Model-based analysis of the effective pressure on effective thermal conductivity of porous media

Accurate characterization of the effective thermal conductivity (ETC) of porous media is crucial for analyzing heat transfer involved in the scientific, technological, and engineering fields. For example, ETC is a fundamental parameter for characterizing energy exploitation and utilization, such as the coupled thermo-hydro-mechanical-chemical process. During the energy extraction from the deep subsurface, the effective pressure (the difference between the confining pressure and the pore pressure) will alter the microstructure of the porous medium, which will then change its ETC value. In light of the intrinsic randomness and disorder in the distribution of grains and pores in the deep subsurface, many researchers have focused on heat conduction to develop theoretical models of ETC. Less attention has been paid to the thermal and mechanical coupling processes. In this paper, a novel analytical model was derived to study the effect of effective pressure on ETC of porous materials based on fractal theory, Laplace′s equation and the theory of elastic mechanics. The newly developed ETC model considered the effective pressure, the liquid saturation, and the microstructure parameters. The model has also been validated against the experimental results. The model demonstrated that effective pressure increases the ETC of a given porous medium. Moreover, there is a larger change in ETC in porous materials with a smaller initial porosity compared to porous materials with a larger initial porosity. This work constitutes a comprehensive investigation of pressure-dependent ETC, which is a key issue in heat transfer in porous media.