Surface Conduction Model for Fractal Porous Media

The 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. Plain Language Summary Electrical conductivity tomography is a powerful method to characterize porous media in the realm of geophysics. In absence of conduction mechanisms on the surface of the grains, the conductivity of a porous material is connected to porosity through a relationship known as Archie's law. Surface conductivity associated with conduction along the electrical double layer coating the surface of the grains is related to the specific surface area of the material. Based on fractal theory, we develop a new power law relationship between the surface conductivity and the specific surface area. This theory can improve our ability to interpret electrical conductivity data at various scales and to connect electrical properties to permeability. Key Points We developed a power law relationship between surface conductivity and specific surface area The exponent of this relationship is related to the porosity/cementation exponent and to the fractal dimension of the pore network The electrical properties entering the newly developed conductivity model can be used to predict permeability