Hollow fiber gas permeator with countercurrent or cocurrent flow: series solutions

The problems in the numerical solution of boundary value problems encountered in hollow fiber binary gas permeatbrs having cocurrent or countercurrent permeate flow with axial pressure drop inside the fiber bore are discussed. A series solution technique is developed to express each product composition and the pressure ratio as a power series in terms of a dimensionless membrane area for shell side constant-pressure feed flow. Cocurrent or countercurrent rating or design problems require the solution of elther one algebraic equation, two coupled algebraic equations, or three coupled algebraic equations to determine the unknown quantities of interest. Calculated product and reject compositions, stage cuts, and closed-end pressure ratios compare quite well with those from numerical solutions for practically useful low to moderate cuts over a wide range of parameters. Cocurrent rating calculations requiring solution of only one algebraic equation are recommended for shortcut procedures since flow pattern effects are significant but not large.