Determination of kozeny constant based on porosity and pore to throat size ratio in porous medium with rectangular rods

Abstract

Kozeny-Carman permeability equation is an important relation for the determination of permeability in porous media. In this study, the permeabilities of porous media that contains rectangular rods are determined, numerically. The applicability of Kozeny-Carman equation for the periodic porous media is investigated and the effects of porosity and pore to throat size ratio on Kozeny constant are studied. The continuity and Navier- Stokes equations are solved to determine the velocity and pressure fields in the voids between the rods. Based on the obtained flow field, the permeability values for different porosities from 0.2 to 0.9 and pore to throat size ratio values from 1.63 to 7.46 are computed. Then Kozeny constants for different porous media with various porosity and pore to throat size ratios are obtained and a relationship between Kozeny constant, porosity and pore to throat size ratio is constructed. The study reveals that the pore to throat size ratio is an important geometrical parameter that should be taken into account for deriving a correlation for permeability. The suggestion of a fixed value for Kozeny constant makes the application of Kozeny-Carman permeability equation too narrow for a very specific porous medium. However, it is possible to apply the Kozeny-Carman permeability equation for wide ranges of porous media with different geometrical parameters (various porosity, hydraulic diameter, particle size and aspect ratio) if Kozeny constant is a function of two parameters as porosity and pore to throat size ratios.