A physically-based fractal model for predicting the electrical conductivity in partially saturated frozen porous media

Macro-scale transport properties (e.g., electrical conductivity, effective excess charge density and hydraulic conductivity) can be conceptualized as capillary bundle models, in which the pore structure of porous medium is viewed as a bundle of capillary tubes of varying sizes. This approach can be used to understand and address the relationship between the petrophysical properties and the geometry of soil phases. When the temperature of porous medium decreases below the freezing temperature, the soil physical properties (transport properties) change drastically. This is attributed to the complexity of the heterogeneous formation of ice in the porous medium. Therefore, understanding better pore ice formation from microscale insights is crucial to describe the evolution of electrical conductivity with temperature in frozen porous medium. In this study, we consider that capillary radius and tortuous length follow fractal distributions, and that total conductance at the microscale scale is determined by the Gibbs-Thomson and Young-Laplace effects as well as by the surface complexation model. A new capillary bundle model is then proposed using an upscaling procedure, which considers the effects of both bulk and surface conductions. Based primarily on an electrical resistance apparatus and the NMR method, a series of laboratory experiments are carried out to study the influence of initial water saturation and salinity on electrical conductivity under unfrozen and frozen conditions. Additionally, the rationality and validity of the proposed model were successfully verified with published data in the literature and experimental data of this study. Our new physically-based model for electrical conductivity opens up new possibilities to interpret electrical and electromagnetic monitoring to easily infer changes in key variables such as liquid water content and moisture gradients.