Comparative Study of Modified Simulated Moving Bed Systems at

Ind. Eng. Chem. Res. 2006, 45, 6251-6265

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Comparative Study of Modified Simulated Moving Bed Systems at Optimal Conditions for the Separation of Ternary Mixtures of Xylene Isomers Anjushri S. Kurup, K. Hidajat, and Ajay K. Ray* Department of Chemical and Biomolecular Engineering, National UniVersity of Singapore, 4 Engineering DriVe 4, Singapore 117576

In this paper, separation of a ternary mixture based on simulated moving bed (SMB) technology is studied. The conventional four-zone SMB system for binary separation was modified into different configurations to facilitate simultaneous collection of all three components. The performances of these systems were compared at optimal conditions based on multiobjective optimization for an industrial-scale separation of C8 aromatics. Simultaneous recovery of p-xylene, ethylbenzene, and mixtures of o- and m-xylene with the highest possible purities are considered. The effect of a reflux stream addition containing one of the components is also investigated. It was observed that, as the separation becomes more difficult, the five-zone SMB performs better than the modified four-zone SMB for ternary separation, while at the same time consuming a lesser amount of desorbent. Efficacies in overall performances of the different modified SMB configurations are discussed. Rigorous multiobjective optimization is performed using a nontraditional optimization technique based on an adaptation of a genetic algorithm, elitist nondominated sorting genetic algorithm with jumping genes. Introduction The simulated moving bed1 (SMB) technology, developed in the early 1960s by the Universal Oil Products Company, is a process chromatographic method that enables a mixture of substances to be continuously separated into two fractions. The SMB basically consists of packed columns interconnected to each other that are arranged in a circular array as shown in Figure 1. Switching of the ports is done to mimic the countercurrent motion between the solid and the fluid phase. Figure 1 shows a four-zone SMB system with eight columns. The inlet and outlet ports divide the circular array of the columns into four sections. Using a suitable combination of adsorbent and desorbent, the feed stream is separated into two withdrawal streams containing the pure components of a binary or pseudobinary mixture. The SMB principle of continuous separation to obtain pure substances has been implemented successfully to various industrial-scale separations, such as in the pharmaceutical industry (for chiral compounds such as steroids, peptides, and antibiotics), the food industry (for fatty acids and carbohydrate mixtures such as a fructose-glucose mixture), the petrochemical industry (for C8 hydrocarbons, e.g., xylene/ toluene), and the biochemical industry (for citric acid, phenylalanine, etc.). The SMB is a well-established separation technology for the separation of binary mixtures. The four-zone SMB for binary separation has been extensively studied by many groups and is now well-understood.2-6 However, the use of SMB systems for multicomponent separations has not been studied extensively. The major limitation of an SMB is the inability to purify a ternary mixture into three different pure fractions in a single unit. As a consequence, several concepts have been proposed to achieve this goal through various modifications keeping the advantages of SMB. Hashimoto et al.3 employed a four-zone conventional SMB, but packed with two different adsorbents, while Kearney and Hieb7 used a variation of the working flow rates with respect to time within a given switching period. * Correspondingauthor.Fax: +6567791936.E-mail: [email protected].

Figure 1. Four-zone eight-column conventional simulated moving bed (SMB) system for binary separation.

Nicoud8 developed an SMB concept consisting of five zones by adding a side stream for the collection of the component with the intermediate adsorption affinity. Nicoud et al.9 also described extending on the concept of five zones by additionally changing the desorbent strength in the five zones. Another concept developed is based on a novel operation technique, wherein the feed is discontinuously added only during a part of the total cycle time while operating in the batch chromatographic mode. For the remaining cycle time, the system is switched to the SMB mode of operation with no feed. This process was commercialized by the Japan Organo Company. Mata and Rodrigues10 developed a pseudo-SMB model based on the above discontinuous process. Wooley et al.11 proposed a nine-zone SMB for the separation of sugars from acetic acid and sulfuric acid produced from a biomass hydrolyzate. Hritzko et al.12 have presented a standing wave design of a tandem SMB process for the multicomponent separation. Wankat13 developed

10.1021/ie0505413 CCC: $33.50 © 2006 American Chemical Society Published on Web 08/01/2006

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Ind. Eng. Chem. Res., Vol. 45, No. 18, 2006

Figure 2. Schematic diagram of modified simulated moving bed system: (a) modified configuration 1 (MC1) and (b) modified configuration 2 (MC2)

seven cascades of SMB system for ternary separation based on linear isotherms and established minimum desorbent usage and productivity based on an equilibrium model. Kim et al.14 developed three cases of single cascades, similar to the approach described by Nicoud8 and Beste and Arlt,15 and determined (using equilibrium theory) favorable conditions to achieve good separations for these designs. Kim et al.14 simulated the system using Aspen Chromatography and studied the effect of different feed compositions and the mass-transfer rates. However, they only considered linear isotherms. Recently, Kurup et al.16 extended the work of Kim et al.14 in the presence of several nonidealities such as high mass-transfer resistance, lower adsorption selectivity, nonlinearity in adsorption isotherm, etc. Besides, they compared the performances of the modified SMB systems at optimal conditions considering multiple objectives. However, Kurup et al.16 studied modified SMB systems assuming just one column in each section. In the application of SMB systems for industrial processes, one generally requires more than one column in each section. The reasons for having multiple columns can be numerous. Ruthven and Ching2 claimed that at least two columns per section are required to provide

enough flexibility in achieving countercurrent separation. Moreover, having more columns in each section helps in revamping the performance deterioration caused by the presence of nonidealities in real systems, such as low mass-transfer rates, high degree of nonlinearity in adsorption isotherms, etc. In our earlier paper,16 two different modified configurations of SMBs for ternary separation systems were studied at optimal conditions (considering multiple objectives), where we considered only one column per section for a hypothetical separation problem in which degree of separation difficulty, adsorption isotherm, and mass-transfer rates were assumed arbitrarily. In this paper, we first extend our earlier study16 on modified SMB systems under nonideal conditions to include more than one column per section for the hypothetical separation problem. It is important to see the effect of having multiple columns in different sections on the performance of the modified configurations. Subsequently, further modifications for an SMB are proposed, and the modified systems are investigated for the separation of C8 aromatics17,18 at optimal conditions. The optimization studies were performed considering multiple objectives19-21 using an elitist nondominated sorting based genetic algorithm with jumping genes,20,21

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Figure 3. Schematic diagram of further modification of MC2 configuration: (a) modified configuration MC2A and (b) modified configuration MC2B

and it is needless to emphasize the importance of multiobjective optimization either at the operating stage or at the design stage for any SMB system.22-29 Modified SMB Systems To achieve separation between the components in the conventional four-section SMB system (Figure 1), the internal flow rates of the fluid phases within the four sections, and the switching time, ts (which defines the imaginary solid-phase velocity), have to be specified appropriately. The two modified configurations of SMB systems described by Kim et al.14 are studied under optimal conditions for nonideal systems for ternary separation by Kurup et al.16 and are shown in Figure 2 parts a and b. Throughout this work, we have assumed that the feed consists of a ternary mixture of components A, B, and C, with A being the least-adsorbed component, C being the mostadsorbed component, and B being the component with intermediate adsorption affinity compared to A and C. The first modified configuration, MC1 (Figure 2a), is a fivezone cascade system. It is very similar to the conventional fourzone SMB (Figure 1) used for binary separation except that, for the recovery of the intermediate component B, an additional

section is present. An additional product outlet port is added in Section Q for the collection of the middle component B. Hence, one can consider Section Q of a conventional SMB to be split into two sections, Q1 and Q2, because of the addition of the additional port. Similar to the conventional SMB, each zone in MC1 also contains at least one fixed column (bed) and has to fulfill distinct specified tasks, i.e., in Sections Q1, Q2, and R, countercurrent separation takes place, while in Sections P and S, as usual the solid and the fluid phases are regenerated, respectively. To achieve separation between the components, the internal flow rates of the fluid phases have to be specified such that there is countercurrent separation between B and C in Section Q1 and separations between A and B in Sections Q2 and R. The second modified configuration, MC2 (Figure 2b), is a four-zone system similar to a conventional SMB system (Figure 1) except that it differs from the traditional four-zone SMB because of the break between Sections P and Q and the use of an additional desorbent stream, D2. This system is more like a batch chromatographic column since there is no recycle of desorbent within the system. However, even in this configuration, the solids do still move countercurrently because of the switching of the ports, similar to the conventional SMB. The component with the least adsorption affinity, A, is collected

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Table 1. Description of the Multiobjective Optimization Problems for the Hypothetical Ternary Separation Problem problem no.

objective function

decision variables

fixed parameters

MC1-P1

max(PurA + PurC) max PurB

MC2-P1


dcol ) 1.38 cm, Lcol ) 166.67 cm Ncol ) 7, p/q1/q2/r/s ) 3/1/1/1/1 QF ) 60 cm3/min QS ) 33.33 cm3/min same as MC1-P1 except Ncol ) 6, p/q/r/s ) 3/1/1/1, and QS is not fixed

MC2A-P1


MC2B-P1


3 e ts e 8 min 30 e QRa e 150 cm3/min 280 e QD e 700 cm3/min 50 e QEx1 e 500 cm3/min 3 e ts e 8 min 0.19 e tp/ts e 0.82 30 e QRa e 150 cm3/min 20 e QD1 e 100 cm3/min 240 e QD2 e 600 cm3/min 3 e ts e 8 min 30 e QRa e 150 cm3/min 20 e QD1 e 100 cm3/min 240 e QD2 e 600 cm3/min 1 e p1 e 2 same as MC2A-P1 and 0.19 e tp/ts e 0.82

as usual at the raffinate port. However, the product collection at the extract port is such that the component with intermediate adsorption capacity, B, is collected for some period (0 < t < tp), while the most strongly adsorbed component, C, is collected for the remainder of the switching time (tp < t < ts) (as shown in Figure 2b). The collection time of intermediate product B, tp, is decided based on the breakthrough time of C, i.e., the time the most strongly adsorbed component C starts to desorb. This process is repeated for every switching of the ports. MC1 is almost similar to the conventional four-zone SMB except that there is an additional section, and hence, having more columns in each section in MC1 will have a similar effect to that of having multiple columns in a four-zone conventional SMB. When designed properly, MC1 with multiple columns should either give better or at least equal performance in terms of purity (or recovery) of the desired product streams when compared with MC1 having only one column in each section. However, this does not necessarily hold true for configuration MC2. When there is only one column in Section P, the function of this section is equivalent to a single-column chromatographic fixed bed within the time of one switching. The desorbent elutes the two components that have peaks separated along the length of the column. However, when multiple columns are present, these peaks are spread along the section across different columns. Since the switching operation is done by moving the ports by each column (and not by section), one can see that component C (the most strongly adsorbed component) in this case cannot be collected in the similar fashion as described for configuration MC2 with one column in each section. Hence, it is necessary to modify configuration MC2 slightly to facilitate collection of component C at the location where higher purities of C can be obtained. Two modifications are proposed and are shown in Figure 3, as MC2A and MC2B. Both the modifications are based on the fact that, when there are multiple columns, it is improper to have the same outlet stream for both components B and C, and hence, C must be collected upstream of the collection port for component B. The presence of this additional outlet port for C splits Section P into two Subsections, P1 and P2. The modified configuration MC2A (Figure 3a) is almost similar to MC1, barring the fact that Section P and Section Q are disconnected. However, the modified configuration MC2B (Figure 3b) is more like MC2. In this case, B is collected from the end of Section P for some time until tp (≡ ethylbenzene > m-xylene > o-xylene (least strongly adsorbed). Following the earlier convention for the hypothetical ternary separation example, one can identify (m-xylene + o-xylene) as component A (component with least affinity for adsorption), ethylbenzene as component B (component with intermediate affinity), and p-xylene as component C (most strongly adsorbed

Table 3. Description of the Multiobjective Optimization Problems for the Ternary Separation of C8 Aromatics problem no.

objective function

decision variables

constraints

fixed parameters

MC1-P2

max(Pur_moX + Pur_pX) max(Pur_EB)

Pur_moX g 60% CmoX,Ex2 e 1%

MC2A-P2


dcol ) 4.117 m, Lcol ) 1.135 m Ncol ) 27, p/q1/q2/r/s ) 6/6/6/6/3 QF ) 0.3 m3/min QS ) 5.39 m3/min same as MC1-P2 except p1/p2/q/r/s ) 6/6/6/6/3 and QS is not fixed

MC2B-P2


1 e ts e 2 min 0.8 e QRa e 3 m3/min 2.8 e QD e 5 m3/min 0.1 e QEx1 e 3 m3/min same as MC1-P2 and 5.5 e QD1 e 7 m3/min 2.8 e QD2 e 6 m3/min 0.5 e QEx1 e 6 m3/min same as MC2A-P2 and 0.19 e tp/ts e 0.82

Pur_moX g 60% CmoX,Ex2 e 1% Pur_moX g 60% CmoX,Ex2 e 1%

same as MC2A-P2


Figure 7. Pareto optimal solutions and the corresponding decision variables for the ternary separation of C8 aromatics (Problem MC1-P2). Table 4. Recovery and Purity Values for Few Selected Points from the Pareto for MC1-P2

a

point

Pur_EB

Pur_moX

Pur_pX

Rec_EB

Rec_moX

Rec_pX

Rec_pXTa

7A 7B 7C

85.2 75.7 55.4

94.8 97.4 98.1

90.3 98.8 99.9

57.3 85.9 90.4

100 100 100

93.5 83.5 57.5

99.3 99.4 99.6

Calculated by considering p-xylene from both extract streams, Ex1 and Ex2.

Figure 8. Concentration profiles of the four components of C8 aromatics in MC1 at cyclic steady state (at the middle of the switching time) corresponding to the optimal point 7A shown in Figure 7.

component). The purity and recovery of the stream collecting m-xylene plus o-xylene were named as Pur_moX and Rec_moX, respectively. Similarly, the purities and recoveries for ethylbenzene and p-xylene were named as Pur_EB, Rec_EB, and Pur_pX, Rec_pX, respectively. On the basis of similar sensitivity studies as in Problem 1, it was observed that both Pur_moX and Pur_pX are conflicting with respect to Pur_EB. When high Pur_moX and high Pur_pX can be achieved, Pur_EB is low. Moreover, it is easier to obtain high Pur_moX and high Pur_pX, but it is difficult to obtain very high Pur_EB. Hence, the optimization problem was formulated similar to the one discussed earlier in Problem 1, viz., maximizing the total purity of streams containing m-xylene plus o-xylene (Pur_moX) and p-xylene (Pur_pX) as one objective function while simultaneously maximizing Pur_EB as the other objective function. However, it was observed that, because of the difficulty in separation between m-xylene and ethylbenzene, the stream collecting ethylbenzene was contaminated with m-xylene. It is important that the ethylbenzene stream be devoid of m-xylene and o-xylene. However, contamination of this stream with

p-xylene may be acceptable, since in that case, one can still separate p-xylene from ethylbenzene by passing it through another SMB binary separation unit. Hence, two constraints were incorporated in the optimization formulation as CmoX,Ex2 e 1% and Pur_moX g 60%. The second constraint is added with the intention that more of ethylbenzene is pushed toward the extract stream, thus increasing its recovery. The mathematical formulations of the different optimization problems explained above are summarized in Table 3. The various results obtained are discussed below. Note that configuration MC2 was not considered for this problem for obvious reasons, as explained before with Problem 1. Instead, application of the modified configurations, MC2A and MC2B, are considered and discussed below. (a) Problem MC1-P2: Ternary Separation of C8 Aromatics in MC1. Figure 7 shows Pareto optimal solutions and corresponding decision variable plots for the separation of C8 aromatics in configuration MC1. The figure shows that the performance of the system is not very good compared to the results obtained with Problem 1. This is expected since, in this case, the separation is difficult because the adsorption selectivity is quite low in addition to the nonlinearity in the adsorption isotherm. The maximum Pur_EB achievable is 85.2% when Pur_moX and Pur_pX are 94.7% and 90.3%, respectively. The maximum Pur_moX and Pur_pX achievable are 98.11% and 99.4%, respectively, but then Pur_EB drops to 55.4%. One can also observe that, along the Pareto curve, as Pur_EB increases, QD decreases. A similar observation was made in our earlier study.16 The optimum values for the decision variables, ts, QRa, and QEx1, were found to be almost constant along the Pareto. The respective values are ts ≈ 1.0 min, QRa ≈ 1.8 m3/min, and QEx1 ≈ 2.2 m3/min. The respective recoveries of m-xylene and o-xylene, ethylbenzene, and p-xylene for three representative points (shown in Figure 7) along the Pareto line are given in Table 4. Recovery of p-xylene at the extract stream Ex1 as well as total p-xylene recovery calculated by adding the amount of

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Figure 9. Pareto optimal solutions and the corresponding decision variables for the ternary separation of C8 aromatics in MC2A and MC2B (Problems MC2A-P2 and MC2B-P2). Table 5. Recovery and Purity Values for Few Selected Points from the Pareto for MC2A-P2 and MC2B-P2 config.

point

Pur_EB

Pur_moX

Pur_pX

Rec_EB

Rec_moX

Rec_pX

Rec_pXT

MC2A

9A 9B 9C 9D

39.0 36.4 39.5 36.9

97.4 97.9 98.2 98.3

71.1 99.9 67.2 99.8

60.8 89.6 40.6 90.0

100 100 100 100

42.8 7.4 62.4 8.6

98.6 99.2 98.6 98.6

MC2B

Table 6. Comparison of Performances between MC1, MC2A, and MC2B for the Separation of C8 Aromatics MC1

Figure 10. Concentration profiles of the four components of C8 aromatics in MC2A at cyclic steady state (at the middle of the switching time) corresponding to the optimal point 9A shown in Figure 9.

p-xylene recovered at both extract streams (Ex1 and Ex2) is reported in Table 4. The tabulated data show that, although the recovery values of p-xylene may not look very attractive at Ex1, the total p-xylene recovery is almost 100%. The extract stream (Ex2), which contains both ethylbenzene and p-xylene, can be further separated into pure streams of ethylbenzene and p-xylene in another (four-zone) SMB binary unit. This is inevitable, since it is impossible to achieve 100% purity of ethylbenzene at the extract port Ex2, and consequently, this stream will always be contaminated with p-xylene. One should also recollect that the

Pur_EB (%) Pur_moX (%) Pur_pX (%) Rec_EB (%) Rec_moX (%) Rec_pX (%) Ncol Lcol (m) QD (m3/min) ARb (m3) 104 Prc (min-1) DRd

85.2 94.8 90.3 57.3 100 93.5 27 1.135 3.93 408 7.35 13.1

55.4 98.1 99.9 90.4 100 57.5 27 1.135 4.53 408 7.35 15.1

MC2A 39.0 97.4 71.1 60.8 100 42.8 27 1.135 9.22a 408 7.35 30.7

36.4 97.9 99.9 89.6 100 7.4 27 1.135 11.94a 408 7.35 39.8

MC2B 39.5 98.2 67.2 40.6 100 62.4 27 1.135 9.11a 408 7.35 30.4

36.9 98.3 99.8 90.0 100 8.6 27 1.135 9.91a 408 7.35 33.0

b Adsorbent requirement, AR (m3) ) a Q (m3/min) ) Q D D1 + QD2. NcolVcol. c Productivity, Pr [(m3/min of feed)/(m3 of solid)] ) QF/AR. d Desorbent requirement, DR [(m3/min)/(m3/min of feed)] ) Q /Q . D F

feed concentration of the C8 aromatics is more biased toward not-so-desirable m-xylene (49.7%), while amounts of p-xylene (23.6%) and ethylbenzene (14%) are present in much lower concentrations. This obviously has an adverse effect on the overall separation process, making the recovery of ethylbenzene and p-xylene more difficult. Figure 8 shows the internal concentration profiles of p-xylene, m-xylene, o-xylene, and ethylbenzene for one of the points on the Pareto (Point 7A shown in Figure 7), where Pur_moX ≈ 94.8%, Pur_EB ≈


Figure 11. Schematic diagram of modified SMB configurations when a reflux stream is added: (a) modified configuration 3 (MC3) and (b) modified configuration 4 (MC4A).

Table 7. Description of the Multiobjective Optimization Problems for the Ternary Separation of C8 Aromatics on Modified Configurations with Reflux Streams problem no.

objective function

decision variables

constraints

fixed parameters

MC3-P2


1 e ts e 2 min 0.8 e QRa e 3 m3/min 2.8 e QD e 5 m3/min 0.1 e QEx1 e 3 m3/min 0.01 e QRe e 0.1 m3/min 1e q21 e 4 same as MC3-P2 and 5.5 e QD1 e 7 m3/min 2.8 e QD2 e 6 m3/min 0.5 e QEx1 e 6 m3/min 1e q2 e 4 same as MC4A-P2 and 0.19 e tp/ts e 0.82

Pur_moX g 60%

same as MC1-P2

MC4A-P2


MC4B-P2


85.2%, and Pur_pX ≈ 90.3%. It can be seen that the collection stream for ethylbenzene, the extract port Ex2, is always contaminated with at least small amount of p-xylene. Considering these facts, the five-zone SMB configuration when coupled with another SMB in series can be a very attractive option for the simultaneous recovery of p-xylene and ethylbenzene from the mixture of C8 aromatics.

CmoX, Ex2 e 1%

same as MC1-P2

same as MC1-P2

(b) Problems MC2A-P2 and MC2B-P2: Ternary Separation of C8 Aromatics in MC2A and MC2B. Similar twoobjective optimization problems were formulated for the separation of C8 aromatics in the proposed modified configurations MC2A and MC2B. The detailed mathematical formulations described as MC2A-P2 and MC2B-P2 are given in Table 3. The Pareto optimal solutions and the corresponding decision

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Figure 12. Pareto optimal solutions and the corresponding decision variables for the ternary separation of C8 aromatics in configuration MC3 (Problem MC3-P2) when additional reflux stream is used.

variables are shown in Figure 9. One can see that the performance achieved in this case is quite poor. It is seen that high Pur_EB cannot be achieved with this system, even though high values of Pur_moX and Pur_pX can be obtained. For example, the maximum Pur_EB achievable is only 39.4% with Pur_pX dropping to as low as 67.3%, although Pur_moX remains more or less constant ∼98% all along the Pareto. The highest Pur_pX achievable is 99.8% (when Pur_moX ≈ 98.3%), but Pur_EB at that time reduces to as low as 36.9%. Once again, it can be observed that MC2B performs slightly better than MC2A when Pur_pX is considered. For both MC2A and MC2B, the optimum values for decision variables ts, QRa, and QD1 were found to be almost constant. The values for MC2A are ts ) 1.1 min, QRa ) 1.74 m3/min, and QD1 ) 6.4 m3/min. The respective optimal values for MC2B are 1.1 min, 1.2 m3/min, and 6.3 m3/ min. The recoveries of m-xylene plus o-xylene, ethylbenzene, and p-xylene for two extreme points on the Pareto for both MC2A and MC2B are given in Table 5. One can see that, for lower values of purity of ethylbenzene, Rec_pX decreases very drastically if one considers the p-xylene collection stream (Ex1) alone. However, recovery of p-xylene collectively in both extract streams (Rec_pXT) is quite high (∼99%). Figure 10 shows the internal concentration profiles of the four components of C8 aromatics for one of the optimal points for MC2A configuration on the Pareto (point 9A in Figure 9), where Pur_moX ≈ 97.4%, Pur_EB ≈ 39.0%, and Pur_pX ≈ 71.1%. From the concentration profile, one can see that the dilution of the components is very high for these systems when compared to Figure 8. From the optimal solutions, it is quite clear that modified five-zone SMB configuration, MC1, is a much better option for the separation

of C8 aromatics compared to MC2 and its modified versions, MC2A and MC2B. MC1 results in much higher purities of ethylbenzene along with high values for Pur_moX and Pur_pX compared to MC2. Table 6 shows the performance comparison between the two configurations in the case of separation of C8 aromatics. Two points corresponding to the highest and lowest purity of the stream containing ethylbenzene are chosen from the Pareto curves obtained for MC1, MC2A, and MC2B. Parameters such as the adsorbent requirement, productivity, and desorbent requirement are tabulated. It can be seen that the desorbent requirements for the configurations MC2A and MC2B are almost twice that of MC1. This result is also in agreement with the observations made for Problem 1 discussed in the earlier paper,16 where it was found that, as the separation becomes more difficult, MC1 performs better than MC2 while at the same time consuming a lesser amount of desorbent. Effect of Addition of a Reflux Stream Containing Pure Ethylbenzene. Nicoud30 explained the importance of introducing a reflux stream rich in one of the components to the conventional four-zone SMB for binary separation. For systems which involve competitive adsorption isotherms, a low concentration of one of the components compared with the other causes a lowering of the adsorption selectivity. In such cases, it is difficult to obtain high purities and high recoveries. For example, we consider a binary system with components A and B (A is the weakly adsorbed component and is present in a large amount in the feed mixture) that have to be separated in a conventional four-zone SMB system (as in Figure 1) comprising Sections P, Q, R, and S. If an additional section is created


Figure 13. Pareto optimal solutions and the corresponding decision variables for the ternary separation of C8 aromatics in configuration MC4A and MC4B (Problems MC4A-P2 and MC4B-P2) when an additional reflux stream is used.

between Sections P and Q by introducing a reflux stream that is rich in component B, a drastic adjustment in the concentration profile takes place. The concentration of B increases at the extract withdrawal point, and as a result, component A is more diluted with regard to component B. Generally, component B elutes component A better than the desorbent does. Thus, separation between A and B can be improved by adding this reflux stream, facilitating the collection of B with high purity. From the results obtained for the modified configurations, MC2A and MC2B, it was observed that high purity and recovery of component B is very difficult to obtain for nonideal systems such as mixture of C8 aromatics. The feed composition for the C8 aromatics is such that component A (m-xylene + o-xylene) dominates the feed mixture. It will, therefore, be worthwhile to see the effect of addition of a reflux stream containing pure ethylbenzene. The configurations MC1, MC2A, and MC2B were accordingly further modified to form new configurations, MC3, MC4A, and MC4B. The modified configurations MC3 and MC4A are shown in Figure 11. The configuration MC4B is not shown for brevity, as it is easy to visualize configuration MC4B based on MC4A (similar to the difference in configuration of MC2B from MC2A). Table 7 summarizes new optimization problems formulated similar to the optimization exercise performed earlier. (a) Problem MC3-P2: Ternary Separation of C8 Aromatics in MC3. This problem (MC3-P2) was solved to see the effect of adding a reflux stream to the five-zone SMB system. Results obtained from the optimization study are shown in Figure 12. Three Pareto points (corresponding to minimum, middle, and maximum Pur_EB values) obtained in problem MC1-P1 are also shown in Figure 12. One can see that, by adding a reflux stream

(as shown in Figure 11a), Pur_EB and Pur_pX can be improved. Rec_moX was seen to be almost 100%. The plots for Rec_EB and Rec_pX are also shown in Figure 12. When compared with the results obtained from the problem MC1-P2, the figure shows that Rec_EB has improved drastically because of the introduction of an additional reflux stream. However, Rec_pX drops significantly when compared to MC1-P2 as Pur_EB decreases. However, one will always tend to operate the system such that one can get both Pur_pX and Pur_EB as high as possible, at which point the Rec_pX value seems to be reasonably good. The column configuration chosen was 6/6/4/2/6/3 for p1/p2/ q1/q2/r/s, i.e., six columns in Section Q for MC1-P2 were divided between Sections Q1 and Q2 as four and two columns, respectively, for MC3-P2. The reflux flow rate was found to be insensitive, and the values were chosen between 0.08 and 0.09 m3/min. Optimum values for the decision variables such as ts and QRa were found to be ∼1.06 min and ∼1.84 m3/min, respectively, while the values of desorbent flow rate are shown in Figure 12. (b) Problems MC4A-P2 and MC4B-P2 (Effect of Additional Reflux Stream on MC2A and MC2B): Ternary Separation of C8 Aromatics in MC4A and MC4B. Similar two-objective optimization problems were formulated for the separation of C8 aromatics in the proposed modified configurations MC4A and MC4B to find out the effect of addition of the reflux stream. The detailed mathematical formulations described as MC4A-P2 and MC4B-P2 are given in Table 7. The Pareto optimal solutions and the corresponding decision variables are shown in Figure 13. The improvement in the system performance is more pronounced in this case than in the previous optimization run. One can see that much higher Pur_EB can be

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obtained with the addition of reflux. The maximum Pur_EB is ∼66% in MC4A and MC4B as compared to 40% in MC2A. Rec_moX is ∼100%, irrespective of whether additional reflux is used or not. The variations of Rec_EB and Rec_pX when reflux stream is used are also shown in Figure 13. As seen in the previous case, it is observed here too that, although Rec_EB increases, Rec_pX decreases quite drastically. In the earlier case (MC3-P2), when Pur_EB was high, the Rec_pX was seen to be comparable with the system without a reflux stream (MC1P2). However, in this case, it is seen that, even at high Pur_EB values, Rec_pX is much lower than the system without a reflux stream (MC2A-P2). The optimal values of the decision values such as ts, QRa, and QD1 were seen to be around 1.1 min, 1.41 m3/min, and 6.23 m3/min, respectively, for MC4A-P2 and around 1.08 min, 1.33 m3/min, and 6.37 m3/min, respectively, for problem MC4BP2. QEx1 for MC4A-P2 was seen to be 3.38 m3/min, while tp/ts was found to be 0.62. The optimal column configuration was seen to be 6/6/4/2/6/3, while the optimal reflux flow rate was seen to be 0.09 m3/min.

All the optimization studies were performed considering multiple objectives using an elitist nondominated sorting genetic algorithm with jumping genes. Appendix The mass balance equations are as follows:

∂qi,k ψk ∂2Ci,k ∂Ci,k ∂Ci,k +υ ) - ψk 2 ∂θ ∂θ Pek ∂χ ∂χ

(A1)

∂qi,k / - qi,k) ) R(qi,k ∂θ

(A2)

where χ ) z/Lcol and θ ) t/ts. The boundary conditions are as follows: in ) Ci,k(0,θ) Ci,χ

∂Ci,k (1,θ) ) 0 ∂χ

Conclusions In our earlier article, separation of a ternary mixture using two different modified configurations of an SMB system was studied, and the performances of the two configurations were compared at optimal conditions for varying degrees of difficulty in separation (adsorption selectivity), mass-transfer resistance, and nonlinearity in adsorption isotherm. Performances of the systems were optimized using multiple objectives, and it was observed that, in general, MC1 performed better than MC2. However, studies were performed assuming only one column per section. In this paper, we first extend our earlier study on modified SMB systems under nonideal conditions to include more than one column per section for the hypothetical separation problem. It was found that, when multiple columns are present in Section P, configuration MC1 performs better than when only one column is present. However, performances for configuration MC2 deteriorate. Two new configurations (MC2A and MC2B) were proposed, and it was found that both perform better in terms of achieving better purity of the most strongly adsorbed component for any particular value of purity for the intermediate component. Moreover, MC2B performs slightly better than MC2A. Subsequently, the modified systems were investigated for the separation of C8 aromatics at optimal conditions to recover simultaneously p-xylene and ethylbenzene. It was found that the modified five-zone SMB configuration, MC1, is a much better option for the separation of C8 aromatics compared to MC2 and its modified versions, MC2A and MC2B. MC1 results in much higher purities of ethylbenzene along with high values for Pur_moX and Pur_pX compared to MC2. It was observed that, as the separation becomes more difficult, MC1 performs better than MC2 while at the same time consuming a lesser amount of desorbent. An attempt was also made to enhance the performance of the modified systems by adding a reflux stream containing pure ethylbenzene. It was observed that, though Pur_EB and Rec_EB can be improved, it results in a decrease in the recovery of p-xylene, particularly for MC2. MC1, however, seems to show high recovery of p-xylene when the Pur_EB is high. Thus, it can be concluded that using a reflux stream containing pure ethylbenzene can improve the Pur_EB and Rec_EB with the system which already delivers high Pur_pX with some loss of p-xylene into the stream collecting ethylbenzene.

1 ∂Ci,k Pek ∂χ

(A3)

(A4)

The initial conditions are as follows: 0 0 (χ) and qi,k(χ,0) ) qi,k (χ) Ci,k(χ,0) ) Ci,k

(A5)

The dimensionless parameters used in the above equations are as follows:

ψk ) UFzts/Lcol, R ) khts, and Pek ) UFkLcol/Daxk

(A6)

The adsorption isotherm is as follows:

qmBiCi,k

/ ) qi,k

NC

1+

BlCl,k ∑ l)1

Nomenclature B ) Langmuir adsorption constant, cm3/g C ) fluid phase concentration, g/cm3 dcol ) diameter of the column, cm dp ) particle diameter, cm ka ) mass-transport coefficient (LDF), min-1 Lcol ) column length, cm Pe ) Peclet number Pur ) purity q ) adsorbed-phase concentration, g/cm3 qm ) adsorbed-phase saturation concentration, g/cm3 Q ) flow rate, cm3/min Rec ) recovery ts ) switching period, min UF ) fluid interstitial velocity, cm/min us ) solid velocity, cm/min Greek Letters ) bed porosity F ) density of adsorbent, g/cm3 Superscripts and Subscripts D ) eluent/desorbent Ex ) extract

(A7)


F ) feed P, Q, R, S ) sections of the SMB system Ra ) raffinate Literature Cited (1) Broughton, D. B.; Gerhold, C. G. Continuous sorption process employing fix beds of sorbent and moving inlets and outlets. U.S. Patent 2,985,589, 1961. (2) Ruthven, D. M.; Ching, C. B. Countercurrent and Simulated Countercurrent Adsorption Separation Processes. Chem. Eng. Sci. 1989, 44, 1011-1038. (3) Hashimoto, K.; Adachi, S.; Shirai, Y.; Morishita, M. Operation and Design of Simulated Moving Bed Adsorbers. In PreparatiVe and Production Scale Chromatography; Ganetsos, G., Barker, P. E., Eds.; Marcel Dekker: New York, 1993; pp 273-300. (4) Fish, B. B.; Carr, R. W.; Aris, R. Design and performance of a simulated countercurrent moving bed separator. AIChE J. 1993, 39 (11), 1783-1790. (5) Storti, G.; Mazzotti, M.; Morbidelli, M.; Carra, S. Robust design of binary countercurrent adsorption separation processes. AIChE J. 1993, 39, 471-492. (6) Charton, F.; Nicoud, R.-M. Complete design of a simulated moving bed. J. Chromatogr. A 1995, 702, 97-112. (7) Kearney, M.; Hieb, K. L. Time variable simulated moving bed process. U.S. Patent 5,102,553, 1992. (8) Nicoud, R.-M. Simulated Moving-Bed Chromatography for Biomolecules. In Handbook of Bioseparations; Ahuja, S., Ed.; Academic Press: San Diego, CA, 2000; pp 475-509. (9) Nicoud, R.-M.; Perrut, M.; Hotier, G. Method and device for fractionating a mixture in a simulated fluidized bed in the presence of a compressed gas, a supercritical fluid or a subcritical fluid. WO Patent 93/ 22022, 1993. (10) Mata, V. G.; Rodrigues, A. E. Separation of ternary mixtures by pseudo-simulated moving bed chromatography. J. Chromatogr. A 2001, 939, 23-40. (11) Wooley, R.; Ma, Z.; Wang, N.-H. L. A Nine-Zone Simulated Moving Bed for the Recovery of Glucose and Xylose from Biomass Hydrolyzate. Ind. Eng. Chem. Res. 1998, 37, 3699-3709. (12) Hritzko, B. J.; Xie, Y.; Wooley, R.; Wang, N.-H. L. Standing Wave Design of Tandem SMB Processes for Mult-component Fractionation: Linear Systems. AIChE J. 2002, 48 (12), 2769-2787. (13) Wankat, P. C. Simulated Moving Bed Cascades for Ternary Separations. Ind. Eng. Chem. Res. 2001, 40, 6185-6193. (14) Kim, J. K.; Zang, Y.; Wankat, P. C. Single-Cascade Simulated Moving Bed Systems for the Separation of Ternary Mixtures. Ind. Eng. Chem. Res. 2003, 42, 4849-4860. (15) Beste, Y. A.; Arlt, W. Side-Stream Simulated Moving-Bed Chromatography for Multicomponent Separation. Chem. Eng Technol. 2002, 25, 956-962. (16) Kurup, A. S.; Hidajat, K.; Ray, A. K. A comparative study of modified simulated moving bed systems at optimal conditions for the separation of ternary mixtures under nonideal conditions. Ind. Eng. Chem. Res. 2006, 45, 3902-3915.

(17) Minceva, M.; Rodrigues, A. E. Modeling and simulation of a simulated moving bed for the separation of p-xylene. Ind. Eng. Chem. Res. 2002, 41, 3454-3461. (18) Kurup, A. S.; Hidajat, K.; Ray, A. K. Optimal operation of an industrial-scale Parex process for the recovery of p-xylene from a mixture of C8 aromatics. Ind. Eng. Chem. Res. 2004, 44, 5703-5714. (19) Chankong, V.; Haimes, Y. Y. MultiobjectiVe Decision Makings Theory and Methodology; Elsevier: New York, 1983. (20) Bhaskar, V.; Gupta, S. K.; Ray, A. K. Applications of multiobjective optimization in chemical engineering. ReV. Chem. Eng. 2000, 16, 1-54. (21) Deb, K. Multi-objectiVe optimization using eVolutionary algorithms; Wiley: New York, 2001. (22) Kasat, R. B.; Gupta, S. K. Multiobjective optimization of an industrial fluidized bed catalytic cracking unit (FCCU) using genetic algorithm (GA) with the jumping genes operator. Comput. Chem. Eng. 2003, 27, 1785-1800. (23) Nandasana, A. D.; Ray, A. K.; Gupta, S. K. Applications of the Nondominated Sorting Genetic Algorithm (NSGA) in Chemical Reaction Engineering. Int. J. Chem. React. Eng. 2003, 1 (R2); www.bepress.com/ ijcre/vol1/R2/. (24) Zhang, Z.; Hidajat, K.; Ray, A. K.; Morbidelli, M. Multi-objective Optimization of Simulated Moving Bed system and Varicol process for Chiral Separation. AIChE J. 2002, 48 (12), 2800-2816. (25) Subramani, H. J.; Hidajat, K.; Ray, A. K. Optimization of Reactive SMB and Varicol Systems. Comput. Chem. Eng. 2003, 27 (12), 18831901. (26) Yu, W.; Hidajat, K.; Ray, A. K. Application of Multi-objective Optimization in the Design and Operation of Reactive SMB and its Experimental Verification. Ind. Eng. Chem. Res. 2003, 42, 6823-6831. (27) Wongso, F.; Hidajat, K.; Ray, A. K. Application of multi-objective optimization in the design of simulated moving bed for chiral drug separation. Bioeng. Biotechnol. 2004, 87 (6), 704-722. (28) Yan, Z.; Hidajat, K.; Ray, A. K. Optimal design and operation of SMB bioreactor: Production of high fructose syrup by isomerization of glucose. Biochem. Eng. J. 2004, 21, 111-121. (29) Kurup, A. S.; Subramani, H. J.; Hidajat, K.; Ray, A. K. Optimization of reactive SMB and Varicol for sucrose inversion. Chem. Eng. J. 2005, 108, 19-33. (30) Nicoud, R.-M. Simulated Moving Bed (SMB)sSome Possible Applications for Biotechnology. In Bioseparation and Bioprocessing Handbook; Subramanian, G., Ed.; Wiley-VCH: New York, 1998; pp 3-39. (31) Coello, C. A.; Veldhuizen, D. A. V.; Lamont, G. B. EVolutionary Algorithms for SolVing Multi-objectiVe Problems; Kluwer Academic Publishers: New York, 2002. (32) Azevedo, D. C. S.; Neves, S. B.; Ravagnani, S. P.; Cavalcante, C. V., Jr.; Rodrigues, A. E. The influence of dead zones of simulated moving bed units. Fundamentals of adsorption 6; Elsevier: Amsterdam, The Netherlands, 1998; pp 521-526.

ReceiVed for reView May 9, 2005 ReVised manuscript receiVed April 5, 2006 Accepted June 26, 2006 IE0505413

Comparative Study of Modified Simulated Moving Bed Systems at

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