Significance of shape factor on permeability anisotropy of sand: representative elementary volume study for pore-scale analysis

Abstract

This paper is a study of determination of representative elementary volume (REV) size suitable for pore-scale flow simulation (PFS) and evaluation of permeability anisotropy for sand based on Kozeny–Carman (KC) equation. We extracted small digitized samples for PFS from the 3D structures of Toyoura sand and glass beads obtained by X-ray computed tomography. Using the digitized samples with various sizes, we performed a series of flow simulations. We characterized the sample size using the ratio of the porous length L to the median grain diameter $$D_{50}$$ . The $$L/D_{50}$$ of REV was determined on the basis of statistical evaluation on coefficients of variations of the simulated values of void ratio, specific surface, hydraulic conductivity and hydraulic tortuosity. We confirmed that the hydraulic properties obtained from the PFS using the REV size determined agreed well with the past experimental studies. We also conducted PFSs in the horizontal direction to evaluate the permeability anisotropy. We clarified that the shape factor in the KC equation has a strong influence on permeability anisotropy even though previous studies treated hydraulic tortuosity as the only factor that affects the permeability anisotropy.