A Fractal Model for Effective Thermal Conductivity in Complex Geothermal Media

Abstract

Thermal conductivity is an important macroscopic thermo-physical parameter due to its significant effects on the temperature field distribution and heat flow magnitude in the material at heat conduction equilibrium. However, because of the extremely complex pore structure and disordered pore distribution, a well-accepted relationship between effective thermal conductivity (ETC) and geometric structural parameters is still lack. In this study, a novel fractal model with variation pore diameter is established systematically based on the assumption that the rough elements of wall surface, pore size distribution and capillary tortuosity follow the fractal scaling law. Thermal-electrical analogy is introduced to predict the ETC of unsaturated geothermal media. The proposed model explicitly relates the ETC to the microstructural parameters (relative roughness, porosity, fractal dimensions and radius fluctuation amplitude) and fluid properties. The proposed model is validated by comparing with existing experimental data. A parametric analysis is performed for presenting the effects of the structural parameters and fluid properties on the ETC. The results show that pore structure has significant effect on ETC of unsaturated porous media. ETC gradually decreases with the increment of porosity, relative roughness, and fractal dimensions. The present study improves the accuracy in predicting ETC and sheds light on the heat transfer mechanisms of geothermal media.