Electrical conductivity, spontaneous potential and ionic diffusion in porous media

Abstract

Abstract A consistent set of equations describing electrical conduction, spontaneous potential and ionic diffusion phenomena in porous media, with a particular emphasis given to surface electrical phenomena, is presented. The porous medium is assumed to consist of an insulating matrix and an inter-connected pore volume that is saturated with an electrolyte. When in contact with an electrolyte solution, mineral surfaces have an excess of charge that is balanced by mobile ions in an electrical diffuse layer (EDL). Electrical conduction and ionic diffusion in this diffuse layer can contribute substantially to the effective electrical conductivity of the porous medium, and can play an important role in the strength of several spontaneous electrical potentials (i.e., membrane potential, streaming potential, and thermo-electric potential) and ionic diffusion phenomena. Our surface electrical properties model is based on a thermodynamic description of surface chemical reactions and electrical diffuse layer processes. As an example, we consider an amphoteric mineral surface described by a three-site-type model. We derive the fractional occupancies of positive, negative and neutral sites, and the fractional ionic diffuse layer densities on the surface as a function of the salinity and the pH. The surface charge density at a given pH, is found to be dependent on the electrolyte concentration. Finally, parameters of interest in describing macroscopic effects (effective electrical conductivity, spontaneous potential coupling coefficients and effective diffusion coefficient), are related to the previously mentioned properties, via the mineral surface electrical potential (called the Stern potential).