Numerical estimation of electrical conductivity in saturated porous media with a 2-D lattice gas

Abstract

A 2-D lattice gas is used to calculate the effective electrical conductivity of saturated porous media as a function of porosity and conductivity ratio [Formula: see text] between the pore‐filling fluid and the solid matrix for various microscopic structures of the pore space. The way the solid phase is introduced allows the porosity ϕ to take any value between 0 and 1 and the geometry of the pore structure to be as complex as desired. The results are presented in terms of the formation factor [Formula: see text], with [Formula: see text] the effective conductivity of the saturated rock and [Formula: see text] the conductivity of the fluid. It is shown that the formation factor F as a function of the porosity ϕ follows a power law [Formula: see text], equivalent to the empirical Archie’s law. The exponent m varies with the microgeometry of the pore space and could therefore reflect the microstructure at the macroscopic scale. The prefactor a of the power law, however, is close to 1 regardless of the microstructure. For a given microgeometry of the pore space, the variation of the residual electrical conductivity of the solid matrix induced by a finite conductivity ratio [Formula: see text] does not significantly influence the variation of the effective conductivity of the fluid‐solid binary mixture unless the porosity is low.