Numerical modeling of multifrequency complex dielectric permittivity dispersion of clay-rich rocks

Abstract

Dielectric permittivity measurements in sedimentary rocks are dominated by mineralogy, the volumetric concentration and spatial distribution of solids and fluids, and interfacial polarization. Conventional interpretation models oversimplify these factors, leading to uncertainties in estimates of formation properties such as hydrocarbon reserves. Interpretation challenges are magnified in clay-rich rocks, such as shaly sands and organic-rich mudrocks, due to convoluted rock fabric and mineralogical composition. However, the impact of fabric features and mineralogy on broadband permittivity is not well understood. Therefore, the main objective of this work is to develop a numerical framework to quantify the impact of different minerals and corresponding spatial distribution on the multifrequency complex permittivity of clay-rich rocks. We have solved the quasielectrostatic approximation to Maxwell’s equations in the frequency domain through the finite-volume method. We also introduce a workflow to calculate the effective admittance of the clay network. Furthermore, we derive an equation to incorporate the induced polarization effect into the effective admittance of pyrite particles. Finally, we perform a sensitivity analysis of the complex permittivity of clay-rich rocks in the frequency range from 100 Hz to 1 GHz to the volumetric concentration and spatial distribution of clays, cation exchange capacity (CEC), volumetric concentration of pyrite, and the orientation of the electric field. The simulation results confirm that the presence of clay minerals affects the permittivity and conductivity of the rocks. However, clays can enhance or diminish electrical conductivity values at different frequencies depending on their intrinsic properties and spatial distribution. For instance, laminations significantly enhance permittivity in the sub-MHz frequency range, but their effect is imperceptible at 1 GHz. The CEC variation affects conductivity in the entire frequency range from 100 Hz to 1 GHz and the permittivity at sub-MHz frequencies. A volumetric concentration of pyrite of 5% can enhance permittivity and conductivity at 100 Hz by approximately 50% and 30%, respectively.