Developing a new form of the Kozeny–Carman parameter for structured porous media through lattice-Boltzmann modeling

Abstract

The semi-empirical Kozeny–Carman (KC) equation is a commonly-used relationship for determining permeability as a function of porosity for granular porous materials. This model features a material-specific fitting parameter, CKC, which is generally treated as a constant coefficient. Recent studies, however, have shown that CKC is not constant and could be a varying function of porosity. We used lattice-Boltzmann (LB) modeling to calculate the absolute permeability of two simulated porous structures: periodic arrays of (a) staggered parallel infinite cylinders and (b) spheres. We then identified various functional forms of CKC, and for each form, we performed a regression analysis in order to fit the function to the permeability values determined from the LB simulations. From this analysis, we extracted optimal fitting parameters for each function that minimized the error between permeability values obtained from the KC model and the LB simulations. All linear and non-linear functional forms proposed in this work improve the predictability of the KC model. An algebraic function for CKC provided the most accurate prediction of the KC porosity–permeability relationship for the geometries examined.