Application of Hierarchical Homogenization Technique in Thermal Conductivity Computation for Micro-Computed Tomography (Micro-CT) Images of Porous Media

Thermal properties play a critical role in environments and processes involving heat exchange and transfer. Heat transport in porous media has been a subject of extensive study due to its significant impact on applications ranging from in situ hydrocarbon production to geothermal energy projects. Micro-CT imaging has become a powerful tool for characterizing porous media, with its use increasingly expanding in recent years, driven by progress in computational techniques. Homogenization approaches provide a powerful means to analyze transport phenomena in Micro-CT images, offering reliable accuracy while reducing computational errors. In this study, the application of the hierarchical homogenization (HH) technique for thermal conductivity was explored. Various sources of error, including the choice of homogenization scale and numerical conditions such as padding thickness, were systematically investigated and compared to validation dataset acquired by Micro-CT data and high-fidelity direct numerical simulations. The results indicated less than 5% error in the first-order single-stage HH approach for all studied material schemas. Hyperbolic trend of the error was observed with the order of homogenization. Subsequently, telescopic hierarchical homogenization (THH) was found effective as a new approach for more complex systems with a negligible (less than 1.5%) error compared to single-stage HH. Furthermore, the HH error was investigated for a set of 19 synthetic and real samples to assess the effect of porosity and porosity variation in subsamples on the final error values, and a mathematical model was obtained for each of the material schemas. Results showed that in the similar porosity cases, sample with the higher dispersion of porosity will result in more error of thermal conductivity through HH procedure.