Mechanistic model of multi-frequency complex conductivity of porous media containing water-wet nonconductive and conductive particles at various water saturations

Abstract

Electrically conductive particles, such as pyrites, and surface-charge-bearing nonconductive particles, such as clays, are commonly present in water-bearing subsurface formations. Under an external electric field generated by electromagnetic measurement tool, these particles give rise to interfacial polarization (IFP) effects, which causes frequency dispersion of effective conductivity and effective permittivity of the mixture containing such particles. The neglect of IFP effects can lead to inaccurate estimation of petrophysical properties of formations, especially in clay- and pyrite- rich formations. In this paper, we developed a mechanistic model that couples surface-conductance-assisted interfacial polarization (SCAIP) model with perfectly polarized interfacial polarization (PPIP) model to estimate effective conductivity and effective permittivity of homogeneous formations containing both nonconductive and conductive particles at various fluids saturations. The model is developed based on the Poisson-Nernst-Planck (PNP) equations for a dilute solution in a weak electrical field regime to calculate the dipolarizability of the representative volume comprising a single isolated spherical particle in an electrolyte host. Then the effective medium theory is used to determine effective complex conductivity of the whole mixture. The result shows that the conductive particles dominate the frequency dispersion of complex conductivity due to IFP effects compared to nonconductive particles.