A Central Limit Theorem for Multiscaled Permeability

  • S. M. Kozlov
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 114)


Recent experiments of Noetinger and Jacquin [7] showed high accuracy of the effective three-dimensional permeability formula given by the cube of the average of the third root of local permeability. Here, a model of a locally multiscaled lognormal permeability is proposed for which this formula is asymptotically exact. The model reflects the real situation of many (asymptotically infinite) length scales of heterogeneties.


Central Limit Theorem Effective Permeability Random Operator Homogenization Theory Local Permeability 
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  1. [1]
    Dagan G. Flow and Transport in Porous Formations. Springer-Verlag, Berlin, New York, 1989.CrossRefGoogle Scholar
  2. [2]
    Kozlov S. M. Averaging of random operators. Matern. Sbornik, 109(2): 188–203, 1979.Google Scholar
  3. [3]
    Kozlov S. M. The method of averaging and random walks in inhomogeneous environments. Russian Math. Surveys, 40(2):73–145, 1985.CrossRefGoogle Scholar
  4. [4]
    Koziov S. M. Geometric aspects of homogenization. Russian Math. Surveys, 44(2):91–144, 1989.CrossRefGoogle Scholar
  5. [5]
    Landau L. D., Lifshitz E. M. Electrodynamics of Continuous Media. Course of Theoretical Physics 8. Pergamon Press, New York, 1984.Google Scholar
  6. [6]
    Matheron G. Éléments pour une Theorie des Milieux Poreux. Masson, Paris, 1967.Google Scholar
  7. [7]
    Noetinger B., Jacquin C. Experimental tests of a simple permeability composition formula. Society of Petroleum Engineers Preprint SPE 22841, 1991.Google Scholar
  8. [8]
    Novikov S. P., Dubrovin B. A., Fomenko A. T. Modern Geometry. Nauka, Moscow, 1979. In Russian.Google Scholar
  9. [9]
    Stauffer D. Introduction to Percolation Theory. Taylor and Francis Ltd., London, 1985.CrossRefGoogle Scholar
  10. [10]
    Zhykov V. V., Kozlov S. M., Oleinik O. A. Homogenization of Differential Operators. Springer-Verlag, Berlin, New York, 1993.Google Scholar

Copyright information

© Springer Basel AG 1993

Authors and Affiliations

  • S. M. Kozlov
    • 1
  1. 1.Laboratoire APT, URA CNRS 225Université de Provence Aix Marseille IMarseille CedexFrance

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