Hybrid Simulated Moving Bed and Chromatography Systems for

Ind. Eng. Chem. Res. 2006, 45, 8713-8722

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Hybrid Simulated Moving Bed and Chromatography Systems for Center-Cut Separation from Quaternary 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

Three simulated moving bed (SMB) cascade systems with two trains are studied to separate only one of the intermediate retained components from a quaternary mixture. The three systems are a cascade with two fourzone SMBs (4 + 4), a cascade with a two-zone SMB/chromatography and a four-zone SMB (2 + 4), and a cascade with a single-column analogue and a four-zone SMB (1 + 4). To reduce desorbent use, an unwanted product containing desorbent is recycled from the second train to the first train. The minimum Dtotal/F is calculated with the local equilibrium model. Optimum operating conditions are determined with a binary coded genetic algorithm for separation of a model system of nucleosides. In the optimization, purity and recovery were simulated by Aspen Chromatography. Compared to the system 4 + 4, the separation constraints of systems 1 + 4 and 2 + 4 were more restrictive, but they used less desorbent at the same product purity and same productivity. For example, for a product purity of 95.0%, desorbent to feed ratios for systems 2 + 4 and 1 + 4 were 6.07 and 8.33, respectively, while that of system 4 + 4 was 14.26. In addition, systems 1 + 4 and 2 + 4 require fewer columns than system 4 + 4. Introduction The simulated moving bed (SMB), which is a continuous chromatography process, has been successfully applied to hydrocarbon separations and become an important research subject in bioseparation and chiral separation1,2 since UOP introduced the first commercial SMB.3 Studies of multicomponent separations are increasing, although most applications are for binary separations (Figure 1a). For complete ternary separation, the obvious approach is to couple two SMBs in various configurations.4-6 The standard cascade with two four-zone SMBs is shown in Figure 1b. There has been considerable interest in single-train systems with fewer zones. Masuda et al.7 patented a single four-zone SMB process for fractional separation that has been commercialized by Organo Corp., Tokyo, Japan. This system uses a discontinuous feed stream for ternary mixtures. A continuous five-zone SMB is a more recent system for ternary separation and has been extensively studied.8-12 A different approach for ternary separations is the development of a high productivity, hybrid twozone SMB/chromatography system.13 All of the single-train systems require fewer columns than the standard cascade with two four-zone SMBs, but to produce pure products the separation factor between the intermediate and most retained component must be large. The ternary cascades were also extended to complete quaternary separations.4,9 In bioseparations, it is frequently required to separate only one component from a multicomponent mixture. Examples are insulin purification14,15 and sugar separation from biomass hydrolyzate.16 If only the most or least retained component is desired, the standard four-zone SMB (Figure 1a) can be used, although larger amounts of desorbent are required than for a binary separation.4,17 If a middle component is the only desired product, which is called center-cut separation in this study, there are three general ways to separate it. The first method is to adjust * To whom correspondence should be addressed. Tel: 765-494-7422. E-mail: [email protected].

Figure 1. (a) Standard binary four-zone SMB. (b) Standard coupled cascade with two four-zone SMBs for complete ternary separation. Switching of ports is not shown.

the adsorbent properties to make the desired component the least or most retained component. For example, UOP adjusted the adsorbent to make p-xylene most retained to separate it from a mixture of p-xylene, o-xylene, m-xylene, and ethylbenzene.18 However, this approach may not be possible or may be very time-consuming. The second method is using a cascade with multiple SMBs, which was used, for example, in studies of insulin purification and sugar separation.14-16 This design is robust, but it requires many columns, and determining operating conditions is complex. The last approach is using a single system such as a two-zone SMB/chromatography hybrid system to do center cuts of ternary phenol systems although high selectivity between the intermediate and most retained components is required.19 In this study, we briefly review the center-cut two-zone SMB/ chromatography system and design a single-column system that

10.1021/ie0513705 CCC: $33.50 © 2006 American Chemical Society Published on Web 11/11/2006

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Ind. Eng. Chem. Res., Vol. 45, No. 25, 2006

Table 1. System and Operating Informationa

a

nucleosides

2′-deoxycytidine (A), 2′-deoxyguanosine (B), 2′-deoxythymidine (C), 2′-deoxyadenosine (E)

adsorbent desorbent length of column (L), cm column diameter (Dcol),cm total voidage () particle diameter (dp), µm fluid density (F), g/cm3 viscosity (µ), cP axial dispersion constant (Dax), cm2/min mass transfer coefficient, 1/s linear isotherm constant at T ) 30 °C separation factor, R′ (eq 5) feed concentration, g/L

source 30RPC water with 4% ethanol 15.0 0.46 0.80 30.0 1.0 1.0 Chung and Wen correlation (eq 2) apkA ) 1.0, apkB ) 0.5, apkC ) 0.5, apkE ) 0.1 KA ) 3.15, KB ) 7.40, KC ) 9.60, KE ) 27.7 R′AB ) 1.59, R′BC ) 1.19, R′CE ) 2.33 1.0

Data for equilibrium and from ref 11.

mimics this two-zone system. We also study the effect of recycling an unwanted product in multiple train cascades to reduce desorbent usage. Then, we apply these concepts to centercut separation of a quaternary mixture of nucleosides. Theory and Simulation Model for SMB Center-cut separation from a quaternary mixture is required for chiral separations when there are two chiral centers12,20,21 and one of the intermediate components is desired. Although, ternary separation systems can be used for this purification by considering either the two strongest retained components or the two weakest retained components as a single pseudo-component, they will require large amounts of desorbent to obtain high purity and recovery if the separation of the two middle components is much more difficult than the other separations.4,17 To describe concentration changes in a chromatography column, we used the single-porosity model:22,23

∂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 Chung and Wen correlation was used to estimate dispersion effects:24

Pedp )

0.2 0.011 0.48 + Re (10-3 < Re < 103)

(2)

The solid diffusion lumped-parameter mass transfer model was used:11

∂qi ) km,iap(qi* - qi) ∂t

is particularly simple:22,23

ui,j,k )

(4)

[ ]

where Vjk is the superficial velocity in column j for step k (see Figures 3 and 5), Ki is the linear equilibrium constant (qi ) KiCi), and Gi is the constant to determine the velocity of solute. Since the model assumes rapid mass transfer and negligible dispersion, it is only used for visualization and initial estimates. Complete numerical simulations are used to optimize the separation. The model system used in this study was the quaternary mixture of nucleosides: 2′-deoxycytidine (dC), 2′-deoxyguanosine (dG), 2′-deoxythymidine (dT), and 2′-deoxyadenosine (dA).11 Components dC, dG, dT, and dA are the least (A), the first intermediate (B), the second intermediate (C), and the most (E) retained components, respectively. For modeling purposes, it was assumed that the only desired product is 2′-deoxyguanosine (B). Although the difficulty of separation is generally classified by the selectivity, Ri,j ) Kj/Ki, we will use R′i,j defined as4

R′i,j )

ui Gi ) g 1.0 uj Gj

(5)

which is a better measure for small Ki. System, operating, and separation factors are given in Table 1. The BC separation is clearly the most difficult separation. The operation of each system is represented by desorbent to feed ratio (Dtotal/F), purity (PB), recovery (RB), and productivity. They are defined as follows:

(3)

The numerical solution of these differential equations was obtained by a biased upwind differencing scheme (BUDS) using Aspen Chromatography version 12.1. In the simulations, 60 nodes per column were used, and the integration step was tsw/ 2000. Numerical studies showed that these conditions were sufficient to obtain good numerical accuracy. Computation time depends on the number of columns, size of buffer tanks, and operating conditions but was typically 120-150 min to reach cyclic steady state. The dead volume effect was not considered. Various versions of the local equilibrium model have been widely used to analyze and visualize SMB systems.10-13,19-23,25-29 The solute velocity for a single-porosity model of a linear system

Vjk ) GiVjk 1- 1+ Ki

PB (%) )

[

]

CB in B product stream × C A + CB + CC + CE 100 (6a)

RB (%) )

[CB × QB] in B product stream [CB × Qfeed] in feed stream

productivity )

× 100 (6b)

product rate volume of adsorbent

(6c)

In this study, the productivity was fixed by changing feed flow rates for each system with the fixed column length (L ) 15

Ind. Eng. Chem. Res., Vol. 45, No. 25, 2006 8715

feed stream for train 2 and the CED recycle stream for train 1 approximately constant. Constraints for the first train in both panels a and b of Figure 2 are the same as for binary A-B separation:4

uA1 ) MAFuport

(MAF e 1)

(7a)

uB2 ) MBFuport

(MBF e 1)

(7b)

uA3 ) MATuport

(MAT g 1)

(7c)

uB4 ) MBTuport

(MBT g 1)

(7d)

where the average port velocity uport ) L/tsw and uij is the velocity of solute i in column j. The minimum D/F of train 1 can be calculated by setting the multipliers Mij ) 1. For linear systems setting, Mij ) 1 is equivalent to finding the vertex in Triangle theory10,11 while changing the Mij values as indicated moves one inside the triangle. The result is (D/F)min,1 ) 1.0, which is the same as for the binary A-B separation and is much smaller than (D/F)min,1 ) 5.78 for the A-BCE separation. The first trains in Figure 2 have low minimum desorbent requirement because components C and E are not separated. The second four-zone cascade (Figure 2) separates the BCE mixture into B and CE products, and constraints for the separation are as follows:

Figure 2. Combined cascades with two four-zone SMBs to separate only the middle component B from a quaternary mixture (system 4 + 4). Switching of ports is not shown. (a) Cascade without recycle. (b) Cascade with recycle.

cm), and PB and Dtotal/F of the systems were compared with a constraint for the minimum value of RB. System Configurations for the Center-Cut Separation Systems 4 + 4 (Cascades with Two Four-Zone SMBs without and with Recycle). For a cascade with multiple fourzone SMBs, there can be several configurations to purify one of the intermediate components from a quaternary mixture, and the design depends on isotherm values. For this quaternary mixture of nucleosides, a cascade that first separates the feed into ACE and BCE mixtures in train 1 (CE circulates throughout this SMB) and then the BCE mixture into B and CE products in train 2 (Figure 2a) proved to be the simplest four-zone cascade in this study. If pure C product is desired, separating the feed into ABC and ABE in train 1 and then separating the ABC mixture into AB and C products in train 2 is the equivalent configuration. We next modified the system (Figure 2a) by recycling the unwanted product CE, which contains large amounts of desorbent D (Figure 2b). Although this recycle would not be possible for complete quaternary separations and nonlinear systems, it will reduce the use of desorbent for the center-cut separation without a drop in efficiency for linear isotherms. In Figure 2b, desorbent D1 is optional, and the two stirred tanks were used to keep the concentrations of the BCED

uB1′ ) MBF′uport′

(MBF′ e 1)

(8a)

uC2′ ) MCF′uport′

(MCF′ e 1)

(8b)

uB3′ ) MBT′uport′

(MBT′ g 1)

(8c)

uE4′ ) MET′uport′

(MET′ g 1)

(8d)

The minimum D/F of train 2 (Mij ) 1) is 9.23, which is much larger than the minimum D/F ) 1.0 for a standard binary fourzone SMB separating B and C. For B-C binary separation, eq 8d becomes uC4′ ) MCT′uport′, and fluid velocity to satisfy this is much less than for eq 8d; thus, removal of the E requires considerable additional desorbent. The total minimum Dtotal/F for the system in Figure 2a is 10.23. Assuming densities are constant, the mass balances for the recycle system in Figure 2b are as follows:

V2 ) V3 + Vfeed

(9a)

V1 ) V2 - VACE product

(9b)

V3 ) V4 - VBCE product

(9c)

V4 ) V1 + VCE recycle + Vdesorbent 1

(9d)

V2′ ) V3′ + VBCE product

(9e)

V1′ ) V2′ - VB product

(9f)

V3′ ) V4′ - VCE product - VCE recycle

(9g)

8716


V4′ ) V1′ + Vdesorbent 2

(9h)

Vfeed + Vdesorbent 1 + Vdesorbent 2 ) VACE product + VB product + VCE product (9i) In eq 9d, since desorbent use in train 1 is reduced by the amount of recycled CED, the minimum Dtotal/F is decreased from 10.23 without the recycle (Figure 2a) to 9.23 with the recycle (Figure 2b). System 2 + 4 (Cascade with the Two-Zone SMB/Chromatography and Four-Zone SMB). A recycled cascade that combines the two-zone SMB/chromatography (Figure 3) and the standard four-zone SMB (Figure 1a) systems was studied for the purification of the intermediate component. The twozone system was originally designed for complete ternary separations in case of easy B-C separation;13 however, the system is easily modified for center-cut separations, and the modified system has less restrictive separation constraints than the original two-zone system.19 In Figure 3, A and B are separated by a SMB approach (the switching and remixing with the feed keep the mass transfer zone inside the column) while the B-C separation is chromatographic (the B-C mass transfer zone leaves the system). During step a, the slowest component C from the previous feed step exits with the fast moving component A at the top of zone 1, and AB is recycled by remixing with feed. During step b, AC mixture and B are produced at the exits of zones 1 and 2, respectively. Therefore, the two-zone system has discontinuous feed and product streams that are common in most cyclic adsorption processes.30 Two two-zone systems can be used in parallel for a continuous feed stream,31 or a buffer tank can be used when the system is connected with other systems having continuous streams. For the center-cut separation from the quaternary mixture, it is difficult to obtain both high purity and recovery of B by using only the two-zone system since the B-C separation (R′BC ) 1.19) is difficult.19 A rational alternative is to separate the feed into AE and BC mixtures in the two-zone SMB/chromatography, and then separate the BC mixture into B and C products in the four-zone SMB. Like the system 4 + 4, desorbent use can be significantly reduced by recycling the unwanted product C + D to train 1 (Figure 4). Since the C product in the four-zone SMB is recycled and used in addition to D as mobile phase in the two-zone system, component C exits throughout the entire cycle while B component exits during only step b. In the simulations, two large buffer tanks were used between the two trains to keep the feed to the four-zone SMB and the recycle stream concentrations constant. The effects of tank size were studied previously.19 Separation constraints for the two-zone system in system 2 + 4 are

V1aGAta ) MAFL (no constraint for MAF)

Figure 3. Integrated two-zone SMB/chromatography system for centercut separation from a ternary mixture.18 Reprinted with permission from ref 13. Copyright 2005, American Chemical Society.

Figure 4. Combined cascade with two-zone SMB/chromatography and binary four-zone SMB with recycle to separate only the middle component B from a quaternary mixture (system 2 + 4). Switching of ports is not shown.

V1aGEta + V1bGEtb + V2aGEta + V2bGEtb ) MEFL (MEF e 1, E not breakthrough) (10e) 2V1bGEtb + 2V2aGEta + V2bGEtb + V1aGEta ) METL (MET g 1, trailing edge of E exits column before B product) (10f) Separation constraints of train 2 are the same as eqs 8a-d except that eq 8d refers to component C:

(10a)

V1bGAtb + V2aGAta ) MATL (MAT g 1, trailing edge of A exits column) (10b) V1aGBta + V1bGBtb ) MBFL (MBF e 1, B not breakthrough) (10c) V1bGBtb + V2aGBta + V2bGBtb ) MBTL (MBT g 1, trailing edge of B exits column) (10d)

uC4′ ) MCT′uport′

(MCT′ g 1)

(11)

The equations for mass balances can be developed in a fashion similar to system 4 + 4. System 1 + 4 (Cascade with the One-Column Analogue and Four-Zone SMB). For the standard four-zone SMB for binary separations, alternative systems using one chromatography column have been studied.25-28,32-35 A one-column analogue that can mimic any SMB has been developed with both mixed and unmixed reservoirs for binary25-27 and ternary separations.28 We first extend the analogue to the center-cut,


Figure 7. Combined cascade with the one-column analogue and the binary four-zone SMB to separate only the middle component B from a quaternary mixture (system 1 + 4). Switching of ports is not shown.

Figure 5. Single-column chromatograph with recycle analogous to the twozone SMB/chromatography system for center-cut separation from a ternary mixture. (a) Analogue of the two-zone SMB/chromatography with four steps. (b) Simplified analogue system with three steps.

Figure 8. System configuration of the one-column analogue with an unmixed reservoir for system 1 + 4.

of the one-column analogue in the system 1 + 4 are as follows:

VaGAta ) MAFL (MAF g 1, A breakthrough) (12a) VbGAtb ) MATL (MAT g 1, trailing edge of A exits column) (12b) VaGBta ) MBFL (MBF e 1, B not breakthrough) Figure 6. Local equilibrium solutions for the center-cut, ternary analogue. Shown for one complete cycle in Figure 5b (s, A; ‚‚‚‚, B; - - -, C).

two-zone SMB/chromatography system and then use an analogue plus a four-zone SMB for the quaternary separation. Figure 3 shows a complete cycle of the center-cut, ternary twozone system, which was redesigned by using a single column and a tank (Figure 5a). The tank in step c is used to recycle the AB mass transfer zone to mix it with the feed to improve the separation. In the one-column analogue, since steps a and b both produce AC mixtures, they can be merged into one step (Figure 5b). Like the two-zone SMB/chromatography system, the analogue has discontinuous feed and products. The movements of the three solutes (A, B, C) for Figure 5b based on the local equilibrium model are shown in Figure 6. System 1 + 4 shown in Figure 7 separates the quaternary mixture to produce the B product in the same way as system 2 + 4 (Figure 4). The one-column analogue is now adapted to separate the quaternary mixture into ACE and BC, and then the difficult B-C separation is done in the standard binary fourzone SMB. Since the unwanted product C + D is recycled, C exits the analogue throughout the cycle. Separation constraints

(12c)

VbGBtb + VcGBtc ) MBTL (MBT g 1, trailing edge of B exits column) (12d) VaGEta + VbGEtb + VcGEtc ) MEFL (MEF e 1, E not breakthrough) (12e) VbGEtb + VcGEtc + VaGEta + VbGEtb ) METL (MET g 1, trailing edge of E exits column) (12f) Component C is not involved in the analogue constraints. The second train (four-zone SMB) separates the BC mixture into B and C products and has the normal binary constraints. Since concentration profiles are destroyed in a mixed tank, B purity may be reduced. A number of mixed tanks can be used to keep the profiles, but this complicates the system and may not be practical.25 Instead of many mixed reservoirs, a plugflow tank can be used to increase the efficiency of the onecolumn system.28,34,35 In our study, a column (Dcol ) 1.0 cm) packed with glass beads (dp ) 100 µm) was used as an unmixed reservoir for the one-column analogue. The column length was

8718


Table 2. Optimized Switching Times and Flow Rates (cm3/min) with Different Dtotal/F Values Section a: System 4 + 4 (Figure 5) (Qfeed ) 0.067 cm3/min, CA ) CB ) CC ) CE ) 1.0 g/L) 1st train

2nd train

Dtotal/F

tsw (min)

QR1

QD1,opt

QACE

QBCE

tsw′ (min)

QR2

QD2

QB

QCE

QCErecycle

9.50 11.30 13.90 16.27

31.78 28.90 25.43 25.43

0.112 0.121 0.134 0.134

0.000 0.000 0.000 0.000

0.065 0.067 0.080 0.080

0.069 0.080 0.087 0.087

15.97 13.43 11.16 9.73

0.356 0.423 0.504 0.573

0.634 0.753 0.927 1.085

0.096 0.094 0.097 0.111

0.539 0.659 0.817 0.961

0.067 0.080 0.100 0.100

Section b: System 2 + 4 (Figure 6) (Qfeed ) 0.1 cm3/min, CA ) CB ) CC ) CE ) 1.0 g/L) 1st train

2nd train

Dtotal/F

tsw (min)

QACE1

QD1,opt

QACE2

QBC

QD3,opt

tsw′ (min)

QR′

QD′

QB

QC

QCrecycle

3.39 4.27 6.34 8.83 14.22

42.38 42.38 38.09 35.76 30.53

0.267 0.267 0.273 0.286 0.275

0.167 0.000 0.000 0.000 0.000

0.000 0.000 0.023 0.030 0.093

0.142 0.142 0.204 0.284 0.332

0.028 0.000 0.000 0.000 0.000

15.43 9.80 6.84 4.90 3.54

0.368 0.535 0.766 1.071 1.366

0.071 0.213 0.305 0.427 0.664

0.085 0.120 0.172 0.241 0.424

0.000 0.009 0.046 0.093 0.152

0.057 0.155 0.189 0.235 0.254

Section c: System 1 + 4 (Figures 7 and 8) (Qfeed ) 0.125 cm3/min, CA ) CB ) CC ) CE ) 1.0 g/L) 1st train

2nd train

Dtotal/F

tsw (min)

QACE

QABCE

QD1,opt

QBC

QD2,opt

tsw′(min)

QR′

QD′

QB

QC

QCrecycle

3.41 4.44 6.09 8.48 13.05

50.85 50.85 43.39 41.52 34.94

0.328 0.328 0.390 0.397 0.467

0.203 0.203 0.265 0.272 0.342

0.203 0.000 0.000 0.000 0.000

0.185 0.185 0.235 0.353 0.408

0.038 0.000 0.000 0.000 0.000

17.78 11.29 6.99 5.92 4.32

0.320 0.464 0.777 0.886 1.118

0.062 0.185 0.254 0.353 0.544

0.074 0.104 0.164 0.201 0.347

0.000 0.013 0.001 0.062 0.083

0.049 0.129 0.167 0.208 0.250

calculated from the flow rate and the step time of step b. For the unmixed reservoir, axial dispersion was estimated by the Chung and Wen correlation (eq 2). Although several designs can be used to combine the unmixed reservoir with the onecolumn system, the system shown in Figure 8 was used. In this system, the ACED product is split into two parts. The additional ACED product during step b is required to balance the unmixed reservoir. Results and Discussion Optimization. The minimum Dtotal/F values for the three systems were determined from the local equilibrium model constraints. Since separation at the minimum Dtotal/F will not be perfect when mass transfer resistance and axial dispersion are finite, the separation needs further optimization. Optimization tools such as the triangle theory plus optimization,29 standing

Figure 9. Purity of B (2′-deoxyguanosine) in B product vs Dtotal/F in the system 4 + 4 (1, with recycle of CE product (2); 2, without recycle of CE product (b)). Productivities are the same for both systems.

wave design,17,36 on-line optimization,37 and genetic algorithm38 have been developed. In this research, a binary coded genetic algorithm was used to maximize PB with constraints for RB, Dtotal/F, and productivity.38-41 The local equilibrium model gave useful information about the proper range of each variable, which helped the genetic algorithm find the optimum values faster. The objective and constraints are as follows:

objective: maximize PB (%) subject to: Dtotal/F ) constant

(13a)

Qfeed ) constant

(13b)

RB (%) g 90.0 %

(13c)

Qij and tj g 0

(13d)

The constraints 13a-d were specified with the fixed column length (L ) 15 cm) in order to compare purities of the systems with identical productivity and desorbent use and similar recoveries. Although the maximum pressure drop or maximum flow rate is often included in the constraints, operating conditions were first optimized without a limit of pressure drop, and then the systems were scaled to the maximum pressure drop limits. As mentioned, it takes 120-150 min to reach cyclic steady state for an integrated system with buffer tanks and recycle. Thus, although the global optimum may not be obtained, trains 1 and 2 were optimized separately to reduce the computation time, which was 10-15 min for each train. First, train 1 was simulated with various D/F values, and four D/F values were chosen between the minimum D/F and D/F where the PB for train 1 is almost constant. Then, train 2 was optimized with the results of train 1 to find the maximum PB. In these steps, RB g 95.0% for each train was used for systems 1 + 4 and 2 + 4 so that RB,total g 90.0%. However, in the system 4 + 4 RB,1 g 99.0% and RB,2 g 91.0% were used because the A-B separation in train 1 is much easier than the B-CE separation.


Figure 10. Concentration profiles exiting of the second column from the top of the first train in the system 4 + 4 with one column per zone (Figure 2) for the nucleosides mixture (0, A; O, B; +, C; -, E). The dashed lines are concentration profiles in the system without the recycle of the CE product.

For the genetic algorithm, 50 chromosomes were used, and it took around 20 generations to obtain the optimum values. The computer program for the genetic algorithm was formulated with Visual Basic and Excel and combined with Aspen Chromatography to evaluate the variables. Table 2 shows the optimized switching times and flow rates of the three systems. The maximum pressure drop that occurs in zone 4 of train 2 was less than 16 bar for the operating conditions. For further study, it may be useful to develop faster optimization methods for large systems with multiple trains, additional recycle streams, and buffer tanks; however, faster optimization needs to be balanced against development time. Comparison. Figure 9 shows the effect of recycling the CE product stream in the system 4 + 4. As a result of the recycle, the minimum Dtotal/F was decreased from 10.23 to 9.23. At the same Dtotal/F values the recycled system has higher purities PB than the system without recycle. This is particularly significant at low desorbent rates. The concentration profiles exiting train 1 of the system 4 + 4 are shown in Figure 10. While the profiles

Figure 11. Purity for B (2′-deoxyguanosine) in B product vs Dtotal/F in the recycled systems with one column per zone in both trains (1, system 4 + 4 (9); 2, system 2 + 4 (2); 3, system 1 + 4 (b)).

of A and B were not changed by recycle, the concentrations of C and E were increased in the recycled system. At high desorbent rates the simpler cascade without recycle is probably preferable to the recycle cascade. Figure 11 compares the three recycled systems showing the effect of Dtotal/F on PB. Recycling the C product decreased the minimum Dtotal/F from 5.78 to 3.09 for the system 1 + 4 and from 4.51 to 3.09 for the system 2 + 4, respectively. The recovery values RB (Table 3) ranged from 91.3 to 92.3 with average 91.7% for system 1 + 4 with a mixed tank, from 89.9 to 91.9 with average 91.1% for system 2 + 4, and from 89.9 to 92.2 with average 90.7% for system 4 + 4. The recoveries for system 1 + 4 with an unmixed tank were all below 90%. For PB in the range of 90-95%, Dtotal/F values for systems 2 + 4 and 1 + 4 are much smaller than that of system 4 + 4. However, PB values were almost constant or slightly decreased for Dtotal/F > 9.0, and PB values such as 99.0% or higher could not be achieved with systems 2 + 4 and 1 + 4 with one column per zone in the four-zone SMB. The B-C and B-CE separations in train 2 are the most difficult separations (R′BC ) 1.19) in this study. The main

Table 3. Simulation Results system 4 + 4 train 2 configuration 1-1-1-1 (unmixed tank used in train 1) 2-2-2-2 a

system 2 + 4

system 1 + 4a

Dtotal/F

9.50

11.30

13.90

16.27

3.39

4.27

6.34

8.83

14.22

3.41

4.44

6.09

8.48

13.05

PB (%) RB (%) PB (%) RB (%) PB (%) RB (%)

71.2 89.9

83.5 90.7

94.9 90.0

96.2 92.2

68.8 91.7

90.6 91.9

95.7 91.4

96.1 90.7

95.5 89.9

72.3 93.4

83.9 96.0

98.6 97.7

99.5 98.8

70.6 93.3

92.3 94.9

97.7 94.4

98.9 93.8

98.9 93.4

64.0 91.7 65.4 88.4 65.9 93.6

84.4 92.3 87.1 89.6 86.3 95.0

91.2 91.8 92.1 88.1 95.3 92.5

95.3 91.4 95.3 88.2 97.6 94.6

94.6 91.3 94.2 86.9 97.7 94.2

First set of results uses a mixed tank in train 1.

Table 4. Comparison of the Three Systemsa system 4 + 4b

system 2 + 4b

system 1 + 4b,c

configuration of train 2

1-1-1-1

2-2-2-2

1-1-1-1

2-2-2-2

1-1-1-1

2-2-2-2

(Dtotal/F)min Dtotal/F for PB ) 95.0% RB (%) for PB ) 95.0% ∆Pmax(bar)d for PB ) 95.0% (number of columns)min

9.23 14.26 90.2 4.40 8

13.27 97.3 4.13 12

3.09 6.07 91.5 4.89 6

5.29 94.7 4.32 10

3.09 8.33 91.4 5.85 5

6.06 92.6 5.06 9

a Productivity ) 0.00334 cm3/cm3‚min in all systems. b Train 1 has one column per zone for both 1-1-1-1 and 2-2-2-2 configurations. c A mixed tank was used for train 1 of system 1 + 4. d Total pressure drop of train 2.

8720


Table 5. Scaling for the Same Pressure Drop, ∆Pmax ) 10.0 Bar system 4 + 4a

system 2 + 4a

system 1 + 4a,b

configuration of train 2

1-1-1-1

2-2-2-2

1-1-1-1

2-2-2-2

1-1-1-1

2-2-2-2

Dtotal/F a ) dp,new/dp,old g ) Qnew/Qold PB (%) for ∆Pmaxc ) 10.0 bar RB (%) for ∆Pmaxc ) 10.0 bar productivity (cm3/cm3‚min) for ∆Pmaxc ) 10.0 bar

14.26 0.815 1.507 95.2 92.0 0.00503

13.27 0.802 1.555 95.3 97.3 0.00519

6.07 0.836 1.429 95.1 91.7 0.00477

5.29 0.811 1.522 94.8 94.6 0.00508

8.33 0.875 1.308 94.7 91.5 0.00437

6.06 0.843 1.406 94.9 92.3 0.00470

a Train 1 has one column per zone for both 1-1-1-1 and 2-2-2-2 configurations. b A mixed tank was used for train 1 of system 1 + 4. c Total pressure drop of train 2.

+ 4. Thus, for the quaternary mixture of the nucleosides with PB ) 95% and RB > 90%, systems 2 + 4 and 1 + 4 will probably reduce both capital and operating costs. The maximum pressure drop of the column can be utilized by adding more pumps to the loop to increase productivity.31 In Table 4, the maximum pressure drop for PB ) 95% and productivity ) 0.00334 cm3/cm3‚min is approximately 4-5 bar, which is lower than the maximum pressure drop of 10 bar for the adsorbent, SOURCE 30RPC.42 To utilize the pressure limit and to compare the systems at the same pressure drop, SMB scaling rules were applied. When pore diffusion controls, the scaling factors and equations are31

a)

dp,new Lnew Dcol,new Qj,new b) c) g) (14a-d) dp,old Lold Dcol,old Qj,old

RP ) Figure 12. Purity for B (2′-deoxyguanosine) in B product vs Dtotal/F with one column per zone in train 1 and two columns per zone in train 2 (1, system 4 + 4 (9); 2, system 2 + 4 (2); 3, system 1 + 4 (b)).

contaminant in the B product is component C. Thus, to improve the separation we used two columns per zone for train 2 (2-22-2). To keep productivity constant, the column length in train 2 was halved (Lcol ) 7.5 cm) while there is no change in train 1. The results are shown in Figure 12 and Table 3. For the system 2 + 4, purity PB was increased from 96.1% to 98.9% at Dtotal/F ) 8.83, and recovery RB was increased to 93.8% when two columns per zone were used in train 2. The average RB and PB values of the systems 1 + 4 and 4 + 4 were also increased. For the one-column analogue in system 1 + 4, use of an unmixed reservoir instead of the mixed reservoir is expected to improve the separation since it retains the concentration profile. Table 3 shows B purities for both mixed and unmixed reservoirs when one column per zone was used. Although PB increased in the low Dtotal/F region, the unmixed reservoir did not improve PB for Dtotal/F > 8.48. In the low Dtotal/F region, the fraction of C in the B product decreased which increased PB. For Dtotal/F > 8.48, the contamination of B product with component E prevented further increases in purity. In addition, RB was lower with an unmixed tank because of dispersion in the tank. Thus, the unmixed reservoir resulted in little improvement. Table 4 compares the three systems at the same productivity and same purity. The values Dtotal/F for PB ) 95% and (Dtotal/ F)min for systems 2 + 4 and 1 + 4 are much smaller than those of system 4 + 4. System 4 + 4 shows considerable improvement on recovery RB when two columns were used for each zone of train 2. In system 1 + 4, the pressure drop in train 2, where the maximum pressure drop occurs, is slightly larger than the other systems when one pump is used in the recycle loop. However, systems 2 + 4 and 1 + 4 require fewer columns than system 4

∆Pj,new (L/LMTZ)j,new bc2 bg ) 2 2 RN ) ) ∆Pj,old a c (L/LMTZ)j,old a2g (15a,b)

where j indicates the zone. In the scaling procedure, while the column length and diameter are fixed (b ) c ) 1.0), the scaling factors a and g are varied for ∆Pnew ) 10.0 bar, and RN ) 1.0 for the same PB ) 95.0% used in Table 4. The results (Table 5) show that the three systems have similar productivities for the same pressure drop and similar PB values. Although system 4 + 4 has a slightly higher productivity, it requires approximately twice as much desorbent as systems 1 + 4 and 2 + 4 for PB ) 95.0%. In addition, system 1 + 4 and 2 + 4 have fewer columns, which is advantageous when adsorbent replacement is frequent as required in campaigns. Conclusions The simulation results showed that the combined SMB systems 1 + 4 and 2 + 4 can be used for center-cut separation from a quaternary mixture. Although the separation constraints of these systems are more complex than those of the classical 4 + 4 SMB cascade, they showed higher B purities at low Dtotal/F values and require fewer columns. In these three cascade systems, the unwanted product which contains large amounts of desorbent is recycled from train 2 to train 1. Compared to systems without recycle, the recycled systems use less desorbent and have higher B purities at the same Dtotal/F and productivity. In addition, purity and recovery increase when two columns per zone are used for train 2 where the difficult B-C or B-CE separation is done. Systems 1 + 4 and 2 + 4 may require buffer tanks because of their discontinuous feed and product streams in train 1, and system 4 + 4 needs a tank to produce a constant BC concentration between trains 1 and 2. These new designs probably reduce both capital and operating costs.


Acknowledgment This research was partially supported by NSF Grant CTS0211208. We thank our colleagues Nadia Abunasser, Weihua Jin, and Jeung Kun Kim, who offered useful suggestions in this research. Nomenclature a ) ratio of particle diameters in two designs ) dP,new/dP,old b ) ratio of column lengths in two designs ) Lnew/Lold C ) solute concentration in the liquid phase, g/cm3 c ) ratio of column diameters in two designs ) Dcol,new/Dcol,old Dax ) axial dispersion coefficient, cm2/s Dcol ) column 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 ) [1 + (1 - )‚Ki/]-1 g ) ratio of volumetric flow rates in two designs ) Qj,new/Qj,old Ki ) linear equilibrium parameter ) qi/Ci L ) column length, cm M ) multiplier PB ) purity of B in B product, % Pedp ) Peclet number based on particle diameter ) dpV/Dax Q ) volumetric flow rate, cm3/min q ) solute concentration on solid phase, g/(cm3 of particles) RB ) recovery of B in B product, % Re ) Reynolds number ) dpVF/µ RN ) ratio of the fractional bed use in two designs ) (L/LMTZ)new/(L/LMTZ)old RP ) ratio of pressure drop in two designs ) ∆Pj,new/∆Pj,old tsw ) switching time of train 1, s tsw′ ) switching time of train 2, s u ) solute velocity, cm/s V ) interstitial velocity, cm/s z ) axial coordinate, cm Greek Symbols R ) selectivity based on isotherms R′ ) 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, E j ) zones in SMB; j ) 1, 1′, 2, 2′, 3, 3′, 4, 4′ k ) step; k ) a, b, c x ) front (F) or trailing (T) edge Literature Cited (1) Nicoud, R. M. Simulated moving-bed chromatography for biomolecules. In Handbook of Bioseparations; Ahuja, S., Ed.; Academic Press: San Diego, 2000, p 475. (2) Juza, M.; Mazzotti, M.; Morbidelli, M. Simulated moving-bed chromatography and its application to chirotechnology. Trends Biotechnol. 2000, 18, 108. (3) Broughton, D. B. Molex: case history of a process. Chem. Eng. Prog. 1968, 64 (8), 60. (4) Wankat, P. C. Simulated moving bed cascades for ternary separations. Ind. Eng. Chem. Res. 2001, 40, 6185. (5) Nicolaos, A.; Muhr, L.; Gotteland, P.; Nicoud, R. M.; Bailly, M. Application of equilibrium theory to ternary moving bed configurations (four

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ReceiVed for reView December 9, 2005 ReVised manuscript receiVed September 12, 2006 Accepted October 2, 2006 IE0513705

Hybrid Simulated Moving Bed and Chromatography Systems for

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