Porous medium model of a hollow-fiber water filtration system

Abstract

A new model for fluid flow of a liquid through a hollow fiber filtration cluster has been set forth and numerically implemented. The key feature of the approach is modeling of the intrinsic permeability of the individual fibers. This fiber permeability, in addition to the geometrically based permeability of the cluster, gives rise to a situation characterized by two scales of permeability. The fluid mechanic problem is governed by the Navier-Stokes equations supplemented by pressure loss terms for the fiber wall given by the Darcy porous medium model. A number of independent parameters were investigated: the Reynolds number, the magnitude of the permeability, the geometric arrangement of the fibers, the center-to-center separation distances of the fibers, the outer to inner diameter ratio of each fiber, and the boundary condition at the inner surface of a fiber. It was found that for reasonable values of the prescribed intrinsic permeability, significant reductions in the pressure drop occur. Also considerably affected are the patterns of fluid flow within the fiber cluster. It was found that the fiber permeabilities have a major impact on the pressure drop results, suggesting predictions based on the impermeable fibers are, for the most part, in error.