Determination of electrical conductivity of double-porosity formations by using generalized differential effective medium approximation

Abstract

Abstract In this paper, we propose an approach for simulating the effective electrical conductivity of porous rocks. This approach is based on the Generalized Differential Effective Medium (GDEM) method that allows us to calculate the effective conductivity of a rock up to the percolation threshold. We consider a porous medium composed of a porous matrix with small scale pores (primary pores) and large-scale pores placed in the matrix (secondary pores). For double porosity formations we applied two-step homogenization scheme starting from the smallest scale of inclusions. At the first step, we apply a model composed by a conductive host and two types of inclusions placed in it: nonconductive grains and pores with a conductive fluid. The electrical conductivities of the host and saturating fluid are equal. At the second homogenization step we consider the conductive host with effective electrical conductivity determined at the first step and large-scale inclusions with conductivity corresponded to the pore saturating fluid. To take into account the percolation for the secondary pore system we introduce two types of inclusions. For porosities less than the critical porosity (secondary pores are disconnected), we consider spheroids that describe secondary pores of different shapes (vugs and cracks). For porosities more than the critical value, we additionally introduce infinite ellipsoidal cylinders that ensure the pore connectivity. Application of the proposed model allows us to take into account the void percolation for a porous matrix and the percolation threshold for a secondary pore system that we consider as an advantage of the proposed method with comparison of Archie law or classical micromechanical methods.