Batch Distillation in a Column with a Side Withdrawal for Separation of

The separation of a ternary mixture with a decomposing reaction was investigated in a batch distillation column with a side withdrawal (BDS). The proc...
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Ind. Eng. Chem. Res. 2009, 48, 5111–5116

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Batch Distillation in a Column with a Side Withdrawal for Separation of a Ternary Mixture with a Decomposing Reaction Xianbao Cui,* Ying Zhang, Tianyang Feng, and Zhicai Yang State Key Laboratory of Chemical Engineering, School of Chemical Engineering and Technology, Tianjin UniVersity, Tianjin 300072, China

The separation of a ternary mixture with a decomposing reaction was investigated in a batch distillation column with a side withdrawal (BDS). The process was simulated by a constant molar holdup model solved by the GEAR integration method and optimized by a simulated annealing algorithm. Comparing to the batch rectifier and middle vessel batch distillation column, BDS is favorable for the purification of an intermediate component from light and heavy impurities with a decomposing reaction. The effects of top reflux ratio and side reflux ratio were also investigated. Different combinations of top and side reflux ratio result in different types of product withdrawal, and the optimal operation tends to be in a large top reflux ratio and a small side reflux ratio. 1. Introduction Batch distillation is an important unit operation frequently used for high-value-added, low-volume specialty chemicals. The most outstanding feature of batch distillation is its flexibility, which is useful to deal with variations in feedstock or product specification. Furthermore, it provides a simple procedure to handle several mixtures just by switching the operating conditions of the column. The transient nature of batch distillation allows the column to be configured in a number of different ways, such as a batch rectifier, batch stripper, and middle vessel batch distillation column (see Figure 1). The most common used batch distillation column is a batch rectifier (BR; see Figure 1a); the initial charge is placed in the reboiler, and the distillate is sequentially removed from the top of the column. In the case of a batch stripper (see Figure 1b), the original mixture is fed in the storage vessel at the top of the column and the products are withdrawn from the bottom of column sequentially. Sorensen and Skogestad1 compared the batch rectifier and batch stripper for the separation of binary mixtures. They concluded that the batch stripper was found to yield the shortest batch time for the separations where the light component was present in a small amount in the feed. The middle vessel batch distillation column (MVBD; see Figure 1c) was proposed by Robinson and Gilliland2 and studied by many authors in recent years. Davidyan et al.,3 Meski and Morari,4 Barolo et al.,5-7 Phimister and Seider,8,9 and Kim and Diwekar10 studied the features and behavior of this type of batch distillation column. The MVBD is a combination of a batch rectifier and a batch stripper with considerable operating flexibility. There are also some other configurations proposed in recent years. Wittgens et al.11 proposed a multivessel batch distillation column. Cui and Yang12 described a batch rectifier with a side withdrawal and a cold still pot for the separation of heat-unstable material (see Figure 1d). Demicoli and Stichlmair13 demonstrated a type of batch distillation column with a side withdrawal and two charges (see Figure 1e). The column can be visualized as a batch stripper placed on the top of a batch rectifier. In the chemical industry, many kinds of chemicals are heatunstable. When they are heated, some reactions such as * To whom correspondence should be addressed. Tel.: 86-2227404493. Fax: 86-22-27404493. E-mail: [email protected].

decomposition or polymerization will occur, and the reaction rates of such reactions are different. If the reaction rate is large, the chemicals are usually separated by molecular distillation or another “cold separation process” such as crystallization and extraction. If the reaction rate is small, the mixture can be separated by batch distillation and special consideration should be taken to reduce the contamination produced by the undesired reactions. Batch distillation column with a side withdrawal (BDS; see Figure 1f) is a candidate for separation and purification of a heat-unstable product with a slightly decomposing reaction. The intermediate component can be withdrawn from the middle of the column in advance in BDS. The configuration of BDS is simple and easy to control. In this paper, we aim to study the characteristics of BDS for purification of a heat-unstable intermediate component from light and heavy impurities. 2. Operation Steps of BDS The batch distillation in BDS is different from the conventional batch distillation in BR. There is only one reflux in BR, while in BDS, there are two refluxes: one is the top reflux, the same as that in BR at the top of the column, and the other is side reflux, in the middle section of the column. BDS is more flexible than BR, so that the operation steps of BDS are more complicated. The operation steps of BDS are illustrated by considering the separation of a ternary mixture of A, B, and C in which B is the product and A and C are light and heavy impurities, respectively. The general operation steps are as follows: (1) Operating the column at total reflux. (2) Operating the column with a finite top internal reflux ratio RT1 and infinite side internal reflux ratio, to withdraw the concentrated light component A. (3) When the concentration of component B in the side withdrawal stage is greater than a specified purity xBS, operating the column with a finite side internal reflux ratio RS, to withdraw product cut from the side withdrawal. The product is collected in the side receiver. In this period, the instantaneous concentration of component B in side withdrawal will attain a maximum value xBMS; thereafter, it will decrease with distillation time. (4) When the concentration of component B at the top of the column is greater than a specified purity xBD, the product cut is

10.1021/ie8017934 CCC: $40.75  2009 American Chemical Society Published on Web 04/17/2009

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Figure 2. Product withdrawal types in BDS.

(6) When the purity of the product collected in the top receiver Dav Spec xDav B satisfies |xB - xp | e ε and the instantaneous concentration of component B withdrawn from the top of the column is less than xBMD or only a little residue left in the still pot, the operation is terminated. The steps described above are the general steps for the operation of BDS. Because the product can be withdrawn from the side withdrawal or the top of the column, three cases will occur (see Figure 2): (a) the product is only withdrawn from the side withdrawal during the whole distillation process; (b) the product is withdrawn from the side withdrawal first and then it is withdrawn from the top of the column; (c) the product is withdrawn from the side withdrawal and the top of the column, in a specific period the product can be simultaneously withdrawn from the top and side withdrawal of the column. The top internal reflux ratio RT1 and RT2 described above are defined as ratios of the liquid flow rate to vapor flow rate at the top the column, and they reflect the common reflux ratios. The side internal reflux ratio RS is defined as RS )

Figure 1. Different batch column configurations.

withdrawn from the top and the top internal reflux ratio is changed to R2T. The product is collected in the top receiver. The instantaneous concentration of component B withdrawn from the top of the column will attain a maximum value xBMD; thereafter, it will decrease with distillation time. In this period, sometimes the product cuts are simultaneously withdrawn from the top of the column and the side withdrawal. (5) When the purity of the product collected in the side receiver xBSav satisfies the product specification xPSpec with |xBSav xPSpec| e ε and the instantaneous concentration of component B withdrawn from the side withdrawal is less than xBMS, the side withdrawal is terminated.

LN′ S LN S

(1)

Where, LNS is the liquid flow rate that leaves the side withdrawal stage (See Figure 3). LN′ S ) LNS - DNS

(2)

Where, DNS is the side withdrawal flow rate. 3. Dynamic Model A general batch distillation model is used (available in the Supporting Information). It contains N stages, N feeds, N vapor side withdrawals, and N liquid side withdrawals. The model is

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14,15

same as that of Luyben. Because there is a decomposing reaction that occurs during the distillation processes, the steady state is hard to attain during the total reflux period, the time of the total reflux for all the cases is assumed to be the same, and set to 0.5 h in our calculations. 4. Optimization The objective function is the recovery of the product, which is defined as follows: Figure 3. Scheme of a side withdrawal stage.

Ry )

based on the following assumptions: equilibrium stage column, constant relative volatility, constant molar liquid holdup on each stage, negligible vapor holdup and fluid dynamic lags, and adiabatic operation. It is resolved by the GEAR integration method. The model is employed to simulate the batch distillation process in BDS, BR, and the MVBD, in order to compare the characteristics of BDS to BD and MVBD. The column has 15 theoretical stages, numbered from top to bottom. The initial charge contains three components A, B, and C, with a decomposing reaction: BfA The reaction rate is expressed by the following equation: rB,j ) kHjxB,j

(3)

where rB,j is the reaction rate of component B on stage j (mol · h-1); Hj is molar holdup on stage j (mol); xB,j is the mole fraction of component B on stage j; and k is a constant of the reaction rate (h-1). The initial feedstock is 300 mol, the mole fractions of the feedstock are as follows: A 0.05, B 0.9, C 0.05. The holdup on each stage of the column Hj is 1 mol, and the liquid holdup in the condenser is 10 mol. For the MVBD, the liquid holdups in the reboiler and condenser are both 10 mol. The vapor flow rate is 100 mol · h-1. The product purity specification xpSpec is 0.99. The BDS is operated under piecewise constant refluxes, and the operation steps of such a process are presented in section 2. The top internal reflux ratios RT1 and RT2 and the side internal reflux ratio RS are constant. The conventional batch distillation in BR is operated under a piecewise constant reflux. When the concentration of component B in the distillate is less than a specified purity xBD, the distillate is collected as an impurity cut, and the internal reflux ratio in this period is R1T. When the concentration of component B is greater than or equal to xBD, the distillate is collected as a product cut and the internal reflux ratio is changed to RT2. In this period, the concentration of component B in the distillate will attain a maximum value xMD B ; thereafter, it decreases. When the concentration of the product collected in the receiver xBDav satisfies |xBDav - xpSpec| e 1 × 10-4 and the concentration of component B in distillate is less than xBMD, the process is terminated. The MVBD column is operated under constant reflux and reboiler ratios. The middle vessel is also considered as an equilibrium stage. The impurities are withdrawn from the top and the bottom under constant internal reflux ratio RT1 and constant internal reboiler ratio RB1 until the concentration of component B in the middle vessel xBMav satisfies |xBMav - xpSpec| e 1 × 10-4. At the beginning of the startup period (t ) 0), compositions on all theoretical stages, condenser, and reboiler are assumed equal to the initial charge concentration. This assumption is the

PB

(4)

Fx0B

Where, Ry is the recovery of the product (component B), PB is the amount of product obtained, F is the amount of feedstock, and xB0 is the mole fraction of component B in the feedstock. The optimal operation in terms of maximum recovery can be stated as follows: (5)

max Ry subject to

Spec -4 |xDav B - xP | e 1 × 10

(6)

Spec -4 |xSav B - xP | e 1 × 10

(7)

0 e t e tf

(8)

The constraints listed above are based on BDS, for batch distillation in BR and MVBD, the constraints should be replaced by the corresponding forms. The objective function is the same as that for the maximum distillate problem where the amount of distillate of a specified concentration for a specified time is maximized. In our calculation, the distillation time tf is 7.5 h. The parameters to be optimized for BDS are RT1, RT2, RS, xBD, and xBS, while for BR, the parameters to be optimized are RT1, RT2, and xBD, and for MVBD, they are are RT1 and RB1. The batch distillation is optimized by the simulated annealing algorithm. Hanke and Li16 first used this method to resolve the optimal operation problem in batch distillation. Miladi and Mujtaba17 used such method to solve the optimization of design and operation policies of batch distillation with fixed product demand. Simulated annealing (SA) is a stochastic optimization method based on the analogy with the annealing of metals. We used an improved simulated annealing method proposed by Corana18 and Du19 to resolve the optimization problem (details are available in the Supporting Information). 5. Comparison of BDS to BR and MVBD for the Separation of a Ternary Mixture with a Decomposing Reaction Batch distillation in BDS, BR, and MVBD were simulated by the dynamic model described in section 3 and optimized by SA. The optimal results are illustrated in Table 1. In order to compare BDS to BR and MVBD, the recovery enhancement of BDS to BR REBS and that of BDS to MVBD REMS are defined as follows: RBS E ) RMS E )

RBDS - RBR y y RBR y

× 100%

RBDS - RMVBD y y RMVBD y

× 100%

(9)

(10)

The optimal recoveries of product in BDS are greater than those in BR and MVBD as shown in Table 1. The recovery

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Table 1. Comparison of BDS to BR and MVBD Columns for the Separation of a Ternary Mixture with a Decomposing Reaction optimal Ry (%) run no.

reaction rate constant k (h-1)

volatility (A:B:C)

BR

MVBD

BDS

RBS E (%)

RMS E (%)

1 2 3 4 5 6

0.002 0.002 0.002 0.003 0.003 0.003

9:3:1 9:4.5:1 9:2:1 9:3:1 9:4.5:1 9:2:1

68.68 44.70 61.08 54.95 33.34 40.92

77.64 (NMV ) 9) 50.69 (NMV ) 9) 53.29 (NMV ) 8) 67.72 (NMV ) 9) 39.48 (NMV ) 9) 49.37 (NMV ) 8)

94.29 (NS ) 9) 81.29 (NS ) 9) 86.10 (NS ) 7) 93.52 (NS ) 9) 75.65 (NS ) 9) 84.96 (NS ) 7)

37.29 81.85 40.96 70.19 126.9 107.6

21.45 60.37 61.57 38.10 91.62 72.09

Table 2. Optimal Operational Parameters of BR, MVBD, and BDS Columns for the Separation of a Ternary Mixture with a Decomposing Reaction BR

MVBD

BDS

run no.

reaction rate constant k (h-1)

volatility (A:B:C)

R1T

R2T

xBD

R1T

RB1

R1T

1 2 3 4 5 6

0.02 0.02 0.02 0.03 0.03 0.03

9:3:1 9:4.5:1 9:2:1 9:3:1 9:4.5:1 9:2:1

0.7845 0.7323 0.6255 0.7264 0.6971 0.5838

0.4340 0.2712 0.6238 0.4458 0.3014 0.6716

0.9480 0.9666 0.9777 0.9664 0.9722 0.9846

0.9741 0.8486 0.9834 0.9699 0.8048 0.9793

0.9476 0.9690 0.8643 0.9185 0.9701 0.8564

0.9899 0.7397 0.9833 0.9873 0.8259 0.9801

enhancements of BDS to BR are in the range of 37.29%-126.9%, and the recovery enhancements of BDS to MVBD column are in the range of 21.45%-91.62%. The recovery enhancements REBS and REMS increase with the constant of reaction rate k, but the optimal recoveries of product decrease with the constant of the reaction rate, k. Therefore, BDS is favored compared to BR and MVBD for the separation of a ternary system containing a small amount of light and heavy impurities with a slightly decomposing reaction. Table 2 lists the optimal operational parameters of BR, MVBD, and BDS for the separation of a ternary mixture with a decomposing reaction. For all runs of BDS, the products are obtained in the side receiver. The instantaneous concentration of component B at the top in BDS for runs 1, 3, 4, and 6 can not reach xBD in the whole process, so that RT2 have no values. The instantaneous concentration of component B at the top in BDS for runs 2 and 5 can reach xBD, but the values of xBD are low and the values of RT2 are large, so that the purities of distillates collected in the top receiver cannot satisfy the product specification and all the products are obtained in the side receiver. Why is the recovery of product in BDS greater than that in BR? The reason is that BDS has a side withdrawal; it is more flexible than BR. In the case when a heat-unstable intermediate component is separated from light and heavy impurities in BR, at first, the light component A is concentrated and withdrawn from the top, then the intermediate component B is concentrated to a specified purity and withdrawn from the top as the product. Since the holdup in the still pot is large and the temperature is high, most of the decomposing reaction occurs in the still pot, the light component A produced by component B is concentrated by the column to a relative high concentration at the top of the column, component B is continually contaminated by the light impurity A, and it is difficult to attain the product specification. In some cases, the distillate cannot reach the product purity specification during the whole distillation process. Due to the concentration of the light impurity decrease from the top to the bottom of the column, when the light component A has a relatively high concentration at the top, it may have a low concentration in the middle section and the intermediate component B will have a high concentration in the middle section of the column. As shown in Figure 4, when the purity of the intermediate component B is still low at the top, its purity in a middle stage is high, so it is possible to withdraw it from

R2T 0.9701 0.9766

RS

xBD

xBS

0.5883 0.4495 0.6652 0.5886 0.4845 0.6635

0.8851 0.8120 0.8701 0.9217 0.8297 0.9700

0.9709 0.9794 0.9649 0.9736 0.9802 0.9698

Figure 4. Concentration path in BR for separation of a ternary mixture with a decomposing reaction (RAB ) RBC ) 3, k ) 0.002 h-1).

the middle stage in advance as a product cut. However, the product cannot be withdrawn from the middle section of the column in advance in BR; it is withdrawn only from the top of the column until the light impurity cut is completely removed. There is a side withdrawal in BDS, so the intermediate component can be withdrawn from the side withdrawal stage in advance (see Figure 5; the side withdrawal stage is stage 9). The operation of BDS is different from that of BR. There are three periods in Figure 4. The BR is operated at total reflux in period 1, the light impurity A is concentrated and withdrawn from the column in period 2, and the intermediate component B is withdrawn as product in period 3. The separation process in BDS shown in Figure 5 also contains three periods. In period 1, the BDS is operated at total reflux. In period 2, the light impurity A is concentrated and withdrawn from the top. In period 3, the intermediate component B is withdrawn from a side withdrawal (stage 9) as product, while the light impurity A is still withdrawn from the top until the end of the process. Figure 5 shows that the product (component B) is totally withdrawn from the side withdrawal and the light impurity A is withdrawn from the top of column. The top internal reflux ratio is large so that the light impurity can be concentrated to a higher concentration than that in BR.

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Figure 5. Concentration path in BDS (NS ) 9) for separation of a ternary mixture with a decomposing reaction (RAB ) RBC ) 3, k ) 0.002 h-1).

6. Effects of Parameters for BDS The location of the side withdrawal is an important structure parameter for BDS. There is an optimal location of the side withdrawal in BDS. The optimal side withdrawal stage in BDS resembles that in a batch distillation column with a side withdrawal and two charges and the optimal middle vessel stage in MVBD. Barolo7 and Demicoli13 discussed the optimal feed stage in MVBD and the optimal side withdrawal stage in a batch distillation column with a side withdrawal and two charges. The optimal side withdrawal stage is mainly related to the relative volatilities of the components. Generally, if the relative volatilities RAB ) RBC, the optimal stage is near the middle point of the column. If RAB > RBC, the upper section of the column is shorter and the position of the optimal side withdrawal stage would shift upward, and vice versa. The top and side internal reflux ratios are important operational parameters for BDS. Different reflux ratio combinations result in different types of product withdrawal. As described above, three types of product withdrawal occur in BDS operation. The product is withdrawn only from the side withdrawal stage in optimal operation (see Figures 5 and 2a). During such an operation, the top internal reflux ratio is very large and the side internal reflux ratio is small, the light impurity A is concentrated to a high concentration at the top of the column, and the product (component B) is withdrawn only from the side withdrawal stage, so that the recovery of the product is very high. If the operation is not in an optimal mode, the other two types of product withdrawal will occur (See Figure 6). There are five periods in Figure 6a and b. The BDS is operated in total reflux in period 1, the light impurity is withdrawn from the top of column in period 2, the product is withdrawn from the side withdrawal while the light impurity is still withdrawn from the top in period 3, and the product is withdrawn from the top in period 5. In period 4, the two figures are different. In Figure 6a, the light impurity is still withdrawn from the top, no product is withdrawn from the side withdrawal stage. In Figure 6b, the product is withdrawn from the top and side withdrawal stages simultaneously. Therefore, the product withdrawal types in Figure 6a are the same as those in Figure 2b, and the product withdrawal type in Figure 6b is the same as that in Figure 2c. Different reflux ratio combinations result in the difference of the two figures. Comparing Figure 5 to Figure 6a and b, we can see that RT1 decreases, while RS increases. Therefore, when RT1 is large enough and RS is small enough, the product is withdrawn only from the side withdrawal stage; while RT1 is

Figure 6. Concentration path in BDS (NS ) 9) for separation of a mixture with a decomposing reaction by different product withdrawal types (RAB ) RBC ) 3, k ) 0.002 h-1).

small enough and RS is large enough, the product can be withdrawn from the top and side withdrawals simultaneously in a period of time; while in other cases, the product can be withdrawn from the top and side withdrawals, respectively. In all of our calculations, the optimal operations tend to be with a large top internal reflux ratio and small side internal reflux ratio, and the product is only withdrawn from the side withdrawal stage. 7. Conclusions (1) BDS is favored for the purification of an intermediate component from light and heavy impurities with a decomposing reaction. In order to reduce the contamination of the light component produced by the decomposing reaction, the product can be withdrawn from side withdrawal in BDS. The recovery of the product in BDS is larger than that in the BR and MVBD columns. (2) The performance of BDS is investigated. Different combinations of top and side reflux ratios result in different types of product withdrawal, and the optimal operation of BDS for the purification of an intermediate component from light and heavy impurities with a decomposing reaction tends to be with a large top reflux ratio and small side reflux ratio.

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Notation -1

k ) constant of reaction rate, h PB ) the amount of product, mol R1T ) top internal reflux ratio for slop cut R2T ) top internal reflux ratio for product cut rB,j ) reaction rate for component B on stage j, mol.h-1 RBS E ) recovery enhancement of BDS to BR RMS E ) recovery enhancement of BDS to MVBD RS ) side internal reflux ratio Ry ) recovery of the product t ) distillation time, h xB,j ) liquid composition of component B on stage j, mol fraction xBD ) purity of component B in distillate, above which the product cut is collected, mol fraction xBDav ) the average concentration of the product in the top receiver, mol fraction xMav B ) the average concentration of the product in the middle vessel, mol fraction xSav B ) the average concentration of the product in the side receiver, mol fraction xBS ) purity of product on side withdrawal stage, above which the product cut is collected, mol fraction xPSpec ) product purity specification Greek Letters RAB ) relative volatility of component A to B RBC ) relative volatility of component B to C

Supporting Information Available: Details of the optimization problem. This material is available free of charge via the Internet at http://pubs.acs.org. Literature Cited (1) Sorensen, E.; Skogestad, S. Comparison of regular and inverted batch distillation. Chem. Eng. Sci. 1996, 51, 4949–4962. (2) Robinson, C. S.; Gilliland, E. R. Elements of fractional distillation, 4th ed.; McGraw-Hill Book Co.: New York, 1950. (3) Davidyan, A. G; Kiva, V. N.; Meski, G. A. Batch distillation in a column with a middle vessel. Chem. Eng. Sci. 1994, 49, 3033–3051.

(4) Meski, G. A.; Morari, M. Design and operation of a batch distillation column with a middle vessel. Comput. Chem. Eng. 1995, 19, s597-602. (5) Barolo, M.; Guarise, G. B.; Rienzi, S. A. Running batch distillation in a column with a middle vessel. Ind. Eng. Chem. Res. 1996, 35, 4612– 4618. (6) Barolo, M.; Guarise, G. B.; Rienzi, S. A. Understanding the dynamics of a batch distillation column with a middle vessel. Comput. Chem. Eng. 1998, 22, s37–44. (7) Barolo, M.; Guarise, G. B.; Ribon, N. Some issues in the design and operation of a batch distillation column with a middle vessel. Comput. Chem. Eng. 1996, 20, s37–42. (8) Phimister, J. R.; Seider, W. D. Distillate-bottoms control of middlevessel distillation columns. Ind. Eng. Chem. Res. 2000, 39, 1840–1849. (9) Phimister, J. R.; Seider, W. D. Semicontinuous, middle-vessel distillation of ternary mixtures. AIChE J. 2000, 46, 1508–1520. (10) Kim, K. J.; Diwekar, U. M. Comparing batch distillation configurations: parametric study involving multiple objectives. AIChE J. 2000, 46, 2475–2488. (11) Wittgens, B.; Litto, R.; Sørensen, E.; Skogestad, S. Total reflux operation of multivessel batch distillation. Comput. Chem. Eng. 1996, 20, s1041-1046. (12) Cui, X. B.; Yang, Z. C. Batch distillation with a side withdrawal and cold still pot for heat sensitiVe materials. Chinese patent 200310122030.1, Dec 31, 2003. (13) Demicoli, D.; Stichlmair, J. Separation of ternary mixtures in a batch distillation column with side withdrawal. Comput. Chem. Eng. 2004, 28, 643–650. (14) Luyben, W. L. Some practical aspects of optimal batch distillation design. Ind. Eng. Chem. Process Des. DeV. 1971, 10, 54–59. (15) Luyben, W. L. Multicomponent batch distillation. 1. Ternary system with slop recycle. Ind. Eng. Chem. Res. 1988, 27, 642–647. (16) Hanke, M.; Li, P. Simulated annealing for the optimization of batch distillation process. Comput. Chem. Eng. 2000, 24, 1–8. (17) Miladi, M. M.; Mujtaba, I. M. Optimization of design and operation policies of binary batch distillation with fixed product demand. Comput. Chem. Eng. 2004, 28, 2377–2390. (18) Corana, A.; Marchesi, M.; Martini, C. Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithm. ACM Trans. Math. Soft. 1987, 13, 262–280. (19) Du, H. B.; Xue, D. F.; Yao, P. J. Improved adaptive simulated annealing for algorithm for MINLP problems in process synthesis. J. Chem. Eng. Chin. UniV. 2002, 16, 106–110.

ReceiVed for reView November 23, 2008 ReVised manuscript receiVed March 21, 2009 Accepted April 07, 2009 IE8017934