A New Numerical Simulation Framework to Model the Electric Interfacial Polarization Effects and Corresponding Impacts on Complex Dielectric Permittivity Measurements in Sedimentary Rocks

Abstract

A thorough understanding of the interplay between polarization mechanisms is pivotal for the interpretation of electrical measurements, since sub-megahertz electrical measurements in sedimentary rocks are dominated by interfacial polarization mechanisms. Nonetheless, rock-physics models oversimplify pore-network geometry and the interaction of electric double layers relating to adjacent grains. Numerical algorithms present the best possible framework in which to characterize the electrical response of sedimentary rocks, avoiding the constraints intrinsic to rock-physics models. Recently, an algorithm was introduced that can simulate the interactions of electric fields with the ions in solution. The sub-kilohertz permittivity enhancement in sedimentary rocks is dominated by Stern-layer polarization, but a model for the polarization mechanism associated with the Stern layer has not been developed. Hence, the aim of this paper is to develop and test a numerical simulation framework to quantify the influence of Stern- and diffuse-layer polarization, temperature, ion concentration, and pore-network geometry on multi-frequency complex electrical measurements. The algorithm numerically solves the Poisson–Nernst–Planck equations in the time domain and a mineral-dependent electrochemical adsorption/desorption equilibrium model to determine surface charge distribution. Then, the numerical simulator is utilized to perform a sensitivity analysis to quantify the influence of electrolyte and interfacial properties on the permittivity of pore-scale samples at different frequencies.