Membrane Gas Separation Selectivity a and the Pressure Ratio

Illustration 8.8 Membrane Gas Separation Selectivity a and the Pressure Ratio 0 

It has previously been indicated (see Table 8.2) that membrane-based gas separation processes, while still of considerable complexity, can be modeled at the level of ODEs. This is because the principal transport resistance resides within the membrane itself and because the mass balances need therefore be concerned only with concentration changes in the direction of flow. These equations, however, must be supplemented by force balances to take account of the nonlinear pressure drop associated with permeation processes. The resulting set of ODEs will generally have to be solved numerically. We do not take up this problem here but instead acquaint the reader with two important system parameters that provide useful information for a preliminary assessment of these operations. These parameters are the pressure ratio ( ) and the membrane selectivity a. 

The pressure ratio is an operational parameter and is defined as the ratio of feed pressure to that prevailing on the permeate side, i.e.. 

Selectivity a, on the other hand, is a property of the membrane and deals with the relation between compositions, usually expressed as mole fractions i/i, on either side of the barrier. Its definition, at least in its form, is identical to that of relative volatility, which was seen in coimection with vapor-liquid equilibria (see Equation 6.20a). For a two-component system, it is given by the relation 

We start by noting that gas permeahon is driven by a concentration or partial pressure difference across the membrane, i.e., it is a process based on diffusion, and not on D Arcy-type bulk flow. For diffusion to take place, the feed partial pressure must be higher than that on the permeate side i.e., we must have 

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