Multi-Frequency Modeling of Dielectric Measurements in the Presence of Complex Rock Fabric and Composition

Abstract

The low-frequency dielectric response of sedimentary rocks is dominated by rock fabric, volumetric concentrations of fluids and minerals, and interfacial properties. The rock physics models for interpretation of multi-frequency complex permittivity measurements generally rely on simplified geometries for which analytical solutions are obtainable. Consequently, interpretation of permittivity measurements can be challenging in reservoirs with complex pore structure, mineralogy, and mixed-wet conditions. The objectives of this paper include the development of a rigorous numerical simulation framework to enhance the interpretation of multi-frequency, complex dielectric permittivity measurements and also to quantify the influence of polarization of the electric double layer, lithology, fluid properties, and pore-network geometry on dielectric permittivity measurements. We develop a simulator to calculate permittivity dispersion of sedimentary rocks by applying a combination of finite-difference and finite-volume methods to solve the non-linear Poisson and Nernst- Planck equations in the time domain. We perform a sensitivity analysis of dielectric permittivity to the dominant mineral (e.g., quartz, calcite), pore geometry, and fluid properties (e.g., salt concentration). The main contribution of this paper consists of introducing a simulator that provides the complete and accurate description of electric field, ionic distribution, and effective dielectric permittivity in porous media for enhanced petrophysical interpretation of electromagnetic measurements. Results suggest that incorporating the introduced simulation into a workflow for broadband interpretation of dielectric measurements can improve petrophysical evaluation in formations with complex lithology, rock fabric, and in mixed-wet rocks. This unique approach provides a more rigorous characterization of the dielectric permittivity of rocks than previously documented analytical and numerical models.