Interpretation of complex dielectric permittivity measurements is challenging in clay-rich rocks, such as shaly sands and organic-rich mudrocks, due to complex rock fabric and mineralogical composition, which are overlooked by conventional interpretation models. For instance, the impact of fabric features (e.g., laminations, structural/dispersed shale) and diverse constitution (e.g., clay, kerogen, pyrite, brine) to the broadband complex permittivity is not well understood. Therefore, the main objective of this work is to develop a framework capable of reliably quantifying the impact of different minerals and their corresponding spatial distribution on the multi-frequency complex dielectric permittivity measurements in clay-rich rocks.To achieve the aforementioned objective, we introduce a numerical algorithm to compute the dielectric dispersion in 3D pore-scale images of clay-rich rocks. We numerically solve the quasi-electrostatic approximation to Maxwell's equations in the frequency domain through the finite volume method. The clay particles are often sub-resolution in most imaging methods. Therefore, we introduce a workflow to calculate the effective admittance of the clay network. Furthermore, we derive a new equation to incorporate the induced polarization effect into the effective admittance of pyrite particles. Finally, we perform a sensitivity analysis of the complex dielectric 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. Results showed that clays can enhance or diminish electrical conductivity values at different frequencies depending on their intrinsic properties and spatial distribution. Laminations, for instance, significantly enhance dielectric permittivity in the sub-MHz frequency range, but their effect is imperceptible at 1 GHz. Furthermore, the impact of the variation of CEC on permittivity is approximately proportional at 100Hz but negligible at 1 GHz.
Complex dielectric permittivity measurements from ground-penetrating radar data to estimate snow liquid water content in the pendular regime
