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

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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.

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Notes

  1. These involve selecting and parameterising a mathematical function that has the ‘best’ statistical fit to a set of data points, possibly subject to constraints.

  2. Hubbert’s original curve was hand drawn, but his later articles used more formal techniques.

  3. If the discovery rate was constant and if fields were discovered precisely in the descending order of size, the field-rank and discovery projection techniques would be identical. But the advantage of discovery projection is that it does not require data on individual fields.

  4. Exploration is very rarely unrestricted in aggregate regions. For example, the US imposes far fewer restrictions than most countries, but the Arctic National Wildlife Refuge, the eastern Gulf of Mexico, much of the western offshore and many onshore areas in the Rockies are off-limits for environmental reasons (Mills, 2008).

  5. Non-linear regression is straightforward with modern computer technology, but the earlier literature uses simpler methods such as the linear transformation of the functional form followed by a linear regression (Hubbert, 1982). If the production or discovery cycle is well advanced, then it is possible to estimate the URR through visual identification of the asymptote to which the curve is trending (Bentley, 2009).

  6. Hubbert (1982) begins with an assumed parabolic relationship between production and cumulative production and uses this to derive a logistic equation for cumulative production over time. However, this formal derivation came more than 20 years after he first referred to the logistic model (Hubbert, 1959; Sorrell and Speirs, 2009).

  7. Wiorkowski (1981) compared a ‘Generalized Richards’ model (which can take an exponential, logistic, or Gompertz form depending on the parameters chosen) with a cumulative Weibull and found that they fit the US cumulative production data equally well but led to significantly different URR estimates (445 and 235 Gb, respectively).

  8. Cleveland and Kaufmann (1991) fitted a logistic curve to the US production data through to 1988 and found that the adjusted R 2 changed only from 0.9880 to 0.9909 as the value of the URR varied from 160 to 250 billion barrels.

  9. ‘…Because petroleum exploration in the US began very early, because the initial exploration and discoveries occurred in what has proved to be relatively minor basins, because early drilling technology was very limited in its drilling depth capabilities, and because discoveries in the major basins only hit their stride between 1910 in 1950, the US comes closest to a symmetric discovery curve of any major oil producing country or region’ (Nehring, 2006a, b, c).

  10. Including the cumulative length of exploratory drilling (Hubbert, 1967), the total number of exploratory wells (Ryan, 1973), the number of successful exploratory wells (Moore, 1962), the cumulative length of successful exploratory wells (Stitt, 1982) or the cumulative length of all wells (i.e. both exploratory and development) (Cleveland, 1992). A distinction may also be made between the first exploratory well to be drilled (‘new field wildcats’ or NFWs) and subsequent wells.

  11. Laherrère (2004a, b) states that the creaming curve was invented by Shell in the 1980s, but variants of this approach have been used in the oil industry for much longer period (Arps and Roberts, 1958; Arps and others, 1971; Odell and Rosing, 1980; Harbaugh and others, 1995). Two employees of Shell published a paper on ‘the creaming method’ in 1981, but this describes a highly sophisticated (and not widely used) discovery process model that relies on Monte Carlo simulation of trends in both success rates and average field sizes and assumes a lognormal field size distribution (Meisner and Demirmen, 1981).

  12. The IEA (2008) reports that, over the last 50 years, the global average success rate has increased from one in six exploratory wells to one in three. Similarly, Lynch (2002) reports that the average success rate in the US increased by 50% between 1992 and 2002 and Forbes and Zampelli (2000) report that the US offshore success rate doubled between 1978 and 1995. In an econometric analysis, Forbes and Zampelli (2000) estimate that, over the period of 1986–1995, technological progress increased the US offshore success rate by 8.3%/year.

  13. The names of the regions are withheld due to data confidentiality.

  14. Goodness of fit was measured using simple R 2. However, we recognise that this is not the best measure to use when comparing ‘non-nested’ models, such as a logistic versus a Gompertz (Kennedy, 2003).

  15. For example, Epple and Hansen (1981), MacAvoy and Pindyck (1973), Walls (1994) and Mohn and Osmundsen (2008).

  16. For example, between 1957 and 1968, the ‘prorationing’ decisions of the Texas Railroad Commission shut in more than 50% of Texan oil-producing capacity.

  17. A notable exception is Dées and others (2007).

References

  • 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 

  • 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 

  • 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 

  • Arps, J. J., 1956, Estimation of primary oil reserves: Trans. AIME, v. 207, p. 182–191.

    Google Scholar 

  • 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 

  • 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 

  • 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 

  • Bass, F. M., 1969, A new product growth model for consumer durables: Manage. Sci., v. 15, p. 215–227.

    Google Scholar 

  • 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 

  • Bentley, R. W., 2009, A primer on oil peaking: UK Energy Research Centre, London.

    Google Scholar 

  • 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 

  • 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 

  • Brandt, A. R., 2007, Testing Hubbert: Energy Policy, v. 35, no. 5, p. 3074–3088.

    Google Scholar 

  • 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 

  • 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 

  • Campbell, C. J., 1997, The coming oil crisis: Multi-Science Publishing & Petroconsultants.

  • 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 

  • Campbell, C. J., and Heapes, S., 2008, An atlas of oil and gas depletion: Jeremy Mills Publishing, Huddersfield.

    Google Scholar 

  • 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 

  • 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 

  • Cavallo, A. J., 2005a, Hubbert’s model: uses, meanings, and limits. 1: Oil Gas J., v. 103, no. 21, p. 22–24.

    Google Scholar 

  • Cavallo, A. J., 2005b, Hubbert’s model: uses, meanings, and limits. 2: Oil Gas J., v. 103, no. 22, p. 20–25.

    Google Scholar 

  • Charpentier, R. R., 2003, The future of petroleum: optimism, pessimism, or something else? US Geological Survey.

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • Cramer Barton, C., and La Pointe, P. R., 1995, Fractals in petroleum geology and earth processes: Springer.

  • 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 

  • Deffeyes, K. S. (2005). Beyond oil; the view from Hubbert’s peak: Hill and Wang, New York, NY.

  • 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 

  • Drew, L. J., 1997, Undiscovered petroleum and mineral resources: assessment and controversy: Springer.

  • 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 

  • 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 

  • Epple, D., and Hansen, L. P., 1981. Econometrics of exhaustible resource supply: a theory and an application. Final Report: United States: 63 p.

  • Fisher, F. M., 1964, Supply and costs in the US petroleum industry: John Hopkins University Press, Baltimore.

    Google Scholar 

  • 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 

  • 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 

  • Gautier, D. L., 2004, Oil and natural gas resource assessment: geological methods, in Cleveland, C. J., ed., The Encyclopedia of Energy: Edward Elgar, Cheltenham.

  • 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 

  • Harbaugh, J. W., Davies, J. C., and Wendebourg, J., 1995, Computing risk for oil prospects: Pergamon Press, Oxford.

    Google Scholar 

  • 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 

  • Hendricks, T. A., 1965, Resources of oil, gas and natural gas liquids in the United States and the world, US Geological Survey Circular 522.

  • 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.

  • 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.

  • 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.

  • Hubbert, M. K., 1966, Reply to J.M. Ryan: AAPG Bull., v. 18, p. 284–286.

    Google Scholar 

  • Hubbert, M. K., 1967, Degree of advancement of petroleum exploration in United States: AAPG Bull., v. 51, p. 2207–2227.

    Google Scholar 

  • 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 

  • Hubbert, M. K., 1974, U.S. Energy Resources: a review as of 1972: U.S. Government Printing Office, Washington.

  • 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.

  • 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.

  • IEA, 2008, World Energy Outlook 2008: International Energy Agency, OECD, Paris.

    Google Scholar 

  • 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 

  • 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 

  • Ivanhoe, L. F., 1996, Updated Hubbert curves analyze world oil supply: World Oil, v. 217, no. 11, p. 91–94.

    Google Scholar 

  • 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.

  • Kaufman, G. M., 2005, Where have we been? Where are we going?: Nat. Resour. Res., v. 14, no. 3, p. 145–151.

    Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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 

  • Kennedy, P., 2003, A guide to econometrics: Blackwell, Oxford.

    Google Scholar 

  • 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 

  • Laherrère, J. H., 1996, Discovery and production trends: OPEC Bull., February, p. 7–11.

  • 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 

  • 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 

  • Laherrère, J. H., 2000b, Learn strengths, weaknesses to understand Hubbert curve: Oil Gas J., v. 98, no. 16, p. 63–64.

    Google Scholar 

  • Laherrère, J., 2001, Estimates of oil reserves. Paper presented at the EMF/IEA/IEW meeting.

  • Laherrère, J., 2002a, Forecasting future production from past discovery: Int. J. Global Energy Issues, v. 18, no. 2–4, p. 218–238.

    Google Scholar 

  • 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 

  • Laherrère, J., 2003, Future of oil supplies: Energy Explor. Exploit., v. 21, no. 3, p. 227–267.

    Google Scholar 

  • Laherrère, J., 2004a, The future of oil: Int. J. Veh. Des., v. 35, no. 1–2, p. 9–26.

    Google Scholar 

  • Laherrère, J., 2004b, Oil and natural gas resource assessment: production growth cycle models, in Cleveland, C. J., ed., Encyclopaedia of Energy: Elsevier, Amsterdam.

  • 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.

  • 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 

  • 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.

  • Lynch, M. C., 2002, Forecasting oil supply: theory and practice: Q. Rev. Econ. Finance, v. 42, no. 2, p. 373–389.

    Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • Meyer, P. S., 1994, Bi-logistic growth: Technol. Forecast. Soc. Change, v. 47, p. 89–102.

    Google Scholar 

  • 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 

  • Mills, R. M., 2008, The myth of the oil crisis: Praeger Publishers, Westport, CT, USA.

    Google Scholar 

  • 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 

  • 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 

  • 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 

  • Moore, C. L., 1962, Method for evaluating US crude oil resources and projecting domestic crude oil availability: US Department of the Interior.

  • Moore, C. L., 1966, Projections of US petroleum supply to 1980: Office of Oil and Gas, Washington, DC.

    Google Scholar 

  • 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 

  • 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 

  • 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 

  • Nelder, J. A., 1971, The fitting of a generalisation of the logistics curve: Biometrics, v. 17, p. 89–110.

    Google Scholar 

  • NPC, 1995, Research development and demonstration needs of the oil and gas industry: National Petroleum Council, Washington, DC.

    Google Scholar 

  • 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 

  • 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).

  • Pesaran, M. H., and Samiei, H., 1995, Forecasting ultimate resource recovery: Int. J. Forecast., v. 11, no. 4, p. 543–555.

    Google Scholar 

  • Pike, R., 2006, Have we underestimated the environmental challenge? Petrol. Rev., June, p. 26–27.

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • Rogner, H. H., 1997, An assessment of world hydrocarbon resources: Annu. Rev. Energy Environ., v. 22, p. 217–262.

    Google Scholar 

  • 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 

  • 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 

  • 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 

  • Ryan, J. T., 1973, An analysis of crude oil discovery rates in Alberta: AAPG Bull., v. 21, p. 219–235.

  • 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.

  • Sneddon, J. W., Sarg, F., and Ying, X., 2003, Exploration play analysis from a sequence stratigraphic perspective: Search and Discovery (Article 40079).

  • Sorrell, S., and Speirs, J., 2009, Methods for estimating ultimately recoverable resources: UK Energy Research Centre, London.

    Google Scholar 

  • 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 

  • 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.

  • Strahan, D., 2007, The Last Oil Shock; a survival guide to the imminent extinction of petroleum man: John Murray, London.

    Google Scholar 

  • Thompson, E., Sorrell, S., and Speirs, J., 2009a, Definition and interpretation of reserve estimates: UK Energy Research Centre, London.

    Google Scholar 

  • Thompson, E., Sorrell, S., and Speirs, J., 2009b, The nature and importance of reserve growth: UK Energy Research Centre, London.

    Google Scholar 

  • Tsoularis, A., and Wallace, J., 2002, Analysis of logistic growth models: Math. Biosci., v. 179, no. 1, p. 21–55.

    Google Scholar 

  • 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 

  • 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.

  • 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 

  • 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 

  • 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 

  • Weeks, L. G., 1952, Factors of sedimentary basin development that control oil occurence: AAPG Bull., v. 36, p. 2017–2124.

    Google Scholar 

  • 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 

  • 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.

  • White, D. A., and Gehman, H. M., 1979, Methods of estimating oil and gas resources: AAPG Bull., v. 63, p. 2183–2192.

    Google Scholar 

  • 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 

  • Zapp, A. D., 1962, Future petroleum producing capacity of the United States. Geological Survey Bulletin: United States Geological Survey, Washington, D.C., 36 p.

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Acknowledgments

This article is based on a comprehensive review of the curve-fitting literature by Sorrell and Speirs (2009) which in turn formed part of wide-ranging study of global oil depletion by the UK Energy Research Centre (Sorrell and others, 2009). The authors would like to thank the UK Research Councils for their financial support, IHS Energy for allowing the publication of data from their PEPS database, Fabiana Gordon for her help on statistical issues, and Roger Bentley, Richard Miller, Jean Laherrère and Robert Kaufmann for their helpful comments on earlier drafts. The usual disclaimers apply.

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Authors and Affiliations

  1. Sussex Energy Group, SPRU (Science & Technology Policy Research), Freeman Centre, University of Sussex, Falmer, Brighton, BN1 9QE, UK

    Steve Sorrell

  2. Imperial College Centre for Environmental Policy and Technology (ICCEPT), Imperial College London, South Kensington Campus, Exhibition Road, London, SW7 2AZ, UK

    Jamie Speirs

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  1. Steve Sorrell
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  2. Jamie Speirs
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Correspondence to Steve Sorrell.

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Sorrell, S., Speirs, J. Hubbert’s Legacy: A Review of Curve-Fitting Methods to Estimate Ultimately Recoverable Resources. Nat Resour Res 19, 209–230 (2010). https://doi.org/10.1007/s11053-010-9123-z

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