Modelling reactive distillation

R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5203transformed variables presented by Barbosa andDoherty (1987b). In order to save calculation time, theorder of the model was reduced using an orthogonalcollocation method. Some calculations were done for anideal quaternary system. The reduced order model wasveri"ed against a `rigorousa model and a reasonablygood match was found. No extensive numerical dynamicdata are presented.Grosser, Doherty and Malone (1987) use a dynamicmodel based on the following assumptions: the mixture reaches reaction and phase equilibriuminstantaneously on each tray; the solutions are dilute (thus the temperature changecan be ignored); the liquid hold-up is constant on each tray (the vaporhold-up is ignored); constant molar over#ow (modi"ed somewhat) relatesthe #ows from stage to stage.They study the separation by RD of close-boiling mixturessuch as mixtures of xylenes, C4 hydrocarbons, andchlorobenzenes. They report that RD is an attractivealternative to conventional distillation when the relativevolatility is less than 1.06. RD of close-boiling mixtureshas also been studied by Terrill, Sylvestre and Doherty(1985) who suggest that it is possible to separate m- andp-xylene using sodium in a column with very few equilibriumstages. Cleary and Doherty (1985) provided experimentalsupport for this conclusion.Kumar and Daoutidis (1999) presented a comprehensivedynamic EQ stage model of an ethylene glycol RDcolumn. They compare a model that includes vaporphasebalances to a more conventional model that ignoresthe vapor hold-up and suggest that it is important toinclude the vapor phase in order to more accuratelymodel the process dynamics. The major thrust of thiswork is the design of a control system that performs wellwith stability in the high-purity region.Moe, Hauan, Lien and Hertzberg (1995) discuss possiblenumerical problems when developing dynamicmodels of RD based on phase and chemical equilibriumprinciples.3.5. Batch reactive distillationBatch reactive distillation, an inherently unsteadystateprocess has been studied by Corrigan and Ferris(1969), Egly, Ruby and Seid (1979), Cuille and Reklaitis(1986), Reuter, Wozny and Jeromin (1989), Albet, LeLann, Joulia and Koehret (1991); Machiettoand Mujtaba (1992); Mujtaba and Machietto (1992);S+rensen and Skogestad (1992, 1994); S+rensen,Machietto, Stuart and Skogestad (1996); Patlasov (1996);Bollyn and Wright (1998); Xu and Dudukovic (1999) andWajge and Reklaitis (1999), and Venimadhavan, Maloneand Doherty (1999b).Corrigan and Ferris (1969) provided a limited quantityof data for the methanol acetic acid esteri"cation reactionin an Oldershaw column. The paper does not includeany attempt at modelling the process. The modelsof Albet et al. (1991) and of Mujtaba and Machietto(1992) allow for changes in the component hold-ups butassume constant liquid molar hold-ups. These modelsalso use steady-state energy balances. Reuter, Woznyand Jeromin (1989) develop the most complete EQstage model of batch RD that includes the hold-upof both phases and process controller equations. Arelaxation method is used to solve the unsteadystatemodel equations while Newton's method is used tosolve the steady-state equations at each time step. A comparisonwith some dynamic product composition datafor a transesteri"cation plant shows good agreementwith the calculated product composition. Cuille andReklaitis (1986) neglect the vapor-phase hold-up, assumethat the volumetric hold-up on each stage is constant,and assume pressure drops and stage e$ciencies to beconstant. The DAE system was solved using the LSODInumerical integration routine. Egly et al. (1979),Machietto and Mujtaba (1992), and Mujtaba andMachietto (1992) look at the optimal design and operationof batch RD.S+rensen and Skogestad (1992, 1994) and S+rensenet al. (1996) consider the controllability of batch RD.Bollyn and Wright (1998) develop a model of a batch RDprocess for the synthesis of the ethyl ester of pentenoicacid. In this process the reaction occurs only in thereboiler and not at all in the column itself. Thus, themodel is somewhat simpler than other dynamic modelsthat are discussed here. Xu and Dudukovic (1999) developeda dynamic model for semi-batch photo RD. TheDAE equations that formed their model were solvedusing the LSODI routine. Wajge and Reklaitis (1999)describe in detail a package called RDBOPT for thedesign of operation policies for reactive batch distillation.The model is essentially the same as that used by Cuilleand Reklaitis (1986), but the DAE system of model equationsis solved using the DASPK solver.Venimadhavan et al. (1999b) examined a novel distillatepolicy and propose a new re#ux policy for equimolarreactions. For the special case of butyl acetate productionthe new policies lead to complete conversion of thereactants and high-purity products that are unobtainableby conventional methods.3.6. Primarily experimental papersIn addition to the papers cited above, there are someothers whose main thrust is on providing experimentaldata, and in which the modelling activity provides onlya supporting role.Carra et al. (1979b) and Carra, Morbidelli,Santacesaria & Buzzi (1979a) studied the synthesis of