Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Petroleum exploration models—Estimation and applications


Three statistical models of oil and gas exploration prevail in the literature: field size distribution, “exploration function,” and “effectiveness of exploration” models. They may have many functional forms and may be used for prediction and planning results of future exploration activity. A review of American and Soviet literature of exploration models is presented with special emphasis on functions suitable for countries which, like Poland, are not rich in oil and gas. Two new procedures are proposed: a method for assessing field size distribution and a method for simultaneous interval estimation of parameters of the exploration function. The methods complement existing ones as they are suited to areas that are not rich in hydrocarbons. Examples of application to exploration of two Polish petroliferous basins are given.

This is a preview of subscription content, log in to check access.


  1. Arps, J. J. and Roberts, T. G., 1958, Economics of Drilling for Cretaceous Oil on East Flank of Denver-Julesburg Basin:Am. Assoc. Petr. Geol. Bull., v. 42, p. 2549–2566.

  2. Arps, J. J., Mortada, M., and Smith, A. E., 1971, Relationship between Proved Reserves and Exploratory Effort:J. Petr. Technol., v. 23, p. 671–675.

  3. Attanasi, E. D. and Drew, L. J., 1985, Lognormal Field Size Distributions as a Consequence of Economic Truncation:Math. Geol., v. 17, p. 335–351.

  4. Attanasi, E. D., Garland, T. M., Wood, J. H., Dietzman, W. D., and Hicks, J. N., 1981, Economics and Resource Appraisal—The Case of the Permian Basin:J. Petr. Technol., v. 33, p. 603–616.

  5. Babalyan, G. G. and Glazunov, V. I., 1982, Forecasting of Deep Oil Well Drilling Effectiveness:Neftegaz. Geol. Geofiz., No. 2, p. 5–8 (in Russian).

  6. Balasanov, V. A. and Kamenecki, S. G., 1977, Some Problems of Forecasting Methodology of Oil Field Discoverable Reserves:Ekon. Neft. Promst., no. 9, p. 26–28 (in Russian).

  7. Barouch, E. and Kaufman, G. M., 1978, The Interface Between Geostatistical Modeling of Oil and Gas Discovery and Economics:Math. Geol., v. 10, p. 611–627.

  8. Baturin, J. N., Morozova, M. N., and Sokolova, T. V., 1982, Relationship between Exploratory Drilling Volume and Discovered Reserves:Neftegaz. Geol. Geofiz., no. 12, p. 1–2 (in Russian).

  9. Baymukhametov, K. S. and Sattarov, M. M., 1975, About Some Probabilistic-statistical Model for Forecasting of Oil Reserves Increase:Geol. Neft. Gaz., no. 3, p. 27–32 (in Russian).

  10. Buyalov, N. I. and Korchagin, V. I., 1985, Structure of Oil and Gas Drilling Activity as a Function of Reserves Recognition Degree:Neftegaz. Geol. Geofiz. Burene, no. 7, p. 1–4 (in Russian).

  11. Collins, D. R., 1985, Changes in Drilling Density and Discovery Rates Through Time:Math. Geol., v. 17, p. 375–393.

  12. Drew, L. J., Root, D. H., and Bawiec, W. J., 1979, Estimating Future Rates of Petroleum Discoveries in the Permian Basin: SPE Paper No. 7722.

  13. Eremenko, N. A., Krylov, N. A., Kuvykin, J. S., and Stasenko, V. V., 1979, Forecasting Method of Petroleum Exploration Effectiveness:Geol. Neft. Gaz., no. 1, p. 7–13 (in Russian).

  14. Haun, J. D. (Ed.), 1975, Methods of Estimating the Volume of Undiscovered Oil and Gas Resources:AAPG Stud. Geol., no. 1., 204 p.

  15. Hubbert, M. K., 1967, Degree of Advancement of Petroleum Exploration in USA:Bull. Am. Assoc. Petr. Geol., v. 51, p. 2207–2215.

  16. Ivanhoe, L. F., 1976, Oil/Gas Potential in Basins Estimated:Oil Gas J., no. 49, p. 154–155.

  17. Jones, D. A., Buck, N. A., and Kelsey, J. H., 1982a, Choosing an Optimum Exploration Strategy:World Oil, v. 195, p. 71–86.

  18. Jones, D. A., Buck, N. A., and Kelsey, J. H., 1982b, Model to Evaluate Exploration Strategies:Bull. Am. Assoc. Petr. Geol., v. 66, p. 317–331.

  19. Kontorovich, A. E. and Demin, V. I., 1977, Estimation Method of Number and Size Distribution of Oil and Gas Fields in Large Oil and Gas Basins:Geol. Neft. Gaz., no. 12, p. 18–26 (in Russian).

  20. Kontorovich, A. E., Demin, V. I., and Strakhov, I. A., 1985, Rules Governing the Discoveries of Oil and Gas Fields of Various Size in Oil and Gas Basins:Geol. Geofiz., no. 11, p. 3–16 (in Russian).

  21. Korchagin, V. I., 1984, Forecasting the Number and Size of Oil and Gas Deposits:Geol. Neft. Gaz., no. 12, p. 30–33 (in Russian).

  22. Krige, D. G., 1951, A Statistical Approach to Some Basic Mine Valuation Problems on the Witwatersrand:J. Chem. Met. Min. Soc. S. Afr., v. 52, p. 119–139.

  23. Krylov, N. A., 1982, About the Notion “Prospecting Orientation” in Oil and Gas Fields Exploration:Geol. Neft. Gaz., no. 11, p. 17–22 (in Russian).

  24. Lee, P. J. and Wang, P. C. C., 1983a, Probabilistic Formulation of a Method for the Evaluation of Petroleum Resources:Math. Geol., v. 15, p. 163–181.

  25. Lee, P. J. and Wang, P. C. C., 1983b, Conditional Analysis for Petroleum Resource Evaluations:Math. Geol., v. 15, p. 349–361.

  26. Lee, P. J. and Wang, P. C. C., 1985, Prediction of Oil or Gas Pool Sizes when Discovery Record is Available:Math. Geol., v. 17, p. 95–113.

  27. Leybson, M. G., 1982, A Method of Long-Range Petroleum Exploration Planning:Geol. Neft. Gaz., no. 11, p. 12–17 (in Russian).

  28. Megil, R. E., 1971,An Introduction to Exploration Economics: Petroleum Publishing Co., Tulsa, 159 p.

  29. Nesterov, I. I., Shpilman, V. I., Myasnikova, G. P., Plavnik, G. I., Zavgorodnaya, L. D., Krasnova, G. N., and Sudat, L. G., 1977, New Characteristics of Potential Resources:Geol. Neft. Gaz., no. 12, p. 26–32 (in Russian).

  30. Rapoport, L. A. and Grender G. C., 1977, The Impact of Assumptions About Oil Exploration on Projections of Long-Range Energy Supplies in the United States:Math. Geol., v. 9, p. 429–439.

  31. Schoeffler, J., 1971, La “bonnè technique” et le hasard:Rev. AFTP, no. 207, p. 15–20.

  32. Schuenemeyer, J. H. and Drew, L. J., 1983, A Procedure to Estimate the Parent Population of the Size of Oil and Gas Fields as Revealed by a Study of Economic Truncation:Math. Geol., v. 15, p. 145–161.

  33. Seber, G. A. F., 1977,Linear Regression Analysis, Wiley, New York, 480 p.

  34. Selicki, A. G., 1978, Forecasting of optimum oil exploration volume:Geol. Neft. Gaz., no. 11, p. 10–14 (in Russian).

  35. Shpilman, V. I. 1982,Quantitative Forecast of Oil and Gas Occurrence: Nedra, Moscow, 214 p. (in Russian).

  36. Theil, H., 1971,Principles of Econometrics, Wiley, New York, 736 p.

  37. Wiorkowski, J. J., 1981, Estimating Volumes of Remaining Fossil Fuel Resources: A Critical Review:J. Am. Stat. Assoc., v. 76, p. 534–559.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Łucki, Z., Szkutnik, Z. Petroleum exploration models—Estimation and applications. Math Geol 21, 495–512 (1989).

Download citation

Key words

  • Exploration models
  • resource evaluation
  • maximum likelihood estimates