Design and Control of a Methyl Tertiary Butyl Ether (MTBE

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Ind. Eng. Chem. Res. 2007, 46, 2508-2519

Design and Control of a Methyl Tertiary Butyl Ether (MTBE) Decomposition Reactive Distillation Column Kejin Huang*,† and San-Jang Wang‡ School of Information Science and Technology, Beijing UniVersity of Chemical Technology, Beijing 100029, People’s Republic of China, and Department of Chemical and Material Engineering, Ta Hwa Institute of Technology, Chiunglin, Hsinchu 307, Taiwan

The synthesis, design, and control of a reactive distillation column for decomposing methyl tertiary butyl ether into isobutylene and methanol are reported in this work. Because the reaction is highly endothermic, it is advantageous to consider cautiously internal heat integration between the reaction and separation operations during process synthesis the and design, thereby necessitating deliberate determination of the feed location and judicious distribution of reactive section along the height of the process (Huang et al. AIChE J. 2006, 52, 2518). Through extensive comparison with a simple process design in which the reactive section is located between the rectifying section and the stripping section, it is demonstrated that a substantial reduction of capital investment and energy consumption can be achieved with this strategy of process development. Process dynamics and operation of the resultant process design were further investigated, and a noticeable improvement was gained in process controllability. The major reason for this improvement can be attributed to the fact that a more synergistic relationship has been evolved between the reaction and separation operations in the pursuit of further internal heat integration during process synthesis and design. 1. Introduction

Table 1. Physical Properties of the MTBE Decomposition Reacting Mixture (P ) 1100 kPa)

The combination of reaction and separation operations is a primary thrust that endows a reactive distillation column with many advantages over process design using a conventional design philosophy, e.g., a fixed-bed reactor followed by a number of distillation columns.1-7 Unfortunately, it also gives rise to a complicated coordination problem in process development between the reaction and separation operations. In fact, if the coordination problem is not tackled effectively in process synthesis and design, a considerable degradation in system performance might be experienced, as has already been pointed out by a number of studies.8-11 In the case of a reactive distillation column involving reactions with highly thermal effects, combination of the reaction and separation operations can even exhibit a dominant influence on the possibility of internal heat integration between the two operations and, thus, the thermodynamic efficiency of the resultant process design. Although some designs of reactive distillation columns are frequently quoted to display a relatively higher thermodynamic efficiency than those based on conventional designs, the potential energy savings and cost reductions might have been lowered substantially if the released/needed heat of reactions has not been used/supplied in an appropriate way.12-15 Generally speaking, the currently available approaches for the synthesis and design of reactive distillation columns fall into three broad categories:16,17 those based on graphical/topological consideration,18-23 those based on various optimization techniques,24-29 and those based on heuristic evolutionary principles.30-33 All of these methods have their merits and demerits, and which one should be chosen depends heavily on the thermodynamic characteristics of the reacting system at hand and the design objectives to be pursued in process development. Recently, we * To whom correspondence should be addressed. Tel.: +86-106443-4726. Fax: +86-10-6448-7805. E-mail: [email protected]. † Beijing University of Chemical Technology. ‡ Ta Hwa Institute of Technology.

parameter boiling point (K) enthalpy of vaporization at 298 K (MJ kmol-1) conversion rate at 426.73 K (mol %)

MTBE MEOH IBUT 426.3 29.73 68

413.6 38.02

348.1 20.27

proposed a heuristic evolutionary method for the synthesis and design of a reactive distillation column involving reactions with highly thermal effects.34,35 This approach stresses the importance of the issue of combining the reaction and separation operations and attempts to find an appropriate solution according to a thermodynamic point of view (or, more precisely, maximization of the effect of internal heat integration between the reaction and separation operations). By means of a number of case studies, it has been demonstrated that the proposed method can truly yield an effective process design in a number of trial-anderror searches and that the resultant process designs are even found to be comparable in system performance to those derived in terms of a mixed-integer nonlinear programming (MINLP) formulation. Owing to the refinement of the relationship between the reaction and separation operations, it is reasonable to anticipate that process dynamics and controllability could also be improved when compared to a process design obtained by simply distributing the reactive section between the rectifying section and the stripping section (called the basic process design in this work). Although it is impossible to prove definitively the rationale of this expectation because of the great versatility of reacting systems that exist and the various design objectives specified, to understand and be aware of the possibility is still of practical significance to the development of reactive distillation columns because it might be an inherent property of reinforcing internal heat integration between the reaction and separation operations involved. It might even stimulate process designers to pay more attention to the coordination problem (or, more precisely, internal heat integration) in process synthesis and design without any additional concerns about the issues of

10.1021/ie061204c CCC: $37.00 © 2007 American Chemical Society Published on Web 03/21/2007

Ind. Eng. Chem. Res., Vol. 46, No. 8, 2007 2509 Table 2. Nominal Operating Conditions of the MTBE Decomposition Reactive Distillation Column process design parameter

Figure 1. Basic process design for an MTBE decomposition reactive distillation column.

process dynamics and controllability. In fact, the possibility was already illustrated in our recent work by means of two hypothetical reactive distillation columns containing a highly exothermic reaction and a highly endothermic reaction.36 To demonstrate further the possibility, we plan to investigate the synthesis, design, and operation of a number of reactive distillation columns involving reactions with highly thermal effects. In this work, a reactive distillation column that decomposes methyl tertiary butyl ether (MTBE) into isobutylene (IBUT) and methanol (MEOH) is chosen and studied, because this decomposition reaction has to proceed with the input of a large amount of thermal energy and appears to be a suitable reaction for the examination of the reinforcement of internal heat integration between the reaction and separation operations during process synthesis and design. Even though the ban on the production of MTBE has already taken effect in the U.S. and caused the synthesis and decomposition of MTBE by reactive distillation systems to no longer be of great significance, these reactions can still be used as useful examples to interpret the static and dynamic effects of internal heat integration between the reaction and separation operations of a reactive distillation column. The results obtained could have strong implications for the synthesis, design, and control of other reactive distillation columns involving reactions with highly thermal effects. MTBE decomposition (eq 1)

MTBE (C5H12O) T MEOH (CH3OH) + IBUT (i-C4H8) ∆HR,298 ) 37.7 × 103 kJ/kmol (1) used to be a preferred method of producing isobutylene because it can easily be integrated into the refinery and petrochemical sources of isobutylene-containing C4 streams.37-40 Either a homogeneous catalyst such as sulfuric acid or a heterogeneous catalyst, e.g., a strongly acidic macroporous ion-exchange resin, can be employed in this reaction. In this work, the reaction catalyzed by sulfuric acid was investigated. Usually, two side reactions can occur within this reaction system.41,42 One is the dimerization of isobutylene (eq 2), forming a byproduct of diisobutylene (DIB, a mixture of the isomers 2,2,4-trimethyl1-pentene and 2,2,4-trimethyl-2-pentene).

2IBUT (i-C4H8) T DIB (C8H16)

(2)

pressure of the top stage (kPa) pressure drop per stage (kPa) number of stages rectifying section reactive section stripping section holdup (m3) stage condenser reboiler feed flow rate (mol/s) feed location feed pressure (kPa) feed temperature (K) feed thermal condition MYBE conversion rate (%) top-product composition (IBUT, mole fraction) top temperature (K) reflux flow rate (mol s-1) top-product flow rate (mol s-1) bottom-product composition (MEOH, mole fraction) bottom-product flow rate (mol s-1) bottom temperature (K) condenser duty (MW) reboiler duty (MW)

5/6/5

8(5)/6(4)/5

1100 50

1100 50

5 6 5

3 11 5

9.13-15.59 155.59 91.34 100 7 1114.6 426.73 1.0 94.36 0.94

0.40-0.46 4.50 4.50 100 14 1114.6 426.73 1.0 94.03 0.94

342.55 7280.54 100.37 0.94

342.71 287.23 100.03 0.94

93.98 412.50 132.90 133.30

94.00 412.50 6.98 7.39

The other is the dehydration of methanol (eq 3), leading to the formation of dimethyl ether (DME).

2(MEOH) (CH3OH) T DME (C2H6O) + H2O

(3)

By choosing suitable operating conditions, for instance, a low enough operating pressure and thus a low enough temperature, together with a small amount of catalyst employed in the reactive section, the side reaction of methanol dehydration can be completely suppressed, so that only a very small amount of DIB is formed. Hence, for the simplification of process simulation and analysis, only the primary reaction (eq 1) was considered in the synthesis, design, and control studies of the MTBE decomposition reactive distillation column in the following. Some relevant physical properties of the MTBE decomposition reaction mixture are collected in Table 1. The objective of the current work was to explore the synthesis, design, and control of a reactive distillation column for decomposing MTBE into isobutylene and methanol, with special emphasis on the effects of internal heat integration between the reaction and separation operations on the process dynamics and controllability. After a brief introduction on the principle of seeking further heat integration within a reactive distillation column, process synthesis and design for the MTBE decomposition reactive distillation column is discussed. Steady-state operability, open-loop process dynamics, and closed-loop control are then examined sequentially for the resultant process design by means of intensive comparisons with the basic process design obtained by simply distributing the reactive section between the rectifying section and the stripping section. The implications of seeking further internal heat integration between the reaction and separation operations involved in the MTBE decomposition

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Ind. Eng. Chem. Res., Vol. 46, No. 8, 2007

Figure 3. Strengthening internal heat integration for the MTBE decomposition reactive distillation column: (9) superposition of reactive stages on the rectifying section, (O) descent of MTBE feed location from the top of the reactive section.

Figure 2. Profiles of temperature, liquid and vapor flow rates, and liquid composition for process designs 5/6/5 and 5(5)/6(4)/5.

reactive distillation column are indicated, and some concluding remarks are made in the last section of the article. 2. Heuristic Evolutionary Principle for the Synthesis and Design of a Reactive Distillation Column Involving Reactions with Highly Thermal Effects For a conventional distillation column, the rectifying section (or the equivalent section in the case of a multiple-feed distillation column) releases heat during operation and is thus reasonable to be seen as a potential heat source. In contrast, the stripping section (or the equivalent section in the case of a multiple-feed distillation column) absorbs heat during operation and is thus reasonable to be seen as a potential heat sink. On the basis of this thermodynamic interpretation, various thermodynamically efficient distillation columns have been derived by means of heat integration between, for example, the rectifying section and the stripping section (i.e., internal heat integration),43-46 the rectifying section and an external heat sink (i.e., external heat integration), and the stripping section and an external heat source (i.e., external heat integration).47,48 For a reactive distillation column involving reactions with highly thermal effects, the heat of reactions can be treated as either an internal heat source (in the case of exothermic reactions) or an internal heat sink (in the case of endothermic reactions), thereby creating an opportunity for the consideration of internal heat integration between the reaction and separation operations. Superimposing reactive stages onto separating stages in the rectifying/stripping section can serve to meet this purpose. In

contrast to the synthesis and design of internally/externally heatintegrated distillation columns, process development requires almost no additional capital investment but merely a delicate combination between the reaction and separation operations. Two design options usually exist to meet this requirement in process synthesis and design. One is to extend the reactive section to either the rectifying section (in the case of endothermic reactions) or the stripping section (in the case of exothermic reactions) in terms of the detailed reaction system at hand. The other is to deliberately choose the feed location of the relevant reactant in the reactive section (in the case of a multiple-feed reactive distillation column). Both of these design options affect the superposition of reactive stages onto the separating stages in the rectifying/stripping section, thereby enabling the identification of an appropriate degree of internal heat integration (more specifically, the method of combination) between the reaction and separation operations within a number of trialand-error searches. In terms of the above principle for strengthening internal heat integration between the reaction and separation operations, process synthesis and design can be carried out in a heuristic evolutionary manner for a reactive distillation column involving reactions with highly thermal effects. At the beginning, a basic process design with three distinct sections (i.e., a rectifying section and a stripping section, separated by a central reactive section) and feeds of reactants at the ends of the reactive section is selected according to an economic objective or general guideline. Then, with the combinatorial utilization of the two methods for reinforcing internal heat integration between the reaction and separation operations, the distribution of the reactive section is searched until the process configuration with the minimum energy consumption is found. If the process design obtained is satisfactory, then the process synthesis and design is finished; otherwise, a new basic process design should be chosen, and the above search procedure is repeated. In general, the trial-and-error search method appears to be quite robust and effective and could be employed for the synthesis and design of any reactive distillation columns involving reactions with highly thermal effects.

Ind. Eng. Chem. Res., Vol. 46, No. 8, 2007 2511 Table 3. Effect of Reinforcing Internal Heat Integration on System Performance evaluation (%) process design

process configuration

condenser duty (MW)

reboiler duty (MW)

condenser

reboiler

basic process design lowering the MTBE feed location four stages from the top of the reactive section superimposing five reactive stages onto the rectifying section combinatorial use of the above methods final process design

5/6/5 5/6(4)/5 5(5)/6/5 5(5)/6(4)/5 8(5)/6(4)/5

132.90 12.73 7.96 7.29 6.98

133.30 13.15 8.25 7.59 7.39

100 9.58 5.99 5.49 5.25

100 9.87 6.19 5.69 5.54

To clearly represent the evolutionary process during process synthesis and design, we make use of the unified notation Nr(n1)/Nrea(n2)/Ns(n3), throughout this work. This notation can also be used to represent different process designs with and without further internal heat integration between the reaction and separation operations. Here, Nr, Nrea, and Ns represent the numbers of stages in the rectifying, reactive, and stripping sections, respectively, of a process design. The numbers in parentheses, n1 and n3, represent the superposition of additional reactive stages on the rectifying and stripping sections, respectively, and n2 denotes the movement of the feed location of the relevant reactant within the reactive section. It is further stipulated here that the solid lines represent the static and dynamic responses of the reactive distillation column developed through the reinforcement of internal heat integration between the reaction and separation operations, and the dashed lines represent the static and dynamic responses of the basic process design with the reactive section situated directly between the rectifying section and the stripping section. 3. Basic Process Design It should be mentioned here that, although the configuration of the basic process design is specified strictly in the preceding section, it is actually not a necessary requirement for the application of the proposed principle in process synthesis and design. In fact, the basic process design can be arbitrarily specified without influencing the results of the process synthesis and design. Figure 1 depicts a basic process design for the MTBE decomposition reactive distillation column, and Table 2 lists the specifications for process synthesis and design. At the beginning, the MTBE decomposition reactive distillation column is assumed to contain a three-section configuration, 5/6/ 5, in addition to a total condenser at the top and a partial reboiler at the bottom. The pure MTBE reactant (q ) 1) is fed onto the top of the reactive section according to the conventional design practice, because it is the heaviest boiler of the reacting mixture.31,39 The top and bottom products are specified at 94 mol % IBUT and 94 mol % MEOH, respectively, to maintain an overall conversion rate of 94 mol % (in terms of MTBE). In this work, the static and dynamic simulation of the MTBE decomposition reactive distillation column was carried out using the commercial ChemCad software. The liquid-phase activities were calculated using the UNIQUAC model with the binary interaction parameters reported by Rehfinger and Hoffmann.49 Every reactive stage was assumed to be in chemical equilibrium and the following equation was used to represent the temperature dependence of the reaction equilibrium constant50

ln Keq ) 16.33 -

6820 T

(4)

Searches for the operating conditions that satisfy the given design specification were conducted for the basic process design, 5/6/5, and the calculation results obtained are also included in

Table 2. It is noted that an excessively high reflux ratio, R ) RR/d ) 7280.54/100.37 ) 72.54, results, signifying that the basic process design has an extremely low thermodynamic efficiency. Increases in the numbers of stages in the rectifying and stripping section were attempted, and no substantial reduction in energy consumption could be secured. The complicated thermodynamic properties of the reacting mixture and strong interaction between the reaction and separation operations are considered to be the main reasons for this poor performance. In Figure 2, the steady-state profiles of the temperature, liquid and vapor flow rates, and liquid composition are depicted for the basic process design, 5/6/5. Although the fresh feed of MTBE was introduced onto the top of the reactive section, a high presence of MTBE actually formed in the low part of the MTBE decomposition reactive distillation column, which is unfavorable to the forward (decomposition) reaction in the top part of the reactive section. This is apparently an inherent drawback of the basic process design that is closely related to the combination between the reaction and separation operations. To circumvent this deficiency, one has to deliberately determine the feed location of MTBE and judiciously distribute the reactive section along the height of the apparatus during the synthesis and design of an MTBE decomposition reactive distillation column. 4. Synthesis and Design of the MTBE Decomposition Reactive Distillation Column Because MTBE decomposition into isobutylene and methanol is a highly endothermic reaction, it is advantageous to consider further internal heat integration between the reactive section and the rectifying section during process synthesis and design. A certain amount of heat could be recovered from the rectifying section and then used to drive the decomposition reaction forward, thereby decreasing the heat duty of the reboiler and facilitating the reduction of process irreversibility associated with the separation operation. Moreover, the consideration of further internal heat integration between the reactive section and the rectifying section also helps to lessen the negative factors of reactive distillation columns for endothermic reactions, for instance, the relatively large temperature driving forces from the bottom reboiler to the reactive section and the frequent need for intermediate heat exchangers.51,52 The effects of seeking further internal heat integration between the reaction and separation operations are well illustrated in Figure 3. With regard to the descent of MTBE feed location from the top of the reactive section, the basic process design, 5/6/5, displays an inconsistent variation in system performance, and the heat duties of the condenser and reboiler reach their minimum values simultaneously at stage 11. For the superposition of additional reactive stages onto the rectifying section, the heat duties of the condenser and reboiler decrease monotonically, and it is therefore reasonable to allow the MTBE decomposition to occur on all stages in the rectifying section.

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Figure 4. Profiles of net reaction rates in the MTBE decomposition reactive distillation column.

Figure 5. Resultant process design, 8(5)/6(4)/5, obtained by seeking further internal heat integration.

In Table 3, the effects of seeking further internal heat integration between the reactive section and the rectifying section are reported in great detail. In comparison to the basic process design, 5/6/5, the heat duties of the condenser and reboiler are reduced by 90.42% and 90.13%, respectively, when the MTBE feed location is moved from stage 7 to stage 11 [i.e., in process design 5/6(4)/5]. With the replacement of all stages in the rectifying section by reactive stages [i.e., in process design 5(5)/6/5], the heat duties of the condenser and reboiler are diminished by 94.01% and 93.81%, respectively. The combinatorial application of these two methods [i.e., in process design 5(5)/6(4)/5] secures the largest reduction of energy consumption, with decreases of 94.51% in the condenser and 94.31% in the reboiler. In Figure 4, the effects of seeking further internal heat integration are illustrated through comparison of the profiles of net reaction rates. As can be seen, in the basic process design, 5/6/5, the forward (decomposition) reaction occurs excessively on the bottom stage of the reactive section and leads to the occurrence of the backward (synthesis) reaction on the rest of the reactive stages, apparently representing an inappropriate combination between the reaction and separation operations. Only after further internal heat integration is sought is this defect removed and an effective method of combining the reaction and separation operation derived, thereby enabling a substantial improvement of the thermodynamic efficiency of the MTBE decomposition reactive distillation column. In Figure 2, the steady-state profiles of temperature, liquid and vapor flow rates, and liquid composition are also depicted for process design 5(5)/

Figure 6. Profiles of temperature, liquid and vapor flow rates, and liquid composition for the resultant process design, 8(5)/6(4)/5.

Table 4. Relative Gain Array for Process Design 5/6/5 manipulated variables controlled variables xIBUT xMEOH

RR

QREB

33.05 -32.05

-32.05 33.05

6(4)/5. It is readily understood that a relatively high distribution of MTBE is now formed in the common section between the reactive section and the rectifying section, hence facilitating the forward reaction and reducing the possibility of isobutylene dimerization simultaneously in the top part of the reactive section. Recently, Qi et al.53 also reported a very similar configuration for an MTBE decomposition reactive distillation column. Recall that seeking further heat integration in a distillation column actually reduces the driving forces for mass transfer in the rectifying/stripping section where internal/external heat integration is employed;54,55 it is therefore necessary to compensate appropriately for the mass-transfer driving forces during the synthesis and design of the MTBE decomposition reactive distillation column. A straightforward method is to add a number of separating stages to the rectifying section, and the appropriate number should be determined in terms of detailed simulation analysis. In this situation, three separating stages were found to be sufficient for the rectifying section, leading to a final process design of 8(5)/6(4)/5. The process configuration of the MTBE decomposition reactive distillation column is depicted

Ind. Eng. Chem. Res., Vol. 46, No. 8, 2007 2513 Table 5. Relative Gain Array for Process Design, 8(5)/6(4)/5 manipulated variables controlled variables xIBUT xMEOH

RR

QREB

1.71 -0.71

-0.71 1.71

in Figure 5, and its nominal steady-state operating conditions are also reported in Table 2. As can be seen, the liquid holdups on stages (including those on the top condenser and bottom reboiler) are substantially reduced (by a factor ranging from 20.30 to 34.57) after the reinforcement of internal heat integration between the reaction and separation operations, thus illustrating the paramount importance of process synthesis and design on the efficacy of process intensification. Here, the sizing of the MTBE decomposition reactive distillation column was carried out with a builtin function of the ChemCad software. In particular, the criterion that the flood percent on each stage is not allowed to exceed 75% at the nominal operating conditions was employed to calculate some design parameters regarding the column geometry, such as stage diameter, stage spacing, weir height, downcomer side width, and so on. The liquid holdups were then estimated from the determined column geometry. In Figure 6, the steady-state profiles of temperature, liquid and vapor flow rates, and liquid composition are illustrated. In comparison to the basic process design, 5/6/5, the heat duty of the reboiler has been reduced by 94.46%, in addition to a 94.75% reduction of the heat duty of the condenser (cf., Table 3), thereby securing a simultaneous reduction of capital investment and operating cost. It can readily be seen that the addition of three separating stages to the rectifying section gives a certain redundancy to process design 8(5)/6(4)/5. The fairly small improvement in the thermodynamic efficiency from process design 5(5)/6(4)/5 to process design 8(5)/6(4)/5 also indicates the dominant effect of the combination between the reaction and separation operations on the synthesis and design of a reactive distillation column involving reactions with highly thermal effects. 5. Steady-State Operation Analysis Relative gain array (RGA) is a good measure of interactions between different control loops and is thus a useful indication of process controllability.56,57 In Tables 4 and 5, the RGA is reported for the two process designs, 5/6/5 and 8(5)/6(4)/5, respectively, of the MTBE decomposition reactive distillation column. It is noted that the first element of the RGA, λ1,1, is reduced dramatically from 33.05 in the basic process design, 5/6/5, to 1.71 in process design 8(5)/6(4)/5 obtained after the reinforcement of internal heat integration between the reaction and separation operations. This indicates that the severity of the interactions between the top and bottom control loops is alleviated in the decentralized control of the MTBE decomposition reactive distillation column, thereby reflecting a potential improvement in process controllability. Because the magnitude of λ1,1 is also an indication of the sensitivity to process uncertainties, the dramatic reduction in the size of λ1,1 points out that process sensitivity is, to a certain extent, suppressed after the reinforcement of internal heat integration in the MTBE decomposition reactive distillation column. In terms of the RGA values, one can readily see that the top-product composition, xIBUT, should be controlled with the reflux flow rate, RR, and the bottom-product composition, xMEOH, should be controlled with the heat duty of the reboiler, QREB, for both process designs, i.e., 5/6/5 and 8(5)/6(4)/5, of the MTBE decomposition reactive

Figure 7. Steady-state relationships between the reflux flow rate and the product compositions.

distillation column. The dynamic performance of the decentralized control system is examined later in section 7. In Figure 7, the steady-state relationships between the reflux flow rate and the compositions of the top and bottom products are displayed for the heat duties of the reboiler maintained at their nominal steady-state values. For the basic process design, 5/6/5, input multiplicity was observed between the top-product composition, xIBUT, and the reflux flow rate, RR, around the nominal steady state. With increasing reflux flow rate, the purity of the top product cannot be enhanced much higher than the given product specification (in other words, a saturation phenomenon occurs between xIBUT and RR). After the reinforcement of internal heat integration between the reaction and separation operations in process design 8(5)/6(4)/5, not only does the phenomenon of input multiplicity disappear, but the saturation phenomenon is also completely suppressed. Moreover, the degree of linearity between the composition of the bottom product, xMEOH, and the reflux flow rate, RR, is also improved to a certain extent. In Figure 8, the steady-state relationships between the heat duties of the reboiler and the compositions of the top and bottom products are displayed for the reflux flow rates maintained at their nominal steady-state values. It is readily seen that the linearity between the heat duty of the reboiler, QREB, and the composition of the bottom product, xMEOH, is substantially enhanced after the elaboration of process design through further internal heat integration between the reaction and separation operations. Whereas in the basic process design, 5/6/5, input multiplicity and saturation were found between the top-product composition, xIBUT, and the heat duty of the reboiler, QREB, the same phenomena were not found in process design 8(5)/6(4)/5. These interesting outcomes indicate that the reinforcement of internal heat integration can truly have a favorable influence on the process dynamics and controllability of the MTBE decomposition reactive distillation column. 6. Open-Loop Process Dynamics On the basis of the nominal steady states, open-loop process dynamics is examined for process designs 5/6/5 and 8(5)/6(4)/5

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Figure 8. Steady-state relationships between the heat duty of the reboiler and the product compositions.

Figure 10. Open-loop dynamic responses to a (0.001 step change in the heat duty of the reboiler (black lines, positive change; gray lines, negative change).

larger diameter and thus more liquid holdups on stages (including those in the top condenser and bottom reboiler) than the latter, hence decreasing the response speed considerably. 6.2. Transient Responses to a (0.001 Step Change in the Reboiler Duty. In Figure 10, the transient responses of process designs 5/6/5 and 8(5)/6(4)/5 to a step change of (0.001 in the heat duty of the reboiler are compared. Regarding the top product, initial inverse responses were again found in the former and were completely removed in the latter. Although the MTBE decomposition reactive distillation column should be controlled with the decentralized control configuration (xIBUT-RR, xMEOHQREB), as suggested by the RGA analysis in section 5, the nonminimum phase behavior between the top-product composition, xIBUT, and the heat duty of the reboiler, QREB, can still give rise to a negative effect on process controllability. The basic process design, 5/6/5, still exhibits much more sluggish responses than process design 8(5)/6(4)/5 under these conditions. 7. Closed-Loop Control

Figure 9. Open-loop dynamic responses to a (0.001 step change in the reflux flow rate (black lines, positive change; gray lines, negative change).

through the introduction of a number of individual step disturbances to the MTBE decomposition reactive distillation column. 6.1. Transient Responses to a (0.001 Step Change in the Reflux Flow Rate. In Figure 9, the transient responses of process designs 5/6/5 and 8(5)/6(4)/5 are compared when they are subject, respectively, to a step change of (0.001 in the reflux flow rate. In the former, initial inverse responses were found in the top product, which is likely to exert a strong detrimental effect on process operation. With the reinforcement of internal heat integration between the reaction and separation operations in the latter, this nonminimum phase behavior was avoided completely. Much more sluggish responses (i.e., much larger time constants) were noticed for the former compared to the latter. This is because the relatively large vapor and liquid loads in the former necessitate a reactive distillation column with a

7.1. Control System Design. A number of decentralized control systems can be synthesized and designed for the MTBE decomposition reactive distillation column, including direct composition control, indirect composition (i.e., temperaturebased) control, and their various alternatives.58-61 Direct composition control is employed here, because the same conversion rate of MTBE can be strictly maintained between process designs 5/6/5 and 8(5)/6(4)/5 in any situation, thus providing a fair basis for comparative studies of process controllability. Figure 11 presents a sketch of a control configuration in which the purities of both the top and the bottom products are measured and controlled. In accordance with the RGA analysis in section 5, the composition of the isobutylene component is controlled by manipulating the reflux flow rate in the top control loop. In the bottom control loop, the composition of the methanol component is controlled by manipulating the heat duty of the reboiler. The levels of the reflux drum and the bottom reboiler are controlled by the distillate and bottom-product flow rates, respectively. The dynamics of concentration measurements was assumed to be

Ind. Eng. Chem. Res., Vol. 46, No. 8, 2007 2515

Figure 11. Control schemes for the MTBE decomposition reactive distillation column: (a) process design 5/6/5, (b) process design 8(5)/6(4)/ 5.

two first-order lags of 30 s each, in series. The transmitter span of all composition measurements was taken to be 0.12, and all control valves were designed to be half-open at the nominal steady states. Proportional-only (P) controllers were used for all level control loops, and proportional plus integral (PI) controllers were adopted for the top and bottom composition control loops. The PI control systems were tuned in a sequential manner.62 For each control loop, a relay-feedback test was performed to obtain the ultimate gain and ultimate frequency. The following equations were then used to calculate the tuning parameters of the PI controllers

KC )

KCU 3

(5.1)

TI )

PCU 0.5

(5.2)

where KC and TI represent the proportional gain and integral time, respectively, and KCU and PCU are the ultimate gain and ultimate period, respectively. 7.2. Dynamic Responses to a Step Change of (0.005 in the Set Points of the Top and Bottom Control Loops. In Figure 12, the closed-loop responses of process designs 5/6/5

Figure 12. Dynamic responses to a (0.005 step change in the set point of the top control loop (black lines, positive change; gray lines, negative change).

and 8(5)/6(4)/5 to a step change of (0.005 in the set point of the top control system are compared. For process design 5/6/5, the top product failed to reach a purity of 0.945 even though a substantial increase occurred in the reflux flow rate, in good accordance with the steady-state operation analysis in section 5. In particular, an initial oscillation occurred, giving rise to a drastic deviation from the nominal steady state. The complicated interactions between the reaction and separation operations and the multiple steady states are considered to be the primary reasons for the unusual dynamic behavior. Although the top product could, in principle, attain a purity of 0.935, the transition from 0.94 to 0.935 seemed to be very difficult and timeconsuming, even though the reflux flow rate experienced a considerable decrease (note also the large deviation caused in the composition of the bottom product). For process design 8(5)/ 6(4)/5, a fairly smooth transition was realized between the different specifications on the top product, with a reasonable settling time and tolerable interactions with the bottom control

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Figure 13. Dynamic responses to a (10% step change in the feed flow rate of MTBE (black lines, positive change; gray lines, negative change).

loop. At the new steady states reached, this process design still appeared to be much more thermodynamically efficient than the basic process design, 5/6/5 (cf., the new steady-state values of the manipulated variables: RR and QREB). With regard to the dynamic responses to a step change of (0.005 in the set point of the bottom control loop (although not shown here), the basic process design, 5/6/5, appeared to be likely to track the new set points on the bottom product, but still with a very long settling time. For process design 8(5)/ 6(4)/5, a much quicker transition was found between the different specifications on the bottom product. At the new steady states reached, process design 8(5)/6(4)/5 still appeared to be much more thermodynamically efficient than the basic process design, 5/6/5. 7.3. Dynamic Responses to a Step Change of (10% in the Feed Flow Rate of MTBE. In Figure 13, the closed-loop responses of process designs 5/6/5 and 8(5)/6(4)/5 to a step change of (10% in the feed flow rate of MTBE are compared. In the case of the negative perturbation in the feed flow rate,

both process designs could ultimately reject the disturbance and maintain the compositions of the top and the bottom products simultaneously at their specified set points. Whereas the basic process design, 5/6/5, exhibits long settling times in the top and the bottom control loops, process design 8(5)/6(4)/5 displays relatively large deviations in the top and bottom control loops for the first 4 h. In the case of the positive perturbation in the feed flow rate, the basic process design, 5/6/5, again displays a very long settling time, as well as a large offset in the bottom control loop. Process design 8(5)/6(4)/5 shows a response that is quite similar to the response to the negative perturbation in the feed flow rate. The inappropriate combination between the reaction and separation operations should account for the sluggish responses in process design 5/6/5. At the new steady states reached, process design 8(5)/6(4)/5 still appears to be much more thermodynamically efficient than process design 5/6/5. It is noted that, around the time of 13.5 h, a sudden change takes place within the basic process design, 5/6/5, bringing about drastic changes in the compositions of the top and bottom products. The input multiplicity and intricate interactions between the reaction and separation operations are considered to be responsible for the unusual dynamic behavior. Similar phenomena were also observed in the foregoing set-pointtracking studies in the bottom control loop. For process design 8(5)/6(4)/5, no such a phenomenon has yet been found. 7.4. Dynamic Responses to a Step Change in Feed Composition from (0, 0, 1.0) to (0.05, 0.05, 0.9). This scenario represents one of the most critical situations for examining the performance of internal heat integration between the reaction and separation operations involved in the MTBE decomposition reactive distillation column, because the profiles of temperature and liquid composition can be disturbed substantially in both static and dynamic states. In Figure 14, the closed-loop responses of process designs 5/6/5 and 8(5)/6(4)/5 to a change in the feed from a pure-component flow of MTBE (100 mol %) to a mixed flow of IBUT (5 mol %), MEOH (5 mol %), and MTBE (90 mol %). The basic process design, 5/6/5, was only slightly disturbed under these conditions, but it still presented a much long settling time and a sluggish response in the bottom control loop. In the case of process design 8(5)/6(4)/5, although it was disturbed more severely than process design 5/6/5 (for example, in the presence of relatively large deviations in both the top and the bottom control loops for the first 3 h, primarily attributable to the relatively small liquid holdups on the stages, in the condenser, and in the reboiler), the control systems could quickly set back the product compositions, giving a much shorter settling time and zero offset. Despite the dramatic changes in the operating conditions, process design 8(5)/6(4)/5 could still operate in a more thermodynamically efficient way than the basic process design, 5/6/5, demonstrating that the steady-state behavior of the combination between the reaction and separation operations is not as sensitive to changes in the feed composition for the case of the MTBE decomposition reactive distillation column. 8. Discussion The improvement in process dynamics and controllability from process design 5/6/5 to process design 8(5)/6(4)/5 should certainly be attributed to the refined relationship between the reaction and separation operations involved in the MTBE decomposition reactive distillation column. Simply distributing the reactive section between the rectifying section and the stripping section (e.g., as in the basic process design, 5/6/5) is,

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the rectifying section and the reactive section, a more coordinated relationship is evolved and the severity of interactions between the two combined operations is alleviated. This is why complicated process dynamic behavior was not observed in process design 8(5)/6(4)/5, thereby bringing about favorable influences on process operation. This outcome, together with the relative insensitivity of the resultant process design to changes in operating conditions, makes the reinforcement of internal heat integration a good candidate method for the synthesis and design of a reactive distillation column containing reactions with highly thermal effects. 9. Conclusions By means of synthesis, design, and control studies of a reactive distillation column for decomposing MTBE into isobutylene and methanol, it has been shown that seeking further internal heat integration between the reaction and separation operations can be an effective philosophy for the synthesis and design of a reactive distillation column containing a reaction with highly thermal effects. Apart from the increased thermodynamic efficiency and the reduced capital investment, both process dynamics and controllability were improved with the reinforcement of internal heat integration between the reaction and separation operations. The reason for this improvement stems solely from the well-coordinated relationship evolved during the trial-and-error search in the process synthesis and design. Future work will be centered on synthesis, design, and control studies of more complicated reactive distillation columns involving reactions with highly thermal effects. Experimentbased examinations of internal heat integration between the reaction and separation operations involved in a reactive distillation column are also needed in the future. Acknowledgment The authors are grateful to Dr. Hiroyuki Kodama and Dr. Yoshihiko Nagata [Research Institute for Human Science and Biomedical Engineering, National Institute of Advanced Industrial Science and Technology (AIST) of Japan] for their helpful comments. Nomenclature Figure 14. Dynamic responses to a step change in the feed composition from (0, 0, 1.0) to (0.05, 0.05, 0.9).

in general, unlikely to yield an appropriate combination between the reaction and separation operations and quite possibly leads to a strong conflict (or interaction) between the two operations, thereby giving rise to complicated process dynamics and sometimes great difficulties in process operation. For the MTBE decomposition reactive distillation column, the combination problem actually happens between the rectifying section and the reactive section. This is why complicated process dynamic behavior was primarily found in the top product of the basic process design, 5/6/5, including the saturation phenomenon (or the input multiplicity) between the top-product composition and the reflux flow rate/reboiler heat duty, the nonminimum phase behavior of the top-product composition to the changes in the reflux flow rate/reboiler heat duty, the unusual dynamic behavior of sudden changes in the composition of end products, and so forth. The complicated dynamics and uncertainties are bound to degrade the controllability of the basic process design, 5/6/ 5. With the reinforcement of internal heat integration between

b ) bottom withdrawal (mol s-1) d ) distillate flow rate (mol s-1) F ) feed flow rate of a reactant (mol s-1) ∆H ) heat of reaction (kJ kmol-1) KC ) proportional gain KCU ) ultimate gain Keq ) equilibrium constant L ) liquid flow rate (mol s-1) n ) number of stages N ) number of stages P ) pressure (kPa) PCU ) ultimate period (s) q ) feed thermal condition Q ) reboiler duty (MW) R ) reflux ratio RR ) reflux flow rate (mol s-1) T ) temperature (K) TI ) integral time (s) V ) vapor flow rate (mol s-1) x ) liquid composition zF ) feed composition

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ReceiVed for reView September 14, 2006 ReVised manuscript receiVed December 11, 2006 Accepted December 19, 2006 IE061204C

Design and Control of a Methyl Tertiary Butyl Ether (MTBE

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