Control of Quaternary Reactive Distillation Columns: Effects of Number

Article pubs.acs.org/IECR

Control of Quaternary Reactive Distillation Columns: Effects of Number and Location of Temperature Loops Baris Demirel and Devrim B. Kaymak* Department of Chemical Engineering, Istanbul Technical University, 34469, Maslak, Istanbul, Turkey ABSTRACT: The most frequently studied ideal system for reactive distillation columns is the quaternary system with two reactants and two products. The vast majority of reactive distillation literature on control uses two-point inferential control structures with conventional tray selection techniques such as singular value decomposition (SVD) and relative gain array (RGA) analysis. Another common practice for the ideal systems is the assumption of constant relative volatilities. This paper compares two control structures with different number of temperature loops and two alternative sets of tray locations, in terms of the controllability of systems with temperature-dependent relative volatilities. It is observed that a three-point inferential control structure with a new set of tray locations based on a semisystematic method improves the control performance for all three systems studied. This improvement is particularly significant in the purity of the distillate stream as the temperature dependency increases.

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INTRODUCTION Distillation is one of the premier separation methods in the chemical industry; it has been extensively studied for almost a century. Skogestad pointed out three typical issues in the distillation control that must be addressed by the engineers.1 The first issue is the control structure problem, including the decisions on what the remaining control degrees of freedom should be after all liquid levels and gas pressures are controlled. The second issue involves the number of compositions to be controlled. Although there are studies in the literature with control structures including composition controllers, temperatures are widely used in the industry to provide inferential control of compositions. Thus, the third isssue is the number of temperature loops to be closed and the decision on the location of temperature sensors. Luyben discussed five alternative criteria, which are the most widely used in practice, for selecting the best tray locations, and compared them using several case studies.2 On the other hand, reactive distillation columns have received a considerable attention for the past two decades, and there is a rapid growth in the studies on dynamics and controllability of this process. Accordingly, alternative control structures have been evaluated in the literature. Some of these configurations include composition control loops, while the others are inferential temperature control structures. As far as we know, with two exceptions, all the reactive distillation control literature focused on the inferential temperature control structures (it does not matter if they investigate generic or real chemical systems) include only the two-point temperature control structures. Most of these studies use conventional techniques such as sensitivity analysis (SA), singular value decomposition (SVD) method, and relative gain array (RGA) analysis to select the best tray locations.3−9 In addition, only constant (temperature-independent) relative volatilities are used for the generic chemical systems. The first exception is a three-point temperature control structure suggested by Kumar and Kaistha.10 They investigated two different configurations of a three-point temperature © 2013 American Chemical Society

control structure for an ideal quaternary system with a constant relative volatility of 2. They used sensitivity analysis to pair the controlled variables with the corresponding manipulated variables. The manipulated variables of the first configuration are selected as fresh feed streams of the light and heavy reactants (FA0 and FB0) and reflux rate (R), while the second configuration has the fresh B feed flow (FB0), vapor boilup (VS) and reflux rate (R) as the manipulated variables. Although these control structures provide a stable column operation, they cannot maintain the distillate and bottoms product purities for large throughput changes. Based on our knowledge on twopoint temperature control structures,11 we believe that the significant deviation from the purity specification is because of the wrong selection of manipulated variables. The second exception is another three-point temperature control structure suggested by Kookos.12 The manipulated variables of this structure are vapor boilup (VS), fresh A feed flow (FA0), and distillate flow rate (D). Instead of widely used methods such as SA/SVD/RGA, a systematic methodology previously proposed by Kookos13 is used to determine the controlled temperatures, and then the pairing problem is solved. The results show that there are significant changes in the locations of controlled temperatures. It is claimed that this control structure with the new set of tray locations outperforms all previously proposed structures. In addition, it is indicated that this methodology has benefits such as minimizing the economic penalty associated with product overpurification. The case study to which the systematic methodology is applied is an ideal reactive distillation column presented in the literature.11 This is a column for a quaternary system with a constant relative volatility of 2. Received: Revised: Accepted: Published: 5943

November 28, 2012 February 22, 2013 March 26, 2013 March 26, 2013 dx.doi.org/10.1021/ie3032789 | Ind. Eng. Chem. Res. 2013, 52, 5943−5950

Industrial & Engineering Chemistry Research

Article

Recently, Kaymak et al. studied the effect of temperaturedependent relative volatilities on inferential temperature control of reactive distillation columns.14 They used a twopoint temperature control structure, where fresh feed stream of the light reactant (FA0) and vapor boilup (VS) are the manipulated variables, for the ideal quaternary system. Their results illustrated that the magnitude of the offset in final product purities increases significantly with the increase in the temperature dependence of relative volatilities. It is seen that this is especially true for the distillate product purity. The purpose of this study is to examine if a three-point inferential control structure and/or alternative control tray locations can decrease the magnitude of the offset in final product purities for systems with temperature-dependent relative volatilities. For this purpose, two different types of inferential control structures and two different sets of control tray locations are explored. The control structures studied in this paper are the two-point and three-point inferential control structures. The control tray locations are selected based on the SVD method and Kookos’ suggestions. The comparison is made using three ideal systems with different temperature-dependent relative volatilities.

The kinetic parameters and Antoine constants for three different temperature-dependent relative volatility (α390) cases are reported in Table 1. The details of developing

PROCESS STUDIED A schematic of the ideal reactive distillation column is given in Figure 1. The column consists of stripping, reactive, and

temperature-dependent relative volatility (α390) are given in the literature.15 Table 2 gives the optimum design parameters and important operating conditions for these three cases.

Table 1. Physical and Chemical Data parameter

value

activation energy (J mol−1) forward reverse specific reaction rate at 366 K (kmol s−1 kmol−1) forward reverse chemical equilibrium constant at 366 K heat of reaction (J mol−1) heat of vaporization (J mol−1) Vapor Pressure Constants α390 = 2.00 A B C D

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α390 = 1.75

125520 167360 0.008 0.004 2 −41840 29053.7 α390 = 1.50

AVP

BVP

AVP

BVP

AVP

BVP

12.34 11.65 10.96 13.04

3862.00 3862.00 3862.00 3862.00

12.34 12.40 12.45 12.30

3862.00 4100.07 4338.13 3623.93

12.34 13.26 14.17 11.44

3862.00 4374.90 4887.80 3349.10

Table 2. Optimum Design Parameters NS NRX NR P VS R

α390 = 2.00

α390 = 1.75

α390 = 1.50

5 7 5 8.5 28.79 bar 33.43 mol/s

7 9 6 8.0 36.07 bar 40.70 mol/s

9 13 6 7.0 48.80 bar 53.43 mol/s

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CONTROL STRUCTURES Fresh feed stream FB0 acts as the production rate handle in all the control structures. Two-point control structure is given in Figure 2A. Column base and reflux drum levels are controlled by manipulating the bottoms and reflux rates, respectively. A ratio control keeps the distillate in ratio with the reflux. Fresh feed stream FA0 and vapor boilup VS are used to control the temperatures of two selected trays. This control structure is labeled CS2T-C. Two different versions of the three-point control structure are used, depending on the tray selection method that is applied. For the case of using SVD criteria, a three-point control structure given in Figure 2B is proposed. Here, the reflux drum level is controlled by the distillate rate and the reflux rate is used to constitute the third temperature loop. This resulting control structure is labeled CS3T-C. Second version of the three-point control structures is given in Figure 2C. It is the control structure proposed by Kookos12 and labeled CS3T-S. It differs from CS3T-C in that the distillate is used to control a third temperature, while the reflux rate is manipulated to control the reflux drum level. The column base and reflux drum levels are controlled using P-only controllers with a proportional gain of 2. Since pressure dynamics are

Figure 1. Schematic of the ideal reactive distillation column.

rectifying sections. The numbering of the trays is bottom-up, excluding the reboiler and condenser. The reaction A + B ↔ C + D occurs only on the reactive section. The light reactant A and the heavy reactant B are fed from the bottom and top stages of reactive section, respectively. Both feed streams have a flow rate of 12.6 mol/s. The light product C leaves the column from the distillate, while the heavy product D is removed from the bottoms. Both products have a purity of 95 mol % and a flow rate of 12.6 mol/s. 5944

dx.doi.org/10.1021/ie3032789 | Ind. Eng. Chem. Res. 2013, 52, 5943−5950


Article

Figure 2. Two-point and three-point control structures: (A) CS2T-C, (B) CS3T-C, and (C) CS3T-S.

Figure 3. Sensitivity analysis and SVD results for α390 = 2.00: (A) CS2T-C and (B) CS3T-C.

obtained based on the widely used SVD criterion. The SA and SVD results of two-point control structure for the system with α390 = 2.00 are given in Figure 3A. SA result illustrates that both process gains have two peaks at the same locations (tray 4 and tray 13). In addition, SVD result indicates an extra tray location (tray 10) besides tray 14 to pair with VS. Conclusions from previous studies suggest to use a reactive tray instead of a rectifying tray.5 Thus, the pairings of the two-point control structure are selected as T4/FA0 and T10/VS. It is observed that SA and SVD methods for other systems (α390 = 1.75 and 1.50) display similar results. Figure 3B shows SA and SVD results for three-point control structure of the system with α390 = 2.00.

much faster than the others, a perfect pressure control is assumed. Proportional-integral (PI) controllers are used in the temperature loops with two 60-s lags. Relay feedback method is applied to tune the temperature loops. The loops are tuned individually. Then, the Tyreus−Luyben controller settings are used to set the controller gain and the reset time.

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SELECTION OF TEMPERATURE SENSOR LOCATIONS

As mentioned previously, two different sets of locations are used in this study for tray temperature control. The first set is 5945



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Table 3. Temperature Loops and Tuning Parametersa

It is seen that tray 3 is the location with biggest gains and tray 13 has the second biggest gains for all three inputs (FA0, VS, and R). However, no third location is observed according to SA results. The SVD criteria give coherent results with SA for two of the pairings: T3/FA0 and T14/R. On the other hand, it suggests five different tray locations to pair with VS. These are tray 15, tray 12, tray 5, tray 2, and tray 9, starting from the one with the highest U value. However, it is clearly seen that four of these five trays are too close to other pairings (the unsuitability of these selections has been also tested by dynamic simulations). Thus, tray 9 is selected to be paired with VS. It is seen that the results of the SA and SVD methods for other systems (α390 = 1.75 and 1.50) are also similar. The second set is based on a semisystematic method using a priori knowledge from the literature and engineering intuition. In a recent paper, Kookos presented an application of a systematic methodology for optimal control structure selection of a reactive distillation column, where the problem is defined as a mixed integer nonlinear programming (MINP) problem.12 The controlled variables are found as the temperatures on the first tray of stripping section, the first tray of reactive section and the last tray of rectifying section. Each controlled temperature is paired with the manipulated variable that is actually feed to the corresponding tray. In other words, the pairings of this control structure are proposed as T1/VS, T6/FA0, and T17/D for the system with α390 = 2.00. Based on this knowledge, we decide to examine the same pairings for systems with different relative volatilities (α390 = 1.75 and 1.50). Accordingly, temperatures of the first tray, the fresh A feed tray, and the top tray of the column are controlled by manipulating the vapor boilup, fresh A feed flow, and distillate stream, respectively. In addition, a two-point control structure version of these locations is investigated, where the first tray of stripping section is paired with the vapor boilup and the first tray of reactive section is paired with the fresh A feed flow. In this case, a ratio control keeps the distillate proportional to the reflux, and the control structure is labeled CS2T-S. Table 3 reports the proposed temperature loops and resulting controller tunings for these control structures.

CS

MV

CV

ultimate gain, KU

2T-C 2T-C

VS FA0

T10 T4

2T-S 2T-S

VS FA0

T1 T6

6.09 11.61

4.17 4.33

3T-C 3T-C 3T-C

VS FA0 R

T9 T3 T14

2.60 2.80 1.65

8.58 5.92 5.92

3T-S 3T-S 3T-S

VS FA0 D

T1 T6 T17

4.17 4.33 15.33

2T-C 2T-C

VS FA0

T13 T5

6.07 11.53 14.77 = 1.75 8.04 3.85

2T-S 2T-S

VS FA0

T1 T8

11.84 22.60

4.42 4.00

3T-C 3T-C 3T-C

VS FA0 R

T12 T5 T18

4.02 3.85 1.67

9.33 6.42 6.00

3T-S 3T-S 3T-S

VS FA0 D

T1 T8 T22

4.42 4.00 15.08

2T-C 2T-C

VS FA0

T17 T6

11.96 22.75 16.24 = 1.50 15.20 7.04

2T-S 2T-S

VS FA0

T1 T10

23.43 39.30

4.67 4.00

3T-C 3T-C 3T-C

VS FA0 R

T17 T6 T25

6.84 7.08 2.04

9.17 6.58 5.67

3T-S 3T-S 3T-S

VS FA0 D

T1 T10 T28

23.84 39.14 22.34

4.67 4.00 13.58

α390

α390

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RESULTS AND DISCUSSIONS The following results are for the system with a relative volatility of α390 = 2.00. In the figures of this section, controlled variables are given as the variation of temperatures from corresponding steady-state values (ΔT = T − TSS). One of the major disturbances is the change in the throughput manipulator. The closed-loop response for a +20% change in the throughput manipulator for CS2T-C and CS3T-C is shown in Figure 4A. Solid blue line defines CS2T-C, while dashed red line labels CS3T-C. A stable response is obtained for both control structures. CS2T-C reaches the final steady state within 4 h, while it takes slightly longer time for CS3T-C. Controlled temperatures recover back to their set points. The fresh feed flow rate FA0 is increased as the fresh feed flow rate FB0 increases, as the throughput manipulator. In addition, more vapor boilup VS and reflux R are required. However, the results of both control structures show deviations in the product purities. Final deviation in distillate purity is larger than the one in the bottoms purity for both control structures. A comparison of the product purities for CS2T-C and CS3T-C shows that CS3T-C does not provide any significant improvement. Moreover, CS2T-C provides smaller transient deviation and tighter product purity control in the distillate.

ultimate period, PU

α390 = 2.00 4.46 2.69

6.25 5.83

6.50 6.42

6.08 6.67

a

The span of temperature measurements is 50 K and all valves are 50% open at steady state.

Figure 4B gives the closed-loop response of CS2T-C and CS3T-C for a −20% change in throughput manipulator. A stable response with the final steady state reached within 4 h is obtained for both control structures. There is a decrease in fresh feed flow rate FA0, vapor boilup VS, and reflux R. Although the transient behaviors are similar, CS3T-C provides tighter product purity control in the bottoms. On the other hand, similar distillate purities and related dynamic behaviors are observed for both CS2T-C and CS3T-C. It is seen that the final deviation in distillate purity is larger than that in bottoms purity for both control structures. It is noticed that the maximum transient deviations are bigger when a −20% throughput change is applied. Figure 5A shows the performance of CS2T-S and CS3T-S for a +20% change in throughput handle. The solid blue line in the figure defines CS2T-S, while the dashed red line in the figure 5946



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Figure 4. Change in throughput manipulator for CS2T-C and CS3T-C: (A) +20% and (B) −20%.

labels CS3T-S. It is seen that the manipulated variables settle down to their new values with a small oscillation. Their values are similar with those obtained by CS2T-C and CS3T-C. The temperatures and product purities reach the final steady state within 3 h. The bottoms purity is maintained quite close to its specification for both control structures. The results of CS2T-S illustrate significant deviation in the distillate purity. It is even bigger than the deviations of CS2T-C and CS3T-C. On the other hand, using CS3T-S results in tighter distillate product purity control, compared to other control structures. There is a significant improvement in the distillate purity where the deviation is within 0.2% of its specification. The closed-loop response for a −20% change in throughput manipulator for CS2T-S and CS3T-S is shown in Figure 5B.

A stable response is observed for both control structures. The decrease in the throughput handle results in a decrease in the fresh feed flow rate FA0, vapor boilup VS, and reflux R. The temperatures recover back to their set points within 3 h. Both control structures provide tight product purity control in the bottoms. However, the result of CS2T-S shows that the distillate purity cannot be held as close to its specification with the control structures CS2T-C and CS3T-C. On the other hand, a significant improvement is observed in the distillate purity for CS3T-S. It settles down to a final steady state, which is within 0.2% of its specification. Another major disturbance is the change in the fresh feed composition. Figure 6 demonstrates what happens when the composition z0B of the fresh feed F0B is changed from pure B 5947



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Figure 5. Change in throughput manipulator for CS2T-S and CS3T-S: (A) +20% and (B) −20%.

control structures are significantly smaller than the deviations of CS2T-C and CS3T-C. In addition, the results show that the purity of the bottoms product with CS2T-S is held closer to its specification when it is compared with CS3T-S. In general, the results of other ideal systems (α390 = 1.75 and 1.50) show similar dynamic transient behaviors. Thus, they are not demonstrated in this study. Instead, the steady-state deviations of product purities for three systems with different temperaturedependent volatilities (α390 = 2.00, 1.75, and 1.50) against the disturbances are reported in Table 4. A general view of the results shows that the deviations in bottoms purity are significantly smaller than that of distillate purity. The deviation in bottoms purity does not exceed 0.4% of its design value. The only exceptation is the results of CS2T-C for the change in z0B. Among the four control structures,

(z0B,B = 1.00) to a mixture of of A and B (z0B,A = 0.05 and z0B,B = 0.95) for CS2T-C and CS3T-C. The temperatures of both control structures recover back to their set points. For both control structures, the flow rate F0A decreases to compensate for the extra amount of A in feed stream F0B. However, it is seen that the decrease in F0A with CS2T-C is very small, which is not enough to satisfy the stoichiometry between reactants. This results in a big accumulation of component A through the column and tremendous deviation in both product purities. On the other hand, the bottoms purity is maintained close to the desired value with CS3T-C, while the distillate purity cannot be held close enough to its specification. Results of CS2T-S and CS3T-S for the same size of the same disturbance are given in Figure 7. It is clearly seen that the deviations in product purity using these 5948



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Figure 6. Change in fresh feed composition z0B for CS2T-C and CS3T-C: 5% A in F0B.

Figure 7. Change in fresh feed composition z0B for CS2T-S and CS3T-S: 5% A in F0B.

biggest deviations in distillate purity for any value of α390. On the other hand, CS3T-S significantly improves the control performance and decreases the deviation to one-third of CS2TC for any value of α390. Thus, tighter distillate product purity control is achieved where the deviation is within 0.35% of its design value. For the change in z0B, CS2T-C has the worst dynamic results, with more than 1% deviation from the design value being observed, even for the best α390 case. It is seen that the use of CS3T-S improves the controllability by keeping the deviation within 1% of the design value, even for the worst α390 case.

CS2T-C gives the biggest deviations in bottoms purity for any type of disturbance and for any value of α390. However, no significant changes are observed among the results of other control structures, where the final bottoms purity is held within 0.25% of the design value. The effect of control structures on the control performance is more visible in the case of distillate purity. For the changes in throughput manipulator (±20% change in VS), the deviation in distillate purity increases as the dependence of the relative volatility on temperature increases, regardless of the control structure. Among the four control structures, CS2T-S gives the 5949



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(6) Huang, K.; Wang, S. J. Design and control of a methyl tertiary butyl ether (MTBE) decomposition reactive distillation column. Ind. Eng. Chem. Res. 2007, 46, 2508−2519. (7) Chen, C. S.; Yu, C. C. Effects of relative volatility on design and control of reactive distillation systems with ternary decomposition reactions. Ind. Eng. Chem. Res. 2008, 47, 4830−4844. (8) Kumar, M. V. P.; Kaistha, N. Reactive distillation column design for controllability: A case study. Chem. Eng. Proc. 2009, 606−616. (9) Hsu, K. Y.; Hsiao, Y. C.; Chien, I. L. Design and control of dimethyl carbonate−methanol separation via extractive distillation in the dimethyl carbonate reactive distillation process. Ind. Eng. Chem. Res. 2010, 49, 735−749. (10) Kumar, M. V. P.; Kaistha, N. Decentralized control of a kinetically controlled ideal reactive distillation column. Chem. Eng. Sci. 2008, 228−243. (11) Kaymak, D. B.; Yilmaz, D.; Gürer, A. Z. Inferential temperature control structures for different types of two-reactant reactive distillation systems. Ind. Eng. Chem. Res. 2011, 50, 6777−6793. (12) Kookos, I. K. Control structure selection of an ideal reactive distillation column. Ind. Eng. Chem. Res. 2011, 50, 11193−11200. (13) Kookos, I. K. Real-time regulatory control structure selection based on economics. Ind. Eng. Chem. Res. 2005, 44, 3993−4000. (14) Kaymak, D. B.; Yilmaz, D.; Gürer, A. Z. Effect of temperaturedependent relative volatilities on inferential temperature control of reactive distillation columns. Ind. Eng. Chem. Res. 2011, 50, 8138− 8152. (15) Kaymak, D. B.; Luyben, W. L.; Smith, O. J. Effect of relative volatility on the quantitative comparison of reactive distillation and conventional multi-unit systems. Ind. Eng. Chem. Res. 2004, 43, 3151− 3162.

Table 4. Steady-State Deviations |xB,D| CS

20% in VS

−20% in VS

CS2T-C CS3T-C CS2T-S CS3T-S

0.0021 0.0017 0.0004 0.0007

0.0022 0.0007 0.0003 0.0006


0.0022 0.0004 0.0008 0.0008

0.0026 0.0009 0.0007 0.0008


0.0033 0.0006 0.0013 0.0015

0.0038 0.0017 0.0012 0.0014

|xD,C| A in z0B α390 = 2.00 0.0202 0.0003 0.0002 0.0013 α390 = 1.75 0.0129 0.0020 0.0013 0.0022 α390 = 1.50 0.0120 0.0005 0.0011 0.0022

20% in VS

−20% in VS

A in z0B

0.0052 0.0069 0.0071 0.0018

0.0051 0.0054 0.0074 0.0020

0.0329 0.0097 0.0034 0.0042

0.0075 0.0064 0.0090 0.0024

0.0073 0.0057 0.0095 0.0026

0.0109 0.0092 0.0071 0.0053

0.0105 0.0076 0.0123 0.0034

0.0101 0.0063 0.0129 0.0036

0.0110 0.0089 0.0076 0.0063

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CONCLUSIONS The results of a recent paper illustrated that the magnitude of the offset in final product purities increases significantly with the increase in the temperature-dependency of relative volatilities for quaternary reactive distillation columns. In this study, two control structures with different number of temperature loops and two different sets of control tray locations have been explored to obtain better control performance. The steady-state deviations of product purities have been used as a comparison metric. An overall improvement is observed in terms of tighter product purity control by using three-point inferential control structures (CS3T-C and CS3T-S), compared to the widely used two-point inferential control structure (CS2T-C). Furthermore, CS3T-S results in a significant improvement in the distillate purity control for all temperature-dependent relative volatility cases, especially against the changes in the throughput manipulator. Thus, CS3T-S is found superior to other control structures studied for the quaternary systems.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +90-212-285-3539. Fax: +90-212-285-2925. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Skogested, S. The dos and dont’s of distillation column control. Chem. Eng. Res. Des. 2007, 85, 13−23. (2) Luyben, W. L. Evaluation of criteria for selecting temperature control trays in distillation columns. J. Process Control 2006, 16, 115− 134. (3) Al-Arfaj, M. A.; Luyben, W. L. Design and control of an olefin metathesis reactive distillation column. Chem. Eng. Sci. 2002, 715−733. (4) Huang, S. G.; Kuo, C. L.; Hung, S. B.; Chen, Y. W.; Yu, C. C. Temperature control of heterogeneous reactive column. AIChE J. 2004, 2203−2216. (5) Kaymak, D. B.; Luyben, W. L. Evaluation of a two-temperature control structure for a two-reactant/two-product type of reactive distillation column. Chem. Eng. Sci. 2006, 4432−4450. 5950


Control of Quaternary Reactive Distillation Columns: Effects of Number

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