Thermal conductivity modeling in variably saturated porous media

Abstract:

Modeling effective thermal conductivity under variably saturated conditions is essential to study heat transfer in natural sediments, soils, and rocks. The effective thermal conductivity in completely dry and fully saturated porous media is an integrated quantity representing the complex behavior of two conducting phases, i.e., pore fluid (either air or water) and solid matrix. Under partially saturated conditions, however, the effective thermal conductivity becomes even more complicated since three phases (air, water, and solid matrix) conduct heat simultaneously. In this study, we invoke an upscaling treatment called percolation-based effective-medium approximation to model the effective thermal conductivity in fully and partially saturated porous media. Our theoretical porosity- and saturation-dependent models contain endmember properties, such as air, solid matrix, and saturating fluid thermal conductivities, a percolation exponent t, and a percolation threshold. Comparing our theory with 216 porosity-dependent thermal conductivity measurements and 25 saturation-dependent thermal conductivity datasets indicate excellent match between theory and experiments. Our results show that the effective thermal conductivity under fully and partially saturated conditions follows nonuniversal behavior. This means the value of t changes from medium to medium and depends not only on topological and geometrical properties of the medium but also characteristics of the saturating fluid.