A fractal model of effective thermal conductivity for porous media with various liquid saturation

Abstract

Thermal conduction in porous media has received wide attention in science and engineering in the past decades. Previous models of the effective thermal conductivity of porous media contain empirical parameters typically with ambiguous or even no physical rationales. This study proposes a theoretical model of effective thermal conductivity in porous media with various liquid saturation based on the fractal geometry theory. This theoretical model considers geometrical parameters of porous media, including porosity, liquid saturation, fractal dimensions for both the granular matrix and liquid phases, and tortuosity fractal dimension of the liquid phase. Effects of these geometrical parameters on the effective thermal conductivity of porous media are also evaluated. This proposed fractal model has been validated using published experimental data, compared with previous models, and thus provides a physics-based theoretical model that can provide insight to geoscience and thermophysics studies on thermal conduction in porous media.