Membranes binary countercurrent flow

Calculation of the degree of separation of a binary mixture in a membrane module for cocurrent or countercurrent flow patterns involves the numerical solution of a system of two nonlinear, coupled, ordinary differential equations (Walawender and Stem, 1972). For a given cut, the best separation is achieved with countercurrent flow, followed by crossflow, cocurrent flow, and perfect mixing, in that order. The crossflow case is considered to be a good, conservative estimate of module membrane performance (Seader and Henley, 2006). 

Countercurrent and Cocurrent Plug Flows. The model equations for these flow patterns cannot be solved analytically. Oishi and coworkers first derived the general model eqnstions for a binary-component system with porous media.19 Walawenderand Stem,16 Blaisdell and Kammermeyer,1 and Pan and Habgood17 later reported solutions for similar membrane separators. The cocurrent-counteicurrent combiner inu flow pattern also lies been studied by Pen ned Habgood.17... 

Consider a countercurrent gas permeator as well as a cocurrent gas permeator for the separation of a particular binary gas mixture at feed pressure Pf and permeate pressure Pp. Assume that there are no pressure drops on either the feed side or the permeate side. If the pressure ratio y 0, show that the separation achieved would be independent of the flow pattern. Assume a symmetric membrane with constant values of permeances. Will the situation be any different if we used the crossflow permeator of Section 7.2.1.1 ... 

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