Ind. Eng. Chem. Res. 2000, 39, 3953-3957
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COMMENTARIES Reactive Distillation
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Introduction Combining reaction and distillation is an old idea that has received renewed attention in recent years. Figure 1shows the rate of growth in the literature and patents (U.S. only). [Ten years ago it was possible to write a brief paper that included most of the known literature on reactive distillation. This is no longer possible because several hundreds of papers have been published in recent years. These are not cited here in the interest of brevity but have been recently reviewed.1] Reactive or catalytic distillation has captured the imagination of many recently because of the demonstrated potential for capital productivity improvements (from enhanced overall rates, by overcoming very low reaction equilibrium constants and by avoiding or eliminating difficult separations), selectivity improvements (which reduce excess raw materials use and byproduct formation), reduced energy use, and the reduction or elimination of solvents. Some of these advantages are realized by using reaction to improve separation, e.g., overcoming azeotropes or reacting away contaminants; others are realized by using separation to improve reactions, e.g., overcoming reaction equilibrium limitations, improving selectivity, or removing catalyst poisons. The potential is greatest when both aspects are important. [Similar progress has been made in other reaction-separation technologies, such as simulated moving bed reactors, reactive membranes, reactive crystallization, etc., and several interesting applications have been commercialized. In our view we can look forward to rapid progress in this technology sector over the next 5 years. In fact, this will be essential in some areas to meet increased productivity and environmental objectives.] Classic success stories in reactive distillation are the Eastman Chemical Co.’s methyl acetate reactive distillation process and processes for the synthesis of fuel ethers. Some of the improvements are so dramatic, 5 times lower investment and 5 times lower energy use for the Eastman process,2 that we might ask if all chemical processes should be based on simultaneous reaction and separation instead of more traditional separate steps. The answer is no, because combining reaction and distillation is not always advantageous; in some cases it may not even be feasible! A key question is, “How can we decide quickly whether reactive distillation is a good process concept?” This question is addressed mainly by studies in conceptual design, which is the major focus of this commentary. We also describe briefly how this fits into a larger scheme for the development of reactive distillation, because there is significant activity and progress on those related issues. The appropriate starting point is the treatment of feasibility and identification of the minimal data requirements for a reliable answer. Progress in the * To whom correspondence should be addressed. Telephone: (413) 545-0838. Fax: (413) 545-1133. E-mail:
[email protected].
Figure 1. Publications or U.S. patents including reactive or catalytic distillation. A total of 562 publications for the period of 1970-1999, as listed in the Engineering Index; May 2000. A total of 571 U.S. patents for the period of 1971-2000 (through June 26, 2000).
understanding of distillation systems using geometric methods, particularly for nonideal and azeotropic mixtures without reactions, provides a basis for developing conceptual designs rapidly. The goal of separation system synthesis is to discover the best way to separate a mixture subject to the process objectives and constraints. In academia this is often translated into finding the globally optimal separation system over all structural (process devices and their interconnections) and continuous (design variables) variations. Industry usually has the more modest objective of finding a process system that gives a significant competitive edge in the current marketplace and using this to develop a world-class process. Part of the separation system synthesis is combinatorial. For example, an ideal mixture of three components can be separated in either of two simple alternatives, lightest first or heaviest first. With more components to separate, the number of alternative sequences grows quickly into the hundreds of thousands. Recent work provides novel new and more operable complex column configurations with significant improvements in efficiency.3 Naturally, the combinatorial aspect of the problem has led to many optimization-based approaches for distillation system design, which have been studied extensively for ideal mixtures. Nonideal and azeotropic mixtures require more than a solution for the combinatorial aspects of the problem. A feasibility analysis is equally important; fortunately, new methods and tools are available. An effective geometric method uses the residue curve map (RCM) or the closely related “distillation path” diagram. These represent the composition profiles at total reflux in packed or staged columns, respectively. For example, consider a ternary mixture of components A, B, and C
10.1021/ie000633m CCC: $19.00 © 2000 American Chemical Society Published on Web 09/08/2000
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in order of increasing boiling point. Suppose that each binary pair has a minimum boiling azeotrope and that there is also a ternary azeotrope which boils lower than any other point in the mixture. (There are many examples of this sort of behavior.) The RCM feasibility analysis shows that for such a mixture it is possible to obtain pure A, pure B, or pure C (depending on the composition of the feed) but that they can be obtained only as a bottoms product! While this is no surprise for component C, it is neither an expected nor intuitive result for components A or B. Thus, alternatives such as removing A overhead in the first column are impossible. Furthermore, other alternatives that are impossible for ideal mixtures, such as removing A as a bottoms product, are feasible. Using column pinch tracking methods, it has been possible to extend these methods to finite reflux feasibility. Counterintuitive behavior is also found in reactive distillations. For example, in catalytic distillation for methyl tert-butyl ether (MTBE) production, the ether product can be collected as either a distillate or a bottoms product, depending on the feed composition. Understanding and classifying such effects is a key for feasibility analysis in reactive distillation. Fortunately, the RCM and related methods developed for azeotropic distillation are also useful as an element of understanding systems with chemical reactions. A major criticism of geometric methods such as the RCM is their graphical nature, which led to the impression that the methods are restricted to ternary mixtures. However, recent generalizations of the ideas to higher dimensions eliminate this concern. Mixtures with an arbitrary number of components are treated using algorithmic methods combined with techniques from linear algebra.6,7 These approaches have been demonstrated on mixtures with up to six components containing many azeotropes, and there is no inherent limitation on using them for mixtures with even more components, except for the existence of reliable physical properties information. Once alternative feasible splits have been identified, they must be organized in some systematic way and then evaluated. Two common representations are the state task network (STN) and superstructure methods,8,9 often solved by mathematical programming approaches. Computer-aided design and optimization among alternatives is fairly mature for separation systems, with several academic tools and related commercial implementations now available. All of these rely on a knowledge of feasibility and a technology for generating process alternatives. This is an active area of study for reactive distillation. Reactive Distillation An effective way of decomposing the design and development of reactive distillation involves four stages: (1) feasibility and alternatives, (2) conceptual design and evaluation, (3) equipment selection and hardware design, and (4) operability and control. Step 1: Feasibility and Alternatives. The feasible product compositions from a reactive distillation are determined for a given feed, column pressure, and Damko¨hler number. [This dimensionless number, Da, captures the effects of production rate, liquid holdup, and catalyst concentration in a ratio of characteristic times.10 Da , 1 corresponds to little or no extent of reaction, while Da . 1 approaches chemical reaction equilibrium. More dimensionless numbers relevant to reactive distillation are discussed by Sundmacher et
al.11] It is often possible to vary these quantities parametrically to enlarge the design space. In this step, knowledge of the basic process chemistry and the phase equilibrium is vital, and feasibility studies often suggest experiments. Feasibility analysis in reactive distillation must incorporate all of the features for ideal and azeotropic mixtures, as well as new phenomena caused by the introduction of chemical reactions. One of the most famous applications of reactive distillation technology is the Eastman methyl acetate process.12 This process is a radical departure from traditional technology that had been a genuine economic success for over 15 years. One hybrid reactive distillation device replaced an entire flowsheet consisting of 11 major units plus all of their heat exchangers, control systems, pumps, intermediate storage tanks, etc. Similar successes have been achieved by other companies making other products, but they have often chosen to keep the technology a trade secret. The main reason that the old technology to make methyl acetate was so complicated and expensive is the existence of azeotropes in the reactor effluent mixture, consisting of acetic acid + methanol (both unreacted reactants due to the reaction equilibrium limitation) and methyl acetate + water (both products). The azeotrope between methyl acetate and water is of vital concern because this must be broken in order to obtain pure products. However, in reactive distillation this azeotrope disappears because it reacts into a four-component mixture, thereby “destroying” the azeotrope. This is an enormous benefit of carrying out reaction simultaneously with distillation that cannot be achieved by carrying out these steps sequentially. Other benefits also occur, as described by ref 2. This is not the complete story for feasibility. Surprisingly, reaction can induce the formation of azeotropes that were not there to begin with! This phenomenon has now been well-documented from theory, models, and experiments13 and adds a major new consideration to feasibility analysis in reactive distillation. Such “reactive azeotropes” pose the same difficulties and limitations in reactive distillation that azeotropes pose in traditional nonreactive distillation. In the reaction equilibrium limit, all of the effects can be captured effectively using residue curve maps or their higher dimensional generalizations along with pinch tracking methods that are especially tailored to this case, from which it is possible to devise sequences. Extensions of the approaches developed by refs 6 and 7 could clearly be devised. However, this has not happened because many research groups are correctly focused on a much more important question: “What is the effect of chemical kinetics on feasibility?”14 A comprehensive answer to this question will also provide splits and sequences at the reaction equilibrium limit as well as in the other limit of no reaction. Although it is possible to construct hypothetical systems where nothing unexpected happens in the kinetic regime [for example, an ideal mixture of A, B, C, and D reacts according to the chemistry A + B ) C + D; if C is the lightest component and D is the heaviest, no new reactive azeotropes are introduced; the feasible splits at reaction equilibrium are exactly what we would expect; C is produced as the distillate and D as the bottoms], this is the exception not the norm. On the basis of the results of well-established methods for assessing feasibility in the limit of no reaction and in the limit of equilibrium reaction, we know that the feasible separation systems are generally different in these cases. [This is caused by several effects in isolation
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or combination: (1) The reaction stoichiometry. For example, the reaction A ) B + C cannot have pure A as a feasible product because as A is enriched it will decompose to form B and C. This happens in the MTBE chemistry. (2) The disappearance of azeotropes between two reactants or two products because of chemical reaction. This happens in methyl acetate chemistry. (3) The appearance of reactive azeotropes. This happens in isopropyl acetate chemistry.] Thus, there are one or more transitions in the kinetic regime, and different separation system structures appear for different ranges of the Damko¨hler number. The practical implication is that the feasibility and product purities for a reactive distillation may depend on the production rate, the liquid holdup, and the catalyst concentration. For example, in some applications the desired product purities are not feasible if there is too little catalyst in the column or if there is too much! This means that there can be a finite range of feasibility in terms of the residence time, which can give fundamental upper and lower limits to the production rate. It is vital to have sufficient data and analysis at the conceptual design stage to provide a good estimate of the range of operability before a process alternative is selected for further study. A close approach to reaction equilibrium is achieved for very long residence times (small production rates or large holdups), for very fast reactions (aided by large amounts of catalyst), or both. Normally, it is not desirable to operate commercial devices under these conditions, and so the question of what happens to the feasible splits in the finite rate regime is critical. An open question is, how do we detect the feasible splits in the kinetic regime and keep track of them in a meaningful way that makes constructing sequences easy? Currently, three geometric methods are being pioneered to capture this: bifurcation theoretic methods, difference-point methods, and attainable region methods. Bifurcation theoretic methods are an abstraction of residue curve map feasibility analysis, and these rely on numerical “continuation” methods for solutions. The general properties and calculation methods developed for bifurcation studies in general nonlinear systems are very useful in the application of these methods to distillation with and without chemical reactions. It is clear how higher dimensional problems are treated, though some physical insight is lost in those cases. Difference-point methods are powerful tools with a long history of utility in the analysis and understanding of separation systems. The more problem-specific nature of this approach may lead to more powerful results with further study. Attainable region methods seek to incorporate separations into very powerful geometric approaches for finding all of the feasible compositions from any combination of reaction and mixing. Higher dimensions also provide significant challenges for this approach. At the moment, none of the approaches is completely satisfactory for application to realistic column configurations and for any number of components and reactions. Side reactions and selectivity effects are especially important issues, and these have no counterpart in the sequencing of nonreactive columns. Several parallel efforts in academic research groups, usually in collaboration with industry, are focused on resolving these issues, and new methods should be forthcoming. The process synthesis stage seeks alternatives that deserve more detailed evaluation (rather like the early phases of the architectural stage of a building). Results from the feasibility studies are used to identify and organize alternative column sequences, which generally
include fully reactive columns, nonreactive columns, and/or hybrid columns (both reactive and nonreactive sections in the same device). There should be at least as many alternatives as for nonideal and azeotropic distillation and probably a lot more. Systematic methods are vital. Step 2: Conceptual Design and Evaluation. Conceptual design methods estimate equipment sizes (number of reactive stages, number of nonreactive stages, and column diameter), feed flows and locations, heating and cooling loads, catalyst concentrations, and liquid holdups. This provides the basis for an economic evaluation and ranking of the process alternatives from step 1. Geometric methods based on composition profiles15 have been demonstrated for ternary systems, and difference-point methods16 have been used for binary systems. The further development of these methods would be very useful, but significant further progress seems to require additional technology. One possibility is to rely on mathematical programming to find solutions, either fully or partially optimized. This typically requires great care in model formulation and solution, at least for a general method, because feasibility constraints and model sensitivities can pose major difficulties in model convergence. For example, Ciric and Gu17 used an MINLP approach to find equipment sizes and feed addition policies for ethylene glycol synthesis via reactive distillation. Cardoso et al.18 used a simulated annealing approach for the same application. At the moment, these methods have the upper hand for finding designs of realistic complexity, though they do not provide much insight compared to geometric or difference-point methods. There is much more to say on all of these methods, though much of it is too detailed for this commentary. The combination of an optimization-based approach with insights from the other methods may be the most promising direction for further work. Step 3: Equipment Selection and Hardware Design. The ranking of alternatives in step 2 is used to decide if more detailed studies of one, or perhaps a few, alternative(s) is warranted. The most fruitful approach combines high-fidelity models incorporating hydrodynamics and mass transfer with new hardware designs and tests. The hydrodynamics and masstransfer models demand new data because conditions are frequently outside the bounds of known correlations for distillation design. For example, large liquid holdups and multiphase flow over supported heterogeneous catalysts are major issues.19 Simulation methods have matured significantly in the past decade, and columns of realistic complexity can be simulated, including the effects of tray hydraulics, mass transfer between liquid and vapor and between fluid and solid catalyst, etc.1 An important general observation from these models is that many reactive distillation systems exhibit multiple steady states. Recent studies show that some of the calculated multiple steady states are not found in models that incorporate realistic constraints. However, it is clear that some multiple steady states do occur for chemistries with small heats of reaction (e.g., methyl acetate synthesis), with large heats of reaction (e.g., ethylene glycol synthesis), and with intermediate heats of reaction (e.g., MTBE synthesis). Experiments confirm these predictions for fuel ethers.20 Along with greater detail in modeling, many studies have focused on new hardware designs. This has led to novel new designs for packings and supports to accom-
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modate heterogeneous catalysts, which improve contacting for multiphase reacting mixtures. Step 4: Operability and Control. Operability analysis normally includes multiple simulation steps at increasing levels of detail. A key issue at this step is to check the robustness of the design, i.e., the ability to maintain product purities and conversion in a desired range in the face of disturbances in production rate, feed composition, and other connections to the environment. Process control remains an important issue, and there are two main considerations. The first is to ensure that disturbances in operating parameters do not change the feasible split. This is intimately related to the design choices and the availability of sufficient data on rates of reaction and mass transfer.1 The second is to understand the multiplicity and stability of solutions which have been predicted and, in some cases, measured. Despite progress in modeling, there are few results to guide practical decisions on operating strategies, control system design, instrumentation, etc. For instance, little work has been done to ensure that the right measurements are available to detect this multiplicity and to avoid sending the column to a lower conversion steady state. In fact, only two of the papers in the data from Figure 1 focus on operability or control. Concluding Remarks There are significant opportunities for research and development in reactive distillation. From our viewpoint, the most important unsolved problems are as follows: Experiments. Sometimes the best answer to a design question is to do an experiment; furthermore, sometimes the best way to plan an experiment is to develop a design model. For reactive distillation, some of these experiments must be in support of feasibility studies, e.g., phase and reaction equilibrium, adsorption equilibria for heterogeneous catalysts, reaction rates, and selectivity information. A critical decision at this point is the choice of a rapid and useful batch experiment to support the design development. For instance, batch kinetic studies in closed systems often result in selectivity losses far in excess of those possible with byproduct removal in reactive distillation. A batch reactive distillation is more informative on this aspect, though not preferred for building a database of kinetic parameters. Pilot-scale reactive distillation columns are expensive to construct and maintain. However, with the current state of the art, it is inconceivable that any company would build a new reactive distillation process without a pilot test. This should focus on mass transfer and hydrodynamics. A combination of simulation and experiment design, leading to a small number of pilot tests, is the sensible current approach. A challenge for the future is to develop simpler experimental validation procedures without the need for full-scale pilot plants. Phase Equilibrium. For catalyzed reactions, vaporliquid equilibrium models can be assembled from the constituent binary pair interactions in a way similar to that for nonreactive mixtures. The resulting models seem to give quite good results for esterifiation and etherification reactions, ethylene glycol synthesis, etc. When they do not, it is typically because of a shortage of data and the models can be improved as new information for the individual binary pairs becomes available. However, self-catalyzed reactions such as formaldehyde chemistry, chlorination chemistries, etc., are much more difficult to model because the individual binary pairs cannot be measured separately because the reaction spontaneously occurs. Although significant
progress has been made on vapor-liquid equilibrium models for formaldehyde chemistry in recent years,21 little is known about other self-catalyzed reactions, several of which have a good potential for reactive distillation technology. One promising avenue that could provide a general framework for modeling these kinds of mixtures is the reaction-ensemble Monte Carlo simulation methods.22,23 Reaction Rates and Catalysis. Heterogeneous catalysts give more flexibility for devising hybrid reactive distillation columns at the expense of mass-transfer limitations. A significant advantage can be gained in reactive distillation with catalysts that are more active at the relatively low temperatures where distillation is effective. Many of the reactive distillations currently carried out have relatively long reaction times, on the order of an hour, so that significant gains in productivity with more effective catalysts can be expected. These catalysts should probably be different from those in conventional processes in many cases because the temperatures, pressures, and flow conditions are different. However, that is not the case today, and a fruitful area of research should be the development of catalysts specifically tailored for use in the multiphase conditions inherent in reactive distillations. Along with catalyst development, the influence of side reactions on selectivity, for both homogeneous and catalytic reactions, needs further study. The conditions used in a traditional chemistry and catalyst development effort may promote very different side reactions, or extent of those reactions, from those that will prevail in a reactive distillation. Little is known about experimental protocols to systematically and reliably address this. Equipment Design. For effective mass transfer with heterogeneous catalysts, a number of novel supports have been devised, and numerous patents and technologies are available. It is often unclear which of these is a better choice, and general guidelines would be very useful. These should also address the important issue of catalyst deactivation through fouling or poisoning because regeneration or replacement is significantly more difficult than that in conventional reactors. Hydrodynamics and its interactions with the reaction rate, e.g., getting effective phase disengagement, good mixing and sufficient holdup for the intended extents of reaction, cannot typically be done by modeling alone. Experiments can be done more effectively with some insights from models, but many open questions remain, e.g., how to decide the scale for pilot experiments and how to reliably scale-up the results. Alternatives and Conceptual Design. At the moment, there are relatively few general methods available for generating all feasible alternatives, but some systematic studies are published. This is a very hard problem to solve in the general form stated earlier, and it is reasonable to expect that methods will be slower in coming. A promising approach is the modular representation framework being developed by Pistikopoulos and coworkers.24 This approach combines the feasibility step and the sequencing step in a single algorithmic approach. The idea is to replace column sections with inequalities that feasible sections must obey. This sidesteps the need to specify the many internal design variables for each section (number of stages, liquid and vapor rates, stage holdups, catalyst concentrations, etc.), thereby simplifying the problem formulation at the conceptual design stage. This approach is especially appealing for complex systems, like reactive distillation,
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where so many variables influence the behavior of each column section. A drawback is that the resulting feasible sequences may be difficult to evaluate and rank because relatively little is known about those very design variables! Nevertheless, the methodology has already achieved success by inventing known reactive distillation system structures for methyl acetate production as well as novel structures for the production of ethyl acetate. It is possible to imagine that the geometric feasibility methods could be linked to a synthesis methodology (in a similar way that residue curve maps have been for nonreactive distillations), but so far not much has developed along these lines. Energy management has received surprisingly little systematic study on aspects specifically for reactive distillation, although traditional methods for distillation, heat, and power integration are useful. For exothermic reactions, one might expect to capture the heat released by reaction to drive the separation. This may be possible, but the reaction must take place at temperatures higher than the boiling point of the bottoms product for complete integration. Furthermore, the reaction requirements for cooling or heating may not correspond to the preferred reflux or reboil requirements needed for the separation. Heuristics for the use of reactive distillation would also be useful for the early stages of conceptual design. Some early work does address general guidelines, e.g., Xu et al.,25 and it may be possible to expand these substantially using the methods and tools developed in the past decade. The main question posed at the beginning of this paper (“How can one decide quickly whether reactive distillation is a good process concept?”) is only partly answered. One of the great challenges for this technology is to develop feasibility and synthesis methods that will complete the answer. Acknowledgment We are grateful to J. J. Siirola and colleagues, to R. Taylor, and to B. Bessling for valuable suggestions on the first draft of this commentary. Literature Cited (1) Taylor, R.; Krishna, R. Modelling Reactive Distillation. Chem. Eng. Sci. 2000, 55, in press. (2) Siirola, J. J. An Industrial Perspective on Process Synthesis. In Foundations of Computer-Aided Process Design; Biegler, L. T., Doherty, M. F., Eds.; AIChE Symposium Series 304; AIChE: New York, 1995. (3) Agrawal, R.; Fidkowski, Z. T. More Operable Arrangements of Fully Thermally Coupled Distillation Columns. AIChE J. 1998, 44, 2565. (4) Wahnschafft, O. M.; Koehler, J. W.; Blass, E.; Westerberg, A. W. The Product Composition Regions for Single-Feed Azeotropic Distillation Columns. Ind. Eng. Chem. Res. 1992, 31, 2345. (5) Fidkowski, Z. T.; Doherty, M. F.; Malone, M. F. Feasibility of Separations for Distillation of Nonideal Ternary Mixtures. AIChE J. 1993, 39, 1303.
(6) Safrit, B. T.; Westerberg, A. W. Algorithm for Generating the Distillation Regions for Multicomponent Mixtures. Ind. Eng. Chem. Res. 1997, 36, 1827. (7) Rooks, R. E.; Julka, V.; Doherty, M. F.; Malone, M. F. Structure of Distillation Regions for Multicomponent Azeotropic Mixtures. AIChE J. 1998, 44, 1382. (8) Sargent, R. W. H. A Functional Approach to Process Synthesis and Its Application to Distillation Systems. Comput. Chem. Eng. 1998, 22, 31. (9) Novak, Z.; Kravanja, Z.; Grossmann, I. E. Simultaneous Synthesis of Distillation Sequences in Overall Process Schemes Using an Improved MINLP Approach. Comput. Chem. Eng. 1996, 20, 1425. (10) Damko¨hler, G. Stro¨mungs und Wa¨rmeu¨bergangsprobleme in Chemischer Technik und Forschung. Chem. Ing. Tech. 1939, 12, 469. (11) Sundmacher, K.; Rihko, L. K.; Hoffmann, U. Classification of Reactive Distillation Processes by Dimensionless Numbers. Chem. Eng. Commun. 1994, 127, 151. (12) Agreda, V. H.; Partin, L. R.; Heise, W. H. High-Purity Methyl Acetate via Reactive Distillation. Chem. Eng. Prog. 1990, 86, 40. (13) Song, W.; Huss, R.; Doherty, M. F.; Malone, M. F. Discovery of a Reactive Azeotrope. Nature 1997, 388, 561. (14) Bessling, B.; Loning, J.-M.; Ohligschlager, A.; Schembecker, G.; Sundmacher, K. Investigations on the Synthesis of Methyl Acetate in a Heterogeneous Reactive Distillation Process. Chem. Eng. Technol. 1998, 21, 393. (15) Okasinski, M. J.; Doherty, M. F. Design Method for Kinetically Controlled Staged Reactive Distillation Columns. Ind. Eng. Chem. Res. 1998, 37, 2821. (16) Lee, J. W.; Hauan, S.; Westerberg, A. W. Graphical Methods for Reaction Distribution in a Reactive Distillation Column. AIChE J. 2000, 46, 1218. (17) Ciric, A. R.; Gu, D. Synthesis of nonequilibrium reactive distillation processes by MINLP optimization. AIChE J. 1994, 40, 1479. (18) Cardoso, M. F.; Salcedo, R. L.; de Azevedo, S. F.; Barbosa, D. Optimization of Reactive Distillation Processes with Simulated Annealing. Chem. Eng. Sci. 2000, 55, in press. (19) Moritz, P.; Bessling, B.; Schembecker, G. Fluiddynamische Betrachtung von Katalysatortraegernd bei der Reaktivdistillation (Fluid dynamic Considerations about Catalyst Packing in Reactive Distillation). Chem. Ing. Tech. 1999, 71, 1479. (20) Mohl, K.-D.; Kienle, A.; Gilles, E.-D.; Rapmund, P.; Sundmacher, K.; Hoffmann, U. Steady-State Multiplicities in Reactive Distillation Columns for the Production of Fuel Ethers MTBE and TAME: Theoretical Analysis and Experimental Verification. Chem. Eng. J. 1999, 72, 1029. (21) Albert, M.; Garcia, B. C.; Kreiter, C.; Maurer, G. VaporLiquid and Chemical Equilibria of Formaldehyde-Water Mixtures. AIChE J. 1999, 45, 3019. (22) Lisal, M.; Smith, W. R.; Nezbeda, I. Molecular Simulation of Multicomponent Reaction and Phase Equilibria in MTBE Ternary System. AIChE J. 2000, 46, 866. (23) Johnson, J. K.; Panagiotopoulos, A. Z.; Gubbins, K. Reactive Canonical Monte Carlo. Mol. Phys. 1994, 81, 717. (24) Ismail, S. R.; Pistikopoulos, E. N.; Papalexandri, K. P. Modular Representation Synthesis Framework for Homogeneous Azeotropic Distillation. AIChE J. 1999, 45, 1701. (25) Xu, X.; Zhu, B.; Chen, H. Reactive Distillation. Shiyou Huagong 1985, 14, 480.
Michael F. Malone* and Michael F. Doherty Department of Chemical Engineering University of Massachusetts Amherst, Massachusetts 01003-3110 IE000633M
