Quantitative comparison of dynamic controllability between a reactive distillation column and a conventional multi-unit process

Quantitative comparison of dynamic controllability between a reactive distillation column and a conventional multi-unit process

Available online at www.sciencedirect.com Computers and Chemical Engineering 32 (2008) 1456–1470 Quantitative comparison of dynamic controllability ...

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Available online at www.sciencedirect.com

Computers and Chemical Engineering 32 (2008) 1456–1470

Quantitative comparison of dynamic controllability between a reactive distillation column and a conventional multi-unit process Devrim B. Kaymak 1 , William L. Luyben ∗ Process Modeling and Control Center, Department of Chemical Engineering, Lehigh University, Bethlehem, PA 18015, United States Received 8 June 2005; received in revised form 15 June 2007; accepted 21 June 2007 Available online 5 July 2007

Abstract A comparison of the steady-state economic optimum designs of two alternative chemical processes was presented in a previous paper [Kaymak, D. B., & Luyben, W. L. (2004). A quantitative comparison of reactive distillation with conventional multi-unit reactor/column/recycle systems for different chemical equilibrium constants. Industrial & Engineering Chemistry Research, 43, 2493–2507]. A generic exothermic reversible reaction A + B ↔ C + D occurs in both flowsheets, which consist of a conventional multi-unit reactor/separator/recycle structure and a reactive distillation column. Results showed that the reactive distillation process is significantly less expensive than the conventional process for a wide range of the chemical equilibrium constant when there is no mismatch between the temperature favorable for reaction and the temperature favorable for vapor–liquid separation. A reactive distillation column has fewer control degrees of freedom than a conventional multi-unit system. Therefore a reactive distillation column may have worse dynamic response than a conventional process. The purpose of this paper is to compare the dynamic controllability of these two alternative processes. Three different chemical equilibrium constants are considered. Several control structures are developed for each flowsheet, and their effectiveness is evaluated. Disturbances in production rate and fresh feed compositions are considered. The conventional multi-unit process provides significantly better control. The operability region is much larger, there is less variability in product quality and the dynamic responses are faster than those of the reactive column. Thus, these results demonstrate that there is a significant trade-off in this system between optimum economic steady-state design and dynamic controllability. © 2007 Elsevier Ltd. All rights reserved. Keywords: Process control; Plantwide control; Reactive distillation; Simulation

1. Introduction There are multiple unit operations and recycle streams in most of the chemical plants. Although significant research has been done regarding the design and control of individual process units like reactors and distillation columns, plantwide design and control of multi-unit processes are still developing areas. They present challenging tasks because of the interaction among individual units. A heuristic plantwide control procedure has ∗

Corresponding author. Tel.: +1 610 758 4256; fax: +1 610 758 5057. E-mail address: [email protected] (W.L. Luyben). 1 Present address: Department of Chemical Engineering, Istanbul Technical University, 34469 Maslak, Istanbul, Turkey. 0098-1354/$ – see front matter © 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.compchemeng.2007.06.022

been suggested (Luyben, Tyr´eus, & Luyben, 1999) and applied to several typically complex chemical processes. Economic and environmental considerations have forced industry to focus on technologies based on process intensification. Reactive distillation column has been the subject of many papers in recent years because of its potential for process intensification. However, reactive distillation can be applied to a limited number of systems because of several limitations. Since reaction and separation occur simultaneously in the same column, the temperatures that are favorable for these two operations should match. If there is a mismatch, reactive distillation becomes economically unfavorable (Kaymak et al., 2004). The steady-state design and openloop dynamics of reactive columns have been studied widely for many years. However, it

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Nomenclature AVP,j BVP,j B D F FJ F0j F F0j kF kR KC KEQ Mi NR NRX NS NT P Pjs R RDC t Ti TR TAC T VR VS VS xB,j xD,j xSS zj z0j z0j

Antoine constant of component j Antoine constant of component j bottoms flow rate in the column (mol/s) distillate flow rate for ideal process (mol/s) effluent flow rate from the reactor (mol/s) flow rate of cooling water (mol/s) fresh feed flow rate of reactant j (mol/s) change in the reactor effluent F change in the fresh feed stream F0j specific reaction rate of forward reaction (kmol s−1 kmol−1 ) specific reaction rate of reverse reaction (kmol s−1 kmol−1 ) controller gain equilibrium constant reactive tray holdup (mol) number of the rectifying trays number of the reactive trays number of the stripping trays total number of trays in the column column pressure (bar) vapor pressure of component j (bar) reflux (mol/s) reactive distillation column time (h) column temperature on tray i (K) temperature of the reactor (K) total annual cost change in the temperature molar holdup of the reactor (kmol) vapor boilup (mol/s) change in the vapor boilup bottoms composition of component j distillate composition of component j steady-state composition of a component mole fraction of component j in the reactor fresh feed mole fraction of component j change in the composition of fresh feed stream F0j

Greek letters relative volatility of component j αj αR pre-exponential factor τI reset time (min)

has only been in the last decade that a number of papers dealing with the closedloop control of reactive distillation column have begun to appear where most of these studies focused on specific reactive distillation chemistries (Al-Arfaj & Luyben, 2002; Sneesby, Tade, & Smith, 2000; Vora & Daoutidis, 2001; Wang & Wong, 2006; Zeng, Kuo, & Chien, 2006). Kaymak and Luyben (2004) quantitatively compared the steady-state designs of two different process flowsheets: (1) a

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conventional multi-unit reactor/separator/recycle structure, and (2) a reactive distillation column. Both of the flowsheets were designed to achieve the steady-state economic objective of minimum total annual cost. Cases covering a wide range of chemical equilibrium constant KEQ were considered. Relative volatilities were assumed to be constant. Results showed that the reactive distillation column is significantly less expensive, by a factor of over three, than the conventional process for all values of the chemical equilibrium constant. However, a reactive distillation column has fewer control degrees of freedom than a conventional multi-unit system. Therefore a reactive distillation column may have worse dynamic response than a conventional process. The purpose of this paper is to compare the dynamic controllability of these two alternative processes by developing several control structures. Since design based on the steady-state optima may result in plants with poor controllability properties, there have been several papers (Arbel, Rinard, & Shinnar, 1997; Cheng & Yu, 2003; Russel, Henriksen, Jorgensen, & Gani, 2002; Seferlis & Grievink, 2001) addressing the importance of the interaction between design and control. The resiliency, operability, interaction among control loops and determination of variable pairing (selection of controlled and manipulated variables) are important issues for the controllability of multivariable systems, which should be considered in addition to the steady-state economics of the system. Several methods have been developed for the analysis of multivariable processes using steady-state properties (Lau, Alverez, & Jensen, 1985; Skogestad & Morari, 1987; Solovyev & Lewin, 2003; Stanley, Marino-Galarraga, & McAvoy, 1985; Subramanian & Georgakis, 2005). This study uses a simulationbased approach, and singular value decomposition (SVD) and relative gain array (RGA) methods are applied to determine the variable pairings of the reactive distillation column and to check loop interactions. The effectiveness of different control structures is explored in the face of different types of disturbances. Control effectiveness is evaluated in terms of two criteria. First, the system does not shut down as a result of the disturbance. Second, purities of both product streams do not drop below a lower specification limit. This paper also demonstrates how the capacity-based economic approach developed by Elliott and Luyben (1995) can be used to quantitatively incorporate dynamic controllability into process economics for comparing the two alternative processes. This paper is an extension of the study by Kaymak and Luyben (2004), where the steady-state designs of a hypothetical case with two-reactant/two-product type of chemistry were quantitatively compared using two different process flowsheets. The aim of starting with a simple, generic system was to strip away the vapor–liquid equilibrium complexities so that the fundamental differences between the two flowsheets could be fairly compared. However, three different kinetic cases are studied with chemical equilibrium constants varying over a wide range (KEQ between 0.5 and 10). Thus, although this study does not directly aim to represent any real industrial reactive distillation system, the results presented may be useful especially for ideal/slightly nonideal real two-reactant/two-product type processes for a wide range of chemical equilibrium constants.

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Table 1 Physical data for ideal process Activation energy of reaction (cal/mol) Forward Reverse Specific reaction rate at 366 K Forward Reverse

30,000 40,000

(kmol s−1

kmol−1 ) 0.008 0.004

Average heat of reaction (cal/mol) Average heat of vaporization (cal/mol) Molecular weight of the mixture (g/mol) Ideal gas constant (cal/(mol K))

−10,000 6944 50 1.987

Relative volatilities αA αB αC αD

4 2 8 1

Vapor pressure constantsa

A

B

C

D

AVP BVP

12.34 3862

11.65 3862

13.04 3862

10.96 3862

a

lnPjs = AVP,j − BVP,j /Td with temperature in K and vapor pressure in bar.

specified as 0.008 kmol s−1 kmol−1 at 366 K. The reverse reaction rate at this temperature is varied by selecting a specific value of (KEQ )366 . (kR )366 =

(kF )366 (KEQ )366

(3)

In this paper, we considered three different (KEQ )366 values: 0.5, 2.0 and 10.0. For each value of (KEQ )366 , a different value of the pre-exponential factor αR is calculated. Both reaction rates are temperature dependent, and the reverse reaction rate is different for each case of (KEQ )366 selected. The reverse reaction rate is more temperature dependent than the forward reaction rate since the reaction is exothermic. There are two different process flowsheets studied: a conventional multi-unit reactor/separator/recycle structure and a reactive distillation column. The design objective for both flowsheets is to obtain 95% conversion for fixed fresh feed flow rates of pure reactants of 12.6 mol/s. It should be noticed that both flowsheets have identical feeds and produce identical products. In addition, the economic factors (energy cost and capital cost of columns and heat exchangers) are the same in both processes. 2.1. Conventional process

2. Process studied The reversible liquid-phase reaction considered is A+B⇔C+D

(1)

Ideal vapor–liquid equilibrium is assumed with constant volatilities, where the reactants are intermediate boiling between the two products. The relative volatilities are αC = 8, αA = 4, αB = 2, αD = 1

(2)

Kinetic and physical properties and vapor–liquid equilibrium parameters are given in Table 1. The forward reaction rate is

The process given in the left side of Fig. 1 is the conventional multi-unit process studied in this paper. The reaction occurs in a continuous stirred tank reactor (CSTR) with holdup VR . There are two fresh feed streams F0A and F0B that contain pure reactants A and B, respectively. A recycle stream D2 returns from a downstream unit and is also fed to the reactor. The reactor effluent contains a multi-component mixture, since complete one-pass conversion is not achieved. Two columns are needed to separate the two products from the intermediate boiling reactants. The effluent is fed to the first distillation column in which product C is taken overhead in the distillate with the desired

Fig. 1. Process flowsheets: (a) conventional process, (b) reactive distillation column.

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95 mol% C. The impurity in the distillate is mostly component A. The reactants A and B and heavy product D in the feed leave in the bottoms. This stream is fed to the second column, which produces a bottoms stream of D with the desired 95 mol% purity, and a distillate of mostly reactants A and B is recycled back to the reactor. The impurities of product components C and D in the recycle stream are both 5 mol%. The steady-state economic optimization of this multi-unit process was obtained in Kaymak and Luyben (2004) with the following optimization variables: molar holdup in the reactor VR , composition of the reactant B in the reactor zB and reactor temperature TR . A grid-search optimization strategy was used to find the optimum values of the three design optimization variables. Table 2 summarizes the optimization results of the conventional process for all three kinetic cases. Design heuristics were used in the optimization of the conventional process. The number of trays in each column was set equal to twice the minimum number. The reflux ratio was set equal to 1.2 times the minimum. To determine the initial conditions for the columns in the dynamic simulations, the rigorous steady-state Wang-Henke method was used. Notice that the TAC decreases as the chemical equilibrium constant increases. The economics of this conventional process are compared with those of a reactive distillation column in the next section.

is introduced at the top of the reactive section. The light product C leaves in the distillate, while the heavy product D is removed in the bottoms. Reactive tray holdup Mi is 1000 mol, which gives reasonable tray liquid heights (∼0.1 m). For the reactive distillation column, there are three optimization variables: the column pressure P, the number of reactive trays NRX , and the number of the separating (stripping/rectifying) trays NS (or NR ). The numbers of stripping and rectifying trays are assumed to be the same because the relative volatilities between the key components in the two sections are the same. Simultaneous solution of the very large set of nonlinear and algebraic equations is difficult, especially with the high degree of nonlinearity due to reaction kinetics. The relaxation method, which is efficient and robust in solving this large set of equations, is used to calculate mole fractions and temperature profiles throughout the column. In general, relaxation methods use the equilibrium stage model equations in unsteady-state form and integrate them numerically until the steady-state solution is found. Optimum steady-state results of the reactive distillation column for three different kinetic cases are given in Table 3. Notice that the TAC decreases as the chemical equilibrium constant increases. Comparing the results of Table 2 with those of Table 3 shows a very significant economic advantage for reactive distillation.

2.2. Reactive distillation column

3. Control structures

The flowsheet of reactive distillation is shown on the right side of Fig. 1. The column is fed with two pure reactant fresh feed streams F0A and F0B . There is a reactive zone between the stripping and rectifying sections. The light reactant A is fed to the bottom tray of the reactive zone, while the heavy reactant B

Conventional linear PI controllers in a decentralized (SISO) environment are used in all control structures. All level controllers are proportional-only with gains of 2 for the columns and 10 for the reactor. Temperature and composition controllers are tuned using the Tyreus–Luyben tuning method. The relayfeedback method is used to obtain the ultimate gain and ultimate period. Two first-order measurement lags of 60-s each are used in all temperature loops. A 3 min dead-time is used for the composition analyzer. Valves are designed to be half open at steady state.

Table 2 Optimization results of conventional design (KEQ )366

0.5

2.0

10.0

Design variables TR (K) VR (kmol) zB

356.0 222.5 0.275

367.0 102.5 0.225

379.0 60.0 0.150

13 50.56 37.96 1.09 13 66.14 25.33 1.58

13 39.56 26.96 0.97 13 44.42 21.54 1.30

13 31.66 19.06 0.86 13 27.82 16.37 1.03

Design parameters NT1 VS1 (mol/s) R1 (mol/s) DC1 (m) NT2 VS2 (mol/s) R2 (mol/s) DC2 (m)

Table 3 Optimization results of reactive distillation design (KEQ )366

0.5

2.0

10.0

Design variables NR and NS NRX P (bar)

5 14 6.5

5 7 8.5

6 4 12.0

Design parameters NT VS (mol/s) R (mol/s) DC (m)

24 36.05 40.68 0.91

17 28.82 33.45 0.80

16 21.36 26.00 0.67

Capital cost (US$ 103 ) Reactor Heat exchanger Column Tray

358.6 630.1 293.3 9.5

221.3 509.6 245.8 7.3

158.6 407.2 202.4 5.5

Capital cost (US$ 103 ) Heat exchanger Column Tray

269.7 158.9 4.8

241.0 104.5 2.7

209.2 83.3 2.0

Energy cost (US$ 103 /year) TAC (US$ 103 /year)

502.9 933.4

361.9 689.9

256.3 514.2

Energy cost (US$ 103 /year) TAC (US$ 103 /year)

155.3 299.8

124.2 240.3

92.0 190.2

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Fig. 2. Control structure: CS2.

The effectiveness of the control structures studied in this paper is demonstrated by using dynamic simulations and subjecting the processes to production rate changes (F0j , F or VS ) and feed composition disturbances (z0A and z0B ). 3.1. Conventional process Two alternative plantwide control schemes are developed and tested for the conventional process in this paper. Most of the loops in these control structures are identical and are shown in Fig. 2. 1. Reactor temperature is controlled by manipulating the cooling water flow rate. 2. Reactor level is controlled by manipulating the fresh feed F0B . 3. The fresh feed stream F0A is ratioed to the fresh feed stream F0B . 4. The reactor effluent F is flow controlled and serves as the production rate handle. 5. The reflux drum levels for both columns are controlled by distillate flows, and the base levels are controlled by bottoms flows. 6. Inferential control of product compositions in both columns is achieved by selecting an appropriate control tray. In the first column the tray is selected in the rectifying section where a significant break in the temperature profile occurs, while it is chosen in the stripping section for the second column. These

tray temperatures are controlled by changing the reboiler heat inputs. 7. Column reflux flows are ratioed to column feeds with a lag. 8. The column pressures are controlled by manipulating the condenser heat duty. The two control structures are different only in what sets the ratio of the two fresh feeds. In the first structure (CS1) the ratio is set by a composition controller that maintains the concentration of reactant A in the reactor zA . Because composition analyzers are expensive, require high maintenance and introduce deadtime into the control loop, it is desirable to use inferential temperature measurements instead of direct composition measurements whenever possible. Fig. 2 gives the alternative control structure that eliminates the need for the composition analyzer. In this control structure (CS2), the temperature of the top tray in the second column is used to infer the composition of A, and the ratio of the fresh feed streams is set by this temperature controller. The rest of the control loops used in this structure are identical to the ones used in CS1. For both of these control structures, the flow controller in the reactor effluent stream is the product-rate handle. It also prevents the snowball effect. However, the disadvantage of these structures is that the production rate cannot be directly set. 3.2. Reactive distillation column The two control structures applied to the reactive column studied in this paper are shown in Fig. 3. Many of the loops are common to both control schemes.

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Fig. 3. Control structures: (a) CS5, (b) CS7.

1. Reflux-drum level is controlled by reflux flow rate. The reflux ratio is over two for all the design cases, so this structure is recommended by distillation control heuristics. 2. Reflux ratio is controlled by measuring the reflux flow rate, multiplying this by the reciprocal of the desired reflux ratio and sending this signal to a remote-set cascade flow controller on the distillate stream. 3. Base level is controlled by bottoms flow rate. 4. Pressure is controlled by condenser heat removal. The two control structures differ in how the fresh feed streams and the reboiler heat inputs are manipulated. In the scheme shown on the left in Fig. 3 (CS5), the temperature of a tray near the bottom of the column is used to infer bottoms product purity, and it is controlled by manipulating the vapor boilup. This tray is selected in the stripping section where a significant break in the temperature profile occurs. Distillate purity is not controlled. The fresh feed F0B is flow controlled. This is the production rate handle. The flow rate of the other fresh feed F0A is manipulated by a composition controller than maintains the concentration of component A at the bottom tray of the reactive zone in the column. When a distillation column is designed for “neat” operation (no excess of either reactant), the column acts like a pure integrator with respect to the reactants. If 1 mol of B is fed to the system, exactly 1 mol of A is required. Therefore, some feedback of information about reactant inventory inside the system is required for an effective control system. In the CS5 control

structure, a composition analyzer is used so that the inventory of component A in the system can be detected and feedback can be used to prevent the gradual buildup or depletion of reactant A. As mentioned in the previous section, it is desirable to use inferential temperature measurements instead of direct composition measurements whenever possible. The control scheme given on the right side of Fig. 3 shows an alternative control structure (CS7) for reactive distillation column in which two temperature controllers manipulate the two fresh feed flow rates to maintain the temperatures on two trays in the column. Reboiler heat-input is flow controlled and serves as the production rate handle. The locations of the trays whose temperatures are to be controlled are selected by applying Singular Value Decomposition (SVD) analysis to the column. One disadvantage of this structure is that the production rate cannot be directly set. A recent paper (Kaymak & Luyben, 2006) gives a detailed analysis of the CS7 control scheme. 4. Results for base kinetic case (KEQ )366 = 2.00 In this section, we compare the dynamic controllability of the two different flowsheets for the base kinetic case where chemical equilibrium constant (KEQ )366 is equal to 2. First, alternative control structures of each flowsheet are compared for that specific process. Then the results of using the best structure for each flowsheet are compared. The response times of systems to the disturbances, transient drops of purities and operability regions of both processes are presented.

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Fig. 4. Comparison of CS1 and CS2: 20% step increase in production rate handle.

4.1. Comparison of control structures for conventional process In the conventional process the temperature of Tray 11 in the first column and the temperature of Tray 3 in the second column are controlled by manipulating the vapor boilups. In control structure CS1, reactor composition zA is measured and controlled by changing the ratio of the fresh feeds. In control structure CS2, the temperature of Tray 13 near the top of the second column is used to infer the composition of A in the top of the column. This gives a measure of the inventory of component A in the system. Fig. 4 gives a direct comparison between CS1 and CS2 for a +20% increase in the flow rate of the reactor effluent F. The responses are essentially identical because of the ratio used between the two fresh feeds. This increase is handled easily with the system settling at a steady state in about 3 h. The purities of both products are maintained close to the desired 95% specification. The minimum transient purity xB2,D of the D product from the bottom of the second column is about 94.3 mol%. Fig. 5 compares the responses of the CS1 and CS2 structures when the disturbance is a change in feed composition. The composition of the fresh feed F0A is changed from pure A to 90 mol% A and 10 mol% B. Both control structures handle this disturbance. As expected, the CS1 structure detects this composition disturbance more quickly. This provides faster response and a smaller transient changes in the purities of both product streams compared to CS2. However, the changes in product purities are very small. Although control structure CS2 is slightly slower than control structure CS1 for changes in the composition of the fresh feeds,

it never goes too far from the original steady-state values. It also has the significant advantage of not using a composition analyzer. Therefore, in the following sections, control structure CS2 is used as the control structure of the conventional process for making comparisons with the reactive distillation column. 4.2. Comparison of control structures for reactive column For the CS5 control structure, the temperature of Tray 3 in the stripping section is controlled by manipulating the vapor boilup, while the concentration of reactant A on Tray 6 is controlled by manipulating the fresh feed flow rate stream F0A . The production rate handle is the flow rate of the fresh feed F0B . For the control structure CS7, the SVD results suggest that the temperatures of Tray 4 and Tray 10 should be controlled by fresh feeds F0A and F0B , respectively. The production rate handle is the vapor boilup VS . Fig. 6 presents the responses of both control structures to a 5% step decrease in the production rate (F0B or VS ). The 5% decrease can be easily handled by the CS5 structure, and the system settles down to a steady state in about 2 h (solid lines). The purities of both products are maintained close to the desired 95% specification. However, the robustness of the CS7 control structure is poor (dashed lines). When a negative step change is applied to vapor boilup VS , Tray 10 temperature starts to decrease. That decrease in temperature results also in a decrease of fresh feed stream F0B . This negative disturbance shuts off the F0B stream completely in a short time, and the system shuts down. Similar results occur for feed composition disturbances. Although the CS7 control structure can handle very small disturbances, it does not provide stable dynamic

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Fig. 5. Comparison of CS1 and CS2: 10% step change in fresh feed composition z0A .

controllability for disturbances that are typical in most chemical processes. Thus, we conclude that the CS7 structure is not as good as the CS5 structure for the optimal design of the reactive column with the base case kinetics (KEQ )366 = 2.

4.3. Comparison of dynamic controllability for different flowsheets Different control structures for each process flowsheet have been discussed in the previous sections. It has been seen that both

Fig. 6. Comparison of CS5 and CS7: 5% step decrease in production rate handle.

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Fig. 7. Comparison of CS2 and CS5: 20% step increase in production rate handle.

the CS1 and CS2 structures can handle disturbances with similar abilities for the conventional process. Since the CS2 structure has the advantage of not requiring a composition analyzer, it is used in this section. However, there is a big difference in controllability of the reactive column with the two different control structures presented in this paper. For the base kinetic case, the CS7 structure is not able to handle the disturbances that can be easily handled by the CS5 structure. Therefore, only the CS2 and CS5 structures are compared in this section. Fig. 7 gives a direct comparison of the performances of the two flowsheets using the CS2 and CS5 control structures. The disturbance is a 20% step increase in the production rate handle (F or F0B ). Results show that 20% increase can be handled by both control structures. With the increase in the production rate, controlled temperatures and compositions decrease immediately. This decrease results in an increase in fresh feed streams and vapor boilups. Both control structures show smooth responses, and all the variables settle down to their steady-state values easily. The final steady-state purities of both products are maintained close to the desired 95% specification. While conventional process settles down to the new steady state in 2 h, it takes slightly longer for the reactive distillation process. There is also a larger transient drop in bottoms purity xB,D in the reactive distillation column to about 92 mol% D, which lasts for about 2 h. Similar results were obtained for a 20% decrease in production. Fig. 8 compares the two processes for feed composition disturbances. The left two graphs give product purities for the conventional process. The right two graphs give product purities for the reactive distillation column. The top two graphs are for

a change in the composition of the fresh feed F0A from pure component A to a mixture of 90% A and 10% B. The bottom two graphs are for a change in the composition of the fresh feed F0B from pure component B to a mixture of 90% B and 10% A. Both control structures have smooth responses to these disturbances. Almost no change is observed in the product purities of the conventional process. For the z0A disturbance, there is a large transient drop in bottoms purity xB,D in the reactive column, but it ends up within the desired specification limits. However, the distillate purity xD,C goes below the 94% limit. For the z0B disturbance, the reactive column has a transient drop in distillate purity to less than 93 mol% C and is below the minimum specification of 94 mol% for about 1.5 h. These results demonstrate that the conventional process has better dynamic controllability than the reactive distillation column. 4.4. Rangeability It is important to evaluate the region of disturbances for which the control system is able to provide stable effective control and to maintain reasonable conversions and product purities. This property of a control structure is called “rangeability”. The first type of disturbance studied to explore the rangeability of two processes is a range of ± step changes in the production rate handle. Results show that very large changes, up to ±50%, can be handled by the conventional process. The purities of both products are maintained within 1% of the desired 95% specification. The second type of disturbance is a range of compositions

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Fig. 8. Comparison of CS2 and CS5: 10% step change in fresh feed compositions.

of the two fresh feeds F0A and F0B by adding impurities of other reactants up to 25%. The conventional multi-unit process gives dynamically stable responses also to this type of disturbances, and both product purities stay very close to the desired specifications.

However, the operability region of the reactive column with control structure CS5 is more limited. Results indicate that very large negative changes, up to −50%, in the production rate handle (fresh feed stream F0B ) can be handled with product purities within 1% of the desired 95% specification. The top two graphs

Fig. 9. Step changes for RDC.

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in Fig. 9 shows that the system also stays dynamically stable for large increases in the fresh feed stream F0B , but disturbances larger than 35% result in a decrease in distillate purity below the lower specification limit. However, for both disturbance magnitudes there are large transient drops in bottoms purity down to 90 mol%, which last for about 2 h. The middle graphs in Fig. 9 show the responses of the reactive distillation process for changes in composition of fresh feed F0A from pure component A to a mixture of components A and B. Although the system is dynamically stable for a wide range of this disturbance, disturbances larger than 5 mol% of B in the feed stream F0A result in a decrease in distillate purity below 94% while the bottoms purity is around specification. The lower graphs of Fig. 9 show the responses of the reactive column to changes in composition of fresh feed F0B . This disturbance can be as large as 20% of A in F0B while still maintaining product purities greater than 94 mol% at the new steady state. However, there are large transient drops in distillate purity down to less than 91 mol% even for a 15% disturbance. Fig. 10 presents the operability regions for the two processes using control structure CS2 for the conventional process and control structure CS5 for the reactive distillation process. The abscissa is a change in production rate from the nominal design value. The ordinate represents changes in the compositions of the two fresh feeds. The zero location corresponds to both feed being pure. Moving up on the ordinate represents making the F0B fresh feed impure by adding component A. Moving down on the ordinate represents making the F0A fresh feed impure by adding component B. The conventional process is able to provide effective control for the entire region shown in the plot (positive and negative changes in production rate of 50% and 25 mol% impurities in the two fresh feeds). However, the reactive column can handle only a limited area of the space, as indicated by the region surrounded with the border. These borders are set by a minimum purity of either product that drops below 94%, not by system shut downs.

Fig. 10. Operability region of RDC.

4.5. Capacity-based economic approach The desirability of simultaneously designing the plant with its control structure has been recognized for many years. However, if there is a conflict between steady-state economic design and controllability of different designs, we need a quantitative method for resolving the issue. The two alternative processes considered in this paper illustrate the usual dilemma. The reactive distillation process has much more favorable steady-state economics. However, product quality variability is much larger than for the conventional process. This variability may require reworking of the offspecification product or even produce disposal costs. These will increase the required size of the plant to make a specified amount of on-specification product and increase energy costs. The problem is how to quantitatively incorporate dynamic controllability into the steady-state economic design. Elliott and Luyben (1995) described the capacity-based economic approach to this problem. A sequence of expected disturbances in imposed on both processes, and the fraction of the time that each has products outside of specifications is determined by dynamic simulations of both of the plants with their appropriate control structures. The fraction of the time that the process has offspecification products can be quantitatively determined, and the appropriate economic penalties can be applied to assess which process has the lowest costs when considering both dynamics and steady-state performance. An insightful way to find what type of disturbance disturbs the process the most is to determine the closed-loop regulator frequency response. Sinusoidal load disturbances are imposed on the process over a range of frequencies. At low frequencies the control system will attenuate the disturbance. At high frequencies the process capacitance will filter out the disturbances. There is an intermediate range of frequencies where the product purities are most strongly affected. Fig. 11 illustrates this methodology for the two processes considered in this paper. The disturbance is a sine wave of magnitude 20% of the production rate handle (F or F0B ). The plots

Fig. 11. Closed-loop regulator transfer functions relating maximum product purity deviation.

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Fig. 12. Time responses of both processes to peak load disturbances.

show the maximum deviation of either product purities from their steady-state values for each frequency. These results clearly show that the conventional process exhibits much less variability over the whole frequency range, while the reactive column has much larger product quality variability. If the maximum allowable deviation is 1 mol%, the reactive column is outside the limit over a very wide range of frequencies. The frequency at the peak in the curve represents the worst case. Fig. 12 gives the time responses of both flowsheets to sinusoidal production disturbances with 20% magnitudes at their worst-case frequeny: 8 radians/h for the conventional process and 1.8 radians/h for the reactive column. The plots show that the variations of purities in both products are within 1% of the desired limit for the conventional process even at the worstcase frequency. However, the reactive distillation column has huge deviations from the desired products purities. The bottoms purity xB,D is off-specification for almost 50% of the time, while the distillate purity xD,C is off-specification more than 80% of the time. This amount of off-specification material would make the process completely uneconomical. Of course this is the worst-case disturbance. If we select the sequence of disturbances shown in the upper two graphs in Fig. 13 in both production rate and feed composition, the performance of the reactive column is perhaps more typical of what could be expected in a real plant environment. The period is smaller than the worst-case period, and the magnitude of disturbances are selected randomly. Both disturbances are applied to the system simultaneously. As the lower graphs in Fig. 13 show, these disturbances affect the system less than the worst-case disturbance. The fraction of time that the products are outside the specified lower limit is around 25% for both products. If two small distillation columns are required to reprocess the off-specification products, energy cost is increased from

US$ 124,200/year to US$ 139,100/year and capital investment is increased from US$ 348,200 to US$ 485,600. The total annual cost increases from US$ 240,300/year to US$ 301,000/year. This is still much lower than the conventional process. If the off-specification material could not be recovered, disposal costs could be quite high and more fresh reactants would be required to produce the desired amount of products. Therefore, in some systems, the cost of the variability could be very large, which would make the reactive distillation process uneconomical. 5. Results for other kinetics cases A detailed discussion has been presented in the previous sections when the chemical equilibrium constant is (KEQ )366 = 2. In this section other kinetic cases are briefly discussed: (KEQ )366 = 0.5 and 10. Similar procedures are used for the design of the control structures. The results are qualitatively the same for all three kinetic cases. Tables 1 and 2 give the optimum economic steady-state designs for both flowsheets and for all three kinetic cases. Tables 4 and 5 give the controller tuning parameters for both flowsheets and for all three kinetic cases. 5.1. Kinetic case (KEQ )366 = 0.50 The CS2 control structure is used in the conventional multiunit process. The temperatures of Tray 11 in the first column and of Tray 3 in the second column are controlled by the vapor boilup. The temperature of Tray 13 at the top of the second column is used to infer the composition of A in the system. This temperature controller resets the ratio of the two fresh feeds. Both the CS5 and the CS7 control structures are evaluated in the reactive distillation column. In the CS5 structure, Tray 3

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Fig. 13. Disturbance series with 15 min period and time response of RDC.

in the stripping section is controlled by manipulating the vapor boilup. The concentration of reactant A at lowest reactive tray (Tray 6) is controlled by manipulating the flow rate of fresh feed F0A . In the CS7 structure, the SVD analysis suggests the use of Tray 3 paired with the fresh feed flow rate F0A and Tray 20 paired with the fresh feed flow rate F0B . Controller gains and reset times calculated from the relay-feedback test data give reasonable results for both trays. The upper plots in Fig. 14 compare the responses of the two processes for a positive 10% step change in production rate. The conventional process is the solid curves labeled CS2. The reactive column using the CS7 control structure is the dotted lines, and the dash-dot lines use the CS5 control structure. Although Table 4 Tuning parameters for conventional processa

Table 5 Tuning parameters for reactive distillation processa

(KEQ )366

Pairing

KC

τ I (min)

0.5

F0A –zA F0A –T2,13 FJ –TR VS1 –T1,11 VS2 –T2,3

6.37 29.15 31.56 3.71 3.09

24.20 115.13 47.30 13.20 11.37

F0A –zA F0A –T2,13 FJ –TR VS1 –T1,11 VS2 –T2,3

3.11 10.93 15.61 4.73 3.52

22.00 134.20 43.63 12.10 10.63

F0A –zA F0A –T2,13 FJ –TR VS1 –T1,11 VS2 –T2,3

2.12 3.65 9.83 6.40 4.61

20.53 134.57 40.70 11.37 9.53

2.0

10.0

a

there is a big transient drop in distillate purity with the reactive column using the CS7 structure, all three control structures are able to handle this disturbance and to settle down the purities within 1% of the desired 95% specification. The conventional process comes to the new steady state in less than 2 h. It takes more than 5 h for the reactive column to settle out with either structure. As the plots in the middle line of Fig. 15 show, a 15% disturbance results in the reactive column shutting down when the CS7 structure is used. The conventional process settles down in less than 2 h, but the reactive column takes more than 7 h. The lowest plots in Fig. 14 give the responses for a very large 50% step change in production rate. The conventional process is well controlled. The reactive column exhibits very large

Controller gains are dimensionless using temperature transmitter spans 50 K, composition transmitter spans 0.2 and valve sizes twice the steady-state flow rates.

(KEQ )366

CS

Pairing

0.5

5

F0A –x6,A VS –T3

0.09 0.55

20.72 9.72

7

F0A –T3 F0B –T20

1.24 10.00

11.92 9.72

5

F0A –x6,A VS –T3

0.10 0.50

20.17 9.53

7

F0A –T4 F0B –T10

0.86 40.23

12.83 8.43

5

F0A –x7,A VS –T3

0.13 0.58

17.60 9.72

7

F0A –T3 F0B –T9 F0B –T13

0.62 3.55 0.21

15.95 17.60 214.13

2.0

10.0

a

KC

τ I (min)

Controller gains are dimensionless using temperature transmitter spans 50 K, composition transmitter spans 0.2 and valve sizes twice the steady-state flow rates.

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Fig. 14. Comparison of CS2, CS5 and CS7 for KEQ = 0.50: step increase in production rate handle.

transient drops in the purities of both products, and the distillate purity at the new steady state is below specification. Similar responses are obtained for feed composition disturbances. These results illustrate that the conventional process can handle very large disturbances compared to the reactive distillation column.

5.2. Kinetic case (KEQ )366 = 10.00 For the conventional process, the temperature of Tray 11 in the first column is paired with vapor boilup VS1 , and the temperature of Tray 3 in the second column is paired with vapor boilup VS2 . The fresh feed stream F0A is ratioed to the fresh feed stream

Fig. 15. Comparison of CS2, CS5 and CS7 for KEQ = 10: step decrease in production rate handle.

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F0B , and the ratio is set by the temperature controller on the top tray of second column (Tray 13). For the CS5 control structure of the reactive column, the fresh feed F0A is manipulated to control the concentration of reactant A on Tray 7. The vapor boilup is manipulated to control the temperature of Tray 3. For the CS7 structure, SVD analysis suggests controlling the temperatures on Tray 3 and Tray 13 by the fresh feeds F0A and F0B , respectively. Controller gains and reset times calculated from the relay-feedback test data give reasonable results for Tray 3. However, as can be seen from Table 5, the T13 /F0B pairing is not a good choice because the unrealistically large reset time, which is the result of inverse response of the openloop transfer function. Therefore, Tray 9 in the reactive zone is selected as secondary sensitive region, which gives reasonable relay-feedback test results. The upper plots in Fig. 15 show the responses of two processes for a negative 5% step change in production rate. Although there is a transient drop in distillate purity of the reactive column using the CS7 control structure, all three control structures are able to handle this disturbance and to settle down with product purities within 1% of the desired 95% specification. The conventional system comes to a new steady state in a short time. It takes about 3 h for the reactive column with either control structure to come to steady state. The lower plots of Fig. 15 give responses when the disturbance is a 10% decrease in production rate. The reactive column with control structure CS7 shuts down. Similar results are found for feed composition disturbances. The conventional process handles disturbances much better than the reactive distillation column. The CS5 structure in the reactive column handles disturbances better that the CS7 structure. 6. Conclusions The robustness and rangeability of a multi-unit reactor/column/recycle process and a reactive distillation column are compared for different values of chemical equilibrium constants. In this study, we assumed an ideal system with constant relative volatilities (α = 2). The reactive distillation column studied operates in the “neat” mode (no excess reactant). Several control structures are developed and tested for both flowsheets. These control structures are compared in the face of disturbances in production rate and fresh feed compositions. Results show that the control structure without a composition analyzer in the conventional multi-unit process works as well as the control structure with a composition analyzer. The conventional process provides a wide operability region. Since a reactive distillation system has a smaller number of control degrees of freedom than a conventional multi-unit system, its controllability is more difficult and its operability region is much smaller. Product quality variability is larger. These results show that there is a significant trade-off between the optimal economic steady-state design and the dynamic con-

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