Modelling Reactive Distillation

*Corresponding author. Tel.: #31-20-525-7007; fax: #31-20-525-5604.

E-mail address: [email protected] (R. Krishna).

Chemical Engineering Science 55 (2000) 5183}5229

Review

Modelling reactive distillation

R. Taylor!,", R. Krishna#,*!Department of Chemical Engineering, Clarkson University, Potsdam, NY 13699-5705, USA

"Department of Chemical Technology, University of Twente, 7500 AE Enschede, The Netherlands#Department of Chemical Engineering, University of Amsterdam, Nieuwe Achtergracht 166, 1018 WV Amsterdam, The Netherlands

Received 8 October 1999; accepted 12 April 2000

Abstract

The design and operation issues for reactive distillation systems are considerably more complex than those involved for eitherconventional reactors or conventional distillation columns. The introduction of an in situ separation function within the reaction zoneleads to complex interactions between vapor}liquid equilibrium, vapor}liquid mass transfer, intra-catalyst di!usion (for heterogen-eously catalysed processes) and chemical kinetics. Such interactions have been shown to lead to the phenomenon of multiplesteady-states and complex dynamics, which have been veri"ed in experimental laboratory and pilot plant units. We trace thedevelopment of models that have been used for design of reactive distillation columns and suggest future research directions. ( 2000Elsevier Science Ltd. All rights reserved.

Keywords: Reactive distillation; Equilibrium stage model; Non-equilibrium stage model; Multiple steady-states; Maxwell}Stefan equations

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51841.1. Why RD? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51851.2. The constraints and di$culties in RD implementation . . . . . . . . . . . . . . . . . . . . . . . . 51871.3. The complexity of RD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51881.4. Practical design considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5188

1.4.1. Installation, containment and removal of the catalyst . . . . . . . . . . . . . . . . . . . 51881.4.2. E$cient contacting of liquid with catalyst particles . . . . . . . . . . . . . . . . . . . . . 51891.4.3. Good vapor/liquid contacting in the reactive zone . . . . . . . . . . . . . . . . . . . . . 51891.4.4. &&Low'' pressure drop through the catalytically packed reactive section . . . . . . 51891.4.5. Su$cient liquid hold-up in the reactive section . . . . . . . . . . . . . . . . . . . . . . . . 51891.4.6. Designing for catalyst deactivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5189

1.5. Hardware aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51891.5.1. Catalytically packed RD columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51901.5.2. Trays or downcomers to hold catalyst particles . . . . . . . . . . . . . . . . . . . . . . . 5193

2. Thermodynamics of reactive distillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5194

3. Equilibrium (EQ) stage models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51963.1. The EQ stage model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51963.2. Steady-state algorithms and applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51973.3. Multiple steady-states with the EQ model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5200

0009-2509/00/$ - see front matter ( 2000 Elsevier Science Ltd. All rights reserved.PII: S 0 0 0 9 - 2 5 0 9 ( 0 0 ) 0 0 1 2 0 - 2

3.4. Primarily dynamic models and applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52013.5. Batch reactive distillationm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52033.6. Primarily experimental papers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52033.7. Use of e$ciencies in RD models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5205

4. Mass transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5205

5. Non-equilibrium (NEQ) stage modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52085.1. The conventional NEQ model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52085.2. NEQ modelling of RD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52095.3. NEQ models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52095.4. NEQ cell model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52125.5. Pseudo-homogeneous vs. heterogeneous NEQ modelling . . . . . . . . . . . . . . . . . . . . . . 52135.6. Dynamics NEQ models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5214

6. Reactive distillation design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52166.1. Conceptual design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52166.2. Graphical design methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52186.3. Design via optimisation methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52186.4. From conceptual design to column design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52186.5. RD design in industrial practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5219

7. Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5219

Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5220

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5221

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5221

1. Introduction

The versatility of the fractionating column in thedual role of continuous reactor and separator asapplied to chemical processing is well established.

Berman, Isbenjian, Sedo! and Othmer (1948a)

The quote with which we begin this review appeared inprint more than "ve decades ago! It provides an interest-ing historical perspective because in more recent times wehave seen an explosion of interest in the subject of react-ive distillation, and a veritable plethora of papershave appeared in the last 12 years alone. The recentinterest in this process can be attributed in part to thegrowing commercial importance of reactive distillation,and in part to a keynote paper by Doherty and Buzad(1992), who reviewed the literature to that time. Morethan half of the over 300 references cited in this reviewhave appeared after 1992. Thus, one of the objectivesof this article is to provide an up-date to their workwith a review of more recent developments in reactivedistillation.

The term catalytic distillation is also used for suchsystems where a catalyst (homogeneous or heterogen-eous) is used to accelerate the reaction. In this review we

use the generic name reactive distillation, with the acro-nym RD, to cover both catalysed or uncatalysed reac-tions systems.

The "rst patents date back to the 1920s (Backhaus,1921, 1922, 1923a,b). Early journal articles are by Keyes(1932), Leyes and Othmer (1945a,b), Schniep, Dunningand Lathrop (1945), Berman, Melnychuk & Othmer(1948b) and Berman et al. (1948a). The "rst publicationsdeal mainly with homogeneous self-catalysed reactionssuch as esteri"cations, trans-esteri"cations, and hydroly-sis. Heterogeneous catalysis in RD is a more recentdevelopment and was "rst described by Spes (1966).

The main focus of this review is on the modelling ofRD processes. We have tried to be comprehensive in ourcoverage, but it would be nearly impossible to cite everypaper even in this fairly well-de"ned niche. This reviewdoes not attempt quite such comprehensive coverage ofthe literature devoted more to RD catalysis and kineticsstudies, although some of the works in these sub-"eldsnecessarily are included in our review to some extent.

Descriptions of speci"c RD processes also are largelybeyond our scope (see, for example, Sharma (1985), Stich-lmair and Frey (1999) for reviews and Bart and Resil(1997) discuss an unusual application). Introductoryoverviews of RD and RD design and equipment are by

5184 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229

Fig. 1. Processing schemes for a reaction sequence A#B H C#D where C and D are both desired products. (a) Typical con"guration ofa conventional process consisting of a reactor followed by a distillation train. (b) The reactive distillation con"guration. The components A, C, D andB have increasing boiling points. The reactive sections are indicated by grid lines. Adapted from Stichlmair and Frey (1999).

Fair (1998), Hauan and Hildebrandt (1999), and byTowler and Frey (2000). The non-English language liter-ature also is less well served here. Fortunately, many ofthe papers in the German and Russian literature havebeen translated into English. Overviews of parts of theextensive Russian literature on RD (in English) are bySera"mov, Pisarenko and Timofeev (1993), Sera"mov,Pisarenko and Kardona (1999a), and Timofeev,Sera"mov and Solokhin (1994).

A short section on RD thermodynamics is followed bya much longer one on equilibrium (EQ) stage modelling.A brief discussion on e$ciencies in RD leads to anoutline of mass transfer considerations and an overviewof non-equilibrium (NEQ) modelling of RD processes.We end with some comments on RD design methods. Webegin, however, with an appreciation of the bene"ts ofRD.

1.1. Why RD?

Let us begin by considering a reversible reactionscheme: A#B H C#D where the boiling points of thecomponents follow the sequence A, C, D and B. Thetraditional #ow-sheet for this process consists of a reac-tor followed by a sequence of distillation columns; seeFig. 1(a). The mixture of A and B is fed to the reactor,where the reaction takes place in the presence of a cata-lyst and reaches equilibrium. A distillation train is re-quired to produce pure products C and D. The unreactedcomponents, A and B, are recycled back to the reactor. Inpractice the distillation train could be much more com-

plex than the one portrayed in Fig. 1(a) if one or moreazeotropes are formed in the mixture. The alternative RDcon"guration is shown in Fig. 1(b). The RD columnconsists of a reactive section in the middle with non-reactive rectifying and stripping sections at the top andbottom. The task of the rectifying section is to recoverreactant B from the product stream C. In the strippingsection, the reactant A is stripped from the productstream D. In the reactive section the products are separ-ated in situ, driving the equilibrium to the right and preven-ting any undesired side reactions between the reactantsA (or B) with the product C (or D). For a properly designedRD column, virtually 100% conversion can be achieved.

The most spectacular example of the bene"ts of RD isin the production of methyl acetate. The acid catalysedreaction MeOH#AcOH H MeOAc#H

2O was tradi-

tionally carried out using the processing scheme shownin Fig. 2(a), which consists of one reactor and a trainof nine distillation columns. In the RD implementation(see Fig. 2(b)) only one column is required and nearly100% conversion of the reactant is achieved. The capitaland operating costs are signi"cantly reduced (Siirola,1995).

For the acid catalysed reaction between iso-butene andmethanol to form methyl tert-butyl ether: iso-butene#MeOH H MTBE, the traditional reactor-fol-lowed-by-distillation concept is particularly complex forthis case because the reaction mixture leaving the reactorforms three minimum boiling azeotropes. The RD imple-mentation requires only one column to which thebutenes feed (consisting of a mixture of n-butene, which is

R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5185

Fig. 2. Processing schemes for the esteri"cation reactionMeOH#AcOH H MeOAc#H

2O. (a) Conventional processing

scheme consisting of one reactor followed by nine distillation columns.(b) The reactive distillation con"guration. The reactive sections areindicated by grid lines. Adapted from Siirola (1995).

Fig. 3. (a) Reactive distillation concept for synthesis of MTBE from theacid-catalysed reaction between MeOH and iso-butene. The butenefeed is a mixture of reactive iso-butene and non-reactive n-butene. (b)Reactive distillation concept for the hydration of ethylene oxide toethylene glycol. (c) Reactive distillation concept for reaction betweenbenzene and propene to form cumene. (d) Reactive distillation conceptfor reaction production of propylene oxide from propylene chlorohyd-rin and lime. The reactive sections are indicated by grid lines.

non-reactive, and iso-butene which is reactive) and meth-anol are fed near the bottom of the reactive section. TheRD concept shown in Fig. 3(a) is capable of achievingclose to 100% conversion of iso-butene and methanol,along with suppression of the formation of the unwanteddimethyl ether (Sundmacher, 1995). Also, some of theazeotropes in the mixture are `reacted awaya (Doherty& Buzad, 1992).

For the hydration of ethylene oxide to mono-ethyleneglycol: EO#H

2OPEG, the RD concept, shown in

Fig. 3(b) is advantageous for two reasons (Ciric & Gu,1994). Firstly, the side reaction EO#EGPDEG is sup-pressed because the concentration of EO in the liquid-phase is kept low because of its high volatility. Secondly,the high heat of reaction is utilised to vaporise theliquid-phase mixtures on the trays. To achieve the sameselectivity to EG in a conventional liquid-phase plug-#ow reactor would require the use of 60% excess water(Ciric & Gu, 1994). Similar bene"ts are also realised forthe hydration of iso-butene to tert-butanol (Velo, Puig-janer & Recasens, 1988) and hydration of 2-methyl-2-butene to tert-amyl alcohol (Gonzalez & Fair, 1997).

Several alkylation reactions, aromatic#ole"n H al-kyl aromatic, are best carried out using the RD conceptnot only because of the shift in the reaction equilibriumdue to in situ separation but also due to the fact that theundesirable side reaction, alkyl aromatic#ole"n H di-alkyl aromatic, is suppressed. The reaction of propenewith benzene to form cumene, benzene#propene HCumene (Shoemaker & Jones, 1987; see Fig. 3(c)), isadvantageously carried out in a RD column because notonly is the formation of the undesirable di-isopropylben-zene suppressed, but also the problems posed by highexothermicity of the reaction for operation in a conven-tional packed-bed reactor are avoided. Hot spots andrunaway problems are alleviated in the RD conceptwhere liquid vaporisation acts as a thermal #ywheel. Thealkylation of iso-butane to iso-octane, iso-butane#n-butene H iso-octane, is another reaction that bene"tsfrom a RD implementation because in situ separation ofthe product prevents further alkylation: iso-octane#n-butene H C

12H

24(Doherty & Buzad, 1992).

The reaction between propylene chlorohydrin (PCH)and Ca(OH)

2to produce propylene oxide (PO) is best

implemented in an RD column, see Fig. 3(d). Here thedesired product PO is stripped from the liquid-phase byuse of live steam, suppressing hydrolysis to propyleneglycol (Bezzo, Bertucco, Forlin & Barolo, 1999).

Co-current gas}liquid down#ow trickle-bed reactorsare widely applied for hydroprocessing of heavy oils. Thisco-current mode of operation is disadvantageous in mosthydroprocesses (Krishna & Sie, 1994), and counter-cur-rent #ow of gas and liquid would be much more desirable(cf. Fig. 4). This is because reactions such as hydrodesul-phurisation and hydrogenation are inhibited by hydro-gen sulphide formed, even when using the so-calledsulphur-tolerant catalyst of the mixed sulphide type. Theremoval of sulphur from heavy oil generally follows sec-ond-order kinetics in sulphur concentration, which isa re#ection of the presence of a variety of sulphur con-taining compounds with di!erent reactivities. The sec-ond-order kinetics imply that a relatively largeproportion of sulphur is removed in an early stage ofthe process (due to conversion of the bulk of reactive


Fig. 4. Hydrodesulphurisation of gas oil carried out in (a) co-current trickle-bed reactor and (b) counter-current RD unit.

molecules) while removal of the remaining sulphur takesplace much more slowly in later stages. This means thatthe bulk of the H

2S is generated in a small inlet part of

the bed and that this H2S exerts its inhibiting in#uence in

the remaining part of the bed. Fig. 4(a) shows the partialpressure of H

2S in the gas phase. It can be seen that in

co-current operation the larger part of the bed operatesunder a H

2S-rich regime. The situation is clearly more

favourable in the counter-current mode of operationsince in this case the major part of the bed operates in theH

2S lean regime. The co-current mode of operation is

particularly unfavourable since the inhibiting e!ect isstrongest in the region where the refractory compoundshave to be converted, which calls for the highest activity.A similar situation exists in hydrocracking. The by-prod-uct of conversion of nitrogen containing organic com-pounds, viz., ammonia, is a very strong inhibitor forhydrogenation and particularly for hydrocracking reac-tions. For the hydrogenation of aromatics too the co-current operation is unfavourable. This is not only sofrom a kinetic point of view (inhibition by H

2S and

NH3), but also because of thermodynamics (Trambouze,

1990). Deep removal of aromatics from an oil fractiongenerally is limited by thermodynamic equilibrium. Inthe co-current mode of operation the partial pressure ofH

2at the exit end of the reactor is lowest because of the

combined e!ects of pressure drop, hydrogen consump-tion and build up of gaseous components other than H

2(H

2S, NH

3, H

2O, light hydrocarbons).

The counter-current reactor shown in Fig. 4(b) is es-sentially a RD column wherein the H

2S is stripped from

the liquid-phase at the bottom and carried to the top.The quantitative advantages of the RD implementationfor hydroprocessing are brought out in a design studycarried out by Van Hasselt (1999). For a 20,000 bbl/dhydrodesulphurisation unit with a target conversion of98% conversion of sulphur compounds, the catalyst vol-ume required for a conventional trickle-bed reactor is

about 600 m3. For counter-current RD implementationthe catalyst volume is reduced to about 450 m3.

From the foregoing examples, the bene"ts of RD canbe summarised as follows:

(a) Simpli"cation or elimination of the separation sys-tem can lead to signi"cant capital savings.

(b) Improved conversion of reactant approaching100%. This increase in conversion gives a bene"t inreduced recycle costs.

(c) Improved selectivity. Removing one of the productsfrom the reaction mixture or maintaining a low con-centration of one of the reagents can lead to reduc-tion of the rates of side reactions and hence improvedselectivity for the desired products.

(d) Signi"cantly reduced catalyst requirement for thesame degree of conversion.

(e) Avoidance of azeotropes. RD is particularly advant-ageous when the reactor product is a mixture ofspecies that can form several azeotropes with eachother. RD conditions can allow the azeotropes to be`reacted awaya in a single vessel.

(f) Reduced by-product formation.(g) Heat integration bene"ts. If the reaction is exother-

mic, the heat of reaction can be used to provide theheat of vaporisation and reduce the reboiler duty.

(h) Avoidance of hot spots and runaways using liquidvaporisation as thermal #y wheel.

1.2. The constraints and dizculties in RD implementation

Against the above-mentioned advantages of RD, thereare several constraints and foreseen di$culties (Towler& Frey, 2000):

(a) Volatility constraints. The reagents and productsmust have suitable volatility to maintain high con-centrations of reactants and low concentrations ofproducts in the reaction zone.


Fig. 5. Transport processes in RD. (a) homogeneous liquid-phasereaction, and (b) heterogeneous catalysed reactions. Adapted fromSundmacher (1995).

Fig. 6. Length and time scales in RD. Adapted from Sundmacher(1995).

(b) Residence time requirement. If the residence time forthe reaction is long, a large column size and largetray hold-ups will be needed and it may be moreeconomic to use a reactor-separator arrangement.

(c) Scale up to large #ows. It is di$cult to design RDprocesses for very large #ow rates because of liquiddistribution problems in packed RD columns.

(d) Process conditions mismatch. In some processes theoptimum conditions of temperature and pressure fordistillation may be far from optimal for reaction andvice versa.

1.3. The complexity of RD

The design and operation issues for RD systems areconsiderably more complex than those involved foreither conventional reactors or conventional distillationcolumns. The introduction of an in situ separation func-tion within the reaction zone leads to complex interac-tions between vapor}liquid equilibrium, vapor}liquidmass transfer, intra-catalyst di!usion (for heterogeneous-ly catalysed processes) and chemical kinetics. Fig. 5shows the various transfer processes in homogeneousand heterogeneous RD. In heterogeneous RD the prob-lem is exacerbated by the fact that these transfer pro-cesses occur at length scales varying from 1 nm (porediameter in gels, say) to say a few meters (column dimen-sions); see Fig. 6. The time scales vary from 1 ms (di!u-sion within gels) to say a few hours (column dynamics).The phenomena at di!erent scales interact with eachother. Such interactions, along with the strong non-

linearities introduced by the coupling between di!usionand chemical kinetics in counter-current contacting, havebeen shown to lead to the phenomenon of multiplesteady-states and complex dynamics, which have beenveri"ed in experimental laboratory and pilot plant units(Bravo, Pyhalathi & Jaervelin, 1993; Mohl et al., 1999;Rapmund, Sundmacher & Ho!mann, 1998). Successfulcommercialisation of RD technology requires careful at-tention to the modelling aspects, including column dy-namics, even at the conceptual design stage (Doherty& Buzad, 1992; Roat, Downs, Vogel & Doss, 1986). Aswill be shown later many of the reactor and distillationparadigms do not translate easily to RD. The potentialadvantages of RD could be nulli"ed by improper choiceof feed stage, re#ux, amount of catalyst, boilup rate, etc.Thus, it is possible to decrease conversion by increasingthe amount of catalyst under certain circumstances(Higler, Taylor & Krishna, 1999b). Increased separationcapability could decrease process performance (Sneesby,TadeH , Datta & Smith, 1998a).

1.4. Practical design considerations

Towler and Frey (2000) have highlighted some of thepractical issues in implementing a large-scale RD ap-plication. These are discussed below.

1.4.1. Installation, containment and removal of the catalystIt is important to allow easy installation and removal

of the RD equipment and catalyst. If the catalyst under-goes deactivation, the regeneration is most convenientlydone ex situ and so there must be provision for easyremoval and installation of catalyst particles. Reactive


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.

distillation is often passed over as a processing optionbecause the catalyst life would require frequent shut-downs. 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 channell-ing. 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 hot-spots and runaways and allow even catalyst ageing.The requirement of good radial mixing has an im-pact on the choice of the packing con"guration andgeometry. For example, frequent criss-crossing mix-ing patterns 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 equilib-

rium-limited then 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 section

This 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.

1.4.5. Suzcient liquid hold-up in the reactive sectionThe liquid hold-up, mean residence time, and liquid

residence time distribution are all important in determin-ing the 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 desir-

able to allow on-line catalyst removal and regeneration,

such devices have not been commercialised as yet. Cata-lyst deactivation 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 col-umn pressure)

1.5. Hardware aspects

Before modelling aspects can be considered, carefulattention needs to be paid to hardware design aspects.Towler and Frey (2000) have presented an excellent sum-mary of hardware design aspects of RD columns. Someof the important issues are discussed below.

For homogeneous RD processes, counter-current va-por}liquid contacting, with su$cient degree of staging inthe vapor and liquid-phases, can be achieved in a multi-tray column (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; Stich-lmair & 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 pro-cess for methyl acetate manufacture specially designedhigh liquid hold-up trays are used (Agreda, Partin& Heise, 1990).


Fig. 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 de-

sign poses considerable challenges. The catalyst particlesizes used in such operations are usually in the 1}3 mmrange. 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 (Buch-holz, 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"ca-tion, hydrogenation and alkylation of aromatic com-pounds (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 con-cept have been made over the years (Johnson, 1993;Crossland, Gildert & Hearn, 1995). The hydrodynam-ics, kinetics, and mass transfer characteristics of bale-type packings have recently been published in theopen literature (Subawalla, Gonzalez, Seibert & Fair,1997; Xu, Zhao & Tian, 1997, 1999).


Fig. 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 rectangu-lar crimped wire gauze sealed around the edge, there-

by forming 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 re-quired height. 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).


Fig. 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://ct-cr4.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 sand-wich structures (Higler et al., 1999a).

Another alternative is to make the packing itself cata-lytically active. This is the strategy adopted by Flato and

Ho!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


Fig. 15. Catalyst envelopes placed along the liquid #ow path. For photographs of this con"guration, along with CFD animations of the #ow visit theweb site: http://ct-cr4.chem.uva.nl/kattray.

mechanical stresses inside the resin. An alternative con-"guration is the glass-supported precipitated polymerprepared by precipitation of styrene-divinylbenzenecopolymer, which is subsequently activated by chlorsul-phonic acid. Another possibility is to coat structuredpacking with zeolite catalysts (Oudshoorn, 1999); seeFig. 14(b). This concept has not been put into practice forthe following reasons (Towler & Frey, 2000):

1. The amount of catalyst that can be loaded in a columnin this manner is small compared to addition of cata-lyst pills or homogenous catalyst.

2. Coating or impregnation of catalyst materials onmetal surfaces is expensive.

3. Production of catalyst materials in the shape of distil-lation packings is also expensive.

4. There is currently no generic manufacturing methodthat can economically produce di!erent catalyst ma-terials as coatings or structured packings.

The catalyst can also be `casta into a monolith form andused for counter-current vapor}liquid contacting,Lebens (1999) has developed a monolith constructionconsisting of #uted tubes; see Fig. 14(c).

1.5.2. Trays or downcomers to hold catalyst particlesThe catalyst envelopes can be placed in a trayed RD

column and many con"gurations have been proposed.

1. Vertically disposed catalyst containing envelopes canbe placed along the direction of the liquid #ow pathacross a tray (Jones, 1985); see Fig. 15. These envel-opes are almost completely immersed in the froth onthe tray, ensuring good contact between liquid andcatalyst. Furthermore, since the vapor and liquid-phase pass along the packed catalyst in the envelopes,

and not through them, the pressure drop is not excess-ive.

2. Catalyst envelopes can be placed within the down-comers (Carland, 1994); see Fig. 16(a). The primarydrawback with installing the catalyst within down-comers is the limited volume available for catalystinventory. Each `stagea can be regarded as a reactiondevice (downcomer) followed by a separation section(froth on the tray).

3. Catalyst envelopes can be placed near the exit of thedowncomer (Asselineau, Mikitenko, Viltard &Zuliani, 1994); see Fig. 16(b). Catalyst inventory isnecessarily limited. The vapor does not pass throughthe catalyst envelopes.

4. Trays and packed catalyst sections can also be used onalternate stages (Nocca, Leonard, Gaillard &Amigues, 1989, 1991; Quang, Amigues, Gaillard, Leo-nard & Nocca, 1989); see Fig. 16 (c). The vapor #owsthrough the packed section through a central chimneywithout contacting the catalyst. The liquid from theseparation trays is distributed evenly into the packedreactive section below by a distribution device.

5. Other designs have been proposed for tray columnswith catalyst containing pockets or regions that are#uidised by the up#owing liquid (Quang et al., 1989;Marion, Viltard, Travers, Harter and Forestiere, 1998;Jones, 1992a,b). Catalyst attrition is a concern ina #uidised environment, but this can be taken care ofby "ltration of the liquid and by make-up of thecatalyst.

In the tray con"gurations discussed above, the packed(or #uidised) catalyst containing envelopes are essentiallyvapor free. Furthermore, the vapor}liquid contactinge$ciency can be considered practically unimpaired by


Fig. 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, stan-dard tray 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 de-termines the extent of reaction on the stages.

2. Thermodynamics of reactive distillation

An introductory review of RD thermodynamics wasprovided by Frey and Stichlmair (1999a) (see, alterna-tively, Stichlmair & Fair, 1998).

The classical thermodynamic problem of determiningthe equilibrium conditions of multiple phases in equilib-rium with 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 litera-ture review by Seider and Widagdo (1996). Two morerecent developments are noted below.

Perez-Cisneros, Gani & Michelsen (1997a) discuss aninteresting approach to the phase and chemical equilib-rium problem. Their method uses chemical &elements'rather than the actual components. The chemical ele-ments are the molecule parts that remain invariant dur-

ing the reaction. The actual molecules are formed fromdi!erent combinations of elements. A bene"t of this ap-proach is 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 equilib-rium solution, 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) con-siders the in#uence of a single reversible chemical reac-tion on vapor}liquid equilibria. The second paper(Barbosa & Doherty, 1987b) introduces a set of trans-formed composition variables that are particularly usefulin the construction of thermodynamic diagrams for reac-ting mixtures. For a system in which the componentstake part in either of the following reactions

A#B H C, (1)

A#B H C#D (2)

the following transformation is de"ned:

ZiQ

zi/l

i!z

k/l

klk!l

Tzk

. (3)


ziis the mole fraction of species i in either the vapor or

liquid-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 by

dXi

dq"X

i!>

i, (4)

where Xiis the transformed composition of species i in

the liquid-phase and >iis the transformed composition

for the vapor phase. q 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): À system is azeotropic when it canbe distilled (or condensed) without change of composi-tiona. The conditions for the existence of a reactive azeo-trope (and all other stationary points in the reactivemixture) are most easily expressed in terms of the trans-formed composition variables:

Xi">

i. (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 from

dxi

dt"

<

;(x

i!y

i)#

r+j/1

rj(l

i,j!x

i

c+k/1

lk,j

), (6)

where < is the molar #ow rate in the vapor and ; is themolar liquid hold-up. These equations are more conve-niently expressed in terms of actual mole fractions, ratherthan the transformed composition variables de"nedabove. It will be apparent that the heating policy greatly

in#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 by

Da";k

1<

, (7)

where k1is 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 trajecto-ries of residue curves of equilibrium distillation withnonequilibrium reversible reaction in the liquid-phase.Rev shows that there can be a continuous line of station-ary points 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 num-ber of stable nodes as a function of Damkohler numberand pressure.

Residue curve maps and heterogeneous kinetics inmethyl acetate synthesis were measured by Song,


Fig. 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 models

The 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 con-cerned with the extension of this standard model todistillation accompanied by chemical reaction(s).

3.1. The EQ stage model

A 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 pro-cess is 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 acro-nym referring to the di!erent types of equation. TheM equations are the material balance equations; the totalmaterial balance takes the form

d;j

dt"<

j`1#¸

j~1#F

j!(1#rV

j)<

j!(1#rL

j)¸

j

#

r+

m/1

c+i/1

li,m

Rm,j

ej. (8)

;j

is the hold-up on stage j. With very few exceptions,;

jis considered to be the hold-up only of the liquid-

phase. It is more important to include the hold-up of thevapor phase at higher pressures. The component materialbalance (neglecting the vapor hold-up) is

d;jxi,j

dt"<

j`1yi,j`1

#¸j~1

xi,j~1

#Fjzi,j

!(1#rVj)<

jyi,j!(1#rL

j)¸

jxi,j#

r+

m/1

li,m

Rm,j

ej. (9)

In the material balance equations given above rj

is theratio of sidestream #ow to interstage #ow:

rVj"SV

j/<

j, rL

j"SL

j/¸

j, (10)

li,m

represents the stoichiometric coe$cient of compon-ent i in reaction m and e

jrepresents the reaction volume.

The E equations are the phase equilibrium relations

yi,j"K

i,jxi,j

. (11)


Fig. 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

c+i/1

xi,j"1,

c+i/1

yi,j"1. (12)

The enthalpy balance is given by

d;jH

jdt

"<j`1

HVj`1

#¸j~1

HLj~1

#FjHF

j

!(1#rVj)<

jHV

j!(1#rL

j)¸

jHL

j!Q

j. (13)

The superscripted H's are the enthalpies of the appropri-ate phase. 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 addi-tional term 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 automati-cally and no separate term is needed.

Under steady-state conditions all of the time deriva-tives in 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 applications

Much of the early literature on RD modelling is con-cerned primarily with the development of methods forsolving the steady-state EQ stage model. For the mostpart such methods are more or less straightforward ex-tensions of 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 men-tioned most 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 re-lated to 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


of 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 com-putations. 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 reac-tions. Suzuki's method was used by Babcock and Clump(1978). The so-called h method developed for conven-tional distillation columns by Holland and his manycollaborators (see, Holland, 1963, 1981) was extended toRD operations by Komatsu and Holland (1977) andnamed the multi-h}g 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 computa-tional problems associated with multiple columns. Sav-kovic-Stevanovic, Mis\ ic-Vukovic, Boncic-Caricic, Tris\ ovicand Jezdic (1992) used the h 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 simulta-neously using 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 equa-tions in unsteady-state form and integrating numericallyuntil the steady-state solution has been found (Komatsu,1977; Jelinek & Hlavacek, 1976). Komatsu compares his

EQ 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 sub-set of 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 pa-pers. Takamatsu, Hashimoto and Kinoshita (1984) andKinoshita (1985) used a similar approach to model col-umns for an unusual application: heavy water enrich-ment using 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$-cult to 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) de-scribes physical 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 locat-ing multiple steady-states (Pisarenko, Anokhina& Sera"mov, 1993).

Alejski, Szymanowski and Bogacki (1988) used a min-imisation method due to Powell (1965) to solve theMESH equations. This approach is, however, rather slowto converge. Numerical results for the esteri"cation of


Fig. 19. Equilibrium stage model used by Davies et al. (1979).

acetic 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 dia-meter and 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 agree-ment with the shape of the pro"les measured byKomatsu, although there are some signi"cant quantitat-ive di!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 com-bined with Newton's method for computing the variablesat each time step. A comparison between the numericalresults of Alejski (1991a) obtained with an equilibrium-cells-in-series model 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 pro-vided for 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, loca-tion of feed inlets, number of theoretical stages and distil-late rate upon the yield, selectivity and productdistribution. As has been reported elsewhere, the columnpressure is an important factor that strongly a!ects reac-tion rates 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 vari-ables. Four examples demonstrate that RADFRAC canbe applied to a wide variety of reactive separation pro-cesses. 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. Simula-tion results 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 steady-state behaviour of an actual industrial RD column pro-ducing propylene oxide from propylene chlorohydrinand calcium hydroxide. The thermodynamic propertiesof this system are complicated by the presence of electro-lytes in 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 vari-ation on the standard EQ stage model that is depicted inFig. 19. The vapor/liquid contacting section is modelledas a conventional vapor}liquid equilibrium stage (with-out reaction). The outgoing liquid stream passes to a re-actor where chemical equilibrium is established. Thestream leaving this reactor passes on to the next equilib-rium stage. 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 values


Fig. 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).

is 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 evalu-ates the transformed variables.

3.3. Multiple steady-states with the EQ model

Multiple 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 experi-mental veri"cation of their existence has been forthcom-ing. 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 dis-cussions of 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), vary-ing the 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 multipli-city is 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 steady-states, but Kumar and Daoutidis (1999) found ònlya"ve!

GuK ttinger and Morari (1997, 1999a,b) develop theso-called R/R analysis for RD columns. The two


Fig. 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).

in"nities refer to in"nite internal #ow rates and an in"-nite number of stages and the method is for the predic-tion of MSS in distillation. GuK ttinger and Morari (1997)extended prior work of Morari and co-workers that wasrestricted to conventional distillation operations to de-velop a 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 methodo-logy is 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 equa-tions and uses homotopy methods as well as intervalcomputing techniques to identify the highest order singu-larity.

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 nu-merical bifurcation 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 equilib-rium prevails. 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 pro-duce TAME, but not in the MTBE process. The mea-sured steady-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 steady-state, 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 applications

Savkovic-Stevanovic (1982) put forth an unsteady-state EQ 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 un-steady-state conditions.

Ruiz, Basualdo and Scenna (1995) describe a softwarepackage called READYS (REActive Distillation dY-namic Simulator) for which an EQ stage model is used


which adopts the assumption of physical equilibrium,ideal mixing, thermal equilibrium with a chemical reac-tion con"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 pro-gram can 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-Cis-neros, 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 chem-ical and 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 com-putational methods; rather its focus is on some of theparameters that are important in RD modelling. Forexample, they discuss the e!ect of thermodynamic mod-els and 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 dy-namic process 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 negli-gible vapor-phase hold-up and perfect mixing of the twophases. Departures from phase equilibrium could be han-

dled by 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 ob-tained in a pilot-scale column for the esteri"cation ofethanol with acetic acid and sulphuric acid as homogene-ous catalyst. 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 syn-thesis of ETBE using an EQ stage model that they solvewith SpeedUp. Simulation results are compared to re-sults obtained 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 compan-ion paper Sneesby, TadeH , Datta and Smith (1997b) devel-op a 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 pre-vented using appropriate control strategies. Sneesby et al.(1998a) show that an increase in fractionation (by in-creasing re#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 sim-pli"ed dynamic model for an RD column. Vapor hold-ups, 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


transformed 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:

f the mixture reaches reaction and phase equilibriuminstantaneously on each tray;

f the solutions are dilute (thus the temperature changecan be ignored);

f the liquid hold-up is constant on each tray (the vaporhold-up is ignored);

f constant molar over#ow (modi"ed somewhat) relatesthe #ows from stage to stage.

They study the separation by RD of close-boiling mix-tures such 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 equilib-rium stages. Cleary and Doherty (1985) provided experi-mental support for this conclusion.

Kumar and Daoutidis (1999) presented a comprehens-ive dynamic EQ stage model of an ethylene glycol RDcolumn. They compare a model that includes vapor-phase balances to a more conventional model that ignor-es the 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 pos-sible numerical problems when developing dynamicmodels of RD based on phase and chemical equilibriumprinciples.

3.5. Batch reactive distillation

Batch reactive distillation, an inherently unsteady-state process 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 reac-tion in an Oldershaw column. The paper does not in-clude any 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 unsteady-state model equations while Newton's method is used tosolve the steady-state equations at each time step. A com-parison with 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 opera-tion of 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) de-veloped a 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 equa-tions is solved using the DASPK solver.

Venimadhavan et al. (1999b) examined a novel distil-late policy and propose a new re#ux policy for equimolarreactions. For the special case of butyl acetate produc-tion the new policies lead to complete conversion of thereactants and high-purity products that are unobtainableby conventional methods.

3.6. Primarily experimental papers

In 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


propylene 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 col-umn. 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 col-umn packed 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 com-plexation with tri#uroacetic acid. Newton's method wasused to solve the EQ stage model equations. A compan-ion paper (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 laboratory-scale column. 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 iso-butene conversion 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 in

height and 15 cm in diameter. The catalyst was AmberliteXAD ion-exchange resin. Composition pro"les are pro-vided for a few experimental runs. Some of the experi-ments show 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 pro-prietary simulation program FLOWBAT, but compari-sons with 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 stan-dard RD 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 produc-tion of tert-amyl-alcohol from water and iso-amylenes.Their paper provides an unusually comprehensive de-scription of 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 agree-ment with the data. A parametric study showed the e!ectof varying the feed composition and other importantoperational parameters.

Gaspillo, Abella and Goto (1999) studied experi-mentally the dehydrogenation of 2-propanol to acetoneand hydrogen in a small-scale RD column. The separ-ation of 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.


3.7. Use of ezciencies in RD models

Some 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 equilib-rium equations incorporate a stage e$ciency factor.There are many di!erent de"nitions of the stage e$cien-cy; that of Murphree is most often used in EQ stagesimulation:

EMVi

"

yiL!y

iEyHi!y

iE

; i"1,2,2, n, (14)

where yiL

is the average composition of the vapor leavingthe tray, y

iEis the composition of the vapor entering the

tray and yHi

is the composition of the vapor in equilib-rium with 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$ciency prediction method; this paper illus-trates the complex nature of component e$ciencies. Forpacked columns it is common to use the height equiva-lent to 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 funda-mentally sound methods for estimating either e$cienciesor HETPs in RD operations. Davies et al. (1979) em-ployed a conventional binary e$ciency predictionmethod in the absence of anything better. In general, thepresence of chemical reactions will have an in#uence onthe component e$ciencies. This is illustrated by calcu-lations of the component e$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 (dis-cussed below), 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 non-reactive case. For the non-reactive column the compon-ent e$ciencies are close to one another and in the range0.5}0.65. The smallest molecule, water, has the highestcomponent e$ciency. The component e$ciencies of EO

and EG lie in between those of water and DEG. For RDoperation, the component e$ciencies show great vari-ation between the di!erent components. Clearly,chemical reactions in#uence the values of the componente$ciencies in a complex and unpredictable way. Thisaspect has also been highlighted in the simulations pre-sented by 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 transfer

For the purposes of this discussion it su$ces to adopta "lm model description of the transport processes inRD. Representative "lm pro"les for homogeneous sys-tems are shown in Fig. 5(a), and for heterogeneous sys-tems in 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 respec-tively are given by

yi

R¹V

LkVi

Lz"

c+k/1

yiNV

k!y

kNV

icVtnV

i,k

(15)

and

xi

R¹L

LkLi

Lz"

c+k/1

xiNL

k!x

kNL

icLtnL

i,k

, (16)

where xiand y

iare the mole fractions of species i in the

liquid and vapor phases, respectively. The ni,k

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 com-ponent is obtained by the summation equations for bothphases. At the vapor}liquid interface we have the conti-nuity equations

NViDI"NL

iDI. (17)

For a homogeneous system, the molar #uxes in the liquid"lm may change due to any chemical reaction that takesplace there

LNi

Lz"

r+

m/1

li,m

Rm

. (18)


Fig. 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 re-action modelled 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 some-times are written in greatly simpli"ed form

Ni"!c

tD

i,%&&

Lxi

Lz. (19)

This expression ignores the coupling between the speciesgradients as well as mass transfer by convection. D

i,%&&is

an e!ective di!usivity and it should be regarded as


a 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 ana-lytical solutions 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 form

NLi"k

iE

i(xI

i!xL

i), (20)

where ki

is the mass transfer coe$cient and Ei

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

ithat can be used in all situations. Indeed, in many

cases it is not even possible to obtain analytical expres-sions for the enhancement factor, even for the much-simpli"ed constitutive 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 simul-taneous chemical reaction modelled using the simplerconstitutive relation given by Eq. (19). E!ective di!us-ivity models 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:

Ji"!c

t

c~1+k/1

Di,k

Lxi

Lz, (21)

where Ji

is the molar di!usion #ux of speciesi (N

i"J

i#x

iN

t) and the D

i,kare the Fick di!usion

coe$cients for the multicomponent mixture. The Fickdi!usion coe$cients can be related to the binary MSdi!usion coe$cients; see Taylor and Krishna (1993) fordetails of this. Solutions of Eq. (21) and the continuityequation (18) are known for a few cases involving simul-taneous di!usion and reaction (see, for example, Toor,1965; Kenig & Gorak, 1995, 1997). In most cases ofpractical signi"cance Eq. (21) is just as di$cult to solve asthe full MS equations and it is necessary to employnumerical methods here as well.

A rigorous approach to modelling heterogeneous sys-tems (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 is

unnecessary 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 reac-tion in 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 inter-face will 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 cata-lyst as 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 vari-ations across 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:

xi

R¹

Lki

Lz#

xi

R¹

<i

Lp

Lz#

xi

gB0

Di,e

"

c+k/1

xiN

k!x

kN

ictne

i,k

!

Ni

ctDe

i

, (22)

where Deiis the e!ective Knudsen di!usion coe$cient for

species i in the porous catalyst.The mass transfer rates are obtained by multiplying

the #uxes by the interfacial area of the catalyst particles.This is not as straightforward, as it looks, since, depend-ing on 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


Fig. 23. The non-equilibrium stage (cell) for homogeneous liquid-phasereaction.

uncertainty in the parameters that appear in theequations. Berg and Harris (1993) have developed a de-tailed model of di!usion and reaction in MTBE syn-thesis. However, their model focuses only on thetransport and reaction issues and they have not de-veloped a 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 car-ried out 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-ex-change resin. Catalyst e!ectiveness factors and selectiv-ities computed 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 va-por}liquid-porous catalyst 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 intro-duce àrti"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 pack-ing and that the main resistance to mass transfer is on theliquid side.

5. Non-equilibrium (NEQ) stage modelling

The 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).

5.1. The conventional NEQ model

It 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 cross-section of a packed column. The component molar bal-ances for the vapor and liquid-phases are

<jyi,j!<

j`1yi,j`1

!f Vi,j#N V

i,j"0, (23)

¸jxi,j!¸

j~1xi,j~1

!f Li,j!N L

i,j"0, (24)

where Ni,j

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 N

i,jare obtained from the Max-

well}Stefan (16) modi"ed as follows:

xi,j

R¹j

LkLi,j

Lg"

c+k/1

xi,j

N Lk,j

!xk,j

N Li,j

cLt,j

(iLi,k

a)j

(25)

with a similar relation for the vapor phase. The iLi,k

rep-resents the mass transfer coe$cient of the i!k pair inthe liquid-phase; this coe$cient is estimated from in-formation on the corresponding Maxwell}Stefan di!us-ivity nL

i,kusing the standard procedures discussed in

Taylor 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 equa-tions for both phases. The enthalpy balances for bothvapor and liquid-phases are

<jHV

j!<

j`1HV

j`1!FV

jHVF

j#E V

j#QV

j"0, (26)

¸jHL

j!¸

j~1HL

j~1!FL

jHLF

j!EL

j#QL

j"0. (27)


The interphase energy transfer rates Ej

(equal in bothphases) have conductive and convective contributions

E Lj"!hL

ja

L¹L

Lg#

c+i/1

N Li,j

HLi,j

(28)

with a similar relation for the vapor phase. hLj

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 sub-cooled (Taylor et al., 1994).

At the vapor}liquid interface we assume phase equilib-rium

yi,j

DI"K

i,jxi,j

DI, (29)

where the subscript I denotes the equilibrium composi-tions and K

i,jis the vapor}liquid equilibrium ratio for

component 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 liquid-phase and equations expressing the continuity of #uxes ofmass and energy across the interface. Furthermore, in theNEQ model we take account of the pressure drop acrossa stage

pj!p

j~1!(*p

j~1)"0, (30)

where pj

and pj~1

are the stage pressures and *pj~1

isthe 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 de-sign information 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 re-view of early applications of NEQ models is available inTaylor & Krishna (1993, Chapter 14).

5.2. NEQ modelling of RD

Building an NEQ model of a reactive separation pro-cess is not as straightforward as it is for the EQ stagemodel in which we simply (or not so simply) add a term

to account for reaction to the liquid-phase material bal-ances. For a reactive separation process, we "rst need toknow whether the reaction is heterogeneous or homo-geneous.

For homogeneous systems the component molar bal-ance for the liquid-phase becomes

¸jxi,j!¸

j~1xi,j~1

!fLi,j!NL

i,j!

r+

m/1

li,m

Rm,j

ej"0,

(31)

where Rm,j

is the rate of reaction m on stage j. li,m

repres-ents the stoichiometric coe$cient of component i in reac-tion m and e

jrepresents 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"ca-tions and 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 re-quired for 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 equilib-rium (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 bal-ance is as given above and e

jis given by the total amount

of 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 (sur-face area, 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 models

Sawistowski and Pilavakis (1979, 1988) modelleda packed RD column for the esteri"cation of methanoland acetic acid to methyl acetate. They used an e!ective


di!usivity method for their mass transfer model. Unlessthe equilibrium constant has some unconventional def-inition, the reaction equation given in their "rst paperrepresents an irreversible reaction. The system of di!er-ential equations 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 sep-aration modelling (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 col-umn with bag-type porous catalyst. Theirs is a pseudo-homogeneous model 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 prop-erties for 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 concentra-tion, temperature and #ux pro"les. Only for the temper-ature pro"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 mea-sured for 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 descrip-tion of multicomponent mass transfer and the simplere!ective di!usivity models. However, they also concludethat there can be signi"cant di!erences between EQ and

NEQ 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 conver-sion.

Lee and Dudukovic (1998) described an NEQ modelfor homogeneous RD in tray columns. The Max-well}Stefan equations are used to describe interphasetransport, with the AIChE correlations used for the bi-nary (Maxwell}Stefan) mass transfer coe$cients. New-ton's method and homotopy continuation are used tosolve the model equations. A close agreement betweenthe predictions of EQ and NEQ models was found onlywhen the tray e$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 opera-tion of RD in tray columns. The DAE equations weresolved by use of an implicit Euler method combined withhomotopy-continuation. Murphree e$ciencies cal-culated from 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$ciency calculation to account for di!usion and reac-tion in the catalyst. A large number of correlations for themass transfer coe$cients in di!erent types of columninternal are available in the program. Stage hy-drodynamic models included in the package are:

f completely mixed vapor and liquid;f completely mixed liquid, plug-#ow vapor;f mixed pool model for the liquid-phase;f 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 experi-mental data (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,


and/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 introduc-tion of 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 oscil-lations were 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 de-tailed NEQ stage model for vapor}liquid}porous cata-lyst systems. 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 bal-ances. 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 simu-late some 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 reac-tion in 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 Hof-fmann (1999) used both EQ stage (with Murphree e$-ciency) and NEQ models to simulate the MTBE andTAME processes. The reactions were handled using bothquasi-homogeneous and heterogeneous methods. Simu-lation results were compared to experimental data ob-tained in two laboratory-scale columns. A detailed NEQmodel was needed to describe the TAME process, butboth NEQ and the EQ stage (with an e$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 ac-counts for axial dispersion along the column, the disper-sion coe$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 interfa-ces. 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 accom-panies the 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 pilot-scale column with 6 mm Intalox saddles and a reactivesection containing bale-type packing. It was found thatthe DAA production rate was controlled by mass trans-fer. DAA selectivity was in#uenced by the liquid distribu-tion. 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 dis-tillation, although it is interesting to note that the mater-ial balances 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 trans-fer between 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


Fig. 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).

coe$cients being estimated using the correlations ofOnda, Takeuchi and Okumoto (1968). The model equa-tions were solved simultaneously. A predicted temper-ature pro"le appears to be in good agreement with onedetermined experimentally. However, it must be remem-bered that the all important mass transfer coe$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 condensa-tion rate are important design variables for this RDprocess, and that the DAA selectivity would have im-proved if 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 steady-states SS-1 (high conversion), SS-2 (intermediate conver-sion) and SS-3 (low conversion) were found. The desiredhigh-conversion steady-state solution (SS-1) corresponds

to 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 model

An 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 temper-ature, 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 trans-fer. 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 disper-sion due to the vapor jets and bubbles. In packed sec-tions, maldistribution of internal vapor and liquid #ows


Fig. 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 col-umns.

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#u-ence of #ow patterns and maldistribution on the distilla-tion process.

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 approxi-mated using di!erent #ow splitting policies.

A schematic diagram of the unit cell for a vapor}liquid}porous catalyst system is shown in Fig. 27. Each

cell 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 Max-well}Stefan equations are used for calculation of themass transfer rates through each "lm. Thermodynamicequilibrium is assumed only at the vapor}liquid inter-face. Mass transfer inside the porous catalyst may bedescribed with the dusty #uid model described above.

The unit cell for homogeneous systems (and for hetero-geneous systems modelled as though they were homo-geneous) 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 present-ed in 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 forma-tion. 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 opera-tion in 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#u-ence on 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 NEQmodelling

Higler, 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


Fig. 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 cata-lyst is 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 ignored

C A case one in which the Knudsen di!usion coe$cientis a factor "ve times smaller than the smallest of the

Maxwell}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 iso-butene as 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 conver-sion. 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 models

Kreul, Gorak, Dittrich and Barton (1998) described anNEQ model for RD in packed columns. Theirs is a dy-namic model 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


Fig. 29. Comparison of the results for conversion of iso-butene ob-tained by 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 Knud-sen contribution. Adapted from Higler, Krishna and Taylor (2000).

Fig. 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).

describe a two-phase model in which di!usion and reac-tion to and within the solid catalyst is not accounted forby additional equations (and parameters), but their ef-fects are 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 di-mension (the column height) using the method of lines.The model equations were solved using the equation-based modelling environment ABACUS (Allgor, Berrera,Barton & Evans, 1996). The paper by Kreul et al. in-cludes a limited comparison with some unsteady-statedata for a methyl acetate column. The results shown inthe paper suggest that their dynamic model is well able to

describe 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 ex-periments there 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 sub-models for 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 simul-taneous transport and reaction of 10 di!erent species.Schneider, Kenig and Gorak (1999) used the Max-well}Stefan approach 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


Prevost (1998) brie#y addressed some numerical prob-lems that 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 design

Design 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 design

Barbosa and Doherty (1988c) developed the "xed-point method for the design of single-feed RD columns.The method is based on the following assumptions:

f the column is adiabatic;f the molar heat of vaporisation is constant;f the heat of mixing is negligible;f sensible heat e!ects can be ignored;f the heat of reaction is negligible compared to the

enthalpy of the vapor;f the feed is a saturated liquid;f phase equilibrium is achieved on each stage;f 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 equa-tions written around a stage in each section of the col-umn (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 section

Xi,j"

rHj#1

rHj

>i,j!

1

rHj

>i,D

(32)

and for the stripping section the material balance reads

Xi,j`1

"

sHj

sHj#1

>i,j!

1

sHj#1

Xi,B

. (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"ned

as follows:

rHj"

¸j(l

k!l

Txk,j

)

D(lk!l

Tyk,D

), sH

j"

<(lk!l

Tyk,j

)

B(lk!l

Txk,B

). (34)

Barbosa and Doherty convert these equations to di!er-ential form. To determine a feasible design the equationsare integrated numerically starting with the desired prod-uct composition. They illustrate their design procedurefor a quaternary system shown in Fig. 30(a). If the trajec-tories intersect, as shown in Fig. 30(b), then the resultingcolumn is feasible, if the trajectories fail to intersect, thenno column will produce the desired products (Fig. 30(c)).The minimum re#ux can be found from the special caseof two trajectories that just touch each other (Fig. 30(d)).

A number of extensions of the approach of Barbosaand Doherty (1988c) have appeared in the literature.Barbosa and Doherty (1988d) extend their ownmethodology to double-feed columns. Buzad andDoherty (1994, 1995) and Doherty and Buzad (1994)provide a further extension in order to handle kineticallycontrolled reactions in three-component systems. Ungand Doherty (1995e) consider RD processes involvingmultiple reactions. Okasinski and Doherty (1998) relaxsome of the assumptions underlying the methods ofBarbosa, Buzad, and Doherty. They develop a systematicmethod for the design of kinetically controlled staged RDcolumns while taking into account a single liquid-phasereaction, heat e!ects, non-ideal phase equilibrium, anda range of liquid-phase hold-ups on the di!erent stages.The Damkohler number de"ned for the entire column isa key parameter in their approach. Melles, Grievink andSchrans (2000) also relaxed the uniform hold-up assump-tion by allowing di!erent hold-ups per section of thecolumn (not on each tray), taking into account heate!ects, and non-zero stoichiometric sum reactions.

The design of RD columns in which the feed streamcontains species that do not react at all was addressed byEspinosa, Aguirre and Perez (1995a,b). Most of themethods cited above are based on an assumption that thereaction takes place on all stages in the column.Espinosa, Aguirre and Perez (1996) described a methodof dealing with columns in which the reaction takes placeonly in a central portion of the column. The latter issue wasrevisited by Espinosa, Aguirre, Frey and Stichlmair (1999)who proposed a design method for a column with a reactivesection, a stripping section, and two rectifying sections.

Mahajani and Kolah (1996) extended the methods ofDoherty and co-workers for packed RD columns. Anassumption in their method is that liquid-phase backmix-ing is totally absent. It is pertinent to note that the overallmethodology and some important results (e.g. minimumre#ux) are unchanged from the methods for tray col-umns. Mahajani (1999b) also addresses the design of RDprocesses for multicomponent kinetically controlled re-active systems.


Fig. 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 & Hildeb-randt, 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 ap-proach to 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 com-position of any particular phase is given by the vectorequation

dx

dt"mix#sep#rx (35)

where x is the composition of the phase in question, andmix, sep, and rx are vectors that represent the composi-tion changes due to mixing, separation, and reaction,respectively. For these vectors Hauan et al. (2000b) write

mix"M(xF!x0), (36)

rx"R(m!x0+l), (37)

sep"[S](x!y), (38)

where M is a scalar equal to the relative amounts ofmaterial being mixed, x0 is the current composition andxF is the feed composition, and R is a scalar that dependson such things as catalyst activity, hold-up, and temper-ature. [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 possi-bility, 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


di!erence between an arbitrary composition and a singu-lar point. 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 react-ive/separation processes. In their approach an RD pro-cess (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) illus-trate their 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) com-bine heuristic 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 sys-tem and 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 illus-trate it 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 methods

A 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 methods

RD 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 ordi-nary distillation processes may be inappropriate for RD.Gumus and Ciric (1997) used a bilevel optimisation pro-cedure to 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 nitroben-zene to aniline, in which the resulting aniline}nitroben-zene}water system 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 com-position and 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 calcu-lations once the empirical formulae have been construc-ted (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 design

Until 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: pres-sure, reactive zone location, reactant feed ratio, feed


Table 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. Use

a re#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:

<#!5

"

m#!5

o#!5

5. Determine the reactive zone height from the calculated catalyst volume and estimated diameter.

h#!5

"

<#!5

(p4)d2

#0-

6. Determine the number of reactive stages by dividing the total reactive zone height by the catalytic packing HETP.

N#!5

"

h#!5

HETP#!5

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 velocity

and 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 design-ing an 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: èach system has certain character-istics that 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 recom-mend using NEQ or rate-based models for this purpose.

6.5. RD design in industrial practice

At the time the Eastman methyl acetate process wasdeveloped there were no commercially available simula-tion programs 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 simu-lation program. Computer programs to model a com-plete RD 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 accu-rately predict the performance of commercial RD pro-cesses in 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 remarks

Belck (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 un-certainty inherent in the experimental determination ofreaction rate constants and liquid}vapor diagrams


also 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 compo-nents * 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 re-marks even 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. How-ever, 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 simula-tion.

Column hardware choice can have a signi"cant in#u-ence on 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 appreci-ated is the fact that the design methodology for RD traycolumns is fundamentally di!erent from that of conven-tional trays. Liquid residence time and residence timedistributions are more important in RD. The froth re-gime is to be preferred to the spray regime for RDapplications; this is opposite to the design wisdom nor-mally adopted for conventional distillation. Though thephenomena of MSS has received considerable attentionin the literature, it is possible that not all of the steady-states can 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. Pseudo-homogeneous reaction 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 pack-ings such 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 avail-able already, detailed information on the hydrodynamicsand mass transfer parameters for the various hardwarecon"gurations sketched in Figs. 10}16, is woefully lack-ing in the open literature. Paradoxically, such informa-tion has vital consequences for the conversion and

selectivity 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 hydrodyn-amics and 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 pro-cess models.

Notation

a interfacial area, m2

B bottoms #ow, mol s~1

B0

permeability, m2

c number of components, dimensionlessct

total concentration, mol m~3

D distillate #ow, mol sv1Da Damkohler number, dimensionlessD

i,%&&e!ective Fick di!usivity, m2 s~1

nei

e!ective Knudsen di!usivity in porous catalyst,m2 sv1

ni,k

Maxwell}Stefan di!usivity, m2 s~1

Ei

enhancement factor, dimensionlessE energy #ux, W m~2

E energy transfer rate, J s~1

EMVi

overall Murphree tray e$ciency, dimensionlessh#-

clear liquid height, mFV vapor feedstream, mol s~1

FL liquid feedstream, mol s~1

f component feed stream, mol s~1

hw

weir height, mh heat transfer coe$cient, W m~2 K~1

H molar enthalpy, J mol~1

k1

pseudo-"rst-order reaction rate constant, s~1

K vapor}liquid equilibrium constant, dimension-less

¸ liquid #ow rate, mol s~1

¸M

interchange liquid #ow rate between horizon-tal rows of cells, mol s~1

Ni

molar #ux of species i, mol m~2 s~1

N Mass transfer rate, mol s~1

pj

stage pressure, PaQ heat duty, J s~1

r number of reactions, dimensionlessrj

ratio of side stream #ow to interstage #ow onstage j, dimensionless

rHj

transformed re#ux ratio, dimensionlessR

m,jreaction rate, mol m~3 s~1


R gas constant, J mol~1 K~1

sHj

transformed stripping ratio, dimensionlessS side draw-o!, mol s~1

t time, s¹ temperature, K; molar hold-up, mol< vapor #owrate, mol s~1

= weir length, mx mole fraction in the liquid}phase, dimensionlessx mole fraction vector, dimensionlessX transformed liquid-phase mole fraction, di-

mensionlessy mole fraction in the vapor-phase, dimensionless> transformed vapor-phase mole fraction, di-

mensionlessz mole fraction in either vapor or liquid-phase,

dimensionlessZ transformed mole fraction, dimensionless

Greek letters

e reaction volume, m3

ci

activity coe$cient of species i, dimensionlessC thermodynamic correction factor for binary

mixture, dimensionless[C] matrix of thermodynamic factors, dimensionlessi mass transfer coe$cient, m s~1

k chemical potential, J mol~1

l stoichiometric coe$cient, dimensionlessq dimensionless residence time, dimensionlessg viscosity of #uid mixture, Pa sg distance along di!usion path, dimensionless

Subscripts

e! e!ectivei component indexI referring to interfacej stage indexk alternative component indexm reaction indext total

Superscripts

F referring to feed stream¸ referring to liquid-phase< referring to vapor-phase

List of abbreviations

DAE di!erential-algebraic equationsDEG diethylene glycolEG ethylene glycolEQ equilibriumEO ethylene oxide

MeOH methanolMeOAc methyl acetateAcOH acetic acidHETP height of a theoretical plateHTU height of a transfer unitMS Maxwell}StefanMSS multiple steady-statesMTBE methyl tert-butyl etherNEQ non-equilibriumRD reactive distillationSRK Soave}Redlich}KwongTAME tertiary amyl ether

Acknowledgements

RT 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 Nether-lands Organisation for Scienti"c Research (NWO) in theform of a `programmasubsidiea for research on reactiveseparations.

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Modelling Reactive Distillation