Conductivity in partially saturated porous media described by porosity, electrolyte saturation and saturation-dependent tortuosity and constriction factor

Abstract

Modelling the relationships among bulk conductivity, electrolyte conductivity, porosity and fractional electrolyte-saturation continues to be based on empirical relationships such as Archie's law or the Bruggeman correlation. Several authors have attempted to connect such empirical models to first principles. This article presents a complete first principles-based description of conductivity in partially saturated porous media. A geometrical factor is introduced which, together with porosity and saturation, describes the conductivity of partially saturated porous media. This geometrical factor is separated into two intrinsic geometrical descriptors of the electrolyte distribution accounting for tortuosity and constriction. This tortuosity and constriction factor are obtained from integration over the electrical field lines traversing the electrolyte. Bulk and saturation-dependent conductance descriptions are illustrated using three-dimensional pore space models and simulated fluid distributions. Describing conductance through porosity, saturation and a geometrical factor, decomposed into separate terms accounting for tortuosity and constrictivity, permits more insightful understanding of conductance in partially saturated porous media. Use and efficacy of this full conductance description is illustrated throughout this article.