Temperature Control of the BTX Divided-Wall Column - American

Ind. Eng. Chem. Res. 2010, 49, 189–203

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Temperature Control of the BTX Divided-Wall Column Hao Ling Department of Petroleum Processing, East China UniVersity of Science and Technology, Shanghai 200237, China

William L. Luyben* Department of Chemical Engineering, Lehigh UniVersity, Bethlehem, PennsylVania 18015

The control of a divided-wall column is more difficult than the control of a conventional two-column separation sequence for the separation of ternary mixtures because there is more interaction among control loops. In a previous paper, a control structure using four composition loops was shown to provide effective control of the purities of the three product streams and also achieve minimum energy consumption for both feed flow rate and feed composition disturbances. The numerical example studied the separation of benzene, toluene, and o-xylene. The four manipulated variables were reflux flow rate (R), side-stream flow rate (S), reboiler heat input (QR), and liquid split (βL) at the top of the wall. In this paper we explore the use of temperatures to avoid expensive and high-maintenance composition analyzers. Two types of temperature control structures are studied. In the first, three temperatures located in the main column and one temperature on the prefractionator side of the wall are used to adjust the four manipulated variables. Feed flow rate disturbances are well handled with this structure, but product purities start to deviate significantly from their desired values for feed composition changes greater than about 10%. In the second control structure, four differential temperature control loops are used. Performance is improved and disturbances of 20% in feed composition are well handled with only small deviations in product purities. This structure also handles large changes in column operating pressure. 1. Introduction The divided-wall column is an important example of process intensification. Both energy consumption and capital cost can be reduced in some systems compared to a conventional twocolumn direct separation sequence. Wolff and Skogestad1 pointed out that the divided-wall column has four control degrees of freedom: reflux R, vapor boilup V, side stream S, and liquid split βL. These four control degrees of freedom can be used to control four variables during the operation of the column. The purities of all three product streams should be controlled. The fourth degree of freedom can be used to achieve minimum energy consumption as feed compositions change. Our previous work2 illustrated that four composition control loops provided good dynamic performance in the face of feed flow rate and feed composition disturbances. However, online composition analyzers are expensive, require high maintenance, and can introduce long time delays. Temperature measurements are inexpensive and reliable and provide rapid responses. However, they only provide an estimation of composition. In a binary system at constant pressure, knowing the temperature fixes the composition. In a ternary system, which is the situation in the divided-wall column, this is no longer the case. Therefore, it is not surprising that control structures using only temperatures should not perform well for changes in feed composition. Several papers discuss the use of temperature control in divided-wall columns. Abdul Mutalib et al.3 reported using temperatures instead of compositions as the controlled variables to study the methanol/isopropanol/butanol system in a 23-stage column with 98.5 mol % purities. They attempted to control * To whom correspondence should be addressed. Tel.: (610) 7584256. Fax: (610) 758-5057. E-mail: [email protected].

only two temperatures in the system, while keeping the sidestream flow rate S constant. The authors suggested overrefluxing as a way to overcome deviations in product purities for feed composition changes. Adrian et al.4 reported experimental studies of the butanol/ pentanol/hexanol system in the BASF miniplant laboratory. They used a three-temperature control scheme. One temperature was located in the prefractionator side of the wall above the feed tray to prevent the heavy boiling component from passing the upper edge of the divided wall. The second temperature was above the side-stream drawoff tray in the main column side of the wall to monitor the separation between the lightest and the intermediate components. The third temperature was in the stripping section to ensure that none of the intermediate component drops out the bottom of the column. At the same time, holding this temperature helps to keep the lightest component from passing the lower edge of the wall on the prefractionator side. They explored conventional proportional integral derivative (PID) control in which the three manipulated variables used were R, S, and βL. They also studied model predictive control (MPC) in which these three variables and QR were used. Their experimental results showed that stable regulatory temperature control was achieved for both feed flow rate and feed composition disturbances. However, they do not report what happened to product compositions. Wang and Wong5 studied the ethanol/n-propanol/n-butanol system with very high product purities of 99.9 mol % being specified. The authors explored the use of temperature control instead of composition control using PID control structures. A temperature in the prefractionator and two temperatures in the main column were selected. A temperature in the bottom section of the prefractionator was controlled by manipulating reboiler heat input. A temperature in the rectifying section was controlled

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by manipulating R. A temperature near the base of the column was controlled by manipulating S. Liquid split βL was not manipulated. Stable control was achieved and products returned to their desired purity levels for feed flow rate changes. However, large product purity deviations were reported for feed composition disturbances. The authors recommended a temperature/composition cascade control structure to solve this problem. The above literature review illustrates that there have been very few studies of the use of temperature control in dividedwall columns. None of these papers presents a solution to the problem of large product purity deviations by only using temperature control with PID control structures. In our previous study of the benzene-toluene-o-xylene (BTX) system, we proposed four composition control loops, three impurity levels in the three product streams and one composition in the prefractionator. Simulation results show that the control scheme works well while keeping the energy consumption very close to the optimal point. The obvious question to be answered is, can temperature measurements be used instead of composition measurements? In a binary system at constant pressure, the temperature and the composition are uniquely related. This is not the case in a ternary system, which make inferential composition control using temperature measurements more complex. This problem has been studied in conventional distillation columns for many years. Yu and Luyben6 examined temperature control of multicomponent systems with sharp temperature profiles and recommended the use of multiple temperatures. The purpose of this paper is to apply this technology to a divided-wall column. The numerical example is the BTX system. There are four available manipulated variables (R, S, QR, and βL), so four temperatures or combinations of temperature can be controlled.

Figure 1. Divided-wall column flowsheet.

2. Steady-State Design Figure 1 gives the steady-state design of the divided-wall column studied in this paper. The industrially important ternary separation of benzene, toluene, and o-xylene (BTX) is used as a numerical example. The normal boiling points of these three components are 353, 385, and 419 K, respectively, so the separation is a fairly easy one with relative volatilities RB/RT/RX of about 7.1/2.2/1. The feed conditions are a flow rate of 1 kmol/s, a composition of 30/ 30/40 mol % B/T/X, and a temperature of 358 K. Product purities are 99 mol %. All simulations use rigorous distillation column models in Aspen Plus with Chao-Seader physical properties. The divided-wall column is simulated using a stripping column (with only a reboiler), two absorber columns in parallel (without any reboiler or condenser), and a rectifying column (with only a condenser). Condenser pressure is set at 0.37 atm, which gives a refluxdrum temperature (322 K) that is high enough to permit the use of cooling water in the overhead condenser. The column has a total of 46 stages, using Aspen notation of the condenser being stage 1 and the reboiler stage 46. A tray pressure drop of 0.0068 atm is assumed, giving a base pressure of 0.67 atm and a base temperature of 404 K. The rectifying section runs from stage 2 to stage 9. The wall runs from stage 10 down to stage 33. The stripping section runs from stage 34 to stage 45. The feed is fed at stage 21 in the prefractionator side of the wall, and the side stream is withdrawn from stage 20 on the other side of the wall.

Figure 2. (a) Temperature profiles in divided-wall column. (b) Composition profiles in divided-wall column.


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Figure 3. (a) Singular value decomposition analysis for main column. (b) Singular value decomposition analysis for prefractionator.

The reflux ratio is 2.84, and the reboiler heat input is 35.69 MW. The liquid split ratio is 0.353, and the vapor split ratio is 0.627 in this optimum economic design. Thus the wall is not located at the middle of the cross-sectional area of the column. More of the vapor from the stripping section goes up through the prefractionator side of the wall than through the side-stream side of the wall. The diameter of the column is 7.37 m. Figure 2 gives composition and temperature profiles in all sections of the column. The details of the optimum economic design of the dividedwall column are given in our previous paper.2 In the Aspen Plus simulations, the “Design Spec/Vary” functions are used for specifying the desired impurity levels in the three

products. The reflux ratio is varied to control distillate impurity, the side-stream flow rate is varied to control sidestream impurity, and the reboiler heat input is varied to control bottom impurity. With these three products held at their specified values, the liquid split ratio is varied over a range of values to find what liquid split ratio gives the minimum energy consumption. 3. Selecting Temperature Control Trays In our previous paper, four compositions are controlled. Now we wish to see if a four-temperature control structure will work. There are several criteria that can be used for

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Ind. Eng. Chem. Res., Vol. 49, No. 1, 2010 Table 1. Liquid Compositions on the Control Stages stage

B (mole fraction)

T (mole fraction)

X (mole fraction)

7 (main column) 15 (prefractionator) 27 (main column) 39 (main column)

0.517 236 0.256 168 0.000 255 2.15 × 10-6

0.482 438 0.504 115 0.709 559 0.275 617

0.000 326 0.239 717 0.290 186 0.724 38

4. Differential Temperature Control

Figure 4. Temperature control structure.

selecting which trays to hold at constant temperature.7,8 We use sensitivity analysis and singular value decomposition (SVD) criteria for selecting the four control trays.8,9 For sensitivity analysis, a very small change (0.1%) is made in one of the four variables in the system that can be used manipulated (R, S, QR, and βL), while keeping the other three inputs fixed. The Aspen Plus simulation is run, and the new temperatures on all the trays are determined. The change in each tray temperature divided by the change in the manipulated variable gives the steady-state gain for that tray. Note that there are two gain matrices, one for the main column and one for the prefractionator. The main column matrix has 46 rows and four columns. The prefractionator matrix has 23 rows and four columns. Each matrix is decomposed using the SVD program in Matlab into three matrices: K ) UΣVT. The four U vectors are plotted against tray number. Figure 3a gives results for the main column (the stripping section, the side-stream side of the wall, and the rectifying section). The top two graphs show the temperature profile and the slope (the difference between the temperatures on adjacent trays). The largest slope occurs at stage 7. Stage 40 also has a peak, which is a little bit lower than stage 7. The third peak is located at stage 27. The middle two graphs in Figure 3a show the sensitivity criteria. The steady-state gains for the heat input QR and the reflux R are given in the left graph. The steadystate gains for the side stream S and the liquid split βL are given in the right graph. There are peaks at stages 7, 27, and 39. The bottom two graphs in Figure 3a give four U vectors that indicate the sensitive trays in the column. The sensitive locations are stages 7, 27, and 39. From these results and from a consideration of the dynamic relationships between the location of the temperatures and the manipulated variables, the control structure selected controls stage 7 temperature with reflux, stage 27 temperature with side stream, and stage 39 temperature with reboiler heat input. Figure 3b gives results for the prefractionator side of the wall. The temperature profile and slope are given in the top two graphs. The steady-state gains for the four inputs are given in the middle two graphs. The SVD results are given in the bottom two graphs. The sensitive stages are 15 and 23. Since stage 15 is closer to the top of the prefractionator, dynamic considerations suggest that stage 15 temperature should be controlled by the liquid split ratio βL. Figure 4 shows the temperature control structure.

Dynamic simulation results presented in the next section will show that the temperature control structure discussed above, which controls the temperatures on four stages in the dividedwall column, is capable of handling feed flow rate changes well. However, it is not effective for feed composition changes larger than 10%. Table 1 shows the steady-state liquid composition on stages 7, 27, and 39 of the main column and on stage 15 of prefractionator. When feed flow rate changes occur, these compositions remain essentially the same when product purities are at their desired values and energy consumption is minimized. However, when feed composition changes occur, all of these compositions must change to attain the three impurity specifications and minimize energy consumption. This requires that the temperatures on these trays must also change and explains why controlling fixed temperatures does not handle feed composition disturbances. One solution to this problem is to use a cascade temperature/composition control structure, but this requires composition measurements. In this section we will explore another alternative: the use of differential temperatures. This method has been applied for many years in conventional multicomponent distillation columns.6 The use of temperature differences in divided-wall columns was briefly mentioned by Halvorsen and Skogestad.10 They found that the optimum values of differential temperature varied with feed composition, which implies that differential temperature is not a good candidate to control. No dynamic simulation results were presented. Figure 5 shows how the temperatures on various stages in the column change for changes in the benzene composition of the feed while holding the three product impurities at their desired Values and also minimizing energy consumption. The base case has a feed composition of 30 mol % benzene, 30 mol % toluene, and 40 mol % o-xylene. As the benzene composition is changed in Figure 5, the other two feed compositions are changed and kept in the same ratio of 30/40 to make the total add to 100 mol %. The top left graph in Figure 5 shows that the temperature on stage 7 should increase about 2 K as benzene feed composition zB decreases from 30 to 24 mol %. If the set point of the stage 7 temperature controller is fixed and this benzene disturbance occurs, the set point temperature is 2 K lower than what is required to maintain product purities. This results in more reflux being used than is necessary and product impurity is lower than specified. This phenomenon is more serious for the temperature of stage 15 in the prefractionator (lower right graph in Figure 5) where the liquid split ratio βL is the manipulated variable. A fixed temperature set point would result in a temperature on stage 15 that is 4 K too low as zB changes from 0.3 to 0.36. If the temperature set point is not adjusted, large deviations of product purity and energy consumption will occur. As the curves shown in Figure 5 illustrate, adjacent trays show similar changes in the required temperature as feed composition changes. This suggests that the temperature


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Figure 5. Required tray temperatures for changes in benzene feed compositions.

Figure 6. SVD analysis for selection of differential temperature locations.

difference between two trays will not change much for different feed compositions. The selection of which differential temperatures is critical. Using two trays that are close together gives ∆T’s that are almost constant over the range of feed compositions. However, the temperature differences are very small and would be sensitive

to other factors, such as small amounts of non-key components. On the other hand, using two trays that are far apart gives larger ∆T’s. However, the lines are not as parallel, so the ∆T’s are not as constant over the range of feed compositions. The procedure developed for selecting the tray locations for the differential temperature control structure uses SVD analysis.

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Figure 7. Aspen Dynamics implementation of TC structure.

Each of the four loops has two temperatures. The first is selected as discussed in the previous section for the four-temperature control structure. The four stages selected are stages 7, 27, and 39 in the main column and stage 15 in the prefractionator (see Figure 4). We call these reference temperatures TR7, TR27, TR39, and TRP15. The steady-state gains between each of these four temperatures and the four manipulated variables (R, S, QR, and βL) are calculated. For example, for stage 7 the four gains are K7,∆T/∆R, K7,∆T/∆S, K7,∆T/∆QR, and K7,∆T/∆βL. The gains for temperatures on all the other stages in the column are also known. Let us define the gains for stage n as Kn,∆T/∆R, Kn,∆T/∆S, Kn,∆T/∆QR, and Kn,∆T/∆βL. Then the difference between the gains for stage 7 and the gains for stage n are calculated. Applying this for all of the other stages generates a matrix of gain differences, which we call ∆K7. This matrix has 46 rows and 4 columns. Finally SVD analysis gives U1 values for each of the stages in the column. The stage that has the largest U1 is selected for the differential temperature control between it and stage 7. The procedure is repeated for the other three reference temperatures using the matrices ∆K27, ∆K39, and ∆KP15. Figure 6 shows how the U1 values for the four differential temperatures vary with the location of the second temperature

used for the differential temperature measurement. Stages 7 and 39 have two lines. The solid line is for the main column and the dashed line is for the prefractionator. The top left graph in Figure 6 give results for which stage temperature should be used with the stage 7 temperature to generate a differential temperature measurement to be controlled by manipulating reflux. The sensitive stages are 19 in the main column and 11 in the prefractionator. Since stage 11 in the prefractionator is physically closer to stage 7, its dynamics should be similar to those of stage 7, so the differential Table 2. Energy Cost Comparison between Composition Control, Single Temperature Control, and Differential Temperature Control CC

base flow-20% flow+20% B+20% B-20% T+20% T-20% X+20% X-20%

STC

DTC

QR, MW

QR, MW

∆QR, MW

QR, MW

∆QR, MW

35.46 28.42 42.44 34.70 36.70 37.32 33.26 34.84 36.49

35.46 28.29 42.72 34.20 37.45 37.83 33.45 34.54 36.08

0.00 -0.13 0.28 -0.50 0.74 0.51 0.19 -0.30 -0.41

35.46 28.43 42.46 34.68 36.71 37.20 33.99 35.07 36.31

0.00 0.00 0.02 -0.02 0.00 -0.12 0.73 0.23 -0.18

Ind. Eng. Chem. Res., Vol. 49, No. 1, 2010 Table 3. TC Controller Tuning Parameters control loop

controlled variable

manipulated variable

controller gain KC

controller integral time τI (min)

TC1 TC2 TC3 TC4

T7 T27 T39 T15P

R S QR βL

2.81 6.79 6.53 5.23

14.5 25.1 7.9 31.7

temperature for the loop is selected to be ∆TR ) TP11 - T7. Reflux is the manipulated variable that controls this differential temperature. The other three graphs in Figure 6 show that the other three temperature differentials are ∆TS ) T32 - T27 controlled

Figure 8. 10% feed flow rate disturbances using TC.

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by manipulating S, ∆TQR ) T39 - T34 controlled by manipulating QR, and ∆TβL ) TP15 - T7 controlled by manipulating βL. These locations are selected based on sensitivity and proximity to the reference temperature so that dynamic responses will be similar. A comparison of the energy consumption for the three control structures is given in Table 2. The reboiler duties of both the STC and DTC methods keep the reboiler duty very close to the results found with the composition control (CC) structure. All values in Table 2 are the final reboiler duties when the dynamic simulations reach steady-state conditions. These results show that energy consumption deviations for STC are a little bit higher, except the case of T-20%, than those of DTC. This is

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Figure 9. 10% benzene feed composition disturbances using TC.

because DTC can handle temperature deviation and pressure disturbance problems. The dynamic control results given in the next section show that the DTC structure provides excellent energy consumption minimization while keeping the purities of products very close to their specified values. 5. Dynamic Control Results Both the conventional temperature control (TC) and the differential temperature control (DTC) structures are implemented in Aspen Dynamics using conventional PID controllers. Fictitious pumps, compressors, control valves, and pressure and liquid level controllers are added, as discussed in our previous

paper,2 to achieve the necessary liquid and vapor flows in and out of the divided-wall sections. Feed-forward ratio schemes (QR/F and R/F ratios) are also employed in order to reduce the transient deviation in bottoms and distillate purity. All temperature control loops each have a 1-min dead time. The four interacting loops are tuned using a sequential method. The QR loop is tuned first since it affects all of the other variables. A relay-feedback test is run, and Tyreus-Luyben tuning is applied. Then, with this loop on automatic, the R loop is tuned using the same procedure. Then with both the QR and R loops on automatic, the S loop is tuned. Finally, with the other three loops on automatic, the βL loop is tuned. This sequential procedure


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Figure 10. 10% toluene feed composition disturbances using TC.

is used for both the temperature control and the differential control structures. 5.1. Conventional Temperature Control. Figure 7 shows the Aspen Dynamics implementation of the conventional temperature control structure with four temperatures controlled. Three temperatures (stages 7, 27, and 39) in the main column and one temperature in the prefractionator (stage 15) are controlled. Table 3 gives controller tuning results for all four loops. Figures 8-11 give the responses of the divided-wall column for 10% changes in throughput and 10% feed composition disturbances. In Figure 8, increases and decreases of 10% in the feed flow rate are made at time equal to 1 h. Stable regulatory control is achieved with product purities returning

to very close to their specifications in about 4 h. This is almost twice as fast as when direct composition control is used2 because the composition measurement dead time is 5 min, while the temperature measurement dead time is only 1 min. This speeds up the response of the system. The small composition deviations are due to changes in pressure at the temperature control trays since tray pressure drop varies with vapor and liquid rates in the Aspen Dynamics model. All tray temperatures return to their set points. The manipulated variables R, S, and QR all end up at new steady-state levels that are 10% higher or lower than the original. Thus, these variables ratio up and down directly with the feed flow rate. However, the liquid split ends up at exactly the same value for rate changes. Thus the conventional temperature control structure handles throughput changes well.

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Figure 11. 10% xylene feed composition disturbances using TC.

Figures 9-11 give results for 10% changes in feed composition of the three components. For example, in Figure 9 the benzene feed composition is changed from 30 to 33 mol %, while the other two compositions are changed to maintain the same ratio of compositions. Figures 9 and 10 indicate that the product purity deviations are all small and acceptable for 10% disturbances in benzene and toluene. Product purity returns to 99 ( 0.2% levels. However, Figure 11 shows that product purity deviations are larger for the disturbances in xylene feed composition compared with other cases. The side-stream purity deviations are the largest (second graph from the top on the left in Figure 11).

These results illustrate that the conventional temperature control structure results in product purity offsets for feed composition disturbances. 5.2. Differential Temperature Control. The differential temperature control structure (DTC) is shown in Figure 12, and the Aspen Dynamics implementation is shown in Figure 13. This structure measures eight temperatures and calculates four differentials. For example, the controlled differential temperature for reflux, ∆TR, is the temperature difference between stage 11 in the prefractionator and stage 7 in the main column (TP11 T7). The other three differential temperatures (∆TQR, ∆TS, and ∆TLS) are calculated in the same way, using the appropriate


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Table 4. DTC Controller Tuning Parameters

Figure 12. DTC control structure.

stage temperatures. The four loops are sequentially tuned (QR, R, S, and βL). Table 4 gives controller tuning results. Figure 14 shows the controller faceplates in the DTC control structure.

Figure 13. Aspen Dynamics implementation of DTC structure.

control loop

controlled variable

manipulated variable

controller gain KC

controller integral time τI (min)

DTC1 DTC2 DTC3 DTC4

∆TR ∆TS ∆TQR ∆TβL

R S QR βL

0.44 0.52 0.54 1.12

15.8 22.4 13.2 31.7

Figures 15-18 give direct comparisons between the conventional TC control structure (with four temperatures controlled) and the differential DTC control structure (with four differential temperatures controlled) when throughput or feed composition is increased or decreased 20%. Note that these disturbances are twice as large as those used in the previous section. The solid lines are for the TC temperature control system, and the dashed lines are for the DTC differential temperature control system. Figure 15 shows that both control structure do a good job in maintaining product purities. The DTC structure is somewhat better than the TC structure as regards the purity of the side stream (the lower two graphs in Figure 15). Figure 16 compares the two structures for benzene feed composition disturbances. The results demonstrate that the DTC

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Figure 14. Aspen Dynamics faceplates with DTC structure.

Figure 15. Comparison of TC and DTC for 20% feed flow rate disturbances.

structure is much better than the TC structure. Deviations of products purities are decreased to very small levels. Figures 17

and 18 show similar results for toluene or xylene feed composition disturbances.


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Figure 16. Comparison of TC and DTC for 20% benzene feed composition disturbances.

Figure 17. Comparison of TC and DTC for 20% toluene feed composition disturbances.

These results demonstrate that the control of four differential temperatures in the BTX divided-wall column provides more effective control than controlling four tray temperatures. 5.3. Pressure Disturbance. Temperatures depend on both composition and pressure, and the tray pressures change as liquid and vapor flow rates change. Therefore controlling a temperature may result in poor composition control if pressures are not constant.

However, taking the difference between two temperatures provides a degree of pressure compensation because both temperatures are affected by pressure in the same way. The differential temperature control structure provides this advantage. Figure 19 demonstrates this effect. At time equal to 1 h, the set point of the column pressure controller is changed by 2000 Pa. The DTC structure handles this disturbance much better than the TC structure.

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Figure 18. Comparison of TC and DTC for 20% xylene feed composition disturbances.

Figure 19. Comparison of TC and DTC for pressure disturbances.

6. Conclusion This paper extends the work of our previous paper in which direct composition control of the BTX divided-wall column was demonstrated to provide good product purity control. Now temperatures instead of compositions are measured. A conventional structure in which four temperatures are controlled is shown to handle throughput changes but

cannot handle realistically large disturbances in feed composition. A differential control structure is developed in which four temperature differences are controlled. Simulation results for the BTX system show that this structure provides effective product purity control for feed flow rate and feed composition disturbances. It also handles changes in pressure.


Acknowledgment H.L. appreciates the China State Scholarship Fund and The National Basic Research Program of China (973 Program, Contract No. 2006CB202501) for the scholar visiting financial support. Literature Cited (1) Wolff, E. A.; Skogestad, S. Operation of integrated three-product (Petlyuk) distillation columns. Ind. Eng. Chem. Res. 1995, 34, 2094–2103. (2) Ling, H.; Luyben, W. L. New control structure for divided-wall columns. Ind. Eng. Chem. Res. 2009, 48, 6034. (3) Abdul Mutalib, M. I.; Zeglam, A. O.; Smith, R. Operation and control of dividing wall columns Part 2: Simulation and pilot plant studies using temperature control. Trans. Inst. Chem. Eng. Part A 1998, 76, 319–334. (4) Adrian, T.; Schoenmakers, H.; Boll, M. Model predictive control of integrated unit operations: Control of a divided wall column. Chem. Eng. Process. 2004, 43, 347–355.

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(5) Wang, S.; Wong, D. Controllability and energy efficiency of highpurity divided wall column. Chem. Eng. Sci. 2007, 62, 1010–1025. (6) Yu, C. C.; Luyben, W. L. Use of multiple temperatures for the control of multicomponent distillation columns. Ind. Eng. Chem. Process Des. DeV. 1984, 23, 590–597. (7) Luyben, W. L. Distillation Design and Control using Aspen Simulation; Wiley: New York, 2006. (8) Luyben, W. L. Evaluation of criteria for selecting temperature control trays in distillation columns. J. Process Control 2006, 16, 115–134. (9) Moore, C. F. Selection of controlled and manipulated variables. In Practical Distillation Control; Van Nostrand Reinhold: New York, 1992; Chapter 2. (10) Halvorsen, I. J.; Skogestad, S. Optimal operation of Petlyuk distillation: steady-state behavior. J. Process Control 1999, 9, 407–424.

ReceiVed for reView January 23, 2009 ReVised manuscript receiVed August 9, 2009 Accepted October 23, 2009 IE900125W

Temperature Control of the BTX Divided-Wall Column - American

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