A theoretical model for electrical conductivity of a weakly transversely isotropic porous medium with two conducting phases

Electrical properties of porous media consisting of solid and fluid phases have been continuously investigated in the study of geomaterials given their strong link to pore space characteristics (e.g. pore size and connectivity). Over the past decades, numerous theoretical models have been developed to determine the electrical conductivity of the porous media as a function of conductivities of their constituents and their relative proportions. In this paper, we present a new theoretical model to calculate the electrical conductivity of a weakly transversely isotropic (TI) porous medium with two conducting phases. We first use the well-established series and parallel electrical connections, together with a newly introduced coefficient g, to construct a conductive cell that represents the porous medium's microscopic structure. We then obtain the macroscopic weakly TI conductivity stacking these cells in one dimension. We innovatively introduce a normal probability distribution to simulate the distribution of porosities across cells. Good agreement between our theoretical predictions and literature data validates the model for weakly TI porous media. We also show that series and parallel connections of the solid and liquid phases provide reliable building blocks for more advanced models, and that using a normal distribution to simulate electrical anisotropy in quasi-isotropic or weakly TI porous media is viable. Finally, we use the model to study the effects of key variables on weakly TI conductivity. We find that increasing the coefficient g reduces electrical conductivity and that the electrical anisotropy coefficient attains its maximum at 50 per cent porosity in weakly TI porous media with two conducting phases.