Membrane Separations Technology: Single-Stage, Multistage, and Differential Permeation

Appendix 4: Multistage Membrane Separations

The calculations here are confined to two components, the key components, designated i and j (with the components in general designated i).

The feed composition, membrane permeability, and operating pressure levels are assigned as before, and a trial-and-error bubble-point type calculation performed for V/F = 0. This results in a value for V ?, which is not directly required for determining the degree of separation, other than being incorporated into the K-values but would be necessary in further determining membrane areal requirements. Thus, the bubble-point type calculation simultaneously establishes the values for K i and K j, which are used in the separation calculations.

The number of stages n is in turn to be assigned for the rectifying section and the number of stages m for the stripping section (the feed-stream location is n + 1 = m + 1).

RECTIFYING SECTION

The trial-and-error calculation for the rectifying section is made dependent on L/ V, for both components i and j, in terms of the absorbing factors A i and A j. The calculations may be represented as follows, more or less in spreadsheet notation, in terms of component i only:


Now distinguishing between components i and j:


It is required, as a check, that


If the degree of convergence to unity is not satisfactory, then the trial value for L/D or L/V can be adjusted; in fact,...

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