Applications of percolation-based effective-medium approximation to electrical conductivity in porous media with surface conduction

Electrical conductivity, $\sigma$, has been widely used to estimate hydraulic conductivity in porous media as well as to interpret subsurface low- and high-conductivity zones. $\sigma$ in a porous medium is impacted by the complicated relationship between the surface conductivity of solids, as the low-conductivity component which is significant at dry conditions, and bulk conductivity through the pore space, as the high conductivity component. As water saturation increases from completely dry to fully saturated, the effect of the bulk conductivity on electrical conductivity substantially increases. In this study, for the first time, we propose applications of a percolation-based effective-medium approximation (P-EMA) to describe the saturation dependence of $\sigma$ in porous media with significant surface conduction. The proposed P-EMA model estimates were compared to 16 data sets including three numerically simulated sets and thirteen measured sets. There was substantial agreement between the theory and the data, with scaling exponents ranging from 0.18 to 2.39, indicating non-universal behavior. The saturation-dependent $\sigma$ values of packed clay loam soil samples were estimated with the P-EMA model. The P-EMA estimated values were in reasonable agreement with the measured values.