Modelling reactive distillation

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5210 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229di!usivity method for their mass transfer model. Unlessthe equilibrium constant has some unconventional definition,the reaction equation given in their "rst paperrepresents an irreversible reaction. The system of di!erentialequations that constitute their model was solvednumerically. Their second paper includes parametricstudies that show how conversion changes as a functionof catalyst #ow rate, pressure, feed composition, re#uxratio, reboil ratio, feed #ow rates, and feed position.In 1990 ASPEN Technology Inc. introduced theRATEFRAC model for rate-based multicomponent separationmodelling (Sivasubramanian & Boston, 1990).RATEFRAC appears to be based on the NEQ model ofKrishnamurthy and Taylor (1985) with the addition ofequations to account for the e!ect of reaction on masstransfer, and chemical equilibrium constraints (if needed).Zheng and Xu (1992b) have used an NEQ model tosimulate catalytic distillation operations in a packed columnwith bag-type porous catalyst. Theirs is a pseudohomogeneousmodel very similar to that describedabove. Vapor}liquid mass transfer is modelled using theMS equations. However, it is not completely clear howthe reaction is modelled. Elsewhere in the paper it isstated that liquid}solid mass transfer coe$cients in thecatalyst bed are computed from a correlation derived intheir "rst paper (Zheng & Xu, 1992a). Yet no equationsor terms for mass transfer from the liquid to thecatalyst appear anywhere else in the paper. It is possiblethat the reaction is treated pseudo-homogeneously wheree!ects of reaction on mass transfer (and the e!ectsof mass transfer on reaction) in the catalyst are lumpedinto the bulk liquid reaction term. Thermodynamic propertiesfor the liquid-phase are described with theUNIFAC model and the virial equation is used for thevapor phase. The resulting set of algebraic equations wassolved using Newton's method. They model productionof MTBE and provide numerically calculated concentration,temperature and #ux pro"les. Only for the temperaturepro"le is there any comparison with experimentaldata.Zhu and Shen (1995) discussed the modi"cation of theNEQ model of Krishnamurthy and Taylor (1985) tohandle RD. Few precise details are provided, however,and it is impossible to be sure how the presence ofreaction(s) modi"es any of the NEQ model equations.Simulation results appear to show reasonable agreementwith temperature and liquid composition pro"les measuredfor the esteri"cation of ethanol and acetic acidcarried out in an Oldershaw column.Kreul, Gorak and Barton (1999a) used an NEQ modelof homogeneous RD and, via a series of case studies,studied the importance of various model simpli"cations.They found little di!erence between the full MS descriptionof multicomponent mass transfer and the simplere!ective di!usivity models. However, they also concludethat there can be signi"cant di!erences between EQ andNEQ models, and that the additional e!ort of the morecomplicated NEQ approach is justi"ed.Baur et al. (1999) have compared the EQ and the NEQmodels for the MTBE process. They underlined somecounter-intuitive features of RD processes. For example,for a methanol feed location yielding a low-conversionsteady-state, the introduction of mass transfer resistance(i.e. use of the NEQ model), leads to a conversion higherthan that predicted by the EQ model; see Fig. 20 (b). Theintroduction of a mass transfer resistance alleviatesa `bad situationa and has the e!ect of improving conversion.Lee and Dudukovic (1998) described an NEQ modelfor homogeneous RD in tray columns. The Maxwell}Stefanequations are used to describe interphasetransport, with the AIChE correlations used for the binary(Maxwell}Stefan) mass transfer coe$cients. Newton'smethod and homotopy continuation are used tosolve the model equations. A close agreement betweenthe predictions of EQ and NEQ models was found onlywhen the tray e$ciency could be correctly predicted forthe EQ model. In a subsequent paper Lee andDudukovic (1999) extend the dynamic NEQ model ofKooijman and Taylor (1995) to cover the dynamic operationof RD in tray columns. The DAE equations weresolved by use of an implicit Euler method combined withhomotopy-continuation. Murphree e$ciencies calculatedfrom the results of a simulation of the productionof ethyl acetate were not constant with time.Kenig et al. (1999) described a software package for thesynthesis and design of RD operations. The package isone of the results of a major research program on RDsupported by the European Union under the BRITE-EURAM program. The designer part of the package isbased on an NEQ model that accounts for possiblereaction in the mass transfer "lm and includes a catalyste$ciency calculation to account for di!usion and reactionin the catalyst. A large number of correlations for themass transfer coe$cients in di!erent types of columninternal are available in the program. Stage hydrodynamicmodels included in the package are: completely mixed vapor and liquid; completely mixed liquid, plug-#ow vapor; mixed pool model for the liquid-phase; eddy di!usion model for the liquid-phase.No mathematical details of the model are provided in thepaper. The model equations are solved using Newton'smethod. The program is illustrated by modelling theMTBE process and a comparison with some experimentaldata (numerical values not given) shows excellentagreement with the calculated pro"les.Schenk, Gani, Bogle and Pistikopolous (1999) describein considerable detail a hybrid-modelling environment inwhich distillation-type processes can be simulated usinga combination of steady-state, dynamic, EQ stage,
R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5211and/or rate-based models. Two of the three examplesthat illustrate their paper concern RD (ethyl acetateproduction and an MTBE column). The models arecompared to experimental data of Suzuki et al. (1971).The agreement between the pro"les obtained with therate-based model and the data is very encouraging.The authors do, however, demonstrate a sensitivity of thecomputed pro"les to the activity coe$cient model used.A particularly novel feature of their paper is the introductionof Gibbs energy pro"les in the column.In an interesting experimental study Sundmacher andHo!mann (1995) obtained oscillatory behaviour ofa packed laboratory-scale distillation column. The oscillationswere encountered in the MTBE process as well asin the distillation of non-reactive binary mixtures. Itappears likely that these oscillations originate from thehydrodynamics in their packed RD column. The authorsuse an NEQ model for non-reactive distillation thatcompletely neglects mass transfer in the liquid-phase and,by extension, any e!ects due to reaction. The modelequations were solved by a relaxation method, the resultsused to demonstrate multiple steady-states. The NEQmodel does not provide an explanation for the observedoscillations.Sundmacher and Ho!mann (1996) presented a detailedNEQ stage model for vapor}liquid}porous catalystsystems. The model di!ers from that described aboveonly in that the phases are assumed to be in thermalequilibrium with each other. This means that sensibleheat transfer between phases is ignored and that theoverall energy balance replaces the individual phase balances.Mass transfer in the vapor and liquid-phases ismodelled using an explicit approximate solution of theMaxwell}Stefan equations (see Chapter 8 of Taylor andKrishna (1993) for details). The system of equations issolved via a pseudo-relaxation method using the DAEsolver LIMEX cited earlier. The model is used to simulatesome data obtained on a laboratory-scale MTBEcolumn. One of the conclusions from this study is that itis absolutely necessary to account for di!usion and reactionin the porous catalyst (modelled in this paper usingthe catalyst e!ectiveness factor approach developed inother papers from these authors and discussed above).The in#uence of side reactions on RD processes hasbeen investigated by Schoenmakers (1982), Sundmacher,Ho!mann and co-workers (Sundmacher, Uhde &Ho!mann, 1999; Oost, Sundmacher & Ho!mann, 1995;Oost & Ho!mann, 1996). Sundmacher, Uhde and Hoffmann(1999) used both EQ stage (with Murphree e$ciency)and NEQ models to simulate the MTBE andTAME processes. The reactions were handled using bothquasi-homogeneous and heterogeneous methods. Simulationresults were compared to experimental data obtainedin two laboratory-scale columns. A detailed NEQmodel was needed to describe the TAME process, butboth NEQ and the EQ stage (with an e$ciency of 0.8)model could adequately represent the MTBE process. Inthe latter case it was necessary to account for the catalyste!ectiveness along the packing. The authors concludethat it is necessary to account for the side reactions in RDprocess design.Bart and LandschuK tzer (1996) studied the esteri"cationreaction of acetic acid and propanol to propyl acetate,catalysed by an exchange resin in a packed column. Masstransfer across the vapor}liquid interface and betweenliquid bulk and catalyst surface is described with theMaxwell}Stefan equations. The reaction is assumed totake place only at the catalyst surface and is modelledwith an Eley}Rideal kinetic expression. Their model accountsfor axial dispersion along the column, the dispersioncoe$cient being obtained from a Bodensteinrelation that was determined experimentally for theirmodel column.Yu, Zhou and Tan (1997) developed a steady-stateNEQ model that takes into account mass transfer fromthe bulk liquid to the catalyst. Separate rate equationsare written for the vapor}liquid and liquid}solid interfaces.Empirical methods are used for estimating theliquid}solid (and other) phase mass transfer coe$cients.Di!usion within the catalyst phase is ignored. The systemof non-linear equations is solved by a Newton homotopymethod. The solitary numerical example that accompaniesthe paper concerns the reactive stripping processfor the production of Bisphenol-A.Ng, Rempel and their co-workers at the University ofWaterloo (Huang, Podrebarac, Ng & Rempel, 1998a;Huang, Yang, Ng & Rempel, 1998b; Podrebarac et al.,1998a,b) have carried out an in-depth study of the aldolcondensation of acetone to diacetone alcohol (DAA) andmesityl oxide. Experiments were carried out in a pilotscalecolumn with 6 mm Intalox saddles and a reactivesection containing bale-type packing. It was found thatthe DAA production rate was controlled by mass transfer.DAA selectivity was in#uenced by the liquid distribution.Correlations for the solid}liquid mass transfercoe$cients and for the overall mass transfer coe$cientsfor the vapor}liquid transport were developed by Huanget al. (1998a). Their papers also include the developmentof an NEQ model. The model appears to be derived fromthe Krishnamurthy}Taylor model for conventional distillation,although it is interesting to note that the materialbalances are expressed in terms of the mass #ows andmass fractions and include a separate term for the rate ofvaporisation caused by the heat of reaction. Mass transferbetween vapor and liquid-phases is described bya single overall mass transfer coe$cient for each species,a correlation for which was derived for their column.They assume that the rate of reaction is equal to the rateof mass transfer to the catalyst surface and correlationsfor the liquid}solid mass transfer coe$cients were alsodeveloped. Mass transfer in the non-reactive sections wasmodelled using a "lm model for each phase; mass transfer
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