Theoretical and Numerical Study on Electrical Resistivity Measurement of Cylindrical Rock Core Samples Using Perimeter Electrodes

Abstract

The estimation of hydraulic and mechanical properties of bedrock is important for the evaluation of energy-related structures, including high-level nuclear waste repositories, hydraulic fracturing wells, and gas-hydrate production wells. The hydraulic conductivity and stress–strain curves of rocks are conventionally measured through laboratory tests on cylindrical samples. Both ASTM standards for hydraulic conductivity and compressive strength involve the use of the planar bases of a cylindrical sample. Hence, an alternative test method is required for the simultaneous measurement of hydraulic conductivity and stress–strain curves. This study proposes a novel electrical resistivity estimation method using two perimeter electrodes for the estimation of hydraulic properties. The theoretical background for the perimeter electrode setup is derived and the COMSOL MultiPhysics® finite element numerical simulation tool is employed to verify the derived theoretical equation. The accuracy of the numerical simulation tool is first validated by simulating the ASTM standard testing method for electrical resistivity. The electrical resistance values derived from the theoretical equation and numerical simulation are compared for different electrical resistivity and electrode radius. The assumed equidistant, circular equipotential surface results in a theoretical lower bound for the measured electrical resistance in the cylindrical specimen. The introduction of a phenomenological distortion factor to correct for the theoretical equipotential surface results in a good fit with the numerical simulation results. The effects of electrode length and equivalent strap electrodes were investigated to assess the applicability of the suggested method for laboratory testing. Consequently, this study presents an effective alternative theoretical assessment method for the lower bound electrical resistivity of cylindrical rock core samples under confining conditions when the installation of base electrodes is infeasible.