Theory of ionic-surface electrical conduction in porous media

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Abstract
We present a model describing ionic electrical conduction in porous media, with particular emphasis given to surface conduction. The porous medium is assumed to consist of an insulating matrix and an interconnected pore volume that is saturated with an electrolyte. When in contact with an electrolyte, mineral surfaces get an excess of charge that is balanced by mobile ions in an electrical diffuse layer above the surface. Electrical conduction in this diffuse layer can contribute substantially to the effective electrical conductivity of the porous medium. Our surface conduction model is based on a description of surface chemical reactions and electrical diffuse layer processes. For this purpose, we consider an amphoteric mineral surface described by a five-site-type model. We derive the fractional occupancies of positive, negative, and neutral sites on the surface, and the fractional ionic diffuse layer densities, as a function of the salinity and the pH. Finally, the specific surface conductance used to describe the surface electrical conduction is related to the previously mentioned properties, via the electrical surface potential, and is found to be dependent on the electrolyte concentration and pH.