Control of Ternary Reactive Distillation Columns with and without

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Ind. Eng. Chem. Res. 2007, 46, 5576-5590

Control of Ternary Reactive Distillation Columns with and without Chemically Inert Components William L. Luyben* Department of Chemical Engineering, Lehigh UniVersity, Bethlehem, PennsylVania 18015

Dynamic control structures of many types of reactive distillation columns have been studied in the literature. Both ideal hypothetical chemical systems and real chemical systems have been investigated. Most papers that involve ideal systems consider the quaternary ideal two-reactant, two-product chemistry A + B T C + D. This paper explores the control of an ideal ternary system with the chemistry A + B T C. Two cases are considered. In the first, there are only three components. In the second, the feed contains another component that does not participate in the reaction but does have a major impact on the structure of the column and the vapor-liquid phase equilibrium. A recent paper [Luyben, W. L. Ind. Eng. Chem. Res. in review] explored the effects of several kinetic and design parameters on the steady-state design of these ternary systems. Significant differences were observed between the systems with and without chemically inert components. The current paper demonstrates that the control structures for these two systems are also quite different. Of particular importance is the finding that a two-temperature control structure provides effective control for the ternary system without inerts; however, this structure does not work when inerts are present, indicating that a direct composition measurement of a column internal composition is required for effective control. 1. Introduction

Table 1. Kinetic and Vapor-Liquid Equilibrium Parameters for Ternary System without Inerts

The number of papers that involve reactive distillation has grown dramatically in the past decade. Both real chemical systems and ideal hypothetical systems have been studied. The most frequently studied ideal system is the four-component quaternary system with two reactants and two products:

A+BTC+D Reactants A and B are fed into the middle reactive section of the column, light product C goes overhead in the distillate, and heavy product D goes out the bottom. There have been relatively few papers that address the ideal three-component ternary system with two reactants but only one product:

A+BTC Many of the high-capacity industrial reactive columns have this type of chemistry. Three important applications are the production of methyl tert-butyl ether (MTBE) from isobutene and methanol, the production of ethyl tert-butyl ether (ETBE) from isobutene and ethanol, and the production of tert-amyl methyl ether (TAME) from methanol and isoamylenes. Few papers1-5 have explored the control of these systems. Although there are only three components involved in the reaction, in many of the A + B T C systems there more than three components in the column because the feed streams contain other components. These components are “inert” from the standpoint of the reaction, but they are not inert from the standpoint of their effect on the vapor-liquid equilibrium in the column. These inert components are present in the olefin feed streams that contain the reactive C4 and C5 iso-olefins in all of the industrial examples previously cited. The reason for their presence is the great difficulty in separating the desired iso-olefin from the other components. For example, in the MTBE and ETBE cases, the isobutene is typically produced in * To whom correspondence should be addressed. Tel.: 610-7584256. Fax: 610-758-5057. E-mail address: [email protected].

parameter activation energy forward backward specific reaction rate at 366 K forward backward chemical equilibrium constant at 366 K heat of reaction heat of vaporization molecular weight vapor-pressure constants A B C

value 30 kcal/mol 40 kcal/mol 0.008 kmol s-1 kmol-1 0.0004 kmol s-1 kmol-1 20 -10 kcal/mol 6.944 kcal/mol 50 g/mol Aj ) 12.34, Bj ) 3862 Aj ) 11.45, Bj ) 3862 Aj ) 10.96, Bj ) 3862

Table 2. Steady-State Conditions and Design Parameters for the Base Case parameter fresh feed flow rate of A, F0A fresh feed flow rate of B, F0B distillate flow rate, D bottoms flow rate, B vapor boilup, VS reflux flow rate, R overhead vapor flow rate, VNT number of stripping trays, NS number of reactive trays, NRX number of rectifying trays, NR liquid holdup on reactive trays, MRX column diameter pressure, P composition (mole fraction) A B C

value 12.63 mol/s 12.82 mol/s 0 mol/s 12.857 mol/s 62.03 mol/s 80.17 mol/s 80.17 mol/s 5 9 0 1000 mol 1.09 m 8 bar reflux ) 0.8725, bottoms ) 0.0025 reflux ) 0.0928, bottoms ) 0.0175 reflux ) 0.0347, bottoms ) 0.9800

a catalytic cracker in a refinery, along with many other C4 components (isobutane, n-butane, and n-butene). All of these C4 components have very similar boiling points. Their separa-

10.1021/ie070443c CCC: $37.00 © 2007 American Chemical Society Published on Web 07/25/2007

Ind. Eng. Chem. Res., Vol. 46, No. 17, 2007 5577

Figure 1. Flowsheet for a ternary reactive distillation column without inerts. Table 3. Controller Tuning Parameters: Ternary without Inerts Loop 1

KU PU (min) KC τI (min) SP

CS1

CS2

CS3

controlled variable ) xB(C); manipulated variable ) VS

controlled variable ) temperature tray 3; manipulated variable ) VS

controlled variable ) temperature tray 3; manipulated variable ) F0A

9.1 5.0 1.0 11 0.98

2.6 2.0 0.8 4.4 422 (K)

12 2.7 3.6 6.0 422.1 (K)

Loop 2


CS1

CS2

CS3

controlled variable ) x(5,A); manipulated variable ) F0A


controlled variable ) temperature tray 5; manipulated variable ) F0B

1.8 3.0 0.5 6.6 0.38

1.8 3.0 0.5 6.6 0.38

2.6 17 0.83 37 398.8 (K)

A+BTC

has two streams leaving the column. One contains the product (C) and the other contains the inerts. Wang et al.1 studied the control of the MTBE reactive distillation column and recommended a control structure that uses both a tray temperature and an internal composition. The temperature was controlled by the reboiler duty, and the internal composition was controlled by adjusting the C4 fresh feed stream. This is one of the control structures evaluated in this paper. Note that the vapor-liquid equilibrium in the systems studied in this paper is assumed to be ideal with constant relative volatilities. There are no azeotropes.

We will first discuss the control of the ternary system without inerts to get some insights into how changing from a twoproduct, two-reactant system (quaternary) to a one-product, tworeactant (ternary) system impacts the control structure required for reactive distillation columns. Unlike the quaternary column with distillate and bottoms products, the ternary column without inerts has only one product stream leaving the column. The control structure used in the ternary system is quite different from that used in the quaternary system. We will then explore the ternary system with inerts present in one of the feed streams. The reactive distillation column now

2. Ternary System without Inerts 2.1. Column Configuration. In the two-reactant, two-product quaternary reaction system, the column has both bottoms and distillate products coming from the two ends of the column. The two reactant feed streams are fed into the middle section of the column. With a one-product reaction system without inerts, the column has only a bottoms product or a distillate product. If the product component C is heavier than the reactant components A and B, there is a bottoms stream but no distillate. The column operates at total reflux with all the overhead vapor condensed and returned to the column as reflux. There is no

tion using distillation would be very energy-intensive. Therefore, a mixture of all of these C4 components is fed to the reactive distillation column, and the chemically inert components are removed as a product stream from the column. A recent paper6 illustrates the effects of several kinetic and design parameters on the steady-state design of ideal ternary reactive distillation columns. Two cases were studied: one without inert components in the feed and one with inerts. The chemistry considered is the reversible, exothermic, liquid-phase reaction

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Ind. Eng. Chem. Res., Vol. 46, No. 17, 2007

Figure 2. (A) Composition and (B) temperature profiles for the ternary reaction (A + B T C) without inerts.

need to have a rectifying section because there is no distillate and no need to maintain any composition at the top of the column. Therefore, the column configuration in the two-reactant, oneproduct ternary system without inerts is quite different than the two-reactant, two-product quaternary configuration. 2.2. Chemistry and Phase Equilibrium Parameters. Table 1 gives kinetic and vapor-liquid phase equilibrium parameters that have been used in the numerical case considered in this paper. The overall reaction rate on the nth tray (Rn) is dependent on the molar holdup (MRX), the specific forward and backward reaction rates (kF and kB, respectively), and the liquid mole fractions.

Rn ) MRX(kFxnAxnB - kBxnC)

(1)

The equilibrium constant at 366 K ((KEQ)366) is 20. The relative volatilities are constant at 2 between adjacent components.

RA > RB > RC

(2)

Product C is the high-boiling component, so it is removed from the bottom of the column. 2.3. Equipment Sizes and Steady-State Conditions. The ternary system without inerts has two feed streams and a bottoms stream, but there is no distillate. Figure 1 shows the flowsheet. The purity of the bottoms product is 98 mol % C. The production rate of C is set at 12.6 mol/s, which gives a bottoms flow rate of 12.86 mol/s. The column has five stripping trays and nine reactive trays and operates at a pressure of 8 bar. The liquid holdup on the reactive trays is 1000 mol and that on the stripping trays is 654 mol. The column diameter is 1.09 m, as calculated from vapor loading limitations. This diameter gives a reasonable liquid height (in terms of hydraulics) on the reactive trays of 0.077 m with the 1000 mol of liquid holdup. The holdups in the base and reflux drum are sized to provide 5 min of holdup when they are half full. The bottoms purity is 98 mol % C with impurities of 0.25 mol % A and 1.75 mol % B. The fresh feeds are F0A ) 12.63 mol/s and F0B ) 12.82 mol/s. The vapor boilup required to


Figure 3. Schematic diagram of control structure CS1.

Figure 4. Results of control structure CS1: (A) +20% ∆F0B, (B) -20% ∆F0B, (C) z0A(B) ) 0.05, and (D) z0A(C) ) 0.05.

achieve the bottoms purity is 62.03 mol/s, and the reflux flow rate is 80.17 mol/s, which is the overhead vapor rate. Table 2 gives conditions for the base case. Note that the reflux composition is primarily the lightest component (A), but some of the other two components are also present. Figure 2 gives the composition and temperature profiles. Equimolal overflow is assumed, so the liquid and vapor rates are constant in the nonreactive stripping section of the column. However, there are changes in the liquid and vapor flow rates in the reactive section because of two effects: (1) the reaction

is not equimolar (one mole of product is produced by the consumption of two moles of reactant), and (2) the exothermic reaction causes vaporization of some of the liquid. Therefore, the vapor rates increase as they flow up the column and the liquid rates decrease as they flow down the column. λ Vn ) Vn-1 R (3) ∆HV n λ Ln ) Ln+1 - Rn + R (4) ∆HV n

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Figure 6. Results of control structure CS2: (A) +20% ∆F0B, (B) -20% ∆F0B, (C) z0A(B) ) 0.05, and (D) z0A(C) ) 0.05.

In the following sections, three alternative control structures are explored. The primary objective is to maintain the specified purity of the bottoms product at 98 mol % C in the face of disturbances in the production rate and feed compositions.

2.4. Control Structure CS1. Figure 3 shows a control structure that uses two direct composition measurements. The purity of the bottoms product (in units of mol % C) is measured and controlled by vapor boilup. The composition of A on tray



Table 4. Steady-State Conditions and Design Parameters with Inerts parameter fresh feed flow rate of A, F0A composition of F0A (mol % A/mol % I) fresh feed flow rate of B, F0B distillate flow rate, D bottoms flow rate, B vapor boilup, VS reflux flow rate, R stripping trays, NS reactive trays, NRX rectifying trays, NR internal control tray, NC composition on control tray (mole fraction A) (KEQ)366 liquid holdup on reactive trays, MRX column diameter pressure, P vapor-pressure constants A B C I product composition (mole fraction) A B C I

value 24.51 mol/s 50/50 12.60 mol/s 12.58 mol/s 12.39 mol/s 65.10 mol/s 70 mol/s 5 15 5 6 0.30 50 2000 mol 1.11 m 8 bar Aj ) 12.34, Bj ) 3862 Aj ) 11.65, Bj ) 3862 Aj ) 10.96, Bj ) 3862 Aj ) 12.34, Bj ) 3862 distillate, xDj ) 0.0017; bottoms, xBj ) 0.0017 distillate, xDj ) 0.0204; bottoms, xBj ) 0.0163 distillate, xDj ) 0; bottoms, xBj ) 0.9800 distillate, xDj ) 0.9719; bottoms, xBj ) 0.0020

5 is measured and controlled by the flow rate of fresh feed F0A. The throughput is set by controlling the flow of fresh feed F0B. The reflux drum level is controlled by manipulating the reflux flow rate, and the base level is controlled by manipulating the bottoms flow rate. Tray 5 is selected because this is the location where the composition of A is changing rapidly from tray to tray. The steady-state composition is 38 mol % A. Two 0.5-min firstorder composition measurement lags are inserted in both composition control loops. The composition transmitter spans are 20 mol %. All valves are 50% open at steady state. The controllers are tuned by running relay-feedback tests. Values of ultimate gains and periods are given in the first two

columns of Table 3. Tyreus-Luyben tuning is used in most cases; however, some loops are detuned to give larger closedloop damping coefficients. Results for the CS1 control structure are given in Figure 4. In Figure 4A, the disturbance is a positive 20% step change in the throughput handle, F0B, at a time of 10 min. The purity of the bottoms product decreases to ∼97.5 mol % C during the transient but recovers back to its specified value of 98 mol % C within ∼2 h. The fresh feed flow rate F0A of A is increased by the x(5,A) controller to bring in the required amount of A to react with the increased input of B. More vapor boilup VS and reflux R are required. Reflux composition xDj changes very little. Figure 4B gives results for a negative 20% step change in F0B. The control performance is essentially the same as that observed for the positive disturbance. Figure 4C shows what happens when the composition z0A of the fresh feed F0A is changed from pure A (z0A(A) ) 1) to a mixture of A and B (z0A(A) ) 0.95 and z0A(B) ) 0.05). The x(5,A) controller increases the F0A flow rate to compensate for the lower amount of A in that stream. Because more B is coming into the system, more product C is produced and the bottoms flow rate increases. More vapor boilup and reflux are required. Figure 4D shows what happens when the composition z0A of the fresh feed F0A is changed from pure A (z0A(A) ) 1) to a mixture of A and C (z0A(A) ) 0.95 and z0A(C) ) 0.05). The x(5,A) controller increases the F0A flow rate to compensate for the lower amount of A in that stream. Because the same amount of B is coming into the system, the same amount of product C is produced in the reaction; however, the small additional amount of C in the feed produces a small increase in the bottoms flow rate. The CS1 control structure successfully handles these fairly large disturbances. But it has the disadvantage of requiring two on-line composition measurements. In the following sections, we explore using temperature measurements instead of composition measurements. Compositions are much more difficult and expensive to measure than temperatures, so it is highly desirable to find control schemes that provide effective control using only temperatures whenever possible; however, this is not always the case. 2.5. Control Structure CS2. Figure 5 shows a control structure in which, instead of measuring the bottoms composition, the temperature at tray 3 is controlled by manipulating vapor boilup. The temperature profile shown in Figure 2B is changing rapidly from tray to tray at this location, so it should provide a good indication of the composition of the heavy component C at a tray near the location from which the product is removed. The setpoint of this T(3) temperature controller is 422 K. Relay-feedback testing yields the tuning parameters given in Table 3. The span of the temperature transmitter is 50 K. Figure 6 shows the performance of this CS2 control structure for the same four disturbances considered in the previous section. Because the bottoms composition is not directly measured and we are only holding the temperature constant, there is no guarantee that the composition of the bottoms will be held exactly at its specification. However, for the throughput disturbances (changes in F0B), the bottoms purity is maintained quite close to its specification. There is more of an offset in the bottoms composition for the two feed composition disturbances, but this small drop in product purity may be quite acceptable. Thus, the use of a temperature in the stripping section may eliminate the need for a direct composition measurement of the bottoms.

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Figure 8. Steady-state gains for the ternary reaction without inerts.

Figure 9. Results of control structure CS3 (T3 and T5): (A) +20% ∆VS, (B) -20% ∆VS, (C) z0A(B) ) 0.05, and (D) z0A(C) ) 0.05.

2.6. Control Structure CS3. In a previous paper,7 a twotemperature control structure was investigated for the quaternary two-product, two-reactant system. We demonstrated that an internal composition measurement is not required in that system

to provide the precise balancing of the stoichiometry of the reaction, i.e., feeding exactly the right amount of reactants so that no excess of one or the other accumulates in the column. Will a similar two-temperature control structure be effective in


Figure 10. SVD analysis.

Figure 11. Results of control structure CS3 (T3 and T12): (A) +20% ∆VS, (B) -20% ∆VS, (C) z0A(B) ) 0.05, and (D) z0A(C) ) 0.05.

the ternary system without inerts? This structure is shown in Figure 7. The two fresh feeds are manipulated to control the temperatures on two trays.

The first issue is to find what trays to control. The steadystate gains between tray temperatures and the three input variables (vapor boilup and the flow rates of the two fresh feed

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Figure 12. Flowsheet for a ternary reactive distillation column with inerts.

streams) are calculated numerically. Figure 8 shows the steadystate gains between tray temperatures throughout the column and the three inputs to the column: vapor boilup and the fresh feed flow rates F0A and F0B. It is necessary to make very small changes to get accurate gains; i.e., gain values do not change as the size of the change in the input is decreased. These results show that tray 4 is the most sensitive for vapor boilup changes. Tray 3 is the most sensitive to changes in F0A, and tray 5 is the most sensitive to changes in F0B. Therefore, these locations are selected, as shown in Figure 7. The two singular values for this control structure are σ1 ) 142 and σ2 ) 17, giving a condition number of 8.4, which indicates that this control structure should perform adequately. Figure 9 demonstrates that this control structure provides quite acceptable control in the face of all four of the disturbances. Stable base-level regulatory control is attained. The bottoms purity is maintained close to the desired value for all of the disturbances. Figure 10 shows the U vectors from the SVD analysis. The most-sensitive locations are trays 3 and 5, which are those suggested by the steady-state gains. However, there is a third location at tray 12 that is indicated as being sensitive. This is unexpected because the gains in this region, as shown in Figure 8, are all quite small. However, the ∆T/∆F0B gain at tray 12 is the largest of the three. Therefore, the control structure was evaluated in which the temperature at tray 5 is controlled by manipulating F0A and temperature at tray 12 is controlled by manipulating F0B. The results given in Figure 11 demonstrate that this selection of control trays does provide stable base-level regulatory control. However, the purity of the bottoms product is not held as close to its specification as with the original chose of trays 3 and 5. This is particularly true for the changes in feed composition. 3. Ternary System with Inerts The first part of this paper considered the case in which the fresh feed streams of both reactants A and B are pure. In most of the real commercial reactive distillation systems, the lighter

Figure 13. (A) Composition and (B) temperature profiles for the ternary reaction (A + B T C) with inerts.

reactant A is fed with other components that are inert in terms of the reaction but have volatilities that are quite similar to


Figure 14. Schematic diagram of control structure CS1-RR. Table 5. Controller Tuning Parameters: Ternary with Inerts Loop 1


CS1

CS2

CS3

controlled variable ) xB(C); manipulated variable ) VS

controlled variable ) temperature tray 3; manipulated variable ) VS

controlled variable ) temperature tray 5; manipulated variable ) F0A

4.0 6.0 0.5 13 0.98

1.6 2.5 0.125 5.5 418.5 (K)

5.3 3.0 1.6 6.6 339.4 (K)

Loop 2


CS1

CS2

CS3



controlled variable ) temperature tray 13; manipulated variable ) F0B

11 3.0 2.0 6.6 0.30

11 3.0 2.0 6.6 0.30

9.1 55 2.8 100 387.5 (K)

that of component A. We assume that the fresh feed stream F0A is a mixture of reactant A and an inert component I, which is not involved in the reaction. The volatility of I is assumed to be identical to that of A, so both of these components are lighter than the other reactant B and the product C. The composition of this feed stream is z0A(j) and is a 50/50 mixture of reactant A and chemically inert I. 3.1. Column Configuration. In the ternary reaction system without inerts, the column has only a bottoms product in which the heavy product C is removed and has only stripping and reactive zones. In the ternary reaction system with inerts, the column has both distillate and bottoms streams. Figure 12 gives the flowsheet of the reactive column. The heavy product C exits the bottom with some impurities of the other components (mostly B). Because the inert component I has the same volatility as the low-boiling component A, it is removed from the column in a distillate stream. The reactive distillation column has all three zones: a stripping zone to keep light components A, I, and B from dropping out the bottom, a reactive zone in which the reaction occurs, and a rectifying zone to keep the heavier component (B) from escaping out the top. It is important to note that any component A that leaves the top of the reactive zone will go overhead with the inert I. The

rectifying section cannot keep component A from escaping. It can only keep reactant B from being lost in the distillate. 3.2. Chemistry and Phase Equilibrium Parameters. The chemical kinetics are slightly modified from those used in the case without inerts. Because the presence of the inert decreases the concentrations of the reactants, the reaction rates will be smaller. Therefore, the chemical equilibrium constant (KEQ)366 is increased from 20 to 50 to compensate for the lower reactant concentrations. The holdup on the reactive trays is also increased from 1000 mol to 2000 mol. In addition, the number of reactive trays is increased from 9 to 15. The volatility of I is identical to A, so the vapor-pressure constants used for I are the same as those used for A (see Table 1). There are 5 stripping trays, 15 reactive trays, and 5 rectifying trays. The column diameter is 1.1 m. With a liquid height of 0.05 m on the stripping and rectifying trays, the holdup on these trays is 670 mol. The holdup on the reactive trays is 2000 mol, which gives a liquid height of 0.15 m. The holdups in the column base (23.2 kmol) and reflux drum (24.8 kmol) are sized to give 5 min of residence time when 50% full, based on the total liquid that is entering. In the reflux drum, this is the sum of the reflux and distillate flow rates. Steady-state conditions and design parameters are given in Table 4.

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Figure 15. Results for (A) control structure CS1 (with inerts) with fixed reflux, +20% ∆F0B, and for control structure CS1-RR: (B) +20% ∆F0B, (C) -20% ∆F0B, (D) z0A(I) ) 0.45, (E) z0A(I) ) 0.55, and (F) z0B(A) ) 0.05.

Figure 13 gives the liquid composition and temperature profiles. The concentration of A is the highest at tray 6, where it is fed. The concentration of inert I increases throughout the reactive and rectifying stages, particularly in the rectifying stages where B is prevented from being lost in the overhead. Note that there is a slight increase in the concentration of A in the rectifying section. Any A that leaves the reactive zone cannot be prevented from going overhead with the I because the two have the same volatility.

In the following sections, three alternative control structures are explored. The primary objectives in the face of disturbances in production rate and feed compositions are (1) to maintain the specified purity of the bottoms product at 98 mol % C and (2) to avoid losses of reactants in the distillate. 3.3. Control Structure CS1. Figure 14 shows a control structure that uses two direct composition measurements. The purity of the bottoms product (expressed in mol % C) is measured and controlled by vapor boilup. The composition of A on tray 6 (30 mol % A) is measured and controlled by the


Figure 16. Schematic diagram of control structure CS2-RR.

flow rate of fresh feed F0A. The throughput is set by flow controlling the fresh feed F0B. Reflux drum level is controlled by manipulating the distillate flow rate, and base level is controlled by manipulating bottoms flow rate. Two alternative structures are evaluated with this control scheme. In the first, the reflux flow rate is simply fixed. In the second, shown in Figure 14, the reflux ratio is controlled. This is achieved by measuring the distillate flow rate, multiplying this signal in the “ratio” element by the desired reflux ratio. The output signal from the ratio changes the setpoint of the reflux flow controller. The steady-state reflux ratio is 70/12.58 ) 5.58. The bottoms composition is 98 mol % C. The distillate composition is 97.19 mol % I, which means that there are only small losses of reactants A and B in the distillate. Two 0.5 min first-order composition measurement lags are inserted in both composition control loops. Composition transmitter spans are 20 mol %. All valves are 50% open at steady state. The controllers are tuned by running relay-feedback tests. Values of ultimate gains and periods are given in Table 5. Tyreus-Luyben tuning is used in most cases; however, some loops are detuned to give larger closed-loop damping coefficients. Figure 15A gives the response of the system with the fixed reflux flow rate (not a constant reflux ratio) to a +20% change in the production rate handle F0B. The bottoms composition is maintained at its specified value, but the bottom left graph shows that the inert composition of the distillate drops drastically to ∼87 mol % I. This means large amounts of the reactants are being lost out the top of the column. The distillate flow rate increases, as does the fresh feed F0A and vapor boilup. The production of product C only increases by 8% (the bottoms flow rate increases from 12.39 mol/s to 13.5 mol/s), despite the 20% increase in the amount of B fed. The losses of both reactants are very large. Implementing the reflux-ratio strategy improves the situation, as shown in Figure 15B. The distillate inert composition only decreases to ∼96.8 mol % I. The bottoms flow rate increases to 14.9 mol/s, which should be compared with the 13.5 mol/s flow rate observed in the fixed reflux control structure. Figures 15C-F give the response to other disturbances in the production rate and feed compositions.

In Figure 15C, the production rate handle F0B is reduced by 20%, and the control system provides very effective control. In Figure 15D, the fresh feed F0A contains less I, so the distillate rate decreases and less F0A is fed for a fixed value of F0B. The production rate, as reflected in the bottoms flow rate, decreases slightly, even with the fixed amount of B coming into the system with F0B held constant. This occurs because more B is lost in the distillate. (See the lower left plot in Figure 15D. Note that, in this figure, the time of the simulation has been increased to 10 h.) In Figure 15E, more I is included in the fresh feed F0A and both the distillate rate and F0A increase. In Figure 15F, the fresh feed F0B is changed from pure B to z0B(A) ) 0.05 and z0B(B) ) 0.95. Because less B is fed into the reactor, the production rate decreases (the bottoms and distillate flow rates drop) and less F0A is fed into the reactor. The bottoms purity is unchanged, but the concentration of I in the distillate slightly decreases. 3.4. Control Structure CS2. Figure 16 shows a control structure in which the temperature at tray 3 is controlled instead of direct composition control of the bottoms composition. Figure 17 shows that this “inferential” control scheme does a good job of maintaining product purity and keeping reactant losses low for production rate changes (see Figures 17A and 17B). However, the performance of this control structure for feed composition disturbances is somewhat poor. As shown in Figures 17C-E, both the bottoms and distillate compositions change significantly, which indicates a change in conversion and losses of reactants. 3.5. Control Structure CS3. The final control structure studied is the two-temperature scheme that eliminates the need for composition measurements. This control structure works quite well in both the quaternary system and the ternary system without inerts. Will it work as well in the ternary system with inerts? To determine what control trays to select, steady-state gains are calculated and SVD analysis is performed. Figure 18A gives the steady-state gains for all trays in the column. These results indicate that the effects of both F0A and F0B are largest around trays 3 and 4. These two locations are too close together to provide independent temperature measurements. Calculating the

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Figure 17. Results of control structure CS2-RR (with inerts): (A) +20% ∆F0B, (B) -20% ∆F0B, (C) z0A(I) ) 0.45, (D) z0A(I) ) 0.55, and (E) z0B(A) ) 0.05.

two U vectors in the SVD analysis for the two inputs F0A and F0B gives the results shown in Figure 18B. The two sensitive locations are indicated as trays 3 and 5. These are also very close together, but the singular values of the gain matrix are 219 and 76, which gives a reasonable condition number. This control structure was tested without success. The temperature on tray 3 was controlled by manipulating F0A. The process gain in negative, so the controller gain should be negative (direct acting: an increase in temperature increases

F0A). This loop was tuned and worked well when the other temperature loop was in manual mode. The second temperature loop controls tray 5 by manipulating F0B. The process gain in positive, so the controller gain should be positive (reverse acting: an increase in temperature decreases F0B). This loop did not work, as illustrated in Figure 19. The tray 3 temperature controller is in manual mode (i.e., F0A is fixed). No disturbance is made. After ∼10 min, the temperature on tray 5 begins to decrease. The tray 5 temperature controller increases F0B up to its limit (twice the steady-state value), but


Figure 18. (A) Steady-state gains with inerts; (B) SVD analysis of the ternary reaction with inerts.

Figure 19. Results of control structure CS3-RR (with inerts); T5 to F0B loop unstable.

the temperature does not recover. We were unable to make this control structure work using trays 3 and 5.

There is a slight hump in the U1 curve at tray 13 (shown in Figure 18B). We tested a control structure that used F0A to control the temperature of tray 5 and F0B to control the temperature of tray 13. These two loops were successfully tuned, but the tray 13 controller had a very large ultimate period (55 min). Table 5 gives the controller tuning parameters. The performance of this control structure is given in Figure 20A for a +20% change in VS. The system is stable, but the bottoms purity and distillate purity are not well-controlled. Figure 20B shows that the response to a 20% decrease in VS is even worse in terms of product purity. The bottoms composition decreases to 76 mol % C, while the distillate composition slightly decreases. These results demonstrate that a two-temperature control scheme does not provide effective control of the ternary system with inerts. The two-temperature control structure works for the quaternary system and for the ternary without inerts, but not for the ternary with inerts. The same conclusion was observed by Al-Arfaj and Luyben3 for the ETBE system and by Wang et al.1 for the MTBE system.

5590


Figure 20. Results of control structure CS3-RR (with inerts) using T5 and T13: (A) +20% ∆VS and (B) -20% ∆VS.

4. Conclusion Two different ternary systems have been explored. Both have two reactants and one product. However, one has an additional component coming in with one of the feeds that is not involved in the reaction. It is “inert” as far as the chemistry is concerned. However, it dilutes the concentrations of the reactants and the products; thus, it does affect the overall reaction rates. More importantly, the presence of the inert component has a major impact on both the structure of the column (two outlet streams are required instead of one) and the vapor-liquid phase equilibrium. As this paper illustrates, it also has a profound effect on the control structure required for adequate control. Literature Cited (1) Wang, S. J.; Wong, D. S. H.; Lee, E. K. Effect of interaction multiplicity on control system design for a MTBE reactive distillation column. J. Process Control 2003, 13, 503-515.

(2) Sneesby, M. G.; Tade, M. O.; Smith, T. N. Two-point control of a reactive distillation column for composition and conversion. J. Process Control 1999, 9. (3) Al-Arfaj, M. A.; Luyben, W. L. Control study of ethyl tert-butyl ether reactive distillation. Ind. Eng. Chem. Res. 2002, 41, 3784-3796. (4) Al-Arfaj, M. A.; Luyben, W. L. Plantwide control for TAME production using reactive distillation. AIChE J. 2004, 50, 7, 1462. (5) Luyben, W. L. Comparison of pressure-swing and extractivedistillation methods for methanol-recovery systems in the TAME reactivedistillation process. Ind. Eng. Chem. Res. 2005, 44, 5715-5725. (6) Luyben, W. L. Effect of kinetic and design parameters on ternary reactive distillation columns. Ind. Eng. Chem. Res., in review. (7) 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, 61, 4432-4450.

ReceiVed for reView March 27, 2007 ReVised manuscript receiVed May 17, 2007 Accepted May 30, 2007 IE070443C

Control of Ternary Reactive Distillation Columns with and without

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