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

With regard to chemically reacting systems, what is called a membrane reactor can selectively remove one or another of the products, shifting the conversion to the right. As presented in Chapter 5, a feed-reject crossflow with point permeation is the preferable embodiment, with the effects varying with position (that is, area) along the membrane.
Consider the general case of a chemical reaction bimolecular in both directions, which can be represented by
where the capital letters denote the components involved. The reacting system can be homogeneous or catalyzed, that is to say, heterogeneous. Furthermore, for convenience, let the conversion be maintained at a chemical equilibrium, which shifts to the right as one or another of the products is selectively removed. In other words, the rate of removal of the component is slower than the rate of reaction and hence controlling.
Removal of both products from the confines of the reacting system also shifts the conversion to the right, even though the removal of only one component, say, component S, first is considered.
Generally speaking, the reaction equilibrium constant K can be viewed as
where ? represents the absolute activities, to be further specified. In terms of the reaction rate constant k 1 for the forward reaction and k 2 for the reverse reaction, the convention is K = k 1/k 2. For gaseous systems, partial pressures constitute the convention used, and the reaction equilibrium constant is subscripted K. In liquid...