Chromatography for Center-Cut Separation from

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Ind. Eng. Chem. Res. 2006, 45, 1426-1433

Two-Zone SMB/Chromatography for Center-Cut Separation from Ternary Mixtures: Linear Isotherm Systems Jin Seok Hur and Phillip C. Wankat* Purdue UniVersity, School of Chemical Engineering, Forney Hall of Chemical Engineering (FRNY), 480 Stadium Mall DriVe, West Lafayette, Indiana 47907-2100

A center-cut two-zone simulated moving bed (SMB)/chromatography system and a recycled cascade with two four-zone SMBs were designed to purify only the intermediate retained component in ternary mixtures. The operating conditions, productivity, and minimum ratio of total flow rate of desorbent to feed flow rate (Dtotal/F) were determined with the local equilibrium model, and purity and recovery were simulated by Aspen Chromatography. Compared to complete ternary separation, the separation constraints of the center-cut twozone SMB/chromatography were less restrictive, and it showed higher purity of the intermediate retained component. For example, the purity was increased by 3.3% in the center-cut two-zone system for Dtotal/F ) 4.0. Compared to complete ternary separation, the recycled cascade with two four-zone SMBs reduced the desorbent usage by recycling a dilute, unwanted product. For example, the minimum Dtotal/F value was decreased from 2.9 in the standard cascade to 1.0 in the recycled cascade. The center-cut two-zone SMB/chromatography showed exhibited comparable purity, recovery, and productivity as the recycled cascade with two four-zone SMBs, but a larger Dtotal/F value was required. Introduction Since UOP introduced the first commercial simulated moving bed (SMB) system for hydrocarbon separations,1 SMB systems have been widely studied, especially for binary separations. Its higher efficiency and lower desorbent usage, compared to batch chromatography systems, have resulted in many commercial applications.2,3 Various configurations of coupled SMB cascades have been proposed and analyzed for multicomponent separations.4-7 Masuda et al.8 patented a single cascade process for fractional separation that has been commercialized by Organo Corp., Tokyo, Japan. Five-zone SMBs for ternary separations have been studied extensively;3,9-11 however, they produce a pure intermediate product only when the separation factor between the intermediate and most retained component is quite large. In our previous study, we introduced a high-productivity, twozone SMB/chromatography hybrid system, and compared the results to a cascade of two two-zone SMBs and to a cascade of two four-zone SMBs.12 If only the most or least retained component is desired, a single SMB can be used. UOP adjusted the adsorbent to make p-xylene the most retained to separate p-xylene from a mixture of p-xylene, o-xylene, m-xylene, and ethylbenzene.13 Adjustment of the adsorbent may not be possible. Examples are insulin purification14,15 and sugar separation from biomass hydrolyzate.4 When a cascade with two four-zone SMBs is used to separate the components, the system requires at least eight columns, and determining operating conditions is complex. Thus, a single SMB cascade would be preferred if it can produce the desired purity with reasonable desorbent-to-feed ratios. We have designed a semicontinuous center-cut two-zone SMB/chromatography system and a recycled cascade with two four-zone SMBs to separate the intermediate retained component from ternary mixtures. The purity and recovery of the systems * To whom correspondence should be addressed. Tel.: 765-4947422. E-mail: [email protected].

were compared at the same productivity and ratio of total flow rate of desorbent to feed flow rate (Dtotal/F). Simulation Model A phenolic mixture (phenol, 2-phenylethanol, and 3-phenyl1-propanol) was chosen for this study. The components phenol (A), 2-phenylethanol (B), and 3-phenyl-1-propanol (C) are the least-retained, intermediate, and most-retained components, respectively. The stationary phase is Kromasil 100-5C18, and the mobile phase is methanol-water (50:50).16 As a model for other separations, it was assumed that the only desired product is 2-phenylethanol (B). System and operating parameters are given in Table 1. The following solute mass balance for the single porosity model was used:2,17

∂Ci ∂2Ci ∂qi ∂(VCi) + (1 - ) +  - Dax,i 2 ) 0 ∂t ∂t ∂z ∂z



(1)

The subscript i indicates the different solutes, C and q are the solute concentrations in liquid and solid phases, and Dax is the axial dispersion coefficient. The equivalent number of theoretical plates (Np) was used for the combined mass-transfer and dispersion effects in the original data.16 However, with the very small particles used,16 the average of the apparent dispersion coefficients calculated from the number of theoretical plates (PeL ) 2 N) was very close to the estimated dispersion coefficient from the Chung and Wen correlation. Thus, we used this correlation to estimate dispersion effects, and the mass-transfer resistance was assumed to be negligible. The Chung and Wen correlation is18

Pedp )

0.2 0.011 0.48 + Re  

(2)

The numerical solution of these differential equations was obtained by a biased upwind differencing scheme (BUDS), using

10.1021/ie058046u CCC: $33.50 © 2006 American Chemical Society Published on Web 01/20/2006

Ind. Eng. Chem. Res., Vol. 45, No. 4, 2006 1427 Table 1. System and Operating Parametersa

a

parameter

phenolic systemb

length of column, L column diameter, Dcol total voidage,  particle diameter, dp fluid density, F viscosity, µ axial dispersion coefficient, Dax (cm2/min) linear isotherm constant, Ki, at T ) 21 °C feed concentration

25 cm 0.46 cm 0.54 10.0 µm 1.0 g/cm3 1.9 cP Chung and Wen correlation (eq 2) KA ) 2.15 cm3/cm3, KB ) 3.61 cm3/cm3, KC ) 6.85 cm3/cm3 5.0 g/L

Data for equilibrium and  taken from ref 16. b The phenol system consists of phenol (A), 2-phenylethanol (B), and 3-phenyl-1-propanol (C).

Aspen Chromatography Version 12.1. In the simulations, the effect of extra-column dead volume was not considered. The initial values for velocities were determined by the local equilibrium model. The solute velocity for a single porosity model of a linear system is1,17

usolute i,zone j,step k )

Vjk ) GiVjk 1- 1+ Ki 

(

)

(3)

where Vjk is the superficial velocity in column j for step k, Ki is the linear equilibrium constant (qi ) KiCi), and Gi is the constant to determine the velocity of the solute. Because the model assumes rapid mass transfer and negligible dispersion, the initial values for velocities do not guarantee perfect separations. Thus, operating conditions must be optimized when mass transfer and dispersion affect the separation. Although the difficulty of separation is generally classified by the selectivity, RAB ) KB/KA, this measure does not properly represent the difficulty for small Ki. A better measure is R′AB, which is defined as5

uA GA g 1.0 R′AB ) ) uB GB

(4)

The separations of the two binary pairs of the phenolic mixture (R′AB ) 1.44 and R′AB ) 1.68) were both considered moderately difficult. The operation of each system is represented by the Dtotal/F value, the purity-recovery index (PRI), and the productivity. We have defined the PRI value as the average of the purity and recovery of B in product B, PRI ) (purity of B in product B (%)) + (recovery of B in product B (%)) 2

(5) and the productivity is defined as

Figure 1. Integrated two-zone SMB/chromatography system for complete ternary separations. (Reprinted, with permission, from ref 12, Copyright 2005, American Chemical Society.)

the B-C separation is easy. The local equilibrium constraints for the complete separation, written in terms of multipliers, are as follows:12

V1aGAta ) MAFL

(MAF e 1, A not breakthrough)

(7a)

V1bGAtb + V2aGAta ) MATL (MAT g 1, trailing edge of A exits column) (7b) V1aGBta + V1bGBtb ) MBFL (MBF e 1, B not breakthrough) (7c) V1bGBtb + V2aGBta + V2bGBtb ) MBTL (MBT g 1, trailing edge of B exits column) (7d) V1aGCta + V1bGCtb + V2aGCta + V2bGCtb ) MCFL (MCF e 1, C not breakthrough) (7e)

(6)

V1bGCtb + V2aGCta + V2bGCtb + V1aGCta ) MCTL (MCT g 1, trailing edge of C exits column) (7f)

In the previous work,12 we designed a semicontinuous twozone SMB/chromatography system (Figure 1) for complete ternary separations, and the movements of the three solutes are shown in eq 7. In this integrated system, A and B are separated by a SMB approach (the switching and remixing with the feed keep the mass-transfer zone inside the column), whereas the B-C separation is chromatographic (the B-C mass-transfer zone leaves the system).12 Thus, the system is preferred when

The parameters Mix are multipliers for the front and trailing edge of component i (x ) front (F) or trailing edge (T)). Similar linear multipliers have been used by Ruthven and Ching19 (who referred to them as γ) and Zhong and Guiochon20 (who referred to them as β). In eqs 7e and 7f, MCF and MCT both should be 1 for complete ternary separations. Thus, the dispersion of component C makes products A and B impure when mass-transfer resistance and axial dispersion exist. However, MCF and MCT are not required to be 1 for the purification of only the intermediate component B. If these multipliers are larger than 1 (Figure 2b), the solute

volumetric flow rate of feed productivity ) total adsorbent volume Two-Zone SMB/Chromatography System for the Intermediate Retained Component

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Figure 4. Center-cut two-zone SMB/chromatography system for the separation of only the intermediate retained component in ternary mixtures.

Figure 2. Local equilibrium solutions for the integrated two-zone SMB/ chromatography system: (a) MCF ) MCT ) 1, (b) MCF ) MCT > 1, and (c) MCF ) MCT < 1. Data shown for one complete cycle for top column in Figure 1. Data from product A are represented by the thick solid line, product B are represented by the dotted line, and product C is denoted by the thin solid line.

MCF () MCT) for complete ternary separation in the two-zone SMB/chromatography system (see Figure 1) at Dtotal/F ) 4.0. The operating conditions for MCF ) MCT ) 1 were taken from ref 12, and then we decreased the value of parameter MCF () MCT). The purity of B with MCF ) 0.97 was 3.3% larger than that with MCF ) 1.0, whereas the recovery is almost constant. Thus, the PRI was increased by 1.6%. The center-cut two-zone SMB/chromatography system is shown in Figure 4. For the purification of only component B, it is not necessary to keep MAF e 1 and MCT g 1, because components A and C exit from the system in the same product stream. Thus, for the separation of B, eqs 7a and 7f become

V1aGAta ) MAFL

(no constraint for MAF)

(8a)

V1bGCtb + V2aGCta + V2bGCtb + V1aGCta ) MCTL (MCT ) MCF e 1, trailing edge of C does not have to exit column) (8b) If the fluid density is constant, the mass balances become

Figure 3. Purity and recovery of B (2-phenylethanol) in product B versus MCF () MCT) in the integrated two-zone SMB/chromatography for complete ternary separations for Dtotal/F ) 4.0.

velocity of component C becomes faster and it may contaminate product B. If they are less than 1 (Figure 2c), the solute velocity of component C becomes slower and it may contaminate product A; however, on the other hand, this increases the purity of B in product B. This analysis was a hint of how to modify the twozone system for obtaining only product B with high purity. Figure 3 shows the purity and recovery of B in product B with

V1a ) V2a + Vfeed

(9a)

V1a ) VAC product 1

(9b)

V1b ) VAC product 2

(9c)

V2b ) VB product

(9d)

For the center-cut system (Figure 4), specifying the feed flow rate and the column length and diameter results in five unknown variables (V1a, V2a, V1b, V2b, and ta ) tb) and six equations (7b, 7c, 7d, 7e () 8b), 8a, and 9a). Thus, one of the equations is not independent. Because the condition for MAF is not restrictive, we have chosen eqs 7b, 7c, 7d, 7e () 8b), and 9a to determine the minimum Dtotal/F value. The operating conditions were determined by optimizing the flow rates and switching time in the genetic algorithm. Before showing the initial calculations and the simulations, we will consider an alternate process. Cascade with Two Four-Zone Simulated Moving Beds for the Intermediate Retained Component The standard cascade with two four-zone SMBs for complete ternary separations is shown in Figure 5. In this system, train 1

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binary A-B separation:

uA1′ ) MAF′uport′

(MAF′ e 1)

(11a)

uA3′ ) MAT′uport′

(MAT′ g 1)

(11b)

uB2′ ) MBF′uport′

(MBF′ e 1)

(11c)

uB4′ ) MBT′uport′

(MBT′ g 1)

(11d)

Equations 10 and 11 were used to determine the value of (Dtotal/ F)min. For the standard, complete separation cascade with two four-zone SMBs, because the first train was designed to separate the feed into mixture AB and product C, uA1 was used instead of uB1 in eq 10a. The minimum desorbent use of the standard, complete separation system was 2.9. However, in the system that had train 1 separate the ternary feed into mixture AB and product AC, it was reduced by 31% ((Dtotal/F)min ) 2.0), and in the recycled system that was purifying only the intermediate component, it was reduced by 34% more ((Dtotal/F)min ) 1.0), compared to the standard, complete separation system. The local and overall mass balances are

Figure 5. Standard coupled cascade with two four-zone SMBs for complete ternary separation. Switching of ports in the two SMBs is not shown.

separates the ternary feed into product AB [or product A] and product C [or BC], and component AB [or BC] is separated into products A [or B] and B [or C] in train 2. For purification of only the intermediate retained component, some reduction in desorbent use is possible by having train 1 separate the ternary feed into products AB and AC [or into products AC and BC], and then product AB is separated into products A and B [or product BC is separated into products B and C] in train 2. The B-C separation for the phenols is easier than the A-B separation; therefore, the first train was designed for the B-C separation (Figure 6a). Compared to the standard cascade with two four-zone SMBs, this system consumes less desorbent, because train 1 is performing only a binary separation.14,19 We next modified the system by recycling products A + D (Figure 6a) or C + D (Figure 6b) to train 1. Additional desorbent can also be added in train 1, if desired. If this recycle were tried in a standard, complete separation cascade with two four-zone SMBs, complete ternary separation cannot be achieved, because product C is contaminated by the recycle of A [or A is contaminated by the recycled C]. Constraints for the first train are the same as those for a binary B-C separation:

uB1 ) MBFuport

(MBF e 1)

(10a)

uB3 ) MBTuport

(MBT g 1)

(10b)

uC2 ) MCFuport

(MCF e 1)

(10c)

uC4 ) MCTuport

(MCT g 1)

(10d)

V2 ) V3 + Vfeed

(12a)

V1 ) V2 - VAB product

(12b)

V3 ) V4 - VAC product

(12c)

V4 ) V1 + VA recycle + Vdesorbent 1

(12d)

V2′ ) V3′ + VAB product

(12e)

V1′ ) V2′ - VA product - VA recycle

(12f)

V3′ ) V4′ - VB product

(12g)

V4′ ) V1′ + Vdesorbent 2

(12h)

Vfeed + Vdesorbent 1 + Vdesorbent 2 ) VA product + VB product + VAC product (12i) where Vfeed, VAB product, VAC product, VA recycle, VA product, VB product, and Vdesorbent are the interstitial velocities that these streams would have in the column. The use of desorbent in the first train is optional and is dependent on the operating conditions. When we specify the feed flow rate and the column length and diameter, we have 11 unknown variables (V1, V2, V3, V4, V1′, V2′, V3′, V4′, VA recycle, tsw1, and tsw2) for the specified Mix values. The next section explains how the Mix values were determined for the cascade with two four-zone SMBs. The equations for Figure 6b can be developed in a similar fashion. For Figure 6b, the first train has equations that are identical to those for binary separation for products A from B, whereas the second train is a binary separation of B from C. Optimization and Results

where the average port velocity is defined as uport ) L/tsw and uij is the velocity of solute i in column j. The second four-zone cascade separates the mixture AB into products A and B, and constraints for the separation are those for

1. Two-Zone SMB/Chromatography. At minimum Dtotal/F values, the separation will be perfect if mass-transfer resistance and axial dispersion are negligible. However, if they are finite, the separation will not be perfect and must be optimized. Although many optimization tools such as the standing wave design21,22 and the triangle method23 have been developed, we used a genetic algorithm (GA)24-26 for the two-zone SMB/ chromatography systems to maximize the PRI with fixed Dtotal/F values. Objective and constraints for the center-cut two-zone

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Figure 6. Recycled cascade with two four-zone SMBs for purification of only the intermediate component in ternary mixtures: (a) B-C separation is easier and (b) A-B separation is easier. Switching of ports in the SMBs is not shown. Table 2. Optimized Switching Times and Flow Rates, Relative to the Dtotal/F Values (a) Center-Cut Two-Zone SMB/Chromatography System (Figure 4) (QFeed ) 0.5 cm3/min, CA ) CB ) CC ) 5.0 g/L, ta ) tb ) tsw/2) Dtotal/F

tsw (min)

QAC2

QD1

3.28 4.00 5.00 7.00

11.16 9.44 7.89 5.46

1.027 1.150 1.225 1.817

0.527 0.650 0.725 1.317

Flow Rates (cm3/min) QAC1 () QD2) 0.611 0.710 0.963 1.277

QB () QD3)

B purity (%)

B yield (%)

PRIa (%)

0.500 0.641 0.813 0.906

98.2 98.9 99.5 99.6

93.4 99.6 99.9 99.9

95.8 99.2 99.8 99.8

(b) Recycled Cascade with Two Four-Zone SMBs (Figure 6a) (QFeed ) 1.0 cm3/min, CA ) CB ) CC ) 5.0 g/L) Dtotal/F

tsw (min)

1.00 2.16 2.80 3.28 4.00 5.00 7.00

6.19 5.19 4.54 4.54 4.54 4.54 4.54

a

Flow Rate, 1st Train (cm3/min) QR1 QD1 QAB QAC 1.477 1.173 1.304 1.304 1.304 1.304 1.304

0.000 0.060 0.105 0.000 0.000 0.000 0.000

1.000 1.659 1.845 1.845 1.845 1.845 1.845

1.000 1.241 1.455 1.455 1.455 1.455 1.455

tsw′ (min)

QR2

2.79 1.48 1.23 1.09 0.95 0.82 0.63

2.277 4.189 4.998 5.536 6.211 7.145 9.011

Flow Rate, 2nd Train (cm3/min) QD2 QA QA recycle 1.000 2.100 2.700 3.277 4.000 5.000 7.000

0.000 0.000 0.000 0.132 0.428 0.838 1.658

1.000 1.840 2.195 2.300 2.300 2.300 2.300

QB

B purity (%)

B yield (%)

PRIa (%)

1.000 1.919 2.350 2.690 3.117 3.707 4.887

93.1 98.3 99.3 99.9 99.8 99.9 99.9

93.1 98.9 99.5 99.5 99.9 99.8 99.8

93.1 98.6 99.4 99.8 99.8 99.8 99.9

Purity-recovery index.

SMB/chromatography are as follows:

Objective: Subject to:

maximize the purity-recovery index (PRI) Dtotal Q2a + Q1b + Q2b ) ) constant F QFeed

(13a)

Qfeed ) Q1a - Q2a ) constant

(13b)

Q1a, Q2a, Q1b, Q2b, ta ) tb g 0

(13c)

There are five unknown variables (Q1a, Q2a, Q1b, Q2b, ta () tb)) and two equality constraints; therefore, we have three independent variables. In this study, Q1b () QD2), Q2b () QD3) and ta () tb) were chosen to be controlled, while Q1a and Q2a () QD1) were calculated by the equalities (eqs 13a and 13b). We then checked if they are positive (eq 13c). The optimum values of the variables were evaluated by combining GA and Aspen

Chromatography. The computer program for the generic algorithm was formulated with Visual Basic Application (VBA) in Excel, because Aspen Chromatography can be connected and controlled by the VBA. Table 2a shows the optimized switching time and flow rates of the modified two-zone SMB/chromatography system. 2. Recycled, Intermediate Recovery Cascade with Two Four-Zone SMBs. For the cascade with two four-zone SMBs (see Figure 6), the concentrations and fractions in stream AB and in recycled stream A varied throughout the switching time if the trains are directly connected without buffer tanks. This can result in irregular oscillation in product concentrations. Figure 7 shows the irregular oscillation of B concentration in B product for Dtotal/F ) 4.0 (see the conditions in Table 2b). Generally, large stirred tanks can be used to reduce the oscillation and keep the concentrations constant. Figure 8 shows results when a buffer tank is used to reduce the oscillation of

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Figure 7. Concentration of B (2-phenylethanol) in product B for the recycled cascade with two four-zone, directly connected SMBs without buffer tanks (Dtotal/F ) 4.0).

Figure 9. Concentration of B (2-phenylethanol) in product B for the recycled, intermediate component cascade with two four-zone SMBs when a tank (m ) 5) is used for product B and the switching times are congruent (n ) 5).

Figure 8. Concentration of B (2-phenylethanol) in product B for the recycled, intermediate component cascade with two four-zone SMBs when a buffer tank is used on the B product line. Figure 10. Purity-recovery index (PRI) for B versus Dtotal/F for the standard coupled cascade with two four-zone SMBs (Figure 5) and the recycled, intermediate component cascade with two four-zone SMBs including recycle of product A (Figure 6a).

product B in train 2. The variable m is defined as

m)

Vtank QBtsw′

(14)

where Vtank is the initial volume of desorbent in the tank, QB the flow rate of product B, and tsw′ the switching time of train 2. For m ) 5, the oscillation was significantly reduced, whereas, for m ) 50, it almost disappeared. However, the system required significantly more time to reach the cyclic steady state with a large tank. Another way to reduce the irregular oscillation is by adjusting the cycle times. If tsw > tsw′, we defined n as

n)

tsw tsw′

(15)

When tsw ) tsw′ (n ) 1), concentrations of the AB stream are identical for each switching time at cyclic steady state. If n is an integer, the switching times are congruent and the oscillation becomes regular, because the average concentration for n switching times is constant at the cyclic steady state. Thus, only a small tank (e.g., with m ) 5) was needed to remove the oscillation, and the system quickly reached the cyclic steady state. Figure 9 shows concentration of B in product B with m ) n ) 5. When tsw′ was adjusted for n ) 5, the column length L in train 2 was changed to keep uport′ (which is equal to L/tsw′) constant. In the remainder of this study, all columns are identical, to keep the productivity constant, and Vtank (Dtank ) 5 cm and

Htank ) 10 cm) is big enough to remove the oscillation for various operating conditions. For the standard cascade with two four-zone SMBs (Figure 5), train 1 was simulated with various D/F values, and then four D/F values were chosen between the minimum D/F value and D/F value where the PRI for train 1 is almost constant. Train 2 was simulated with the results of train 1 to find the maximum PRIs. Flow rates were varied to optimize the PRIs at each Dtotal/F value by changing Mix one after the other. The recycled cascade with two four-zone SMBs (see Figure 6) was optimized in the same manner. However, the use of desorbent in train 1 was reduced because of the recycling of the A stream (Figure 6a). Figure 10 shows the effect of recycling the product A stream in the cascade with two four-zone SMBs. The minimum Dtotal/F value was decreased from 2.9 to 1.0 by the recycling of A, but the PRI at the minimum Dtotal/F value was also decreased by 1.6%. This occurs because the fraction of A in the AB product stream increases in the recycled system. The recycled, intermediate component cascade system used less desorbent than the standard, complete separation cascade at the same B PRI for Dtotal/F < 6.0. In other words, the recycled system has a higher PRI for B than the standard system at the same Dtotal/F and same productivity. This is particularly significant at low desorbent rates.

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the two modified systems and the total column length was fixed so that the productivity was kept constant. Although the addition of more columns did not improve the PRI of the center-cut twozone SMB/chromatography, the recycled, intermediate component cascade with two four-zone SMBs increased both the purity and the recovery when two columns per zone were used. Discussion and Conclusions

Figure 11. PRI for B versus Dtotal/F for the center-cut two zone-SMB/ chromatography (Figure 3) and the recycled, intermediate component cascade with two four-zone SMBs (Figure 5). Flow rates are optimized for each Dtotal/F value (Table 2). Table 3. Minimum Dtotal/F Value and the Dtotal/F Value for B (PRI ) 99.0%) of Each System with a Productivity of 3.01 × 10-2 cm3/(cm3 min) center-cut two-zone SMB/chromatography

recycled cascade with two four-zone SMBs

3.28 4.00

1.00 2.47

minimum Dtotal/F Dtotal/F for PRI ) 99.0%

Table 4. Purity and Recovery of B When Various Column Configurations Were Used for the Systems Producing Only Pure B at Their Minimum Dtotal/F Values (see Table 3), Respectively, with the Same Productivity (3.01 × 10-2 cm3/(cm3 min)) column configuration 1-1 2-1 1-2 2-2 1-1-1-1 2-2-2-2

purity of B in B product (%)

recovery of B in B product (%)

Center-Cut Two-Zone SMB/Chromatography 98.2 93.4 97.5 94.1 97.2 92.1 93.4 93.0 Recycled Cascade with Two Four-Zone SMBs 93.1 93.1 95.0 94.7

PRI of B (%) 95.8 95.8 94.6 93.2 93.1 94.9

A comparison of the center-cut two-zone SMB/chromatography (Figure 4) with the recycled, intermediate component cascade with two four-zone SMBs (Figure 6), showing the effect of Dtotal/F on the B PRI, is presented in Figure 11. The B PRIs of the recycled cascade with two four-zone SMBs were almost constant for Dtotal/F g 4.0, whereas the PRI of the center-cut two-zone SMB/chromatography increased until Dtotal/F ) 5.0. For Dtotal/F g 5.0, the two systems had almost the same PRI. Table 3 shows the minimum Dtotal/F value and the Dtotal/F value for PRI ) 99.0%. The minimum Dtotal/F value was determined from the local equilibrium analysis, using Mix ) 1 at the same productivity. Although the minimum Dtotal/F value of the center-cut two-zone SMB/chromatography system was 228% larger than that of the recycled cascade with two fourzone SMBs, the center-cut two-zone system required only 62% more desorbent than the modified two four-zone SMBs for PRI ) 99.0% (see Figure 11). For binary four-zone SMBs, it is well-known that the purity can be improved by using multiple columns per zone. To apply this for the systems producing only pure B product, different column configurations were tested (see Table 4). In this table, simulations were performed at the minimum Dtotal/F values of

The results of these simulations show that the center-cut twozone SMB/chromatography system can be used for the separation of the intermediate retained component in ternary mixtures. The system showed similar purities and recoveries but higher Dtotal/F values, when compared to the recycled, intermediate component cascade with two four-zone SMBs; however, the center-cut two-zone SMB/chromatography system is simpler. For example, in the optimization step with a fixed feed flow rate and constant Dtotal/F value, the center-cut two-zone system has only three variables to be optimized. Unfortunately, the minimum Dtotal/F value of the center-cut two-zone system can be quite large for mixtures with small selectivities, and it may not be possible to satisfy the equilibrium constraints for some isotherms. The recycled, intermediate component cascade with two fourzone SMBs used less desorbent than the standard complete separation cascade with two four-zone SMBs and had an higher PRI than the center-cut two-zone SMB/chromatography at the same Dtotal/F value and same productivity. In addition, the purity and recovery were increased when multiple columns per zone were used. Unfortunately, this is the most complex system that was studied. The center-cut two-zone SMB/chromatography system may have advantages in determining optimum operating conditions and in capital cost if the extra cost of recovering desorbent is not excessive; however, the separation constraints are more restrictive than for the recycled, intermediate component cascade with two four-zone SMBs. The recycled two, four-zone SMB cascade requires significantly less desorbent for the same purities and recoveries than the standard, complete separation cascade of two four-zone SMBs, although the recycle stream may make operation of the recycled, intermediate component cascade with two four-zone SMB more difficult to operate. Acknowledgment This research was supported by NSF Grant CTS-0211208. We thank our colleagues Nadia Abunasser, Weihua Jin, and Jeung Kun Kim, who offered useful suggestions in this research. Notation C ) solute concentration in the liquid phase (g/cm3) Dax ) axial dispersion coefficient (cm2/s) Dcol ) column diameter (cm) Dtank ) tank diameter (cm) Dtotal/F ) ratio of total flow rate of desorbent to feed flow rate dp ) particle diameter (cm) Gi ) constant for determining the velocity of solute; Gi ) [1 + (1 - )Ki/]-1 Htank ) height of desorbent in a tank (cm) Ki ) linear equilibrium parameter; Ki ) qi/Ci L ) column length (cm) M ) multiplier m ) ratio of initial volume of tank to volume of B for a switching time; m ) Vtank/(QBtsw′) Np ) number of theoretical plates

Ind. Eng. Chem. Res., Vol. 45, No. 4, 2006 1433

n ) ratio of switching times for train 1 and 2; n ) tsw/tsw′ Pedp ) Peclet number based on particle diameter; Pedp ) dpV/ Dax PeL ) Peclet number based on column length; PeL )LV/Dax Q ) volumetric flow rate (cm3/min) q ) solute concentration on the solid phase (g/(cm3 of particles)) Re ) Reynolds number; Re ) dpVF/µ tsw ) switching time of train 1 (s) tsw′ ) switching time of train 2 (s) u ) solute velocity (cm/s) Vtank ) volume of desorbent in a tank (cm3) V ) interstitial velocity (cm/s) z ) axial coordinate (cm) Greek Symbols RAB ) selectivity based on isotherms R′AB ) selectivity based on solute velocities  ) total bed void fraction F ) fluid density (g/cm3) µ ) fluid viscosity (g/(cm s)) Subscripts i ) solute; i ) A, B, C j ) zones in SMB; j ) 1, 1′, 2, 2′, 3, 3′, 4, 4′ k ) step; k ) a, b x ) front (F) or trailing edge (T) Literature Cited (1) Broughton, D. B. Molex: Case History of a Process. Chem. Eng. Prog. 1968, 64 (8), 60. (2) Wankat, P. C. Large-Scale Adsorption and Chromatography; CRC Press: Boca Raton, FL, 1986; Chapter 6. (3) 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. (4) Wooley, R.; Ma, Z.; Wang, N.-H. L. A Nine-Zone Simulating Moving Bed for the Recovery of Glucose and Xylose from Biomass Hydrolyzate. Ind. Eng. Chem. Res. 1998, 37, 3699. (5) Wankat, P. C. Simulated Moving Bed Cascades for Ternary Separations. Ind. Eng. Chem. Res. 2001, 40, 6185. (6) Nicolaos, A.; Muhr, L.; Gotteland, P.; Nicoud, R. M.; Bailly, M. Application of Equilibrium Theory to Ternary Moving Bed Configurations (four+four, five+four, eight and nine zones): I. Linear Case. J. Chromatogr., A 2001, 908, 71. (7) Nicolaos, A.; Muhr, L.; Gotteland, P.; Nicoud, R. M.; Bailly, M. Application of Equilibrium Theory to Ternary Moving Bed Configurations (4+4, 5+4, 8 and 9 zones): II. Langmuir Case. J. Chromatogr., A 2001, 908, 87. (8) Masuda, T.; Sonobe, T.; Matsuda, F.; Horie, M. Process for Fractional Separation of Multi-Component Fluid Mixture. U.S. Patent No. 5,198,120, 1993.

(9) Kim, J. K.; Zang, Y.; Wankat, P. C. Single-Cascade Simulated Moving Bed Systems for the Separation of Ternary Mixtures. Ind. Eng. Chem. Res. 2004, 42, 4849. (10) Abel, S.; Babler, M. U.; Arpagaus, C.; Mazzotti, M.; Stadler, J. Two-Fraction and Three Fraction Continuous Simulated Moving Bed Separation of Nucleosides. J. Chromatogr., A 2004, 1043, 201. (11) Paraedes, G.; Abel, S.; Babler, M. U.; Mazzotti, M.; Morbidelli, M.; Stadler J. Analysis of a Simulated Moving Bed Operation for ThreeFraction Separations (3F-SMB). Ind. Eng. Chem. Res. 2004, 43, 6157. (12) Hur, J. S.; Wankat, P. C. New Design of Simulated Moving Bed (SMB) for Ternary Separations. Ind. Eng. Chem. Res. 2005, 44, 1906. (13) Broughton, D. B.; Neuzil, R. W.; Pharis J. M.; Brearley, C. S. The Parex Process for Recovering Paraxylene. Chem. Eng. Prog. 1970, 66, 70. (14) Xie, Y.; Mun, S.; Kim, J.; Wang, N.-H. L. Standing Wave Design and Experimental Validation of a Tandem Simulated Moving Bed Process for Insulin Purification. Biotechnol. Prog. 2002, 18, 1332. (15) Mun, S.; Xie, Y.; Wang, N.-H. L. Robust Pinched-Wave Design of a Size-Exclusion Simulated Moving-Bed Process for Insulin Purification. Ind. Eng. Chem. Res. 2003, 42, 3129. (16) Lisec, O.; Hugo, P.; Seidel-Morgenstern, A. Frontal Analysis Method to Determine Competitive Adsorption Isotherms. J. Chromatogr., A 2001, 908, 19. (17) Wankat, P. C. Rate-Controlled Separations; Kluwer Academic Publishers: Amsterdam, 1990; Chapter 6. (18) Chung, S. F.; Wen, C. Y. Longitudinal Dispersion of Liquid Flowing Through Fixed and Fluidized Beds. AIChE J. 1968, 14, 857. (19) Ruthven, D. M.; Ching, C. B. Counter-Current and Simulated Counter-Current Adsorption Separation Processes. Chem. Eng. Sci. 1989, 44, 1011. (20) Zhong, G.; Guiochon, G. Analytical Solution For The Linear Ideal Model of Simulated Bed Chromatography. Chem. Eng. Sci. 1996, 51, 4307. (21) Hritzko, B.; Xie, Y.; Wooley, R.; Wang, N.-H. L. Standing Wave Design of Tandem SMB for Linear Multicomponent Systems. AIChE J. 2002, 48, 2769. (22) Ma, Z.; Wang, N.-H. L. Standing Wave Analysis of SMB Chromatography: Linear System. AIChE J. 1997, 43, 2488. (23) Mazzotti, M.; Storti, G.; Morbidelli, M. Optimal Operation of Simulated Moving Bed Units for Nonlinear Chromatographic Separations. J. Chromatogr. A 1997, 769, 3. (24) Goldberg, D. E. Genetic Algorithms in Search, Optimization, and Machine Learning; Addison-Wesley Longman, Inc.: Reading, MA, 1989; Chapter 3. (25) Chambers, L. The Practical Handbook of Genetic Algorithms Applications; CRC Press: Boca Raton, FL, 2000; Chapter 2. (26) Osyczka, A. EVolutionary Algorithms for Single and Multicriteria Design Optimization; Physica-Verlag Heidelberg: New York, 2002; Chapters 2 and 3.

ReceiVed for reView May 9, 2005 ReVised manuscript receiVed December 15, 2005 Accepted December 19, 2005 IE058046U