Frequency‐Dependent Electric Properties of Microscale Rock Models for Frequencies from One Millihertz to Ten Kilohertz

Abstract

In this study, spectral induced polarization (SIP) spectra were generated numerically to better understand how actual rock microstructure and electrolyte properties in rock pores affect the spectral pattern, i.e., the characteristic relaxation time of polarization as well as the polarization strength of a rock pore system. The dynamics of charge carriers in three‐dimensional pore systems were simulated using a frequency‐dependent formulation of the Nernst–Planck–Poisson (NPP) ion‐transport equations. Basically, a pore‐system model of alternating stacked cylinders of two different sizes was studied considering the electrical double layer (EDL). A reduced cationic mobility—resulting from increased adsorption of these cations at the rock–water interface—was assumed within the EDL. By solving the NPP equations using the finite element method, complex resistivity phase spectra were generated. Subsequently, the effect of pore structural properties and electrolyte conductivity on the magnitude and frequency position of the characteristic resistivity phase minimum of rocks was studied. The following results were found: First, regarding pore geometry, the characteristic frequency of the phase minimum fmin decreases with increasing pore length of the large pore. Second, both small pores having a radius of a few Debye lengths combined with larger pores are needed to ensure detectable phase amplitudes. Third, with regard to electrolyte concentration, the phase amplitude is inversely proportional to the concentration, whereas fmin remains constant. Because the studied model does not provide a direct and exclusive link between the simulated electrical properties and pore throat size, further research is needed here to specify a convincing SIP interpretation method for improved permeability estimation.