A Framework for Pore-Scale Simulation of Effective Electrical Conductivity and Permittivity of Porous Media in the Frequency Range From 1 mHz to 1 GHz

Geoelectrical methods are broadly used in earth sciences for various purposes. To correctly interpret field geoelectrical data, it is essential to have a mechanistic understanding of the effective electrical conductivity and permittivity of geological materials over a broad frequency range. Recently, the pore-scale numerical simulation, which utilizes the digital microstructural images of the material, has become a powerful tool in studying the effective electrical properties of geological media. However, it is still difficult to incorporate surface-related electrochemical processes in a pore-scale simulation. In this study, we develop a general framework to consider these electrochemical processes in pore-scale simulations, which enable the calculation of broadband effective electrical conductivity and permittivity of porous geological media. A Berea sandstone sample is utilized to demonstrate the use of the proposed framework. Laboratory experiments of the effective electrical conductivity and permittivity of the sample in the frequency range from 10⁻³ to 10⁹ Hz provided valuable measurement data for validating the simulation. The good agreement between our simulated spectra and the experimental data provides validation for the numerical simulation to reproduce the variations in the effective electrical conductivity and permittivity of porous geological materials induced by both the electrochemical polarizations and the interfacial polarization. This work thus provides a useful tool for studying the effective electrical properties of porous geological materials featuring complex microstructures.