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Accurate prediction of permeability and thermal conductivity of porous materials is essential for the design and optimisation of various engineering systems in energy, environmental and infrastructure applications. This study presents a discrete multi-physics modelling framework that enables direct prediction of these properties from microstructural information alone, without recourse to fitting against experimental data of fluid flow and heat transfer. The method is based on combinatorial differential forms defined on a cell complex, allowing local conservation laws to be enforced while capturing material and interfacial non-linearities. Representative elementary volumes (REVs) were statistically reconstructed from high-resolution X-ray computed tomography (XCT) of two sandstone types, with mineralogical composition derived from X-ray diffraction (XRD) analysis. Local transport properties were assigned based on pore geometry and mineral-specific conductivities, incorporating realistic mixing rules at interfaces. Simulations across 30 stochastic microstructural realisations per specimen of rock yielded permeability and thermal conductivity estimates that captured experimental trends and magnitudes without calibration. The results demonstrate the predictive capability and robustness of the approach, offering a viable pathway for microstructure-informed design and digital characterisation of porous and fractured geomaterials. The central scientific contribution is a unified discrete operator formulation in which permeability and thermal conductivity emerge from the same mathematical structure, providing a physically consistent basis for modelling transport in heterogeneous and fractured rock materials.
Liu et al. (Sat,) studied this question.