Electrical conductivity of percolating two-component rock-like materials

Abstract

Many heterogeneous materials such as rocks lose the electrical conductivity when their porosity tends to its critical value (void percolation). We present a new approach for the calculation of the effective conductivity taking into account the effect of the void percolation. This approach is based on the generalized differential effective medium method. In this paper, we have introduced a model of a porous material composed by a conducting host (phase 0) (it is a conducting fluid in the case of rocks) and ellipsoidal inclusions of two types embedded in it. Inclusions of the first type (phase 1) are represented by solid grains with low conductivity and inclusions of the second type (phase 2) have the same conductivity as the host. As the solid grain concentration increases, the host concentration decreases and it tends to zero near the critical porosity. We have calculated the conductivities of isotropic and anisotropic heterogeneous materials in a wide range of porosity. The comparison of our results with the experimental data for sedimentary rocks and metal–insulator composites has shown their good coincidence.