Transport of water and ions in partially water-saturated porous media. Part 3. Electrical conductivity

In hydrogeophysics, we need a reliable petrophysical model connecting (non-linearly) the conductivity of a porous material (like a soil) to the conductivity of the pore water and the water saturation. Classical models are too simplistic especially at low salinities. The convexity of the electrical conductivity of a porous material as a function of the pore water conductivity is due to both a textural effect and the dependence of the specific surface conductivity on salinity. The textural effect arises because of a change in the distribution of pore network conductances with salinity. From volume averaging arguments, it is possible to provide a general equation for the conductivity of porous materials. This approximation is based on a Padé approximant, connecting low and high salinity asymptotic limits for which a rigorous analysis can be made based on four fundamental textural parameters. We discuss the connection between this volume averaging model and empirical models as well as with the differential effective medium (DEM) solution for granular media. The DEM captures the non-linear behavior of the conductivity curve with only two parameters but it is strictly valid for granular materials only. We compare the models with finite element computations using two three-dimensional pore geometries with continuous and discontinuous solid surfaces, respectively. Finally the models are compared to experimental data.