Modelling reactive distillation

5194 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229Fig. 16. Counter-current vapor}liquid}catalyst contacting in trayed columns. (a) catalyst in envelopes inside downcomers, (b) tray contacting withcatalyst placed in wire gauze envelopes near the liquid exit from the downcomers and (C) alternating packed layers of catalyst and trays.the presence of the catalyst envelopes. Therefore, standardtray design procedures (Lockett, 1986; Stichlmair& Fair, 1998) can be applied without major modi"cation.Care must be exercised, however, in making a properestimation of the liquid}catalyst contact time, which determinesthe extent of reaction on the stages.2. Thermodynamics of reactive distillationAn introductory review of RD thermodynamics wasprovided by Frey and Stichlmair (1999a) (see, alternatively,Stichlmair & Fair, 1998).The classical thermodynamic problem of determiningthe equilibrium conditions of multiple phases in equilibriumwith each other is addressed in standard texts (see,e.g., Walas, 1985; Sandler, 1999) and not considered here.The equally important, and computationally more di$cult,problem of "nding the composition of a mixture inchemical equilibrium has also been well studied. Readersare referred to the text of Smith and Missen (1982). Thecombined problem of determining the equilibrium pointsin a multiphase mixture in the presence of equilibriumchemical reactions has been the subject of a recent literaturereview by Seider and Widagdo (1996). Two morerecent developments are noted below.Perez-Cisneros, Gani & Michelsen (1997a) discuss aninteresting approach to the phase and chemical equilibriumproblem. Their method uses chemical &elements'rather than the actual components. The chemical elementsare the molecule parts that remain invariant duringthe reaction. The actual molecules are formed fromdi!erent combinations of elements. A bene"t of this approachis that the chemical and physical equilibriumproblem in the reactive mixture is identical to a strictlyphysical equilibrium model.McDonald and Floudas (1997) present an algorithmthat is theoretically guaranteed to "nd the global equilibriumsolution, and illustrate GLOPEQ, a computer codethat implements their algorithm for cases where theliquid-phase can be described by a Gibbs excess energymodel.The e!ect that equilibrium chemical reactions haveon two-phase systems has been considered at lengthby Doherty and coworkers (Barbosa & Doherty, 1987a,b, 1988a}d, 1990; Doherty, 1990; Ung & Doherty,1995a}e).The "rst paper by Barbosa and Doherty (1987a) considersthe in#uence of a single reversible chemical reactionon vapor}liquid equilibria. The second paper(Barbosa & Doherty, 1987b) introduces a set of transformedcomposition variables that are particularly usefulin the construction of thermodynamic diagrams for reactingmixtures. For a system in which the componentstake part in either of the following reactionsA#B C, (1)A#B C#D (2)the following transformation is de"ned:Z Q z /ν !z /ν ν !ν z . (3)