TABLE OF CONTENTS A multistage membrane operation can be represented in similar fashion to a multistage, plate-to-plate, stepwise or stagewise distillation column or operation, although at first glance this may not appear readily evident. Moreover, by viewing and phrasing membrane separations in the terms used for distillation, the membrane separation derivations and calculations can be similarly systematized and similarly simplified. This requires the modification and utilization of the K-value concept as developed in the previous chapter, whereby the techniques for vapor-liquid flash vaporization calculations are adapted to single-stage membrane separations. The arguments are further pursued in this chapter, beginning with a review of multistage distillation.
A multistage distillation column can be represented schematically as diagrammed in Figure 4.1. The complete column is shown, with a condenser to produce external liquid reflux at the top and a reboiler at the bottom to produce an external recycle vapor phase. In the customary parlance, the section above the feed plate or feed point is called the rectifying (or absorbing) section, and the section below is called the stripping section. The usual symbolism is to denote the vapor phase or its molar flow rate by V or 
, and the liquid phase or its molar flow rate by L or 
, for the rectifying and stripping sections, respectively.
In sum, distillation is a countercurrent vapor-liquid operation with the external reflux of a condensed liquid...
