journal of MEMBRANE SCIENCE ELSEVIER Journal of Membrane Science 125 (1997) 275-291 Mathematical modeling of gas separation permeators - for radial crossflow, countercurrent, and cocurrent hollow fiber membrane modules Mathews J. Thundyil, William J. Koros * Department of Chemical Engineering, The Universi~ of Texas at Austin, Austin, TX 78712, USA Received 5 February 1996; revised 22 July 1996; accepted 22 July 1996 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 compositions 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. Incorpora- tion 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. Keywords: Gas separation; Membrane module modeling; Cocurrent; Countercurrent; Radial crossflow; Succession of states; Finite element method I. Introduction The separation of gases by means of permselec- tive membranes is an important unit operation in the industrial separation of gases. Membrane based sepa- rations are important in natural gas processing (carbon dioxide enrichment in enhanced oil recovery, natural gas sweetening), nitrogen production from * Corresponding author. air, hydrogen streams in refinery and petrochemical process streams as well as in ammonia and methanol process streams [1,2] among others. The success of membrane based processes for separation is depen- dent on two factors: the discovery of high intrinsic permeability and selectivity membrane materials; and providing appropriate engineering tools to select ap- propriate membrane configurations and flow pat- terns. Commercially, gas separation permeators are op- 0376-7388/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved. PII S0376-7388(96)002 1 8-9