An Extended Kozeny-Carman Model for Gas Permeability in Micro/Nano-porous Media

Abstract

Gas transport in micropores/nanopores deviates from classical continuum calculations due to nonequilibrium in gas dynamics. In such a case, transport can be classified by the Knudsen number (Kn) as the ratio of gas mean free path and characteristic flow diameter. The well-known Klinkenberg correction and its successors estimate deviation from existing permeability values as a function of Kn through a vast number of modeling attempts. However, the nonequilibrium in a porous system cannot be simply modeled using the classical definition of the Kn number calculated from Darcy's definition of the pore size or hydraulic diameter. Instead, a proper flow dimension should consider pore connectivity in order to characterize the rarefaction level. This study performs a wide range of pore-level analysis of gas dynamics with different porosities, pore sizes, and pore throat sizes at different Kn values in the slip flow regime. First, intrinsic permeability values were calculated without any rarefaction effect and an extended Kozeny-Carman model was developed by formulating the Kozeny-Carman constant by porosity and pore to throat size ratio. Permeability increased by increasing the porosity and decreasing the pore to throat size ratio. Next, velocity slip was applied on pore surfaces to calculate apparent permeability values. Permeability increased by increasing Kn at different rates depending on the pore parameters. While the characterization by the Kn value calculated with pore height or hydraulic diameter did not display unified behavior, relating permeability values with the Kn number calculated from the equivalent height definition created a general characterization based on the porosity independent from the pore to throat size ratio. Next, we extended the Klinkenberg equation by calculating unknown Klinkenberg coefficients which were found as a simple first order function of porosity regardless of the corresponding pore connectivity. The extended model as a combination of Kozeny-Carman for intrinsic permeability and Klinkenberg for apparent permeability correction yielded successful results. Published under license by AIP Publishing.