Analysis of Control Properties of Thermally Coupled Distillation

The control properties of thermally coupled distillation sequences for the separation of quaternary mixtures of hydrocarbons were compared to those of...
0 downloads 0 Views 514KB Size
Download PDF
Ind. Eng. Chem. Res. 2005, 44, 391-399

391

Analysis of Control Properties of Thermally Coupled Distillation Sequences for Four-Component Mixtures† J. Carlos Ca´ rdenas, Salvador Herna´ ndez,* Iva´ n R. Gudin ˜ o-Mares, Fernando Esparza-Herna´ ndez, Carmen Y. Irianda-Araujo, and Luis Miguel Domı´nguez-Lira Facultad de Quı´mica, Universidad de Guanajuato, Noria Alta s/n, Guanajuato, Gto., Me´ xico 36050

The control properties of thermally coupled distillation sequences for the separation of quaternary mixtures of hydrocarbons were compared to those of conventional distillation sequences. Two thermally coupled systems were investigated: a thermally coupled distillation sequence with side columns and a Petlyuk-type column. The preliminary steady-state design of the thermally coupled distillation sequences was obtained by starting from a conventional distillation sequence and then optimizing for minimum energy consumption. The control properties of the sequences considered were obtained by using the singular value decomposition technique and closed-loop dynamic simulations under feedback control. It was found that, for some frequencies, the thermally coupled distillation sequences present theoretical control properties similar to those of conventional distillation sequences, i.e., similar minimum singular values and condition numbers. Also, both types of distillation sequences show interactions when relative gain arrays were obtained. Then, when both types of distillation sequences were studied under the action of proportional integral controllers, the thermally coupled sequences also presented optimum dynamic responses similar to those obtained in the conventional distillation scheme. As a result, it can be concluded that thermally coupled distillation sequences can present theoretical control properties similar to those obtained in conventional distillation sequences. This result is significant because it lets one establish that the energy savings predicted for thermally coupled distillation sequences are achieved without introducing additional control problems. Introduction

Design of Thermally Coupled Distillation Sequences

A common problem in process systems engineering is the separation of a ternary mixture. This can be done by using two conventional distillation sequences, the direct and indirect distillation sequences. It is well known that these types of distillation sequences require large amounts of energy to achieve separation. To reduce these energy demands, thermally coupled distillation sequences (TCDS) can be used instead. It has been proved that thermal coupling can reduce energy demands between 30 and 50% depending upon the composition of the mixture to be separated.1-4 There are three TCDS that have been explored in detail: (i) the thermally coupled distillation sequence using a side rectifier, (ii) the thermally coupled distillation scheme involving a side stripper, and (iii) the fully thermally coupled distillation sequence or Petlyuk system. Significant work has been reported on the development of methods for the design and optimization of TCDS systems5-8 and their control schemes.9-12 As a result, some large companies such as BASF are using this technology for the design of new plants.13 To extend these ideas for the separation of mixtures with more than three components, current research efforts focus on the design and control of new TCDS.14-16

† A preliminary version of this paper was presented at the ESCAPE-14 Conference, Lisbon, May 16-19, 2004. * To whom correspondence should be addressed. Tel. (+52-473) 732-0006 Ext. 8142. Fax (+52-473) 732-0006 Ext. 8108. E-mail: [email protected].

A quaternary mixture can be separated using five conventional distillation sequences as indicated in Figure 1. Thermally coupled distillation sequences can be obtained from the conventional distillation sequences by removing a condenser and introducing a liquid recycle stream. Similarly, a reboiler can be replaced by using a vapor recycle stream. As reported by Rong et al.,17 there are many thermally coupled distillation sequences for the separation of quaternary mixtures. We have selected two thermally coupled distillation sequences which, in principle, can be more easily implemented: the TCDS-SR/SS (Figure 2) and the Petlyuk column (Figure 3). The Petlyuk-type column can be implemented through the dividing-wall column proposed by Kaibel.13 This option can reduce both energy and capital costs. The TCDS-SR/SS system is important because additional energy savings can be obtained through the use of both thermal couplings and heat integration (Figure 4) as shown in the work of Rong et al..18 Both thermally coupled distillation sequences can be obtained from the conventional distillation sequence indicated in Figure 1D as reported in Blancarte-Palacios et al..16 The method for the preliminary design of the TCDS schemes uses the separation sections of a conventional distillation sequence (CDS, Figure 5) on which a distillation column performs the split AB/CD (sections 1 and 2 of column C-1 of Figure 5) and two additional columns perform the binary separations A/B (sections 3 and 4 of column C-2 of Figure 5) and C/D (sections 5 and 6 of column C-3 of Figure 5), respectively. For instance, for

10.1021/ie049928g CCC: $30.25 © 2005 American Chemical Society Published on Web 12/23/2004

392

Ind. Eng. Chem. Res., Vol. 44, No. 2, 2005

Figure 1. Conventional distillation sequences for the separation of quaternary mixtures.

the preliminary design of the new TCDS scheme with a side stripper and a side rectifier of Figure 2, the sequence includes a main column (C-1) with sections 1 and 2 of the conventional distillation column that performs the split AB/CD plus the stages of the rectifying section 3 of the column for the separation A/B and the stages of stripping section 6 of the column that performs the split C/D. This main column is then thermally coupled through one liquid and one vapor interconnecting streams (LF and VF) to the stripping stages of section 4 of the column for the separation A/B and the rectifying section 5 of the column that separates

the binary mixture C/D, correspondingly. Finally, the flows of the two interconnecting streams are varied until the minimum energy consumption for the TCDS is obtained. The procedure for the TCDS with a prefractionator is similar to the one we describe here, but for this type of sequence, we need section 7 of Figure 3, which is not present in the conventional distillation sequence. Section 7 is equivalent to the stages for total reflux in the binary separation B/C. Such a separation is not included in the conventional distillation sequence of Figure 5. The complete design and optimization methods are described in Blancarte-Palacios et al..16

Ind. Eng. Chem. Res., Vol. 44, No. 2, 2005 393

Figure 2. TCDS-SR/SS.

Figure 4. Thermally coupled and heat-integrated distillation sequence for four-component mixtures.

Figure 3. TCDS-PR.

The new energy-efficient designs of the TCDS options are subjected to a controllability analysis of their theoretical control properties using the singular value decomposition (SVD) technique in the frequency domain. The minimum singular value and the condition number obtained through the use of the SVD method for conventional distillation sequences and the two TCDS schemes allow us to detect the design with the best theoretical control properties. These optimum designs were also tested under the action of feedback controllers. Theoretical Control Properties The optimized designs of the three distillation sequences (TCDS-SR/SS, TCDS-PR, CDS) were subjected to a controllability analysis using SVD. This technique requires transfer functions that are grouped into a transfer function matrix. For the distillation sequences presented in this work, four controlled variables were

Figure 5. CDS.

considered, the product compositions of A-D. Similarly, four manipulated variables were defined, the reflux ratios and the heat duties supplied to the reboilers for the systems of Figures 2 and 5 and, in the case of the TCDS-PR (Figure 3), the side streams of products B and C. The SVD technique implies that any complex matrix can be decomposed into three matrices:

G(ωj) ) V(ωj)Σ(ωj)WH(ωj)

(1)

where Σ ) diag(σ1, σ2, ........, σn), σi is the singular value of G(ωj) ) λ1/2[G(ωj)‚G(ωj)H], σ1 > σ2 > ......... > σn > 0, and r e n; V ) (v1, v2, ....) is the matrix of left singular vectors, and W ) (w1, w2....) is the matrix of right singular vectors. Two parameters of interest in chemical process control are the minimum singular value (σ*) and

394

Ind. Eng. Chem. Res., Vol. 44, No. 2, 2005

Table 1. Steady-State Design Variables for the Three Distillation Sequences Studied TCDS-SR/SS column C-1 section 1 ) 8 section 2 ) 5 section 3 ) 9 section 6 ) 8 reflux ratio ) 8.27 reboiler duty ) 679.6 kW LF ) 28.60 kmol/h VF ) 56.75 kmol/h column C-2 section 4 ) 8 reboiler duty)93.47 kW column C-3 section 5 ) 11 reflux ratio ) 1.90

TCDS-PR

CDS

column C-1 section 1 ) 8 section 2 ) 5

column C-1 section 1 ) 8 section 2 ) 5 reflux ratio ) 1.2 reboiler duty ) 325 kW

column C-2 section 3 ) 9 section 4 ) 8 section 5 ) 11 section 6 ) 8 section 7 ) 12 reflux ratio ) 11.59 reboiler duty ) 851.1 kW liquid side product ) 11.29 kmol/h LF ) 31.78 kmol/h VF ) 54.48 kmol/h

the ratio of maximum to minimum singular values or condition number (γ*):

γ* ) σ*/σ*

column C-2 section 3 ) 9 section 4 ) 8 reflux ratio ) 2.038 reboiler duty ) 266.6 kW column C-3 section 5 ) 11 section 6 ) 8 reflux ratio ) 3.243 reboiler duty ) 388.4 kW

Table 2. Transfer Function Matrix for CDS reflux ratio 1

reboiler duty 1

reflux ratio 2

reboiler duty 2

(2)

A

1.3616 0.69s + 1

-3.0888 0.6s + 1

0

0

The minimum singular value is a measure of the invertibility of the system and, therefore, represents a measure of potential problems of the system under the action of feedback controllers. The condition number represents the sensitivity of the system under uncertainties in process parameters and modeling errors. Systems with high values of condition numbers tend to increase these types of error. Then, systems with high values of σ* and low values of γ* are preferred.

B

-1.4752 0.86s + 1

1.2704 0.45s + 1

0

0

C

0

0

1.5832 0.95s + 1

-3.9144 1.32s + 1

D

0

0

-3.0904 1.21s + 1

1.98 0.76s + 1

Dynamic Analysis The design of the TCDS schemes was first developed following the approach proposed by Blancarte-Palacios et al..16 The design method involves a search procedure on the interconnection streams LF and VF (Figures 2 and 3) until a minimum energy consumption is detected. The resulting structures provided the designs that were then subjected to the dynamic analysis through the use of Aspen Dynamics 11.1.

Figure 6. Energy optimization of the TCDS-SR/SS.

As a case study, a four-component mixture of npentane, n-hexane, n-heptane, and n-octane was considered, with a feed flow rate of 45.5 kmol/h as saturated liquid at 23.6 psia, and an equimolar composition. It was used as a design pressure of 21.1 psia in all columns in order to use cooling water in the condensers. Also, a pressure drop of 5 psia in the column was assumed. The specified product purities for components A-D were 98, 95, 95, and 98 mol %, respectively. Since the feed involves a hydrocarbon mixture, the Chao-Seader correlation was used for the prediction of thermodynamic properties.19 As far as energy consumption is concerned, the optimized steady-state design for the TCDS-SR/SS option provides energy savings of ∼20% with respect to the best energy-efficient sequence based on conventional distillation columns. With respect to the dynamic analysis of the integrated sequences and its comparison to the CDS, the section of closed-loop dynamic responses presented here consists of two stages. In the first part, operation for a single closed loop using a PI controller was considered. The gain and reset time of the controller were optimized to minimize the IAE value for a positive set point change.20 For the second part of the study, two or more closed loops were added to the distillation schemes. Tuning up the controllers with an optimization criterion is a difficult task for this case, so the following procedure was used. First, product A was initially considered under closed-loop operation with the other three components operating under open-loop mode; optimal parameters for the PI controller were obtained for this control loop from the IAE minimization criterion. Then, products A and B were assumed to operate under closed loop, and the parameters of the PI controller for product B were obtained, keeping the previous values for the composition control loop of product A, and with C and D free of

Ind. Eng. Chem. Res., Vol. 44, No. 2, 2005 395 Table 3. Transfer Function Matrix for TCDS-SR/SS reflux ratio 1

reboiler duty 1

reflux ratio 2

reboiler duty 2

A

2.6276 1.5s + 1

-3.9888 0.6s + 1

-3.574 (4.09s + 1)(1.68s + 1)

-9.48 7.96 + 1.3s + 1 3.95s + 1

B

0.3904 3.4008 0.35s + 1 15s + 1

1.9644 3.13s + 1

0.276 (4s + 1)(0.12s + 1)

-4 4.84 + 0.84s + 1 4s + 1

C

-0.824 1.2396 + 0.65s + 1 4.57s + 1

-0.232 0.7 + 2s + 1 20s + 1

1.63 2.9s + 1

0.776 7.7628 0.18s + 1 6.11s + 1

D

-4.9264 4.0696 + 2.2s + 1 7.6s + 1

-4.34 (3.66s + 1)(3.66s + 1)

-6.0304 6.7s + 1

3.4264 1.63s + 1

control loops. The procedure continued until the four components were analyzed under closed-loop operation, and the full set of gains and integral times were used for the test of the multivariable control problem with four control loops. It is important to establish that studying a quaternary mixture of hydrocarbons is a suitable example, given the applications of the hydrocarbon mixtures in the petrochemical industry.2,22

Table 4. Transfer Function Matrix for TCDS-PR reflux ratio 1

liquid side stream 1

A

0.9494 2.69s + 1

-1.0332 2.44s + 1

0.0449 12.35s + 1

0.54e-1.11s 12.26s + 1

B

0.6364 0.97s + 1

-0.8484 1.16s + 1

-1 4.56s + 1

-0.156 0.4324 + 0.09s + 1 4.1s + 1

C

0.6535 1.17s + 1

0.6832 1.23s + 1

0.7628 4.85s + 1

-0.42 0.8532 + 3.1s + 1 27.66s + 1

D

-0.6758 2.15s + 1

0.9704 3.71s + 1

1.1148 10.05s + 1

12.88 10.5s + 1

Results and Discussion In the first part of the study, the theoretical control properties of conventional and thermally coupled distillation sequences were obtained. In the second part of the study, the distillation sequences were studied under the action of proportional integral controllers for changes in set points or disturbances in the feed for one or more closed loops. Singular Value Decomposition. The SVD technique requires transfer function matrices, which are generated by implementing step changes in the manipulated variables of the optimum design of the distillation sequences (base designs) and registering the dynamic responses of the four products.20,21 Figure 6 shows the minimization of the energy consumption for the case of the TCDS-SR/SS sequence shown in Figure 2 in order to obtain the steady-state design. It is

liquid side stream 2 -1.29s

reboiler duty 1

important to emphasize that energy requirements in the reboiler depend strongly on the LF, once a value of the VF has been set. During the search for the optimum energy consumption, four design specifications for product purities A-D were set in order to avoid deviations in the required purities. For the case of the TCDS-SR/ SS, one can fix a value of VF and only perform a complete search on LF. For this case study, the TCDSSR/SS scheme has an energy consumption 20% less than that of the CDS. As can be seen in Figure 3, the steady state of TCDS-PR can be obtained also by varying the two interconnecting streams. Table 1 presents the design variables required in the dynamic simulation.

Figure 7. Minimum singular values for the three distillation schemes.

396

Ind. Eng. Chem. Res., Vol. 44, No. 2, 2005

Figure 8. Condition number for the three distillation schemes.

Figure 10. Control loops in the TCDS-PR.

Figure 9. Control loops in the TCDS-SR/SS.

Also, residence times of 5 min for liquid holdups were assumed as recommended by Luyben.21 After the optimum designs were obtained, open-loop dynamic simulations were carried out in Aspen Dynamics 11.1 in order to obtain the transfer function matrix. For the case study considered here, Table 2 shows the transfer function matrix generated by using step changes in the manipulated variable and recording the dynamic behavior of the four product compositions (A-D). The transfer function matrix shown in Table 2 corresponds to the CDS. It can be noted that the dynamic responses can be adjusted to first-order systems without dead time. When the integrated distillation systems were considered, it was found that the dynamic responses can be adjusted to first, first plus dead time, second, or parallel processes. An important observation is that

Figure 11. Control loops in the CDS.

severe inverse responses are presented in the TCDSSR/SS scheme as indicated in Table 3. Moreover, the TCDS-PR presented dead times in some responses (Table 4). It is clear that those dynamic responses could in principle deteriorate the closed-loop responses. The matrices were subjected to SVD in the frequency domain and it was found, at intermediate frequencies, that the TCDS-SR/SS presented values of σ* similar to those of the CDS as indicated in Figure 7. As a result, we can expect that the TCDS-SR/SS presents similar theoretical control properties similar to those obtained in the

Ind. Eng. Chem. Res., Vol. 44, No. 2, 2005 397

Figure 12. Closed-loop responses for a positive set point change in product composition A. Table 5. Tuning Parameters Obtained for Each Control Loop control loop

TCDS-SR/SS

TCDS-PR

CDS

A

gain integral time gain integral time gain integral time gain integral time

9.92 kmol/kmol 0.5 h 4.67 kW 2.83 h 3.42 kmol/kmol 0.083 h 883.48 kW 0.083 h

13.90 kmol/kmol 0.45 h 2.258 kmol/h 0.75 h 2.258 kmol/h 0.75 h 936.21 kW 0.33 h

B C D

CDS for some changes in the set points. According to the values of σ*, good dynamic behavior can be expected in the integrated TCDS-SR/SS sequence in contrast to that presented by the conventional distillation sequence. For the case of γ*, Figure 8 shows that the TCDS options tend to be better conditioned for intermediate frequencies, which implies that some disturbances can be eliminated more easily than others. Notice that, at intermediate frequencies, the TCDS options presented values similar to those presented in the CDS sequence. However, the γ* is in general better for the CDS. To complete the study of the theoretical control properties, relative gain arrays were obtained for the three distillation sequences. Matrices 3-5 show the RGA for the CDS, TCDS-SR/SS, and TCDS-PR, respectively. As we can see, the CDS sequence (matrix 3) presents interactions because positive values of the relative gains are greater than 1.

[

-0.6119 1.6119 ACDS ) 0 0

[

1.6120 -0.6119 0 0

2.2063 -1.5377 ATCDS-Sr/SS ) -0.1695 0.5007

[

0.0263 0.3855 ATCDS-PR ) 0.5590 0.0289

0 0 -0.3497 1.3498

-6.1295 3.0269 -0.3027 4.4055

0.9373 -0.4738 0.5322 0.0006

0 0 (3) 1.3496 -0.3498

4.6901 -0.3517 0.7587 -4.0970

0.0353 1.0613 -0.0896 -0.0070

0.2330 -0.1375 0.7133 0.1908 (4)

0.0008 0.0226 -0.0015 0.9775 (5)

When the TCDS-SR/SS sequence is considered, values of the relative gains for components A, B, and D (rows 1, 2, and 4 of matrix 4) are greater than 1, which imply large interactions. Also, the negative values cause negative interactions. For the TCDS-PR option (matrix 5), interactions are presented in the intermediate components (B and C) due to relative gains less than 1.

2.44 kmol/kmol 0.50 h 239.94 kW 0.66 h 0.64 kmol/kmol 1.33 h 427.24 kW 0.167 h

From relative gains, we can conclude that significant interactions are present in both conventional and thermally coupled distillation sequences. Results for One or More Closed Loops. As part of the control loops implemented within Aspen Dynamics, PI pressure controllers (which use the pressure at the top of the column manipulated with the heat duty in the condenser as control loops) were included and perfect control level in the reflux drum and the bottoms accumulator of the column was assumed21 (with distillate and bottoms flow rates as the corresponding manipulated variables). In the dynamic simulations, LF and VF were fixed, but LF can be manipulated23 in order to guarantee minimum energy consumption. Composition control tasks were then the subject of the dynamic analysis. Product compositions represented the controlled variables, which were tied to manipulated variables given by the corresponding reflux ratios, reboiler heat duties, and sidestream flow rate for the integrated sequences. Standard control loops were used for the distillation sequences: (a) top productreflux ratio, (b) sidestream puritysidestream flow rate, and (c) bottom productheat duty (see Figures 9-11). PI controllers were used for each loop, and their parameters were tuned to minimize the IAE criterion.20 By using Aspen Dynamics 11.1, the values of the controller gains (Kc) and the reset times (τi) that minimized IAE values for each design were found. Those tuning parameters are presented in Table 5. Figure 12 shows the optimal responses for all sequences when a positive set point change of 0.01 was implemented in product composition A with compositions B-D under open-loop operation. The IAE values obtained for the TCDS-SR/SS, TCDS-PR, and CDS are 4.47 × 10-4, 2.52 × 10-4, and 5.26 × 10-4, respectively. It is clear that, according to these values, the TCDS-PR has a better response than the other schemes and that the TCDS schemes outperform the response of the CDS. Although all responses show oscillations, the TCDS-PR reaches the new steady state faster than the other sequences. Figures 13-15 show typical dynamic responses of product compositions A-C when the distillation sequences were studied under the action of four closed

398

Ind. Eng. Chem. Res., Vol. 44, No. 2, 2005

Figure 13. Closed-loop responses for component A for four closed loops.

Figure 14. Closed-loop responses for component B for four closed loops.

Figure 15. Closed-loop responses for component C for four closed loops.

Figure 16. Closed-loop responses for a disturbance in the feed composition of component D (four closed loops).

loops. A positive set point change of magnitude 0.01 was implemented in product compositions A-C while the composition of product D was kept constant but also under closed-loop operation. In the case of component A, we can observe that the three distillation sequences reach the new steady state, but the integrated sequences present oscillatory responses (Figure 13). For product composition B, all sequences can achieve the change imposed in the set point (Figure 14), but the TCDS-SR/ SS has an oscillatory response and the largest stabilization time. The TCDS-PR presents a dynamic response which is similar to that obtained for the CDS. For

product purities C and D, the TCDS-SR/SS exhibits dynamic responses very similar to those obtained in the CDS scheme, as can be seen in Figure 15. In the case of disturbances in the feed composition for four closed loops, the flow of component D is increased (3%) and the flows corresponding to A-C are lowered (1% each) in order to keep the total feed flow as constant. Figure 16 shows the dynamic responses. One can note that the TCDS-SR/SS scheme presents better responses than those of the CDS scheme and the TCDS-PR sequence. These results are in agreement with the theoretical control properties obtained by SVD.

Ind. Eng. Chem. Res., Vol. 44, No. 2, 2005 399

Conclusions The theoretical control properties and closed-loop responses for one conventional and two thermally coupled distillation sequences were obtained. The theoretical control properties, obtained from the SVD method, indicate that the TCDS with side columns present good control properties in comparison to those of the conventional distillation sequences; i. e., the integrated sequence presents similar minimum singular values in comparison to those obtained in the conventional distillation sequence for intermediate frequencies. Also, interactions in both types of distillation sequences were found because of relative gains different from 1. For the case of changes in set points and disturbances, some dynamic responses of the TCDS schemes were better that those of the CDS according to IAE criteria. These results are significant because they let us establish that the TCDS schemes not only require energy demands lower than conventional distillation sequences but also present theoretical control properties similar to those of the conventional distillation sequence used in the preliminary design of the TCDS schemes. Acknowledgment The authors acknowledge financial support received from Conacyt and Concyteg, Mexico. A prelimary version of this paper was presented at the ESCAPE-14 Conference, Lisbon, May 16-19, 2004. Literature Cited (1) Tedder, D. W.; Rudd, D. F. Parametric Studies in Industrial Distillation: Part I. Design Comparisons. AIChE J. 1978, 24, 303. (2) Triantafyllou, C.; Smith, R. The Design and Optimisation of Fully Thermally Coupled Distillation Columns. Trans Inst. Chem. Eng. 1992, 70, 118. (3) Wolff, E. A.; Skogestad, S. Operation of Integrated ThreeProduct (Petlyuk) Distillation Columns. Ind. Eng. Chem. Res. 1995, 34, 2094. (4) Annakou, O.; Mizsey, P. Rigorous Comparative Study of Energy-Integrated Distillation Schemes. Ind. Eng. Chem. Res. 1996, 35, 1877. (5) Du¨nnebier, G.; Pantelides, C. C. Optimal Design of Thermally Coupled Distillation Columns. Ind. Eng. Chem. Res. 1999, 38, 162. (6) Herna´ndez, S.; Jime´nez, A. Design of Optimal ThermallyCoupled Distillation Systems Using a Dynamic Model. Trans. Inst. Chem. Eng. 1996, 74, 357. (7) Herna´ndez, S.; Jime´nez, A. Design of Energy-Efficient Petlyuk Systems. Comput. Chem. Eng. 1999a, 23, 1005.

(8) Caballero, J. A.; Grossmann, I. E. Generalized Disjunctive Programming Model for the Optimal Synthesis of Thermally Linked Distillation Columns. Ind. Eng. Chem. Res. 2001, 40, 2260. (9) Herna´ndez, S.; Jime´nez, A. Controllability Analysis of Thermally Coupled Distillation Systems. Ind. Eng. Chem. Res. 1999b, 38, 3957 (10) Jime´nez, A.; Herna´ndez, S.; Montoy, F. A.; Zavala-Garcı´a, M. Analysis of Control Properties of Conventional and Nonconventional Distillation Sequences. Ind. Eng. Chem. Res. 2001, 40, 3757. (11) Serra, M.; Espun˜a, A.; Puigjaner, L. Controllability of Different Multicomponent Distillation Arrangements. Ind. Eng. Chem. Res. 2003, 42, 1773. (12) Emtir, M.; Mizsey, P.; Rev, E.; Fonyo, Z. Economic and Controllability Investigation and Comparison of Energy-Integrated Distillation Schemes. Chem. Biochem. Eng. Q. J. 2003, 17, 31. (13) Kaibel, G. Proc. ESCAPE-12 (Computer Aided Process Engineering, 10); Grievink, J., Schijndel, J. V., Eds.; Elsevier: Amsterdam, 2002; p 9. (14) Rong, B. G.; Kraslawski, A. Optimal Design of Distillation Flowsheets with a Lower Number of Thermal Couplings for Multicomponent Separations. Ind. Eng. Chem. Res. 2002, 41, 5716. (15) Rong, B. G.; Kraslawski, A. Partially Thermally Coupled Distillation Systems for Multicomponent Separations. AIChE J. 2003, 49, 1340. (16) Blancarte-Palacios, J. L.; Bautista-Valde´s, M. N.; Herna´ndez, S.; Rico-Ramı´rez, V.; Jime´nez, A. Energy-Efficient Designs of Thermally Coupled Distillation Sequences for Four-Component Mixtures. Ind. Eng. Chem. Res. 2003, 42, 5157. (17) Rong, B. G.; Kraslawski, A.; Turunen, I. Synthesis of Functionally Distinct Thermally Coupled Configurations for Quaternary Distillation. Ind. Eng. Chem. Res. 2003, 42, 1204. (18) Rong, B. G.; Kraslawski, A.; Turunen, I. Synthesis of HeatIntegrated Thermally Coupled Distillation Systems for Multicomponent Separations. Ind. Eng. Chem. Res. 2003, 42, 4329. (19) Seader, J. D.; Henley, E. Separation Process Principles; John Wiley and Sons: New York, 1998. (20) Stephanopoulos, G. Chemical Process Control. An Introduction to Theory and Practice; Prentice Hall Inc.: Englewood Cliffs, NJ, 1984. (21) Luyben, W. L. Practical Distillation Control; Van Nostrand Reinhold: New York, 1992. (22) Harmsen, G. J. Industrial Best Practices of Conceptual Process Design. Chem. Eng. Processes 2004, 43, 671. (23) Abdul Mutalib, M. I.; Zeglam, O. A., Smith, R. Operation and Control of Divided Wall Distillation Columns: Part II Simulation and Pilot Plant Studies Using Temperature Control. Trans. Inst. Chem. Eng. 1998, 76, 319.

Received for review January 22, 2004 Revised manuscript received November 4, 2004 Accepted November 4, 2004 IE049928G