Alternative flow model of anisotropic porous media

Abstract

Porous flow is typically analyzed by the Kozeny–Carman equation using geometric variables, such as hydraulic diameter and tortuosity. The hydraulic tortuosity was first described by Kozeny, and later redefined by Carman as the tortuosity square term in the Kozeny–Carman equation. However, the revised term correlating the flow velocity with path length square would be physically ambiguous. Moreover, the hydraulic diameter, which is directly correlated to the permeability and interstitial velocity in the Kozeny–Carman equation, is an isotropic constant property; thus, it should be verified whether the isotropic hydraulic diameter can reasonably correlate each anisotropic directional flow feature passing through heterogeneous complex media. Accordingly, the Kozeny–Carman equation was theoretically examined and experimentally verified in this study to obtain the proper correlation based on the definitions of truly equivalent diameter and tortuosity. Therefore, the effective variables of porous media were presented, and it confirmed that the effective diameter corresponded to the physically equivalent diameter of anisotropic porous media. Moreover, using the mass conservation relation, it was verified that Kozeny's tortuosity is exactly associated with the truly equivalent flow model, and then the Kozeny constant must be differently defined from the original Kozeny equation. Accordingly, the Kozeny–Carman equation was improved by appertaining either effective diameter or tortuosity, and the momentum conservation relation was used to verify it. The pore-scale simulations using 5-sorts of 25-series porous media models were performed to test the validity of derived effective variables and revised equations. Finally, the alternative flow model of anisotropic porous media was presented using equivalent geometric and frictional flow variables. Subsequently, their practical and more accurate estimations were achieved by introducing the concentric annulus flow model under the special hydraulic condition. The new variables and relations are expected to be usefully applied to various porous flow analyses, such as interstitial velocity estimations, geometric condition variations, flow regime changes, and anisotropic heat and multiphase flows.