Quantifying the Impacts of Stern and Diffuse Layer Polarization on Multi-Frequency Dielectric Permittivity and Electrical Conductivity of Rock-Fluid Systems

Abstract

AbstractA thorough understanding of the interplay between polarization mechanisms is crucial for interpretation of electrical measurements because sub-MHz electrical measurements in sedimentary rocks are dominated by interfacial polarization mechanisms. However, rock-physics models oversimplify pore-network geometry and the interaction of electric double layers (EDL) pertaining to adjacent grains. The impact of these simplifications on the assessment of petrophysical properties, such as hydrocarbon reserves, is difficult to quantify and often unknown. Numerical algorithms present the ideal framework to characterize the electrical response of sedimentary rocks, circumventing the limitations intrinsic to rock-physics models. Our recently developed algorithm simulates the interactions of electric fields with the ions in solution. However, a model for the polarization mechanism associated with the Stern layer has not been developed. The sub-kHz permittivity enhancement in sedimentary rocks is dominated by Stern layer polarization. Therefore, the objective of this paper is to develop a numerical simulation framework capable of quantifying the influence of Stern- and diffuse-layer polarization, temperature, ion concentration, and pore-network geometry on multi-frequency complex electrical measurements.We developed a numerical simulator to compute time-dependent behavior of electric field, ion concentration, and interfacial polarization mechanisms in sedimentary rocks. The algorithm numerically solves the Poisson-Nernst-Planck (PNP) equations in the time domain conjointly with a mineral-dependent electrochemical adsorption/desorption equilibrium model. Then, we use the numerical simulator to perform a sensitivity analysis to quantify the influence of electrolyte and interfacial properties on the permittivity of pore-scale samples at different frequencies. Results demonstrated that the joint effect of Stern layer ion concentration and corresponding mobility dominates sub-MHz dielectric response of rocks. The low-frequency permittivity enhancement due to the EDL can sweep several orders of magnitude. The Stern layer polarization acts as a macroscopic (i.e., at the grain scale) dipole created by counterions wading around the surface of the grains due to an externally applied electric field. Therefore, the grain shape and corresponding orientation relative to the electric field significantly affect the behavior of macroscopic Stern layer dipoles. Reliable interpretation of multi-frequency electrical measurements can provide insights in mineralogy, fluid typing, grain size, and interfacial properties. Time-domain numerical modeling of complex permittivity dispersion can greatly enhance interpretation of multi-frequency dielectric measurements.