Multifrequency Analytical Forward Modeling of Dielectric Permittivity Dispersion in Mixed-Wet Sedimentary Rocks

Abstract

Summary The dominant wettability of reservoir rocks is one of the main factors affecting the spatial distribution of fluids inside the pore space. More specifically, wettability controls the fluid type that coats the surface of the grains and, hence, the establishment of an electric double layer (EDL) at the solid–liquid interface. These factors, namely fluid distribution and EDL, affect the conductivity and permittivity of the rock in unique ways. Therefore, interpretation of multifrequency complex permittivity measurements can be used to quantify the wettability and parameters affecting the double layer (e.g., grain size) in addition to porosity and fluid saturation. In this paper, we introduce an analytical model to reliably characterize the dielectric permittivity dispersion of mixed-wet sedimentary rocks. The analytical derivation of the rock-physics model results in physically meaningful parameters, associated with either microscopic polarization mechanisms or pore-network geometry. We incorporate the contribution of the complex impedance associated with the EDL to the complex permittivity of the rock through a mechanistic model of Stern and Gouy-Chapman layers. Then, we quantify the contribution of different fluid and grain types to the electrical response of sedimentary rocks through Hanai–Bruggeman effective medium model. The sequential application of Hanai-Bruggeman is specifically designed to make the dependence of complex permittivity on wettability explicit. We successfully verified the reliability of the new analytical model using experimental measurements performed on two water-wet and two hydrocarbon-wet sandstone core samples. The experimental measurements were in agreement with the complex permittivity calculated using the new analytical model in the frequency range of 100 Hz to 10 MHz. Furthermore, the introduced model provides a physical interpretation to the experimentally detectable influence of wettability on the complex dielectric permittivity of rocks. Consequently, the outcomes of this paper will enhance petrophysical evaluation in mixed-wet formations by providing a novel interpretation method for complex permittivity dispersion measurements.