Rank-two tensorial shape descriptors: Insights into anisotropic permeability tensor characterization

The permeability of an anisotropy porous microstructure is expressed as a symmetric tensor of rank two. Compared with a specific scalar or a combination of several scalars, a homogeneous and symmetric tensorial descriptor is more suitable for characterizing the anisotropy permeability tensor. Unlike prior work, our method integrates advanced three-dimensional pore mesh generation from X-ray computed tomography images of sand-packing sample and desiccation cracked soil, creating twenty-seven representative elementary volume meshes. Using the finite element method, we numerically simulate the permeability tensor for each mesh and validate our results by showing strong correlations between Minkowski tensor (MT) descriptor W20,2 and permeability tensor: Pearson correlation coefficients of 0.763 for sand-packing sample and 0.854 for desiccation cracked soil. Additionally, we compare our approach with conventional permeability prediction methods and demonstrate that MTs provide a more detailed understanding of permeability anisotropy. This approach offers new insights into the anisotropy of permeability and provides a more robust framework for characterizing heterogeneous porous materials in both geophysical and engineering applications.