Modelling reactive distillation

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5220 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229also tends to make the value of such calculationsquestionable. Whether or not the experimental workand calculation time * for a detailed computation ofsuch a process in a system with four or more components* can be justi"ed or not will then ultimatelydepend upon the economic importance of theproducts.There remains more than a grain of truth to these remarkseven today, when the computer, which wouldmake its mark in chemical engineering soon after thesewords were written, has largely rendered moot the issueof computational cost.There are a variety of models now available in theliterature for screening, analysis, design and optimisationof RD columns. Each model has its place in the processdevelopment cycle. Residue curve maps are invaluablefor initial screening and #owsheet development. EQmodels have their place for preliminary designs. However,recent NEQ modelling works have exposed thelimitations of EQ models for "nal design and for thedevelopment of control strategies. NEQ models havebeen used for commercial RD plant design and simulation.Column hardware choice can have a signi"cant in#uenceon the conversion and selectivity; such aspects canbe properly described only by the NEQ cell model. It isinsu$ciently realised in the literature that say for trayRD columns, the tray design can be deliberately chosento improve conversion and selectivity. Even less appreciatedis the fact that the design methodology for RD traycolumns is fundamentally di!erent from that of conventionaltrays. Liquid residence time and residence timedistributions are more important in RD. The froth regimeis to be preferred to the spray regime for RDapplications; this is opposite to the design wisdom normallyadopted for conventional distillation. Though thephenomena of MSS has received considerable attentionin the literature, it is possible that not all of the steadystatescan be realised in practice due to hydraulicaspects, which are taken into account in the NEQmodel. For relatively fast reactions, it is essential toproperly model intra-particle di!usion e!ects. Pseudohomogeneousreaction models may be inadequate forfast reactions. RD columns using dumped (random)packings are susceptible to maldistribution and there isa case to be made for choosing regular structured packingssuch as that shown in Fig. 13. For proper descriptionof the column dynamics, it is essential to adopt the NEQmodel.Though sophisticated NEQ design models are availablealready, detailed information on the hydrodynamicsand mass transfer parameters for the various hardwarecon"gurations sketched in Figs. 10}16, is woefully lackingin the open literature. Paradoxically, such informationhas vital consequences for the conversion andselectivity of RD columns. There is a crying need forresearch in this area. It is perhaps worth noting here thatmodern tools of computational #uid dynamics could beinvaluable in developing better insights into hydrodynamicsand mass transfer in RD columns (Van Baten& Krishna, 2000; Higler, A.P., et al., 1999a; Krishna, VanBaten, Ellenberger, Higler & Taylor, 1999).Besides more research on hydrodynamics and masstransfer, there is need for more experimental work withthe express purpose of model validation. In such processstudies, parameters need to be measured along the heightof RD columns. Too often measurements are con"ned tofeed and product stream conditions. Such data cannotserve as a reliable discriminant of computer-based processmodels.NotationaBB cc DDaD n n E EEh FFfh hHk K¸¸N p Qrr rH R interfacial area, mbottoms #ow, mol spermeability, mnumber of components, dimensionlesstotal concentration, mol mdistillate #ow, mol sDamkohler number, dimensionlesse!ective Fick di!usivity, m se!ective Knudsen di!usivity in porous catalyst,m sMaxwell}Stefan di!usivity, m senhancement factor, dimensionlessenergy #ux, W menergy transfer rate, J soverall Murphree tray e$ciency, dimensionlessclear liquid height, mvapor feedstream, mol sliquid feedstream, mol scomponent feed stream, mol sweir height, mheat transfer coe$cient, W m Kmolar enthalpy, J molpseudo-"rst-order reaction rate constant, svapor}liquid equilibrium constant, dimensionlessliquid #ow rate, mol sinterchange liquid #ow rate between horizontalrows of cells, mol smolar #ux of species i, mol m sMass transfer rate, mol sstage pressure, Paheat duty, J snumber of reactions, dimensionlessratio of side stream #ow to interstage #ow onstage j, dimensionlesstransformed re#ux ratio, dimensionlessreaction rate, mol m s
R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5221R gas constant, J mol KsH transformed stripping ratio, dimensionlessS side draw-o!, mol st time, s¹ temperature, K; molar hold-up, mol< vapor #owrate, mol s= weir length, mx mole fraction in the liquid}phase, dimensionlessx mole fraction vector, dimensionlessX transformed liquid-phase mole fraction, dimensionlessy mole fraction in the vapor-phase, dimensionless> transformed vapor-phase mole fraction, dimensionlessz mole fraction in either vapor or liquid-phase,dimensionlessZ transformed mole fraction, dimensionlessGreek lettersεγ Γ[Γ]κμντηηSubscriptsreaction volume, mactivity coe$cient of species i, dimensionlessthermodynamic correction factor for binarymixture, dimensionlessmatrix of thermodynamic factors, dimensionlessmass transfer coe$cient, m schemical potential, J molstoichiometric coe$cient, dimensionlessdimensionless residence time, dimensionlessviscosity of #uid mixture, Pa sdistance along di!usion path, dimensionlesse! e!ectivei component indexI referring to interfacej stage indexk alternative component indexm reaction indext totalSuperscriptsF referring to feed stream¸ referring to liquid-phase< referring to vapor-phaseList of abbreviationsDAEDEGEGEQEOdi!erential-algebraic equationsdiethylene glycolethylene glycolequilibriumethylene oxideMeOHMeOAcAcOHHETPHTUMSMSSMTBENEQRDSRKTAMEmethanolmethyl acetateacetic acidheight of a theoretical plateheight of a transfer unitMaxwell}Stefanmultiple steady-statesmethyl tert-butyl ethernon-equilibriumreactive distillationSoave}Redlich}Kwongtertiary amyl etherAcknowledgementsRT and RK would like to express their appreciation toArnoud Higler and Richard Baur for their considerableassistance in the preparation of this paper. RT's researchin RD was partially supported by BP-Amoco Chemicals.RK acknowledges "nancial support from the NetherlandsOrganisation for Scienti"c Research (NWO) in theform of a `programmasubsidiea for research on reactiveseparations.ReferencesAbufares, A. A., & Douglas, P. L. (1995). Mathematical modeling andsimulation of an MTBE catalytic distillation process usingSPEEDUP and AspenPlus. Chemical Engineering Research andDesign, Transactions of the Institution on Chemical Engineers Part A,73, 3}12.Agreda, V. H., Partin, L. R., & Heise, W. H. (1990). High-purity methylacetate via reactive distillation. Chemical Engineering Progress,86(2), 40}46.Albet, J. M., Le Lann, J. M., Joulia, X., and Koehret, B. (1991). Rigoroussimulation of multicomponent multisequence batch reactive distillation.Proceedings of COPE '91, Barcelona, Spain (pp. 75}80).Alejski, K. (1991a). Computation of the reacting distillation columnusing a liquid mixing model on the plates. Computers and ChemicalEngineering, 15, 313}323.Alejski, K. (1991b). Analysis of complex chemical-reactions in distillationcolumn. 1. Parallel reactions. Inzynieria Chemiczna i Procesowa,12, 617}631.Alejski, K., & Duprat, F. (1996). Dynamic simulation of the multicomponentreactive distillation. Chemical Engineering Science, 51,4237}4252.Alejski, K., & Szymanowski, J. (1988). Comparison of selected methodsof reacting distillation column computing. Inzynieria Chemicznai Procesowa, 10, 55}73.Alejski, K., & Szymanowski, J. (1989). Analysis of chemical-reactioncourse in distillation column. Inzynieria Chemiczna i Procesowa, 9,565}584.Alejski, K., Szymanowski, J., & Bogacki, M. (1988). The application ofa minimization method for solving reactive distillation problems.Computers and Chemical Engineering, 12, 833}839.Allgor, R. J., Berrera, M. J., Barton, P. I., & Evans, L. B. (1996). Optimalbatch process development. Computers and Chemical Engineering,20, 885}896.
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