Batch Distillation in a Batch Stripper with a Side Withdrawal for

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Ind. Eng. Chem. Res. 2010, 49, 6521–6529

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Batch Distillation in a Batch Stripper with a Side Withdrawal for Purification of Heat-Unstable Compounds Xianbao Cui,* Xiaokai Zhang, Ying Zhang, and Tianyang Feng State Key Laboratory of Chemical Engineering, School of Chemical Engineering and Technology, Tianjin UniVersity, Tianjin 300072, People’s Republic of China

Batch distillation in a batch stripper with a side withdrawal (BSS) for the purification of heat-unstable compounds from light and heavy impurities was investigated. The batch distillation process was simulated by a dimensionless dynamic model and optimized by simulated annealing algorithm. Batch distillation in a BSS was compared with that in a batch stripper (BS) for the purification of heat-unstable compounds with different types of degradation reactions. The recovery of heat-unstable compounds in a BSS is larger than that in a BS, especially in the case of the heat-unstable compound converting to a heavy impurity. Compared with batch distillation in a batch rectifier with a side withdrawal (BRS), batch distillation in a BSS is more suitable for purification of heat-unstable compounds that convert to a light impurity. The effects of operational and design parameters for batch distillation in a BSS were discussed according to the simulation results, such as the temperature in the top storage vessel, the location of the side withdrawal stage, the holdup in the reboiler, the reboiler ratio, and the side reflux ratio. 1. Introduction Many types of chemicals are thermodynamically unstable, and the types of degradation reactions that they undergo at elevated temperatures are numerous. Decomposition, polymerization, isomerization, and cyclization reactions can occur when the heat-unstable compounds are heated at elevated temperatures.1 The separation and purification of heat-unstable compounds are performed according to the degradation reaction rates of the heat-unstable compounds. If the degradation reaction rates are large, molecular distillation, crystallization, extraction and membrane separation processes are preferred; however, these separation processes are one-stage separation processes. If the degradation reaction rates of the heat-unstable compounds are small, batch distillation is a good choice, because its flexibility allows for different types of column configurations; furthermore, batch distillation is a multistage separation process. Most of the substances that are purified by distillation are particularly prone to heat damage, and this proneness is responsible for their heat sensitivity. Thermal hazard is contributed by temperature and time. Hickman and Embree2 proposed the concept of decomposition hazard D to compare the different hazards of decomposition in various stills. King1 proposed a stability index (IS) to describe the degradation hazard, based on the decomposition hazard D. He also proposed a degradation index ID to characterize distillation equipment. The degradation index ID for distillation equipment should always be less than the stability index IS, to perform a successful separation of a mixture containing heat-unstable compounds. Noworyta3 proposed a method to quantitatively determine the distillation process requirements. They defined a nonheatsensitivity factor, which consisted of the reaction factor and the apparatus operation factor. The reaction factor includes parameters that indicate the heat sensitivity of the substance. Based on this value, materials can be classified in relation to heat damage. The apparatus operation factor is a function of the process operation parameters and the apparatus used. The value * To whom correspondence should be addressed. Tel.: 86-2227404493. E-mail: [email protected].

of this factor permits us to determine whether given equipment may be applied to the distillation of heat-sensitive compounds. Batch distillation is widely used for the production of fine chemicals and specialized products such as alcoholic beverages, essential oils, perfumes, and pharmaceutical and petroleum products. It is the most-frequent separation method in batch processes.4 The batch distillation apparatus can be configured many different ways, e.g., batch rectifier, batch stripper (BS),5,6 middle vessel column,7-14 multivessel column,15 and side withdrawal column.16,17 Many of the fine chemicals and specialized products are heat-unstable; the degradation reaction rate of such chemicals are small, and the compositions of feedstock often vary for different batches with some impurities that are hard to separate. The batch distillation process can be used in such cases, and the configuration of the apparatus and process should be carefully considered. Generally, the heatunstable compound can be purified via high vacuum distillation to reduce the temperature, but the vacuum is limited; further reduction of the degradation reaction rate lies on the proper process and apparatus. In this paper, we aim to study the purification of heat-unstable compounds in a batch stripper with a side withdrawal (BSS). In section 2, the operation steps of batch distillation in a BSS are presented. The simulation and optimization methods are described in section 3. Comparisons of batch distillation in a BSS with that in a BS and in a batch rectifier with a side withdrawal (BRS) for purification of a heat-unstable intermediate component from its light and heavy impurities are presented in sections 4 and 5, respectively. The effects of parameters for batch distillation in a BSS for the purification of heat-unstable compounds are discussed in section 6. 2. Operation Steps of Batch Distillation in a Batch Stripper with a Side Withdrawal Batch distillation in a batch stripper with a side withdrawal (BSS) is different from that in a batch stripper (BS). There is only one withdrawal in the reboiler for BS, whereas, for BSS, there are two withdrawals: one is in the reboiler, the same as that in BS, and the other is side withdrawal, in the middle section

10.1021/ie901558c  2010 American Chemical Society Published on Web 06/22/2010

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of the column. Since BSS is more flexible than BS, the operation steps of BSS are more complicated. The operation steps of the BSS are presented by considering the separation of a ternary mixture of A, B, and C in which B is the product, A and C are light and heavy impurities, respectively. The operation steps are as follows: (1) Operating the column at total reboiler ratio. (2) Operating the column with a finite internal reboiler ratio RN1 and infinite internal side reflux ratio, to withdraw the concentrated heavy component C from the reboiler. (3) When the concentration of component B on the side withdrawal stage is greater than a specified purity xBS (product cut location specification for side withdrawal), operating the column with a finite internal side reflux ratio RS, to withdraw product B from the side withdrawal stage. The instantaneous concentration of component B in side withdrawal increases with distillation time until it reaches a maximum value xMS B , and then it decreases with distillation time. (4) When the concentration of component B in the reboiler is greater than a specified purity xBB (product cut location specification for reboiler), the product B is withdrawn from the reboiler, and the reboiler ratio is changed to RN2 . The instantaneous concentration of component B withdrawn from the reboiler increases with distillation time, until it reaches a maximum value xBMB, then it decreases with distillation time. In this period, sometimes the product cuts are simultaneously withdrawn from the reboiler and the side withdrawal. (5) When the purity of the product (component B) 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. (6) When the purity of the product collected in the bottom receiver xBBav satisfies |xBBav - xPSpec| e ε and the instantaneous concentration of component B withdrawn from the reboiler is less than xBMB, or only a little residue left in top storage vessel, the operation is terminated. 3. Dynamic Model and Optimization 3.1. Dynamic Model. A dimensionless model (see the Appendix) is derived based on the following assumptions: equilibrium stage column, constant vapor flow on each stage, constant molar liquid holdup on each stage, negligible vapor holdup and fluid dynamic lags, and adiabatic operation. The dimensionless model is used to simulate batch distillation in a BSS and a BS. The column has 15 theoretical stages, numbered from top to the bottom. The initial charge contains three components A, B, and C, with reactions

Table 1. Thermodynamic Data for the Ternary Mixture Antoine Constantsa index of component

boiling point (K)

a

b

c

A B C

353.25 383.78 417.56

6.01907 6.08627 6.13132

1204.682 1349.122 1480.155

-53.072 -53.154 -58.804

a Note: The Antoine equation is described as follows: log10 P ) a b/(c + T), where P is the pressure (given in units of kPa) and T is the temperature (in Kelvin).

Suppose t0 ) 1 h, qA ) qC ) 0, and qB ) 1; then, the dimensionless reaction rate is simplified to R*j )

( )

rj Ea ) k0 exp H*x V RT j j,B

(2)

The activation energy is Ea ) 150 kJ/mol, and the gas constant is R ) 0.008314 kJ mol-1 K-1. The amount of feedstock is unity, and the mole fraction of feedstock is 0.05 A, 0.9 B, and 0.05 C. The holdup on each stage of the column (H*j ) is 0.005, and the holdup in the reboiler is 0.02, unless otherwise stated. The distilled mixture is considered to be an ideal mixture, and the Antoine constants of components A, B, and C are shown in Table 1. The BSS is operated under piecewise constant reboiler ratios, and the operation steps of such a process are presented in section 2. The internal reboiler ratios (RN1 and RN2 ) and the internal side reflux ratio (RS) are constant. 3.2. Optimization. The objective function is the recovery of the product, which is defined as Ry )

PB H*0x0B

)

PB x0B

(3)

where Ry is the recovery of the product (component B), PB the amount of product obtained, H*0 the dimensionless feedstock (H0/H0), and xB0 the mole fraction of component B in the feedstock. The optimal operation in terms of maximum recovery can be stated as: max Ry

(4)

Spec |xBav | e 1 × 10-4 B - xp

(5)

Spec |xSav | e 1 × 10-4 B - xp

(6)

τfL e τf e τfU

(7)

subject to

B f C or B f A The dimensionless reaction rate is expressed by R*j )

( )∏

rj Hj )k V V

( )( ) ∏ ( ) ∏

Ea Hj /H0 xqj,ii ) RT V/H0 Ea H*t0 xqj,ii (1) k0 exp RT j

xqj,ii ) k0 exp -

where Ea is the activation energy, k0 the reaction rate constant, H*j the dimensionless holdup on stage j, H0 the feed charge, t0 a reference time (which stands for the time needed to totally evaporate the feed stock), V the vapor flow rate, Hj the liquid holdup on stage j, and qi an empirical constant.

The objective function is almost the same as the maximum distillate problem, where the amount of distillate of a specified concentration for a specified time is maximized. τf is the total dimensionless distillation time. In our calculation, the dimenL sionless distillation time τU f is 6.5, while τf is zero. The product Spec purity specification xp is 0.98. The parameters to be optimized for BSS are RN1 , RN2 , RS, xBB and xBS ; for BS, the parameters to be optimized are RN1 , RN2 , and xBB. The purities xBB and xBS stand for the cut location. Bonny18 found that the amount of product obtained in batch distillation was affected by the cut locations, and there were optimal cut locations in batch distillation. Therefore, the cut locations xBB and xBS are also optimized in our calculations. Since a degradation reaction occurs during the distillation process, in some cases, the recovery of the product

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Table 2. Comparison of Batch Distillation in BSS and BS with Component B Converting to Component C TTOP (K)

NS

k0 (h-1)

1

2

RN

RN

RS

B

xB

S

xB

RY

RyE (%)

Batch Distillation in BS 1×1019 0.8303 0.5925 BPa 303.15 1×1019 0.9746 0.3342 363.15 1×1019 0.9634 0.3105

0.9560 0.6044 0.7534

0.1258 0.8597 0.8043

Batch Distillation in BSS 8 BPa 1×1019 0.9223 8 303.15 1×1019 0.9859 8 363.15 1×1019 0.9823 a

0.8299 0.9895 0.9719 0.3733 196.7 0.6541 0.9837 0.9712 0.9099 5.839 0.8091 0.9276 0.9568 0.8952 11.30

The abbreviation “BP” denotes bubble point.

will reach its maximum value when the total distillation time is less than τfU. Therefore, the total dimensionless distillation time is set to a range in the optimization. The batch distillation is optimized by the simulated annealing algorithm. Simulated annealing (SA) is a stochastic optimization method and based on the analogy with the annealing of metals. Hanke and Li19 first used this method to resolve the optimal operation problem in batch distillation. Miladi and Mujtaba20 used such a method to solve the optimization of design and operation policies of batch distillation with fixed product demand. Cui et al.17 used an improved simulated annealing method proposed by Corana21 and Du22 to resolve the optimization problem in batch distillation, and the same method was used in the optimization of batch distillation in BS and BSS in this paper. 4. Comparison of Batch Distillation in BSS with That in BS for the Purification of Heat-Unstable Compounds Batch distillation in BS and BSS was simulated by the dimensionless dynamic model and optimized by SA. Two types of reactions were considered in the batch distillation process: (1) Heat-unstable compound converts to heavy impurity, B fC (2) Heat-unstable compound converts to light impurity, B f A To compare BSS with BS, the recovery enhancement of BSS to BS is defined as follows: REy (%) )

- RBS RBSS y y RBS y

× 100

(8)

4.1. Intermediate Component Converts to Heavy Impurity (B f C). The optimization results of batch distillation in a BS and a BSS with the intermediate component converting to a heavy component, are shown in Table 2. Table 2 shows that the recovery of the intermediate component in a BSS is higher than that in a BS. When the mixture in the top storage vessel is kept at its bubble point, the recovery of product (component B) in a BSS is ∼3 times that in a BS. When the mixture in the top storage vessel is kept in a cold state, the recovery enhancements are 5.8%-11.3%, and the recovery enhancement increase with the increasing temperatures in the top storage vessel. The feedstock is stored in a top storage vessel for batch distillation in a BS or BSS. The mixture stored in the top storage vessel can be kept at the bubble point or at a given temperature by adjusting the heat-transfer area of the condenser and the flow rate of cold water in the condenser. When the mixture in the top storage vessel is stored in a temperature below its bubble point, the reflux should be heated to its bubble point before it

Figure 1. Variation of (a) temperature and (b) reaction rate for batch distillation in a BS (B converts to C, TTOP ) bp (bubble point); RY ) 0.1258).

returns to the column; otherwise, some of the vapor at the top of the column will be condensed by the cold reflux. Figures 1-4 illustrate the temperatures and dimensionless reaction rates in the top storage vessel (j ) 1) and reboiler (j ) 15), and on stage 8 for batch distillation in a BS or BSS. The areas below the dimensionless reaction rate curves stand for the amount of intermediate component reacted in the distillation process. When the temperature in the top storage vessel is at the bubble point, the amount of intermediate component reacted in the top storage vessel is the largest, since the holdup in the top storage vessel is the largest, as shown in Figures 1 and 3. The dimensionless reaction rate on stage 8 is very low; because the holdup on stage 8 is very small (actually, the holdups in other stages except for the top storage vessel and reboiler are the same as stage 8), the amount of intermediate component reacted on theses stages are also very small. However, in the reboiler, the temperature is the highest and the holdup is larger than that in stage 8, so the amount of intermediate component reacted in the reboiler is larger than that in stage 8. If the temperature in the top storage vessel is reduced from the bubble point to 303.15 K, the dimensionless reaction rate in the top storage vessel is greatly reduced (comparing Figures 2b and 4b with Figures 1b and 3b), and the dimensionless reaction rate in the top storage vessel is almost zero at 303.15 K (see Figures 2b and 4b). When the reaction rate in the top storage vessel is reduced, the recovery of the product will increase. Comparing Figure 3 with Figure 1, we found that, although the recovery of product in a BSS is larger than that in a BS, the reaction rate in a BSS is not less than that in a BS. That implies the difference of recoveries in a BSS and a BS is mainly due to the difference in column configuration.

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Figure 3. Variation of (a) temperature and (b) reaction rate for batch distillation in a BSS (B converts to C, TTOP ) bp (bubble point), NS ) 8; RY ) 0.3733). Figure 2. Variation of (a) temperature and (b) reaction rate for batch distillation in a BS (B converts to C, TTOP ) 303.15 K; RY ) 0.8597).

Batch distillation in a BSS has more freedom than that in a BS. The product is withdrawn only from the reboiler in BS; however, the product can be withdrawn from the side withdrawal or the reboiler in a BSS. When intermediate component B converts to heavy component C, the product is withdrawn from the side withdrawal in a BSS; it avoids withdrawing the product from the high-temperature high-holdup reboiler. In the reboiler, component B will decompose to C; furthermore, component C continually produced by component B in the column will also be concentrated herein. Therefore, it is difficult to concentrate component B to a high concentration in the reboiler. Consequently, the recovery of the intermediate component in a BSS is larger than that in a BS. The operations of batch distillation in a BS and a BSS are different. There are three periods for batch distillation in a BS (see Figure 5). The column is operated at total reboiler ratio in period 1, then the heavy impurity is concentrated and removed from the reboiler in period 2 until the intermediate component reaches the product cut specification, and then the product is withdrawn from the reboiler until the termination criteria are satisfied. There are also three periods for batch distillation in a BSS (see Figure 6). The column is operated at total reboiler ratio in period 1 (the same as that in a BS), then the heavy impurity is concentrated and removed from the reboiler in period 2 until the intermediate component reaches the product cut specification on side withdrawal stage, and then the product is withdrawn from the side withdrawal stage and the concentrated heavy impurity is still removed from the reboiler in period 3. Figure 6 shows that the product is only withdrawn from the side withdrawal stage, during the distillation process.

4.2. Intermediate Component Converts to Light Impurity (B f A). If the intermediate component converts to light impurity, the recovery of the product is sufficiently large, even if it is purified in a BS with the mixture in the top storage vessel stored in the bubble point state (see Table 3). The recoveries of the product increase only slightly as the temperature in the top storage vessel decreases from the bubble point to a low temperature in BS or BSS. The recovery of the product in a BSS is larger than that in a BS, but the recovery enhancement is very small (see Table 3). Consequently, if the intermediate component converts to light impurity, BSS has only a slight advantage over BS. The operation of batch distillation in a BS with component B converting to light impurity A (see Figure 7) is similar to that with component B converting to heavy impurity C, but the amount of product obtained is larger. The operation of batch distillation in a BSS with intermediate component converting to light impurity (see Figure 8) is different from that with intermediate component converting to heavy impurity. There are four periods in Figure 8. The column is operated at total reboiler ratio in period 1, the heavy component is concentrated and removed from the reboiler with the product withdrawn from the side withdrawal stage simultaneously in period 2, the heavy impurity is continually removed from the reboiler but no side withdrawal product is obtained in period 3, the product is withdrawn from the reboiler in period 4 until the termination criteria is satisfied. 5. Comparison of Batch Distillation in Batch Rectifier with a Side Withdrawal (BRS) with That in BSS for the Purification of Heat-Unstable Compounds We have investigated batch distillation in a batch rectifier with a side withdrawal (BRS) for purification of a heat-unstable compound with a decomposing reaction.17 The recovery of the

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Figure 6. Concentration path in a BSS for separation of a ternary mixture with an intermediate component converting to heavy impurity. Table 3. Comparison of Batch Distillation in BSS and BS with Component B Converting to Component A TTOP (K)

NS

k0 (h-1)

RN1

RN2

RS

xBB

xBS

RY

RyE (%)

Batch Distillation in a BS 1 × 1019 0.9583 0.7344 BPa 303.15 1 × 1019 0.9745 0.6853

0.7913 0.6058

0.8336 0.8943

Batch Distillation in a BSS 8 BPa 1 × 1019 0.9743 0.8174 0.8282 0.9196 0.9548 0.8522 2.23 8 303.15 1 × 1019 0.9859 0.1311 0.6541 0.9837 0.9712 0.9099 1.74 a

The abbreviation “BP” denotes bubble point.

Figure 4. Variation of (a) temperature and (b) reaction rate for batch distillation in a BSS (B converts to C, TTOP ) 303.15 K, NS ) 8; RY ) 0.9099).

Figure 7. Concentration path in a BS for separation of a ternary mixture with an intermediate component converting to light impurity.

Figure 5. Concentration path in a BS for separation of a ternary mixture with an intermediate component converting to heavy impurity.

heat-unstable compound in a BRS is higher than that in a conventional batch rectifier. Now we compare batch distillation in a BRS with that in a BSS for the purification of a heat-unstable compound from light and heavy impurities. As discussed in the above section, two types of reactions are considered. If the heat-unstable compound converts to light impurity, the recovery of the heat-unstable compound in a BSS is greater than that in a BRS, as shown in Table 4. The reaction rate is also expressed by eq 2 in section 3.1. When the reaction constant k0 is 1 × 1019 h-1, the recovery of the product is 0.6924 in the BRS; however, the recovery of the product in a BSS with the

top storage vessel kept in bubble point is 0.8522, and the recovery is increased by 23.1%. If the mixture in the top storage vessel in a BSS is stored in a cold state (TTOP ) 303.15 K), the recovery is 0.9099, which represents an increase of 31.4%. If the reaction constant k0 is large (5 × 1019 h-1), no product is obtained in a BRS; however, some product can be obtained in a BSS, and the recoveries of the product are 0.5400 and 0.7693, with the mixture in the top storage vessel kept at the bubble point state and at 303.15 K. If the mixture is separated by a BSS, the product continually converts to light impurity, but the concentration of the light component decreases down the column, the concentration of the light component in the reboiler is the lowest, and the light impurity produced by the intermediate component hardly contaminates the heavy and intermediate component in the

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Ind. Eng. Chem. Res., Vol. 49, No. 14, 2010 Table 5. Batch Distillation in a BRS and a BSS for Separation of a Ternary Mixture with Component B Converting to Component Ca TTOP (K)

k0 (h-1)

RN1

RN2

xBB

xBS

RY

0.8268 0.9750

0.8293 0.9790

0.8681 0.0067

0.9719 0.9815 0.9712 0.9660

0.3733 0.0061 0.9099 0.7853

RS

Batch Distillation in a BRS BP BP

1×1019 5×1019

0.9328 0.9500

BP BP 303.15 303.15

1×1019 5×1019 1×1019 5×1019

0.9223 0.8643 0.9859 0.9545

0.6215 0.6000

0.5745 0.9000

Batch Distillation in a BSS 0.8299 0.8959 0.6541 0.7376

0.9895 0.9570 0.9837 0.9277

a Note: holdups in the condenser or reboiler for a BRS or a BSS are 0.02, respectively. The side withdrawal stage NS ) 8. The abbreviation “BP” denotes bubble point.

Figure 8. Concentration path in a BSS for separation of a ternary mixture with an intermediate component converting to light impurity. Table 4. Batch Distillation in a BRS and a BSS for Separation of a Ternary Mixture with Component B Converting to Component Aa TTOP (K)

k0 (h-1)

RN1

RN2

xBB

xBS

RY

0.9394

0.9660

0.6924 0.0

0.9548 0.9813 0.9712 0.9735

0.8522 0.5400 0.9099 0.7693

RS

Batch Distillation in a BRS BP BP

1×1019 5×1019

0.9523

BP BP 303.15 303.15

1×1019 5×1019 1×1019 5×1019

0.9743 0.9403 0.9859 0.9559

0.7855

Batch Distillation in a BSS 0.8174 0.8103 0.1311 0.5959

0.8282 0.6744 0.6541 0.8169

0.9196 0.9156 0.9837 0.9192

a Note: holdups in the condenser or reboiler for a BRS or a BSS are 0.02, respectively. The side withdrawal stage NS ) 8. The abbreviation “BP” denotes bubble point.

reboiler, so it is easier to remove the heavy impurity from the reboiler in a BSS than to remove light impurity from the top of the column in a BRS. It is one of the reasons why the recovery of the product in a BSS is larger than that in a BRS when the intermediate component converts to light impurity. In a distillation process, the temperature in the condenser is the lowest in terms of the temperatures in the column, and the temperature in the reboiler is the highest. In a BRS, the light impurity is removed first, and the temperature in the reboiler increases during the distillation process, and the mixture to be separated is stored in the reboiler, so that the amount of product reacted is relatively large. In a BSS, the mixture to be separated is stored in the top storage vessel, and the temperature in the top storage vessel is the lowest, even if it is in a bubble point state, the reaction rate of the product in the top storage vessel is low, and the amount of the product converted is low; furthermore, the mixture in the top storage vessel can be kept in a low temperature, the reaction rate of the product can be greatly reduced. Based on the analysis above, we can conclude that a BSS is more suitable for the purification of a heat-unstable compound, which decomposes to light impurity from its light and heavy impurities. Batch distillation in a BRS and a BSS is different from those discussed above, if the heat-unstable compound converts to heavy impurity (see Table 5). The results show that the recovery of the product in a BRS is larger than that in a BSS with the mixture in the top storage vessel stored at the bubble point state. However, the recovery of the product in a BRS is lower than that in a BSS with the mixture in the top storage vessel stored at a low temperature. If the temperature of the mixture in the top storage vessel in BSS is low, the amount of product reacted

can be greatly reduced and, consequently, the recovery of the product is large. If the mixture in the top storage vessel is stored in a bubble point state, the situation is different. In such cases, the product in the top storage vessel continually converts to heavy impurity, and it is concentrated down the column; the heavy impurity produced by the product greatly affects the separation of the heavy impurity from the product, and more product accompanied by the heavy impurity should be removed from the reboiler before the concentration of the product in the side withdrawal stage reaches the product purity specification. In a BRS, since the product converts to heavy impurity, the concentration of the heavy impurity decreases up the column; the heavy impurity produced by the product does not have much effect on the concentration of the product in the middle section of the column, the purity of the product in the middle section is mainly affected by the light impurity. It is easier to remove light impurity from the top of the column in a BRS than to remove the continually produced heavy impurity from the reboiler in a BSS. Consequently, if the intermediate component converts to heavy impurity, the recovery of the product in a BRS is larger than that in a BSS with the mixture in the top storage vessel is stored in a bubble point state. Based on the analysis above, regardless of whether the intermediate component converts to light or heavy impurity, a BSS is more suitable than a BRS for the purification of a heatunstable compound from its light and heavy impurities, if the mixture in the top storage vessel is stored at a temperature far below the bubble point. However, the operation of a BSS is more difficult than that of a BRS, since the liquid flow from the top storage vessel to the column and the liquid removed from the reboiler and side withdrawal should be carefully controlled. The operation of a BRS is easier; in some cases, such as the reaction rate is small and the intermediate component converts to heavy impurity, BRS is also a good choice. 6. Effects of Parameters for Batch Distillation in a Batch Stripper with a Side Withdrawal for Purification of Heat-Unstable Compounds Batch distillation in a BSS can be used to purify a heatunstable compound that converts to light or heavy impurities. The effects of the parameters for batch distillation in a BSS are discussed in this section. 6.1. Effect of Temperature in the Top Storage Vessel. The temperature of the mixture in the top storage vessel is an important factor for batch distillation in a BSS. The mixture in the top storage vessel can be kept at various temperatures by adjusting the area of the condenser and the flow rate of the cold water in the condenser. The reaction rate decreases with the decreasing temperature in the top storage vessel; consequently,

Ind. Eng. Chem. Res., Vol. 49, No. 14, 2010

Table 8. Effect of Holdup in the Reboiler in a BSS on the Recovery of the Product with Component B Converting to Component C

Table 6. Effect of Side Withdrawal Stages in a BSS with Component B Converting to Component C NS TTOP(K) 5 6 7 8 9 10

343.15 343.15 343.15 343.15 343.15 343.15

k0(h-1)

RN1

1 × 10 1 × 1019 1 × 1019 1 × 1019 1 × 1019 1 × 1019 19

RN2

0.9845 0.9890 0.9885 0.9867 0.9828 0.9758

RS 0.8736 0.8382 0.8303 0.6655 0.6655 0.6373

xBB 0.9349 0.9245 0.9427 0.9054 0.9694 0.9371

xBS 0.9021 0.9566 0.9531 0.9691 0.9594 0.9578

RY 0.8625 0.9100 0.9103 0.9096 0.9024 0.8845

6 7 8 9 10 a

TTOP (K) k0 (h-1) Bp Bp Bp Bp Bp

1 × 1019 1 × 1019 1 × 1019 1 × 1019 1 × 1019

RN1 0.9667 0.9728 0.9743 0.9716 0.9631

RN2 0.7937 0.9021 0.8174 0.7146 0.8936

RS 0.8987 0.8481 0.8282 0.8245 0.7129

xBB 0.9130 0.9114 0.9196 0.9248 0.9325

xBS 0.9651 0.9453 0.9548 0.9019 0.9659

H* N NS 0.01 0.02 0.03 0.04 0.05

8 8 8 8 8

TTOP (K)

k0 (h-1)

RN1

RN2

RS

xBB

xBS

RY

343.15 343.15 343.15 343.15 343.15

1 × 1019 1 × 1019 1 × 1019 1 × 1019 1 × 1019

0.9855 0.9869 0.9839 0.9882 0.9893

0.6544 0.2753 0.3712 0.3306 0.8770

0.6400 0.6676 0.7574 0.7984 0.7867

0.9472 0.9155 0.9932 0.9427 0.9488

0.9780 0.9674 0.9676 0.9048 0.9167

0.9012 0.9118 0.8974 0.8975 0.8930

Table 9. Effect of Holdup in Reboiler in BSS on the Recovery of the Product with Component B Converting to Component A

Table 7. Effect of Side Withdrawal Stages in a BSS with Component B Converting to Component Aa NS

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RY 0.8293 0.8499 0.8522 0.8479 0.8351

The abbreviation “BP” denotes the boiling point.

the recovery of the product increases. This has been discussed in section 4 (see Tables 2 and 3). However, the lower the temperature in the top storage vessel, the more energy must be consumed in the distillation process. In practice, the mixture in the top storage vessel should be kept in a moderate temperature, at which the reaction rate is low enough. 6.2. Effect of Location of Side Withdrawal Stage. The location of the side withdrawal stage is an important design parameter for a BSS. Cui et al.17 discussed the optimal side withdrawal stage for a BRS. The optimal side withdrawal stage in a BRS is mainly related to the relative volatilities of the components. In a BRS, 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. Since the mixture is mainly separated in the column, the effects of relative volatilities on the optimal side withdrawal stage in a BSS are similar to that in a BRS. Tables 6 and 7 show the effects of a side withdrawal stage in a BSS. Since the relative volatilities RABand RBC are almost equal in our calculation, the optimal stages are near the middle point of the column. 6.3. Effects of Reboiler Ratio and Side Reflux Ratio. The reboiler ratio and side reflux ratio are important operation parameters for a BSS. The reboiler ratio and side reflux ratio can affect each other, and different combinations of reboiler ratio and side reflux ratio result in different types of product withdrawal. If the intermediate component converts to heavy impurity, the product is only withdrawn from the side withdrawal stage in the optimal operation mode for a BSS. This is the same as that in a BRS for purification of the intermediate component from light and heavy impurities with a decomposing reaction, which is discussed in our previous paper.17 If the intermediate component converts to light impurity, the product is withdrawn from the side withdrawal stage first and then it is withdrawn from the reboiler in optimal operation mode for a BSS. Other combinations of reboiler ratio and side reflux ratio that are not in optimal operation mode will result in other types of product withdrawal; for example, the product can be withdrawn from the reboiler and the side withdrawal stage simultaneously in a period of the distillation process with some combinations of the reboiler and side reflux ratios. 6.4. Effect of Holdup in the Reboiler. The effect of holdup in the reboiler on the recovery of the product is illustrated in Tables 8 and 9. The holdup in the reboiler has little effect on

TTOP H* N NS (K) 0.01 0.02 0.03 0.04 0.05 a

8 8 8 8 8

Bp Bp Bp Bp Bp

k0 (h-1)

RN1

RN2

RS

xBB

xBS

RY

1 × 10 1 × 1019 1 × 1019 1 × 1019 1 × 1019

0.9743 0.9743 0.9855 0.9893 0.9890

0.8174 0.8174 0.8278 0.8042 0.3231

0.8282 0.8282 0.8611 0.8479 0.8238

0.9195 0.9195 0.9442 0.9457 0.9125

0.9548 0.9548 0.9251 0.9671 0.9735

0.8812 0.8522 0.8121 0.8104 0.7921

19

The abbreviation “Bp” denotes the boiling point.

the recovery of the product (see Table 8), when the intermediate component converts to heavy impurity. However, the recoveries of the product increase as the holdups in the reboiler decrease, if the intermediate component converts to light impurity (see Table 9). This results from the different product withdrawal types in a BSS. When the intermediate component converts to heavy impurity, the product is only withdrawn from the side withdrawal stage in an optimal operation mode, so the holdup in the reboiler has little effect on the recovery of the product. When the intermediate component converts to light impurity, the product is withdrawn from the side withdrawal stage and the reboiler in an optimal operation mode, and the holdup in the reboiler affects the product withdrawn from the reboiler. When the holdup in the reboiler increases, the recovery of the product withdrawn from the reboiler greatly decreases, and the total recovery of the product decreases, even if the recovery of the product withdrawn from the side withdrawal stage may increase. Sorensen5 noted that the holdup in the reboiler in a batch stripper must be very low, but a sufficiently low holdup in the reboiler may be difficult to achieve in practice. The same problem also occurs in a BSS, if the intermediate component converts to light impurity. Our research group developed a type of low hold up reboiler called “wet-type dry still”, where the liquid distilled in the reboiler is directly heated by immiscible liquid filled in the reboiler.23 In this paper, the “wet-type dry still” is not considered in our calculation; however, in practice, this type of reboiler may be used in a BSS. 7. Conclusion Batch distillation in a batch stripper with a side withdrawal (BSS) can be used for the purification of heat-unstable compounds from light and heavy impurities. The process was simulated by a dimensionless dynamic model and optimized by simulated annealing (SA). The results show that the recovery of heat-unstable compounds in a BSS is larger than that in a batch stripper (BS), especially in the case of the heat-unstable compound converting to heavy impurity. The configuration of the column should be matched with the type of the degradation reaction. Compared with batch distillation in a batch rectifier with a side withdrawal (BRS), batch distillation in a BSS is more suitable for purification of a heat-unstable compound that converts to light impurity. The effects of operational and design parameters for batch distillation in a BSS were also investigated. The recovery of the product increases with the decreasing temperature in the top storage vessel. There is an optimal side

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Ind. Eng. Chem. Res., Vol. 49, No. 14, 2010

withdrawal stage in a BSS, and the optimal side withdrawal stage is determined by the relative volatilities of the components. The product withdrawal type is relative to the reboiler ratio, side reflux ratio, and the type of the degradation reaction. The holdup in the reboiler has little effect on the recovery of the product, if the intermediate component converts to heavy impurity. When the intermediate component converts to light impurity, the recoveries of the product increase as the holdups in the reboiler decrease. Notation Parameters a, b, c ) constants of the Antoine equation E a ) activation energy (kJ/mol) H0 ) amount of feedstock (mol) Hj ) holdup on stage j (mol) Hj* ) dimensionless holdup on stage j k0 ) reaction rate constant (h-1) NS ) side withdrawal stage Rj* ) dimensionless reaction rate on stage j RN ) internal reboiler ratio RS ) internal side reflux ratio Ry ) recovery of the product RyE ) recovery enhancement t0 ) reference time (h) TTOP ) temperature in the top storage vessel (K) V ) vapor flow rate (mol/h) xBB ) purity of component B in the reboiler, a cut location for product withdrawn from the reboiler xBBav ) average purity of product collected in the bottom receiver xBMB ) maximum purity of component B in the reboiler during product withdrawal period xBMS ) maximum purity of component B on side withdrawal stage during product withdrawal period xSB ) purity of component B on side withdrawal stage, a cut location for product withdrawn from the side withdrawal stage xBSav ) average purity of product collected in the side receiver xj,i ) liquid composition of component i on stage j xSpec ) product purity specification p

Figure A1. Scheme of a batch stripper with side withdrawals.

whole (see Figure A1), the mass balance of the condenser and storage vessel is as follows: d(H1x1,i) ) VK2,ix2,i - L1x1,i + νir1 dt

(i ) 1, ..., c)

(A3) where H is the molar holdup, V the vapor flow rate, L the liquid flow rate, ν a stoichiometric number, r the reaction rate, x the liquid composition, and K the equilibrium constant. dH1 ) V - L1 + νTr1 dt

(A4)

where

Greek Letters τf ) total dimensionless distillation time

c

νT )

Appendix

∑ν

(A5)

i

i)1

Figure A1 shows a batch distillation column provided with N theoretical stages and N side withdrawals. A storage vessel is placed at the top of the column, and a mixture consisting of c components is loaded into the storage vessel. The model is based on the following assumptions: equilibrium stage column, constant vapor flow on each stage, constant molar liquid holdup on each stage, negligible vapor holdup and fluid dynamic lags, adiabatic operation. Suppose the following reaction occurred:

∑νA

i i

)0

(A1)

∏x

qi j,i

H1

dx1,i ) VK2,ix2,i - x1,i(V + νTr1) + νir1 dt

(A6)

For theoretical stage j: Hj

dxj,i ) Wj-1Lj-1xj-1,i + VKj+1,ixj+1,i - Ljxj,i - VKj,ixj,i + dt νirj (j ) 2, ..., N - 1; i ) 1, ..., c) (A7)

where W is the liquid ratio. If the side withdrawal stage is stage M, the internal side reflux ratio RS is

The reaction rate is expressed by rj ) kHj

Combining eqs A3 and A4, we obtained

(A2)

where qi is an empirical constant. Mass balance: The condenser can be placed in the storage vessel, so that the condenser and the storage vessel can be considered as a

RS ) WM Wj-1Lj-1 - Lj + νTrj ) 0 For the reboiler:

(A8) (j ) 2, ..., N - 1) (A9)

Ind. Eng. Chem. Res., Vol. 49, No. 14, 2010

HN

dxN,i ) WN-1LN-1xN-1,i - VKN,ixN,i + νirN dt LNxN,i (i ) 1, ..., c) (A10)

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The dimensionless mathematical model consists of eqs A17, A18, and A20-A22, which is solved using a GEAR integration method. The dimensionless model shows that the processes are identical with the same parameters: H*j ,t0, Wj, k0, Ea, Vi, and qi.

The internal reboiler ratio is RN ) WN ) 1 -

LN V

(A11)

Substituting eq A11 into A10, we obtain HN

dxN,i ) WN-1LN-1xN-1,i - VxN,i[KN,i + (1 - WN)] + νirN dt (A12) WN-1LN-1 - (2 - WN)V + νTrN ) 0

(A13)

Phase equilibrium: yj,i ) Kj,ixj,i

(A14)

Summation equation: c

∑x

j,i

-1)0

(A15)

-1)0

(A16)

i)1 c

∑y

j,i

i)1

SupposeL*j ) Lj/V; then, according to eqs A9and A13, we obtain L*N-1 ) L*j-1 )

(2 - WN) - (νTrN /V) WN-1

L*j - (νTrj /V) Wj-1

(A17)

(j ) N - 1, ..., 2)

(A18)

Suppose dτ )

V dt dt ) 0 0 H t

(A19)

where H0 is the feed charge, t0 a reference time (the time needed to totally evaporate the feed stock), and τ the dimensionless distillation time. Suppose H*j ) Hj/H0, eqs A6, A7, and A12 can be changed to dimensionless equations: H*1 H*j

(

)

νTr1 νir1 dx1,i ) K2,ix2,i - x1,i 1 + + V V dτ

(A20)

νirj dxj,i ) Wj-1L*j-1xj-1,i - (L*j + Kj,i)xj,i + Kj+1,ixj+1,i + V dτ (A21)

H*N

νirN dxN,i ) WN-1L*N-1xN-1,i - xN,i[KN,i + (1 - WN)] + V dτ (A22)

For the reaction item:

( )( ( )

)∏

Ea Hj /H0 xqj,ii ) RT V/H0 Ea H*t0 k0 exp xqj,ii (A23) RT j where Ea is the activation energy and k0 is the reaction rate constant.

R*j )

Hj rj )k V V

∏x

qi j,i

) k0 exp -

∏

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ReceiVed for reView October 6, 2009 ReVised manuscript receiVed March 25, 2010 Accepted May 25, 2010 IE901558C