Abstract
Permeable sedimentary rocks can often be modeled as an impermeable rock matrix cut by a system of an irregular system of interconnected, irregularly shaped, water‐saturated pore spaces. I represent this system by a multiphase effective medium that is compatible with Archie’s Law for electrical conductivity. My effective medium is an extention of the self‐similar Sen, Scalar, and Cohen model which characterizes sedimentary rocks as a water suspension of spherical solid grains. My generalized multiphase model includes two important components: open water spherelike pockets, which significantly increase the porosity but add little to the electrical conductivity, and thin films surrounding the grains and water‐filled cracks, which contribute little to the porosity but significantly to the electrical conductivity. By perturbing the relative balance between these two model components, I am able to represent a range of aggregates for which I can construct effective media that are consistent with the electrical conductivity predicted by Archie’s Law.
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