Thermal conductivity in porous media: Percolation‐based effective‐medium approximation

Abstract Knowledge of porosity and saturation‐dependent thermal conductivities is necessary to investigate heat and water transfer in natural porous media such as rocks and soils. Thermal conductivity in a porous medium is affected by the complicated relationship between the topology and geometry of the pore space and the solid matrix. However, as water content increases from completely dry to fully saturated, the effect of the liquid phase on thermal conductivity may increase substantially. Although various methods have been proposed to model the porosity and saturation dependence of thermal conductivity, most are empirical or quasiphysical. In this study, we present a theoretical upscaling framework from percolation theory and the effective‐medium approximation, which is called percolation‐based effective‐medium approximation (P‐EMA). The proposed model predicts the thermal conductivity in porous media from endmember properties (e.g., air, solid matrix, and saturating fluid thermal conductivities), a scaling exponent, and a percolation threshold. In order to evaluate our porosity and saturation‐dependent models, we compare our theory with 193 porosity‐dependent thermal conductivity measurements and 25 saturation‐dependent thermal conductivity data sets and find excellent match. We also find values for the scaling exponent different than the universal value of 2, in insulator‐conductor systems, and also different from 0.76, the exponent in conductor‐superconductor mixtures, in three dimensions. These results indicate that the thermal conductivity under fully and partially saturated conditions conforms to nonuniversal behavior. This means the value of the scaling exponent changes from medium to medium and depends not only on structural and geometrical properties of the medium but also characteristics (e.g., wetting or nonwetting) of the saturating fluid.