Application of space renormalisation technique for spatiotemporal analysis of effective thermal conductivity in multiphase porous materials

Effective thermal conductivity (‾k) is a critical parameter influencing heat transfer in multiphase porous materials. This study introduces a computational approach using the space renormalisation technique to derive ‾k from segmented X-ray micro-CT images of porous media. By accounting for pore-scale heterogeneity, this approach enables detailed spatiotemporal analysis of ‾k in different porous structures. The application of this technique is demonstrated through the prediction and spatiotemporal analysis of ‾k in three different porous rock samples experiencing multiphase fluid flow: (i) steady-state two-phase flow in Estaillades carbonate, (ii) sequential flooding in Bentheimer sandstone, and (iii) immiscible three-phase flow in Ketton limestone. Results show distinct directional variations in ‾k according to phase saturations and redistributions, highlighting the sensitivity of the approach to the microstructural characteristics of porous media. The space renormalisation technique efficiently predicts ‾k with significantly reduced computational costs compared to traditional finite difference methods, making it suitable for real-time applications. The findings provide deeper insights into the dynamic heat transfer mechanisms in heterogeneous porous systems, with implications for various porous media applications such as enhanced oil recovery, geothermal energy extraction, and the design of heat exchangers in engineering systems.