Elucidating Pore-Scale Mechanisms Governing the Saturation-Dependence of Complex Conductivity

Petrophysical models linking geophysical observables to subsurface hydraulic states are fundamental to the interpretation of hydrogeophysical data. For electrical methods, power-law formulations such as Archie’s law are commonly used to relate different components of complex conductivity to water saturation, with the associated saturation exponents in these power laws describing the saturation-dependent behavior of complex conductivity. However, due to the lack of the ability to directly visualize pore-scale fluid distributions for traditional laboratory or field investigations, the physical origin and variability of these saturation exponents remain poorly understood, which hinders reliable interpretation of geoelectrical data in dynamic or heterogeneous subsurface environments.

In this contribution, we present results from our recent studies that quantitatively investigate how pore-scale fluid and interface distribution govern the saturation dependence of complex conductivity. First, a dedicated milli-fluidic micromodel was developed to enable simultaneous spectral IP measurements and direct visualization of pore-scale fluid configurations during drainage and imbibition. By combining laboratory observations with finite-element and pore-network simulations, we demonstrate quantitatively that both the in-phase and quadrature saturation exponents are controlled by the rate of change of pore-water connectivity with saturation. In parallel, by extending Archie’s laws to interfacial polarization using fractal theories, we establish that surface and quadrature conductivity in fractal porous media follow power-law relationships with specific surface area, with the corresponding exponents linked to the pore-volume fractal dimension. Building on these results, we further explore a commonly observed yet poorly explained anomaly in IP measurements: the decrease of quadrature conductivity (or normalized chargeability) with increasing saturation during drying. Using desiccation experiments combined with pore-network modeling, we show that this anomalous behavior arises from a coupled mechanism involving the sequential drying of pores of different characteristic sizes and the persistence of thin water films on solid surfaces.

Together, these studies advance the petrophysical understanding of IP signatures by linking macroscopic electrical parameters to microscale fluid topology and interfacial processes. Our findings underscore the importance of incorporating pore-scale fluid connectivity and interfacial effects into petrophysical models, thereby improving the quantitative interpretation of geoelectrical data in hydrogeological, biogeochemical, and reservoir monitoring applications.