Membrane permeation relationships

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 generally of a distribution coefficient (also denotable as K or fC,) for relating the component mole fraction composition in one liquid phase to that in the other. Albeit concentrations constitute the usual mode of expression for liquids, concentrations are transformable to mole fractions via the equation of state as applied to a liquid or a more-dense single phase. However, the membrane permeation rate or flux balance modifies into the same format as for gaseous systems to yield the fC-value form 

The single-stage membrane unit becomes equivalent to a so-called flash vaporization. The flash vaporization calculation itself is straightforward, with the vapor and liquid phases assumed at equilibrium, as presented in a number of references. The limits correspond to the dewpoint and bubble-point calculations for vapor-liquid equilibrium, which are special or limiting cases for the flash vaporization calculation. The object, therefore, is to adapt the membrane calculation to the techniques for the flash vaporization calculation and thereby take advantage of the relative simplicity of the latter, as is demonstrated in Chapter 3. 

Other procedures and calculation techniques have been developed for both stagewise and differential permeation, as are presented by S.-T. Hwang and K. Kammermeyer, but these are not pursued here, inasmuch as the analogy is to be made specific to vapor-liquid mass transfer unit operations. In this way, the conventions and techniques already developed for mass transfer operations can be more readily utilized. Note also that the symbols and terminology used for membrane permeation have evolved through the years and perforce vary from one author to another. 

In Process Design and Optimization, R. Rautenbach explores the uses of cascade operations, without and with reflux, and of operations as a continuum. These and other embodiments, and their modes of operation and calculation, are detailed in subsequent chapters. 

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Membrane Permeation Relationships I 57 Effect of Compressibility Factor... 

Table A2.1 Excel Spreadsheet Designators and Formulas for Membrane Permeation Relationship Calculations for Example 2.1...

Membrane Permeation Relationships I 269 Table A2.8 Membrane Permeation Relationships— Example 2.4... 

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