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 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 emerged as an innovative technique for characterizing porous media, with its adoption growing in recent years due to advancements in computational methods. 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. 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 sub samples 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.