Internal Heat Integration and Controllability of Double Feed Reactive

Aug 28, 2008 - The impact of altering feed tray locations (for the purpose of saving energy) on the controllability of double feed reactive distillati...
3 downloads 12 Views 2MB Size
Download PDF
7294

Ind. Eng. Chem. Res. 2008, 47, 7294–7303

Internal Heat Integration and Controllability of Double Feed Reactive Distillation Columns, 1. Effect of Feed Tray Location M. V. Pavan Kumar and N. Kaistha* Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India

The impact of altering feed tray locations (for the purpose of saving energy) on the controllability of double feed reactive distillation (RD) columns is evaluated for two case studies: a hypothetical ideal RD column and a methyl acetate RD column. Energy savings of 18.3% and 36.4% over the conventional design (feed immediately above and below the reactive zone) is achieved for the ideal and methyl acetate systems, respectively. A steady-state bifurcation analysis shows that, for both systems, output multiplicity, with respect to reboiler duty, occurs at a fixed reflux rate for the different designs (conventional/altered feed tray location). The output multiplicity is eliminated at a fixed reflux ratio. Closed-loop dynamic simulation results show that the controllability of the internally heat integrated ideal RD column deteriorates, compared to the conventional design. Unlike the conventional design, temperature-based inferential control is infeasible and compositionbased control structures must be used. For the methyl acetate column, on the other hand, heat integration by altering the feed locations entails no loss in controllability using two-point temperature inferential control. Introduction Reactive distillation (RD) is now established as a promising design alternative for process integration/intensification.1–4 It is economically attractive when the reaction kinetics favor a high reaction rate at the tray bubble temperature and the vapor-liquid equilibrium (VLE) is such that the reactant(s) can be pushed back into the reactive section and prevented from escaping the column (internal recycle of reactants). In addition, azeotropes may be “reacted away,” significantly the separation task. Eastman’s methyl acetate process is a classic commercial success that replaced a conventional process that consisted of a reactor followed by a nine-column separation section with a single RD column.4 The capital and operating costs are reported to be one-fifth of the cost of the conventional process. Given its economic potential, significant research effort in the past two decades has focused on development of RD processes for different chemicals.5 Commercially, RD has been successfully used for esterification and etherification processes.6 A key challenge in RD process development is the need to consider controllability issues at the design stage itself. The interaction between reaction and separation causes high nonlinearity, often resulting in steady-state multiplicity.7–15 The potential controlled variables such as tray temperatures/ compositions can exhibit output/input multiplicity, with respect to one or more potential control inputs (such as the feed rate(s), reboiler duty, or reflux rate), because of process gain sign reversal. The control system may then succumb to nonlinear dynamic phenomena such as “wrong”’ control action,13,14 a steady-state transition,13 or a limit cycle,16 compromising its robustness. In the worst-case scenario, where no control structure performs satisfactorily, the column design itself may need to be altered to mitigate the nonlinear effects. However, the interaction between RD column design and controllability is not well-understood and is an active research area. Recent research in RD design has shown that the proper choice of the column design degrees-of-freedom can lead to significant energy savings. Cheng and Yu17 showed that, for a double feed ideal RD column, the conventional design with the * To whom correspondence should be addressed. Fax: 0091-5122590104. E-mail address: [email protected].

heavy and light reactant feed immediately above and below the reactive section, respectively, may be altered to allow feeds into the reactive zone, with maximum energy savings in the range of 6%-47%. Alternatively, the total catalyst may be redistributed to extend the reactive section into the stripping (rectifying) section with exothermic (endothermic) reaction heat on the extension trays, reducing the energy consumption. A combination of feed tray location alteration and catalyst redistribution for reactive zone extension may also be used to maximize the energy savings. Huang et al.18 have shown that extending the reactive section into the stripping (rectifying) section for an exothermic (endothermic) double feed ideal RD column results in significant energy savings. Huang et al.19 have also shown that the combination of feed tray location alteration and reactive zone extension by catalyst redistribution leads to substantial energy savings for real double feed RD systems such as a methyl tert-butyl ether (MTBE) column and an ethylene glycol column. It is demonstrated that the energy-efficient designs may be controlled using appropriate decentralized control structures.20–22 However, a systematic comparison of the controllability of the designs is lacking, and the impact of internal heat integration on overall column controllability is not clear. This article compares the controllability of a conventional double feed RD column design with an internally heat integrated design obtained by altering the feed tray locations. The hypothetical ideal RD column23 and a methyl acetate column are used as example case studies. It is highlighted that, to the best of our knowledge, the methyl acetate RD system has not been studied for internal heat integration. Also, for both RD systems, we particularly focus on temperature inferential control, which has much practical relevance in an industrial setting. In the following, the conventional design and the internally heat integrated design obtained by altering the feed tray locations are described for the ideal and methyl acetate RD systems. A bifurcation study of the input-output relations of the two designs is then presented. Two-point temperature inferential control structures are then synthesized for both the RD systems. The closed-loop response to large-throughput changes is then evaluated. The two designs are compared in terms of the steadystate deviation, as well as the integral absolute error (IAE) of

10.1021/ie071638n CCC: $40.75  2008 American Chemical Society Published on Web 08/28/2008

Ind. Eng. Chem. Res., Vol. 47, No. 19, 2008 7295

Figure 1. Schematic of a conventional double feed reactive distillation (RD) column.

the product purity. The results from the two case studies are contrasted in the Discussion. The article concludes by summarizing the main results from the two case studies. Steady-State Column Designs A schematic of the double feed RD column with rectifying, reactive, and stripping sections is shown in Figure 1. In the conventional design, the fresh heavy reactant is fed immediately above the reactive section, while the fresh light reactant is fed immediately below the reactive zone. Table 1 summarizes the reaction kinetics and other model details for the ideal and methyl acetate systems studied in this work. The reaction chemistry for both systems is of the type A + B T C + D. For the methyl acetate system, methanol, acetic acid, methyl acetate, and water correspond to components A, B, C, and D, respectively. Both the RD systems are operated with the pure reactants being fed in exact stoichiometric amounts. The equilibrium stage model is used to simulate the columns. The conventional column design and operating conditions for the two RD systems are summarized in Table 2. The conventional feed location design for the ideal RD system is taken from the work of Kaymak and Luyben24 and consists of 5 rectifying trays, 10 reactive trays, and 5 stripping trays, with a catalyst loading of 0.7 kmol per reactive tray. The two fresh feeds are perfectly stoichiometric and are fed at the rate of 12.6 mol/s each. The distillate rate is specified to equal the fresh feed rate (i.e., 12.6 mol/s) and the reflux ratio is adjusted to 2.718 for 95 mol% pure distillate and bottoms streams. The conventional methyl acetate RD column design consists of 7 rectifying trays, 18 reactive trays, and 10 stripping trays, with a catalyst loading of 300 kg per reactive tray. Each feed is perfectly stoichiometric at a rate of 300 kmol/h. The distillate rate is 308.63 kmol/h and the reflux ratio is set at 2.287 for a distillate methyl acetate purity of 95 mol%. The corresponding bottoms water purity is 96.3 mol%. The basic column design with the fresh feeds immediately above and below the reactive zone is internally heat integrated by allowing the feeds to be introduced into the reactive zone to minimize the reboiler duty. To maintain consistency across the different designs, the two column specifications are chosen so that the main product rate and purity remain the same as that

for the conventional design. Accordingly, the distillate (main product) flow rate specification is kept constant and the reflux ratio specification is adjusted for a 95 mol% pure distillate. For the energy-saving design, it turns out that the bottoms purity does not change for the ideal RD system, whereas, for the methyl acetate system, a slight decrease occurs. Figure 2 plots the reboiler duty, with respect to the lower feed location, with the top feed tray location being varied as a parameter. For the ideal RD system, the minimum reboiler duty design is obtained for the higher feed moving down by 3 trays and the lower feed moving up by 3 trays into the reactive section from their respective conventional locations (immediately above and below the reactive section). The optimized design for the methyl acetate RD system is obtained for the lower methanol feed moving up by 5 trays into the reactive section. The higher acetic acid feed location remains unaltered from its conventional location immediately above the reactive section, because moving the feed tray causes the reboiler duty to increase, regardless of the lower feed location. Table 3 summarizes the key operating conditions for the internally heat integrated designs for the ideal and methyl acetate example columns. The vapor boilup is reduced by 18.34% and 36.40% over the conventional design for the ideal and methyl acetate systems, respectively. Altering the feed tray locations can thus result in significant energy savings for the studied RD systems. The conventional and internally heat integrated column designs obtained by altering the feed tray locations are subjected to a bifurcation analysis and rigorous closed-loop dynamic simulations to evaluate their controllability. For convenient reference, the conventional design is referred to as Design A, whereas the optimized feed tray location design is referred to as Design B. Bifurcation Analysis The simplest control schemes result with a fixed reflux rate or a fixed reflux ratio policy. In view of the possibility of steadystate multiplicity, the variation in the product purity, with respect to the reboiler duty, (Qr), is obtained for Design A and Design B of the two example systems. The input-output (IO) relations are obtained for a fixed reflux rate as well as a fixed reflux ratio policy, and they are generated using homotopy continuation.15 For the ideal RD column, the IO relations for both Design A and Design B in Figure 3 show that output multiplicity occurs at a fixed reflux rate, signifying the highly nonlinear nature of the process. A fixed reflux ratio policy mitigates the nonlinearity, and the IO relations do not exhibit output multiplicity. However, input multiplicity in the two product purities is observed. The IO relations at a fixed reflux rate and fixed reflux ratio for the two designs of the methyl acetate column in Figure 4 show that output multiplicity occurs at a fixed reflux rate. As with the ideal system, the output multiplicity is eliminated for a fixed reflux ratio policy in the two designs. These results suggest that maintaining (or adjusting) the reflux ratio should be preferred over the reflux rate for good operability. Control Structure Synthesis Temperature Inferential Control Structures. Two-point temperature inferential control structures using a fixed reflux ratio policy are now synthesized for Design A and Design B of the ideal and methyl acetate RD systems. To ensure a fair controllability comparison between the designs, the closed-loop performance of the best structure for a design should be compared with the best structure for the other design(s).

7296 Ind. Eng. Chem. Res., Vol. 47, No. 19, 2008 Table 1. VLE and Reaction Details of the RD Systems ideal RD column reaction stoichiometry relative volatility

A+BTC+D RD/RB/RA/RC ) 1:2:4:8; temperature-independent

liquid-phase activity vapor phase reaction kinetics

ideal ideal rC (mol s-1 mol-1) ) kfxAxB - kbxCxD

methyl acetate RD column HAc + MeOH T H2O + MeOAc temperature-dependent (extended Antoine equation used to estimate the saturated vapor pressure) Wilson ideal with Marek’s methoda rMeOAc )

(

)

aMeOAcawater Keq (1 + KHAcaAcOH + KMeOHaMeOH + KMeOAcaMeOAc + Kwaterawater)2 Mckf aHAcaMeOH -

kf ) 2.4260 × 1016 e15098.1/T, kb ) 2.11768 × 10-6 e5032.47/T -41840 kJ/kmol, temperature-independent

heat of reaction a

KHOAc ) 3.18, KMeOH ) 4.95, Kwater ) 10.5, KMeOAc ) 0.82, kf (kmol/kgcat/h) ) 69.42 × 109 e-52275.93/(RT), Keq ) 2.32 e782.98/ T -33566.80 kJ/kmol at 330 K, temperature-dependent

Accounts for vapor-phase dimerization of acetic acid.

Table 2. Base-case RD parameter

ideal RD column

methyl acetate RD column

flow rate of feeds NE/NRX/NS design feed tray locations catalyst loading per reactive tray pressure reflux ratio distillate rate reboiler duty product purities

FA ) FB ) 12.6 mol/s 5/10/5 nFA ) 6; nFB ) 15 0.7 kmol

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

8.5 bar 2.718 12.6 mol/s 0.86086 MW xC, D ) xD, B ) 0.95

1.013 bar 2.287 308.63 kmol/h 5.7616 MW XMeOAc, D ) 0.95; xwater, B ) 0.963

However, the best control structure for a particular design is not known a priori. Indeed, if Design B consumes significantly less energy than Design A, it is quite possible that the best

Table 3. Salient Design Parameters of Internally Heat Integrated RD Column design parameter

ideal RD column

methyl acetate RD column

flow rate of feeds NE/NRX/NS design feed tray locations catalyst loading per reactive tray pressure reflux ratio distillate rate reboiler duty product purities

FA ) FB ) 12.6 mol/s 5/10/5 nFA ) 9; nFB ) 12 0.7 kmol

FHAc ) FMeOH ) 300 kmol/h 7/18/10 nFMeOH )16; nFHAc ) 28 300 kg

8.5 bar 2.287 12.6 mol/s 0.7030 MW xc, D ) xD, B ) 0.95

1.013 bar 1.4877 308.63 kmol/h 3.6639 MW xc, D ) 0.95xD, B ) 0.96-4

control structure for the two designs is different. In light of the same, the closed-loop performance of all reasonable two-point temperature control structures must be evaluated. For fixed-reflux-ratio two-point temperature control, any two of the column inputs (namely, the reboiler duty and the two fresh feeds) can be used to control a suitable tray temperature. The remaining third input is then the throughput manipulator. Accordingly, there are three basic control structures with the reboiler duty, the light reactant feed, or the heavy reactant feed as the throughput manipulator. These basic control structures are shown in Figure 5 and labeled, in order, CS1, CS2, and CS4, for convenient reference. The control tray locations and loop pairings are chosen from sensitivity analysis.25 Briefly, for a given throughput manipulator, the maximum sensitivity tray temperature is paired with the corresponding control input. The remaining input is then paired with an appropriate highsensitivity tray temperature. The Niederlinski Index (NI) may be used to eliminate unworkable input-output (IO) pairings. We also propose the vector, -K-1 · kTP (where K is the 2 × 2 steady-state gain matrix for the control structure IO pairings and kTP is the 2 × 1 gain vector of the controlled tray temperatures, with respect to the throughput manipulator), as additional criteria for eliminating unworkable IO pairings. Without any loss of generality, if u1 and u2 are the two manipulated variables and u3 is the throughput manipulator, we have, in the close vicinity of the base-case steady state,

[ ] [

][ ] [ ]

∆T1 K11 K12 ∆u1 K13 ) + ∆u3 ∆T2 K21 K22 ∆u2 K23

(1)

or, in matrix notation, Figure 2. Variation of reboiler duty, with respect to the lower feed location for a fixed top feed location: (a) ideal RD column and (b) methyl acetate RD column.

∆T ) K∆u + kTP∆u3

(2)

For a unit change in the throughput manipulator (∆u3 ) 1), the change in the manipulated variables necessary for the

Ind. Eng. Chem. Res., Vol. 47, No. 19, 2008 7297

Figure 3. Variation of product purities with respect to changes reboiler duty at a fixed reflux ratio and reflux rate for ideal RD column designs: (a) Design A and (b) Design B.

Figure 4. Variation of product purity, with respect to changes in reboiler duty at a fixed reflux ratio and reflux rate for methyl acetate RD column designs: (a) Design A and (b) Design B.

controlled temperatures to remain at the setpoint (∆T) is obtained from the aforementioned equation as ∆u ) -K-1 · kTP -1

(3)

Therefore, the vector -K · kTP is the change in the control inputs per unit change in the throughput manipulator. Clearly, if any element of the vector is negative, the control structure is unworkable, because a throughput increase (decrease) requires all other inputs to increase (decrease) in tandem. Also, the closer the vector element values are to 1, the more-balanced the control structure is, in that a unit change in the throughput manipulator causes a unit change in the control inputs. Figure 6 plots the tray temperature sensitivities, with respect to the reboiler duty and the two fresh feeds of the two designs for the example RD systems. For the ideal RD column, even as rectifying tray temperatures are sensitive, a severe inverse response to FB occurs. Also, input multiplicity causes a steadystate transition/wrong control action for moderately large throughput changes. Controlling a reactive tray temperature instead significantly improves the magnitude of the throughput

change that is handled. Accordingly, in the IO pairings for the ideal RD system, the most-sensitive reactive tray temperature is controlled (instead of a rectifying tray). The resulting IO pairings in CS1, CS2, and CS4 are noted in Table 4. Also, the condition number (CN), the Niederlinski Index (NI), and the vector -K-1 · kTP for the IO pairings are reported in Table 4. For the ideal RD system, the negative elements of -K-1 · kTP in all the structures for Design B show that the two-point temperature control structures are unworkable. On the other hand, the condition number, NI, and -K-1 · kTP values for the conventional feed tray location design (Design A) are acceptable. Internal heat integration by altering the feed tray locations causes temperature inferential control of the ideal RD system to be infeasible. Therefore, the controllability of the ideal RD system is adversely affected. For the methyl acetate system, the CN, NI, and -K-1 · kTP values for the different control structures for Design A and Design B are acceptable and comparable. This suggests that temperature inferential control for both designs should be possible.

7298 Ind. Eng. Chem. Res., Vol. 47, No. 19, 2008

Figure 5. Schematic of the temperature control structures: (a) CS1, (b) CS2, and (c) CS3.

Figure 6. Tray temperature sensitivities of the double feed RD column designs under study: (a) ideal and (b) methyl acetate.

Composition Control Structure. Huang et al.20 recently showed that three-point composition control can be used to regulate an internally heat-integrated ideal RD column. Because temperature inferential control is infeasible for Design B of the ideal RD system, the application of three-point composition control is considered. The control structure studied here is shown in Figure 7. The reflux ratio and vapor boilup are adjusted to maintain the distillate purity and the bottoms purity, respectively, while FB controls a sensitive reactive tray composition (tray 11 for Design A and Tray 15 for Design B). Composition-based control of the methyl acetate column is not studied, because temperature inferential control is feasible for both the designs.

Table 4. Control-Loop Pairings in the Control Structure (CS) and Its Niderlinski Index (NI), Condition Number (CN), and the Vector -(K-1 · kTP)T CS

NI

-(K-1kTP)T

CN

Ideal RD Column, Design A CS1 CS2 CS4

T11-FB; T3-FA T11-Qr; T3-FA T11-FB; T3-Qr

CS1 CS2 CS4

T14-FB; T6-FA T14-Qr; T6-FA T14-FB; T6-Qr

CS1 CS2 CS4

T18-FHAc; T2-FMeOH T18-Qr; T2-FMeOH T18-FHAc; T2-Qr

CS1 CS2 CS4

T13-FHAc; T2-FMeOH T13-Qr; T2-FMeOH T13-FHAc; T2-Qr

0.785 1.542 1.396

16.24 18.33 6.905

[0.955 0.972] [1.047 1.018] [0.982 1.029]

Ideal RD Column, Design B 1.989 1.957 -0.033

4.423 1.620 213.3

[-2.9601 0.011] [-0.338 -0.004] [-253.8 85.74]

Methyl Acetate RD Column, Design A

Closed-Loop Dynamic Simulation Results Dynamic Simulation and Controller Tuning. The closedloop performance of the proposed control structures is evaluated from rigorous dynamic simulations using the equilibrium tray model. The rigorous dynamic tray material and energy balance equations, along with the VLE constraints, are solved using the method of Jhon and Lee.26 Two 1-min (6 min) lags in series

loop pairings

0.984 1.006 3.348

2.215 1.435 1.786

[1.050 1.009] [0.952 0.960] [1.041 0.991]

Methyl Acetate RD Column, Design B 1.000 0.998 1.508

2.710 3.540 1.481

[1.006 0.981] [0.994 0.975] [1.026 1.0195]

Ind. Eng. Chem. Res., Vol. 47, No. 19, 2008 7299 Table 5. Tuning Parameters for (a) Temperature/Composition Loops for Ideal RD Designs and (b) Temperature Loops for Methyl Acetate RD Column Designs design

control loop

KCTL

τITL (min)

Design B

Distillate Purity

f

(a)Tuning Parameters of Temperature/Composition Loops for Ideal RD Designs Design A

Table 6. Final Product Purity and Its Integral Absolute Error (IAE) for a (20% Throughput Change for Ideal RD Column Design A

T11-FB T3-FA T3-Qr T11-Qr xD, B-Qr xc, D-L/D xB,11-FB

7.1531 0.9969 0.5875 3.2632 1.1063 0.925 0.4063

16.5 18.48 12.54 12.28 55.22 102.96 64.24

2 2 2 2 2 2 2

xD, B-Qr xc, D-L/D xB,11-FB

1.475 1.6594 0.6031

59.4 102.08 65.12

1 1 1

(b) Tuning Parameters of Temperature Loops for Methyl Acetate RD Column Designs Design A CS1 CS1 CS2 CS2 CS4 CS4

T18-FHAc T2-FMeOH T18-Qr T2-FMeOH T18-FHAc T2-Qr

0.105 1.720 0.829 1.720 0.103 0.331

299.64 26.53 15.84 26.53 337.92 25.97

1 1 4 4 2 5

Design B CS1 CS1 CS2 CS2 CS4 CS4

T18-FHAc T2-FMeOH T18-Qr T2-FMeOH T18-FHAc T2-Qr

0.175 1.130 1.794 1.130 3.344 0.655

162.58 42.24 31.65 42.24 27.45 23.5

1 1 3 3 2 5

are applied to all temperature (composition) measurements. Perfect pressure and flow control is assumed. This is reasonable, considering the relatively much faster dynamics of the pressure and flow loops, compared to the temperature/composition loops. The pressure drop across the column is assumed to be negligible. All valves are 50% open at the base case. The reboiler and reflux drum are sized for a 5-min liquid residence time at 50% level for the base-case flows. The corresponding levels are controlled using the distillate and bottoms flow rates, respectively. Both the level controllers are P only with a gain of 2 (percent valve

Figure 7. Schematic of three composition control structures for the ideal RD column.

Bottoms Purity

integral absolute final integral absolute final steady error, IAE steady value error, IAE value CS1 +20% CS1 -20%

1.4938 1.395

0.9427 0.9573

1.1143 1.6464

0.9486 0.9517

CS2 +20% CS2 -20%

0.322 0.5517

0.9422 0.9575

0.3503 0.6338

0.9486 0.9518

CS4 +20% CS4 -20%

1.5417 1.6510

0.9424 0.9575

1.2620 0.7923

0.9486 0.9518

opening change per percent level change). The temperature/ composition loops are tuned using the relay feedback test to obtain the ultimate gain (KU) and period (PU). The Tyreus-Luyben (TL) controller tuning parameters are then empirically detuned by a factor f to obtain the controller gain KC )

KU 3.2 × f

(4)

and the reset time τI ) 2.2 × f × PU

(5)

for reasonable closed-loop performance. The detuning is necessary to avoid sustained oscillations in the closed-loop response. Consistent with the suggestions by Kaymak and Luyben,27 the two temperature loops are tuned individually (i.e., the other loop is on manual) for the ideal RD system, while, for the methyl acetate system, sequential tuning (i.e., the stripping loop is tuned with the reactive loop on manual and then the reactive loop is tuned with the stripping loop on automatic) is used. Table 5 tabulates the controller tuning parameters and detuning factor for the ideal and methyl acetate RD systems. Closed-Loop Results. In this section, the closed-loop response results for a large (20% change in the throughput manipulator are compared for the two designs. The steady-state deviation and the integral absolute error (IAE) of the distillate and bottoms purity are used as metrics for a quantitative comparison. Ideal RD System. Table 6 reports the steady-state product purity and its IAE for the two ideal RD designs. Data for CS1, CS2, and CS4 are not reported for Design B, because of the infeasibility of temperature inferential control, as discussed previously. For Design A, the steady-state distillate/bottoms purity values are comparable for all the two-point temperature inferential control structures. In terms of tightness of control, the IAE values for the distillate purity (main product) are the least for CS2, so that the control structure may be considered the best for tight distillate purity control. The closed-loop response of control structures CS1, CS2, and CS4 to a (20% throughput change for Design A is shown in Figure 8. The response is complete within ∼2 h for all the structures with the final distillate purity being within 1% of its design value. For tighter product purity control, a temperature in the rectifying section may be controlled by adjusting the reflux ratio. Alternatively, the reflux ratio may be adjusted in response to distillate purity deviations. A comparison of the IAE values using the three-composition control structure shows that the distillate and bottoms product purity control is noticeably tighter for Design A (data not shown). Figure 9 plots the closed-loop response of the threecomposition control structure to a (20% throughput change for Design A and Design B. The response is complete within

7300 Ind. Eng. Chem. Res., Vol. 47, No. 19, 2008 Table 7. Final Product Purity and Its IAE for a (20% Throughput Change for the Methyl Acetate RD Column Designs Distillate Purity

Bottoms Purity

integral absolute error, IAE

final steady value

integral absolute error, IAE

final steady value

34.58 90.73 4.726 5.302

0.9500 0.9755 0.9511 0.9752

29.97 101.15 6.263 5.92

0.9510 0.9685 0.9513 0.9684

Design A CS1 CS1 CS2 CS2

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

45.91 21.49 1.682 5.703

CS1 CS1 CS2 CS2

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

16.76 1.530 0.3538 1.10

0.9505 0.9495 0.9506 0.9494 Design B 0.9484 0.9516 0.9484 0.9516

∼10 h for Design A, while the response completion time for Design B is much higher (at ∼20 h). Note that if the Tyreus-Luyben (TL) controller settings are directly applied (no detuning) to the composition controllers in Design B, an oscillatory closed-loop response is obtained. Detuning the stoichiometric balancing loop by a factor of 4 gives a smooth response, as seen in Figure 9. A well-behaved closed-loop response is obtained for Design A, without any detuning. The superior product purity control in Design A is also clearly evident in Figure 9. The results clearly suggest that Design A is more controllable than Design B. The infeasibility of twopoint temperature control for Design B also suggests that Design A is inherently more controllable. For the ideal RD system, internal heat integration by adjusting the feed tray locations results in a marked deterioration in column controllability.

Figure 8. Closed-loop response of control structures (a) CS1, (b) CS2, and (c) CS4 for a (20% change in the throughput manipulator for the ideal RD column, Design A.

Figure 9. Closed-loop response for a (20% throughput change using three composition control schemes for the ideal RD case: (a) Design A and (b) Design B.

Ind. Eng. Chem. Res., Vol. 47, No. 19, 2008 7301

Figure 10. Closed-loop response of temperature control structures ((a) CS1 and (b) CS2) to a (20% throughput change for the methyl acetate RD column, Design A.

Methyl Acetate System. The closed-loop response of the CS1 and CS2 control structures for the methyl acetate column, Design A, is shown in Figure 10. The corresponding response for Design B is shown in Figure 11. Results for the CS4 control structure are not shown, because more than 100 h are required for the response of Design A to be completed. For the internally heat integrated Design B, the closed-loop response is extremely sensitive to the loop tunings. If the stripping loop is tuned tightly, the reboiler duty valve saturates for a 20% throughput increase within ∼2 h. On the other hand, detuning the stripping loop causes the control system to succumb to the “wrong” control action for a throughput decrease. The control system works only for a small range of tuning parameters of the two loops. Given that the dynamics of processes change over time, an initially properly tuned CS4 control structure may fail after some time has elapsed, because of process drifts. Thus, the CS4 control structure is not practical for the methyl acetate system. For Design A, the CS1 response requires >40 h for completion. On the other hand, the CS2 response is completed within