Liquid distribution and redistribution in packed columns-I Theoretical

Abstract

When liquid is uniformly distributed at the top of a packed column it is found that there is a preferential flow to the wall, and early theoretical work has suggested that the observed radial velocity is proportional to the radial gradient of axial velocity. A set of consistent boundary conditions has not been found. In this paper the experimental observation of preferential liquid flow is interpreted as a difference in permeability between the wall and bulk region of packing, and the existence of a potential for liquid redistribution is inferred from an examination of experimental work on two-phase flow in porous media, and of the internal consistency of the early relation between radial velocity and the radial gradient of axial velocity. The existence of a potential for liquid redistribution, and a difference in permeability between the wall and bulk regions are shown to lead to a differential equation describing liquid distribution in the packing, defined by consistent and well-posed boundary conditions that are determined from the physical analysis.The solution to the partial differential equation describing redistribution from an initial axisymmetric distribution is given.