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Separation Process Engineering: Includes Mass Transfer Analysis, Third Edition by Phillip C. Wankat

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17.7.1 Binary Cross-Flow Permeation

Spiral-wound membrane units are very close to cross-flow operation with an unmixed permeate (Figure 17-18A). We can approximate this cross-flow system as a series of N well-mixed stages as shown in Figure 17-19A. Since we know how to solve each of the well-mixed stages in Figure 17-19A, we can add all the results to find the behavior of the cross-flow system. Since a complicated analytical solution exists for binary cross-flow gas permeation (Geankoplis, 2003; Hwang and Kammermeyer, 1984), we can check the accuracy of our numerical solution.

For a design problem (cut is specified and membrane area is unknown) solution is easiest if we make the permeate flow rate Fp,j for each small well-mixed stage the same ...

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