Advertisement

Nonrenewable Resources

, Volume 5, Issue 2, pp 103–115 | Cite as

An analytical approximation of the distribution of total hydrocarbon discoveries as a function of discovery number

  • E. Chungcharoen
  • J. D. Fuller
Articles
  • 20 Downloads

Abstract

Recently, Manly's method has been successfully applied to hydrocarbon exploration modeling in order to approximate the expected value and the standard deviation of the total amount of hydrocarbons discovered. This method is much faster than running prolonged simulations normally required by the probabilistic model of the hydrocarbon discovery process, and the results are very accurate. This paper extends the usefulness of the approximation method by developing an approximate analytical model of the whole probability distribution of the total volume of hydrocarbons discovered. The mean and the standard deviation from Manly's approximation are used to help set the parameters of a family of beta distributions, to represent the distributions of the total amount of hydrocarbons discovered from the beginning to the end of the exploration process in an area. Three real datasets—the Nova Scotian Shelf from offshore northeastern Canada, the Bistcho Play, and the Zama Play from northwestern Canada—are chosen to verify the methodology developed. Confidence intervals of the forecast for each number of discovered fields are constructed from the analytical approximation and compared with confidence intervals generated by the simulation. Sensitivity analyses are performed to show that the idea of using a family of beta distributions is a robust approximation.

Key Words

Exploration crude oil natural gas 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arps, J. J., and Roberts, T. G., 1958, Economics of drilling for cretaceous oil on east flank of denver-julesburg basin: AAPG Bulletin, v. 42, n. 11, p. 2549–2566.Google Scholar
  2. Attanasi, E. D., Drew, L. J., and Schuenemeyer, J. H., 1980, Petroleum resource appraisal and discovery rate forecasting in partially explored regions—An application to supply modeling: U.S. Geological Survey Professional Paper, 1138A-C.Google Scholar
  3. Barouch, E., and Kaufman, G. M., 1976, Probabilistic modeling of oil and gas discovery,in Roberts, F. S., ed., SIAM, p. 248–260.Google Scholar
  4. Bickel, P. J., Nair, V. N., and Wang, P. C. C., 1992, Nonparametric inference under biased sampling from a finite population: The Annals of Statistics, v. 20, n. 2, p. 853–878.Google Scholar
  5. Bradley, J. V., 1968, Distribution-free statistical tests: Englewood Cliffs, NJ, Prentice-Hall, 388 p.Google Scholar
  6. Chungcharoen, E., 1994, Approximating the distributions of the total amount of hydrocarbons discovered by a family of beta distributions: Master's thesis, University of Waterloo, Waterloo, Canada, 149 p.Google Scholar
  7. Fuller, J. D., 1991, A rapid method to simulate exploration for hydrocarbons,in Breton, M., and Zaccour, G., eds., Advances in operations research in the oil and gas industry, p. 51–62.Google Scholar
  8. Fuller, J. D., and Wang, F., 1991, A Probabilistic model of petroleum discovery: Nonrenewable Resources, v. 1, p. 325–330.Google Scholar
  9. Johnson, N. L., and Kotz, S., 1970, Continuous univariate distributions-II: Boston, Houghton Mifflin, 306 p.Google Scholar
  10. Kaufman, G. M., Balcer, Y., and Kruyt, D., 1975, A probabilistic model of oil and gas discovery,in Haun, J. D., ed., Methods of estimating the volume of undiscovered oil and gas resources: AAPG Studies in Geology, n. 1, p. 113–142.Google Scholar
  11. Law, A. M., and Kelton, W. D., 1991, Simulation modeling and analysis: New York, McGraw-Hill, 759 p.Google Scholar
  12. Lee, P. J., and Wang, P. C. C., 1983a, Probabilistic formulation of a method for the evaluation of petroleum resources: Journal of the International Society for Mathematical Geology, v. 15, n. 1, p. 163–181.Google Scholar
  13. Lee, P. J., and Wang, P. C. C., 1983b, Conditional analysis for petroleum resource evaluations: Journal of the International Society for Mathematical Geology, v. 15, n. 2, p. 349–361.Google Scholar
  14. Lee, P. J., and Wang, P. C. C., 1985, Prediction of oil or gas pool sizes when discovery record is available: Journal of the International Society for Mathematical Geology, v. 17, n. 2, p. 95–113.Google Scholar
  15. Macdonald, D. G., Power, M., and Fuller, J. D., 1994, A new discovery process approach to forecasting hydrocarbon discoveries: Resource and Energy Economics, v. 16, p. 147–166.Google Scholar
  16. Manly, B. F. J., 1974, A model for certain types of selection experiments: Biometrics, v. 30, p. 281–294.Google Scholar
  17. Ninpong, R., 1992, Assessing the accuracy of a rapid approximation for simulating hydrocarbons exploration: thesis, University of Waterloo, Waterloo, Canada, PhD 259 p.Google Scholar
  18. Ninpong, R., Power, M., and Fuller, J. D., 1992, A rapid approximation for predicting the hydrocarbon discovery rate: Part 1-assessing the accuracy: Natural Resource Modeling, v. 6, n. 3, p. 285–303.Google Scholar
  19. O'Carroll, F. M., and Smith, J. L., 1980, Probabilistic methods for estimating undiscovered petroleum resources: Advance in the Economics of Energy and Resources, v. 3, p. 31–63.Google Scholar
  20. Power, M., 1990, Modeling natural gas exploration and development on the Scotian Shelf; PhD thesis, University of Waterloo, Waterloo, Canada, 289 p.Google Scholar
  21. Power, M., and Fuller, J. D., 1991, Predicting the discoveries and finding costs of natural gas: the example of the Scotian Shelf: The Energy Journal, v. 12, n. 3, p. 77–93.Google Scholar
  22. Rabinowitz, D., 1991, Using exploration history to estimate undiscovered resources: Mathematical Geology, v. 23, n. 2, p. 257–274.Google Scholar
  23. Smith, J. L., 1980, A probabilistic model of oil discovery: Review of Economics, and Statistics, v. 62, n. 4, p. 587–594.Google Scholar

Copyright information

© International Association for Mathematical Geology 1996

Authors and Affiliations

  • E. Chungcharoen
    • 1
  • J. D. Fuller
    • 1
  1. 1.Department of Management SciencesUniversity of WaterlooWaterlooCanada

Personalised recommendations