Internal Heat Integration and Controllability of Double Feed Reactive

Aug 28, 2008 - and methyl acetate RD systems. The exploitation of the available design degrees of freedom (namely, catalyst redistribution for reactiv...
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Ind. Eng. Chem. Res. 2008, 47, 7304–7311

Internal Heat Integration and Controllability of Double Feed Reactive Distillation Columns, 2. Effect of Catalyst Redistribution M. V. Pavan Kumar and Nitin Kaistha* Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India

The effect of internal heat integration by catalyst redistribution on the controllability of an ideal and a methyl acetate reactive distillation (RD) column is studied. Conventional designs with feeds immediately above and below the reactive section are internally heat integrated by (a) extending the reactive section into the stripping section with catalyst redistribution, followed by (b) altering the feed tray locations. For the ideal RD system, only reactive section extension results in a design with a reboiler energy savings of 7.7%. The design obtained by reactive section extension followed by altered feed tray locations gives greater energy savings of 18.2%. For the methyl acetate system, simple reactive section extension with no change in the feed tray locations gives the most energy-efficient design with an energy savings of 39.7%. A comparison of the closed-loop performance of the two-point temperature control structures for the different designs demonstrates that temperature inferential control can be used to regulate the internally heat-integrated designs of both the ideal and methyl acetate systems. The controllability of the ideal RD column with full internal heat integration (both items (a) and (b) above) is found to be inferior to the conventional design. For the methyl acetate system, the controllability of the internally heat-integrated design is improved, relative to the conventional design. Introduction In double feed reactive distillation (RD) systems such as esterification columns, typically, the light and heavy reactants are fed, respectively, immediately below and above the reactive section. Recent literature reports show that significant energy savings are possible by altering the conventional design to allow feeds into the reactive section as well as by catalyst redistribution to extend the reactive section into the stripping (rectifying) section for an exothermic (endothermic) reaction.1–3 In other words, the column design degrees of freedom can be exploited toward further internal heat integration for reduced capital and operating costs. Although internal heat integration is economically beneficial, its impact on the overall controllability of the RD process is not well-understood. The issue is particularly relevant, because RD systems are known to be highly nonlinear and routinely exhibit steady-state multiplicity.4–9 The multiplicity makes the process vulnerable to nonlinear dynamic phenomena such as “wrong” control action10 or a steady-state transition under closed-loop operation,11 severely compromising control system robustness. Therefore, proper evaluation of the controllability of internally heat-integrated RD columns is imperative to ensure that the column designs, while being economical, are operable in practice. In Part 1 of this article series,12 the impact of internal heat integration by allowing reactant feeds into the reactive zone on the controllability of a hypothetical ideal and a methyl acetate RD column was studied. Another possibility for internal heat integration of RD systems with exothermic reactions is to extend the reactive section into the stripping section with catalyst redistribution.1 The reaction heat released on the extension trays reduces the reboiler vaporization load. In this work, the impact of catalyst redistribution for reduced energy consumption on column controllability is evaluated for the double feed ideal13 and methyl acetate RD systems. The exploitation of the available * To whom correspondence should be addressed. Tel.: 91-512-2597432. Fax: 91-512-259-0104. E-mail: [email protected].

design degrees of freedom (namely, catalyst redistribution for reactive zone extension and altered feed tray locations) toward internal heat integration, and its effect on controllability using temperature inferential control, is systematically addressed for the two example systems. The work is relevant in that the methyl acetate RD system has not been analyzed from the perspective of internal heat integration and its effect on controllability, to the best of our knowledge. For the ideal RD system, Huang et al.2 have shown that a three-composition control structure can be used to regulate the internally heat-integrated column designs. However, the applicability of temperature inferential control instead of composition-based control has not been considered. The article is organized as follows. Internally heat-integrated designs via extension of the reactive section into the stripping section and then additionally by adjustment of the feed tray locations are obtained first. Two-point temperature control structures are then synthesized and their closed-loop responses are quantitatively compared for large throughput changes. The main inferences from the results are finally summarized in the conclusions. Internally Heat-Integrated Designs The conventional column design (Design A) for both the ideal and methyl acetate RD systems is the same as that described in our previous work.12 The reader is referred to that article for details regarding the model, design, and operating conditions. Briefly, Design A consists of 5 rectifying trays, 10 reactive trays, and 5 stripping trays, with a catalyst loading of 0.7 kmol per tray for the ideal RD system. The corresponding figures for the methyl acetate RD column design are 7 rectifying trays, 18 reactive trays, and 10 stripping trays, with a catalyst loading of 300 kg per tray. Design A serves as the baseline for comparing the reduction in reboiler duty and the closed-loop control performance of the internally heat-integrated designs. For internal heat integration, the reactive section is extended into the stripping section with the total amount of catalyst being

10.1021/ie071639f CCC: $40.75  2008 American Chemical Society Published on Web 08/28/2008

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Figure 2. Variation in reboiler duty with alteration of feed tray locations in the ideal RD column, Design C. Table 1. Key Parameters of Ideal RD Column Designs Studied Ideal RD Column parameter

Figure 1. Variation in reboiler duty by reactive section extension into stripping section with catalyst redistribution: (a) ideal RD column and (b) methyl acetate RD column.

redistributed equally among all the reactive trays. The design with the lowest reboiler duty is then the best heat-integrated design obtained by extension of the reactive section with catalyst redistribution. This design is referenced as Design C, in continuation with the labels given to the designs in our earlier work.12 Design C can be further internally heat-integrated by altering the location of the two feed trays. The least reboiler duty design obtained in this manner exploits the available degrees of freedom of the design (namely, reactive section extension with catalyst redistribution and altered feed tray locations) and is referenced as Design D. Figure 1 plots the variation in reboiler duty with the number of reactive trays extended into the stripping section for the ideal and methyl acetate RD systems. The minimum reboiler duty design for the ideal system is obtained for three extension trays, with a 7.7% reduction in energy consumption. For the methyl acetate RD column, the corresponding design is obtained for eight extension trays, with a 39.7% energy savings. Figure 2 plots the variation in reboiler duty as the lower feed tray location is altered for Design C with the higher feed tray location being varied as a parameter for the ideal RD system. Design D, which corresponds to the minimum reboiler duty, is thus obtained for the lower feed tray moving up by 4 trays and the higher feed tray moving down by 2 trays, with respect to Design C. The reduction in reboiler duty is 18.2%, relative to the conventional design, Design A. For the methyl acetate RD system, altering either of the feed tray locations in Design C causes the reboiler duty to increase. Therefore, Design C and Design D are identical. Table 1 summarizes the key design and operating parameters of the conventional (Design A) and internally heat-integrated designs (Design C and Design D) for the ideal RD system.

feed flow rate (FA ) FB) NE/NRX/NS feed tray locations catalyst loading per tray pressure reflux ratio distillate rate reboiler duty distillate purity, xC, D

Design A 12.6 mol/s

Design C 12.6 mol/s

Design D 12.6 mol/s

5/10/5 5/13/2 5/13/2 nFA ) 6; nFB ) 15 nFA ) 6; nFB ) 15 nFA ) 9; nFB ) 13 0.7 kmol 0.5385 kmol 0.5385 kmol 8.5 bar 2.718 12.6 mol/s 0.86086 MW 0.95

8.5 bar 2.5374 12.6 mol/s 0.7947 MW 0.95

8.5 bar 2.29 12.6 mol/s 0.7040 MW 0.95

Table 2. Key Parameters of the Methyl Acetate RD Column Designs Studied Value parameter

Design A

Design C

flow rate of feeds

FHAc ) FMeOH ) 300 kmol/h 7/18/10 nFMeOH ) 11; nFHAc ) 28 300 kg

FHAc ) FMeOH ) 300 kmol/h 7/26/2 nFMeOH ) 11; nFHAc ) 28 207.7 kg

1.013 2.287 308.63 kmol/h 5.7616 MW

1.013 1.4158 308.63 kmol/h 3.4754 MW

0.950 0.963

0.950 0.960

NE/NRX/NS feed tray locations catalyst loading per tray pressure, bar reflux ratio distillate rate reboiler duty product purity, xMeOAc, D xwater, B

Notice that Design D, obtained by appropriately utilizing the available degrees of freedom of the design (namely, reactive zone extension and feed tray location alteration) is significantly more energy-efficient than Design C, which exploits only the former. Clearly, from the economic perspective, Design D should be preferred over Design C. From the viewpoint of controllability however, Design C may be superior. This is particularly relevant, considering the deterioration in controllability by feed tray location alteration, as observed in our previous work.12 Accordingly, both these designs are evaluated for closed-loop control performance using two-point temperature inferential control in the following. Table 2tabulates the main design and operating conditions for Design A and Design C of the methyl acetate column. Note that Design D is identical to Design C for the methyl acetate system.

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Figure 4. Open-loop and closed-loop sensitivity of tray temperatures, with respect to FB. Table 3. Control Structure Loop Pairings and the Corresponding Niederlinski Index (NI), Condition Number (CN), and -(K-1 · kTP)T Vector control structure

loop pairings

NI

CN

-(K-1 · kTP)T

Ideal RD Column, Design C CS1 CS2 CS4

T10-FB; T2-FA T10-Qr; T2-FA T10-FB; T2-Qr

CS1 CS2 CS4

T11-FB; T5-FA T11-Qr; T5-FA T11-FB; T5-Qr

CS1 CS2 CS4

T5-FHAc; T2-FMeOH T5-Qr; T2-FMeOH T5-FHAc; T2-Qr

0.9398 1.031 2.945

11.38 9.433 3.568

[1.0386 0.7117] [0.9628 0.6852] [1.4594 1.4051]

Ideal RD Column, Design D 2.6227 0.3294 3.4205

51.5547 87.2706 25.5717

[0.7886 0.8391] [1.2683 1.0643] [0.9397 1.1917]

Methyl Acetate RD Column, Design C

Figure 3. Tray temperature sensitivity profiles of example RD systems: (a) ideal and (b) methyl acetate.

Design A and Design C are compared for their closed-loop performance, using two-point temperature inferential control. Two-Point Temperature Inferential Control Structures There are three possible control structures with the reboiler duty or one of the two fresh feeds as the throughput manipulator. Given a throughput manipulator, the remaining two inputs control two sensitive tray temperatures. The three resulting structures corresponding to the reboiler duty, the heavy reactant feed, and the light reactant feed as the throughput manipulator are labeled, respectively, CS1, CS2, and CS4. Figure 3 plots the tray temperature sensitivities, with respect to the three inputs, at a constant reflux ratio for the internally heat-integrated design(s) of the ideal and methyl acetate RD systems. For the ideal RD system, a sensitive reactive tray

0.9902 1.2527 1.0388

1.76 3.26 1.99

[0.989 0.9656] [1.011 0.9964] [1.0242 1.0356]

temperature must be controlled, even as rectifying tray temperatures exhibit higher sensitivity. This is because the latter exhibit a severe inverse response and input multiplicity, with respect to the heavy reactant feed.14 The ideal RD column Design D sensitivities in Figure 3 show that the reactive tray temperature sensitivities are very low. In particular, the sensitivity is almost zero, with respect to the heavy reactant feed FB. This suggests that, unlike Design C (and the conventional design), it may be difficult to control a reactive tray temperature using FB, which is a manipulated variable for control structures CS1 and CS4. However, it has been shown that, because of the high interaction between the reaction and separation in RD systems, the sensitivity may change significantly, depending on whether other loops are in “manual” or “auto” mode.15,16 We determined that the sensitivity of the reactive trays to FB improves if a sensitive tray temperature below the lower feed is held constant (for example, using reboiler duty Qr, as in control structure CS4). This is verified from Figure 4, which plots the temperature sensitivity, with respect to FB, holding T5 constant (Qr is adjusted). The temperature of reactive tray 11 between the two fresh feeds exhibits good sensitivity, with respect to FB. For the methyl acetate column, Design C, the tray temperature sensitivities are well-behaved. The sensitivity profiles are not collinear, and, with respect to every input, a sensitive tray temperature location (or zone) is clearly evident. The input-output (IO) pairings used in each of the three structures are noted in Table 3 for the example RD systems. To quantify the interaction between the two loops, the Niederlinski Index (NI), the condition number (CN), and the

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-K · kTP vector are noted in the table. The derivation and meaning of the latter has been described in detail in our earlier work.12 For the ideal RD system, notice that the CN values of all three control structures in Design D is noticeably higher than that for Design C, which suggests collinearity. The collinearity is also evident in the sensitivity plot (see Figure 3). Also, the -K-1 · kTP elements are closer to 1 for all structures in Design C, which implies better balance with a unit change in the throughput manipulator causing a unit change in the control inputs. The data suggest that Design C may be more controllable than Design D. Even so, the fact that the -K-1 · kTP elements are positive in all the control structures for Design D suggests that temperature inferential control may be feasible. This is in direct contrast to the infeasibility of two-point temperature inferential control of Design B obtained by adjusting only the feed tray locations in our previous work.12 Therefore, catalyst redistribution gives approximately the same reduction in reboiler duty (18.3% for Design B and 18.2% for Design D) while improving controllability with temperature inferential control being feasible. For the methyl acetate column, Design C, the CN of all the control structures is not too large, which suggests relative independence of the two loops for small deviations around the base-case steady state. The NI value for all the structures is surprisingly close to 1, which indicates that the interaction between the two loops in the vicinity of the base-case steady state is only one-way. Also, the -K-1 · kTP element values of all the structures are close to 1, which indicates a well-balanced control system. Therefore, temperature inferential control is likely to work well for the methyl acetate column, Design C. Closed-Loop Dynamics Simulation Results Dynamic Simulation and Controller Tuning. As in Part 1,12 rigorous dynamic simulations are performed using the method of Jhon and Lee.17 The distillate and bottoms flow rates control the reflux drum and bottom sump levels, respectively. The reflux drum and bottoms sumps are sized for a 5-min holdup (at the 50% level) under the base-case conditions. The level controllers are P only with a gain of 2. Perfect pressure and flow control is assumed as the dynamics are much faster than the slow temperature loops. Pressure drop across the column is neglected. Two first-order lags of 1 min each are applied in series to the temperature measurements. All the temperature loops are tuned using the Tyreus-Luyben (TL) settings.18 The ultimate gain and period for the loops are obtained from the relay feedback test.19 Table 4 reports the control-structurespecific tuning parameters and detuning factors for the ideal/ methyl acetate RD column designs. For the methyl acetate system, the stripping loop is individually tuned, followed by sequential tuning14 of the reactive loop for control structures CS1 and CS4. Both loops are tuned individually for control structure CS2. For the ideal RD system, in all of the control structures, both the temperature loops are tuned individually. Closed-Loop Results. The two-point temperature inferential control structures are tested for large (20% step throughput changes, the principal load disturbance. The steady-state deviation and the integral absolute error (IAE) of the product purities are used to quantify the control performance. Ideal RD System. The closed-loop response of the two-point temperature control structures CS1, CS2, and CS4 of the ideal column, Design C and Design D, is shown in Figures 5 and 6, respectively. The large throughput changes in either direction are handled properly by all of the structures for both Design C

Table 4. Controller Tuning Parameters control structure

τI

f

21.1200 18.6912 15.312 18.6912 21.1200 11.55

1 1 1 1 1 1

32.60 19.48 19.05 19.48 32.60 11.22

2 1 1 1 2 1

Kc Ideal RD Column, Design C

CS1 CS1 CS2 CS2 CS4 CS4

T10-FB T2-FA T10-Qr T2-FA T10-FB T2-Qr

4.1167 0.7862 2.3255 0.7862 4.1167 0.5738

Ideal RD Column, Design D CS1 CS1 CS2 CS2 CS4 CS4

T11-FB T5-FA T11-Qr T5-FA T11-FB T5-Qr

3.4167 0.6919 1.8955 0.6919 3.4167 0.6197

Methyl Acetate RD Column, Design C CS1 CS1 CS2 CS2 CS4 CS4

T5-FHAc T2-FMeOH T5-Qr T2-FMeOH T5-FHAc T2-Qr

0.3375 0.5314 0.9492 0.5314 1.534 1.205

130.94 54.98 16.5 54.98 27.50 16.95

1 1 3 2 2 5

and Design D. All the responses are complete within ∼4 h. In the dynamic simulations, all the control structures were determined to work well for the TL controller settings with no detuning of the temperature controllers (i.e., f ) 1) in Design C. In Design D, however, the reactive tray temperature control loop must be detuned, or else the “wrong” control action occurs for control structures CS1 and CS4 with the two control inputs moving in opposite directions and saturating, instead of moving in tandem for a 20% throughput decrease. Table 5 tabulates the steady-state product purity and IAE of the distillate and bottoms purity for Design C and Design D. To facilitate comparison with the conventional design, the corresponding data for Design A are also reported in the table. The final steady-state purity is within 1% of the design value for Design A and Design C, whereas for Design D, the deviation is >1% (∼1.1%). The steady-state distillate purity deviation for a 20% throughput change increases in the following order: Design A, Design C, and Design D. The distillate purity IAE values in Table 5 may be considered to be comparable for Design A and Design C, whereas, for Design D, the values are significantly higher for either a throughput increase or a decrease in all the evaluated control structures. The bottoms purity IAE values for Design D are consistently higher than those for Design C for all the structures. The IAE data also suggest that the tightest distillate purity control for all the designs is obtained using control structure CS2. The superior performance of control structure CS2 may be attributed to the fast dynamic response of both of the temperature loops to the control inputs, the reboiler duty, and the light reactant feed. In control structures CS1 and CS4, the dynamics of the reactive tray temperature control loop is relatively much slower. This can be verified from the controller reset times shown in Table 4. The steady-state deviation in the product purities in Table 5 for the two-point temperature control structures suggests that the column operating conditions need further adjustment to minimize the deviations and ensure on-spec distillate and bottoms purities. Table 6 tabulates the percent change in reboiler duty if the operating conditions are adjusted for on-spec product purities for Design A, Design C, and Design D for a 20% throughput change. One would expect that the 20% throughput change would result in a corresponding ∼20% change in the reboiler duty. The only exception to this trend in Table 6 is a

7308 Ind. Eng. Chem. Res., Vol. 47, No. 19, 2008

Figure 5. Closed-loop response to a (20% throughput change of two point temperature control structures for the ideal RD column, Design C: (a) CS1, (b) CS2, and (c) CS4.

20% throughput increase in Design D that required double the increase in the reboiler duty. Therefore, the significant (∼20%) internal heat-integration advantage under the base-case operating conditions for Design D gets significantly diluted for a large production rate increase. On the other hand, the balanced change in the reboiler duty in Design C suggests that the internal heatintegration advantage is retained for large throughput changes. These results, in totality, suggest that Design D is inferior to Design A and Design C, in terms of controllability. Both Design A and Design C are controllable, using temperature inferential control. To compensate for the slightly higher steady-state product purity deviations in Design C (see Table 5), the column may be operated at an incrementally higher reflux ratio. The corresponding increase in the reboiler duty for the same distillate product purity deviation to a 20% throughput increase is only marginal (∼2%). Given that the base-case Design C reboiler

Figure 6. Closed-loop response to a (20% throughput change of two point temperature control structures for the ideal RD column, Design D: (a) CS1, (b) CS2, and (c) CS4.

duty is 7.7% less than that for Design A, the energy advantage is retained, even at the slightly higher reflux ratio. Design C, which is obtained from catalyst redistribution, to extend the reactive zone into the stripping section, is therefore considered to the best overall in that it consumes less energy and its controllability using two-point temperature inferential control is comparable to Design A (conventional design). Methyl Acetate RD System. The closed-loop response of control structures CS1 and CS2 for Design C to a 20% throughput change is plotted in Figure 7. Both structures handle the throughput change well, with the control inputs increasing or decreasing in tandem. For control structure CS1, the response is completed within 15 h. The response completion time for control structure CS2 is also approximately the same. Control structure CS4 was determined to work only for a narrow range of tuning parameters similar to Design B in our previous work.12

Ind. Eng. Chem. Res., Vol. 47, No. 19, 2008 7309 Table 5. Steady-State Distillate and Bottoms Purity and Its Integral Absolute Error (IAE) for Throughput Changes for the Ideal RD Column Designs Distillate Purity control structure

IAE

final steady value

Table 7. Steady-State Distillate and Bottoms Purity and Its Integral Absolute Error (IAE) for Throughput Changes for the Methyl Acetate RD Column Designs

Bottoms Purity IAE

final steady value

0.3625 0.5223 0.0844 0.2060 0.1832 0.0801

0.9492 0.9510 0.9491 0.9510 0.9491 0.9510

Distillate Purity control structure

throughput change

final steady value

+20% -20% +20% -20%

45.91 21.49 1.682 5.703

Design C CS1 CS1 CS2 CS2 CS4 CS4

+20% -20% +20% -20% +20% -20%

1.1985 1.4894 0.5866 0.9447 1.2960 1.5130

0.9410 0.9587 0.9403 0.9590 0.9405 0.9590

+20% -20% +20% -20% +20% -20%

2.1922 1.1272 1.2898 1.3873 1.2728 2.7399

0.9364 0.9584 0.9377 0.9606 0.9355 0.9587

1.6361 1.3153 2.0426 1.1251 1.7064 1.8039

0.9512 0.9550 0.9478 0.9533 0.9511 0.9551

Table 6. Percent Increment in Reboiler Duty for a (20% Throughput Change with On-Spec Distillate Purity (95%) for Ideal RD Column Designs Percentage Increment (%)

Design A Design C Design D

IAE

IAE

0.9505 0.9495 0.9506 0.9494

34.58 90.73 4.726 5.302

0.9500 0.9755 0.9511 0.9752

11.54 16.96 16.11 10.58

0.9493 0.9687 0.9494 0.9687

Design A

Design D CS1 CS1 CS2 CS2 CS4 CS4

Bottoms Purity final steady value

20% increase

20% decrease

21.02 21.31 40.02

-20.68 -20.83 -22.35

Table 7 reports the steady-state distillate and bottoms purity and the corresponding IAE for the two-point temperature

CS1 CS1 CS2 CS2

Design C CS1 CS1 CS2 CS2

+20% -20% +20% -20%

0.8632 0.7996 1.4159 1.6545

0.9465 0.9533 0.9465 0.9533

inferential control structures. For comparison, the data for the conventional design, Design A, are also reported in the table. The steady-state distillate product purity deviations, relative to a 20% throughput change, are higher for Design C (∼0.35%) compared to that for Design A (∼0.05%). To compensate for the same, Design C can be operated at a slightly higher reflux ratio, so that the steady-state distillate purity does not decrease below 95% for the worst-case disturbance, which is a 20% throughput increase. The reboiler duty increases only slightly (∼2%) over its base-case value for the slight increase in reflux ratio. The same does not significantly alter the substantially lower (∼40%) reboiler duty in Design C (compared to Design A). A comparison of the IAE values shows that the distillate product purity control is tighter for both control structures CS1 and CS2 for Design C. The improvement in the control performance of control structure CS1 is particularly impressive. These results suggest that, from the perspective of both energy savings and controllability, the internally heat-integrated design, Design C, obtained by reactive zone extension into the stripping section by catalyst redistribution, is superior to the conventional design, Design A. Discussion

Figure 7. Closed-loop response to a (20% throughput change of two point temperature control structures for the methyl acetate RD column, Design C: (a) CS1 and (b) CS2.

At this point, it is worthwhile to recapitulate and discuss the salient findings of the impact of internal heat integration on controllability of the ideal and methyl acetate double feed RD columns. Including our earlier work,12 four column designs have been considered: (i) conventional Design A, with the heavy and light reactant being fed immediately above and below the reactive zone; (ii) the internally heat-integrated Design B, which is obtained by altering the feed tray locations in Design A; (iii) the internally heat-integrated Design C, which is obtained by extending the Design A reactive zone into the stripping section with catalyst redistribution; and (iv) the internally heat-integrated Design D, obtained by altering the feed tray locations of Design C. These four designs are distinct for the ideal RD system while for the methyl acetate RD system, Design C and Design D are identical. The results for the ideal RD system seem to suggest that catalyst redistribution onto the stripping trays tends to improve controllability. Therefore, temperature inferential control works for Design C (catalyst redistribution + feed location alteration) while it is infeasible for Design B (feed tray location alteration only). Also, temperature inferential control works well for Design C (catalyst redistribution only), even as the design consumes less reboiler energy. On the other hand, internal heat integration by alteration of feed tray locations seems to adversely

7310 Ind. Eng. Chem. Res., Vol. 47, No. 19, 2008 Table 8. Open-Loop Temperature and Acetic Acid Mole Fraction Sensitivities of Controlled Reactive Tray for Methyl Acetate RD Column Designs ∂Tn/∂FHAc (K/%)

(∂xHAc/∂FHAc)|n (mol fraction/%)

(∂xHAc/∂Qr)|n (mol fraction/%)

-4.21 -1.55 -2.24

-0.0210 0.0146 0.0181

0.0217 -0.0081 -0.0082

Design A Design B Design C

Figure 8. Bifurcation diagram of distillate and bottoms purity, with respect to reboiler duty for methyl acetate column Design C.

affect controllability. The infeasibility of temperature inferential control for Design B (feed tray location alteration only), compared to Design A (conventional), and the inferior controllability of Design D (extension + feed location alteration), compared to Design C (extension only), suggest the same. The ideal RD case study results also suggest that due caution must be exercised in seeking internal heat integration. The most energy-efficient designs, Design B and Design D with ∼18% energy savings, exhibit poor controllability. On the other hand, Design C, with a comparatively smaller energy savings of 7.7%, exhibits good controllability. These findings also suggest that controllability issues should be considered at the column design stage. The results for the methyl acetate RD system are much more encouraging in that internal heat integration by either feed tray location alteration or by catalyst redistribution gives significant energy savings with improved controllability compared to the conventional design. Huang et al.2 have emphasized that internal heat integration gives more-refined relationships between reaction and separation, with a consequent improvement in controllability. Figure 8 plots the bifurcation diagram of the distillate and bottoms purity, with respect to the reboiler duty at constant reflux rate and constant reflux ratio for Design C. Notice that, for this most energy-efficient design, no output multiplicity occurs with respect to the base-case operating condition at a fixed reflux rate. On the other hand, Design A and Design B exhibit output multiplicity, as previously observed.12 If the reboiler duty changes as a large negative pulse with the fresh feeds and reflux rate at their base-case values, Designs A and B would settle at the low distillate purity steady state, whereas Design C would return to its base-case steady state. An openloop steady-state transition10 is avoided in Design C. Thus, in some sense, the dynamic behavior of Design C is better than that of the other two designs. Another interesting feature of the methyl acetate case study is the marked improvement in the closed-loop dynamic response of control structure CS1 from Design A to Design B to Design C. The reactive control tray temperature location for Design A, Design B, and Design C is tray 18, tray 13, and tray 5, respectively. The latter two tray locations are below the methanol feed tray (tray 11). Table 8 notes the reactive control tray temperature and acetic acid mole fraction sensitivity. The

tray temperature sensitivities are negative for all the designs. The composition sensitivity is positive for Design B and Design C and negative for Design A. If the reboiler duty is increased, the control tray temperature increases and the acetic acid feed increases to bring the temperature back down. The control tray acetic acid composition for Design B and Design C decreases and the increasing acetic acid feed helps to restore the composition. On the other hand, for Design A, the tray acetic acid composition increases so that the temperature control action and the direction of composition response do not match. This mismatch helps in partially explaining the improvement in control performance of the internally heat-integrated designs over the conventional design using control structure CS1. Last but not least, we emphasize that, for both the ideal and methyl acetate systems, the control performance of control structure CS2 was determined to be the best, in terms of the tightness of the product purity control that is achieved. In both systems, the dynamic response of the control tray temperatures to the corresponding manipulated variables (the light reactant feed and the reboiler duty) is fast. On the other hand, the dynamic response of the control tray locations to the heavy reactant feed, which is a manipulated variable in control structures CS1 and CS4, is noticeably slower. The discussion highlights the crucial role of the choice of the manipulation handle on control performance. Conclusions In conclusion, catalyst redistribution to extend the reactive section into the stripping section results in a reduction of 7.7% and 39.7% in the reboiler duty of the ideal and methyl acetate reactive distillation (RD) columns, respectively. Further internal heat integration with an 18.2% reduction in reboiler duty is achieved for the ideal RD column by altering the feed tray locations. All the internally heat-integrated column designs can be regulated using two-point temperature inferential control. For the ideal RD system, the controllability of the design with only reactive zone extension is comparable to the conventional design. The controllability of the design obtained by further altering the feed tray locations is inferior. For the methyl acetate system, internal heat integration by only catalyst redistribution for reactive zone extension gives the most energy-efficient design. The controllability of this design is superior to the conventional design. The results illustrate that, for both of the double feed RD columns studied, internal heat integration, when done appropriately, involves no loss in controllability. Acknowledgment The financial support from the Department of Science and Technology, Government of India, is gratefully acknowledged. Literature Cited (1) Huang, K.; Iwakabe, K.; Nakaiwa, M.; Tsutsumi, A. Towards Further Internal Heat Integration in Design of Reactive Distillation Columns;Part 1: The Design Principle. Chem. Eng. Sci. 2005, 60, 4901.

Ind. Eng. Chem. Res., Vol. 47, No. 19, 2008 7311 (2) Huang, K.; Nakaiwa, M.; Tsutsumi, A. Towards Further Internal Heat Integration in Design of Reactive Distillation Columns;Part 2: The Process Dynamics and Operation. Chem. Eng. Sci. 2006, 61, 5377. (3) Huang, K.; Nakaiwa, M.; Wang, S. J.; Tsutsumi, A. Reactive Distillation Design with Considerations of Heats of Reaction. AIChE J. 2006, 53, 2518. (4) Ciric, A. R.; Miao, P. Steady-State Multiplicities in an Ethylene Glycol Reactive Distillation Column. Ind. Eng. Chem. Res. 1994, 33, 2738. (5) Guttinger, T. E.; Morari, M. Predicting Multiple Steady-States in Distillation: Singularity Analysis and Reactive Systems. Comput. Chem. Eng. 1997, 21, 995. (6) Jacobs, R.; Krishna, R. Multiple Solutions in Reactive Distillation for Methyl tert-Butyl Ether Synthesis. Ind. Eng. Chem. Res. 1993, 32, 1706. (7) Hauan, S.; Hertxberg, T.; Lien, K. M. Why Methyl-tert-Butyl-Ether Production by Reactive Distillation May Yield Multiple Solutions. Ind. Eng. Chem. Res. 1995, 34, 987. (8) 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 Validation. Chem. Eng. Sci. 1999, 54, 1029. (9) Singh, B. P.; Singh, R.; Kumar, M. V. P.; Kaistha, N. Steady State Analysis of Reactive Distillation Using Homotopy Continuation. Chem. Eng. Res. Des. 2005, 83, 959. (10) Pavan Kumar, M. V.; Kaistha, N. Role of Multiplicity in Reactive Distillation Control System Design. J. Process Control 2008, 18, 692. (11) Pavan Kumar, M. V.; Kaistha, N. Steady State Multiplicity and Its Implications on the Control of an Ideal Reactive Distillation Column. Ind. Eng. Chem. Res. 2008, 47, 2778.

(12) Pavan Kumar, M. V.; Kaistha, N. Internal Heat Integration and Controllability of Double Feed Reactive Distillation Columns, 1. Effect of Feed Tray Locations. Ind. Eng. Chem. Res. 2008, 47, 7294. (13) Luyben, W. L. Economic and Dynamic Impact of the Use of Excess Reactant in Reactive Distillation Systems. Ind. Eng. Chem. Res. 2000, 39, 2935. (14) Kaymak, D. B.; Luyben, W. L. Comparison of Two Types of Two Temperature Control Structures for Reactive Distillation Columns. Ind. Eng. Chem. Res. 2005, 44, 4625. (15) Singh, R.; Kumar, M. V. P.; Kaistha, N. Steady-State Reactive Distillation Simulation Using the Napthali-Sandholm Method. Can. J. Chem. Eng. 2007, 85, 75. (16) Lee, H. Y.; Huang, H. P.; Chien, I. L. Control of Reactive Distillation Process for Production of Ethyl Acetate. J. Process Control 2007, 17, 363. (17) Jhon, Y. H.; Lee, T. H. Dynamic Simulation for Reactive Distillation with ETBE Synthesis. Sep. Purif. Technol. 2003, 31, 301. (18) Tyreus, B. D.; Luyben, W. L. Tuning PI Controllers for Integrator/ Dead Time Processes. Ind. Eng. Chem. Res. 1992, 31, 2625–2628. (19) Astrom, K. J.; Hagglund, T. Automatic Tuning of Simple Regulators with Specifications on Phase and Amplitude Margins. Automatica 1984, 20, 645.

ReceiVed for reView December 2, 2007 ReVised manuscript receiVed May 30, 2008 Accepted June 16, 2008 IE071639F