Series Solutions for a Gas Permeator with Countercurrent and Cocurrent Flow

The difficulties In the numerical solution of differential equations for countercurrent binary gas permeatorsare discussed. For a permeator with countercurrent or cocurrent flow of a binary gas mixture without axial pressure drops, a series solution technique Is introduced to express each product composition as a power series in terms of a dimensionless membrane area. For countercurrent flow over a wide range of parameters, computed product compositions and fractions of the feed mixture permeating the membranes compare very well with those from a numerical solution of the governing equations for small to moderate permeate fractions in the range considered practical. For ideal separation factors of 2, 5, 10, 25, and 80, significant deviations occur at fractions larger than 0.7, 0.5, 0.33, 0.25, and 0.15, respectively, at a pressure ratio of around 0.1 and a more-permeable-component feed mole fraction around 0.2. Cocurrent flow predictions are excellent at somewhat lower permeate fractions. Preliminary countercurrent permeator design or rating problems will require solution of only one or two cubic equations.