To provide a critical assessment of electrical resistivity logging measurements in shaly sands, a theoretical, patchy-charge model is derived to quantify the surface conductivity of clay minerals. The proposed model instills a molecular rigor into the general framework of the widely-used, semi-theoretical approach of Waxman and Smits. The most significant contribution of the patchy-charge model is its physical explanation for the characteristic convex curvature observed from experimental measurements on the change of the effective conductivity of water-saturated shaly sands with the change of the conductivity of the equilibrating brine. We attribute the major portion of the extra conductivity to two-dimensional translation of counterions along the inner Helmholtz plane (IHP). By representing isomorphic substitution within the clay lattice as patches of periodically varying charge, an electrical activation barrier to migration along the IHP is identified. It is the variation of this electrical barrier to surface diffusion with changing ionic strength which gives rise to the curvature seen in the experiments. The patchy-charge model predictions for overall reservoir formation conductivities yield excellent agreement with experimental data on water-saturated shaly sands over a bulk conductivity range from 0.1 S/m to 10 S/m with the benefit of only one adjustable parameter. Model calculations are readily extended to predict oil saturations for measured resistivity ratios of shaly reservoir formations.

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