Designs of Simulated-Moving-Bed Cascades for Quaternary Separations

Ind. Eng. Chem. Res. 2004, 43, 1071-1080

1071

Designs of Simulated-Moving-Bed Cascades for Quaternary Separations Jeung Kun Kim and Phillip C. Wankat* School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907-2050

Although basic architecture is important for all simulated-moving-bed (SMB) systems, it is particularly important for the separation of multicomponent mixtures because there are not yet standard schemes. New designs are proposed for SMB cascades separating quaternary mixtures. The local equilibrium model is used to determine the minimum desorbent-to-feed ratios (D/F) and productivities for 21 different SMB systems with linear isotherms. An easy-split SMB cascade can theoretically achieve the thermodynamic minimum D/F ) 3.0. On the basis of the results, tentative selection rules for SMB systems are proposed for quaternary separations with linear isotherms. Detailed simulations agreed qualitatively with the equilibrium model predictions. Simulated-moving-bed (SMB) systems were developed as an efficient method for doing large-scale chromatographic separation, particularly of binary mixtures.1 Recently, SMB technology has been applied in the food, biotechnology, pharmaceuticals, and fine chemical industries.2-5 A schematic diagram of the four-zone SMB for binary separation is shown in Figure 1. The design of SMB systems for binary separations has been extensively studied by many groups and is now well understood.6-10 On the other hand, the use of SMB cascades for multicomponent systems has not been extensively studied. Wooley et al.11 developed a nine-zone system for separations of two sugars (glucose and xylose) from biomass hydrolyzate. Extensive comparisons of theory and experiments were made for ternary systems, and a few experiments were done with a quaternary system (acetic acid, glucose, xylose, and sulfuric acid). Nicoud12 discussed a five-zone system with side streams for the separation of ternary mixtures. Mata and Rodrigues13 developed a pseudo-SMB model of the JO process developed by Japan Organo Co. for the separation of a ternary mixture and addressed the effects of operating conditions and mass-transfer coefficients on the process performance. Because ternary separations are now being done commercially with SMB cascades, it is appropriate to consider the next step: quaternary separations. Industrially significant separations that might use a quaternary SMB cascade include purification of biomass hydrolyzate11 and separation of complex sugar mixtures. The sequencing of distillation columns for a fraction of multicomponent mixtures has been extensively studied.14-18 Because there is a weak analogy between distillation and SMB systems, it is natural to apply distillation sequences for the initial development of SMB sequences for the separation of multicomponent mixtures. Wankat19 proposed a number of new SMB cascades for ternary separations that were initially based on distillation sequences. He determined the minimum * To whom correspondence should be addressed. Tel.: 765494-7422. Fax: 765-494-0805. E-mail: [email protected].

Figure 1. SMB for binary separation.

desorbent usage and the productivity for linear systems and found that modifications in the sequences were necessary. The goals of this paper are to develop new designs of SMB cascades for quaternary systems and to determine the productivity and minimum desorbent-to-feed ratio, D/F, for each cascade for complete separation. The initial screening studies use the equilibrium model with linear isotherms. Complete simulations with Aspen Chromatography are done for a few designs to check the conclusions of the equilibrium model. New Designs Twenty-one SMB designs for complete separation of four-component systems are shown in Figures 2-6. For simplicity, all systems are shown with one column per zone; of course, the number of columns per zone can be increased to any desired value. Component A is the weakest adsorbed, and E is the strongest. D is the desorbent. Figure 2 illustrates the straightforward use of the analogy with distillation to develop 12-zone systems with one product stream for each product. The configurations in parts a-e of Figure 2 differ by the order in which pure products are removed. Figure 3 illustrates 13-zone systems with two product streams for one of the components. The use of an additional product stream reduces the feed flow to the next SMB unit, thus decreasing the need for desorbent. The addition of the extra product stream is not analogous

10.1021/ie020863w CCC: $27.50 © 2004 American Chemical Society Published on Web 01/20/2004

1072 Ind. Eng. Chem. Res., Vol. 43, No. 4, 2004

Figure 2. (a) 12-zone SMB for complete quaternary separations: middle split. (b) 12-zone SMB for complete quaternary separations: remove heavies first. (c) 12-zone SMB for complete quaternary separations: remove heavy and then light components. (d) 12-zone SMB for complete quaternary separations: remove lights. (e) 12-zone SMB for complete quaternary separations: remove light and then heavy components before final separation.

to distillation practice but has been done for ternary SMB systems.11,19 The configurations in parts a-f of Figure 3 also differ by the order in which pure products are removed. Figure 4 illustrates 14-zone systems with either two product streams for two components or three product streams for one component. The additional product streams again reduce feed rates to the next SMB, reducing desorbent use. Figure 5 illustrates two 19-zone systems that use an easy-split ternary separation.19 The easy-split process is analogous to distillation, but the use of additional product withdrawals is not. Figure 6a illustrates a 28-zone system that uses easysplit separations for both the quaternary and ternary separations. Parts b and c of Figure 6 extend the easysplit configuration by first (Figure 6b) withdrawing two additional pure products from the first train of the 30zone cascade. Figure 6c adds the withdrawal of binary mixtures from the first train in a 32-zone cascade. This step was not employed for ternary SMB systems19 and

is not analogous to distillation. Although extensive, this catalog of designs is not encyclopaedic. Local Equilibrium Solution The equilibrium solution has been extensively applied to analyze SMB systems with both linear and nonlinear isotherms.6,7,9,19 The linear equilibrium solution is easily developed for all of the schemes shown Figures 2-6. To easily compare these cascades, this paper is restricted to linear isotherms although the cascades would be applicable to nonlinear isotherms. The goal of the linear analysis is to find the conditions that minimize desorbent usage and then compare the minimum desorbentto-feed ratio, (D/F)min, and the productivity for each cascade. The equilibrium model assumes very rapid mass transfer and negligible dispersion so that the adsorbate concentration q is always in equilibrium with the solute concentration c outside the adsorbent particles. Thus,

Ind. Eng. Chem. Res., Vol. 43, No. 4, 2004 1073

Figure 3. (a) 13-zone SMB for complete quaternary separations: corresponds to Figure 2b but with an extra A product in train 2. (b) 13-zone SMB for complete quaternary separations: corresponds to Figure 2b but with an extra A product in train 1. (c) 13-zone SMB for complete quaternary separations: corresponds to Figure 2c but with an extra C product in train 2. (d) 13-zone SMB for complete quaternary separations: corresponds to Figure 2c but with an extra A product in train 1. (e) 13-zone SMB for complete quaternary separations: corresponds to Figure 2d but with an extra E product in train 1. (f) 13-zone SMB for complete quaternary separations: corresponds to Figure 2e but with an extra E product in train 1.

for systems separating based on equilibrium differences, the equilibrium solution represents the best separation possible. For linear isotherms, the solute velocity19 is

vj

usolute i,zone j ) 1+

1 - e (1 - e)(1 - p) K + FsKi e p Di e (1a)

where the average port velocity is uport ) L/tsw. If masstransfer rates are very high and dispersion is low, the conditions in eq 2 will ensure complete separation of solutes A-B and C-E. The interstitial velocities are related to mass balances. Assuming that the densities of the liquid mixtures are identical

v1 ) v2 - vABprd, v2 ) v3 + vF, v3 ) v4 - vCEprd, v4 ) v1 + vD (3a-d)

where Ki ) qi/ci. It is convenient to write this as

uij ) (constanti)vj ) Civj

(1b)

As an illustration of this well-known procedure, consider the quaternary SMB shown in Figure 2a. Train 1 separates components A and B from C and E. We want

uA1 e uport, uA2 g uport, uB2 g uport, uC2 e uport, uE2 e uport, uA3 g uport, uB3 g uport, uC3 e uport, uE3 e uport, uE4 g uport (2a-j)

The velocities of products, feed, and desorbent input are related to their volumetric rates by equations of the form

vF )

F eAC

where AC ) πdcol2/4

(4)

Because v2 is greater than v3, eqs 2b, 2c, 2e, 2f, 2h, and 2i are automatically satisfied if eqs 2d and 2g are satisfied, respectively. Thus, the four eqs 2a, 2d, 2g, and 2j are sufficient. The minimum amount of desorbent


Figure 4. (a) 14-zone SMB for complete quaternary separations: corresponds to Figure 2a but with extra A and E products in train 1. (b) 14-zone SMB for complete quaternary separations: corresponds to Figure 3a but with an extra A product in train 1. (c) 14-zone SMB for complete quaternary separations: corresponds to Figure 3c but with an extra A product in train 1. (d) 14-zone SMB for complete quaternary separations: corresponds to Figure 3e but with an extra E product in train 2. (e) 14-zone SMB for complete quaternary separations: corresponds to Figure 3f but with an extra B product in train 2.

under ideal conditions can be found by using the equality signs in these four relationships. For a known feed rate F, simultaneously solving eqs 1b, 2d, 2g, 3b, and 4 results in

v2 ) CBvF/(CB - CC), uport ) CCv2 ) CCCBvF/(CB - CC), v3 ) v2 - vF (5a-c) Once the optimum value of uport has been determined, the velocities in zones 1 and 4 can be found from eqs 1a and 2a,j.

v1 ) uport/CA, v4 ) uport/CE

(6a,b)

Thereupon, vABprd, vCEprd, and vD can be determined from

eqs 3a, 3c, and 3d. The column length is related to the port velocity and the switching time by L ) uporttsw. The feeds to trains 2 and 3 are the AB and CE products from train 1, respectively. Because the three trains are likely to have columns of different diameter, the new volumetric feed rates are calculated as

Ftrn2 ) (vABprdeAC)trn1, Ftrn3 ) (vCEprdeAC)trn1 (7a,b) The feed velocities vF,trn2 and vF,trn3 are found from eq 4. Trains 2 and 3 do binary separations and can be designed by standard procedures. The total amount of desorbent is

Dtotal ) Dtrn1 + Dtrn2 + Dtrn3

(8)

Ind. Eng. Chem. Res., Vol. 43, No. 4, 2004 1075

Figure 5. (a) 19-zone SMB for complete quaternary separations with three A products, two B products, and two C products. (b) 19-zone SMB for complete quaternary separations with three E products, two B products, and two C products.

which allows the value of (Dtotal/F)min to be calculated. The volumetric productivity of the system is defined as

productivity )

volume feed/time total adsorbent volume

(9)

signs are used. Substituting eq 1b into eqs 11a-h, we obtain

v1 ) uport/CA, v2 ) uport/CB, v3 ) uport/CC, v4 ) uport/CE, v5 ) uport/CA, v6 ) uport/CB, v7 ) uport/CC, v8 ) uport/CE (12a-h)

where the total adsorbent volume is calculated from The velocity relationships (with constant density) are

total adsorbent volume ) [(no. of columns)ACL]trn1 + [(no. of columns)ACL]trn2 + [(no. of columns)ACL]trn3 (10) Switching times and column lengths can be different in each train. For the local equilibrium solution, the switching time (or column length) can be arbitrarily specified. To compare the productivities for all systems, we used an arbitrarily chosen constant switching time of 7.5 min. Column diameters were sized so that the maximum velocity in each train was 100 cm/min. These choices do not affect the calculated values of D/F. When the calculations are programmed in a spreadsheet, D/F and productivity can easily be determined for any input conditions. The 32-zone easy-split system shown in Figure 6c is a special case because it always has the lowest D/F, equal to 3.00 for all cases because the easy-split configuration with appropriate product withdrawals does not require extra desorbent and each of the seven trains can be optimized. The minimized desorbent-to-feed ratios D/F can be estimated from the equilibrium model. Appropriate solute velocity equations for train 1 of Figure 6c are

uA1 e uport, uB2 e uport, uC3 e uport, uE4 e uport, uA5 g uport, uB6 g uport, uC7 g uport, uE8 g uport (11a-h) To find the minimum amount of desorbent, the equal

v1 ) v2 - Aprd/AC, v2 ) v3 - FAB,trn1/AC, v3 ) v4 - FABC/AC, v4 ) v5 - Ftrn1/AC, v5 ) v6 - FBCE/AC, v6 ) v7 - FCE,trn1/AC, v7 ) v8 - Eprd/AC, v8 ) v1 + D1/AC (13a-h) At the feed point for train 1, we can simultaneously solve eqs 12d, 12e, and 13d. The resulting value of uport is

uport )

Ftrn1/AC 1/CE - 1/CA

(14)

Now all of the velocities are easily determined from eq 12 and the product flow rates and D1 from eq 13. The total amount of desorbent required is

Dtotal ) D1 + D2 + D3 + D4 + D5 + D6

(15)

Because the minimum amount of desorbent for complete separation in a linear ternary easy-split SMB system (including the corresponding binary SMBs) is 2 × feed rate19 and the minimum amount of desorbent for a linear system is the feed rate, eq 15 becomes

Dtotal ) D1 + 2FBCE + 2FABC + FAB,trn1 + FCE,trn1 (16) Upon substitution in the feed rate from eq 13 and the velocities from eq 12, this becomes

[(

Dtotal,min ) uportAC 3

)]

1 1 CE CA

(17a)


Figure 6. (a) 28-zone SMB for complete quaternary separations: easy split. (b) 30-zone SMB for complete quaternary separations: easy split with removal of A and E products in train 1. (c) 32-zone SMB for complete quaternary separations: easy split with removal of A and E products and removal of intermediate streams AB and CE in train 1.

Upon substitution in eq 14

Dtotal,min )

[(

Ftrn1 1 1 3 1/CE - 1/CA CE CA

)]

) 3Ftrn1 (17b)

This is remarkable because (Dtotal/F)min ) 3.00 is the thermodynamic limit without adding energy to the system. In a sense, the SMB in Figure 6c is analogous to an optimized Petlyuk distillation system with all

columns operating at minimum reflux; however, it is superior because the linear isotherms allow the operation to be reversible. Results of Equilibrium Calculations One goal of this paper is to find which cascade has the minimum value of D/F and the highest productivity for a number of different separation problems for quaternary systems. The difficulty of linear separations

Ind. Eng. Chem. Res., Vol. 43, No. 4, 2004 1077 Table 1. Results of Equilibrium Solutions for 12-Zone SMB Systems strategy

Figure 2a Figure 2b Figure 2c Figure 2d Figure 2e

(D/F)min productivity (D/F)min productivity (D/F)min productivity (D/F)min productivity (D/F)min productivity

A-B: difficult B-C: easy C-E: difficult

A-B: easy B-C: easy C-E: easy

A-B: easy B-C: difficult C-E: easy

A-B: difficult B-C: difficult C-E: easy

A-B: easy B-C: difficult C-E: difficult

A-B: difficult B-C; difficult C-E: difficult

3.33 3.94 × 10-4 26.71 5.48 × 10-5 602.18 2.90 × 10-5 125.44 4.31 × 10-5 403.20 4.77 × 10-5

11.50 8.61 × 10-3 4.59 7.68 × 10-3 14.44 5.17 × 10-3 231.00 1.22 × 10-3 68.25 2.06 × 10-3

84.00 6.57 × 10-4 22.64 7.64 × 10-4 4.11 1.28 × 10-3 381.80 1.83 × 10-4 16.77 3.57 × 10-4

70.82 1.38 × 10-4 5.10 1.73 × 10-4 5.50 1.67 × 10-4 2649.60 7.23 × 10-6 116.36 1.41 × 10-5

20.20 5.13 × 10-4 157.09 1.07 × 10-4 28.51 1.74 × 10-4 6.66 5.39 × 10-4 5.00 8.07 × 10-4

7.02 1.14 × 10-4 13.18 6.09 × 10-5 14.22 5.92 × 10-5 17.21 5.33 × 10-5 12.94 7.71 × 10-5

Table 2. Results of Equilibrium Solutions for 13-Zone SMB Systems strategy

Figure 3a Figure 3b Figure 3c Figure 3d Figure 3e Figure 3f

(D/F)min productivity (D/F)min productivity (D/F)min productivity (D/F)min productivity (D/F)min productivity (D/F)min productivity







26.45 5.06 × 10-5 26.24 5.59 × 10-5 314.18 4.56 × 10-5 586.73 2.96 × 10-5 115.47 4.71 × 10-5 616.4 2.93 × 10-5

4.27 8.74 × 10-3 4.44 7.99 × 10-3 9.19 7.68 × 10-3 169.44 4.59 × 10-4 71.00 3.84 × 10-3 33.5 4.99 × 10-3

13.20 1.18 × 10-3 18.77 9.30 × 10-4 3.94 1.39 × 10-3 37.39 4.68 × 10-4 82.60 8.43 × 10-4 7.87 1.52 × 10-3

4.14 2.27 × 10-4 4.99 1.77 × 10-4 4.34 2.25 × 10-4 5.39 1.72 × 10-4 181.20 1.01 × 10-4 42.73 1.59 × 10-4

91.64 1.60 × 10-4 41.18 3.99 × 10-4 27.35 1.88 × 10-4 13.05 5.85 × 10-4 6.04 6.01 × 10-4 5.61 6.19 × 10-4

10.69 7.80 × 10-5 10.02 8.11 × 10-5 11.22 7.72 × 10-5 10.75 7.89 × 10-5 12.13 7.64 × 10-5 11.33 7.84 × 10-5

Table 3. Results of Equilibrium Solutions for 14 Zone SMB Systems strategy

Figure 4a Figure 4b Figure 4c Figure 4d Figure 4e








3.16 4.06 × 10-4 25.98 5.71 × 10-5 306.23 4.66 × 10-5 110.93 5.07 × 10-5 361.40 4.36 × 10-5

7.25 1.09 × 10-2 4.13 9.08 × 10-3 8.81 7.99 × 10-3 51.00 4.99 × 10-3 32.25 5.40 × 10-3

43.50 1.25 × 10-3 11.05 1.42 × 10-3 3.46 1.68 × 10-3 45.20 1.29 × 10-3 7.83 1.55 × 10-3

36.91 2.17 × 10-4 4.06 2.33 × 10-4 4.25 2.30 × 10-4 111.90 1.41 × 10-4 42.66 1.61 × 10-4

11.60 8.18 × 10-4 26.86 5.51 × 10-4 12.80 6.18 × 10-4 4.79 7.96 × 10-4 4.58 8.04 × 10-4

5.01 1.63 × 10-4 8.29 1.02 × 10-4 8.65 1.01 × 10-4 9.82 9.68 × 10-5 9.42 9.76 × 10-5

can be classified based on the selectivity

Rik ) Ki/Kk g 1.0

(18)

Somewhat arbitrarily, when R ) 1.1, the separation was considered difficult, and when R ) 4.0, it was easy. The value of KA was arbitrarily chosen as 1.2. We then investigated the six cases where A-B, B-C, and C-E separations could be difficult or easy. The calculated values of the minimum D/F and productivity for the equilibrium analysis of the linear quaternary SMB systems are shown in Tables 1-4. The ratio D/F is important because desorbent usage or desorbent recovery is the most important operating cost. The productivity includes an important capital cost, the amount of adsorbent required. Minimizing D/F and maximizing productivity will often minimize the cost of the SMB system. There are general trends in Tables 1-4. As noted previously, the 32-zone easy-split system in Figure 6c always has the lowest (D/F)min (3.0) and fairly high

productivity. The 28-zone easy-split system shown in Figure 6a always has (D/F)min equal to 5.00 (Table 4). The 30-zone easy-split system shown in Figure 6b always has (D/F)min and productivity values between the 28-zone SMB system and the 32-zone SMB system (Table 4). From the equilibrium theory results when the A-B and C-E separations are approximately of equal difficulty and the B-C separation is easy, Figures 4a and 2a are the second-best systems [(D/F)min ) 3.16 in Table 3 and 3.33 in Table 1, respectively]. The center-split system with additional product withdrawals in Figure 4a has the highest productivity and is much simpler than the easy-split system in Figure 6c. When all separations are easy, Figure 6c has both the lowest (D/F)min and the highest productivity while the easy-split systems in Figures 6b and 5a are the secondbest systems [(D/F)min ) 3.38 and 3.81 in Table 4, respectively]. The best of the simpler cascades is Figure 4b [(D/F)min ) 4.13 in Table 3]. When the A-B and C-E separations are easy and

1078 Ind. Eng. Chem. Res., Vol. 43, No. 4, 2004 Table 4. Results of Equilibrium Solutions for SMB Systems (easy-split) strategy

Figure 5a (19-zone) Figure 5b (19-zone) Figure 6a (28-zone) Figure 6b (30-zone) Figure 6c (32-zone)








25.73 6.01 × 10-5 106.4 5.44 × 10-5 5.0 4.04 × 10-4 4.72 4.18 × 10-4 3.00 4.27 × 10-4

3.81 1.08 × 10-2 31.00 5.80 × 10-3 5.0 1.05 × 10-2 3.38 1.26 × 10-2 3.00 1.34 × 10-2

3.32 1.88 × 10-3 7.80 1.58 × 10-3 5.0 9.84 × 10-4 3.05 1.85 × 10-3 3.00 1.93 × 10-3

3.12 3.02 × 10-4 42.6 1.63 × 10-4 5.0 1.98 × 10-4 3.06 3.03 × 10-4 3.00 3.11 × 10-4

12.55 9.88 × 10-4 3.55 1.01 × 10-3 5.0 7.30 × 10-4 3.21 1.11 × 10-3 3.00 1.23 × 10-3

6.55 1.58 × 10-4 7.51 1.17 × 10-4 5.0 1.49 × 10-4 3.66 2.01 × 10-4 3.00 2.44 × 10-4

the B-C separation is difficult, Figure 6c again has the lowest (D/F)min and the highest productivity while the easy-split systems in Figures 6b [(D/F)min ) 3.05] and 5a [(D/F)min ) 3.32] are the second-best systems with productivities close to that of Figure 6c. The best 14zone system is Figure 4c [(D/F)min ) 3.46]. When the A-B and B-C separations are difficult and the C-E separation is easy, Figure 6c again has the lowest (D/F)min and the highest productivity while the easy-split systems in Figures 6b [(D/F)min ) 3.06] and 5a [(D/F)min ) 3.12] are very close. The best of the simpler cascades is Figure 4b [(D/F)min ) 4.06 in Table 3]. When the A-B separation is easy and B-C and C-E separations are difficult, Figure 6c has the lowest D/F and the highest productivity while the easy-split systems in Figures 6b [(D/F)min ) 3.21] and 5b [(D/F)min ) 3.55] are the second-best systems. The best 14-zone cascade is Figure 4e [(D/F)min ) 4.58]. When the A-B, B-C, and C-E separations are all difficult, Figure 6c again has the lowest (D/F)min and the highest productivity while the easy-split system in Figure 6b [(D/F)min ) 3.66] is the second-best system. The best 14-zone system is Figure 4a [(D/F)min ) 5.01].

Table 5. Conditions of Simulation for Figures 2a and 4aa dimension column diameter, cm Figure 2a Figure 4a

column length, cm

train 1

train 2

train 3

train 1

train 2

train 3

2.79 2.79

4.82 4.22

5.24 4.44

558.77 558.77

803.99 803.99

558.77 558.77

a F ) 60 cm3/min, t sw ) 10.3 min, e) 0.45, p) 0.00, and RP ) 0.0011 cm.

Table 6. Aspen Chromatography Simulation of Dextran T9 (A), Dextran T6 (B), Raffinose (C), and Fructose (E) Separation Using a 12-Zone Base Case SMB (Figure 2a) at Ideal Minimum Desorbent Flow Ratesa A (%)

B (%)

AB feed CE feed

49.14 0.89

Train 1 47.16 2.49 1.21 1.56 47.70 49.85

C (%)

E (%)

flow rate (mL/min) 78.18 83.64

A product B product

88.08 10.57

9.58 85.40

Train 2 1.57 2.80

0.77 1.23

78.18 78.18

C product E product

1.27 0.91

2.24 1.44

Train 3 83.28 13.21 12.75 84.89

83.64 83.64

a D/F ) 4.39, productivity ) 2.49 × 10-4, feed flow rate (F) ) 60 mL/min, switching time (tsw) ) 10.3 min, and 2 columns/zone.

Detailed Simulations More detailed simulations were done using the commercially available chromatography/SMB software package Aspen Chromatography version 11.1. This package is a dynamic simulator that solves the algebraic and partial differential equations for SMBs. The SMB train receiving the fresh feed was simulated first. The feed streams [e.g., F′(AB) and F′′(CE) in Figure 2a] were treated as if they were sent to a holding tank and were well-mixed. The concentrations of these feeds were obtained as the average concentrations of the products from the first train. In actual practice, the concentrations in the tanks would cycle with a period equal to tsw. Model simulations were performed for the separation of dextran T9, dextran T6, raffinose, and fructose in water using silica gel. We used equilibrium and masstransfer data given by Ching et al.,20 who reported experimental results for the continuous separation of three carbohydrate mixtures (fructose-dextran, raffinose-dextran, and fructose-raffinose) with silica gel as the sorbent and deionized water as the eluent. The equilibrium constants are Kdextran T9 ) 0.13, Kdextran T6 ) 0.23, Kraffinose ) 0.56, and Kfructose ) 0.69. The masstransfer constants ki (min-1) are kdextran T9 ) 0.60, kdextran T6 ) 2.84, kraffinose ) 3.42, and kfructose ) 5.52.

The SMB systems were simulated with two columns per zone. A common switching time of 10.3 min was used so that productivities are directly comparable. The feed rate for the laboratory-scale system was 60 mL/ min. The feed contained 50 g/L of each solute. The SMB systems were designed for the minimum D/F values calculated from the local equilibrium theory. The resulting flow rates, column lengths, and column diameters were then used as the input for Aspen Chromatography (Table 5). In industrial-scale separations, the much higher feed rate will require much larger column diameters and hence more reasonable ratios of length/ diameter. The simulation results at minimum D/F are shown in Tables 6 and 7. As expected, the simulations show that the products are not pure when the minimum desorbent flow rates are set. Higher purities are easily obtained by increasing D/F and/or the number of columns per zone. The results allow comparison of the two SMB systems shown in Figures 2a and 4a. From the results of simulation, the purities of each component for the 12-zone system shown in Figure 2a are as follows: A, 88.08%; B, 85.40%; C, 83.28%; E, 84.89%. For the 14-zone system shown in Figure 4a, the average purities are as follows: A, 86.70%; B, 87.43%; C, 85.88%; E, 83.41%. The 14-zone system has higher B and C

Ind. Eng. Chem. Res., Vol. 43, No. 4, 2004 1079 Table 7. Aspen Chromatography Simulation of Dextran T9 (A), Dextran T6 (B), Raffinose (C), and Fructose (E) Separation Using a 14-Zone SMB (Figure 4a) at Ideal Minimum Desorbent Flow Ratesa A (%)

B (%)

C (%)

E (%)

18.18 60.00 60.00 23.64

0.50 0.69

60.00 60.00

Train 3 85.88 10.89 15.43 82.06

60.00 60.00

A product AB feed CE feed E product

87.15 44.44 0.54 1.52

10.88 51.97 1.90 0.00

Train 1 0.00 1.96 2.87 0.72 53.16 44.39 14.13 84.35

A product B product

86.10 8.88

11.44 87.43

Train 2 1.96 3.00

C product E product

0.71 0.60

2.53 1.91

flow rate (mL/min)

a D/F ) 3.70, productivity ) 3.00 × 10-4, feed flow rate (F) ) 60 mL/min, switching time (tsw) ) 10.3 min, and 2 columns/zone.

product purities despite operating at a significantly lower D/F value. Thus, for this separation of dextran T9, dextran T6, raffinose, and fructose, the 14-zone system is preferable. This result agrees qualitatively with the equilibrium calculations because the dextran T9 (A)-dextran T6 (B) and the raffinose (C)-fructose (E) separations are difficult compared to the relatively easy dextran T6 (B)-raffinose (C) separation. Heuristics Heuristics have been extensively used for the design of separation sequences,14-18,21 although only the distillation heuristics have been extensively tested.16,17 On the basis of the results in the previous sections, the following tentative heuristics are proposed for quaternary SMB separations. 1. Since the 32-zone easy-split system (Figure 6c) always has the lowest value of (D/F)min and one of the higher productivities, consider it even though it is a complex cascade. 2. The additional options to consider depend on the separation. (a) If all separations are difficult or the A-B and C-E separations are considerably more difficult than the B-C separation, consider the 14-zone center-split system (Figure 4a). (b) If all separations are easy, consider the 19-zone system in Figure 5a and the 14-zone direct sequence in Figure 4b. (c) If the C-E separation is considerably less difficult than both the A-B and B-C separations, consider the 19-zone system in Figure 5a and the 14-zone systems in parts b and c in Figure 4. (d) If the B-C separation is considerably more difficult than both the A-B and C-E separations, consider the 19-zone system in Figure 5a and the 14-zone sequence in Figure 4c. (e) If the A-B separation is considerably easier than both the B-C and C-E separations, consider the 19zone system in Figure 5b and the 14-zone systems in parts d and e of Figure 4. These heuristics must be considered tentative because they are based on the analysis of systems with linear isotherms and were done only for the SMB cascades in this paper.

Figure 7. 60-zone SMB for complete five-component separation using an easy-split system for all components. (Dtotal/F)min ) 4.0 for linear isotherms.

Conclusions and Extensions New designs for SMB cascades to completely separate a quaternary mixture are proposed. The proposed designs can be easily realized based on the proven SMB technology. The equilibrium theory can be used to eliminate cascades that are poor choices for a given separation. The same theory can also be used to determine the exact range of operation parameters for the fractionation of each individual component and to estimate desorbent flow rates for SMB systems with one or more columns per zone. The 32-zone cascade shown in Figure 6c is remarkable because it can always be optimized to operate at an ideal D/F ) 3.0. For quaternary separations without the addition of energy, this represents the thermodynamic minimum amount of desorbent. However, in actual practice, the simpler 14-zone systems (particularly Figure 4a) or 19-zone systems (Figure 5a or 5b) may be less expensive because fewer columns are required. In addition, the simpler SMB systems will probably be easier to operate. The easy-split systems for ternary19 and quaternary separations (Figure 6c) that operate at the thermodynamic minimum D/F can be extended to additional components. The 10-train, 60-zone easy-split system shown in Figure 7 for five components will always have the lowest D/F, equal to 4.00 for all values of linear equilibrium constants because the easy-split configuration with additional product withdrawals does not require extra desorbent and each of the seven trains can be optimized. This easy-split idea can be extended to a six-component separation with 15 trains and 100 zones,


and so forth. In general, to operate at the thermodynamic minimum D/F, the corresponding easy-split system for an N-component separation will have

no. of trains ) 1 + 2 + ... + N - 1

(19)

no. of zones ) 1 (2N) + 2 [2(N - 1)] + ... + (N - 1) (4) (20) Although probably not of practical interest, these extensions illustrate the minimum desorbent use that is possible without the addition of energy to the cascade. Thus, they should be useful limiting conditions when designing SMB cascades. Acknowledgment This research was partially supported by NSF Grant CTS-9815844. Notation AC ) cross-sectional area of the column, m2 ci ) concentration of species i in liquid, g/m3 Ci ) constant for determining the velocity of solute i, eqs 1a and 1b dcol ) column diameter, m D ) volumetric flow rate of fresh desorbent, m3/s F ) volumetric flow rate of the feed, m3/s KDi ) steric hindrance factor; KDi ) 0 if molecules are excluded from all pores and KDi ) 1.0 if molecules have free access to all pores Ki ) qi/ci, linear equilibrium constant, g of adsorbent/m3 of solution ki ) overall mass-transfer coefficient, min-1 L ) length of each column, m N ) number of components qi ) amount adsorbed, g of solute/g of adsorbent Rp ) particle radius, cm tsw ) switching time, s ui ) velocity of the solute, m/s uport ) port velocity ) L/tsw, m/s vj ) interstitial fluid velocity in zone j, m/s Greek Symbols Rik ) selectivity ) Ki/Kk e ) external porosity p ) particle porosity Fs ) solid density, kg/m3 Subscripts A, B, C, E, i, k ) solutes total ) total flow rate to all trains trn1, trn2, trn3 ) conditions in train 1, train 2, and train 3 1, 2, 3, ..., 8 ) zones in SMB

Literature Cited (1) Broughton, D. B. Continuous sorption process employing fix beds of sorbent and moving inlets and outlets. U.S. Patent 2,985,589, 1961.

(2) Coelho, M. S.; Azevedo, D. C. S.; Teixeira, J. A.; Rodrigues, A. Dextran and fructose separation on an SMB continuous chromatographic unit. Biochem. Eng. J. 2002, 3625, 1. (3) Khattabi, S.; Cherrak, D. E.; Mihlbachler, K.; Guiochon, G. Enantioseparation of 1-phenyl-1-propanol by simulated moving bed under linear and nonlinear conditions. J. Chromatogr. A 2002, 893, 307. (4) Gottschlich, N.; Kasche, V. Purification of monoclonal antibodies by simulated moving-bed chromatography. J. Chromatogr. A 1997, 765, 201. (5) Pais, L. S.; Loureiro, J. M.; Rodrigues, A. Separation of 1,1′bi-2-naphthol enantiomers by continuous chromatography in simulated moving bed. Chem. Eng. Sci. 1997, 52, 245. (6) Mazzoti, M.; Storti, G.; Morbidelli, M. Optimal Operation of Simulated Moving Bed Units for Nonlinear Chromatographic Separations. J. Chromatogr. A 1997, 769, 3. (7) Migliorini, C.; Mazzoti, M.; Morbidelli, M. Robust Design of Countercurrent Adsorption Separation Processes. AIChE J. 2000, 46, 1384. (8) Nicoud, R.-M.; Charton, F. Complete design of a simulated moving bed. J. Chromatogr. A 1995, 702, 97. (9) Ruthven, D. M.; Ching, C. B. Countercurrent and Simulated Countercurrent Adsorption Separation Processes. Chem. Eng. Sci. 1989, 44, 1011. (10) Xie, Y.; Wu, D.-J.; Ma, Z.; Wang, N.-H. L. Extended Standing Wave Design Method for Simulated Moving Bed Chromatography: Linear Systems. Ind. Eng. Chem. Res. 2000, 39, 1993. (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. (12) Nicoud, R. M. Simulated Moving-Bed Chromatography for Biomolecules. In Handbook of Bioseparations; Ahuja, S., Ed.; Academic Press: San Diego, 2000; pp 475-509. (13) Mata, V. G.; Rodrigues, A. E. Separation of ternary mixtures by pseudo-simulated moving bed chromatography. J. Chromatogr. A 2001, 939, 23. (14) Seader, J. D.; Westerberg, A. W. A Combined Heuristic and Evolutionary Strategy for Synthesis of Simple Separation Sequences. AIChE J. 1977, 23, 951. (15) Tedder, D. W.; Rudd, D. F. Parametric Studies in Industrial Distillation: Part 1. Design Comparisons. AIChE J. 1978, 24, 303. (16) Malone, M. F.; Glonos, K.; Marquez, F. E.; Douglas, J. M. Simple, Analytical Criteria for the Sequencing of Distillation Columns. AIChE J. 1985, 31, 683. (17) Douglas, J. M. Conceptual Design of Chemical Processes; McGraw-Hill: New York, 1988; Chapter 7. (18) Agrawal, R. Thermally Coupled Distillation with Reduced Number of Intercolumn Vapor Transfer. AIChE J. 2000, 46, 2198. (19) Wankat, P. C. Simulated Moving Bed Cascades for Ternary Separations. Ind. Eng. Chem. Res. 2001, 40, 6185. (20) Ching, C. B.; Chu, K. H.; Hidajat, K.; Uddin, M. S. Comparative Study of Flow Schemes for a Simulated Countercurrent Adsorption Separation Process. AIChE J. 1992, 38, 1744. (21) Wankat, P. C. Rate-Controlled Separations; Kluwer: Amsterdam, The Netherlands, 1990; Chapter 14.

Received for review October 30, 2002 Revised manuscript received November 24, 2003 Accepted December 5, 2003 IE020863W

Designs of Simulated-Moving-Bed Cascades for Quaternary Separations

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