Electrical conductivity models in saturated porous media: A review

Electrical transport properties of saturated porous media, such as soils, rocks and fractured networks, typically composed of a non-conductive solid matrix and a conductive brine in the pore space, have numerous applications in reservoir engineering and petrophysics. One of the widely used electrical conductivity models is the empirical Archie's law that has a practical application in well-log interpretation of reservoir rocks. The Archie equation does not take into account the contributions of clay minerals, isolated porosity, heterogeneity in grains and pores and their distributions, as well as anisotropy. In the literature, either some modifications were presented to apply Archie's law to tight and clay-rich reservoirs or more modern models were developed to describe electrical conductivity in such reservoirs. In the former, a number of empirically derived parameters were proposed, which typically vary from one reservoir to another. In the latter, theoretical improvements by including detailed characteristics of pore space morphology led to developing more complex electrical conductivity models. Such models enabled us to address the electrical properties in a wider range of potential reservoir rocks through theoretical parameters related to key reservoir-defining petrophysical properties. This paper presents a review of the electrical conductivity models developed using fractal, percolation and effective medium theories. Key results obtained by comparing experiential and theoretical models with experiments/simulations, as well as advantages and drawbacks of each model are analyzed. Approaches to obtaining more reasonable electrical conductivity models are discussed. Experiments suggest more complex relationships between electrical conductivity and porosity than experiential models, particularly in low-porosity formations. However, the available theoretical models combined with simulations do provide insight to how microscale physics affects macroscale electrical conductivity in porous media.