Design and Control of Entrainer-Added Reactive Distillation for Fatty

A special case of input multiplicity, in which a set of design specifications can be achieved by an infinite but bounded set of operating conditions, ...
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Design and Control of Entrainer-Added Reactive Distillation for Fatty Ester Production San-Jang Wang*,† and David S. H. Wong‡ Department of Chemical and Material Engineering, Ta Hwa Institute of Technology, Chiunglin, Hsinchu 307, Taiwan, Republic of China, and Department of Chemical Engineering, National Tsing Hua UniVersity, Hsinchu 300, Taiwan, Republic of China

Substantial energy reduction and high-purity isopropyl palmitate can be obtained by using an entrainer-added reactive distillation process. A special case of input multiplicity, in which a set of design specifications can be achieved by an infinite but bounded set of operating conditions, is found. Plantwide dynamics show that entrainer inventory in the reactive distillation column is self-regulatory, provided that the organic phase liquid level is controlled without offset. A simple plantwide control scheme with three temperature control loops, PI decanter level control, and conventional level control in the reboiler will be sufficient to maintain purities of the fatty ester and water products. 1. Introduction 1.1. Motive. Reactive distillation has become one of the extensively researched process intensification methods due to its ability to reduce energy consumption and number of process units. One of the processes that can make effective use of reactive distillation is the production of fatty esters. Fatty esters are important fine chemicals used in the manufacturing of cosmetics, detergents, and surfactants. Batch processes are currently used to produce the esters. A costly posttreatment by distillation is necessary for the reuse of excess alcohol reactant and product purification. However, use of reactive distillation only may not solve the problem. Since the product water forms a low boiling azeotrope with the low molecular weight alcohol, reaction conversion is limited and ester purity obtained is low due to the water reflux along with unreacted alcohol. If an entrainer, such as cyclohexane, is used to break the wateralcohol azeotrope, conversion will be enhanced and subsequent separation will be easy. Recently, Dimian et al.1 demonstrated the effectiveness of the entrainer use in reactive distillation. The main purpose of the study is to investigate the design and control of the entrainer-added reactive distillation process. 1.2. Design and Control of Reactive Distillation. Research on reactive distillation has been comprehensively reviewed by Doherty and Buzad2 and Taylor and Krishna.3 The process exhibits nonlinear characteristics such as multiple steady states and high sensitivity to operating variables due to the coupling between separation and chemical reaction.4-14 Various methods of controlling reactive distillation have been proposed. For example, the two-point control scheme,15 nonlinear control strategy,16-19 adaptive control,20 and robust proportionalintegral (PI)21 control configuration were used in controlling ethylene glycol, ethyl acetate, isopropyl alcohol, and ethyl tertbutyl ether reactive distillation processes, respectively. The keys to controlling a reactive distillation column are to maintain the product purity and the correct stoichiometric balance between the reactant feeds. Stoichiometric balance control can be achieved using feed ratio control. However, Al-Arfaj and * To whom correspondence should be addressed. Tel.: +886-35927700, ext. 2853. Fax: +886-3-5927310. E-mail: cewsj@ et4.thit.edu.tw. † Ta Hwa Institute of Technology. ‡ National Tsing Hua University.

Luyben22 pointed out that a feed ratio control scheme is a feedforward scheme with no assurance that correct stoichiometric balance is maintained in case of feed flow measurement bias. The use of a composition analyzer in the reactive zone to maintain stoichiometric balance was advocated. They also have studied a number of reactive distillation columns23-27 and found that effective control can be provided by the simple PI control schemes. Using a methyl tert-butyl ether synthesis column as an example, Wang et al.28 found that interaction multiplicity between stoichiometric balance and product quality control loops must be eliminated for such a linear control strategy to work. In an equilibrium controlled reactive distillation column, the reaction rate is infinite. Therefore the net extent of reaction, which is nonzero,29 will not be affected by the residence in the reactive section. The nominal temperature and composition profiles will not be affected if all flow rates are increased in the same proportion. However, when the reaction is kinetically controlled, the reaction rate is finite and the temperature and composition profiles will change even if stoichiometric balance of the feeds can be maintained.30 Set-point adjustment of the internal composition control loop by either final product purity feedback30 or direct throughput rate feedforward control31 becomes necessary. 1.3. Design and Control of Azeotropic Distillation. Heterogeneous azeotropic distillation is commonly used in industry to separate azeotropic mixtures. Research in azeotropic distillation was reviewed comprehensively by Widagdo and Seider.32 As reactive distillation, the system showed complex characteristics such as parametric sensitivity, multiple steady states, long transient, and nonlinear dynamics. Bozenhardt33 used average temperature control, on-line break point control, and five feedforward control loops for the ethanol dehydration system using ether as an entrainer. Rovaglio et al.34 proposed average temperature control and two feedforward control loops for the same system but using benzene as the entrainer. They also reported the importance of the entrainer inventory for good controller performance. Chien et al.35 proposed an inverse double temperature loop control strategy for the isopropyl alcohol + water system using cyclohexane as the entrainer. Kurooka et al.36 applied nonlinear control strategy to the heterogeneous azeotropic distillation column that separates a three-component mixture of water, n-butyl acetate, and acetic acid. Ulrich and Morari37 examined the influence of the fourth component

10.1021/ie060626j CCC: $33.50 © 2006 American Chemical Society Published on Web 11/03/2006

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Figure 1. Entrainer-enhanced reactive distillation process for synthesis of isopropyl palmitate.

impurities on the operation and control of a heterogeneous azeotropic distillation column for dewatering a heavy-boiling organic using methyl tert-butyl ether as a light entrainer. Recently, Chien et al.38 investigated the design and control strategy of an acetic acid dehydration system by heterogeneous azeotropic distillation. Different inventory control strategies using organic reflux and entrainer makeup flows were analyzed. 1.4. Scope and Organization. To our knowledge, there have been, up to now, no discussions on the control strategy of entrainer-added reactive distillation in the open literature. In this study we will investigate the design and control of an entrainer-added reactive distillation process for the production of isopropyl palmitate by the reaction of isopropyl alcohol and palmitic acid. Isopropyl palmitate is used as an excellent solvent for mineral oil, silicone, and lanolin. With good characteristics in absorption, it is widely used in cosmetics and topical medicinal preparations for which good absorption through the skin is required. This paper is organized in the following fashion. In the next section, the base case design of such an entraineradded reactive distillation process will be presented. We shall show that there are an infinite set of steady states that satisfy the design specifications, due to the fact that the entrainer is neither fed in nor lost. In section 3, dynamic simulations of the reactive distillation column, without taking into account the effect of stripper, will be presented. We show that the desired specifications cannot be achieved even if stoichiometric balance and bottom temperature can be maintained, due to changes in entrainer inventory in the reactive distillation column. In section 4, plantwide control with the stripper included will be studied. Self-regulating behavior is found as long as there are no serious offsets in the decanter levels. There is no need for an extra control loop to maintain the correct entrainer inventory. A summary of findings is given in section 5. 2. Base Case Design 2.1. Thermodynamic and Kinetic Model. The reaction involved is given by

palmitic acid + isopropyl alcohol h (PaAcid) (IPA) isopropyl palmitate + water (PaEster) The above reaction is an endothermic reaction. The reversible

reaction needs to be catalyzed by strong acids. The kinetic equation given by Aafaqi et al.39 is used:

r ) 1.50 × 105 exp(-4903.8/T)CPaAcidCIPA 2.13 exp(-1069.3/T)CPaEsterCH2O (1) where r, Ci, and T are the reaction rate, molar concentration of the i component, and temperature, respectively. The process is simulated using ChemCad. The liquid phase activities were calculated by using UNIFAC. 2.2. Process Flow Sheet. To design a feasible process, a very large number of stages in reaction, rectification, and stripping zones is initially used in the reactive distillation column to guarantee high reaction extent, homogeneous azeotrope formed at the column top, and desired isopropyl palmitate purity at the column bottom. The reboiler duty under this condition is regarded as an approximate minimum reboiler duty. The number of stages in each zone is then reduced to the point where actual reboiler duty is about 10% higher than the minimum reboiler duty and further decrease in number of stages results in a large increase of reboiler duty. The column is operated at 1 atm, and its pressure drop is assumed to be 0.305 atm. A reactive distillation column consisting of 55 stages, including a total condenser, a partial reboiler, and 53 column stages, is used for the synthesis of fatty ester. Stages 1-10 are the rectification zone, stages 11-50 are the reaction zone, and stages 51-55 form the stripping zone. Pure palmitic acid and isopropyl alcohol, high and low boiling reactants, at 25 °C and 1 atm are fed to stages 11 and 50, respectively, numbering from the column top. Designed feed rates of 100 kmol/h are used for both reactants. In this reaction, the heaviest component is isopropyl palmitate, which is withdrawn from the bottom. The unreacted reactant, isopropyl alcohol, and water form a homogeneous azeotrope at the column top. Recycling the isopropyl alcohol carries a large amount of water into the reaction zone. Therefore, the reaction conversion is limited. Hence if an entrainer is not used, low conversion, low isopropyl palmitate (∼40 mol %), and high reboiler duty (∼300 GJ/h) are required. If an entrainer, cyclohexane, is added, the column top product is a ternary heterogeneous azeotrope of cyclohexane, isopropyl alcohol, and water. Vapor from the top of the column will condense and split into two liquid phases. The liquid of the

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Table 1. Feasible Operating Ranges at Different Throughput Rates throughput rate (kmol/h)

entrainer in organic reflux (kmol/h)

entrainer in aqueous distillate (kmol/h)

reboiler duty (GJ/h)

entrainer composition in organic phase of decanter

80 100 120

1054-760 1139-952 1281-1145

0.146-0.307 0.194-0.384 0.261-0.460

122.2-66.0 123.3-82.7 126.4-99.4

0.390-0.574 0.430-0.574 0.482-0.574

aqueous phase is drawn off as the distillate and fed into a stripper column with five stages. The organic phase liquid, mainly consisting of unreacted isopropyl alcohol and entrainer, is totally refluxed back to the reactive column. The use of entrainer increases the amount of water removal and internal recycle amount of isopropyl alcohol. Reaction rate is then enhanced by the entrainer due to the higher reactant concentration in the reaction zone. High-purity isopropyl palmitate, 99 mol %, can be obtained at the bottom. A large amount of water with purity up to 99.9 mol % is produced at the stripper bottom. The overhead with totally recovered entrainer, unreacted isopropyl alcohol, and small amount of water is fed back to the condenser of the reactive distillation column. Figure 1 illustrates the basic flow sheet of the entrainer-added reactive distillation process. 2.3. Operability Analysis. It should be noted that there is no net entrainer loss in the above process. The bottom product of the reactive distillation column is 99 mol % isopropyl palmitate with the impurities being palmitic acid and isopropyl alcohol. The bottom product of the stripper column is 99.9 mol % water with the impurity being isopropyl alcohol. There is no need for the entrainer makeup. Furthermore, the desired products (isopropyl palmitate with purity 99 mol % and water with purity 99.9 mol %) can be obtained for a continuous spectrum of steady states with the amount of entrainer recovery from the stripper overhead ranging between 0.194 and 0.384 kmol/h. The corresponding composition profiles of isopropyl alcohol in the reactive distillation column are shown in Figure 2. This is a very special case of input multiplicity in which a specific set of design specifications, for a given feed condition, can be achieved by an infinite but bounded set of operational inputs. The reboiler duty decreases if the entrainer recycle increases. The ranges of feasible inputs at different throughput rates are shown in Table 1. A robust design for nominal reactant feeds of 100 kmol/h can be achieved when the nominal operating value of entrainer recycle amount is chosen at the median value of 0.289 kmol/h, with reboiler duty equal to 87.4 GJ/h and cyclohexane composition in the organic phase of the decanter equal to 54.8 mol %. Steady-state analysis found that the highpurity isopropyl palmitate can also be obtained for the nominal entrainer recycle amount even when there are (20% changes in reactant feeds. If entrainer recycle is chosen to be greater

Figure 2. Composition profiles of isopropyl alcohol in the reactive distillation column with different amounts of entrainer recovery.

than 0.307 kmol/h, reboiler duty can be further decreased but the column will be inoperable if the throughput rate is less than 80 kmol/h. Further decrease of the entrainer recovery will increase the reboiler duty, but the flexibility of the design will not be enhanced. For example, if the entrainer recovery is less than 0.261 kmol/h, the column will not be operable when the throughput rate is increased beyond 120 kmol/h. 3. Single Column Control In this section, the control of a stand-alone entrainer-added reactive distillation column is studied. In the reactive distillation column, the liquid of the organic phase is totally refluxed and the entrainer recycle from the stripper column is considered as a makeup feed. For a reactive distillation column in the kinetic regime, the desired steady-state temperature or composition profile changes when the feed rate changes and product purity is kept at its designed value.30 Hence there are three keys to controlling such a column: (1) to maintain the product quality, (2) to maintain the correct stoichiometric balance between the feeds, and (3) to account for possible changes in control objective when throughput rate changes.

Figure 3. (a) Changes of T55 with respect to reboiler duty and (b) sensitivity of desired set-point values of T55 to throughput rate changes under stoichiometric balance condition.

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and sufficient sensitivity with respect to the feed ratio set point. Figure 4 shows that the temperature of stage 54, T54(1), has high sensitivity and near-linear behavior with isopropyl alcohol/ palmitic acid feed ratio and is very insensitive to throughput rate changes under the stoichiometric balance condition. Hence it was chosen as the controlled variable of the outer cascade loop of stoichiometric balance control. Figure 5 shows the basic control scheme where control loops are designed by PI controllers for the entrainer-added reactive distillation column designed by the above steady-state analysis. Column pressure is controlled by manipulating the coolant flow rate. The level of organic phase, the level of aqueous phase, and the base level are maintained by changing the organic reflux flow rate, aqueous distillate flow rate, and bottom flow rate, respectively. Temperature control of stage 55 is implemented by manipulating reboiler duty. Feed ratio + temperature control is used to maintain the temperature at stage 54 by manipulating the isopropyl alcohol feed flow rate. Entrainer + isopropyl alcohol recovery feed is flow controlled. In the control system of a distillation column, level, pressure, and flow control belong to inventory control maintaining the basic operation of the column. Thus, in the following discussion, emphasis is placed on the response of the temperature control strategy used to maintain product quality and reactant conversion. The controllers were tuned using a sequential design approach.40 For each controller, a relay-feedback test41 is performed to obtain ultimate gain and ultimate frequency. The following equations are used to calculate the tuning parameters of PI controllers:

Figure 4. (a) Changes of T54 with respect to isopropyl alcohol/palmitic acid feed ratio and (b) sensitivity of desired set-point values of T54 to throughput rate changes under stoichiometric balance condition.

To maintain high-purity isopropyl palmitate at the column bottom, a temperature loop can be used, in which the temperature of a stage inside the column is maintained by manipulating the reboiler duty. The input-output relation between stage temperature and reboiler duty should have a near-linear relationship without multiplicity and sufficient sensitivity around the nominal operating condition. Furthermore, the temperature set point should be insensitive or invariant to throughput rate changes under the stoichiometric balance condition.30 Open loop tests show that the temperature of stage 55, T55(1), is a qualified candidate as the controlled variable (Figure 3). The stoichiometric balance between the reactant feeds must be maintained when operating a reactive distillation column. Feed ratio control is the simplest way to maintain the balance. However, when there is a measurement bias in the feed flow rate, the feed ratio control scheme will not be able to keep the desired feed ratio. To overcome this problem, Al-Arfaj and Luyben22 suggested that the reactant composition of some column stage be controlled by the reactant feed flow. In industrial applications, temperature control is usually used instead of composition control. The reason is that most product analyzers, such as gas chromatographs, suffer from large measurement delays and high investment and maintenance cost. The internal composition loop can be replaced by an internal temperature loop. Furthermore, to have better control performance, we use a cascade scheme in which the set point of a feedfoward flow-ratio controller is used as the manipulated variable of the internal temperature control. Hence the internal stage temperature selected should have a near-linear relationship

Kc ) Kcu/3

(2)

TI ) Pu/0.5

(3)

where Kc and TI represent proportional gain and integral time, respectively, and Kcu and Pu are ultimate gain and ultimate period, respectively. Figure 6 shows the dynamic responses under the basic control scheme for (10% changes in the set point of palmitic acid flow when entrainer + isopropyl alcohol recovery feed is fixed. The controlled temperature variables can quickly return to their respective set points. However, the bottom isopropyl palmitate composition cannot be maintained at its designed value. When the flow rates of two reactants are increased, more cyclohexane is needed to remove the additional water formed. If the flow rates of two reactants are decreased, less cyclohexane is required inside the column. It seems that entrainer inventory control is required. The issue of entrainer inventory control has been discussed by Rovaglio et al.34 in an azeotropic distillation column. 4. Plantwide Control The results shown in the previous section indicate that inventory control of entrainer is necessary for the entraineradded reactive distillation column alone. However, it should be pointed out that entrainer lost in the aqueous distillate is actually recovered in the stripper column. Since high-purity products (ester and water) are obtained at the bottom of the reactive distillation column and stripper column, there is no entrainer loss in the entrainer-added reactive distillation process as a whole. Hence, plantwide control performance is expected to be different from single column performance. Figure 7 shows the dynamic responses for (10% changes in the set point of palmitic acid flow with the stripper column included. In the plantwide process, the entrainer + isopropyl alcohol recovery feed is not flow controlled and is equal to the distillate flow of the stripper column. In the stripper column, the base level is

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Figure 5. Basic control scheme for entrainer-added reactive distillation column.

Figure 6. Dynamic responses of the stand-alone reactive distillation column under the basic control scheme for (10% changes in the set point of palmitic acid flow with stripper recovery feed being fixed.

maintained by changing the bottom flow rate. The temperature of stage 5, T5(2), is controlled by manipulating reboiler duty to maintain the water purity. The controlled stage temperatures can quickly return to their respective set points. There is little change in the uncontrolled entrainer composition in the organic

phase, and only a slight offset is observed in bottom isopropyl palmitate purity. In other words, since entrainer loss of the entire process is negligible and the decanter levels are controlled, the amounts of entrainer in the reactive distillation and stripper columns are self-regulatory. Entrainer inventory control in the

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Figure 7. Plantwide dynamic responses of the reactive distillation process for (10% changes in the set point of palmitic acid flow with decanter level under PI control.

reactive distillation column is not necessary. The content and property of the recycled stream were also analyzed, and we found that recycle flow rate almost proportionally increases or decreases with the reactant feed flow rate at final steady state when the throughput rate was changed. In addition, there are only very little changes in the component compositions of the recycled stream compared with those at nominal operating condition. Hence, the recycle flow acts as a self-regulating response to changes in various throughput rates. This explains why the proposed strategy works in the plantwide process. The effect of recycle on the design of controller of a reactor/ separator system was well exposed by Luyben et al.42 They characterized chemical components into three types: reactants, products, and inerts. Since excess reactants are recycled to ensure complete consumption, the system acts as an integrator and does not exhibit self-regulating behavior in terms of reactants. In such systems, the recycle stream, consisting mainly of reactants, will exhibit large disturbances to small disturbances

in the feed. Such a phenomenon is known as the “snowball effect”. A heuristic rule commonly used to prevent the effect is to fix the flow rate of a recycle stream. In our system, the recycle stream exhibits self-regulating behavior rather than a snowball effect. No flow control is used in either recycle loop (between the decanter and the reactive distillation column, and the other between the decanter and the stripper). This is because the recycle stream contains a new type of chemical component, the entrainer, which is neither fed nor lost, but merely distributed between the reactive distillation column, the decanter, and the stripper. As shown in the previous paragraph, this distribution is self-regulating rather than snowballing. Thus flow control in the recycle loops is not necessary. In the above study, the accumulator levels are tightly controlled by a PI controller. In practice, liquid levels are usually controlled by a P controller only. Some offset in the liquid level is usually allowed for conventional column operation. However, if there is an offset in the liquid level of the organic phase, the

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Figure 8. Plantwide dynamic responses of the reactive distillation process for (10% changes in the set point of palmitic acid flow with decanter level under P control.

entrainer amount returned to the entrainer-added reactive distillation column changes. The self-regulatory behavior will be lost. Figure 8 shows the dynamic responses for the same disturbances and control scheme as in Figure 7 except that the liquid level of the organic phase is under P control. Even though controlled stage temperatures can be maintained at their respective set points, a larger offset is observed in the bottom isopropyl palmitate purity. Similar dynamic simulation tests indicate that the offset in the isopropyl palmitate purity increases with the offset in the liquid level of the organic phase. 5. Conclusions The process characteristics and control strategies of an entrainer-added reactive distillation for the synthesis of fatty ester are investigated in the study. Substantial energy reduction and high-purity isopropyl palmitate can be obtained by adding an entrainer that forms a minimum boiling heterogeneous azeotrope with isopropyl alcohol and water. The bottom products

of the reactive distillation column and stripper column are highpurity isopropyl palmitate and water. There is no net entrainer loss in the plantwide process, and therefore entrainer makeup is unnecessary. Furthermore, the desired products can be obtained for a continuous spectrum of steady states with different amounts of entrainer recycle. The keys of controlling the entrainer-added reactive distillation column, in which the reaction is kinetically controlled, are to (i) maintain the quality of bottom product, (ii) maintain the proper ratio between the feed rates, (iii) account for possible changes in control objective when throughput rate changes, and (iv) maintain a proper entrainer inventory in the reactive distillation column. Product quality can be maintained by controlling the bottom temperature. Maintenance of feed ratio can be implemented by a cascade scheme. The inner loop is a feed ratio control of the two reactants, and the outer loop controls an internal stage temperature. Maintenance of a proper entrainer inventory can be achieved provided that the liquid level

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of the organic phase is controlled and there is no offset. This is due to the fact that there is no net entrainer loss in the above process. If there is too much entrainer in the reactive distillation column, the amount of organic phase accumulated in the decanter will decrease; level control will reduce the organic phase recycle. Since the desired product purity can be achieved with a range of entrainer recycle, this robustness allows the process to self-regulate the entrainer inventory in the reactive distillation column. Acknowledgment This work is supported by the National Science Council of R.O.C. under Grant NSC-93-2214-E-233-001. Nomenclature Ci ) molar concentration of i component (mol/L) Kc ) proportional gain Kcu ) ultimate gain Pu ) ultimate period r ) reaction rate (mol/L‚h) T ) temperature (K) T54(1), T55(1) ) temperature of stages 54 and 55 in reactive distillation column T5(2) ) temperature of stage 5 in stripper column TI ) integral time Literature Cited (1) Dimian, A. C.; Omota, F.; Bliek, A. Entrainer-Enhanced Reactive Distillation. Chem. Eng. Process. 2004, 43, 411. (2) Doherty, M. F.; Buzad, G. Reactive Distillation by Design. Chem. Eng. Res. Des. 1992, 70, 448. (3) Taylor, R.; Krishna, R. Modelling Reactive Distillation. Chem. Eng. Sci. 2000, 55, 5183. (4) Hauan, S.; Schrans, S. M.; Lien, K. M. Dynamic Evidence of the Multiplicity Mechanism in Methyl tert-Butyl Ether Reactive Distillation. Ind. Eng. Chem. Res. 1997, 36, 3995. (5) Mohl, K. D.; Kienle, A.; Gilles, E. D.; Rapmund, P.; Sundmacher, K.; Hoffmann, U. Nonlinear Dynamics of Reactive Distillation Processes for the Production of Fuel Ethers. Comput. Chem. Eng. 1997, 21, S989. (6) Mohl, K. D.; Kienle, A.; Gilles, E. D. Multiple Steady States in a Reactive Distillation Column for the Production of the Fuel Ether TAME I. Theoretical Analysis. Chem. Eng. Technol. 1998, 21, 133. (7) Rapmund, P.; Sundmacher, K.; Hoffmann, U. Multiple Steady States in a Reactive Distillation Column for the Production of the Fuel Ether TAME Part II: Experimental Validation. Chem. Eng. Technol. 1998, 21, 136. (8) Sneesby, M. G.; Tade´, M. O.; Datta, R.; Smith, T. N. Multiplicity and Pseudo-Multiplicity in MTBE and ETBE Reactive Distillation. Chem. Eng. Res. Des. 1998, 76, 525. (9) Sneesby, M. G.; Tade´, M. O.; Datta, R.; Smith, T. N. Steady-State Transitions in the Reactive Distillation of MTBE. Comput. Chem. Eng. 1998, 22, 879. (10) Eldarsi, H. S.; Douglas, P. L. Methyl-tert-Butyl-Ether Catalytic Distillation Column Part I: Multiple Steady States. Chem. Eng. Res. Des. 1998, 76, 509. (11) Rosendo, M. L.; Jose, A. R. On the Steady-State Multiplicities for an Ethylene Glycol Reactive Distillation Column. Ind. Eng. Chem. Res. 1999, 38, 451. (12) Chen, F.; Huss, R. S.; Doherty, M. F.; Malone, M. F.Multiple Steady States in Reactive Distillation: Kinetic Effects. Comput. Chem. Eng. 2002, 26, 81. (13) Baur, R.; Taylor, R.; Krishna, R. Bifurcation Analysis for TAME Synthesis in a Reactive Distillation Column: Comparison of PseudoHomogeneous and Heterogeneous Reaction Kinetics Models. Chem. Eng. Process. 2003, 42, 211. (14) Huss, R. S.; Chen, F.; Malone, M. F.; Doherty, M. F. Reactive Distillation for Methyl Acetate Production. Comput. Chem. Eng. 2003, 27, 1855. (15) Sneesby, M. G.; Tade´, M. O.; Smith, T. N. Two-Point Control of a Reactive Distillation Column for Composition and Conversion. J. Process Control 1999, 9, 19.

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ReceiVed for reView May 19, 2006 ReVised manuscript receiVed August 10, 2006 Accepted September 29, 2006 IE060626J