Numerical modeling of multifrequency complex dielectric permittivity dispersion of sedimentary rocks

Abstract

The dielectric response of rocks results from electric double layer (EDL), Maxwell-Wagner (MW), and dipolar polarizations. The EDL polarization is a function of solid-fluid interfaces, pore water, and pore geometry. MW and dipolar polarizations are functions of charge accumulation at the interface between materials with contrasting impedances and the volumetric concentration of its constituents, respectively. However, conventional interpretation of dielectric measurements only accounts for volumetric concentrations of rock components and their permittivities, not interfacial properties such as wettability. Numerical simulations of the dielectric response of rocks provide an ideal framework to quantify the impact of wettability and water saturation ([Formula: see text]) on electric polarization mechanisms. Therefore, we have developed a numerical simulation method to compute pore-scale dielectric dispersion effects in the interval from 100 Hz to 1 GHz including effects of pore structure, [Formula: see text], and wettability on permittivity measurements. We solve the quasielectrostatic Maxwell’s equations in 3D pore-scale rock images in the frequency domain using the finite-volume method. Then, we verify simulation results for a spherical material by comparing to the corresponding analytical solution. Additionally, we introduce a technique to incorporate [Formula: see text]-polarization to the simulation and we verify it by comparing pore-scale simulation results to experimental measurements on a Berea sandstone sample. Finally, we quantify the impact of [Formula: see text] and wettability on broadband dielectric permittivity measurements through pore-scale numerical simulations. The numerical simulation results show that mixed-wet rocks are more sensitive than water-wet rocks to changes in [Formula: see text] at sub-MHz frequencies. Furthermore, permittivity and conductivity of mixed-wet rocks have weaker and stronger dispersive behaviors, respectively, when compared to water-wet rocks. Finally, numerical simulations indicate that conductivity of mixed-wet rocks can vary by three orders of magnitude from 100 Hz to 1 GHz. Therefore, Archie’s equation calibrated at the wrong frequency could lead to water saturation errors of up to 73%.