### Tuesday, 12 October 2004 - 9:15 AM

### This presentation is part of : Torquato Symposium

### Spatial Correlations and Fluid Permeability Estimates

**James G. Berryman**, University of California, Lawrence Livermore National Laboratory, University of California, Lawrence Livermore National Laboratory, P. O. Box 808 L-200, Livermore, CA 94551-9900
Image processing methods have been used very effectively to estimate physical properties such as fluid permeabilty of isotropic porous materials such as sandstones. Anisotropic materials can also be analyzed in order to estimate their properties, but additional care and more well-chosen images of cross sections are required to obtain adequate results. For stationary and translationally invariant anisotropic media, the overall specific surface area can be obtained from radial averages of the two-point correlation function in the full three-dimensional volume. Formulas relating the derivative of the planar correlation functions to surface area integrals are known. When the pore surface normal is uniformly distributed (as is the case for any distribution of spherical voids), these formulas can be used to relate specific surface area to easily measureable quantities from any single representative cross section. When the surface normal is not distributed uniformly (as would be the case for an oriented distribution of ellipsoidal voids), valid estimates of specific surface area are obtained by averaging measurements on three orthogonal cross sections. And, although layered materials are not translationally invariant in the direction of the layering, nevertheless averages of cross sections may be used to obtain the specific surface area for a transversely isotropic rock. The same basic methods of analysis can be used either on thin sections or to simplify quantitative analysis of three-dimensional volumes of pore structure data obtained by means of x-ray microtomography methods, using only a few representative cross sections chosen from the full three-dimensional data set.

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