Skip to main content

Creating Reservoir Simulations with Fractal Characteristics

  • Chapter
Fractals in Petroleum Geology and Earth Processes

Abstract

Reservoir characterization is in many ways like a game of poker, an estimate of a set of data from incomplete information on which money is wagered. A gambler may know a little information (his cards, certain cards turned face up for the other players, the distribution of cards in suits in a 52–card deck), and he is required to wager money based upon his reconstruction of what cards he thinks the other players hold. If the poker player is good at using this sparse hard information, and additional soft information like the size of a competing player’s bets and voice inflections, then there is a good change he will win money over the course of the game. Reservoir characterization shares many of these same elements: exceedingly little hard information from wells, additional soft information from seismic and geological concepts, the need to reconstruct information from these sources, reconstructions that contain inherent uncertainty, and the potential for winning or losing large sums of money over the life of the game (field).

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Barnsley, M., Fractals Everywhere, Academic Press, Boston (1988).

    MATH  Google Scholar 

  • Barton, C. C., and Larsen, E., Fractal geometry of two-dimensional fracture networks at Yucca Mountain, southwestern Nevada, Int. Symp. on Fundamentals of Rock Joints, pp. 77–84, Björkliden/Oslo, September 1985.

    Google Scholar 

  • Burrough, P. A., Fractal dimensions of landscapes and other environmental data, Nature 19, 240–242 (1981).

    Article  ADS  Google Scholar 

  • Crane, S. D., and Tubman, K. M., Reservoir variability and modeling with fractals, SPE 20606, 65th Ann. Tech. Conf., New Orleans, Louisiana, September 1990.

    Google Scholar 

  • Dershowitz, W. S., Interpretation and synthesis of discrete fracture orientation, size, shape, spatial structure and hydrologic data by forward modeling, ISRM Int. Conf. on Fractured and Jointed Rock Masses, Lake Tahoe, California, June 1992.

    Google Scholar 

  • Dershowitz, W. S., Hurley, N., and Been, K., Stochastic discrete fracture modelling of heterogeneous and fractured reservoirs, Third European Conference on the Mathematics of Oil Recovery, Delft, The Netherlands, June 1992.

    Google Scholar 

  • Dershowitz, W. S., Lee, G., Geier, J., Hitchcock, S., and La Pointe, P., FracMan Version 2.4 Interactive Discrete Feature Data Analysis, Geometric Modeling and Exploration Simulation, Golder Associates Inc., Redmond, Washington (1994).

    Google Scholar 

  • Dershowitz, W. S., Redus, K., Wallmann, P., La Pointe, P., and Axelsson, C.-L., The implication of fractal dimension in hydrology and rock mechanics, Swedish Nuclear Fuel and Waste Management Co. Tech. Report 92-17, Stockholm, Sweden (1992).

    Google Scholar 

  • Dershowitz, W. S., Roberds, W., and Black, J., Application of discrete fracture analysis to site characterization, ASCE 1991 Geotech. Eng. Congress, Boulder, Colorado, June 1991.

    Google Scholar 

  • Doe, T. W., Dershowitz, W. S., Wallmann, P. C., La Pointe, P. R., Lee, G., and Thomas, A., Heisei-5 Progress Report prepared by Golder Associates Inc., Redmond, Washington to PNC Power Reactor and Nuclear Fuel Development Corp., Tokyo, Japan (1994).

    Google Scholar 

  • Dubrule, O., A review of stochastic models for petroleum reservoirs, in: Geostatistics (M. Armstrong, ed.), Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 493–506 (1988).

    Google Scholar 

  • Dupuy, M., and Lefebvre du Prey, E., L’anisotropic d’ecoulement en milieu poreux presentant des intercalations horizontales discontinues, Third Meeting of the ARTFP, pp. 23–26, Pau, France, September 1968.

    Google Scholar 

  • Goff, J. A., Comment on “Fractal mapping of digitized images: Application to the topography of Arizona and comparison with synthetic images” by J. Huang and D. L. Turcotte, J Geophys. Res. 95(B4), 5159 (1990).

    Article  ADS  Google Scholar 

  • Gubin, L. G., Polyak, B. T., and Raik, E. V., The method of projections for finding the common point of convex sets, USSR Comp. Math. and Math. Phys. (English Trans.) 7, 1–24 (1967).

    Article  Google Scholar 

  • Haldorsen, H. H., Reservoir characterization procedures for numerical simulation, Ph.D. thesis, U. Texas-Austin (1983).

    Google Scholar 

  • Hewett, T. A., Fractal distributions of reservoir heterogeneity and their influence on fluid transport, SPE 15385, 61st Ann. Tech. Conf. New Orleans, Louisiana, October 1986.

    Google Scholar 

  • Hewett, T. A., and Behrens, R. A., Conditional simulation of reservoir heterogeneity with fractals, SPE 18326, 63rd Ann. Tech. Conf., Houston, Texas, October 1988.

    Google Scholar 

  • Hohn, M. E., Geostatistics and Petroleum Geology, Van Nostrand Reinhold, New York (1988).

    Google Scholar 

  • Huang, J., and Turcotte, D. L., Fractal mapping of digitized images: Application to the topography of Arizona and comparison with synthetic images, J. Geophys. Res. 94(B6), 7491–7495 (1989).

    Article  ADS  Google Scholar 

  • Huang, J., and Turcotte, D. L., Reply, J. Geophys. Res. 95(B4), 5161 (1990).

    Article  ADS  Google Scholar 

  • Journel, A. G., Geostatistics for conditional simulation of ore bodies, Econ. Geol. 69, 673–687 (1974).

    Article  Google Scholar 

  • Journel, A. G., and Alabert, F. G., Focusing on spatial connectivity of extreme-valued attributes: stochastic indicator models of reservoir heterogeneities, SPE 18324, 63rd Ann. Tech. Conf., Houston, Texas, October 1988.

    Google Scholar 

  • Journel, A. G., and Huijbregts, C. J., Mining Geostatistics, Academic Press, London (1978).

    Google Scholar 

  • Krige, D.G., A statistical approach to some basic mine valuation problems on the Witwatersrand, J. Chem. Metall. Min. Soc. S. Afr. 52, 119–139 (1951).

    Google Scholar 

  • La Pointe, P. R., Dershowitz, W. S., and Wallmann, P. C., Flow and connectivity properties of fracture networks as a function of the fractal dimension [abstract], Geological Society of America Annual Meeting, Boston, Massachusetts, October 1993, Abstract No. 15395 (1993).

    Google Scholar 

  • Long, J. C. S., Doughty, C., Hestir, K., and Martel, S., Modeling heterogeneous and fractured reservoirs with inverse methods based on iterated function systems, Reservoir Characterization III, pp. 471–503, Penwell Books, Tulsa, Oklahoma (1991).

    Google Scholar 

  • Malinverno, A., A simple method to estimate the fractal dimension of a self-affine series, Geophys. Res. Lett. 17, 1953–1956 (1990).

    Article  ADS  Google Scholar 

  • Malinverno, A., and Rossi, D. J., Applications of projection onto convex sets to stochastic inversion, SPE 25659, Middle East Oil Show, Bahrain, April 1993.

    Google Scholar 

  • Mandelbrot, B. B., Statistical methodology for non-periodic cycles: from the covariance to R/S analysis, Ann. Econ. Soc. Meas. 1, 259–290 (1972).

    Google Scholar 

  • Mandelbrot, B. B., The Fractal Geometry of Nature, Freeman, San Francisco (1982).

    MATH  Google Scholar 

  • Mandelbrot, B. B., and Van Ness, J. W., Fractional Brownian motion, fractional noises and applications, SIAM Rev. 10, 422–437 (1968).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Matheron, G., The Theory of Regionalized Variables and Its Applications, Les Cahiers du Centre de Morphologie Mathématique, fascicule 5, Centre de Géostatistque, Fontainebleau (1971).

    Google Scholar 

  • Menke, W., Applications of the POCS inversion method to interpolating topography and other geophysical fields, Geophys. Res. Lett. 18, 435–438 (1991).

    Article  ADS  Google Scholar 

  • Oliver, D., Fractal Grafics, Version 1.6 (1990).

    Google Scholar 

  • Peitgen, H.-O., Jurgens, H., and Saupe, D., Fractals for the Classroom, Springer-Verlag, New York (1992).

    Book  Google Scholar 

  • Perez, G., and Kelkar, M., Assessing distributions of reservoir properties using horizontal well data, Reservoir Characterization III, pp. 399–436, Penwell Books, Tulsa, Oklahoma (1991).

    Google Scholar 

  • Reiss, L. H., Reservoir engineering in fractured reservoirs, French Institute of Petroleum (Institut Français du Petrole) (1976).

    Google Scholar 

  • Voss, R. F., Fractals in nature: From characterization to simulation, in: The Science of Fractal Images (H. O. Peitgen and D. Saupe, eds.), Springer-Verlag, New York, pp. 21–70 (1988).

    Chapter  Google Scholar 

  • Warren, J. E., and Root, P. J., The behavior of naturally fractured reservoirs, Soc. Petrol. Eng. J. 3, 245–255 (1963).

    Google Scholar 

  • Youla, D. C., Generalized image restoration by the method of alternating orthogonal projections, IEEE Trans. Circ. Sys. CAS-25, 694–702 (1978).

    Article  MathSciNet  Google Scholar 

  • Youla, D. C., and Webb, H., Image restoration by the method of convex projections, Part 1—Theory, IEEE Trans. Med Imag. MI-1, 81–94 (1982).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer Science+Business Media New York

About this chapter

Cite this chapter

La Pointe, P.R., Barton, C.C. (1995). Creating Reservoir Simulations with Fractal Characteristics. In: Barton, C.C., La Pointe, P.R. (eds) Fractals in Petroleum Geology and Earth Processes. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1815-0_12

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-1815-0_12

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-5733-9

  • Online ISBN: 978-1-4615-1815-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics