The modification of the Kozeny-Carman equation through the lattice Boltzmann simulation and experimental verification

Abstract

In this paper, the numerical simulation based on the lattice Boltzmann method (LBM) and experimental studies are conducted to investigate the permeability of porous media with sphere packing. The accuracy of LBM is verified through the comparison of theoretical solutions and the numerical result of flat channel flows. The resolution and the size of representative element volume used for simulation are evaluated. Then, the effects of porosity and particle size on the permeability of porous media are studied through the combination of LBM and discrete element method, and the factors that affect the fluid flow in porous media are explored. It is found that there are very high linear correlations between n3/(1-n)2 and permeability. Meanwhile, the relationship between the particle size, d, and permeability is also established. The physical constant, Ck, is found closely related to the porosity, n, based on which, the modification of the Kozeny-Carman (K-C) equation is proposed. After that, the constant head test is conducted for the glass beads with different porosity and particle size distribution, and the proposed equation is validated. The experimental results show that the modified K-C equation presents a higher accuracy than the classical K-C equation for the porous media from sphere packing.