Electrical Resistivity of a Partially Saturated Porous Medium at Subzero Temperatures

Abstract

Core Ideas We collected resistivity data at a range of temperatures and initial saturations. Archie's equation was modified to include temperature dependence below 0°C. Bulk resistivity was used to estimate unfrozen water content and fluid resistivity. At subzero temperatures, unfrozen water content is independent of initial saturation. Ion exclusion from ice explains the dependence of resistivity on initial saturation. Electrical resistivity tomography has been used in many frozen ground applications to delineate frozen and unfrozen areas of the subsurface and monitor changes with time. In these studies, the amount of unfrozen water remaining in the pore space at subzero temperatures is often a parameter of interest. To interpret resistivity data quantitatively in terms of unfrozen water content, it is necessary to establish a relationship between bulk resistivity, subzero temperature, and liquid water saturation. In the literature, a consensus has not been reached on the form of this relationship, and a better understanding of the mechanisms controlling the resistivity of frozen ground is needed. This study used a unique laboratory apparatus to collect electrical resistivity tomography data for a uniform porous medium at temperatures from −20 to 25°C for a range of initial water saturations. Archie's equation was modified to include the effects of temperature above and below 0°C. Resistivity data collected below 0°C were used to estimate temperature‐dependent liquid water saturation and fluid resistivity. The amount of unfrozen water remaining at a given temperature was not related to initial water saturation and was nearly identical for all initial saturations at temperatures below about −5°C. The dependence of resistivity–temperature curves on initial water saturation at subzero temperatures was caused by differences in fluid resistivity as a result of ion exclusion during freezing. The relationships established in this study provide insight into the physical mechanisms that govern the resistivity of porous media at subzero temperatures and a starting point for quantitative analysis of resistivity data collected in frozen ground.