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 dielectric response of rocks provides an ideal framework to quantify the impact of wettability and water saturation ( Sw) on electric polarization mechanisms. Therefore, in this paper we introduce a numerical simulation method to compute pore-scale dielectric dispersion effects in the interval from 100 Hz to 1 GHz including impacts of pore structure, Sw, and wettability on permittivity measurements. We solve the quasi-electrostatic Maxwell's equations in three-dimensional (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 with the corresponding analytical solution. Additionally, we introduce a technique to incorporate α-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 Sw 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 Sw 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 73%.
Numerical Simulation of Abrikosov Vortex at Columnar Defect in Superconductor
