Surface Conduction Model for Fractal Porous Media

Abstract

AbstractThe electrical conductivity of natural water‐saturated porous materials has two contributions, one associated with conduction in the pore network and a second one associated with the electrical double layer coating the surface of the mineral grains, and called surface conductivity. We model the effect of material texture on surface conductivity based on fractal theory. We demonstrate that surface conductivity obeys a power‐law dependence (that we called surface Archie's law) on the specific surface area. The power exponent is theoretically related to the porosity exponent entering Archie's law and to the fractal dimension of the pore network. A permeability model is derived by combining the new surface Archie's law and the Kozeny‐Carman model. We show that our model is consistent with both numerical finite element simulations on synthetic porous media and experimental data.