Quantitative Evaluation of the Effect of Pore Fluids Distribution on Complex Conductivity Saturation Exponents.

The induced polarization (IP) method holds a strong potential to better characterize the critical zone of our planet especially in areas characterized by multi‐phase flow. Power‐law relationships between the bulk, surface, and quadrature conductivities versus the pore water saturation are potentially useable to map the subsurface water content distribution. However, the saturation exponents n and p in these power‐law relationships have been observed to vary with the texture of geomaterials and the wettabilities of pore fluids. Traditional experimental setups in the laboratory do not allow to independently visualize the pore fluid distribution. Therefore, the physical interpretations of the two saturation exponents have remained unclear. We developed a novel milli‐fluidic micromodel using clay‐coated glass beads that exhibit excellent visibility and high IP response. Through laboratory experiments, we simultaneously determined the micromodel complex conductivity and acquired the corresponding pore‐scale fluid distributions generated by drainage and imbibition through such class of porous materials. Finite‐element simulations of complex conductivity based on the upscaling of the complex surface conductance of grains were conducted to determine the saturation exponents under ideal pore fluid distributions. Results indicate that saturation exponents n and p vary depending on the ganglia size of the insulating fluids. The saturation exponents n and p exhibit power‐law relationships with the change rate of pore water connectivity with saturation, which is calculated through the computation of the derivative of Euler characteristics. These findings provide a new physical explanation to the relationships between the saturation exponents and the microscopic fluid distributions within the geomaterials. Plain Language Summary: Water saturation of porous bodies can be related to the complex conductivity through power‐law relationships. The existence of these power‐law relationships has been clearly documented in the literature. They are critical in the realm of hydrogeophysics to better characterize the critical zone of the solid Earth. However, the values of the saturation exponents in these power‐laws have been observed to vary with different material textures and no underlying mechanisms have been able to explain these variations to date. This lack of physical understanding could limit the applicability of the induced polarization method to characterize the critical zone especially when immiscible fluid phases are present. To tackle this, we developed a milli‐fluidic pore model that allows investigating the saturation exponents while monitoring the pore‐scale fluid distributions. Together with numerical simulations for ideal fluid distribution cases, we found a relationship between the saturation exponents and a microscopic pore parameter called "change rate of the pore water connectivity with saturation." These findings suggest that when estimating subsurface water saturation from electrical parameters, taking the pore fluid distribution into account can significantly improve the estimation accuracy, therefore enhancing the efficiency of geo‐electrical applications for a better characterization of hydrocarbon contaminated aquifers and oil reservoirs. Key Points: A micromodel setup allows for simultaneous pore fluid visualization and complex electrical conductivity measurementThe two saturation exponents for the in‐phase and quadrature conductivities are correlated with the ganglia size of the insulating phaseA power‐law‐type relationship between the saturation exponents and the change rate of water connectivity with saturation is demonstrated [ABSTRACT FROM AUTHOR]