The hydroelectric problem of porous rocks: thermodynamic approach and introduction of a percolation threshold

Abstract

An electrical field is produced in response to groundwater flow in porous materials such as soils and permeable rocks. This electrical field is due to the relative displacement between the charged mineral grains and the pore water, which drags the excess of electrical charge located in the close vicinity of the pore water/mineral interface in the so-called electrical double layer. In this note, I take the hydroelectric problem back to its thermodynamic roots by showing how the hydroelectric equations can be derived from the Gibbs-Duhem equation. In addition, I suggest that the introduction of a percolation porosity may improve the description of the material properties of granular porous materials entering the coupled hydroelectric problem at the macro-scale. Comparison between the proposed model and a set of laboratory data available from the literature are in agreement for a reasonable choice of specific parameters.