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

Appendix 7: Countercurrent Flow with Recycle

The preliminaries more or less follow the spreadsheet calculations as presented in Appendix 4. The same feed composition is used, and the same dimensionless permeability and reject and permeate pressures (plus membrane thickness) are given.

The calculations are therefore the same up to and including the bubble-point type determination for the feedstream F, which also establishes the (same) value for the permeate flux V ? (and the corresponding K-values).

However, from this point on, a degree of separation is assigned in terms first of ( x D), and then (x B)., along with specifying the external recycle ratios L/D and V/B, and the necessary membrane areas are determined by analytic integration, for both the rectifying sections and stripping sections.

At the end of the dimensionless area calculation, absolute permeability and pressure values are assigned in terms of a conversion (or divisor factor) for a specified membrane thickness, also as in Appendix 4. The area so calculated in cm is placed on the basis of 1 gram-mole per second of feedstream.

RECTIFYING SECTION

The derived integration in terms of component i is


where y varies from its value at the feed location (y = Kx F) to its final value x D. The area A 2 is designated the area for the rectification section.

Integration is from the feed location toward the more-permeable product end, designated D, with A viewed as positive.

The value of V

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