ANALYTICAL ELECTRICAL CONDUCTIVITY MODELS FOR SINGLE-PHASE AND MULTI-PHASE FRACTAL POROUS MEDIA

Archie's law is commonly applied to predict electrical conductivity of rock by correlating the homogeneous, water-wet reservoir rock conductivity with its porosity and saturation. However, Archie's law is an empirical model consisting of unknown cementation exponent and saturation exponent. In this study, we propose analytical electrical conductivity models for both single-phase and multi-phase porous media based on the fractal theory. The established electrical conductivity model for fractal porous media saturated with a single fluid phase is the function of several factors including pore fluid electrical conductivity, porosity, pore fractal dimension and tortuosity fractal dimension. The established electrical conductivity model for fractal porous media containing multiple fluid phases is the function of wetting fluid saturation, contact angle and pore shape apart from the factors for saturated fractal porous media condition. The calculated formation factor based on the proposed model correlates well with the sandstone experimental data.