Hierarchical unsymmetrical effective medium approximations for the electrical conductivity of water-saturated porous rocks
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A two-level unsymmetrical effective medium approximation scheme is developed to model the electrical conductivity of sedimentary rocks with pore space interconnected and water-filled. The scheme takes into account certain observed features of the rock geometry, which appears to be a suspension of open water sphere-like pockets, or platelet-like cracks of secondary porosity, in the mass of solid grains surrounded by the thin water films. The pockets contribute much to the porosity but little to the conductivity in contrast with the thin films surrounding the grains, or the cracks and fractures of secondary porosity, the latest are the most conducting effective. The models are flexible enough to explain the behavior of the rocks described by the empirical Archie's law.
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