Evaluation of electrical conductivity of shaly sands using the theory of mixtures

On the basis of the theory of mixtures, an equation is proposed for the electrical conductivity of shaly sands. Using a simple shaly sand model, Waxman and Smits, Hill and Milburnʹs core data and regression analysis, the equation was specified. It was fitted using core data for water conductivity within 0.2 to 25 S/m. The equation satisfies core data with a mean relative error of about 3%. The theory of mixtures allows clarification of the physical meaning of the cementation exponent representing it as the coefficient of mixing of shaly sand components. The saturation exponent was represented as the coefficient of mixing of the pore fluids. In clean sands, the derived equation is reduced to the Archie–Dahnov equation. The equation allows one to derive the effective porosity of cores which in turn exhibits good correlation with water permeability. The working hypothesis that shale porosity has the same magnitude as the total porosity of the shaly sands was assumed. It allows to evaluate shale content of core samples from their electrical conductivity without using destructive analysis. The derived shale content correlates with the cation exchange capacity and mixture exponent. The equation can be combined with nonelectrical equations used in sonic, density and neutron logs, and applied in log analysis.