The microstructure of granular media, including grain’s shape- and size- polydispersities, orientation, and area fraction can potentially affect its permeability. However, few studies consider the coupling effects of these features. This work employs geometrical probability and stereology to establish quantitative relationships between the above microstructural features and the geometric tortuosity of the two-dimensional granular media containing superellipse, superoval, and polygon grains. Then the lattice Boltzmann method (LBM) is used to determine the permeabilities of these granular media. By combining the tortuosity model and the LBM-derived permeabilities, modified K-C equations are formulated to predict the permeability and the shape factor, considering the grain’s shape- and size- polydispersities, orientation, and area fraction. The reliability of these methods can be verified by comparing with both our simulations and available experimental, theoretical, and numerical data reported in the literature. The findings implicate that the tortuosity and permeability of the granular media are strongly correlated with the grain’s shape, orientation, and area fraction but unaffected by the size polydispersity and spatial arrangement of grains. Only circularity is not enough to derive a unified formula for considering the impact of grain shape on tortuosity and permeability, other shape parameters need to be explored in the future.
 

Geometric tortuosity; Konzey-Carman equation; Shape and size ploydispersities; Grain orientation; Lattice Boltzmann method; Ganular media