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. Taylorº', R. Krishna°* ºDepartment 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 either conventional reactors or conventional distillation columns. The introduction of an in situ separation function within the reaction zone leads to complex interactions between vapor}liquid equilibrium, vapor}liquid mass transfer, intra-catalyst di!usion (for heterogeneously catalysed processes) and chemical kinetics. Such interactions have been shown to lead to the phenomenon of multiple steady-states and complex dynamics, which have been veri"ed in experimental laboratory and pilot plant units. We trace the development of models that have been used for design of reactive distillation columns and suggest future research directions. 2000 Elsevier Science Ltd. All rights reserved. Keywords: Reactive distillation; Equilibrium stage model; Non-equilibrium stage model; Multiple steady-states; Maxwell}Stefan equations Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5184 1.1. Why RD? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5185 1.2. The constraints and di$culties in RD implementation . . . . . . . . . . . . . . . . . . . . . . . . 5187 1.3. The complexity of RD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5188 1.4. Practical design considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5188 1.4.1. Installation, containment and removal of the catalyst . . . . . . . . . . . . . . . . . . . 5188 1.4.2. E$cient contacting of liquid with catalyst particles . . . . . . . . . . . . . . . . . . . . . 5189 1.4.3. Good vapor/liquid contacting in the reactive zone . . . . . . . . . . . . . . . . . . . . . 5189 1.4.4. &&Low'' pressure drop through the catalytically packed reactive section . . . . . . 5189 1.4.5. Su$cient liquid hold-up in the reactive section . . . . . . . . . . . . . . . . . . . . . . . . 5189 1.4.6. Designing for catalyst deactivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5189 1.5. Hardware aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5189 1.5.1. Catalytically packed RD columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5190 1.5.2. Trays or downcomers to hold catalyst particles . . . . . . . . . . . . . . . . . . . . . . . 5193 2. Thermodynamics of reactive distillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5194 3. Equilibrium (EQ) stage models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5196 3.1. The EQ stage model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5196 3.2. Steady-state algorithms and applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5197 3.3. Multiple steady-states with the EQ model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5200 0009-2509/00/$- 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5201 3.5. Batch reactive distillationm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5203 3.6. Primarily experimental papers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5203 3.7. Use of e$ciencies in RD models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5205 4. Mass transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5205 5. Non-equilibrium (NEQ) stage modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5208 5.1. The conventional NEQ model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5208 5.2. NEQ modelling of RD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5209 5.3. NEQ models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5209 5.4. NEQ cell model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5212 5.5. Pseudo-homogeneous vs. heterogeneous NEQ modelling . . . . . . . . . . . . . . . . . . . . . . 5213 5.6. Dynamics NEQ models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5214 6. Reactive distillation design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5216 6.1. Conceptual design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5216 6.2. Graphical design methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5218 6.3. Design via optimisation methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5218 6.4. From conceptual design to column design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5218 6.5. 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 the dual role of continuous reactor and separator as applied to chemical processing is well established. Berman, Isbenjian, Sedo! and Othmer (1948a) The quote with which we begin this review appeared in print more than "ve decades ago! It provides an interesting historical perspective because in more recent times we have seen an explosion of interest in the subject of reactive distillation, and a veritable plethora of papers have appeared in the last 12 years alone. The recent interest in this process can be attributed in part to the growing commercial importance of reactive distillation, and in part to a keynote paper by Doherty and Buzad (1992), who reviewed the literature to that time. More than half of the over 300 references cited in this review have appeared after 1992. Thus, one of the objectives of this article is to provide an up-date to their work with a review of more recent developments in reactive distillation. The term catalytic distillation is also used for such systems where a catalyst (homogeneous or heterogeneous) is used to accelerate the reaction. In this review we use the generic name reactive distillation, with the acronym RD, to cover both catalysed or uncatalysed reactions 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, Dunning and Lathrop (1945), Berman, Melnychuk & Othmer (1948b) and Berman et al. (1948a). The "rst publications deal mainly with homogeneous self-catalysed reactions such as esteri"cations, trans-esteri"cations, and hydrolysis. Heterogeneous catalysis in RD is a more recent development and was "rst described by Spes (1966). The main focus of this review is on the modelling of RD processes. We have tried to be comprehensive in our coverage, but it would be nearly impossible to cite every paper even in this fairly well-de"ned niche. This review does not attempt quite such comprehensive coverage of the literature devoted more to RD catalysis and kinetics studies, although some of the works in these sub-"elds necessarily are included in our review to some extent. Descriptions of speci"c RD processes also are largely beyond our scope (see, for example, Sharma (1985), Stich- lmair and Frey (1999) for reviews and Bart and Resil (1997) discuss an unusual application). Introductory overviews 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 &C#D where C and D are both desired products. (a) Typical con"guration of a conventional process consisting of a reactor followed by a distillation train. (b) The reactive distillation con"guration. The components A, C, D and B 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 by Towler and Frey (2000). The non-English language literature also is less well served here. Fortunately, many of the papers in the German and Russian literature have been translated into English. Overviews of parts of the extensive Russian literature on RD (in English) are by Sera"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 by a much longer one on equilibrium (EQ) stage modelling. A brief discussion on e$ciencies in RD leads to an outline of mass transfer considerations and an overview of non-equilibrium (NEQ) modelling of RD processes. We end with some comments on RD design methods. We begin, however, with an appreciation of the bene"ts of RD. 1.1. Why RD? Let us begin by considering a reversible reaction scheme: A#B &C#D where the boiling points of the components follow the sequence A, C, D and B. The traditional #ow-sheet for this process consists of a reactor followed by a sequence of distillation columns; see Fig. 1(a). The mixture of A and B is fed to the reactor, where the reaction takes place in the presence of a catalyst and reaches equilibrium. A distillation train is required to produce pure products C and D. The unreacted components, A and B, are recycled back to the reactor. In practice the distillation train could be much more complex than the one portrayed in Fig. 1(a) if one or more azeotropes are formed in the mixture. The alternative RD con"guration is shown in Fig. 1(b). The RD column consists of a reactive section in the middle with non- reactive rectifying and stripping sections at the top and bottom. The task of the rectifying section is to recover reactant B from the product stream C. In the stripping section, the reactant A is stripped from the product stream D. In the reactive section the products are separated in situ, driving the equilibrium to the right and preventing any undesired side reactions between the reactants A (or B) with the product C (or D). For a properly designed RD column, virtually 100% conversion can be achieved. The most spectacular example of the bene"ts of RD is in the production of methyl acetate. The acid catalysed reaction MeOH#AcOH&MeOAc#H O was tradi- tionally carried out using the processing scheme shown in Fig. 2(a), which consists of one reactor and a train of nine distillation columns. In the RD implementation (see Fig. 2(b)) only one column is required and nearly 100% conversion of the reactant is achieved. The capital and operating costs are signi"cantly reduced (Siirola, 1995). For the acid catalysed reaction between iso-butene and methanol to form methyl tert-butyl ether: iso- butene#MeOH&MTBE, the traditional reactor-followed-by-distillation concept is particularly complex for this case because the reaction mixture leaving the reactor forms three minimum boiling azeotropes. The RD implementation requires only one column to which the butenes 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 reaction MeOH#AcOH&MeOAc#H O. (a) Conventional processing scheme consisting of one reactor followed by nine distillation columns. (b) The reactive distillation con"guration. The reactive sections are indicated by grid lines. Adapted from Siirola (1995). Fig. 3. (a) Reactive distillation concept for synthesis of MTBE from the acid-catalysed reaction between MeOH and iso-butene. The butene feed is a mixture of reactive iso-butene and non-reactive n-butene. (b) Reactive distillation concept for the hydration of ethylene oxide to ethylene glycol. (c) Reactive distillation concept for reaction between benzene and propene to form cumene. (d) Reactive distillation concept for reaction production of propylene oxide from propylene chlorohydrin and lime. The reactive sections are indicated by grid lines. non-reactive, and iso-butene which is reactive) and methanol are fed near the bottom of the reactive section. The RD concept shown in Fig. 3(a) is capable of achieving close to 100% conversion of iso-butene and methanol, along with suppression of the formation of the unwanted dimethyl ether (Sundmacher, 1995). Also, some of the azeotropes in the mixture are `reacted awaya (Doherty & Buzad, 1992). For the hydration of ethylene oxide to mono-ethylene glycol: EO#H OPEG, the RD concept, shown in Fig. 3(b) is advantageous for two reasons (Ciric & Gu, 1994). Firstly, the side reaction EO#EGPDEG is suppressed 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 the liquid-phase mixtures on the trays. To achieve the same selectivity 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 for the 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 &alkyl aromatic, are best carried out using the RD concept not only because of the shift in the reaction equilibrium due to in situ separation but also due to the fact that the undesirable side reaction, alkyl aromatic#ole"n &dialkyl aromatic, is suppressed. The reaction of propene with benzene to form cumene, benzene#propene & Cumene (Shoemaker & Jones, 1987; see Fig. 3(c)), is advantageously carried out in a RD column because not only is the formation of the undesirable di-isopropylbenzene suppressed, but also the problems posed by high exothermicity of the reaction for operation in a conventional packed-bed reactor are avoided. Hot spots and runaway problems are alleviated in the RD concept where liquid vaporisation acts as a thermal #ywheel. The alkylation of iso-butane to iso-octane, iso-butane#n- butene &iso-octane, is another reaction that bene"ts from a RD implementation because in situ separation of the product prevents further alkylation: iso-octane#n- butene &C H (Doherty & Buzad, 1992). The reaction between propylene chlorohydrin (PCH) and Ca(OH) to produce propylene oxide (PO) is best implemented in an RD column, see Fig. 3(d). Here the desired product PO is stripped from the liquid-phase by use of live steam, suppressing hydrolysis to propylene glycol (Bezzo, Bertucco, Forlin & Barolo, 1999). Co-current gas}liquid down#ow trickle-bed reactors are widely applied for hydroprocessing of heavy oils. This co-current mode of operation is disadvantageous in most hydroprocesses (Krishna & Sie, 1994), and counter-current #ow of gas and liquid would be much more desirable (cf. Fig. 4). This is because reactions such as hydrodesulphurisation and hydrogenation are inhibited by hydrogen sulphide formed, even when using the so-called sulphur-tolerant catalyst of the mixed sulphide type. The removal of sulphur from heavy oil generally follows second-order kinetics in sulphur concentration, which is a re#ection of the presence of a variety of sulphur containing compounds with di!erent reactivities. The second-order kinetics imply that a relatively large proportion of sulphur is removed in an early stage of the process (due to conversion of the bulk of reactive 5186 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 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 takes place much more slowly in later stages. This means that the bulk of the H S is generated in a small inlet part of the bed and that this H S exerts its inhibiting in#uence in the remaining part of the bed. Fig. 4(a) shows the partial pressure of H S in the gas phase. It can be seen that in co-current operation the larger part of the bed operates under a H S-rich regime. The situation is clearly more favourable in the counter-current mode of operation since in this case the major part of the bed operates in the H S lean regime. The co-current mode of operation is particularly unfavourable since the inhibiting e!ect is strongest in the region where the refractory compounds have to be converted, which calls for the highest activity. A similar situation exists in hydrocracking. The by-product of conversion of nitrogen containing organic compounds, viz., ammonia, is a very strong inhibitor for hydrogenation and particularly for hydrocracking reactions. For the hydrogenation of aromatics too the co- current operation is unfavourable. This is not only so from a kinetic point of view (inhibition by H S and NH ), but also because of thermodynamics (Trambouze, 1990). Deep removal of aromatics from an oil fraction generally is limited by thermodynamic equilibrium. In the co-current mode of operation the partial pressure of H at the exit end of the reactor is lowest because of the combined e!ects of pressure drop, hydrogen consumption and build up of gaseous components other than H (H S, NH , H O, light hydrocarbons). The counter-current reactor shown in Fig. 4(b) is essentially a RD column wherein the H S is stripped from the liquid-phase at the bottom and carried to the top. The quantitative advantages of the RD implementation for hydroprocessing are brought out in a design study carried out by Van Hasselt (1999). For a 20,000 bbl/d hydrodesulphurisation unit with a target conversion of 98% conversion of sulphur compounds, the catalyst volume required for a conventional trickle-bed reactor is about 600 m. For counter-current RD implementation the catalyst volume is reduced to about 450 m. From the foregoing examples, the bene"ts of RD can be summarised as follows: (a) Simpli"cation or elimination of the separation system can lead to signi"cant capital savings. (b) Improved conversion of reactant approaching 100%. This increase in conversion gives a bene"t in reduced recycle costs. (c) Improved selectivity. Removing one of the products from the reaction mixture or maintaining a low concentration of one of the reagents can lead to reduction of the rates of side reactions and hence improved selectivity for the desired products. (d) Signi"cantly reduced catalyst requirement for the same degree of conversion. (e) Avoidance of azeotropes. RD is particularly advantageous when the reactor product is a mixture of species that can form several azeotropes with each other. 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 exothermic, the heat of reaction can be used to provide the heat of vaporisation and reduce the reboiler duty. (h) Avoidance of hot spots and runaways using liquid vaporisation as thermal #y wheel. 1.2. The constraints and dizculties in RD implementation Against the above-mentioned advantages of RD, there are several constraints and foreseen di$culties (Towler & Frey, 2000): (a) Volatility constraints. The reagents and products must have suitable volatility to maintain high concentrations of reactants and low concentrations of products in the reaction zone. R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5187 Fig. 5. Transport processes in RD. (a) homogeneous liquid-phase reaction, and (b) heterogeneous catalysed reactions. Adapted from Sundmacher (1995). Fig. 6. Length and time scales in RD. Adapted from Sundmacher (1995). (b) Residence time requirement. If the residence time for the reaction is long, a large column size and large tray hold-ups will be needed and it may be more economic to use a reactor-separator arrangement. (c) Scale up to large #ows. It is di$cult to design RD processes for very large #ow rates because of liquid distribution problems in packed RD columns. (d) Process conditions mismatch. In some processes the optimum conditions of temperature and pressure for distillation may be far from optimal for reaction and vice versa. 1.3. The complexity of RD The design and operation issues for RD systems are considerably more complex than those involved for either conventional reactors or conventional distillation columns. The introduction of an in situ separation function within the reaction zone leads to complex interactions between vapor}liquid equilibrium, vapor}liquid mass transfer, intra-catalyst di!usion (for heterogeneously catalysed processes) and chemical kinetics. Fig. 5 shows the various transfer processes in homogeneous and heterogeneous RD. In heterogeneous RD the problem is exacerbated by the fact that these transfer processes occur at length scales varying from 1 nm (pore diameter in gels, say) to say a few meters (column dimensions); 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 each other. Such interactions, along with the strong non- linearities introduced by the coupling between di!usion and chemical kinetics in counter-current contacting, have been shown to lead to the phenomenon of multiple steady-states and complex dynamics, which have been veri"ed in experimental laboratory and pilot plant units (Bravo, Pyhalathi & Jaervelin, 1993; Mohl et al., 1999; Rapmund, Sundmacher & Ho!mann, 1998). Successful commercialisation of RD technology requires careful attention to the modelling aspects, including column dynamics, even at the conceptual design stage (Doherty & Buzad, 1992; Roat, Downs, Vogel & Doss, 1986). As will be shown later many of the reactor and distillation paradigms do not translate easily to RD. The potential advantages of RD could be nulli"ed by improper choice of feed stage, re#ux, amount of catalyst, boilup rate, etc. Thus, it is possible to decrease conversion by increasing the amount of catalyst under certain circumstances (Higler, Taylor & Krishna, 1999b). Increased separation capability could decrease process performance (Sneesby, TadeH , Datta & Smith, 1998a). 1.4. Practical design considerations Towler and Frey (2000) have highlighted some of the practical issues in implementing a large-scale RD application. These are discussed below. 1.4.1. Installation, containment and removal of the catalyst It is important to allow easy installation and removal of the RD equipment and catalyst. If the catalyst undergoes deactivation, the regeneration is most conveniently done ex situ and so there must be provision for easy removal and installation of catalyst particles. Reactive 5188 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 Fig. 7. Counter-current vapor}liquid contacting in trayed columns. Animations of CFD simulations of #ows on the tray can be viewed on our web site: http://ct-cr4.chem.uva.nl/sievetrayCFD. distillation is often passed over as a processing option because the catalyst life would require frequent shutdowns. An RD device that allowed on-stream removal of catalyst would answer this concern. 1.4.2. Ezcient contacting of liquid with catalyst particles The hardware design must ensure that the following `wish-lista is met. (a) Good liquid distribution and avoidance of channelling. Liquid maldistribution can be expected to have a more severe e!ect in RD than in conventional distillation (Podrebarac, Ng & Rempel, 1998a,b). (b) Good radial dispersion of liquid through the catalyst bed. This is required in order to avoid reactor hotspots and runaways and allow even catalyst ageing. The requirement of good radial mixing has an impact on the choice of the packing con"guration and geometry. For example, frequent criss-crossing mixing patterns may be desirable, as is realised in some hardware con"gurations discussed in Section 1.5. 1.4.3. Good vapor/liquid contacting in the reactive zone If the reaction rate is fast and the reaction is equilibrium-limited then the required size of the reactive zone is strongly in#uenced by the e!ectiveness of the vapor} liquid contacting. Vapor}liquid contacting becomes less important for slower reactions. Commonly used devices for good vapor}liquid contacting are the same as for conventional distillation and include structured packing, random packing and distillation trays. 1.4.4. `Lowa pressure drop through the catalytically packed reactive section This problem arises because of the need to use small catalyst particles in the 1}3 mm range in order to avoid intra-particle di!usional limitations. Counter-current operation in catalyst beds packed with such small-sized particles has to be specially con"gured in order to avoid problems 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 section The liquid hold-up, mean residence time, and liquid residence time distribution are all important in determining the conversion and selectivity of RD. This is in sharp contrast with conventional distillation where liquid hold-up and RTD are often irrelevant as the vapor} liquid mass transfer is usually `controlleda by the vapor side resistance. For trayed RD columns the preferred regime of operation would be the froth regime whereas for conventional distillation we usually adopt the spray regime. 1.4.6. Designing for catalyst deactivation Even though, as discussed in Section 1.4.1, it is desirable 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 design stage by use of excess catalyst. Besides adding excess catalyst, the reaction severity can be increased by (a) increasing re#ux, leading to increased residence time and (b) increasing reaction temperature (by increase of column pressure) 1.5. Hardware aspects Before modelling aspects can be considered, careful attention needs to be paid to hardware design aspects. Towler and Frey (2000) have presented an excellent summary of hardware design aspects of RD columns. Some of the important issues are discussed below. For homogeneous RD processes, counter-current vapor}liquid contacting, with su$cient degree of staging in the vapor and liquid-phases, can be achieved in a multitray column (cf. Fig. 7) or a column with random or structured packings (cf. Fig. 8). The hardware design information can be found in the standard sources for conventional distillation design (Lockett, 1986; Stich- lmair & Fair, 1998). The Hatta number for most RD applications is expected to be smaller than about unity (Sundmacher, Rihko & Ho!mann, 1994) and the froth regime is usually to be preferred on the trays (cf. Fig. 9) because of the desire to maintain high liquid hold-up on the trays. High liquid hold-ups could be realised by use of bubble caps, reverse #ow trays with additional sumps to provide ample tray residence time. In the Eastman process for methyl acetate manufacture specially designed high liquid hold-up trays are used (Agreda, Partin & Heise, 1990). R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5189 Fig. 8. Counter-current vapor}liquid contacting in packed columns. Fig. 9. Flow regimes on trays. 1.5.1. Catalytically packed RD columns For heterogeneously catalysed processes, hardware design poses considerable challenges. The catalyst particle sizes used in such operations are usually in the 1}3 mm range. Larger particle sizes lead to intra-particle di!usion limitations. To overcome the limitations of #ooding the catalyst particles have to be enveloped within wire gauze envelopes. Most commonly the catalyst envelopes are packed inside the column. Almost every conceivable shape of these catalyst envelopes has been patented; some basic shapes are shown in Figs. 10}14. These structures are: 1. Porous spheres "lled with catalyst inside them (Buch- holz, Pinaire & Ulowetz, 1995; Johnson, 1993); see Fig. 10(a). 2. Cylindrical shaped envelopes with catalyst inside them (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 with catalyst (Van Hasselt, 1999); see Fig. 11(a). 5. Horizontally disposed wire-mesh tubes containing catalyst (Buchholz et al., 1995; Groten, Booker & Crossland, 1998; Hearn, 1993); see Fig. 11(b). 6. Catalyst particles enclosed in cloth wrapped in the form of bales (Johnson & Dallas, 1994; Smith, 1985). This is the con"guration used by Chemical Research and Licensing in their RD technology for etheri"cation, hydrogenation and alkylation of aromatic compounds (Shoemaker & Jones, 1987). The catalyst is held together by "breglass cloth. Pockets are sewn into a folded cloth and then solid catalyst is loaded into the pockets. The pockets are sewn shut after loading the catalyst and the resulting belt or `catalyst quilta is rolled with alternating layers of steel mesh to form a cylinder of `catalyst balesa as shown in Fig. 12. The steel mesh creates void volume to allow for vapor tra$c and vapor/liquid contacting. Scores of these bales are installed in the reactive zone of a typical commercial RD column. Bales are piled on top of each other to give the required height necessary to achieve the desired extent of reaction. When the catalyst is spent the column is shut down and the bales are manually removed and replaced with bales containing fresh catalyst. Improvements to the catalyst bale concept have been made over the years (Johnson, 1993; Crossland, Gildert & Hearn, 1995). The hydrodynamics, kinetics, and mass transfer characteristics of bale- type packings have recently been published in the open literature (Subawalla, Gonzalez, Seibert & Fair, 1997; Xu, Zhao & Tian, 1997, 1999). 5190 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 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 corrugated sheets of wire gauze (Stringaro, 1991, 1995; Gelbein & Buchholz, 1991; Johnson & Dallas, 1994); see Fig. 13. Such structures are being licensed by Sulzer (called KATAPAK-S) and Koch-Glitsch (called KATAMAX). They consist of two pieces of rectangular crimped wire gauze sealed around the edge, thereby forming a pocket of the order of 1}5 cm wide between the two screens. These catalyst `sandwichesa or `wafersa are bound together in cubes. The resulting cubes are transported to the distillation column and installed as a monolith inside the column to the required height. When the catalyst is spent, the column is shut down and the packing is manually removed and replaced with packing containing fresh catalyst. Information on the #uid dynamics, mixing and mass transfer in such structures is available in the open literature (Bart & LandschuK tzer, 1996; Ellenberger & Krishna, 1999; DeGarmo, Parulekar and Pinjala, 1992; Higler, Krishna, Ellenberger & Taylor, 1999a; Moritz & Hasse, 1999). The important advantage of the structured catalyst sandwich structures over the catalyst bales is with respect to radial distribution of liquid. Within the catalyst sandwiches, the liquid follows a criss-crossing #ow path. The radial dispersion is about an order of magnitude higher than in conventional packed beds (Van Gulijk, 1998). R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5191 Fig. 13. Structured catalyst-sandwiches. (a) Catalyst sandwiched between two corrugated wire gauze sheets. (b) The wire gauze sheets are joined together and sewn on all four sides. (c) The sandwich elements arranged into a cubical collection. (d) The sandwich elements arranged in a round collection. 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 catalyst monolith tubes. Furthermore, frequent criss-crossing leads to a signi"- cant improvement in mass transfer within the sandwich structures (Higler et al., 1999a). Another alternative is to make the packing itself catalytically 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 are made catalytically active; see Fig. 14(a). The catalyst rings can be prepared by block polymerisation in the annular space. Their activity is quite high, however, osmotic swelling processes can cause breakage by producing large 5192 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 Fig. 15. Catalyst envelopes placed along the liquid #ow path. For photographs of this con"guration, along with CFD animations of the #ow visit the web site: http://ct-cr4.chem.uva.nl/kattray. mechanical stresses inside the resin. An alternative con- "guration is the glass-supported precipitated polymer prepared by precipitation of styrene-divinylbenzene copolymer, which is subsequently activated by chlorsulphonic acid. Another possibility is to coat structured packing with zeolite catalysts (Oudshoorn, 1999); see Fig. 14(b). This concept has not been put into practice for the following reasons (Towler & Frey, 2000): 1. The amount of catalyst that can be loaded in a column in this manner is small compared to addition of catalyst pills or homogenous catalyst. 2. Coating or impregnation of catalyst materials on metal surfaces is expensive. 3. Production of catalyst materials in the shape of distillation packings is also expensive. 4. There is currently no generic manufacturing method that can economically produce di!erent catalyst materials as coatings or structured packings. The catalyst can also be `casta into a monolith form and used for counter-current vapor}liquid contacting, Lebens (1999) has developed a monolith construction consisting of #uted tubes; see Fig. 14(c). 1.5.2. Trays or downcomers to hold catalyst particles The catalyst envelopes can be placed in a trayed RD column and many con"gurations have been proposed. 1. Vertically disposed catalyst containing envelopes can be placed along the direction of the liquid #ow path across a tray (Jones, 1985); see Fig. 15. These envelopes are almost completely immersed in the froth on the tray, ensuring good contact between liquid and catalyst. Furthermore, since the vapor and liquid- phase pass along the packed catalyst in the envelopes, and not through them, the pressure drop is not excessive. 2. Catalyst envelopes can be placed within the downcomers (Carland, 1994); see Fig. 16(a). The primary drawback with installing the catalyst within downcomers is the limited volume available for catalyst inventory. Each `stagea can be regarded as a reaction device (downcomer) followed by a separation section (froth on the tray). 3. Catalyst envelopes can be placed near the exit of the downcomer (Asselineau, Mikitenko, Viltard & Zuliani, 1994); see Fig. 16(b). Catalyst inventory is necessarily limited. The vapor does not pass through the catalyst envelopes. 4. Trays and packed catalyst sections can also be used on alternate stages (Nocca, Leonard, Gaillard & Amigues, 1989, 1991; Quang, Amigues, Gaillard, Leo- nard & Nocca, 1989); see Fig. 16 (c). The vapor #ows through the packed section through a central chimney without contacting the catalyst. The liquid from the separation trays is distributed evenly into the packed reactive section below by a distribution device. 5. Other designs have been proposed for tray columns with 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 in a #uidised environment, but this can be taken care of by "ltration of the liquid and by make-up of the catalyst. In the tray con"gurations discussed above, the packed (or #uidised) catalyst containing envelopes are essentially vapor free. Furthermore, the vapor}liquid contacting e$ciency can be considered practically unimpaired by R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5193 Fig. 16. Counter-current vapor}liquid}catalyst contacting in trayed columns. (a) catalyst in envelopes inside downcomers, (b) tray contacting with catalyst placed in wire gauze envelopes near the liquid exit from the downcomers and (C) alternating packed layers of catalyst and trays. the presence of the catalyst envelopes. Therefore, standard tray design procedures (Lockett, 1986; Stichlmair & Fair, 1998) can be applied without major modi"cation. Care must be exercised, however, in making a proper estimation of the liquid}catalyst contact time, which determines the extent of reaction on the stages. 2. Thermodynamics of reactive distillation An introductory review of RD thermodynamics was provided by Frey and Stichlmair (1999a) (see, alternatively, Stichlmair & Fair, 1998). The classical thermodynamic problem of determining the equilibrium conditions of multiple phases in equilibrium with each other is addressed in standard texts (see, e.g., Walas, 1985; Sandler, 1999) and not considered here. The equally important, and computationally more di$- cult, problem of "nding the composition of a mixture in chemical equilibrium has also been well studied. Readers are referred to the text of Smith and Missen (1982). The combined problem of determining the equilibrium points in a multiphase mixture in the presence of equilibrium chemical reactions has been the subject of a recent literature review by Seider and Widagdo (1996). Two more recent developments are noted below. Perez-Cisneros, Gani & Michelsen (1997a) discuss an interesting approach to the phase and chemical equilibrium problem. Their method uses chemical &elements' rather than the actual components. The chemical elements are the molecule parts that remain invariant during the reaction. The actual molecules are formed from di!erent combinations of elements. A bene"t of this approach is that the chemical and physical equilibrium problem in the reactive mixture is identical to a strictly physical equilibrium model. McDonald and Floudas (1997) present an algorithm that is theoretically guaranteed to "nd the global equilibrium solution, and illustrate GLOPEQ, a computer code that implements their algorithm for cases where the liquid-phase can be described by a Gibbs excess energy model. The e!ect that equilibrium chemical reactions have on two-phase systems has been considered at length by Doherty and coworkers (Barbosa & Doherty, 1987a, b, 1988a}d, 1990; Doherty, 1990; Ung & Doherty, 1995a}e). The "rst paper by Barbosa and Doherty (1987a) considers the in#uence of a single reversible chemical reaction on vapor}liquid equilibria. The second paper (Barbosa & Doherty, 1987b) introduces a set of transformed composition variables that are particularly useful in the construction of thermodynamic diagrams for reacting mixtures. For a system in which the components take part in either of the following reactions A#B &C, (1) A#B &C#D (2) the following transformation is de"ned: Z G Q z G /v G !z I /v I v I !v 2 z I . (3) 5194 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 z G is the mole fraction of species i in either the vapor or liquid-phase as appropriate and the subscript k refers to the index of the reference component (one whose stoichiometric coe$cient is non-zero). In terms of the transformed composition variables the material balance equations that describe a simple open evaporation in a reacting mixture are given by dX G dt "X G !> G , (4) where X G is the transformed composition of species i in the liquid-phase and > G is the transformed composition for the vapor phase. t is a dimensionless time. Numerical solution of these equations yields the residue curves for the system. Barbosa and Doherty (1987a) consider two di!erent de"nitions of an azeotrope and adopt the de"nition given by Rowlinson (1969): À system is azeotropic when it can be distilled (or condensed) without change of compositiona. The conditions for the existence of a reactive azeotrope (and all other stationary points in the reactive mixture) are most easily expressed in terms of the transformed composition variables: X G "> G . (5) It is interesting to observe that reactive azeotropes can occur even for ideal mixtures (Barbosa & Doherty, 1987a, 1988a). Further, non-reactive azeotropes can disappear when chemical reactions occur. A reactive azeotrope has been found for the system isopropanol} isopropyl acetate}water}acetic acid (Song, Huss, Doherty & Malone, 1997). The in#uence the reaction equilibrium constant has on the existence and location of reactive azeotropes was investigated for single reaction systems by Okasinski and Doherty (1997a,b). Barbosa and Doherty (1988a) provide a method for the construction of phase diagrams for reactive mixtures. Doherty (1990) develops the topological constraints for such diagrams. Ung & Doherty (1995a}e) have extended the methods of Barbosa and Doherty to deal with mixtures with arbitrary numbers of components and reactions. The in#uence of homogeneous reaction kinetics on chemical phase equilibria and reactive azeotropy was discussed by Venimadhavan, Buzad, Doherty and Malone (1994) and Rev (1994). The residue curves are obtained from dx G dt " < ; (x G !y G )# P H r H (v GH !x G A I v IH ), (6) where < is the molar #ow rate in the vapor and ; is the molar liquid hold-up. These equations are more conveniently expressed in terms of actual mole fractions, rather than the transformed composition variables de"ned above. It will be apparent that the heating policy greatly in#uences the rate of vapor removal and the value of the equilibrium and reaction rate constants and, through this, the trajectories of the residue curves. Although it is not obvious from Eq. (6), it is the Damkohler number that emerges as the important parameter in the location of the residue curves for such systems. The Damkohler number is de"ned by Da" ;k < , (7) where k is a pseudo-"rst-order reaction rate constant. The Damkohler number is a measure for the rate of reaction relative to the rate of product removal. Low Damkohler numbers are indicative of systems that are controlled by the phase equilibrium; a high Da indicates a system that is approaching chemical equilibrium (see Towler & Frey, 2000). Venimadhavan, Malone & Doherty (1999a) employed a bifurcation analysis to investigate in a systematic way the feasibility of RD for systems with multiple chemical reactions. Feasible separations are classi"ed as a function of the Damkohler number. For the MTBE system they show that there is a critical value of the Damkohler number that leads to the disappearance of a distillation boundary. For the synthesis of isopropyl acetate there exists a critical value of the Damkohler number for the occurrence of a reactive azeotrope. Frey and Stichlmair (1999b) describe a graphical method for the determination of reactive azeotropes in systems that do not reach equilibrium. Lee, Hauan & Westerberg (2000e) discussed circumventing reactive azeotropes. Rev (1994) looks at the general patterns of the trajectories of residue curves of equilibrium distillation with nonequilibrium reversible reaction in the liquid-phase. Rev shows that there can be a continuous line of stationary points belonging to di!erent ratios of the evaporation rate and reaction rate. Points on this line are called kinetic azeotropes. A reactive azeotrope exists when this line intersects with the surface determining chemical equilibrium. Thiel, Sundmacher & Ho!mann (1997a,b) compute the residue curves for the heterogeneously catalysed RD of MTBE, TAME and ETBE and "nd them to have signi"cantly di!erent shapes to the homogeneously catalysed residue curves (Venimadhavan et al., 1994). They also note the importance of the Damkohler number and the operating pressure. These parameters in#uence the existence and location of "xed points in the residue curve map as seen in Fig. 17 adapted from Thiel et al. (1997a). An analysis was carried out to forecast the number of stable nodes as a function of Damkohler number and pressure. Residue curve maps and heterogeneous kinetics in methyl acetate synthesis were measured by Song, R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5195 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 kinetically controlled cases are qualitatively similar to the curves for the equilibrium case. Thus, the production of methyl acetate by RD can be carried out in either regime. Open evaporation accompanied by liquid-phase chemical 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 stage model for conventional (i.e. non-reactive) distillation has been 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 concerned with the extension of this standard model to distillation accompanied by chemical reaction(s). 3.1. The EQ stage model A schematic diagram of an equilibrium stage is shown in Fig. 18(a). Vapor from the stage below and liquid from the stage above are brought into contact on the stage together with any fresh or recycle feeds. The vapor and liquid streams leaving the stage are assumed to be in equilibrium with each other. A complete separation process is modelled as a sequence of s of these equilibrium stages (Fig. 18(b)). The equations that model equilibrium stages are known as the MESH equations, MESH being an acronym referring to the di!erent types of equation. The M equations are the material balance equations; the total material balance takes the form d; H dt "< H> #¸ H\ #F H !(1#r4 H )< H !(1#r* H )¸ H # P K A G v GK R KH c H . (8) ; H is the hold-up on stage j. With very few exceptions, ; H is considered to be the hold-up only of the liquid- phase. It is more important to include the hold-up of the vapor phase at higher pressures. The component material balance (neglecting the vapor hold-up) is d; H x GH dt "< H> y GH> #¸ H\ x GH\ #F H z GH !(1#r4 H )< H y GH !(1#r* H )¸ H x GH # P K v GK R KH c H . (9) In the material balance equations given above r H is the ratio of sidestream #ow to interstage #ow: r4 H "S4 H /< H , r* H "S* H /¸ H , (10) v GK represents the stoichiometric coe$cient of component i in reaction m and c H represents the reaction volume. The E equations are the phase equilibrium relations y GH "K GH x GH . (11) 5196 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 Fig. 18. (a) The equilibrium stage. (b) Multi-stage distillation column. Chemical reaction equilibrium is not considered in many of the early papers because it is more di$cult to model. There are, however, some exceptions to this statement and such works are noted below. The S equations are the summation equations A G x GH "1, A G y GH "1. (12) The enthalpy balance is given by d; H H H dt "< H> H4 H> #¸ H\ H* H\ #F H H$ H !(1#r4 H )< H H4 H !(1#r* H )¸ H H* H !Q H . (13) The superscripted H's are the enthalpies of the appropriate phase. The enthalpy in the time derivative on the left-hand side represents the total enthalpy of the stage but, for the reasons given above, this will normally be the liquid-phase enthalpy. Some authors include an additional term in the energy balance for the heat of reaction. However, if the enthalpies are referred to their elemental state then the heat of reaction is accounted for automatically and no separate term is needed. Under steady-state conditions all of the time derivatives in the above equations are equal to zero. Some authors include additional equations in their (mostly unsteady-state) models. For example, pressure drop, controller equations and so on. 3.2. Steady-state algorithms and applications Much of the early literature on RD modelling is concerned primarily with the development of methods for solving the steady-state EQ stage model. For the most part such methods are more or less straightforward extensions of methods that had been developed for solving conventional distillation problems. The number of examples that illustrate most of the early papers usually is rather limited, both in number as well as in the type of RD process considered (most often it is an esteri"cation reaction). Only rarely is there any attempt to compare the results of simulations to experimental data (some exceptions are noted below). More and more of the more recent modelling studies are carried out using one or other commercial simulation package: Aspen Plus, Pro/II, HYSYS, and SpeedUp are the packages mentioned most often in the papers discussed in what follows. Tray-to-tray calculations were carried out by hand by Berman et al. (1948a); Marek (1954), and Belck (1955). Marek also presents an elaborate graphical method related to the McCabe}Thiele method for conventional binary distillation. Berman et al. (1948a) considered the production of dibutyl phthalate, extensive data for which system had been reported by Berman et al. (1948b). We may identify several classes of computer-based methods that have been developed for solving the EQ stage model equations; these methods are discussed brie#y in what follows. Readers are referred to the review R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5197 of Seader (1985) for background and original literature citations. Brief reviews of early RD algorithms are by Holland (1981) and by Hunek, Foldes and Sawinsky (1979). Short-cut methods involve a number of simplifying assumptions that are made in order to derive simple approximate equations that can be used for rapid computations. It is quite di$cult to derive generic short-cut procedures for RD because of the many ways in which chemical reactions in#uence the process (see, however, Ciric & Spencer, 1995). Bock and Wozny (1997) show that the assumption of chemical equilibrium, often made in developing short cut methods, is inappropriate for many RD processes. Tearing methods involve dividing the model equations into groups to be solved separately. A brief description of computer based tray-to-tray calculations for the RD of ethylene oxide and water was given by Corrigan and Miller (1968). Tray-to-tray calculations and parametric studies for the simulation and optimisation of an RD column for trioxane synthesis are described by Hu, Zhou & Yuan (1999). The bubble-point method of Wang and Henke (1966) was extended by Suzuki, Yagi, Komatsu and Hirata (1971) to be able to deal with chemical reactions. Suzuki's method was used by Babcock and Clump (1978). The so-called 0 method developed for conventional distillation columns by Holland and his many collaborators (see, Holland, 1963, 1981) was extended to RD operations by Komatsu and Holland (1977) and named the multi-0}n method. The method is applied to the esteri"cation of acetic acid. Other papers from this group are Izarraz, Bentzen, Anthony and Holland (1980) and Mommessin, Bentzen, Anthony and Holland (1980). Mommessin and Holland (1983) discuss the computational problems associated with multiple columns. Sav- kovic-Stevanovic, Mis\ic-Vukovic, Boncic-Caricic, Tris\ovic and Jezdic (1992) used the 0 method to model an esteri"- cation of acetic acid and ethanol carried out in a glass column that was 33 mm in diameter and 1000 mm tall. The calculated temperature pro"le and product compositions are in good agreement with the measured quantities. Solving all of the independent equations simultaneously using Newton's method (or a variant thereof) nowadays is an approach used very widely by authors of many of the more recent papers in this "eld (see, for example, Pilavachi, Schenk, Perez-Cisneros and Gani, 1997; Lee & Dudukovic, 1998). Holland (1981) provides a cursory description of this approach to RD simulation. More details and illustrative examples are to be found in the works of Block (1977); Block and Hegner (1977); Kaibel, Mayer and Seid (1979) and Simandl and Svrcek (1991). Relaxation methods involve writing the MESH equations in unsteady-state form and integrating numerically until the steady-state solution has been found (Komatsu, 1977; Jelinek & Hlavacek, 1976). Komatsu compares his EQ stage model calculations to his own experimental data for one experiment showing that the EQ model composition pro"les are qualitatively correct. The authors from Prague provide three numerical examples involving esteri"cation processes. Relaxation methods are not often used because they are considered to be too demanding of computer time. They are, of course, closely related to dynamic models. Bogacki, Alejski & Szymanowski (1989) used the Adams}Moulton numerical integration method to integrate a simpli"ed dynamic model that neglects the enthalpy balance to a steady-state solution. Numerical results for a single example are compared to numerical results obtained by Komatsu (1977). There also exists a class of algorithm that really is a combination of equation tearing and simultaneous solution in that Newton's method is used to solve a subset of the MESH equations, but in which other methods are used to solve the remaining equations. Papers by Nelson (1971), Kinoshita, Hashimoto and Takamatsu (1983), and by Tierney and Riquelme (1982) fall into this category. Very few RD examples accompany these papers. Takamatsu, Hashimoto and Kinoshita (1984) and Kinoshita (1985) used a similar approach to model columns for an unusual application: heavy water enrichment using hydrophobic catalysts. Isla and Irazoqui (1996) use Newton's method to solve the equations that model what they refer to as a `partial equilibriuma stage. However, despite the new name, theirs is essentially the same EQ model employed by almost everyone else in that the exiting streams are in phase equilibrium, but not in chemical equilibrium with each other. Parametric studies involving the e!ects of catalyst load and distribution, operating pressure and re#ux ratio are reported. Homotopy-continuation methods are employed most often for solving problems that are considered very di$- cult to solve with other methods (e.g. Newton's). For more details about this method, the reader is referred to Wayburn and Seader (1987). Homotopy-continuation was "rst applied to RD operations by Chang and Seader (1988). Their paper is illustrated by a number of case studies involving the esteri"cation of acetic acid and ethanol to ethyl acetate and water. Bondy (1991) describes physical continuation approaches to solving RD problems. Lee and Dudukovic (1998) have also used homotopy continuation to solve both EQ and NEQ models of RD operations. Continuation methods are also useful for studying parametric sensitivity (see, for example, Sneesby, TadeH and Smith, 1997c) and for locat- ing multiple steady-states (Pisarenko, Anokhina & Sera"mov, 1993). Alejski, Szymanowski and Bogacki (1988) used a minimisation method due to Powell (1965) to solve the MESHequations. This approach is, however, rather slow to converge. Numerical results for the esteri"cation of 5198 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 Fig. 19. Equilibrium stage model used by Davies et al. (1979). acetic acid with ethanol were compared with data from Komatsu (1977). Komatsu carried out experiments on the esteri"cation system of acetic acid and ethanol. The experiments were carried out in a column of 7 trays each with a single bubble cap. The trays had an inside diameter and spacing of 140 mm. Liquid-phase composition pro"les are provided for "ve experiments. There are also 3 sets of data for a #ash RD. Alejski et al. (1988), as well as Simandl and Svrcek (1991), show that the shape of the pro"les obtained by the EQ model is largely in agreement with the shape of the pro"les measured by Komatsu, although there are some signi"cant quantitative 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 #ow across a tray by a sequence of mixing cells, each of which is considered to be a non-equilibrium cell. Departures from equilibrium were handled through the calculation (in the usual way) of the point e$ciency. The model equations were solved using a relaxation method combined with Newton's method for computing the variables at each time step. A comparison between the numerical results of Alejski (1991a) obtained with an equilibriumcells-in-series model and the experimental data of Marek (1956) shows that the assumption of complete mixing on the tray is much less successful than the multi-cell model at predicting the actual composition pro"les. Marek (1956) had described a plant for the production of acetic anhydride. Experimental composition pro"les are provided for a single set of operating conditions. Alejski (1991b) investigated the steady-state properties of an RD column in which parallel reactions take place. It was assumed that reactions occur in the liquid-phase and the reactions are rate controlling. Each stage was assumed to be perfectly mixed, and the interstage #ows were equimolar. The vapor leaving any stage was in physical equilibrium with the liquid in this stage. Alejksi looked at the in#uence of reactants' volatilities, reaction equilibrium constants, reaction rates, re#ux ratio, location of feed inlets, number of theoretical stages and distillate rate upon the yield, selectivity and product distribution. As has been reported elsewhere, the column pressure is an important factor that strongly a!ects reaction rates by changing the column temperature pro"le. Venkataraman, Chan and Boston (1990) describe the inside-out algorithmknown as RADFRACthat is part of the commercial program Aspen Plus. Inside-out methods involve the introduction of new parameters into the model equations to be used as primary iteration variables. Four examples demonstrate that RADFRAC can be applied to a wide variety of reactive separation processes. RADFRAC is able to handle both equilibrium reactions as well as kinetically limited reactions. Simandl and Svrcek (1991) provide more details of their own implementation of an inside-out method for RD simulation. RADFRAC has been used by many other authors. Quitain, Itoh & Goto (1999a) modelled a small-scale column used to produce ETBE from bioethanol. Simula- tion results are compared to experimental data. A second paper (Quitain, Itoh & Goto, 1999b) used RADRAC to model 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 producing propylene oxide from propylene chlorohydrin and calcium hydroxide. The thermodynamic properties of this system are complicated by the presence of electrolytes in the liquid-phase and by salting out e!ects. Reaction kinetics were modelled using the expressions reported by Carra, Santacesaria, Morbidelli and Cavalli (1979b). By adjusting the Murphree e$ciency the authors were able to obtain the best possible agreement between the plant data and the simulations. Davies, Jenkins and Dilfanian (1979) describe a variation on the standard EQ stage model that is depicted in Fig. 19. The vapor/liquid contacting section is modelled as a conventional vapor}liquid equilibrium stage (without reaction). The outgoing liquid stream passes to a reactor where chemical equilibrium is established. The stream leaving this reactor passes on to the next equilibrium stage. The disadvantage of this approach is that it fails to properly account for the in#uence that chemical equilibrium has on vapor}liquid equilibrium (and vice versa). The model is used to predict the temperature and composition pro"les in a 76 mm diameter column in which formaldehyde is reacting with water and methanol. Good agreement between predicted and measured values R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5199 Fig. 20. (a) Con"guration of the MTBE synthesis column, following Jacobs and Krishna (1993). The column consists of 17 stages. (a) High- and low-conversion branches obtained by EQ and NEQ simulations. The bottoms #ow in these simulations was "xed at 203 mol/s. The details of the calculations are given in Baur et al. (1999). is claimed, but the "gures provided in their paper are small and hard to read. Barbosa and Doherty (1988d) point out that the EQ stage model equations (including those that account for simultaneous phase and chemical equilibrium) can be rewritten so that they are identical in form to the EQ model equations in the absence of chemical reactions. The actual #ows and compositions are replaced by the transformed #ows and compositions, the latter being de"ned by Eq. (3). The advantage of this approach is that existing algorithms and programs can be used to solve the equations. All that is required is to replace that part of the program that carries out the phase equilibrium calculations with a new procedure that computes the phase and chemical equilibrium computation and evaluates the transformed variables. 3.3. Multiple steady-states with the EQ model Multiple steady-states (MSS) in conventional distillation have been known from simulation and theoretical studies dating back to the 1970s and have been a topic of considerable interest in the distillation community. However, it is only recently that experimental veri"cation of their existence has been forthcoming. It is beyond the scope of this article to review this body of literature; readers are referred to GuK ttinger (1998) for citations of the original literature and discussions of the di!erent kinds of multiplicity that have been found. The "rst report of MSS in RD appeared in the Russian literature. Pisarenko, Epifanova and Sera"mov (1988a) found three steady-states for an RD column with just one product stream, two of which were stable. Timofeev, Solokhin and Kalerin (1988) provided a simple analysis of their RD column con"guration. Karpilovsky, Pisarenko and Sera"mov (1997) developed an analysis of single-product columns at in"nite re#ux. Pisarenko et al. (1993) used homotopy methods to locate MSS in RD with more conventional con"gurations. RADFRAC has been used by, among others, Jacobs and 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 in RD columns. For MTBE synthesis using the Jacobs} Krishna column con"guration, shown in Fig. 20(a), varying the location of the stage to which methanol is fed results in either a high or low conversion. When the methanol is fed to stages 10 or 11, steady-state multiplicity is observed (Baur, Higler, Taylor & Krishna, 1999). Explanation for the occurrence of MSS in the MTBE process was provided by Hauan et al. (1995, 1997). The ethylene glycol RD process also appears to be particularly 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 the so-called R/R analysis for RD columns. The two 5200 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 Fig. 21. (a) Multiple steady-states in TAME synthesis. Experimental data on low- and high-conversion steady-states. (b) Response of TAME column to 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 of Mohl 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 prediction of MSS in distillation. GuK ttinger and Morari (1997) extended prior work of Morari and co-workers that was restricted to conventional distillation operations to develop a uni"ed approach to the prediction of MSS in systems involving equilibrium chemical reactions. The method is applied to the MTBE process studied by others; they conclude that the MSS are easily avoided by selecting appropriate control strategies. The methodology is further re"ned and developed by GuK ttinger and Morari (1999a,b). The "rst of these two papers deals with what the authors call non-hybrid columns, in which the reaction is assumed to take place on every stage of the column. The second paper relaxes this restriction and considers MSS in columns with a reactive section, and non-reactive stripping and recti"cation sections. Gehrke and Marquardt (1997) developed a method based on singularity theory for elucidating the possible causes of MSS in a single equilibrium stage RD process. Their method requires no analytical solution of the equations and uses homotopy methods as well as interval computing techniques to identify the highest order singularity. Mohl et al. (1997) and Mohl, Kienle & Gilles (1998) implemented a dynamic EQ model (with Murphree-type e$ciencies) in the DIVA simulator and carried out a numerical bifurcation and stability analysis on the MTBE and TAME processes. They also show that the window of opportunity for MSS to actually occur in the MTBE process is quite small. For the TAME process MSS occur in the kinetic regime and vanish when chemical equilibrium prevails. The window of opportunity for MSS in the TAME process is larger than for the MTBE process. Experimental con"rmation of MSS in RD has been provided by Thiel et al. (1997) and Rapmund et al. (1998). Mohl et al. (1999) used a pilot-scale column used to produce MTBE and TAME. Multiple steady-states were found experimentally when the column was used to produce TAME, but not in the MTBE process. The measured steady-state temperature pro"les for the low and high steady-states for the TAME process are shown in Fig. 21(a). For a column operating at the low steady- state, a pulse injection of pure TAME for a short period results 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 RD in 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 which one component takes part in an association reaction in both phases. Euler's method was used to integrate the di!erential equations. A comparison with data for the acetic acid}benzene system shows good agreement with the model, but no actual data are provided. One of the "rst papers to discuss dynamic simulation of RD processes is the work of Roat et al. (1986). Their model integrates the control system equations with the column model equations. Using the Eastman methyl acetate process, they show that control schemes with good steady-state characteristics may fail under unsteady-state conditions. Ruiz, Basualdo and Scenna (1995) describe a software package called READYS (REActive Distillation dY- namic Simulator) for which an EQ stage model is used R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5201 which adopts the assumption of physical equilibrium, ideal mixing, thermal equilibrium with a chemical reaction con"ned to the liquid-phase. Column hydraulics is accounted for through a pressure drop equation and departures from equilibrium can be modelled using a Murphree-type e$ciency factor. Extensive numerical results are provided. The authors state that their program can be used to study unsteady and unstable column operations such as start-up, shutdown and abnormal hydraulic column behaviour. The package allows for a number of standard thermodynamic property packs as well as user-supplied models. Scenna, Ruiz and Benz (1998) employ READYS to study the start-up of RD columns. They show that the start-up policy can have a strong in#uence on the ultimate steady-state behaviour by 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 own somewhat di!erent approach to the EQ model. Their model uses chemical &elements' rather than the actual components. The chemical elements are the molecule parts that remain invariant during the reaction. The actual molecules are formed from di!erent combinations of elements. A bene"t of this approach is that the chemical and physical equilibrium problem in the reactive mixture is identical to a strictly physical equilibrium model. A comparison with the RD data of Suzuki et al. (1971) is provided and it is noted that these data are di$cult to match unless the `"tteda activity coe$cient model is used. Gani, Jepsen and Perez-Cisneros (1998) described a generalised reactive separation unit model. Theirs is an unsteady-state EQ stage model that can handle systems both with and without reactions and with more than two #uid phases. The methodology is quite unique in that it is based on the element approach of Perez-Cisneros et al. (1997b). Several numerical examples cover a range of simulation problems. Pilavachi et al. (1997) use the same approach, but their paper does not dwell on the computational methods; rather its focus is on some of the parameters that are important in RD modelling. For example, they discuss the e!ect of thermodynamic models and their parameters on RD simulation. Abufares and Douglas (1995) use an EQ stage model for steady-state and dynamic modelling of an RD column for production of MTBE. The steady-state model is RADFRAC from Aspen Plus. The unsteady-state model equations are solved using SpeedUp, a commercial dynamic process simulation program. The focus of this paper is the transient response of the system. Alejski and Duprat (1996) described a dynamic model for modelling kinetically controlled RD processes. The model is based on the conventional assumptions of negligible vapor-phase hold-up and perfect mixing of the two phases. Departures from phase equilibriumcould be handled by speci"cation of a vaporisation e$ciency, and corrections of the conversion due to imperfect mixing are accounted for using a `conversion e$ciencya, the latter being calculated from an eddy di!usion model in terms of the Peclet number. The model is compared to data obtained in a pilot-scale column for the esteri"cation of ethanol with acetic acid and sulphuric acid as homogeneous catalyst. Column start-up and disturbances of continuous operation were investigated. The dynamic temperature pro"les are in reasonable agreement with the data, but the predicted dynamic concentration pro- "les are very di!erent from the observed pro"les. Alejski and Duprat (1996) also recommend that tray hydraulics be accounted for in any dynamic model of RD. Schrans, de Wolf & Baur (1996) carried out dynamic simulations, using SPEEDUP, of the MTBE synthesis process using essentially the Jacobs}Krishna column con"guration shown in Fig. 20(a). Their simulations showed that increase in the iso-butene feed by 4% leads to oscillatory behaviour. A further increase of iso-butene feed by 5% causes a jump from the high-conversion steady-state to the lower one. Hauan, Schrans and Lien (1997) also showed oscillatory behaviour and suggested that it is due to an internal recycle of MTBE in the reactive zone. Sneesby, TadeH , Datta & Smith (1997a) model the synthesis of ETBE using an EQ stage model that they solve with SpeedUp. Simulation results are compared to results obtained with the commercial simulation program Pro/II. Homotopy methods are used to investigate the e!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 companion paper Sneesby, TadeH , Datta and Smith (1997b) develop a dynamic model of the same process using SpeedUp. Their dynamic model assumes that reaction equilibrium is attained on all stages, neglecting reaction kinetics. The authors recommend including control issues early in the design process. Subsequent papers from this group look at multiple steady-states in RD (Sneesby, TadeH & Smith, 1998c}e). Sneesby et al. (1998d) (as well as Bartlett and Wahnscha!t (1998) using RADFRAC) report that the transition from one steady-state to another can be prevented using appropriate control strategies. Sneesby et al. (1998a) show that an increase in fractionation (by increasing re#ux ratios, or numbers of equilibrium stages) does not always lead to improved performance of RD columns. This is exactly opposite to the situation in conventional distillation. Espinosa, Martinez and Perez (1994) presented a simpli"ed dynamic model for an RD column. Vapor hold- ups, heat losses to the environment and the heat of reaction were neglected. In addition, equimolar over#ow and physical and chemical equilibrium were assumed. The resulting equations were rewritten in terms of the 5202 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 transformed variables presented by Barbosa and Doherty (1987b). In order to save calculation time, the order of the model was reduced using an orthogonal collocation method. Some calculations were done for an ideal quaternary system. The reduced order model was veri"ed against a `rigorousa model and a reasonably good match was found. No extensive numerical dynamic data are presented. Grosser, Doherty and Malone (1987) use a dynamic model based on the following assumptions: E the mixture reaches reaction and phase equilibrium instantaneously on each tray; E the solutions are dilute (thus the temperature change can be ignored); E the liquid hold-up is constant on each tray (the vapor hold-up is ignored); E constant molar over#ow (modi"ed somewhat) relates the #ows from stage to stage. They study the separation by RD of close-boiling mixtures such as mixtures of xylenes, C4 hydrocarbons, and chlorobenzenes. They report that RD is an attractive alternative to conventional distillation when the relative volatility is less than 1.06. RD of close-boiling mixtures has also been studied by Terrill, Sylvestre and Doherty (1985) who suggest that it is possible to separate m- and p-xylene using sodium in a column with very few equilibrium stages. Cleary and Doherty (1985) provided experimental support for this conclusion. Kumar and Daoutidis (1999) presented a comprehensive dynamic EQ stage model of an ethylene glycol RD column. They compare a model that includes vapor- phase balances to a more conventional model that ignores the vapor hold-up and suggest that it is important to include the vapor phase in order to more accurately model the process dynamics. The major thrust of this work is the design of a control system that performs well with stability in the high-purity region. Moe, Hauan, Lien and Hertzberg (1995) discuss possible numerical problems when developing dynamic models of RD based on phase and chemical equilibrium principles. 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, Le Lann, Joulia and Koehret (1991); Machietto and 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) and Wajge and Reklaitis (1999), and Venimadhavan, Malone and Doherty (1999b). Corrigan and Ferris (1969) provided a limited quantity of data for the methanol acetic acid esteri"cation reaction in an Oldershaw column. The paper does not include any attempt at modelling the process. The models of Albet et al. (1991) and of Mujtaba and Machietto (1992) allow for changes in the component hold-ups but assume constant liquid molar hold-ups. These models also use steady-state energy balances. Reuter, Wozny and Jeromin (1989) develop the most complete EQ stage model of batch RD that includes the hold-up of both phases and process controller equations. A relaxation method is used to solve the unsteady- state model equations while Newton's method is used to solve the steady-state equations at each time step. A comparison with some dynamic product composition data for a transesteri"cation plant shows good agreement with the calculated product composition. Cuille and Reklaitis (1986) neglect the vapor-phase hold-up, assume that the volumetric hold-up on each stage is constant, and assume pressure drops and stage e$ciencies to be constant. The DAE system was solved using the LSODI numerical integration routine. Egly et al. (1979), Machietto and Mujtaba (1992), and Mujtaba and Machietto (1992) look at the optimal design and operation of batch RD. S+rensen and Skogestad (1992, 1994) and S+rensen et al. (1996) consider the controllability of batch RD. Bollyn and Wright (1998) develop a model of a batch RD process for the synthesis of the ethyl ester of pentenoic acid. In this process the reaction occurs only in the reboiler and not at all in the column itself. Thus, the model is somewhat simpler than other dynamic models that are discussed here. Xu and Dudukovic (1999) developed a dynamic model for semi-batch photo RD. The DAE equations that formed their model were solved using the LSODI routine. Wajge and Reklaitis (1999) describe in detail a package called RDBOPT for the design of operation policies for reactive batch distillation. The model is essentially the same as that used by Cuille and Reklaitis (1986), but the DAE system of model equations is solved using the DASPK solver. Venimadhavan et al. (1999b) examined a novel distillate policy and propose a new re#ux policy for equimolar reactions. For the special case of butyl acetate production the new policies lead to complete conversion of the reactants and high-purity products that are unobtainable by conventional methods. 3.6. Primarily experimental papers In addition to the papers cited above, there are some others whose main thrust is on providing experimental data, and in which the modelling activity provides only a supporting role. Carra et al. (1979b) and Carra, Morbidelli, Santacesaria & Buzzi (1979a) studied the synthesis of R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5203 propylene oxide from propylene chlorohydrins in an RD column. Reaction kinetics of this reaction were derived and presented in the "rst paper; A limited quantity of column data is reported in their second paper. Few details of the column design are given other than to say the column was a continuous multistage micropilot column. The authors used Newton's method to solve the equations that model the synthesis of propylene oxide from propylene chlorohydrins in an RD column. A good match was found between simulation results and top and bottom stream composition data obtained in the two experiments for which they provide data. However, it must be remembered that matching only top and bottom compositions is not a particularly good test of a complete column model. A much more demanding test is to be able to predict observed composition pro"les along the length of a column. Neumann and Sasson (1984) used the method of Suzuki et al. (1971) to model the production of methyl acetate by methanol esteri"cation in a small-scale column packed with an acidic organic acid polymer catalyst. A limited quantity of experimental data is included in the paper. Duprat and Gau (1991b) study the separation of close-boiling mixtures using RD. The process studied is the separation of 3-picoline and 4-picoline through complexation with tri#uroacetic acid. Newton's method was used to solve the EQ stage model equations. A companion paper (Duprat & Gau, 1991a) provides equilibrium data for this system. RD of close-boiling mixtures (m- and p-xylene) has also been studied by Saito, Michishita & Maeda (1971). Fuchigami (1990) reported top and bottom column temperature and composition data for 13 experiments for the methyl acetate process carried out in a laboratory- scale column. No attempt to model the column is provided. Flato and Ho!mann (1992) discuss the development and start-up of a small-scale packed distillation column for the production of MTBE. The manufacture of the Raschig ring-shaped packing elements is described in some detail, as is the control system installed around their column. Experimental results are provided for the mole percent of MTBE as a function of time, the iso- butene conversion and MTBE selectivity as a function of methanol/iso-butene ratio in the feed, and data showing the e!ect of pressure on iso-butene conversion. Krafczyk and Ghmeling (1994) used RADFRAC to model an experimental column with 2 m of KATAPAK- S with bubble cap trays above and below. The main goal of this study was to test the feasibility of heterogeneous RD for methyl acetate production. No data are provided that could be useful to other investigators. Bravo et al. (1993) provide some preliminary results obtained from a catalytic distillation pilot plant used to produce TAME. The pilot-scale column was 11 m in height and 15 cm in diameter. The catalyst was Amberlite XAD ion-exchange resin. Composition pro"les are provided for a few experimental runs. Some of the experiments show composition pro"les that appear almost #at, indicating little composition change from stage to stage. Pekkanen (1995a) refers to such regions as `reactive pinchesa. The experiments were simulated with the proprietary simulation program FLOWBAT, but comparisons with the data are provided for only one experiment. Insu$cient data are available for others to attempt a simulation using anything other than an EQ model. Bart and Reidetschlager (1995) used RADFRAC to model experiments involving the esteri"cation of succinic anhydride with methanol to produce dimethyl succinate and water in laboratory-scale column. When tray ef- "ciencies were speci"ed, the simulations could be made to agree with the experimental composition pro"les. Simulations are used to compare the performance of several di!erent plant designs. They suggest that a standard RD column is preferable to a reactor/column for fast reactions and high relative volatilities. Acetalisation of formaldehyde with methanol in batch and continuous RD columns was studied by Kolah, Mahajani & Sharma (1996). Their paper provides more data than usually is the case in experimental papers. The column was modelled using the transformed composition approach of Ung & Doherty (1995), with the calculation of the minimum re#ux and of the number of stages. Gonzalez and Fair (1997) present data for the production of tert-amyl-alcohol from water and iso-amylenes. Their paper provides an unusually comprehensive description of the experimental work carried out. The RD column has an internal diameter of 5.1 cm and a total length of 2.25 m. The column was loaded with bales of catalytic packing similar to that shown in Fig. 12. In some of their experiments the column was loaded with 6 bales, in others just 2, the rest of the column being "lled with Sulzer BX gauze packing. An important conclusion from their experimental work is that over design of an RD column can lead to unacceptably low yields of the desired products, with correspondingly high yields of undesired products. Gonzalez, Subawalla and Fair (1997) used the RADFRACmodel in Aspen Plus to simulate the process. The simulation results were in reasonable agreement with the data. A parametric study showed the e!ect of varying the feed composition and other important operational parameters. Gaspillo, Abella and Goto (1999) studied experimentally the dehydrogenation of 2-propanol to acetone and hydrogen in a small-scale RD column. The separation of acetone from 2-propanol is strongly in#uenced by the feed #ow rate, the re#ux ratio, and the temperature of the heat source. The motivation for the study was to investigate the possibility of using the system in chemical heat pump. 5204 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 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) use a modi"ed EQ stage model in which the phase equilibrium equations incorporate a stage e$ciency factor. There are many di!erent de"nitions of the stage e$ciency; that of Murphree is most often used in EQ stage simulation: E+4 G " y G* !y G# yH G !y G# ; i"1,2, 2 , n, (14) where y G* is the average composition of the vapor leaving the tray, y G# is the composition of the vapor entering the tray and yH G is the composition of the vapor in equilibrium with the liquid leaving the tray. Since the mole fractions add to unity, only (n!1) of the Murphree component e$ciencies are independent. For distillation of systems with three or more species, the component e$ciencies are almost always unequal to one another and these can routinely assume values greater than unity or less than zero (Taylor & Krishna, 1993). Ilme, Keskinen, Markkanen & Aittamaa (1997) simulated an industrial MTBE (non-reactive) distillation column using an EQ stage model using a more rigorous multicomponent (matrix) e$ciency prediction method; this paper illustrates the complex nature of component e$ciencies. For packed columns it is common to use the height equivalent to a theoretical plate (HETP). The behaviour of HETPs in multicomponent mixtures is closely related to the behaviour of stage e$ciencies. To the best of our knowledge there are no fundamentally sound methods for estimating either e$ciencies or HETPs in RD operations. Davies et al. (1979) employed a conventional binary e$ciency prediction method in the absence of anything better. In general, the presence of chemical reactions will have an in#uence on the component e$ciencies. This is illustrated by calculations of the component e$ciencies for an RD column for hydration of ethylene oxide (EO) with water to mono-ethylene glycol (EG). In situ distillation is used to suppress the unwanted side reaction to diethylene glycol (DEG) produced from the reaction EO#EGPDEG. Using a rigorous non-equilibrium (NEQ) model (discussed below), the component e$ciencies were calculated for an RD column (using the con"guration described by Baur et al., 1999) and also for a column in which the reactions were deliberately suppressed. The component e$ciencies for EO, Water, EG and DEG, calculated from the NEQ model are shown in Fig. 22 with "lled symbols for the RD case and with open symbols for the non- reactive case. For the non-reactive column the component e$ciencies are close to one another and in the range 0.5}0.65. The smallest molecule, water, has the highest component e$ciency. The component e$ciencies of EO and EG lie in between those of water and DEG. For RD operation, the component e$ciencies show great variation between the di!erent components. Clearly, chemical reactions in#uence the values of the component e$ciencies in a complex and unpredictable way. This aspect has also been highlighted in the simulations presented by Higler, Taylor and Krishna (1998). For a more complete understanding of RD processes it is necessary to consider in detail the interaction between mass transfer and chemical reaction. We take up this subject next. 4. Mass transfer For the purposes of this discussion it su$ces to adopt a "lm model description of the transport processes in RD. Representative "lm pro"les for homogeneous systems are shown in Fig. 5(a), and for heterogeneous systems in Fig. 5(b). In homogeneous RD processes the reaction takes place only in the liquid-phase. If it is su$ciently rapid, the reaction will also take place in the liquid "lm adjacent to the phase interface. Very fast reactions may occur only in the "lm. A slow reaction also takes place in the "lm but its in#uence on the mass transfer process can safely be ignored. The most fundamentally sound way to model mass transfer in multicomponent systems is to use the Maxwell}Stefan theory (see Krishna & Wesselingh, 1997; Taylor & Krishna, 1993). The Maxwell}Stefan equations for mass transfer in the vapor and liquid-phases respectively are given by y G 1¹4 cj4 G cz " A I y G N4 I !y I N4 G c4 R n4 GI (15) and x G 1¹* cj* G cz " A I x G N* I !x I N* G c* R n* GI , (16) where x G and y G are the mole fractions of species i in the liquid and vapor phases, respectively. The n GI represents the corresponding Maxwell}Stefan di!usivity of the i!k pair in the appropriate phase. Only c!1 of Eqs. (15) and (16) are independent; the mole fraction of the last component is obtained by the summation equations for both phases. At the vapor}liquid interface we have the continuity equations -4 G ¦ ' "-* G ¦ ' . (17) For a homogeneous system, the molar #uxes in the liquid "lm may change due to any chemical reaction that takes place there cN G cz " P K v GK R K . (18) R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5205 Fig. 22. Component e$ciencies for EO, water, EG and DEG for reactive and non-reactive operation. The RD column con"guration is shown in Fig. 24(a). Unpublished results of Baur, Taylor and Krishna (2000). For most reactive distillations the change in the #uxes through the "lm will not be signi"cant because the Hatta numbers are smaller than unity (Sundmacher et al., 1994). The composition pro"le with the `di!usiona "lm will be nearly linear. For other reactive separation processes (e.g. reactive absorption) the composition change in the "lm will be very important. It will not always be clear in advance in which regime a particular process will be operating, and the regime may even vary from stage to stage. Thus, the most general approach is to solve the MS and continuity equations simultaneously for all cases involving homogeneous reactions. Eqs. (16) and (18) form a system of non-linear coupled di!erential equations that must be solved numerically in most cases. Frank, Kuipers, Versteeg and van Swaaij (1995b) and Frank, Kuipers, Krishna and van Swaaij (1995a) provide perhaps the most comprehensive study of simultaneous mass (and heat) transfer with chemical reaction modelled using the MS equations. They report that thermal e!ects can a!ect mass transfer rates by as much as a factor of 30! In view of their complexity, the MS equations sometimes are written in greatly simpli"ed form N G "!c R D G°'' cx G cz . (19) This expression ignores the coupling between the species gradients as well as mass transfer by convection. D G°'' is an e!ective di!usivity and it should be regarded as 5206 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 a function of the binary MS di!usion coe$cients, the mixture composition, and the mass transfer rates themselves. However, if, as is usually done, we assume the e!ective di!usivity to be constant, then analytical solutions to Eqs. (18) and (19) may be derived. Indeed, the literature on mass transfer with chemical reaction based on these two equations is vast and such equations often are used. Results usually are expressed in the form N* G "k G E G (x' G !x* G ), (20) where k G is the mass transfer coe$cient and E G is an enhancement factor that accounts for the in#uence of chemical reaction on the molar #uxes. Among other things, enhancement factors depend quite strongly on the reaction kinetics; thus, there is no universal expression for E G that can be used in all situations. Indeed, in many cases it is not even possible to obtain analytical expressions for the enhancement factor, even for the muchsimpli"ed constitutive relation given by Eq. (19). Danckwerts (1970) and Van Swaaij and Versteeg (1992) review the "eld of mass transfer with chemical reaction. Frank, Kuipers, Krishna and van Swaaij (1995a) cite other studies of non-isothermal mass transfer with simultaneous chemical reaction modelled using the simpler constitutive relation given by Eq. (19). E!ective di!usivity models of this sort have been used with some success in the modelling of amine-based gas treating processes (see, for example, Cornelisse, Beenackers, van Beckum & van Swaaij, 1980; Carey, Hermes & Rochelle, 1991; Altiqi, Sabri, Bouhamra & Alper, 1994 and the extensive lists of references in these papers). A more rigorous approach to modelling mass transfer in multicomponent systems is a!orded by the generalized Fick's law: J G "!c R A\ I D GI cx G cz , (21) where J G is the molar di!usion #ux of species i (N G "J G #x G N R ) and the D GI are the Fick di!usion coe$cients for the multicomponent mixture. The Fick di!usion coe$cients can be related to the binary MS di!usion coe$cients; see Taylor and Krishna (1993) for details of this. Solutions of Eq. (21) and the continuity equation (18) are known for a few cases involving simultaneous di!usion and reaction (see, for example, Toor, 1965; Kenig & Gorak, 1995, 1997). In most cases of practical signi"cance Eq. (21) is just as di$cult to solve as the full MS equations and it is necessary to employ numerical methods here as well. A rigorous approach to modelling heterogeneous systems (Fig. 5(b)) would involve a complete description of mass transport to the catalyst and di!usion and reaction inside the catalyst particles, if the catalyst is porous, or reaction at the surface if it is not. In either case it is unnecessary to allow for reaction in the vapor or liquid "lms as described above. For all cases involving a heterogeneous reaction we may model transport through the vapor}liquid interface using the MS equations given above (assuming no reaction in the liquid "lm). We also need to model di!usion of reactants to and products away from the solid catalyst surface using a separate set of di!usion equations. For those cases where the reaction takes place at the catalyst surface the boundary conditions at the liquid}solid interface will be determined by the reaction kinetics. However, if the reaction takes place inside a porous catalyst then we need to model di!usion and reaction inside the catalyst as well as transport from the bulk liquid to/from the catalyst surface. Modelling multicomponent mass transfer in porous media is complicated when the mean free path length of the molecules is of the order of magnitude of the pore diameter. The di$culties posed by this case may be circumvented by a method originally introduced by Maxwell (1866) and developed further by Mason and co-workers (see Mason & Malinauskas, 1983). Maxwell suggested that the porous material itself be described as a supplementary `dusta species, consisting of very large molecules that are kept motionless by some unspeci"ed external force. The Chapman}Enskog kinetic theory is then applied to the new pseudo-gas mixture, in which the interaction between the dust and gas molecules simulates the interaction between the solid matrix and the gas species. In addition, one is no longer faced with the problem of #ux and composition variations across a pore and problems related to catalyst geometry. The dusty #uid model as developed by Krishna and Wesselingh (1997) is a modi"cation of the dusty gas model so as to be able to model liquid-phase di!usion in porous media. For a non-ideal mixture we have: x G 1¹ cj G cz # x G 1¹ < G cp cz # x G n B D GC " A I x G N I !x I N G c R nC GI ! N G c R DC G , (22) where DC G is 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, depending on the geometry of the catalyst, the cross-sectional area can change along the di!usion path. It is necessary to take catalyst geometry into account in the solution of these equations. The dusty gas model is often used as the basis for the calculation of a catalyst e!ectiveness factor (Jackson, 1977). The extension to non-ideal #uids noted above has not been used as often, partly because of the greater R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5207 Fig. 23. The non-equilibrium stage (cell) for homogeneous liquid-phase reaction. uncertainty in the parameters that appear in the equations. Berg and Harris (1993) have developed a detailed model of di!usion and reaction in MTBE synthesis. However, their model focuses only on the transport and reaction issues and they have not developed 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 carried out an extensive study of mass transfer and activity in and around RD catalysts. Sundmacher and Ho!mann (1992) recommend the MS equations over Fick's law for modelling mass transfer in the liquid-phase surrounding an ion-exchange catalyst particle. The reaction is modelled by an activity-based Langmuir}Hinshelwood expression derived from an extensive experimental study by Reh"nger and Ho!mann (1990a,b). The model is used to determine the catalyst e!ectiveness factor, and the model is in good agreement with extensive experimental data. Sundmacher and Ho!mann (1994a) developed a detailed model to investigate the interaction between mass and energy transport and reaction in an ion-exchange resin. Catalyst e!ectiveness factors and selectivities computed from the model are in good agreement with experimental data for MTBE formation obtained in a CSTR. In other papers Sundmacher & Ho!mann (1994, 1995) use the Maxwell}Stefan equations as a basis for a "lms-in-series mass transfer model for a vapor}liquid-porous catalyst system. However, di!usion in the catalyst is described using an e!ective di!usivity model 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 component consumption term, corrected by the catalyst e$ciency. The reaction term is evaluated at bulk liquid conditions. Non-idealities in the liquid-phase were described with the UNIQUACequation. The SRKequation of state was used for the gas phase. Sundmacher and Ho!mann introduce àrti"cial inertia termsa into the interface mass balances in order to create a system of di!erential and algebraic equations (DAEs). The DAE system was solved with the LIMEX solver (Deu#hard, Hairer & Zugck, 1987). Important conclusions from their theoretical work are that the mass transfer resistance inside the catalyst can vary signi"cantly along the packing and that the main resistance to mass transfer is on the liquid side. 5. Non-equilibrium (NEQ) stage modelling The NEQ stage model for RD follows the philosophy of 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 the NEQ model for conventional distillation operations. A schematic representation of the NEQ stage is shown in Fig. 23. This NEQ stage may represent a tray or a crosssection of a packed column. The component molar balances for the vapor and liquid-phases are < H y GH !< H> y GH> !f 4 GH #-4 GH "0, (23) ¸ H x GH !¸ H\ x GH\ !f * GH !-* GH "0, (24) where - GH is the interfacial mass transfer rate and is the product of the molar #ux and the net interfacial area. The overall molar balances are obtained by summing Eqs. (23) and (24) over the total number (c) of components in the mixture. The - GH are obtained from the Max- well}Stefan (16) modi"ed as follows: x GH 1¹ H cj* GH cn " A I x GH -* IH !x IH -* GH c* RH («* GI a) H (25) with a similar relation for the vapor phase. The «* GI represents the mass transfer coe$cient of the i!k pair in the liquid-phase; this coe$cient is estimated from information on the corresponding Maxwell}Stefan di!usivity n* GI using the standard procedures discussed in Taylor and Krishna (1993). a is the interfacial area. Only c!1 of Eq. (25) are independent. The mole fraction of the last component is obtained by the summation equations for both phases. The enthalpy balances for both vapor and liquid-phases are < H H4 H !< H> H4 H> !F4 H H4$ H #$4 H #Q4 H "0, (26) ¸ H H* H !¸ H\ H* H\ !F* H H*$ H !$* H #Q* H "0. (27) 5208 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 The interphase energy transfer rates $ H (equal in both phases) have conductive and convective contributions $* H "!h* H a c¹* cn # A G -* GH H* GH (28) with a similar relation for the vapor phase. h* H is the heat transfer coe$cient in the liquid-phase. The conductive contributions are ignored in some modelling studies. This omission results in liquid-phases being (predicted to be) slightly superheated and vapor phases that are subcooled (Taylor et al., 1994). At the vapor}liquid interface we assume phase equilibrium y GH ¦ ' "K GH x GH ¦ ' , (29) where the subscript I denotes the equilibrium compositions and K GH is the vapor}liquid equilibrium ratio for component i on stage j. The K-values are evaluated at the temperature, pressure and composition of the interface from appropriate thermodynamic models (the same models used in conventional equilibrium stage models). In addition to Eqs. (23)}(29), we have the summation equations for the mole fractions in the vapor and liquid- phase and equations expressing the continuity of #uxes of mass and energy across the interface. Furthermore, in the NEQ model we take account of the pressure drop across a stage p H !p H\ !(Ap H\ )"0, (30) where p H and p H\ are the stage pressures and Ap H\ is the pressure drop per tray from stage (j!1) to stage j. The pressure drop over the stage is considered to be a function of the stage #ows, the physical properties and the hardware design. In the NEQ model, hardware design information must be speci"ed so that mass transfer coe$cients, interfacial areas, liquid hold-ups, etc. can be calculated. The NEQ model requires thermodynamic properties, not only for calculation of phase equilibrium but also for calculation of driving forces for mass transfer and, in RD, for taking into account the e!ect of non-ideal component behaviour in the calculation of reaction rates and chemical equilibriumconstants. In addition, physical properties such as surface tension, di!usion coe$cients, viscosities, etc. for calculation of mass (and heat) transfer coe$cients and interfacial areas are required. The steady-state model equations most often are solved using Newton's method or by homotopy-continuation. A review of early applications of NEQ models is available in Taylor & Krishna (1993, Chapter 14). 5.2. NEQ modelling of RD Building an NEQ model of a reactive separation process is not as straightforward as it is for the EQ stage model in which we simply (or not so simply) add a term to account for reaction to the liquid-phase material balances. For a reactive separation process, we "rst need to know whether the reaction is heterogeneous or homogeneous. For homogeneous systems the component molar balance for the liquid-phase becomes ¸ H x GH !¸ H\ x GH\ !f* GH !-* GH ! P K v GK R KH c H "0, (31) where R KH is the rate of reaction m on stage j. v GK represents the stoichiometric coe$cient of component i in reaction m and c H represents the reaction volume on stage j. For homogeneous reactions this is given by the total liquid hold-up on stage j and, in an NEQ model, is obtained directly from the column internals speci"cations and appropriate hydrodynamic correlations. If it is su$ciently rapid, the reaction will also take place in the liquid "lm adjacent to the phase interface, and very fast reactions may occur only in the "lm. In either case the continuity equations for the "lm are required for taking into account the e!ect of the reaction on the interphase mass transfer rates. The combined set of MS and continuity equations usually must be solved numerically. The phase equilibrium equations for the interface may need to be modi"ed for the in#uence of additional species on the thermodynamic properties at the interface. Amine-based gas treating again provides a case in point where reactions in the liquid-phase create additional species (including ions) that a!ect the interfacial equilibrium (Glasscock & Rochelle, 1989). For a heterogeneous reaction, there are two options for the description of the reaction term. The simplest approach is to treat the reaction pseudo-homogeneously, whereby catalyst di!usion and reaction is lumped into an overall reaction term. For heterogeneous reactions that are modelled in this way the liquid-phase material balance is as given above and c H is given by the total amount of catalyst present on the stage under consideration. In this case, one only needs to specify catalyst mass and activity. A more rigorous approach would involve the use of the dusty #uid model discussed above if the catalyst is porous, or reaction at the surface if not. In this case one also needs information about the catalyst geometry (surface area, mean pore diameter, etc). In either case it is unnecessary to allow for reaction in the vapor}liquid "lm and the vapor}liquid transport equations are exactly as given above. 5.3. NEQ models Sawistowski and Pilavakis (1979, 1988) modelled a packed RD column for the esteri"cation of methanol and acetic acid to methyl acetate. They used an e!ective R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5209 di!usivity method for their mass transfer model. Unless the equilibrium constant has some unconventional definition, the reaction equation given in their "rst paper represents an irreversible reaction. The system of di!erential equations that constitute their model was solved numerically. Their second paper includes parametric studies that show how conversion changes as a function of catalyst #ow rate, pressure, feed composition, re#ux ratio, reboil ratio, feed #ow rates, and feed position. In 1990 ASPEN Technology Inc. introduced the RATEFRAC model for rate-based multicomponent separation modelling (Sivasubramanian & Boston, 1990). RATEFRAC appears to be based on the NEQ model of Krishnamurthy and Taylor (1985) with the addition of equations to account for the e!ect of reaction on mass transfer, and chemical equilibriumconstraints (if needed). Zheng and Xu (1992b) have used an NEQ model to simulate catalytic distillation operations in a packed column with bag-type porous catalyst. Theirs is a pseudo- homogeneous model very similar to that described above. Vapor}liquid mass transfer is modelled using the MS equations. However, it is not completely clear how the reaction is modelled. Elsewhere in the paper it is stated that liquid}solid mass transfer coe$cients in the catalyst bed are computed from a correlation derived in their "rst paper (Zheng & Xu, 1992a). Yet no equations or terms for mass transfer from the liquid to the catalyst appear anywhere else in the paper. It is possible that the reaction is treated pseudo-homogeneously where e!ects of reaction on mass transfer (and the e!ects of mass transfer on reaction) in the catalyst are lumped into the bulk liquid reaction term. Thermodynamic properties for the liquid-phase are described with the UNIFAC model and the virial equation is used for the vapor phase. The resulting set of algebraic equations was solved using Newton's method. They model production of MTBE and provide numerically calculated concentration, temperature and #ux pro"les. Only for the temperature pro"le is there any comparison with experimental data. Zhu and Shen (1995) discussed the modi"cation of the NEQ model of Krishnamurthy and Taylor (1985) to handle RD. Few precise details are provided, however, and it is impossible to be sure how the presence of reaction(s) modi"es any of the NEQ model equations. Simulation results appear to show reasonable agreement with temperature and liquid composition pro"les measured for the esteri"cation of ethanol and acetic acid carried out in an Oldershaw column. Kreul, Gorak and Barton (1999a) used an NEQ model of 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 description of multicomponent mass transfer and the simpler e!ective di!usivity models. However, they also conclude that there can be signi"cant di!erences between EQ and NEQ models, and that the additional e!ort of the more complicated NEQ approach is justi"ed. Baur et al. (1999) have compared the EQ and the NEQ models for the MTBE process. They underlined some counter-intuitive features of RD processes. For example, for a methanol feed location yielding a low-conversion steady-state, the introduction of mass transfer resistance (i.e. use of the NEQ model), leads to a conversion higher than that predicted by the EQ model; see Fig. 20 (b). The introduction of a mass transfer resistance alleviates a `bad situationa and has the e!ect of improving conversion. Lee and Dudukovic (1998) described an NEQ model for homogeneous RD in tray columns. The Max- well}Stefan equations are used to describe interphase transport, with the AIChE correlations used for the binary (Maxwell}Stefan) mass transfer coe$cients. New- ton's method and homotopy continuation are used to solve the model equations. A close agreement between the predictions of EQ and NEQ models was found only when the tray e$ciency could be correctly predicted for the EQ model. In a subsequent paper Lee and Dudukovic (1999) extend the dynamic NEQ model of Kooijman and Taylor (1995) to cover the dynamic operation of RD in tray columns. The DAE equations were solved by use of an implicit Euler method combined with homotopy-continuation. Murphree e$ciencies calculated from the results of a simulation of the production of ethyl acetate were not constant with time. Kenig et al. (1999) described a software package for the synthesis and design of RD operations. The package is one of the results of a major research program on RD supported by the European Union under the BRITE- EURAM program. The designer part of the package is based on an NEQ model that accounts for possible reaction in the mass transfer "lm and includes a catalyst e$ciency calculation to account for di!usion and reaction in the catalyst. A large number of correlations for the mass transfer coe$cients in di!erent types of column internal are available in the program. Stage hydrodynamic models included in the package are: E completely mixed vapor and liquid; E completely mixed liquid, plug-#ow vapor; E mixed pool model for the liquid-phase; E eddy di!usion model for the liquid-phase. No mathematical details of the model are provided in the paper. The model equations are solved using Newton's method. The program is illustrated by modelling the MTBE process and a comparison with some experimental data (numerical values not given) shows excellent agreement with the calculated pro"les. Schenk, Gani, Bogle and Pistikopolous (1999) describe in considerable detail a hybrid-modelling environment in which distillation-type processes can be simulated using a combination of steady-state, dynamic, EQ stage, 5210 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 and/or rate-based models. Two of the three examples that illustrate their paper concern RD (ethyl acetate production and an MTBE column). The models are compared to experimental data of Suzuki et al. (1971). The agreement between the pro"les obtained with the rate-based model and the data is very encouraging. The authors do, however, demonstrate a sensitivity of the computed pro"les to the activity coe$cient model used. A particularly novel feature of their paper is the introduction of Gibbs energy pro"les in the column. In an interesting experimental study Sundmacher and Ho!mann (1995) obtained oscillatory behaviour of a packed laboratory-scale distillation column. The oscillations were encountered in the MTBE process as well as in the distillation of non-reactive binary mixtures. It appears likely that these oscillations originate from the hydrodynamics in their packed RD column. The authors use an NEQ model for non-reactive distillation that completely neglects mass transfer in the liquid-phase and, by extension, any e!ects due to reaction. The model equations were solved by a relaxation method, the results used to demonstrate multiple steady-states. The NEQ model does not provide an explanation for the observed oscillations. Sundmacher and Ho!mann (1996) presented a detailed NEQ stage model for vapor}liquid}porous catalyst systems. The model di!ers from that described above only in that the phases are assumed to be in thermal equilibrium with each other. This means that sensible heat transfer between phases is ignored and that the overall energy balance replaces the individual phase balances. Mass transfer in the vapor and liquid-phases is modelled using an explicit approximate solution of the Maxwell}Stefan equations (see Chapter 8 of Taylor and Krishna (1993) for details). The system of equations is solved via a pseudo-relaxation method using the DAE solver LIMEX cited earlier. The model is used to simulate some data obtained on a laboratory-scale MTBE column. One of the conclusions from this study is that it is absolutely necessary to account for di!usion and reaction in the porous catalyst (modelled in this paper using the catalyst e!ectiveness factor approach developed in other papers from these authors and discussed above). The in#uence of side reactions on RD processes has been 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$- ciency) and NEQ models to simulate the MTBE and TAME processes. The reactions were handled using both quasi-homogeneous and heterogeneous methods. Simu- lation results were compared to experimental data obtained in two laboratory-scale columns. A detailed NEQ model was needed to describe the TAME process, but both NEQ and the EQ stage (with an e$ciency of 0.8) model could adequately represent the MTBE process. In the latter case it was necessary to account for the catalyst e!ectiveness along the packing. The authors conclude that it is necessary to account for the side reactions in RD process design. Bart and LandschuK tzer (1996) studied the esteri"cation reaction of acetic acid and propanol to propyl acetate, catalysed by an exchange resin in a packed column. Mass transfer across the vapor}liquid interface and between liquid bulk and catalyst surface is described with the Maxwell}Stefan equations. The reaction is assumed to take place only at the catalyst surface and is modelled with an Eley}Rideal kinetic expression. Their model accounts for axial dispersion along the column, the dispersion coe$cient being obtained from a Bodenstein relation that was determined experimentally for their model column. Yu, Zhou and Tan (1997) developed a steady-state NEQ model that takes into account mass transfer from the bulk liquid to the catalyst. Separate rate equations are written for the vapor}liquid and liquid}solid interfaces. Empirical methods are used for estimating the liquid}solid (and other) phase mass transfer coe$cients. Di!usion within the catalyst phase is ignored. The system of non-linear equations is solved by a Newton homotopy method. The solitary numerical example that accompanies the paper concerns the reactive stripping process for the production of Bisphenol-A. Ng, Rempel and their co-workers at the University of Waterloo (Huang, Podrebarac, Ng & Rempel, 1998a; Huang, Yang, Ng & Rempel, 1998b; Podrebarac et al., 1998a,b) have carried out an in-depth study of the aldol condensation of acetone to diacetone alcohol (DAA) and mesityl oxide. Experiments were carried out in a pilot- scale column with 6 mm Intalox saddles and a reactive section containing bale-type packing. It was found that the DAA production rate was controlled by mass transfer. DAA selectivity was in#uenced by the liquid distribution. Correlations for the solid}liquid mass transfer coe$cients and for the overall mass transfer coe$cients for the vapor}liquid transport were developed by Huang et al. (1998a). Their papers also include the development of an NEQ model. The model appears to be derived from the Krishnamurthy}Taylor model for conventional distillation, although it is interesting to note that the material balances are expressed in terms of the mass #ows and mass fractions and include a separate term for the rate of vaporisation caused by the heat of reaction. Mass transfer between vapor and liquid-phases is described by a single overall mass transfer coe$cient for each species, a correlation for which was derived for their column. They assume that the rate of reaction is equal to the rate of mass transfer to the catalyst surface and correlations for the liquid}solid mass transfer coe$cients were also developed. Mass transfer in the non-reactive sections was modelled using a "lm model for each phase; mass transfer R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5211 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-phase molar #ow. (c) Non-equilibrium model calculations for the ethylene glycol process for a column of diameter 1.7 m showing the corresponding column pro"les. Details of the simulations are available in Baur, Higler, Taylor and Krishna (1999). coe$cients being estimated using the correlations of Onda, Takeuchi and Okumoto (1968). The model equations were solved simultaneously. A predicted temperature pro"le appears to be in good agreement with one determined experimentally. However, it must be remembered that the all important mass transfer coe$cients were "tted to data obtained in their own column. Thus, the true predictive abilities of their model are untested. It is reported that the amount of catalyst and the condensation rate are important design variables for this RD process, and that the DAA selectivity would have improved if the liquid}catalyst mass transfer improved. Podrebarac et al. (1998b) modelled the reactive section as a plug-#ow reactor with radial dispersion. The set of di!erential and algebraic equations was solved using the gPROMS system. The authors were able to "t their own experimental data quite well. However, the model could not be used for predictive purposes due, it was claimed, to the random nature of the #ow in a packed column. The recent study of Baur et al. (1999) comparing the EQ and NEQ models for hydration of ethylene oxide to ethylene glycol throws a new light on the phenomena on MSS and the importance of using the NEQ model. For the Ciric and Gu (1994) con"guration for the ethylene glycol column (see Fig. 24(a)), multiple steady-states are found with both EQ and NEQ models. Three steady- states SS-1 (high conversion), SS-2 (intermediate conversion) and SS-3 (low conversion) were found. The desired high-conversion steady-state solution (SS-1) corresponds to high column temperatures and lowest molar #ow rate of the vapor up the column. Let us now consider the NEQ model simulations for the 1.7 m diameter column con"guration. For this chosen column diameter, only one solution, SS-1, can be realised in the column. The other solutions SS-2 and SS-3 could not be realised in the NEQ 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 chosen to be 3 m, only the lowest conversion steady-state can be realised! 5.4. NEQ cell model An issue that is not adequately addressed by most NEQ models is that of vapor and liquid #ow patterns on distillation trays or maldistribution in packed columns. Since reaction rates and chemical equilibrium constants are dependent on the local concentrations and temperature, they may vary along the #ow path of liquid on a tray, or from side to side of a packed column. For such systems the residence time distribution could be very important, as well as a proper description of mass transfer. On distillation trays, vapor will rise in plug-#ow through a layer of froth. The froth will pass through the liquid more or less in plug-#ow, with some axial dispersion due to the vapor jets and bubbles. In packed sections, maldistribution of internal vapor and liquid #ows 5212 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 Fig. 25. The non-equilibrium cell model of Higler, Krishna and Taylor (1999a). over the cross-sectional area of the column can lead to loss of interfacial area. This is known to be one of the main reasons for inadequate performance of packed columns. To deal with this shortcoming of earlier models, Higler, Taylor and Krishna (1999c) and Higler, Krishna and Taylor (1999a,b) developed an NEQ cell model. The distinguishing feature of this model is that stages are divided into a number of contacting cells, as shown in Fig. 25. These cells describe just a small section of the tray or packing, and by choosing an appropriate connection pattern, one can very easily study the in#u- ence of #ow patterns and maldistribution on the distillation process. Flow patterns on distillation trays are modelled by choosing an appropriate number of cells in each #ow direction. A column of cells can model plug-#ow in the vapor phase, and multiple columns of cells can model plug-#ow in the liquid-phase as depicted in Fig. 26. Backmixing may also be taken into account by using an appropriate number of cells. This may be derived from calculating an equivalent number of cells from eddy di!usion models. Flow patterns in packed columns are evaluated by means of a natural #ow model. The #ows are split up according to the ratio of the cell surface areas between the cells. Various #ow patterns may be approximated 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 for heterogeneous systems described above. The bulk of both vapor and liquid-phases is assumed to be completely mixed. Mass transfer resistances are located in "lms near the vapor/liquid and liquid/solid interfaces, and the Max- well}Stefan equations are used for calculation of the mass transfer rates through each "lm. Thermodynamic equilibrium is assumed only at the vapor}liquid interface. Mass transfer inside the porous catalyst may be described with the dusty #uid model described above. The unit cell for homogeneous systems (and for heterogeneous systems modelled as though they were homogeneous) is as depicted in Fig. 23. The equations for each cell are essentially as given above. For RD, the staging in the liquid-phase could have a signi"cant in#uence on the reaction selectivity. This is emphasised in the study by Baur et al. (1999) of the in#uence of hardware design on the formation of the by-product DEG in the hydration column (sieve tray) shown in Fig. 24(a). Their simulation results are presented in Fig. 28. For "ve mixing cells in both vapor and liquid-phases (which corresponds closely to plug-#ow conditions for either phase), the formation of by-product DEG is reduced while the conversion to EG is increased. Removing the mass transfer resistances, i.e. assuming the EQ model, gives the best performance with respect to conversion and selectivity; see the point towards the bottom right of Fig. 28. Reaction selectivity can be in- #uenced by tray hardware design. Decreasing the weir height from 80 mm (base case) to 50 mm decreases formation of EG and increases by-product DEG formation. This reduction is due to a lowering in the interfacial area with decreasing weir height. Increasing the weir height from 80 to 100 mm leads to improved conversion and improved selectivity. High weir heights, and operation in the froth regime, are generally to be preferred in RD operations. Increasing the number of passes from 1 to 2 increases by-product formation; see the top point in Fig. 28. This is because the liquid load per weir length is reduced by 50%. This reduction in the liquid load leads to a reduction in the clear liquid height and lowering in the total interfacial area, which has a detrimental in#u- ence on both the conversion and selectivity. It appears that the usual design rules for conventional distillation column design cannot be carried over to RD columns because, for a column of 1.7 m diameter the conventional design philosophy would be to use two passes for the liquid #ow. 5.5. Pseudo-homogeneous vs. heterogeneous NEQ modelling Higler, Krishna and Taylor (2000) used the dusty #uid equations to model di!usion and reaction in porous catalysts in RD. The MTBE process (following the con"guration of Jacobs and Krishna (1993) shown in R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5213 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 catalysed reaction. Fig. 20(a)) was simulated under three di!erent sets of assumptions: A A pseudo-homogeneous approach, in which the catalyst is neglected and the reaction rate is evaluated at liquid bulk conditions. B A case in which the Knudsen di!usion coe$cient is large, in which case the mass transfer interaction with the catalyst is ignored C A case one in which the Knudsen di!usion coe$cient is a factor "ve times smaller than the smallest of the Maxwell}Stefan di!usion coe$cients. The value of the Knudsen di!usion coe$cient is assumed to be the same for all components. Shown in Fig. 29 is the steady-state conversion of iso- butene as a function of the bottom product #owrate. The multiple steady-state region has disappeared for the dusty #uid model, and the Knudsen di!usion term has a substantial in#uence on the results of the dusty #uid model simulations. This may be explained by the fact that, in the lower branch of the multiple steady-state region, MTBE is consumed in part of the column. The rate of consumption of MTBEis very much in#uenced by additional mass transfer resistances. Additional mass transfer resistances, therefore result in a higher conversion. This is not the case for the TAME process where the reaction rate is very much lower than it is for MTBE and mass transfer in#uences are not signi"cant. Multiple steady-states have been found experimentally for an RD column used to produce TAME, but not in the MTBE process (Rapmund et al., 1998), appearing to con"rm the results shown in Fig. 29. 5.6. Dynamic NEQ models Kreul, Gorak, Dittrich and Barton (1998) described an NEQ model for RD in packed columns. Theirs is a dynamic model that, as is usual in such models, neglects the hold-up in the vapor-phase. Their paper addresses the problems of modelling mass transfer and reaction in a vapor}liquid}porous catalyst system. In addition, they 5214 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 Fig. 29. Comparison of the results for conversion of iso-butene obtained by three di!erent model formulations for taking account of chemical reactions: (A) pseudo-homogeneous, (B) dusty #uid model without 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 ethylene glycol (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, Taylor and Krishna (1999). describe a two-phase model in which di!usion and reaction to and within the solid catalyst is not accounted for by additional equations (and parameters), but their effects are lumped into a kinetic term that appears in the liquid-phase material balances. The choice of which of these two approaches was adopted for their simulations is not completely clear. The material balances (partial di!erential equations) are discretised in the spatial dimension (the column height) using the method of lines. The model equations were solved using the equationbased modelling environment ABACUS (Allgor, Berrera, Barton & Evans, 1996). The paper by Kreul et al. includes a limited comparison with some unsteady-state data for a methyl acetate column. The results shown in the paper suggest that their dynamic model is well able to describe the product composition transients. The actual experimental data are not provided in the paper. Kreul, Gorak and Barton (1999b) described an NEQ model to study batch distillation. In essence, the model is an extension and generalisation of the dynamic NEQ models of Kooijman and Taylor (1995) for tray columns and Pelkonen, Gorak, Kooijman and Taylor (1997) for packed columns. The MS equations were used to model vapor and liquid-phase mass transfer. The model system was implemented and solved using the ABACUS system. The paper includes extensive comparisons of true model predictions of experiments performed in a pilot plant column involving the system methanol}acetic acid} methyl acetate}water. Under the conditions in the experiments there was essentially no liquid-phase chemical reaction; vapor-phase dimerisation was, however, taken into account. The agreement between the predicted and measured compositions is exceptionally good. Strictly speaking, reactive absorption falls outside the scope of this review. However, NEQ models as outlined above apply more or less unchanged in principle to reactive absorption and RD alike. The only di!erences between the models are the inclusion of di!erent submodels for the reaction kinetics and thermodynamic properties. A nitric acid recovery plant modelled by Wiesner, Wittig and Gorak (1996) and by Kenig and Gorak (1997) involves nine di!erent reactions and simultaneous transport and reaction of 10 di!erent species. Schneider, Kenig and Gorak (1999) used the Max- well}Stefan approach to model the dynamics of reactive absorption processes. Of particular interest in their model is the inclusion of the gradient of the electrical potential in the Maxwell}Stefan equations and the electro-neutrality equation that must be satis"ed at all points in the liquid due to the presence of ions in the processes they model. Rascol, Meyer, Le Lann and R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5215 Prevost (1998) brie#y addressed some numerical problems that can be encountered in the simulation of reactive absorption using NEQ models. We have already noted the success (using e!ective di!usivities and enhancement factor approaches to mass transfer with reaction) of NEQ models of amine-based gas treating processes (Carey et al., 1991; Altiqi et al., 1994). 6. Reactive distillation design Design and simulation of RD operations are very di!erent types of calculation, calling for very di!erent approaches. Most conceptual design models are based on the EQ stage model described above. However, as discussed below, some recent developments have opened up the possibility of using NEQ models for RD design, and a limited number of papers suggest that NEQ models already have a place in industrial RD design practice. 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: E the column is adiabatic; E the molar heat of vaporisation is constant; E the heat of mixing is negligible; E sensible heat e!ects can be ignored; E the heat of reaction is negligible compared to the enthalpy of the vapor; E the feed is a saturated liquid; E phase equilibrium is achieved on each stage; E the column operates with a partial condenser. These assumptions ensure that the vapor and liquid #ows inside the column are constant, thereby permitting the energy balances to be solved essentially independent of the remaining stage equations. The "xed-point method uses material balance equations written around a stage in each section of the column (above and below the feed stage) and the corresponding end of the column. With reference to Fig. 18(a), for example, we have, for the rectifying section X GH " rH H #1 rH H > GH ! 1 rH H > G" (32) and for the stripping section the material balance reads X GH> " sH H sH H #1 > GH ! 1 sH H #1 X G . (33) Note that these equations have been written in terms of the transformed composition variables de"ned by Eq. (3). The transformed re#ux and stripping ratios are de"ned as follows: rH H " ¸ H (v I !v 2 x IH ) D(v I !v 2 y I" ) , sH H " <(v I !v 2 y IH ) B(v I !v 2 x I ) . (34) Barbosa and Doherty convert these equations to di!erential form. To determine a feasible design the equations are integrated numerically starting with the desired product composition. They illustrate their design procedure for a quaternary system shown in Fig. 30(a). If the trajectories intersect, as shown in Fig. 30(b), then the resulting column is feasible, if the trajectories fail to intersect, then no column will produce the desired products (Fig. 30(c)). The minimum re#ux can be found from the special case of two trajectories that just touch each other (Fig. 30(d)). A number of extensions of the approach of Barbosa and Doherty (1988c) have appeared in the literature. Barbosa and Doherty (1988d) extend their own methodology to double-feed columns. Buzad and Doherty (1994, 1995) and Doherty and Buzad (1994) provide a further extension in order to handle kinetically controlled reactions in three-component systems. Ung and Doherty (1995e) consider RD processes involving multiple reactions. Okasinski and Doherty (1998) relax some of the assumptions underlying the methods of Barbosa, Buzad, and Doherty. They develop a systematic method for the design of kinetically controlled staged RD columns while taking into account a single liquid-phase reaction, heat e!ects, non-ideal phase equilibrium, and a range of liquid-phase hold-ups on the di!erent stages. The Damkohler number de"ned for the entire column is a key parameter in their approach. Melles, Grievink and Schrans (2000) also relaxed the uniform hold-up assumption by allowing di!erent hold-ups per section of the column (not on each tray), taking into account heat e!ects, and non-zero stoichiometric sum reactions. The design of RD columns in which the feed stream contains species that do not react at all was addressed by Espinosa, Aguirre and Perez (1995a,b). Most of the methods cited above are based on an assumption that the reaction takes place on all stages in the column. Espinosa, Aguirre and Perez (1996) described a method of dealing with columns in which the reaction takes place only in a central portion of the column. The latter issue was revisited by Espinosa, Aguirre, Frey and Stichlmair (1999) who proposed a design method for a column with a reactive section, a stripping section, and two rectifying sections. Mahajani and Kolah (1996) extended the methods of Doherty and co-workers for packed RD columns. An assumption in their method is that liquid-phase backmixing is totally absent. It is pertinent to note that the overall methodology and some important results (e.g. minimum re#ux) are unchanged from the methods for tray columns. Mahajani (1999b) also addresses the design of RD processes for multicomponent kinetically controlled reactive systems. 5216 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 Fig. 30. Column pro"les in RD design (Doherty method). The attainable region approach to reactor network feasibility is based on geometric properties and has been studied in depth mainly by Glasser, Hildebrandt, and their co-workers (see, for example, Glasser & Hildeb- randt, 1997; Feinberg & Hildebrandt, 1997; Feinberg, 1999). McGregor, Glasser & Hildebrandt (1997) and Nisoli, Malone and Doherty (1997) apply the attainable region approach in order to develop a systematic approach to identifying the feasible compositions that can be obtained in RD processes. Once again, the Damkohler number 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-based method for the analysis and design of reactive separation processes. Within this framework the change in the composition of any particular phase is given by the vector equation dx dt "mix#sep#rx (35) where x is the composition of the phase in question, and mix, sep, and rx are vectors that represent the composition changes due to mixing, separation, and reaction, respectively. For these vectors Hauan et al. (2000b) write mix"M(x F !x), (36) rx"R(!xv), (37) sep"[S](x!y), (38) where M is a scalar equal to the relative amounts of material being mixed, x is the current composition and x F is the feed composition, and R is a scalar that depends on such things as catalyst activity, hold-up, and temperature. [S] is matrix of component speci"c mass transfer rates. If the phases are assumed to be in equilibrium then [S] reduces to a simple scalar. The direction of these combined vectors indicates the feasibility of a particular process; their length is a measure of the process e$ciency. Hauan and Lien (1998) illustrated their methodology with an analysis of the MTBE process. More interestingly, this formulation admits the possibility, so far unexplored, of using a properly formulated model of mass transfer in multicomponent systems as discussed above. A "xed point exists when the mix, sep, and rx vectors nullify each other. 0"mix#sep#rx. (39) When the reaction and separation vectors have zero magnitude then the "xed point is an equilibrium point. A kinetic "xed point (azeotrope) arises when all three vectors have non-zero magnitudes, but still nullify each other. The location of these kinetic "xed points has a direct in#uence on the product compositions that can be realised in an RD column (see, also, Mahajani, 1999a). Hauan et al. (2000b) have provided a comprehensive analysis of the kinds of "xed point that can arise from cancellation of di!erent combinations of these vectors. They also introduce the reaction di!erence point as the R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5217 di!erence between an arbitrary composition and a singular point. The use of these di!erence points in RD process design 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-based modelling framework that is able to capture hybrid reactive/separation processes. In their approach an RD process (here meaning more than just a single RD column) is synthesised from a collection of modules that involve reaction, reaction and separation, or only separation. In this context a module does not necessarily represent a single model stage, but a collection of such stages. Either EQ or NEQ stage models could be used in this approach. Papalexandri and Pistikopolous (1996) illustrate their methodology with the design of an ethylene glycol column, while Ismail et al. (1999) considered the production of ethyl acetate from acetic acid and ethanol. Bessling, Schembecker and Simmrock (1997a,b) combine heuristic rules, numerical computation, and RD line diagrams to study the feasibility of RD processes. They devise a method for identifying RD processes in which the RD column needs to be divided into reactive and non-reactive sections. Bessling, Loning, Ohligschlager, Schembecker and Sundmacher (1998) use these RD line diagrams to identify the main process parameters and to provide a basis for an experimental study in the methyl acetate process. The signi"cant in#uence of the re#ux ratio on conversion is shown by simulation using an EQ stage model and by experiments in a small-scale column that 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 developed a method they call static analysis. It is the result of an extensive investigation of the thermodynamic and topological structure of distillation diagrams. The method requires very little fundamental data on the system and is based on an assumption that the vapor and liquid #ow rates in the column are very large. As a result of this assumption the composition change caused by the reaction is small on each stage and can be neglected. The desired product compositions, extent of reaction, and number of stages need not be "xed a priori. The most accessible work from this group is the paper by Giessler et al. (1998) who outline the steps of the method and illustrate it with a case study of the MTBE process. Giessler et 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#uence of inerts can also be considered with this approach. 6.2. Graphical design methods A graphical (Ponchon}Savarit type) design procedure for RD columns based on the transformed composition variables of Barbosa & Doherty (1988) is described by Espinosa, Scenna and Perez (1993). The MTBE process is used to illustrate their method. Lee, Hauan, Lien and Westerberg (2000a,b) and Lee et al. (2000d) have recently presented an in-depth analysis of the classical Ponchon-Savarit and McCabe}Thiele graphical methods for RD systems. 6.3. Design via optimisation methods RD design via optimisation methods has been the subject of a few studies. Ciric and Gu (1994) formulated a mixed integer nonlinear programming model, solution of which yields the optimal number of EQ stages, feed rates and re#ux ratios at a minimal annual cost. To the best of our knowledge this was the "rst paper that combines RD column design and cost estimation, thereby emphasizing the fact that the usual optimisation techniques for ordinary distillation processes may be inappropriate for RD. Gumus and Ciric (1997) used a bilevel optimisation procedure to explore the design of RD columns that could have more than one liquid-phase. The number of phases and the phase equilibria were determined by minimising the Gibbs free energy. Their paper was illustrated by considering the liquid-phase hydrogenation of nitrobenzene to aniline, in which the resulting aniline}nitrobenzene}water system can split into two liquid-phases. Eldarsi and Douglas (1998b) used the optimisation capability in Aspen Plus to optimise an MTBE column. Their study indicated that the market price of the MTBE product, the cost of the butylenes, the isobutylene composition and utility costs all in#uence the MTBE column pro"t. Pekkanen (1995b) described a local optimisation method for the design of RD. Duprat, Gassend & Gau (1988) constructed a set of empirical formulae that was used to optimise an RD process for the separation of the close-boiling mixture of 3-picoline and 4-picoline. The latter method leads to the most rapid optimisation calculations once the empirical formulae have been constructed (by "tting the results of rigorous model simulations). However, the di!erences between RD processes means that the formulae developed for one process have no value for modelling others. 6.4. From conceptual design to column design Until recently, a procedure to go from a viable EQ stage design to an actual column design was not available in the literature. An important paper by Subawalla and Fair (1999) addresses this issue with a lengthy discussion of the importance of several key design parameters: pressure, reactive zone location, reactant feed ratio, feed 5218 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 Table 1 Procedure 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: < °º' " m °º' j °º' 5. Determine the reactive zone height from the calculated catalyst volume and estimated diameter. h °º' " < °º' ( )d °º' 6. Determine the number of reactive stages by dividing the total reactive zone height by the catalytic packing HETP. N °º' " h °º' HETP °º' 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 maximumvapor 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 there is 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 column diameter, 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 change in 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 desired conversion 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, and HETP. Their detailed step-by-step procedure for designing an RD column is summarised in Table 1. Their paper includes a case study in which their design procedure is applied to the production of TAME. The authors make the important point that their procedure is not applicable to all RD processes: èach system has certain characteristics that make the use of one or more of these guidelines di$culta. Step 7 in Table 1 should be singled out for particular attention as the one that relies on the models discussed in this article. At the end of their paper the authors recommend using NEQ or rate-based models for this purpose. 6.5. RD design in industrial practice At the time the Eastman methyl acetate process was developed there were no commercially available simulation programs capable of modelling RD operations. Agreda et al. (1990) reported that stage-to-stage hand calculations were done using #ash and reaction programs to calculate the vapor and liquid compositions in the reactive section. The conventional distillation column sections were modelled using an existing EQ model simulation program. Computer programs to model a complete RD column had to be developed in-house at the same time as pilot plant work was being carried out. Pinjala, DeGarmo, Ulowetz, Marker and Luebke (1992) used the NEQ model RATEFRAC to model MTBEand TAMEprocesses in columns "lled with Koch KataMax packing. Very little information on the form of the model is provided (i.e. how the reaction is brought into the model, the actual kinetic expressions are left to the imagination. Limited comparisons with pilot-plant data look quite good. However, the data are provided in such a way as to render them unusable in independent modelling studies. Frey, Ozmen, Hamm, Pinjala and DeGarmo (1993) have reported that RATEFRAC has been used to accurately predict the performance of commercial RD processes in Germany and Texas, and that the model has been validated for the design of TAME, ETBE, and TAEE units with data from semi-commercial operations. 7. Concluding remarks Belck (1955) concludes his paper describing a hand calculation method for RD columns with the following words: 2 as the complexity of the system increases, the calculation becomes increasingly di$cult 2 the uncertainty inherent in the experimental determination of reaction rate constants and liquid}vapor diagrams R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5219 also tends to make the value of such calculations questionable. Whether or not the experimental work and calculation time * for a detailed computation of such a process in a system with four or more components * can be justi"ed or not will then ultimately depend upon the economic importance of the products. There remains more than a grain of truth to these remarks even today, when the computer, which would make its mark in chemical engineering soon after these words were written, has largely rendered moot the issue of computational cost. There are a variety of models now available in the literature for screening, analysis, design and optimisation of RD columns. Each model has its place in the process development cycle. Residue curve maps are invaluable for initial screening and #owsheet development. EQ models have their place for preliminary designs. How- ever, recent NEQ modelling works have exposed the limitations of EQ models for "nal design and for the development of control strategies. NEQ models have been used for commercial RD plant design and simulation. Column hardware choice can have a signi"cant in#u- ence on the conversion and selectivity; such aspects can be properly described only by the NEQ cell model. It is insu$ciently realised in the literature that say for tray RD columns, the tray design can be deliberately chosen to improve conversion and selectivity. Even less appreciated is the fact that the design methodology for RD tray columns is fundamentally di!erent from that of conventional trays. Liquid residence time and residence time distributions are more important in RD. The froth regime is to be preferred to the spray regime for RD applications; this is opposite to the design wisdom normally adopted for conventional distillation. Though the phenomena of MSS has received considerable attention in the literature, it is possible that not all of the steady- states can be realised in practice due to hydraulic aspects, which are taken into account in the NEQ model. For relatively fast reactions, it is essential to properly model intra-particle di!usion e!ects. Pseudo- homogeneous reaction models may be inadequate for fast reactions. RD columns using dumped (random) packings are susceptible to maldistribution and there is a case to be made for choosing regular structured packings such as that shown in Fig. 13. For proper description of the column dynamics, it is essential to adopt the NEQ model. Though sophisticated NEQ design models are available already, detailed information on the hydrodynamics and mass transfer parameters for the various hardware con"gurations sketched in Figs. 10}16, is woefully lacking in the open literature. Paradoxically, such information has vital consequences for the conversion and selectivity of RD columns. There is a crying need for research in this area. It is perhaps worth noting here that modern tools of computational #uid dynamics could be invaluable in developing better insights into hydrodynamics and mass transfer in RD columns (Van Baten & Krishna, 2000; Higler, A.P., et al., 1999a; Krishna, Van Baten, Ellenberger, Higler & Taylor, 1999). Besides more research on hydrodynamics and mass transfer, there is need for more experimental work with the express purpose of model validation. In such process studies, parameters need to be measured along the height of RD columns. Too often measurements are con"ned to feed and product stream conditions. Such data cannot serve as a reliable discriminant of computer-based process models. Notation a interfacial area, m B bottoms #ow, mol s\ B permeability, m c number of components, dimensionless c R total concentration, mol m\ D distillate #ow, mol s¯ Da Damkohler number, dimensionless D G°'' e!ective Fick di!usivity, m s\ nC G e!ective Knudsen di!usivity in porous catalyst, m s¯ n GI Maxwell}Stefan di!usivity, m s\ E G enhancement factor, dimensionless E energy #ux, W m\ $ energy transfer rate, J s\ E+4 G overall Murphree tray e$ciency, dimensionless h °' clear liquid height, m F4 vapor feedstream, mol s\ F* liquid feedstream, mol s\ f component feed stream, mol s\ h U weir height, m h heat transfer coe$cient, W m\ K\ H molar enthalpy, J mol\ k pseudo-"rst-order reaction rate constant, s\ K vapor}liquid equilibrium constant, dimensionless ¸ liquid #ow rate, mol s\ ¸ + interchange liquid #ow rate between horizontal rows of cells, mol s\ N G molar #ux of species i, mol m\ s\ - Mass transfer rate, mol s\ p H stage pressure, Pa Q heat duty, J s\ r number of reactions, dimensionless r H ratio of side stream #ow to interstage #ow on stage j, dimensionless rH H transformed re#ux ratio, dimensionless R KH reaction rate, mol m\ s\ 5220 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 R gas constant, J mol\ K\ sH H transformed stripping ratio, dimensionless S side draw-o!, mol s\ t time, s ¹ temperature, K ; molar hold-up, mol < vapor #owrate, mol s\ = weir length, m x mole fraction in the liquid}phase, dimensionless x mole fraction vector, dimensionless X transformed liquid-phase mole fraction, dimensionless y mole fraction in the vapor-phase, dimensionless > transformed vapor-phase mole fraction, dimensionless z mole fraction in either vapor or liquid-phase, dimensionless Z transformed mole fraction, dimensionless Greek letters c reaction volume, m ¸ G activity coe$cient of species i, dimensionless thermodynamic correction factor for binary mixture, dimensionless [] matrix of thermodynamic factors, dimensionless « mass transfer coe$cient, m s\ j chemical potential, J mol\ v stoichiometric coe$cient, dimensionless t dimensionless residence time, dimensionless n viscosity of #uid mixture, Pa s n distance along di!usion path, dimensionless Subscripts e! e!ective i component index I referring to interface j stage index k alternative component index m reaction index t total Superscripts F referring to feed stream ¸ referring to liquid-phase < referring to vapor-phase List of abbreviations DAE di!erential-algebraic equations DEG diethylene glycol EG ethylene glycol EQ equilibrium EO ethylene oxide MeOH methanol MeOAc methyl acetate AcOH acetic acid HETP height of a theoretical plate HTU height of a transfer unit MS Maxwell}Stefan MSS multiple steady-states MTBE methyl tert-butyl ether NEQ non-equilibrium RD reactive distillation SRK Soave}Redlich}Kwong TAME tertiary amyl ether Acknowledgements RT and RK would like to express their appreciation to Arnoud Higler and Richard Baur for their considerable assistance in the preparation of this paper. 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Analysis of reactive systems with selective exchange of material with the ambient medium. Theoretical Foundations of Chemical Engineering, 28, 416}420. Timofeev, V. S., Solokhin, A. V., & Kalerin, E. A. (1988). Multiple steady states in the reaction-recti"cation process. Theoretical Foun- dations of Chemical Engineering, 22, 488}492. Toor, H. L. (1965). Dual di!usion - reaction coupling in "rst order multicomponent systems. Chemical Engineering Science, 20, 941}951. Towler, G. P., & Frey, S. J. (2000). Reactive distillation. In S. Kul- prathipanja, Reactive separation processes. Philadelphia: Taylor and Francis (Chapter 2). Trambouze, P. (1990). Countercurrent two-phase #ow "xed bed catalytic reactors. Chemical Engineering Science, 45, 2269}2275. Ung, S., & Doherty, M. F. (1995a). Vapor liquid phase equilibrium in systems with multiple chemical reactions. Chemical Engineering Science, 50, 23}48. Ung, S., & Doherty, M. F. (1995b). Theory of phase equilibria in multireaction systems. 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Chemical Engineering Research and Design, Transactions of the Institution of Chemical Engineers, Part A, 70, 465}470. Zhu, J., & Shen, F. (1995). The modelling and simulation of reactive distillation processes. A.I.Ch.E. Symposium Series No. 304, vol. 91 (pp. 297}300). R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5229 5184 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 3.4. 3.5. 3.6. 3.7. Primarily dynamic models and applications Batch reactive distillationm . . . . . . . . . . . . . Primarily experimental papers . . . . . . . . . . . Use of e$ciencies in RD models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5201 5203 5203 5205 5205 5208 5208 5209 5209 5212 5213 5214 5216 5216 5218 5218 5218 5219 5219 5220 5221 5221 4. Mass transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Non-equilibrium (NEQ) stage modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. The conventional NEQ model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. NEQ modelling of RD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. NEQ models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4. NEQ cell model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5. Pseudo-homogeneous vs. heterogeneous NEQ modelling . . . . . . . . . . . . . . . . . . . . . . 5.6. Dynamics NEQ models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. Reactive distillation design . . . . . . . . . . . . . . . . . 6.1. Conceptual design . . . . . . . . . . . . . . . . . . . 6.2. Graphical design methods . . . . . . . . . . . . . 6.3. Design via optimisation methods . . . . . . . 6.4. From conceptual design to column design 6.5. RD design in industrial practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Introduction The versatility of the fractionating column in the dual role of continuous reactor and separator as applied to chemical processing is well established. Berman, Isbenjian, Sedo! and Othmer (1948a) The quote with which we begin this review appeared in print more than "ve decades ago! It provides an interesting historical perspective because in more recent times we have seen an explosion of interest in the subject of reactive distillation, and a veritable plethora of papers have appeared in the last 12 years alone. The recent interest in this process can be attributed in part to the growing commercial importance of reactive distillation, and in part to a keynote paper by Doherty and Buzad (1992), who reviewed the literature to that time. More than half of the over 300 references cited in this review have appeared after 1992. Thus, one of the objectives of this article is to provide an up-date to their work with a review of more recent developments in reactive distillation. The term catalytic distillation is also used for such systems where a catalyst (homogeneous or heterogeneous) is used to accelerate the reaction. In this review we use the generic name reactive distillation, with the acronym RD, to cover both catalysed or uncatalysed reactions 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, Dunning and Lathrop (1945), Berman, Melnychuk & Othmer (1948b) and Berman et al. (1948a). The "rst publications deal mainly with homogeneous self-catalysed reactions such as esteri"cations, trans-esteri"cations, and hydrolysis. Heterogeneous catalysis in RD is a more recent development and was "rst described by Spes (1966). The main focus of this review is on the modelling of RD processes. We have tried to be comprehensive in our coverage, but it would be nearly impossible to cite every paper even in this fairly well-de"ned niche. This review does not attempt quite such comprehensive coverage of the literature devoted more to RD catalysis and kinetics studies, although some of the works in these sub-"elds necessarily are included in our review to some extent. Descriptions of speci"c RD processes also are largely beyond our scope (see, for example, Sharma (1985), Stichlmair and Frey (1999) for reviews and Bart and Resil (1997) discuss an unusual application). Introductory overviews of RD and RD design and equipment are by R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5185 Fair (1998), Hauan and Hildebrandt (1999), and by Towler and Frey (2000). The non-English language literature also is less well served here. Fortunately, many of the papers in the German and Russian literature have been translated into English. Overviews of parts of the extensive Russian literature on RD (in English) are by Sera"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 by a much longer one on equilibrium (EQ) stage modelling. A brief discussion on e$ciencies in RD leads to an outline of mass transfer considerations and an overview of non-equilibrium (NEQ) modelling of RD processes. We end with some comments on RD design methods. We begin, however, with an appreciation of the bene"ts of RD. 1.1. Why RD? Let us begin by considering a reversible reaction scheme: A#B & C#D where the boiling points of the components follow the sequence A, C, D and B. The traditional #ow-sheet for this process consists of a reactor followed by a sequence of distillation columns; see Fig. 1(a). The mixture of A and B is fed to the reactor, where the reaction takes place in the presence of a catalyst and reaches equilibrium. A distillation train is required to produce pure products C and D. The unreacted components, A and B, are recycled back to the reactor. In practice the distillation train could be much more complex than the one portrayed in Fig. 1(a) if one or more azeotropes are formed in the mixture. The alternative RD con"guration is shown in Fig. 1(b). The RD column consists of a reactive section in the middle with nonreactive rectifying and stripping sections at the top and bottom. The task of the rectifying section is to recover reactant B from the product stream C. In the stripping section, the reactant A is stripped from the product stream D. In the reactive section the products are separated in situ, driving the equilibrium to the right and preventing any undesired side reactions between the reactants A (or B) with the product C (or D). For a properly designed RD column, virtually 100% conversion can be achieved. The most spectacular example of the bene"ts of RD is in the production of methyl acetate. The acid catalysed reaction MeOH#AcOH & MeOAc#H O was tradi tionally carried out using the processing scheme shown in Fig. 2(a), which consists of one reactor and a train of nine distillation columns. In the RD implementation (see Fig. 2(b)) only one column is required and nearly 100% conversion of the reactant is achieved. The capital and operating costs are signi"cantly reduced (Siirola, 1995). For the acid catalysed reaction between iso-butene and methanol to form methyl tert-butyl ether: isobutene#MeOH & MTBE, the traditional reactor-followed-by-distillation concept is particularly complex for this case because the reaction mixture leaving the reactor forms three minimum boiling azeotropes. The RD implementation requires only one column to which the butenes feed (consisting of a mixture of n-butene, which is Fig. 1. Processing schemes for a reaction sequence A#B & C#D where C and D are both desired products. (a) Typical con"guration of a conventional process consisting of a reactor followed by a distillation train. (b) The reactive distillation con"guration. The components A, C, D and B have increasing boiling points. The reactive sections are indicated by grid lines. Adapted from Stichlmair and Frey (1999). 5186 R. Taylor, R. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 Fig. 2. Processing schemes for the esteri"cation reaction MeOH#AcOH & MeOAc#H O. (a) Conventional processing scheme consisting of one reactor followed by nine distillation columns. (b) The reactive distillation con"guration. The reactive sections are indicated by grid lines. Adapted from Siirola (1995). Fig. 3. (a) Reactive distillation concept for synthesis of MTBE from the acid-catalysed reaction between MeOH and iso-butene. The butene feed is a mixture of reactive iso-butene and non-reactive n-butene. (b) Reactive distillation concept for the hydration of ethylene oxide to ethylene glycol. (c) Reactive distillation concept for reaction between benzene and propene to form cumene. (d) Reactive distillation concept for reaction production of propylene oxide from propylene chlorohydrin and lime. The reactive sections are indicated by grid lines. non-reactive, and iso-butene which is reactive) and methanol are fed near the bottom of the reactive section. The RD concept shown in Fig. 3(a) is capable of achieving close to 100% conversion of iso-butene and methanol, along with suppression of the formation of the unwanted dimethyl ether (Sundmacher, 1995). Also, some of the azeotropes in the mixture are `reacted awaya (Doherty & Buzad, 1992). For the hydration of ethylene oxide to mono-ethylene glycol: EO#H OPEG, the RD concept, shown in Fig. 3(b) is advantageous for two reasons (Ciric & Gu, 1994). Firstly, the side reaction EO#EGPDEG is suppressed because the concentration of EO in the liquidphase is kept low because of its high volatility. Secondly, the high heat of reaction is utilised to vaporise the liquid-phase mixtures on the trays. To achieve the same selectivity 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 for the hydration of iso-butene to tert-butanol (Velo, Puigjaner & Recasens, 1988) and hydration of 2-methyl-2butene to tert-amyl alcohol (Gonzalez & Fair, 1997). Several alkylation reactions, aromatic#ole"n & alkyl aromatic, are best carried out using the RD concept not only because of the shift in the reaction equilibrium due to in situ separation but also due to the fact that the undesirable side reaction, alkyl aromatic#ole"n & dialkyl aromatic, is suppressed. The reaction of propene with benzene to form cumene, benzene#propene & Cumene (Shoemaker & Jones, 1987; see Fig. 3(c)), is advantageously carried out in a RD column because not only is the formation of the undesirable di-isopropylbenzene suppressed, but also the problems posed by high exothermicity of the reaction for operation in a conventional packed-bed reactor are avoided. Hot spots and runaway problems are alleviated in the RD concept where liquid vaporisation acts as a thermal #ywheel. The alkylation of iso-butane to iso-octane, iso-butane#nbutene & iso-octane, is another reaction that bene"ts from a RD implementation because in situ separation of the product prevents further alkylation: iso-octane#nbutene & C H (Doherty & Buzad, 1992). The reaction between propylene chlorohydrin (PCH) and Ca(OH) to produce propylene oxide (PO) is best implemented in an RD column, see Fig. 3(d). Here the desired product PO is stripped from the liquid-phase by use of live steam, suppressing hydrolysis to propylene glycol (Bezzo, Bertucco, Forlin & Barolo, 1999). Co-current gas}liquid down#ow trickle-bed reactors are widely applied for hydroprocessing of heavy oils. This co-current mode of operation is disadvantageous in most hydroprocesses (Krishna & Sie, 1994), and counter-current #ow of gas and liquid would be much more desirable (cf. Fig. 4). This is because reactions such as hydrodesulphurisation and hydrogenation are inhibited by hydrogen sulphide formed, even when using the so-called sulphur-tolerant catalyst of the mixed sulphide type. The removal of sulphur from heavy oil generally follows second-order kinetics in sulphur concentration, which is a re#ection of the presence of a variety of sulphur containing compounds with di!erent reactivities. The second-order kinetics imply that a relatively large proportion of sulphur is removed in an early stage of the process (due to conversion of the bulk of reactive Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5187 Fig. 4(b) is essentially a RD column wherein the H S is stripped from the liquid-phase at the bottom and carried to the top. R. Taylor. RD conditions can allow the azeotropes to be `reacted awaya in a single vessel. . ammonia. For a 20. The quantitative advantages of the RD implementation for hydroprocessing are brought out in a design study carried out by Van Hasselt (1999). This increase in conversion gives a bene"t in reduced recycle costs.R. RD is particularly advantageous when the reactor product is a mixture of species that can form several azeotropes with each other. molecules) while removal of the remaining sulphur takes place much more slowly in later stages. (h) Avoidance of hot spots and runaways using liquid vaporisation as thermal #y wheel.000 bbl/d hydrodesulphurisation unit with a target conversion of 98% conversion of sulphur compounds. The constraints and dizculties in RD implementation Against the above-mentioned advantages of RD. the catalyst volume required for a conventional trickle-bed reactor is about 600 m. The counter-current reactor shown in Fig. (c) Improved selectivity. For counter-current RD implementation the catalyst volume is reduced to about 450 m. The co-current mode of operation is particularly unfavourable since the inhibiting e!ect is strongest in the region where the refractory compounds have to be converted. The situation is clearly more favourable in the counter-current mode of operation since in this case the major part of the bed operates in the H S lean regime. It can be seen that in co-current operation the larger part of the bed operates under a H S-rich regime. viz. hydrogen consumption and build up of gaseous components other than H (H S. This means that the bulk of the H S is generated in a small inlet part of the bed and that this H S exerts its inhibiting in#uence in the remaining part of the bed. the heat of reaction can be used to provide the heat of vaporisation and reduce the reboiler duty.. NH . From the foregoing examples. (g) Heat integration bene"ts. This is not only so from a kinetic point of view (inhibition by H S and NH ). If the reaction is exothermic. Hydrodesulphurisation of gas oil carried out in (a) co-current trickle-bed reactor and (b) counter-current RD unit. (d) Signi"cantly reduced catalyst requirement for the same degree of conversion. H O. The reagents and products must have suitable volatility to maintain high concentrations of reactants and low concentrations of products in the reaction zone. but also because of thermodynamics (Trambouze. the bene"ts of RD can be summarised as follows: (a) Simpli"cation or elimination of the separation system can lead to signi"cant capital savings. is a very strong inhibitor for hydrogenation and particularly for hydrocracking reactions. The by-product of conversion of nitrogen containing organic compounds. 2000): (a) Volatility constraints. 4. 1990). (f) Reduced by-product formation. which calls for the highest activity. (b) Improved conversion of reactant approaching 100%. Fig. A similar situation exists in hydrocracking. In the co-current mode of operation the partial pressure of H at the exit end of the reactor is lowest because of the combined e!ects of pressure drop. Deep removal of aromatics from an oil fraction generally is limited by thermodynamic equilibrium. 4(a) shows the partial pressure of H S in the gas phase. light hydrocarbons). 1. (e) Avoidance of azeotropes. there are several constraints and foreseen di$culties (Towler & Frey. For the hydrogenation of aromatics too the cocurrent operation is unfavourable.2. Removing one of the products from the reaction mixture or maintaining a low concentration of one of the reagents can lead to reduction of the rates of side reactions and hence improved selectivity for the desired products. say) to say a few meters (column dimensions). 6. It is di$cult to design RD processes for very large #ow rates because of liquid distribution problems in packed RD columns. (a) homogeneous liquid-phase reaction. Taylor & Krishna..5188 R. which have been veri"ed in experimental laboratory and pilot plant units (Bravo. 1993. a large column size and large tray hold-ups will be needed and it may be more economic to use a reactor-separator arrangement. Practical design considerations Towler and Frey (2000) have highlighted some of the practical issues in implementing a large-scale RD application. it is possible to decrease conversion by increasing the amount of catalyst under certain circumstances (Higler. . 1. etc. Rapmund. re#ux. Reactive Fig. Such interactions. Datta & Smith. linearities introduced by the coupling between di!usion and chemical kinetics in counter-current contacting. Taylor. Adapted from Sundmacher (1995). The phenomena at di!erent scales interact with each other. R. have been shown to lead to the phenomenon of multiple steady-states and complex dynamics. along with the strong non- Fig. Thus. Increased separation capability could decrease process performance (Sneesby. 1999. containment and removal of the catalyst It is important to allow easy installation and removal of the RD equipment and catalyst. amount of catalyst. In heterogeneous RD the problem is exacerbated by the fact that these transfer processes occur at length scales varying from 1 nm (pore diameter in gels. 6. 5 shows the various transfer processes in homogeneous and heterogeneous RD. 1986). Successful commercialisation of RD technology requires careful attention to the modelling aspects. Vogel & Doss. Mohl et al. 1. see Fig. boilup rate. Roat. If the residence time for the reaction is long. Installation. and (b) heterogeneous catalysed reactions. even at the conceptual design stage (Doherty & Buzad. In some processes the optimum conditions of temperature and pressure for distillation may be far from optimal for reaction and vice versa. H 1. (d) Process conditions mismatch. including column dynamics. vapor}liquid mass transfer.3. As will be shown later many of the reactor and distillation paradigms do not translate easily to RD. 1998). Tade.4. The introduction of an in situ separation function within the reaction zone leads to complex interactions between vapor}liquid equilibrium.4. The time scales vary from 1 ms (di!usion within gels) to say a few hours (column dynamics). 1992. the regeneration is most conveniently done ex situ and so there must be provision for easy removal and installation of catalyst particles. 5. These are discussed below. intra-catalyst di!usion (for heterogeneously catalysed processes) and chemical kinetics. Adapted from Sundmacher (1995). Pyhalathi & Jaervelin. Downs. 1999b).1. 1998a). (c) Scale up to large #ows. The complexity of RD The design and operation issues for RD systems are considerably more complex than those involved for either conventional reactors or conventional distillation columns. Fig. Length and time scales in RD. If the catalyst undergoes deactivation. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 (b) Residence time requirement. Sundmacher & Ho!mann. Transport processes in RD. The potential advantages of RD could be nulli"ed by improper choice of feed stage. as discussed in Section 1. 1990).5. Stichlmair & Fair. Fig. The hardware design information can be found in the standard sources for conventional distillation design (Lockett. For example. Ezcient contacting of liquid with catalyst particles The hardware design must ensure that the following `wish-lista is met. leading to increased residence time and (b) increasing reaction temperature (by increase of column pressure) 1. such devices have not been commercialised as yet. These con"gurations are discussed in Section 1. 1998a. This is required in order to avoid reactor hotspots and runaways and allow even catalyst ageing. and liquid residence time distribution are all important in determining the conversion and selectivity of RD.4. R. careful attention needs to be paid to hardware design aspects. For trayed RD columns the preferred regime of operation would be the froth regime whereas for conventional distillation we usually adopt the spray regime. Commonly used devices for good vapor}liquid contacting are the same as for conventional distillation and include structured packing.b). Hardware aspects Before modelling aspects can be considered.uva. mean residence time. The requirement of good radial mixing has an impact on the choice of the packing con"guration and geometry. Designing for catalyst deactivation Even though.4. High liquid hold-ups could be realised by use of bubble caps. Towler and Frey (2000) have presented an excellent summary of hardware design aspects of RD columns. 1986. Ng & Rempel. Counter-current operation in catalyst beds packed with such small-sized particles has to be specially con"gured in order to avoid problems of excessive pressure drop and `#oodinga. (b) Good radial dispersion of liquid through the catalyst bed. 9) because of the desire to maintain high liquid hold-up on the trays. 1994) and the froth regime is usually to be preferred on the trays (cf. (a) Good liquid distribution and avoidance of channelling.1. the reaction severity can be increased by (a) increasing re#ux. can be achieved in a multitray column (cf. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5189 distillation is often passed over as a processing option because the catalyst life would require frequent shutdowns. For homogeneous RD processes.4. random packing and distillation trays. counter-current vapor}liquid contacting.chem. 8). 7. 1. Counter-current vapor}liquid contacting in trayed columns. Fig. 1. 1. reverse #ow trays with additional sumps to provide ample tray residence time. it is desirable to allow on-line catalyst removal and regeneration. Partin & Heise.4. The Hatta number for most RD applications is expected to be smaller than about unity (Sundmacher. Catalyst deactivation is therefore accounted for in the design stage by use of excess catalyst. as is realised in some hardware con"gurations discussed in Section 1. Some of the important issues are discussed below. An RD device that allowed on-stream removal of catalyst would answer this concern. In the Eastman process for methyl acetate manufacture specially designed high liquid hold-up trays are used (Agreda.4. Taylor.5.5.R.4. Fig. 1. Fig. Liquid maldistribution can be expected to have a more severe e!ect in RD than in conventional distillation (Podrebarac. 7) or a column with random or structured packings (cf.3. Good vapor/liquid contacting in the reactive zone If the reaction rate is fast and the reaction is equilibrium-limited then the required size of the reactive zone is strongly in#uenced by the e!ectiveness of the vapor} liquid contacting. Suzcient liquid hold-up in the reactive section The liquid hold-up. Vapor}liquid contacting becomes less important for slower reactions. Animations of CFD simulations of #ows on the tray can be viewed on our web site: http://ct-cr4.6. 1. Rihko & Ho!mann. `Lowa pressure drop through the catalytically packed reactive section This problem arises because of the need to use small catalyst particles in the 1}3 mm range in order to avoid intra-particle di!usional limitations.nl/sievetrayCFD.5. with su$cient degree of staging in the vapor and liquid-phases. This is in sharp contrast with conventional distillation where liquid hold-up and RTD are often irrelevant as the vapor} liquid mass transfer is usually `controlleda by the vapor side resistance. 1998). frequent criss-crossing mixing patterns may be desirable. Besides adding excess catalyst. .4.2. Booker & Crossland. 9. Most commonly the catalyst envelopes are packed inside the column. 10(c). hydrogenation and alkylation of aromatic compounds (Shoemaker & Jones. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 Fig. The catalyst is held together by "breglass cloth. Johnson. Catalytically packed RD columns For heterogeneously catalysed processes. 10}14. Smith. Scores of these bales are installed in the reactive zone of a typical commercial RD column. hardware design poses considerable challenges. 1995.. "lled with catalyst (Van Hasselt. Wire gauze envelopes with various shapes: spheres. The catalyst particle sizes used in such operations are usually in the 1}3 mm range. 12. This is the con"guration used by Chemical Research and Licensing in their RD technology for etheri"cation. Horizontally disposed wire-mesh tubes containing catalyst (Buchholz et al.5. kinetics. 1995. 4. 1994. The hydrodynamics. 1993). 5. (Smith. 1999). Cylindrical shaped envelopes with catalyst inside them (Johnson. Larger particle sizes lead to intra-particle di!usion limitations. Almost every conceivable shape of these catalyst envelopes has been patented. 1999). Hearn. Groten. 1993). Counter-current vapor}liquid contacting in packed columns. 1998.5190 R. Horizontally disposed wire-mesh `guttersa. These structures are: 1. 1. see Fig. see Fig. Taylor. doughnuts. Bales are piled on top of each other to give the required height necessary to achieve the desired extent of reaction. Crossland. Pockets are sewn into a folded cloth and then solid catalyst is loaded into the pockets. some basic shapes are shown in Figs. 1985). 6. 2. The pockets are sewn shut after loading the catalyst and the resulting belt or `catalyst quilta is rolled with alternating layers of steel mesh to form a cylinder of `catalyst balesa as shown in Fig. 8. and mass transfer characteristics of baletype packings have recently been published in the open literature (Subawalla. 11(a). 1997. 10(b). R. Xu. Flow regimes on trays. Zhao & Tian. 1987). see Fig. The steel mesh creates void volume to allow for vapor tra$c and vapor/liquid contacting.1. Gildert & Hearn. see Fig. 1997. 1993). 1984). Porous spheres "lled with catalyst inside them (Buchholz. etc. 1995). Gonzalez. To overcome the limitations of #ooding the catalyst particles have to be enveloped within wire gauze envelopes. 3. Catalyst particles enclosed in cloth wrapped in the form of bales (Johnson & Dallas. 11(b). . 10(a). When the catalyst is spent the column is shut down and the bales are manually removed and replaced with bales containing fresh catalyst. Seibert & Fair. tablets. see Fig. Pinaire & Ulowetz. Improvements to the catalyst bale concept have been made over the years (Johnson. Fig. 1993. 7. Catalyst particles need to be enveloped in wire gauze packings and placed inside RD columns. These catalyst `sandwichesa or `wafersa are bound together in cubes. Johnson & Dallas. Parulekar and Pinjala. 1999. Ellenberger & Taylor. The radial dispersion is about an order of magnitude higher than in conventional packed beds (Van Gulijk. Higler. the liquid follows a criss-crossing #ow path. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5191 Fig. 12. Horizontally disposed (a) wire gauze gutters and (b) wire gauze tubes containing catalyst. 13. When the catalyst is spent. The important advantage of the structured catalyst sandwich structures over the catalyst bales is with respect to radial distribution of liquid. 1998). 10. Within the catalyst sandwiches. 1995. They consist of two pieces of rectangular crimped wire gauze sealed around the edge. Catalyst particles sandwiched between corrugated sheets of wire gauze (Stringaro. Catalyst bales licensed by Chemical Research and Licensing. Fig. 1992. Gelbein & Buchholz. 11. mixing and mass transfer in such structures is available in the open literature (Bart & Landschutzer. thereby forming a pocket of the order of 1}5 cm wide between the two screens. . R. 1991. Various `tea-baga con"gurations. Information on the #uid dynamics. Ellenberger K & Krishna. Such structures are being licensed by Sulzer (called KATAPAK-S) and Koch-Glitsch (called KATAMAX). 1999). DeGarmo. Fig. the column is shut down and the packing is manually removed and replaced with packing containing fresh catalyst. Taylor. 1999a. 1996. The resulting cubes are transported to the distillation column and installed as a monolith inside the column to the required height. 1994). Krishna. see Fig. 1991. Moritz & Hasse.R. nl/strucsim. 14(a). R. 1999a). 14.. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 Fig. however. Structured catalyst-sandwiches. Adapted from Sundmacher (1995). (b) Structured packings coated with catalyst. This is the strategy adopted by Flato and Ho!mann (1992) and Sundmacher and Ho!mann (1994a.5192 R. (c) Fluted catalyst monolith tubes. (c) The sandwich elements arranged into a cubical collection.chem. Furthermore. The catalyst rings can be prepared by block polymerisation in the annular space. (d) The sandwich elements arranged in a round collection. see Fig. Fig.uva. osmotic swelling processes can cause breakage by producing large . 13. Another alternative is to make the packing itself catalytically active. (a) Catalyst sandwiched between two corrugated wire gauze sheets. Taylor. Photographs of the structure. frequent criss-crossing leads to a signi"cant improvement in mass transfer within the sandwich structures (Higler et al. along with CFD simulations of the liquid #ow within the sandwiches can be viewed at: http://ctcr4. Their activity is quite high. (b) The wire gauze sheets are joined together and sewn on all four sides. (a) Catalytically active Raschig ring.b) wherein the Raschig ring-shaped packings are made catalytically active. ensuring good contact between liquid and catalyst. but this can be taken care of by "ltration of the liquid and by make-up of the catalyst.uva. 4. Catalyst envelopes placed along the liquid #ow path. 1. 3. which is subsequently activated by chlorsulphonic acid.. along with CFD animations of the #ow visit the web site: http://ct-cr4. Viltard & Zuliani.R. Other designs have been proposed for tray columns with catalyst containing pockets or regions that are #uidised by the up#owing liquid (Quang et al.b). Catalyst envelopes can be placed near the exit of the downcomer (Asselineau. see Fig. Catalyst envelopes can be placed within the downcomers (Carland. This concept has not been put into practice for the following reasons (Towler & Frey. 3. 14(b). 1985). Furthermore. The vapor #ows through the packed section through a central chimney without contacting the catalyst. Trays or downcomers to hold catalyst particles The catalyst envelopes can be placed in a trayed RD column and many con"gurations have been proposed. 14(c). Furthermore. 1994). since the vapor and liquidphase pass along the packed catalyst in the envelopes. see Fig. 16 (c).2. In the tray con"gurations discussed above. Catalyst attrition is a concern in a #uidised environment. 1994). 1989. Leonard & Nocca. 2000): 1. Vertically disposed catalyst containing envelopes can be placed along the direction of the liquid #ow path across a tray (Jones. see Fig. For photographs of this con"guration. 15. Viltard. 5. 1989.chem. Gaillard. These envelopes are almost completely immersed in the froth on the tray. Amigues. and not through them.nl/kattray. 1. The amount of catalyst that can be loaded in a column in this manner is small compared to addition of catalyst pills or homogenous catalyst. Each `stagea can be regarded as a reaction device (downcomer) followed by a separation section (froth on the tray). Leonard. 4. 1991. Production of catalyst materials in the shape of distillation packings is also expensive. the vapor}liquid contacting e$ciency can be considered practically unimpaired by Fig. The liquid from the separation trays is distributed evenly into the packed reactive section below by a distribution device. see Fig. There is currently no generic manufacturing method that can economically produce di!erent catalyst materials as coatings or structured packings. 16(b). Catalyst inventory is necessarily limited. Gaillard & Amigues. Jones. see Fig. The primary drawback with installing the catalyst within downcomers is the limited volume available for catalyst inventory. R. 1998. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5193 mechanical stresses inside the resin. Another possibility is to coat structured packing with zeolite catalysts (Oudshoorn. the pressure drop is not excessive. Quang. Marion. Coating or impregnation of catalyst materials on metal surfaces is expensive. An alternative con"guration is the glass-supported precipitated polymer prepared by precipitation of styrene-divinylbenzene copolymer. . 1989). 1992a. the packed (or #uidised) catalyst containing envelopes are essentially vapor free. The catalyst can also be `casta into a monolith form and used for counter-current vapor}liquid contacting. Lebens (1999) has developed a monolith construction consisting of #uted tubes. Mikitenko. 2. Travers. 15. 1999). Taylor. Harter and Forestiere. see Fig. 2.5. Trays and packed catalyst sections can also be used on alternate stages (Nocca. 16(a). The vapor does not pass through the catalyst envelopes. Sandler. The classical thermodynamic problem of determining the equilibrium conditions of multiple phases in equilibrium with each other is addressed in standard texts (see. The second paper (Barbosa & Doherty. 1990. Two more recent developments are noted below. The combined problem of determining the equilibrium points in a multiphase mixture in the presence of equilibrium chemical reactions has been the subject of a recent literature review by Seider and Widagdo (1996). the presence of the catalyst envelopes. 2. b. Care must be exercised. and computationally more di$cult. and illustrate GLOPEQ.5194 R. 1999) and not considered here. Perez-Cisneros. in making a proper estimation of the liquid}catalyst contact time. Stichlmair & Fair. 1987b) introduces a set of transformed composition variables that are particularly useful in the construction of thermodynamic diagrams for reacting mixtures. McDonald and Floudas (1997) present an algorithm that is theoretically guaranteed to "nd the global equilibrium solution. 1995a}e). Stichlmair & Fair. alternatively. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 Fig. Counter-current vapor}liquid}catalyst contacting in trayed columns. 1988a}d. however.. Ung & Doherty. The e!ect that equilibrium chemical reactions have on two-phase systems has been considered at length by Doherty and coworkers (Barbosa & Doherty. 16.g. which determines the extent of reaction on the stages. ZQ G G G ! z I 2 I (3) (1) (2) . 1987a. (b) tray contacting with catalyst placed in wire gauze envelopes near the liquid exit from the downcomers and (C) alternating packed layers of catalyst and trays. 1986. Thermodynamics of reactive distillation An introductory review of RD thermodynamics was provided by Frey and Stichlmair (1999a) (see. problem of "nding the composition of a mixture in chemical equilibrium has also been well studied. Walas. Taylor. (a) catalyst in envelopes inside downcomers. 1985. A bene"t of this approach is that the chemical and physical equilibrium problem in the reactive mixture is identical to a strictly physical equilibrium model. The "rst paper by Barbosa and Doherty (1987a) considers the in#uence of a single reversible chemical reaction on vapor}liquid equilibria. 1998). a computer code that implements their algorithm for cases where the liquid-phase can be described by a Gibbs excess energy model. For a system in which the components take part in either of the following reactions A#B & C. The equally important. Doherty. Their method uses chemical &elements' rather than the actual components. The chemical elements are the molecule parts that remain invariant during the reaction. e. The actual molecules are formed from di!erent combinations of elements. Readers are referred to the text of Smith and Missen (1982). Therefore. standard tray design procedures (Lockett. 1998) can be applied without major modi"cation. A#B & C#D the following transformation is de"ned: z / !z / I I . 1990. R. Gani & Michelsen (1997a) discuss an interesting approach to the phase and chemical equilibrium problem. . 1994). < (7) where X is the transformed composition of species i in G the liquid-phase and > is the transformed composition G for the vapor phase.. Malone & Doherty (1999a) employed a bifurcation analysis to investigate in a systematic way the feasibility of RD for systems with multiple chemical reactions. The in#uence of homogeneous reaction kinetics on chemical phase equilibria and reactive azeotropy was discussed by Venimadhavan. Huss. For the MTBE system they show that there is a critical value of the Damkohler number that leads to the disappearance of a distillation boundary. Rev shows that there can be a continuous line of stationary points belonging to di!erent ratios of the evaporation rate and reaction rate. (6). Low Damkohler numbers are indicative of systems that are controlled by the phase equilibrium. Doherty and Malone (1994) and Rev (1994). A reactive azeotrope has been found for the system isopropanol} isopropyl acetate}water}acetic acid (Song. G H I where < is the molar #ow rate in the vapor and . a high Da indicates a system that is approaching chemical equilibrium (see Towler & Frey. They also note the importance of the Damkohler number and the operating pressure. Taylor.R. the trajectories of the residue curves. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5195 z is the mole fraction of species i in either the vapor or G liquid-phase as appropriate and the subscript k refers to the index of the reference component (one whose stoichiometric coe$cient is non-zero). Frey and Stichlmair (1999b) describe a graphical method for the determination of reactive azeotropes in systems that do not reach equilibrium. Residue curve maps and heterogeneous kinetics in methyl acetate synthesis were measured by Song. through this. Lee. Buzad. (5) G G It is interesting to observe that reactive azeotropes can occur even for ideal mixtures (Barbosa & Doherty. For the synthesis of isopropyl acetate there exists a critical value of the Damkohler number for the occurrence of a reactive azeotrope. is a dimensionless time. 17 adapted from Thiel et al. These equations are more conveniently expressed in terms of actual mole fractions. The Damkohler number is de"ned by . In terms of the transformed composition variables the material balance equations that describe a simple open evaporation in a reacting mixture are given by dX G "X !> . Venimadhavan. It will be apparent that the heating policy greatly where k is a pseudo-"rst-order reaction rate constant. An analysis was carried out to forecast the number of stable nodes as a function of Damkohler number and pressure. The conditions for the existence of a reactive azeotrope (and all other stationary points in the reactive mixture) are most easily expressed in terms of the transformed composition variables: X "> . Barbosa and Doherty (1988a) provide a method for the construction of phase diagrams for reactive mixtures. 1988a). Doherty & Malone. Thiel. Although it is not obvious from Eq.b) compute the residue curves for the heterogeneously catalysed RD of MTBE. Barbosa and Doherty (1987a) consider two di!erent de"nitions of an azeotrope and adopt the de"nition given by Rowlinson (1969): À system is azeotropic when it can be distilled (or condensed) without change of compositiona. Further. TAME and ETBE and "nd them to have signi"cantly di!erent shapes to the homogeneously catalysed residue curves (Venimadhavan et al. Hauan & Westerberg (2000e) discussed circumventing reactive azeotropes. non-reactive azeotropes can disappear when chemical reactions occur. The Damkohler number is a measure for the rate of reaction relative to the rate of product removal.b). 1987a. is the molar liquid hold-up. R. A reactive azeotrope exists when this line intersects with the surface determining chemical equilibrium. Sundmacher & Ho!mann (1997a.k Da" . The residue curves are obtained from dx < P A G " (x !y )# r ( !x ). 1997). Ung & Doherty (1995a}e) have extended the methods of Barbosa and Doherty to deal with mixtures with arbitrary numbers of components and reactions. it is the Damkohler number that emerges as the important parameter in the location of the residue curves for such systems. (6) G H GH G IH dt . (1997a). The in#uence the reaction equilibrium constant has on the existence and location of reactive azeotropes was investigated for single reaction systems by Okasinski and Doherty (1997a. Numerical solution of these equations yields the residue curves for the system. 2000). Doherty (1990) develops the topological constraints for such diagrams. rather than the transformed composition variables de"ned above. These parameters in#uence the existence and location of "xed points in the residue curve map as seen in Fig. Points on this line are called kinetic azeotropes. Feasible separations are classi"ed as a function of the Damkohler number. G G d (4) in#uences the rate of vapor removal and the value of the equilibrium and reaction rate constants and. Rev (1994) looks at the general patterns of the trajectories of residue curves of equilibrium distillation with nonequilibrium reversible reaction in the liquid-phase. 3. for example. 18(b)). the total material balance takes the form d. 1985. (9) H H GH H H GH GK KH H K In the material balance equations given above r is the H ratio of sidestream #ow to interstage #ow: r4"S4/< . Here we are concerned with the extension of this standard model to distillation accompanied by chemical reaction(s). Equilibrium (EQ) stage models The development and application of the EQ stage model for conventional (i. The vapor and liquid streams leaving the stage are assumed to be in equilibrium with each other. Taylor & Lucia. (1997a). With very few exceptions. (8) GK KH H K G . The EQ stage model A schematic diagram of an equilibrium stage is shown in Fig. The equations that model equilibrium stages are known as the MESH equations. R. the production of methyl acetate by RD can be carried out in either regime. r*"S*/¸ . Residue curves for the homogeneously and heterogeneously catalysed MTBE synthesis. is the hold-up on stage j. 17. non-reactive) distillation has been described in several textbooks (see. The component material balance (neglecting the vapor hold-up) is d.b). 1981. Blagov. x H GH "< y #¸ x #F z H> GH> H\ GH\ H GH dt P !(1#r4)< y !(1#r*)¸ x # R . It is more important to include the hold-up of the vapor phase at higher pressures. H "< #¸ #F !(1#r4)< !(1#r*)¸ H> H\ H H H H H dt P A # R . GH GH GH (11) 3. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 Fig. They found that the residue curves for the kinetically controlled cases are qualitatively similar to the curves for the equilibrium case. Holland. H . (10) H H H H H H represents the stoichiometric coe$cient of componGK ent i in reaction m and represents the reaction volume. 18(a). 1994). Malone and Doherty (1998).e. Seader. Henley & Seader.1. The M equations are the material balance equations. Epifanova & Sera"mov (1988b) and Solokhin.5196 R. Taylor. A complete separation process is modelled as a sequence of s of these equilibrium stages (Fig. H The E equations are the phase equilibrium relations y "K x . Seader & Henley. is considered to be the hold-up only of the liquidH phase. Venimadhavan. After Thiel et al. MESH being an acronym referring to the di!erent types of equation. Manning. Open evaporation accompanied by liquid-phase chemical reactions has also been studied by Pisarenko. 1998) and reviews (Wang & Wang. 1963. 1981. Thus. Vapor from the stage below and liquid from the stage above are brought into contact on the stage together with any fresh or recycle feeds. . 1980. Sera"mov & Timofeev (1990a. HYSYS. R. this will normally be the liquid-phase enthalpy. H H H "< H4 #¸ H* #F H$ H> H> H\ H\ H H dt !(1#r4)< H4!(1#r*)¸ H*!Q . For example. GH (12) 3. The enthalpy in the time derivative on the left-hand side represents the total enthalpy of the stage but. some exceptions to this statement and such works are noted below. however. these methods are discussed brie#y in what follows. Marek (1954).R. H H H H H H H (13) The superscripted H's are the enthalpies of the appropriate phase. However. Berman et al. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5197 Fig. Only rarely is there any attempt to compare the results of simulations to experimental data (some exceptions are noted below). 18. Tray-to-tray calculations were carried out by hand by Berman et al. and SpeedUp are the packages mentioned most often in the papers discussed in what follows. controller equations and so on. We may identify several classes of computer-based methods that have been developed for solving the EQ stage model equations. Marek also presents an elaborate graphical method related to the McCabe}Thiele method for conventional binary distillation. The number of examples that illustrate most of the early papers usually is rather limited. Readers are referred to the review G G The enthalpy balance is given by d. More and more of the more recent modelling studies are carried out using one or other commercial simulation package: Aspen Plus. . There are. (1948a) considered the production of dibutyl phthalate. Taylor. The S equations are the summation equations A x "1. extensive data for which system had been reported by Berman et al. Some authors include an additional term in the energy balance for the heat of reaction. Steady-state algorithms and applications Much of the early literature on RD modelling is concerned primarily with the development of methods for solving the steady-state EQ stage model. both in number as well as in the type of RD process considered (most often it is an esteri"cation reaction).2. for the reasons given above. Under steady-state conditions all of the time derivatives in the above equations are equal to zero. Pro/II. Some authors include additional equations in their (mostly unsteady-state) models. (1948b). (b) Multi-stage distillation column. For the most part such methods are more or less straightforward extensions of methods that had been developed for solving conventional distillation problems. if the enthalpies are referred to their elemental state then the heat of reaction is accounted for automatically and no separate term is needed. (a) The equilibrium stage. Chemical reaction equilibrium is not considered in many of the early papers because it is more di$cult to model. and Belck (1955). GH A y "1. (1948a). pressure drop. 5198 R. The method is applied to the esteri"cation of acetic acid.g. Parametric studies involving the e!ects of catalyst load and distribution. Zhou & Yuan (1999). More details and illustrative examples are to be found in the works of Block (1977). Relaxation methods involve writing the MESH equations in unsteady-state form and integrating numerically until the steady-state solution has been found (Komatsu. Bock and Wozny (1997) show that the assumption of chemical equilibrium. Very few RD examples accompany these papers. Numerical results for a single example are compared to numerical results obtained by Komatsu (1977). Short-cut methods involve a number of simplifying assumptions that are made in order to derive simple approximate equations that can be used for rapid computations. closely related to dynamic models. Sneesby. Solving all of the independent equations simultaneously using Newton's method (or a variant thereof) nowadays is an approach used very widely by authors of many of the more recent papers in this "eld (see. Takamatsu. Mayer and Seid (1979) and Simandl and Svrcek (1991). 1976). Savkovic-Stevanovic. This approach is. There also exists a class of algorithm that really is a combination of equation tearing and simultaneous solution in that Newton's method is used to solve a subset of the MESH equations. often made in developing short cut methods. but not in chemical equilibrium with each other. Szymanowski and Bogacki (1988) used a minimisation method due to Powell (1965) to solve the MESH equations. the reader is referred to Wayburn and Seader (1987). 1993). Mis\ ic-Vukovic. Holland (1981) provides a cursory description of this approach to RD simulation. Bentzen. Papers by Nelson (1971). Homotopy-continuation methods are employed most often for solving problems that are considered very di$cult to solve with other methods (e. Yagi. The bubble-point method of Wang and Henke (1966) was extended by Suzuki. However. Perez-Cisneros and Gani. Komatsu and Hirata (1971) to be able to deal with chemical reactions. 1995). 1963. theirs is essentially the same EQ model employed by almost everyone else in that the exiting streams are in phase equilibrium. operating pressure and re#ux ratio are reported. Tade and Smith. 1977. Relaxation methods are not often used because they are considered to be too demanding of computer time. 1998). Tray-to-tray calculations and parametric studies for the simulation and optimisation of an RD column for trioxane synthesis are described by Hu. Hashimoto and Kinoshita (1984) and Kinoshita (1985) used a similar approach to model columns for an unusual application: heavy water enrichment using hydrophobic catalysts. for example. Pilavachi. is inappropriate for many RD processes. Bogacki. despite the new name.} method. Foldes and Sawinsky (1979). Tris\ ovic and Jezdic (1992) used the method to model an esteri"cation of acetic acid and ethanol carried out in a glass column that was 33 mm in diameter and 1000 mm tall. Ciric & Spencer. 1997. Block and Hegner (1977). The calculated temperature pro"le and product compositions are in good agreement with the measured quantities. Tearing methods involve dividing the model equations into groups to be solved separately. Kinoshita. but in which other methods are used to solve the remaining equations. Brief reviews of early RD algorithms are by Holland (1981) and by Hunek. Newton's). rather slow to converge. Holland. Suzuki's method was used by Babcock and Clump (1978). Other papers from this group are Izarraz. however. and by Tierney and Riquelme (1982) fall into this category. Isla and Irazoqui (1996) use Newton's method to solve the equations that model what they refer to as a `partial equilibriuma stage. Bondy (1991) describes physical continuation approaches to solving RD problems. Anthony and Holland (1980) and Mommessin. Alejski. Hashimoto and Takamatsu (1983). Mommessin and Holland (1983) discuss the computational problems associated with multiple columns. Homotopy-continuation was "rst applied to RD operations by Chang and Seader (1988). 1981) was extended to RD operations by Komatsu and Holland (1977) and named the multi. of course. Numerical results for the esteri"cation of . however. Bentzen. R. Anokhina & Sera"mov. Kaibel. For more details about this method. for example. Lee & Dudukovic. Their paper is illustrated by a number of case studies involving the esteri"cation of acetic acid and ethanol to ethyl acetate and water. Komatsu compares his EQ stage model calculations to his own experimental data for one experiment showing that the EQ model composition pro"les are qualitatively correct. A brief description of computer based tray-to-tray calculations for the RD of ethylene oxide and water was given by Corrigan and Miller (1968). Boncic-Caricic. Anthony and Holland (1980). 1997c) and for locatH ing multiple steady-states (Pisarenko. The so-called method developed for conventional distillation columns by Holland and his many collaborators (see. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 of Seader (1985) for background and original literature citations. The authors from Prague provide three numerical examples involving esteri"cation processes. Continuation methods are also useful for studying parametric sensitivity (see. Jelinek & Hlavacek. Schenk. Lee and Dudukovic (1998) have also used homotopy continuation to solve both EQ and NEQ models of RD operations. Taylor. It is quite di$cult to derive generic short-cut procedures for RD because of the many ways in which chemical reactions in#uence the process (see. Alejski & Szymanowski (1989) used the Adams}Moulton numerical integration method to integrate a simpli"ed dynamic model that neglects the enthalpy balance to a steady-state solution. They are. Equilibrium stage model used by Davies et al. Quitain. Four examples demonstrate that RADFRAC can be applied to a wide variety of reactive separation processes. Simulation results are compared to experimental data. reaction rates. Venkataraman. The trays had an inside diameter and spacing of 140 mm. 1999b) used RADRAC to model an industrial-scale version of the same process. Experimental composition pro"les are provided for a single set of operating conditions. show that the shape of the pro"les obtained by the EQ model is largely in agreement with the shape of the pro"les measured by Komatsu. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5199 acetic acid with ethanol were compared with data from Komatsu (1977). Komatsu carried out experiments on the esteri"cation system of acetic acid and ethanol. and the interstage #ows were equimolar. Bezzo et al. The model is used to predict the temperature and composition pro"les in a 76 mm diameter column in which formaldehyde is reacting with water and methanol. Itoh & Goto. The model equations were solved using a relaxation method combined with Newton's method for computing the variables at each time step. Itoh & Goto (1999a) modelled a small-scale column used to produce ETBE from bioethanol. RADFRAC has been used by many other authors. Davies.R. Santacesaria. The outgoing liquid stream passes to a reactor where chemical equilibrium is established. RADFRAC is able to handle both equilibrium reactions as well as kinetically limited reactions. Jenkins and Dilfanian (1979) describe a variation on the standard EQ stage model that is depicted in Fig. selectivity and product distribution. although there are some signi"cant quantitative di!erences. 19. Simandl and Svrcek (1991) provide more details of their own implementation of an inside-out method for RD simulation. Alejski (1991b) investigated the steady-state properties of an RD column in which parallel reactions take place. Alejski and Szymanowski (1988. re#ux ratio. each of which is considered to be a non-equilibrium cell. Departures from equilibrium were handled through the calculation (in the usual way) of the point e$ciency. (1979). (1988). Each stage was assumed to be perfectly mixed. Inside-out methods involve the introduction of new parameters into the model equations to be used as primary iteration variables. Reaction kinetics were modelled using the expressions reported by Carra. There are also 3 sets of data for a #ash RD. 19. The thermodynamic properties of this system are complicated by the presence of electrolytes in the liquid-phase and by salting out e!ects. It was assumed that reactions occur in the liquid-phase and the reactions are rate controlling. Alejksi looked at the in#uence of reactants' volatilities. as well as Simandl and Svrcek (1991). Good agreement between predicted and measured values Fig. A comparison between the numerical results of Alejski (1991a) obtained with an equilibriumcells-in-series model and the experimental data of Marek (1956) shows that the assumption of complete mixing on the tray is much less successful than the multi-cell model at predicting the actual composition pro"les. Morbidelli and Cavalli (1979b). reaction equilibrium constants. number of theoretical stages and distillate rate upon the yield. R. Chan and Boston (1990) describe the inside-out algorithm known as RADFRAC that is part of the commercial program Aspen Plus. . Liquid-phase composition pro"les are provided for "ve experiments. the column pressure is an important factor that strongly a!ects reaction rates by changing the column temperature pro"le. 1989) provide a brief (in Polish) review of RD algorithms. In a later paper Alejski (1991a) models the liquid #ow across a tray by a sequence of mixing cells. The vapor/liquid contacting section is modelled as a conventional vapor}liquid equilibrium stage (without reaction). (1999) used RADFRAC to study the steadystate behaviour of an actual industrial RD column producing propylene oxide from propylene chlorohydrin and calcium hydroxide. The experiments were carried out in a column of 7 trays each with a single bubble cap. Alejski et al. The disadvantage of this approach is that it fails to properly account for the in#uence that chemical equilibrium has on vapor}liquid equilibrium (and vice versa). The stream leaving this reactor passes on to the next equilibrium stage. Marek (1956) had described a plant for the production of acetic anhydride. Taylor. A second paper (Quitain. location of feed inlets. By adjusting the Murphree e$ciency the authors were able to obtain the best possible agreement between the plant data and the simulations. As has been reported elsewhere. The vapor leaving any stage was in physical equilibrium with the liquid in this stage. b) develop the K so-called R/R analysis for RD columns.3. 1997). Hertzberg and Lien (1995. Barbosa and Doherty (1988d) point out that the EQ stage model equations (including those that account for simultaneous phase and chemical equilibrium) can be rewritten so that they are identical in form to the EQ model equations in the absence of chemical reactions. the latter being de"ned by Eq. Perez-Cisneros. 1999). It is beyond the scope of this article to review this body of literature. The ethylene glycol RD process also appears to be particularly interesting for the investigation of MSS. The advantage of this approach is that existing algorithms and programs can be used to solve the equations. among others. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 is claimed. RADFRAC has been used by. The details of the calculations are given in Baur et al. Timofeev. The actual #ows and compositions are replaced by the transformed #ows and compositions. (a) High. Pisarenko. (3). The "rst report of MSS in RD appeared in the Russian literature. Schenk and Gani (1997b) and Eldarsi and Douglas (1998a) for investigation of multiplicity of steady-states in RD columns. 20(a). Pisarenko et al. varying the location of the stage to which methanol is fed results in either a high or low conversion. (1993) used homotopy methods to locate MSS in RD with more conventional con"gurations. it is only recently that experimental veri"cation of their existence has been forthcoming. steady-state multiplicity is observed (Baur. Multiple steady-states with the EQ model Multiple steady-states (MSS) in conventional distillation have been known from simulation and theoretical studies dating back to the 1970s and have been a topic of considerable interest in the distillation community. Taylor & Krishna. The bottoms #ow in these simulations was "xed at 203 mol/s.5200 R. R. Epifanova and Sera"mov (1988a) found three steady-states for an RD column with just one product stream. Kerkhof and Mak (1993). However. The column consists of 17 stages. two of which were stable. 1997). Higler. Taylor. 3. Karpilovsky. following Jacobs and Krishna (1993). Jacobs and Krishna (1993). but the "gures provided in their paper are small and hard to read. Nijhuis. (1999). Explanation for the occurrence of MSS in the MTBE process was provided by Hauan et al. Solokhin and Kalerin (1988) provided a simple analysis of their RD column con"guration. (a) Con"guration of the MTBE synthesis column. Pisarenko and Sera"mov (1997) developed an analysis of single-product columns at in"nite re#ux. shown in Fig. The two Fig. readers are referred to Guttinger K (1998) for citations of the original literature and discussions of the di!erent kinds of multiplicity that have been found. For MTBE synthesis using the Jacobs} Krishna column con"guration. (1995. Hauan. 20. . but Kumar and Daoutidis (1999) found ònlya "ve! Guttinger and Morari (1997.and low-conversion branches obtained by EQ and NEQ simulations. 1999a. Ciric and Miao (1994) found as many as nine steadystates. All that is required is to replace that part of the program that carries out the phase equilibrium calculations with a new procedure that computes the phase and chemical equilibrium computation and evaluates the transformed variables. When the methanol is fed to stages 10 or 11. For the TAME process MSS occur in the kinetic regime and vanish when chemical equilibrium prevails. Experimental data on low. The measured steady-state temperature pro"les for the low and high steady-states for the TAME process are shown in Fig. (b) Response of TAME column to injection of pure TAME in the feed during the period 860}920 min. (1999) used a pilot-scale column used to produce MTBE and TAME. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5201 in"nities refer to in"nite internal #ow rates and an in"nite number of stages and the method is for the prediction of MSS in distillation. The window of opportunity for MSS in the TAME process is larger than for the MTBE process. Gehrke and Marquardt (1997) developed a method based on singularity theory for elucidating the possible causes of MSS in a single equilibrium stage RD process. (a) Multiple steady-states in TAME synthesis. Kienle & Gilles (1998) implemented a dynamic EQ model (with Murphree-type e$ciencies) in the DIVA simulator and carried out a numerical bifurcation and stability analysis on the MTBE and TAME processes. Ruiz. Basualdo and Scenna (1995) describe a software package called READYS (REActive Distillation dYnamic Simulator) for which an EQ stage model is used Fig. and non-reactive stripping and recti"cation sections. R. The methodology is further re"ned and developed by Guttinger and K Morari (1999a. 21(a). . in which the reaction is assumed to take place on every stage of the column. Primarily dynamic models and applications Savkovic-Stevanovic (1982) put forth an unsteadystate EQ stage model of a distillation process in which one component takes part in an association reaction in both phases. see Fig.and high-conversion steady-states. They also show that the window of opportunity for MSS to actually occur in the MTBE process is quite small. We will have more to say on the subject of MSS in RD in a later section on NEQ modelling.R. (1999). Their method requires no analytical solution of the equations and uses homotopy methods as well as interval computing techniques to identify the highest order singularity. 3. Taylor. Euler's method was used to integrate the di!erential equations. (1997) and Mohl. The column shifts from a low steady-state to the higher one. 21. Using the Eastman methyl acetate process. Measurements of Mohl et al. (1986). Experimental con"rmation of MSS in RD has been provided by Thiel et al. but not in the MTBE process. Guttinger and Morari (1997) K extended prior work of Morari and co-workers that was restricted to conventional distillation operations to develop a uni"ed approach to the prediction of MSS in systems involving equilibrium chemical reactions. but no actual data are provided. a pulse injection of pure TAME for a short period results in a shift from the low to the higher steady-state. Mohl et al.4. Their model integrates the control system equations with the column model equations. (1998). they show that control schemes with good steady-state characteristics may fail under unsteady-state conditions. One of the "rst papers to discuss dynamic simulation of RD processes is the work of Roat et al. A comparison with data for the acetic acid}benzene system shows good agreement with the model. 21(b). they conclude that the MSS are easily avoided by selecting appropriate control strategies. Mohl et al. For a column operating at the low steadystate. The second paper relaxes this restriction and considers MSS in columns with a reactive section. Multiple steady-states were found experimentally when the column was used to produce TAME. The method is applied to the MTBE process studied by others.b). (1997) and Rapmund et al. The "rst of these two papers deals with what the authors call non-hybrid columns. Espinosa. The package allows for a number of standard thermodynamic property packs as well as user-supplied models. Their dynamic model assumes that reaction equilibrium is attained on all stages. Martinez and Perez (1994) presented a simpli"ed dynamic model for an RD column. but their paper does not dwell on the computational methods. ideal mixing. Column hydraulics is accounted for through a pressure drop equation and departures from equilibrium can be modelled using a Murphree-type e$ciency factor. (1997b). 20(a). READYS and Aspen Plus were used by Perez-Cisneros. (1998a) show that an increase in fractionation (by increasing re#ux ratios. The dynamic temperature pro"les are in reasonable agreement with the data. The resulting equations were rewritten in terms of the . The model is based on the conventional assumptions of negligible vapor-phase hold-up and perfect mixing of the two phases. The actual molecules are formed from di!erent combinations of elements. the latter being calculated from an eddy di!usion model in terms of the Peclet number. Schrans and Lien (1997) also showed oscillatory behaviour and suggested that it is due to an internal recycle of MTBE in the reactive zone. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 which adopts the assumption of physical equilibrium.5202 R. The authors state that their program can be used to study unsteady and unstable column operations such as start-up. equimolar over#ow and physical and chemical equilibrium were assumed. This is exactly opposite to the situation in conventional distillation. de Wolf & Baur (1996) carried out dynamic simulations. The focus of this paper is the transient response of the system. heat losses to the environment and the heat of reaction were neglected. and corrections of the conversion due to imperfect mixing are accounted for using a `conversion e$ciencya. neglecting reaction kinetics. Their simulations showed that increase in the iso-butene feed by 4% leads to oscillatory behaviour. The chemical elements are the molecule parts that remain invariant during the reaction. Subsequent papers from this group look at multiple steady-states in RD (Sneesby. Tade & Smith. The unsteady-state model equations are solved using SpeedUp. thermal equilibrium with a chemical reaction con"ned to the liquid-phase. Alejski and Duprat (1996) described a dynamic model for modelling kinetically controlled RD processes. Gani and Pilavachi (1996) and PerezCisneros et al. Gani. In a companion paper Sneesby. using SPEEDUP. Tade. Theirs is an unsteady-state EQ stage model that can handle systems both with and without reactions and with more than two #uid phases. In addition. (1997b) who also discussed their own somewhat di!erent approach to the EQ model. Sneesby et al. A process design methodology is suggested. or numbers of equilibrium stages) does not always lead to improved performance of RD columns. H 1998c}e). number of equilibrium stages * reactive or non-reactive. A bene"t of this approach is that the chemical and physical equilibrium problem in the reactive mixture is identical to a strictly physical equilibrium model. shutdown and abnormal hydraulic column behaviour. Departures from phase equilibrium could be handled by speci"cation of a vaporisation e$ciency. Ruiz and Benz (1998) employ READYS to study the start-up of RD columns. Abufares and Douglas (1995) use an EQ stage model for steady-state and dynamic modelling of an RD column for production of MTBE. (1997) use the same approach. Their model uses chemical &elements' rather than the actual components. Vapor holdups. The model is compared to data obtained in a pilot-scale column for the esteri"cation of ethanol with acetic acid and sulphuric acid as homogeneous catalyst. Column start-up and disturbances of continuous operation were investigated. rather its focus is on some of the parameters that are important in RD modelling. they discuss the e!ect of thermodynamic models and their parameters on RD simulation. of the MTBE synthesis process using essentially the Jacobs}Krishna column con"guration shown in Fig. R. Schrans. Tade. The steady-state model is RADFRAC from Aspen Plus. Simulation results are compared to results obtained with the commercial simulation program Pro/II. Schenk. ethanol excess. A comparison with the RD data of Suzuki et al. Jepsen and Perez-Cisneros (1998) described a generalised reactive separation unit model. For example. Sneesby et al. They show that the start-up policy can have a strong in#uence on the ultimate steady-state behaviour by sending the column to an undesirable operating point. but the predicted dynamic concentration pro"les are very di!erent from the observed pro"les. Pilavachi et al. Several numerical examples cover a range of simulation problems. (1971) is provided and it is noted that these data are di$cult to match unless the `"tteda activity coe$cient model is used. Taylor. Datta & Smith (1997a) model the synH thesis of ETBE using an EQ stage model that they solve with SpeedUp. Alejski and Duprat (1996) also recommend that tray hydraulics be accounted for in any dynamic model of RD. The methodology is quite unique in that it is based on the element approach of Perez-Cisneros et al. a commercial dynamic process simulation program. Sneesby. Homotopy methods are used to investigate the e!ects of important design variables (feed composition. pressure. Extensive numerical results are provided. The authors recommend including control issues early in the design process. reboiler duty and so on). Datta and Smith (1997b) develH op a dynamic model of the same process using SpeedUp. Hauan. Scenna. (1998d) (as well as Bartlett and Wahnscha!t (1998) using RADFRAC) report that the transition from one steady-state to another can be prevented using appropriate control strategies. A further increase of iso-butene feed by 5% causes a jump from the high-conversion steady-state to the lower one. For the special case of butyl acetate production the new policies lead to complete conversion of the reactants and high-purity products that are unobtainable by conventional methods. Thus. Bollyn and Wright (1998) develop a model of a batch RD process for the synthesis of the ethyl ester of pentenoic acid. Mujtaba and Machietto (1992). E the solutions are dilute (thus the temperature change can be ignored). C4 hydrocarbons. there are some others whose main thrust is on providing experimental data. and in which the modelling activity provides only a supporting role. the model is somewhat simpler than other dynamic models that are discussed here. and assume pressure drops and stage e$ciencies to be constant. In order to save calculation time. 1994).and p-xylene using sodium in a column with very few equilibrium stages. an inherently unsteadystate process has been studied by Corrigan and Ferris (1969). Venimadhavan et al. Morbidelli. Wozny and Jeromin (1989) develop the most complete EQ stage model of batch RD that includes the hold-up of both phases and process controller equations. Cleary and Doherty (1985) provided experimental support for this conclusion. Machietto and Mujtaba (1992). Cuille and Reklaitis (1986) neglect the vapor-phase hold-up. (1979b) and Carra. Kumar and Daoutidis (1999) presented a comprehensive dynamic EQ stage model of an ethylene glycol RD column. Le Lann. Egly. 3.06. E the liquid hold-up is constant on each tray (the vapor hold-up is ignored). (1999b) examined a novel distillate policy and propose a new re#ux policy for equimolar reactions. Malone and Doherty (1999b). Joulia and Koehret (1991). Sylvestre and Doherty (1985) who suggest that it is possible to separate m. Grosser.5. S+rensen and Skogestad (1992. Primarily experimental papers In addition to the papers cited above. Reuter. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5203 transformed variables presented by Barbosa and Doherty (1987b). Lien and Hertzberg (1995) discuss possible numerical problems when developing dynamic models of RD based on phase and chemical equilibrium principles. They report that RD is an attractive alternative to conventional distillation when the relative volatility is less than 1. The DAE equations that formed their model were solved using the LSODI routine. A relaxation method is used to solve the unsteadystate model equations while Newton's method is used to solve the steady-state equations at each time step. R. Albet. 3. RD of close-boiling mixtures has also been studied by Terrill.R. (1979). Some calculations were done for an ideal quaternary system. The DAE system was solved using the LSODI numerical integration routine. but the DAE system of model equations is solved using the DASPK solver. No extensive numerical dynamic data are presented. Wajge and Reklaitis (1999) describe in detail a package called RDBOPT for the design of operation policies for reactive batch distillation. and Mujtaba and Machietto (1992) look at the optimal design and operation of batch RD. Carra et al. Moe. Egly et al. Xu and Dudukovic (1999) developed a dynamic model for semi-batch photo RD. The model is essentially the same as that used by Cuille and Reklaitis (1986). and Venimadhavan. Doherty and Malone (1987) use a dynamic model based on the following assumptions: E the mixture reaches reaction and phase equilibrium instantaneously on each tray. E constant molar over#ow (modi"ed somewhat) relates the #ows from stage to stage. S+rensen and Skogestad (1992. the order of the model was reduced using an orthogonal collocation method. and chlorobenzenes. Xu and Dudukovic (1999) and Wajge and Reklaitis (1999).6. Machietto and Mujtaba (1992). Batch reactive distillation Batch reactive distillation. Machietto. 1994) and S+rensen et al. Reuter. Santacesaria & Buzzi (1979a) studied the synthesis of . Cuille and Reklaitis (1986). Corrigan and Ferris (1969) provided a limited quantity of data for the methanol acetic acid esteri"cation reaction in an Oldershaw column. assume that the volumetric hold-up on each stage is constant. A comparison with some dynamic product composition data for a transesteri"cation plant shows good agreement with the calculated product composition. Bollyn and Wright (1998). The reduced order model was veri"ed against a `rigorousa model and a reasonably good match was found. Hauan. The paper does not include any attempt at modelling the process. These models also use steady-state energy balances. Patlasov (1996). In this process the reaction occurs only in the reboiler and not at all in the column itself. Stuart and Skogestad (1996). S+rensen. The major thrust of this work is the design of a control system that performs well with stability in the high-purity region. (1996) consider the controllability of batch RD. They study the separation by RD of close-boiling mixtures such as mixtures of xylenes. Wozny and Jeromin (1989). The models of Albet et al. (1991) and of Mujtaba and Machietto (1992) allow for changes in the component hold-ups but assume constant liquid molar hold-ups. Ruby and Seid (1979). They compare a model that includes vaporphase balances to a more conventional model that ignores the vapor hold-up and suggest that it is important to include the vapor phase in order to more accurately model the process dynamics. Taylor. 12. the isobutene conversion and MTBE selectivity as a function of methanol/iso-butene ratio in the feed. indicating little composition change from stage to stage. (1971) to model the production of methyl acetate by methanol esteri"cation in a small-scale column packed with an acidic organic acid polymer catalyst.25 m. Mahajani & Sharma (1996). . but comparisons with the data are provided for only one experiment. Acetalisation of formaldehyde with methanol in batch and continuous RD columns was studied by Kolah. The process studied is the separation of 3-picoline and 4-picoline through complexation with tri#uroacetic acid. the re#ux ratio. Simulations are used to compare the performance of several di!erent plant designs. Bravo et al. it must be remembered that matching only top and bottom compositions is not a particularly good test of a complete column model. Their paper provides more data than usually is the case in experimental papers. Flato and Ho!mann (1992) discuss the development and start-up of a small-scale packed distillation column for the production of MTBE. Composition pro"les are provided for a few experimental runs. Their paper provides an unusually comprehensive description of the experimental work carried out. Gonzalez and Fair (1997) present data for the production of tert-amyl-alcohol from water and iso-amylenes. Krafczyk and Ghmeling (1994) used RADFRAC to model an experimental column with 2 m of KATAPAKS with bubble cap trays above and below. Insu$cient data are available for others to attempt a simulation using anything other than an EQ model. Gaspillo. the simulations could be made to agree with the experimental composition pro"les. Michishita & Maeda (1971). No attempt to model the column is provided. The separation of acetone from 2-propanol is strongly in#uenced by the feed #ow rate. A good match was found between simulation results and top and bottom stream composition data obtained in the two experiments for which they provide data. Taylor. The authors used Newton's method to solve the equations that model the synthesis of propylene oxide from propylene chlorohydrins in an RD column. Bart and Reidetschlager (1995) used RADFRAC to model experiments involving the esteri"cation of succinic anhydride with methanol to produce dimethyl succinate and water in laboratory-scale column. The simulation results were in reasonable agreement with the data. Experimental results are provided for the mole percent of MTBE as a function of time. The pilot-scale column was 11 m in height and 15 cm in diameter. with the calculation of the minimum re#ux and of the number of stages. Few details of the column design are given other than to say the column was a continuous multistage micropilot column. Duprat and Gau (1991b) study the separation of close-boiling mixtures using RD. Pekkanen (1995a) refers to such regions as `reactive pinchesa. and the temperature of the heat source.5204 R. A limited quantity of column data is reported in their second paper. (1993) provide some preliminary results obtained from a catalytic distillation pilot plant used to produce TAME. The column was modelled using the transformed composition approach of Ung & Doherty (1995). The manufacture of the Raschig ring-shaped packing elements is described in some detail. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 propylene oxide from propylene chlorohydrins in an RD column.and p-xylene) has also been studied by Saito. A companion paper (Duprat & Gau. Newton's method was used to solve the EQ stage model equations. No data are provided that could be useful to other investigators. Gonzalez. They suggest that a standard RD column is preferable to a reactor/column for fast reactions and high relative volatilities. However. The column was loaded with bales of catalytic packing similar to that shown in Fig. R. The motivation for the study was to investigate the possibility of using the system in chemical heat pump. RD of close-boiling mixtures (m. Abella and Goto (1999) studied experimentally the dehydrogenation of 2-propanol to acetone and hydrogen in a small-scale RD column. A limited quantity of experimental data is included in the paper. in others just 2. An important conclusion from their experimental work is that over design of an RD column can lead to unacceptably low yields of the desired products. with correspondingly high yields of undesired products. The main goal of this study was to test the feasibility of heterogeneous RD for methyl acetate production. When tray ef"ciencies were speci"ed. Fuchigami (1990) reported top and bottom column temperature and composition data for 13 experiments for the methyl acetate process carried out in a laboratoryscale column. The experiments were simulated with the proprietary simulation program FLOWBAT. The RD column has an internal diameter of 5.1 cm and a total length of 2. In some of their experiments the column was loaded with 6 bales. The catalyst was Amberlite XAD ion-exchange resin. and data showing the e!ect of pressure on iso-butene conversion. A parametric study showed the e!ect of varying the feed composition and other important operational parameters. A much more demanding test is to be able to predict observed composition pro"les along the length of a column. Subawalla and Fair (1997) used the RADFRAC model in Aspen Plus to simulate the process. as is the control system installed around their column. Some of the experiments show composition pro"les that appear almost #at. 1991a) provides equilibrium data for this system. Reaction kinetics of this reaction were derived and presented in the "rst paper. the rest of the column being "lled with Sulzer BX gauze packing. Neumann and Sasson (1984) used the method of Suzuki et al. (17) G ' G ' For a homogeneous system.. Using a rigorous non-equilibrium (NEQ) model (discussed below). 1993). i"1.2. respectively. Water. A slow reaction also takes place in the "lm but its in#uence on the mass transfer process can safely be ignored. E+4" G* G yH!y G G# (14) and EG lie in between those of water and DEG. For packed columns it is common to use the height equivalent to a theoretical plate (HETP). The component e$ciencies of EO 4. y is the composition of the vapor entering the G# tray and yH is the composition of the vapor in equilibG rium with the liquid leaving the tray. 22 with "lled symbols for the RD case and with open symbols for the nonreactive case. This is illustrated by calculations of the component e$ciencies for an RD column for hydration of ethylene oxide (EO) with water to mono-ethylene glycol (EG). Keskinen. (1979) employed a conventional binary e$ciency prediction method in the absence of anything better. For the non-reactive column the component e$ciencies are close to one another and in the range 0. 1997. Isla & Irazoqui. The Maxwell}Stefan equations for mass transfer in the vapor and liquid-phases respectively are given by y * 4 A y N4!y N4 G G" G I I G c4n4 1¹4 *z R GI I and (15) x * * A x N*!x N* G G" G I I G . that of Murphree is most often used in EQ stage simulation: y !y G# . calculated from the NEQ model are shown in Fig. Ruiz et al. To the best of our knowledge there are no fundamentally sound methods for estimating either e$ciencies or HETPs in RD operations. In general. and for heterogeneous systems in Fig. Taylor. If it is su$ciently rapid. For a more complete understanding of RD processes it is necessary to consider in detail the interaction between mass transfer and chemical reaction.g. (16) 1¹* *z c*n* R GI I where x and y are the mole fractions of species i in the G G liquid and vapor phases. water. GK K *z K (18) . Since the mole fractions add to unity. We take up this subject next. the molar #uxes in the liquid "lm may change due to any chemical reaction that takes place there *N P G" R . At the vapor}liquid interface we have the continuity equations . For distillation of systems with three or more species.65. 1999) and also for a column in which the reactions were deliberately suppressed. R. this paper illustrates the complex nature of component e$ciencies. Taylor & Krishna. Lee & Dudukovic. 1993). Representative "lm pro"les for homogeneous systems are shown in Fig. has the highest component e$ciency. 5(a). The most fundamentally sound way to model mass transfer in multicomponent systems is to use the Maxwell}Stefan theory (see Krishna & Wesselingh. the component e$ciencies show great variation between the di!erent components. Use of ezciencies in RD models Some authors (e. The smallest molecule. Ilme. Clearly. the component e$ciencies were calculated for an RD column (using the con"guration described by Baur et al. For RD operation.. the mole fraction of the last component is obtained by the summation equations for both phases.2. where y is the average composition of the vapor leaving G* the tray. the presence of chemical reactions will have an in#uence on the component e$ciencies. (15) and (16) are independent. Mass transfer For the purposes of this discussion it su$ces to adopt a "lm model description of the transport processes in RD.R.4" ". The behaviour of HETPs in multicomponent mixtures is closely related to the behaviour of stage e$ciencies.. Davies et al. 1995. Only c!1 of Eqs. n. Very fast reactions may occur only in the "lm. The n represents GI the corresponding Maxwell}Stefan di!usivity of the i!k pair in the appropriate phase. the reaction will also take place in the liquid "lm adjacent to the phase interface. EG and DEG. Markkanen & Aittamaa (1997) simulated an industrial MTBE (non-reactive) distillation column using an EQ stage model using a more rigorous multicomponent (matrix) e$ciency prediction method. Reuter et al. the component e$ciencies are almost always unequal to one another and these can routinely assume values greater than unity or less than zero (Taylor & Krishna. chemical reactions in#uence the values of the component e$ciencies in a complex and unpredictable way. 5(b). 1989. Taylor and Krishna (1998). In situ distillation is used to suppress the unwanted side reaction to diethylene glycol (DEG) produced from the reaction EO#EG P DEG. 1996. only (n!1) of the Murphree component e$ciencies are independent. In homogeneous RD processes the reaction takes place only in the liquid-phase.5}0.7. There are many di!erent de"nitions of the stage e$ciency. The component e$ciencies for EO. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5205 3. 1998) use a modi"ed EQ stage model in which the phase equilibrium equations incorporate a stage e$ciency factor. This aspect has also been highlighted in the simulations presented by Higler.*" . Eqs. the most general approach is to solve the MS and continuity equations simultaneously for all cases involving homogeneous reactions. Kuipers.5206 R. Taylor. D is G an e!ective di!usivity and it should be regarded as . and the regime may even vary from stage to stage. It will not always be clear in advance in which regime a particular process will be operating. (16) and (18) form a system of non-linear coupled di!erential equations that must be solved numerically in most cases. 22.g. *z (19) This expression ignores the coupling between the species gradients as well as mass transfer by convection. 24(a). For most reactive distillations the change in the #uxes through the "lm will not be signi"cant because the Hatta numbers are smaller than unity (Sundmacher et al. reactive absorption) the composition change in the "lm will be very important. the MS equations sometimes are written in greatly simpli"ed form N "!c D G R G *x G . water. Component e$ciencies for EO. 1994). The composition pro"le with the `di!usiona "lm will be nearly linear. They report that thermal e!ects can a!ect mass transfer rates by as much as a factor of 30! In view of their complexity. Kuipers. R.. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 Fig. Taylor and Krishna (2000). Frank. Thus. Unpublished results of Baur. Versteeg and van Swaaij (1995b) and Frank. EG and DEG for reactive and non-reactive operation. Krishna and van Swaaij (1995a) provide perhaps the most comprehensive study of simultaneous mass (and heat) transfer with chemical reaction modelled using the MS equations. The RD column con"guration is shown in Fig. For other reactive separation processes (e. E!ective di!usivity models of this sort have been used with some success in the modelling of amine-based gas treating processes (see. For a non-ideal mixture we have: x * x *p x B G G# G < # G 1¹ *z 1¹ G *z D GC A x N !x N N G I I G! G .R. enhancement factors depend quite strongly on the reaction kinetics. A rigorous approach to modelling heterogeneous systems (Fig. 5(b)) would involve a complete description of mass transport to the catalyst and di!usion and reaction inside the catalyst particles. or reaction at the surface if it is not. Hermes & Rochelle. thus. in many G cases it is not even possible to obtain analytical expressions for the enhancement factor. Solutions of Eq. A more rigorous approach to modelling mass transfer in multicomponent systems is a!orded by the generalized Fick's law: J "!c G R A\ *x G . Toor. Among other things. The dusty #uid model as developed by Krishna and Wesselingh (1997) is a modi"cation of the dusty gas model so as to be able to model liquid-phase di!usion in porous media. see Taylor and Krishna (1993) for details of this. Krishna and van Swaaij (1995a) cite other studies of non-isothermal mass transfer with simultaneous chemical reaction modelled using the simpler constitutive relation given by Eq. 1965. The Fick di!usion coe$cients can be related to the binary MS di!usion coe$cients. (19). 1977). Carey. there is no universal expression for E that can be used in all situations. It is necessary to take catalyst geometry into account in the solution of these equations. R. Frank. the literature on mass transfer with chemical reaction based on these two equations is vast and such equations often are used. (21) is just as di$cult to solve as the full MS equations and it is necessary to employ numerical methods here as well. we assume the e!ective di!usivity to be constant. The dusty gas model is often used as the basis for the calculation of a catalyst e!ectiveness factor (Jackson. if the catalyst is porous. as it looks. Bouhamra & Alper. 1994 and the extensive lists of references in these papers). The Chapman}Enskog kinetic theory is then applied to the new pseudo-gas mixture. Results usually are expressed in the form N*"k E (x'!x*). Beenackers. D GI *z (21) unnecessary to allow for reaction in the vapor or liquid "lms as described above. then analytical solutions to Eqs. 1995. The mass transfer rates are obtained by multiplying the #uxes by the interfacial area of the catalyst particles. Altiqi. for example. Modelling multicomponent mass transfer in porous media is complicated when the mean free path length of the molecules is of the order of magnitude of the pore diameter. However. and the mass transfer rates themselves. For those cases where the reaction takes place at the catalyst surface the boundary conditions at the liquid}solid interface will be determined by the reaction kinetics. consisting of very large molecules that are kept motionless by some unspeci"ed external force. The extension to non-ideal #uids noted above has not been used as often. (20) G G G G G where k is the mass transfer coe$cient and E is an G G enhancement factor that accounts for the in#uence of chemical reaction on the molar #uxes. since. For all cases involving a heterogeneous reaction we may model transport through the vapor}liquid interface using the MS equations given above (assuming no reaction in the liquid "lm). one is no longer faced with the problem of #ux and composition variations across a pore and problems related to catalyst geometry. in which the interaction between the dust and gas molecules simulates the interaction between the solid matrix and the gas species. 1991. the mixture composition. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5207 a function of the binary MS di!usion coe$cients. if. if the reaction takes place inside a porous catalyst then we need to model di!usion and reaction inside the catalyst as well as transport from the bulk liquid to/from the catalyst surface. (21) and the continuity equation (18) are known for a few cases involving simultaneous di!usion and reaction (see. Kenig & Gorak. as is usually done. (18) and (19) may be derived. 1983). Cornelisse. In either case it is . the cross-sectional area can change along the di!usion path. Danckwerts (1970) and Van Swaaij and Versteeg (1992) review the "eld of mass transfer with chemical reaction. van Beckum & van Swaaij. We also need to model di!usion of reactants to and products away from the solid catalyst surface using a separate set of di!usion equations. Indeed. (19). even for the muchsimpli"ed constitutive relation given by Eq. In most cases of practical signi"cance Eq. for example. depending on the geometry of the catalyst. In addition. 1997). This is not as straightforward. Sabri. Kuipers. 1980. The di$culties posed by this case may be circumvented by a method originally introduced by Maxwell (1866) and developed further by Mason and co-workers (see Mason & Malinauskas. " (22) c nC c DC R GI R G I where DC is the e!ective Knudsen di!usion coe$cient for G species i in the porous catalyst. Indeed. Maxwell suggested that the porous material itself be described as a supplementary `dusta species. Taylor. However. partly because of the greater I where J is the molar di!usion #ux of species G i (N "J #x N ) and the D are the Fick di!usion G G G R GI coe$cients for the multicomponent mixture. 1993. The reaction term is evaluated at bulk liquid conditions. 23.* "0.* GH GH " GH IH IH GH (25) 1¹ * c* ( * a) H RH GI H I with a similar relation for the vapor phase. 1985.b. (23) and (24) over the total number (c) of components in the mixture. 1998). However. The SRK equation of state was used for the gas phase. Taylor. Catalyst e!ectiveness factors and selectivities computed from the model are in good agreement with experimental data for MTBE formation obtained in a CSTR. Taylor & Krishna. this coe$cient is estimated from information on the corresponding Maxwell}Stefan di!usivity n* using the standard procedures discussed in GI Taylor and Krishna (1993). The non-equilibrium stage (cell) for homogeneous liquid-phase reaction. 1994a.* !x . Important conclusions from their theoretical work are that the mass transfer resistance inside the catalyst can vary signi"cantly along the packing and that the main resistance to mass transfer is on the liquid side.1. The overall molar balances are obtained by summing Eqs. (24) H GH H\ GH\ GH GH where . The model is used to determine the catalyst e!ectiveness factor. Zhang & Ho!mann. H H H> H> H H H H ¸ H*!¸ H* !F*H*$!$ *#Q*"0. R. Kooijman & Hung. Sundmacher and Ho!mann (1992) recommend the MS equations over Fick's law for modelling mass transfer in the liquid-phase surrounding an ion-exchange catalyst particle.is the interfacial mass transfer rate and is the GH product of the molar #ux and the net interfacial area.5208 R. 1995.are obtained from the MaxGH well}Stefan (16) modi"ed as follows: x * * A x . Sundmacher and Ho!mann introduce àrti"cial inertia termsa into the interface mass balances in order to create a system of di!erential and algebraic equations (DAEs). 1993. a is the interfacial area. Ho!mann and their co-workers (Sundmacher & Ho!mann. and the model is in good agreement with extensive experimental data. 1987). Sundmacher. Non-idealities in the liquid-phase were described with the UNIQUAC equation. The * repGI resents the mass transfer coe$cient of the i!k pair in the liquid-phase.4 "0. However. A schematic representation of the NEQ stage is shown in Fig. In other papers Sundmacher & Ho!mann (1994. 1994. Non-equilibrium (NEQ) stage modelling The NEQ stage model for RD follows the philosophy of rate-based models for conventional distillation (Krishnamurthy & Taylor. The component molar balances for the vapor and liquid-phases are < y !< y !f 4 #. H H H\ H\ H H H H (26) (27) 5. . The e!ect of the reaction is lumped into a component consumption term. Only c!1 of Eq. 1995) have carried out an extensive study of mass transfer and activity in and around RD catalysts.. The reaction is modelled by an activity-based Langmuir}Hinshelwood expression derived from an extensive experimental study by Reh"nger and Ho!mann (1990a. The enthalpy balances for both vapor and liquid-phases are < H4!< H 4 !F4H4$#$ 4#Q 4"0. Hairer & Zugck. 1995) use the Maxwell}Stefan equations as a basis for a "lms-in-series mass transfer model for a vapor}liquid-porous catalyst system. Berg and Harris (1993) have developed a detailed model of di!usion and reaction in MTBE synthesis. This NEQ stage may represent a tray or a crosssection of a packed column. Fig. di!usion in the catalyst is described using an e!ective di!usivity model that is equivalent to a rearrangement of the dusty #uid model while ignoring the Knudsen di!usion terms. The conventional NEQ model It will be helpful to begin with a brief review of the NEQ model for conventional distillation operations. (23) H GH H> GH> GH GH ¸ x !¸ x !f * !. The DAE system was solved with the LIMEX solver (Deu#hard. their model focuses only on the transport and reaction issues and they have not developed a complete column/process model. Sundmacher.b). corrected by the catalyst e$ciency. 5. Taylor. Sundmacher and Ho!mann (1994a) developed a detailed model to investigate the interaction between mass and energy transport and reaction in an ion-exchange resin. The . 1992. 23. The mole fraction of the last component is obtained by the summation equations for both phases. Seader & Henley. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 uncertainty in the parameters that appear in the equations. 1994. Sundmacher et al. (25) are independent. The steady-state model equations most often are solved using Newton's method or by homotopy-continuation. H For homogeneous reactions this is given by the total liquid hold-up on stage j and. A more rigorous approach would involve the use of the dusty #uid model discussed above if the catalyst is porous. whereby catalyst di!usion and reaction is lumped into an overall reaction term. In either case the continuity equations for the "lm are required for taking into account the e!ect of the reaction on the interphase mass transfer rates. In this case. 5. The simplest approach is to treat the reaction pseudo-homogeneously.2. Chapter 14). viscosities.3.R. The phase equilibrium equations for the interface may need to be modi"ed for the in#uence of additional species on the thermodynamic properties at the interface. one only needs to specify catalyst mass and activity. (30) H H\ H\ where p and p are the stage pressures and p is H H\ H\ the pressure drop per tray from stage (j!1) to stage j. (23)}(29). pressure and composition of the interface from appropriate thermodynamic models (the same models used in conventional equilibrium stage models). In the NEQ model. In addition. etc. The NEQ model requires thermodynamic properties. not only for calculation of phase equilibrium but also for calculation of driving forces for mass transfer and. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5209 The interphase energy transfer rates $ (equal in both H phases) have conductive and convective contributions A *¹* $ *"!h*a # . 1988) modelled a packed RD column for the esteri"cation of methanol and acetic acid to methyl acetate. At the vapor}liquid interface we assume phase equilibrium y " "K x " .. hardware design information must be speci"ed so that mass transfer coe$cients. A review of early applications of NEQ models is available in Taylor & Krishna (1993. interfacial areas. The pressure drop over the stage is considered to be a function of the stage #ows. in an NEQ model. Amine-based gas treating again provides a case in point where reactions in the liquid-phase create additional species (including ions) that a!ect the interfacial equilibrium (Glasscock & Rochelle. etc. for taking into account the e!ect of non-ideal component behaviour in the calculation of reaction rates and chemical equilibrium constants. and very fast reactions may occur only in the "lm. For homogeneous systems the component molar balance for the liquid-phase becomes P ¸ x !¸ x !f* !-* ! R "0. 5. R. NEQ models Sawistowski and Pilavakis (1979. The combined set of MS and continuity equations usually must be solved numerically. This omission results in liquid-phases being (predicted to be) slightly superheated and vapor phases that are subcooled (Taylor et al.* H* (28) H * GH GH H G with a similar relation for the vapor phase. (29) GH ' GH GH ' where the subscript I denotes the equilibrium compositions and K is the vapor}liquid equilibrium ratio for GH component i on stage j. The K-values are evaluated at the temperature. 1989). If it is su$ciently rapid. for calculation of mass (and heat) transfer coe$cients and interfacial areas are required. In addition to Eqs. in the NEQ model we take account of the pressure drop across a stage p !p !( p )"0. we "rst need to know whether the reaction is heterogeneous or homogeneous. For a heterogeneous reaction. Furthermore. In this case one also needs information about the catalyst geometry (surface area. there are two options for the description of the reaction term. the reaction will also take place in the liquid "lm adjacent to the phase interface. mean pore diameter. etc). liquid hold-ups. NEQ modelling of RD Building an NEQ model of a reactive separation process is not as straightforward as it is for the EQ stage model in which we simply (or not so simply) add a term to account for reaction to the liquid-phase material balances. is obtained directly from the column internals speci"cations and appropriate hydrodynamic correlations. h* is the heat H transfer coe$cient in the liquid-phase. physical properties such as surface tension. 1994). di!usion coe$cients. the physical properties and the hardware design. For heterogeneous reactions that are modelled in this way the liquid-phase material balance is as given above and is given by the total amount H of catalyst present on the stage under consideration. They used an e!ective . The conductive contributions are ignored in some modelling studies. Taylor. or reaction at the surface if not. represKH GK ents the stoichiometric coe$cient of component i in reaction m and represents the reaction volume on stage j. in RD. In either case it is unnecessary to allow for reaction in the vapor}liquid "lm and the vapor}liquid transport equations are exactly as given above. we have the summation equations for the mole fractions in the vapor and liquidphase and equations expressing the continuity of #uxes of mass and energy across the interface. For a reactive separation process. H GH H\ GH\ GH GH GK KH H K (31) where R is the rate of reaction m on stage j. can be calculated. The DAE equations were solved by use of an implicit Euler method combined with homotopy-continuation. the reaction equation given in their "rst paper represents an irreversible reaction. eddy di!usion model for the liquid-phase. The resulting set of algebraic equations was solved using Newton's method. completely mixed liquid. temperature and #ux pro"les. Lee and Dudukovic (1998) described an NEQ model for homogeneous RD in tray columns. Yet no equations or terms for mass transfer from the liquid to the catalyst appear anywhere else in the paper. 1992a). Baur et al. plug-#ow vapor. Simulation results appear to show reasonable agreement with temperature and liquid composition pro"les measured for the esteri"cation of ethanol and acetic acid carried out in an Oldershaw column.5210 R. pressure. (1999) described a software package for the synthesis and design of RD operations. leads to a conversion higher than that predicted by the EQ model. Kreul. RATEFRAC appears to be based on the NEQ model of Krishnamurthy and Taylor (1985) with the addition of equations to account for the e!ect of reaction on mass transfer. Few precise details are provided. Kenig et al. The designer part of the package is based on an NEQ model that accounts for possible reaction in the mass transfer "lm and includes a catalyst e$ciency calculation to account for di!usion and reaction in the catalyst. and chemical equilibrium constraints (if needed). for a methanol feed location yielding a low-conversion steady-state. 20 (b). introduced the RATEFRAC model for rate-based multicomponent separation modelling (Sivasubramanian & Boston. It is possible that the reaction is treated pseudo-homogeneously where e!ects of reaction on mass transfer (and the e!ects of mass transfer on reaction) in the catalyst are lumped into the bulk liquid reaction term. The model equations are solved using Newton's method. feed composition. feed #ow rates. The introduction of a mass transfer resistance alleviates a `bad situationa and has the e!ect of improving conversion.e. Taylor. However. Zheng and Xu (1992b) have used an NEQ model to simulate catalytic distillation operations in a packed column with bag-type porous catalyst. 1990). In 1990 ASPEN Technology Inc. No mathematical details of the model are provided in the paper. A large number of correlations for the mass transfer coe$cients in di!erent types of column internal are available in the program. use of the NEQ model). Theirs is a pseudohomogeneous model very similar to that described above. Bogle and Pistikopolous (1999) describe in considerable detail a hybrid-modelling environment in which distillation-type processes can be simulated using a combination of steady-state. and feed position. The program is illustrated by modelling the MTBE process and a comparison with some experimental data (numerical values not given) shows excellent agreement with the calculated pro"les. They model production of MTBE and provide numerically calculated concentration. They underlined some counter-intuitive features of RD processes. via a series of case studies. Elsewhere in the paper it is stated that liquid}solid mass transfer coe$cients in the catalyst bed are computed from a correlation derived in their "rst paper (Zheng & Xu. Vapor}liquid mass transfer is modelled using the MS equations. (1999) have compared the EQ and the NEQ models for the MTBE process. mixed pool model for the liquid-phase. Gani. R. A close agreement between the predictions of EQ and NEQ models was found only when the tray e$ciency could be correctly predicted for the EQ model. re#ux ratio. the introduction of mass transfer resistance (i. Schenk. and it is impossible to be sure how the presence of reaction(s) modi"es any of the NEQ model equations. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 di!usivity method for their mass transfer model. it is not completely clear how the reaction is modelled. studied the importance of various model simpli"cations. In a subsequent paper Lee and Dudukovic (1999) extend the dynamic NEQ model of Kooijman and Taylor (1995) to cover the dynamic operation of RD in tray columns. The package is one of the results of a major research program on RD supported by the European Union under the BRITEEURAM program. Newton's method and homotopy continuation are used to solve the model equations. Zhu and Shen (1995) discussed the modi"cation of the NEQ model of Krishnamurthy and Taylor (1985) to handle RD. Only for the temperature pro"le is there any comparison with experimental data. reboil ratio. Thermodynamic properties for the liquid-phase are described with the UNIFAC model and the virial equation is used for the vapor phase. however. Unless the equilibrium constant has some unconventional definition. Their second paper includes parametric studies that show how conversion changes as a function of catalyst #ow rate. and that the additional e!ort of the more complicated NEQ approach is justi"ed. Stage hydrodynamic models included in the package are: E E E E completely mixed vapor and liquid. They found little di!erence between the full MS description of multicomponent mass transfer and the simpler e!ective di!usivity models. For example. . with the AIChE correlations used for the binary (Maxwell}Stefan) mass transfer coe$cients. However. The system of di!erential equations that constitute their model was solved numerically. The Maxwell}Stefan equations are used to describe interphase transport. Gorak and Barton (1999a) used an NEQ model of homogeneous RD and. see Fig. EQ stage. dynamic. they also conclude that there can be signi"cant di!erences between EQ and NEQ models. Murphree e$ciencies calculated from the results of a simulation of the production of ethyl acetate were not constant with time. however. Sundmacher and Ho!mann (1996) presented a detailed NEQ stage model for vapor}liquid}porous catalyst systems. Their model accounts for axial dispersion along the column. Mass transfer across the vapor}liquid interface and between liquid bulk and catalyst surface is described with the Maxwell}Stefan equations. The agreement between the pro"les obtained with the rate-based model and the data is very encouraging. 1995. Experiments were carried out in a pilotscale column with 6 mm Intalox saddles and a reactive section containing bale-type packing. The system of equations is solved via a pseudo-relaxation method using the DAE solver LIMEX cited earlier. Mass transfer in the non-reactive sections was modelled using a "lm model for each phase. Uhde and Hoffmann (1999) used both EQ stage (with Murphree e$ciency) and NEQ models to simulate the MTBE and TAME processes. Their papers also include the development of an NEQ model. It was found that the DAA production rate was controlled by mass transfer. The reactions were handled using both quasi-homogeneous and heterogeneous methods. Rempel and their co-workers at the University of Waterloo (Huang. 1996). Di!usion within the catalyst phase is ignored. Sundmacher & Ho!mann. It appears likely that these oscillations originate from the hydrodynamics in their packed RD column. A detailed NEQ model was needed to describe the TAME process. The NEQ model does not provide an explanation for the observed oscillations. Zhou and Tan (1997) developed a steady-state NEQ model that takes into account mass transfer from the bulk liquid to the catalyst. Sundmacher. Correlations for the solid}liquid mass transfer coe$cients and for the overall mass transfer coe$cients for the vapor}liquid transport were developed by Huang et al. a correlation for which was derived for their column. catalysed by an exchange resin in a packed column. demonstrate a sensitivity of the computed pro"les to the activity coe$cient model used. Mass transfer between vapor and liquid-phases is described by a single overall mass transfer coe$cient for each species. The model equations were solved by a relaxation method. Simulation results were compared to experimental data obtained in two laboratory-scale columns.R. Podrebarac et al. Empirical methods are used for estimating the liquid}solid (and other) phase mass transfer coe$cients. Sundmacher. but both NEQ and the EQ stage (with an e$ciency of 0. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5211 and/or rate-based models. Separate rate equations are written for the vapor}liquid and liquid}solid interfaces. Yu. by extension. R. Oost. The model appears to be derived from the Krishnamurthy}Taylor model for conventional distillation. mass transfer . A particularly novel feature of their paper is the introduction of Gibbs energy pro"les in the column. 1998a. DAA selectivity was in#uenced by the liquid distribution. (1998a). The reaction is assumed to take place only at the catalyst surface and is modelled with an Eley}Rideal kinetic expression. Two of the three examples that illustrate their paper concern RD (ethyl acetate production and an MTBE column). 1998a. Ng. The authors conclude that it is necessary to account for the side reactions in RD process design.b) have carried out an in-depth study of the aldol condensation of acetone to diacetone alcohol (DAA) and mesityl oxide. Ho!mann and co-workers (Sundmacher. although it is interesting to note that the material balances are expressed in terms of the mass #ows and mass fractions and include a separate term for the rate of vaporisation caused by the heat of reaction. The system of non-linear equations is solved by a Newton homotopy method. Podrebarac. Ng & Rempel. The models are compared to experimental data of Suzuki et al. In an interesting experimental study Sundmacher and Ho!mann (1995) obtained oscillatory behaviour of a packed laboratory-scale distillation column. Ng & Rempel. 1998b. The authors do. (1971). In the latter case it was necessary to account for the catalyst e!ectiveness along the packing. Bart and Landschutzer (1996) studied the esteri"cation K reaction of acetic acid and propanol to propyl acetate. One of the conclusions from this study is that it is absolutely necessary to account for di!usion and reaction in the porous catalyst (modelled in this paper using the catalyst e!ectiveness factor approach developed in other papers from these authors and discussed above). Yang. The in#uence of side reactions on RD processes has been investigated by Schoenmakers (1982). Huang. This means that sensible heat transfer between phases is ignored and that the overall energy balance replaces the individual phase balances. Taylor. Mass transfer in the vapor and liquid-phases is modelled using an explicit approximate solution of the Maxwell}Stefan equations (see Chapter 8 of Taylor and Krishna (1993) for details). the dispersion coe$cient being obtained from a Bodenstein relation that was determined experimentally for their model column. Uhde & Ho!mann. Oost & Ho!mann.. The oscillations were encountered in the MTBE process as well as in the distillation of non-reactive binary mixtures.8) model could adequately represent the MTBE process. They assume that the rate of reaction is equal to the rate of mass transfer to the catalyst surface and correlations for the liquid}solid mass transfer coe$cients were also developed. 1999. The authors use an NEQ model for non-reactive distillation that completely neglects mass transfer in the liquid-phase and. any e!ects due to reaction. The model is used to simulate some data obtained on a laboratory-scale MTBE column. The solitary numerical example that accompanies the paper concerns the reactive stripping process for the production of Bisphenol-A. The model di!ers from that described above only in that the phases are assumed to be in thermal equilibrium with each other. the results used to demonstrate multiple steady-states. Baur et al. SS-1. and that the DAA selectivity would have improved if the liquid}catalyst mass transfer improved. can be realised in the column. Since reaction rates and chemical equilibrium constants are dependent on the local concentrations and temperature. the #ooding boundaries are drawn in Fig. The other solutions SS-2 and SS-3 could not be realised in the NEQ because for the higher vapor #ows.4. However. (1999) also show that if the column diameter was chosen to be 3 m. The authors were able to "t their own experimental data quite well. 24(c). It is reported that the amount of catalyst and the condensation rate are important design variables for this RD process. only one solution. Taylor. A predicted temperature pro"le appears to be in good agreement with one determined experimentally.7 m diameter column con"guration. The recent study of Baur et al. SS-2 (intermediate conversion) and SS-3 (low conversion) were found. (1999) comparing the EQ and NEQ models for hydration of ethylene oxide to ethylene glycol throws a new light on the phenomena on MSS and the importance of using the NEQ model. Podrebarac et al. with some axial dispersion due to the vapor jets and bubbles. The model equations were solved simultaneously. Three steadystates SS-1 (high conversion). 24(a)). Let us now consider the NEQ model simulations for the 1. The desired high-conversion steady-state solution (SS-1) corresponds to high column temperatures and lowest molar #ow rate of the vapor up the column. (a) Con"guration of reactive distillation column for hydration of ethylene oxide to ethylene glycol used by Ciric and Miao (1994). . to the random nature of the #ow in a packed column. The froth will pass through the liquid more or less in plug-#ow. R. For the Ciric and Gu (1994) con"guration for the ethylene glycol column (see Fig. NEQ cell model An issue that is not adequately addressed by most NEQ models is that of vapor and liquid #ow patterns on distillation trays or maldistribution in packed columns. the column #oods in some (SS-2) or all (SS-3) of the stages. In packed sections. they may vary along the #ow path of liquid on a tray. 24. On distillation trays. Details of the simulations are available in Baur. multiple steady-states are found with both EQ and NEQ models. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 coe$cients being estimated using the correlations of Onda. (1998b) modelled the reactive section as a plug-#ow reactor with radial dispersion. temperature and vapor-phase molar #ow. maldistribution of internal vapor and liquid #ows Fig. (b) Equilibrium model calculations for the ethylene glycol process showing column pro"les for liquid-phase mole fraction. (c) Non-equilibrium model calculations for the ethylene glycol process for a column of diameter 1.7 m showing the corresponding column pro"les.5212 R. The set of di!erential and algebraic equations was solved using the gPROMS system. However. it was claimed. it must be remembered that the all important mass transfer coe$cients were "tted to data obtained in their own column. or from side to side of a packed column. only the lowest conversion steady-state can be realised! 5. the model could not be used for predictive purposes due. Taylor and Krishna (1999). Thus. Takeuchi and Okumoto (1968). the true predictive abilities of their model are untested. Higler. as well as a proper description of mass transfer. vapor will rise in plug-#ow through a layer of froth. For such systems the residence time distribution could be very important. For this chosen column diameter. This may be derived from calculating an equivalent number of cells from eddy di!usion models.R. Mass transfer resistances are located in "lms near the vapor/liquid and liquid/solid interfaces. (1999) of the in#uence of hardware design on the formation of the by-product DEG in the hydration column (sieve tray) shown in Fig. 23. Various #ow patterns may be approximated using di!erent #ow splitting policies. 25. Backmixing may also be taken into account by using an appropriate number of cells. The distinguishing feature of this model is that stages are divided into a number of contacting cells. Increasing the weir height from 80 to 100 mm leads to improved conversion and improved selectivity.e. Flow patterns in packed columns are evaluated by means of a natural #ow model. To deal with this shortcoming of earlier models. Flow patterns on distillation trays are modelled by choosing an appropriate number of cells in each #ow direction. For RD. Pseudo-homogeneous vs. 28. Decreasing the weir height from 80 mm (base case) to 50 mm decreases formation of EG and increases by-product DEG formation. Each cell is modelled essentially using the NEQ model for heterogeneous systems described above. 26. heterogeneous NEQ modelling Higler. This is because the liquid load per weir length is reduced by 50%. A schematic diagram of the unit cell for a vapor} liquid}porous catalyst system is shown in Fig. Krishna and Taylor (1999a. The #ows are split up according to the ratio of the cell surface areas between the cells. High weir heights. are generally to be preferred in RD operations. which has a detrimental in#uence on both the conversion and selectivity. This is known to be one of the main reasons for inadequate performance of packed columns. A column of cells can model plug-#ow in the vapor phase. Their simulation results are presented in Fig. This is emphasised in the study by Baur et al. Removing the mass transfer resistances. 27. Reaction selectivity can be in#uenced by tray hardware design. 24(a). the staging in the liquid-phase could have a signi"cant in#uence on the reaction selectivity. and by choosing an appropriate connection pattern.5. These cells describe just a small section of the tray or packing. see the top point in Fig.b) developed an NEQ cell model. the formation of by-product DEG is reduced while the conversion to EG is increased. one can very easily study the in#uence of #ow patterns and maldistribution on the distillation process. R. and operation in the froth regime. and the Maxwell}Stefan equations are used for calculation of the mass transfer rates through each "lm. Increasing the number of passes from 1 to 2 increases by-product formation. The equations for each cell are essentially as given above. This reduction is due to a lowering in the interfacial area with decreasing weir height. It appears that the usual design rules for conventional distillation column design cannot be carried over to RD columns because. The non-equilibrium cell model of Higler. assuming the EQ model. see the point towards the bottom right of Fig. Krishna and Taylor (2000) used the dusty #uid equations to model di!usion and reaction in porous catalysts in RD. for a column of 1. 28. 28. 5. over the cross-sectional area of the column can lead to loss of interfacial area. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5213 Fig. Krishna and Taylor (1999a). gives the best performance with respect to conversion and selectivity. 25. The bulk of both vapor and liquid-phases is assumed to be completely mixed. as shown in Fig. For "ve mixing cells in both vapor and liquid-phases (which corresponds closely to plug-#ow conditions for either phase). This reduction in the liquid load leads to a reduction in the clear liquid height and lowering in the total interfacial area. Taylor. i. Mass transfer inside the porous catalyst may be described with the dusty #uid model described above. and multiple columns of cells can model plug-#ow in the liquid-phase as depicted in Fig. Higler. Thermodynamic equilibrium is assumed only at the vapor}liquid interface.7 m diameter the conventional design philosophy would be to use two passes for the liquid #ow. The unit cell for homogeneous systems (and for heterogeneous systems modelled as though they were homogeneous) is as depicted in Fig. Taylor and Krishna (1999c) and Higler. The MTBE process (following the con"guration of Jacobs and Krishna (1993) shown in . The value of the Knudsen di!usion coe$cient is assumed to be the same for all components. 1998). neglects the hold-up in the vapor-phase.5214 R. Their paper addresses the problems of modelling mass transfer and reaction in a vapor}liquid}porous catalyst system. in which the catalyst is neglected and the reaction rate is evaluated at liquid bulk conditions. Fig. In addition. Taylor. The multiple steady-state region has disappeared for the dusty #uid model. as is usual in such models. 20(a)) was simulated under three di!erent sets of assumptions: A A pseudo-homogeneous approach. This is not the case for the TAME process where the reaction rate is very much lower than it is for MTBE and mass transfer in#uences are not signi"cant. in the lower branch of the multiple steady-state region. The non-equilibrium stage (cell) for heterogeneous catalysed reaction.6. This may be explained by the fact that. 27. Additional mass transfer resistances. Multiple steady-states have been found experimentally for an RD column used to produce TAME. B A case in which the Knudsen di!usion coe$cient is large. they . The rate of consumption of MTBE is very much in#uenced by additional mass transfer resistances. Details of #ows in and out of multiple cells used to model the hydrodynamics of trayed columns. appearing to con"rm the results shown in Fig. therefore result in a higher conversion. Gorak. Dynamic NEQ models Kreul. 5. Dittrich and Barton (1998) described an NEQ model for RD in packed columns. 26. and the Knudsen di!usion term has a substantial in#uence on the results of the dusty #uid model simulations. Fig. MTBE is consumed in part of the column. Theirs is a dynamic model that. R. but not in the MTBE process (Rapmund et al. in which case the mass transfer interaction with the catalyst is ignored C A case one in which the Knudsen di!usion coe$cient is a factor "ve times smaller than the smallest of the Maxwell}Stefan di!usion coe$cients. 29. 29 is the steady-state conversion of isobutene as a function of the bottom product #owrate.. Shown in Fig. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 Fig. (B) dusty #uid model without Knudsen contribution.7 m) is that shown in Fig. the model is an extension and generalisation of the dynamic NEQ models of Kooijman and Taylor (1995) for tray columns and Pelkonen. The actual experimental data are not provided in the paper. The material balances (partial di!erential equations) are discretised in the spatial dimension (the column height) using the method of lines. Berrera. 1996). The only di!erences between the models are the inclusion of di!erent submodels for the reaction kinetics and thermodynamic properties. 24(a). Taylor. The MS equations were used to model vapor and liquid-phase mass transfer. Kenig and Gorak (1999) used the Maxwell}Stefan approach to model the dynamics of reactive absorption processes. however. Adapted from Higler. The results shown in the paper suggest that their dynamic model is well able to describe the product composition transients. The model system was implemented and solved using the ABACUS system. describe a two-phase model in which di!usion and reaction to and within the solid catalyst is not accounted for by additional equations (and parameters). Kreul. and (C) dusty #uid model with Knudsen contribution. The model equations were solved using the equationbased modelling environment ABACUS (Allgor. 28. 29. Strictly speaking. The agreement between the predicted and measured compositions is exceptionally good. Krishna and Taylor (2000). Of particular interest in their model is the inclusion of the gradient of the electrical potential in the Maxwell}Stefan equations and the electro-neutrality equation that must be satis"ed at all points in the liquid due to the presence of ions in the processes they model. Higler.R. includes a limited comparison with some unsteady-state data for a methyl acetate column. Taylor and Krishna (1999). but their effects are lumped into a kinetic term that appears in the liquid-phase material balances. taken into account. Comparison of the results for conversion of iso-butene obtained by three di!erent model formulations for taking account of chemical reactions: (A) pseudo-homogeneous. Under the conditions in the experiments there was essentially no liquid-phase chemical reaction. The paper by Kreul et al. Kooijman and Taylor (1997) for packed columns. Wittig and Gorak (1996) and by Kenig and Gorak (1997) involves nine di!erent reactions and simultaneous transport and reaction of 10 di!erent species. Fig. Barton & Evans. The choice of which of these two approaches was adopted for their simulations is not completely clear. However. Gorak. Le Lann and . vapor-phase dimerisation was. Gorak and Barton (1999b) described an NEQ model to study batch distillation. Meyer. In essence. reactive absorption falls outside the scope of this review. Schneider. The paper includes extensive comparisons of true model predictions of experiments performed in a pilot plant column involving the system methanol}acetic acid} methyl acetate}water. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5215 Fig. R. The column con"guration (diameter"1. Rascol. Details of the simulations are available in Baur. A nitric acid recovery plant modelled by Wiesner. In#uence of tray hardware and number of mixing cells on the formation of by-product DEG in the hydration of ethylene oxide to ethylene glycol (EG). NEQ models as outlined above apply more or less unchanged in principle to reactive absorption and RD alike. as shown in Fig. and non-zero stoichiometric sum reactions. It is pertinent to note that the overall methodology and some important results (e. heat e!ects. 1995) and Doherty and Buzad (1994) provide a further extension in order to handle kinetically controlled reactions in three-component systems. for example. Aguirre and Perez (1995a. 1994). then the resulting column is feasible. Most of the methods cited above are based on an assumption that the reaction takes place on all stages in the column. To determine a feasible design the equations are integrated numerically starting with the desired product composition. Ung and Doherty (1995e) consider RD processes involving multiple reactions. Buzad. as discussed below. for the rectifying section rH#1 1 X "H > ! > (32) GH GH rH G" rH H H and for the stripping section the material balance reads sH 1 X " H > ! X . They develop a systematic method for the design of kinetically controlled staged RD columns while taking into account a single liquid-phase reaction.. Most conceptual design models are based on the EQ stage model described above. Mahajani and Kolah (1996) extended the methods of Doherty and co-workers for packed RD columns. and Doherty. Barbosa and Doherty (1988d) extend their own methodology to double-feed columns. rH" H I H H D( ! y ) B( ! x ) I 2 I" I 2 I (34) 6. and a limited number of papers suggest that NEQ models already have a place in industrial RD design practice. non-ideal phase equilibrium. then no column will produce the desired products (Fig. taking into account heat e!ects. . thereby permitting the energy balances to be solved essentially independent of the remaining stage equations. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 Prevost (1998) brie#y addressed some numerical problems that can be encountered in the simulation of reactive absorption using NEQ models. The method is based on the following assumptions: E E E E E the column is adiabatic. With reference to Fig. If the trajectories intersect. Grievink and Schrans (2000) also relaxed the uniform hold-up assumption by allowing di!erent hold-ups per section of the column (not on each tray). Mahajani (1999b) also addresses the design of RD processes for multicomponent kinetically controlled reactive systems. The Damkohler number de"ned for the entire column is a key parameter in their approach. a stripping section. some recent developments have opened up the possibility of using NEQ models for RD design. Frey and Stichlmair (1999) who proposed a design method for a column with a reactive section. The minimum re#ux can be found from the special case of two trajectories that just touch each other (Fig. 30(b). Altiqi et al. we have. The transformed re#ux and stripping ratios are de"ned Barbosa and Doherty convert these equations to di!erential form. minimum re#ux) are unchanged from the methods for tray columns. Buzad and Doherty (1994. E phase equilibrium is achieved on each stage. the molar heat of vaporisation is constant. However. sH" I 2 IH . (3). We have already noted the success (using e!ective di!usivities and enhancement factor approaches to mass transfer with reaction) of NEQ models of amine-based gas treating processes (Carey et al.b). The latter issue was revisited by Espinosa. The design of RD columns in which the feed stream contains species that do not react at all was addressed by Espinosa. E the feed is a saturated liquid. 30(a). A number of extensions of the approach of Barbosa and Doherty (1988c) have appeared in the literature. The "xed-point method uses material balance equations written around a stage in each section of the column (above and below the feed stage) and the corresponding end of the column. 1991. the heat of reaction is negligible compared to the enthalpy of the vapor. 30(c)). calling for very di!erent approaches. Aguirre. the heat of mixing is negligible. if the trajectories fail to intersect.. sensible heat e!ects can be ignored. R. as follows: ¸( ! x ) <( ! y ) 2 IH .1.5216 R. Okasinski and Doherty (1998) relax some of the assumptions underlying the methods of Barbosa. and two rectifying sections. E the column operates with a partial condenser. Aguirre and Perez (1996) described a method of dealing with columns in which the reaction takes place only in a central portion of the column. Espinosa. An assumption in their method is that liquid-phase backmixing is totally absent. 6. Reactive distillation design Design and simulation of RD operations are very di!erent types of calculation. and a range of liquid-phase hold-ups on the di!erent stages. Taylor. 30(d)). They illustrate their design procedure for a quaternary system shown in Fig. These assumptions ensure that the vapor and liquid #ows inside the column are constant.g. Conceptual design Barbosa and Doherty (1988c) developed the "xedpoint method for the design of single-feed RD columns. Melles. 18(a). (33) GH> sH#1 GH sH#1 G H H Note that these equations have been written in terms of the transformed composition variables de"ned by Eq. hold-up. and temperature. McGregor. The direction of these combined vectors indicates the feasibility of a particular process. ). Once again. and reaction. More interestingly. Malone and Doherty (1997) apply the attainable region approach in order to develop a systematic approach to identifying the feasible compositions that can be obtained in RD processes. sep. 0"mix#sep#rx. 1998. also. [S] is matrix of component speci"c mass transfer rates. Feinberg. Hauan. but still nullify each other. rx"R( !x sep"[S](x!y). 1999a). Column pro"les in RD design (Doherty method). A kinetic "xed point (azeotrope) arises when all three vectors have non-zero magnitudes. separation. Within this framework the change in the composition of any particular phase is given by the vector equation dx "mix#sep#rx dt (35) where M is a scalar equal to the relative amounts of material being mixed. sep. The attainable region approach to reactor network feasibility is based on geometric properties and has been studied in depth mainly by Glasser. 1998. If the phases are assumed to be in equilibrium then [S] reduces to a simple scalar. their length is a measure of the process e$ciency. (36) (37) (38) When the reaction and separation vectors have zero magnitude then the "xed point is an equilibrium point. Feinberg & Hildebrandt. 1997. Hauan et al. and mix. 30.R. respectively. (39) where x is the composition of the phase in question. Hauan & Lien. Glasser & Hildebrandt (1997) and Nisoli. so far unexplored. R. Taylor. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 5217 Fig. for example. Mahajani. this formulation admits the possibility. For these vectors Hauan et al. (2000b) write mix"M(xF!x). Hildebrandt. 1996. 1999). of using a properly formulated model of mass transfer in multicomponent systems as discussed above. and R is a scalar that depends on such things as catalyst activity. Hauan and co-workers (see Hauan. Hauan and Lien (1998) illustrated their methodology with an analysis of the MTBE process. The location of these kinetic "xed points has a direct in#uence on the product compositions that can be realised in an RD column (see. Westerberg & Lien. 1997. and rx vectors nullify each other. Glasser & Hildebrandt. (2000b) have provided a comprehensive analysis of the kinds of "xed point that can arise from cancellation of di!erent combinations of these vectors. They also introduce the reaction di!erence point as the . 2000b) have developed what they call a phenomena-based method for the analysis and design of reactive separation processes. A "xed point exists when the mix. and rx are vectors that represent the composition changes due to mixing. x is the current composition and xF is the feed composition. the Damkohler number emerges as the important parameter. and their co-workers (see. 1999. reaction and separation. An important paper by Subawalla and Fair (1999) addresses this issue with a lengthy discussion of the importance of several key design parameters: pressure. b. Their paper was illustrated by considering the liquid-phase hydrogenation of nitrobenzene to aniline. Danilov & Sera"mov. Pisarenko & Kulov. 1999) have developed a phenomena-based modelling framework that is able to capture hybrid reactive/separation processes. As a result of this assumption the composition change caused by the reaction is small on each stage and can be neglected.. 6. The MTBE process is used to illustrate their method. 1996. Scenna and Perez (1993). Sera"mov. The in#uence of inerts can also be considered with this approach. Hauan. Pisarenko. Duprat. Schembecker and Simmrock (1997a. Graphical design methods A graphical (Ponchon}Savarit type) design procedure for RD columns based on the transformed composition variables of Barbosa & Doherty (1988) is described by Espinosa. Patlasov & Sera"mov. They devise a method for identifying RD processes in which the RD column needs to be divided into reactive and non-reactive sections.b) and Lee et al. extent of reaction. In this context a module does not necessarily represent a single model stage. Schembecker and Sundmacher (1998) use these RD line diagrams to identify the main process parameters and to provide a basis for an experimental study in the methyl acetate process. ethylene glycol. The method requires very little fundamental data on the system and is based on an assumption that the vapor and liquid #ow rates in the column are very large. 1999a) have developed a method they call static analysis. a procedure to go from a viable EQ stage design to an actual column design was not available in the literature. Papalexandri and Pistikopolous (1996) illustrate their methodology with the design of an ethylene glycol column. 6. (1999) considered the production of ethyl acetate from acetic acid and ethanol. Eldarsi and Douglas (1998b) used the optimisation capability in Aspen Plus to optimise an MTBE column. The most accessible work from this group is the paper by Giessler et al. Design via optimisation methods RD design via optimisation methods has been the subject of a few studies.. The use of these di!erence points in RD process design is the subject of two recent papers by Hauan. and number of stages need not be "xed a priori. (1999) applied the method to "ve other RD processes: the production of acetic acid. Giessler et al. Pisarenko et al. reactant feed ratio. Either EQ or NEQ stage models could be used in this approach.5218 R. Ohligschlager. (1998) who outline the steps of the method and illustrate it with a case study of the MTBE process. feed rates and re#ux ratios at a minimal annual cost. Pistikopolous and co-workers (see Papalexandri & Pistikopolous. 6. From conceptual design to column design Until recently. Giessler et al. 1997. reactive zone location. Lee. It is the result of an extensive investigation of the thermodynamic and topological structure of distillation diagrams. or only separation. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 di!erence between an arbitrary composition and a singular point. Westerberg and Lien (2000a) and by Lee. 1998. and butyl acetate. Bessling. feed . Pistikopolous & Papalexandri. in which the resulting aniline}nitrobenzene}water system can split into two liquid-phases. 1988a. Sera"mov et al. 1995. the cost of the butylenes. Pisarenko & Sera"mov. Taylor. 1980. cumene.2. Loning. However. Ismail. Their study indicated that the market price of the MTBE product. but a collection of such stages. Ciric. while Ismail et al.. Ciric and Gu (1994) formulated a mixed integer nonlinear programming model. Lien and Westerberg (2000c). 1988. To the best of our knowledge this was the "rst paper that combines RD column design and cost estimation. Sera"mov and co-workers (Balashov & Sera"mov. Bessling. Lien and Westerberg (2000a. The signi"cant in#uence of the re#ux ratio on conversion is shown by simulation using an EQ stage model and by experiments in a small-scale column that employed packing in the form of Raschig rings. (2000d) have recently presented an in-depth analysis of the classical Ponchon-Savarit and McCabe}Thiele graphical methods for RD systems. The latter method leads to the most rapid optimisation calculations once the empirical formulae have been constructed (by "tting the results of rigorous model simulations). Pekkanen (1995b) described a local optimisation method for the design of RD. Hauan.4. thereby emphasizing the fact that the usual optimisation techniques for ordinary distillation processes may be inappropriate for RD.b) combine heuristic rules. and RD line diagrams to study the feasibility of RD processes.3. In their approach an RD process (here meaning more than just a single RD column) is synthesised from a collection of modules that involve reaction. the di!erences between RD processes means that the formulae developed for one process have no value for modelling others. the isobutylene composition and utility costs all in#uence the MTBE column pro"t. 1981. Balashov. The number of phases and the phase equilibria were determined by minimising the Gibbs free energy. R. Gassend & Gau (1988) constructed a set of empirical formulae that was used to optimise an RD process for the separation of the close-boiling mixture of 3-picoline and 4-picoline. Gumus and Ciric (1997) used a bilevel optimisation procedure to explore the design of RD columns that could have more than one liquid-phase. The desired product compositions. 1999b. numerical computation. solution of which yields the optimal number of EQ stages. 1992. 1996. ethyl or methyl acetate. 4. R. 3. Estimate the catalyst volume from the catalyst mass and maximum packing catalyst density: m < " Determine the reactive zone height from the calculated catalyst volume and estimated diameter. Specify the distillate and bottom product compositions and determine minimum re#ux requirements using the Underwood method. < h " ( )d . 5219 Assume that the column feed stream consists of a prereacted mixture of products and reactants at a desired conversion. re#ux ratio. and column diameter (from: Subawalla and Fair. 1999) 1. Taylor. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 Table 1 Procedure to estimate the reactive zone height. Estimate the diameter form the maximum allowable vapor velocity (80% of #ood velocity). 2. Use a re#ux ratio 20% greater than the minimum re#ux ratio as an initial estimate to determine column vapor and liquid velocities.R. the data are provided in such a way as to render them unusable in independent modelling studies. reactive zone height. 7. If the conversion decreases. At the end of their paper the authors recommend using NEQ or rate-based models for this purpose. DeGarmo. Go to step 10. (1990) reported that stage-to-stage hand calculations were done using #ash and reaction programs to calculate the vapor and liquid compositions in the reactive section. 6. and stripping stages. Determine the number of reactive stages by dividing the total reactive zone height by the catalytic packing HETP.5. go to step 9. Their paper includes a case study in which their design procedure is applied to the production of TAME.e. re#ux ratio. 8. Computer programs to model a complete RD column had to be developed in-house at the same time as pilot plant work was being carried out. Increase the re#ux ratio by 10%. then we have reliable estimates for the reactive zone height. Limited comparisons with pilot-plant data look quite good. reaction. Simulate a reactive column with the calculated number of recti"cation. Marker and Luebke (1992) used the NEQ model RATEFRAC to model MTBE and TAME processes in columns "lled with Koch KataMax packing. Pinjala and DeGarmo (1993) have reported that RATEFRAC has been used to accurately predict the performance of commercial RD processes in Germany and Texas. Concluding remarks Belck (1955) concludes his paper describing a hand calculation method for RD columns with the following words: 2as the complexity of the system increases. If the conversion decreases with increasing re#ux. number of equilibrium stages. The conventional distillation column sections were modelled using an existing EQ model simulation program. Very little information on the form of the model is provided (i. and that the model has been validated for the design of TAME. If the desired conversion is not attained. 9. Pinjala. ETBE. Agreda et al. 10. and repeat steps 4}7. calculate a new maximum vapor velocity and column diameter. The authors make the important point that their procedure is not applicable to all RD processes: èach system has certain characteristics that make the use of one or more of these guidelines di$culta. Frey. catalyst mass. 7. and HETP. re#ux ratio and column diameter. Keep increasing the re#ux ratio in 10% increments and repeating steps 4}7 (if necessary) until there is no charge in conversion. location. the calculation becomes increasingly di$cult 2 the uncertainty inherent in the experimental determination of reaction rate constants and liquid}vapor diagrams . However. calculate the new maximum vapor velocity and column diameter and repeat steps 4}7. column diameter. decrease the re#ux ratio by 10%. 6. how the reaction is brought into the model. Their detailed step-by-step procedure for designing an RD column is summarised in Table 1. Ulowetz. and TAEE units with data from semi-commercial operations. Ozmen. Step 7 in Table 1 should be singled out for particular attention as the one that relies on the models discussed in this article. If the desired conversion is attained. increase the catalyst mass and repeat the procedure starting with step 3. the actual kinetic expressions are left to the imagination. Keep decreasing the re#ux ratio in 10% increments and repeating steps 4}7 (if necessary) until there is no change in conversion. h N " HETP 5. Go to step 10. If the conversion increases. RD design in industrial practice At the time the Eastman methyl acetate process was developed there were no commercially available simulation programs capable of modelling RD operations. Hamm. it is essential to adopt the NEQ model. There remains more than a grain of truth to these remarks even today. Taylor. Besides more research on hydrodynamics and mass transfer. Each model has its place in the process development cycle. 2000. when the computer. this is opposite to the design wisdom normally adopted for conventional distillation. Too often measurements are con"ned to feed and product stream conditions. Higler. Krishna.. Liquid residence time and residence time distributions are more important in RD. Pseudohomogeneous reaction models may be inadequate for fast reactions. Though sophisticated NEQ design models are available already. such information has vital consequences for the conversion and selectivity of RD columns. Column hardware choice can have a signi"cant in#uence on the conversion and selectivity. parameters need to be measured along the height of RD columns. The froth regime is to be preferred to the spray regime for RD applications. Higler & Taylor. detailed information on the hydrodynamics and mass transfer parameters for the various hardware con"gurations sketched in Figs. However. 13. design and optimisation of RD columns. which are taken into account in the NEQ model. which would make its mark in chemical engineering soon after these words were written. There is a crying need for research in this area. EQ models have their place for preliminary designs. et al. analysis. R. Residue curve maps are invaluable for initial screening and #owsheet development. It is perhaps worth noting here that modern tools of computational #uid dynamics could be invaluable in developing better insights into hydrodynamics and mass transfer in RD columns (Van Baten & Krishna. is woefully lacking in the open literature. It is insu$ciently realised in the literature that say for tray RD columns.5220 R. RD columns using dumped (random) packings are susceptible to maldistribution and there is a case to be made for choosing regular structured packings such as that shown in Fig. Van Baten. For relatively fast reactions.. 1999). 1999a. A. the tray design can be deliberately chosen to improve conversion and selectivity. it is possible that not all of the steadystates can be realised in practice due to hydraulic aspects. For proper description of the column dynamics. recent NEQ modelling works have exposed the limitations of EQ models for "nal design and for the development of control strategies. Whether or not the experimental work and calculation time * for a detailed computation of such a process in a system with four or more components * can be justi"ed or not will then ultimately depend upon the economic importance of the products. There are a variety of models now available in the literature for screening. 10}16. Paradoxically. Notation a B B c c R D Da D G nC G n GI E G E $ E+4 G h . Even less appreciated is the fact that the design methodology for RD tray columns is fundamentally di!erent from that of conventional trays. there is need for more experimental work with the express purpose of model validation. NEQ models have been used for commercial RD plant design and simulation. Ellenberger. Though the phenomena of MSS has received considerable attention in the literature. Krishna / Chemical Engineering Science 55 (2000) 5183}5229 also tends to make the value of such calculations questionable. Such data cannot serve as a reliable discriminant of computer-based process models. it is essential to properly model intra-particle di!usion e!ects. has largely rendered moot the issue of computational cost. such aspects can be properly described only by the NEQ cell model.P. In such process studies. m number of components. mol m\ s\ . dimensionless ratio of side stream #ow to interstage #ow on stage j. J mol\ pseudo-"rst-order reaction rate constant. mol s\ permeability. m s\ e!ective Knudsen di!usivity in porous catalyst. mol s\ interchange liquid #ow rate between horizontal rows of cells. s\ vapor}liquid equilibrium constant. dimensionless transformed re#ux ratio. dimensionless reaction rate. mol s\ molar #ux of species i. dimensionless energy #ux. m heat transfer coe$cient. mol s\ liquid feedstream. mol sU Damkohler number. mol m\ distillate #ow. dimensionless total concentration. dimensionless e!ective Fick di!usivity. Pa heat duty. mol s\ weir height. dimensionless liquid #ow rate. mol s\ component feed stream. J s\ overall Murphree tray e$ciency. m s\ enhancement factor. m sU Maxwell}Stefan di!usivity. m bottoms #ow. dimensionless clear liquid height. mol m\ s\ Mass transfer rate. J s\ number of reactions. W m\ energy transfer rate. m vapor feedstream. mol s\ stage pressure. W m\ K\ molar enthalpy. F4 F* f h U h H k K ¸ ¸ + N G p H Q r r H rH H R KH interfacial area. M. V. mol vapor #owrate. Agreda. The application of a minimization method for solving reactive distillation problems.R. J. 313}323. 75}80). mol s\ time. 885}896. & Douglas.. & Evans. Analysis of chemical-reaction course in distillation column. Spain (pp. dimensionless thermodynamic correction factor for binary mixture. 73. Alejski.. Partin. Rigorous simulation of multicomponent multisequence batch reactive distillation.. dimensionless MeOH MeOAc AcOH HETP HTU MS MSS MTBE NEQ RD SRK TAME methanol methyl acetate acetic acid height of a theoretical plate height of a transfer unit Maxwell}Stefan multiple steady-states methyl tert-butyl ether non-equilibrium reactive distillation Soave}Redlich}Kwong tertiary amyl ether Acknowledgements RT and RK would like to express their appreciation to Arnoud Higler and Richard Baur for their considerable assistance in the preparation of this paper. Comparison of selected methods of reacting distillation column computing.. Taylor. 51. Berrera. 565}584. Alejski.. & Bogacki. I. J. J. 40}46. (1988). Joulia. (1991).. RT's research in RD was partially supported by BP-Amoco Chemicals.. 9. m activity coe$cient of species i. Allgor. dimensionless G [ ] References Abufares. Alejski. dimensionless transformed vapor-phase mole fraction. Inzynieria Chemiczna i Procesowa. 55}73. Mathematical modeling and simulation of an MTBE catalytic distillation process using SPEEDUP and AspenPlus. Computers and Chemical Engineering.. J. 12. 833}839. Subscripts e! i I j k m t e!ective component index referring to interface stage index alternative component index reaction index total Superscripts F ¸ < referring to feed stream referring to liquid-phase referring to vapor-phase List of abbreviations DAE DEG EG EQ EO di!erential-algebraic equations diethylene glycol ethylene glycol equilibrium ethylene oxide . J. B. B. mol s\ weir length. Le Lann. Alejski. Transactions of the Institution on Chemical Engineers Part A. dimensionless mass transfer coe$cient.. 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