Tubular and hollow-fiber modules can be arranged to have approximately countercurrent flow patterns (Figure 17-18c). Since these flow patterns are an advantage in equilibrium-staged systems, we would expect that they might be an advantage in membrane separations also. Example 17-11 showed that this is true. The staged model for countercurrent flow is shown in Figure 17-19c. Coker et al. (1998) present a solution method for a staged model for countercurrent, multicomponent permeation when the membrane area is known but the cut is unknown, and show that N = 100 is usually sufficient.
Developing a design method for a binary, countercurrent permeator is challenging. Typically the values of Fin, yr,0, pp, pr, PA