Modeling the Frequency‐Dependent Effective Excess Charge Density in Partially Saturated Porous Media

Abstract

AbstractIn the context of seismoelectric and self‐potential surveying, the effective excess charge density and the electrokinetic coupling coefficient are key parameters relating the measured electrical potential and the hydraulic characteristics of the explored porous media. In this work, we present a novel flux averaging approach that permits to estimate the frequency‐dependent effective excess charge density in partially saturated porous media. For this, we conceptualize the porous medium as a partially saturated bundle of capillary tubes under oscillatory flux conditions. We account for the pore size distribution (PSD) to determine the capillary‐pressure saturation relationship of the corresponding medium, which, in turn, permits to determine the pore scale saturation. We then solve the Navier‐Stokes equations within the saturated capillaries and, by means of a flux‐averaging procedure, obtain upscaled expressions for: (a) the effective excess charge density, (b) the effective permeability, and (c) the electrokinetic coupling coefficient, which are functions of the saturation and the probing frequency. We analyze and explain the characteristics of these functions for three different PSDs: fractal, lognormal, and double lognormal. It is shown that the PSD characteristics have a strong effect on the corresponding electrokinetic response. The proposed flux‐averaging approach has an excellent capability for reproducing experimental measurements and models in the literature, which are otherwise based on well‐known empirical relationships. The results of this work constitute a useful framework for the interpretation of electrokinetic signals in partially saturated media.