The permeability tensor for anisotropic nonuniform porous media

Abstract

This paper describes a study of the permeability of anisotropic, nonuniform porous media. The approach is through a statistical model of the microstructure of the porous media. Using a capillary-type model with a distribution of pore sizes and orientations, we show that the permeability can be described by a second-order symmetric tensor regardless of the preferential orientation of the pores in the microstructure. We also show that an ergodic assumptions is not always true—spatial averages cannot generally be interchanged with mathematical expectations.