Effective medium approximation for the electromagnetic properties of rocks with surface conductivity

Abstract

We present an approach to calculate the complex dielectric permittivity of a microheterogeneous rock composed of non-conductive solid grains with surface conductivity and a conductive liquid.

We have calculated the effective electrical properties of a rock using the model that consider the complex structure of the conducting double layer between a solid grain and the electrolyte in the pores. The influence of two parts of double layer: the Stern (inner) layer on the solid surface and the diffuse (outer) layer was considered.

Previously, the Differential Effective Medium (DEM) scheme was used to calculate the effective conductivity and dielectric permittivity. In contrast, we have adopted the Effective Medium Approximation (EMA) method for calculation of the effective electromagnetic properties of a rock with high inclusion concentration. This method allows one to describe both elastic and electromagnetic properties of the rock based on the unified model of the pore space.

The calculations were performed both for the rock model with a fixed grain size and for the model with a fractal distribution of grain sizes.

Our calculations have shown that the value of the dielectric permittivity in the low frequency range depends on the concentration and dimension of solid grains. However, the frequency-dispersion behavior is a function of the inclusion size only and it does not relate to the inclusion concentration in the porosity range typical for sedimentary rocks. This effect confirms the feasibility of the determination of the inclusion concentration and dimension by using the dielectric permeability and electrical conductivity dispersion curves.