Natural Resources Research

, Volume 19, Issue 3, pp 209–230

Hubbert’s Legacy: A Review of Curve-Fitting Methods to Estimate Ultimately Recoverable Resources

Article

Abstract

A growing number of commentators are forecasting a near-term peak and subsequent terminal decline in the global production of conventional oil as a result of the physical depletion of the resource. These forecasts frequently rely on the estimates of the ultimately recoverable resources (URR) of different regions, obtained through the use of curve-fitting to historical trends in discovery or production. Curve-fitting was originally pioneered by M. King Hubbert in the context of an earlier debate about the future of the US oil production. However, despite their widespread use, curve-fitting techniques remain the subject of considerable controversy. This article classifies and explains these techniques and identifies both their relative suitability in different circumstances and the level of confidence that may be placed in their results. This article discusses the interpretation and importance of the URR estimates, indicates the relationship between curve fitting and other methods of estimating the URR and classifies the techniques into three groups. It then investigates each group in turn, indicating their historical origins, contemporary application and major strengths and weaknesses. The article then uses illustrative data from a number of oil-producing regions to assess whether these techniques produce consistent results as well as highlight some of the statistical issues raised and suggesting how they may be addressed. The article concludes that the applicability of curve-fitting techniques is more limited than adherents claim and that the confidence bounds on the results are wider than usually assumed.

Keywords

Petroleum resource estimation peak oil 

References

  1. Ahlbrandt, T. S., and Klett, T. R., 2005, Comparison of methods used to estimate conventional undiscovered petroleum resources: world examples: Nat. Resour. Res., v. 14, no. 3, p. 187–210.Google Scholar
  2. Aleklett, K., Höök, M., Jakobsson, K., Lardelli, M., Snowden, S., and Söderbergh, B., 2009, The peak of the oil age: analysing the world oil production reference scenario in World Energy Outlook 2008: Energy Policy, v. 38, no. 3, p. 1398–1414.Google Scholar
  3. Arps, J. J., 1945, Analysis of decline curves, transactions of the American institute of mining: Metall. Petrol. Eng., v. 160, pp. 228–247.Google Scholar
  4. Arps, J. J., 1956, Estimation of primary oil reserves: Trans. AIME, v. 207, p. 182–191.Google Scholar
  5. Arps, J. J., and Roberts, T. J., 1958, Economics of drilling for Cretaceous oil on the east flank of Denver-Julesberg basin: AAPG Bull., v. 42, no. 11, p. 2549–2566.Google Scholar
  6. Arps, J. J., Mortada, M., and Smith, A. E., 1971, Relationship between proved reserves and exploratory effort: J. Petrol. Technol., v. 23, no. 6, p. 671–675.Google Scholar
  7. Bartlett, A. A., 2000, An analysis of US and world oil production patterns using Hubbert-style curves: Math. Geol., v. 32, no. 1, p. 1–17.Google Scholar
  8. Bass, F. M., 1969, A new product growth model for consumer durables: Manage. Sci., v. 15, p. 215–227.Google Scholar
  9. Baxter, G. G., Cargill, A. H. C., Hart, P. E., Kaufmann, G. M., and Urquidi-Barrau, F., 1978, Workshop on the Delphi method: J. Int. Assoc. Math. Geol., v. 10, no. 5, p. 581–587.Google Scholar
  10. Bentley, R. W., 2009, A primer on oil peaking: UK Energy Research Centre, London.Google Scholar
  11. Bentley, R. W., Mannan, S. A., and Wheeler, S. J., 2007, Assessing the date of the global oil peak: the need to use 2P reserves: Energy Policy, v. 35, no. 12, p. 6364–6382.Google Scholar
  12. Bowden, G., 1985, The social construction of validity in estimates of US crude oil reserves: Soc. Stud. Sci., v. 15, no. 2, p. 207–240.Google Scholar
  13. Brandt, A. R., 2007, Testing Hubbert: Energy Policy, v. 35, no. 5, p. 3074–3088.Google Scholar
  14. Byrd, L. T., Kumar, R. M., Williams, A. F., and Moore, D. L., 1985, US oil and gas finding and development costs 1973–1982, lower 48 onshore and offshore: J. Petrol. Technol., v. 31, p. 2040–2048.Google Scholar
  15. Campbell, C. J., 1996, Status of world oil depletion at the end of 1995: Energy Explor. Exploit., v. 14, no. 1, p. 63–81.Google Scholar
  16. Campbell, C. J., 1997, The coming oil crisis: Multi-Science Publishing & Petroconsultants.Google Scholar
  17. Campbell, C. J., 2002, The assessment and importance of oil depletion: Energy Explor. Exploit., v. 20–1, no. 6–1, p. 407–435.Google Scholar
  18. Campbell, C. J., and Heapes, S., 2008, An atlas of oil and gas depletion: Jeremy Mills Publishing, Huddersfield.Google Scholar
  19. Carlson, W. B., 2007, Analysis of world oil production based on the fitting of the logistic function and its derivatives: Energy Sources B Econ. Plann. Policy, v. 2, no. 4, p. 421–428.Google Scholar
  20. Cavallo, A. J., 2004, Hubbert’s petroleum production model: an evaluation and implications for world oil production forecasts: Nat. Resour. Res., v. 13, no. 4, p. 211–221.Google Scholar
  21. Cavallo, A. J., 2005a, Hubbert’s model: uses, meanings, and limits. 1: Oil Gas J., v. 103, no. 21, p. 22–24.Google Scholar
  22. Cavallo, A. J., 2005b, Hubbert’s model: uses, meanings, and limits. 2: Oil Gas J., v. 103, no. 22, p. 20–25.Google Scholar
  23. Charpentier, R. R., 2003, The future of petroleum: optimism, pessimism, or something else? US Geological Survey.Google Scholar
  24. Charpentier, R. L., Dolton, G. L., and Ulmishek, G. F., 1995, Annotated bibliography of methodology for assessment of undiscovered oil and gas resources: Nat. Resour. Res., v. 4, no. 2, p. 154–186.Google Scholar
  25. Cleveland, C. J., 1991, Physical and economic aspects of resource quality: the cost of oil supply in the lower 48 United States, 1936–1988: Resour. Energy, v. 13, no. 2, p. 163–188.Google Scholar
  26. Cleveland, C. J., 1992, Yield per effort for additions to crude-oil reserves in the lower 48 united-states, 1946–1989: AAPG Bull., v. 76, no. 6, p. 948–958.Google Scholar
  27. Cleveland, C. J., and Kaufmann, R. K., 1991, Forecasting ultimate oil recovery and its rate of production: incorporating economic forces into the models of M. King Hubbert: Energy J., v. 12, no. 2, p. 17–46.Google Scholar
  28. Cleveland, C. J., and Kaufmann, R. K., 1997, Natural gas in the US: how far can technology stretch the resource base: Energy J., v. 18, no. 2, p. 89–108.Google Scholar
  29. Cramer Barton, C., and La Pointe, P. R., 1995, Fractals in petroleum geology and earth processes: Springer.Google Scholar
  30. Dées, S., Karadeloglou, P., Kaufmann, R. K., and Sánchez, M., 2007, Modelling the world oil market: assessment of a quarterly econometric model: Energy Policy, v. 35, no. 1, p. 178–191.Google Scholar
  31. Deffeyes, K. S. (2005). Beyond oil; the view from Hubbert’s peak: Hill and Wang, New York, NY.Google Scholar
  32. Divi, R. S., 2004, Probabilistic methods in petroleum resource assessment, with some examples using data from the Arabian region: J. Petrol. Sci. Eng., v. 42, no. 2–4, p. 95–106.Google Scholar
  33. Drew, L. J., 1997, Undiscovered petroleum and mineral resources: assessment and controversy: Springer.Google Scholar
  34. Drew, L. J., and Schuenemeyer, J. H., 1992, A petroleum discovery rate forecast revisited-the problem of field growth: Nonrenew. Resour., v. 1, no. 1, p. 51–60.Google Scholar
  35. Drew, L. J., and Schuenemeyer, J. H., 1993, The evolution and use of discovery process models at the US Geological Survey: AAPG Bull., v. 77, no. 3, p. 467–478.Google Scholar
  36. Epple, D., and Hansen, L. P., 1981. Econometrics of exhaustible resource supply: a theory and an application. Final Report: United States: 63 p.Google Scholar
  37. Fisher, F. M., 1964, Supply and costs in the US petroleum industry: John Hopkins University Press, Baltimore.Google Scholar
  38. Forbes, K. F., and Zampelli, E. M., 2000, Technology and the exploratory success rate in the U.S. offshore: Energy J. v. 21, no. 1, p. 109–120.Google Scholar
  39. Forman, D., and Hinde, A. L., 1985, Improved statistical method for assessment of undiscovered petroleum resources: AAPG Bull., v. 69, no. 1, p. 106–118.Google Scholar
  40. Gautier, D. L., 2004, Oil and natural gas resource assessment: geological methods, in Cleveland, C. J., ed., The Encyclopedia of Energy: Edward Elgar, Cheltenham.Google Scholar
  41. Gowdy, J., and Roxana, J., 2007, Technology and petroleum exhaustion: evidence from two mega-oilfields: Energy, v. 32, no. 8, p. 1448–1454.Google Scholar
  42. Harbaugh, J. W., Davies, J. C., and Wendebourg, J., 1995, Computing risk for oil prospects: Pergamon Press, Oxford.Google Scholar
  43. Harris, d. P., 1977, Conventional crude oil resources of the United States: recent estimates, method for estimation and policy considerations: Mater. Soc., v. 1, p. 263–286.Google Scholar
  44. Hendricks, T. A., 1965, Resources of oil, gas and natural gas liquids in the United States and the world, US Geological Survey Circular 522.Google Scholar
  45. Hubbert, M. K., 1956, Nuclear energy and the fossil fuels, in Meeting of the Southern District, Division of Production, American Petroleum Institute, San Antonio, TX: Shell Development Company.Google Scholar
  46. Hubbert, M. K., 1959, Techniques of prediction with application to the petroleum industry, in 44th Annual Meeting of the American Association of Petroleum Geologists, Dallas, TX: Shell Development Company.Google Scholar
  47. Hubbert, M. K., 1962, Energy resources: A report to the committee on Natural Resources of the National Academy of Sciences: National Research Council, United States, 153 p.Google Scholar
  48. Hubbert, M. K., 1966, Reply to J.M. Ryan: AAPG Bull., v. 18, p. 284–286.Google Scholar
  49. Hubbert, M. K., 1967, Degree of advancement of petroleum exploration in United States: AAPG Bull., v. 51, p. 2207–2227.Google Scholar
  50. Hubbert, M. K., 1968, Degree of advancement of petroleum exploration in United States; Natural gases of North America. Part 4. Papers of general scope: Memoir AAPG, v. 9, no. 2, p. 2149–2170.Google Scholar
  51. Hubbert, M. K., 1974, U.S. Energy Resources: a review as of 1972: U.S. Government Printing Office, Washington.Google Scholar
  52. Hubbert, M. K., 1979, Hubbert estimates from 1956 to 1974 of US oil and gas, in Grenon, M., ed., Methods and Models for Assessing Energy Resources: Pergamon Press, Oxford.Google Scholar
  53. Hubbert, M. K., 1982, Techniques of prediction as applied to production of oil and gas: NBS Special Publication, US Department of Commerce, v. 631, p. 1–121.Google Scholar
  54. IEA, 2008, World Energy Outlook 2008: International Energy Agency, OECD, Paris.Google Scholar
  55. Iledare, O., and Pulsipher, A. G., 1999, Sources of change in productivity of petroleum exploration and development in the U.S. onshore Louisiana, 1977–1994: Energy Econ., v. 21, no. 3, p. 261–272.Google Scholar
  56. Imam, A., Startzman, R. A., and Barrufet, M. A., 2004, Multicyclic Hubbert model shows global conventional gas output peaking in 2019: Oil Gas J., v. 102, no. 31, p. 20–28.Google Scholar
  57. Ivanhoe, L. F., 1996, Updated Hubbert curves analyze world oil supply: World Oil, v. 217, no. 11, p. 91–94.Google Scholar
  58. Kaufman, G. M., 1975, Models and methods for estimating undiscovered oil and gas: what they do when do not do, in First IIASA Conference on Energy Resources, Laxenburg, Austria: International Institute for Applied Systems Analysis.Google Scholar
  59. Kaufman, G. M., 2005, Where have we been? Where are we going?: Nat. Resour. Res., v. 14, no. 3, p. 145–151.Google Scholar
  60. Kaufmann, R. K., 1991, Oil production in the lower 48 states: reconciling curve fitting and econometric models: Resour. Energy, v. 13, no. 1, p. 111–127.Google Scholar
  61. Kaufmann, R. K., and Cleveland, C. J., 1991, Policies to increase US oil production: likely to fail, damage the economy, and damage the environment: Annu. Rev. Energy Environ., v. 16, p. 379–400.Google Scholar
  62. Kaufmann, R. K., and Cleveland, C. J., 2001, Oil production in the lower 48 states: economic, geological, and institutional determinants: Energy J., v. 22, no. 1, p. 27–49.Google Scholar
  63. Kemp, A. G., and Kasim, A. S., 2005, Are decline rates really exponential? Evidence from the UK continental shelf: Energy J., v. 26, no. 1, p. 27–50.Google Scholar
  64. Kennedy, P., 2003, A guide to econometrics: Blackwell, Oxford.Google Scholar
  65. Klett, T. R., and Gautier, D. L., 2005, Reserve growth in oil fields of the North Sea: Petrol. Geosci., v. 11, no. 2, p. 179–190.Google Scholar
  66. Laherrère, J. H., 1996, Discovery and production trends: OPEC Bull., February, p. 7–11.Google Scholar
  67. Laherrère, J. H., 1999, World oil supply—what goes up must come down, but when will it peak?: Oil Gas J., v. 97, no. 5, p. 57–64.Google Scholar
  68. Laherrère, J., 2000a, Distribution of field sizes in a petroleum system; parabolic fractal, lognormal or stretched exponential?: Mar. Petrol. Geol., v. 17, no. 4, p. 539–546.Google Scholar
  69. Laherrère, J. H., 2000b, Learn strengths, weaknesses to understand Hubbert curve: Oil Gas J., v. 98, no. 16, p. 63–64.Google Scholar
  70. Laherrère, J., 2001, Estimates of oil reserves. Paper presented at the EMF/IEA/IEW meeting.Google Scholar
  71. Laherrère, J., 2002a, Forecasting future production from past discovery: Int. J. Global Energy Issues, v. 18, no. 2–4, p. 218–238.Google Scholar
  72. Laherrère, J. H., 2002b, Modelling future liquids production from extrapolation of the past and from ultimates: Energy Explor. Exploit., v. 20, no. 6, p. 457–479.Google Scholar
  73. Laherrère, J., 2003, Future of oil supplies: Energy Explor. Exploit., v. 21, no. 3, p. 227–267.Google Scholar
  74. Laherrère, J., 2004a, The future of oil: Int. J. Veh. Des., v. 35, no. 1–2, p. 9–26.Google Scholar
  75. Laherrère, J., 2004b, Oil and natural gas resource assessment: production growth cycle models, in Cleveland, C. J., ed., Encyclopaedia of Energy: Elsevier, Amsterdam.Google Scholar
  76. Laherrère, J. H., 2005, Forecasting production from discovery, in ASPO IV International Workshop on Oil and Gas Depletion, Lisbon: Association for the Study of Peak Oil.Google Scholar
  77. Li, K., and Horne, R. N., 2007, Comparison and verification of production prediction models: J. Petrol. Sci. Eng., v. 55, p. 213–220.Google Scholar
  78. Lore, G. L., Ross, K. M., Bascle, B. J., Nixon, L. D., and Klazynski, R. J., 1996, Summary of the 1995 assessment of the conventional recoverable hydrocarbon resources of the Gulf of Mexico and Atlantic Continental Shelf, Minerals Management Service.Google Scholar
  79. Lynch, M. C., 2002, Forecasting oil supply: theory and practice: Q. Rev. Econ. Finance, v. 42, no. 2, p. 373–389.Google Scholar
  80. Lynch, M. C., 2003, Petroleum resources pessimism debunked in Hubbert model and Hubbert modelers’ assessment: Oil Gas J., v. 101, no. 27, p. 38–47.Google Scholar
  81. MacAvoy, P. W., and Pindyck, R. S., 1973, Alternative regulatory policies for dealing with the natural gas shortage: Bell J. Econ. Manage. Sci., v. 4, no. 2, p. 454–498.Google Scholar
  82. Managi, S., Opaluch, J. J., Jin, D., and Grigalunas, T. A., 2004, Technological change and depletion in offshore oil and gas: J. Environ. Econ. Manage., v. 47, p. 388–409.Google Scholar
  83. Managi, S., Opaluch, J. J., Jin, D., and Grigalunas, T. A., 2005, Technological change and petroleum exploration in the Gulf of Mexico: Energy Policy, v. 33, no. 5, p. 619–632.Google Scholar
  84. Meade, N. M., 1984, The use of growth curves in forecasting market development—a review and appraisal: J. Forecast., v. 3, p. 49–451.Google Scholar
  85. Meisner, J., and Demirmen, F., 1981, The creaming method: a procedure to forecast future oil and gas discoveries in mature exploration provinces: J. R. Stat. Soc. A, v. 144, no. 1, p. 1–31.Google Scholar
  86. Meyer, P. S., 1994, Bi-logistic growth: Technol. Forecast. Soc. Change, v. 47, p. 89–102.Google Scholar
  87. Meyer, P. S., Yung, J. W., and Ausbel, J. H., 1999, A primer on logistic growth and substitution: the mathematics of the loglet lab software: Technol. Forecast. Soc. Change, v. 61, p. 247–271.Google Scholar
  88. Mills, R. M., 2008, The myth of the oil crisis: Praeger Publishers, Westport, CT, USA.Google Scholar
  89. Mohn, K., and Osmundsen, P., 2008, Exploration economics in a regulated petroleum province: the case of the Norwegian Continental Shelf: Energy Econ., v. 30, no. 2, p. 303–320.Google Scholar
  90. Mohr, S. H., and Evans, G. M., 2007, Mathematical model forecasts year conventional oil will peak: Oil Gas J., v. 105, no. 17, p. 45–46.Google Scholar
  91. Mohr, S., and Evans, G., 2008, Peak Oil: testing Hubbert’s curve via theoretical modeling: Nat. Resour. Res., v. 17, no. 1, p. 1–11.Google Scholar
  92. Moore, C. L., 1962, Method for evaluating US crude oil resources and projecting domestic crude oil availability: US Department of the Interior.Google Scholar
  93. Moore, C. L., 1966, Projections of US petroleum supply to 1980: Office of Oil and Gas, Washington, DC.Google Scholar
  94. Nehring, R., 2006a, How Hubbert method fails to predict oil production in the Permian Basin: Oil Gas J., v. 104, no. 15, p. 30–35.Google Scholar
  95. Nehring, R., 2006b, Post-Hubbert challenge is to find new methods to predict production, EUR: Oil Gas J., v. 104, no. 16, p. 43–46.Google Scholar
  96. Nehring, R., 2006c, Two basins show Hubbert’s method underestimates future oil production: Oil Gas J., v. 104, no. 13, p. 37–42.Google Scholar
  97. Nelder, J. A., 1971, The fitting of a generalisation of the logistics curve: Biometrics, v. 17, p. 89–110.Google Scholar
  98. NPC, 1995, Research development and demonstration needs of the oil and gas industry: National Petroleum Council, Washington, DC.Google Scholar
  99. Odell, P. R., and Rosing, K. E., 1980, The future of oil: a simulation study of the interrelationships of resources, reserves, and use, 1980–2080: Nichols Publishing Co, New York.Google Scholar
  100. Patzek, T. W., 2008, Exponential growth, energetic Hubbert cycles and the advancement of technology: Arch. Min. Sci. Polish Acad. Sci., v. 22 (Accepted for publication May 3, 2008).Google Scholar
  101. Pesaran, M. H., and Samiei, H., 1995, Forecasting ultimate resource recovery: Int. J. Forecast., v. 11, no. 4, p. 543–555.Google Scholar
  102. Pike, R., 2006, Have we underestimated the environmental challenge? Petrol. Rev., June, p. 26–27.Google Scholar
  103. Power, M., 1992, Lognormality in the observed size distribution of oil and gas pools as a consequence of sampling bias, Math. Geol., v. 24, no. 8, p. 929–945.Google Scholar
  104. Power, M., and Fuller, J. D., 1992a, A review of methods for estimating hydrocarbon supply: J Forecasting, v. 4, no. 2, p. 128–145.Google Scholar
  105. Power, M., and Fuller, J. D., 1992b, A comparison of models for forecasting the discovery of hydrocarbon deposits: J. Forecast., v. 11, p. 183–193.Google Scholar
  106. Power, M., and Jewkes, E., 1992, Simulating the discovery rate implications of technological innovation in oil and gas exploration: Technol. Forecast. Soc. Change, v. 41, no. 2, p. 161–175.Google Scholar
  107. Priest, T., 2007, Extraction not creation: the history of offshore petroleum in the Gulf of Mexico: Enterp. Soc., v. 8, no. 2, p. 227–267.Google Scholar
  108. Reynolds, D. B., and Kolodziej, M., 2008, Former Soviet Union oil production and GDP decline: granger causality and multi-cycle Hubbert curve: Energy Econ., v. 30, no. 2, p. 271–289.Google Scholar
  109. Rogner, H. H., 1997, An assessment of world hydrocarbon resources: Annu. Rev. Energy Environ., v. 22, p. 217–262.Google Scholar
  110. Root, D. H., and Mast, R. F., 1993, Future growth in know oil and gas fields: AAPG Bull., v. 77, no. 3, p. 479–484.Google Scholar
  111. Ryan, J. M., 1965, National Academy report on energy resources: discussion of limitations of logistic projections: Bull. Assoc. Petrol. Geol., v. 49, p. 1713–1727.Google Scholar
  112. Ryan, J. M., 1966, Limitations of statistical methods for predicting petroleum and natural gas reserves and availability: J. Petrol. Technol., v. 18, no. 3, p. 231–237.Google Scholar
  113. Ryan, J. T., 1973, An analysis of crude oil discovery rates in Alberta: AAPG Bull., v. 21, p. 219–235.Google Scholar
  114. Schuenemeyer, J. H., and Drew, L. J., 1994, Description of a discovery process modelling procedure to forecast future oil and gas incorporating field growth, US Geological Survey, Open File Report, p. 98–111.Google Scholar
  115. Sneddon, J. W., Sarg, F., and Ying, X., 2003, Exploration play analysis from a sequence stratigraphic perspective: Search and Discovery (Article 40079).Google Scholar
  116. Sorrell, S., and Speirs, J., 2009, Methods for estimating ultimately recoverable resources: UK Energy Research Centre, London.Google Scholar
  117. Sorrell, S., Speirs, J., Bentley, R. W., Brandt, A. R., and Miller, R. G., 2009, Global oil depletion: an assessment of the evidence for a near-term peak in global oil production: UK Energy Research Centre, London.Google Scholar
  118. Stitt, W., 1982, Current problems in oil and gas modelling, in Gass, S. I., ed., Oil and Gas Supply Modelling: National Bureau of Standard Special Publication, Maryland, v. 631, p. 142–170.Google Scholar
  119. Strahan, D., 2007, The Last Oil Shock; a survival guide to the imminent extinction of petroleum man: John Murray, London.Google Scholar
  120. Thompson, E., Sorrell, S., and Speirs, J., 2009a, Definition and interpretation of reserve estimates: UK Energy Research Centre, London.Google Scholar
  121. Thompson, E., Sorrell, S., and Speirs, J., 2009b, The nature and importance of reserve growth: UK Energy Research Centre, London.Google Scholar
  122. Tsoularis, A., and Wallace, J., 2002, Analysis of logistic growth models: Math. Biosci., v. 179, no. 1, p. 21–55.Google Scholar
  123. USGS, 2000, USGS World Petroleum Assessment 2000: description and results by USGS World Energy Assessment Team: U.S. Geological Survey, Reston, VA, USA.Google Scholar
  124. Verma, M. K., 2003, Modified Arrington method for calculating reserve growth; a new model for United States oil and gas fields: U.S. Geological Survey, Reston, VA, 14 p.Google Scholar
  125. Verma, M. K., 2005, A new reserve growth model for United States oil and gas fields: Nat. Resour. Res., v. 14, no. 2, p. 77–89.Google Scholar
  126. Walls, M. A., 1992, Modeling and forecasting the supply of oil and gas: a survey of existing approaches: Resour. Energy, v. 14, no. 3, p. 287–309.Google Scholar
  127. Walls, M. A., 1994, Using a ‘hybrid’ approach to model oil and gas supply: a case study of the Gulf of Mexico outer continental shelf: Land Econ., v. 70, no. 1, p. 1–19.Google Scholar
  128. Weeks, L. G., 1952, Factors of sedimentary basin development that control oil occurence: AAPG Bull., v. 36, p. 2017–2124.Google Scholar
  129. Wendebourg, J., and Lamiraux, C., 2002, Estimating the ultimate recoverable reserves of the Paris Basin, France: Oil Gas Sci. Technol., v. 57, no. 6, p. 621–629.Google Scholar
  130. White, L. P., 1981, A play approach to hydrocarbon resource assessment and evaluation, in Ramsay, J. B., ed., The Economics of Exploration for Energy Resources: JAI Press, Greenwich, p. 51–68.Google Scholar
  131. White, D. A., and Gehman, H. M., 1979, Methods of estimating oil and gas resources: AAPG Bull., v. 63, p. 2183–2192.Google Scholar
  132. Wiorkowski, J. J., 1981, Estimating volumes of remaining fossil fuel resources: a critical review: J. Am. Stat. Assoc., v. 76, no. 375, p. 534–547.Google Scholar
  133. Zapp, A. D., 1962, Future petroleum producing capacity of the United States. Geological Survey Bulletin: United States Geological Survey, Washington, D.C., 36 p.Google Scholar

Copyright information

© International Association for Mathematical Geology 2010

Authors and Affiliations

  1. 1.Sussex Energy Group, SPRU (Science & Technology Policy Research), Freeman CentreUniversity of SussexFalmerUK
  2. 2.Imperial College Centre for Environmental Policy and Technology (ICCEPT), Imperial College LondonLondonUK

Personalised recommendations