Electrolytic Conduction in Partially Saturated Shaly Formations

Abstract

Abstract An essential feature of electrical conduction in shaly sands is the fact that the surface and bulk tortuosities are not identical as assumed in most empirical models. For an arbitrary geometry of insulating, but charged, objects immersed in an electrolyte for which diffusion currents are important, the DC electrical conductivity problem can be mapped into a superposition of two ordinary conduction problems without diffusion currents but with conductive surface layers. We apply this mapping to a generalization of the grain consolidation model in which a shaly sand is modelled by a three dimensional periodic array of charged overlapping spherical grains. We solve numerically for the electrical conductivity, σ, as a function of the porosity ϕ, brine salinity σw, charge density Qv, and water saturation Sw. The results of these calculations provide a basis for new empirical saturation equations which can be used in exploration geophysics.