Minkowski Functionals as Analytical Predictors of Permeability in Porous Microstructures

Understanding the relationship between microstructure and macroscopic properties in porous media remains crucial for numerous applications in geoscience and engineering. For example, accurate predictability of permeability is essential for optimizing fluid flow processes in applications such as hydrocarbon recovery, groundwater management, and carbon or energy storage. The Kozeny-Carman equation has long served as a fundamental tool for predicting permeability based on porosity and specific surface area, with an empirical adjusted constant for different types of materials. Modifications to the equation have been introduced to improve the predictability on selected materials, but they become more specific and introduce new parameters. In this study, we explore an alternative analytical formulation that links permeability directly to Minkowski functionals (MFs), which are known to be more general systematic descriptors of porous media microstructure. Utilizing a database of simulated granular and cemented microstructures, we evaluate permeability predictions based on this MF-based formulation. We show a strong correlation between the functionals and the hydraulic properties, based on very simple assumptions. Despite the motion invariant limitation of the MFs that we confirm in our anisotropic case study, this contribution highlights the potential of MFs as a generalisation of rock typing for permeability prediction.