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

In 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. Plain Language Summary Seismic waves travel throughout the Earth deforming the rocks in their passage. If rocks are porous, permeable, and contain fluids in their pores, as is the case in many geological formations, the wave's passage may induce oscillatory fluid flow. Minerals composing rocks are commonly electrically charged and, thus, the flowing fluid can result in an electrical field. Interestingly, measuring this electrical field at the Earth's surface may permit to characterize the hydromechanical properties of geological formations of interest, motivating the so-called seismoelectric method. The effective excess charge that is mobilized by the fluid motion depends on the frequency content of the wave, and models exist to estimate this dependence in terms of the rock and fluid properties. However, in many scenarios in Earth sciences, rocks contain two immiscible fluid phases, such as, water and air, for which frequency-dependent effective excess charge density models based on pore-scale physics are missing in the literature. In this paper, we derive such a model and show that it is able to reproduce previous estimates and experimental data.

Automated summary

This study introduces a novel flux averaging approach to estimate the frequency-dependent effective excess charge density in partially saturated porous media. The upscaling method based on pore-scale physics shows promising results and could be applied to interpret electrokinetic signals in geological formations.