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UBC Theses and Dissertations

The economics of industry petroleum exploration Eglington, Peter Cheston 1975

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'TEE ECONOMICS OF INDUSTRY PETROLEUM EXPLORATION by PETER CHESTON EGLINGTON B.Con., McGill University, 1961 S.M., Massachusetts Institute of Technology, 3.965 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS' FOR -TiE DEGREE OF DOCTOR OF PHILOSOPHY. in the Departnient of Economics We accept this thesis as conforming to the required s^andfiAi THE UNIVERSITY OF BRITISH COLUMBIA August, 1975 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of £C6A/ Q^< ^ > The University of British Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 ABSTRACT This thesis examines various features of the market for petroleum reserves, i n theory and empirically for the time period 1947-1970 i n Alberta, Canada. The main thrust of analysis i s directed towards the.industry supply process i n the reserves market which results from the a c t i v i t i e s of exploration comp-anies. In particular the thesis focusses attention on the activity of New Fie l d Wildcatting. A t o t a l l y new data bank regarding o i l and gas exploration i n Alberta i s estab-lished, containing many items of information which have net previously been available and whose lack was considered a major stumbling block i n analysing the petroleum exploration process. For example, the data f i l e s show the d i -rection of search of exploratory wells, towards either o i l or gas, the class of well which discovered each petroleum pool, the company which was the prin-c i p a l operator of the discovery well, the cost of wells, etc. Thus, i t was possible to analyse the discovery sequence from well class, etc. to the discovered pool and i t s detailed reserves characteristics. With.this data bank an original and unique approach amongst studies of o i l and gas supply and exploration was possible. The study isolates the geolog-i c a l and economic factors which contribute to the incentives and costs of participants i n the market for reserves. I t should be noted that the data bank, on computer tape and described i n a 130 page manual, can be obtained upon request from the author. The hitherto unavailable d e t a i l of this data invites further analysis. On the demand side of the reserves market, data was generated which allowed a detailed estimation of the price incentive to explore for reserves. This included consideration of production delays, expected well productivities, royalties, operating costs, joint products, income taxes, etc. I t i s established that New Field Wildcat wells may be viewed as the primary discovery a c t i v i t y of the petroleum reserves market. A main objective of the thesis i s to define the components of the economic market for reserves so that empirical tests may be conducted to demonstrate the economic linkages between the incentives to explore for o i l and gas and the rates of wildcat d r i l l i n g and subsequent reserves discovered. This objective i s met by providing an extensive descriptive and s t a t i s t i c a l backdrop of the o i l and natural gas industry i n Alberta, developing theoret-i c a l economic models of petroleum exploration and production, and then f i t -ting econometric equations to estimate the e l a s t i c i t y and shifting of the i n -dustry' s short run petroleum reserves supply function. I t i s shown that the short run e l a s t i c i t y between the reserves price incent-ive to explore and New Field Wildcatting for o i l averaged between 0.3 and 0.4 during the period i n Alberta. The comparable e l a s t i c i t y for natural gas was around 0.1. We stress, however, that these e l a s t i c i t i e s may be rather un-important out of their context of a shifting supply function. They do not remain constant as a region i s depleted and the rate at which the supply function shifts as a region i s explored w i l l be more significant i n deter-nriiung the longer run petroleum supply than the short run e l a s t i c i t y . Such shifting of the supply function i s also estimated. Secondary objectives are to examine the exploration characteristics of large companies compared to the others. S t a t i s t i c a l analysis shows that the "Big Eight" companies have realized higher success ratios i n New Field Wildcatting, have discovered much larger o i l and gas pools and have done considerably more geophysics on their land holdings than.other companies. Many other features of the petroleum discovery process, such as the s t a t i s t -i c a l nature of the populations of pools discovered i n sequential time periods, are also^examined. Thesis Supervisor - i i i -TABLE OF CONTENTS • CHAPTER PAGE 1. INTRODUCTION 1.1 Review of Literature J 1.1 . 1.2 Objectives and Conclusions 1.6 1.2.1 Supply Function i n Reserves Market 1.6 1.2.2 Demand Price for Reserves 1.7 1.2.3 Size of Discoveries 1.7 1.2.4 Success Ratios and Directionality 1.8 1.2.5 Large Companies 1.9 2. INDUSTRY INCENTIVES TO EXPLORE 2.1.1 Overview of the Markets 2.1 2.2.1 Products i n the Markets 2.2 2.3.1 Outline of Market Processes 2.3 2.4.1 Government Market for Reserves i n Place 2.5 2.5.1 Non-Homogeneity of Reserves i n Place 2.6 2.6.1 Recoverable Reserves A v a i l a b i l i t y 2.8 2.6.2 From Existing Reserves i n Place 2.8 2.6.3 From Expected Reserves Discoveries 2.9 2.6.4 Depletion of Reserves 2.12 2.6.5 Change i n Demand Price for Reserves .2.12 2.7.1 Production Output Supply Function . 2.13 3. ECONOMIC MODEL OF PETROLEUM EXPLORATION BY A FIRM 3.1.1 Exploration Sequence 3.1 3.2.1 Exploration Expenditures -Definitions 3.1 3.2.2 Exploration Revenues - Definitions 3.2 3.3.1 Production Process of Exploration 3.4 3.3.2 Generalized Reserves Production Function 3.4 - i v -3.3.3 Inventory of Undrilled Prospects 3.5 3.3.4 The State of Nature 3.11 3.3.5 Exploration D r i l l i n g 3.14 3.4.1 Form of Exploration Success Function 3.17 3.4.2 Exploration Directionality 3.19 3.4.3 Form of Exploration Reserves Production i Function 3.20 3.5.1 Optimal Rate of Exploratory D r i l l i n g 3.21 4. ECONOMIC MODEL OF PETROLEUM PRODUCTION FROM KNOWN RESERVES IN PLACE 4.1.1 Introduction 4.1 4.2.1 Generalized Production Function 4.1 4.2.2 Prices and Costs 4.2 4.2.3 Profit Decisions 4.3 4.2.4 Cost Curves 4.4 4.2.5 Period of Pra-vuction of Mine 4.4. 4.2.6 The Finite Reserves Model 4.5 4.2.7 An O i l Production Model 4.6 4.3.1 The Demand Price for Recoverable O i l Reserves 4.8 RECOVERABLE RESERVES MARKET - EMPIRICAL ANALYSIS OF DEMAND FACTORS 5.1.1 The Demand for Recoverable Reserves 5.1 5.1.2 Income Tax Considerations 5.1 5.1.3 Joint Products i n Reservoir : Production 5.4 5.1.4 Aggregate Industry Demand for Reserves 5.5 5.1.5 Demand for O i l Reseives 5.6 5.1.6 Demand for Natural Gas Reserves 5.12 5.2.1 Measurement of Variables 5.14 5.2.2 Measurement of Reserves 5.15 5.2.3 Wellhead Prices - Summary 5.16 5.2.4 Crude O i l Prices 5.18 - V -5.2.5 Natural Gas Prices 5.24 5.2.6 Price Deflator 5.32 5.2.7 Operating Costs E Rentals 5.33 5.2.8 Royalty Rates 5.33 5.2.9 Development Wells 5 Surface Equipment 5.37 5.2.10 Gas Plant Costs 5.37 5.2.11 Productivity of Wells 5.37 5.2.12 Cost of Money 5.38 5.2.13 Income Tax Rates 5.38 5.2.14 Industry Life Index £ Appreciation 5.41 5.2.15 Production Delays i n O i l 5.46 5.2.16 Production Delays i n Gas 5.49 6. RECOVERABLE RESERVES MARKET - EMPIRICAL ANALYSIS OF SUPPLY FACTORS 6.1.1 Supply of New Reserves from Exploration 6.1 6.1.2 Aggregate Industry Supply of Reserves 6.3 6.2.1 Measurement of Variables 6.4 6.3.1 Annual Rate of Exploratory D r i l l i n g 6.5 6.3.2 The Both Intent 6.8 6.4.1 D r i l l i n g Efficiency, Cost £ Depth of Exploratory Wells 6.10 6.5.1 The Inventory of Undrilled Prospects 6.14 6.5.2 Geophysics Activit y 6.14 6.5.3 Bonus Payments 6.18 6.6.1 Success Rate i n Finding New Pools 6.23 6.7.1 Population of O i l £ Gas Pools i n Ground 6.28 6.7.2 Average Size of Pools 6.33 6.8.1 Directionality, Success Ratios S Pool Size 6.39 :. 6.8.2 New Field Wildcats 6.39 6.8.3 Size of Pools Discovered 6.44 6.8.4 The Large Companies 8 Directionality 6.47 6.8.5 New Pool Wildcats, Extension Wells & Tests 6.50 - v i -7. ALTERNATIVE PETROLEUM SUPPLY FUNCTIONS -7.1.1 Theoretical Considerations 7.1 7.1.2 Long Run Supply Potential 7.1 7.1.3 Short Run Supply Curve 7.2 7.1.4 Short and Long Run Supply 7.2 7.2.1 Two Previous Analyses of Discovery Rates S Finding Costs i n Alberta 7.6 7.3.1 Van de Panne's Analysis 7.8 7.3.2 Rate of Discovery 7.8 7.3.3 Finding Costs 7.8 7.3.4 Estimate of Ultimate Reserves 7.12 7.3.5 Interpretation of Equation Constants 7.12 7.4.1 Actual Annual Average Discovery Rates 7.13 7.4.2 Rate of Discovery 7.13 7.4.3 Finding Costs 7.16 7.4.4 Estimate of Ultimate Reserves 7.16 7.5.1 Ryan's Analysis 7.21 7.5.2 Rate of Discovery 7.21 7.5.3 Finding Costs 7.24 7.5.4 Estimate of Ultimate Reserves 7.24 7.5.5 Interpretation of Equation Constants 7.26 8. ECONOMETRIC MODELS 8.1.1 Introduction 8.1 8.2.1 O i l Reserves Supply Function 8.2 8.2.2 O i l Pool Size 8.3 8.2.3 Gas Pool Size 8.6 8.2.4 Reserves Equation Results 8.7 8.2.5 D r i l l i n g Equation Results 8.10 8.2.6 Inventory of Undrilled Prospects i n D r i l l i n g Equations 8.14 8.2.7 Summary of Time Series Analysis 8.19 8.3.1 Cross Section Econometrics 8.20 8.3.2 Introduction to Cross Section Results 8.21 - v i i -8.3.3 L i s t of Symbols Used 8.22 8.3.4 Cross Section Results 8.24 8.3.5 Mixed Cross Section and Time Series Results 8.30 8.3.6 Summary of Cross Section Analysis 8.31 9. APPENDIX 9.1 O i l Prorationing i n Alberta 9.1 9.1.1 Introduction 9.1 9.1.2 The 1950 Proration Plan 9.4 9.1.3 The "Residual MPR" Plan (the 1957 Plan) 9.6 9.1.4 The 1964 Proration Plan 9.7 9.1.5 Summary 9.10 9.2 Note on Geology S Western Canadian Sedimentary Basin 9.11 9.2.1 Introduction 9.11 9.2.2 Basic Principles of Petroleum Geology 9.11 9.2.3 Western Canadian Sedimentary Basin 9.19 BIBLIOGRAPHY - V1X1 -LIST OF TABLES TABLE 5.1 Estimated Demand Price for Reserves 5.2 Gas Input Data 5.3 O i l Input Data 5.4 . Economic Input Data 5.5 Ill u s t r a t i v e Relationship between O i l Wellhead Price £ Demand Price for Recoverable Reserves 5.6 Average Wellhead Prices (current $) i n Alberta, 1946-1970 5.7 Posted Field Prices for Redwater, Alberta, Crude O i l 1948-1969 5.8 Alberta Crude O i l 5.9 I n i t i a l Marketable Natural Gas Discoveries, by Year, Alberta, 1945-1970 5.10 By-Products of Natural Gas per BCF of Pipeline Gas, Production i n Alberta, 1946-1970 5.11 Wellhead Value of Natural Gas, Pentanes Plus, Propane, Butane and Sulphur i n Alberta 1946-1970 5.12 Canadian Wholesale Price Index 5.13 O i l Royalty Schedules 5.14 Average Royalty Rates on Wellhead Value of Crude O i l , Pipeline Gas £ Gas Byproducts i n Alberta, 1946-1970 5.15 Capable Wells £ Production i n Alberta, 1946-1970 5.16 Cost of Money £ Income Taxes 5.17 Remaining Recoverable Reserves Life Indexes i n Alberta, 1947-1970 5.18 Apparent Periods of Production of Twelve Largest O i l Fields i n Alberta 6.1 Annual Rate of Exploratory D r i l l i n g by A l l Companies i n Alberta, 1946-1970 6.2 Annual Rate of Exploratory D r i l l i n g by the 'Big Eight Companies i n Alberta, 1946-1970 6.3 New Field Wildcat D r i l l i n g Costs £ D r i l l Rig Productivity i n Alberta, 1946-1970 - i x -6.4 New Pool Wildcat, Extension 8 Test Well D r i l l i n g Costs S D r i l l Rig Productivity In Alberta, 1946-1970 6.12 6.5 Geophysics Crew Weeks"Activity by Companies i n Alberta, 1946-1970 * . 6.16 6.6 Large Companies Share of Geophysics Crew Weeks S Exploratory D r i l l i n g i n Alberta, 1946-1970 6.17 6.7 Estimated Bonus Payments Applicable to O i l Prospects i n Alberta, 1946-1970 6.21 6.8 Estimated Bonus Payments Applicable to Natural Gas Prospects i n Alberta, 1946-1970 6.22 6.9 Annual Rate of D r i l l i n g Success i n Finding O i l Pools by A l l Companies i n Alberta, 1946-1970 6.24 6.10 Annual Rate of D r i l l i n g Success i n Finding Gas Pools by A l l Companies i n Alberta, 1946-1970 6.25 6.11 Annual Rate of D r i l l i n g Success i n Finding O i l Pools by Big Eight Companies i n Alberta, 1946-1970 6.26 6.12 Annual Rate of D r i l l i n g Success i n Finding Gas Pools by Big Eight Companies i n Alberta, 1946-1970 6.27 6.13 O i l Pools Discovered i n Alberta by A l l D r i l l i n g 1946 to 1970, i n Five Year Periods 6.30 6.14 Non-Associated Gas Pools Discovered i n Alberta by A l l D r i l l i n g , 1946 to 1970, i n Five Year Periods 6.32 6.15 Marketable O i l Reserves Discovered by A l l New Field Wildcats i n Alberta, 1946-1970 6.36 6.16 Marketable Non-Associated Gas Reserves Discovered by A l l New Field Wildcats i n Alberta, 1946-1970 6.37 6.17 Average Size of Pools Discovered by A l l New Field Wildcats i n Alberta, 1946-1970 6.38 6.18 New Field Wildcats i n Alberta, 1945-1961 6.40 6.19 New Field Wildcats i n Alberta, 1962-1970 6.40 6.20 New Field Wildcats i n Alberta, 1945-1970 6.41 6.21 Average Size of Pools Discovered by New Field Wildcats i n Alberta, 1945-1961 6.45 6.22 Average Size of Pools Discovered by New Field Wildcats i n Alberta, 1962-1970 6.45 6.23 Primary Recoverable Crude O i l Reserves £ I n i t i a l Recoverable Reserves of Natural Gas Discovered by New Field Wildcats i n Alberta, 1945-1970 6.46 6.24 Big Eight Companies: New Field Wildcats i n Alberta, 1945-1970, Pools Discovered 6.47 - X -6.25 Other Companies : New Field Wildcats i n Alberta, 1945-1970, Pools Discovered 6.48 6.26 'Oil £ Gas Discovered by New Field Wildcats i n Alberta, 1945-1970, by the Big Eight Companies 6.49 6.27 O i l S Gas Discovered by New Field Wildcats i n Alberta, 1945-1970, by Other Companies 6.50 6.28 New Pool Wildcats, Extensions 6 Tests, i n Alberta, 1945-1970, Successes according to "Shows" 6.51 6.29 New Field Wildcats i n Alberta, 1945-1970, Successes according to "Shows" 6.51 6.30 Average Size of Pools Discovered by New Pool Wildcats. Extensions £ Tests i n Alberta, 1945-1970 6.53 7.1 Cumulative Wells £ Reserves, Discovery Rates £ Cost (Van de Panne) 7.11 7.2 Actual O i l £ Gas Discovery Rates i n Alberta 7.11 7.3 Data for Actual O i l Finding Costs- i n Alberta, for Appreciated Recoverable O i l Reserves 7.19 7.4 Data for Actual Gas Finding Costs i n Alberta, for Appreciated.Recoverable Gas Reserves 7.20 7.5 Cumulative Reserves, Rates of Discovery £ Finding Costs for the Plays i n Alberta (Ryan) 7.23 8.1 Components of Inventory of Undrilled O i l Prospects 8.16 8.2 Bonus Contribution to Inventory of Undrilled Gas Prospects 8.17 8.3 Equations Explaining Number of Successes 8.31 9.1 Alberta O i l £ Gas Production 9.1 9.2 Disposition of Alberta Crude O i l Production, 1947-1951 9.2 9.3 Production £ Capacity, Leduc £ Redwater Fields i n 1950 9.3 - x i -LIST OF FIGURES FIGURE PAGE 2.1 Diagram of Supply Process 2.1 2.2 Remaining Reserves i n Place 2.7 2.3 Remaining Recoverable Reserves Av a i l a b i l i t y from Reserves i n Place 2.9 2.4 Expected Remaining Recoverable Reserves Av a i l a b i l i t y from New Exploration 2.10 2.5 Intermediate Period Output Supply Function, for a Region 2.13 311 Joint Product Transformation Curve 3.16 4.1 Termination of Production from Mine 4.5 5.1 Crude O i l Output Market i n Toronto 1950's £ 1960's 5.22 5.2 Idealized Industry Production from a Region 5.42 5.3 Natural Gas Production £ Capacity i n Alberta 1945 to 1970 5.51 6.1 Expected Recoverable Reserves of O i l Short-Run Supply Curve 6.2 6.2 Annual Exploratory D r i l l i n g Rates of A l l Intents, by A l l Companies i n Alberta, 1945-1970 6.5 6.3 Proportion of New Field Wildcats designated as having Both Intent i n Alberta, 1945-1970 6.9 6.4 Average Feet Drilled per D r i l l Rig Day i n Alberta, by New Field Wildcats 6.13 6.5 Exploration i n Libya, 1956-1966 6.15 6.6 Comparison of Size-Frequency Distributions of Probable Ultimate Recoverable O i l Reserves i n Alberta, at 1965 6.29 6.7 O i l Pools of A l l Geological Zones i n Populations according to Discovery Dates i n 5 year period i n Alberta 6.31 6.8 Non-Associated Gas Pools of A l l Geological Zones, Discovered between 1945 £ 1970 i n Alberta 6.34 x i i -6.9 Average Size of O i l Pools -Discovered by New Field Wildcats i n Alberta, 1945-1970 6.35 6.10 New Field Wildcat Success Ratio £ Directionality According to Pools Discovered, by O i l Intent D r i l l i n g i n Alberta, 1945-1970 6.43 6.11 Directionality of New Field Wildcat 8 New Pool Wildcat D r i l l i n g for O i l i n Alberta, 1945-1970 6.52 7.1 Short Run and Long Run Supply 7.2 7.2 Stochastic Nature of Supply Curves 7.4 7.3 Rates of Discovery i n Alberta by Van de Panne's Model 7.9 7.4 Projected Finding Costs i n Alberta by Van de Panne's Model (Reserves Potential Schedule) 7.10 7.5 Actual Annual Average O i l Discovery Rates by A l l Exploratory Wells i n Alberta 7.14 7.6 Actual Annual Average Gas Discovery Rates by A l l Exploratory Wells i n Alberta 7.15 7.7 Actual Annual Average O i l Finding Costs by O i l Intent Exploratory Wells i n Alberta 7.17 7.8 Actual Annual Average Gas Finding Costs by Gas Intent Exploratory Wells i n Alberta 7.18 7.9 Rates of Discovery for O i l Plays i n Alberta by Ryan's Model 7.22 7.10 Finding Costs for O i l Plays i n Alberta by Ryan's Model 7.25 8.1 Linear Approximation to Theoretical Short Run O i l Reserves Supply Function 8.8 9.1 Economic £ Minimum Well Allowances under the 1950, 1957 £ 1964 Proration Plans, Province of Alberta 9.5 9.2 Structural O i l 8 Gas Traps (Cross Section) 9.13 9.3 Stratigraphic O i l 8 Gas Traps (Cross Section) 9.13 9.4 . Palebgeologic Map with Structure Contours on Unconformity 9.17 9.5 O i l Trapped by Folded Top of Porous Dolomite("e"> £ Unconformity 9.17 - X l l i -9.6 Differential Entrapment (Cross Section) 9.18 9.7 Influence of Water Movement on Trapping Conditions (Cross Section) 9.19 9.8 Sedimentary Basins, Western Canada .9.21 9.9 Generalized Stratigraphic Column and Cross Section, Central Alberta 9.22 - xiv -•ACKNOWLEDGEMENTS I wish to acknowledge the guidance and cooperation extended to me by my thesis committee members; Dr. R.S. Uhler, Dr. P.G. Bradley, and Dr. K. Nagatani, with particular mention for the comments and c r i -ticisms of Russ Uhler. In addition, I wish to thank the many other persons who aided me i n the preparation of this work. I am.deeply indebted to the Federal Department of Energy, Mines and Resources who provided financial assistance particularly for the preparation of the very extensive data base which was computerized for this thesis. Ralph Toombs of EMR was most helpful i n this matter. Several research assistants aided me i n preparation and analysis of the data including Merritt Cluff and • Lynda Walsworth. For typing and related assistance I am forever indebted to Ritsuko Sato. CHAPTER 1 INTRODUCTION 1.1 Review of Literature 1.2 Objectives and Conclusions 1.2.1 Supply Function i n Reserves Market 1.2.2 Demand Price for Reserves 1.2.3 Size of Discoveries 1.2.4 Success Ratios and Directionality 1.2.5 Large Companies 2 1. INTRODUCTION. 1.1 REVIEW OF LITERATURE This thesis examines various features of the market for petroleum reserves, i n theory and empirically for the time period 1947-1S70 i n Alberta, Canada. The main thrust of analysis i s directed towards the industry supply process i n the reserves market which results from the a c t i v i t i e s of exploration companies. In particular the thesis focusses attention on the a c t i v i t y of New Field Wildcatting. This approach is.original and unique amongst studies of petroleum supply and exploration i n that i t isolates the incentives and costs of participants i n the market for reserves i n which exploration takes place. For example, the demand side of the market for reserves i s the derived demand of producing companies who are viewed as either e x p l i c i t l y or i m p l i c i t l y purchasing reserves for development and production. The derived demand price for reserves i s , therefore, the appropriate price variable i n analysis of exploration incentives. This thesis, i n Chapters 4 and 5, examines i n detail the linkage between the wellhead prices (for flow output of production) and the demand price for reserves i n the ground (as discovered by the explorationist). No previous studies have undertaken this approach, but rather they have assumed that wellhead prices were suitable price variables which would indicate the price incentive for the explorationist. While a f a i r amount of industry trading of reserves i n the ground takes place there i s l i t t l e published information on the prices at which reserves change hands. There i s , however, good data on the wellhead prices that producers obtain for delivering a flow output. This means that any study of exploration should include consideration of the development process so that a r e a l i s t i c estimate of the market or shadow price value of discovered reserves can be made. This i s particularly important i f development and production have been controlled by other than market forces, by prorationing for example. - 1.2 - 3 Fisher (in 1964) and Erickson (in 1968 )r f i t t e d econometric models to the U.S. data with equations explaining the rate of exploratory d r i l l i n g , the average success r a t i o , and the average reserves discovered per well. They used data which was a mixture of cross-section and time series for the 5 petroleum d i s t r i c t s of the U.S. for the period. 1946-1955." These models have major deficiencies. The price variables used are wellhead prices. Their equations do not include depletion of prospects as d r i l l i n g cumu-lates which means that their models imply the possi b i l i t y of a steady state condition in. which discoveries proceed continually at a steady rate, which i s impossible. Their models are f i t t e d with a mixture of cross-section and time series data. Both Fisher and Erickson attempt to estimate a wellhead price e l a s t i c i t y of new reserves from exploratory d r i l l i n g . Erickson's innovation i n the Fisher model was to introduce a variable which reflected the participation of large firms i n d r i l l i n g , and t h i s variable did emerge as highly significant. • Both Fisher and Erickson also discuss the inventory of prospects available to a firm but they do not systematically develop this concept. In this thesis we define an inventory of prospects and show how i t can be measured empirically. We also examine data for large firms i n considerably more det a i l than has hitherto been possible. We also show that the greater intensity of geo-physics expenditure on property held by the larger firms may account for their higher success ratios. F.M. Fisher, Supply and Ports i n the U.S. Petroleum Industry, Two Econometric  Studies, Baltimore, Johns Hopkins Press, 1964 E.W. Erickson, Economic Incentives, Industrial Structure and t'ne Supply of Crude O i l Discoveries i n the U.S., 1946 - 1958/59, Unpublished Ph D Thesis, Vanderbilt U., 1968 - 1.3 - 4 On various occasions i t has been shown that .small firms i n the U.S. d r i l l with a lower average success ratio for smaller prospects than large firms.* Shearer showed "that the Canadian situation i n 1946-1954 was similar.*" He also suggested that there are economies of scale i n geophysical research which were not availa-ble to firms with limited access to capital at that time. We examine these hypotheses for the Canadian industry i n much greater detail than was previously possible either i n the U.S. or i n Canada. I t should be pointed out that the back up data established on computer f i l e s for "this thesis i s much more detailed and complete izhan has ever been available previously for studies of petroleum exploration. A description of the data . tapes consisting of a Manual of some 130 pages i s available from the author. J.W. McKie, "Market Structure and Uncertainty i n O i l and Gas Exploration", Quarterly Journal of Economics, Vol. 74, No. 4, Nov. 1960, pp 543 - 571 R.A. Shearer, "Nationality, Size of Firm, and Exploration for Petroleum i n Western Canada, 1946 - 1954", Canadian Journal of Economics and P o l i t i c a l Science, Vol. 30, No. 2, May 1964, pp 226 1.4 - 5 •Erickson and Spann (in 1971) studied the U.S. gas industry. Their study is, notable i n treating the joint production nature of o i l and natural gas i n the exploration phase. I t was found, however, that the price of gas was not significant i n any of the equations. They explained the signs of their coef-ficients as resulting from firms' decision processes acting upon their i n -ventories of undrilled prospects, expanding on the original suggestions of Fisher and Erickson's earlier wo"rk with crude o i l . * I t should be pbijated out that, ex ante, i t i s often not known whether a prospect, i f i t i s successfully d r i l l e d , might yi e l d o i l or gas. Hence, almost always the expected returns from exploratory d r i l l i n g w i l l be influenced by the prices of both o i l and natural gas. In earlier stages of the industry the potential revenues from gas were often negligible through lack of pipelines and small regional markets. Crude o i l , on the other hand, can always be trucked to market i f no other means of transportation are available. I t seern^ to be generally accepted i n the industry that exploration can be directed towards either o i l or gas. That i s , the discovery of o i l pools and gas pools i s not a joint cost production process with fixed proportions. In the very earliest stages of exploration i n a new region i t may be that costs are incurred with l i t t l e or no understanding as to whether gas or o i l dis-coveries may be made, but as regional geology becomes understood through both pre-drilling and d r i l l i n g exploration i t becomes known whether an area, or geological horizon, i s gas-prone or oil-prone. For example, with existing knowledge, i t appears unlikely that one would discover numerous gas pools i n south eastern Saskatchewan. North eastern B r i t i s h Columbia i s regarded as • a gas-prone area, but much of Alberta presents a mixed bag. Part of the s t a t i s t i c a l analysis of Chapter 6 deals with this topic of "direc-ti o n a l i t y " i n detail which has not previously been possible. The analysis follows up the suggestions of D. Khazzoom i n his paper on directionality i n the U.S. industry. We show, for example, that a considerable amount of natural gas was discovered i n Alberta by exploration directed towards finding o i l . ** E.W. Erickson, and R.M. Spann, "Supply Response i n a Regulated Industry: the Case of Natural Gas", The Be l l Journal of Economics and Management Science, Vol 2, No 1, Spring 1571 * J.D.Khazzoom, "Gas Production Directionality", Public U t i l i t i e s Fortnightly, . Vol. 84, No. 13, December 18, 1969, pp 20-25 1.5 - 6 Chapter 2 defines the Reserves-Market which i s the subject area of this thesis and shows how i t links with the production Output Market. The nature of the short and long run supply functions for reserves are outlined. In Chapter 3 an economic model of petroleum exploration i s outlined, mainly with the objective of identifying variables which should be considered i n a reserves supply equation for' the industry. Chapter 4 describes an economic model of petroleum production. This model i s developed to provide a framework for connecting wellhead prices i n the Output Market with the demand prices for reserves i n the reserves market. Chapter 5 employs the theoretical production model of Chapter 4 plus a great deal of empirical data to derive estimates of the demand prices for o i l and gas reserves :_n Alberta for the period 1347-1970. These are shown i n Table 5.1. Many empirical features of the Alberta petroleum industry which have not been quantified and analysed previously ar<_ discussed. Chapter 6 i s a discussion.of empirical factors on the supply side of the Alberta Reserves Market. An extensive "tabular analysis i s made of success ratios i n exploratory d r i l l i n g ; comparing New Field Wildcats with other classes of wells, comparing the success ratios of large companies with others and so forth. The directionality of exploratory d r i l l i n g i s also examined. Chapter 7 outlines the theoretical supply function of reserves developed i n this thesis, and then discusses other studies of the Alberta discovery process. Chapter 8 d i s t i l l s the preceeding descriptive analysis into econometric equations The main equations use time series data and they lead to estimates of the short run e l a s t i c i t y between changes i n the prices, of o i l and gas and the annual rate of New Field Wildcatting. A secondary set of equations examines a cross section of data across companies and the purpose i s to estimate the contribution of geo-physics (predrilling investment) to success rates i n d r i l l i n g . -.1.6 - 7 1.2 OBJECTIVES AND CONCLUSIONS 1.2.1 SUPPLY FUNCTION IN RESERVES MARKET A primary objective of thi s thesis i s to define the components of the economic market for petroleum reserves, in general terms and specifically for Alberta i n the period 1947-1970, so that empirical tests may be conducted to demon-strate the economic linkages between the incentives to explore for o i l and gas and rates of wildcat d r i l l i n g . The principal d i f f i c u l t y i n analysing the demand side of this market i s to define and quantify the price incentive which motivates the explorer. We do not stress the problem of r i s k faced by the individual firm when d r i l l i n g a particular prospect but we focus on the revenue incentive available to the industry of explorationists. The supply side activity which we have emphasized i s New Field Wildcatting. This objective i s mat by providing an extensive descriptive and s t a t i s t i c a l backdrop of the o i l and gas industry i n Alberta and then f i t t i n g econometric equations to estimate the el a s t i c i t y and shifting of the industry's short run reserves supply function. I t i s shown i n Chapter 8 that the short run e l a s t i c i t y between the reserves price incentive to explore and New Field Wildcatting for o i l averaged between 6.3 and 0.4 during the period i n Alberta. The comparable e l a s t i c i t y for natural gas was around 0.1. We stress, however, that these e l a s t i c i t i e s may be rather unimportant out of their context of a shifting supply function. They do not remain constant as a region i s depleted and the rate at which the supply function shifts as a region i s explored w i l l be more significant i n determining the longer run petroleum supply than the short run e l a s t i c i t y . The equations of Chapter 8 also provide a measure of the shifting of the short run supply functions and thereby show the relationship between the short run functions and the long run supply potential of a region which i s the principal subject of Chapter 7. - 1.7 - 8 •While Fisher and Erickson simply discuss the concept of an industry inventory of undrilled prospects, we proceed to define and estimate some of the com- :. ponents of this inventory i n the course of developing the supply functions. 1.2.2 DEMAND PRICE FOR RESERVES As mentioned, a particularly significant part of this thesis (Chapter 5) i s the estimation of the true price incentive for exploration. The theoretical and empirical model takes cognizance of the whole breadth of factors which impinge on the producer's demand price for new reserves. These factors include f i e l d operating costs, development costs, well productivities, length of production l i f e , royalty rates, income taxes, the cost of money, delays before i n i t i a l production, the production of joint products, etc. 1.2.3 SIZE OF DISCOVERIES One question posed at the start of this thesis work was whether the decline i n o i l discoveries (and exploration by the major corporations) i n Alberta i n the late 1960's was a result mainly of economic factors rather than geological depletion. I t becomes clear from our results that although the incentive to explore for o i l was tending to decline, the principal cause of the worsening discovery performance of the industry was the decline i n the average size of o i l pool discovered. Chapter 8 f i t s equations to estimate the expected pool sizes which the industry faced through the period. We also analyse the s t a t i s t i c a l characteristics of the populations of pools discovered i n five year intervals through 1946-1970, i n Chapter 6. The data shows that the five year successive populations of o i l pools are each approximately lognormal but with smaller and smaller means through time. The populations of gas pools do not show as marked a decline i n mean size over the period. This data with other results dealing with d r i l l i n g directionality shows how the search for o i l was more intensive and systematic during the study period. Also, by comparing the expected pool sizes within a play to those over a sequence of plays we show the very rapid decline of pool sizes as discoveries are made within a play, and how the succeeding o i l plays have yielded smaller average pool sizes. 1.2.4 SUCCESS RATIOS AND DIRECTIONALITY The success r a t i o i n d r i l l i n g describes the chance that exploratory wells w i l l , make discoveries of either gas or o i l , and directionality measures the degree to which the industry can direct i t s search towards the discovery of either gas or o i l reserves, separately. The extent to which the industry can direct i t s search towards the discovery of o i l or gas separately i s an important aspect of the supply function. I f directionality were very low the apparent incentive to explore may only be remotely linked to the rate of d r i l l i n g and subsequent discoveries. The analysis of Chapter 6 show that directionality i n both o i l and gas intent d r i l l i n g was f a i r l y high, although o i l directionality has been lower than gas. We find that New Field Wildcat wells have a success ratio and directionality lower than New Pool Wildcats, and that within the class of New Field Wildcats the directionality of discoveries i s positively correlated with the success r a t i o . In the period 1945-1961 New Field Wildcats had a success ratio of 14.6% i n finding o i l or gas pools — 5.2% for o i l pools and 9.4% for gas pools. In the later period, 1962-1970, their success ratio was 10.8%, with 4.9% for o i l pools and 5.9% for gas pools. Using our measures of discovery, Chapter 6 demonstrates the extremely important role of New Field Wildcat wells (rather than other classes of exploratory wells) i n the petroleum discovery process. The data also indicates that some 95% of o i l reserves i n Alberta have been discovered by o i l intent wells. But, i n addition, o i l intent wells have dis-covered some 23% of the non-associated gas reserves, and about 52% of the associated and solution gas reserves. Overall they discovered some 30% of a l l - 1.9 - 10 gas reserves. That i s , the c i l - p r o f i t motivated search for o i l has been res-ponsible for almost a l l the o i l reserves, and has augmented the gas supply to some extent. 1.2.5 LARGE COMPANIES In Chapter 6 we find that while the large companies (the Big Eight) have had a higher success ratio than the others, the factor which markedly separates them as explorers i s the size of discovery. The Big Eight discovered much larger o i l .pools (4-5 times) and gas pools (2 times) than the others. We also find that the Big Eight did considerably more geophysics per well than the smaller firms. In Chapter 8 we f i t equations to company cross section data which shows that geophysics per acreage purchased was a significant determinant of a company's success ratio i n New Field Wildcatting. The data indicates that the larger companies tend to invest proportionately more i n pre-drilling a c t i v i t i e s and thereby they increase their success ratios, their directionality, and the size of pools discovered. CHAPTER 2 INDUSTRY INCENTIVES TO EXPLORE Overview of the Markets Products i n the Markets Outline of Market Processes Government Market for Reserves i n Place Non-Homogeneity of Reserves i n Place Recoverable Reserves A v a i l a b i l i t y From Existing Reserves i n Place From Expected Reserves Discoveries Depletion of Reserves Change i n Demand Price for Reserves Production Output Supply Function 12 SYMBOLS USED IN CHAPTER 2 NOTE: The indexes t and T are used to denote the time to which a variable applies. P Wellhead Price for O i l (Price for flow production), ° $/Bbl throughput • P Demand Price for Recoverable O i l Reserves, $/Bbl i n '° ground R . Reserves i n Place, Barrels i n the ground r Production-Reserves Ratio 13 2. INDUSTRY INCENTIVES TO EXPLORE  2.1.1. OVERVIEW OF THE MARKETS The supply side of the petroleum industry may be considered as a process whereby Possible Reserves — unexplored but believed to exist — i n the earth's crust are converted into delivered crude o i l , natural gas, or natural gas byproducts. In the f i r s t stage, predrilling and exploration d r i l l i n g investment serve to produce Reserves i n Place. Then development d r i l l i n g converts some of the discovered Reserves i n Place to Recoverable Reserves (or "Proved Reserves"). Development d r i l l i n g and subsequent operation of the development wells also provide the means of delivering production output to the wellhead. The supply process may be viewed as consisting of (at least) two markets. There i s an asset Kiarket for reserves i n the ground and a production flow market for a rate of output flow at the wellhead. This i s il l u s t r a t e d below. FIGURE 2.1 DIAGRAM OF SUPPLY PROCESS Asset; Reserves Market Possible Exploration Reserves Reserves ^ i n Place Flow; Output Market Development Recoverable ~> Reserves Production Output In the case of crude o i l production, the demand for output at the wellhead i s that of refiners, who then make refined petroleum products. The demand for o i l reserves i n the asset market i s by crude o i l producers, who develop and operate the o i l f i e l d s . Natural gas reserves are purchased by producers and production i s sold to u t i l i t i e s . - 2.2. 14 We refer to the prices set by the..two markets as the price per flow output and the price per reserve i n the ground. Thus; for o i l we have dollars per barrel output and dollars per barrel i n ground; for gas we have cents per MCF output and cents per MCF i n ground. Clearly, the demand for reserves i n the ground i s a derived or "intermediate" demand of the petroleum f i e l d operators and the demand for flow output i s an intermediate demand of refiners (or u t i l i t i e s ) . We view the asset Reserves Market as that i n which the "explorationist" i s active. The flow Output Market i s the terrain of the "producer". While the integrated companies participate i n both markets, there are many small companies active i n exploration i n the Reserves Market. The industry becomes less concent-rated as the stage of production i s further upstream from refining. This thesis focusses attention on the Reserves Market and especially on the supply side of the Reserves Market. However, because petroleum prices are generally available only for the Output Market, considerable effort has been given to estimating the derived demand (or demand price) of producers for reserves. Before pursuing the discussion of the markets further i t i s appropriate to out--line b r i e f l y some of the complications of joint production and product definition which w i l l be examined i n detail l a t e r , but should not be ignored even at this stage. 2.2.1. PRODUCTS IN THE MARKETS There are 4 major products which are traded separately i n the Output Market. These are; Crude O i l , Natural Gas, Natural Gas Liquids, and Sulphur: Natural Gas Liquids (which include Condensate, Pentanes Plus, Propane and Butane) and Sulphur are produced from Natural Gas reserves. . Natural Gas (and i t s byproducts) may be produced from Solution Gas reserves, which are gas reserves i n solution i n o i l reserves; from Associated Gas reserves which are reserves of gas capping an o i l pool; or from Non-Associated Gas reserves which are reserves of gas i n separate gas pools without o i l reserves. - 2.3 - 15 Natural Gas i t s e l f , whatever i t s source, i s processed to extract the byproducts i f any, and usually requires cleaning before i t i s saleable as "pipeline gas". Crude o i l generally requires some separation and cleaning before i t i s saleable "at the wellhead". In many instances a l l 4 major products are present i n the reserves of a pool. For example, an o i l pool may have solution gas which provides valuable gas byproducts. Obviously, the value of reserves, especially gas reserves, may be influenced significantly by the value of gas byproducts. The above factors bear on the incentive for explorationists to direct exploration towards prospects with various expected product potentials. However, there i s always a degree of uncertainty whether a petroleum prospect may yield gas or o i l , separately or i n combination, i f indeed i t turns out to be "wet". After a geological region has been f a i r l y well explored the characteristics of a prospect can often be anticipated correctly. In other words, the explorationist -can direct his efforts towards the discovery of either o i l or gas, although not with certainty. The explorationist's ex ante d r i l l i n g intention i s called his d r i l l Intent. This may be Intent O i l , Intent Gas, or Intent Both. The degree to which d r i l l i n g Intent i s f u l f i l l e d by discoveries i s called the "directionality" of d r i l l i n g . Another aspect worth noting at this point i s that the quality of petroleum reserves ranges widely. This may be a matter of production capability such as reservoir porosity, or relating to characteristics of the petroleum i t s e l f such as the gravity of o i l . Subsequent sections of this thesis w i l l return to examine i n detail the above features of petroleum products as they impinge on the Reserves Market. 2.3.1. OUTLINE OF MAP.KET PROCESSES To examine the interplay between the Reserves Market and the Output Market we now consider a producer firm on the supply side of the Output Market. - 2.4 - 16 We put aside complications of joint production i n either the Reserves Market or the Output Market and we discuss crude o i l reserves and production. The firm needs Recoverable (or Proved) Reserves for the purpose of making profits by producing and selling a flow of output. Proved Reserves may be obtained by the development d r i l l i n g of known Reserves i n Place. The firm may already own some undeveloped Reserves i n Place which could be developed. Or,, i t could purchase some undeveloped Reserves i n Place i n the Reserves Market. '': Or, i t could undertake i t s own exploration. The firm w i l l plan to invest optimally i n the various methods of obtaining Proved Reserves. For our purposes, there are 4 ways: 1) Prove up existing Reserves i n Place already owned by the firm, by development d r i l l i n g . ** 2) Purchase Reserves i n Place i n the Reserves Market and then develop them. 3) Undertake New Pool Wildcatting.. Test Wells or Extension Wells to discover new Reserves i n Place, on a structural feature or other typo of trap which i s already producing o i l or gas. Then develop the new reserves into Proved Reserves. 4) Undertake New Field Wildcatting on a structural feature or other type of trap which has not previously produced o i l or gas. Then develop the new reserves into Proved Reserves. When this type of trading actually occurs between firms the reserves are usually developed or p a r t i a l l y developed. We include enhanced recovery investments with development d r i l l i n g . We should mention that a more, general view of the intensive p o s s i b i l i t i e s for production from known reserves would include conversion of other energy sources than conventional crude o i l and natural gas into petroleum products. The gassification of coal and the exploitation of the Alberta Oil Sands are two good examples. I t i s important to recognize that there are abundant energy Reserves i n Place. The adequacy of petroleum.supply i s a matter of costs. - 2.5 - 17 I t can be seen that the uncertainty attached to each alternative ranges from being ndnimal i n the f i r s t method to considerable i n the case of New Field Wildcatting. At any point i n time, the firm would seek the cheapest o i l production, i n a sense which includes an evaluation of uncertainty, by an appropriate combination of investments i n the four alternatives. Theoretically, i f the cost of uncertainty were included i n each marginal cost then marginal costs i n each ac t i v i t y should be equalized and made equal to the marginal return from additional production. In equilibrium the firm would purchase reserves i n the Reserves Market for a price per barrel i n the ground that would just allow the firm to develop and produce output so that i t received i t s cost of money on the marginal investment. Also i t would engage i n the other alternatives up to the same equivalent "demand price" for reserves i n the ground. Viewing firms as not partici.pating i n hoth markets, which i s the same as viewing the exploration departments of firms as separate from their production depart-ments, we see that the supply side of the Reserves i n Place Market consist of the a c t i v i t i e s of explorationists, and that the demand side i s the demand for reserves of producers. Since producers i n any particular region (of Canada) are small relative to the world petroleum market, (and there are numerous explorationists) the demand for reserves w i l l be i n f i n i t e l y elastic at a price determined by netting back the world market price (and expected future prices) to the wellhead i n the region, and deducting development and operating costs, i n appropriate present value terms. Thus, the demand price for reserves, at any time, i s the price per reserves i n the. ground which new pool producers would pay for new reserves. 2.4.1. GOVERNMENT MARKET FOR RESERVES IN PLACE While some trading of Reserves i n Place occurs between firms, the most obvious market for Reserves i n Place i s established by the Alberta government. When a firm makes a commercial discovery, the exploration permits covering that land . area must be converted to production leases. On conversion, however, 50% of the acreage reverts to the Alberta government. Then, from time to time, the province - 2.6 - 18 auctions producing leases on this acreage. This supply of Reserves i n Place and industry's demand make a market i n which the price i s industry's Bonus Bids. These bids are lump sum payments for a given acreage and consequently they are often • quoted on a price per acre basis, but we may view them as prices for expected' reserves i n the ground. To i l l u s t r a t e ; Campbell Watkins has analysed the Bonus Payments for several pools i n the Rainbow area of Alberta.* Three of the pools were developed after leases for their reserves were purchased i n 1966, 1967 and 1968. The Bonus pay-ments were between 3.08<:/Bbl i n the ground and 16-lOt/Bbl i n the ground for o i l Reserves i n Place. With Recovery Factors (Recoverable Reserves divided by Reserves i n Place) of 30% to 48% i n Watkins1 examples, these Bonus payments were between 8.79<7Bbl in the ground and 40.25<:/Bbl i n the ground for Recoverable Reserves i n the ground. In Chapter 5 we estimate that the average demand price for Recoverable Reserves i n Alberta was around 30<-/Bbl i n the ground i n 1965. See Table 5.1. 2.5.1. NON-HOMOGENEITY Or RESERVES IN PLACE When speaking of an average demand price for Recoverable Reserves we imply an average quality of reserve. In this sense we assume that Recoverable Reserves are homogeneous. Reserves i n Place, however, which include not-economically-recoverable reserves must be considered as heterogeneous. The demand price for Recoverable Reserves (P R Q ^) i s the average price that a producer would pay for undeveloped Recoverable Reserves. As outlined, the Recoverable Reserves may be supplied either from known Reserves i n Place or from exploration for new reserves. Consider now the supply from Reserves i n Place. The heterogeneous inventory of Reserves i n Place can be represented by a figure l i k e Figure 2.2. We assume that the supplier (owner of the Reserves i n Place) undertaked investments such as enhanced recovery schemes which would make the reserves equivalent to an average Recoverable Reserve for subsequent development by the producer. The producers have a single demand price for the average Recoverable Reserve. * G.C. Watkins, "Direct Government Revenue from Petroleum - Alberta and the Middle East", Unpublished Paper, Calgary, 1973. - 2.7 - 19 FIGURE 2.2 bOX> ft) CQ -co-§£ o <u (1) w OS o +•> CD rH 8 & > •P o •H O R,o,t .L 0 R, R, REMAINING .RESERVES IN PLACE -\/v-Rr 4 R. 5 "6 *x7 Remaining Reserves i n Place, at time t Barrels i n the ground Thus the cost axis of Figure 2.2 shows the unit cost (implicitly) incurred by the reserve supplier that would make the Reserve i n Place equivalent to the average Recoverable Reserve." Figure 2.2 i s scaled, to i l l u s t r a t e the Alberta situation i n 1970 when some 20% of Reserves i n Place (OR^) were economically recoverable by primary means and some 10% (R^R2) were recoverable by enhanced recovery. The reserves re-presented by 01^ 2 a r e shown to be supplied at less than the Recoverable Reserves price of P p . But some 70% of Reserves i n Place (R 0R 7) are shown as not being economically recoverable, at that price. An interesting discussion of a resource conversion function which converts non-homogeneous resources to a standard resource i s given i n H.J. Barnett and C. Morse, Scarcity and Growth, The Economics of Natural Resource A v a i l a b i l i t y , Baltimore, J. Hopkins Press, 1963, pp. 109-115. - 2.8 - 20 A producer would be w i l l i n g to pay P p . for average Recoverable Reserves and an owner of reserves such as those i n OR^  would receive a quasi-rent. I f a producer paid P R q ^ for reserves of the quality indicated by R2Rg the supplier would take a loss because of the costs he would have to incur to con-vert his poor quality reserves to average Recoverable Reserves. Thus the Reserves i n Place (R2R7) remain uneconomical to recover. In recognizing that Reserves i n Place are heterogeneous we blur the idea of a single market with one price for Reserves i n Place. We have, however, defined a market for Recoverable Reserves, and i t i s this market which we view as the Reserves Market for purposes of this thesis. That i s ; we view explo-rationists as searching for Recoverable Reserves which when discovered are sold to producers. Also we view producers as developing Recoverable Reserves from existing Reserves i n Place. Both sources of Recoverable Reserves are l i k e l y to show increasing costs. 2.6.1. RECOVERABLE RESERVES AVAILABILITY •2.6.2. FROM EXISTING RESERVES IN PLACE By joining the top mid-points of each bar i n Figure 2.2 we may derive an appro-ximation to a "Recoverable. Reserves A v a i l a b i l i t y from Reserves i n Place Schedule." This i s shown i n Figure 2.3. - Z . 3 - 21 FIGURE 2.3 REMAINING RECOVERABLE RESERVES AVAILABILITY FROM EXISTING RESERVES IN PLACE •H CO iH 3 •v. -co-4-> CO 8 •rl R,o,t Demand Price for Recoverable Reserves R2 Remaining Recoverable Reserves from Existing Reserves i n Place, at time t , Bbls i n ground 2.6.3. FROM EXPECTED RESERVES DISCOVERIES The Recoverable Reserves Av a i l a b i l i t y Schedule of Figure 2.3 i s upward sloping because of the mixed quality of existing remaining Reserves i n Place, at time t. I t does not result from changing exploration costs per unit of reserves. In fact, exploration costs have been considered as sunk and irrelevant. - 2.10 - 22 Looking to the future, however, i f we measure the size of new discoveries accord-ing to their expected (appreciated) Recoverable Reserves (at current prices), we may estimate a schedule of Expected Recoverable Reserves A v a i l a b i l i t y from New Exploration, as follows: FIGURE 2.4 EXPECTED REMAINING RECOVERABLE RESERVES AVAILABILITY FROM NEW EXPLORATION Demand Price for Recoverable Reserves Expected Recoverable Reserves from New Exploration, Bbls i n ground The definition of this schedule differs from that shown i n Figure 2.3 because Figure 2.4 assumes that newly discovered reserves are homogeneous as to their estimated recoverability at existing prices, whereas Figure 2.3 assumes, reserves are made homogeneous by appropriate investment over the range of unit costs. Consequently, i t i s incorrect to sum the schedules of Figure 2.3 and Figure 2.4. with a view.to obtain a comprehensive reserves ava i l a b i l i t y schedule from existing and expected new reserves. - 2.11 - 23 Schedule 2.4 i s t i l t e d anticlockwise from a true schedule reflecting both sets of factors. That i s , at prices higher than P D . more reserves would be available, K,o,r but below P_ , there would be less reserves. R,o,t However, i n the subsequent analysis we ignore such a refinement. We focus at-tention on the finding costs to discover Recoverable Reserves, assuming that the range of prices considered does not change the recovery factor of reserves discovered. Figure 2.4 must be interpreted as applying to a span of time. I f the time span i s long Figure 2.4 provides information about the ultimate Recoverable Reserves which are expected to be discovered i n future years, i n a region. I f the time period were one year i t would show the expected finding cost of Recoverable Reserves at various levels of annual exploratory d r i l l i n g . As the time period were shorter the curve would be steeper.* Interpreting Figure 2.4 as showing annual finding costs, at time t , means that the incentive of Pv, . i s available for explorationists to undertake annual K,o,t d r i l l i n g up to the rate where expected Recoverable Reserves to be found are OR^ . That i s , we can expect annual exploratory d r i l l i n g to add OR^  reserves to the lower-part of the schedule i n Figure 2.3, below the demand price of P p .. Note that whatever Recoverable Reserves are actually discovered w i l l , by defini-tion, be added to the lower part of the schedule i n Figure 2.3. * The nature of this supply curve i s explained i n more detail i n Sections 6.1 - and 7.1. - 2.12 24 Of course, exploration w i l l also discover Reserves i n Place which are not economically recoverable at or below P^ ^. These reserves, which are not depicted i n Figure 2.4, would rotate the schedule of Figure 2.3, above the P^ Q ^ unit cost, rightwards. Overall, the discoveries resulting from exploration w i l l s hift the entire schedule of Figure 2.3 rightwards. 2.6.4. DEPLETION OF RESERVES The other source of change i n Remaining Recoverable Reserves a v a i l a b i l i t y i s depletion by production. Note that, at time t , the reserves OR2 i n Figure 2.3 would be developed and supporting output, but the reserves with unit costs (to become recoverable) above P-p, Q ^ would be undeveloped or "beyond economic reach". Consequently, as time passes, production depletion shifts the lower' portion of the supply schedule i n Figure 2.3, leftwards. 2.6.5. CHANGE IN DEMAND PRICE FOR RESERVES Consider an increase i n the demand price for Recoverable Reserves, perhaps stenming from an increase i n the wellhead price. An upward sh i f t of P i n Figure 2.3 would increase the conversion of existing K , 0 , t Reserves i n Place to Recoverable Reserves and provide a concomitant increase i n Output. In Figure 2.4, the incentive to explore would increase and'we expect discoveries to s h i f t the schedule of Figure 2.3 rightwards more than would otherwise be the case. Also, we .might expect the rate of production (and depletion) from Recoverable Reserves to increase which would tend to shi f t the lower part of the schedule i n Figure 2.3 leftwards more rapidly. - 2.13 ~ 25 2.7.1. PRODUCTION OUTPUT SUPPLY FUNCTION Assuming, as before, that Recoverable Reserves are homogeneous, the Reserves Avai l a b i l i t y Schedule of Figure 2.3 can indicate, at any time, the Output supply curve. That i s , we can map the schedule of Figure 2.3 into an Output supply function of the type usually used i n economics but with the qualification that i t applies only at a single point i n time. I t only applies when the underlying Reserves i n Place inventory has the given characteristics. FIGURE 2.5 INTERMEDIATE PERIOD OUTPUT SUPPLY FUNCTION, FOR A REGION f o & -CO-Ol o •H "8 S H W cS •»-> •d 5 very short run supply by increasing production/ reserves ratio 4 production depletes Recoverable Reserves supply at time t by developing existing Reserves i n Place exploration augments Reserves i n Place Production Rate Bbls/yr - 2.14. - 26 This upward sloping supply curve shows a r i s i n g unit cost associated with higher production rates as a result of lower quality Reserves i n Place being converted to Recoverable Reserves, at time t , to increase the production rate. I t i s an intermediate term supply curve which permits changes i n development d r i l l i n g but not changes i n the Reserves i n Place. We have assumed that the production to reserves ratio (r) i s constant. We should allow, however, that i n the very short run, before production could be increased by converting Reserves i n Place to Recoverable Reserves, as a response to a rise i n the wellhead price, the ratio of production to reserves would probably be increased. That i s , firms would expand the rate of production up their short run marginal cost curves by increasing production rates from the existing developed reserves. The very short run industry supply function would be above the intermediate run supply curve, as shown by the dotted line i n Figure 2.5 * Again, consider a r i s e i n the wellhead price, from PQ. F i r s t , there could be a very short run response by companies increasing their production to reserves ratios. Then further Reserves i n Place would be proved up perhaps mainly by the introduction of enhanced recovery schemes. Production would then be back on the "intermediate" supply curve. However, over time, depletion and exploration would both increase and the degree to which the supply curve would shift at the new level of production w i l l depend upon the success of exploration. A f u l l equilibrium in this regional market would be given by supply remaining constant at the wellhead demand price determined by the "world" market. This would require exploration to be adequately successful to stave off the depletion effect, without shifting industry marginal costs of production. A masters thesis from the University of Calgary, Alberta, estimates the shape of this very short run supply function for Alberta i n 1972. M.W. Edwards, Alberta Short Run Crude Oil Supply - 1972, Calgary, Alberta, University of Calgary Unpublished Masters Thesis, 1973. , CHAPTER 3 ECONOMIC MODEL OF PETROLEUM EXPLORATION BY A FIRM Exploration Sequence Exploration Expenditures - Definitions Exploration Revenues - Definitions Production Process of Exploration Generalized Reserves Production Function Inventory of Undrilled Prospects The State of Nature Exploration D r i l l i n g Form of Exploration Success Function Exploration Directionality Form of Exploration Reserves Production Function Optimal Rate of Exploratory D r i l l i n g 28 SYMBOLS, USED IN CHAPTER 3 NOTE: The indexes t and T are used to denote the time to which a variable applies. A Q , A G See page 3.18 B Exploration Budget of Firm, $ 8 Proportion of a Pool Expected to be Controlled after Discovery ^13'^14 Empirical Constants Reflecting the Degree to which Geophysics Augments Each Inventory of Prospects Dg I n i t i a l Number of Gas Pools i n a Region D I n i t i a l Number of O i l Pools i n a Region o o D_ Estimated Undiscovered Gas Pools b,t D . Estimated Undiscovered O i l Pools o,t G Geophysics Activity, crew weeks H Q Expected Percent O i l Intent Directionality Ig Inventory of Undrilled Prospects of Gas at Beginning of Period t I Inventory of Undrilled Prospects of O i l at Beginning of Period t k Q(.),kg(.) Poisson Intensities for O i l and Gas Success Rates, respectively k (.) Expected O i l Success Rate Function from O i l Intent o,o - ...,. ' D r i l l i n g k Expected Gas Success Rate Function from O i l Intent D r i l l i n g L Land Acquisition,acres Lg Land Acquisition for Gas Prospects,acres L Q Land Acquisition for O i l Prospects,acres u Mean of the Underlying Normal Distribution of the Log of the Variable 29 SYMBOLS USED IN CHAPTER,3, page 2 Vig Estimated I n i t i a l Mean Parameter for Gas u Estimated I n i t i a l Mean Parameter for O i l o y„ . Estimated Mean Parameter for Gas b,r u . Estimated Mean Parameter for O i l o,t N„ Number of Gas Pools Discovered by A l l Intents of b D r i l l i n g N Number of O i l Pools Discovered by A l l Intents of ° D r i l l i n g II Profits from O i l Intent D r i l l i n g , $ o °' P B Wellhead Price of Butane, $/Bbl P Price Per Crew Week of Geophysics, $/crew week P G Wellhead Price of Gas, C/MCF P^ Price of Land Acquisition, $/acre PT n Price of Land Acquisition for Gas Prospects,$/acre P. Price of Land Acquisition for O i l Prospects,$/acre Li,0 P Q Wellhead Price of O i l , $/Bbl output . Pp Wellhead Price of Propane, $/Bbl output P Wellhead Price of Pentanes Plus, $/Ebl output pp * P Wellhead Price of Sulphur, $/L'.Ton output s P„ R Demand Price for Recoverable Reserves of Butane, K ' B $/Bbl i n ground P^ g Demand Price for Recoverable Reserves of Gas, <7MCF ' i n ground P^ • Demand Price for Recoverable Reserves of O i l , $/Bbl * i n ground P p Demand Price for Recoverable Reserves of Propane, K , P $/Bbl i n ground 30 SYMBOLS USED IN CHAPTER 3,, page 3 P R Demand Price for Recoverable Reserves of Pentanes K , p p Plus, $/Bbl i n ground P c Demand Price for Recoverable Reserves of Sulphur, $/L.Ton i n ground P D r i l l i n g Cost of Well with.Oil Intent, $/well P r D r i l l i n g Cost of Well with Gas Intent, $/well P Vector of Costs of Wells for O i l , Gas and Both Intents, $/well Rg Q Reserves of Butane i n Gas Pools, Bbls i n ground Rg Q Reserves of Butane i n O i l Pools, Bbls i n ground R„ n Reserves of Gas i n Gas Pools,MCF i n ground Rg Q Reserves of Gas i n O i l Pools, MCF i n ground R Reserves of O i l i n O i l Pools, Bbls i n ground 0 , 0 °^ R p Reserves of Propane i n Gas Pools, Bbls i n ground Rp o . Reserves of Propane i n O i l Pools, Bbls i n ground R g Reserves of Pentanes Plus i n Gas Pools, Bbls i n p p ' ground R Reserves of Pentanes Plus i n O i l Pools,Bbls i n p p ' ground Rg g Reserves of Sulphur i n Gas Pools, L.Tons i n ground Rg Q Reserves of Sulphur i n O i l Pools, L.Tons i n ground S th G,G, i Reserves of a Single Pool or Size of i Gas Pool, MCF i n ground *f~"K S p . Reserves of Gas i n the -v O i l Pool, MCF i n ground S . Reserves of O i l i n the.-£th O i l Pool,Bbls i n ground o , 0 , *• S p r Firm's Anticipated Average Gas Pool Size from Gas 9 Intent D r i l l i n g , MCF i n ground Firm's Anticipated Average Gas Pool Size from O i l Intent Drilling,MCF i n ground Firm's Anticipated Average O i l Pool Size from O i l Intent D r i l l i n g , Bbls i n ground Variance Parameter of the Underlying Normal D i s t r i -bution of the Log of the Variable Variance Parameter of the Underlying Normal D i s t r i -bution of the Log of Gas Pool Size Variance Parameter of the Underlying Normal D i s t r i -bution of the Log of O i l Pool Size Proxy of the State of Nature Regarding Gas Pools Proxy of the State of Nature Regarding O i l Pools Dummy Stochastic Variable Sum of Rates of D r i l l i n g with O i l , Gas and Both Intents,wells Vector of Rates of D r i l l i n g with O i l , Gas and Both Intents, wells Rate of D r i l l i n g with .Both Intent, wells Rate of Non-Successes with Both Intent D r i l l i n g , dry wells Rate of Success Gas with Both Intent D r i l l i n g , gas pools Rate of Success O i l with Both Intent D r i l l i n g , o i l pools Rate of D r i l l i n g with Gas Intent, wells Rate of Non-Successes with Gas Intent D r i l l i n g , dry wells Rate of Success Gas .with Gas Intent D r i l l i n g , gas pools Rate of Success O i l with Gas Intent D r i l l i n g , o i l pools 32 SYMBOLS USED IN CHAPTER 3, page 5 X Q Rate of D r i l l i n g with O i l Intent, wells X N Rate of Non-Successes with O i l Intent Drilling,dry °'D wells X n Rate of Success Gas with O i l Intent D r i l l i n g , gas °'G pools X Rate of Success O i l with O i l Intent D r i l l i n g , o i l °>° pools 33 3. ECONOMIC MODEL OF PETROLEUM EXPLORATION BYA FIRM 3.1.1. EXPLORATION SEQUENCE The main components of the exploration process may be outlined as follows: Pre-Drill Investment i n : Land, Permits, etc. Geology £ Geophysics, etc. D r i l l Exploratory Wells with Intent: Oil Gas Both Discover: Oil Oil & Associated Gas, plus NGL's £ Sulphur Oil £ Solution Gas, plus NGL's £ Sulphur Non-Associated Gas, plus NGL's £ Sulphur Nothing (Dry Hole) The exploration firm (or part of a firm) invests, i n pre-drilling and d r i l l i n g a c t i v i t y with the goal of producing reserves of the various petroleum products. 3.2.1. EXPLORATION EXPENDITURES - DEFINITIONS In any year in a given region, an exploration firm divides i t s budget between Land, Geology and Geophysics, and D r i l l i n g . These expenditures are defined as follows: The Exploration Budget, B^ ($), gees to: 1) Purchase of "acreage" which i s required for obtaining the right to d r i l l and to own the production from any discoveries. Much of this expenditure constitutes capitalized "economic rent" payments i n the - 3.2 - 34 form of Bonuses. We c a l l this investment Land Acquisition, L^. I t i s measured by acres, but we usually use -the dollars worth which i s Lt*PL 5t i.e. acres times price per acre. When Land Acquisition i s specifically for o i l prospects i t i s defined L Q ^ with a price PL,o,t » f° r S a s prospects i t i s defined L ^ t with price PL,G,t-2) Investment i n information gathering a c t i v i t y , a l l of which we include under the name of Geophysics, Gt, which has been the method used most by the industry i n the study time period. We measure Geophysics by the units of "crew weeks". The price per crew week i s Pg,t* 3) Investment i n exploratory wells. We are primarily concerned wi.th wells classed as New Field Wildcats (and sometimes with New Pool Wildcats, Test Wells and Extension Wells). A l l wells have a stated intention of search; i.e. for Crude O i l , Natural Gas,, or for "Both". We use the symbols Xo^ts G^,t» t t o r e ^ e r the rate of d r i l l i n g for each class. The sum of the rates i s defined as X-t, and Xf. i s the vector of the three rates. The price or cost of wells i s denoted by Px,o,t9 e - t c» a n c^ the vector of prices by P v + . —x,x We have Bt = L f P L , t + ^ ^ g . t + £f£x,t ( 3 , 1 ) 3.2.2. EXPLORATION REVENUES - DEFINITIONS 1) Exploratory d r i l l i n g during a time period t may yie l d reserves of o i l , gas, and gas byproducts. These are represented by reserves; R . , R,, j . R ,, R ,, R_ , , R„ , o,o,t G,o,t pp,o,t' p,o,t' BiO,t S,o,t. That i s ; reserves of crude o i l , pipeline gas, Pentanes Plus, Propane, Butane and Sulphur, i n o i l pools. Reserves i n gas pools are RG,G,t> ^ , 6 ^ ' RP>G,t> RB,G,t, RS,G,t-The reserves i n a single pool, or the size of the i t h pool, i s given by So,o,i f° r °il ^  "the i t h o i l pool; S Q j Q j i for gas i n the i t h o i l pool, and so forth. - 3.3 - 35 2) When an exploratory well discovers a new pool we term this d r i l l i n g outcome a success. I f the pool contains o i l i n commercial quantities (whether or not i t also has gas reserves with the o i l ) we designate the pool as an o i l pool and the discovery as a "success o i l " . A "success gas" signifies the discovery of a non-associated gas pool. The rate that each type of d r i l l i n g obtains success i s denoted as follows: ^o,o,tj ^G,o,t> xB,o,t ^ o r "success o i l " when d r i l l i n g intent was O i l , Gas or Both, and XQ^Q^, ^G,G,f *B,G,t for "success gas" for the three d r i l l i n g intents. The rate, of non-successes i s given by ^OjD,^ ^ j D j t * xB,D,f As an example, we may have o i l intent d r i l l i n g Xo,t which discovers o i l pools Xo. 0 ; (t5 but with associated gas which i s produced and processed to obtain pipeline gas plus the four gas byproducts. These o i l pools would have reserves of O i l , Gas, Pentanes Plus, Propane, Butane, and Sulphur. Consequently the value of these reserves depends on the proportion of each product and their relevant prices. We assume prices and unit costs to be exogeneously determined outside of the firm, and to be constant within the time period t , which i s usually taken to be one year. 3) Wellhead prices, at time t , are denoted by P0,t» PG,t» p^p,t» ^ p,t> ^B,t> ^S t "t^e demand prices for recoverable reserves of each product a^e P R j 0 } t , P R j G j t , P R j p p j t , P R j P j t , P R ) B ) t , P R ) S ) t-To use notation which always accounts for the joint products from pool production i s very cumbersome. In our analysis we view production from reservoirs to take place i n fixed proportions, given the reservoir characteristics. Therefore, for simplicity we speak of o i l pools and gas pools and we ignore discussion of the joint products as much as possible. For example, i n the theoretical exposition we may speak of the value. of the i t h o i l pool as: >o,o,i,f*R,o,t - 3.4 - 36 which i s the o i l reserves size of the i t h o i l pool times the demand price for o i l reserves, at time t . For convenience we ignore the value of any joint products. Of course, we must f u l l y include them i n our empirical analysis, however. 3.3.1. PRODUCTION PROCESS OF EXPLORATION In any time period t (say one year) the firm establishes i t s exploration budget and divides i t between Land Acquisition, Geophysics, and Exploratory D r i l l i n g . The current Land Acquisition and Geophysics expenditures, however, are not relevant to current d r i l l i n g . The success of current d r i l l i n g i s determined by previous Land Acquisition and Geophysics and by the degree to which those expenditures provide current d r i l l i n g potential. Such potential i s conditional upon the State of Nature. 3.3.2. GENERALIZED RESERVES PRODUCTION FUNCTION We can classify the inputs going to produce new reserves i n time t , as 1) the firm's Inventory of Undrilled Prospects 2) the firm's D r i l l i n g during time t 3) the State of Nature The inventory of Undrilled Prospects i s a function of the cumulated unused information gathered by the firm, and the firm's unexploited investments i n land holdings. The State of Nature measures the number and size of remaining undiscovered hydrocarbon pools i n the region. Accordingly, the firm's production function can be written for o i l reserves i n o i l pools, as follows: * *o,o,t = R(x t, i C j t , e 0 9 t , u t) (3.2) The vector 6p,t i s o n e subset of two i n the vector 6£. The other vector i s §G,t , for~gas pool information. - 3 . 5 - 37 where I 0 j-t i s the firm's Inventory of Undrilled Prospects at the beginning of the period, and 6^  ^  i s the proxy for the State of Nature regarding o i l pools at time t , and U^ i s the dummy stochastic variable which shows that the function R(.) doesn't map the inputs deterministically into the output. The production function means that the input rates determine the parameters of the s t a t i s t i c a l distribution according to which the output of new reserves w i l l be distributed. 3.3.3. INVENTORY OF UNDRILLED PROSPECTS The firm's Inventory of Undrilled Prospects ( o i l or gas prone) i s viewed as being a function of the firm's prior expenditures for Land Acquisition and for Geo-physics, and of variables representing the degree that prospects have been used up (i.e. d r i l l e d ) . 1) Geophysics: Assuming the firm has a given Land Acquisition history, i t s cumulated expenditures on Geophysics provide an indicator of the pre-drilling information (or Inventory of Prospects) which i t has gathered. The Inventory of Undrilled Prospects, however, gets used up as prospects are d r i l l e d . Some prospects may turn out to be pools (about 10% - 15% of d r i l l e d prospects i n Alberta), but most of them are dry. Each exploratory well and especially each New Field Wildcat provides evidence of a prospect being used up. Indeed, Gamer and Campbell have defined a prospect as " geological anomoly which can be evaluated with a single exploratory well".* Consequently, the variable of cumulated exploratory wells d r i l l e d by the firm indicates the drawing down of o i l or gas prospects from i t s inventory. 2) Land Acquisition: The foregoing assumed that the firms had a given history of Land Acquisi-tion. Land Acquisition, however, may play a v i t a l role i n providing * C.R. Garner and T.J. Campbell, Economic Evaluation and Plarcr'ng Exploration Programs, Oil S Gas Journal, June 4, 1973, pp 94. - 3.6 38 undrilled prospects for the firm's inventory. * Most of the Land Acquisition payments are Bonus payments to the provincial government which are payments for expected reserves, based on estimates of the economic potential of land areas. Dichotomizing the situation we can view Bonus payments as being a) Payments for production leases, as discussed i n Section 2.4.1 where they were compared with the producer's demand price for Recoverable Reserves. b) Payments for exploration rights (and the option for subsequent lease rights on part of the exploration acreage i f exploration i s successful). In the f i r s t case we may assune that finding costs following the Bonus payments are negligible. In effect, the producer simply buys expected reserves i n the ground, which i s the same thing as undrilled prospects.. The dollar amount of Land Acquisition payments for Bonuses, divided by the demand price for reserves and the expected average size of pool, should approximate the expected number of pools which are being purchased, i f no finding costs would be needed. ** Supposing that the producer's expectations were correct, then the variable * Without farm-in provisions i t would be a necessary condition before a firm could consider any prospects. Note that the aggregate industry's Bonus payments serve to transfer prospects from the provincial government (i.e. outside of the industry) to the industry. ** We have ignored the delay between. Bonus payments and i n i t i a l exploration i n this formulation. We consider income tax complications i n Chapter 5. Only since 1963 have Bonus payments been wholly deductible for income tax purpose. o,t L,o,t TETS T - 3.7 - 39 would approximate the number of o i l pools (wet prospects) which had been purchased by Oil Bonus payments for production leases, at time T. In the foregoing we assumed there were no finding costs which means that no -dry holes were expected or that the success ratio i n d r i l l i n g the pros-pects which were purchased was 100%. i.e. no exploration was needed. This i s a limiting case because i n practice even Bonuses for production leases are paid for (what turn out to be) dry prospects. In the second case Bonuses are paid for exploration d r i l l i n g rights (described i n more detail i n Section 6.5.3). The number of prospects being bought includes dry prospects as well as pools. Therefore we have to allow for the cost of exploratory wells. Also we have to take into account that the explorationist cannot appropriate a l l of the pools discovered. Usually, only half the acreage under exploration permit can be leased (according to a checker-board pattern). We assume that the proportion 8 of a psol can be expected to be controlled after discovery, and we assume that geophysics costs are not included here. Then, again assuming that expectations are correct, we have the variable T-l L ..PT n . _._ o,t L,o,t  * P p ^ +.E(S^ n +).E-(Xrt „ . ).B - P v t=0 R,o,t o,o,t o,o,t o,t x,o,t which would approximate the number of o i l prospects (wet or dry) which had been purchased by O i l Bonus payments for exploration rights, up to time T. This variable i s derived as follows. We have equation (3.28) for expected Profit of the explorationist from O i l intent d r i l l i n g . Suppose we ignore the possi b i l i t y of finding gas pools when d r i l l i n g o i l prospects, then equation (3.28) i s ; EOT m) = Pp T.E(X o ^ T).E(S n rn) — P _ T.X T (3.3) o,I RjO,i o,o,± o,o,i x,o,i o,i This formulation ignores the po s s i b i l i t y of finding gas pools when d r i l l i n g for o i l . ,3.8' - 40 where we haven't spelled out the components of the expected success rate and expected pool size. Then the expected profit per O i l intent well i s ; E^o/P _ PR,o >T- E ( Xo,o,T ) , E ( So,o >T ) " PX,o,T (3.4) Xo,T Xo,T but each O i l intent well d r i l l s an o i l prospect so this i s also the ex-pected profit per recognised prospect. We can assume that the explorationist (in a competitive auction) would pay an amount up to but not greater than the expected profit for a Bonus. I f he paid a Bonus equal to the ex-pected profit we have; Lo,T"PL,o,T (3.5) Number of Prospects = E ( no,T ) | Xo,T which, after allowing for leasing provisions that only permit some 3 of a pool to be appropriated, gives us the variable on page 3.7. As before, exploratory d r i l l i n g can be assumed to deplete the exploration prospects which are obtained through Bonus payments. Our argument leads to the specification of possible equations for the Inventory of Undrilled Prospects (for New Field Wildcatting) as follows: Oil Prospects, at time T; T-l L ..P. . j = j- o,t L,o,t O,T A ~ P I TTETS TTTETX JX J . B - p " ' tr=0 R,o,t o,o,t o,o,t o,t x,o st T-l T-l + b.,-. Z G. - Z X . (3.6) 1 3 1HJ t t-0 °'t Gas Prospects, at time T; j = *1a,t'PL,G,t  G > T 1-0 PR,6,f E (^S,G,t ,* E ( XG,6,t / XG,t )- 0 " P x,G,t T-l T-l + b 1 u. Z G. - Z XR (3.7) where b^3 and b^4 are empirical constants reflecting the degree to which geophysics augments each inventory. * Also, we require that Lj. > 0. Such requirements may influence the functional form for estimation of this variable. We use cumulated Geophysics Crew weeks, T-l Z G^  , as the Geophysics variable rather than dollars worth of Geophysics. t=0 r The expected size of pool variables E(S Q 0 j-t) and ECSg^tOs refer to the size of pools expected from prospects purchased at time t . Note, the above definition ignores byproducts. The model states that, on balance, exploratory d r i l l i n g depletes the inventory of undrilled prospects. This may be questioned; especially when prospects * Note, we have assumed that there are two d r i l l i n g intents, O il and Gas. i.e. We may consider the Both intent as included with the Oil intent. - 3.10 - 42 represent stratigraphic traps whose identification may depend on information from d r i l l i n g . Structural traps are normally identifiable from predrilling investment (e.g. by geophysics). We do not deny that d r i l l i n g provides information about the existence of pros-pects, but we argue that, i f a l l predrilling investment were unchanged, less than one new prospect would be added for every prospect which i s d r i l l e d . This i s net to say that an important discovery may not provide the impetus for an entirely unexpected play, but i n such a case, we argue, the discovery would stimulate predrilling investment which would lead thereafter to the d r i l l i n g of new prospects. This implies that i f exploratory d r i l l i n g were maintained without any investment i n Land or Geophysics, the inventory of undrilled prospects would run down, eventually containing only prospects which were judged to be either too uncertain or too small to d r i l l . Most of the remaining prospects, i n this situation, are l i k e l y to be small but relatively certain (e.g. the Milk River gas prospects in Alberta), which reflects the distribution of pools according to size i n nature. * I t should be pointed out that this approach to the "learning" or "information" aspect of the exploration problem, has two substantial improvements over previous models. I t does not impose any particular learning pattern on the model. That i s , i t does not preclude any number of peaks i n d r i l l i n g success during the exploration history of a region. Indeed the inventory of prospects (and d r i l l i n g success) may continually run down from the outset i f d r i l l i n g always depletes prospects faster than they are gathered. Or, d r i l l i n g success may reflect the inventory * See F.M. Fisher, Supply S Costs i n the U.S. Petroleum Industry: Two Econometric Studies, Baltimore, J. Hopkins Press, 1964, pp. 5 and pp. 26. Generally speaking, a situation of "run-down" prospects (but with increasing economic incentive) appears to have existed i n Alberta since about 1970. As shown i n Chapter 6 the major companies, i n particular, have drastically reduced their participation i n geophysics. Their uncertain prospects have been farmed out but their small certain prospects have been d r i l l e d at a rapid pace. - 3.11 - 43 of prospects by f i r s t r i s i n g , then gradually f a l l i n g o f f , then r i s i n g again etc. as the balance between additions to the inventory of undrilled prospects and d r i l l i n g fluctuates. < It separates measurement of the information component i n d r i l l i n g from the depletion of actual prospects from nature as pools are discovered. 3.3.4. THE STATE OF NATURE 1) Frequency of Occurrence of Pools: We view the production function as being not only a matter of effort applied to an inventory of prospects, but also conditional upon the actual or estimated State of Nature i n the region. Note that the State of Nature i s outside of the control of the firm. The discoveries of a l l fir^ms i n a region deplete that region's inventory i n the ground of undiscovered pools. Thus government action, for example, could influence the overall depletion rate by influencing the industry rate of d r i l l i n g , but no single firm could control i t . The firm's inventory of undrilled prospects, however, i s controlled by i t s investments i n predrilling a c t i v i t i e s or by d r i l l i n g prospects. The inventory of undiscovered pools i n the ground w i l l partly over-lap with the firm's (or industry's) inventory of undrilled prospects. - 3.12 - 44 We knew that the discovery of pools must diminish the number of remaining undiscovered pools. I f we had a means of estimating the i n i t i a l number of pools i n a region, then the estimated number of undiscovered pools would simply be the i n i t i a l number less the number of pools discovered. I f DQ represents the i n i t i a l number of o i l pools i n a region, then D Q ^, would be the estimated undiscovered pools at time t , as follows: J T-l D „ = D - I EN . + ) N s'X . + L + X n _,_ (3.8) o,T o j ^  o,:,t ' o,t o,o,x ^S,o,t B,o,t where j refers to the J firms which have previously (from time T = 0 to t = T-l) made discoveries i n the region. A similar argument applies to gas pools: J T-l DG,T " DG " * ^ G . j . t > NG,t = Xo,G,t + XG,G,t + \<S9t (3.9) 2) Size Distribution of Pools: For theoretical purposes we assume that the i n i t i a l distribution of pools by size i n a region i s according to the lognormal.*. I t i s also an empirical fact that population of pools discovered i n sequential time periods (say of 5 years) are approximately lognormal, but usually with declining mean sizes. The characteristics of pool size distribu-tion i n Alberta i s examined i n some detail i n Chapter 6. I f pool discoveries, at any time, are distributed lognormally by size, we have: 2 So,o,T 1 3 FL ( So,o,T I "o.T^o.T* , and ( 3 ' 1 0 )  SG,G,T 1 3 FL(SG,G,T ' yG,T'°G,T) ( 3 - n ) A number of analyses including those i n Section 6.7 support this assumption. - '3.13 - 45 where the parameters u and a 2 are those of the underlying normal d i s t r i -bution of the log of the variable. Then we hypothesize that: J T-l yo,T = yo " b l l ' ? ^o9t , and (3.12) yG,T = y G - b 1 2 - [ ^ , t ( 3 ' 1 3 ) where u and u are the estimated i n i t i a l parameters i n nature. The G O expected size of pools w i l l be: ^S.G.T' " " » 1 WG + H i - b12-| > ( 3 ' 1 5 ) Our concern, however, i s the nature of the firm's expectations about pool sizes. Following the argument above for o i l pools, we rewrite (3.14) as: J T-l (3.16) W = e ^ { ^ 8 - b n - ^ N o , t } where S 0 ^ T i s the firm's anticipated average o i l pool size from o i l intent d r i l l i n g , and we assume that the variance i s taken as constant.* * For the industry i n Alberta 1948 - 1969, for pools discovered by NFW; - _ 2 J T-l S - - exp" {10.9- - -9 x 10" .E t N } MSTB o,o,T . j tK) °' - 3.14 - 46 We have argued that the firm estimates a smaller average pool size from year to year. Within a play this would be a reasonable policy, which i s abundantly supported by our data and other studies. Since there i s no way to anticipate the beginning of a new play,such a strategy would always be reasonable. When a new play occurred the industry would be surprised (happily) by discoveries which would usually be much larger than previously. Thereafter, however, pool size would decline again from the new peak.* As far as pool size i s concerned within a play, the selection of prospects follows a course where f i r s t a broad mesh sieve i s used to pick out the largest prospects. After d r i l l i n g those, the smaller prospects are identified, and so on. Thus the State of Nature, which we have previously called 8 and 6,, . consists —O , T -va ,T of two measurements for each of o i l and gas. The o i l State of Nature i s given by D „ and S _,, and the gas State of Nature i s given by D0 „ and Sn „. 3.3.5. EXPLORATION DRILLING The firm's decision variables, at any time, are the three d r i l l i n g rates, the current Geophysics expenditures and the amount of Land Acquisitions. But, because current d r i l l i n g i s assumed not to be affected by current Land Acquisition and Geophysics, the d r i l l i n g decisions may be considered separately. * The actual decline rates i n Alberta are examined i n detail i n Chapter 8. 3.15 - 47 Each d r i l l i n g decision w i l l be a function of the exogenous variables l i k e prices and costs, and predetermined variables l i k e the firm's Inventory of Prospects and the (estimated) State of Nature. Over the longer view, however, the decisions regarding Geophysics and Land Acquisition are interdependent with d r i l l i n g . Briefly stated, the firm desires to strike an optimal balance over a period of time (say 5-10 years) between i t s cumulated investments i n each activity. Current investment i n Land Acquisition and Geophysics boosts the Inventory of Prospects for future d r i l l i n g . * To c l a r i f y these points, we have assumed that the Inventory of Prospects consists of discrete prospects which may be increased i n number by further Geophysics or Land Acquisition but which w i l l not be otherwise changed by these a c t i v i t i e s . The probabilities of success i n d r i l l i n g a prospect i n terms of whether i t i s l i k e l y to be a wet hydrocarbon reservoir and of what size are estimated by the firm according to i t s estimates of the State of Nature. Thus, given no budget constraint, i f d r i l l i n g appears to be profitable to the firm i t should definitely be undertaken. In r e a l i t y there may also be some d r i l l -ing which would be marginal on i t s own expected p r o f i t a b i l i t y but i t might be expected to provide information about the State of Nature for assessing prospect p r o f i t a b i l i t y for future d r i l l i n g . We don't include this p o s s i b i l i t y i n our model. Further, our model does not deal with prospects one at a time but considers the firm to undertake a d r i l l i n g program or annual rate of d r i l l i n g . Consequently, d r i l l i n g only for information would probably be insignificant i n this model, even i f i t were possible to include i t . We note that core d r i l l i n g crew weeks are included i n our Geophysics variable. These assumptions mean that the firm i n our model, wouldn't undertake any wildcat d r i l l i n g i f no prospects were expected to be profitable. Theoretically this suggests that the problem i s one i n the realm of' Calculus of Variations. Such an approach i n the context of our study would seem to be grandiose, however. - 3.16 - 48 This approach means that the current d r i l l i n g decision i s a function of prices, costs, the Inventory of Undrilled Prospects and the State of Nature. Also, we could include a function or coefficient representing the firm's attitude toward risk. For example, i f the firm were a r i s k averter i t might value the variance or skewness of expected profits negatively. Then, some negative coefficient associated with variance would become one of the arguments i n the optimum d r i l l i n g decision function.* In general we regard d r i l l i n g as producing the products of o i l reserves and gas reserves j o i n t l y according to a probabilistic production process. Previous analysts have viewed exploratory d r i l l i n g i n this way, using the standard joint product theory. They have argued that -"Shifts i n exploratory effort from prospects with high expected oil/gas discovery ratios to prospects with lower ratios are movements along a product transformation curve", l i k e that i n Figure 3.1. ** FIGURE 3.1 JOINT PRODUCT TRANSFORMATION CURVE C E ^ t 5 * Empirically we may wish to identify such a r i s k coefficient with size of firm. • •  ** E.W. Erickson and R.M. Spann, "Supply Response i n a Regulated Industry: The Case of Natural Gas", The Bell Journal of Economics £ Management  Science, Vol. 2, No. 1, Spring 1971, pp 96. - 3.17 - 49 Our data provides d r i l l i n g information by intent. D r i l l i n g i s classed as either O i l intent, Gas intent, or Both intent. Thus, we define three separate ac t i v i t i e s which together provide the firm with a more or less continuous expected product transformation curve. Oi l intent d r i l l i n g might yi e l d a point l i k e A; Both intent a point l i k e B; and Gas intent a point l i k e C, at any time. Around each point would be an area of l i k e l y outcomes according to the probabilistic nature of the process, but to examine this concept l e t us view the problem i n an "expectations" sense. Each d r i l l i n g intent i s an activity which produces some of both products i n propor-tions determined by the rate of d r i l l i n g , the firm's Inventory of Undrilled Prospects and the State of Nature. Thus, assuming costs of each a c t i v i t y are independent, we may consider each d r i l l i n g intent as an independent a c t i v i t y yielding expected profits which the firm would attempt to maximize separately. 3.4.1. FORM OF EXPLORATION SUCCESS FUNCTION A possible s t a t i s t i c a l specification for the Success function, suggested by R.S. Uhler, uses the Poisson distribution." Consider o i l intent d r i l l i n g , and suppose that the number of d r i l l i n g successes (i.e. pools discovered) i s Poisson with intensity determined by the rate of D r i l l i n g , the Inventory of Undrilled Prospects and the undiscovered pools i n the ground (i.e. one component of the State of Nature). Thus we have, (e .(k (.)) °) o PCX b,o,t = A X (3.17) ft R.S. Uhler, "Production, Reserves, and Economic Return i n a Petroleum Exploration and Reservoir Development Program" , unpublished Paper, U.B.C., March 1972, - 3.18 - 50 —kp(.) Ap (e b .(kp(.)) b) Ptt p . = Ap|X^ . ,1 . ,Dp . ) = - (3.18) o,G,t G1 0,t' o,t G,t . , for A q , Ag = 0,1,2,..., but we assume that the probabilities are such that A Q, A„ cannot exceed X .. G o,t The terms k (.) and k_,(.) are the Poisson intensities which we postulate to O (o be functions with general form as follows: O i l Success Rate from O i l Intent D r i l l i n g ; k (.) T = k T , I mjD T) (3.19) o,o T o,o o,l o,l o,l Gas Success Rate from O i l Intent D r i l l i n g ; W-'T-WVT'V'V' (3-20) To i l l u s t r a t e the theoretical application of these equations we suppose the following particular functional forms. b2 b 3 b5 ko,o (' )T = bl- Xo,T- Io,T- Do,T .'. (3.21) Gas Success Rate from O i l Intent D r i l l i n g : V ( ^ = - K v b 7 t ^ 0 ( 3 - 2 2 ) Ko,GV';T D6' o,T' o,T,JJG,T The expected rate of success from o i l intent d r i l l i n g i s k Q (.)^ for o i l pools and k Q g(.)rp for gas pools. We anticipate that b2 and b^ would be positive and less than one. - 3.19 - 51 3.4.2. EXPLORATION DIRECTIONALITY Directionality measures the extent to which new pool discoveries conform to the well operator's expectations prior to d r i l l i n g . For example, a firm searching for gas which discovers 15 pools of which 12 are gas and 3 are o i l i s said to have an 80% directionality (i.e. ^ which i s the proportion of pools which conform to the d r i l l i n g intent. In our model the expected ratio of o i l pools to gas pools from O i l intent d r i l l i n g would be: b3 b5 k (.)m b. .1 _.D _ b0-b^ o,o T _ f 1 o,T o,T . 2 7 (3.23) b 8 b 1 Q ;-Xo,T ko,G ( , )T V ^ T ^ C T I f b2 = b7 o i l and gas pools would be expected to be produced i n a fixed proportion, at any level of d r i l l i n g , at a given point i n time, according to the term i n brackets i n equation (3.23). In such a case the "Activities" i n Figure 3.1 could be represented by straight line rays from the origin through the .points A, B, or C 0 . . . . . . . The expected percent Oil intent directionality would be: b3 b5 b ri 0 i T. D o i T.ioo ( 3 w ) Note that H T w i l l change as the Inventory of Undrilled Prospects and the State o,i of Nature regarding o i l pools and gas pools change over time. - 3.20 - 52 I f b2 4s b7, the expected directionality i s variable with the rate of d r i l l i n g , at a point i n time.. We would have, b3 b5 b,.I \V T.100 H 1 °'A °? T (3.25) b l " 3 D'5 + b l " 8 > ^ 2  b l , : L o , r D o , T 'l56-io,T*L,G,T-X6,T This means that the products of o i l pools and gas pools are not expected to be produced i n fixed proportions. 3.U.3. FORM OF RESERVES PRODUCTION FUNCTION We can now bring together the variables of D r i l l i n g , the Inventory of Undrilled Prospects and the State of Nature, to specify the functional form of the firm's reserves production function. Consider again, the O i l intent d r i l l i n g . From equation (3.21) we have an expected success rate i n finding o i l pools, and from equation (3.16) we have, the firm's anticipated average pool size. The product of success rate and average pool size gives us the expected reserves. Thus, with the i l l u s t r a t i v e forms of equations (3.21) and (3.22) the expected reserves of O i l and Gas from O i l intent d r i l l i n g are:' b 2 bo br o,o,l 1 o,i o,i o,i o,o,i 1>7 bp b-.n ^  E ( IW = b6-Xo,T-To,T-DG,T-§G,G,T ( 3 ' 2 7 ) and there would be a pair of similar equations for Gas intent d r i l l i n g and for Both intent d r i l l i n g . - 3.21 - 53 •3.5.1. OPTIMAL RATE OF EXPLORATORY DRILLING The expected profits from O i l intent d r i l l i n g w i l l be: m o J - V , r ^ - x ^ r I o ! r D o ! r i o , o , T - P b7 b8 b10 -+" PR,G,T'V Xo J ^ o / r ^ G / r SG,G,T -B " Px,o,T*Xo,T (3.28) Without e x p l i c i t l y accounting for r i s k , and assuming that b 2= by , we have: 6E(nQ T) b 2 - l b 3 b 5 £' b g b 1 Q . g x 7 °b2- Xo,T • ( PR,o )T , br Io,T' Do,T , So,o,T. + ^ C ^ r V ^ r ^ T " ^ , ^ ' 3 o,T = P m for max. (3.29). x,o,T so, with b 0 + 1.0 -1 b3 b 5 . b R b 1 Q ~ l - b 2 X m = { P (Pp „ m.bu.I m.D^ _.§ + PR. p m-b-.I m.D p m.S p m ) .$ } o,T x,o,T 2 R,o,T 1 o,T o,T o,o,T K sb,l b o,i b,l o,b,i (3.30) - 3.22 - 54 As our model has been defined i t seems reasonable to view b 0= b„ which allows for the changing expected proportions of discoveries to be gas or o i l pools over time, but postulates that production i s expected to be i n fixed proportions at any point i n time, given the intent of d r i l l i n g . Furthermore we can consider Gas intent and Both intent d r i l l i n g in a similar manner, except that the directionality measure of equation (3.24) would not be applicable to the Both intent d r i l l i n g . We note, however', equations (3.28), (3.29) and (3.30) do not incorporate a measure of r i s k . We have derived the theoretical equation (3.30) i n order to 'shew the explanatory variables which should be considered i n attempting to explain the rate of exploratory d r i l l i n g . We do not regard the particular functional form as more than an example of how the equation mighx be written for empirical testing. I t i s a stepping off point for the empirical tests which follow i n Chapter 8. .CHAPTER 4 ECONOMIC MODEL OF PETROLEUM PRODUCTION FROM'KNOWN RESERVES IN PLACE Introduction Generalized Production Function Prices and Costs Profit Decisions Cost Curves Period of Production of Mine The Finite Reserves Model An O i l Production Model The Demand Price for Recoverable O i l Reserves 56 SYMBOLS USED IN CHAPTER H Note: The indexes t and T are used to denote the time to which a variable applies. r 1 Wage Rate, Unit Cost of Variable Input or Variable Cost i n Production, e.g. Variable Cost Per Well or Variable Cost Per Bbl r 2 Unit Cost of "Mine Shafts" or Development Wells, $000/Well C Total Cost of Production, $ A Number of Years of Delay between Discovery and I n i t i a l Production, years G Grade of Ore, Proportionality Factor between 0 and 1 -£ Interest Rate or Cost of Money, percent per year L Labor or Variable Input N. 3 Mine Shafts or Wells Installed at tame 3 1 ^o Optimal Number of Wells Po Wellhead Price of O i l , $/Bbl output p R,o Demand Price for Recoverable O i l Reserves, $/Bbl i n ground p Price of Metal of Production Output, $/Unit of output no Present Value Profit at time 0, $ Q Annual Productivity Per Well, 000 Bbls/year or MMCF/year S Reserve Size of Mine or Pool, or Appreciated Recoverable Reserve i n the Pool, units of reserves i n ground T Period of Production, years 57 SYMBOLS USED IN CHAPTER 4, page. 2 U Rate of Production of Ore W Cumulative Production of Ore Y Rate of Production of Metal 4. .ECONOMIC MODEL OF PETROLEUM PRODUCTION FROM KNOW RESERVES IN PLACE 4.1.1. INTRODUCTION The reason for developing an economic model of production from Reserves i n Place i s to provide a framework for linking wellhead prices i n the Output Market with the demand prices for reserves i n the Reserves Market. We begin by describing a generalized theory of production from known reserves. We refer to ore production from a mine, and the model i s general, but of course, our special interest i s petroleum production. 4.2.1. GENERALIZED PRODUCTION FUNCTION Suppose that ore production i s a function of investment i n mine shafts ( o i l wells), miners employed (i.e. variable, factors), and cumulated production. As production cumulates more variable factors must be employed to maintain any given rate of production of ore. In o i l production this could be represented by pumps working harder as pool pressure declines. • We have, N. Mine shafts or wells installed at time j . Labor or variable inputs used at time t Uj. Rate of production of ore at time t . Then the production function of ore i s : t t U. =U( I N.. , L. , m dt) (4.1) x j=o : ^ 0 t where time 0 i s the i n i t i a l year of development, and the p a r t i a l derivatives are: IN J U . U^O , U ^ O u2>o , u2"<o u3>o , u3"<o The production function of "metal" (or saleable concentrate), or crude o i l from o i l production i s : Y t=U t.G t (4.2) where Y^ i s Rate of Production of metal at time t i s Grade of ore at time t ; i.e. the proportion of "metal" i n the mine's output. In o i l production the grade of ore might reflect the water content of barrels of throughput of wells. As pools are depleted the water to o i l ratio often increases markedly. The grade of ore may be considered a function of cumulated production: G t = G(£Jtdt) G'<0, G">0 (4.3) 4.2.2. PRICES £ COSTS Prices, and unit costs, considered exogenous to the firm are: P^ price of metal at time t , supposed constant and expected to remain, i.e. P^ = P C-^  ^  wage rate or unit cost of variable input, supposed.constant, i.e. C l j t = C 1 - 4.3 - 60 i t interest rate or cost of money, assumed constant, i.e. %^ =•£ C 2 ^ unit cost of "mine shafts", or development wells, i.e. C 2 t = C 2 4.2.3. PROFIT DECISIONS Assume that a l l investment i n mine shafts (development wells) i s made at time 0, but that LL. can be changed by varying the variable input during the l i f e of the fixed f a c i l i t i e s . Then, Present Value Profit i s : T T T n = / {P.U(N.L. ,/U.dt).G(/U.dt) - C r L . } . e _ i t d t - N .C 0 (4.4) O Q O t Q t o t I t O 2 which the firm would aim to maximize by choice of N Q and L^ ., t = 0,1,...., T. Parenthetically, i t may be of interest that equation (4.4) can be simplified and generalized i n a manner suitable for calculus of variations.* t Define /Utdt = W , then U t = W (4.5) o and we may rewrite equation (4.4) as: T . n = /II(W(t),W(t),t).e~ dt - N.C 0 (4.6) O o o z which can be solved for a maximum by Euler's equation. The results, however, are not i n t u i t i v e l y meaningful and Figure 4.1 probably il l u s t r a t e s the nature of the optimization decision as well as possible. * See Gordon, R.L. » "A Reinterpretation of the Pure Theory of Exhaustion", Journal of P o l i t i c a l Economy, Vol. 75, No. 3, June, 1967, pp. 274-286. - 4.4 - 61 4.2.4. COST CURVES The t o t a l cost function w i l l have the general form t t C. = C(U. ,ZN. ,/U^dt) (4.7) x x o J o given the exogenous prices and unit costs, t t The ZNj and /U-^dt variables may be viewed as shi f t parameters i n a normal cost function. The shi f t parameter /U^dt i s indirectly controlled by the t ° decision maker and EN.: i s directly controlled. o J 4.2.5. PERIOD OF PRODUCTION OF MINE From equation (4.4) we can see that, i f N Q i s sunk, the decision maker would extend the Period of Production u n t i l t t P.U(N ,L. ,/U.dt).G(/U^.dt) - C, . L. -= 0 (4.8) O T o T O although 1^ . were adjusted optimally. This must be where t o t a l variable costs (C^.Lj.) are optimally adjusted by changes i n the variable input and are equal to to t a l revenue. Or, i n the more usual format, the average variable cost would equal average revenue. This i s ill u s t r a t e d i n Figure 4.1. - 4.5 - 62 FIGURE 4.1 TERMINATION OF PRODUCTION FROM MINE $ per unit ore The arrows indicate how the curves shift as production i s cumulated. Note that the Period of Production may be prolonged i f i t were profitable, or feasible, to put additional capital i n place at time T. This would shift the production function and thus move the Average Variable Cost curve downwards. 4.2.6. THE FINITE RESERVES MODEL In contrast to much of the economics literature on this matter, we have not assumed a f i n i t e reserve i n the above. The fixed reserve model i s a special case of the production function of equation (4.1). Production i s supposed to become discontinuously impossible when t /U1.dt>S, where S i s the reserve size of the mine or pool. Or, i n terms of the o x cost function, equation (4.7), costs would become i n f i n i t e l y large i f cumulated production were greater than S. It appears that, empirically, the f i n i t e reserves model i s almost never a close representation of real production conditions. Raw ores of a l l kinds are vastly greater than those which are deemed to be economically recoverable at any time. For example, the Recoverable Oil Reserves i n Alberta are some 30% of Known Reserves i n Place. 4.2.7. AN OIL PRODUCTION MODEL The non-finite reserves model i s d i f f i c u l t to use for empirical purposes because i t recognizes that ore bodies are heterogeneous as to grade, and i t i s d i f f i c u l t , i f not impossible, to obtain or work with such data. As a result, for purposes of quantification, the size of reserves, such as o i l reserves, are usually measured by their estimated economically Recoverable Reserves, assuming existing prices and unit costs, but with some "reasonable expectations" for future prices, costs and technological improvement. The estimated Recoverable Reserve gives us one point on a schedule of grades which should represent the heterogeneity of the Reserves i n Place. For our purposes i n examining the Alberta situation during the 1945-1970 period we make the following assumptions and simplifications. F i r s t , we assume that expectations of future real costs, prices, well productivities, and the Period of Production are based on the current industry averages. We assume reserves to be f i n i t e and measured by their Appreciated Recoverable Reserve.* Development wells are assumed to be installed at the commencement of production. I n i t i a l development may be delayed after discovery of a pool but i n the case of o i l production i n Alberta the i n i t i a l delay was negligible. I n i t i a l gas pool production, however, has been delayed significantly. * Appreciated Recoverable Reserve i s defined i n Section 5.2.14 - 4.7 - 64 We also assume that variable costs are constant over the production l i f e of the pool, and that variable inputs are not a decision instrument. Accordingly, i n line with prorationing (and the actual industry experience), we assume that o i l pools are produced at a constant rate of output. Thus, the Production Function i s : U t = U = U(N Q) - 0 The production f u n c t i o n may appear as f o l l o w s : U • i o O I N Number of Wells o where T i s the Period of Production, T = S/U. S i s the Appreciated Recoverable Reserve i n the pool. Assuming also that G^  = 1.0 which means the grade of barrels produced i s unity and remains constant over the Period of Production. Then T /U tdt*S T /U +dt>S o L (4.9) Y t = Y = U t.G t=U (4.10) - 4.8 - 65 Exogenous prices are P 0,t ^  *o wh^0*1 ^ s "the wellhead price of crude o i l ; C 2 the unit cost of a development well; C]_ the unit variable cost per barrel production; i i s the interest rate. Then the present value profit i s : T II =/(P„ - C, ).U(N ) . e _ i t d t - C0.N (4.11) O r> O 1 O I O and T = S/U(N ) (4.12) o where the producer chooses the number of development wells which maximizes n . We can integrate equation (4.11) nr-N ^ -£.S/U(N0) n = (P - C.,). u ^ o j . ( l - .2 ) - C 2.N 0 (4.13) O O 1 ^ z u Then differentiate with respect to N Q and equate to zero; 6n n 6U 1 - i S / U ( N ) S -£S/U(N ) 7 ^ = ( P - C, ^  { - . ( 1 - e ) .e }- C 2 = 0 % o 1 6N 0 i : u ( N o ) 2 (4.14) This 1st order condition gives an equation for the optimal N , which i s a func-JPTT O t i o n of P q S Cp C 2, i, S, j^- , given the function U ( N Q ) . 4.3.1. THE DEMAND PRICE FOR RECOVERABLE OIL RESERVES The producer's demand price for the Recoverable Reserves i n the pool w i l l be equal to the present value profits divided by the reserve. That i s ; IL, , given that N was chosen optimally. (4.15) R,o s ° - 4.9 - 66 Dividng equation (4.13) by S, we have P = n o R,o — where N G means optimal NQ. I f i n i t i a l production were delayed by A years the right hand side of equation (4.16) would be multiplied by e"^^. The producer would have to hold the reserve idle for A years and therefore would only pay a lower price for the reserves. For empirical purposes we have data on well productivities and the Period of Production. Consequently, we can rewrite equation (4.16) as follows: { (P - C , ) . — . ( 1 - e ~ i T ) - — } . e ' i A (4.17) ° 1. i.T T.Q where Q = ^ — i s the annual productivity per w e l l , and ^  = T And A i s the delay time i n years between the discovery and i n i t i a l pool develop-ment. Thus we can derive a price for Recoverable Reserves on the basis of observations on wellhead price, variable unit production cost, an appropriate cost of money, the Period of Production, well productivity, the unit cost of development wells, and the delay time between discovery and i n i t i a l production. In Chapter 5 we also consider income taxes, joint products and natural gas production. = (P - C1).Hi!i£l.(l - e ) - C 2 - N o ° 1 i.S S (4.16) R,o 67 CHAPTER 5 RECOVERABLE RESERVES MARKET-EMPIRICAL ANALYSIS OF DEMAND FACTORS The Demand f o r Recoverable Reserves Income Tax Considerations J o i n t Products i n R e s e r v o i r Production Aggregate Industry Demand f o r Reserves Demand f o r O i l Reserves Demand f o r N a t u r a l Gas Reserves 5.2.1 Measurement of V a r i a b l e s 5.2.2 Measurement of Reserves 5.2.3 Wellhead P r i c e s - Summary 5.2.4 Crude O i l P r i c e s 5.2.5 N a t u r a l Gas P r i c e s 5.2.6 P r i c e D e f l a t o r 5.2.7 Operating Costs S Rentals 5.2.8 Royalty Rates 5.2.9 Development Wells 8 Surface Equipment 5.2.10 Gas Pla n t Costs 5.2.11 P r o d u c t i v i t y of Wells 5.2.12 Cost of Money 5.2.13 Income Tax Rates 5.2.14 Industry L i f e Index S A p p r e c i a t i o n 5.2.15 Production Delays i n O i l 5.2.16 Production Delays i n Gas 5.1.1 5.1.2 5.1.3 5.1.4 5.1.5 5.1.6 68 SYMBOLS USED IN CHAPTER 5 Note: The indexes t and T are used to denote the time to which a variable applies a Capital Cost Allowance for Income Tax, a fraction between 0 and 1 1 Operating Costs Excluding Royalties, O i l Wells, $/Bbl r 2 Development D r i l l i n g Costs, $000/well p 3 Development Surface Equipment, $000/well C4 Rental Costs, O i l Pools, $/Bbl output C 5 O i l Royalty Rate, fraction between 0 and 1 C 6 Gas Royalty Rate, fraction between 0 and 1 C7 Gas Well Operating Costs, $/MCF output C8 Rental Costs, Gas Pools, $/MCF output C9 Gas Plant Capital Costs, $/Annual MCF C10 Gas Plant Operating Costs, $/MCF output ^1,^2 Dummy Variables to Account for Changes i n Income Tax Regulations, zero or 1 AG Number of Years of Delay between Discovery and I n i t i a l Production of Gas, years Ao Number of Years of Delay between Discovery and I n i t i a l Production of O i l , years F Capital tax Factor, a fraction between 0 and 1 1 Capital Tax Factor for Equipment, fraction between 0 and 1 69 SYMBOLS USED IN CHAPTER 5, page 2 p 2 Capital Tax Factor for Gas Plants, fraction between 0 and 1 i Interest Rate or Cost of Money, percent per year L Life Index - Ratio of Remaining Recoverable Reserves to Current Annual Production PG Wellhead Price of Gas, t/MCF output Po Wellhead Price of O i l , $/Bbl output P R,G Demand Price for Gas Reserves, C/MCF m ground P R,o Demand Price for O i l Reserves, $/Bbl i n ground G^ Annual Productivity Gas Wells, MMCF/year ^o Annual Productivity O i l Wells, 000 Bbls/year x Effective Income Tax Rate, fraction between 0 and 1 T G Period of Production i n Gas Pools, years T o Period of Production i n O i l Pools, years 70 RECOVERABLE RESERVES MARKET - EMPIRICAL ANALYSIS OF. DEMAND FACTORS 5.1.1. THE DEMAND FOR RECOVERABLE RESERVES In Chapter 4 we derived the equation (4.17) for the producer firm's demand price for the Recoverable Oil Reserves i n a pool. In Section 5.1 we now expand the theoretical model to include empirically related complications such as including additional cost categories, allowing for the impact of income taxes, and allow-ing for gas pool production and joint products. Also, we now consider the aggregate demand of industry for reserves rather than the demand of a single producer firm for the reserves i n a single pool. Section 5.2. describes the various problems of empirical interpretation, data . selection and data analysis, which were required to estimate the demand prices i n the o i l and gas Reserves Markets. The discussion also provides an empirical backdrop for understanding the other s t a t i s t i c a l and econometric analyses of this thesis. 5.1.2. INCOME TAX CONSIDERATIONS An aspect of some significance i n estimating the demand price for Recoverable Reserves has been that Bonus Payments, or any payments to acquire reserves, only became f u l l y deductible for income tax purposes i n 1963. When Bonus payments were tax deductible, producers would be w i l l i n g to pay more for reserves than otherwise. Other income tax regulations, and the varying income tax rate over the 1947-1970 period, must also have influenced a producer's demand price for reserves. For o i l production five cost categories are required i n the demand price equation to treat the impact of income taxes, as follows: Operating Costs excluding Royalties, o i l wells Development D r i l l i n g Costs including well casing Development Surface Equipment such as gathering lines Rental Costs, o i l pools Royalty Rats, o i l - 5.2 - 71 Producers' deductions for income tax purposes have been allowed, as: 1) From 1947-1970, one third of Taxable Income after a l l other allow-ances could be deducted as "Depletion Allowance". Hence the effective income tax rate during most of the 1960's was 33 1/3% (see Table 5.4). 2) With some minor exceptions Capital Cost Allowances have been: Surface Equipment 30 % Gas Plant 6 % 3) Development D r i l l i n g Costs including well casing, Operating Costs and. Royalties have been deductible as expenses for tax purposes, during the period. 4) Rentals payments were not deductible for tax up to 1949. From 1950 to 1962 Rentals were deductible to a maximum annual payment not exceeding $1.00 per acre. Since 1963 Rentals have been deductible as expenses without restrictions. 5) Bonus Payments, or payments to acquire reserves from another company (rather than from the government), made prior to 1952 were not deductible for tax purposes. From 1952 to 1962 they were deductible only i f there was no well on the location and the land was surrendered i n the year for which the deduction was claimed. Since 1963 Bonus payments have been deductible without restrictions. To capture the above effects we introduce the following additional variables: T^ . Effective income tax rate on taxable income, after the 1/3 deple-tion allowance F Capital Tax Factor, which represents the tax effect of Capital Cost Allowances which are calculated on a diminishing balance basis on investment expenditures. I t i s derived as follows: — 5.3 — 72 A $1 expenditure chargeable against income immediately has the effect of reducing income taxes otherwise payable by $1*T where x i s the income tax rate. A $1 chargeable to capital and subject to CCA. also reduces income taxes by $1*T, but not immediately. The tax savings are spread out over a long period of time as the CCA. i s claimed. We can describe this process by applying a Capital Tax Factor to the capital expenditure. The Capital Tax Factor converts capital expenditures to their net.present worth by allowing for future income tax reductions stemming from the expenditure i n present worth terms. I t i s defined as: 2 n 1 r - i - a , T . { l + a ' T + ( 1 ~ a ) + ... +( 1 " a ) > (5.D 1 + i 1 +• i 1 + i 1 + i where a i s the CCA., T i s Income Tax rate and i i s cost of money. When>n-*» , summation of the above geometric progression allows us to write: a.T F = 1 (5.2) n-x» a + i We can use equation (5.2) as the Capital Tax Factor. Note that i t i s a function of the CCA., the income tax-rate and the cost of money. With a = 0.30, T = 0.30, i = 0.15, then F = 0.8 which i s to say that the after tax present value cash outflow equivalent of a $1 spent on a capital item i s $1><F = 1x0.8 = 80 cents. Note that i f the CCA. =1 which means that an item i s expensed for tax purposes, the after tax outflow would be the expense less tax savings collected at the end of one year. The above formula-tio n assumes that taxes are paid at the end of each year. F^ Capital Tax Factor for Equipment, which has a Capital Cost Allowance, a^ = 0.30 Dummy variable; equal to zero i n period up to 1949, equal to one i n 1950 and thereafter T>2 Dummy variable; equal to zero i n period up to 1962, equal to one i n 1963 and thereafter For gas production the following cost categories are required: C6 Gas Royalty Rate C7 Gas Well Operating Costs C8 Rental Costs, Gas pools °S Gas Plant Capital Costs C10 Gas Plant Operating Costs F2 Capital Tax Factor for Gas Plants, which have a Capital Cost Allowance, = 0.06 5.1.3. JOINT" PRODUCTS IN RESERVOIR PRODUCTION Thus far the theoretical model embodied i n equation (4.17) has not e x p l i c i t l y made provision for byproducts i n reservoir production. Crude o i l production often includes the production of Condensate (the light ends of the crude: C5, Cg, C7's), and Natural Gas either from solution or from a gas cap. The Natural Gas may then be processed to yie l d Natural Gas Liquids and . Sulphur. With existing data i t i s d i f f i c u l t to identify Condensate separately from Crude and i n any event the price has been close to the crude price. There-fore o i l pools may be regarded as having potentially marketable natural gas, either i n the form of solution gas or cap gas. Such gas may yie l d the byproducts of Natural Gas Liquids and Sulphur. Many o i l pools, however, do not provide marketable gas. We define gas pools as pools which have marketable .gas reserves but not o i l . These are Non-Associated Gas Pools. Gas pools always produce Pipeline Gas, and most of them produce Natural Gas Liquids and Sulphur. While i t i s true that the joint products of either gas or o i l pools may be produced i n variable proportions, for our purposes which are to concentrate examination on the exploration end of the industry we regard the outputs of the pool production process as being produced i n fixed proportions i n any given pool. Note that we are treating production as having fixed proportions of joint products, given the reserve characteristics of each pool, but exploration as yielding joint products ( o i l or gas reserves) i n proportions varying with the intent of wildcat wells. I t should also be mentioned that while the assumption of fixed proportions i n output production i s reasonable, the production propor-tions of Propane and Butane can be varied over a f a i r l y wide range with any given reserves characteristics. Consequently, the foregoing production models remain valid except that the output unit refers to a composite of the joint products. Likewise, variable costs and prices should be interpreted to apply to the joint product. For example, i f gas byproducts are produced with gas the variable production cost should include the gas gathering and processing costs as well as the byproduct variable costs. 5.1.4. AGGREGATE INDUSTRY DEMAND FOR RESERVES The equation (4.17) was derived i n the context of production from a single pool. We want to derive an equation which represents the price which an explorationist could expect to receive i f he makes a discovery. Basically we assume that the explorationist expects to receive the demand price for reserves which was implied by the most recently available aggregate industry production s t a t i s t i c s . We assume that these are last year's s t a t i s t i c s . Thus, the expected demand price i s assumed to be that implied by the average industry production characteristics of the previous year. Consequently we interpret the variables i n equation (4.17) as averages for the industry. - 5.6 - 75 5.1.5. DEMAND FOR OIL RESERVES We can now write the complete equation for the explorationist's expected demand price for o i l reserves. P P - { — p — - ( 1 ~ e ^ 0 ) . ^ - T ) . ( P 0 . ( 1 - C 5) - C X ) - (1 - D^.O.Cj (1 - T).C 2 + F!.C 3 -i*o }.— (5.3) V 9 o 1 - D 2 - T where the right-hand variables are evaluated for the time period preceding the period to which P R j 0 applies. The units of P R j Q are $/Bbl i n ground. Table 5.1 shows the results of equation (5.3), evaluated according to the data i n Tables 5.3 and 5.4 for the province of Alberta, 1946 to 1970. I t can be seen that the estimated demand price for o i l reserves has been rather constant over the period although tending to decline. I t i s interesting to examine the linkage between the crude o i l wellhead price and the reserves demand price with some i l l u s t r a t i v e values. Consider the data for 1970 from Tables 5.3 and 5.4, and l e t us increase the wellhead price from $2.57/Bbl Output to $6.50/Bbl. T A B L E 5 . 1 ESTIMATED DEMAND PRICE FOR RESERVES At Constant Prices (1950) Current Prices c— Y E A 1 ? OEMAN0 P ' T C E F O " OIL ^ F S ^ V F S P E H A H O P O K E F O » G A S R F S E R / F S OEHASO P R I C E F O " O I L RESERVES DEMAND P * I C E FDR GAS RESERVES s/nnt I N S R O J M I C E N T S / M C F IN GR0JN9 $ / " R L IN GROUND C E N T S / M C F I N GROUND 191.6 .6«.95 . 2 6 9 7 .1.271. .1771. 191.7 .5973 . 3219 .1.623 .251.3 191.8 1.015l» .5 769 .9296 .5283 19<»9 .611.5 .3 751 .5770 .3522 1950 ,5611 . 0 1 1 5 .5011 . 3 1 1 5 1951 .(•13? . 0 2 5 2 .1.699 . 3 2 8 6 1952 .2613 .1.3)1. .3010 .1)638 \ 1953 .2765 .3121 .2169 .3261 1951. .3 736 . 7 2 3 9 .3838 .71.38 1955 .<il<i& 1 .2621 .1.298 1 .32S9 1906 .391'« 1 .0021 .1.181 1.0701. 1957 .3005 . 6 6 9 7 .3235 .7211 1951 .251.? .751.5 .271.2 • J13S 1959 .21.33 . 5 1 0 7 . 2656 .5576 1960 .1997 . 6 5 1 3 .2163 . 9 3 0 7 1961 .1877 I . C329 .2071. 1 . U 1 0 1962 .23A6 1 .6556 .2712 1.8811. 1963 .31.62 3.1.1.05 .1.009 3.901.1. 196l» .3503 3 . 8 0 H .1.070 i . . '«2J7 1965 .2536 <>. 0881 .3007 1..SI.65 1966 .1933 •t.1516 .23(52 5 .1009 1967 .1980 I..2396 .21.76 5. 30 IS 1968 .11.1.1 3 . 7 2 1 7 .1950 I..7562 v 1969 .136> I. 0 9 75 .1122 ^.11.18 1970 .11.01 2 . 5 0 3 3 .2011 3 .3306 CO TABLE 5.2 GAS INPUT DATA f 1 YEAR MELLHEAO P ° T C F S / M C F ( P G ) ROYALTY PATF OYPRO" . (C6 I WELL OPES . COST $/HCF CC7 I RENTALS ? T C . t / « C F « C 5 » N E L L O P O O I J : T I V I T Y M M C F / W W ( O G I PERIOD O F P R O D . YRS. ( T G I DEVELOP. HELL COST S K / W E L L f c O SURF. E Q U I P . C O S T $ K / H E L L ( C 3 ) S / l » L A N T : D S T S ; F / Y R I C 9 I PLANT 0 » E R . COST S /HCFtC IO ) DELAY 3 E r . I N I T . p i m . YRS. «6<^l 19b6 . 1000 .0000 .021. .003 170 .0 » 8 . 0 50.n 1h.fl .1 b . m i l 3 19h7 . icon . 0 ) 0 0 .021. . 003 170 .0 28. 0 50.0 l h . O . l b .031 3 19b8 . 1 0 5 5 .0000 .021. . 003 1 8 0 . 0 28 .0 50.0 l h . O • l h .0 39 3 _19<t9 . 1 0 ? « . 0000 .02>. . 003 1*0.0 2 7 . 5 50.0 ih .n .1 b .0 3 ) b noo .09.79 . 0 000 .021. . 003 130.0 27.0 50.0 l h . O . l b .0 32 5 1951 .0975 .0 355 .021. . 003 180 .0 2 6 . 5 50.0 l h . O .lh . 0 3 ) 7 195? . 130 1 .01.85 .028 .003 n n . n 26 .0 53.7 12.7 .15 .0 77 7 1153 .131 6 .0<»93 .029 .003 1 8 0 . 7 2 5 . 5 65.2 16.0 .16 . 0 2 7 7 1 >5b . 130 1 .053<» .020 . 0 0 3 187. 3 25 .0 60.1 17.0 . l h . 0 1 7 8 1955 .136.3 .0'.68 .022 . 0 0 3 7 1 B . 9 21. .5 60.8 l h . 5 .10 .011. 8 195fi . 1391 .0 ' .57 .023 .003 2 1 9 . 9 ?h.O 73.2 20 . h .11 .017 8 1957 .15?! . .0 393 .0 23 .003 ' 3 0 . 8 2 3 . 5 89.8 25.3 • l"? .022 8 195 8 . 1«. U 0 • 0<t86 .019 .003 265 . 3 23 .0 82.1 20.0 .15 .02? 8 1959 . 1 2 9 7 .0538 .016 .003 30"». 9 2 2 . 5 78.2 73.2 .18 .02? 8 I960 . 1 3 6 0 • 05b0 .015 .002 'hi .1 22.0 90.«. 23 .h .16 . 0 1 7 9 1961 . 1710 .0575 .012 .002 38 8. B 21.8 105.2 ?h .3 . l h .025 9 1962 . 1 8 6 9 .0752 .010 . 0 0 2 h 9 6 . 5 21.6 79.3 20.0 . l b .0 2? S 1963 . 2399 .0863 .011 .002 1.85.1 2 l . l i 86.6 23.3 . l h .021 8 196«. . 2 5 7 7 .081.3 .01} .002 1.81. 6 21 .2 79.7 ?7 .2 .15 .0 2? 8 1965 . 2 7 0 h .0901 .010 .002 (.76.7 21.0 91.6 37 .9 .16 .021 7 1966 . 2 9 7 2 .081.8 .011 .0C2 U71 .7 20 .8 111.1 hh.6 .ie .0 23 6 1967 . 3 2 9 8 .081.6 .011 .001 1.72. 7 2 0 . 6 93.8 56.2 .23 .0 2'4 5 196 A . 3 b 3 h .0856 .013 .001 4 5 2 . 5 20.1. 89.3 73.8 .32 .02(1 h 1969 .311.7 .0816 .01? .001 b i l . b 20 .2 80.8 88.2 .31 . 0 2 ? 3 .1970 . 2 9 1 7 .0879 .015 .001 1.71.5 20.0 76.1. 85.5 .30 . 0 2 3 2 J TABLE 5.3 OIL INPUT DATA f YEAR HELLHEAn PRICE S/RRL tPO) ROYALTY RATE RATin<05) HELL O P E ? . C O S T S / 9 9 L « 0 t » RENTALS " T J . J / R 9 L <CI.) W;LL O ^ O vH I I T I V I T Y MEBL/Y/Wl<QO> PF^IOO O P >RDO. Y R S U - O ) 9EVEL0P . M ; L l COST $ K / H E L L t C 2 l S1IPF. EO.UIP.COST JK/MELLCC3) OELAY B E F . IM IT .PROO. Y R S . ( A O ) 191(6 1.90 .055 .260 .11.7 1 6 . 0 2 7 10.0 50.0 11.. 0 0 191.7 1.99 .355 .250 .11.7 1 2 . 71.9 30.0 50.0 ik.O a 19UB 3.1.7 .051 . 2 5 7 .276 I d . 61.3 35.0 50.0 It..0 G 191.9 3.0 2 . 071 .38 5 . 359 1 5 . 8 6 2 t.0.0 50.0 11.. 0 0 1950 3 .09 .071. . 3 J 9 .1.11 13 . 585 S.5.0 50.0 11.. 0 a 1951 2 .88 . 1 0 5 .312 .3*1 15 .772 1.3.0 50.0 l i . . 0 0 1952 2.51. .111 .31 8 .383 16 . 0 3U V I .0 53.2 1 2 . 7 0 1953 2 . 3 9 . 1 0 2 .305 .372 17 . 031 39.0 65.2 16.0 0 1951. 2 . 6 7 .101. • 3U0 . 2 6 9 1 7 . 2 8 6 37 .0 60.1 17.0 0 1955 2.1.7 . 115 . 2 5 7 .221 1 8 , 3 8 5 35.0 60.8 H . 5 0 1956 2.1.9 .121 .251 .212 19 . 1.1.1. J U . 0 73.2 20.1. 0 1957 2 .66 .122 . 2 5 6 . 2 6 9 1 7 . 0 6 7 33 .0 89.8 25 .3 0 1956 2 . M .100 . 316 . 326 1 3. 180 32.0 82.1 20.0 0 1959 2.53 . 1 0 2 .356 . 3 d . 1 3.975 31 .0 78.2 23 .2 0 1960 2.31. .0 99 .33 8 . 297 1 3. 213 30.0 90.1. 23.1. 0 1961 2 .35 .101. .310 .2 36 11.. " 8 7 29 .0 105.2 21.. 3 0 196? 2.1.6 .130 .32 5 .281 1 5 . 2 7 5 26.0 79.3 20 .0 0 1963 2 . 5 6 .126 .359 .270 11.. 750 2 7.0 86.8 23 .3 0 1961. 2 . 5 6 . 1 2 9 . 31.0 .295 lit.1.30 26 .0 79.7 27 .2 0 1965 2 .55 .131, .32 2 .378 11.. 385 25 .0 91.6 37 .9 0 1966 2 . 5 7 .1 31. . 3 J 3 .318 1 5 . 3 8 5 2i». 0 111.1 1.1.. 6 0 . 1967 2 . 5 6 .11.8 .301 .281 I 7. 986 ?3 .0 93.8 56 .2 0 1968 2 . 5 7 .11.6 . 326 .266 18. ?5<» 23 .0 89.3 73.8 0 1969 2 . 5 7 .152 .233 . 2 * 5 2 0 . 0 9 0 22 .0 80.8 38.2 0 ,1970 2 . 5 7 . 1 5 5 .306 . 2C H 2 3 . 3 0 5 2? .C 76.1. 85 .5 o TABLE 5.4 ECONOMIC INPUT DATA • INTEREST INCOME CAPITAL COST ALLOWANCE "R ICE DUN1Y1 OUMMY2 YEAR RATE TAX RATE SURF E Q U I » SAS PLANTS TNOEX (I I <T«U I ( A l l (A2I (PII O i l (021 191.6 .05bt . ' 0 0 .700 . CF.0 171Q J n i9«»r .0b97 .203 .330 .060 1633 0 19U8 .0b89 .209 .300 . 060 193b a 0 19b9 .0505 .••2 0 .35 0 .060 1983 , fl 1950 • 0b91 .229 .300 . 0 6 0 7112 i 0 1951 .0501 .30b .300 .060 2b02 l 0 1952 .062? .3b7 .70 0 .060 7260 , n 1953 .0620 .727 .700 .060 2207 i 0 195b .0627 .727 .700 .060 2170 i 0 1955 .0560 .713 .30 0 .060 2189 , 0 1956 .0581 .713 .300 . C 6 ) .''256 i 0 1957 .0731 .713 .300 . 0 6 0 227b t 0 19?8,_ .0706 .717 .70 0 .060 7278 , 0 1959 .0731 .733 ,300 .060 2306 i 0 1960 .0660 .337 .300 .060 2309 I 0 1961 .07B5 .733 .70 0 .060 7333 t 0 1962 .07b6 .733 .300 .060 21.00 1 0 1963 .0753 .737 .300 .060 7bb6 1 1 196 b .0755 . 737 . 700 .060 2b5b t ! 1965 .0766 .737 .300 .060 750b 1 1 1966 .08b7 .733 .30 0 • P63 2595 1 • 1 1967 .0956 .737 .70 0 .060 ? 6 b l t ! 1966 .1063 .757 .730 .063 2599 1 1 1969 . l t b 5 .757 .300 .960 782b 1 1 J 9 7 0 .1301 . 761 .70 0 .060 »86b I 1 - 5 . 1 1 - 80 TABLE 5.5 ILLUSTRATIVE RELATIONSHIP BETWEEN OIL WELLHEAD PRICE 8 DEMAND PRICE FOR RECOVERABLE RESERVES* OBSERVED WELLHEAD PRICE DEMAND PRICE FOR OIL RESERVES PR,o ELASTICITY OF P^ on P p ^  o R,o ($/Bbl Output) 2.57 3.00 4.00 5.00 6.00 6.50 ($/Bbl i n Ground) 0.202 0.321 0.600 0.878 1.156 1.296 (0.2783xP o/P R 5 O) 3.5 2.6 1.9 1.6 1.4 1.4 In 1970 the average wellhead price was about $2.57/Bbl output, which would give an implied reserves price of about 20 cents. This i s the price at which the producer could afford to purchase Recoverable Reserves i n the ground and then break even at 13% rate of return as a result of production. Substituting the i l l u s t r a t i v e values into equation (5.3), we have; P p . - -0.5135 + 0.2783Po " , $/Bbl i n ground (5.4) which means that, for every 1 cent change i n wellhead price there i s a 0.28 of a cent change i n the demand price for.Recoverable Reserves. Note that at a well-head price of less than $1.85 Bbl output the demand price for Reserves would be zero. Note that the Period of Production has been assumed to remain unchanged although wellhead prices were changed. The demand price for Recoverable Reserves should be calculated with the appropriate optimum Period of Production for each wellhead price. This would tend to reduce the e l a s t i c i t i e s s l i g h t l y . - 5 . 1 2 - 8 1 The relationship (5.4) i s linear i n the neighbourhood of the chosen levels of development but the e l a s t i c i t y of P q on P R j D i s greater than one because of the cost elements embodied i n the constant terms of equation (5.4). I f the fixed development costs were ignored the e l a s t i c i t y would be less but s t i l l greater •than unity. Only by ignoring a l l costs would the e l a s t i c i t y be unity. When costs are small relative to wellhead price the e l a s t i c i t y i s close to one, as il l u s t r a t e d i n Table 5.5. Before 1963 Bonus Payments and Rentals were not f u l l y deductible. Assuming that they were not deductible at a l l , which would probably have been the producer's assumption when contemplating the purchase of reserves, our dummy variable D 2 would equal zero and demand price for reserves would be less than otherwise. The increase of Pp^ 0 i n 1963 over 1962 (in Table 5.1) results largely from this taxation change. 5.1.6. DEMAND FOR NATURAL GAS RESERVES We treat gas production "from non-associated gas pools with the same kind of equation as equation (5.3). However, there are some significant additional capital costs i n the form of gas plant investments. The equation for the demand price for gas reserves i s as follows: PR,G = { "TTJT * ( 1 " e ~ i T G ) - C ( 1 " T).CP G.(1 " C6> - C 7 - C 1 0 ) - (1 - DjO.Cg] (1 - T ) . C 2 + F1.C3 * F2.C9.QG e" I AG — ————————————————j. (5.5) TG.QG 1 - D 2 - T where the units of P R j G are $/MCF in ground. Note that the gas plant capital cost, Cg, i s the cost of gas plants per new MCF/yr' For example, from Table 5.2 we see that a new annual throughput of 1 MCF required a gas plant investment of 30 cents. - 5 . 13 - 82 From Table 5.1 i t can be seen that the demand price for gas reserves was negligible i n the earlier years of the period, but that i t rose considerably by the mid and late 1960's. The price peaked i n 1967 largely as a result of the high sulphur price. We might mention that our f i r s t estimates of the non-associated gas reserves demand price gave negative prices for 1949, 1950 and 1951. In other words, there appeared to be absolutely no gas related profit incentive to search for non-associated gas reserves. This would not role out some incentive to d r i l l New Field Wildcats with Intent Gas because there was always some chance of find-ing o i l and the demand price for o i l reserves was relatively high. According to our exploratory d r i l l i n g data there was a t o t a l of 196 New Field Wildcats with Intent Gas i n the three years, compared to 547 NFW with Intent Oil or Both. In any event we reestimated the average gas pool cost characteristics i n such a way that none of the estimated gas reserve demand prices were negative, but the year to year relative prices were unchanged. * During the ea r l i e r period a tremendous amount of gas reserves were found i n conjunction with o i l . By 1955, for example, more than half the province's gas reserves were either associated gas or solution gas.** This i s discussed further i n Section 5.2.5. The e l a s t i c i t y linkage between the gas wellhead price and the demand price for gas reserves would be similar to the o i l . * The negative average demand price for gas may have been r e a l i s t i c . I t i s said that companies which discovered non-associated gas i n this period would attempt not to disclose their discovery i n order to save the cost of i n s t a l l i n g casing as required by the Conservation Board before a potential gas well could be capped. ** See Table 5.9. - 5,14 - 8 3 5.2.1. MEASUREMENT OF VARIABLES Tables 5.2, 5.3 and 5.4 i n the previous section show annual data for the 1946-1970 period for the variables of equations (5.3) and (5.4). We now examine the source of these data series, and provide discussion to support their derivation and use. We consider; . Wellhead Prices of: o i l , gas, Pentanes Plus, Propane, Butane and Sulphur . The mix of products i n joint production from o i l pools and gas pools . Average Variable cost of production, including operating costs, royalties and taxes: from o i l pools, and from gas pools, allowing for the joint products where necessary . Cost of development wells and surface equipment including gathering lines and gas plants: for o i l pools and gas pools . Productivity of o i l wells and gas wells . The cost of money of producers (the appropriate interest rate) . Income tax rates . The Period of Production of o i l pools and gas pools . The delay time between pool discovery and i n i t i a l production, for o i l pools and for gas pools. As mentioned i n Section 5.1.4 we generally assume that the values of these variables during the previous year constitute the expectations of explorationists at January 1st of the current year. This means that i f our model i s close to re a l i t y the estimated demand price for Recoverable Reserves at time t - l would approximate the actual price which would be offered by producers for Recoverable Reserves. This price i s assumed to be the demand price expected by explora-tionists at January 1st of time t . The wellhead prices, the average per unit variable costs, the joint production mix, the cost of development wells and surface equipment, and the productivity of wells can be determined directly from the annual industry data. The cost of - 5 . 1 5 - 84 money i s also relatively easy to approximate (although d i f f i c u l t to estimate exactly). The expected delay time between discovery and i n i t i a l production and the Period of Production, however, cannot be measured directly and require indirect estimation. The measurement of these variables i s discussed below. 5.2.2. MEASUREMENT OF RESERVES We have described the output of exploratory d r i l l i n g as the discovery of Reserves i n Place. * But, as discussed, both i n r e a l i t y and i n our theoretical approach, Reserves i n Place are heterogeneous. In Alberta, for example, there i s wide variation i n the recoverability of Reserves i n Place, ranging from a low of some 16% in the Rundle Carbonates to about 67% i n the Keg River Carbonate Pinnacle reefs, as at 1972. Recoverability has also varied over time. In the 1947-1952 period some 50-60% of I n i t i a l Reserves i n Place were described as economically recoverable as Primary Reserves (i.e. without enhanced recovery methods). In 1953 and up to about 1957, with Pembina and other discoveries, the Primary Recovery Factor was about 10% of I n i t i a l Reserves i n Place. In the 1960's the Primary Recovery Factor averaged, on an annual discovery basis, between 20% and 35%. Some of the Rainbow pools have Factors of over 65%. More generally, a l l mining industries exhibit variation i n the quality of ore bodies which are discovered. The absolute quantity of raw Reserves i n Place may not even be a good guide to the value of a reserve. However, unless we can view the value of discoveries as determined by their size and price per unit of size i t i s extremely d i f f i c u l t to apply any theoretical analysis to the exploration process, or to set up and test hypotheses. We need units of measurement which can unequivocally be linked to the units of the flow production output. For o i l we need to relate; (1) the rate of output of barrels of o i l at the wellhead to the reserve of o i l discovered, and (2) the wellhead price of this o i l throughput to the demand price for reserves of o i l i n the ground. * Geological information i s another output from exploratory d r i l l i n g . - 5.16 - 85 The pool size measure of Reserves i n Place appears to be unusable because of i t s lack of uniformity. But, to measure pool size by Recoverable Reserves, as suggested i n our Production Model, leads to the complication that the Recovery Factor i s i t s e l f partly a function of price. For example, an observation that the average size of pool discovered, measured by Recoverable Reserves, tended to decline over a period when real prices were f a l l i n g could reflect that the Recovery Factors were being scaled down, but we might interpret the data to mean that geologically smaller pools were being discovered. The explorationist may be indifferent to the causes of decline i n the value of discoveries, but for analytical purposes (and projections) i t i s necessary to separate them. As well as price changes, technological improvements, especially i n enhanced recovery methods, could bias the Recovery Factor over a period of time. A pa r t i a l solution to these d i f f i c u l t i e s might be the use of Primary Recoverable . Reserves as a measure of size, but this raises other problems i n that some pools may be greatly undervalued. In the purview of the normal economics market analysis there i s no solution to this measurement d i f f i c u l t y and our subsequent analysis uses the Appreciated Recoverable O i l Reserves and the Appreciated Marketable (Recoverable as pipeline gas) Gas Reserves as the measure of pool size. 5.2.3. WELLHEAD PRICES - SUMMARY Wellhead prices are shown i n Table 5.6. The crude o i l prices are calculated from our data f i l e s which contain prices and production by f i e l d as at January 1st each year. The other prices are calculated from average annual revenue and annual production data contained i n CP.A. Annual Reports and A.E.R.C.B. publica-tions. I t should be noted that the natural gas price i s for "Pipeline Gas" ex the gas plant. Pipeline Gas i s less than actual gas production by amounts of wastes and other losses i n the gas processing sequence. Gas Recoverable Reserves, however, are also measured as Pipeline Gas. The gas producer, at the wellhead, receives the Pipeline Gas price less the gas plant long run operating costs per MCF of Pipeline Gas produced. - 5.17 -TABLE 5.6 AVERAGE I^ ELIHEAD PRICES (current $) IN ALBERTA 1946 - 1970 86 YEAR CRUDE OIL ($/Bbl) PIPELINE GAS «: /MCF) PENTANES PLUS ($/Bbl) PROPANE ($/Bbl) BUTANE ($/Bbl) 1 SULPHUR ($/Ton) 1946 1.90 _ _ 47 1.99 6.76 - - - -48 3.47 6.44 3.31 1.18 - -49 3.02 6.24 3.35 1.15 - -1950 3.09 5.75 3.70 1.15 1.36 51 2.88 6.13 3.23 1.15 1.33 52 2.54 9.28 2.87 1.35 1.35 22.54 53 2.39 9.21 2.93 1.20 1.42. 22.37 54 2.67 9.13 2.90 1.35 1.42 22.39 1 55 2.47 3.32 2.84 1.25 1.40 22.42 ; 56 2.49 9.53 2.87 1.26 1.48 21.45 : 57 2.66 10.17 2.72 1.43 1.03 25.41 . 58 2.60 10.75 2.69 1.48 0.98 22.35 59 2.53 9.49 2.34 1.18 1.14 21.80 1960 2.34 9.66 2.34 1.25 1.30 20.06 61 2.35 12.04 2.36 1.31 1.14 20.26 62 2.46 12.71 2.39 1.38 1.12 14.81 63 2.56 13.93 2.92 1.31 1.23 11.60 64 2.56 14.65 2.58 1.06 1.27 11.04 . 65 2.55 14.54 2.58 1.18 1.18 13.88 66 2.57 15.24 2.60 1.39 1.33 21.56 67 2.56 15.69 2.57 1.64 1.42 30.42 68 2.57 15.71 2.71 1.48 1.39 34.54 69 2.57 15.76 2.69 1.27 1.24 22.94 I 1970 2.57 16.50 2.68 1.32 1.19 8.93 Source: E.M.R. Data F i l e : A.E.R.C.B. Publications; The crude o i l price i s at Jan. 1 each year, averages over the whole year. CP.A. Publications. Other prices are - 5.18 - 87 5.2.4. CRUDE OIL PRICES The pricing system for crude o i l i n North America i s i n broad terms a netback or basing-point system. Market prices are set by the location of a competitive 'interface' where the delivered costs of o i l transported from various sources of supply are equalized. The price at a given source of supply w i l l approximate the market price at the 'interface' less transportation cost to that area. This method of pricing i s bolstered when supply within a source area i s controlled by regulation, as applies when production i s prorated, since competition between alternative supplies from the same area i s eliminated. Historical movements i n Canadian o i l prices may be interpreted i n terms of adjustments to meet competitive forces defining a changing market 'interface'. Thus, the expansion of markets for Alberta o i l since the 1947 Leduc discovery necessitated frequent adjustments i n wellhead prices to meet competition from sources of supply i n the United States, which had previously served areas pene-. trated by Alberta supplies. Up t i l l March 1959, the Sarnia, Ontario area tended to be the market equalization point for competing sources of supply, from which i n general f i e l d prices for Alberta o i l were derived by deduction of transporta-tion costs and after appropriate adjustments for crude o i l quality differentials. Subsequently, the market equalization point tended to move south to the Detroit-Toledo area of the United States. The pattern of wellhead price changes since 1947 i n Alberta induced by these changing market conditions and by alterations i n the Canadian-United States exchange rate i s shown i n Table 5.7 which u t i l i z e s prices for crude o i l from the Redwater f i e l d i n Alberta. The table shows a declining trend i n price, 1948 to 1952, reflecting the easterly direction of the market expansion for Alberta o i l i n competition with alternative American supplies from I l l i n o i s , Oklahoma and Texas: the delivered price of American o i l f e l l , ceteris paribus, the further east markets were from Alberta. Table 5.8 shows average wellhead prices calculated from our own prices f i l e . I t i s of interest that the average API has tended to increase gradually over the period. One degree of API i s worth about 2 cents. - 5.19 - 88 In the 1950's prices f i r s t tended to decline but i n 1956/57 the "Suez C r i s i s " stimulated demand for Canadian crude and output peaked i n 1956 at some 144 million barrels per year. World prices dropped i n 1958-1959 i n a situation of general excess supply. This was a stimulus for the U.S. introduction of manda-tory import controls i n the place of former voluntary controls and for the shaping of the Canadian National Oil Policy i n 1961. The National Energy Board was also formed i n 1959. The world excess supply of crude o i l also pushed the major world exporters together and OPEC was formed i n 1960. Through the early 1960's Canada maintained an informal control over i t s exports to the U.S., but by the end of the decade there was l i t t l e restriction. - 5 .20 -TABLE 5.7 POSTED FIELD PRICES FOR RTO\ZATER, ALBERTA, CRUDE OIL 1948 - 1969 89 YEAR DATE PRICE $ per Barre] COMMENTS 1948 Jan. - Nov. Dec. 3.20 2.68 To make Alberta crude competitive at Winnipeg 1949 Sept. 24 2.88 Devaluation of the Canadian dollar 1950 Oct. 16 2.73 Alteration of exchange rate freeing of the Canadian dollar 1951 Apr. 24 June 1 2.44 2.46 To make Alberta crude competitive with I l l i n o i s crude at Sarnia 1952 Apr. 23 Oct. 15 2.315 2.325 Alteration of exchange rate and meeting competition at Sarnia 1953 Mar. 19 2.385 Alteration of exchange rate and meeting competition at Sarnia July 21 2.645 Increase i n world crude prices reflected at Sarnia 1954 Oct. 15 2.555 Alteration of exchange rate 1955 Jan. 7 2.485 Price change i n I l l i n o i s crude and some adjustment for. alteration of exchange rate Feb. 1 2.49 Adjustment of local Alberta Pipeline t a r i f f change 1957 Jan. 16 2.67 General world price increase reflected at Sarnia Aug. 30 2.63 Alteration of exchange rate 1958 Mar. 24 Apr. 12 2.42 2.56 Reductions i n world posted prices and their impact on crude and product prices i n Canadian markets 1961 Sept. 11 2.52 Decline i n Canadian dollar floating exchange rate 1962 May 10 2.62 Devaluation of Canadian dollar to a pegged rate Source:- G.C. Watkins, Proration and the Economics of O i l Reservoir Development, Province of Alberta, Canada, Mimeo, December 1971, pp. 117. - 5 . 2 1 -TABLE 5.8 ALBERTA CRUDE OIL 9 0 YEAR AVERAGE WELLHEAD PRICE AT JAN. 1 ($/Bbl) AVERAGE API OF PRODUCTION (degrees API) PRODUCTION OF CRUDE OIL (MSTB/YR) 1946 1.90 32.2 6,704 47 1.99 32.8 6,382 48 3.47 36.4 10,505 49 3.02 37.2 19,768 . 1950 3.09 36.5 27,149 51 2.88 36.2 45,836 52 2.54 36.4 58,837 53 2.39 36.9 76,702 54 2.67 36.8 87,593 55 2.47 37.1 112,853 56 2.49 37.4 143,682 57 2.66 37.2 136,766 58 2.60 37.5 112,471 59 2.53 37.6 128,802 1960 2.34 37.4 130,499 61 2.35 37.7 157,813 62 2.46 37.9 165,189 63 2.56 37.9 168,750 64 2.56 37.9 175,145 65 2.55 38.0 183,726 66 2.57 38.2 202,499 67 2.56 38.3 230,479 68 2.57 38.4 250,768 69 2.57 38.3 279,026 1970 2.57 38.4 325,592 Source: A.E.R.C.B., and Prices Computer Files at E M.R. - 5 . 2 2 - 9 1 During the late 1950's and the 1960's the crude o i l market situation i n Toronto (Sarnia) appears to have been similar to the i l l u s t r a t i o n of Figure 5.1. FIGURE 5.1 CRUDE OIL OUTPUT MARKET IN TORONTO 1950's S 1960's Canadian Supply Canadian £ U.S. Demand after 1959 World Supply Q2 Q3 Q4 Annual Output In a free market the Canadian suppliers would have sold the amount and Q^-Qi would have been supplied from world sources, a l l at the world market price i n Toronto of Three overriding factors distorted this situation: . Production prorationing i n Alberta, since 1950 .The National O i l Policy of 1961 . The U.S. O i l Import Program of 1959 - 5.23 - 92 1950 - 1961 From 1950 to 1961 Canadian crude o i l wellhead prices (nominal and real) were rather constant or, i f anything, tended to decline i n response to world market pressures i n Toronto. The Alberta excess supply of reserves was preserved through the provincial prorationing scheme, begun i n 1950. Without prorationing the Canadian supply curve would have been shifted rightwards. Canadian output would have increased and the Toronto market may have been supplied wholly from the West at a lower price. Or much of the market may have been supplied from Canadian sources but at the world price i n Toronto. After 1961 After 1961 the National Oil Policy eliminated world supply competition west of the "Ottawa Valley Line". Principally, this meant that the Toronto market was supplied from Canada.* The Toronto market equilibrium was shifted to some lower demand output l i k e Q2 at the higher price P 2. Also, of course, prorationing was s t i l l enforced and the Alberta supply function was to the l e f t of where i t would be otherwise (not shown i n the Figure), and this further reduced the quantity and increased the Toronto price. Under the above conditions we would not expect Canadian crude to be exported to the U.S. Detroit area because the U.S. could import world crude cheaper than the Toronto price of P 2. However, the U.S. restricted imports of offshore crude and thereby raised the Detroit-Chicago price which meant that i t was economic for Canadian crude to be exported i n increasing amounts to this area over the 1960's, and especially after 1967. The demand function for Canadian crude became l i k e the dashed l i n e i n the Figure. Observance of the Ottawa Valley Line was voluntary and price differentials did encourage the movement of products westwards across the Line. Also heavy fuel o i l s were exempt from the regulation. Thus world prices did exert some downward pressure on the Toronto price in spite of the N.O.P. - 5 . 2 4 - 93 The price P3 was close to or coincident with P 2 u n t i l after 1970, but production increased substantially during the 1960's because the actual Canadian supply function (after prorationing) continually shifted right-wards (not shown i n Figure) as the constraints of prorationing were released i n response to the increases i n quantity demanded. By 1972/73 the Canadian producers were approximately back on the true economic industry supply curve with output about equal to aggregate MER production. I t appears to be indisputable that the Canadian wellhead price was supported higher than i t would have been i n the late 1950's and for most of 1960's. Also, output was restrained to be lower than would have occurred i n a free competitive market. For purposes of estimating the Demand Price for Recoverable Reserves we take the actual wellhead price as i t was, and we consider that the existence of the National O i l Policy and prorationing would have led to price expectations being for a continuation of current prices. The effect of prorationing on production delays i s discussed i n Section 5.2.15. Although gas reserves are frequently discovered j o i n t l y with o i l we view them as insignificant i n the incentive to search for o i l . Consequently, our estimation of demand prices, shown i n Table 5.1, does not include the possible value of associated gas, solution gas or gas byproducts. However, when considering the demand price for gas reserves i n Section 5.2.5., we include the value of gas byproducts which can be a significant incentive. 5.2.5. NATURAL GAS PRICES Like o i l prices, gas wellhead prices were established on the basis of a netback system, where the marketing point was Southern Ontario and Montreal i n most of the period, with a growing influence from U.S. markets during the 1960's. Unlike o i l , gas was sold under long-term contracts. The wellhead price of pipeline gas was approximately constant, at around 9.3C/MCF i n the 1952-1956/57 period. In 1957 the Alberta and Southern Company began purchasing Alberta gas for delivery i n California and same price improvement - 5 . 2 5 - 94 occurred. After 1960, when Trans Canada was on f u l l stream, average wellhead prices continued to increase. The average wellhead price increased from some 12C/MCF i n 1961 to around 16£<7MCF i n 1970 (see Table 5.6). The Alberta industry has exhibited the combination of chronic excess supply and constant or r i s i n g wellhead prices, over the 1945-1970 period. I t i s natural to ask: why and how was the excess gas supply maintained for so many years, without a prorationing scheme i n natural gas? On the supply side, a considerable quantity of gas was discovered as a result of o i l directed search. By the year 1970 only some 26% of marketable gas reserves were solution gas or associated gas, but the percent was 59% i n 1950, 49% i n 1955, 314% i n 1960, and 29% i n 1965 (see Table 5.9). That i s , i n the early 1950fs when the Gas Life Index was so high, some half of the reserves would have been solution or associated gas. These would be proved up as a result of o i l develop-ment d r i l l i n g . Also, s t a t i s t i c a l analysis has shown that some 23% of non-associated gas pool reserves' were discovered by exploratory wells which were searching for o i l . In contrast, some 95% of o i l reserves i n Alberta have been discovered by o i l intent exploratory wells. Such supply factors reflect the degree to which gas and o i l are joint products of the exploration process. Speaking roughly, substantial quantities of gas were made available accidentally i n the early part of our study period. To market these gas reserves, large investments i n gathering systems, processing plants and pipelines would be required. Natural gas processing and transmission costs were extremely high relative to finding and extraction costs, which must have been very low i n many cases. Gas transmission costs are also high relative to the transmission of equivalent BTU's i n o i l , and long distance gas transmission was relatively unknown i n the early 1950's. However, these supply related factors do not wholly explain the maintenance of . excessive reserves. The submissions of companies and other interested parties to the A.E.R.C.B. hear-ing into the f i e l d pricing of natural gas i n 1972 suggest that institutional and - 5.26 - 95 TABLE 5.9 INITIAL MARKETABLE NATURAL GAS  DISCOVERIES, BY YEAR, IN ALBERTA, 1945 - 1970 YEAR NON-ASSOCIATED GAS (BCF) ASSOCIATED GAS (BCF) SOLUTION GAS (BCF) ACCUMULATED ASS. 6 SOL. GAS AS PER CENT OF ALL GAS CUMULATED (%) 1945 24 - _ — 46 209 900 2 79.47 47 136 328 112 78.43 48 407 26 71 64.96 49 403 48 92 57.25 1950 364 614 67 59.42 51 669 106 179 53.50 52 1,824 1,526 420 52.66 53 1,955 1,111 873 51.94 54 1,155 1,647 273 54.01 55 1,864 434 126 49.84 56 1,853 61 8 45.37 57 2,407 201 1 563 42.44 58 2,441 222 308 39.64 59 4,045 216 . 442 35.71 1960 999 74 6 34.75 61 4,078 179 63 31.26 62 2,334 270 99 30.04 63 1,467 185 9 29.29 64 458 81 213 29.46 65 548 341 138 29.88 66 150 80 196 30.23 67 2,53.9 10 48 28.62 68 1,729 12 13 27.61 69 512 287 50 27.82 1970 509 20 - 27.56 35,079 8,979 4,371 Source: E.M.R. Reserves File s . - 5 . 2 7 - 9 6 regulatory arrangements were significant i n restricting the use of available supply.* The A.E.R.C.B. controls the permits for export of gas from Alberta and the N.E.B. licenses exports from Canada. Obviously, i t may take several years for a producer with adequate reserves to fi n a l i z e a contract to export gas. The dominant (monopsonistic). role of Trails Canada i n gas purchasing for export was also viewed as having tended to reduce prices and re s t r i c t production. Doubtless these institutional features of the gas industry have delayed produc-tion and reduced prices. Also, however, we should remember that the rise i n aggregate gas production was contingent upon market penetration i n the large markets of Eastern Canada. There are obvious limits to the rate at which consumers would convert from other fuels to natural gas i n the short run. Despite these limitations, Alberta gas production quadrupled i n the 1947-1956 period, and between 1951 and 1962 the annual production growth rate was actually accelerating, peaking i n 1962 with a whopping rate of 46%. Since 1962 the annual growth rates have ranged between 6% and 17%. Throughout the period natural gas has been sold under long term contracts of between 20 and 30 years. Typical contract clauses were: 1) Base price 2) Specific adjustments; i.e. currency value due to variations i n heating value or 3) Periodic price escalations 4) Prepayments 5) Rate of take 6) Time of i n i t i a l delivery 7) Redetermination 8) Favoured "nation" clauses 9) Other miscellaneous matters project, term of contract ; e.g. take or pay, uncertainty i n A l l of these contract factors influence the present value of a gas contract. * A.E.R.C.B., Report on Field Pricing of Gas i n Alberta, Calgary, Aug. 1972. - 5 . 2 3 - 97 For our purposes we have data on the average sale price of pipeline gas each year and knowledge of typical contract provisions. We focus on the Base Price, the Rate of Take and the Delay to I n i t i a l Delivery. We assume that the Base Price each year i s the same as the average price of current gas sales. The Rate of Take which determines the Period of Production i n our model i s estimated from contracts described i n the Report on Field Pricing of Gas i n Alberta.* The delay to i n i t i a l delivery i s estimated i n Section i5.2.16 and includes a l l delay between the time of discovery to the i n i t i a l delivery, not only any delay which may be described i n sales contracts. Most gas contracts contained a price escalation clause whereby prices would increase by small amounts annually. The length of the contracts being aro»:nd 30 years i n the earlier period indicates, however, that price expectations were essentially for l i t t l e change. The price escalation clauses (around 2% per year) which were supposed to cover cost increases were lower than general i n f l a t i o n rates of the period. Several joint products of natural gas processing have sometimes been significant i n determining the demand price for gas reserves. These are sulphur and the Natural Gas Liquids (NGL's); Unprocessed Condensate, Pentanes Plus, Propane, and Butane. The price of NGL's has varied over our study period to some extent, but the price of sulphur changed markedly, r i s i n g from $14.81/Ton i n 1962 to $34.54/Ton i n 1968, and then declining to $8.93/Ton i n 1970. In addition to price v a r i a b i l i t y the gross sales value of these joint-products has been significant compared to sales of natural gas. Over the 1960's the value of NGL's plus sulphur rose from about half that of gas to more than gas by 1967. In 1968 the value of NGL's plus sulphur sales was some $195.0 million and natural gas sales were $170.9 million. In the case of gas reserves we include the value of a l l gas byproducts i n the unit price of natural gas (see Table 5.2). In effect we use a composite commodity consisting of gas and i t s byproducts i n the proportions i n which they were produced each year. These are shown i n Table 5.10. * A.E.R.C.B., Op. C i t . , Aug. 1972. TABLE 5.10 BY-PRODUCTS OF NATURAL GAS PER BCF OF PIPELINE GAS  PRODUCTION IN ALBERTA, 1916 - 1970 YEAR PENTANES PLUS (MSTB) PROPANE (MSTB) BUTANES (MSTB) SULPHUR (LTONS) 1946 • _ 47 - - -48 12.4 0.2 0 0 49 11.6 1.3 0 0 1950 8.8 2.8 0.7 0 51 9.0 4.4 1.5 0 52 9.1 5.3 2.2 0.1 53 8.3 5.9 2.7 0.2 54 7.8 6.0 2.8 0.2 55 8.1 7.3 4.3 0.2 56 8.0 7.5 3.8 0.3. 57 7.4 7.4 4.4 0.6 58 5.8 5.4 3.5 0.4 59 6.6 5.9 4.4 0.3 1960 6.1 5.8 3.9 0.7 61 10.4 5.6 3.9 0.7 j 62 15.1 4.7 3.3 0.9 | 63 25.1 4.9 3.6 1.5 64 29.7 7.1 6.0 1.9 65 30.4 10.6 7.1 2.0 66 30.2 12.5 8.1 1.9 | 67 29.3 13.1 8.5 2.2 68 29.1 13.6 8.9 2.1 69 29.3 13.4 8.4 2.1 1970 29.4 14.1 8.8 2.2 Source: Calculated from CP.A. Annuals. _ r, of! _ 9 9 We can see from Tables 5.6 and 5.10 that the gross value of pipeline gas (i.e. the price of the gas plus i t s byproducts) i n 1970, for example, was: (16.5 + 29.4x0.268 + 14.1x0.132 + 8.8x0.119 + 2.2x0.893)C/MCF = 29<7MCF The gas composite price i s shown for the period 1948 to 1970 i n Table 5.11. Comparison of Tables 5.6 and 5.11 shows that about half of the gross value (before costs) of the composite commodity has been the value of the pipeline gas, depending of course on the relative prices of the five products. The price per MCF of the composite commodity peaked i n 1968, the year i n which sulphur prices peaked. This composite price i s the relevant wellhead price for evaluating the Demand Price for Recoverable Gas Reserves. - 5.31 - 100 TABLE 5.11 WELLHEAD VALUE OF NATURAL GAS, PENTANES PLUS, PROPANE, BUTANE £ SULPHUR IN ALBERTA 1946 - 1970 YEAR TOTAL VALUE ($000) PRICE FOR COMPOSITE COMMODITY U/MCF of Pipeline Gas) 1946 . _ 47 3,184 -48 4,007 10.55 49 4,218 10.29 1950 4,786 9.39 51 5,554 9.75 52 8,326 13.01 53 9,607 13.16 54 11,449 13.01 55 14,576 13.63 56 15,988 13.91 57 20,565 15.24 58 26,918 14.40 59 32,814 12.97 1960 44,058 13.60 61 72,320 17.10 62 116,585 18.69 63 167,190 23.99 64 202,031 25.77 65 231,956 27.04 66 269,226 29.72 67 . 321,834 32.98 68 365,987 34.34 69 390,821 31.47 1970 427,078 29.97 Source: Calculated from CP.A. Annuals. - 5.32 - 101 5.2.6.. PRICE DEFLATOR TABLE 5.12 CANADIAN WHOLESALE PRICE INDEX YEAR INDEX 1946 138.9 47 163.3 48 193.4 49 198.3 1950 211.2 51 240.2 52 226.0 53 220.7 54 217.0 55 218.9 56 225.6 57 227.4 58 227.8 59 230.6 1960 230.9 61 233.3 62 240.0 63 244.6 64 245.4 65 250.4 66 259.5 67 264.1 68 269.9 69 282.4 1970 286.4 Source: Statistics Canada. - 5 . 3 3 1 0 2 5.2.7. OPERATING COSTS S RENTALS Oil well, gas well and gas plant operating costs per Bbl or MCF of output, shown i n Tables 5.2 and 5.3, were estimated from CP.A. annual s t a t i s t i c s . When industry costs were not assigned to o i l or gas we have apportioned them on the basis of the number of capable wells i n the province each year. Industry rentals payments were estimated from data supplied by the Alberta Department of Mines and Minerals. .Several kinds of rentals are assessed at the different stages of the exploration-production process. In the exploration stage-, rentals of IOC /acre minimum are paid for the renewal of reservation permits, rentals of 25£/acre are paid upon bidding for a Crown Reserve D r i l l i n g Reservation and for i t s extension, and rentals are paid for various other permits. In the production phase, production leases generally carry a rental of $1.0/acre. Most of the rental payments are for production leases and we treat a l l rental payments as production costs. Miscellaneous taxes such as municipal and property taxes are also included with rentals. 5.2.8. ROYALTY RATES We have estimated average o i l royalty rates from o i l well productivity data and from st a t i s t i c s of payments to the provincial government." Note that some 19% of mineral rights i n the province are freehold. Our estimates are shown i n Table 5.14. I t can be seen that the estimates from o i l well productivity data and from government payments correspond closely. We have chosen to use the series based on government payments. The rationale for deriving estimates from o i l well productivities stems from the royalty regulations which related royalties to well productivity, as follows. From 1946 to 1972 the o i l royalty schedules were: * Well productivity refers to production per well - 5.34 - 103 GENERAL PROVISIONS 1946 - May 1951 Royalty rate, as a percentage of production, was equal to the square root of the average daily production of a well, for each day the well had been producing i n the calendar month. EXCEPTIONS 1) I f production stemmed from pools under agreements made prior to September 1930, the royalty rate was 10%. 2) For leases issued by the Province after October 1930, the maximum royalty was 15% and minimum was 5%. However, an option was available to producers to pay a f l a t 12s% over the whole period. 3) I f , as a result of an order by the Conservation Board or other government authority, a well operated intermittently the royalty payable was not to exceed the square root of the monthly average daily production for a l l days of the month. June 1951 - December 31, 1972 After 1951 royalty rates were made according to the following schedules: - 5 . 3 5 -TABLE 5.13 OIL ROYALTY SCHEDULES WELL PRODUCTION (Bbls per month) MONTHLY ROYALTY June 1951 - Mar. 31, 1962 0 - 600 600 - 750 750 950 950 — 1,150 1,150 - 1,500 1,500 - 1,800 1,800 - 4,050 4,050 E over Apr. : 1, 1962 0 750 750 - 2,700 2,700 8 over 31, 1972 5% 14% 30 barrels + of 600 barrels) 51 barrels '+' 17% of excess of excess (i.e. excess 85 barrels 121 barrels 1 9 -2 -6 12 l f t + 18% of excess + 19% of excess 225 barrels + 20% of excess 16 2/3% 8% 60 barrels + 20% of excess over 750 barrels 16 2/3% Source: Alberta Regulation 80/62 as amended by Alberta Regulation 14/65, The Mines and Minerals Act, Petroleum and Natural Gas Royalty Regulations, Province of Alberta. Department of Mines and Minerals, Province of Alberta. In the 1951 to 1962 period, we see that for well output less than 4,050 barrels per month, the effective royalty rate was variable with production. Note that average well productivity was only some 1,000 - 1,500 barrels per month (Table 5.16) at this time. The 1962 royalty changes increased royalty rates. - 5 . 3 6 - 1 0 5 TABLE 5.14 AVERAGE ROYALTY RATES*ON WELLHEAD VALUE OF  CRUDE OIL, PIPELINE GAS S GAS BYPRODUCTS IN ALBERTA, 1946 - 1970 YEAR CONVENTIONAL CRUDE OIL ROYALTY RATES ESTIMATED FROM ROYALTY RATES ESTIMATED FROM PAYMENTS TO GOV'T ON ' COMPOSITE OF GAS S PAYMENTS TO GOV'T. (%) - WELL • PRODUCTIVITY (%) NATURAL GAS (%) GAS BY-PRODUCTS (%) BYPRODUCTS (%) 1946 5.5 N.A. — _ 47 5.5 N.A. - — 48 5.1 N.A. - -49 7.1 N.A. - -1950 7.4 N.A. — . - • 51 10.5 12.0 5.7 3.6 52 11.1 11.7 6.3 1.3 4.9 53 10.2 12.1 6.3 1.9 4.9 54 10.4 12.2 6.8 1.9 5.3 55 11.5 12.5 6.1 1.6 4.7 56 12.1 12.5 5.9 1.6 4.6 57 12.2 12.2 5.2 1.3 3.9 .58 10.0 10.2 ' 6.1 1.2 4.9 59 10.2 10.6 6.6 1.0 5.1 1960 9.9 10.2 7.0 1.4 5.4 61 10.4 11.2 6.2 4.8 5.8 62 13.0 12.9 7.5 7.7 7.5 63 12.6 12.7 9.5 7.4 8.6 64 12.9 12.6 8.8 8.0 8.4 65 13.4 12.5 9.1 8.9 9.0 66 13.4 13.0 8.5 8.4 8.5 1 1 67 14.8 13.7 8.2 8.7 8.5 68 14.6 14.1 8.4 8.7 8.6 69 15.2 14.6 8.6 7.7 8.2 1970 15.5 15.4- 8.9 8.7 8.8 Source: Department of Mines and Minerals, Government of Alberta; Alberta Oil and Gas Picture, 1955-1970: Annual Reports, 19^6-1954, C.P.A. Annuals, and Table 5.16. - 5 . 3 7 - 1 0 6 Natural gas royalties are assessed on raw gas production according to a formula which allows for processing costs and other factors which are sometimes at the discretion of the Minister. I t i s not appropriate to elaborate further for our purposes. The resulting royalty rates on the value of pipeline gas and gas byproducts have been around 85% i n the late 1960's. 5.2.9. DEVELOPMENT WELLS S SURFACE EQUIPMENT The average cost of development wells and surface equipment, shown i n Tables 5.2 and 5.3, was calculated from CP.A. annual s t a t i s t i c s and from well data published by "the A.E.R.C.B. We have not included secondary recovery expenditures with the surface equipment costs. The same costs are. used for gas wells and o i l wells. Average well costs have tended to increase over the period, although they declined from 1967 to 1970. Costs are a function of well depths, remoteness of wells from support f a c i l i t i e s , productivity of d r i l l i n g rigs and daily d r i l l r i g costs. 5.2.10. GAS PLANT COSTS Gas plant capital costs, shown i n Table 5.2, were estimated from CP.A. cost data and plant data published i n Natural Gas Processing i n Canada, E.M.R., Ottawa. The trend of r i s i n g plant costs i n the 1960's was caused partly by the increasing emphasis on gas byproduct production during that time. In 1970 the capital cost was 30.cents per new MCF/year. That i s , 30 cents worth of capital was needed to deliver one MCF per year for the l i f e of the plant. 5.2.11. PRODUCTIVITY OF WELLS Well productivities vary widely from pool to pool i n the province, from a few barrels per day to several thousands. To measure average well productivity we have divided production figures by the reported number of capable wells. Produc-t i v i t i e s are often reported on the basis of producing wells (i.e. wells which were actually producing i n the period), but we have chosen to use capable wells for the production model because i t reflects the d r i l l i n g requirement to develop pools by allowing for well workovers and so forth. _ c no — o .oo - 1 0 7 Table 5.15 shows capable o i l and gas wells and annual production. Tables 5.2 and 5.3 show the resulting well productivities. I t can be seen from Table 5.2 that productivity increases i n gas wells have been particularly pronounced over the period. The gas well productivities for 1946 and 1947 were estimated. O i l well productivities were f a i r l y f l a t over the period but increased i n the late 1960's. Note that since 1970 both gas and o i l well productivities have increased substantially as production has risen towards pool capacities (not shown i n Tables). 5.2.12. COST OF MONEY To reflect the equity i n the producer's capital and possible r i s k elements i n petroleum production, industrial bond yields, shown i n Table 5.16 have been inflated by 40%, to approximate a cost of money to producers. Note that we are not attempting to estimate the "real" cost of money to producers after in f l a t i o n effects, but the discount rate which producers were using when deterniining the price they would pay for reserves. 5.2.13. INCOME TAX RATES The impact of income tax regulations on the demand price for reserves has been outlined i n Section 5.1.2. The effective tax rate over the period i s shown i n Table 5.16. - 5 . 3 9 - 108 TABLE 5.15 CAPABLE WELLS S PRODUCTION IN ALBERTA, 1946 - 1970 CAPABLE WELLS ANNUAL PRODUCTION YEAR OIL GAS OIL GAS (#) • (MMSTB) (BCF) 1946 418 200 6.7 N.A. 47 502 200 6.4 N.A. 48 717 211 10.5 38 49 1,242 228 19.7 41 , 1950 1,995 283 27.1 51 ) 51 2,731 317 45.8 57 52 3,661 356 58.7 64 53 4,504 404 76.7 73 54 5,068 470 87.6 88 55 6,135 ' 489 112.8 107 56 7,390 523 143.7 115 57 8,016 585 136.8 135 58 8,536 705 112.5 187 59 9,217 830 128.8 253 1960 9,878 950 130.5 324 61 10,529 1,088 157.8 423 62 10,809 1,257 165.1 624 63 11,437 1,437 168.7 697 64 12,114 1,628 175.4 784 65 12,771 1,800 183.7 858 66 13,162 1,921 202.5 906 67 13,473 2,065 230.2 976 68 13,733 2,356 250.7 1,066 69 13,897 2,692 279.2 1,242 1970 13,971 3,010 325.6 1,425 Note: Oil i s conventionally produced crude o i l . Gas i s pipeline gas. Source: A.E.R.C.B. - 5 .40 - 109-TABLE 5.16 COST OF MONEY S INCOME! TAXES YEAR BTOUSTRIAL BOND YIELD OF 10 INEUSTRIALS (%) APPROXIMATE COST OF MONEY TO PRODUCERS (%) T I EFFECTIVE INCOME [ TAX RATE (%) 1946 N.A. 5.41 20.0 47 N.A. 4.97 20.0 48 3.49 4.89 20.0 49 3.61 5.05 22.0 1950 3.51 4.91 22.0 51 3.58 5.01 - 30.4 52 4.44 6.22 34.7 53 4.43 6.20 32.7 54 4.48 6.27 32.7 55 4.00 5.60 31.3 56 4.15 5.81 31.3 57 5.22 7.31 31.3 58 5.04 7.06 31.3 59 5.22 7.31 33.3 1960 6.14 6.60 33.3 61 5.61 7.85 33.3 62 5.33 7.46 33.3 63 5.38 7.53 33.3 64 5.39 7.55 33.3 65 5.47 7.66 33.3 66 6.05 8.47 33.3 67 6.83 9.56 33.3 68 7.59 10.63 35.3 69 8.18 11,45 35.7 1970 9.29 13.01 36.0 Note: The Effective Income Tax Rate i s 2/3 times actual income tax rate of corporations i n Alberta, which allows for the "depletion allowance" of 1/3 which has been available throughout the period. Bond yields, cost of money and income tax rates apply to Jan. 1 each year. Source: Bond yields from Bank of Canada "Interest Rate Package". Tax rates calculated from Income Tax Act. 5.41 - 110 5.2.14. INDUSTRY LIFE INDEX S "APPRECIATION" Generally speaking, an apparent excess supply of both o i l and natural gas existed during the period of study. Under such conditions we expect the demand price for Recoverable Reserves to be depressed because producers would be holding an excessive quantity of reserves to meet their current and expected production levels. In terms of our model, the excessive reserves on hand would tend to delay the i n i t i a l production from a new pool and would slow down the rate of production. These changes would depress the incentive to explore for new reserves which i s to say that the demand price for new reserves would be depressed. In the case of o i l production there was seldom more than l i years delay, at the most, from the time of a discovery to i n i t i a l production. Prorationing of o i l demand meant that a pool would always be produced soon after discovery, although at a moderate rate. The o i l Period of Production, however, was certainly extended beyond the normal (optimal) period. Production from non-associated gas pools, unlike o i l pools, frequently was delayed for several years after a discovery. The Period of Production of gas pools was also lengthened, as evidenced by the gas contract terms undertaken i n the 1950's and early 1960's. Before we examine the evidence of delay more closely i n Sections 5.2.15 and 5.2.16 we explain two measures used by the industry; the "Life Index" and "Apprecia-tio n " of Recoverable Reserves. The Industry Life Index: In the aggregate, i f we assume that the industry as a whole i s producing at a steady constant rate from a large number of similar reservoirs, the industry "Life Index", defined as the rat i o of Remaining Proved Recoverable Reserves to current annual production, would equal half the period of production. We may imagine new reservoirs being brought into production at a rate just sufficient to offset those finishing t h e i r l i f e . At any point i n time there would be a schedule of reservoirs with - 5.42 - 1 1 1 a range of Remaining Reserves to production ratios from the maximum to the minimum of 1 year. Over time, as a particular reservoir aged i t s Remaining Reserves to production ratio would decline, but the whole industry would maintain a constant ratio. Consequently, under the assumption of a steady state industry the observed Life Index, L, would indicate that reservoirs are being pro-duced with a Period of Production of 2L. Thus twice the Life Index would provide an empirical estimate of the average Period of Production. I f prices and costs were constant over the l i f e cycle of industry production from a region, production would f i r s t grow, temporarily reach an approximate steady state, and then decline. In the early years the Life Index would be close to a maximum, equal to the Period of Production. The Index would always decline, passing through the steady state phase, and eventually reach zero when production ceased. This i s illustrated i n Figure 5.2. FIGURE 5.2 IDEALIZED INDUSTRY PRODUCTION FROM A REGION Time - 5.43 - 112 I t i s useful to hold this schematic outline of regional industry development i n mind when considering the Alberta data. The model suggests lim i t s within which the observed Life Index should l i e i f the industry were operating e f f i c i e n t l y on i t s supply curve. However, there are important empirical divergencies from the idealized model: Reservoirs discovered i n each year range widely i n size (according to a lognormal distribution) and they have a range of production characteristics; large reservoirs tend to be found i n the early stages of development and they tend to have longer Periods of Production than smaller pools; the joint production of petroleum products both i n exploration and development may cause unavoidable distortions i n the Life Index; changing economic conditions or tech-nological change may shift the regional production p r o f i l e ; the Life Index only measures capacity relative to the steady state and i t i s d i f f i c u l t to judge the stage of exploitation of the regional industry. Appreciation of Recoverable Reserves: Reserves are "proved" (and thus designated as recoverable) by deve--lopment and extension wells which simultaneously provide production capability. Hence, for the most part, new discoveries are only "proved up" slowly over a period of several years. This process of proving up new discoveries means that the i n i t i a l estimates of recoverable reserves, made i n the year of discovery, are typically much less than the recoverable reserves which w i l l eventually be identified. Also, over time, other factors may influence the degree to which reserves i n a pool become recoverable. For example, new methods of enhanced recovery may increase the proportion of Reserves i n Place which may be recovered. This process of augmenting (updating) the i n i t i a l estimates of reservoir size i s termed "appreciation of reserves". In Alberta the average hi s t o r i c a l appreciation of the estimated recoverable reserves size of o i l pools has been some 8.3 times, i n 20 years. Natural gas - 5.44 - 113 pools have been appreciated about 4.1 times. The lower appreciation of gas reserves results partly from the higher recovery factor for gas Reserves i n Place which runs around 60% after surface losses, as compared to the current o i l recovery factor of about 32%. In any year the remaining proved Recoverable Reserves may be sub-stantially less than the remaining appreciated Recoverable Reserves from known pools. This may be il l u s t r a t e d by comparison of Life Indexes for Alberta, as i n Table 5.17, especially during the earlier period. The thrust of the above comments on the Life Index and Appreciation i s that the normal industry proved reserves l i f e index must be interpreted with extreme caution, i f used at a l l . TABLE 5.17 REMAINING RECOVEPABLE RESERVES  LIFE INDEXES IN ALBERTA, 1947 - 1970 (YEARS) OIL LIFE INDEXES GAS LIFE INDEXES YEAR PROVED RESERVES APPRECIATED RESERVES PROVED RESERVES | APPRECIATED | RESERVES 1947 15.1 67.8 103.5 N.A. 48 8.3 122.9 90.0 N.A. 49 18.0 87.0 96.6 N.A. 1950 35.3 76.4 88.0 N.A. 51 26.0 62.7 115.8 172.2 52 25.9 54.0 150.9 211.8 53 24.3 66.1 168.3 221.7 54 24.3 59. M 162.3 241.1 55 21.7 46.1 152.2 218.8 56 19.6 36.6 160.5 229.2 57 21.4 47.1 153.2 219.0 58 25.1 59.0 130.2 175.2 59 24.2 59.9 107.7 147.1 1960 25.3 58.3 96.2 119.3 61 22.2 47.5 73.8 105.0 62 21.9 45.6 51.8 74.6 63 22.5 45.2 47.2 68.8 64 33.2 45.3 44.9 61.4 65 33.0 46.4 43.7 56.9 66 33.3 43.4 42.0 53.6 67 30.9 39.0 40.7 51.9 68 30.4 35.7 40.7 47.4 69 27.5 31.6 33.6 39.5 1970 23.3 26.3 31.8 36.6 Source: Calculated from A.E.R.C.B. data. - 5 . 4 6 - 115 5.2.15. PRODUCTION DELAYS IN OIL As mentioned, delays between discovery and i n i t i a l production were insignificant for o i l pools. The Period of Production of o i l pools, however, appears to have been considerably extended. Evidence of the true Period of Production should not show up i n the observed Remaining Proved Reserves to current production ratio (the normal industry "Life Index") because reserves may be proved up slowly, keeping the normal Life Index at a reasonable, "operating inventory" l e v e l , although the Appreciated Life Index may be very high. However, there i s evidence of some excess supply i n the industry's normal Life Index but this was occasioned primarily by the prorationing regulations of 1950 and 1957 which assigned output to pools on the basis of producing wells; hence overdrilling and overproving up of reserves. The observed Proved Reserves Life Index has generally been between 20 and 35 years which may be reasonable i n the early stages of development i n a region, but would have been uneconomically high during the 1960's without prorationing. During the 1960's production ranged between 37% and 54% (1970) of developed wellhead capacity, although surface equipment and pipelines were not installed for much of the excess well capacity. There i s also a seasonality requirement which has been estimated to account for some 20% of the apparent excess well capacity. Overall i t appears that only i n 1974 has the industry started to produce on i t s true supply curve. The 1973 Life Index was about 12 years. I t i s of interest that Gulf Oil Canada has recommended to the National Energy Board that a Life Index of 10 years would be appropriate for the industry during the coming decade.* This implies a Period of Production of about 20 years. Gulf O i l Canada Limited, Submission to the National Energy Board i n the  Matter of the Exportation of O i l , Dec. 1973, pp. 111-5. - 5 . 4 7 - 116 To assist i n estimating the true Period of Production we have calculated the Appreciated Life Index, shown i n Table 5.17. A comparison of the normal Life Index with the Appreciated Life Index shows the extent that known pools were proved up each year. In 1956, for example, remaining recoverable o i l reserves were subsequently found to be about 2 times remaining reserves proved at that time. That i s , with hindsight, Remaining Appreciated Recoverable Reserves were about twice the Remaining Proved Reserves. This means that only some half of "the potential recoverable reserves i n known pools was developed at that time. In terms of the alternative means of obtaining Proved Reserves, described i n Chapter 2, the intensive development margin must have provided a very elastic supply of Recoverable Reserves at that time. We measure the size of pools by their Appreciated Recoverable Reserves. Hence, the Period of Production would be the time over which the Appreciated Reserve i s produced. In the mid 1950's, at the beginning of the regional production cycle, the Appreciated Life Index ,was around 50 years, but by 1970 i t was about half that amount. Another indication of the Period of Production i s given by examining the produc-tion profiles of the twelve largest o i l fields i n the province. On the basis of the average annual production, from these fields from their dates of f i r s t production to 1970, and their Appreciated Recoverable Reserves, we have the following: - 5.48 - 117 TABLE 5.18 APPARENT PERIODS OF PRODUCTION OF TWELVE LARGEST OIL FIELDS IN ALBERTA INITIAL APPROX. AVERAGE FIELD PRODUCTION DATE PERIOD OF PRODUCTION (year) (years) Pembina 1953 44 Swan H i l l s 1957 39 * Redwater 1948 40 Judy Creek 1959 33 Swan H i l l s S. 1959 39 Bonnie Glen 1952 42 Wizard Lake 1951 54 Mitsue 1964 35 Nip i s i 1956 30 Golden Spike 1949 57 Fenn 1950 42 Leduc-D3 1948 30 These f i e l d s , l i s t e d i n order of size, contain over half of the province's I n i t i a l Recoverable Reserves. The weighted average Period of Production for the pools discovered before 1955 i s 43 years, and after 1955 i s 39 years. This data would tend to overestimate the Period of Production because large pools tend to have longer production lives than small pools. Also, the data refers to fields rather than pools. The Appreciated Life Index fluctuated considerably during the 1950's reflecting the large discoveries but relatively small production levels at that time. I t would be unrealistic to view this index i t s e l f as an indicator of the expected -.5.49 - 118 Period of Production, although we are considering the beginning stages of regional production. Expectations would be relatively constant from year to year and the peaks i n the Life Index reflect the very short run changes i n remaining reserves stemniing from discoveries. I t took about Is to 2 years for o i l pool discoveries to be developed to a steady level of production. Overall, considerable judgement must be exercised to estimate the o i l pool Period of Production. Table 5.18 has shown that the average (ex post) Period of Production of the largest fields was around 40-45 years before 1955. I t i s reasonable, then, that the expected Period of Production i n the early 1950's might have been i n the 45 year range. Pools discovered i n the 1955-1964 period probably had an expected Period of Production i n the 30-35 year range. Pools discovered i n 1965 (Rainbow) and thereabouts have been described by Watkins as having a 25 year Period of Production, and recently (1974) the expected Period of Production has been i n the 20 year range.* On the basis of this evidence we estimate the Period of Production as shown i n Table 5.3. 5.2.16. PRODUCTION DELAYS IN GAS I t i s well known that considerable delays have occurred between the time of discovery of non-associated gas pools and their i n i t i a l production. Typically, a lag of some 2 to 4 years has occurred and i n some cases up to 7 or 8 years.** A factor i n this lag has been delays inherent i n gas plant construction, but mainly i t reflects the excess supply situation which prevailed. In addition, of course, there have been poorer quality gas discoveries which were capped and were not produced at a l l during the period of our analysis. With discount-ing, the value to the explorer of a capped gas discovery may be extremely small. * G.C. Watkins, Op. C i t . , Calgary, 1973. ** A.E.R.C.B. Op. C i t . , Aug., 1972, pp. 5-6 to 5-16. - 5 . 5 0 - 119 The Period of Production on gas contracts declined from the 30 year range i n 1950's to around 20 years i n the late 1960's." Gas well productivity has increased from some 180 MMCF/YR/gaswell i n the early 1950's to some 480 MMCT7 YR/gaswell i n the mid 1960's, as shown i n Table 5.2. Also, the Proportion of gas reserves consisting of associated and solution gas has declinec over the period (Table 5.9). In the case of natural gas pools we have i n i t i a l delays of consequence as well as long Period of Production. Gas Pool Delay before I n i t i a l Production: Using the gas sales contract information to indicate rate of production we can calculate the production capacity of non-associated gas pools i f they had been developed and put into production as soon as they were discovered. A comparison of this "Theoretical" production capacity with the actual production from non-associated gas pools can be made, as i n Figure 5.3. I f we assume that pools are approximately of the same size and that they get to be put on production on a " f i r s t dis-covered f i r s t produced" basis, the gap between the two series indicates the average i n i t i a l delay before production which was experienced. Figure 5.3 shows a maximum i n i t i a l delay of around 8 to 9 years i n the 1955 period. The estimated delays are shown i n Table 5.2. A comparison of the shapes of the two growth paths i s also interesting. While the actual production gives the appearance of r i s i n g exponentially, the theoretical production capacity rose extremely fast at the beginning of the period but has always been increasing at a decreasing rate. Around 1973-1975 actual production w i l l be close to capacity, and clearly, the production growth rate from this region w i l l be modified, whatever discovery rate i s realized. A.E.R.C.B. Op. C i t . , Aug., 1972, pp. 8-17. - 5.51 - 120 FIGURE 5.3 NATURAL GAS PRODUCTION £ CAPACITY IN ALBERTA, 1945 TO 1970 Year - 5.52 - 121 Gas Pool Period of Production: A higher Rate of Take on a gas contract would either increase the rate of production from individual pools or i t would reduce the delay before pools were brought into production. We assume that the higher Rate of Take, shown by contracts, increases the rate of production. Thus, we • interpret an average contract Rate of Take of 1 MMCFD per 10 BCF I n i t i a l Recoverable Reserves as a Period of Production of 27.4 years for a separate gas pool. Accordingly, we estimate the non-associated gas pool Period of Produc-tion on the basis of the reported average contract lengths over the period as shown i n Table 5.2.* A.E.R.C.B., Op. C i t , Aug., 1972, pp. 8-17. 122 CHAPTER 6 RECOVERABLE RESERVES MARKET - EMPIRICAL ANALYSIS OF SUPPLY FACTORS 6.1.1 Supply of New Reserves from E x p l o r a t i o n 6.1.2 Aggregate Industry Supply of Reserves 6.2.1 Measurement o f V a r i a b l e s 6.3.1 Annual Rate of E x p l o r a t o r y . D r i l l i n g 6.3.2 The Both Intent 6.4.1 D r i l l i n g E f f i c i e n c y , Cost £ Depth of E x p l o r a t o r y Wells 6.5.1 The Inventory of U n d r i l l e d Prospects 6.5.2 Geophysics A c t i v i t y 6.5.3 Bonus Payments 6.6.1 Success Rate i n F i n d i n g New Pools 6.7.1 P o p u l a t i o n of O i l £ Gas Pools i n Ground 6.7.2 Average Size of Pools 6.8.1 D i r e c t i o n a l i t y , Success R a t i o s £ Pool Size 6.8.2 New F i e l d Wildcats 6.8.3 S i z e of Pools Discovered 6.8.4 The Large Companies £ D i r e c t i o n a l i t y 6.8.5 New Pool W i l d c a t s , Extension Wells £ Tests 123 SYMBOLS USED IN CHAPTER 6 Note: The indexes t and T are used to denote the time to which a variable applies B Proportion of a Pool Expected to be Controlled after Discovery G^ Estimated Undiscovered Gas Pools *o Estimated Undiscovered O i l Pools ""o Inventory of Undrilled Prospects of O i l at Beginning of Period, number of prospects G^ See page 6.1 ^o See page 6.1 o,o Reserves of O i l i n O i l Pools, Bbls i n ground p R,G Demand Price for Recoverable Reserves of Gas, £/MCF i n ground p R,o Demand Price for Recoverable Reserves of O i l , $/Bbls i n ground PX,o Cost of Wells with O i l Intent, $/Well G,G Firm's Anticipated Average Gas Pool Size from Gas Intent D r i l l i n g , MCF i n ground .a, g o,o Firm's Anticipated Average O i l Pool Size from O i l Intent D r i l l i n g , Bbls i n ground 124 6. RECOVERABLE RESERVES MARKET - EMPIRICAL ANALYSIS OF SUPPLY FACTORS 6.1.1. SUPPLY OF NEW RESERVES FROM EXPLORATION In Chapter 5 we have discussed the empirical factors determining the demand side of the Recoverable Reserves Market. We now turn to analysis of the supply side of the market. In Section 2.6.3 we outlined the demand and supply functions for new reserves from exploration and we sketched them in Figure 2.4. We now bring together the analysis of Chapter 2 with that of Chapter 3 with the purpose of defining the supply function more exactly. In Chapter 3 we derived equations (.3.26) and (3.27) for the exploration firm's production functions for expected reserves of o i l and gas from o i l intent d r i l l -ing. We also derived an equation (3.30) for the firm's optimal rate of o i l intent <±?illing. We can use these relationships to specify the firm's theoretical reserves supply curve from o i l intent d r i l l i n g . We may then consider aggrega-tion of supply curves over a l l firms to obtain an industry supply function. For ease of exposition we consider o i l intent d r i l l i n g only, although the firm has been considered to have three a c t i v i t i e s , O il intent, Gas intent, and Both intent d r i l l i n g which may each produce o i l reserves. The short-run expected o i l supply curve (from o i l intent d r i l l i n g ) i s given by substituting the optimal d r i l l i n g rate from equation (3.30) into the production function (3.26). For convenience, l e t us define; b3 b5 -<J> T= b.,.1 m.D T.S „ o,i l o,l o,l o,o,l (6.1) 'G,T- b6 , 3 :o,r D6,T , S6,G,T (6.2) Then from equations (3.30) and (3.26) we have a supply function relating new expected o i l reserves to the demand price for o i l reserves; - 6.2 - 125 -1 YT,— E(R m) = { b 9.P Y „.(Pp T.6 + P p P T.«j>r).B > 2 . , K 0,o,T 2 X,o,l R,o,T o RjG5T b .(po (.6.3'" The sign of the slope of this supply function depends on whether < 1. I f < 1 we have an upward sloping supply function, perhaps l i k e Figure 6.1. Let us assume this.to be the case. FIGURE 6.1 EXPECTED RECOVERABLE RESERVES OF OIL SHORT-RUN SUPPLY CURVE Expected Recoverable Reserves from New Exploration, i n period T, Bbls i n ground Like equation (3.30) the equation (6.3) i s viewed as a possible functional form for the supply function which i s useful mainly as i t suggests which variables should be' included as explanatory i n the econometric work of Chapter 8. Note that the cost of d r i l l i n g , P v should be the cost after income A , O j i taxes. - 6 . 3 - 126 Note the following "shift parameters" i n the function, equation (6.3): 1) I f the cost of exploratory wells increases the expected supply function shifts leftward. That i s , at any o i l reserves price a lower expected reserves i s indicated. 2) I f the price of gas reserves increases the expected supply function shifts rightwards. 3) An increase i n any of the variables contained i n the <J>'s shifts the expected supply function rightwards. Notably, the Inventory of Undrilled Prospects, Io,T can be manipulated by the firm, for example by undertaking geophysics or by purchasing prospects. The other variables, the D's and S's, reflect the State of Nature i n the region, and they w i l l tend to s h i f t the supply function leftwards as they decrease as a result of prospects being depleted i n a region. Clearly, this expected supply function i s valid only for a limited period of time. As pools are discovered i t shifts leftwards; as the expected pool size declines i t shifts leftwards; and these can be offset only by increasing the Inventory of Undrilled Prospects through geophysics, etc. In a well defined region, l i k e the whole or a part of the sedimentary basin of Alberta, we would expect to observe a l i f e cycle during which the supply curve would f i r s t s h i f t rightwards as the industry builds up an Inventory of Undrilled Prospects, but eventually would sh i f t leftwards as depletion would dominate a l l other effects. 6.1.2. AGGREGATE INDUSTRY SUPPLY OF RESERVES Thus far we have developed the theoretical supply equations i n the context of the behaviour of the firm. For aggregation we simply assume that the industry behaves l i k e our typical firm. I f firms are considered to behave independently this assumption i s theoretically reasonable. However, although there are a large number of small exploration - 6.4 - 127 firms i n Alberta (several hundred), i t seems obvious that they don't make decisions independently. There i s a great deal of joint venture a c t i v i t y and sheeplike behaviour. Also, as shown i n other sections of this thesis, the large companies definitely have different exploitation characteristics from the other firms. In any event, to gain an empirical foothold, we assume that the industry responds as the firm model of Chapter 3 suggests. Thus we view equation (6.3) as an industry supply function (for o i l reserves from o i l intent d r i l l i n g ) where the variables are interpreted as industry aggregates or averages. Often however, we w i l l consider the Big Eight companies separately from other companies. In Chapter 5, we estimated the two price variables and we are new concerned with the data requirements to estimate the other variables and parameters contained i n equation (6.3). 6.2.1. MEASUREMENT OF VARIABLES In the remainder of Chapter 6, we present and discuss the various data series required for analysis of the supply side of the reserves market. We consider; . Annual Rate of Exploratory D r i l l i n g . D r i l l i n g Efficiency, Cost S Depth of Exploratory Wells . The Inventory of Undrilled Prospects; Geophysics S Bonus Payments . Success Rate i n Finding New Pools . Size of New Pools . Directionality, Success Ratios S Pool Size - 6.5 -6.3.1. ANNUAL RATE OF EXPLORATORY DRILLING 128 Our exploratory d r i l l i n g f i l e contains an annual count of wells d r i l l e d , by operator company, by class of well, by the designated intent of d r i l l i n g , and other factors, for the period 1945 to 1970. The number of wells d r i l l e d by a l l companies and by the Big Eight companies are shown i n Tables 6.1 and 6.2. To give an overview of this a c t i v i t y for a l l companies, Figure 6.2 i s presented below. FIGURE 6.2 ANNUAL EXPLORATORY DRILLING RATES OF ALL INTENTS, BY ALL COMPANIES IN ALBERTA, 1945 - 1970 600 400 1 - 1 T I r~ 1 -i 1 i I 1 i 1 1 1 i !' i \ k Pi A W vL a t I 5-1 l _ j t \ it a »• Y. res. t i l e l _ . -J —, / / . . . i t / 1 -» / / \ -X A \ ft / 1 / ( t I V i i / I i * / > I J •x — % - I \ c f / \ t t I I . \ -i f / ~t -* \t- W -X 'ie 1-i if fi 1 d 1 1\ I ~T i 1 r f -V t | > ; / / / ; : 1 f f—• 1 1 -— L- i l - p 1- 1 1 1 1945 1950 1960 1970 Year Source: E.M.R. D r i l l i n g F i l e . TABLE 6.1 ANNUAL RATE OF EXPLORATORY DRILLING BY ALL COMPANIES IN ALBERTA, 1946 - 1970 (# Wells) YEAR NFW INTENT NFW EXT. 8 TEST WELLS INTENT TOTAL OIL GAS BOTH OIL GAS BOTH 1946 21 23 22 7 16 7 96 47 23 17 23 21 16 3 103 48 44 43 34 23 2 3 149 49 62 56 93 21 5. 2 239 1950 67 41 90 51 3 2 254 51 93 99 142 42 20 14 410 52 104 95 186 55 39 34 513 53 118 103 146 46 43 27 483 54 93 97 131 66 36 22 445 55 92 80 144 59 48 37 460 56 111 81 164 43 39 29 467. 57 89 79 212 66 56 37 539 58 81 92 200 44 44 29 490 59 104 88 200 61 58 30 541 1960 92 105 167 69 84 58 575 . 61 112 130 154 69 77 29 571 62 244 128 23 i n 118 4 628 63 264 127 26 137 70 15 639 64 265 156 35 155 108 20 739 65 379 189 48 178 97 18 909 66 387 189 12 139 122 1 850 67 317 90 35 340 114 24 920 68 355 127 75 346 144 49 1,096 69 243 132 77 326 210 71 1,059 1970 157 99 30 226 428 100 1,040 Note: The data series appears to contain a discontinuity i n the Intent c l a s s i f i -cation i n 1962. The to t a l wells d r i l l e d s t a t i s t i c s may d i f f e r from other published data because the well date i s according to r i g release data. There may also be differences i n well type. Source: E.M.R. D r i l l i n g F i l e . - 6.7 - 130 TABLE 6.2 ANNUAL RATE OF EXPLORATORY DRILLING  BY THE BIG EIGHT COMPANIES IN ALBERTA, 1946 - 1970 (# Wells) YEAR NFW INTENT NPW EXT. S TEST WELLS INTENT TOTAL OIL l GAS BOTH OIL GAS BOTH 1946 9 10 6 2 7 7 41 47 8 2 4 6 3 1 24 48 15 16 14 7 0 1 53 49 23 25 24 7 1 1 81 1950 17 16 35 10 1 1 80 51 22 23 56 11 11 5 128 52 26 26 54 . 16 7 7 136 53 44 22 47 6 6 3 128 54 43 26 61 33 11 7 181 55 52 26 49 34 4 7 172 56. 48 33 61 26 3 8 179 57 36 28 88 11 9 11 183 58 42 30 86 10 15 6 189 59 46 20 71 27 15 9 188 1960 32 22 47 16 22 14 153 61 45 30 51 30 18 9 183 62 81 20 3 26 18 1 149 63 85 21 2 56 23 o 187 64 104 42 6 56 32 3 243 65 116 58 19 51 28 6 278 66 120 64 5 40 32 0 261 67 93 20 4 136 32 6 . 291 68 106 23 18 138 26 6 317 69 71 24 9 65 22 6 197 1970 27 9 2 32 18 7 95 Note: Wells are cla s s i f i e d as d r i l l e d by the Big Eight i f the principal well operator was one of the major companies; Imperial, Gulf, Chevron, Mobil, Shell, Texaco, Amoco, and Hudson Bay Oil and Gas. Source: E.M.R. D r i l l i n g F i l e . - 6.8 - 131 One significant feature of this data i s that the New Pool Wildcats, Extension and Test Wells increased at a very rapid rate i n the later part of the period, Wiile the New Field Wildcats peaked i n 1965 and have thereafter tended to decline. 6.3.2. THE BOTH INTENT The intent data i s taken from the computer f i l e s of Imperial O i l (The Omega F i l e ) . The intent designation i s described i n the company's computer manual as follows: " The d r i l l i n g intent i s a one dig i t code designating the purpose for which the well i s being d r i l l e d . The d r i l l i n g intent i s assigned to the well at the time of licensing and i s determined by the Scouting Department with advice, i f necessary, from -the Geological Department." I t can be seen from Tables 6.1 and 6.2 that prior to 1962 (1945-1961) the proportion of New Field Wildcats i n Alberta which were designated as intent Both was substantially higher than i n 1962 and thereafter. As knowledge of regional geology was accumulated we might expect less and less wells to be designated as Both, but the change i s so abrupt from 1961 to 1962 that one suspects a data inconsistency. There are other factors which suggest that the Both group might increase i t s share of a l l exploratory d r i l l i n g over time. The most obvious prospects would be depleted, and the relative r i s e i n the price of gas may have induced more d r i l l i n g for Both. The data shows that within the two periods, from.1945 to 1961, and from 1962 to 1970, the proportion of wells designated as Both tends to increase; although i t did begin dropping after 1957. See Figure 6.3. The most l i k e l y reason for the- change i n the Both group was the introduction of the 1962 Mines and Minerals Act ( f i l e d i n A p r i l to May 1962) which prescribes various detailed provision for exploratory d r i l l i n g which were not previously enforced. In particular, wells d r i l l e d under the 1962 Crown Reserves D r i l l i n g Reservation Regulations were specifically to be d r i l l e d "with a view to the - 6.9 - 132 finding of o i l " . * FIGURE 6.3 PROPORTION OF NEW FIELD WILDCATS  DESIGNATED AS HAVING BOTH INTENT IN ALBERTA, 1945 - 1970 100 1 80 60 40 20 T 1 1 I 1 r 1 i • 1 i 1 II -1, I i i 1 i 1 i 1 ..i • -i s ) / \ { H v v \ / \ / t j y Ia it D i : >c C n t j I r / z: / 0 Da- L. be t. j (i an .19 6 _ ) \ / i / \ / 1 ( i 1 L \ > * \ r < • / •Cr / > S. / t i r t 1 1945 1950 1960 1970 Year Source: Calculated from Table 6.1 * Alberta Regulation 284/62, under the MLnes and Minerals Act, 1962. - 6.10 - 133 Anyway, for empirical analysis we treat the intent classification with due respect. For example, we sometimes consider the 1945-1961 period separately from the 1962-1970 period, or we include the Oil intent with the Both intent and so forth. 6.4.1. DRILLING EFFICIENCY, COST S DEPTH OF EXPLORATORY WELLS By computer analysis of approximately a 100% sample of the Alberta Exploratory Well Data we calculated the feet d r i l l e d per r i g day and the average depth of wells for New Field Wildcats, and for New Pool Wildcats, Extension and Test Wells, by year, for the 1945-1970 period. Also, average annual well costs are given on the E.N.R. D r i l l i n g F i l e . Combining these data sources provided Tables 6.3 and 6.4. These tables show cost estimates for the d r i l l i n g of New Field Wildcat and New Pool Wildcat, Extension and Test Wells without including the cost of production casing or equipment. The d r i l l i n g productivity i s also interesting. * Up u n t i l 1965 the industry i n Alberta maintained a continuous improvement i n productivity. The performance since then, however, has levelled off. Consequently, although the cost per r i g day has risen steadily over the whole period the cost per foot d r i l l e d (in current $) tended to decline to a low of $10.81 (for New Field Wildcats) i n 1962. Since 1965 costs per foot d r i l l e d have been rising . We may. also note that the average f i n a l total depth of New Field Wildcats rose more or less continuously u n t i l 1961, but has declined thereafter. One reason for the declining average depth of a l l wells has been the growing emphasis on shallow gas intent d r i l l i n g during the 1960's. A corporation has always been allowed to deduct a l l d r i l l i n g expenses, including casing, for income tax purposes. Hence after tax d r i l l i n g costs depend on the effective income tax rate (Table 5.4). See Figure 6.4. TABLE 6.3 NEW FIELD WILDCAT DRILLING COSTS  S DRILL RIG PRODUCTIVITY IN ALBERTA, 1946 - 1970 FELT DRILLED AVERAGE DEPTH 1 | AVERAGE COST PER YEAR PER RIG DAY OF WELLS FOOT RIG DAY WELL (FT/DAY) (FT) ($/FT) ($/DAY) ($000/WELL) 1946 84 3,659 16.81 1,412 61.5 47 91 .3,461 20.66 1,880 71.5 48 80 4,012 20.44 1,840 82.0 49 94 4,572 18.13 1,704 82.9 1950 113 4,861 15.61 1,764 75.9 51 109 4,661 16.34 1,781 76.2-52 117 4,476 14.24 1,666 63.7 53 130 4,848 15.70 2,041 76.1 54 131 5,187 15.83 2,073 82.1 55 129 5,686 14.79 1,908 84.1 56 136 5,704 15.60 2,122 89.0 57 153 5,365 15.22 2,329 81.7 58 170 5,521 15.15 2,576 83.6 59 194 5,321 12.34 2,394 65.7 1960 190 6,068 13.22 2,512 80.2 61 211 6,096 11.27 2,378 68.7 62 239 5,567 ' 10.81 2,584 60.2 63 249 5,743 11.40 2,839 65.5 64 260 5,479 14.44 3,754 79.1 65 266 4,859 12.74 3,389 61.9 66 245 4,961 15.77 3,864 78.2 67 248 4,865 19.37 4,804 94.2 68 260 5,077 16.88 4,389 85.7 69 256 5,235 14.80 3,789 77.5 1970 216 5,467 22.48 4,856 122.9 Note: Dollars are non-constant $. D r i l l i n g covers a l l Intents. Depth i s Final Total Depth. Source: Computer Analysis of Alberta E.R.C.B. Well Files and of E.M.R. Dr i l l i n g F i l e . Costs based on Approx. 1/3 sample of a l l d r i l l i n g . - 6.12 - 135 TABLE 6.4 NEW POOL WILDCAT, EXTENSION 6 TEST WELL DRILLING  COSTS S DRILL RIG PRODUCTIVITY IN ALBERTA, 1946 - 1970 FELT DRILLED AVERAGE DEPTH AVERAGE COST PER YEAR PER RIG DAY OF WELLS FOOT RIG DAY WELL (FT/DAY) (FT) ($/FT) ($/DAY) ($000/WELL) 1946 - - - — — 47 N.A. N.A. 14.23 - -48 99 4,374 12.01 1,190 52.5 49 134 4,545 13.31 1,784 60.5 1950 139 4,481 12.24 1,701 54.8 51 142 4,003 13.16 1,869 52.7 52 163 3,981 12.09 1,971 48.1 53 161 4,058 11.07 1,782 44.9 54 173 4,475 12.63 2,185 56.5 55 199 5,274 12.11 2,410 63.9 56 203 5,280 11.50 2,335 60.7 57 218 4,998 12.02 2,620 60.1 58 181 5,440 11.90 2,154 64.7 59 187 5,745 10.65 1,992 61.2 1960 258 5,362 11.05 2,851 59.3 61 273 5,919 11.23 3,066 66.5 62 278 5,879 10.41 2,894 61.2 63 273 5,595 11.41 3,115 63.8 64 318 5,251 11.30 3,593 59.3 65 294 5,238 12.36 3,634 64.7 66 303 4,833 11.50 3,485 55.6 67 280 5,045 14.44 4,043 72.8 68 299 5,000 14.33 4,285 71.7 69 303 4,675 12.34 3,739 57.7 1970 339 4,126 14.56 4,936 60.1 Note: Dollars are non-constant. D r i l l i n g covers a l l Intents. Depth i s Final Total Depth. Source: Computer Analysis of Alberta E.R.C.B. Well Files and of E.M.R. D r i l l i n g F i l e . Costs based on approx. 1/3 sample of a l l d r i l l i n g . - 6.13 - 136 FIGURE 6.4 AVERAGE FEET DRILLED PER DRILL RIG DAY IN ALBERTA, BY NEW FIELD WILDCATS bO rH Millions Ft Drilled by NFW Cumulative, 19U5 - 1970 Source: Analysis of E.M.R. D r i l l i n g F i l e - 6.14 - 137 6.5.1. THE INVENTORY OF UNDRILLED PROSPECTS We have described this inventory i n equation (3.3). Undrilled prospects are assumed to be gathered from undertaking geophysics activity and from Bonus payments. They are depleted by d r i l l i n g . 6.5.2. GEOPHYSICS ACTIVITY I t i s interesting that geophysics ac t i v i t y i n Alberta peaked i n 1952 (Table 6.5). This pattern of geophysics can be compared to that of d r i l l i n g rates shown i n Figure 6.2. Parenthetically, we note that Van Meurs observed a similar pattern for the exploration data for Libya. * He writes; 11 The succession of the different exploration methods can be studied i n the figure below which il l u s t r a t e s exploratory a c t i v i t y i n Libya i n the ten years after 1956. The search for o i l and gas beneath the continental shelf i s characterized by a f i r s t peak of gravimetric surveys, followed by intensive seismic work, with, f i n a l l y , d r i l l i n g needed to prove the presence of productive reservoirs." ft A.P.H. Van Meurs, Petroleum Economics and Offshore Mining Legislation, Amersterdam, Elsevier Publishing Company, .197.1, pp. 7. - 6.15 - 138 FIGURE 6.5  EXPLORATION IN LIBYA, 1956 - 1966 Source: Bull. Am. Assoc. Petrol. Geologists, 1966, pp.1696. A similar figure could be made with the Alberta data. The geophysics ac t i v i t y peaked i n 1952 but New Field Wildcatting peaked i n 1965. Our geophysics data includes gravity and magnetic with seismic but does not include f i e l d geology. Table 6.6 shows the participation of the Big Eight companies i n geophysics i n 15 of the 25 years of the study period. The large companies have always under-taken proportionately more geophysics than wildcatting. But they have also d r i l l e d deeper and more costly wells. - 6.16 - 13S TABLE 6.5 GEOPHYSICS CREW WEEKS ACTIVITY BY  COMPANIES IN ALBERTA, 1946 - 1970 YEAR BY ALL COMPANIES BY BIG EIGHT 1946 400 N.A. 47 695 N.A. 48 1,818 N.A. 49 2,767 N.A. 1950 4,238 2,173 51 5,732 3,441 52 7,0.00 N.A. 53 6,700 N.A. 54 5,404 N.A. 55 4,552 N.A. 56 4,033 2,297 57 3,220 2,478 58 2,075 1,635 59 1,978 1,336 1960 1,819 1,022 61 1,685 859 62 1,870 N.A. 63 1,558 N.A. 64 1,420 948 65 1,593 1,122 66 2,500 1,328 ; 67 2,712 1,385 68 2,280 1,171 69 2,412 802 1970 1,484 462 Sources: International Oil Scouts Association, International Oil and Gas Development Year Book, Exploration Volumes 1947-1970, and Canadian O i l Scouts Association, O i l and Gas Activity i n Canada, Volumes 1963-1970. - 6.17 -TABLE 6.6 LARGE COMPANIES SHARE OF GEOPHYSICS CREW WEEKS S EXPLORATORY DRILLING IN ALBERTA, 1946 - 1970 "BIG EIGHT" COMPANIES SHARE OF YEAR GEOPHYSICS (%) NEW FIELD WILDCAT WELLS (%) ALL EXPLORATORY WELLS (%) 1946 N.A. 37.9 42.7 47 N.A. 22.2 23.3 48 N.A. 37.2 35.6 49 N.A. 34.1 33.9 1950 51.28 34.4 31.5 51 60.04 30.2 31.2 52 N.A. 27.5 26.5 53 N.A. 30.8 26.5 54 N.A. 40.5 40.7 55 N.A. 40.2 37.4 56 56.96 39.9 38.3 57 76.96 40.0 34.0 58 78.80 42.4 38.6 59 67.55 35.0 34.8 1960 57.19 27.8 26.6 61 50.98 31.8 32.1 62 N.A. 26.3 23.7 63 N.A. 25.9 29.3 64 66.76 33.3 32.9 65 79.02 31.3 30.6 66 53.12 32.2 30.7 67 51.07 26.5 31.6 68 51.36 26.4 28.9 69 33.25 23.0 18.6 1970 31.14 13.3 9.1 Source: E.M.R. Exploratory Well F i l e , and International O i l Scouts Associa-t i o n , and Canadian Oil Scouts Association Annuals, 1947 - 1970. - 6.18 - 141 6.5.3 BONUS PAYMENTS From 1946 to 1949, a l l the rights for petroleum and natural gas were disposed of through the Provincial Lands Act and were administered by the Alberta Department of Lands and Mines. Since A p r i l 1, 1949 when the Department of Mines and Minerals was formed (under the Mines and Minerals Act of 1949) to replace the old Alberta Department of Lands and Mines, these regulations have been administered by the Department of Mines and Minerals. The Mines and Minerals Act was rewritten i n 1962, effective June 1, 1962 . and several ammendments concerning land disposal and royalties have taken place. T i t l e to the o i l , gas and other mineral rights underlying lands i n the Province are divided approximately as follows: the Alberta Provincial Government 81%, about 163 million acres, freehold 10% and Federal Government (Natioml Parks and Indian Reservations) 9%. As arrangements for leasing and development of the freehold rights are generally a matter to be settled between the owner and the prospective operator, we do not deal with those here, but we consider the system employed i n obtaining leases and reservations for the exploration and development of Crown-owned properties. Over the period exploration rights have been granted by; Petroleum and Natural Gas Reservations (since 1946) Petroleum and Natural Gas Permits (since 1962) Crown Reserve D r i l l i n g Reservations (since 1954) Crown Reserve Natural Gas Licences (since 1952) Natural Gas Licences (since 1951) Production leases have been granted by; Petroleum and Natural Gas Leases (since 1946) Natural Gas Leases (since 1952) Petroleum Leases (since 1952) The normal process of securing land and production rights i n Alberta i s aligned to the sequence of exploration then development. The alternatives available to companies since 1962 are shown i n the Flow Diagram on page 6.20. - 6.19 - 142 Reservations, permits and licences for exploration rights are disposed of by sealed tender (plus a small fee and a subsequent rental etc.). Such rights also include an option on the part of the explorationist to convert part (or a l l i n some cases) of the exploration area to a production lease. The P, £ N,G. Reservations can convert up to 50% of the area to lease; the P. S N.G. Permits can convert up to 100%, and the Crown Reserve D r i l l i n g Reservations are usually set up to allow for conversion of a maximum of 25%. The conversion option for Gas Licences depends upon the number of commercial gas wells completed. The P. £ N.G. Reservations and Permits are exclusive exploration licences to d r i l l i n any zone for o i l or gas. The Crown Reserve D r i l l i n g Reservations are licences requiring the d r i l l i n g of a test well to a specified formation, i n search of o i l . Both the Natural Gas Licences are for' gas intent wells to specified zones. Production leases are obtained either as a result of exercising the options mentioned above, or by sealed tendering for Crown Reserve lands. Generally, a l l of the rights and leases are made available by sealed tendering. However, the lands posted for tender are often those requested by o i l operators. In each case, the government receives a bonus payment, a f i l i n g fee and rental payments. In most instances there are also performance obligations to be f u l -f i l l e d by the lessee. As the Flow Diagram on page 6.20 shows, there were various options and alternatives available to companies i n securing prospects. The Bonus payments for production leases are obviously for much more certain prospects than Bonuses for exploration rights. However, a l l Bonuses are paid for undrilled prospects and such investments always lead, i n the f i r s t instance, to exploratory d r i l l i n g . The Crown Reserve D r i l l i n g Reservations are primarily for o i l exploration. The P. £ N.G, Reservations and . Permits are for either o i l or gas and the Natural Gas Licences are for gas. The P. £ N.G. leases are mainly for o i l (but not always), and the Natural Gas Leases are for gas. Only a handful of Petroleum Leases have ever been issued. - 6.20 - 143 For lack of better independent information, we assign a l l the Crown Reserve D r i l l i n g Reservations, half the P. 8 N.G. Reservations and Permits, and some two thirds of the P. 8 N.G. Leases to o i l , * and the remainder to gas prospects. The resulting Bonus payments for o i l and gas prospects are shown i n Tables 6.7 and 6.8. FLOW DIAGRAM OF DISPOSAL OF OIL AST) GAS RIGHTS, 197U EXPLORATION RIGHTS i Bonus Bidding j—> | P.&K.6. Reservations J ^ _P.SN.G. Permits Cram Reserve dr i l l i n g Reservations !~If Gas" ""! i Discovered L ... Katural G3S Licence Crown Reserve Natural Gas Licence r if ou Discovered 1 1 _ l I f Gas |_ J_Di5CoveredJ~ PRODUCTION RIGHTS  Bonus Bidding Petroleum and Natural Gas Lease Natural Gas Lease f l f Oil J ^Discovered ! 1 Petroleum Lease * Approximately 2/3 of a l l gross revenue of the industry has been for o i l . A l l Reservations and Permits were for o i l prior to 1953. - 6.21 - 144 TABLE 6.7 ESTIMATED BONUS PAYMENTS APPLICABLE TO OIL  PROSPECTS IN ALBERTA, 1946 - 1970 (in $'000) YEAR CROWN RESERVE DRILLING RESERVATIONS P. 8 N.G. RESERVATIONS 8 PERMITS P. 8 N.G. LEASES TOTAL OIL BONUSES 1946 _ . _ _ mm 47 - - - • -48 - 53 2,070 2,123 49 - 195 13,110 13,305 1950 - 232 24,139 24,371 51 - 265 9,925 10,190 52 • - 153 14,798 14,951 53 - 1,987 • 11,605 13,592 54 7,245 16,582 15,769 39,596 55 8,259 6,772 26,972 42,003 56 3,858 552 44,708 49,118 57 11,503 7,811 27,045 46,359 58 11,882 5,341 18,052 35,275 59 14,241 . 2,889 33,635 50,765 1960 9,227 735 26,507 36,469 61 10,660 240 21,052 31,952 62 11,212 1,656 10,753 23,621 63 18,777 722 17,507 37,006 64 23,660 787 39,875 64,322 65 39,804 - 53,215 93,019 66 21,568 196 51,162 72,926 67 18,692 31 45,069 63,792 68 30,977 704 40,034 71,715 69 44,565 7,039 28,796 80,400 1970 8,069 97 10,359 18,525 Source: Calculated from data provided by Alberta Department of Mines and Minerals. TABLE 6.8 ESTIMATED BONUS PAYMENTS APPLICABLE TO NATURAL  GAS PROSPECTS IN ALBERTA, 1946 - 1970 (in $'000) YEAR P. 8 N.G. RESERVATIONS S PERMITS P. 6 N.G. LEASES NATURAL GAS 1 1 TOTAL ! GAS BONUSES LICENCES LEASES 1946 _ 47 - - - - -48 - 1,019 - - 1,019 49 - 6,457 - - 6,457 1950 - 11,889 - - 11,889 51 - 4,888 - - 4,888 52 153 7,289 - - 7,442 53 1,987 5,716 1,239 232 9,174 54 16,582 7,767 876 31 25,256 55 6,772 13,285 303 9 20,369 56 552 22,021 962 7 23,542 57 7,811 13,320 714 15 21,860 58 5,341 8,891 996 580 15,808 59 2,889 16,567 1,304 303 21,063 1960 735 13,056 3,649 56 17,496 61 240 10,369 1,165 907 12,681 62 1,656 5,296 2,515 67 9,534 63 722 8,622 179 117 9,640 64 787 19,640 - 71 20,498 65 - 26,210 397 35 26,642 66 196 25,199 721 77 26,193 67 31 22,198 1,688 12 23,929 68 704 19,719 1,205 49 21,677 69 7,039 14,183 558 1 21,781 1970 97 5,102 1,952 12 7,163 Source: Calculated from data provided by Alberta Department of Mines and Minerals. - 6.23 - 1H6 6.6.1. SUCCESS RATE IN FINDING NEW POOLS There are various ways to measure the success rate of exploratory wells. The usual measure i n the industry classifies a well as successful i f i t becomes a producer. The problem with such a measure for our purposes i s that the amount of production or the amount of reserves which should be attributed to a produc-ing well cannot be defined except through some kind of arbitrary assignment. Consequently, and especially because our interest i s primarily with New Field Wildcats, we have defined a well as successful i f i t i s the f i r s t well penetrating an o i l or gas pool. In other words, we define wells as successful only i f they discover a new pool. An exploratory well may become a producing well but not be the f i r s t well into a pool. Such a well i s not counted as a discovery well i n our s t a t i s t i c s . Defining successes as discovery wells allows us to associate the reserves of the pool which i s discovered with the successful well. We have given considerable effort to constructing a computer f i l e of o i l and gas pools showing reserves etc. and discovery well information for each pool. As a consequence we have data showing for each d r i l l i n g intent the number and type of pools discovered showing their reserves size and so forth. Tables 6.9 to 6.12 show the number of o i l and gas pools discovered annually by each well class and intent. In this data, as described i n Section 3.2.2, an o i l pool signifies the presence of . recoverable o i l reserves and there may be associated or solution gas reserves, but a gas pool i s defined as a non-associated gas pool. The Oil intent New Field Wildcat success ratio i s shown graphically i n Figure 6.10. - 6.24 - 147 TABLE 6.9 ANNUAL RATE OF DRILLING SUCCESS IN FINDING OIL POOLS  BY ALL COMPANIES IN ALBERTA, 1946 - 1970 (# o i l pools) YEAR N.F.W. N.P.W. EXT. S TEST WELLS TOTAL INTENT INTENT OIL GAS BOTH OIL GAS BOTH 1946 1 1 — — _ 1 3 47 4 - • - - — - 4 48 4 - 1 1 - 1 7 49 10 2 - - - - 12 1950 12 3 3 3 - - 21 51 15 2 1 5 - - 23 52 21 2 6 7 - 1 37 . 53 13 2 6 4 3 1 29 54 14 2 3 5 - 1 25 55 15 4 3 3 - 1 26 56 16 - 5 1 1 3 26 57 9 - 2 8 - 5 24 58 13 - 1 2 - 2 18 59 13 1 4 3 3 5 29 1960 11 1 3 5 3 2 25 61 13 2 2 7 1 1 26 62 13 6 1 4 3 - 27 63 19 3 4 9 5 1 41 64 17 7 1 10 1 2 38 65 18 3 2 13 5 1 42 66 39 3 - 14 3 - 59 67 31 3 1 112 5 1 153 68 15 - 3 122 3 5 148 69 9 - 1 89 3 4 106 1970 16 13 1 30 Source: E.M.R. D r i l l i n g F i l e . - 6.25 - 148 TABLE 6.10 ANNUAL RATE OF DRILLING SUCCESS IN FINDING GAS POOLS  BY ALL COMPANIES IN ALBERTA, 1946 - 1970 (# gas pools) 1 YEAR N.F.W. v — — • ... I N.P.W. EXT. £ TEST WELLS TOTAL INTENT ! 1 f INTENT OIL GAS BOTH OIL GAS BOTH 1946 - 2 1 _ T _ 4 47 - 5 1 - 1 1 8 48 - 4 1 - - - 5 49 1 14 3 2 1 - 21 1950 2 9 1 - - - 12 51 3 29 8 1 1 - 42 52 5 21 8 - 3 3 40 . 53 4 19 7 3 3 - 36 54 4 32 4 1 3 - 44 55 8 20 10 3 4 3 48 56 3 13 12 2 5 8 43 57 3 .16 5 3 5 4 36 58 5 27 4 - 11 2 49 59 9 19 8 1 16 1 54 1960 6 34 10 6 19 2 77 61 6 29 3 2 18 2 60 62 20 9 - 5 17 - 51 63 16 16 4 10 9 1 56 64 11 19 7 4 9 1 51 65 13 23 3 2 17 1 59 66 10 21 1 6 16 - 54 67 15 11 3 17 15 4 65 68 6 16 8 12 15 10 67 69 2 10 3 13 35 4 67 1970 - 3 1 7 48 9 68 Source: E.M.R. D r i l l i n g F i l e . - 6.26 - 149 TABLE 6.11 ANNUAL RATE OF DRILLING SUCCESS IN FINDING OIL POOLS  BY BIG EIGHT COMPANIES IN ALBERTA, 1946 - 1970 (# o i l pools) N.F.W. N.P.W. EXT. 8 TEST WELLS YEAR INTENT INTENT TOTAL OIL GAS BOTH OIL GAS BOTH 1946 - 1 — — 1 2 47 2 - - - • - 2 48 3 - 1 -• - - 4 49 7 - - - - 7 1950 6 2 - 1 - - 9 51 4 2 - 2 - - 8 52 5 ' 2 1 2 - - 10 . 53 4 1 4 2 1 - 12 54 6 2 1 1 - - 10 55 9 2 2 1 - 1 15 56 8 - 2 - 1 - 11 57 1 . - 1 1 - - 3 58 8 - - - - - 8 59 8 1 1 1 1 3 15 1960 4 - 1 3 1 - 9 61 2 - - 4 1 - 7 62 3 2 - - 1 - 6 63 7 1 - 1 1 - 10 64 9 1 - 6 - - 16 65 6 1 1 - - 8 66 20 - - 7 3 - 30 67 16 2 - 73 1 - 92 68 9 - 1 72 - 82 69 4 - - 33 - - 37 1970 - - - 4 1 - 5 Source: E.M.R. D r i l l i n g F i l e . - 6.27 - 150 TABLE 6.12 ANNUAL RATE OF DRILLING SUCCESS IN FINDING GAS POOLS  BY BIG EIGHT COMPANIES IN ALBERTA, 1946 - 1970 (# gas pools) YEAR N.F.W. N.P.W. EXT. 8 TEST WELLS INTENT INTENT TOTAL OIL GAS BOTH OIL ! GAS BOTH 1946 - 1 1 — 1 _ 3 47 - - - - 1 - 1 48 - 2 - - - - 2 49 1 4 - 2 - - 7 1950 - 3 1 - - - 4 51 1 8 4 - 1 - 14 52 5 8 2 - - - 15 53 2 5 5 - 1 - 13 54 1 9 - - 1 - 11 55 5 11 5 1 1 1 24 56 _ 6 5 1 2 3 17 57 10 1 2 3 3 19 58 1 12 2 - 3 1 19 59 4 9 5 5 - 23 1960 4 9 4 3 6 - 26 61 4 11 - 2 1 1 19 62 5 1 - 2 3 - 11 63 4 3 1 6 3 - 17 64 9 9 - - 3 - 21 65 7 7 2 - 5 1 22 66 7 6 - 2 4 - 19 67 6 3 2 6 5 - 22 68 - 7 2 5 1 1 16 69 - 2 - 3 2 1 8 1970 - - - 1 - 2 3 Source: E.M.R. D r i l l i n g F i l e . 6.7.1. POPULATION OF OIL S GAS POOLS IN GROUND McCrossan and others have examined the s t a t i s t i c a l characteristics of o i l and gas pool populations i n Alberta. * McCrossan concludes; " Both the o i l and gas reserves of Western Canada are log-normally distributed. I f the t o t a l reserves are separated into groups made up of single•types of occurrence, these a l l display log-normal distributions as well. The parameters of the distributions vary considerably for different groups of genetically related accumulations. Many of the distribu-tions also appear to be heterogeneous, showing distinct bimodality. Several hypotheses can be offered to explain thi s . For instance, the reserves of the group of smaller sized pools may be under-estimated for lack of sufficient information; secondly, geologically unlike types of pools may be grouped together. I f the former i s the case, an estimate can be made of the additional o i l and gas i n aggre-gate that may be undeveloped i n the smaller under-estimated pools. The degree of bimodality may also indicate the maturity of an exploration play. Other p o s s i b i l i t i e s ai-e also considered. The distribution curves for the t o t a l reserves show only a generalized picture and obscure the characteristics of the individual distributions of the several types of o i l or gas accumulations. " Some of the populations classified by geological zone are shown i n Figure 6.6. R.G. McCrossan, "An Analysis of Size Frequency Distribution of Oil and Gas Reserves of Western Canada", Canadian Journal of Earth Sciences, Vol. 6, No. 2, 1969, pp. 201 - 211. FIGURE 6.6 COMPARISON OF SIZETFREQUENCY DISTRIBUTIONS OF PROBABLE  ULTIMATE RECOVERABLE OIL RESERVES I N ALBERTA, AT 1965 CO v CO r-H 2 O IOT io« io» S — Pool Size (Bbls) Source: R.G. McCrossan, pp. 209 We have also examined the pool characteristics according to geological zone and we concur with McCrossan's findings. Our special interests, however, lead us to report here on the characteristics of populations of pools from a l l zones but discovered during sequential time intervals. For this purpose we undertook a computer analysis of pools discovered i n the 5 year intervals beginning i n 1946. The average results for o i l pools are shown i n Table 6.13. - 6.30 153 TABLE 6.13 OIL POOLS DISCOVERED IN ALBERTA BY ALL DRILLING  1946 to 1970, IN FIVE YEAR PERIODS PRIMARY PLUS ENHANCED RESERVES YEARS 1946-50 1951-55 1956-60 1961-65 1966-70 NO. OF POOLS (#) 46 146 134 214 490 AVERAGE POOL SIZE (MSTB) 44,015 24,893 20,882 . 5,869 2,081 MAXIMUM POOL SIZE (MSTB) 806,000 1,691,000 790,000 352,000 148,200 TOTAL (MMSTB) 2,024.6 3,634.4 2,798.2 1,256.0 1,019.7 1,030 10,420 10,732.9 The largest pools are Redwater D-3 1948, Pembina Cardium A 1953, Swan H i l l s BHL-A 1957, Mitsue Gilwood A 1964, and Rainbow Keg River B 1966. Table 6.13 shows a general trend of declining average pool size. I t i s interesting to plot the 5 year period populations on probability paper, as i n Figure 6.7. I t can be seen that the populations i n the time periods except 1966-1970 appear to conform reasonably well with the lognormal assump-tion. The graph for each period tends to be shifted to the l e f t of the previous period, but the variance (indicated by the slope) i s not substantially changed except i n the last period. The Keg River pinnacle reef discoveries of the 1966-1970 period constitute a markedly different population from the pools from other horizons. This reflects Pembina Cardium reserves. I t i s sometimes disputed whether the reserves are r^eally i n a single pool. - 6.31 - 154 FIGURE 6.7 OIL POOLS OF ALL GEOLOGICAL ZONES IN POPULATIONS  ACCORDING TO DISCOVERY DATES IN 5 YEAR PERIOD IN ALBERTA l i r a -UJ_i_J_!_|_i S B rm TT "4T T7f MM. | | ! . -i-jq U_JJi i JJ::JJTI;I -/•rr •nip 1 • - l_U -H -±li •>-\-7-T T i r 1961-1965 :0* 11 J_!_J. 1946-1950 I ! ! Ti +4 DISCOVERY PERIOD • 1946-1950 X 1951-1955 o 1956-1960 © 1961-1965 n1966-1970 J_L u J _ ! _ a . ff-..L| n 11 i i AVERAGE POOL SIZE (MSTB) 44,015 24,893 20,882 5,869 2,081 POOLS 46 146 134 214 490 -1 Tt-n 44-101 10* 10 3 10" 10 s 10 6 10 7 S = Pool Size, Recoverable Reserves MSTB 10{ - 6.32 - 155 Figure 5.7 demonstrates that the populations of o i l pools which were discovered i n sequential time periods retained lognormal characteristics but with the mean of the population shifted lever each period. This "well-behaved" result i s caused partly because the five year intervals correspond roughly to the sequence of major o i l plays i n the province. But an analysis of pools according to three broad geological classes gives similar results, although more erratic. We divided pools into Upper Cretaceous to Upper Devonian Dl, Upper Devonian D2 £ D3, and Mid Devonian and older. For each geological class we find five year populations which are roughly lognormal and whose means shift lower each time period. The results for gas pools do not show .the same systematic declining average pool size as those for o i l . As discussed i n Section 6.8.2 the search for o i l pools seems to have been more extensive and continuous. This would also be expected from the very low incentive to search for gas, as estimated by the demand price for gas reserves i n Chapter 5. The average gas pool results are shown i n Table 6.14. TABLE 6.14 NON-ASSOCIATED GAS POOLS DISCOVERED IN ALBERTA  BY ALL DRILLING, 1946 to 1970, IN FIVE YEAR PERIODS MARKETABLE RESERVES NO. OF AVERAGE MAXIMUM YEARS POOLS POOL SIZE POOL SIZE TOTAL (#) (BCF) (BCF) (BCF) 1946-50 49 31 380 1,519 1951-55 177 42 1,350 7,434 1956-60 226 52 1,700 11,752 1961-65 227 39 2,400 8,853 1966-70 127 43 1,700 5,461 806 43 35,019 - 6.33 - 156 The largest gas pool i n Alberta, Kaybob S., was discovered i n 1961, some 14 years after Leduc but only some 6 years after the incentive to search for gas was at a l l substantial (see Table 5.1). Rather than show the sequential populations of gas pools, Figure 6.8 shows the population of gas pools discovered i n the 1946-1970 period. The sequential populations appear to con-form to the lognormal but they are d i f f i c u l t to i l l u s t r a t e since they don't shift from period to period. 6.7.2. AVERAGE SIZE OF POOLS The average pool size of the populations i n 5 year intervals can indicate a "long-run" trend i n the size of pools from play to play i n the region. How-ever, the year to year trend i n pool size follows the characteristics of discovery within each play. The year to year decline i n average pool size within a play i s substantially greater than the long-run trend. While the population of pools from the whole or most of the play (in the 5 year interval) w i l l conform to a lognormal, the pools discovered each year are not random samples from the population. Quite the contrary! The largest pools i n the play are usually discovered i n i t s early stages. Figure 6.9 illustrates -these points. The dotted line shows the long-run trend i n the average o i l pool size and the solid lines show the year to year trend within each play. The annual pool size data for -New Field Wildcats i s shown i n Tables 6.15 to 6.17. A play may be defined roughly as the exploration of a specific geological horizon i n a region. In Section 6.8 we discuss further complications of these samples of pools by size. Namely; that the size of pools are significantly different depending on the intent of the discovery well, the class of well, and the size of the exploration company. - 6.34 -FIGURE 6.8 NON-ASSOCIATED GAS POOLS OF ALL GEOLOGICAL ZONES, DISCOVERED BETWEEN 1945 g 1970 IN ALBERTA — 6.35 — FIGURE 6.9 AVERAGE SIZE OF OIL POOLS DISCOVERED BY NEW FIELD WILDCATS IN ALBERTA, 1845 - 1970 1945 1950 1955 1960 1965 1970 Year Source: Tables 6.13 and 6.17 - 6.36 - 159 TABLE 6.15 MARKETABLE OIL, RESERVES DISCOVERED BY ALL NEW  FIELD, .WILDCATS IN ALBERTA, 1946 - 1970 (in MSTB) YEAR OIL INTENT GAS INTENT BOTH INTENT TOTAL PRIMARY ENHANCED PRIMARY r ENHANCED PRIMARY ENHANCED 1946 - - - - - - -47 234,782 64,800 - - - - 299,582 48 844,300 4,480 -' • - - 425 - 849,205 49 366,698 76,220 185 - - - 443,103 1950 355,397 29,800 18,980 6 - 404,183 51 293,423 74,700 24 100 - 368,247 52 629,471 70,613 5,929 - 129 - 706,142 53 1,040,160 877,800 4,761 - 5,555 - 1,928,276 54 75,090 96,000 79,950 8,880 59,390 3,680 322,990 55 34,313 21,693 7,909 - 5,910 3,280 73,105 56 88,395 26,160 - - 12,808 14,300 141,663 57 455,871 651,780 - - 1,071 - 1,108,722 58 195,487 223,500 - - 86 - 419,073 59 185,107 310,850 66 - 399 - 496,422 1960 10,482 3,443 408 758 753 - 15,844 61 26,943 9,310 66 - 784 - 37,103 62 37,038 75,100 719 - 50 - 112,907 63 51,707 30,775 400 - 3,015 7,920 93,817 64 212,139 165,430 2,962 •2,320 8 - . 382,859 65 234,851 153,120 700 - 1,771 - 390,442 66 127,261 12,100 124 - - 139,485 67 27,556 5,415 6,532 - 100 - 39,603 68 10,913 1,670 - - 1,916 - 14,499 69 6,161 - - - - 6,161 1970 - - - - - - -Source: E.M.R. Reserves Files. 0 , o / — 160 TABLE 6.15 MARKETABLE NON-ASSOCIATED GAS RESERVES DISCOVERED BY  ALL NEW FIELD WILDCATS IN ALBERTA, 1946 - 1970 (in BCF) YEAR OIL INTENT GAS INTENT BOTH INTENT TOTAL 1946 - - . 194 13 207 47 - 76 -1 X 77 48 - 381 3 384 j 49 - 386 16 402 1950 2 228 88 318 51 7 533 28 568 | 52 44 1,627 41 1,712 j 53 72 1,539 230 1,841 j 54 16 1,105 . 17 1,138 | 55 686 837 • 280 1,803 i ' j 56 56 505 134 695 57 19 1,509 228 1,756 58 7 1,801 316 2,124 59 793 842 253 1,888 1960 14 547 76 637 61 51 3,563 " 3 3,617 62 2,058 57 - 2,115 63 470 512 5 987 64 256 81 5 342 65 27 303 100 430 66 41 46 - 87 67 1,712 639 - 2,351 68 234 284 22 540 69 15 113 - 128 1970 - 335 - 335 Source: E.M.R. Reserves Files. - 6 . 3 8 - 161 TABLE 6.17 AVERAGE SIZE OF POOLS DISCOVERED BY ALL NEW  FIELD WILDCATS IN ALBERTA, 1946 - 1970 YEAR PRIMARY S ENHANCED RECOVERABLE RESERVES IN OIL POOLS MARKETABLE RESERVES IN NON-ASSOCIATED GAS POOLS # POOLS MSTB # POOLS BCF 1946 2 - 3 69.00 47 4 74,895.50 6 12.83 48 5 169,841.00 5 76.80 49 12 36,925.25 18 22.33 1950 18 22,454.61 12 26.50 51 18 20,458.17 40 14.20 52 29 24,349.72 34 50.35 53 21 91,822.67 30 61.37 54 19 16,999.47 40 28.45 55 22 3,322.95 38 47.45 i 56 21 6,745.86 28 24.82 57 11 100,792.91 24 73,17 58 14 29,933.79 36 59.00 59 18 27,579.00 36 52.44 1960 15 1,056.27 50 12.74 61 17 2,182.53 38 95.18 62 20 5,645.35 29 72.93 63 26 3,608.35 36 27.42 64 25 15,314.36 37 9.24 65 23 16,975.74 39 11.03 66 42 3,321.07 32 2.72 67 35 . 1,131.51 29 81.07 68 18 805.50 30 18.00 69 10 616.10 15 8.53 1970 4 83.75 Source: Tables 6.9, 6.10, 6.15, 6.16. - 6.39 - 162 6.8.1. DIRECTIONALITY, SUCCESS RATIOS 6 POOL SIZE In Section 3.4.2 we introduced the concept of directionality. We now present data which gives a general overview of d r i l l i n g directionality and success rates for New Field Wildcats i n Alberta over the 1945-1970 period. To measure the importance of directionality upon the supply of reserves, we must relate reserves discovered to d r i l l i n g success. Consequently, we define successful wells as those which discover new separate pools, as i n Section 3.2.2. This i s particularly appropriate when considering New Field Wildcats, which are unequivocally searching for new separate pools. I t may not be so pertinent for other exploratory wells such as Extension Wells. The measure of directionality may be defined as "the extent to which new pool discoveries (made by New Field Wildcats) conform to the well operators' expecta-tions prior to d r i l l i n g " . With this measure we can then examine the size of the pools discovered. We begin the analysis by confining our attention to New Field Wildcats i n Alberta, defining successful wells as those which were the f i r s t (according to the r i g release date) to be recorded as entering a pool. As discussed i n Section 6.3.2 the classification of exploratory wells by intent may or may not be consistent from the earlier period up to 1961 to the later period of 1962 to 1970. Consequently the subsequent directionality analysis usually considers the two periods separately. 6.8.2. NEW FIELD WILDCATS In Tables 6.18 and 6.19 we show the average results for the 1945-1961 period and for the 1962-1970 period. - 6.40 - 163 TABLE 6.18 NEW FIELD WILDCATS IN ALBERTA. 1945 - 1961 POOLS DISCOVERED DRILLING FOR WELLS DRILLED OIL GAS DIRECTIONALITY (#) (#) (%) (#) (%) (%) Oil 1,334 184 . 13.8 59 4.4 75.7 Gas 1,244 22 1.8 294 23.6 93.0 Both 2,123 40 1.9 87 4.1 4,701 246 5.2 440 9.4 TABLE 6.19 NEW FIELD WILDCATS IN ALBERTA, 1962 - 1970 POOLS DISCOVERED DRILLING FOR WELLS DRILLED OIL GAS DIRECTIONALITY (#) (#) (%) (#) (%) (%) Oil 2,611 161 6.2 93 3.6 63.4 Gas 1,237 25 2.0 128 10.3 83.7 Both 361 13 3.6 30 8.3 - 4,209 199 4.7 251 6.0 - 6.41 -It can be seen that o i l directionality i s lower than gas directionality and that both of them have declined on the average, from the earlier period to the later. The o i l directionality of 63.4% i n the later period means that 36.6% of pools discovered when searching for o i l were actually non-associated gas pools. Generally, the average success ratios have also declined from the earlier to the later period. Comparing o i l and gas success ratios we see that the o i l success ratios are typically lower than the gas success ratios. In the later period the o i l success ratio when looking for o i l was 6.2% versus the gas success ratio when searching for gas of 10.3%. The diff e r e n t i a l i n these ratios i n the earlier period was about the same but with higher success ratios. By viewing the average data for the whole period 1945 - 1970, we get a good general picture of the h i s t o r i c a l success and directionality patterns, according to the pools discovered, i n the Alberta industry. TABLE 6.20 NEW FIELD WILDCATS IN ALBERTA, .1945 - 1970 POOLS DISCOVERED DRILLING FOR WFT.T.S DRILLED OIL GAS DIRECTIONALITY (#) (%) (#) (%) (%) Oil 3,945 345 8.7 152 3.9 69.4 Gas 2,481 47 1.9 422 17.0 90.0 Both 2,484 53 2.1 117 4.7 8,910 445 5.0 691 7.8 - 6.42 - 165 The t o t a l number of pools discovered by New Field Wildcats was 1,136 of which 445 were o i l pools and 691 were gas pools. Some 20% to 30% of the gas pools, however, are small and may not be commercial producers. These 1,136 pools are somewhat less than half of a l l the pools discovered (by a l l well classes) i n Alberta during the period, but they include most of the petroleum. There i s no s t a t i s t i c a l reason for close to half the pools being o i l pools. This follows primarily from the geology of. the province. Most pools i n Saska-tchewan and Manitoba are o i l pools and most pools i n B r i t i s h Columbia are gas pools. Table 6.20 also suggests how the search for o i l has augmented the gas supply. We see that 3.9% of the Mew Field Wildcats d r i l l e d i n the search for o i l , have found gas pools, and some of these have been large non-associated gas pools. Also some 4.7% of the Both intent wells have found gas pools. The directionality, therefore, appears significantly low i n o i l d r i l l i n g suggesting that o i l explora-tion has shifted the gas supply function. Of course, the importance of the low o i l directionality depends upon the average size of pools, which i s examined i n Section 6.8.3. Over the period 1945 - 1961 o i l directionality closely parallels the o i l intent success ra t i o i n finding o i l pools. Figure 6-.10 shows New Field Wildcat o i l directionality (divided by 5 for convenience) and the o i l intent success ratio declining over the period. A higher and higher proportion of pools discovered when searching for o i l were non-associated gas pools. Although the success ratio i n finding o i l or gas pools rose i n i t i a l l y to the 20% range by 1950/53 and remained thereafter at around that l e v e l , the success ratio i n discovering o i l pools was declining. The evidence suggests that the extensive exploratory margin i n o i l d r i l l i n g has been pushed out relatively more than that for gas. The success ratios i n search-ing gas have been higher; the directionality i n searching gas was higher; and the o i l directionality has tended to decline over time. We note that the apparent upswing i n o i l directionality after 1965 was associated with the Northern Alberta o i l plays, and most recently with a very low success ratio. - 6.43 - 166 FIGURE 6.10 NEW FIELD WILDCAT SUCCESS RATIO S .DIRECTIONALITY ACCORDING  TO POOLS DISCOVERED, BY OIL INTENT DRILLING IN ALBERTA, 1945 - 1970 20 f f 15 10 h 1945 1950 1960 1970 Year Source: Calculated from E.M.R. D r i l l i n g Files - 6.44 - 167 In the earlier period, i n addition to the declining o i l directionality we have a distinct upswing i n the proportion of d r i l l i n g with intent Both (as shown i n Section 6.3.2). Gas intent d r i l l i n g increased i n iinportance only i n 1960 and thereafter, as might be anticipated as a result of the pipeline completions and the running down of excessive gas reserves. In both the earlier and the later periods there appears to have been a relative backlog of gas-prone prospects which remained 3<nown but undrilled longer than o i l prospects. The gas directionality and gas success ratio tend to lag those of o i l d r i l l i n g by a year or two, especially i n the earlier period. Perhaps companies delayed d r i l l i n g the gas-prone prospects during a play and only d r i l l e d them when more geological data ( and well control) became available. Generally, the success ratios appear to be positively correlated with direction-a l i t y . 6.8.3. SIZE OF POOLS DISCOVERED We show the size of pools as measured by Primary Recoverable O i l Reserves, Enhanced Recoverable Oil Reserves, and the I n i t i a l Recoverable Gas Reserves, as appreciated at December, 1971. The average size of pools discovered i n the two time periods are shown i n Tables 6.21 and 6.22. The largest o i l pools have been found by New Field Wildcats d r i l l i n g for o i l . The situation with gas discoveries, however, i s different. According to our data some very large gas pools were discovered i n the 1962-1970 period by wells searching for o i l . These pools were discovered when companies other than the Big Eight were successful i n finding very large gas pools at Edson (Elkton 1962), Marten H i l l s (Wabiskaw 1963), and Strachan (Leduc 1967), as a result of o i l intent New Field Wildcats.* Canadian Petroleum, A p r i l , 1968, pp. 54, suggests that the Strachan Nev Field Wildcat was searching for gas. Our data indicates otherwise. Only the companies themselves really know. - 5 . 1 5 - 168 TABLE 6.21 AVERAGE SIZE OF POOLS DISCOVERED BY NEW  FIELD WILDCATS IN ALBERTA, 1945 - 1961 DRILLING FOR Oil Gas Both OIL RECOVERABLE RESERVES PRIMARY (MSTB) 25,402 5,376 2,185 19,836 ENHANCED (MSTB) 13,570 438 532 10,275 GAS INITIAL RECOVERABLE RESERVES (BCF) 29.9 53.3 19.9 43.6 TABLE 6.22 AVERAGE SIZE OF POOLS DISCOVERED BY NEW  FIELD WILDCATS IN ALBERTA, 1962 - 1970 DRILLING FOR Oil Gas Both OIL RECOVERABLE RESERVES PRIMARY ENHANCED (MSTB) 4,395 457 528 (MSTB) 2,755 93 609 GAS INITIAL RECOVERABLE RESERVES (BCF) 51.8 18.5 4.4 3,648 2,281 29.1 We can bring the foregoing factors together by showing the t o t a l volumes of primary o i l and gas reserves discovered by New Field Wildcats i n the whole 1945 - 1970 period, as shown i n Table 6.23. - 6.46 - 169 TABLE 6.23 PRIMARY RECOVERABLE CRUDE OIL RESERVES S INITIAL RECOVERABLE RESERVES OF NATURAL GAS DISCOVERED BY NEW FIELD WILDCATS IN ALBERTA, 1945 - 1970 DRILLING FOR WELLS DRILLED OIL GAS (#) (MMSTB) (%) (BCF) (%) Oil 3,945 5,381.5 96.0 6,580 24; 9 Gas 2,481 129.7 2.3 18,043 68.1 Both 2,484 94.3 1.7 1,859 7.0 8,910 5,605.5 100.0 26,482 100.0 To put these t o t a l reserves i n perspective we note that the Primary Recoverable Oi l Reserves of 5,605.5 MMSTB are close to 80% of a l l the Alberta reserves discovered i n the period. Another 775 MMSTB was discovered by New Pool Wild-cats, Extension Wells and Test Wells, and a further 800 MMSTB was recorded as being discovered by Development Wells. The I n i t i a l Recoverable Gas Reserves of 26,482 BCF represents some 53% of the gas reserves discovered i n the period. About 5,750 BCF was discovered by New Pool Wildcats, Extensions and Tests, and another 2,847 BCF by Development Wells, leaving a remainder of about 14,900 BCF of which some 8,979 BCF i s associated and 4,371 i s solution gas and the residual i s not accounted for i n our computer f i l e . We can estimate from Table 6.23 that about 76% of a l l Primary Recoverable Oil Reserves were discovered by New Field Wildcats searching for o i l (96.0% x 80%). This i s approximately the same throughout the whole period. This data under-scores the extremely significant role of New Field Wildcatting i n discovering o i l reserves. - 6.47 - 170 On the other hand, the o i l intent d r i l l i n g was f a i r l y important i n discovering gas reserves. The o i l intent New Field Wildcats discovered some 13% of I n i t i a l Recoverable Non-associated Gas Reserves during the period (24.9% x 53%) and some 42% of the associated and solution gas. These observations are consistent with the finding that the o i l directionality was lower than for gas, and i t means that considerable gas reserves (discovered during the 1962 - 1970 period especially) were found independently of gas related economic incentives; i.e. not as a result of the increasing relative price of gas. 6.8.4. THE LARGE COMPANIES 8 DIRECTIONALITY It i s interesting to compare the s t a t i s t i c a l performance of the Big Eight companies (Imperial, Gulf, Chevron, Mobil, Shell, Texaco, Amoco and H.B.O.G.) with the other companies, with the pool discovery data. We begin to see what really separates the companies. Over the whole period (and i n the sub periods) the Big Eight have obtained a higher average success ratio i n a l l categories of New Field Wildcats. TABLE 6.24 BIG EIGHT COMPANIES: NEW FIELD WILDCATS  IN ALBERTA, 1945 - 1970 POOLS DISCOVERED  DRILLING WELLS FOR DRILLED OIL GAS DIRECTIONALITY -(#) (#) (%) an (%) (%) Oil 1,323 150 11.3 66 5.0 69.4 Gas 640 19 3.0 146 22.8 88.5 Both 826 16 1.9 43 5.2 2,789 185 6.6 255 9.1 - 6 . 4 8 - 171 TABLE 6.25 OTHER COMPANIES: NEW FIELD WILDCATS  IN ALBERTA, 1945 - 1970 POOLS DISCOVERED DRILLING FOR WELLS DRILLED OIL GAS DIRECTIONALITY (#) (#) (%) (#) (%) (%) Oil 2,622 195 7.4 86 3.27 69.4 Gas 1,841 28 1.5 276 15.0 90.8 Both 1,658 37 2.2 74 4.5 ' 6,121 260 4.2 436 7.1 The differences between the success ratios of the Big Eight and the other companies are certainly significant, but they are not as large as other writers have reported for the U.S. industry (using other measures of success rati o ) . The o i l directionality i s the same for the large companies as the small, but lower for gas. We should point out that these s t a t i s t i c a l measures do not necessarily indicate superior economic efficiency on the part of the large companies. The large companies may have higher success ratios but be economically less efficient. They may invest too heavily i n predrilling investment and be over-cautious. The substantial performance difference between the companies emerges when we examine the average size of pools discovered by the two groups (Tables 6.26 and 6.27). The average primary Z'.?serves size of o i l pools discovered by the Big Eight i s almost four times that of the others. In the earlier period this d i f f e r e n t i a l was even higher, at about five times. As a result, the Big Eight, while d r i l l i n g about one th i r d of the o i l intent New Field Wildcats, discovered about 72% of the Primary Recoverable Oil Reserves found by a l l New Field Wild-- 6.49 - 172 cats. We might mention that the Big Eight have also tended to d r i l l significantly deeper and more expensive wells. On the average, their New Field Wildcats have been some 30% deeper and relatively even more expensive than those of the other companies. Regarding natural gas discoveries, the picture i s similar but less pronounced. Overall, the Big Eight discovered gas pools of about twice the size of the others. We have mentioned the anomolously large gas pools discovered by the other companies when searching for o i l i n the 1962 - 1970 period. The t o t a l amount of gas discovered by New Field Wildcats by the two groups i s almost the same. The other companies' smaller average pool size does not result simply from the larger absolute number of pools discovered by them, because the to t a l reserves of o i l and gas discovered by the others i s also smaller. TABLE 6.26 OIL S GAS DISCOVERED BY NEW FIELD WILDCATS  IN ALBERTA. 1945 - 1970, BY THE BIG EIGHT COMPANIES DRILLING FOR PRIMARY RECOVERABLE OIL (MMSTB) TOTAL AVERAGE POOL SIZE INITIAL RECOVERABLE GAS (BCF) TOTAL AVERAGE POOL SIZE Oil Gas Both 3,931.0 105.3 25.1 26.2 5.5 1.6 1,530 10,575 1,274 23.2 72.4 29.6 4,061.4 22.0 13,379 52.5 - 6.50 - 173 TABLE 6.27 OIL £ GAS DISCOVERED BY NEW FIELD WILDCATS  IN ALBERTA, 1915 - 1970, BY 'OTHER* COMPANIES DRILLING FOR PRIMARY RECOVERABLE OIL (MMSTB) TOTAL AVERAGE POOL SIZE INITIAL RECOVERABLE GAS (BCF) TOTAL AVERAGE POOL SIZE O i l Gas Both 1,450.5 24.4 69.2 7.4 0.9 1.9 5,050 7,468 585 58.7 27.1 7.9 1,544.1 5.9 13,103 30.1 6.-8.5. NEW POOL WILDCATS, EXTENSION WELLS S TESTS While the data does show that the New Pool Wildcat group had a higher success ratio according to our pool success measure, and that overall the o i l direc-t i o n a l i t y was higher i n New Pool Wildcats than i n New Field Wildcats, we do not analyse that data here. Instead we compare New Field Wildcats and the other exploratory wells on the basis of d r i l l i n g successes defined by i n i t i a l shows. This i s probably a better measure for the. New Pool Wildcats, Extension Wells and Tests because they are not always definitely searching for new separate pools. The results are shown i n Tables 6.28 and 6.29, and i n Figure 6.11. TABLE 6.28 NEW POOL WILDCATS, EXTENSIONS S TESTS, IN ALBERTA, 1945 - 1970 SUCCESSES ACCORDING TO "SHOWS" DRILLING FOR Oil Gas Both WELLS DRILLED (#) 2,713 2,002 667 5,382 OIL 1,217 77 82 1,376 (%) 44.9 3.9 12.3 25.6 GAS '(#) 252 969 152 1,373 (%) 9.3 48.4 22.8 25.5 DIRECTIONALITY (%) 82.9 92.6 TABLE 6.29 NEW FIELD WILDCATS IN ALBERTA, 1945 - 1970 SUCCESSES ACCORDING TO "SHOWS" DRILLING FOR WELLS DRILLED OIL GAS DIRECTIONALITY (#) (#) <%) (#) (%) (%) Oil 3,945 728 18.5 311 7.9 70.1 Gas 2,481 72 .2.9 895 36.1 92.6 Both 2,484 122 4.9 246 9.9 8,910 922 10.4 1,452 16.3 - 6.52 - 175 FIGURE 6.11 DIRECTIONALITY OF NEW FIELD WILDCAT S NEW  POOL WILDCAT DRILLING FOR OIL IN ALBERTA, 1945 - 1970 100 Source: Calculated from E.M.R. D r i l l i n g Files. - 6.53 - 176 While we have compared the well classes according to their success i n obtaining shows, i t i s , however, of interest to consider the average size of pools discovered by the New Pool Wildcat group. The average size of o i l pools discovered by the New Pool Wildcat group was only about one ninth of those found by New Field Wildcats. As a consequence, the New Pool Wildcat group discovered only some 12% of the Primary Recoverable Reserves, but i n some 55% of the o i l pools discovered by exploratory wells over the period. A similar but less exaggerated picture exists regarding gas pools. The New Pool Wildcat group discovered some 38% of the gas pools but only some 18% of the I n i t i a l Gas Reserves. TABLE 6.30 AVERAGE SIZE' OF POOLS DISCOVERED BY NEW POOL  WILDCATS, EXTENSIONS S TESTS IN ALBERTA, 1945 - 1970 OIL GAS " PRIMARY RECOVERABLE INITIAL RECOVERABLE DRILLING FOR RESERVES RESERVES (MSTB) (BCF) Oil 1,589 5.1 Gas 981 13.6 Both 516 27.2 1,449 13.4 177 CHAPTER 7 ALTERNATIVE PETROLEUM SUPPLY FUNCTIONS 7.1.1 Theoretical Considerations 7.1.2 ' Long Run Supply Potential 7.1.3 Short Run Supply Curve 7.1.4 Short and Long Run Supply 7.2.1 Two Previous Analyses of Discovery Rates S Finding Costs i n Alberta 7.3.1 Van de Panne's Analysis 7.3.2 Rate of Discovery 7.3.3 Finding Costs 7.3.4 .. Estimate of Ultimate Reserves 7.3.5 Interpretation of Equation Constants 7.4.1 Actual Annual Average Discovery Rates 7.4.2 Rate of Discovery 7.4.3 Finding Costs 7.4.4 Estimate of Ultimate Reserves 7.5.1 Ryan's Analysis 7.5.2 Rate of Discovery 7.5.3 Finding Costs 7.5.4 Estimate of Ultimate Reserves 7.5.5 Interpretation of Equation Constants 178 SYMBOLS USED IN CHAPTER 7 The indexes t and T are used to denote the time to which a variable applies. Empirically Fitted Constants for Van de Panne's Equation Empirically Fitted Constants for Ryan's Equation Proportion of a Pool Expected to be Controlled after Discovery Demand Price for Recoverable Reserves of Gas, C/MCF i n ground Demand Price for Recoverable O i l Reserves, $/Bbl i n ground Cost of Wells with O i l Intent, $/well See page 6.1 See page 6.1 Reserves of Gas Discovered Per Year, units specified i n text Reserves of O i l Discovered Per Year, units specified i n text Reserves of Crude O i l i n O i l Pools, Bbls i n ground Exploratory Wells Drilled Per Year, Wells 179 7. ALTERNATIVE PETROLEUM SUPPLY  FUNCTIONS 7.1.1 THEORETICAL CONSIDERATIONS There are two supply schedules, based oh Figure 2.4, which may be used to delineate the economic characteristics of a play or series of plays. Fi r s t there i s the schedule with an indefinite time horizon which indicates the ultimate reserves and second there i s a short run schedule which i s usually considered as applying to a single year. The lat t e r shows the expected sup-ply response from the industry i n a short time period during which industry's information i s essentially unchanged. 7.1.2 LONG RUN SUPPLY POTENTIAL On page 2.11 we br i e f l y discussed the supply schedule of Figure 2.4. Viewing Figure 2.4 as a schedule for an indefinite time span i t shows the amount of Recoverable Reserves which would be expected to be discovered over the ex-ploration history of a region (or a play). Such a curve i s sometimes called a Reserves Potential Schedule. For example, i n Figure 2.4, the schedule would show that reserves of Rg are expected to be discovered (eventually) i f the demand price remained at P^ .. The expected marginal cost of finding additional K,o,T reserves beyond Rg i s greater than the expected returns from exploration and hence further exploration would not be profitable. Consider the expected ultimate reserves i n a play. The reserves w i l l be con-tained i n a population of pools. I f pools were discovered i n their order of size which i s often approximately the case since the larger identifiable prospects are usually d r i l l e d earliest, then we can view Figure 2.4 as repres-enting the decline i n pool size and success ratio as the play develops. Exploratory d r i l l i n g would continue as long as the expected pool size and success ratio are sufficient (given the unit costs involved) to yi e l d a finding cost (marginal and average) less than P . R,o,t I t may occur that identifiable plays of considerable physical potential might show expected finding costs everywhere above the demand price for reserves i n that region. This was surely the case for the Canadian Mackenzie Delta region - 7.2 - 180 prior to I960. A play or basin, then, may have considerable geological potential but not be of economic significance. Usually the reserves beyond economic (finding) potential w i l l be contained i n small, scattered, hard-to-identify pools. 7.1.3 SHORT RUN SUPPLY CURVE In the short run context we may think of Figure 2.4 applying to a short time period l i k e one year. This i s a period which i s too short for the complete exploration of a play. In the short run, information available to the industry i s essentially fixed and finding costs w i l l rise.as the rate of exploration i s increased. Thus the short run supply curve w i l l be steeper and to the l e f t of the long run supply potential curve. 7.1.4 SHORT AND LONG RUN SUPPLY We can i l l u s t r a t e the supply process by Figure 7.1 FIGURE 7.1 ' 'SHORT RUN AND LONG RUN SUPPLY T3 0 R.. R„ R R Expected Recoverable Reserves from New Exploration, Bbls i n ground .7.3. - 181 The annual short run industry marginal and average costs are shown by the curves marked MC(i) and AC(i)v The expected reserves i n year one are R^ ; i n year two they are (R^ ~ year three they are (Rg - R2), and i n year four they are. (R^ - Rg). Notice that the expected annual discoveries are smaller and smaller, and that the annual producers1 rent gets smaller u n t i l at R^  i t vanishes. I t . i s the existence of the expected producers' rent which keeps the exploration going i n the region from year to year. The long run supply potential curve i s traced out by the minimum points on the average cost curves. In this example the region i s f u l l y explored, at the demand price of q after four years. I f the demand price for reserves were constant and the realized finding costs were the same as those expected we would observe a series of finding costs given by the intersection of the average cost curves and the lines indicating the quantities, as marked by the X's. These X's trace out the observed long run finding costs. Of course, i t i s extremely unlikely that the realized finding costs would be the same as those expected. Each of the supply curves i s r e a l l y a stochastic curve distributed around curves l i k e those indicated i n Figure 7.1. Given a certain rate of exploratory d r i l l i n g large discoveries may be made i n which case larger than expected reserves with lower finding costs would be realized. Or, unusually small discoveries may lead to smaller reserves with higher finding costs. This i s illustrated by Figure 7.2. » *• The industry cost curves are the sum of firm's cost curves. - 7.M - 182 FIGURE 7.2. •STOCHASTIC NATURE OF SUPPLY CURVES Supply "band" at a certain , / probability of occurrence S t a t i s t i c a l Distributions ' of Finding Costs, given expected reserves of R. and R2 Expected Recoverable Reserves from New Exploration, Bbls i n ground Our equation (6.3) corresponds to the marginal cost curves i n Figure 7.1, As explained on page 6.3 the "shift parameters" i n equation (6.3) determine the location of the expected reserves supply function. The econometric objective i s to estimate the e l a s t i c i t y of an expected reserves supply- function, l i k e this one, i n the neighborhood of the demand price. With equation (6.3) we see that this e l a s t i c i t y changes with a l l the parameters of the equation; -1 1-b, o,o,T = { bo-P- ,.(PT + P. 2"X,o,r^R,o,T'vo,T R,G,T < i > G j T ) . e } "o,T (6.3) - 7.5 - 183 and ffi-(1W. PR,o,T = b2 .PR,o,T 6PR,o,T E ( Ro,o,T ) X- b2 b 2 - i • { b2'PX,o,T-(PR,o,T^o,T + \G9T*GJ'* } ( 7 ' 0 ) Chapter 8 describes the estimation procedure. By necessity, empirical,observations of annual industry finding costs are data bearing on the realized average costs. The data which i s usually examined shows the annual average finding rate of appreciated reserves per exploratory well d r i l l e d . Such data can easily be converted to average finding costs by assigning an appropriate cost to wells d r i l l e d . The papers of Van de Panne and Ryan, described later i n this chapter, f i t em-p i r i c a l curves through such sequential average finding rate data. Their analyses may be useful for estimating the Ultimate Recoverable Reserves of a region or play, but they do not illuminate the e l a s t i c i t y of response of the industry. Previous analysis, l i k e the papers mentioned above, focusses attention on the apparent production relationship between d r i l l i n g and discoveries, but does not deal with the question of how the rate of exploration i s determined. I t may be useful to separate these two aspects of the problem, but the h i s t o r i c a l data i s formed from their conjunction. - 7.6 - 184 7.2.1 TWO PREVIOUS ANALYSES OF DISCOVERY PATES  AND FINDING COSTS' IN ALBERTA To exemplify the studies which have been made of discovery rates for o i l and gas i n the province we now summarize the approaches and the main results of two papers; by C. Van de Panne and J.T. Ryan. We also compare these papers with average actual finding rates.* To relate these analyses to each other and to the question of estimating future long run finding costs i n Alberta, i t i s important to take note of the de-fin i t i o n s of variables, the geographical and geological scope of analysis, and the period of time used by each approach. Each analysis purports to provide a means for forecasting finding costs. Note, at the outset, that Van de Panne examined a l l classes of exploratory wells i n a l l areas of the province for the period 1950 to 1968. Ryan examined New Field Wildcats i n specified geological zones i n the province for the period 1946 to 1969 (i.e. his analysis deals with o i l "plays"). * Van de Panne, C., "The Development of O i l and Gas Reserves i n Alberta", Discussion Paper No. 15, University of Calgary, September, 1971. Ryan, J«T., "An Analysis of Crude O i l Discovery i n Alberta", Unpublished Paper, University of Alberta, 1971. Energy Resources Conservation Board of Alberta, Reserves of Crude O i l , Gas, Natural Gas Liquids and Sulphur, Province of Alberta, Calgary, December, 1972, and 1973 editions. -. 7.7 - 185 In Chapter 7 we use the following symbols: . R Q ^ Reserves of o i l discovered per year, at time t Rg ^ Reserves of gas discovered per year, at time t Note: Van de Panne uses f u l l y Appreciated Recoverable Reserves. Ryan uses Recoverable Reserves appreciated to 1970. The A.E.R.C.B. data uses f u l l y Appreciated Recoverable Reserves. Exploratory wells d r i l l e d per year, at time t Note: Van de Panne uses a l l exploratory wells (i.e. New Field Wildcats, New Pool Wildcats, Extension Wells and Test Wells). Ryan uses New Field Wildcats only. The actual data i s analysed according to intent of d r i l l i n g for a l l classes of exploratory wells. b's The empirically f i t t e d constants are designated as b's, as follows: Constants f i t t e d i n Van de Panne's equation which have interpretive meanings, described under Section 7.3.5., below Constants f i t t e d i n Ryan's equation which have interpretive meanings, described i n Section 7.5.5. 7.8 -- 186 7.3.1. VAN DE PANNE'S ANALYSIS 7.3.2. RATE OF DISCOVERY Using a non-linear least squares method Van de Panne f i t t e d equations to the 1950-1968 Alberta aggregate reserves and d r i l l i n g data for o i l and gas, as follows: T R /Xt/1000dt °'T =2.64(0.86)° MMSTB/well (7.1) . xyioo'o /X /lOOOdt V = 12.04(0.84)° B C T ^ e 1 1 ( 7 ' 2 ) Xj/1000 where R „, i s the rate of discovery of BSTB of Recoverable O i l Reserves, R n „-O , 1 b , 1 i s the rate of discovery of TCF of Recoverable Gas Reserves, and Xj, i s the rate of d r i l l i n g exploratory wells (of a l l classes), a l l per year at time T. These equations are plotted i n Figure 7.3, which i s based on Table 7.1. The curves i n Figure 7.3 are production relationships. They reflect the shifting reserves production function as wells are cumulated. Such a shi f t i s attributed to the depletion of prospects. Note that a cost may be assigned to wells and these relationships may then be used to derive a long run Supply Potential Schedule. Suppose $200,000 per well i s assigned to cover a l l exploration costs and then assume that half the wells are d r i l l e d with intent o i l and half with intent gas. The resulting Supply Potential Curves would be l i k e those i n Figure 7.4. 7.3.3. FINDING COSTS Figure 7,4 shows estimated finding costs for reserves i n the ground according to Van de Panne's equations and the above exploration costs. There were some 12,000 exploratory wells d r i l l e d by 1970. - 7.9 - 187 FIGURE 7.3 RATES OF DISCOVERY IN ALBERTA 3Y VAN DE PANNE'S MODEL Cumulative Wells (thousands), after 1950 Note: Reserves are Appreciated Recoverable Reserves. Source: Table 7.1 - 7 . 1 0 -F I G U R E 7 . 4 P R O J E C T E D F I N D I N G COSTS I N A L B E R T A B Y VAN D E P A N N E ' S MODEL  ( R E S E R V E S P O T E N T E A L S C H E D U L E ) 400 300 200 100 0 f 1 i . • • : ... 1 1 • • 1 , - . • . ,. 1 1 i ' - ; i • . • " 1 • 1 I - . • i , : . ! : : i • ' . • ' • . —^—i - : • i ; • I ! i - ' i . i i : i i i - ' . i • 1 • i ! ' • • • ; i . - • ! i 1 , i — : j J . • ; : ' ; . - 1 j . , , . , .. ; i * • 1 , • • i • , ' - ! : ; I j 1 ' ; • 1 : — f. j. : , . — j . — i ! 1 1 : ; . —1 ! . . • : ' / • ; 1 - ' i i , ! ; j—t— i i . • i i 1 • I 1 - -j 1 • ; , : . i — i — i ! 1 . / ' . ' • ! 1 i i ' ' ' 1 — ; —1 — : — 1 — i — j 7 1 ' i : : i 1 i : I I i . i — ! — 1 — i — ' • — ! — • . / i 1 • : : • i ! i ' • ! i / I " 1 ' ' i ' ' , i ' ! - • • : - — 1 — J — i — 1 : I : : ' i • • / ! : , 1 : / ; i : ; : ; i : 1 ' 1 • ! • ' 1 1 i ' •/'<•• • • i • • . • • , • 1 1 1 — 1 — 1 OIL — l - / . I ' . ; • 1 1 • ' : • • : i I • ! 1 : j 1 / I I I . . . 1 i t ! ' ! : • I I I / • ' M L . ' ! • ' . • • 1 1 • i 1 1 > • 1 ' ' i : .• ; i 1 : • : i • . : ! i > 1 ! : ' • 1 / i I , 1 | i : j / : 1 — i — , I I I : • / ' ! ' • 1 ! : i t ; i ~~I : • GAS • | ] ; l i i i • 1 1 1 • J i i ; j i : , ~1* 1 i ; i l • 1 / ! • • ' / ' . ! 1 j , i / i i I / . . . t — - — t / • ; ' ' 1 1 l i i • / i Jf i . 1 i , . . i i . : : i \ / i ;. • : • i ' ' : ' : ; : ; — 1 — — ! — i — ' — i — : . j 1 1 - 1 . i i . I ; : | ; i . 1 1 i • i • - • , • • : j ' ! ! i S • ; ' I • : 1 - • : ! ; ! I : ; . . : : : - ! - i l l : : 1 1 J< • i > - ^ 1 — i : • i — 5 ' , ,1 i i • i • i 0, 3^- 1 r-!. i 1 ; k — -ft i--*1— ; i i i i " i —I—[—r ! ! • • +-i — - + f t - f t i i ; j j , Cumulative Wells (in thousands) — i i — i — • H V ' A f * ' 1  _ i _ -+--•: : i — j , — — 1 ! ' 1 i 1 ' i ; ! I i i • i — ! ~ i — i — : —1 — \ — • t ' ! ! i i j 1 : ' ; • i : • • .—, i, - •— I • i 1 1 i ' i 1 i _! _ . — H V L ^ 4 . _ _ i ^ _ i . 0 9.27 13.68 15.68 15.65 17.10 0 40.18 56.98 64.00 66.94 68.17 Cumulative Reserves (0il-3STB; Gas-TCF), after 1950 Note: Reserves are Appreciated Recoverable Reserves. Source: Table 7.1 - 7.1-1 - 189 TABLE 7.1. CUMULATIVE WELLS £ RESERVESj DISCOVERY PATES S COST (VAN DE PANNE) CUMULATIVE O I L G A S WELLS DISC. RATE CUM. RES. COST DISC. RATE CUM. RES. COST T (wells ) R 0 j T/X T ( M M S T R / W P !1) T (RSTR) (C/Bbl i n ground) R g y ^ fRPF/wp-i-n T fTCF') (t/MCF i n ground) 0 2.64 0 7.58 12.04 0 1.66 5 1.24 9.27 16.13 5.04 40.18 3.97 10 0.58 13.63 34.48 2.11 56.98 9.48 15 0.27 15.68 74.07 0.88 64.00 22.73 20 0.13 16.65 153.85 0.37 66.94 54.05 •25 0.06 17.10 3.33.33 0.15 68.17 133.33 30 0.03 17.31 666.67 0.06 68.69 333.33 Note: i s i n thousands i n Table 7.1 Source: Calculated from Van de Panne's paper. See f.n. page 7.6. TABLE 7.2 ACTUAL OIL S GAS DISCOVERY RATES IN ALBERTA YEAR OIL DISC.RATE (MMSTB/well) GAS DISC.RATE (BCF/well) YEAR OIL DISC.RATE (MMSTB/well) GAS DISC.RATE (BCF/well) . 1947 4.25 — 1959 2.75 10.8 1948 7.00 - 1960 0*.07 4.3 1949 2.09 - 1961 0.12 . 15.6 1950 1.82 - 1962 0.44 6.5 1951 2.45 2.9 1963 0.64 4.S 1952 0.82 8.6 1964 0.87 . 1.6 1953 5.84 8.0 1965 1.05 2.2 1954 0.61 13.9 1966 0.70 0.9 1955 0.31 6.6 1967 0.60 4.4 1956 0.55 8.2 1968 0.24 1.0 1957 2.93 7.4 1969 0.16 4.0 1958 0.71 7.9 1970 0.08 0.6 Source: A.E.R.C.B. Reserves of Crude O i l , Gas, Natural Gas Liquids and  Sulphur, Province of Alberta, Calgary, Dec, 1972. /.. i t — 190 Note that Figure 7,4 has two horizontal axes. The emulative Reserves axis indicates the expected cumulated reserves for each amount of cumulated d r i l l i n g . 7.3.4. ESTIMATE OF ULTIMATE RESERVES When finding costs increase towards i n f i n i t y we have an estimate of the ultimate Recoverable Reserves. Van de Panne estimates an ultimate o i l reserve of 17-18 BSTB and an ultimate gas reserve of about 71 TCF. Cumulative reserves for a certain number of cumulative wells are obtained by integrating the discovery rate equations (7.1.) and (7.2 )» ss follows: /XVIOCO d t /R d t - Z ' W .(0.86 -1) o °Vt In 0.8.6 B S T B t 7 , 3 ) /Xt/1000 dt L dt - 1 2 - ° 4 .(0.84° "•' -1) o In 0,84 T C F 1 ' ; where a l l variables, constants and units are the same as for equations (7.1) and (7.2). 7.3.5. INTERPRETATION OF EQUATION CONSTANTS As an example consider Van de Panne's equation (7,1) for the rate of o i l dis-coveries. In general form i t i s ; ' v T v /X./1000dt *o>T v v o X MMSTB/well (7.5) ——- = b, .b« Xx/1000 1 2 . T Notice that when ^X^/1000 dt i s very small at the beganning of exploration i n a region the reserves discovery rate i s approximately equal to b^. This i n i t i a l reserves discovery rate must bear a close relationship to the size of the largest pools i n the region, which may be a useful relationship for projecting success rates i n immature regions. -. 7,13 - 191 Also, the constant shows how the reserves discovery rate i s estimated to decline as a result of wells being d r i l l e d . In equation (7.1), b 2 = 0.86 means that i t i s estimated that Appreciated Recoverable O i l Reserves discovered per exploratory well decline by 14% for every one thousand wells d r i l l e d . 7.4.1. ACTUAL ANNUAL AVERAGE DISCOVERY RATES 7.4.2. RATE OF DISCOVERY Van de Panne f i t t e d equations to the aggregate provincial data. We now examine that data, as shown by the A.E.R.C.B. publication Reserves of Crude O i l , Gas , Natural Gas Liquids and Sulphur, Province of Alberta, 1972. The discovery rates for Appreciated Recoverable Reserves by a l l exploratory wells for Alberta according to the A.E.R.C.B. are shown i n Figures 7.5 and 7.6. The erratic nature of these graphs i s explained by the various "plays" which have occurred i n the exploration history of Alberta. The main o i l plays have been: 1947 + Leduc D2, D3 1953 + Pembina Cardium 1957 + Kaybob Beaverhill Lake (Swan H i l l s ) 1964 + Mitsue Gilwood 1965 + Rainbow Keg River I t can be seen that discovery rates i n a play are high at f i r s t but then decline rapidly. Van de Panne's equation "averages" between these plays. I t repre-sents a "long-run" f i t to the data which for forecasting purposes, assumes that new plays (although smaller) w i l l emerge i n the future. In Section 7,5. we look at Ryan's analysis which examines the characteristics of each play. FIGURE 7.5 ACTUAL ANNUAL AVERAGE OIL DISCOVERY RATES BY ALL EXPLORATORY WELLS IN ALBERTA Note: Reserves are Appreciated Recoverable Reserves. Source: Table 7,2, from A.E.R.C.B. - 7 . 1 5 - 1 °, -FIGURE 7.6 ACTUAL ANNUAL AVERAGE'GAS-'PISCOVERY RATES BY ALL EXPLORATORY WELLS IN ALBERTA 1947 48 50 52 54 56 58 60 62 64 66 68 70 YEAR Note: Reserves are Appreciated Recoverable Reserves. Source: Table 7,2, from A,E.R.C.B, r 7 . 1 6 - 194 7.4.3. FINDING COSTS To estimate year by year finding costs we have divided the tot a l exploratory d r i l l i n g costs as reported by CP.A., into costs applicable to o i l intent d r i l l i n g and gas intent d r i l l i n g . This assignment of costs was made on the basis of the EMR D r i l l i n g F i l e , according to the stated intent of wells. The reserves discoveries are those reported by the A.E.R.C.B., consistent with the data shown i n Section 7.4.2. above. The finding costs, shown i n Figures 7.7 and 7.8, are calculated by dividing the assigned costs by the reserves discoveries, year by year. Note that these costs are plotted by year. A comparison of Van de Panne's costs i n Figure 7.4 with the actual year by year costs can be made by assuming that about 12,000 exploratory wells of a l l classes and intents were cumulated by 1970. It can be seen that Van de Panne's costs would be about 50£/Bbl for o i l and 10<7MCF for gas, but the actual i n 1970 was about $1.70/Bbl for o i l and around 25£/MCF.for gas. Actual annual costs reflect the unfolding of plays. I t i s also interesting to compare the estimated demand prices for o i l and for gas with these calculated annual finding costs (Compare Table 5.1 with Figures 7.7 and 7.8). I t can be seen that from 1966-1970 the estimated demand price for o i l was less than the annual finding cost. I t was during this time that the major companies ceased New Field Wildcatting for o i l i n Alberta. 7.4.4. ESTIMATE OF ULTIMATE RESERVES In mid 1974 the A.E.R.C.B. have estimated an Ultimate Recoverable O i l Reserve of 20 BSTB and an Ultimate Recoverable Gas Reserve of 110 TCF. - 7.17 - 195 FIGURE 7.7 ACTUAL ANNUAL AVERAGE OIL FINDING COSTS BY OIL INTENT EXPLORATORY WELLS IN ALBERTA Lake River YEAR Source: Table 7.3 - 7.18 - 19G F I G U R E 7.8 A C T U A L A N N U A L A V E R A G E GAS F I N D I N G COSTS B Y GAS I N T E N T E X P L O R A T O R Y W E L L S I N A L B E R T A Y E A R Source: Table 7.4 - 7.19 - 197 TABLE 7.3 DATA FOR A C T U A L O I L F I N D I N G COSTS I N A L B E R T A , F O R A P P R E C I A T E D R E C O V E R A B L E O I L R E S E R V E S YEAR EXPLORATORY WELLS DRILLED FOR OIL (# wells) FRACTION OF DRILLED WELLS THAT ARE OIL TOTAL ANNUAL COSTS ($ millions) TOTAL ANNUAL OIL COST ($ millions) OIL RESERVES FOUND (MMSTB) FINDING COST tt/Bbl i n ground) 1947 70 .68 18.50 1 12.57 302 4.16 1948 104 .70 31.50 21.99 868 2.53 1949 178 .74 54.50 48.04 444 10.82 1950 210 .83 91.50 75.65 383 19.75 1951 291 .71 107.00 75.94 847 8.97 1952 379 .74 133.50 98.63 361 27.32 1953 337 .70 136.50 95.24 1976 4.82 1954 312 .70 183.50 128.66 223 57.69 1955 332 .72 198.50 143.27 108 132.65 1956 347 .74 204.00 151.58 205 73.94 1957 404 .75 203.50 152.53 1323 11.53 1958 354 .72 201.50 145.57 302 48.20 1959 395 .73 208.50 152.23 1203 12.65 1960 386 .67 188.50 126.54 30 421.80 1961 364 .64 183.00 116.66 46 253.61 • 1962 382 .61 177.50 107.97 191 56.53 1963 442 .69 184.20 127.41 . 271 47.02 1964 475 .64 239.00 153.62 504 30.48 1965 623 .69 309.70 212.26 758 28.00 1966 539 .63 313.80 198.99 458 43.45 1967 716 .79 344.10 267.80 419 63.91 1968 825 .75 349.00 262.71 225 116.76 1969 717 .68 355.80 240.90 151 159.53 1970 513 .49 270.50 133.43 80 166.79 Wells D r i l l e d , Fraction of Dr i l l e d Wells that are O i l , from E.M.R. D r i l l i n g F i l e Total Annual Costs, from CP.A. Annuals, 1955-1970 Total Annual O i l Cost; Column.3 x Column 4 Oil Reserves Found, from A.E.R.CIB. Finding Costs; Column 5 -r Column 6 Source: (1) (2) (3) (4) (5) - 7.20 - 138 TABLE 7.4 DATA FOR ACTUAL GAS FINDING COSTS IN- ALBERTA, FOR APPRECIATED RECOVERABLE GAS RESERVES YEAR EXPLORATORY WELLS DRILLED FOR GAS (# welis) FRACTION OF DRILLED WELLS FOR GAS I TOTAL ANNUAL . COSTS ($ millions) TOTAL ANNUAL GAS COST ($ millions) GAS RESERVES FOUND (BCF) FINDING . COST (t/KCF i n ground-) 1951 119 .29 107.00 31.06 1007 3.08 1952 134 .26 133.50 34.87 3804 0.92 1953 146 .30 136.50 41.26 2700 1.53 1954 133 .30 183.50 54.84 5122 1.07 1955 128 .28 198.50 55.23 2301 2.40 1956 120. .26 204.00 52.42 3066 1.71 1957 135 .25 203.50 50.97 3335 1.53 1958 136 .28 201.50 55.93 3388 1.65 1959 146 .27 208.50 56.27 4726 1.19 1960 189 .33 188.50 • 61.96 1760 3.52 1961 207 .36 183.00 66.34 6161 1.08 1962 246 .39 177.50 69.53 2810 2.47 1963 197 .31 184.20 56.79 2090 2.72 1964 164 .36 239.Q0 85.38 929 9.19 1965 286 .31 309.70 97.44 1587 6.14 1966 311 .37 313.80 114.81 620 18.52 1967 204 .21 344.10 76.30 3067 2.49 1968 271 .25 349.00 66.29 941 9.17 1969 342 .32 355.80 114.90 3861 2.98 1970 527 .51 270.50 137.07 532 25.77 Source: Cl) Wells D r i l l e d , Fraction of D r i l l e d Wells that are Gas, from E.M.R. D r i l l i n g F i l e (2) Total Annual Costs, from CP.A. Annuals, 1955-1970 (3) Total Annual Gas Cost; Column 3 x Column 2 (4) Gas Reserves Found, from A.E.R.C.B.. (5) Finding Costs; Column 5 t Column 6 i - 7.21 - 199 7.5.1. RYAN'S ANALYSIS .7.5.2, RATE OF DISCOVERY _ Ryan also used a least squares method to f i t equations to the Alberta r. discovery data. However, he examined only o i l discoveries and on a play by play basis, from 19H6 to 1969. His drilling variable was New Field Wildcats only. Ryan argued that, given a play is known, "the rate of discovery of oil in the play is proportional to the undiscovered oi l in the play ... ". He fitted an equation which in general form was as follows: °? T -b,.(b u-/R .at) XT/1000 3 H © o,t where R^ -p is the rate of discovery of BSTB to 1970, and X<p is the rate of drilling New classes) per year, at time T. The fitted coefficient values for the plays OIL PLAY; GEOLOGICAL ZONE . MMSTB/well (7.6)' of Recoverable Oil Reserves Appreciated Field Wildcat wells (of a l l intent which were studied are shown below: . COEFFICIENTS  .b3 bn D3 1.068 2.770 D2 1.300 0.583 Viking 1.140 0.232 Cardium W.79Q 1.988 Beaverhill Lake 1.970 2A&0 Gilwood 3.740 0.658 Keg River 0.939 1.106 Misc. 0.117 1.847 The discovery rate equations for each piay are shown in Figure 7.9< - 7 . 2 2 - 2 0 0 FIGURE 7.9 RATES OF DISCOVERY FOR OIL PLAYS IN ALBERTA BY RYAN'S MODEL Cumulative Reserves (BSTB), from beginning of play O D2 Beaverhill Lake Q K e S River © D3 ^ Gilwood ggg Cardium \ 7 Viking Note: Reserves are Appreciated Recoverable Reserves. Source: Table 7.5 TABLE 7.5 aJMULATIVE RESERVES, RATES OF DISCOVERY S FINDING COSTS FOR THE PLAYS IN ALBERTA (RYAN) CUMULATIVE RESERVES (BSTB) 0 0.5 1.0 1.5 2.0 2.5 2.70 D3 PLAY Rate bf Disc. (MMSTB/weli) Cost (t/Bbl) 2.96 6.76 2.42 8.26 1.89 10.58 1.36 14.71 0.822 24.33 0.288 69.44 0.07 285.71 — 0 0.10 0.20 0.30 0.40 0.50 D2 PLAY Rate of Disc. (MMSTB/weli) Cost U/Bbl) 0.758 26.39 0.628 31.85 0.498 40.17 0.368 54.36 0.238 84.07 0.108 185.36 ^ 0 0.04 0.08 0.12 0.16 0.20 VIKING PLAY Rate of Disc. (MMSTB/weli: Cost tt/Bbl) 0.264 75.76 0.219 91.32 0.173 115.61 0.128 156.25 0.082 243.90 0.035 555.56 ~ ' : 0 0.30 0.60 0.90 1.5 1.8 1.980 CARDIUM PLAY Rate of Disc. (MMSTB/weli: Cost U/Bbl) 29.40 0.68 . 24.97 0.80 20.53 0.97 16.09 1.24 7.22 2.77 2.78 7.19 0.12 166.67 " - 0 0.40 0.80 1.2 1.6 2.0 2.4 BEAVER-HILL LAKE PLAY Rate of Disc. (MMSTB/weli: Cost (t/Bbl) 4.85 4.12 4.06 4.93 3.27 6.12 2.48 8.06 1.69 11.83 0.91 21.98 0.12 166.67 ' " ~ . 0 0.10 0.20 0.30 0.40 0.50 0.60 GILWOOD PLAY Rate of Disc. (MMSTB/weli! Cost (C/Bbl) 2.46 8.13 2.09 9.57 1.71 11.70 •1.34 14.93 0.96 20.83 0.59 33.90 0.22 90.91 0 0.20 0.40 0.60 0.80 1.0 KEG . RIVER PLAY Rate of Disc. (MMSTB/weli: Cost (C/Bbl) 1.04 19.23 0.85 23.53 0.66 30.30 0.48 41.67 0.29 68.97 0.10 200.00 Note: Costs are <t/Bbl i n ground. Source: Calculated from Ryan's paper. - 7,24 - 202 Notice that Ryan postulates that the discovery rates decline linearly with cumu-lative reserves within a play. In view of our evidence i n Chapter 8 this seems implausible. 7.5.3. FINDING COSTS Figure 7.10 shows the estimated finding costs on the basis of Ryan's equations for each play. As before we have assumed $200,000 per well for exploration, but a l l wells are assumed to have intent o i l : I t can be seen that finding costs for each play r i s e extremely fast as the play deteriorates. These play related finding costs can be compared to the short run cycles i n the actual finding costs shown i n Figure 7.7. 7.5.4. ESTIMATE OF ULTIMATE RESERVES When finding costs increase substantially, or when the rate of discovery ap-proaches zero for a play we have an estimate of the Ultimate Recoverable Reserves for that play. This can be seen from Figure 7.9. More precisely, we may integrate equation (7.6) to give an equation for cumulative reserves: T T -b-./X./1000dt fR dt = b 4 . ( l - e o T ) BSTB (7.7) o ' T When T i s large we have IRQ ^dt = b^ which i s Ryan's estimate of the Ultimate o ' Reserve for the play, . In Ryan's paper he sums up the Ultimate Reserve estimates for each play to get an estimate of the Ultimate Reserves for Alberta, which i s some 12-13 BSTB of Recoverable Reserves. This represents the lowest estimate of Ultimate Recoverable Reserves which has been made and i t assumes no_newjplavs i - 7:25 - 203 FIGURE 7.10 FINDING COSTS FOR OIL PLAYS IN ALBERTA BY RYAN'S MODEL Cumulative Reserves (BSTB), from beginning of play Q D2 j£\ Beaverhill Lake Q Keg River 0 D3 Gilwood ||g Cardium ^7 Viking Note: Reserves are Appreciated Recoverable Reserves. Source: Table 7,5, - 7.26 - 204 7.5.5. INTERPRETATION OF EQUATION CONSTANTS As mentioned i n Section 7.5.4. the b^ coefficient provides an estimate of the Ultimate Recoverable Reserves for a play. The sum of the coefficients for each play i s an estimate of the Ultimate Recoverable Reserves i n the province. The Table on page 7.21 shows the sum of the b^'s as equal to 11.644 BSTB. Ryan ca l l s the b^ coefficient a proportionality constant. I t shows the proper-t i o n a l i t y between the estimated undiscovered o i l i n the play and the rate of discovery. 205 CHAPTER 8 ECONOMETRIC MODELS 8.1.1 Introduction 8.2.1 O i l Reserves Supply Function 8.2.2 O i l Pool Size 8.2.3 Gas Pool Size 8.2.4 Reserves Equation Results 8.2.5 D r i l l i n g Equation Results 8.2.6 Inventory of Undrilled Prospects i n D r i l l i n g Equations 8.2.7 Summary of Time Series Analysis 8.3.1 Cross Section Econometrics 8.3.2 Introduction to Cross Section Results 8.3.3 L i s t of Symbols Used 8.3.4 Cross Section Results 8.3.5 Mixed Cross Section and Time Series Results 8.3.6 Summary of Cross Section Analysis 206 SYMBOLS USED IN.CHAPTER 8 Note: The indexes t and T are used to denote the time to which a variable applies. DpE^'^'^ Dummy Variables Used i n the Pool Size Equations as follows: O i l Pool Equations: 1946-1952 The Constant Applies 1953-1956 Constant + D 1957-1963 Constant + \ + ® 2 1964-1970 Constant + + D2 + D 3 Gas Pool Equations: 1946-1951 The Constant Applies 1952-1956 Constant + 1957-1960 Constant + ^ + D 2 1961-1966 Constant + 0 . ^ 0 ^ 0 2 1967-1970 Constant + + T>2 + Dg + D^  D Estimated Undiscovered O i l Pools o G. . Geophysics Crew Weeks of % Company i n j Year I'll] G . Average Annual Geophysics Crew Weeks of Company i "Is I Inventory of Undrilled Prospects of O i l at Beginning ° of Period, number of prospects N p Number of Gas Pools Discovered by A l l Intents of D r i l l i n g , pools "th "t3"i N. . Successes of the i Company i n the j Year, number l , t ? of successes N. Average Annual Successes of Company i ' N Number of O i l Pools Discovered by A l l Intents of ° D r i l l i n g P. Total Property Acquired for Expoloration by Company i, v acres P g Demand Price for Recoverable Reserves of Gas, <7MCF ' i n ground 207 SYMBOLS USED IN Q3APTER 8, page 2 P„ Q Demand Price for Recoverable Reserves of O i l , $/Bbl i n ground P v Cost of Wells of Any Intent, $000/well x PB Prospects Variable, number of prospects R_ Reserves of Gas Discovered, BCF i n ground R Reserves of Oi l Discovered, 000 Bbls i n ground R Reserves of O i l Discovered by O i l Intent D r i l l i n g , °'° MMSTB/year S„ c Firm's Anticipated Average Gas Pool Size from Gas b' Intent D r i l l i n g , BCF i n ground S Firm's Anticipated Average O i l Pool Size from O i l 0 , 0 Intent D r i l l i n g , 000 Bbls i n ground X „ Rate of D r i l l i n g with Gas Intent, wells n Rate of Success with Gas Intent, gas pools X . . Number of NFW of the Company i n the 3" Year, wells X . Average Annual Wells D r i l l e d , wells X Q Rate of D r i l l i n g with O i l Intent, wells X Rate, of Success O i l with O i l Intent D r i l l i n g , o i l pools 0 , 0 8. ECONOMETRIC MODELS 208 8.1.1 INTRODUCTION We have now established the theoretical framework and the empirical base to estimate relationships of interest with a view to testing various hypotheses and to estimating the characteristics of the supply function of the Alberta petroleum Reserves Market. Already our discussion of "the data has tested some of the hypotheses which we had at the start. For example; i t has become clear that New Field Wildcats realize substantially lower success ratios than other exploratory wells. Also, while we have established that there has been significant directionality i n exploratory d r i l l i n g , the d i -rectionality i n o i l intent d r i l l i n g was obviously lower than for gas intent.. The discovery data for solution and associated gas and the relatively low d i -rectionality for o i l intent d r i l l i n g has provided previously unavailable evidence of how the excess supply of natural gas stemmed partly from o i l related d r i l l i n g . The data indicates that some 95% of o i l reserves i n Alberta have been discovered by o i l intent wells. But, i n addition, o i l intent wells have discovered some 23% of the non-associated gas reserves, and about 52% of the associated and solution gas reserves. Overall they discovered some 30% of a l l gas reserves. That i s , the o i l - p r o f i t motivated search for o i l has been responsible for almost a l l the o i l reserves, and has augmented the gas supply. I t was also of interest to observe how the directionality i n o i l intent d r i l l i n g tended to decline as the success ratio declined. Although the New Field Wildcats have realized a lower success ratio than the other exploratory wells, they have played an extremely important role i n discovering o i l and gas. Some 76% of a l l Primary Recoverable O i l Reserves were discovered by New Field Wildcats searching for o i l . To some degree this result stems from our definition of a discovery well as the f i r s t well into a pool, but i t does confirm the correctness of our focus on New Field Wildcat d r i l l i n g as the principal supply a c t i v i t y i n the Reserves Market. - 8.2 - 209 I t has also emerged that the largest firms, the Big Eight, have tended to have a sl i g h t l y higher success ratio i n d r i l l i n g and have obtained substantially larger pool discoveries than the other companies. The data suggest that these differences may result from the proportionately larger pre-drilling investment by the Big Eight in geophysics and land holdings. The Big Eight have always done proportionately more geophysics than d r i l l i n g . For example, i n 1960 the Big Eight did 57.2% of the geophysics which was undertaken in Alberta but only did 27.8% of the New Field Wildcat d r i l l i n g . Our analysis of d r i l l i n g efficiency and exploratory well costs has provided un-expected insights into the cost aspects of d r i l l i n g over the period of analysis. We have also discussed the lognormal characteristics of populations of pools discovered i n 5 year intervals. The analysis of. Chapter 5 has provided a tremendous amount of data which was not previously available, such as the analysis of well productivities and royalty rates, but the c l a r i f i c a t i o n and estimation of production delays i s perhaps the most original contribution. 8.2.1. OIL RESERVES SUPPLY FUNCTION The theoretical equation (6.3) suggests the variables which might be included i n an equation representing the reserves supply function. These variables are the o i l reserves price, the gas reserves price, the cost of exploratory wells, and the <f> variables. The <(> variables combine the expected pool sizes and the factors which have been postulated to determine the success ratios. At f i r s t we do not include these determining factors of the success ratios, but rather we include lagged success ratios which stand proxy for the expected success ratios. We f i t linear and log linear equations by regressing the variables; o i l reserves price, gas reserves price, cost of exploratory wells, the lagged New Field Wildcat success ratio in finding o i l pools, the lagged New Field Wildcat success ratio i n finding gas pools, the expected size of o i l pools and the expected size of gas pools, on the reserves discovered by New Field Wildcats. - 3.3 - 210 Each of these variables i s available i n our data base except the expected pool size. We discuss the derivation of this variable below. 8.2.2. OIL POOL SIZE S „ o>Q>T In equation (3.14) we have suggested that the expected pool size i s a function of the cumulated pools discovered. This postulate has a theoretical foundation in recent work of G. Kaufman." We have also f i t t e d equations i n which the pool size i s a function of the cumulated reserves discovered. Both approaches give empirical results of approximately equal significance. We f i r s t tested an equation l i k e equation (3.14) but with cumulated reserves, with the following results: T-l S „ = exp { 11.56 - 0.414 x 10~6 .ER _ } MSTB (8.1) ,0,0,T c 0,T i = 0 t: (20.0) (-4.6) 2 RB =0.49, F=20.8, D.W. = 1.2, NOBS = 22 t n c at 20 d.f. = 1.725 F at 0.05 c r i t i c a l point with (1,20) d.f. =4.351 G.M. Kaufman, Y. Balcer, D. Kruyt, "A Probabilistic Model of the O i l and Gas Discovery Process", Unpublished Paper, M.I.T. May 17, 1974. - 8-.'4 - 211 This equation represents a "long run" f i t a l l through the plays, as i l l u s -trated previously i n Figure 6.9, and consequently the corrected correlation coefficient i s rather low, at 0.49. Also, the error terms tend to be autocorrelated reflecting the unfolding of the four cycles i n the data stemming from the exploration of; Ti^ and D3, Cardium, Reaverhill Lake, Gilwood and Keg River. I f we introduce dummy variables for each of these time periods; 1946-1952, 1953-1956, 1957-1963, 1964-1970, we can approximate the average decline rate of pool size within each play, as follows: , T-l S „ = exp { 12.8 + 3.9D, + 3.3D0 + 1.0DQ - 0.1537 x 10" . .Z" R w > MSTB (8.2) o,o,l r 1 I 6 o,T t = 0 t: (24.9) (-4.1) (4.2) (1.8) (-6.2) 2 RB=0.75, F = 17.0, D.W. = 1.65, NOBS - 22 t Q 5 at 17 d.f. = 1.740 F at 0.05 c r i t i c a l point with (4,17) d.f. = 2.965 Equation (8.2) provides a considerably better s t a t i s t i c a l f i t than (8.1). I t can be seen that following the i n i t i a t i o n of each play the function shifts right-wards as illustrated i n Figure 6.9. The rate of decline of pool size within a play i s almost 4 times as rapid as the long run decline estimated from equation (8.1). I t i s of interest that equation (8.2) f i t s the data of the Keg River play less well than the others. Using the cumulated pools instead of the cumulated reserves we have the following results. - 8.5 - 212 T-l I = exp { 10.94 - 0.9047.x 10~2 .£ N _ } MSTB (8.3) o,o,T r o,l t = 0 t: (25.1) (-4.85) 2 RB =0.52, F=23.5, D.W. = 1.46, NOBS = 22 t n c at 20 d.f. = 1.725 . uo F at 0.05 c r i t i c a l point with (1,20) d.f. = 4.351 Equation (8.3) gives a sl i g h t l y better f i t than (8.1) for the long run pool size decline. With the dummy variables and the cumulated pools variable we have: • T - l S Q Q T = exp { 11.3 + 1.6^ + 2.3D2 + 3.2D3 - 0.0291.Z N q t } MSTB (8.4) t = b' t: (26.9) (2.2) (3.1) (3.4) (-5.5) 2 RB = 0.70, F = 1.3.5, D.W. = l'i74, NOBS = 22 * > 0 5 at 17 d.f. = 1.740 F at 0.05 c r i t i c a l point with (4,17) d.f. = 2.965 2 Equation (8.4) gives a lower RB than equation (8.2), but the error terms are more randomly scattered and the dummy variables are more evenly significant. Notice that the dummies i n equation (8.2) carry smaller and smaller coefficients but those of equation (8.4) get larger. This reflects the tendency over time for the discoveries to be more numerous but smaller. With this formulation the short run decline rate i s some 3g times the long run rate. For the purposes of the econometric modelling which follows we use equation (8.2). - 8.6 - 213 8.2.3 GAS POOL SIZE Sn _ „ As described i n Chapter 6 much of the time period of analysis was dominated by wildcatting for o i l and consequently the long run trend i n discovery sizes does not f i t an equation comparable to those for o i l . The long run trend ap-pears to be almost f l a t . This i s not the case, however, for equations reflecting the unfolding of plays. We have f i t t e d equations as follows: SgjGjT = exp { 3.4 +.1.9^-+ 2.2D2 + 2.0D3 + l.SD^ - 0.000317 Z R Q T" } BCF (8.5) T-l t = 0 t: (11.6) (3.8) (3.4) (2.8) (2.8) (-4.7) RB =0.50, F=5.4, D.W. = 2.2, NOBS = 23 ^ 0 5 at 17 d.f. = 1.740 F at 0.05 c r i t i c a l point with (6,17) d.f. = 2.7 2 I t can be seen that the RB i s considerably lower than the comparable equation for o i l , but the equation i s significant i n every respect. The equation with gas pools instead of reserves i s as follows: T-l Sg G T = exp { 3.5 + 2.6D1 + 2.3D2 + 2.2D3 + 2.5D4 - 0.0155 E Ng T } BCF (8.6) t = 0 t: (12.8) (4.7) (3.9) (3.2) (4.1) (-5.3) 2 RB =0.58, F=6.96, D.W. = 2.4, NOBS = 23 t 0 5 at 17 d.f. = 1.740 - 8.7 - 214 F at 0.05 c r i t i c a l point with (.6,17) d.f. = 2.7 The coefficients i n this equation, are a l l significant and the overall f i t i s rather better than equation (8.5). In the following analysis we use equation (8.6) for the expected gas pool size. 8.2.4 RESERVES EQUATION RESULTS * OIL RESERVES We f i r s t f i t t e d an equation i n a simple additive form as follows; *o,o,T " 1 6 6 ' 8 " 5' 1 PX,T + 1 ' 1 5 7 ' 8 PR,o,T-l t: (.55) (-1.96) (2.72) + 13.5 P„ n „ , - 1,203.8 Xo,o,T-l _ 5 8 > 9 XG,G,T-1 o,T-l- G,T-1 (.44) (-.56) (-.09) + 10.1 x 10 § o ^ T + 2.1 § G j G > j T MMSTB (8.7) (9.79) (1.61) RB2 = .92, F = 28.9, D.W. = 1.75, NOBS = 19 •t n r at 11 d.f. = 1.796 F at 0.05 c r i t i c a l point with (7,11) d.f. = 2.9.5 I t can be seen that cost of d r i l l i n g , the o i l price, and the expected size of o i l pools have significant coefficients. The gas price coefficient i s positive but not significant. Note that the pr-ices and costs variables i n these equations are i n current dollars. A l l the equations have also been f i t t e d with constant dollars, deflated by the Canadian Wholesale index, with results which were essentially unchanged from those reported. -.8.8 - 215 The e l a s t i c i t y of reserves with respect to the demand price for o i l i s close to 1.0 when calculated at the average values for each variable. This supply equation may be illu s t r a t e d as follows: $ PR,o,T .60 .50 .40 .30 .20 .10 FIGURE 8.1 ' LINEAR APPROXIMATION TO •THEORETICAL SHORT RUN OIL RESERVES SUPPLY FUNCTION r~— i , - - • - . - , r ~ 1 — 331333 33 33!" .331.1.3 - 3 313 -. 33 3333 ~z Vith3:S - i — ~ rp • 3337 3333 "i 3 33 33]i!" 3:3 33 33!' : r-/ — 07,O r?B 31B3 3iiinii 3 r~' 33 3 3 4-hfp 333 ' ." ' 133' ~ 3:3 333 3Lrri: 3Ef 131 3.3 133 333 3TJ 3 > i 1 :333 3133 3~3Li. ±i+r. 33 333 33 33 33 -j 33. ~ — - • -r — 33 33*. _i:C .,e a W V • ru. .j i_u!_ 1313 rs-x 133 fir} 3:3 3 3 1 *. 3:1 <31 •\ • 33 :B 33 .777; 3 3 r.3r. 33- 35 •3r-:-H ~77;~ _: ]_( .Tn."b 777:. •:±p;: r*- -33- 33 33 3 3 3 3 331 . : .-. 7777. 33 1T3Z1 -j i-j-1 : " ! ; 333 _r 3 i3 > • 1^3 '• '•- • 31 33: .3; i 331 .33 • ' 7 3 3 3—1 33 3t'l Mi. ; ! ; . IE! 31r •33: 3' 313: r'B .: 31 3 3 33 3:: 3 3 333 3^  77.;7 33|J r3J33 33 33 3 j : 3:1 :3:1 :"[ i i •;•• 3rr 3? 131 31B '•in W 33 F . . . 33 331 131 .: 31 13. 3 3 131 -1 :3.' -7771 13- 13; 33 L i l 3 f j : . r±± _77j7 3 3 j ;4".' ':"J"I J. r-P-r .33 u '3-.33 •:n±i. 133 33 33 3 , ".IXTT|11 100 200 300 400 500 600 700 800 900 MMSTB E(R _) o,OjT The equation may be viewed as a linear approximation to the theoretical supply functions sketched i n Figures 6.1 and 7.1. The shi f t parameter variables with significant coefficients accord to the theory. That i s , an increase i n d r i l l i n g costs shifts the supply curve leftward and an increase i n the ex-pected pool size shifts the curve rightward, as ill u s t r a t e d . As the region has been depleted the expected pool size has declined (in con-cert with the sequence of plays) and the supply curve has shifted leftward. In 1970 when the expected pool size was some 264,000 barrels of recoverable o i l the supply curve would be extremely cH.ose to the price axis i n Figure 8.1. Although we have mentioned that the price e l a s t i c i t y of reserves i s unlikely to remain constant through the l i f e cycle of a region we then f i t t e d a log linear equation. The results were as follows: - 8.9 - 216 Z"Ro,o,T " 2 6' 2 " 4- 1 Z* PX,T + 2 - 3 ^ P R , c , T - l *: (4.0) (-3.0) (2.16) 0.01ZnPR G T _ 1 + n.UU7;/o,o,T-l - n.1.R^*6'6'1"-1 Xo,T-l XG,T-1 (.03) (.61) (-.24) + °-8n*~So,c,T " °-15fofi6,6,T MSTB (8.8) (3.8) (.38) 2 RB =.81, F = 11.8, D.W. = 2.2, NOBS = 19 • t . Q 5 at d.f. = 1.796 F at 0.05 c r i t i c a l point with (7,11) d.f. = 2.95 The same variables are significant here but the e l a s t i c i t y of reserves with respect to the o i l price i s 2.3 rather than about 1.0 in the f i r s t equation. While the coefficient on the o i l price i s significant the log linear speci-fication appears to have biased the coefficient to be unbelievably high. GAS RESERVES The linear additive equation for gas reserves l i k e equation (8.7) gave a negative and completely insignificant coefficient on the demand price for gas, and a RB = 0.47. Consequently we only report the log linear form of the gas equation, as follows: l,iRG,6,T = 1 4 ' 9 ~ ^ ^ X . T +" °Mn\o,T-l (3.1) (-1.56) (.56) Xo,T-l *G,T-1 (1.33) (1.35) (2.22) -°'09lnSo,o,<I + 1-llnh,G,T BCF (8.9) (-.52) (3.63) 2 RB = .63, F=5.5, D.W. = 1.9, NOBS = 19 t Q 5 at 1.1 d.f. = 1.7.96 F at 0.05 c r i t i c a l point with (7,11) d.f. = 2.95 In equation (8.9) the variables; cost of d r i l l i n g , success ratio i n finding gas pools, and the expected size of gas pools have significant coefficients. The demand price for gas i s significant at the .20 l e v e l , but as may be ex-pected from our previous discussions of the gas industry the apparent e l a s t i c i t y i s rather low, at 0.3, i n the period of analysis. 8.2.5 DRILLING EQUATION RESULTS The theoretical equation (3.30) suggests that the same explanatory variables be included i n an equation to explain the rate of New Field Wildcat d r i l l i n g . - 8.11 - 218 OIL DRILLING (OIL INTENT PLUS BOTH INTENT) With the same six explanatory variables as equation (8.7) regressed i n simple linear form on New Field Wildcat d r i l l i n g (Oil + Both intent) the o i l price has a coefficient which i s almost but not quite significant at the .05 le v e l , although the overall f i t of the equation was reasonable with RB2 = 0.64 and F = 5.7. Therefore, we added the variable of lagged NFW d r i l l i n g . The simple linear equation and the log linear equation then gave significant coefficients for the o i l price variable. The simple linear regression gave results as follows: X o > T = 207.3 - 2.3 P X ? T t 227.H P R . 6 j T l l (1.68) (-3.4) (1.85) + 21.9 P D . _ . + 443.3 X°'°' T- 1 + 61.7 XG,G,T-1 K , b , l - ± y y c,T-l AG,T-1 (2.04) (.76) (.36) - 0.4 x 10" 5 I n T - 0.02 l r p T + 0.4 X m -i WELLS (8.10) 0 , 0 , i k,b,l 0,1-1 (.01) (.63) (1.4) RB~= .68, F=5.7, D.W. = 2.36, NOBS = 19 t Q 5 at 10 d.f. = 1.812 F at 0.05 c r i t i c a l point with (8,10) d.f. = 3.072 This equation gives significant coefficients for the two price variables and the cost variable. The pool size variables are completely insignificant. The e l a s t i c i t y of d r i l l i n g with respect to the demand price for o i l at the average variable values i s about 0.3. - 8.12 - 219 A log linear equation with the same 7 variables gave the following result lnXn m — 4.9 ~ 0. 8ZnPY + 0. 5lnPv „ 1 (4.5) (-5.2) (4.1) X X + 0.09 P D _ _ _ + O.lln 0>°> TJ: + Q.QSZW G > G > T - 1 K , b , l - 1 y y P,T-1 AG,T-1 (2.6) (1.7) (1.1) - 0.06Zn§ „ ••+ 0.08Zn§ +. 0.9Z*X (8.11) 0 , 0 , 1 «>V3>i • 5 (-2.2) (1.8) (5.3) 2 RB =0.81, F-10.8, D.W. = 2.8, NOBS = 19 i t n c at 11 d.f. = 1.812 F at 0.05 c r i t i c a l point with (7,11) d.f. - 3.07 This equation estimates an el a s t i c i t y of 0.5 for the wildcat d r i l l i n g response to change i n the demand'price for o i l . "Note that the•elasticity between the wellhead price and d r i l l i n g would be larger because the elasticity' between the wellhead price and the demand price i s greater than one and probably about 3.5 during the period of analysis (see Table 5.5). The implied short run' e l a s t i c i t y between wellhead price and wildcat d r i l l i n g was, therefore, about 1.7. The e l a s t i c i t y of 0.5 between the demand price for o i l and wildcatting for o i l i s higher than the average estimated from equation (8.10) and i s also higher than further estimates which w i l l be discussed below. * Note that we refer to short run e l a s t i c i t i e s throughout Chapter 8. The to t a l effect upon d r i l l i n g of a change i n price, over a l l future time periods, would be larger and w i l l be a function of the coefficient on the lagged d r i l l i n g variable as well as the other variables (notably the o i l pool size variable) which are never constant period to period. - 8.13 - 220 GAS DRILLING (GAS INTENT) The gas d r i l l i n g equations do not give as unequivocally significant linkages between price and drilling.as the o i l equations. In a l l equations the demand price for gas carries a positive coefficient but i t i s not always significant. With the same six explanatory variables as equation (8.7) and the lagged gas d r i l l i n g variable we have the following result for an equation i n simple linear form. X = 184.8 - 1.2 P„ m * 57.2 P, G,T X,T AR,o,T-l (3.1) (-2.8) C.8H) X X + 10.4 P -.firifi.S 0» 0» T" 1 - 7.1 G,G,T-1 o,T-l AG,T-1 (1.92) (-1.8) (-.07) + °- 0 0 0 1 So,o,T - °- 1 7 §G,G,T + °' 2 4 XG,T-1 WELLS (8.12) (.86) (-.80) (1.08) 2 RB =.57, F=4.0, D.W. = 2.3, NOBS = 19 t 0 5 at 10 d.f. = 1.812 F at 0.05 c r i t i c a l point with (8,10) d.f. = 3.072 The e l a s t i c i t y between d r i l l i n g and gas of the variables. The price of o i l has fi c i e n t . The gas d r i l l i n g equation i n log linear with an RB2 = 0.48 and F = 3.07 and the i s 0.033 but not significant. price i s about 0.1 at the average value a positive but not significant coef-form i s considerably less significant coefficient on the demand price for gas - 8.14 - 221 8.2.6 INVENTORY OF UNDRILLED PROSPECTS IN DRILLING EQUATIONS The foregoing equations have, used the variables of lagged o i l success ratio and lagged gas success ratio as proxies for the expected success ratios. We now explore the possi b i l i t y of e x p l i c i t l y incorporating the Inventory of Undrilled Prospects as our explanatory variable. OIL PROSPECTS In Section 3.3.3. we suggested a possible specification for the equation des-cribing the Inventory of Undrilled O i l Prospects, by equation (3.6). Treating equation (3.6)as the simplest formulation which i s possible, we can empirically identify each of the variables on the right hand side of the equation; although not without some complexities for the expected pool size and expected success ratio variables. There remains, however, the unknown parameter b-^ gj and there i s apparently no means of estimating this single parameter because the inventory i t s e l f i s not observable. As a result, the best that can be done i s to treat the components of the inventory separately for econometric purposes. Our calculation (according to equation (3.6) but omitting the P v term) of the A,t bonus contribution to the inventory of prospects i s shown i n Table 8.1. Up to 1954 a negligible number of prospects had been purchased by bonus payments. The series appears reasonable between 1954 and 1968 and indeed the cumulated pros-pects derived i n that period i s approximately equal to the sum of the o i l and both intent New Field Wildcats which were d r i l l e d . In the earlier period prospects were derived mainly through geophysics work. Although, of course, geophysics was important throughout the period. In 1969 and 1970 the series seems to be unreasonably high. This occurs because the demand price for o i l de-clined, the expected pool size f e l l and the success ratio f e l l i n these years. Although i t can be seen that the bonus payments series and the "prospects derived" series are f a i r l y highly correlated there i s a considerable amount of random error i n the "prospect derived" series. As a result we have sometimes used the bonus series rather than the prospects series as an explanatory variable. - 8.15 - 222 The geophysics and d r i l l i n g variables can be introduced separately i n their natural units. Alternatively, we can combine the two variables; and to avoid the problem of scaling the variables so that a meaningful difference could be calculated, we have also tested the variable of cumulated geophysics per cumulated d r i l l i n g (of a l l intents). GAS PROSPECTS As with the o i l prospects we are required to simplify the suggested formu^ lation of equation (3.7) and to consider the components separately. The geophysics activity i s not specific to either o i l or gas exploration and we use the same variable as i n considering the o i l prospects. That i s , we use a l l the geophysics crew weeks, or geophysics per cumulated wells d r i l l e d of a l l intents, i f we employ the d r i l l i n g variable separately we use the gas intent New Field Wildcats. The components of the Inventory of Undrilled Gas Prospects are shown i n Table 8.2. The prospects purchased series appears rather erratic but the numbers are in the correct range, and the sum of prospects from 1952 to 1970 (2,336) i s approximately equal to the gas intent New Field Wildcats d r i l l e d i n that period (2,187). - 8.16 - 223 TABLE 8.1 COMPONENTS OF INVENTORY OF I.H-JDRILLED OIL PROSPECTS Exploration O i l Bonus Bonus Contribution To Cum. Geophysics Payments Inventory Of Prospects Per Cum. NFW .'($000) Annual Cumulative (Crew wks. per well) (Number of Prospects) 1946 - - - 6.06 7 - - - 8.49 8 53 - - 11.65 9 195 .02 .02 12.32 1950 .232 .17 .19 15.05 1 265 .26 .45 15.76 2 153 .48 .93 16.44 3 1^987 12 13 16.82 4 23,827 115 .128 16.82 5 15,031 100 228 16.50 6 4,410 43 217 15.83 7 19,314 217 488 14.93 8 17,223 25 513 13.93 9 17,130 118 631 13.03 1960 9,962 120 751 12.35 1 10,900 357 1,108 11.66 2 12,868 438 1,546 11.11 3 19,499 570 2,116 10.55 4 24,447 380 2,496 9.98 5 39,804 347 2,843 .9.28 . 6 21,764 595 3,438 8.86 7 18,723 567 4,005 8.70 8 31,681 1,228 5,233 8.39 9 51,604 6,143 11,376 8.23 1970 8,166 1,361 12,737 8.13 Note: The 6 factor =0.6 TABLE 8.2  BONUS CONTRIBUTION TO INVENTORY OF UNDRILLED GAS PROSPECTS Exploration Gas Bonus "Payments $000 NIL 1153 3,226 17,458 7,075 1,514 8,525 6,337 4,193 4,384 1,405 4,171 . 901 ' 787 397 917 1,719 1,909 7,597 2,049 Bonus Contribution To Inventory Of Prospects Annual Cumulative (Number of Prospects) 239 239 54 293 394 687 147 834 51 885 507 1,392 60 1,452 70 1,522 124 1,646 60 1,706 115 1,821 15 1,836 10 1,846 8 1,854 35 1,889 97 1,986 13 1,999 151 2,150 186 2,336 - 8.18..- 225 We tested many equations with the additional var5-ables; a l l bonus payments, bonus payments for exploration licences, estimated prospects, geophysics crew weeks, and cumulated geophysics crew weeks per cumulated wells d r i l l e d , with some of the other variables which we have included i n equations (8.7) to (8.12). Generally, the bonus or prospect variables were signed correctly and either significant or close to being significant i n the o i l d r i l l i n g equations, but not i n the gas equations. The geophysics variables were not significant i n either sets of equations. The average e l a s t i c i t y between the o i l price and o i l d r i l l i n g , when the o i l price coefficient was significant, ranged between 0.3 and 0.4. The comparable range for gas d r i l l i n g was between 0.09 and 0.13. An example of a log linear o i l d r i l l i n g equation which includes the prospects variable, identified as PB^, i s shown below. ZnX. = 3.98 - 0.6ZnPY + 0.4ZnPp n „ , o,T X,J. R,o,T-l (3.7) (-3.99) (3.22) + 0.03ZnPBT + O.lSZn + 0.9Z«X ^ o,T-l (1.49) (1.67) (5.2) 2 RB = .74, F = 11.05, D.W. = 2.47, NOBS = 19 t Q 5 at 13 d.f. = 1.771 F at 0.05 c r i t i c a l point with (5,13) d.f = 3.025 The prospects variables, PBp i n equation (8.13) i s significant at the .10 level and the o i l price coefficient i s significant at the .005 le v e l . - 8:19 - 226 8.2.7 SUMMARY OF TIME SERIES ANALYSIS We f i r s t f i t t e d equations to derive variables for the expected pool sizes which could reasonably be assumed by industry at any time. The best f i t t i n g equations; equation (8.2) and equation (8.6) were then used for the expected pool sizes i n the following reserves equations and d r i l l i n g equations. The linear reserves equations indicated that the average short run e l a s t i c i t y of o i l reserves with respect to the demand price for o i l was about 1.0. The log linear equation gave an e l a s t i c i t y of 2.3. I t was stressed, however, that the log linear equation was a poor specification for the supply curve, leading to an over-estimate of the e l a s t i c i t y . The log linear reserves equation for gas gave an e l a s t i c i t y of 0.3. Overall the gas price tended to be less significant and gas reserves apparently showed a lower response to gas prices than o i l reserves to o i l prices. This seems to be consistent with the analysis and discussion of Chapter 6. The o i l d r i l l i n g equations gave an e l a s t i c i t y between d r i l l i n g and the demand price for o i l of between 0.3 and 0.5. We pointed out that the approximate e l a s t i c i t y between wellhead o i l prices and NFW d r i l l i n g was about 1.7 during the period of analysis. The e l a s t i c i t y of gas d r i l l i n g with respect to the demand price for gas was estimated at about 0.1, or less. We then attempted to estimate the number of prospects which were brought into the inventory of the industry through bonus payments. This variable was used i n d r i l l i n g equations i n order to obtain further estimates of the price e l a s t i c i t i e s . The o i l price e l a s t i c i t i e s were between 0.3 and 0.5, as i n equation (8.13). The gas price e l a s t i c i t i e s were between 0.09 and 0.13. These lat t e r estimates tended to corroborate the values estimated i n equations (8.7) to (8.12). I t i s of interest to compare equations l i k e equations (8.7) and (8.10) to the analysis described i n Chapter 7. There i s a direct relationship because equation (8.7) gives an estimate of reserves discovered each year conditional upon the values of the explanatory variables, and equation (8.10) gives estimates of o i l intent wildcat d r i l l i n g . Therefore, the estimated reserves divided by the estimated d r i l l i n g gives us a discovery rate per well, given the values of the explanatory variables. - 8;20 - 227 Holding a l l explanatory variables constant .except the pool size we could project pool size as a function of cumulated reserves, as i n equation (8.1), to y i e l d a projection of annual reserves discovery rates per o i l intent well d r i l l e d , similar to those presented i n Figure 7.3. 8.3.1. CROSS SECTION ECONOMETRICS We have argued i n Section 3.4.1. that the expected success rate of a company from o i l intent d r i l l i n g i s : E ( Xo,o,T ) = ^o.o^o.T^o.T^o,*^ (8.14) I f we now examine a cross-section of companies, at a given point i n time, we may drop the D q ^ variable because i t would apply equally to a l l firms which were d r i l l i n g i n the region. Thus we have the two variables X T and I „ which may o,i o,i z distinguish -the performance of firms, at any time. Our data f i l e s provide data by company for X Q ^. Also, the actual success rate from NFW d r i l l i n g may serve as a proxy for the expected success rate. The com-plexities of the Inventory of Undrilled Prospects variable, described i n Section 8.2. 6, suggest that we should extract the components from the variable, as feasible, for econometric purposes. There are also data limitations because bonus payments are not generally available by company for a cross-section analysis.. Accordingly, data for separate companies was compiled for the following "basic" variables for Alberta: Geophysics Crew Weeks undertaken (1964-1970) "Show" successes of NFW, a l l intents (1964-1970) Number of NFW d r i l l e d , a l l intents (1964-1970) Net land holdings (1970) Permits 8 reservations (property) acquired for exploration (1967+1968) Average depth per NFW, based on dryholes The data of the basic variables above was manipulated into many forms for em-p i r i c a l testing. Except for the Land and Permits and Reservations, the variables were measured by their average annual rate for the period 1964-1970. C . 2 I 228 In the case of the geophysics crew weeks data there were some years i n which the • crew weeks for a company' were not available. In these cases; (1) the company's average annual rate was calculated for those years with data. This rate was then assumed to apply to the whole 1964-1970 period, and (2) the d r i l l i n g , successes, cost and depth data were collected only for the corresponding years with geophysics data. For instance for some companies l i k e .Imperial., which had geophysics data for each year 1964-1970 i n our data f i l e s , there was no problem. However, for some com-panies such as Sun O i l Company, which had data for only six years of the period, a problem arose when attempting to compare such companies to others for which a more complete set of data.was available. The completeness of the geophysics data limited the number of observations usable i n the study. Data was collected for those companies which had geophysics data for at least 2 years of the period 1964-1970. The data for each company was summed over each year of the period; the sum was then divided by the number of years for which the data had been summed to yield an "average" figure which was used as an estimation of the annual rate of the particular a c t i v i t y for a company. In most of the equations we f i t three sets of data. The (A) set i s the collection of the top 10 companies as ranked by the amount of d r i l l i n g . The (B) set of ob-servations consist of the top 15 companies, and the (C) set of observations consist of a l l those companies for which there was complete data. 8.3.2. INTRODUCTION TO CROSS SECTION RESULTS A much larger number of regression equations were tested than we report i n the following Sections. Our discussion tends to focus on useful results leading to the conclusions of Section 8.3.6. In particular we tested certain variables which do not appear i n any of the reported equations. For example we tested the variable of bonus payments instead of acres of permit and reservation property purchased. Because the results were not encouraging and because our approach here i s to view explanatory variables as production process inputs the results are not reported. Also we used variables of feet d r i l l e d and cost of wells d r i l l e d i n the place of wells d r i l l e d , but without any improvement over the equations reported which use wells d r i l l e d as the primary exploratory variable. However, both significant and insignificant equations are discussed as they may shed li g h t on the problem. -8.22 - 229 8.3.3. LIST OF SYMBOLS USED•IN SECTION 8,3 N. . = successes of the i t h company i n j t h year, j = (1, where 1 corresponds to the 1st year for which there was data, and m corresponds to the number of years for which there was data (1964-1970). = ' t o t a l property acquired for exploration by company i i n 1967 and 1968. We use A, B, C, D, unsubscripted, as coefficients i n the regres-sions equations. standard error of the coefficient estimate. a = the correlation coefficient of X to Y. the symbol with a ~, indicated the calculated value. U.. = theoretical error term. NOBS = number of observations PX:Y = In = before a variable indicates the log of the variable (to the base e, unless otherwise specified) - 8.23 - 230 N. vtm m = E N: 3-1 1>>3 m average annual successes of company i. m m G. . = geophysics crew weeks of the i t h company i n the j t h year, t-j 3 3 = (1, ... , m), where 1 corresponds to the 1st year for which there was data and m corresponds to the number of years for which there was data (1964-1970). m G. = EG. . m G E G. . — i m 7=1 G. = — — — = — = average annual geophysics crew weeks m m r-of company ^ . i,3 = number of NFW of the i t h company i n the j t h year, 3 = (l,...,m), where 1 corresponds to the 1st year for which there was data and m to the number of years for which there was data (1964-1970). m X. = E X . . \ m 7=i ^3 X. = - — = — = average annual wells d r i l l e d . m m ^ - 8.24 - 231 8.3.4. CROSS SECTION RESULTS To set the stage we f i r s t examine an equation with only the rate d r i l l i n g as an explanatory variable: N. = A.jS.U. (8.15) This can be written i n log linear form as i n equation (8.16) and the f i t t e d coefficients are shown i n equation (8.17). InN. - Ink ± BlnX. + In U. (8.16) IrN. = -3.2 + 1.692ZnX. (8.17) Is % 2 a: (0.47) (0.20) RB = 0.76 t: (-6.76) (8.34 F = 68.97 D.W. = 1.89 NOBS = 22 t n, at 20 d.f. = 1.725 F at. 0.05 c r i t i c a l point with (1,20).d.f. = 4.35 PN. : X. = 0.8805 ^ i The log-linear equation (8.17)' can be reinterpreted i n the form of equation (8.15) 1.69 N. = 0.041X. (8.18) The equation shows a high degree of significance, and i t indicates substantial increasing returns to scale. In fact the value of the exponent on X^ i s significantly greater than 1, at the 95% confidence le v e l . - 8.25 - 232 After examining various equations we concluded that geophysics and d r i l l i n g explained successes with most significance. The following non-linear equation was tested: B C JL = A.XrG\..U. (8.19) Averaged annual data was used for each variable. Rewritten i n log-linear form we have; ZnfL = Ink + BZnX\ + CZnG\ + Z«u\ (8.20) The (A) set of observations (top 10 companies) yielded the following results: ZnN. = -3.63 + 1.15ZnX. + 0.38ZnG. (8.21) a: (0.68) (0.36) (0.126) RB2 = 0.888 F = 36.60 t: (-5.35) (3.18) (3.04) t n c at 7 d.f. = 1.895 . uo D.W. = 2.60 NOBS = 10 F at 0.05 c r i t i c a l point with (2,7) d.f. = 4.74 p ZnN.:ZnX. = 0 - 8 9 p ZnN.:ZnG. = °' 8 9 p ZnX. :ZnG. = °- 7 4 Rewritten i n the form of equation (8.19), we have; _1.15 _0.38 N. = 0.027X. .G. (8.22) -3.26 - 233 Subject to the limitation that these results are for only 10 observa-tions for the largest 10 companies, a l l s t a t i s t i c a l tests show a high degree of significance. This i s i n spite of the multicollinearity. Apparently the amount of geophysics crew weeks can be regarded as an input activity which, to a degree, can substitute for d r i l l i n g and . which tends to increase the success ratio. When the (B) set of data was used, the significance level of the estimates f e l l (on the whole) but remained significant. However, the adjusted RB2 f e l l to 0.76; the F ratio f e l l to 22.79. These results could be due to greater randomness which more inaccurate data might bring (smaller companies having less accurate data i n our f i l e ) . The (C) set of data ( a l l companies ) 'followed the "trend" set by the (B) set of data. The estimates were less significant. Zn§.= -3.57 + 1.54ZnX. + 0.179ZnG. (8.23). c: (0.588) (0.25) (0.171) RB2 = 0.77 F = 35.21 t: (-6.07) (6.22) (1.05) t Q 5 at 19 d.f. = 1.729 D.W. = 1.86 NOBS = 22 F at 0.05 c r i t i c a l point with (2,19) d.f.- 3.52 P ZnN.rZnX. = °' 8 8 p ZnN.:ZnG. = °' 6 0 p ZnX.:ZnG. = °" 5 7 Note that the increased number of observations tended to make d r i l l i n g more significant with a larger coefficient value, and geophysics less significant with a lower coefficient value. The coefficient on Geophysics has become insignificantly different from zero. - 8,27 - 234 We then tested land holdings as an additional variable but found i t not significant. Consequently, a new variable measuring land acquired (in acres) by each company for exploration purposes i n 1967 and 1968 was sub-stituted, as follows: B C D N. = A.X..G..F..U. (8.24) ^ i ^ % x In log linear form: ZwN. = Ink + BZnX. + CZnG. + DZnP. + InU. (8.25) ^ , ^ ^ ^ ^ The equation was tested for the top 10 companies (set A), the top 15 compa-nies (set B) and a l l companies except three (Set C). The regression with the top 10 companies provided interesting results. The (B) and (C) data sets gave results similar to the (A) set and i t i s instructive to examine the regression runs for the larger data sets. The (B) set of data gave the following results: ZnN. = 0.94 + 1.021ZnX. + 0.31ZnG. - 0.30lZnP\ (8.26) ^ ^ % i p: (0.99) (0.18) (0.08) (0.08) RB2 = 0.88 t: (0.95) (5.69) (3.83) (-3.79) F = 36.89 D.W. = 1.23 NOBS = 15 t Q 5 at 11 d.f. = 1.796 F at 0.05 c r i t i c a l point with (3,11) d.f. = 3.59 p ZnN.:ZnX. = °' 8 3 1 p ZnN.:ZnG. ~ °*71*- P ZnN.:ZnP. = -0.1803 - 8.28 - 235 2 This regression yields encouraging results. The adjusted R i s high for a cross section data model. I t appears that geophysics per acreage purchased i s the important explanatory variable rather than geophysics or land separately. Equation (8.26) rewritten into nonlinear form becomes: 1.02 0.31 -0.30 N. = 2.57X. .G. .P. (8.27) The (G) set of data reduced the significance of the coefficient on geophysics. 2 However, i t was significant at the 90% confidence level. The RB f e l l to 0.77. The estimated coefficients i n equation (8.26) are each significantly different from zero, and the estimated constant i s not significantly different from 1.0. Also, i t can be shown that the coefficient on X. i s not significantly different from 1.0. The coefficient on G., however, i s significantly less than 1.0,.ranging between 0.13 and 0.49 at the 95% confidence level. The coefficient on P. ranges •z, to between -0.48 and -0.12 i n the 95% confidence interval. Consider the results of equation (8.27) rewritten i n the following form. - _1.02 G. 0.31 N^ = 2.75Xi .(-^-) (8.28) Rewriting the equation i n this manner, one may consider the new variable G i as a proxy for the level of intensity of geophysics on land taken up. P£ - 8 . 2 9 - 236 Equations (8,27) and (8.28) provide interesting analysis. I f the equation (8.28) can be viewed as a production function then d r i l l i n g has the following marginal productivity: 3N. 0.02 G. 0.31 — = (1.02) (2.57)X. . ( — — ) 3X". % Pi 0.02 G. 0.31 = .2 . 625?. . ( — — ) (8.29) % P. ^ Taking Imperial O i l as an example, one may calculate the marginal addition to .success for a well d r i l l e d as: = (2.62)(1.039)(0.1058) = 0.288 Therefore, the marginal productivity of d r i l l i n g for Imperial O i l i s 0.288 which we would expect to be somewhat less than the average success r a t i o , which was 0.336*. * I t should be remembered that' this analysis deals with "shows" successes of both o i l and gas. .- 8.30 - 237 8.3.5 ' MIXED CROSS SECTION AND TIME SERIES RESULTS Consider an equation l i k e (8.19) but applying to the year by year data for each company. _B _C N. . = A.X. ..G. ..U. . fo o n A %33 ^ J l 7 ts3 ,^«7 (8.30) and we use the Big Eight Companies ( i = 1,...,8) for the years 1964 to 1970. We now have a possible 56 observations but i n some years some companies had zero successes which reduces the useable observations to 47. The results were as follows: ZnN. . = -2.68 + 0.906ZnX. .+ 0.328ZnG. . (8.31) 2 a: (0.73) (0.097) (0.156) RB = 0.71 (-3.68) (9.350) (2.112) F = 57.2 D.W. =1.64 NOBS = 47 * n c at -44 d.f. = 1.68 . Uo F at 0.05 c r i t i c a l point with (2,44) d.f. = 3.23 Rewritten i n the form of equation (8.30), we have: 0.906 0.328 N. . = 0.069X. . .G. . V o 0„v ^ J J i,3 (8.32) I t can be seen that the equation shows a high degree of significance. The results are similar to equation (8.21),although the coefficient on d r i l l i n g i s now some-what less than one. -8,31 - 238 8.3.6 SUMMARY OF CROSS SECTION ANALYSIS We can summarize the results described i n the previous pages as follows: TABLE 8.3 EQUATIONS EXPLAINING NUMBER OF SUCCESSES Equation No. Data Set Explanatory Variable Coefficients 8.17 8.19 8.23 8.26 8.31 C A C B X 1.69 1.15 1.54 1.02 0.91 0.38 0.18 0.31 0.33 -0.30 * Mixed cross section and time series data for the Big Eight companies. I t can be seen that, with the A,B and mixed cross section and time series data the coefficient on the d r i l l i n g variable was approximately equal to 1.0, and the coefficient on geophysics or geophysics per land area purchased, was ap-proximately 0.3. As a result i t can be said that the success ratio obtained by the larger companies (8-15 largest companies) was a function of the intensity of geophysics undertaken per land area purchased or per well d r i l l e d . The e l a s t i c i t y between geophysics and success r a t i o , however* was considerably less than 1.0 as would be expected, and was about 0.3, indicating a high degree of diminishing returns to increases i n the geophysics input. I t may be noted that the property variables enter the equations negatively when geophysics was included, indicating that the extent of property purchased or held could not explain the higher success ratios of some companies when the rate - 8.32 - 23S of geophysics was also considered. This means that the analysis does not show a l i n k between mere land holdings and more prospects leading to higher success ratios, but rather i t shows that the intensity of geophysics per land holdings was important. 240 CHAPTER 9 APPENDIX 9.1 O i l P r o r a t i o n i n g i n A l b e r t a 9.1.1 I n t r o d u c t i o n 9.1.2 The 1950 P r o r a t i o n Plan 9.1.3 The "Residual MPR" Plan (the 1957 Plan) 9.1.4 The 1964 Plan 9.1.5 Summary 9.2 Note on Geology 6 Western Canadian Sedimentary Basin 9.2.1 I n t r o d u c t i o n g.2.2 Basic P r i n c i p l e s of Petroleum Geology 9.2.3 Western Canadian "Sedimentary Basin 243 9. APPENDIX 9.1 OIL PRORATIONING IN ALBERTA * 9.1.1. INTRODUCTION The Alberta petroleum industry' has been productive for many years but before 1947 the growth pattern was erratic. TABLE 9.1 ALBERTA OIL S GAS PRODUCTION YEAR CRUDE OIL NATURAL GAS (MSTB/YR) (BCF/YR) 1925 171.9 N.A. 1930 1,444.7 N.A. 1935 767.3 N.A. 1940 8,221.0 55.1 1945 7,642.9 62.3 1950 27,149.4 73.3 1955 112,853.1 161.7 1960 130,498.8 420.9 1965 183,729.1 1,082.9 1970 337,625.0 1,425.0 Note: In addition to Crude Oil and Natural Gas, Condensate, Pentanes Plus, Propane, Butane and Sulphur are the major products of the industry. Source: A.E.R.C.B. The ri s e i n o i l production from 1925 to 1930 stemmed from development of Turner Valley and the heavier o i l s from the Wainwright area. By 1935 the Shallower horizons of Turner Valley were mostly depleted, but i n 1936 deeper horizon discoveries were made and o i l production again grew rapidly, reaching a wartime peak i n 1943. This section i s based principally on G.C. Watkins, Op. C i t . , Dec. 1971, pp. 53-91. - 9 . 2 - 242 The f i r s t formal prorationing i n the province pertained to production from the deeper horizons of Turner Valley and was primarily concerned with efficient recovery from the reservoir, rather than with allocation of market demand between reservoirs. The Alberta industry emerged as nationally important following the Leduc discovery i n 1947. Between 1945 and 1950 o i l production increased by about 4 times, and by 1955 i t had increased by some 15 times. The expanding Alberta o i l reserves permitted the rapid penetration of extra provincial markets and by 1951 exports were being made to the U.S. TABLE 9.2 DISPOSITION OF ALBERTA CRUDE OIL PRODUCTION, 1947 - 1951 (yearly average: barrels per day) YEAR ALBERTA SASKATCHEWAN MANITOBA ONTARIO TOTAL 1947 15,527 3,030 - 18,557 1948 20,138 6,480 1,990 - 28,608 1949 31,121 18,689 3,279 - 53,089 1950 37,782 25,768 4,348 - 67,898 1951 41,776 30,376 12,561 37,442 123,414 Source: G.C. Watkins , Op. C i t . , pp. 59. But the growth i n markets was insufficient by late 1949 and early 1950 to keep up with the growth i n productive capacity. Excess productive capacity became apparent, principally i n the Redwater and the Leduc Woodbend D-2 and D-3 f i e l d s , as recorded i n Table 9.3. The development of new f i e l d s , including Golden Spike and Wizard Lake, and the apparent rate of new discoveries i n relation to prospective market growth rendered unlikely any early return to a close balance between productive capacity and demand. *. Including exports to the U.S. of 1,268. - 9.3 - 243 Also the effect of changes to provincial land regulations i n July, 1947 which provided for the surrender to the Crown of one half the Crown acreage under company permit, before conversion to a production lease, may have been to stimulate excessive intensive development well d r i l l i n g at that time. TABLE 9.3 PRODUCTION S CAPACITY, LEDUC S REDWATER FIELDS, i n 1950 * NO. OF CAPABLE PRODUCTIVE EXCESS RESERVOIR . OIL WELLS CAPACITY ** PRODUCTION CAPACITY  (Bbls/day) (Bbls/day) (Bbls/day) (%) Leduc-Woodbend D-2 209 11,410 . D-3 297 28,930 Redwater D-3 733 92,400 Source: G.C. Watkins, Op. C i t . , pp. 59. 7,870 3,540 31.0 20,699 8,231 28.5 29,442 62,958 68.1 See J.H. Dagher, Effect of the National Oil Policy on the Ontario Refining  Industry, unpublished PhD Thesis, McGill University, Montreal, 1968, pp. 244. Imperial Oil owned 75 percent of the Leduc (1947) reservoir, but despite a similar prior land position, owned only 50 percent of Redwater (1948). Imperial stated i t completed 286 producing wells i n Redwater to meet competition from the development of Crown acreage leased to 20 other companies (Ibid, p. 244-5). As determined by Maximum Permissive Rates of Production. - 9 . 4 - 244 ,9.1.2. THE 1950 PRORATION PLAN In response to the excess of productive capacity, i n 1950 the major crude o i l purchasing companies - Br i t i s h American Oil Company and Imperial O i l Limited -commenced limiting the volume of o i l they would purchase from certain f i e l d s . This.system, referred to as a well and pipeline acceptance system, provoked dissatisfaction among several producing companies operating i n the Province. In September and October 1950 the provinces' Petroleum and Natural Gas Conserva-tion Board held hearings and by December 1, 1950 they had introduced a plan for prorationing of o i l production to market demand. The 1950 Plan was based on two factors: well costs and well productive capacity. The f i r s t factor involved assigning to each e l i g i b l e well an 'economic' allowance. The economic allowance was a combination of two concepts expressed at the October hearing: (1) a minimum production allowance for each producing well to cover operating costs; and (2) compensation for well d r i l l i n g and completion costs. The allowance was graduated with well depth, and i s shown i n Figure 9.1. The function adopted was based on a cost analysis of the relation-ship between pool development and operating costs and depth, and was believed to properly reflect the major expenses involved i n d r i l l i n g and operating wells. The economic allowance was fixed for each well and did not vary with market demand, except where the market demand did not exceed the sum of well economic allowances i n the Province. The second factor concerned the allocation of demand remaining after satisfac-tion of the well economic allowances. This residual demand - defined as the difference between t o t a l demand and the t o t a l of the economic allowances, when positive - was allocated among the pools and wells i n proportion to the well or pool productive capacity, as represented by the MPR or MER. The proration plan adopted by the OGCB instituted an economic allowance designed to compensate for well d r i l l i n g , completion and operating costs which would thus guarantee long-term and short-term p r o f i t a b i l i t y for any well d r i l l e d capable of economic operation. This tended to encourage excessive development d r i l l i n g . - q c _ 245 FIGURE 9.1 ECONOMIC S MINIMUM WELL ALLOWANCES UNDER THE  1950, 1957 S 1964 PRORATION PLANS, PROVINCE OF ALBERTA l o a . . '— 190 180. VT • > ' ' 1 ' « 1 1 I 1 « • 1 t ° loco 2,000 3,600 4flOO 5.00O 6.000 7.000 i.OOO ^OOO I0.CO0 11,000 12,000 1 ) 0 0 0 l+OOO 15000 Well Depth (feet) Source: G.C. Watkins, Op. Cit. ,,Dec. 1971, pp. 75. - 9.6 - 246 9.1.3. THE "RESIDUAL MPR" PLAN (THE 1957 PLAN) In 1957 the Board called a hearing to review the main principles of the 1950 Plan and i n particular to consider the role and definition of the economic allowance. * I t reaffirmed i t s belief that an economic allowance should be assigned to a well to cover operating costs and to permit recovery of d r i l l i n g costs over "a reasonable period of time". However, the Board saw l i t t l e j u s t i f i c a t i o n for the indefinite continuance of an economic allowance which would allow the several fold recovery of d r i l l i n g costs. Accordingly, a 'two-stage' economic allowance system involving a distinction between ' i n i t i a l ' and 'operating' allowances was adopted. The i n i t i a l economic allowance was designed to cover well operating costs, a five year pay-out of well d r i l l i n g costs and a two and one-half year pay-out of completion costs. The i n i t i a l allowance was computed using uniform wellhead prices and data on average operating, d r i l l i n g and completion costs, and was graduated by well depth. I t was to apply for seven years following i n i t i a l development of a pool. After this period, the i n i t i a l allowance was reduced to a lower l e v e l , referred to as the operating economic allowance, which was also graduated by well depth. The operating allowance was intended to cover operat-ing costs and a continuation of the two and one-half year pay-out of completion costs. The purpose of the l a t t e r was to reimburse equipment replacement and other additional costs incurred during the l i f e of a well. Thus the distinction between the operating and i n i t i a l economic allowance was the exclusion of the well d r i l l i n g cost component i n the determination of the former. ** The new economic allowances were to be effective on January 1, 1958 but were to be used i n 1958 and 1959 i n conjunction with the method under the 1950 Plan for allocating residual demand. The levels of the i n i t i a l and operating economic allowances as a function of depth are shown i n Figure 9.1. Petroleum and Natural Gas Conservation Board, Province of Alberta, "Prora-tion to Market Demand and the Economic Allowance", Proceedings of Hearings held May 27-28, 1957, Vol. 1 and 2, p. 2. D r i l l i n g costs account for the greater portion of the i n i t i a l cost of a well. - 9.7 - 2 4 7 The Board considered that the adoption of the two-stage economic allowance warranted greater emphasis on the MPR i n determining a pool's share of residual demand. For this reason, the Board endorsed the "residual MPR' plan. Under this plan, the t o t a l production allocated to a well would be the economic allowance plus a fraction of the difference between the MPR and the economic allowance. The fraction was the ratio of a well's MPR less i t s economic allow-ance to the sum of such differences for a l l prorated wells i n the Province. Since the economic allowance constituted a lower l i m i t to the MPR", the differences were never negative. The 'residual MPR' plan was to be f u l l y implemented by January 1, 1960. The 1957 Plan was the f i r s t major change to the Alberta proration plan. No further significant changes were made by the Board from 1957 to 1963. However, towards the end of this period, the need for a review was broached by several companies. 9.1.4. THE 1954 PRORATION PLAN Following the 1963 hearings, the Board issued a comprehensive report out-li n i n g a new proration system (the 1964 Plan). The new system was f u l l y imple-mented by May 1, 1969 and marked a noticeable departure from the system ini t i a t e d i n 1950 and modified i n 1957. The 1957 changes - the introduction of the 'two t i e r ' economic allowances and the 'residual' MPR - though s i g n i f i -cant, were i n essence refinements to the structure of the 1950 proration formula. The Board's 1964 Plan i s described as follows: See Oil and Gas Conservation Board, OGCB Report 65-3, Report and Decision  on Review of Plan for Maximum Oil Production Rate Limitation i n Alberta, March 1955, Calgary, Alberta, p. 39. - 9.8 - 248 Minimum Allowances 1) Purpose: The Board accepted the argument that a minimum well allowance was necessary to avoid premature well abandonment and to permit the completion and operation of wells d r i l l e d i n pools capable of economic operation. The argument that the prime purpose of the minimum allowance was to recover well d r i l l i n g costs or provide an incentive for exploration was rejected. 2) Floor or Basic Allowance: The Board preferred the floor allowance method, arguing i t would satisfy the purpose of a minimum allowance while leaving a greater portion of the t o t a l demand for allocation on the basis of reserves. 3) Magnitude, Depth £ Acreage Dependence: The Board believed the mimjnum allowance should be of sufficient magnitude, but no larger, to satisfy the purpose of allowing continued production from a l l economically capable wells. Consequently, the allowance should generally only reflect recovery of well completion and operating costs and not include recovery of d r i l l i n g costs. Studies of completion and operating costs undertaken by the Board convinced i t that, ceteris paribus, costs did vary more or less as a continuous function of depth. Given the objective of the minimum allowance, the Board concluded that i t should be scaled with depth. The principle of scaling the minimum allowance by the area, allocated to wells was not accepted. - 9 . 9 - 2 4 9 " The ju s t i f i c a t i o n for the minimum allowance l i e s with the well, d r i l l e d on whatever spacing has been authorized." Figure 9.1 shows the Board minimum allowance i n relation to the previous 1957 i n i t i a l and operating economic allowances and the 1950 economic allowance. The two significant points concerning the minimum allowance were: f i r s t , the fact that d r i l l i n g costs were eliminated from the deter-mination of the minimum allowance, which removed any guarantee of irdnimum p r o f i t a b i l i t y for any well d r i l l e d , i n contrast to the 1957 i n i t i a l economic allowance; second, the operation of the minimum allowance as a floor, that i s , s t r i c t l y as a minimum allowable. b) Allocation Among Pools The Board decided a pool's share of t o t a l o i l demand should be determined i n proportion of i t s reserves. For this purpose the pool's reserve was defined as one half of i t s ultimate reserve, plus one half of i t s remaining reserve. The important factor i n this decision was the substantial elimina-tion of the number of wells - and hence well spacing - within a pool as a determinant of a pool's share of demand, i n contrast to the previous schemes involving the MPR and the economic allowance. c) Allocation within Pools The Board rejected the use of ultimate reserves to determine the distribution of production within pools, primarily on the grounds of inherent complexity and administrative d i f f i c u l t i e s . I t adopted the area method modified, when appropriate, by the 'recovery factor'. The la t t e r adjustment was intended to reflect the greater recovery of o i l from those portions of a pool subject to an enchanced recovery scheme. - 9.10 - 250 This method of distribution of the pool allowable - subject of course to the application of the well minimum allowance, i f rele-vant - directly related well allowables within a pool to well spacing. As such, i t marked a radical change. The institution of well allowables which varied i n proportion to spacing removed any incentives which might exist under proration for an operator to d r i l l more wells than necessary to produce his share of the pool allocation. 9.1.5. SUMMARY . Watkins' study of prorationing concludes that the 1950 and 1957 Plans did not provide a general incentive towards excessive development d r i l l i n g , but they did encourage close well spacing i n reservoirs with high reserves per acre density.* Thus, reservoirs with high reserves per acre were overdrilled, and on the average some 1 i n 5 development wells were superfluous. The 1964 Plan, i n contrast, rendered the volume of production allocated to pools essentially independent of the number of wells i n i t , and development d r i l l i n g by 1969, when the 1964 Plan was f u l l y implemented, should have been close to optimal. For the purpose of valuing the worth of discoveries (and thus assessing the impact of prorationing on the incentive to explore), the effect of prorationing i s incorporated into the estimates' of demand price for Recoverable Reserves i n Chapters 4 and 5 through the well productivity, the period of production, and the wellhead price variables. Without prorationing,' well productivity would have been higher, the period of production shorter, but the wellhead price lower. G.C. Watkins, Op. C i t . , Dec. 1971, pp. i i . - 8.11 - 251 9.2 NOTE ON GEOLOGY S WESTERN CANADIAN SEDIMENTARY BASIN * 9.2.1. INTRODUCTION There are several interesting differences between hard rock mining and petroleum mining. Petroleum geology i s basically the same from the Arctic Ocean to the Gulf of Mexico. The contents of a hydrocarbon pool are arranged i n orderly fashion, gas at the top, o i l i n the middle, and water at the bottom. They are usually stored i n large, but poorly defined underground reservoirs. Ore bodies, on the other hand, come i n a variety of shapes and ingredients. They are often restricted to their contact zones, linear fault trends, or narrow fold belts. They occur i n a number of different geological provinces with sharply outlined borders, each with i t s own structural style and mineral associations. The f i r s t exploratory phase i s relatively cheap i n both industries. A decision i s made to spend a few thousand dollars for preliminary geological work. There-after, however, petroleum exploration requires exploratory d r i l l i n g involving considerable sums of money. I f a discovery i s made the production from an o i l pool can usually be predicted with reasonable certainty, whereas a mining discovery leads to considerable further investment and .decision making of high uncertainty. Relatively, the petroleum industry presents more risks earlier than hard rock mining. 9.2.2. BASIC PRINCIPLES OF PETROLEUM GEOLOGY The basic principles of petroleum geology are f a i r l y simple. O i l and natural gas are organic substances and not minerals i n the s t r i c t sense of the word. Their source material consists of animal and plant matter, mostly marine. Therefore, the majority of petroleum liquids and gases are found, together with saltwater, i n marine sediments. Much of this material i s taken from a series of articles by J.E.F. DeWiel i n the Northern Miner, January-June, 1972. - 9 . 1 2 - 252 In order to accumulate i n commercial quantities, o i l and gas need space. However, contrary to popular misconception, petroleum reserves do not commonly occur i n underground caves and rivers, but i n the pores of host rocks, such as sandstones and dolomites. The reservoir f l u i d s , gas, o i l and water, follow the laws of gravity. I f a l l three are present i n a single container, gas i s found at the top, o i l i n the middle, and water at the bottom. Since o i l and gas continue to r i s e through porous rocks u n t i l they are stopped by a barrier before they escape to the surface, one of the most important requirements for a petroleum reservoir i s an impermeable "roof". In order to form a trap, the roof must be concave as viewed from below. Structural Traps: The most obvious petroleum reservoir i s a porous bed under a tight layer, both folded into an arch or anticline (Figure 9.2, on l e f t , A n t i c l i n a l Trap). Where the entire sequence of sediments above the subsurface anticline has been deformed i n the same manner, the structure can be mapped at the surface. But even i f a structure - exists at the surface, i t may be absent at depth. Or, i t may not contain the right combination of porous and impermeable rocks. Or, even i f the anticline does form a trap, i t may be f i l l e d with water. A structural trap can be defined as one whose roof has been shaped by local deformation, not only by folding, but also by faulting. Faults are just as common i n sedimentary as they are i n hard rocks, and the role of faulting i n the formation of petroleum traps i s easy to visualize (Figure 9.2, on right, Fault Trap). Stratigraph Traps: A t o t a l l y different kind of petroleum reservoir i s caused, not by.local struc-ture, but by a change or break i n the porous formation. This type of trap can only be detected by "stratigraphy", the study of layered rocks, and i s there-fore called "stratigraphic trap", either primary or secondary. - 9.13 - 253 FIGURE 9.2 STRUCTURAL OIL S GAS TPAPS (Cross Section) S U R F A-C'E FIGURE 9.3. STRATIGRAPHIC OIL S GAS TRAPS (Cross Section) S U R F A C E Primary stratigraphic traps (Figure 9.3 ) are the product of the environment i n which the sediment i n question was l a i d down. Sandstone lenses of a l l shapes and sizes, for instance, can be the result of wave and current action i n ancient oceans, or they can represent buried deltas or r i v e r channels. Another common type of primary stratigraphic trap was created by the local replacement of lime-stone by dolomite. In dolomites the crystals are less t i g h t l y packed than i n limestones, their pores are therefore larger, and they make excellent o i l and - 9.14 - 254 gas reservoirs. Unfortunately, dolomitization i s a chemical process that i s not too well known, and i s therefore d i f f i c u l t to trace or predict. Sandstones enclosed i n shale, and dolomites enclosed i n limestone, are similar i n many respects, at least as far as the trapping mechanism i s concerned. Another important group of traps i s different, and these are the organic reefs. In the stratigraphic sense, a reef i s a mound-like or layered rock structure b u i l t by corals and other marine organisms. I t can be large, l i k e the Great Barrier Reef off the east coast of Australia, or small, l i k e the a t o l l of Bi k i n i . One of the most famous f o s s i l examples i s the o i l reservoir of Leduc i n Alberta. Traps of this nature f a l l i n the primary stratigraphic category, but since they were b u i l t up above the surrounding sea bottom, often to heights of several hundred feet, they have much i n common with structural traps, and as exploration targets they are i n a class by themselves. In contrast to primary stratigraphic traps, secondary stratigraphic traps are the product of developments that took place long after the deposition of the reservoir rock. In the most important of these developments, ancient layers of sediments were l i f t e d above sea l e v e l , exposed to weathering and erosion for a few million years, and then returned to their aquatic environment and covered with new sediments. The usual result of such "temporary" interruption of the depositional process i s an angular "unconformity" between the older and younger sets of rocks. A reservoir rock, sandwiched between shales, truncated by erosion, and capped by younger shales, can become a trap for migrating petroleum. That i s , i f the capping came before the migration (Figure 9.3, on right). I t i s probably clear by now, that most stratigraphic traps could not exist with-out the help of some regional structure, however subtle. A widespread blanket sand, for instance, would be completely useless from the standpoint of the petroleum geologist, i f i t were absolutely f l a t and horizontal. Only when such a sand has been t i l t e d ever so s l i g h t l y , can the petroleum liquids gather to form a pool at the upper edge of the reservoir. Even in the exploration for s t r a t i -graphic traps, structure i s important. As a matter of fact, i n many cases o i l and gas pools are controlled by a combination of stratigraphic and structural factors. - 9.15 - 255 Secondary Stratigraphic Traps: Not a l l stratigraphic traps are b u i l t , l i k e sand lenses and reefs, right into the formation. Secondary traps, for instance, are the result of developments "that took place long after the deposition and consolidation of the original sediment. The most common example i s the. unconformity' trap. As a type i t i s not d i f f i c u l t to visualize, especially when seen i n cross-section. A porous formation has been truncated by erosion and capped by an impervious shale. But why should such a trap be f i l l e d with anything but water? After a l l , i f our porous dolomite was once exposed, any o i l that i t may have carried at that time must have escaped right then and there. This i s often true, but not always. Exposure does not necessarily mean the complete destruction of an o i l reservoir. Sometimes only gas and other volatile constituents evaporate while the rest of the accumulation remains intact. Another point to remember i s : When o i l , under the ever-increasing pressure of the overburden i s squeezed out of i t s source rock, i t follows the course of least resistance, which i s downward i f that i s where the nearest porosity happens to be. Therefore, a shale over an unconformity trap can be source and cap at the same time. Downward migration can account for the entire content of the trap, and i t can also contribute new light ends to an older pool of heavy residual o i l below. Finally, the earth i s not a s o l i d b a l l of rock and a sedimentary basin i s not a stable fixture. Every movement of the crust i s accompanied by f l u i d adjustments, so that a trap f u l l of water during the Mississippian can very well have become oil-bearing during the Cretaceous. Paleo- S Subgeology: Unconformities are important phenomena i n petroleum exploration because they bring a l l kinds of potential source and reservoir xocks i n contact with each other. To arrive at a clearer picture of these contacts, paleogeologic and sub-geologic maps can be constructed. - 9.16 - 255 A paleogeologic nap shows the pattern created by the truncated strata at the old (paleo) surface, I t i s also called a subcrop map. A subgeologic map depicts the character and extent of the formation or formations directly above the unconformity. I t i s a facies map i n this case also known as a worm's eye map. By combining the two, i t i s theoretically possible to determine where source rocks are i n touch vrith reservoir rocks and where porous beds are capped by impermeable ones. In practice, the paleogeologic map i s the more useful tool. The f i r s t genera-tion of sediments dumped on an old erosional surface i s usually so monotonous, from a regional point of view, that i t i s not worth mapping. At the same time i t can be so diverse, l o c a l l y , that i t i s impossible to map. Regionally, for instance, the pre-Cretaceous unconformity under the Western Prairies i s covered with a uniform sand/shale blanket. Locally, however, the facies of the a l l -important basal Cretaceous changes so quickly from sandy shale to shaly sand that i t i s unmappable. Combination Traps: Figure 9.4 i s a paleogeologic map of the area east of our hypothetical Sand Field. I t shows that the older carbonate sequence has been folded before i t was eroded and then buried under younger sands and shales. As a result, the east-ward sloping unconformity (indicated by structure contours) intersects the curved upper boundary of the dolomite i n such a way that the two together form the roof of a trap that has structural as well as stratigraphic elements (Figure 9.5). Similar combination traps can be expected a l l along the winding subcrop of the porous formation. I f one trap i s wet, the next higher one may be f u l l of o i l and the next higher one gas-bearing, or vice versa.' - 9.17 - 257 FIGURE 9.1 PALEOGEOLOGIC MAP WITH STRUCTURE CONTOURS ON UNCONFORMITY FIGURE 9.5 OIL TRAPPED BY FOLDED TOP OF POROUS DOLOMITE ("e'!) £ UNCONFORMITY Differential Entrapment: When petroleum liquids and gases are expelled from their source and i f they are free to migrate upward, gas as the more mobile end lighter constituent i s i n a better position to reach the nearest trap f i r s t . Even i f that trap i s already f i l l e d with o i l from another source, the gas w i l l r i s e to the top and force the - 9.18 - 258 heavier petroleum to s p i l l over into the next higher trap. Figure 9.6 explains better than words how i t can be that the lowest i n a series of traps i s f i l l e d with gas and the highest with water. FIGURE 9.6 ' DIFFERENTIAL ENTRAPMENT (Cross Section) Hydrodynamics: Moving formation water i s another factor that can lead to an unexpected arrange-ment of reservoir f l u i d s . I t i s elementary knowledge that water moving from intake to outlet through near-surface aquifers, i s part of the hydrological cycle. Less well-known i s the fact that precipitation, instead of taking one of the shorter routes back to the ocean, can be diverted into a deep-reaching detour. There i s conclusive evidence that formation waters are moving northeastward through the Western Canada Sedimentary Basin at a depth of several thousand feet. Rainwater soaked up by Devonian beds i n the Rocky Mountains has a f a i r chance of surfacing again, eventually, i n Devonian outcrops at Lake Winnipegosis, Manitoba. At best, this movement resembles a very slow creep, and one would hardly expect i t to produce enough impulses to play a part i n petroleum geology. And yet, i t can be proved i n theory and demonstrated i n practice, that hydrodynamic flow can defeat conventional trapping mechanisms by t i l t i n g oil/water contacts. By the same token, moving water i t s e l f can become a trapping agent. Figure 9.7 explains this double role. Differential entrapment and hydrodynamic energy are only two of the reasons why petroleum prospects are never fail-proof- It. bears repeating, an underground o i l accumulation cannot be seen. I t i s well hidden. Unless discovered by accident - which happens - i t must be imagined before i t can be found, and the road from figment to confirmation i s paved with stumbling blocks. 9.2.3. WESTERN CANADIAN SEDIMENTARY BASIN  The Sedimentary Cover: Following the contours of the Canadian Shield, whose rocks form the basement of the Western Canada Basin, the sedimentary cover has a slight southwesterly t i l t . This i s the regional structural element needed to cause o i l and gas to gather near the "updip" edges of Cretaceous sand lenses and similar reservoirs. But, there i s also local structure. Below the Cretaceous, at depths of several thousand feet, i s an "unconformity" which resulted from the elevation above sea l e v e l , and erosion, of older Mississippian and Devonian sediments (Figure 9.9 ). When the basal Cretaceous beds were l a i d down on this irregular surface, they were draped over i t s ridges and valleys, so that o i l - and gas-bearing highs often coincide with underlying erosional h i l l s . - 9.20 - 2S0 Cretaceous rocks account for one third of the marketable gas and one quarter of the recoverable o i l reserves of Alberta, but i n the overall picture, the Cretaceous i s only the third most productive system i n Western Canada. The second most productive unit i s the Mississippian. Mississippian petroleum i s produced primarily from two kinds of traps, "struc-t u r a l " and "secondary stratigraphic". During the late Cretaceous disturbance which led to the formation of the Rocky Mountains, the Mississippian limestones and shales under the Alberta foo t h i l l s were folded and faulted into large anti-clines and thrust plates. The Turner Valley f i e l d , whose p a r t i a l discovery i n 1914 touched off the f i r s t Canadian " o i l " boom (actually a gas boom), i s a classic example of a structural trap, and many p r o l i f i c gas pools have since been found i n similar reservoirs. Secondary stratigraphic traps, caused by the truncation of porous Mississippian limestones and their burial under impervious younger sediments, are typical for Weybum, Midale, Steelman, and most other o i l f ields i n southeastern Saskatchewan. The major producing system i s the Devonian. I t contains 60% of the o i l and 30% of the gas i n Western Canada. Devonian petroleum comes mostly from primary stratigraphic traps, and most important among these are the organic reefs of Central Alberta: Leduc, Redwater, Golden Spike, and many others. I t appears that the ancient reef-building organisms preferred a certain narrow depth range and thrived under certain oceanic current conditions, both of which were restricted to linear zones along the bottom of the Devonian sea. This i s why the reefs i n the Edmonton area are arranged l i k e beads on a string, a fact that made i t relatively easy to locate additional reefs, once the Leduc discovery had been d r i l l e d i n 1947. Other Devonian reservoirs are not so obliging. Some of the famous Rainbow reefs i n northwestern Alberta, for instance, measure less than a mile i n diameter, and they are scattered at random throughout the broad Black Creek Basin. Farther west, i n northeastern B r i t i s h Columbia, large gas reserves are trapped i n the dolomitized portions of an extensive limestone platform, where dolomitization follows no recognizable pattern and exploration i s d i f f i c u l t and costly. The best-known example i s the Clarke Lake gas f i e l d near Fort Nelson. - 9.21 - • FIGURE 9.8  SEDIMENTARY BASINS, WESTERN CANADA 261 - 9.22 -FIGURE 9.9 GENERALIZED STRATIGRAPHIC COLUMN £ CROSS-SECTION, CENTRAL ALBERTA 263 BIBLIOGRAPHY 2 6 4 M.A. Adelman, Alaska O i l : Costs and Supply, New York, Praeger, 1971 M.A. Adelman, "Efficiency of Resource Use i n Crude Petroleum", Southern Economic Journal, Vol. 31, October 1964, pp 101-122 M.A. Adelman, "Oil. Prices i n the Long Run (1963-1975)", Journal of Business of University of Chicago, Vol. XXXVII, No. 2, A p r i l 1954, pp 143-161 M.A. Adelman, The Supply and Price of Natural Gas, Oxford, Blackwell, 1962 J. Aitchison, Choice Against Chance, Reading Mass., Addison Wesley, 1970 J. Aitchison, and J.A.C. Brown, The Lognormal Distribution, Cambridge England, Cambridge University Press, 1963 M. A l l a i s , "Method of Appraising Economic Prospects of Mining Exploration over Large Territories", Management  Science, Vol. 3, No. 4, July 1957, pp 285-347 K.J. Arrow, Aspects of the Theory of Risk-Bearing, Helsinki, 1965 P. Balestra and M. Nerlove, "Pooling Cross Section and Time Series Data i n the Estimation of a Dynamic Model: The Demand for Natural Gas", Econometrica, Vol. 34, No. 3, July 1966, pp 585-612 Bank of Canada, Interest Rate Package, Ottawa, Mimeo 1974 H.J. Barnett and C. Morse, Scarcity and Growth, The Economics of Natural Resource Av a i l a b i l i t y , Baltimore, Johns Hopkins Press, 1963 K.H. Borch, The Economics of Uncertainty, Princeton, N.J., Princeton U. Press, 1968 P.G. Bradley, The Economics of Crude Petroleum Production, Amsterdam, North Holland, 1967 P.G. Bradley, "Exploration Models and Petroleum Production Economics", i n M.A. Adelman, ed., Alaskan O i l :  Costs and'Supply, New York, Praeger, 1971, pp 94-122 P.G. Bradley, "Increasing Scarcity: The Case of Energy Resources", American Economic Review, Vol. 63, No. 2, May 1973, pp 119-125 265 P.G. Bradley, and G.M. Kaufman, "Reward and Uncertainty i n Exploration Programs", Second International Symposium of Arctic Geology Paper, San Francisco, February 1971 P.G. Bradley, and G.M. Kaufman,."Two Stochastic Models Useful i n Petroleum Exploration"i Second International Symposium of Arctic Geology Paper, San Francisco, February 1971 G.A. Brown, M. Bucovetsky. J.V. Buller, "The Evaluation of Risk i n Mining Ventures", The  Canadian Institute of Mining and Metallurgy Bulletin, Vol. 63, No. 702j October 1970, pp 1165-1171 ' The Taxation of Mineral Extraction, Ottawa, Queen's Printer, 1966 "A Computer-Oriented System for the Storage and Retrieval of Well Information", Bulletin of  Canadian Petroleum Geology, Vol. 12, No. 4, 1964 pp 847-891 ' C.F. Burk JR., and N.M. Ediger, "Collating Exploration Data", Oilweek, Vol. 17. No. 39, 1966,pp 16-19 O.R. Burt, and R.G. Cuircnings, "Production and Investment i n Natural Resource Industries", American Economic Review, Vol. 60, No. 4, September 1970, pp 576-590 R.W. Campbell. The Economics of Soviet O i l and Gas, Baltimore, J. Hopkins Press, 1968 W.M. Campbell, and F.J. Schuh, "Risk Analysis: Overall Chance of Success Related to Number of Ventures", Society of Petroleum Engineers of AIME Reprint SEE 218,October 1961 Canadian O i l Scouts Association, O i l and Gas Activity i n Canada, Mimeo Annual Volumes 1963-1970 Canadian Petroleum Association, S t a t i s t i c a l Year Books, 1946-1973, Calgary E.C. Capen, and R.V. Clapp, "Shortcomings of Intuition i n Uncertain Environ-ments", Society of Petroleum Engineers of AIME Reprint SPE 3974, October 1972 R.M. Cassie, "Some Uses of Probability Paper i n the Analysis of Size - Frequency Distributions", Australian Journal  Marine Freshwater Res., Vol. 5, 1954, pp 513-522 O i l Fields of Alberta Supplement, 1966, Alberta Society of Petroleum Geologists, Calgary, 1967 K. Chu, and T.H. Naylor, "A Dynamic Model of the Firm", Management Science, Vol,. 11, No. 7, May 1965, pp 736-750 J.R. Century, (ed.) 266 A.C. Cohen JR., K.J. Cohen, J.V. Cowan, J.M. Cozzolino, R.G.. Cummings. J.H. Dagher, L.F. Davis, • "Simplified Estimators for the Normal Dis-tribution When Samples Are Singly Censored or Truncated", Technometrics, Vol. 1, No. 3, 1959, pp 217-237 Computer Models of the Shoe, Leather, Hide  Sequence, Englewood C l i f f s N.J., Prentice H a l l , 1960 "Risk Analysis as Applied to Drilling_and De-veloping an Exploration Prospect", Society of Petroleum Engineers of AIME Reprint SPE 2583, September 1969 "Sequential Search for an Unknown Number of Objects of Non-Uniform Size", Operations Research, Vol. 20, No. 2, March-April 1972, pp 293-308 "Some Extensions of the Economic Theory of Ex-haustible Resources", Western Economic Journal, Vol. 7, No. 3, September 1969, pp 201-210 "Effect of the National O i l Policy on the Ontario Refining Industry", Unpublished PhD Thesis, McGill University., Montreal, 1968 "Economic Judgement and Planning i n North American Petroleum Exploration", Society of Petroleum Engineers of AIME Reprint SPE 2002, August 1967 Department of Energy, Mines and Resources, Natural Gas Processing i n Canada, Ottawa, Queen's Printer, Annual Editions Department of Mines and Minerals, Government of Alberta, Alberta O i l and Gas Picture, 1955-1970, Edmonton J.E.F. De Wiel, G.J. Dickie, J.P. Dowds, M.W. Edwards, "The O i l Business", The Northern Miner, January 13-June 8; 1972, Sec. 1, pp 5 "A Quantitative Geological Analysis of Cretaceous and Jurassic O i l and Gas Pools i n Alberta", Unpublished PhD thesis, Department of Geology, University of Alberta, Edmonton, Spring 1972 "S t a t i s t i c a l Geometry of Petroleum Reservoirs i n Exploration and Exploitation", Journal of Petroleum  Technology, July 1969, pp 841-852 "Alberta Short Run Crude O i l Supply-1972", Un-published Masters Thesis, University of Calgary, Calgary, 1973 267 Energy Resources Conservation Board of Alberta, Report on Field Pricing of Gag i n Alberta, Calgary, August 1972 Energy Resources Conservation Board of Alberta, Reserves of Crude O i l , Gas, Natural Gas Liquids and Sulphur, Province of Alberta, Calgary, December 1972 and 1973 editions E.W. Erickson, "Economic Incentives, Industrial Structure and the Supply of Crude O i l Discoveries i n the U.S., 1946-1958/59", Unpublished PhD Thesis, Vanderbilt University, 1968 E. W. Erickson, and R.M. Spann, "Supply Response i n a Regulated Industry: The Case of Natural Gas", The Be l l Journal of Economics  and Management Science, Vol. 2, No. 1, Spring 1971, pp 94-121 G.K. Erickson, "Alaska's Petroleum Leasing Policy", i n G.S. Harrison ed., Alaska Public Policy, Fairbanks Alaska, In-t i t u t e of Social, Economic and Government Research College, 1971, pp 191-219 D.E. Farrar, The Investment Decision Under Uncertainty, Englewood C l i f f s N.J., Prentice H a l l , 1962 F. M. Fisher, Supply and Costs i n the U.S. Petroleum Industry; Two Econometric Studies, Baltimore, Johns Hopkins Press, 1964 J.W. Forrester, Industrial Dynamics, Cambridge Mass., M.I.T. Press, 1961 P.H. Frankel, O i l , The Facts of L i f e , London, Weidenfeld and Nicolson, 1962 M. Friedman, and L.J. Savage, " U t i l i t y Analysis of Choices Involving Risk", Journal of P o l i t i c a l Economy, Vol. LVI, 1948, pp 279-304 D.B. Furlong, P o l i t i c a l Attacks on the O i l and Gas Industry Today, Mimeo, Speech of September 28, 1971 M. Gaffney, (ed.) Extractive Resources and Taxation, Milwaukee, University of Wisconsin Press, 1967 C.R. Garner, and T.J. Campbell JR., "Economic Evaluation and Planning of Ex-ploration Programs", O i l and Gas Journal, Vol. 71, No. 23, June 4, 1973, pp 94-96 J.P. Getty, My Life and Fortune, London, G. Allen £ Unwin, 1964 268 A.S. Goldberger, R.L. Gordon, E. Gray, L.C. Gray, C.J. Grayson JR., J.C. G r i f f i t h s , J.C. G r i f f i t h s , Gulf O i l Canada Limited, M.T. Halbouty, E.J. Hanson, D.V. Harris, J.E. Hazleton, J.F. H e l l i w e l l , J.M. Henderson, J.M. Henderson, and R.E. Econometric Theory, New York, John Wiley and Sons, Inc., 1966 "A Reinterpretation of the Pure Theory of Exhaustion", Journal of P o l i t i c a l Economy, Vol. 75, No. 3, June 1967, pp 274-286 The Great Canadian O i l Patch, Toronto, Maclean -Hunter, 1970. "Rent Under the Assumption of Exhaustibility", Quarterly Journal of Economics, Vol. 28, May 1914, pp 66-89 Decisions Under Uncertainty: D r i l l i n g Decisions by  O i l and Gas Operators, Cambridge Mass., Harvard Business School Division of Research, 1960 "Exploration for Natural Resources", Operations Research, March-April, 1966, pp 189-209 "S t a t i s t i c a l Approach to the Study of Potential O i l Reservoir Sandstones", Computers i n the Mineral  Industries, Part 2, George A. Parks, ed., Stanford University Publications, Geological Sciences, Vol. 9, No. 2, 1964 Submission to the National Energy Board i n the  Matter of the Exportation of O i l , Mimeo, December 1973 Geology of Giant Petroleum Fields, Memoir 14, American Association of Petroleum Geologists, Tulsa, Oklahoma, November 1970 Dynamic Decade, Toronto, McClelland S Stewart, 1958 "A Probability Model of Mineral Wealth", Transactions:  Society of Mining Engineers, June 1966, pp 199-216 The Economics of the Sulphur Industry, Baltimore, J. Hopkins Press, 1970 Public Policies and Private Investment, Oxford, Clarendon Press, 1968 "A Short-Run Model for the Coal Industry", Review of Economics and S t a t i s t i c s , Vol. 37, November 1955, pp 336-346 Quandt, Microeconomic Theory, A Mathematical Approach, New, York, McGraw-Hill, 1971 269 O.C. Herfindahl, J.D. Hilborn, (ed.) B. Hitchon, H. Hotelling, M.K. Hubbert, M.K. Hubbert, M.K. Hubbert, M.K. Hubbert, J. Johnston, ''Some Fundamentals of Mineral Economics", Land  Economics, Vol. 31, May 1955, pp 131-138 Dusters and Gushers, Toronto, P i t t Publishing, 1968 "F l u i l d Flow i n the Western Canada Sedimentary Basin, 2, Effect of Geology", Water Resource Res., Vol. 5, No. 2, 1969, pp 460-469 "The Economics of Exhaustible Resources", Journal of  P o l i t i c a l Economy, Vol. 39, No. 2, A p r i l 1931, pp 137-175 "Degree of Advancement of Petroleum Exploration i n United States", The American Association of Petroleum  Geologists Bulletin, Vol. 51, No. 11, 1967, pp 2207-2227 "Energy Resources", Report to the Committee on Natural Resources: National Academy of Sciences - National Research Council, Washington D.C., Publication 1000-D, 1962 "Energy Resources of the Earth", Scientific American, Vol. 224, No. 3, September 1971, pp 60-70 "Survey of World Energy Resources", The Canadian Institute of Mining arid Metallurgy TCIM) Bulletin, Vol. 66, No. 735, July 1973, pp 37-53 Econometric Methods, New York, McGraw-Hill, 1963 International O i l Scouts Association, International O i l and Gas Development Year Book, Exploration Volumes 17-40, Austin, Texas, International O i l Scouts Association, 1947-1970 G.M.; Kaufman, Y. Balcer, D. Kruyt, "A Probabilistic Model of the O i l and Gas Discovery Process", Unpublished Paper, Massachusetts Institute of Technology, May 17, 1974 G.M. Kaufman, J.D. Khazzoom, J.D. Khazzoom, St a t i s t i c a l Decision and Related Techniques i n O i l  and Gas Exploration, Englewood C l i f f s N.J., Prentice H a l l , 1963 An Econometric Model of U.S. Natural Gas Supply, Federal Power Commission, Docket No. AR69-1, September 1970 "Gas Production Directionality", Public U t i l i t i e s  Fortnightly, Vol. 84, No. 13, December 18, 1969, pp 20-25 270 "N.T. Khoury, "Prorationing and the Economic Efficiency of Crude O i l Production", Canadian Journal of Economics, Vol. 2, August 1969, pp 443-448 F.H. Knight, Risk, Uncertainty, and Pr o f i t , Boston, Houghton M i f l i n , 1921 W.C. Krumbein, and F.A. Graybill, An Introduction to S t a t i s t i c a l Models i n Geology, New York, McGraw-Hill, 1965 R.G. Kuller,and R.G. Cummings, "An Economic Model of Production and Investment for Petroleum Reservoirs", American Economic Review, Vol. LXIV, No. 1, March 1974, pp 66-79 D.H. Kyle, "Developments i n Western Canada, '67", Canadian Petroleum, Vol. 9, No. 4, A p r i l 1968, pp 51-58 L.H. Larson, (ed.) Gas Fields of Alberta, Alberta Society of Petroleum Geologists, Calgary, 1969 J. Laxer, The Energy Poker Game, Toronto, New Press, 1970 W.R. Lee, "Prorationing and i t s Effects on Investment i n the Canadian O i l Industry",'Unpublished Masters Thesis, University of Bri t i s h Columbia, Vancouver, 1967 H.W. L i l l i e f o r s , "On the Kolmogorov-Smironov Test for Normality with Mean and Variance Unknown", Journal of the American  S t a t i s t i c a l Association, Vol. 62, 1967, pp 399-402 W.F. Lovejoy, "Oil Conservation, Producing Capacity, and National Security", Natural Resources Journal, January 1970, Vol. 10, No. 1, pp 62-96 W.F. Lovejoy, and P.T. Homan, Economic Aspects of O i l Conservation Regulation, Baltimore, RFF-Johns Hopkins, 1967 W.F. Lovejoy, and P.T. Homan, Methods of Estimating Reserves of Crude O i l , Natural Gas, and Natural Gas Liquids, Maryland, J. Hopkins Press, 1965 P.W. MacAvoy, "The Regulation-Induced Shortage of Natural Gas", Journal of Law and Economics, Vol. XTV, No. 1, A p r i l 1971, pp 167-199 A.W. McCray, "Evaluation of Exploratory D r i l l i n g Ventures by St a t i s t i c a l Decision Methods", Society of Petroleum Engineers of AIME Reprint SPE 2220, September 1968 271 R.G. McCrossan, "An Analysis of Size Frequency Distribution of O i l and Gas Reserves of Western Canada", Canadian Journal  of Earth Sciences, Vol. 6, No. 2, 1969, pp 201-211 R.G. McCrossan, and R.P. Glaister, (eds.) Geological History of Western Canada, Alberta Society of Petroleum Geologists, Calgary, 1964 S.L. McDonald, Petroleum Conservation i n the United States: An Economic Analysis, Baltimore, J. Hopkins Press, 1971 J.W. McKie, "Market Structure and Uncertainty i n Oi l and Gas Exploration", Quarterly Journal of Economics, Vol. 74, No. 4, November 1960, pp 543-571 J.W. McKie, and S.L. McDonald, "Petroleum Conservation i n Theory and Practice", Quarterly Journal of Economics, Vol. 76, February 1962, pp 98-121 R.C. Meier, W.T. Newell, and H.C. Pazer, Simulation in.Business and Economics, Englewood C l i f f s N.J., Prentice H a l l , 1969 A.P.H. van Meurs, Petroleum Economics and Offshore Mining Legislation, Amersterdam, Elsevier Publishing Company, 1971 National Energy Board, Energy Supply and Demand i n Canada and Export Demand for Canadian Energy, 1966 to 1990, Ottawa, Queen's Printer, 1969 National Energy Board, Royal Commission on Energy, Second Report, Ottawa, Queen's Printer, July 1959 P.D. Newendorp, "A Decision Criterion for D r i l l i n g Investments", Society of Petroleum Engineers of AIME Reprint SPE 2219, September 1968 P.D. Newendorp, "Risk Analysis i n D r i l l i n g Investment Decisions", Society of Petroleum Engineers of AIME Reprint SPE 1932, July 1967 C.A. Norman, "Economic Analysis of Prudhoe Bay O i l Field", i n M.A. Adelman, ed., Alaskan O i l : Costs and Supply, New York, Praeger, 1971, pp 31-79 .Oil and Gas Conservation Board, Pressure-Depth and Temperature-Depth Relation- ships, Alberta Crude O i l Pools, O i l and Gas Conservation Board, Calgary, 1970. O i l and Gas Conservation Board, Report and Decision on Review of Plan for Maximum O i l Production Rate Limitation i n Alberta, O i l and Gas Conservation Board Report 65-3, Calgary, March 1955 272 •Oil and Gas Conservation Board, Report and Decision on Review of Plan for Proration of O i l to Market Demand i n Alberta, O i l and Gas Conservation Board Mimeo, Calgary, July 1964 C. van de Panne, "The Development of O i l and Gas Reserves i n Alberta", Discussion Paper Series No. 15, University of Calgary, Department of Economics,September 1971 E.T. Penrose, The Large International Firm i n Developing Countries, The International Petroleum Industry, Cambridge Mass.. M.I.T. Press, 1968 Petroleum and Natural Gas Conservation Board, Province of Alberta, "Proration to Market Demand and the Economic Allowance", Proceedings of Hearings held May 27-28, Vol. 1 and 2, 1957 A.R. Plotnick, Petroleum Canadian Markets and U.S. Foreign Trade Policy,. Seattle, University of Washington Press, 1964 T.L. Powrie, F. Roseman, and G. Moynham, "Interactions Among Various Sources of Government Revenue from the O i l Industry", Un-published Paper, University of Alberta, Edmonton, May 1972 G. D. Quirin, Economics of O i l and Gas Development i n Northern Canada, Ottawa, Queen's Printer, January 1962 H. Raiffa, Decision Analysis: Introductory Lectures on Choices Under Uncertainty, Reading Mass., Addison Wesley, 1968 Resources For The Future Inc., Energy Research Needs, Washington, Mimeo5 October 1971 J.T. Ryan, "An Analysis of Crude O i l Discovery i n Alberta", Unpublished Paper, Department of Chemical and Petroleum Engineering, University of Alberta, 1971 J.T. Ryan, "An Estimate of the Potential Conventional Crude O i l i n Alberta", Unpublished Paper, Department of Chemical and Petroleum Engineering, University of Alberta, October 1972 J.T. Ryan, "One View of the Future of the O i l Industry i n Alberta", Unpublished Paper, Department of Chemical and Petroleum Engineering, University of Alberta, October 1971 \ 273 A.D. A.D. Scott, Scott, R.A. Shearer, M.B. Smith, M.B. Smith, V.L. Smith, L.C. Stevens. G.J. B.K. P.G. Stigler, Stone, Natural Resources: The Economics of Conservation, Toronto, University of Toronto Press, 1955 "The Theory of the Mine Under Conditions of Certainty", i n M. Gaffney ed., Extractive Resources and Taxation, Milwaukee, University of Wisconsin Press, 1967, PP 25-62 "Nationality, Size of Firm, and Exploration for Petroleum i n Western Canada, 1946-1954", Canadian  Journal of Economics and P o l i t i c a l Science , Vol. XXX, No. 2, May 1964, pp 211-227 "Parametric U t i l i t y Functions for Decisions Under Uncertainty", Society of Petroleum Engineers of AIME Reprint SPE 3973, October 1972 "Probability Models for Petroleum Investment Decisions", Society of Petroleum Engineers of AIME Reprint SPE 2587, September 1969 "Economics of Production from Natural Resources", American Economic Review, Vol. LXVIII, No. 3, Pt. 1, June 1968, pp 409-431 "Joint Ventures i n the International Petroleum Industry", Society of Petroleum Engineers of AIME Reprint SPE 3975, October 1972 "The Economics of Information", Journal of P o l i t i c a l  Economy, Vol. LXIX, No. 3, June 1961, pp 213-225 Risk, Return, and Equilibrium, Cambridge Mass., M.I.T. Press, 1970 Sutterlin, and J. de Plancke, "The Development of a Flexible Computer-Processible F i l e for the Storage and Retrieval of Mineral Deposits Data", Proc. Symp. on Decision Making i n Mineral Expl. I I , University of B r i t i s h Columbia, February 1969, pp 11-42 R.S. Uhler, "Production, Reserves and Economic Return i n a Petroleum Exploration and Reservoir Development Program", Unpublished Paper, University of B r i t i s h Columbia, March 1972 R.S. J.E. Uhler, and P.G. Bradley, "A Stochastic Model for Deterririning the Economic Prospects of Petroleum Exploration Over Large Regions", Journal of the American S t a t i s t i c a l  Association, Vol. 65, No. 330, June 1970, pp 623-630 Walstrom, and J.T. Mueller,' "Evaluating Uncertainty i n Engineering Cal-culations", Society of Petroleum Engineers of AIME Reprint. SPE 1928, May 1967 274 , G.C. Watkins, G.C. Watkins, ."Direct Government Revenue from Petroleum -Alberta and the Middle East", Unpublished Paper, Calgary, 1973 Proration and the Economics of O i l Reservoir De- velopment, Province of Alberta, Canada, Mimeo, December 1971 G.C. Watkins, and K. Sharp, "The Long-Term Cost of Alberta Conventional Crude O i l " , Journal of Canadian Petroleum Technology, Vol. 9, No. 1, January-March 1970, pp 22-27 R.J. White, (ed.) T.K, Wingnall, J. Williamson, O i l Fields of Alberta, Alberta Society of Petroleum Geologists, Calgary, 1960 "Oil and Gas Exploration, S t a t i s t i c a l Decision Criteria: Applications of Discriminant Analysis i n the Petroleum Industry", Society of Petroleum Engineers of AIME Reprint SPE 2223, September 1968 "Profit, Growth and Sales Maximization", Economica, Vol. 33, February 1966, pp 1-16 The data f i l e s referred to i n the text as E.M.R. f i l e s are those established by the author for purposes of this thesis. 

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