed as pumping rate
increases and/ or reserves remaining decrease ( i. e., decreasing returns to scale) into the
composite cost function. Our general approach was to define a “ wells scalar” that will
multiply the cost function and increase the cost of producing oil if the model chooses
production rates that are high enough to be in the range of decreasing returns to scale. We
defined this scalar as the ratio of the decreasing returns wells surface to the constant
returns wells plane and invoke it only when the ratio is greater than one ( i. e., the cost
function is left unmodified so long as production is in the range of constant returns, but is
scaled upward if production exceeds this range). We also added a user- defined parameter
( the decreasing returns to scale margin, DRTS_ M) to shift the constant returns plane up
or do