Estimation of Undiscovered Hydrocarbon Potential through Fractal Geometry

  • Paul R. La Pointe


Why is there a need to develop yet another resource assessment method, especially one based upon fractal geometry? As pointed out by Bois et al. (1979), the estimation of undiscovered hydrocarbon resources suffers from two fundamental difficulties. First, a sedimentary basin is a complex entity, for which there are only a limited number of measurements on a small subset of physical and geometrical properties for the hydrocarbon system, even after decades of exploration and production. Second, there is no universally accepted causal relation between these variables, and the occurrence and size of undiscovered fields. Rather, the assessor must choose from a variety of empirical models relating the observed variables to undiscovered hydrocarbon. These two shortcomings mean that assessments are still imprecise and uncertain, affording room for both improved accuracy and constraint of uncertainty. Occasionally, the lack of consonance between nature and the empirical model or its limited database may cause an estimate to be unexpectedly inaccurate. Without comparing several independent estimates, it is difficult to guard against being led astray by the difficult-to-detect aberration of any one method in a specific area.


Fractal Dimension Field Size Fractal Geometry Small Field Data Cloud 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Arps, J. J., and Roberts, T. G., Economies of drilling for Cretaceous oil on east flank of the Denver-Julesburg basin, Am. Assoc. Petroleum Geologists Bull. 42, 2549–2566 (1958).Google Scholar
  2. Barton, C. C, La Pointe, P.R., and Malinverno, A., Fractals and Their Use in the Earth Sciences and in the Petroleum Industry, Short Course Manual, American Association of Petroleum Geologists Short Course, Houston, Texas, March 11–13, 1992.Google Scholar
  3. Bethea, R. M., Duran, B. S., and Boullion, T. L. Statistical Methods for Engineers and Scientists, Marcel Dekker, Inc., New York, pp. 351–363 (1985).MATHGoogle Scholar
  4. Bois, C, Cousteau, H., and Perredon, A., Méthodes d’estimation des reserves ultimes, in: Proceedings, 10th World Petroleum Congress, World Petroleum Congress, Bucharest, pp. 279–289 (1979).Google Scholar
  5. Bruno, R., and Raspa, G., Geostatistical characterization of fractal models of surface, in: Geostatistics, Proceedings of the Third International Geostatistics Congress, Kluwer Academic Publishers, Dordrecht, pp. 77–90 (1989).Google Scholar
  6. Burrough, P. A., Fractal dimensions of landscapes and other environmental data, Nature 294, 240–242 (1981).ADSCrossRefGoogle Scholar
  7. CGMM (Centre de Geostatistique, Écoles des Mines de Paris), SIMPACK User’s Guide (1978).Google Scholar
  8. De Vaucouleurs, G., The case for a hierarchical cosmology, Science 167, 1203–1213 (1970).ADSCrossRefGoogle Scholar
  9. Falconer, K. J., Fractal Geometry: Mathematical Foundations and Applications, John Wiley & Sons, Inc., Chichester (1990).MATHGoogle Scholar
  10. Feder, J., Fractals, Plenum Press, New York (1988).MATHGoogle Scholar
  11. Hoaglin, D. C, Mosteller, E, and Tukey, J. W, Exploring Data Tables, Trends and Shapes, John Wiley & Sons, Inc., New York (1985).MATHGoogle Scholar
  12. Journel, A. G., Geostatistics for conditional simulation of ore bodies, Econ. Geol. 69, 673–687 (1973).CrossRefGoogle Scholar
  13. Journel, A. G., and Huijbregts, C, Mining Geostatistics, Academic Press, London (1978).Google Scholar
  14. La Pointe, P.R., Fractals and Their Use in Earth Sciences. Course Notes for Geological Society of America ShortGoogle Scholar
  15. Course No. 4, Annual Meeting, San Diego, California, Oct. 19–20, 1991.Google Scholar
  16. Lee, P. J., and Wang, P. C. C., Probabilistic formulation of a method for the evaluation of petroleum resources, Mathemat. Geol. 15, 163–181 (1983).Google Scholar
  17. Mandelbrot, B. B., The Fractal Geometry of Nature, W.H. Freeman and Company, New York (1983).Google Scholar
  18. Mark, D. M., and Aronson, PB., Scale-dependent fractal dimensions of topographic surfaces: an empirical investigation, with applications in geomorphology and computer mapping, Math. Geol. 16, 671–683 (1984).CrossRefGoogle Scholar
  19. Moore, R. E., Mathematical Elements of Scientific Computing, Holt, Rinehart and Winston, Inc., New York, pp. 91–101 (1975).MATHGoogle Scholar
  20. Neother, G. E., Introduction to Statistics: A Non-Parametric Approach, Houghton Mifflin Co., Boston (1971).Google Scholar
  21. Rendu, J. M. An Introduction to Geostatistical Methods of Mineral Evaluation, South African Institute of Mining and Metallurgy, Johannesburg (1981).Google Scholar
  22. Robert, A. Statistical properties of sediment bed profiles in alluvial channels, Math. Geol. 20, 205–225 (1988).CrossRefGoogle Scholar
  23. Shepherd, J., Creasey, J. W., and Rison, L. K., Comment on “Joint spacing as a method of locating faults”, Geol. 10, 282 (1982).CrossRefGoogle Scholar
  24. White, D. A., and Gehman, H. M., Methods of estimating oil and gas resources, Bull. Am. Assoc. Petroleum Geologists 63, 2183–2192 (1981).Google Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Paul R. La Pointe
    • 1
  1. 1.Golder Associates Inc.RedmondUSA

Personalised recommendations