OVERVIEW

In many respects, single-stage and multistage membrane separations can be viewed as analogous to steady-state flash separations and distillations, as derived and calculated for vapor-liquid systems. By a rearrangement of the membrane permeation rate or flux equation, the result is adaptable to the form used for vapor-liquid phase equilibrium, expressed as the K-value or equilibrium vaporization ratio. Therefore, in the usual notation, assuming perfect mixing in the respective membrane phases involved, y _i = K _ix _i, where K _i is the ratio of the mole fraction of a component in the permeate phase with respect to the mole fraction in the reject or retentate phase. This derivational sequence, detailed in Chapter 3, is basically connected with the idea of permeability in its several embodiments or units and the corresponding rate or flux relationships, which constitute the subject of this chapter.

Both the permeate and reject phases, for the most part, are considered gaseous for the baseline derivations and calculations, but the methodology is equally applicable to gas-liquid or vapor-liquid systems, as in pervapora-tion, and to miscible liquid-liquid systems and solutions of dissolved solids, even to colloids, suspensions, and emulsions. All that is required is a mathematical conversion of permeability units and values, along with component concentrations, to be consistent with the gas-phase format, which is expressed in terms of mole fractions and their partial-pressure difference as the driving force for permeation.

To continue, for liquid-liquid phase equilibria per se, we may speak more...