Model of the constricted unit cell type for isotropic granular porous media

Abstract

AbstractThe constricted unit cell model for isotropic granular porous media developed by Payatakes, Tien, and Turian (1973) is extended here to take in account the random orientation of the flow channels. In the proposed model, each unit cell corresponds to a pore (cavern) and has two coaxial constricted inlet and outlet ports (throats). The unit cells have random dimensions and orientations, the distributions of which can be determined from simple experimental measurements. The flow through a unit cell is assumed to be identical to that through a segment of the corresponding periodically constricted tube. The model is applied to the case of creeping Newtonian flow. The solution to the flow problem is obtained by a collocation method. Permeabilities of typical packings are calculated without use of any adjustable parameters (such as tortuosities, etc.) and are found in excellent agreement with experimental values.