Modelling reactive distillation

R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5189distillation is often passed over as a processing optionbecause the catalyst life would require frequent shutdowns.An RD device that allowed on-stream removal ofcatalyst would answer this concern.1.4.2. Ezcient contacting of liquid with catalyst particlesThe hardware design must ensure that the following`wish-lista is met.(a) Good liquid distribution and avoidance of channelling.Liquid maldistribution can be expected to havea more severe e!ect in RD than in conventionaldistillation (Podrebarac, Ng & Rempel, 1998a,b).(b) Good radial dispersion of liquid through the catalystbed. This is required in order to avoid reactor hotspotsand runaways and allow even catalyst ageing.The requirement of good radial mixing has an impacton the choice of the packing con"guration andgeometry. For example, frequent criss-crossing mixingpatterns may be desirable, as is realised in somehardware con"gurations discussed in Section 1.5.1.4.3. Good vapor/liquid contacting in the reactive zoneIf the reaction rate is fast and the reaction is equilibrium-limitedthen the required size of the reactive zone isstrongly in#uenced by the e!ectiveness of the vapor}liquid contacting. Vapor}liquid contacting becomes lessimportant for slower reactions. Commonly used devicesfor good vapor}liquid contacting are the same as forconventional distillation and include structured packing,random packing and distillation trays.1.4.4. `Lowa pressure drop through the catalyticallypacked reactive sectionThis problem arises because of the need to use smallcatalyst particles in the 1}3 mm range in order to avoidintra-particle di!usional limitations. Counter-currentoperation in catalyst beds packed with such small-sizedparticles has to be specially con"gured in order to avoidproblems of excessive pressure drop and `#oodinga.These con"gurations are discussed in Section 1.5.such devices have not been commercialised as yet. Catalystdeactivation is therefore accounted for in the designstage by use of excess catalyst. Besides adding excesscatalyst, the reaction severity can be increased by (a)increasing re#ux, leading to increased residence time and(b) increasing reaction temperature (by increase of columnpressure)1.5. Hardware aspectsBefore modelling aspects can be considered, carefulattention needs to be paid to hardware design aspects.Towler and Frey (2000) have presented an excellent summaryof hardware design aspects of RD columns. Someof the important issues are discussed below.For homogeneous RD processes, counter-current vapor}liquidcontacting, with su$cient degree of staging inthe vapor and liquid-phases, can be achieved in a multitraycolumn (cf. Fig. 7) or a column with random orstructured packings (cf. Fig. 8). The hardware designinformation can be found in the standard sources forconventional distillation design (Lockett, 1986; Stichlmair& Fair, 1998). The Hatta number for most RDapplications is expected to be smaller than about unity(Sundmacher, Rihko & Ho!mann, 1994) and the frothregime is usually to be preferred on the trays (cf. Fig. 9)because of the desire to maintain high liquid hold-up onthe trays. High liquid hold-ups could be realised by use ofbubble caps, reverse #ow trays with additional sumps toprovide ample tray residence time. In the Eastman processfor methyl acetate manufacture specially designedhigh liquid hold-up trays are used (Agreda, Partin& Heise, 1990).1.4.5. Suzcient liquid hold-up in the reactive sectionThe liquid hold-up, mean residence time, and liquidresidence time distribution are all important in determiningthe conversion and selectivity of RD. This is in sharpcontrast with conventional distillation where liquidhold-up and RTD are often irrelevant as the vapor}liquid mass transfer is usually `controlleda by the vaporside resistance. For trayed RD columns the preferredregime of operation would be the froth regime whereas forconventional distillation we usually adopt the spray regime.1.4.6. Designing for catalyst deactivationEven though, as discussed in Section 1.4.1, it is desirableto allow on-line catalyst removal and regeneration,Fig. 7. Counter-current vapor}liquid contacting in trayed columns.Animations of CFD simulations of #ows on the tray can be viewed onour web site: http://ct-cr4.chem.uva.nl/sievetrayCFD.

5190 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229Fig. 8. Counter-current vapor}liquid contacting in packed columns.Fig. 9. Flow regimes on trays.1.5.1. Catalytically packed RD columnsFor heterogeneously catalysed processes, hardware designposes considerable challenges. The catalyst particlesizes used in such operations are usually in the 1}3mmrange. Larger particle sizes lead to intra-particle di!usionlimitations. To overcome the limitations of #ooding thecatalyst particles have to be enveloped within wire gauzeenvelopes. Most commonly the catalyst envelopesare packed inside the column. Almost every conceivableshape of these catalyst envelopes has been patented; somebasic shapes are shown in Figs. 10}14. These structuresare:1. Porous spheres "lled with catalyst inside them (Buchholz,Pinaire & Ulowetz, 1995; Johnson, 1993); seeFig. 10(a).2. Cylindrical shaped envelopes with catalyst insidethem (Johnson, 1993); see Fig. 10(b).3. Wire gauze envelopes with various shapes: spheres,tablets, doughnuts, etc. (Smith, 1984); see Fig. 10(c).4. Horizontally disposed wire-mesh `guttersa, "lled withcatalyst (Van Hasselt, 1999); see Fig. 11(a).5. Horizontally disposed wire-mesh tubes containingcatalyst (Buchholz et al., 1995; Groten, Booker &Crossland, 1998; Hearn, 1993); see Fig. 11(b).6. Catalyst particles enclosed in cloth wrapped in theform of bales (Johnson & Dallas, 1994; Smith, 1985).This is the con"guration used by Chemical Researchand Licensing in their RD technology for etheri"cation,hydrogenation and alkylation of aromatic compounds(Shoemaker & Jones, 1987). The catalyst isheld together by "breglass cloth. Pockets are sewninto a folded cloth and then solid catalyst is loadedinto the pockets. The pockets are sewn shut afterloading the catalyst and the resulting belt or `catalystquilta is rolled with alternating layers of steel mesh toform a cylinder of `catalyst balesa as shown in Fig. 12.The steel mesh creates void volume to allow for vaportra$c and vapor/liquid contacting. Scores of thesebales are installed in the reactive zone of a typicalcommercial RD column. Bales are piled on top of eachother to give the required height necessary to achievethe desired extent of reaction. When the catalyst isspent the column is shut down and the bales aremanually removed and replaced with bales containingfresh catalyst. Improvements to the catalyst bale concepthave been made over the years (Johnson, 1993;Crossland, Gildert & Hearn, 1995). The hydrodynamics,kinetics, and mass transfer characteristics of baletypepackings have recently been published in theopen literature (Subawalla, Gonzalez, Seibert & Fair,1997; Xu, Zhao & Tian, 1997, 1999).

R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5191Fig. 10. Various `tea-baga con"gurations. Catalyst particles need to be enveloped in wire gauze packings and placed inside RD columns.Fig. 11. Horizontally disposed (a) wire gauze gutters and (b) wire gauze tubes containing catalyst.Fig. 12. Catalyst bales licensed by Chemical Research and Licensing.7. Catalyst particles sandwiched between corrugatedsheets of wire gauze (Stringaro, 1991, 1995; Gelbein& Buchholz, 1991; Johnson & Dallas, 1994); seeFig. 13. Such structures are being licensed by Sulzer(called KATAPAK-S) and Koch-Glitsch (calledKATAMAX). They consist of two pieces of rectangularcrimped wire gauze sealed around the edge, therebyforming a pocket of the order of 1}5 cm widebetween the two screens. These catalyst `sandwichesaor `wafersa are bound together in cubes. The resultingcubes are transported to the distillation column andinstalled as a monolith inside the column to the requiredheight. When the catalyst is spent, the columnis shut down and the packing is manually removedand replaced with packing containing fresh catalyst.Information on the #uid dynamics, mixing and masstransfer in such structures is available in the openliterature (Bart & LandschuK tzer, 1996; Ellenberger& Krishna, 1999; DeGarmo, Parulekar and Pinjala,1992; Higler, Krishna, Ellenberger & Taylor, 1999a;Moritz & Hasse, 1999). The important advantage ofthe structured catalyst sandwich structures over thecatalyst bales is with respect to radial distributionof liquid. Within the catalyst sandwiches, the liquidfollows a criss-crossing #ow path. The radialdispersion is about an order of magnitude higher thanin conventional packed beds (Van Gulijk, 1998).

5192 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229Fig. 13. Structured catalyst-sandwiches. (a) Catalyst sandwiched between two corrugated wire gauze sheets. (b) The wire gauze sheets are joinedtogether and sewn on all four sides. (c) The sandwich elements arranged into a cubical collection. (d) The sandwich elements arranged in a roundcollection. Photographs of the structure, along with CFD simulations of the liquid #ow within the sandwiches can be viewed at: http://ctcr4.chem.uva.nl/strucsim.Fig. 14. (a) Catalytically active Raschig ring. Adapted from Sundmacher (1995). (b) Structured packings coated with catalyst. (c) Fluted catalystmonolith tubes.Furthermore, frequent criss-crossing leads to a signi"-cant improvement in mass transfer within the sandwichstructures (Higler et al., 1999a).Another alternative is to make the packing itself catalyticallyactive. This is the strategy adopted by Flato andHo!mann (1992) and Sundmacher and Ho!mann(1994a,b) wherein the Raschig ring-shaped packings aremade catalytically active; see Fig. 14(a). The catalyst ringscan be prepared by block polymerisation in the annularspace. Their activity is quite high, however, osmoticswelling processes can cause breakage by producing large

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)

R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5195z is the mole fraction of species i in either the vapor orliquid-phase as appropriate and the subscript k refers tothe index of the reference component (one whosestoichiometric coe$cient is non-zero).In terms of the transformed composition variables thematerial balance equations that describe a simple openevaporation in a reacting mixture are given bydX dτ "X !> , (4)where X is the transformed composition of species i inthe liquid-phase and > is the transformed compositionfor the vapor phase. τ is a dimensionless time. Numericalsolution of these equations yields the residue curves forthe system.Barbosa and Doherty (1987a) consider two di!erentde"nitions of an azeotrope and adopt the de"nition givenby Rowlinson (1969): `A system is azeotropic when it canbe distilled (or condensed) without change of compositiona.The conditions for the existence of a reactive azeotrope(and all other stationary points in the reactivemixture) are most easily expressed in terms of the transformedcomposition variables:X "> . (5)It is interesting to observe that reactive azeotropes canoccur even for ideal mixtures (Barbosa & Doherty,1987a, 1988a). Further, non-reactive azeotropes candisappear when chemical reactions occur. A reactiveazeotrope has been found for the system isopropanol}isopropyl acetate}water}acetic acid (Song, Huss,Doherty & Malone, 1997). The in#uence the reactionequilibrium constant has on the existence and location ofreactive azeotropes was investigated for single reactionsystems by Okasinski and Doherty (1997a,b).Barbosa and Doherty (1988a) provide a method for theconstruction of phase diagrams for reactive mixtures.Doherty (1990) develops the topological constraints forsuch diagrams. Ung & Doherty (1995a}e) have extendedthe methods of Barbosa and Doherty to deal withmixtures with arbitrary numbers of components andreactions.The in#uence of homogeneous reaction kinetics onchemical phase equilibria and reactive azeotropy wasdiscussed by Venimadhavan, Buzad, Doherty andMalone (1994) and Rev (1994). The residue curves areobtained fromdx dt "< ; (x !y )# r (ν !x ν ), (6)where < is the molar #ow rate in the vapor and ; is themolar liquid hold-up. These equations are more convenientlyexpressed in terms of actual mole fractions, ratherthan the transformed composition variables de"nedabove. It will be apparent that the heating policy greatlyin#uences the rate of vapor removal and the value of theequilibrium and reaction rate constants and, throughthis, the trajectories of the residue curves. Although it isnot obvious from Eq. (6), it is the Damkohler numberthat emerges as the important parameter in the locationof the residue curves for such systems. The Damkohlernumber is de"ned byDa" ;k < , (7)where k is a pseudo-"rst-order reaction rate constant.The Damkohler number is a measure for the rate ofreaction relative to the rate of product removal. LowDamkohler numbers are indicative of systems that arecontrolled by the phase equilibrium; a high Da indicatesa system that is approaching chemical equilibrium (seeTowler & Frey, 2000).Venimadhavan, Malone & Doherty (1999a) employeda bifurcation analysis to investigate in a systematic waythe feasibility of RD for systems with multiple chemicalreactions. Feasible separations are classi"ed as a functionof the Damkohler number. For the MTBE system theyshow that there is a critical value of the Damkohlernumber that leads to the disappearance of a distillationboundary. For the synthesis of isopropyl acetate thereexists a critical value of the Damkohler number for theoccurrence of a reactive azeotrope.Frey and Stichlmair (1999b) describe a graphicalmethod for the determination of reactive azeotropes insystems that do not reach equilibrium. Lee, Hauan& Westerberg (2000e) discussed circumventing reactiveazeotropes.Rev (1994) looks at the general patterns of the trajectoriesof residue curves of equilibrium distillation withnonequilibrium reversible reaction in the liquid-phase.Rev shows that there can be a continuous line of stationarypoints belonging to di!erent ratios of the evaporationrate and reaction rate. Points on this line are calledkinetic azeotropes. A reactive azeotrope exists when thisline intersects with the surface determining chemicalequilibrium.Thiel, Sundmacher & Ho!mann (1997a,b) computethe residue curves for the heterogeneously catalysed RDof MTBE, TAME and ETBE and "nd them to havesigni"cantly di!erent shapes to the homogeneouslycatalysed residue curves (Venimadhavan et al., 1994).They also note the importance of the Damkohler numberand the operating pressure. These parameters in#uencethe existence and location of "xed points in the residuecurve map as seen in Fig. 17 adapted from Thiel et al.(1997a). An analysis was carried out to forecast the numberof stable nodes as a function of Damkohler numberand pressure.Residue curve maps and heterogeneous kinetics inmethyl acetate synthesis were measured by Song,

5196 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229Fig. 17. Residue curves for the homogeneously and heterogeneously catalysed MTBE synthesis. After Thiel et al. (1997a).Venimadhavan, Manning, Malone and Doherty (1998).They found that the residue curves for the kineticallycontrolled cases are qualitatively similar to the curves forthe equilibrium case. Thus, the production of methylacetate by RD can be carried out in either regime.Open evaporation accompanied by liquid-phasechemical reactions has also been studied by Pisarenko,Epifanova & Sera"mov (1988b) and Solokhin, Blagov,Sera"mov & Timofeev (1990a,b).3. Equilibrium (EQ) stage modelsThe development and application of the EQ stagemodel for conventional (i.e. non-reactive) distillation hasbeen described in several textbooks (see, for example,Holland, 1963, 1981; Henley & Seader, 1981; Seader& Henley, 1998) and reviews (Wang & Wang, 1980;Seader, 1985; Taylor & Lucia, 1994). Here we are concernedwith the extension of this standard model todistillation accompanied by chemical reaction(s).3.1. The EQ stage modelA schematic diagram of an equilibrium stage is shownin Fig. 18(a). Vapor from the stage below and liquid fromthe stage above are brought into contact on the stagetogether with any fresh or recycle feeds. The vapor andliquid streams leaving the stage are assumed to be inequilibrium with each other. A complete separation processis modelled as a sequence of s of these equilibriumstages (Fig. 18(b)).The equations that model equilibrium stages areknown as the MESH equations, MESH being an acronymreferring to the di!erent types of equation. TheM equations are the material balance equations; the totalmaterial balance takes the formd; dt "< #¸ #F !(1#r )< !(1#r )¸# ν R ε . (8) ; is the hold-up on stage j. With very few exceptions,; is considered to be the hold-up only of the liquidphase.It is more important to include the hold-up of thevapor phase at higher pressures. The component materialbalance (neglecting the vapor hold-up) isd; x "< y x #F zdt #¸ !(1#r)< y !(1#r # )¸x ν R ε . (9) In the material balance equations given above r is the ratio of sidestream #ow to interstage #ow:r "S /< , r "S /¸, (10)ν represents the stoichiometric coe$cient of componenti in reaction m and ε represents the reaction volume.The E equations are the phase equilibrium relationsy "K x . (11)

R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5197Fig. 18. (a) The equilibrium stage. (b) Multi-stage distillation column.Chemical reaction equilibrium is not considered in manyof the early papers because it is more di$cult to model.There are, however, some exceptions to this statementand such works are noted below.The S equations are the summation equations x "1, y "1. (12)The enthalpy balance is given byd; H "< H H #F Hdt #¸ !(1#r )< H !(1#r )¸H !Q . (13)The superscripted H's are the enthalpies of the appropriatephase. The enthalpy in the time derivative on theleft-hand side represents the total enthalpy of the stagebut, for the reasons given above, this will normally be theliquid-phase enthalpy. Some authors include an additionalterm in the energy balance for the heat of reaction.However, if the enthalpies are referred to their elementalstate then the heat of reaction is accounted for automaticallyand no separate term is needed.Under steady-state conditions all of the time derivativesin the above equations are equal to zero.Some authors include additional equations in their(mostly unsteady-state) models. For example, pressuredrop, controller equations and so on.3.2. Steady-state algorithms and applicationsMuch of the early literature on RD modelling is concernedprimarily with the development of methods forsolving the steady-state EQ stage model. For the mostpart such methods are more or less straightforward extensionsof methods that had been developed forsolving conventional distillation problems. The numberof examples that illustrate most of the early papersusually is rather limited, both in number as well as inthe type of RD process considered (most often it is anesteri"cation reaction). Only rarely is there any attemptto compare the results of simulations to experimentaldata (some exceptions are noted below). More and moreof the more recent modelling studies are carried out usingone or other commercial simulation package: Aspen Plus,Pro/II, HYSYS, and SpeedUp are the packages mentionedmost often in the papers discussed in what follows.Tray-to-tray calculations were carried out by hand byBerman et al. (1948a); Marek (1954), and Belck (1955).Marek also presents an elaborate graphical method relatedto the McCabe}Thiele method for conventionalbinary distillation. Berman et al. (1948a) considered theproduction of dibutyl phthalate, extensive data for whichsystem had been reported by Berman et al. (1948b).We may identify several classes of computer-basedmethods that have been developed for solving theEQ stage model equations; these methods are discussedbrie#y in what follows. Readers are referred to the review

5198 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229of Seader (1985) for background and original literaturecitations. Brief reviews of early RD algorithms are byHolland (1981) and by Hunek, Foldes and Sawinsky (1979).Short-cut methods involve a number of simplifyingassumptions that are made in order to derive simpleapproximate equations that can be used for rapid computations.It is quite di$cult to derive generic short-cutprocedures for RD because of the many ways in whichchemical reactions in#uence the process (see, however,Ciric & Spencer, 1995). Bock and Wozny (1997) showthat the assumption of chemical equilibrium, often madein developing short cut methods, is inappropriate formany RD processes.Tearing methods involve dividing the model equationsinto groups to be solved separately. A brief description ofcomputer based tray-to-tray calculations for the RD ofethylene oxide and water was given by Corrigan andMiller (1968). Tray-to-tray calculations and parametricstudies for the simulation and optimisation of an RDcolumn for trioxane synthesis are described by Hu, Zhou& Yuan (1999). The bubble-point method of Wang andHenke (1966) was extended by Suzuki, Yagi, Komatsuand Hirata (1971) to be able to deal with chemical reactions.Suzuki's method was used by Babcock and Clump(1978). The so-called θ method developed for conventionaldistillation columns by Holland and his manycollaborators (see, Holland, 1963, 1981) was extended toRD operations by Komatsu and Holland (1977) andnamed the multi-θ}η method. The method is applied tothe esteri"cation of acetic acid. Other papers from thisgroup are Izarraz, Bentzen, Anthony and Holland (1980)and Mommessin, Bentzen, Anthony and Holland (1980).Mommessin and Holland (1983) discuss the computationalproblems associated with multiple columns. Savkovic-Stevanovic,Mis\ ic-Vukovic, Boncic-Caricic, Tris\ ovicand Jezdic (1992) used the θ method to model an esteri"-cation of acetic acid and ethanol carried out in a glasscolumn that was 33 mm in diameter and 1000 mmtall. The calculated temperature pro"le and productcompositions are in good agreement with the measuredquantities.Solving all of the independent equations simultaneouslyusing Newton's method (or a variant thereof)nowadays is an approach used very widely by authors ofmany of the more recent papers in this "eld (see, forexample, Pilavachi, Schenk, Perez-Cisneros and Gani,1997; Lee & Dudukovic, 1998). Holland (1981) providesa cursory description of this approach to RD simulation.More details and illustrative examples are to be found inthe works of Block (1977); Block and Hegner (1977);Kaibel, Mayer and Seid (1979) and Simandl and Svrcek(1991).Relaxation methods involve writing the MESH equationsin unsteady-state form and integrating numericallyuntil the steady-state solution has been found (Komatsu,1977; Jelinek & Hlavacek, 1976). Komatsu compares hisEQ stage model calculations to his own experimentaldata for one experiment showing that the EQ modelcomposition pro"les are qualitatively correct. Theauthors from Prague provide three numerical examplesinvolving esteri"cation processes. Relaxation methodsare not often used because they are considered to betoo demanding of computer time. They are, of course,closely related to dynamic models. Bogacki, Alejski& Szymanowski (1989) used the Adams}Moultonnumerical integration method to integrate a simpli"eddynamic model that neglects the enthalpy balance toa steady-state solution. Numerical results for a singleexample are compared to numerical results obtained byKomatsu (1977).There also exists a class of algorithm that really isa combination of equation tearing and simultaneoussolution in that Newton's method is used to solve a subsetof the MESH equations, but in which other methodsare used to solve the remaining equations. Papers byNelson (1971), Kinoshita, Hashimoto and Takamatsu(1983), and by Tierney and Riquelme (1982) fall into thiscategory. Very few RD examples accompany these papers.Takamatsu, Hashimoto and Kinoshita (1984) andKinoshita (1985) used a similar approach to model columnsfor an unusual application: heavy water enrichmentusing hydrophobic catalysts.Isla and Irazoqui (1996) use Newton's method to solvethe equations that model what they refer to as a `partialequilibriuma stage. However, despite the new name,theirs is essentially the same EQ model employed byalmost everyone else in that the exiting streams are inphase equilibrium, but not in chemical equilibrium witheach other. Parametric studies involving the e!ects ofcatalyst load and distribution, operating pressure andre#ux ratio are reported.Homotopy-continuation methods are employed mostoften for solving problems that are considered very di$cultto solve with other methods (e.g. Newton's). Formore details about this method, the reader is referred toWayburn and Seader (1987). Homotopy-continuationwas "rst applied to RD operations by Chang and Seader(1988). Their paper is illustrated by a number of casestudies involving the esteri"cation of acetic acid andethanol to ethyl acetate and water. Bondy (1991) describesphysical continuation approaches to solving RDproblems. Lee and Dudukovic (1998) have also usedhomotopy continuation to solve both EQ and NEQmodels of RD operations. Continuation methods are alsouseful for studying parametric sensitivity (see, forexample, Sneesby, TadeH and Smith, 1997c) and for locatingmultiple steady-states (Pisarenko, Anokhina& Sera"mov, 1993).Alejski, Szymanowski and Bogacki (1988) used a minimisationmethod due to Powell (1965) to solve theMESH equations. This approach is, however, rather slowto converge. Numerical results for the esteri"cation of

R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5199acetic acid with ethanol were compared with data fromKomatsu (1977). Komatsu carried out experiments onthe esteri"cation system of acetic acid and ethanol. Theexperiments were carried out in a column of 7 trays eachwith a single bubble cap. The trays had an inside diameterand spacing of 140 mm. Liquid-phase compositionpro"les are provided for "ve experiments. There are also3 sets of data for a #ash RD. Alejski et al. (1988), as wellas Simandl and Svrcek (1991), show that the shape of thepro"les obtained by the EQ model is largely in agreementwith the shape of the pro"les measured byKomatsu, although there are some signi"cant quantitativedi!erences. Alejski and Szymanowski (1988, 1989)provide a brief (in Polish) review of RD algorithms.In a later paper Alejski (1991a) models the liquid #owacross a tray by a sequence of mixing cells, each of whichis considered to be a non-equilibrium cell. Departuresfrom equilibrium were handled through the calculation(in the usual way) of the point e$ciency. The modelequations were solved using a relaxation method combinedwith Newton's method for computing the variablesat each time step. A comparison between the numericalresults of Alejski (1991a) obtained with an equilibriumcells-in-seriesmodel and the experimental data of Marek(1956) shows that the assumption of complete mixing onthe tray is much less successful than the multi-cell modelat predicting the actual composition pro"les. Marek(1956) had described a plant for the production of aceticanhydride. Experimental composition pro"les are providedfor a single set of operating conditions.Alejski (1991b) investigated the steady-state propertiesof an RD column in which parallel reactions take place.It was assumed that reactions occur in the liquid-phaseand the reactions are rate controlling. Each stage wasassumed to be perfectly mixed, and the interstage #owswere equimolar. The vapor leaving any stage was inphysical equilibrium with the liquid in this stage. Alejksilooked at the in#uence of reactants' volatilities, reactionequilibrium constants, reaction rates, re#ux ratio, locationof feed inlets, number of theoretical stages and distillaterate upon the yield, selectivity and productdistribution. As has been reported elsewhere, the columnpressure is an important factor that strongly a!ects reactionrates by changing the column temperature pro"le.Venkataraman, Chan and Boston (1990) describe theinside-out algorithm known as RADFRAC that is part ofthe commercial program Aspen Plus. Inside-out methodsinvolve the introduction of new parameters into themodel equations to be used as primary iteration variables.Four examples demonstrate that RADFRAC canbe applied to a wide variety of reactive separation processes.RADFRAC is able to handle both equilibriumreactions as well as kinetically limited reactions. Simandland Svrcek (1991) provide more details of their ownimplementation of an inside-out method for RDsimulation.RADFRAC has been used by many other authors.Quitain, Itoh & Goto (1999a) modelled a small-scalecolumn used to produce ETBE from bioethanol. Simulationresults are compared to experimental data. A secondpaper (Quitain, Itoh & Goto, 1999b) used RADRAC tomodel an industrial-scale version of the same process.Bezzo et al. (1999) used RADFRAC to study the steadystatebehaviour of an actual industrial RD column producingpropylene oxide from propylene chlorohydrinand calcium hydroxide. The thermodynamic propertiesof this system are complicated by the presence of electrolytesin the liquid-phase and by salting out e!ects.Reaction kinetics were modelled using the expressionsreported by Carra, Santacesaria, Morbidelli and Cavalli(1979b). By adjusting the Murphree e$ciency the authorswere able to obtain the best possible agreement betweenthe plant data and the simulations.Davies, Jenkins and Dilfanian (1979) describe a variationon the standard EQ stage model that is depicted inFig. 19. The vapor/liquid contacting section is modelledas a conventional vapor}liquid equilibrium stage (withoutreaction). The outgoing liquid stream passes to a reactorwhere chemical equilibrium is established. Thestream leaving this reactor passes on to the next equilibriumstage. The disadvantage of this approach is that itfails to properly account for the in#uence that chemicalequilibrium has on vapor}liquid equilibrium (and viceversa). The model is used to predict the temperature andcomposition pro"les in a 76 mm diameter column inwhich formaldehyde is reacting with water and methanol.Good agreement between predicted and measured valuesFig. 19. Equilibrium stage model used by Davies et al. (1979).

5200 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229is claimed, but the "gures provided in their paper aresmall and hard to read.Barbosa and Doherty (1988d) point out that the EQstage model equations (including those that account forsimultaneous phase and chemical equilibrium) can berewritten so that they are identical in form to the EQmodel equations in the absence of chemical reactions.The actual #ows and compositions are replaced by thetransformed #ows and compositions, the latter beingde"ned by Eq. (3). The advantage of this approach is thatexisting algorithms and programs can be used to solvethe equations. All that is required is to replace that partof the program that carries out the phase equilibriumcalculations with a new procedure that computes thephase and chemical equilibrium computation and evaluatesthe transformed variables.3.3. Multiple steady-states with the EQ modelMultiple steady-states (MSS) in conventionaldistillation have been known from simulation andtheoretical studies dating back to the 1970s and havebeen a topic of considerable interest in the distillationcommunity. However, it is only recently that experimentalveri"cation of their existence has been forthcoming.It is beyond the scope of this article to review thisbody of literature; readers are referred to GuK ttinger(1998) for citations of the original literature and discussionsof the di!erent kinds of multiplicity that havebeen found.The "rst report of MSS in RD appeared in the Russianliterature. Pisarenko, Epifanova and Sera"mov (1988a)found three steady-states for an RD column with just oneproduct stream, two of which were stable. Timofeev,Solokhin and Kalerin (1988) provided a simple analysisof their RD column con"guration. Karpilovsky,Pisarenko and Sera"mov (1997) developed an analysis ofsingle-product columns at in"nite re#ux. Pisarenko et al.(1993) used homotopy methods to locate MSS in RDwith more conventional con"gurations.RADFRAC has been used by, among others, Jacobsand Krishna (1993); Nijhuis, Kerkhof and Mak (1993),Hauan, Hertzberg and Lien (1995, 1997), Perez-Cisneros,Schenk and Gani (1997b) and Eldarsi and Douglas(1998a) for investigation of multiplicity of steady-states inRD columns. For MTBE synthesis using the Jacobs}Krishna column con"guration, shown in Fig. 20(a), varyingthe location of the stage to which methanol is fedresults in either a high or low conversion. When themethanol is fed to stages 10 or 11, steady-state multiplicityis observed (Baur, Higler, Taylor & Krishna, 1999).Explanation for the occurrence of MSS in the MTBEprocess was provided by Hauan et al. (1995, 1997).The ethylene glycol RD process also appears to beparticularly interesting for the investigation of MSS.Ciric and Miao (1994) found as many as nine steadystates,but Kumar and Daoutidis (1999) found `onlya"ve!GuK ttinger and Morari (1997, 1999a,b) develop theso-called R/R analysis for RD columns. The twoFig. 20. (a) Con"guration of the MTBE synthesis column, following Jacobs and Krishna (1993). The column consists of 17 stages. (a) High- andlow-conversion branches obtained by EQ and NEQ simulations. The bottoms #ow in these simulations was "xed at 203 mol/s. The details of thecalculations are given in Baur et al. (1999).

R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5201in"nities refer to in"nite internal #ow rates and an in"-nite number of stages and the method is for the predictionof MSS in distillation. GuK ttinger and Morari (1997)extended prior work of Morari and co-workers that wasrestricted to conventional distillation operations to developa uni"ed approach to the prediction of MSS insystems involving equilibrium chemical reactions. Themethod is applied to the MTBE process studied byothers; they conclude that the MSS are easily avoided byselecting appropriate control strategies. The methodologyis further re"ned and developed by GuK ttinger andMorari (1999a,b). The "rst of these two papers deals withwhat the authors call non-hybrid columns, in which thereaction is assumed to take place on every stage of thecolumn. The second paper relaxes this restriction andconsiders MSS in columns with a reactive section, andnon-reactive stripping and recti"cation sections.Gehrke and Marquardt (1997) developed a methodbased on singularity theory for elucidating the possiblecauses of MSS in a single equilibrium stage RD process.Their method requires no analytical solution of the equationsand uses homotopy methods as well as intervalcomputing techniques to identify the highest order singularity.Mohl et al. (1997) and Mohl, Kienle & Gilles (1998)implemented a dynamic EQ model (with Murphree-typee$ciencies) in the DIVA simulator and carried out a numericalbifurcation and stability analysis on the MTBEand TAME processes. They also show that the windowof opportunity for MSS to actually occur in the MTBEprocess is quite small. For the TAME process MSS occurin the kinetic regime and vanish when chemical equilibriumprevails. The window of opportunity for MSS in theTAME process is larger than for the MTBE process.Experimental con"rmation of MSS in RD has beenprovided by Thiel et al. (1997) and Rapmund et al. (1998).Mohl et al. (1999) used a pilot-scale column used toproduce MTBE and TAME. Multiple steady-states werefound experimentally when the column was used to produceTAME, but not in the MTBE process. The measuredsteady-state temperature pro"les for the low andhigh steady-states for the TAME process are shown inFig. 21(a). For a column operating at the low steadystate,a pulse injection of pure TAME for a short periodresults in a shift from the low to the higher steady-state;see Fig. 21(b).We will have more to say on the subject of MSS in RDin a later section on NEQ modelling.3.4. Primarily dynamic models and applicationsSavkovic-Stevanovic (1982) put forth an unsteadystateEQ stage model of a distillation process in whichone component takes part in an association reaction inboth phases. Euler's method was used to integrate thedi!erential equations. A comparison with data for theacetic acid}benzene system shows good agreement withthe model, but no actual data are provided.One of the "rst papers to discuss dynamic simulationof RD processes is the work of Roat et al. (1986). Theirmodel integrates the control system equations with thecolumn model equations. Using the Eastman methylacetate process, they show that control schemes withgood steady-state characteristics may fail under unsteady-stateconditions.Ruiz, Basualdo and Scenna (1995) describe a softwarepackage called READYS (REActive Distillation dYnamicSimulator) for which an EQ stage model is usedFig. 21. (a) Multiple steady-states in TAME synthesis. Experimental data on low- and high-conversion steady-states. (b) Response of TAME columnto injection of pure TAME in the feed during the period 860}920 min. The column shifts from a low steady-state to the higher one. Measurements ofMohl et al. (1999).

5202 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229which adopts the assumption of physical equilibrium,ideal mixing, thermal equilibrium with a chemical reactioncon"ned to the liquid-phase. Column hydraulics isaccounted for through a pressure drop equation anddepartures from equilibrium can be modelled usinga Murphree-type e$ciency factor. Extensive numericalresults are provided. The authors state that their programcan be used to study unsteady and unstable columnoperations such as start-up, shutdown and abnormalhydraulic column behaviour. The package allows fora number of standard thermodynamic property packs aswell as user-supplied models. Scenna, Ruiz and Benz(1998) employ READYS to study the start-up of RDcolumns. They show that the start-up policy can havea strong in#uence on the ultimate steady-state behaviourby sending the column to an undesirable operating point.READYS and Aspen Plus were used by Perez-Cisneros,Schenk, Gani and Pilavachi (1996) and Perez-Cisneros et al. (1997b) who also discussed their ownsomewhat di!erent approach to the EQ model. Theirmodel uses chemical &elements' rather than the actualcomponents. The chemical elements are the moleculeparts that remain invariant during the reaction. Theactual molecules are formed from di!erent combinationsof elements. A bene"t of this approach is that the chemicaland physical equilibrium problem in the reactivemixture is identical to a strictly physical equilibriummodel. A comparison with the RD data of Suzuki et al.(1971) is provided and it is noted that these data aredi$cult to match unless the `"tteda activity coe$cientmodel is used.Gani, Jepsen and Perez-Cisneros (1998) describeda generalised reactive separation unit model. Theirs is anunsteady-state EQ stage model that can handle systemsboth with and without reactions and with more than two#uid phases. The methodology is quite unique in that it isbased on the element approach of Perez-Cisneros et al.(1997b). Several numerical examples cover a range ofsimulation problems. Pilavachi et al. (1997) use the sameapproach, but their paper does not dwell on the computationalmethods; rather its focus is on some of theparameters that are important in RD modelling. Forexample, they discuss the e!ect of thermodynamic modelsand their parameters on RD simulation.Abufares and Douglas (1995) use an EQ stage modelfor steady-state and dynamic modelling of an RD columnfor production of MTBE. The steady-state model isRADFRAC from Aspen Plus. The unsteady-state modelequations are solved using SpeedUp, a commercial dynamicprocess simulation program. The focus of thispaper is the transient response of the system.Alejski and Duprat (1996) described a dynamic modelfor modelling kinetically controlled RD processes. Themodel is based on the conventional assumptions of negligiblevapor-phase hold-up and perfect mixing of the twophases. Departures from phase equilibrium could be handledby speci"cation of a vaporisation e$ciency, andcorrections of the conversion due to imperfect mixing areaccounted for using a `conversion e$ciencya, the latterbeing calculated from an eddy di!usion model in terms ofthe Peclet number. The model is compared to data obtainedin a pilot-scale column for the esteri"cation ofethanol with acetic acid and sulphuric acid as homogeneouscatalyst. Column start-up and disturbances ofcontinuous operation were investigated. The dynamictemperature pro"les are in reasonable agreement withthe data, but the predicted dynamic concentration pro-"les are very di!erent from the observed pro"les. Alejskiand Duprat (1996) also recommend that tray hydraulicsbe accounted for in any dynamic model of RD.Schrans, de Wolf & Baur (1996) carried out dynamicsimulations, using SPEEDUP, of the MTBE synthesisprocess using essentially the Jacobs}Krishna columncon"guration shown in Fig. 20(a). Their simulationsshowed that increase in the iso-butene feed by 4% leadsto oscillatory behaviour. A further increase of iso-butenefeed by 5% causes a jump from the high-conversionsteady-state to the lower one. Hauan, Schrans and Lien(1997) also showed oscillatory behaviour and suggestedthat it is due to an internal recycle of MTBE in thereactive zone.Sneesby, TadeH , Datta & Smith (1997a) model the synthesisof ETBE using an EQ stage model that they solvewith SpeedUp. Simulation results are compared to resultsobtained with the commercial simulation programPro/II. Homotopy methods are used to investigate thee!ects of important design variables (feed composition,ethanol excess, pressure, number of equilibrium stages* reactive or non-reactive, reboiler duty and so on).A process design methodology is suggested. In a companionpaper Sneesby, TadeH , Datta and Smith (1997b) developa dynamic model of the same process using SpeedUp.Their dynamic model assumes that reaction equilibriumis attained on all stages, neglecting reaction kinetics. Theauthors recommend including control issues early in thedesign process. Subsequent papers from this group lookat multiple steady-states in RD (Sneesby, TadeH & Smith,1998c}e). Sneesby et al. (1998d) (as well as Bartlett andWahnscha!t (1998) using RADFRAC) report that thetransition from one steady-state to another can be preventedusing appropriate control strategies. Sneesby et al.(1998a) show that an increase in fractionation (by increasingre#ux ratios, or numbers of equilibrium stages)does not always lead to improved performance of RDcolumns. This is exactly opposite to the situation inconventional distillation.Espinosa, Martinez and Perez (1994) presented a simpli"eddynamic model for an RD column. Vapor holdups,heat losses to the environment and the heat ofreaction were neglected. In addition, equimolar over#owand physical and chemical equilibrium were assumed.The resulting equations were rewritten in terms of the

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

5204 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229propylene oxide from propylene chlorohydrins in an RDcolumn. Reaction kinetics of this reaction were derivedand presented in the "rst paper; A limited quantity ofcolumn data is reported in their second paper. Fewdetails of the column design are given other than to saythe column was a continuous multistage micropilot column.The authors used Newton's method to solve theequations that model the synthesis of propylene oxidefrom propylene chlorohydrins in an RD column. A goodmatch was found between simulation results and top andbottom stream composition data obtained in the twoexperiments for which they provide data. However, itmust be remembered that matching only top and bottomcompositions is not a particularly good test of a completecolumn model. A much more demanding test is to be ableto predict observed composition pro"les along the lengthof a column.Neumann and Sasson (1984) used the method ofSuzuki et al. (1971) to model the production of methylacetate by methanol esteri"cation in a small-scale columnpacked with an acidic organic acid polymer catalyst.A limited quantity of experimental data is included in thepaper.Duprat and Gau (1991b) study the separation ofclose-boiling mixtures using RD. The process studied isthe separation of 3-picoline and 4-picoline through complexationwith tri#uroacetic acid. Newton's method wasused to solve the EQ stage model equations. A companionpaper (Duprat & Gau, 1991a) provides equilibriumdata for this system. RD of close-boiling mixtures (m- andp-xylene) has also been studied by Saito, Michishita& Maeda (1971).Fuchigami (1990) reported top and bottom columntemperature and composition data for 13 experiments forthe methyl acetate process carried out in a laboratoryscalecolumn. No attempt to model the column isprovided.Flato and Ho!mann (1992) discuss the developmentand start-up of a small-scale packed distillation columnfor the production of MTBE. The manufacture of theRaschig ring-shaped packing elements is described insome detail, as is the control system installed aroundtheir column. Experimental results are provided for themole percent of MTBE as a function of time, the isobuteneconversion and MTBE selectivity as a function ofmethanol/iso-butene ratio in the feed, and data showingthe e!ect of pressure on iso-butene conversion.Krafczyk and Ghmeling (1994) used RADFRAC tomodel an experimental column with 2 m of KATAPAK-S with bubble cap trays above and below. The main goalof this study was to test the feasibility of heterogeneousRD for methyl acetate production. No data are providedthat could be useful to other investigators.Bravo et al. (1993) provide some preliminary resultsobtained from a catalytic distillation pilot plant used toproduce TAME. The pilot-scale column was 11 m inheight and 15 cm in diameter. The catalyst was AmberliteXAD ion-exchange resin. Composition pro"les are providedfor a few experimental runs. Some of the experimentsshow composition pro"les that appear almost #at,indicating little composition change from stage to stage.Pekkanen (1995a) refers to such regions as `reactivepinchesa. The experiments were simulated with the proprietarysimulation program FLOWBAT, but comparisonswith the data are provided for only one experiment.Insu$cient data are available for others to attempta simulation using anything other than an EQ model.Bart and Reidetschlager (1995) used RADFRAC tomodel experiments involving the esteri"cation of succinicanhydride with methanol to produce dimethyl succinateand water in laboratory-scale column. When tray ef-"ciencies were speci"ed, the simulations could be madeto agree with the experimental composition pro"les.Simulations are used to compare the performance ofseveral di!erent plant designs. They suggest that a standardRD column is preferable to a reactor/column forfast reactions and high relative volatilities.Acetalisation of formaldehyde with methanol in batchand continuous RD columns was studied by Kolah,Mahajani & Sharma (1996). Their paper providesmore data than usually is the case in experimentalpapers. The column was modelled using the transformedcomposition approach of Ung & Doherty (1995), withthe calculation of the minimum re#ux and of the numberof stages.Gonzalez and Fair (1997) present data for the productionof tert-amyl-alcohol from water and iso-amylenes.Their paper provides an unusually comprehensive descriptionof the experimental work carried out. The RDcolumn has an internal diameter of 5.1 cm and a totallength of 2.25 m. The column was loaded with bales ofcatalytic packing similar to that shown in Fig. 12. Insome of their experiments the column was loaded with6 bales, in others just 2, the rest of the column being "lledwith Sulzer BX gauze packing. An important conclusionfrom their experimental work is that over design of anRD column can lead to unacceptably low yields of thedesired products, with correspondingly high yields ofundesired products. Gonzalez, Subawalla and Fair (1997)used the RADFRAC model in Aspen Plus to simulate theprocess. The simulation results were in reasonable agreementwith the data. A parametric study showed the e!ectof varying the feed composition and other importantoperational parameters.Gaspillo, Abella and Goto (1999) studied experimentallythe dehydrogenation of 2-propanol to acetoneand hydrogen in a small-scale RD column. The separationof acetone from 2-propanol is strongly in#uencedby the feed #ow rate, the re#ux ratio, and the temperatureof the heat source. The motivation for the study was toinvestigate the possibility of using the system in chemicalheat pump.

R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 52053.7. Use of ezciencies in RD modelsSome authors (e.g. Reuter et al., 1989; Ruiz et al., 1995;Isla & Irazoqui, 1996; Lee & Dudukovic, 1998) usea modi"ed EQ stage model in which the phase equilibriumequations incorporate a stage e$ciency factor.There are many di!erent de"nitions of the stage e$ciency;that of Murphree is most often used in EQ stagesimulation:E" y !y ; i"1,2,2, n, (14) yH!y where y is the average composition of the vapor leavingthe tray, y is the composition of the vapor entering thetray and yH is the composition of the vapor in equilibriumwith the liquid leaving the tray. Since the molefractions add to unity, only (n!1) of the Murphreecomponent e$ciencies are independent. For distillationof systems with three or more species, the componente$ciencies are almost always unequal to one another andthese can routinely assume values greater than unity orless than zero (Taylor & Krishna, 1993). Ilme, Keskinen,Markkanen & Aittamaa (1997) simulated an industrialMTBE (non-reactive) distillation column using an EQstage model using a more rigorous multicomponent(matrix) e$ciency prediction method; this paper illustratesthe complex nature of component e$ciencies. Forpacked columns it is common to use the height equivalentto a theoretical plate (HETP). The behaviour ofHETPs in multicomponent mixtures is closely related tothe behaviour of stage e$ciencies.To the best of our knowledge there are no fundamentallysound methods for estimating either e$cienciesor HETPs in RD operations. Davies et al. (1979) employeda conventional binary e$ciency predictionmethod in the absence of anything better. In general, thepresence of chemical reactions will have an in#uence onthe component e$ciencies. This is illustrated by calculationsof the component e$ciencies for an RD columnfor hydration of ethylene oxide (EO) with water tomono-ethylene glycol (EG). In situ distillation is used tosuppress the unwanted side reaction to diethylene glycol(DEG) produced from the reaction EO#EG P DEG.Using a rigorous non-equilibrium (NEQ) model (discussedbelow), the component e$ciencies were calculatedfor an RD column (using the con"guration described byBaur et al., 1999) and also for a column in which thereactions were deliberately suppressed. The componente$ciencies for EO, Water, EG and DEG, calculated fromthe NEQ model are shown in Fig. 22 with "lled symbolsfor the RD case and with open symbols for the nonreactivecase. For the non-reactive column the componente$ciencies are close to one another and in the range0.5}0.65. The smallest molecule, water, has the highestcomponent e$ciency. The component e$ciencies of EOand EG lie in between those of water and DEG. For RDoperation, the component e$ciencies show great variationbetween the di!erent components. Clearly,chemical reactions in#uence the values of the componente$ciencies in a complex and unpredictable way. Thisaspect has also been highlighted in the simulations presentedby Higler, Taylor and Krishna (1998).For a more complete understanding of RD processes itis necessary to consider in detail the interaction betweenmass transfer and chemical reaction. We take up thissubject next.4. Mass transferFor the purposes of this discussion it su$ces to adopta "lm model description of the transport processes inRD. Representative "lm pro"les for homogeneous systemsare shown in Fig. 5(a), and for heterogeneous systemsin Fig. 5(b).In homogeneous RD processes the reaction takes placeonly in the liquid-phase. If it is su$ciently rapid, thereaction will also take place in the liquid "lm adjacent tothe phase interface. Very fast reactions may occur only inthe "lm. A slow reaction also takes place in the "lm butits in#uence on the mass transfer process can safely beignored.The most fundamentally sound way to model masstransfer in multicomponent systems is to use theMaxwell}Stefan theory (see Krishna & Wesselingh, 1997;Taylor & Krishna, 1993). The Maxwell}Stefan equationsfor mass transfer in the vapor and liquid-phases respectivelyare given byy μ ¹ z " andx μ ¹ z " y N !y N c n (15)x N !x N c n , (16)where x and y are the mole fractions of species i in theliquid and vapor phases, respectively. The n representsthe corresponding Maxwell}Stefan di!usivity of the i!kpair in the appropriate phase. Only c!1 of Eqs. (15) and(16) are independent; the mole fraction of the last componentis obtained by the summation equations for bothphases. At the vapor}liquid interface we have the continuityequations " . (17) For a homogeneous system, the molar #uxes in the liquid"lm may change due to any chemical reaction that takesplace thereN z " ν R . (18)

5206 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229Fig. 22. Component e$ciencies for EO, water, EG and DEG for reactive and non-reactive operation. The RD column con"guration is shown in Fig.24(a). Unpublished results of Baur, Taylor and Krishna (2000).For most reactive distillations the change in the #uxesthrough the "lm will not be signi"cant because the Hattanumbers are smaller than unity (Sundmacher et al., 1994).The composition pro"le with the `di!usiona "lm will benearly linear. For other reactive separation processes (e.g.reactive absorption) the composition change in the "lmwill be very important. It will not always be clear inadvance in which regime a particular process will beoperating, and the regime may even vary from stage tostage. Thus, the most general approach is to solve the MSand continuity equations simultaneously for all casesinvolving homogeneous reactions.Eqs. (16) and (18) form a system of non-linear coupleddi!erential equations that must be solved numerically inmost cases. Frank, Kuipers, Versteeg and van Swaaij(1995b) and Frank, Kuipers, Krishna and van Swaaij(1995a) provide perhaps the most comprehensive study ofsimultaneous mass (and heat) transfer with chemical reactionmodelled using the MS equations. They reportthat thermal e!ects can a!ect mass transfer rates by asmuch as a factor of 30!In view of their complexity, the MS equations sometimesare written in greatly simpli"ed formN "!c D x z . (19)This expression ignores the coupling between the speciesgradients as well as mass transfer by convection. D isan e!ective di!usivity and it should be regarded as

R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5207a function of the binary MS di!usion coe$cients,the mixture composition, and the mass transferrates themselves. However, if, as is usually done, weassume the e!ective di!usivity to be constant, then analyticalsolutions to Eqs. (18) and (19) may be derived.Indeed, the literature on mass transfer with chemicalreaction based on these two equations is vast and suchequations often are used. Results usually are expressed inthe formN "k E (x !x ), (20)where k is the mass transfer coe$cient and E is anenhancement factor that accounts for the in#uence ofchemical reaction on the molar #uxes. Among otherthings, enhancement factors depend quite strongly on thereaction kinetics; thus, there is no universal expressionfor E that can be used in all situations. Indeed, in manycases it is not even possible to obtain analytical expressionsfor the enhancement factor, even for the muchsimpli"edconstitutive relation given by Eq. (19).Danckwerts (1970) and Van Swaaij and Versteeg (1992)review the "eld of mass transfer with chemical reaction.Frank, Kuipers, Krishna and van Swaaij (1995a) citeother studies of non-isothermal mass transfer with simultaneouschemical reaction modelled using the simplerconstitutive relation given by Eq. (19). E!ective di!usivitymodels of this sort have been used with some successin the modelling of amine-based gas treating processes(see, for example, Cornelisse, Beenackers, van Beckum& van Swaaij, 1980; Carey, Hermes & Rochelle, 1991;Altiqi, Sabri, Bouhamra & Alper, 1994 and the extensivelists of references in these papers).A more rigorous approach to modelling mass transferin multicomponent systems is a!orded by the generalizedFick's law: xJ "!c D z , (21)where J is the molar di!usion #ux of speciesi (N "J #x N ) and the D are the Fick di!usion coe$cients for the multicomponent mixture. The Fickdi!usion coe$cients can be related to the binary MSdi!usion coe$cients; see Taylor and Krishna (1993) fordetails of this. Solutions of Eq. (21) and the continuityequation (18) are known for a few cases involving simultaneousdi!usion and reaction (see, for example, Toor,1965; Kenig & Gorak, 1995, 1997). In most cases ofpractical signi"cance Eq. (21) is just as di$cult to solve asthe full MS equations and it is necessary to employnumerical methods here as well.A rigorous approach to modelling heterogeneous systems(Fig. 5(b)) would involve a complete description ofmass transport to the catalyst and di!usion and reactioninside the catalyst particles, if the catalyst is porous, orreaction at the surface if it is not. In either case it isunnecessary to allow for reaction in the vapor or liquid"lms as described above.For all cases involving a heterogeneous reaction wemay model transport through the vapor}liquid interfaceusing the MS equations given above (assuming no reactionin the liquid "lm). We also need to model di!usion ofreactants to and products away from the solid catalystsurface using a separate set of di!usion equations. Forthose cases where the reaction takes place at the catalystsurface the boundary conditions at the liquid}solid interfacewill be determined by the reaction kinetics. However,if the reaction takes place inside a porous catalyst thenwe need to model di!usion and reaction inside the catalystas well as transport from the bulk liquid to/from thecatalyst surface.Modelling multicomponent mass transfer in porousmedia is complicated when the mean free path length ofthe molecules is of the order of magnitude of the porediameter. The di$culties posed by this case may becircumvented by a method originally introduced byMaxwell (1866) and developed further by Mason andco-workers (see Mason & Malinauskas, 1983). Maxwellsuggested that the porous material itself be describedas a supplementary `dusta species, consisting ofvery large molecules that are kept motionless bysome unspeci"ed external force. The Chapman}Enskogkinetic theory is then applied to the new pseudo-gasmixture, in which the interaction between the dust andgas molecules simulates the interaction between the solidmatrix and the gas species. In addition, one is no longerfaced with the problem of #ux and composition variationsacross a pore and problems related to catalystgeometry.The dusty #uid model as developed by Krishna andWesselingh (1997) is a modi"cation of the dusty gasmodel so as to be able to model liquid-phase di!usion inporous media. For a non-ideal mixture we have:x μ ¹ z # x ¹ < p z #x ηB D " x N !x N ! N , (22)c n c D where D is the e!ective Knudsen di!usion coe$cient forspecies i in the porous catalyst.The mass transfer rates are obtained by multiplyingthe #uxes by the interfacial area of the catalyst particles.This is not as straightforward, as it looks, since, dependingon the geometry of the catalyst, the cross-sectionalarea can change along the di!usion path. It is necessaryto take catalyst geometry into account in the solution ofthese equations.The dusty gas model is often used as the basis for thecalculation of a catalyst e!ectiveness factor (Jackson,1977). The extension to non-ideal #uids noted above hasnot been used as often, partly because of the greater

5208 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229uncertainty in the parameters that appear in theequations. Berg and Harris (1993) have developed a detailedmodel of di!usion and reaction in MTBE synthesis.However, their model focuses only on thetransport and reaction issues and they have not developeda complete column/process model. Sundmacher,Ho!mann and their co-workers (Sundmacher &Ho!mann, 1992, 1993, 1994a,b, 1995; Sundmacher et al.,1994; Sundmacher, Zhang & Ho!mann, 1995) have carriedout an extensive study of mass transfer and activityin and around RD catalysts. Sundmacher and Ho!mann(1992) recommend the MS equations over Fick's law formodelling mass transfer in the liquid-phase surroundingan ion-exchange catalyst particle. The reaction ismodelled by an activity-based Langmuir}Hinshelwoodexpression derived from an extensive experimental studyby Reh"nger and Ho!mann (1990a,b). The model is usedto determine the catalyst e!ectiveness factor, and themodel is in good agreement with extensive experimentaldata. Sundmacher and Ho!mann (1994a) developeda detailed model to investigate the interaction betweenmass and energy transport and reaction in an ion-exchangeresin. Catalyst e!ectiveness factors and selectivitiescomputed from the model are in good agreementwith experimental data for MTBE formation obtained ina CSTR. In other papers Sundmacher & Ho!mann(1994, 1995) use the Maxwell}Stefan equations as a basisfor a "lms-in-series mass transfer model for a vapor}liquid-porouscatalyst system. However, di!usion inthe catalyst is described using an e!ective di!usivitymodel that is equivalent to a rearrangement of the dusty#uid model while ignoring the Knudsen di!usion terms.The e!ect of the reaction is lumped into a componentconsumption term, corrected by the catalyst e$ciency.The reaction term is evaluated at bulk liquid conditions.Non-idealities in the liquid-phase were described withthe UNIQUAC equation. The SRK equation of state wasused for the gas phase. Sundmacher and Ho!mann introduce`arti"cial inertia termsa into the interfacemass balances in order to create a system of di!erentialand algebraic equations (DAEs). The DAE systemwas solved with the LIMEX solver (Deu#hard, Hairer& Zugck, 1987). Important conclusions from theirtheoretical work are that the mass transfer resistanceinside the catalyst can vary signi"cantly along the packingand that the main resistance to mass transfer is on theliquid side.5.1. The conventional NEQ modelIt will be helpful to begin with a brief review of theNEQ model for conventional distillation operations.A schematic representation of the NEQ stage is shown inFig. 23. This NEQ stage may represent a tray or a crosssectionof a packed column. The component molar balancesfor the vapor and liquid-phases are< y !< y !f # "0, (23) x !f ! "0, (24)¸x !¸ where is the interfacial mass transfer rate and is theproduct of the molar #ux and the net interfacial area. Theoverall molar balances are obtained by summing Eqs.(23) and (24) over the total number (c) of components inthe mixture. The are obtained from the Maxwell}Stefan(16) modi"ed as follows:x μ ¹ η " x !x c (κ a) (25)with a similar relation for the vapor phase. The κ representsthe mass transfer coe$cient of the i!k pair inthe liquid-phase; this coe$cient is estimated from informationon the corresponding Maxwell}Stefan di!usivityn using the standard procedures discussed inTaylor and Krishna (1993). a is the interfacial area. Onlyc!1 of Eq. (25) are independent. The mole fraction ofthe last component is obtained by the summation equationsfor both phases. The enthalpy balances for bothvapor and liquid-phases are< H!< H !FH# #Q"0, (26)¸H H !FH!#Q"0. !¸ (27)5. Non-equilibrium (NEQ) stage modellingThe NEQ stage model for RD follows the philosophyof rate-based models for conventional distillation(Krishnamurthy & Taylor, 1985; Taylor & Krishna,1993; Taylor, Kooijman & Hung, 1994; Seader & Henley,1998).Fig. 23. The non-equilibrium stage (cell) for homogeneous liquid-phasereaction.

R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5209The interphase energy transfer rates (equal in bothphases) have conductive and convective contributions "!ha ¹ η # H (28) with a similar relation for the vapor phase. h is the heattransfer coe$cient in the liquid-phase. The conductivecontributions are ignored in some modelling studies.This omission results in liquid-phases being (predicted tobe) slightly superheated and vapor phases that are subcooled(Taylor et al., 1994).At the vapor}liquid interface we assume phase equilibriumy "K x , (29)where the subscript I denotes the equilibrium compositionsand K is the vapor}liquid equilibrium ratio forcomponent i on stage j. The K-values are evaluated at thetemperature, pressure and composition of the interfacefrom appropriate thermodynamic models (the samemodels used in conventional equilibrium stage models).In addition to Eqs. (23)}(29), we have the summationequations for the mole fractions in the vapor and liquidphaseand equations expressing the continuity of #uxes ofmass and energy across the interface. Furthermore, in theNEQ model we take account of the pressure drop acrossa stagep !p !(῀p )"0, (30)where p and p are the stage pressures and ῀p is the pressure drop per tray from stage (j!1) to stage j.The pressure drop over the stage is considered to bea function of the stage #ows, the physical properties andthe hardware design. In the NEQ model, hardware designinformation must be speci"ed so that mass transfercoe$cients, interfacial areas, liquid hold-ups, etc. can becalculated. The NEQ model requires thermodynamicproperties, not only for calculation of phase equilibriumbut also for calculation of driving forces for mass transferand, in RD, for taking into account the e!ect of non-idealcomponent behaviour in the calculation of reaction ratesand chemical equilibrium constants. In addition, physicalproperties such as surface tension, di!usion coe$cients,viscosities, etc. for calculation of mass (and heat) transfercoe$cients and interfacial areas are required. Thesteady-state model equations most often are solved usingNewton's method or by homotopy-continuation. A reviewof early applications of NEQ models is available inTaylor & Krishna (1993, Chapter 14).5.2. NEQ modelling of RDBuilding an NEQ model of a reactive separation processis not as straightforward as it is for the EQ stagemodel in which we simply (or not so simply) add a termto account for reaction to the liquid-phase material balances.For a reactive separation process, we "rst need toknow whether the reaction is heterogeneous or homogeneous.For homogeneous systems the component molar balancefor the liquid-phase becomesx !f ! ! ¸x !¸ ν R ε "0, (31)where R is the rate of reaction m on stage j. ν representsthe stoichiometric coe$cient of component i in reac- tion m and ε represents the reaction volume on stage j.For homogeneous reactions this is given by the totalliquid hold-up on stage j and, in an NEQ model, isobtained directly from the column internals speci"cationsand appropriate hydrodynamic correlations.If it is su$ciently rapid, the reaction will also takeplace in the liquid "lm adjacent to the phase interface,and very fast reactions may occur only in the "lm. Ineither case the continuity equations for the "lm are requiredfor taking into account the e!ect of the reactionon the interphase mass transfer rates. The combined setof MS and continuity equations usually must be solvednumerically.The phase equilibrium equations for the interface mayneed to be modi"ed for the in#uence of additional specieson the thermodynamic properties at the interface.Amine-based gas treating again provides a case in pointwhere reactions in the liquid-phase create additionalspecies (including ions) that a!ect the interfacial equilibrium(Glasscock & Rochelle, 1989).For a heterogeneous reaction, there are two optionsfor the description of the reaction term. The simplestapproach is to treat the reaction pseudo-homogeneously,whereby catalyst di!usion and reaction is lumped into anoverall reaction term. For heterogeneous reactions thatare modelled in this way the liquid-phase material balanceis as given above and ε is given by the total amountof catalyst present on the stage under consideration. Inthis case, one only needs to specify catalyst mass andactivity. A more rigorous approach would involve the useof the dusty #uid model discussed above if the catalyst isporous, or reaction at the surface if not. In this case onealso needs information about the catalyst geometry (surfacearea, mean pore diameter, etc). In either case it isunnecessary to allow for reaction in the vapor}liquid "lmand the vapor}liquid transport equations are exactly asgiven above.5.3. NEQ modelsSawistowski and Pilavakis (1979, 1988) modelleda packed RD column for the esteri"cation of methanoland acetic acid to methyl acetate. They used an e!ective

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

5212 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229coe$cients being estimated using the correlations ofOnda, Takeuchi and Okumoto (1968). The model equationswere solved simultaneously. A predicted temperaturepro"le appears to be in good agreement with onedetermined experimentally. However, it must be rememberedthat the all important mass transfer coe$cientswere "tted to data obtained in their own column. Thus,the true predictive abilities of their model are untested. Itis reported that the amount of catalyst and the condensationrate are important design variables for this RDprocess, and that the DAA selectivity would have improvedif the liquid}catalyst mass transfer improved.Podrebarac et al. (1998b) modelled the reactive sectionas a plug-#ow reactor with radial dispersion. The set ofdi!erential and algebraic equations was solved using thegPROMS system. The authors were able to "t their ownexperimental data quite well. However, the model couldnot be used for predictive purposes due, it was claimed, tothe random nature of the #ow in a packed column.The recent study of Baur et al. (1999) comparing theEQ and NEQ models for hydration of ethylene oxide toethylene glycol throws a new light on the phenomena onMSS and the importance of using the NEQ model. Forthe Ciric and Gu (1994) con"guration for the ethyleneglycol column (see Fig. 24(a)), multiple steady-states arefound with both EQ and NEQ models. Three steadystatesSS-1 (high conversion), SS-2 (intermediate conversion)and SS-3 (low conversion) were found. The desiredhigh-conversion steady-state solution (SS-1) correspondsto high column temperatures and lowest molar #ow rateof the vapor up the column. Let us now consider theNEQ model simulations for the 1.7 m diameter columncon"guration. For this chosen column diameter, onlyone solution, SS-1, can be realised in the column. Theother solutions SS-2 and SS-3 could not be realised in theNEQ because for the higher vapor #ows, the column#oods in some (SS-2) or all (SS-3) of the stages; the#ooding boundaries are drawn in Fig. 24(c). Baur et al.(1999) also show that if the column diameter was chosento be 3 m, only the lowest conversion steady-state can berealised!5.4. NEQ cell modelAn issue that is not adequately addressed by mostNEQ models is that of vapor and liquid #ow patterns ondistillation trays or maldistribution in packed columns.Since reaction rates and chemical equilibrium constantsare dependent on the local concentrations and temperature,they may vary along the #ow path of liquid ona tray, or from side to side of a packed column. For suchsystems the residence time distribution could be veryimportant, as well as a proper description of mass transfer.On distillation trays, vapor will rise in plug-#owthrough a layer of froth. The froth will pass through theliquid more or less in plug-#ow, with some axial dispersiondue to the vapor jets and bubbles. In packed sections,maldistribution of internal vapor and liquid #owsFig. 24. (a) Con"guration of reactive distillation column for hydration of ethylene oxide to ethylene glycol used by Ciric and Miao (1994). (b)Equilibrium model calculations for the ethylene glycol process showing column pro"les for liquid-phase mole fraction, temperature and vapor-phasemolar #ow. (c) Non-equilibrium model calculations for the ethylene glycol process for a column of diameter 1.7 m showing the corresponding columnpro"les. Details of the simulations are available in Baur, Higler, Taylor and Krishna (1999).

R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5213Fig. 25. The non-equilibrium cell model of Higler, Krishna and Taylor(1999a).over the cross-sectional area of the column can lead toloss of interfacial area. This is known to be one of themain reasons for inadequate performance of packed columns.To deal with this shortcoming of earlier models,Higler, Taylor and Krishna (1999c) and Higler,Krishna and Taylor (1999a,b) developed an NEQ cellmodel. The distinguishing feature of this model is thatstages are divided into a number of contacting cells, asshown in Fig. 25. These cells describe just a small sectionof the tray or packing, and by choosing an appropriateconnection pattern, one can very easily study the in#uenceof #ow patterns and maldistribution on the distillationprocess.Flow patterns on distillation trays are modelled bychoosing an appropriate number of cells in each #owdirection. A column of cells can model plug-#ow in thevapor phase, and multiple columns of cells can modelplug-#ow in the liquid-phase as depicted in Fig. 26.Backmixing may also be taken into account by using anappropriate number of cells. This may be derived fromcalculating an equivalent number of cells from eddydi!usion models. Flow patterns in packed columns areevaluated by means of a natural #ow model. The #owsare split up according to the ratio of the cell surface areasbetween the cells. Various #ow patterns may be approximatedusing di!erent #ow splitting policies.A schematic diagram of the unit cell for a vapor}liquid}porous catalyst system is shown in Fig. 27. Eachcell is modelled essentially using the NEQ model forheterogeneous systems described above. The bulk of bothvapor and liquid-phases is assumed to be completelymixed. Mass transfer resistances are located in "lms nearthe vapor/liquid and liquid/solid interfaces, and the Maxwell}Stefanequations are used for calculation of themass transfer rates through each "lm. Thermodynamicequilibrium is assumed only at the vapor}liquid interface.Mass transfer inside the porous catalyst may bedescribed with the dusty #uid model described above.The unit cell for homogeneous systems (and for heterogeneoussystems modelled as though they were homogeneous)is as depicted in Fig. 23. The equations for eachcell are essentially as given above.For RD, the staging in the liquid-phase could havea signi"cant in#uence on the reaction selectivity. This isemphasised in the study by Baur et al. (1999) of thein#uence of hardware design on the formation of theby-product DEG in the hydration column (sieve tray)shown in Fig. 24(a). Their simulation results are presentedin Fig. 28. For "ve mixing cells in both vapor andliquid-phases (which corresponds closely to plug-#owconditions for either phase), the formation of by-productDEG is reduced while the conversion to EG is increased.Removing the mass transfer resistances, i.e. assuming theEQ model, gives the best performance with respect toconversion and selectivity; see the point towards thebottom right of Fig. 28. Reaction selectivity can be in-#uenced by tray hardware design. Decreasing the weirheight from 80 mm (base case) to 50 mm decreasesformation of EG and increases by-product DEG formation.This reduction is due to a lowering in the interfacialarea with decreasing weir height. Increasing the weirheight from 80 to 100 mm leads to improved conversionand improved selectivity. High weir heights, and operationin the froth regime, are generally to be preferred inRD operations. Increasing the number of passes from1 to 2 increases by-product formation; see the top pointin Fig. 28. This is because the liquid load per weir lengthis reduced by 50%. This reduction in the liquid load leadsto a reduction in the clear liquid height and lowering inthe total interfacial area, which has a detrimental in#uenceon both the conversion and selectivity. It appearsthat the usual design rules for conventional distillationcolumn design cannot be carried over to RD columnsbecause, for a column of 1.7 m diameter the conventionaldesign philosophy would be to use two passes for theliquid #ow.5.5. Pseudo-homogeneous vs. heterogeneous NEQmodellingHigler, Krishna and Taylor (2000) used the dusty #uidequations to model di!usion and reaction in porouscatalysts in RD. The MTBE process (following thecon"guration of Jacobs and Krishna (1993) shown in

5214 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229Fig. 26. Details of #ows in and out of multiple cells used to model the hydrodynamics of trayed columns.Fig. 27. The non-equilibrium stage (cell) for heterogeneous catalysedreaction.Fig. 20(a)) was simulated under three di!erent sets ofassumptions:A A pseudo-homogeneous approach, in which the catalystis neglected and the reaction rate is evaluated atliquid bulk conditions.B A case in which the Knudsen di!usion coe$cient islarge, in which case the mass transfer interaction withthe catalyst is ignoredC A case one in which the Knudsen di!usion coe$cientis a factor "ve times smaller than the smallest of theMaxwell}Stefan di!usion coe$cients. The value of theKnudsen di!usion coe$cient is assumed to be thesame for all components.Shown in Fig. 29 is the steady-state conversion of isobuteneas a function of the bottom product #owrate. Themultiple steady-state region has disappeared for thedusty #uid model, and the Knudsen di!usion term hasa substantial in#uence on the results of the dusty #uidmodel simulations. This may be explained by the factthat, in the lower branch of the multiple steady-stateregion, MTBE is consumed in part of the column. Therate of consumption of MTBE is very much in#uenced byadditional mass transfer resistances. Additional masstransfer resistances, therefore result in a higher conversion.This is not the case for the TAME process where thereaction rate is very much lower than it is for MTBE andmass transfer in#uences are not signi"cant. Multiplesteady-states have been found experimentally for an RDcolumn used to produce TAME, but not in the MTBEprocess (Rapmund et al., 1998), appearing to con"rm theresults shown in Fig. 29.5.6. Dynamic NEQ modelsKreul, Gorak, Dittrich and Barton (1998) described anNEQ model for RD in packed columns. Theirs is a dynamicmodel that, as is usual in such models, neglects thehold-up in the vapor-phase. Their paper addresses theproblems of modelling mass transfer and reaction ina vapor}liquid}porous catalyst system. In addition, they

R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5215Fig. 28. In#uence of tray hardware and number of mixing cells on the formation of by-product DEG in the hydration of ethylene oxide to ethyleneglycol (EG). The column con"guration (diameter"1.7 m) is that shown in Fig. 24(a). Details of the simulations are available in Baur, Higler, Taylorand Krishna (1999).Fig. 29. Comparison of the results for conversion of iso-butene obtainedby three di!erent model formulations for taking account ofchemical reactions: (A) pseudo-homogeneous, (B) dusty #uid modelwithout Knudsen contribution, and (C) dusty #uid model with Knudsencontribution. Adapted from Higler, Krishna and Taylor (2000).describe a two-phase model in which di!usion and reactionto and within the solid catalyst is not accounted forby additional equations (and parameters), but their effectsare lumped into a kinetic term that appears in theliquid-phase material balances. The choice of which ofthese two approaches was adopted for their simulationsis not completely clear. The material balances (partialdi!erential equations) are discretised in the spatial dimension(the column height) using the method of lines.The model equations were solved using the equationbasedmodelling environment ABACUS (Allgor, Berrera,Barton & Evans, 1996). The paper by Kreul et al. includesa limited comparison with some unsteady-statedata for a methyl acetate column. The results shown inthe paper suggest that their dynamic model is well able todescribe the product composition transients. The actualexperimental data are not provided in the paper.Kreul, Gorak and Barton (1999b) described an NEQmodel to study batch distillation. In essence, the model isan extension and generalisation of the dynamic NEQmodels of Kooijman and Taylor (1995) for tray columnsand Pelkonen, Gorak, Kooijman and Taylor (1997) forpacked columns. The MS equations were used to modelvapor and liquid-phase mass transfer. The model systemwas implemented and solved using the ABACUS system.The paper includes extensive comparisons of true modelpredictions of experiments performed in a pilot plantcolumn involving the system methanol}acetic acid}methyl acetate}water. Under the conditions in the experimentsthere was essentially no liquid-phase chemicalreaction; vapor-phase dimerisation was, however, takeninto account. The agreement between the predicted andmeasured compositions is exceptionally good.Strictly speaking, reactive absorption falls outside thescope of this review. However, NEQ models as outlinedabove apply more or less unchanged in principle toreactive absorption and RD alike. The only di!erencesbetween the models are the inclusion of di!erent submodelsfor the reaction kinetics and thermodynamicproperties. A nitric acid recovery plant modelled byWiesner, Wittig and Gorak (1996) and by Kenig andGorak (1997) involves nine di!erent reactions and simultaneoustransport and reaction of 10 di!erent species.Schneider, Kenig and Gorak (1999) used the Maxwell}Stefanapproach to model the dynamics of reactiveabsorption processes. Of particular interest in theirmodel is the inclusion of the gradient of the electricalpotential in the Maxwell}Stefan equations and theelectro-neutrality equation that must be satis"ed at allpoints in the liquid due to the presence of ions in theprocesses they model. Rascol, Meyer, Le Lann and

5216 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229Prevost (1998) brie#y addressed some numerical problemsthat can be encountered in the simulation of reactiveabsorption using NEQ models. We have already notedthe success (using e!ective di!usivities and enhancementfactor approaches to mass transfer with reaction) of NEQmodels of amine-based gas treating processes (Careyet al., 1991; Altiqi et al., 1994).6. Reactive distillation designDesign and simulation of RD operations are verydi!erent types of calculation, calling for verydi!erent approaches. Most conceptual design models arebased on the EQ stage model described above. However,as discussed below, some recent developments haveopened up the possibility of using NEQ models for RDdesign, and a limited number of papers suggest that NEQmodels already have a place in industrial RD designpractice.6.1. Conceptual designBarbosa and Doherty (1988c) developed the "xedpointmethod for the design of single-feed RD columns.The method is based on the following assumptions: the column is adiabatic; the molar heat of vaporisation is constant; the heat of mixing is negligible; sensible heat e!ects can be ignored; the heat of reaction is negligible compared to theenthalpy of the vapor; the feed is a saturated liquid; phase equilibrium is achieved on each stage; the column operates with a partial condenser.These assumptions ensure that the vapor and liquid #owsinside the column are constant, thereby permitting theenergy balances to be solved essentially independent ofthe remaining stage equations.The "xed-point method uses material balance equationswritten around a stage in each section of the column(above and below the feed stage) and thecorresponding end of the column. With reference to Fig.18(a), for example, we have, for the rectifying sectionX " rH #1 > ! 1 > (32) rH rH and for the stripping section the material balance readsX "sH sH#1 > ! 1sH#1 X . (33) Note that these equations have been written in terms ofthe transformed composition variables de"ned by Eq. (3).The transformed re#ux and stripping ratios are de"nedas follows:rH "¸ (ν !ν x )D(ν !ν y ) , sH "

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

5218 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229di!erence between an arbitrary composition and a singularpoint. The use of these di!erence points in RD processdesign is the subject of two recent papers by Hauan,Ciric, Westerberg and Lien (2000a) and by Lee, Hauan,Lien and Westerberg (2000c).Pistikopolous and co-workers (see Papalexandri &Pistikopolous, 1996; Ismail, Pistikopolous &Papalexandri, 1999) have developed a phenomena-basedmodelling framework that is able to capture hybrid reactive/separationprocesses. In their approach an RD process(here meaning more than just a single RD column) issynthesised from a collection of modules that involvereaction, reaction and separation, or only separation. Inthis context a module does not necessarily representa single model stage, but a collection of such stages.Either EQ or NEQ stage models could be used in thisapproach. Papalexandri and Pistikopolous (1996) illustratetheir methodology with the design of an ethyleneglycol column, while Ismail et al. (1999) considered theproduction of ethyl acetate from acetic acid and ethanol.Bessling, Schembecker and Simmrock (1997a,b) combineheuristic rules, numerical computation, and RD linediagrams to study the feasibility of RD processes. Theydevise a method for identifying RD processes in whichthe RD column needs to be divided into reactive andnon-reactive sections. Bessling, Loning, Ohligschlager,Schembecker and Sundmacher (1998) use these RD linediagrams to identify the main process parameters and toprovide a basis for an experimental study in the methylacetate process. The signi"cant in#uence of the re#uxratio on conversion is shown by simulation using an EQstage model and by experiments in a small-scale columnthat employed packing in the form of Raschig rings.Sera"mov and co-workers (Balashov & Sera"mov,1980; Balashov, Patlasov & Sera"mov, 1981; Pisarenko& Sera"mov, 1988, 1992; Pisarenko et al., 1988a, b;Pisarenko, Danilov & Sera"mov, 1995, 1996, 1997;Giessler et al., 1998, 1999; Sera"mov, Pisarenko& Kulov, 1999b; Sera"mov et al., 1999a) have developeda method they call static analysis. It is the result of anextensive investigation of the thermodynamic andtopological structure of distillation diagrams. Themethod requires very little fundamental data on the systemand is based on an assumption that the vapor andliquid #ow rates in the column are very large. As a resultof this assumption the composition change caused by thereaction is small on each stage and can be neglected. Thedesired product compositions, extent of reaction, andnumber of stages need not be "xed a priori. The mostaccessible work from this group is the paper by Giessleret al. (1998) who outline the steps of the method and illustrateit with a case study of the MTBE process. Giessleret al. (1999) applied the method to "ve other RD processes:the production of acetic acid, cumene, ethylene glycol,ethyl or methyl acetate, and butyl acetate. The in#uenceof inerts can also be considered with this approach.6.2. Graphical design methodsA graphical (Ponchon}Savarit type) design procedurefor RD columns based on the transformed compositionvariables of Barbosa & Doherty (1988) is described byEspinosa, Scenna and Perez (1993). The MTBE process isused to illustrate their method.Lee, Hauan, Lien and Westerberg (2000a,b) and Leeet al. (2000d) have recently presented an in-depth analysisof the classical Ponchon-Savarit and McCabe}Thielegraphical methods for RD systems.6.3. Design via optimisation methodsRD design via optimisation methods has been thesubject of a few studies. Ciric and Gu (1994) formulateda mixed integer nonlinear programming model, solution ofwhich yields the optimal number of EQ stages, feed ratesand re#ux ratios at a minimal annual cost. To the best ofour knowledge this was the "rst paper that combines RDcolumn design and cost estimation, thereby emphasizingthe fact that the usual optimisation techniques for ordinarydistillation processes may be inappropriate for RD.Gumus and Ciric (1997) used a bilevel optimisation procedureto explore the design of RD columns that couldhave more than one liquid-phase. The number of phasesand the phase equilibria were determined by minimisingthe Gibbs free energy. Their paper was illustrated byconsidering the liquid-phase hydrogenation of nitrobenzeneto aniline, in which the resulting aniline}nitrobenzene}watersystem can split into two liquid-phases.Eldarsi and Douglas (1998b) used the optimisationcapability in Aspen Plus to optimise an MTBE column.Their study indicated that the market price of the MTBEproduct, the cost of the butylenes, the isobutylene compositionand utility costs all in#uence the MTBE columnpro"t. Pekkanen (1995b) described a local optimisationmethod for the design of RD. Duprat, Gassend & Gau(1988) constructed a set of empirical formulae that wasused to optimise an RD process for the separation of theclose-boiling mixture of 3-picoline and 4-picoline. Thelatter method leads to the most rapid optimisation calculationsonce the empirical formulae have been constructed(by "tting the results of rigorous model simulations).However, the di!erences between RD processes meansthat the formulae developed for one process have novalue for modelling others.6.4. From conceptual design to column designUntil recently, a procedure to go from a viable EQstage design to an actual column design was not availablein the literature. An important paper by Subawalla andFair (1999) addresses this issue with a lengthy discussionof the importance of several key design parameters: pressure,reactive zone location, reactant feed ratio, feed

R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5219Table 1Procedure to estimate the reactive zone height, re#ux ratio, and column diameter (from: Subawalla and Fair, 1999)1. Assume that the column feed stream consists of a prereacted mixture of products and reactants at a desired conversion.2. Specify the distillate and bottom product compositions and determine minimum re#ux requirements using the Underwood method. Useare#ux ratio 20% greater than the minimum re#ux ratio as an initial estimate to determine column vapor and liquid velocities.3. Estimate the diameter form the maximum allowable vapor velocity (80% of #ood velocity).4. Estimate the catalyst volume from the catalyst mass and maximum packing catalyst density:< " m ρ 5. Determine the reactive zone height from the calculated catalyst volume and estimated diameter.h " < (π)d 6. Determine the number of reactive stages by dividing the total reactive zone height by the catalytic packing HETP.N "h HETP 7. Simulate a reactive column with the calculated number of recti"cation, reaction, and stripping stages.8. Increase the re#ux ratio by 10%. If the conversion decreases, go to step 9. If the conversion increases, calculate the new maximum vapor velocityand column diameter and repeat steps 4}7. Keep increasing the re#ux ratio in 10% increments and repeating steps 4}7 (if necessary) until thereis no charge in conversion. Go to step 10.9. If the conversion decreases with increasing re#ux, decrease the re#ux ratio by 10%, calculate a new maximum vapor velocity and columndiameter, and repeat steps 4}7. Keep decreasing the re#ux ratio in 10% increments and repeating steps 4}7 (if necessary) until there is no changein conversion. Go to step 10.10. If the desired conversion is attained, then we have reliable estimates for the reactive zone height, re#ux ratio and column diameter. If the desiredconversion is not attained, increase the catalyst mass and repeat the procedure starting with step 3.location, catalyst mass, number of equilibrium stages,reactive zone height, column diameter, re#ux ratio, andHETP. Their detailed step-by-step procedure for designingan RD column is summarised in Table 1. Their paperincludes a case study in which their design procedure isapplied to the production of TAME. The authors makethe important point that their procedure is not applicableto all RD processes: `each system has certain characteristicsthat make the use of one or more of these guidelinesdi$culta.Step 7 in Table 1 should be singled out for particularattention as the one that relies on the models discussed inthis article. At the end of their paper the authors recommendusing NEQ or rate-based models for this purpose.6.5. RD design in industrial practiceAt the time the Eastman methyl acetate process wasdeveloped there were no commercially available simulationprograms capable of modelling RD operations.Agreda et al. (1990) reported that stage-to-stage handcalculations were done using #ash and reaction programsto calculate the vapor and liquid compositions in thereactive section. The conventional distillation columnsections were modelled using an existing EQ model simulationprogram. Computer programs to model a completeRD column had to be developed in-house at thesame time as pilot plant work was being carried out.Pinjala, DeGarmo, Ulowetz, Marker and Luebke(1992) used the NEQ model RATEFRAC to modelMTBE and TAME processes in columns "lled with KochKataMax packing. Very little information on the form ofthe model is provided (i.e. how the reaction is broughtinto the model, the actual kinetic expressions are left tothe imagination. Limited comparisons with pilot-plantdata look quite good. However, the data are provided insuch a way as to render them unusable in independentmodelling studies.Frey, Ozmen, Hamm, Pinjala and DeGarmo (1993)have reported that RATEFRAC has been used to accuratelypredict the performance of commercial RD processesin Germany and Texas, and that the model hasbeen validated for the design of TAME, ETBE, andTAEE units with data from semi-commercial operations.7. Concluding remarksBelck (1955) concludes his paper describing a handcalculation method for RD columns with the followingwords:2as the complexity of the system increases, thecalculation becomes increasingly di$cult 2 the uncertaintyinherent in the experimental determination ofreaction rate constants and liquid}vapor diagrams

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.

5222 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229Altiqi, I., Sabri, M. F., Bouhamra, W., & Alper, E. (1994). Steady-staterate-based modelling for CO /amine absorption-desorption systems.Gas Separation and Purixcation, 8, 3}11.Asselineau, L., Mikitenko, P., Viltard, J. C., & Zuliani, M. (1994) U.S.Patent 5368691: Reactive distillation process and apparatus forcarrying it outBabcock, P. D., & Clump, C. W. (1978). Distillation of chemicallyreactive solutions. In N.N. Li, Recent developments in separationscience, vol. IV (pp. 149}166).Backhaus, A. A. (1921). Continuous processes for the manufacture ofesters, US patent 1400849.Backhaus, A. A. (1922). Apparatus for producing high grade esters, USpatent 1403224.Backhaus, A. A. (1923a). Process for producing high grade esters, USpatent 1454462.Backhaus, A. A. (1923b). Process for esteri"cation, US patent 1454463.Balashov, M. I., Patlasov, V. P., & Sera"mov, L. A. (1981). Rules ofprimary reaction zone spread in continuous combined reactionfractionationprocess. Theoretical Foundations of Chemical Engineering,15, 406}413.Balashov, M. I., & Sera"mov, L. A. (1980). The statics analysis ofcontinuous combined reaction-fractionation process. TheoreticalFoundations of Chemical Engineering, 14, 803}808.Barbosa, D., & Doherty, M. F. (1987a). Theory of phase diagrams andazeotropic conditions for two-phase reactive systems. Proceedingsof the Royal Society London A, 413, 443}458.Barbosa, D., & Doherty, M. F. (1987b). A new set of compositionvariables for the representation of reactive phase diagrams. Proceedingsof the Royal Society London A, 413, 459}464.Barbosa, D., & Doherty, M. F. (1988a). The in#uence of equilibriumchemical reactions on vapor liquid-phase diagrams. Chemical EngineeringScience, 43, 529}540.Barbosa, D., & Doherty, M. F. (1988b). The simple distillation ofhomogeneous reactive mixtures. Chemical Engineering Science, 43,541}550.Barbosa, D., & Doherty, M. F. (1988c). Design and minimum re#uxcalculations for single-feed multicomponent reactive distillation columns.Chemical Engineering Science, 43, 1523}1537.Barbosa, D., & Doherty, M. F. (1988d). Design and minimum re#uxcalculations for double-feed multicomponent reactive distillationcolumns. Chemical Engineering Science, 43, 2377}2389.Barbosa, D., & Doherty, M. F. (1990). Theory of phase diagrams andazeotropic conditions for two-phase reactive systems. Proceedingsof the Royal Society London A, 430, 669}678.Bart, H. -J., & LandschuK tzer, H. (1996). Heterogene Reaktivdestillationmit axialer RuK ckvermischung. Chemie Ingenieur Technik, 68,944}946.Bart, H. -J., & Reidetschlager, J. (1995). Distillation with chemicalreactionand apparatus selection. Separaration Science and Technology,30, 1849}1865.Bart, H. -J., & Resil, H. -O. (1997). Der Hybridprozess Reaktivdestillation/Pervaporationzur Herstellung von CarbonsaK ureestern.Chemie Ingenieur Technik, 69, 824}827.Bartlett, D. A., & Wahnscha!t, O. M. (1998). Dynamic simulation andcontrol strategy evaluation for MTBE reactive distillation. In J.F.Pekny & G.E. Blau, Foundations of computer-aided process operation,AIChE Symposium Series, vol. 320, (pp. 315}321).Van Baten, J. M., & Krishna, R. (2000). Modelling of sieve tray hydraulicsusing computational #uid dynamics. Chemical Engineering Journal,77, 143}152.Baur, R., Higler, A. P., Taylor, R., & Krishna, R. (1999). Comparison ofequilibrium stage and nonequilibrium stage models for reactivedistillation. Chemical Engineering Journal, 76, 33}47.Belck, L. H. (1955). Continuous reactions in distillation equipment.American Institute of Chemical Engineers Journal, 1, 467}470.Berman, S., Isbenjian, H., Sedo!, A., & Othmer, D. F. (1948a). Esteri"-cation. Continuous production of Dibutyl phthalate in a distillationcolumn. Industrial and Engineering Chemistry, 40, 2139}2148.Berman, S., Melnychuk, A., & Othmer, D. F. (1948b). Dibutylphthalate. Reaction rate of catalytic esteri"cation. Industrial andEngineering Chemistry, 40, 1312}1319.Bessling, B., Loning, J. -M., Ohligschlager, A., Schembecker, G., & Sundmacher,K. (1998). Investigations on the synthesis of methyl acetatein a heterogeneous reactive distillation process. Chemical Engineeringand Technolgy, 21, 393}400.Bessling, B., Schembecker, G., & Simmrock, K. H. (1997a). Design ofprocesses with reactive distillation line diagrams. Industrial andEngineering Chemistry Research, 36, 3032}3042.Bessling, B., Schembecker, G., & Simmrock, K. H. (1997b). Design ofreactive distillation processes with reactive and nonreactive distillationzones. Distillation and absorption '97, Institute of ChemicalEngineers Symposium Series, vol. 142 (pp. 675}684).Bezzo, F., Bertucco, A., Forlin, A., & Barolo, M. (1999). Steady-stateanalysis of an industrial reactive distillation column. Separation andPurixcation Technology, 16, 251}260.Block, U. (1977). Carrying out continuous reactions with superposeddistillation. Chemie Ingenieur Technik, 49(2), 151.Block, U., & Hegner, B. (1977). Simulationsmethode fur homogeneFlussigphasenreacktion mit uberlagerter Destillation. Verfahrenstechnik,11(2), 101}104.Bock, H., & Wozny, G. (1997). Analysis of distillation and reactionrate in reactive distillation. Distillation and absorption '97. Instituteof Chemical Engineers Symposium Series, vol. 142 (pp.553}564).Bogacki, M. B., Alejski, K., & Szymanowski, J. (1989). The fast methodof the solution of a reacting distillation problem. Computers andChemical Engineering, 13, 1081}1085.Bollyn, M. P., & Wright, A. R. (1998). Development of a reactiveprocess model for a batch reactive distillation * a case study.Computers and Chemical Engineering, 22, S87}S94.Bondy, R. W. (1991) Physical continuation approaches to solvingreactive distillation problems. Paper presented at the AIChE meeting,Los Angeles.Bravo, J. L., Pyhalathi, A., & Jaervelin, H. (1993). Investigations ina catalytic distillation pilot plant: Vapor/ liquid equilibrium, kineticsand mass transfer issues. Industrial and Engineering ChemistryResearch, 32, 2220}2225.Buchholz, M., Pinaire, R., & Ulowetz, M. A. (1995). Structure andmethod for catalytically reacting #uid streams in mass transferapparatus, European patent 448884B1.Buzad, G., & Doherty, M. F. (1994). Design of three componentkinetically controlled reactive distillation systems using "xed-pointmethods. Chemical Engineering Science, 49, 1947}1963.Buzad, G., & Doherty, M. F. (1995). New tools for the design ofkinetically controlled reactive distillation columns for ternary mixtures.Computers and Chemical Engineering, 19, 395}408.Carey, T. T., Hermes, J. E., & Rochelle, G. T. (1991). A model of acid gasabsorption/stripping using MDEA with added acid. Gas Separationand Purixcation, 5, 95}109.Carland, R. J. (1994). Fractionation tray for catalytic distillation, USpatent 5308451.Carra, S., Morbidelli, M., Santacesaria, E., & Buzzi, G. (1979a). Synthesisof propylene oxide from propylene chlorohydrins * II.Modeling of the distillation with chemical reaction unit. ChemicalEngineering Science, 34, 1133}1140.Carra, S., Santacesaria, E., Morbidelli, M., & Cavalli, L. (1979b).Synthesis of propylene oxide from propylene-chlorohydrins* I Kinetic aspects of the process. Chemical Engineering Science, 34,1123}1132.Chang, Y. A., & Seader, J. D. (1988). Simulation of continuous reactivedistillation by a homotopy continuation method. Computers andChemical Engineering, 12, 1243}1255.Ciric, A. R., & Gu, D. (1994). Synthesis of nonequilibrium reactivedistillation by MINLP optimization. American Institute of ChemicalEngineers Journal, 40, 1479}1487.

R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5223Ciric, A. R., & Miao, P. (1994). Steady-state multiplicities in an ethyleneglycol reactive distillation column. Industrial and Engineering ChemistryResearch, 33, 2738}2748.Ciric, A. R., & Spencer, J. (1995). Shortcut calculations in reactivedistillation. Paper 21d, AIChE National Meeting, Miami Beach.Cleary, W., & Doherty, M. F. (1985). Separation of closely boilingmixtures by reactive distillation. 2. Experiments. Industrial and EngineeringChemistry Process Design & Development, 24, 1071}1173.Cornelisse, R., Beenackers, A. A. C. M., van Beckum, F. P. H., & vanSwaaij, W. P. M. (1980). Numerical calculation of simultaneousmass transfer of two gasses accompanied by complex reversiblereactions. Chemical Engineering Science, 35, 1245}1260.Corrigan, T. E., & Ferris, W. R. (1969). A development study ofmethanol acetic acid esteri"cation. Canadian Journal of ChemicalEngineering, 47, 334}335.Corrigan, T. E., & Miller, J. H. (1968). E!ect of distillation on a chemicalreaction. Industrial and Engineering Chemistry Research ProcessDesign and Development, 7, 383}384.Crossland, C. S., Gildert, G. R., & Hearn, D. (1995). Catalytic distillationstructure, US patent 5431890.Cuille, P. E., & Reklaitis, G. V. (1986). Dynamic simulation of multicomponentbatch recti"cation with chemical reactions. Computersand Chemical Engineering, 10, 389}398.Danckwerts,P.V.(1970).Gas}liquid reactions.NewYork:McGraw-Hill.Davies, B., Jenkins, J. D., & Dilfanian, S. (1979). Distillation withchemical reaction * the distillation of formaldehyde solutions ina sieve plate column. Institute of Chemical Engineers SymposiumSeries, 56, 65}79.Deu#hard, P., Hairer, E., & Zugck, J. (1987). One-step and extrapolationmethods for di!erential-algebraic equations. Numerical Mathematics,51, 501}516.DeGarmo, J. L., Parulekar, V. N., & Pinjala, V. (1992). Considerreactive distillation. Chemical Engineering Progress, 3, 43}50.Doherty, M. F. (1990). Topological theory of phase diagrams for reactingmixtures. Proceedings of the Royal Society London A, 430,669}678.Doherty, M. F., & Buzad, G. (1992). Reactive distillation by design.Chemical Engineering Research and Design, Transactions of the Institutionof Chemical Engineers, Part A, 70, 448}458.Doherty, M. F., & Buzad, G. (1994). New tools for the design ofkinetically controlled reactive distillation columns. Computers andChemical Engineering, 18, S1}S13.Duprat, F., Gassend, R., & Gau, G. (1988). Reactive distillation processoptimization by empirical formulae construction. Computers andChemical Engineering, 11, 1141}1149.Duprat, F., & Gau, G. (1991a). Reactive distillation of pyridine mixtureswith an organic acid. I. Determination of the reactive distillationequilibrium. Canadian Journal of Chemical Engineering, 69,1320}1326.Duprat, F., & Gau, G. (1991b). Reactive distillation of pyridine mixtureswith an organic acid. II. Parametric sensitivity and optimizationof the process. Canadian Journal of Chemical Engineering, 69,1327}1335.Egly, H., Ruby, V., & Seid, B. (1979). Optimum design and operation ofbatch recti"cation accompanied by chemical reaction. Computersand Chemical Engineering, 3, 169}174.Eldarsi, H. S., & Douglas, P. L. (1998a). Methyl-tert-butyl ether catalyticdistillation column. Part I: Multiple steady-states. ChemicalEngineering Research and Design, Transactions of the Institution ofChemical Engineers, Part A, 76, 509}516.Eldarsi, H. S., & Douglas, P. L. (1998b). Methyl-tert-butyl ether catalyticdistillation column. Part II: Optimization. Chemical EngineeringResearch and Design, Transactions of the Institution of ChemicalEngineers, Part A, 76, 517}524.Ellenberger, J., & Krishna, R. (1999). Counter-current operation ofstructured catalytically packed distillation columns: Pressure drop,hold-up and mixing. Chemical Engineering Science, 54, 1339}1345.Espinosa, J., Aguirre, P. A., Frey, T., & Stichlmair, J. (1999). Analysis of"nishing reactive distillation columns. Industrial and EngineeringChemistry Research, 38, 187}196.Espinosa, J., Aguirre, P. A., & Perez, G. A. (1995a). Some aspects inthe design of multicomponent reactive distillation columns includingnon reactive species. Chemical Engineering Science, 50, 469}484.Espinosa, J., Aguirre, P. A., & Perez, G. A. (1995b). Product compositionregions of single feed reactive distillation column: Mixturescontaining inerts. Industrial and Engineering Chemistry Research, 34,853}861.Espinosa, J., Aguirre, P. A., & Perez, G. A. (1996). Some aspects in thedesign of multicomponent reactive distillation columns with a reactingcore: Mixtures containing inerts. Industrial and EngineeringChemistry Research, 35, 4537}4549.Espinosa, J., Martinez, E., & Perez, G. A. (1994). Dynamic behavior ofreactive distillation columns, equilibrium systems. Chemical EngineeringCommunications, 128, 19}42.Espinosa, J., Scenna, N., & Perez, G. A. (1993). Graphical procedure forreactive distillation systems. Chemical Engineering Communications,119, 109}124.Fair, J. R. (1998). Design aspects for reactive distillation * columns forsimultaneous reaction and separation need skilful planning. ChemicalEngineering (New York), 105(11), 158.Feinberg, M. (1999). Recent results in optimal reactor synthesis viaattainable region theory. Chemical Engineering Science, 54,2535}2543.Feinberg, M., & Hildebrandt, D. (1997). Optimal reactor design froma geometric viewpoint * I. Universal properties of the attainableregion. Chemical Engineering Science, 52, 1637}1665.Flato, J., & Ho!mann, U. (1992). Development and start-up of a "xedbed reaction column for manufacturing antiknock enhancer MTBE.Chemical Engineering and Technology, 15, 193}201.Frank, M. J. W., Kuipers, J. A. M., Krishna, R., & van Swaaij, W. P. M.(1995a). Modeling of simultaneous mass and heat transfer withchemical reaction using the Maxwell Stefan theory * II. Nonisothermalstudy. Chemical Engineering Science, 50, 1661}1671.Frank, M. J. W., Kuipers, J. A. M., Versteeg, G., & van Swaaij, W. P. M.(1995b). Modeling of simultaneous mass and heat transfer withchemical reaction using the Maxwell Stefan theory * I. Modeldevelopment and isothermal study. Chemical Engineering Science,50, 1645}1659.Frey, S. J., Ozmen, S. M., Hamm, D. A., Pinjala, V., & DeGarmo, J. L.(1993). Advanced ether technology commercialised. Paper presentedat the world conference on clean fuels and air quality control,Washington, DC.Frey, T., & Stichlmair, J. (1999a). Thermodynamic fundamentals ofreactive distillation. Chemical Engineering and Technology, 22,11}18.Frey, T., & Stichlmair, J. (1999b). Reactive azeotropes in kineticallycontrolled reactive distillation. Chemical Engineering Research andDesign, Transactions of the Institution of Chemical Engineers, Part A,77, 613}618.Fuchigami, Y. (1990). Hydrolysis of methyl acetate in distillation columnpacked with reactive packing of ion exchange resin. Journal ofChemical Engineering Japan, 23, 354}358.Gani, R., Jepsen, T. S., & Perez-Cisneros, E. (1998). A generalizedreactive separation unit model. Modelling and simulation aspects.Computers and Chemical Engineering, 22, S363}S370.Gaspillo, P. -A., Abella, L. C., & Goto, S. (1999). Dehydrogenation of2-propanol in reactive distillation column for chemical heat pump.Journal of Chemical Engineering Japan, 31, 440}444.Gehrke, V., & Marquardt, W. (1997). A singularity theory approach tothe study of reactive distillation. Computers and Chemical Engineering,21, S1001}S1006.Gelbein, A. P., & Buchholz, M. (1991). Process and structure fore!ecting catalytic reactions in distillation structure, US patent5073236.

5224 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229Giessler, S., Danilov, R. Y., Pisarenko, R. Y., Sera"mov, L. A., Hasebe,S., & Hashimoto, I. (1998). Feasibility study of reactive distillationusing the analysis of statics. Industrial and Engineering ChemistryResearch, 37, 2220}2225.Giessler, S., Danilov, R. Y., Pisarenko, R. Y., Sera"mov, L. A., Hasebe,S., & Hashimoto, I. (1999). Feasibile separation modes for variousreactive distillation systems. Industrial and Engineering ChemistryResearch, 38, 4060}4067.Glasscock, D. A., & Rochelle, G. T. (1989). Numerical simulation oftheories for gas absorption with chemical reaction. American Instituteof Chemical Engineers Journal, 35, 1271}1281.Glasser, D., & Hildebrandt, D. (1997). Reactor and process synthesis.Computers and Chemical Engineering, 21, S775}S783.Gonzalez, J. C., & Fair, J. R. (1997). Preparation of tertiary amylalcohol in a reactive distillation column.1. Reaction kinetics, chemicalequilibrium, and mass-transfer issues. Industrial and EngineeringChemistry Research, 36, 3833}3844.Gonzalez, J. C., Subawalla, H., & Fair, J. R. (1997). Preparation oftert-amyl alcohol in a reactive distillation column.2. Experimentaldemonstration and simulation of column characteristics. Industrialand Engineering Chemistry Research, 36, 3845}3853.Grosser, J. H., Doherty, M. F., & Malone, M. F. (1987). Modeling ofreactive distillation systems. Industrial and Engineering ChemistryResearch, 26, 983}989.Groten, W. A., Booker, D., & Crossland, C. S. (1998). Catalytic distillationstructure, US patent 5730843.van Gulijk, C. (1998). Using computational #uid dynamics to calculatetransversal dispersion in a structured packed bed. Computers andChemical Engineering, 22, S767}S770.Gumus, Z. H., & Ciric, A. (1997). Reactive distillation column designwith vapor/liquid/liquid equilibria. Computers and Chemical Engineering,21, S983}S988.GuK ttinger, T. E. (1998). Multiple steady states in azeotropic and reactivedistillation. Dissertation ETH No. 12720, Swiss Federal Institute ofTechnology (ETH), Zurich.GuK ttinger, T. E., & Morari, M. (1997). Predicting multiple steady statesin distillation: Singularity analysis and reactive systems. Computersand Chemical Engineering, 21, S995}S1000.GuK ttinger, T. E., & Morari, M. (1999a). Predicting multiple steadystates in equilibrium reactive distillation. 1. Analysis of nonhybridsystems. Industrial and Engineering Chemistry Research, 38,1633}1648.GuK ttinger, T. E., & Morari, M. (1999b). Predicting multiple steadystatesin equilibrium reactive distillation. 2. Analysis of hybridsystems. Industrial and Engineering Chemistry Research, 38,1649}1665.Van Hasselt, B. (1999). The three-levels-of-porosity reactor. Ph.D. dissertationin Chemical Engineering, Delft University of Technology.Hauan, S. (1998). On the behaviour of reactive distillation systems. Doctoralthesis, Norwegian University of Science and Technology,Trondheim.Hauan, S., Hertzberg, T., & Lien, K. M. (1995). Why methyl-tertbutyl-etherproduction by reactive distillation may yield multiplesolutions. Industrial and Engineering Chemistry Research, 34,987}991.Hauan, S., Hertzberg, T., & Lien, K. M. (1997). Multiplicity in reactivedistillation of MTBE. Computers and Chemical Engineering, 21,1117}1124.Hauan, S., & Hildebrandt, D. (1999). An introduction to reactivedistillation. Chemical Technology (RSA), 8}12.Hauan, S., & Lien, K. M. (1996). Geometric visualization of reactive"xed points. Computers and Chemical Engineering, 20,S133}S138.Hauan, S., & Lien, K. M. (1998). A phenomena based design approachto reactive distillation. Chemical Engineering Research and Design,Transactions of the Institution of Chemical Engineers, Part A, 76,396}407.Hauan, S., Schrans, S., & Lien, K. M. (1997). Dynamic evidence of themultiplicity mechanism in methyl tert-butyl ether reactive distillation.Industrial and Engineering Chemistry Research, 36, 3995}3998.Hauan, S., Ciric, A. R., Westerberg, A. W., & Lien, K. M. (2000a).Di!erence points in extractive and reactive cascades. I * basicproperties and analysis. Chemical Engineering Science, 55,3145}3159.Hauan, S., Westerberg, A. W., & Lien, K. M. (2000b). Phenomenabasedanalysis of "xed points in reactive separation systems. ChemicalEngineering Science, 55, 1053}1075.Hearn, D. (1993). Catalytic distillation machine, US patent 5266546.Henley, E. J., & Seader, J. D. (1981). Equilibrium-stage separation operationsin chemical engineering. New York: Wiley.Higler, A. P., Krishna, R., Ellenberger, J., & Taylor, R. (1999a).Counter-current operation of a structured catalytically packed bedreactor: Liquid-phase mixing and mass transfer. Chemical EngineeringScience, 54, 5145}5152.Higler, A. P., Taylor, R., & Krishna, R. (1998). Modeling of a reactiveseparation process using a nonequilibrium stage model. Computersand Chemical Engineering, 22, S111}S118.Higler, A. P., Taylor, R., & Krishna, R. (1999b). Nonequilibrium Modellingof reactive distillation: Multiple steady states in MTBE synthesis.Chemical Engineering Science, 54, 1389}1395.Higler, A. P., Taylor, R., & Krishna, R. (1999c). The in#uence ofmass transfer and liquid mixing on the performance of reactivedistillation tray column. Chemical Engineering Science, 54,2873}2881.Higler, A., Krishna, R., & Taylor, R. (1999a). A nonequilibrium cellmodel for multicomponent (reactive) separation processes. AmericanInstitute of Chemical Engineers Journal, 45, 2357}2370.Higler, A., Krishna, R., & Taylor, R. (1999b). A non-equilibrium cellmodel for packed distillation columns. The in#uence of maldistribution.Industrial and Engineering Chemistry Research, 38, 3988}3999.Higler, A., Krishna, R., & Taylor, R. (2000). Non-equilibrium modellingof reactive distillation: A dusty #uid model for heterogeneouslycatalysed processes. Industrial and Engineering Chemistry Research,39, 1596}1607.Holland, C. D. (1963). Multicomponent distillation. Englewood Cli!s, NJ:Prentice-Hall.Holland, C. D. (1981). Fundamentals of multicomponent distillation. NewYork: McGraw-Hill.Hu, M., Zhou, X. -G., & Yuan, W. -K. (1999). Simulation and optimizationof a coupled reactor/column system for trioxane synthesis.Chemical Engineering Science, 54, 1353}1358.Huang, C. C., Podrebarac, G. G., Ng, F. F. T., & Rempel, G. L. (1998a).A study of mass transfer behaviour in a catalytic distillation column.Canadian Journal of Chemical Engineering, 76, 323}330.Huang, C. C., Yang, L., Ng, F. F. T., & Rempel, G. L. (1998b).Application of catalytic distillation for the aldol condensation ofacetone: A rate based model in simulating the catalytic distillationperformance under steady state conditions. Chemical EngineeringScience, 53, 3489}3499.Hunek, J., Foldes, P., & Sawinsky, J. (1979). Methods for calculatingreactive distillation. International Chemical Engineering, 19,248}258.Ilme, J. K., Keskinen, K. I., Markkanen, V. L., Aittamaa, J. R. (1997).Simulation of industrial MTBE distillation column using an equilibriumstage model with e$ciency calculation. Distillation andabsorption '97, Institute of Chemical Engineers Symposium Series,vol. 142 (pp. 497}510).Isla, M. A., & Irazoqui, H. A. (1996). Modeling, analysis, and simulationof a methyl tert-butyl ether reactive distillation column. Industrialand Engineering Chemistry Research, 35, 2396}2708.Ismail, S. R., Pistikopolous, E. N., & Papalexandri, K. P. (1999).Synthesis of reactive and combined reactor/separation systems utilizinga mass/heat exchange transfer module. Chemical EngineeringScience, 54, 2721}2729.

R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5225Izarraz, A., Bentzen, G. W., Anthony, R. G., & Holland, C. D. (1980).Solve more distillation problems, Part 9 * when reactions occur.Hydrocarbon Processing, 59(4), 195}203.Jackson, R. (1977). Transport in porous catalysts. Amsterdam: Elsevier.Jacobs, R., & Krishna, R. (1993). Multiple solutions in reactive distillationfor methyl-tert-butyl ether synthesis. Industrial and EngineeringChemistry Research, 32, 1706}1709.Jelinek, J., & Hlavacek, V. (1976). Steady state countercurrent equilibriumstage separation with chemical reaction by relaxation method.Chemical Engineering Communications, 2, 79}85.Johnson, K. H. (1993). Catalytic distillation structure, US patent5189001.Johnson, K. H., & Dallas, A. B. (1994). Catalytic distillation structure,US patent 5348710.Jones, Jr., E. M. (1985). Contact structure for use in catalytic distillation,US patent 4536373.Jones, Jr., E. M. (1992a). Catalytic distillation reactor, US patent 5130102.Jones, Jr., E. M. (1992b). Distillation column reactor, European patent0 402 019 A3.Kaibel, G., Mayer, H. -H., & Seid, B. (1979). Reactions in distillationcolumns. German Chemical Engineering, 2, 180}187.Karpilovsky, O. L., Pisarenko, Y. A., & Sera"mov, L. A. (1997). Multiplesolutions in single-product reactive distillation. Distillation andabsorption '97, Institute of Chemical Engineers Symposium Seriesvol. 142 (pp. 685}694).Kenig, E. Y., & Gorak, A. (1995). A "lm model based approach forsimulation of multicomponent reactive separation processes. ChemicalEngineering and Processing, 34, 97}103.Kenig, E. Y., & Gorak, A. (1997). Modeling of reactive absorption usingthe Maxwell}Stefan equations. Industrial and Engineering ChemistryResearch, 36, 4325}4334.Kenig, E., Jakobsson, K., Banik, P., Aittamaa, J., Gorak, A., Koskinen,M., & Wettman, P. (1999). An integrated tool for synthesis anddesign of reactive distillation. Chemical Engineering Science, 54,1347}1352.Keyes, D. B. (1932). Esteri"cation processes and equipment. Industrialand Engineering Chemistry, 24, 1096}1103.Kinoshita, M. (1985). Simulation procedure for multistage water/hydrogenexchange column for heavy water enrichment accounting forcatalytic and scrubbing e$ciencies. Journal of Nuclear Science andTechnology, 22, 398}405.Kinoshita, M., Hashimoto, I., & Takamatsu, T. (1983). A new simulationprocedure for multicomponent distillation column processingnonideal solutions or reactive solutions. Journal of Chemical EngineeringJapan, 16, 370}377.Kolah, A. K., Mahajani, S. M., & Sharma, M. M. (1996). Acetalizationof formaldehyde with methanol in batch and continuous reactivedistillation. Industrial and Engineering Chemistry Research, 35,3707}3720.Komatsu, H. (1977). Application of the relaxation method of solvingreacting distillation problems. Journal of Chemical EngineeringJapan, 10, 200}205.Komatsu, H., & Holland, C. D. (1977). A new method of convergencefor solving reacting distillation problems. Journal of Chemical EngineeringJapan, 10, 292}297.Kooijman, H. A., & Taylor, R. (1995). A dynamic nonequilibriummodel of tray distillation columns. American Institute of ChemicalEngineers Journal, 41, 1852}1863.Krafczyk, J., & Ghmeling, J. (1994). Einsatz von Katalysatorpakungenfuer die Herstellung von Methylacetat durch reactive Rekti"kation.Chemie Ingenieur Technik, 66, 1372}1375.Kreul, L. U., Gorak, A., & Barton, P. I. (1999a). Modeling of homogeneousreactive separation processes in packed columns. ChemicalEngineering Science, 54, 19}34.Kreul, L. U., Gorak, A., & Barton, P. I. (1999b). Dynamic rate-basedmodel for multicomponent batch distillation. American Institute ofChemical Engineers Journal, 54, 1953}1962.Kreul, L. U., Gorak, A., Dittrich, C., & Barton, P. I. (1998). Dynamiccatalytic distillation: Advanced simulation and experimental validation.Computers and Chemical Engineering, 22, S371}S378.Krishna, R., Van Baten, J. M., Ellenberger, J., Higler, A. P., & Taylor, R.(1999). CFD simulations of sieve tray hydrodynamics. ChemicalEngineering Research and Design, Transactions of the Institution ofChemical Engineers, Part A, 77, 639}646.Krishna, R., & Sie, S. T. (1994). Strategies for multiphase reactorselection. Chemical Engineering Science, 49, 4029}4065.Krishna, R., & Wesselingh, J. A. (1997). The Maxwell}Stefan approachto mass transfer. Chemical Engineering Science, 52, 861}911.Krishnamurthy, R., & Taylor, R. (1985). A Nonequilibrium stage modelof multicomponent separation processes. American Institute ofChemical Engineers Journal, 32, 449}465.Kumar, A., & Daoutidis, P. (1999). Modeling, analysis and control ofethylene glycol reactive distillation column. American Institute ofChemical Engineers Journal, 45, 51}68.Lebens, P. J. M. (1999). Development and design of a monolith reactorforgas}liquid countercurrent operation. Ph.D. dissertation, Delft Universityof Technology, Delft.Lee, J. H., & Dudukovic, M. P. (1998). A comparison of the equilibriumand nonequilibrium models for a multicomponent reactivedistillation column. Computers and Chemical Engineering, 23,159}172.Lee J. H., & Dudukovic, M. P. (1999). Dynamic simulation of a reactivedistillation tray column using a rate-based model. Paper presented atAIChE National meeting, Dallas.Lee, J. W., Hauan, S., Lien, K. M., & Westerberg, A. W. (2000a).Graphical methods for designing reactive distillation columns.I * The Ponchon}Savarit Diagram. Proceedings of the Royal SocietyLondon A, in press.Lee, J. W., Hauan, S., Lien, K. M., & Westerberg, A. W. (2000b).Graphical methods for designing reactive distillation columns.I * The McCabe}Thiele Diagram. Proceedings of the Royal SocietyLondon A, in press.Lee, J. W., Hauan, S., Lien, K. M., & Westerberg, A. W. (2000c).Di!erence points in extractive and reactive cascades. II * Generatingdesign alternatives by the lever rule for reactive systems. ChemicalEngineering Science, 55, 3161}3176.Lee, J. W., Hauan, S., & Westerberg, A. W. (2000d). Reactiondistribution in a reactive distillation column by graphicalmethods. American Institute of Chemical Engineers Journal, 46,1218}1233.Lee, J. W., Hauan, S., & Westerberg, A. W. (2000e). Circumventing anazeotrope in reactive distillation. Industrial and Engineering ChemistryResearch, 39, 1061}1063.Leyes, C. E., & Othmer, D. F. (1945a). Continuous esteri"cation ofbutanol and acetic acid, kinetic and distillation considerations.Transactions of the American Institute of Chemical Engineers, 41,157}196, 481Leyes, C. E., & Othmer, D. F. (1945b). Esteri"cation of butanol andacetic acid. Industrial and Engineering Chemistry, 37, 968}977.Lockett, M. J. (1986). Distillation tray fundamentals. Cambridge, UK:Cambridge University Press.Machietto, S., & Mujtaba, I. (1992). Design and operation policies forbatch distillation. Proceedings of NATO ASI on batch processingsystems engineering, Antalya, Turkey, May 29}June 7.Mahajani, S. M. (1999a). Kinetic azeotropy and design of reactivedistillation columns. Industrial and Engineering Chemistry Research,38, 177}186.Mahajani, S. M. (1999b). Design of reactive distillation columns formulticomponent kinetically controlled reactive systems. ChemicalEngineering Science, 54, 1425}1430.Mahajani, S. M., & Kolah, A. K. (1996). Some design aspects of reactivedistillation columns (RDC). Industrial and Engineering ChemistryResearch, 35, 4587}4596; additions and corrections. Industrial andEngineering Chemistry Research, 36, 2520.

5226 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229Marek, J. (1954). Recti"cation with a chemical reaction. I. Calculationof the number of theoretical plates for continuous plate columns.Collection of Czechoslovak Chemical Communications, 19, 1055}1073.Marek, J. (1956). Recti"cation with a chemical reaction. II. Plantrecti"cation of mixtures of water, acetic acid, acetic anhydride.Collection of Czechoslovak Chemical Communications, 21, 1560}1568.Marion, M. C., Viltard, J. C., Travers, P., Harter, I., & Forestiere, A.(1998). Process and apparatus for reactive distillation with a particulardistribution of liquid and vapor phases, US patent 5776320.Mason, E. A., & Malinauskas, A. P. (1983). Gas transport in porousmedia: The dusty gas model. Amsterdam: Elsevier.McDonald, C. M., & Floudas, C. A. (1997). GLOPEQ: A new computationaltool of the phase and chemical equilibrium problem. Computersand Chemical Engineering, 21, 1}23.McGregor, C., Glasser, D., & Hildebrandt, D. (1997) Process synthesisof a reactive distillation system using attainable region results.Distillation and absorption '97, Institue of Chemical Engineers SymposiumSeries, vol. 142 (pp. 663}674).Melles, S., Grievink, J., & Schrans, S. (2000). Optimisation of theconceptual design of reactive distillation columns. Chemical EngineeringScience, 55, 2089}2097.Moe, H. I., Hauan, S., Lien, K. M., & Hertzberg, T. (1995). Dynamicmodel of a system with phase and reaction equilibrium. Computersand Chemical Engineering, 19, S513}S518.Mohl, K. D., Kienle, A., & Gilles, E. D. (1998). Multiple steady states ina reactive distillation column for the production of the fuel etherTAME I. Theoretical analysis. Chemical Engineering and Technology,21, 133}136.Mohl, K. D., Kienle, A., Gilles, E. D., Rapmund, P., Sundmacher, K.,&Ho!mann, U. (1997). Nonlinear dynamics of reactive distillationprocesses for the production of fuel ethers. Computers and ChemicalEngineering, 21, S989}S994.Mohl, K. D., Kienle, A., Gilles, E. D., Rapmund, P., Sundmacher, K.,&Ho!mann, U. (1999). Steady-state multiplicities in reactive distillationcolumns for the production of fuel ethers MTBE and TAME:Theoretical analysis and experimental veri"cation. Chemical EngineeringScience, 54, 1029}1043.Mommessin, P. E., Bentzen, G. W., Anthony, R. G., & Holland, C. D.(1980). Solve more distillation problems, part 10 * another way tohandle reactions. Hydrocarbon Processing, 59(7), 144}148.Mommessin, P. E., & Holland, C. D. (1983). Solve more distillationproblems, part 13 * multiple columns with reactions. HydrocarbonProcessing, 62(11), 195}200.Moritz, P., & Hasse, H. (1999). Fluid dynamics in reactive distillationpacking Katapak-S. Chemical Engineering Science, 54, 1367}1374.Mujtaba, I., & Machietto, S. (1992). Optimal operation of reactivebatch distillation process. American Institute of Chemical Engineersannual meeting, Miami Beach.Nelson, P. A. (1971). Countercurrent equilibrium stage separation withreaction. American Institute of Chemical Engineers Journal, 17,1043}1049.Neumann, R., & Sasson, Y. (1984). Recovery of dilute acetic acidby esteri"cation in a packed chemorecti"cation column. Industrialand Engineering Chemistry Process Design and Development, 23,654}659.Nijhuis, S. A., Kerkhof, F. P. J. M., & Mak, A. N. S. (1993). Multiplesteady states during reactive distillation of methyl-tert-butylether.Industrial and Engineering Chemistry Research, 32,2767}2774.Nisoli, A., Malone, M. F., & Doherty, M. F. (1997). Attainable regionsfor reaction with separation. American Institute of Chemical EngineersJournal, 43, 374}387.Nocca, J. L., Leonard, J., Gaillard, J. F., & Amigues, P. (1989). Processfor manufacturing a tertiary alkyl ether by reactive distillation, USpatent 4847431.Nocca, J. L., Leonard, J., Gaillard, J. F., & Amigues, P. (1991). Apparatusfor reactive distillation, US patent 5013407.Okasinski, M. J., & Doherty, M. F. (1997a). Thermodynamic behaviorof reactive azeotropes. American Institute of Chemical EngineersJournal, 43, 2227}2238.Okasinski, M. J., & Doherty, M. F. (1997). E!ects of unfavorablethermodynamics on reactive distillation column design. Distillationand absorption '97, Institue of Chemical Engineers SymposiumSeries, vol. 142 (pp. 695}704).Okasinski, M. J., & Doherty, M. F. (1998). Design method for kineticallycontrolled, staged reactive distillation columns. Industrial andEngineering Chemistry Research, 37, 2821}2834.Onda, K., Takeuchi, H., & Okumoto, Y. (1968). Mass transfer coe$cientsbetween gas and liquid phases in packed columns. Journal ofChemical Engineering Japan, 1, 56}62.Oost, C., & Ho!mann, U. (1996). The synthesis of tertiary amyl methylether (TAME): Microkinetics of the reactions. Chemical EngineeringScience, 51, 329}340.Oost, C., Sundmacher, K., & Ho!mann, U. (1995). The synthesis oftertiary amyl methyl ether (TAME): Equilibrium of the multiplereactions. Chemical Engineering and Technology, 18, 110}117.Oudshoorn, O. L. (1999) Zeolite coatings applied in structured catalystpackings. Ph.D. dissertation, Delft University of Technology, Delft.Papalexandri, K. P., & Pistikopolous, E. N. (1996). Generalized modularrepresentation framework for process synthesis. American Instituteof Chemical Engineers Journal, 42, 1010}1032.Patlasov, V. P. (1996). Qualitative analysis of the mathematical modelfor the dynamics of multicomponent batch reactive recti"cation.Theoretical Foundations of Chemical Engineering, 30, 81}88.Pekkanen, M. (1995a). Pinches in reactive distillation: Conditions ofexistence. A.I.Ch.E. Symposium Series No. 304, vol. 91 (pp. 301}304).Pekkanen, M. (1995b). A local optimzation method for the design ofreactive distillation. Computers and Chemical Engineering, 19,S235}S240.Pelkonen, S., Gorak, A., Kooijman, H. A., & Taylor, R. (1997). Operationof a packed distillation column: Modelling and experimentsdistillation. Distillation and absorption '97, Institute of ChemicalEngineers Symposium Series, vol. 142 (pp. 269}277).Perez-Cisneros, E., Gani, R., & Michelsen, M. L. (1997a). Reactiveseparation systems. Part I: Computation of physical and chemicalequilibrium. Chemical Engineering Science, 52, 527}543.Perez-Cisneros, E., Schenk, M., & Gani, R. (1997b). A new approach toreactive distillation simulation. Distillation and absorption '97,Institue of Chemical Engineers Symposium Series, 142 (pp.715}724).Perez-Cisneros, E., Schenk, M., Gani, R., & Pilavachi, P. A. (1996).Aspects of simulation, design and analysis of reactive distillationoperations. Computers and Chemical Engineering, 20, S267}S272.Pilavachi, P. A., Schenk, M., Perez-Cisneros, E., & Gani, R. (1997).Modeling and simulation of reactive distillation operations. Industrialand Engineering Chemistry Research, 36, 3188}3197.Pinjala, V., DeGarmo, J. L., Ulowetz, M. A., Marker, T. L., & Luebke,C. P. (1992). Rate based modeling of reactive distillation operations.AIChE annual meeting, Session 3, Distillation with reaction.Pisarenko, Y. A., Anokhina, E. A., & Sera"mov, L. A. (1993). Search forthe set of stationary states of co-current reaction mass transferprocesses. Theoretical Foundations of Chemical Engineering, 27,539}543.Pisarenko, Y. A., Danilov, R. Y., & Sera"mov, L. A. (1995). In"nitee$ciencyoperating conditions in analysis of statics of reactiverecti"cation. Theoretical Foundations of Chemical Engineering, 29,556}564.Pisarenko, Y. A., Danilov, R. Y., & Sera"mov, L. A. (1996). Possiblemodes of separation in continuous reactive-distillation processes.Theoretical Foundations of Chemical Engineering, 30, 585}592.Pisarenko, Y. A., Danilov, R. Y., & Sera"mov, L. A. (1997). Applicationof the concept of a limiting paths to estimating the feasibility ofsteady states in analyzing the statics of reactive-distillation processes.Theoretical Foundations of Chemical Engineering, 31, 43}48.

R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5227Pisarenko, Y. A., Epifanova, O. A., & Sera"mov, L. A. (1988a). Conditionsfor a steady state in a reactive distillation operation. TheoreticalFoundations of Chemical Engineering, 22, 31}34.Pisarenko, Y. A., Epifanova, O. A., & Sera"mov, L. A. (1988b). Dynamicsof continuous evaporation with a chemical reaction. TheoreticalFoundations of Chemical Engineering, 22, 483}488.Pisarenko, Y. A., & Sera"mov, L. A. (1988). Steady states for a reactivedistillationcolumn with one product stream. Theoretical Foundationsof Chemical Engineering, 21, 281}286.Pisarenko, Y. A., & Sera"mov, L. A. (1992). Statics of systems involvingchemical conversions. Theoretical Foundations of Chemical Engineering,25, 519}527.Podrebarac,G.G.,Ng,F.F.T.,&Rempel,G.L.(1998a).Theproductionof diacetone alcohol with catalytic distillation * Part I: Catalyticdistillation experiments. Chemical Engineering Science, 53, 1067}1075.Podrebarac, G. G., Ng, F. F. T., & Rempel, G. L. (1998b). The productionof diacetone alcohol with catalytic distillation * Part II:A rate-based catalytic distillation model for the reaction zone.Chemical Engineering Science, 53, 1077}1088.Powell, M. J. D. (1965). A method for minimizing a sum of squares ofnonlinear functions without calculating derivatives. Computer Journal,7, 303}307.Quang, D. V., Amigues, P., Gaillard, J. F., Leonard, J., & Nocca, J. L.(1989). Process for manufacturing a tertiary alkyl ether by reactivedistillation, US patent 4847430.Quitain, A., Itoh, H., & Goto, S. (1999a). Reactive distillation forsynthesizing ethyl tert-butyl ether from bioethanol. Journal of ChemicalEngineering Japan, 32, 280}287.Quitain, A., Itoh, H., & Goto, S. (1999b). Industrial-scale simulation ofproposed process for synthesizing ethyl tert-butyl ether from bioethanol.Journal of Chemical Engineering Japan, 32, 539}543.Rapmund, P., Sundmacher, K., & Ho!mann, U. (1998). Multiple steadystates in a reactive distillation column for the production of the fuelether TAME II experimental validation. Chemical Engineering andTechnology, 21, 136}139.Rascol, E., Meyer, M., Le Lann, J. M., & Prevost, M. (1998). Numericalproblems encountered in the simulation of reactive absorption:DAE index reduction and consistent initialisation. Computers andChemical Engineering, 22, S929}S932.Reh"nger, A., & Ho!mann, U. (1990a). Kinetics of methyl-tert-butylether liquid-phase synthesis catalysed by ion exchange resin. I * intrinsicrate expression in liquid phase activities. Chemical EngineeringScience, 45, 1605}1616.Reh"nger, A., & Ho!mann, U. (1990b). Kinetics of methyl-tert-butylether liquid phase synthesis catalysed by ion exchange resin. II* macropore di!usion of MeOH as rate controlling step. ChemicalEngineering Science, 45, 1619}1626.Reuter, E., Wozny, G., & Jeromin, L. (1989). Modeling of multicomponentbatch distillation processes with chemical reaction andtheir control systems. Computers and Chemical Engineering, 13,499}510.Rev, E. (1994). Reactive distillation and kinetic azeotropy. Industrial andEngineering Chemistry Research, 33, 2147}2179.Roat, S. D., Downs, J. J., Vogel, E. F., & Doss, J. E. (1986). Theintegration of rigorous dynamic modeling and control system synthesisfor distillation columns: An industrial approach. In M.Morari, & T. J. McAvoy, Chemical process control * CPC III. NewYork: Elsevier.Rowlinson, J. S. (1969). Liquids and liquid mixtures (2nd ed.). London:Butterworth.Ruiz, C. A., Basualdo, M. S., & Scenna, N. J. (1995). Reactive distillationdynamic simulation. Chemical Engineering Research and Design,Transactions of the Institution of Chemical Engineers, Part A, 73,363}378.Saito, S., Michishita, T., & Maeda, S. (1971). Separation of meta- andpara-xylene mixture by distillation accompanied by chemical reactions.Journal of Chemical Engineering Japan, 4, 37}43.Sandler, S. I. (1999). Chemical and engineering thermodynamics (3rd ed.).New York: Wiley.Savkovic-Stevanovic, J. (1982). Mathematical model of unsteady statedistillation column with association reaction. Proceedings of thethird Austrian}Italian}Yugoslav Congress on chemical engineering,Graz, Austria, Vol. I (pp. 326}332).Savkovic-Stevanovic, J., Mis\ ic-Vukovic, M., Boncic-Caricic, G.,Tris\ ovic, B., & Jezdic, S. (1992). Reactive distillation with ion exchangers.Separation Science and Technology, 27, 613}630.Sawistowski, H., & Pilavakis, P. A. (1979). Distillation with chemicalreaction in a packed column. Institute of Chemical Engineers SymposiumSeries, 56, 4.2/49-63.Sawistowski, H., & Pilavakis, P. A. (1988). Performance of esteri"cationin a reaction-distillation column. Chemical Engineering Science, 43,355}360.Scenna, N. J., Ruiz, C. A., & Benz, S. J. (1998). Dynamic simulation ofstartup procedures of reactive distillation columns. Computers andChemical Engineering, 22, S719}S722.Schenk, M., Gani, R., Bogle, D., & Pistikopolous, E. N. (1999). A hybridmodelling approach for separation systems involving distillation.Chemical Engineering Research and Design, Transactions of the Institutionof Chemical Engineers, Part A, 77, 519}534.Schneider, R., Kenig, E. Y., & Gorak, A. (1999). Dynamic modelling ofreactive absorption with the Maxwell}Stefan approach. ChemicalEngineering Research and Design, Transactions of the Institution ofChemical Engineers, Part A, 77, 633}638.Schniep, L. E., Dunning, J. W., & Lathrop, E. C. (1945). Continuousprocess for acetylation of 2,3-butylene glycol. Industrial and EngineeringChemistry, 37, 872}877.Schoenmakers, H. (1982). Possibilities of suppressing undesired reactionsin distillation columns. Chemie Ingenieur Technik, 54,1196}1197.Schrans, S., de Wolf, S., & Baur, R. (1996). Dynamic simulation ofreactive distillation. An MTBE case study. Computers and ChemicalEngineering, 20, S1619}S1624.Seader, J. D. (1985). The B.C. (Before Computers) and A.D. of equilibrium-stageoperations. Chemical Engineering Education, 19, 88}103.Seader, J. D., & Henley, E. J. (1998). Separation process principles. NewYork: Wiley.Seider, W. D., & Widagdo, S. (1996). Multiphase equilibria of reactivesystems. Fluid Phase Equilibria, 123, 283}303.Sera"mov, L. A., Pisarenko, Y. A., & Kardona, K. A. (1999a). Optimizationof reactive distillation processes. Theoretical Foundations ofChemical Engineering, 33, 455}463.Sera"mov, L. A., Pisarenko, Y. A., & Kulov, N. (1999b).Coupling chemical reaction with distillation: Thermodynamic analysisand practical applications. Chemical Engineering Science, 54,1383}1388.Sera"mov, L. A., Pisarenko, Y. A., & Timofeev, V. S. (1993). Reactionmasstransfer processes: Problems and prospects. Theoretical Foundationsof Chemical Engineering, 27, 1}9.Sharma, M. M. (1985). Separations through reactions. Journal of SeparationProcess Technology, 6, 9}16.Shoemaker, J. D., & Jones, E. M. (1987). Cumene by catalytic distillation.Hydrocarbon Processing, 66, 57}58.Siirola, J. J. (1995). An industrial perspective on process synthesis.A.I.Ch.E. Symposium Series No. 304, Vol. 91 (pp. 222}233).Simandl, J., & Svrcek, W. Y. (1991). Extension of the simultaneoussolution and inside}outside algorithms to distillation with chemicalreactions. Computers and Chemical Engineering, 15, 337}348.Sivasubramanian, M. S., & Boston, J. F. (1990). The heat andmass transfer approach for modeling multicomponent separationprocesses. In H. Th. Bussemaker, & P. D. Iedema, Computerapplications in chemical engineering (pp. 331}336). Amsterdam:Elsevier.Smith, Jr., L. A. (1984). Catalytic distillation structure, US patent4443559.

R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5229Congress on chemical engineering * ECCE-1, May 4}7, Florence,Vol. 2 (pp. 1423}1426).Thiel, C., Sundmacher, K., & Ho!mann, U. (1997a). Residue curve mapsfor heterogeneously catalysed reactive distillation of fuel ethersMTBE and TAME. Chemical Engineering Science, 52, 993}1005.Thiel, C., Sundmacher, K., & Ho!mann, U. (1997b). Synthesis of ETBE:Residue curve maps for the heterogeneously catalysed reactive distillationprocess. Chemical Engineering Journal, 66, 181}191.Tierney, J. W., & Riquelme, G. D. (1982). Calculation methods fordistillation systems with reaction. Chemical Engineering Communication,16, 91}108.Timofeev, V. S., Sera"mov, L. A., & Solokhin, A. V. (1994). Analysis ofreactive systems with selective exchange of material with the ambientmedium. Theoretical Foundations of Chemical Engineering, 28,416}420.Timofeev, V. S., Solokhin, A. V., & Kalerin, E. A. (1988). Multiplesteady states in the reaction-recti"cation process. Theoretical Foundationsof Chemical Engineering, 22, 488}492.Toor, H. L. (1965). Dual di!usion - reaction coupling in "rst ordermulticomponent systems. Chemical Engineering Science, 20,941}951.Towler, G. P., & Frey, S. J. (2000). Reactive distillation. In S. Kulprathipanja,Reactive separation processes. Philadelphia: Taylor andFrancis (Chapter 2).Trambouze, P. (1990). Countercurrent two-phase #ow "xed bed catalyticreactors. Chemical Engineering Science, 45, 2269}2275.Ung, S., & Doherty, M. F. (1995a). Vapor liquid phase equilibrium insystems with multiple chemical reactions. Chemical EngineeringScience, 50, 23}48.Ung, S., & Doherty, M. F. (1995b). Theory of phase equilibriain multireaction systems. Chemical Engineering Science, 50,3201}3216.Ung, S., & Doherty, M. F. (1995c). Calculation of residue curve mapsfor mixtures with multiple equilibrium chemical reactions. Industrialand Engineering Chemistry Research, 34, 3195}3202.Ung, S., & Doherty, M. F. (1995d). Necessary and su$cient conditionsfor reactive azeotropes in multireaction mixtures. American Instituteof Chemical Engineers Journal, 41, 2383}2392.Ung, S., & Doherty, M. F. (1995e). Synthesis of reactive distillationsystems with multiple equilibrium chemical reactions. Industrial andEngineering Chemistry Research, 34, 2555}2565.Velo, E., Puigjaner, L., & Recasens, F. (1988). Inhibition by product inthe liquid-phase hydration of iso-butene to tert-butyl alcohol * kineticsand equilibrium studies. Industrial and Engineering ChemistryResearch, 27, 2224}2231.Venimadhavan, G., Buzad, G., Doherty, M. F., & Malone, M. F.(1994). E!ect of kinetics on residue curve maps for reactive distillation.American Institute of Chemical Engineers Journal, 40,1814}1824.Venimadhavan, G., Malone, M. F., & Doherty, M. F. (1999a). Bifurcationstudy of kinetic e!ects in reactive distillation. American Instituteof Chemical Engineers Journal, 45, 546}556.Venimadhavan, G., Malone, M. F., & Doherty, M. F. (1999b). A noveldistillate policy for batch reactive distillation with application to theproduction of butyl acetate. Industrial and Engineering ChemistryResearch, 38, 714}722.Venkataraman, S., Chan, W. K., & Boston, J. F. (1990). Reactivedistillation using ASPEN PLUS. Chemical Engineering Progress,86(8), 45}54.Wajge, R. M., & Reklaitis, G. V. (1999). RDBOPT: A general purposeobject-oriented module for distributed campaign optimization ofreactive batch distillation. Chemical Engineering Journal, 75, 57}68.Walas, S. M. (1985). Phase equilibria in chemical engineering. Stoneham(MA): Butterworths.Wang, J. C., & Henke, G. E. (1966). Tridiagonal matrix for distillation.Hydrocarbon Processing, 45(8), 155}163, 45(9), 169Wang, J. C., & Wang, Y. L. (1980). A review on the modeling andsimulation of multi-stage separation processes. In W. D. Seider,& R. S. H. Mah, Foundations of computer aided chemical processdesign, vol. II (pp. 121}170).Wayburn, T. L., & Seader, J. D. (1987). Homotopy-continuationmethods for computer aided process design. Computers and ChemicalEngineering, 11, 7}25.Wiesner, U., Wittig, M., & Gorak, A. (1996). Design and optimization ofa nitric acid recovery plant from nitrous waste gases. Computers andChemical Engineering, 20, S1425}S1430.Xu, X., Zhao, Z., & Tian, S. -J. (1997). Study on catalytic distillationprocesses, Part III. Prediction of pressure drop and holdup incatalyst bed. Chemical Engineering Research and Design, Transactionsof the Institution of Chemical Engineers, Part A, 75, 625}629.Xu, X., Zhao, Z., & Tian, S. (1999). Study on catalytic distillationprocesses, Part IV: Axial dispersion of liquid in catalyst bed ofcatalytic distillation column. Chemical Engineering Research andDesign, Transactions of the Institution of Chemical Engineers, Part A,77, 16}20.Xu, Z., & Dudukovic, M. P. (1999). Modeling and simulation of a semibatchphoto reactive distillation. Chemical Engineering Science, 54,1397}1403.Yu, S., Zhou, A., & Tan, Q. (1997). Simulation of multistage catalyticstripping with a nonequilibrium stage model. Computers and ChemicalEngineering, 21, 409}415.Zheng, Y., & Xu, X. (1992a). Study on catalytic distillation processes,Part I: Mass transfer characteristics in catalyst bed within thecolumn. Chemical Engineering Research and Design, Transactions ofthe Institution of Chemical Engineers, Part A, 70, 459}546.Zheng, Y., & Xu, X. (1992b). Study on catalytic distillation processes,Part II: Simulation of catalytic distillation processes, Quasi homogeneousand rate based model. Chemical Engineering Research andDesign, Transactions of the Institution of Chemical Engineers, Part A,70, 465}470.Zhu, J., & Shen, F. (1995). The modelling and simulation of reactivedistillation processes. A.I.Ch.E. Symposium Series No. 304, vol. 91(pp. 297}300).