Percolation Model of Micro Heterogeneous Media

Abstract

Conductivity of a medium (coefficients of permeability and electric conductivity) depends significantly on the pore space structure. In the case of stochastic distribution of conducting channels in the medium, it is possible to describe the topology of the pore space in terms of the percolation theory [25–27, 29, 30]. However the existing percolation models can be applied only if the conducting structural bonds in the medium are sufficiently homogeneous. This is due to the fact that all the theoretical relationships in percolation theory were obtained under the assumption that there are only two types of structural bonds in the medium, namely the conducting and the non-conducting ones. It is also assumed that the intrinsic conductivities of all conducting bonds are equal. At the same time, in the majority of actual media, a commensurate contribution to effective conductivity can be made by groups of conducting bonds whose intrinsic conductivities are notably different. Rocks, which may have many different types of pore space structure, represent an example of such media.