Modelling reactive distillation

R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5217Fig. 30. Column pro"les in RD design (Doherty method).The attainable region approach to reactor networkfeasibility is based on geometric properties and has beenstudied in depth mainly by Glasser, Hildebrandt, andtheir co-workers (see, for example, Glasser & Hildebrandt,1997; Feinberg & Hildebrandt, 1997; Feinberg,1999). McGregor, Glasser & Hildebrandt (1997) andNisoli, Malone and Doherty (1997) apply the attainableregion approach in order to develop a systematic approachto identifying the feasible compositions that canbe obtained in RD processes. Once again, the Damkohlernumber emerges as the important parameter.Hauan and co-workers (see Hauan, 1998; Hauan& Lien, 1996, 1998; Hauan, Westerberg & Lien, 2000b)have developed what they call a phenomena-basedmethod for the analysis and design of reactive separationprocesses. Within this framework the change in the compositionof any particular phase is given by the vectorequationdx"mix#sep#rx (35)dtwhere x is the composition of the phase in question, andmix, sep, and rx are vectors that represent the compositionchanges due to mixing, separation, and reaction,respectively. For these vectors Hauan et al. (2000b) writemix"M(x F !x), (36)rx"R(ν!xν), (37)sep"[S](x!y), (38)where M is a scalar equal to the relative amounts ofmaterial being mixed, x is the current composition andx F is the feed composition, and R is a scalar that dependson such things as catalyst activity, hold-up, and temperature.[S] is matrix of component speci"c mass transferrates. If the phases are assumed to be in equilibrium then[S] reduces to a simple scalar. The direction of thesecombined vectors indicates the feasibility of a particularprocess; their length is a measure of the process e$ciency.Hauan and Lien (1998) illustrated their methodologywith an analysis of the MTBE process.More interestingly, this formulation admits the possibility,so far unexplored, of using a properly formulatedmodel of mass transfer in multicomponent systems asdiscussed above.A "xed point exists when the mix, sep, and rx vectorsnullify each other.0"mix#sep#rx. (39)When the reaction and separation vectors have zeromagnitude then the "xed point is an equilibrium point.A kinetic "xed point (azeotrope) arises when all threevectors have non-zero magnitudes, but still nullify eachother. The location of these kinetic "xed points hasa direct in#uence on the product compositions that canbe realised in an RD column (see, also, Mahajani, 1999a).Hauan et al. (2000b) have provided a comprehensiveanalysis of the kinds of "xed point that can arise fromcancellation of di!erent combinations of these vectors.They also introduce the reaction di!erence point as the