Effective permeability of anisotropic porous materials containing periodically or randomly distributed cracks

Abstract : This paper aims at predicting effective transport properties of fractured porous media based on the information of cracks distribution within the material. The porous materials are assumed to contain aligned impermeable or superpermeable cracks, arranged in parallel layers. Two types of cracks distributions are considered: periodic and random distributions. In the former periodic case, the estimates are analytically derived from the approximation of polarization integral equations, and compare well with a numerical solution. In the latter random case, the estimates show explicit connections to planar structure factors of hard disks, a statistical quantity of phases distribution in Fourier space. Different random ensembles of hard disks are also examined to study how they affect the effective permeability of the material.