Mathematical modeling of gas separation permeators — for radial crossflow, countercurrent, and cocurrent hollow fiber membrane modules

Abstract

A new approach to solve the mass transfer problem posed by the permeation process in a hollow fiber permeator is presented and analyzed. The algorithm models the separation offered for a membrane module, for given gas conditions, simulating the permeate and residue composition and the stage cut. The advantage of the ‘succession of states’ approach utilized here is the option of retroactive incorporation of more complex interactions such as permeate pressure buildup, a pressure, composition and temperature dependent permeability. The two dimensional mass transfer in a radial crossflow permeator has been qualitatively discussed in the past, but it has not been modeled in the literature. The countercurrent, cocurrent and crossflow configurations (all single dimensional mass transfer cases) for gas separation have been modeled in literature primarily by numerical integration of the differential equations over the relevant boundary conditions. Incorporation of nonlinearities such as pressure and permeability variations complicate the mathematics considerably for a single dimension, and make their solution almost impossible in two dimensions. This paper proposes an algorithm that simplifies the understanding of the problem posed, in terms of practical parameters (such as stage cut), and analyses the three flow patterns (radial crossflow, countercurrent, and cocurrent) in detail.