Single-Cascade Simulated Moving Bed Systems for the Separation of

Ind. Eng. Chem. Res. 2003, 42, 4849-4860

4849

Single-Cascade Simulated Moving Bed Systems for the Separation of Ternary Mixtures Jeung Kun Kim, Yifei Zang, and Phillip C. Wankat* School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907-1283

Single-cascade simulated moving bed (SMB) systems with a side-stream withdrawal are developed for separating ternary systems. Several single-cascade SMB systems are studied for the separation of ternary mixtures within the linear range. Design parameters, operating conditions, minimum desorbent-to-feed ratios, and productivities are determined with the local equilibrium theory, and purities are determined through detailed Aspen Chromatography simulations. A series of initial feed compositions are simulated to determine the optimal regions. The single-cascade SMB is particularly applicable when there is little of the most strongly adsorbed component, a significant amount of the middle component, and the separation between these components is easy. A surprising finding is that the purity of the middle-component product is usually higher in an SMB than in a true moving bed. A few quaternary separations with a side-stream SMB followed by a binary SMB are also studied. Single-Cascade SMB Designs for the Separation of Ternary Mixtures

Introduction Simulated moving bed (SMB) systems are an efficient means of performing large-scale chromatographic separation, particularly of binary mixtures. The four-zone SMB for binary separations has been extensively studied by many groups and is now well understood.1-3 On the other hand, the use of SMB systems for multicomponent separations has not been extensively studied. Wooley et al.4 proposed a nine-zone system for glucose-xylose-sulfuric acid-acetic acid separations and reported extensive comparisons of theory and experiments. Masuda et al.5 developed a ternary separation process that was commercialized. Meta and Rodrigues6 proposed a pseudo-SMB model for this process and addressed the effects of operating conditions and mass-transfer coefficients on the process performance. Wankat7 developed seven cascades of SMB systems for ternary separations with linear isotherms and determined the minimum desorbent usage and the productivity using the well-known equilibrium model. Nicoud8 briefly discussed a five-zone system with side streams for the separation of ternary mixtures (Figure 1b). Beste and Arlt9 derived rules for five-zone systems with side streams for the separation of ternary mixtures based on the triangle method,1,2 and they compared simulations with experiments. The objective of this study is to develop single-cascade SMB systems for the separation of ternary mixtures and to determine the favorable conditions for these designs. Local equilibrium theory and detailed simulations with Aspen Chromatography are used to study the behavior of systems with linear isotherms. We extend the work of Beste and Arlt9 by determining the conditions necessary to obtain a pure side-stream product and by developing a new SMB cascade. * To whom correspondence should be addressed. E-mail: [email protected].

Because distillation is the most widely used method for separating liquid mixtures, it has been extensively studied.10-14 Although most systems use N - 1 columns for N-component separations, single distillation towers for separations of ternary mixtures are shown in Figures 1a and 2a.10 The components in the mixture are ranked according to their relative volatilities, that is, A is the most volatile component, and C is the least volatile component. When some of the feed components are present in only trace amounts or only low product purities are required, these column designs might be the most economical alternatives. Tedder and Rudd10 suggested that the single distillation tower shown in Figure 1a is favored when the feed is more than 50% B and less than 5% C. The single distillation tower shown in Figure 2a is favored when the feed is more than 50% B and less than 5% A.10 The weak analogy between distillation and SMB systems can be used to develop designs of new SMB systems and qualitatively predict their behavior for the separation of multicomponent mixtures. Figures 1b and 2b show single-cascade SMB systems for the separation of ternary mixtures that correspond to their distillation analogues. Port locations shift periodically in the same direction as fluid flow. These single-cascade SMB systems are used to separate mixtures in which A is the most weakly adsorbed component and C is the most strongly adsorbed component. In Figure 1b, the fluid velocities and port velocity are set so that solute A moves at a rate higher than uport (column length/ switching period) in zones 2 and 3 but at a lower rate in zone 1, solute B moves at a rate lower than uport in zones 2 and 3 but at a higher rate in zone 4, and solute C moves at a rate lower than uport in zones 2-4 but at a higher rate in zone 5. In Figure 2b, solute A moves at a rate higher than uport in zones 2-4 but at a lower rate in zone 1, solute B moves at a higher rate in zone 2 but at a lower rate in zones 3 and 4, and solute C moves at

10.1021/ie030373j CCC: $25.00 © 2003 American Chemical Society Published on Web 08/29/2003

4850 Ind. Eng. Chem. Res., Vol. 42, No. 20, 2003

Figure 1. Single distillation tower and corresponding SMB cascade for removal of two heavy components: (a) distillation tower, (b) five-zone SMB cascade.

a lower rate in zones 2-4 but at a higher rate in zone 5. If these single-cascade SMB systems were true moving beds (TMBs), the B product stream would have to be contaminated with C (Figure 1b) or A (Figure 2b). An alternative four-zone device with chromatographic development of products B and C is shown in Figure 3. Products B and C will probably be more dilute than in Figure 1b, but this SMB system is simpler and does not requires as large a value of the selectivity to achieve complete separation.

solute is always in equilibrium with the solute in solution outside the adsorbent particles. For systems involving equilibrium-based separations, the resulting solution represents the best separation possible. For linear isotherms, the solute velocity is7

Local Equilibrium Solution

where Ki ) qi/ci. As an illustration of this well-known procedure, consider the five-zone SMB system shown in Figure 1b. If one wants to separate the ternary mixture to obtain pure A and C, the conditions are

The equilibrium model assumes very rapid mass transfer and negligible dispersion so that the adsorbed

usolute i,zone j )

vj

) 1 - e (1 - e)(1 - p) 1+ K + FsKi e p Di e (constanti)vj ) Civj (1)

Ind. Eng. Chem. Res., Vol. 42, No. 20, 2003 4851

Figure 2. Single distillation tower and corresponding SMB cascade for removal of two light components: (a) distillation tower, (b) fivezone SMB cascade.

uA1 ) MA1uport, MA1 e 1

(2a)

uA2 ) MA2uport, uB2 ) MB2uport, MA2 g 1, MB2 e 1 (2b,c) uA3 ) MA3uport, uB3 ) MB3uport, MA3 g 1, MB3 e 1 (2d,e) uB4 ) MB4uport, uC4 ) MC4uport, MB4 g 1, MC4 e 1 (2f,g)

is satisfied with MB2 ) 1, eq 2e is automatically satisfied with MB3 < 1. If mass-transfer rates are very high and axial dispersion is negligible, the conditions in eqs 2 will ensure pure A and C products, but the B product might be contaminated with C. The interstitial velocities are related by mass balances. Assuming that the densities of the liquid mixtures are identical, one can write

v1 ) v2 - vAprd

(3a)

uC5 ) MC5uport, MC5 g 1

(2h)

v2 ) v3 + vF

(3b)

uport ) L/tsw

(2i)

v3 ) v4 - vBprd

(3c)

where the Mij values are multipliers that allow one to use equations instead of inequalities. If MA3 ) 1.0, eq 2b is automatically satisfied with MA2 > 1, and if eq 2c

v4 ) v5 - vCprd

(3d)

v5 ) v1 + vD

(3e)


vD ) v5 - v1

(7)

and the desorbent-to-feed ratio is D/F ) vD/vF. The absolute minimum value of D/F occurs when the multipliers are set equal to 1. To improve the separation, MA3, MB4, and MC5 are made greater than 1, and MA1 and MB2 are made less than 1. Once flow rates are determined, eq 2g is checked. The productivity of the system is defined as

productivity )

feed volume/time ) total adsorbent volume F (8) (no. of columns)AcL

For the local equilibrium solution, the switching time (or column length) can be arbitrarily specified, and the other term can be found from eq 2i. For the SMB shown in Figure 1b, a higher-purity B product can be obtained if an additional constraint is met. In Figure 4, the solute bands predicted by the local equilibrium model are shown. The constraint for the leading edge of the C band is

uC2 + uC3 + uC4 ) MC,leaduport, MC,lead e 1

(9)

Unfortunately, eq 9 overconstrains the system and can be satisfied only when RCB ) KC/KB is large enough. A similar separation of bands is not possible for the SMB in Figure 2b. For the A and B components in Figure 3, the appropriate solute velocity equations are eqs 2a, 2c, and 2d. These three equations plus v2 ) v3 + vF allow one to find v1, v2, v3, and uport for a known vF. The tailing edge of the C band must be removed. The condition for complete removal of C from zone 4 is (Figure 5)

uC3 + uC4 ) MC4uport, MC4 g 1

Figure 3. Modified four-zone SMB for the separation of heavy components.

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

F vF ) where Ac ) πDC2/4 eAc

(4)

Equations 1, 2c, 2d, and 3b can be solved simultaneously with the eqs for the interstitial velocities to determine uport and v2

v2 )

(CA/MA3)vF (CA/MA3) - (CB/MB2)

uport )

(CB/MB2)(CA/MA3)vF (CA/MA3) - (CB/MB2)

(5)

(6)

where vF is assumed to be known. Once the value of uport has been determined, eqs 2a, 2f, and 2h can be used to find the velocities in zones 1, 4, and 5, respectively. The required flow rate of desorbent is

(10)

This equation plus v4 ) v1 + vD2 allow one to calculate v4 and vD2. Product B is removed from time t ) 0 to tp (product time) and product C from tp to tsw, where tp has a value between 0 and tsw. The trailing edge of B must exit the column before tp (Figure 5). After dividing by tsw and using eq 2i, the result is

uB3 + uB4tp/tsw ) MB,Figure 3uport, MB,Figure 3 g 1 (11) The front edge of C should not break through at tp (Figure 5)

uC2 + uC3 + uC4tp/tsw ) MC,Figure 3uport, MC,Figure 3 e 1 (12) Because tp/tsw can be used to satisfy either eq 11 or 12, the other equation overconstrains the system. If RCB ) KC/KB is small, a solution might not exist. The single SMB cascades shown in Figures 1b and 3 will have identical D/F values if v5,Figure 1) v3,Figure 3 + v4,Figure 3, as v1,Figure 1 ) v1,Figure 3. In Figures 1b and 3, respectively

vD,total ) vD ) v5 - v1

(13a)

vD,total ) vD1 + vD2 ) v3 + (v4 - v1)

(13b)

and


Figure 4. Local equilibrium solution for the SMB in Figure 1b satisfying eqs 2a-h and 9. Table 1. Results of Equilibrium Solutions selectivity RBA ) KB/KA 1.1

Figure 5. Local equilibrium solution for the system in Figure 3 satisfying eqs 2a-e and 10-12.

MC4uport CC

Thus, if MC5 ) MC4, the D/F values are identical. However, for a given set of values of RBA and RCB, it might be possible to satisfy the band constraints for Figure 3 but not for Figure 1b.

2.10 6.50 34.0

1.60 × 10-3

1.30 2.50 (10.00)

8.00 × 10-3

4.0

1.1 1.5 4.0

1.13 1.67 (5.00)

4.80 × 10-2

1.1

1.1 1.5 4.0

2.10 6.50 (34.00)

2.00 × 10-3

1.5

1.1 1.5 4.0

1.30 2.50 (10.00)

1.00 × 10-2

4.0

1.1 1.5 4.0

1.13 1.67 (5.00)

6.00 × 10-2

Figure 3b

(14a)

(14b)

Figure 1.1 1.5 4.0

productivity

1.1 1.5 4.0

and

(v3 + v4)Figure 3 )

(D/F)min 1ba

1.5

From eqs 2h and 10

MC5uport v5,Figure 1b ) CC

RCB ) KC/KB

a For Figure 1b, all results satisfy eqs 2a-h, and the results in parentheses also satisfy the constraint on bands (eq 9). b For Figure 3, all results satisfy eqs 2a-e, and the results in parentheses also satisfy eqs 10-12.

Table 2. Minimum Possible Selectivity for the SMB System Shown in Figure 1b to Satisfy the Constraints in Eqs 2a-h and 9 selectivity

Results of Equilibrium Calculations The local equilibrium theory was used to determine design parameters and operating conditions for detailed simulations to investigate the expected feed composition regions of design optimality for single-cascade SMB systems. Design parameters and operating conditions can easily be determined when calculations are programmed in a spreadsheet. The difficulty of linear separations can be classified on the basis of the selectivity

Rik ) Ki/Kk g 1.0

(15)

Somewhat arbitrarily, a separation with R ) 1.1 is considered hard, that with R ) 1.5 is moderate, and that with R ) 4.0 is easy. The values of KA and tsw are arbitrarily chosen as 1.0 and 7.5 min, respectively. The calculated minimum values of (D/F)min and productivity for the equilibrium analysis of the single SMB cascades

RBA ) KB/KA

RCB ) KC/KB

(D/F)min

1.1 1.5 4.0

g4.2 g3.6 g2.8

36.00 8.80 3.33

Table 3. Minimum Possible Selectivity for the SMB System Shown in Figure 3 to Satisfy the Constraints in Eqs 2a-e and 10-12. tp/tsw ) 0.6 selectivity RBA ) KB/KA

RCB ) KC/KB

(D/F)min

1.1 1.5 4.0

g2.50 g1.80 g1.50

17.00 3.40 1.67

shown in Figures 1b and 3 are given in Table 1. The lowest selectivities that allow satisfaction of all constraints are reported in Tables 2 and 3. The SMB system shown in Figure 3 requires a smaller selectivity than the SMB system shown in Figure 1b to satisfy the constraints for perfect ideal separation.

4854 Ind. Eng. Chem. Res., Vol. 42, No. 20, 2003 Table 4. Results of Equilibrium Solutions for Figure 2b selectivity RBA ) KB/KA

RCB ) KC/KB

(D/F)min

productivity

1.1

1.1 1.5 4.0

1.91 1.18 1.03

1.76 × 10-3 8.80 × 10-3 5.28 × 10-2

1.5

1.1 1.5 4.0

4.33 1.67 1.11

2.40 × 10-3 1.20 × 10-2 7.20 × 10-2

4.0

1.1 1.5 4.0

8.50 2.50 1.25

6.40 × 10-3 3.20 × 10-2 1.92 × 10-1

Table 5. System and Operating Parameters for Simulationsa e ) 0.4 Rp ) 0.001 cm

p ) 0.0

FB ) 670 kg/m3 k ) 1.0 × 105 min-1

Ff ) 1000 kg/m3

Five-Zone SMB System (Figure 1b) and Corresponding TMB System (Results in Tables 6, 7, and 9) column length (L) 166.67 cm (D/F)min 5.00 column diameter (Dc) 1.38 cm productivity 4.80 × 10-2 flow rates A product 60 cm3/min desorbent 300 cm3/min B product 60 cm3/min recycle 33.33 cm3/min C product 240 cm3/min Four-Zone SMB System (Figure 3; Results in Tables 8 and 10) column length (L) 166.67 cm (D/F)min column diameter (Dc) 1.38 cm productivity flow rates A product 60 cm3/min desorbent (D1) B product 300 cm3/min desorbent (D2) C product 300 cm3/min

5.00 6.00 × 10-2 33.33 cm3/min 266.67 cm3/min

Five-Zone SMB System (Figure 2b; Results in Tables 10 and 11) column length (L) 41.67 cm (D/F)min 1.25 column diameter (Dc) 1.38 cm productivity 1.92 × 10-1 flow rates A product 15 cm3/min desorbent 75 cm3/min B product 60 cm3/min recycle 8.33 cm3/min C product 60 a

Feed compositions shown in Figure 6 and in Tables 6-8 and

10.

The (D/F)min and productivity values for the equilibrium analysis of single-cascade SMB system shown in Figure 2b are given in Table 4. Remember that these results do not guarantee a pure B product. Simulation Results Simulations were performed with the commercially available chromatography/SMB software package Aspen Chromatography, version 11.1. The single-cascade SMB systems were first designed for the minimum D/F values calculated using local equilibrium theory. The resulting flow rates, column lengths, and column diameters were then used as the inputs for Aspen Chromatography. The SMB systems were simulated with one column per zone. The simulation conditions are listed in Table 5, and the feed compositions are shown in Figure 6. Very rapid mass transfer was assumed, and dispersion was estimated from the Chung and Wen correlation.15 The effect of lower mass-transfer rates is considered later. The results are presented in Tables 6-11. Table 6 shows simulation results for the singlecascade SMB with five zones (Figure 1b). When there is very little component C in the feed (runs 2-5), the A

Figure 6. Initial feed compositions.

product purities increase from 68.65 to 98.23% as the amount of A in the feed increases. The B product purities decrease from 99.21 to 82.93% with increasing feed compositions of the A component (decreasing B). As expected, the simulation results show that neither A nor C is pure when the minimum desorbent flow rates are used. When there is little A component in the feed (runs 6-9), the simulation results show that the A products are not pure. For these runs, the B product purity decreases from 99.51 to 92.23%, and the C product purity increases from 69.92 to 98.37% with decreasing feed composition of B (increasing C). If the target component is A, the feed compositions for points 1, 4, 5, and 10 shown in Figure 6 are favored. For C as the target, the highest purities occur for points 1 and 7-10. For middle component B as the target, points 1-4 and 6-9 give purities greater than 90%. If all three components are targeted, feed composition points 1 and 10 are best. For components A and B as targets, points 1, 4, and 10 are best. For components B and C as targets, points 1 and 8-10 are best. For components A and C as targets, points 1 and 10 are best. Note that the purities can be increased by using D/F > (D/F)min (see Table 9). This is particularly true for products A and C. Table 7 shows the results of the TMB simulations. As expected, a comparison of the SMB and TMB simulations shows that the purities of products A and C are higher in the TMB system. Surprisingly, the B product purity is generally higher in the SMB (except for runs 4 and 5 that contain very large amounts of A). This is a result of the separation of bands of B and C. Table 8 presents the simulation results for Figure 3 when tp/tsw ) 0.33. Note that the A product purity is not affected by tp/tsw. The B product purities are always higher for tp/tsw ) 0.33 than for tp/tsw ) 0.60 (not shown), and the C product purity is also higher in all runs, except for run 6 where the C purity was 84.84% with tp/tsw ) 0.60. The optimum value of tp/tsw probably depends on the equilibrium relationships, mass transfer, and feed concentrations. Feed concentrations appear to affect product purities similarly to the results in Table 6. A comparison of Tables 6 and 8 shows that the fivezone SMB (Figure 1b) generally has higher-purity A and B products, but lower-purity C product at D/F ) (D/F)min ) 5.0.

Ind. Eng. Chem. Res., Vol. 42, No. 20, 2003 4855 Table 6. Simulation Results at (D/F)min ) 5.00 for the Five-Zone SMB System (rBA ) 4.0, rCB ) 4.0) Shown in Figure 1ba A product (%)

B product (%)

C product (%)

run

feed composition

A

B

C

A

B

C

A

B

C

1 2 3 4 5 6 7 8 9 10

0.33-0.34-0.33 0.15-0.80-0.05 0.30-0.65-0.05 0.60-0.35-0.05 0.80-0.15-0.05 0.05-0.80-0.15 0.05-0.65-0.30 0.05-0.35-0.60 0.05-0.15-0.80 0.44-0.14-0.42

88.93 68.65 84.27 95.08 98.23 40.86 43.22 48.85 53.50 94.04

7.62 30.46 15.19 4.61 1.53 54.39 46.74 28.45 13.35 2.49

3.45 0.89 0.54 0.31 0.24 4.75 10.04 22.70 33.15 3.47

3.49 0.70 1.71 6.07 16.70 0.24 0.29 0.52 1.16 10.24

95.27 99.21 98.19 93.75 82.93 99.51 99.10 97.23 92.23 86.28

1.24 0.09 0.10 0.18 0.37 0.25 0.61 2.25 6.61 3.48

2.51 3.56 7.61 17.69 26.46 0.65 0.39 0.22 0.17 2.76

7.33 53.83 46.79 29.29 14.08 29.43 14.55 4.39 1.46 2.49

90.16 42.61 45.60 53.02 59.46 69.92 85.06 95.39 98.37 94.75

a

Conditions in Table 5.

Table 7. Simulation Results at (D/F) ) 5.00 for the TMB System (rBA ) 4.0, rCB ) 4.0) that Corresponds to Figure 1ba A product (%)

B product (%)

C product (%)

run

feed composition

A

B

C

A

B

C

A

B

C

1 2 3 4 5 6 7 8 9 10

0.33-0.34-0.33 0.15-0.80-0.05 0.30-0.65-0.05 0.60-0.35-0.05 0.80-0.15-0.05 0.05-0.80-0.15 0.05-0.65-0.30 0.05-0.35-0.60 0.05-0.15-0.80 0.44-0.14-0.42

96.07 83.89 92.80 98.01 99.41 63.01 66.91 76.35 82.71 98.51

3.33 15.91 7.09 1.93 0.55 35.78 30.58 17.99 9.19 0.90

0.60 0.20 0.11 0.06 0.04 1.21 2.51 5.66 8.10 0.59

1.24 0.37 0.72 2.26 6.24 0.22 0.26 0.38 0.18 2.70

81.31 98.27 97.62 94.74 87.30 95.81 90.51 72.23 45.85 58.42

17.46 1.36 1.66 3.00 6.46 3.97 9.23 27.38 53.97 38.88

0.44 0.15 1.54 5.66 9.16 0.56 0.32 0.17 0.06 0.59

4.68 42.21 36.90 23.60 12.29 19.54 9.07 2.71 0.83 1.72

94.88 57.64 61.56 70.74 78.55 79.90 90.61 97.12 99.11 97.69

a


Table 8. Simulation Results at (D/F)min ) 5.00 and tp/tsw ) 0.33 for the Four-Zone SMB System (rBA ) 4.0, rCB ) 4.0) Shown in Figure 3a A product (%)

B product (%)

C product (%)

run

feed composition

A

B

C

A

B

C

A

B

C

1 2 3 4 5 6 7 8 9 10

0.33-0.34-0.33 0.15-0.80-0.05 0.30-0.65-0.05 0.60-0.35-0.05 0.80-0.15-0.05 0.05-0.80-0.15 0.05-0.65-0.30 0.05-0.35-0.60 0.05-0.15-0.80 0.44-0.14-0.42

84.48 68.38 83.46 94.38 97.64 41.76 41.22 40.17 39.50 89.21

7.33 29.05 14.92 4.69 1.64 47.35 38.10 20.33 8.98 2.54

8.19 2.57 1.62 0.93 0.72 10.89 20.68 39.50 51.52 8.25

2.90 0.62 1.48 5.17 14.08 0.23 0.27 0.47 0.92 7.87

92.14 98.95 98.00 93.90 84.01 98.68 97.21 91.03 77.21 79.30

4.96 0.43 0.52 0.93 1.91 1.09 2.58 8.50 21.87 12.83

3.76 7.21 13.77 26.19 34.00 1.23 0.72 0.38 0.29 4.01

2.82 26.74 21.38 11.23 4.85 16.58 5.85 1.69 0.57 0.97

93.42 66.05 64.85 62.58 61.15 82.19 93.43 97.93 99.14 95.02

a


Table 9 shows the simulation results for SMB systems shown in Figures 1b and 3 when the multipliers are adjusted for better separation of ternary mixtures. The feed composition is 0.3-0.65-0.05 (run 3). The results show that separation performance generally increases with increasing D/F, particularly for Figure 1b. The C product purity rapidly becomes higher for Figure 1b than Figure 3 as D/F increases. The exception is run f, in which the C product is contaminated with B. Table 10 shows the simulation results for the singlecascade SMB system shown in Figure 2b at (D/F)min ) 1.25. Because this value of (D/F)min ensures only the A and C product purities, the generally low purities of the B product are expected. Table 11 shows the simulation results for Figure 2b when D/F is increased. The B product is purest when there is little A and large amounts of B in the feed. The results at D/F ) 5.0 (run e) in Table 11 can be compared with runs 1, 6, and 8 in Tables 6 (Figure 1b) and 8 (Figure 3). The cascade in Figure 2b results in higher purities for the A and C products, but a significantly lower purity for the B product.

The effect of the mass-transfer rates on the SMB shown in Figure 1b is examined in Table 12. The runs labeled a and d with k ) 1.0 × 105 min-1 are identical to runs a and d for Figure 1b in Table 9. For lower masstransfer rates, the purities of products A and C decrease significantly. Mass-transfer rates of 5.0 and 2.8 min-1 are in the normal range, whereas 0.5 is low. Increasing D/F helps recover some of the purity losses for A and C caused by the lower mass-transfer rates. Because multiple columns per zone are commonly used to improve SMB separations, we examined the effect of different SMB configurations for the system shown in Figure 1b at (D/F)min ) 5.0. Because all columns are the same size, additional columns increase the adsorbent volume and decrease the productivity. The results are presented in Table 13. The product purities generally increase as the number of column increases. The average purity is maximized for the 2-2-1-2-2 configuration when the feed composition is 0.33-0.34-0.33 and for the 2-2-2-2-2 configuration for a feed composition of 0.30-0.65-0.05.

4856 Ind. Eng. Chem. Res., Vol. 42, No. 20, 2003 Table 9. Simulation Results for the Single SMB Cascades (rBA ) 4.0, rCB ) 4.0) Shown in Figures 1b and 3 for Run 3 (Feed ) 0.3-0.65-0.05)a Figure 1b multipliers

A product (%)

B product (%)

C product (%)

run

MA1

MB2

MA3

MB4

MC5

D/F

A

B

C

A

B

C

A

B

C

a b c d e f

1.00 0.95 0.90 0.90 0.90 0.90

1.00 0.95 0.95 0.90 0.90 0.90

1.00 1.00 1.00 1.00 1.50 1.50

1.00 1.50 2.00 2.00 1.00 1.00

1.00 1.00 1.00 1.00 1.00 1.50

5.00 5.45 5.48 5.99 8.92 13.82

84.27 89.11 88.02 92.93 92.84 92.90

15.19 10.29 10.21 6.44 7.09 7.10

0.54 0.60 1.77 0.63 0.07 0.001

1.71 1.75 1.66 1.82 0.12 0.04

98.19 97.94 97.77 97.15 99.48 99.94

0.10 0.31 0.57 1.03 0.40 0.02

7.61 8.23 4.42 4.05 4.96 2.64

46.79 0.13 0.13 0.00 0.0041 54.84

45.60 91.64 95.45 95.95 95.04 42.52

Figure 3 (tp/tsw ) 0.33) multipliers

A product (%)

B product (%)

C product (%)

run

MA1

MB2

MA3

MB4

D/F

A

B

C

A

B

C

A

B

C

a b c d e f

1.00 0.95 0.90 0.90 0.90 0.90

1.00 0.95 0.95 0.90 0.90 0.90

1.00 1.00 1.00 1.00 1.50 1.50

1.00 1.00 1.00 1.00 1.00 1.50

5.00 5.45 5.48 5.99 8.92 13.82

83.46 88.08 87.99 92.36 91.54 92.89

14.92 10.18 10.22 5.65 6.99 7.10

1.62 1.74 1.79 1.99 1.47 0.01

1.48 1.45 1.39 1.95 0.08 0.07

98.00 98.05 98.12 97.56 99.52 99.27

0.52 0.50 0.49 0.49 0.40 0.66

13.77 10.47 7.50 7.35 4.25 3.70

21.38 22.32 23.08 22.86 30.38 38.08

64.85 67.21 69.42 69.79 65.37 58.22

a


Table 10. Simulation Results at (D/F)min ) 1.25 for the Five-Zone SMB System (rBA ) 4.0, rCB ) 4.0) Shown in Figure 2ba A product (%)

B product (%)

C product (%)

run

feed composition

A

B

C

A

B

C

A

B

C

1 2 3 4 5 6 7 8 9 10

0.33-0.34-0.33 0.15-0.80-0.05 0.30-0.65-0.05 0.60-0.35-0.05 0.80-0.15-0.05 0.05-0.80-0.15 0.05-0.65-0.30 0.05-0.35-0.60 0.05-0.15-0.80 0.44-0.14-0.42

79.86 63.56 80.80 93.47 97.29 33.09 31.43 28.57 26.94 85.07

8.07 33.24 17.17 5.35 1.79 51.91 40.07 19.61 7.92 2.66

12.07 3.20 2.03 1.18 0.92 15.00 28.50 51.82 65.14 12.27

41.90 13.39 27.53 58.33 80.98 4.83 5.70 8.94 14.39 65.68

51.98 85.96 71.80 40.96 18.28 93.05 89.30 75.38 51.98 25.16

6.12 0.65 0.67 0.71 0.74 2.12 5.00 15.67 33.63 9.16

0.64 1.40 2.91 6.32 8.95 0.19 0.10 0.05 0.04 0.68

2.49 28.15 23.80 13.94 6.35 11.73 5.13 1.44 0.47 0.82

96.87 70.45 73.29 79.74 84.70 88.08 94.77 98.51 99.49 98.50

a


Table 11. Simulation Results for the Five-Zone SMB System (rBA ) 4.0, rCB ) 4.0) Shown in Figure 2ba multipliers

A product (%)

run

MA1

MB2

MA3

MB4

MC5

a b c d e

1.00 0.90 0.90 0.90 0.90

1.00 0.90 0.90 0.90 0.90

1.00 1.00 0.90 0.90 0.90

1.00 1.50 1.50 1.50 1.90

1.00 1.00 1.00 1.50 1.93

a b c d e

1.00 0.90 0.90 0.90 0.90

1.00 0.90 0.90 0.90 0.90

1.00 1.00 0.90 0.90 0.90

1.00 1.50 1.50 1.50 1.90

a b c d e

1.00 0.90 0.90 0.90 0.90

1.00 0.90 0.90 0.90 0.90

1.00 1.00 0.90 0.90 0.90

1.00 1.50 1.50 1.50 1.90

a

D/F

A

B

B product (%) C

A

B

C product (%) C

A

B

C

feed composition 0.33-0.34-0.33 (point 1, Figure 6) 1.25 79.86 8.07 12.07 41.09 51.98 1.57 81.45 3.07 15.48 41.66 51.60 1.90 82.12 3.04 14.84 42.22 53.70 2.94 96.41 3.57 0.02 43.20 54.96 5.00 96.37 3.63 2.3 × 10-6 43.12 54.87

6.12 6.74 4.08 1.84 2.01

0.64 0.16 0.17 0.19 0.20

2.49 0.02 0.02 0.02 1.1 × 10-4

96.87 99.82 99.81 99.79 99.80

1.00 1.00 1.00 1.50 1.93


2.12 2.34 1.38 0.61 0.67

0.19 0.05 0.06 0.07 0.07

11.73 0.08 0.08 0.09 6.0 × 10-4

88.08 99.87 99.86 99.84 99.93

1.00 1.00 1.00 1.50 1.93


15.67 17.09 10.74 5.04 5.47

0.05 0.01 0.01 0.02 0.02

1.44 0.01 0.01 0.01 1.0 × 10-4

98.51 99.98 99.98 99.97 99.98


Four-Component SMB Systems Two SMB designs with nine zones for the complete separation of four-component systems are shown in Figure 7. Component A is the most weakly adsorbed, and E is the most strongly adsorbed. D is the desorbent. These nine-zone SMB systems use Figure 1b or 2b for the initial separation, followed by a binary SMB. They

are similar to the nine-zone ternary SMB,4 but have a different purpose. The SMB system in Figure 7a is designed for the minimum D/F value calculated from local equilibrium theory. The resulting flow rates, column lengths, and column diameter were then used as inputs for Aspen Chromatography. Because the configuration in Figure 7a should work well for feeds that contain a large

Ind. Eng. Chem. Res., Vol. 42, No. 20, 2003 4857 Table 12. Simulation Results for the Single SMB Cascade (rBA ) 4.0, rCB ) 4.0) Shown in Figure 1b for Run 3 (Feed ) 0.3-0.65-0.05) Illustrating the Effect of Mass-Transfer Ratesa multipliers

A product (%)

B product (%)

C product (%)

run

k (min-1)

MA1

MB2

MA3

MB4

MC5

D/F

A

B

C

A

B

C

A

B

C

a a1 a2 a3 d d1 d2 d3

1.0 × 105 5.0 2.8 0.5 1.0 × 105 5.0 2.8 0.5

1.00

1.00

1.00

1.00

1.00

5.00

0.90

0.90

1.00

2.00

1.00

5.99

84.27 67.55 61.44 39.88 92.93 74.68 67.58 41.93

15.19 30.89 36.70 56.35 6.44 23.99 30.87 54.46

0.54 1.56 1.86 3.77 0.63 1.33 1.55 3.61

1.71 3.06 4.09 14.45 1.82 2.92 3.79 13.25

98.19 94.89 92.93 80.49 97.15 92.78 91.21 80.94

0.10 2.05 2.98 5.06 1.03 4.30 5.00 5.81

7.61 7.20 7.54 14.39 4.05 11.65 10.92 13.41

46.79 71.01 75.65 77.65 0.00 27.17 53.64 77.73

45.60 21.79 16.81 7.96 95.95 61.18 35.44 8.86

a


Table 13. Simulation Results at (D/F)min ) 5.00 for Five-Zone SMB System (rBA ) 4.0, rCB ) 4.0) Shown in Figure 1b with Additional Columns/Zonea A product (%) configuration

A

B

B product (%) C

A

B

C product (%) C

1-1-1-1-1 2-2-1-1-2 2-2-1-2-2 2-2-2-2-2

88.93 97.68 99.88 97.75

7.62 1.90 0.10 1.89

feed composition 0.33-0.34-0.33 (point 1) 3.45 3.49 95.27 1.24 0.42 3.01 96.41 0.58 0.12 3.07 96.74 0.19 0.36 0.79 97.85 1.36

1-1-1-1-1 2-2-1-1-2 2-2-1-2-2 2-2-2-2-2

84.27 99.96 95.98 96.03

15.19 0.04 3.96 3.91

feed composition 0.30-0.65-0.05 (point 3) 0.54 1.71 98.19 0.10 7.0 × 10-4 1.56 98.42 0.02 0.06 1.38 98.58 0.04 0.06 0.38 99.51 0.11

a

A

B

C

2.51 0.48 2.3 × 10-7 0.54

7.33 7.62 0.06 1.86

90.16 91.90 99.94 97.60

7.61 1.4 × 10-16 2.51 2.61

46.79 37.95 18.68 18.86

45.60 62.05 78.81 78.53


Table 14. Simulation Results for Nine-Zone System (rBA ) 4.0, rCB ) 4.0, and rBC ) 4.0) Shown in Figure 7aa purity (%) A

B

C

E

Train 1b A product 89.6795 8.9988 5.77 × 10-9 1.3207 BC feed 1.5423 46.7292 50.8657 0.8628 E product 4.5906 3.91 × 10-15 33.1006 62.3088 B product C product

2.3814 83.8259 0.6085 4.1777

Train 2c 13.2063 94.1950

0.5864 1.0188

Table 15. Simulation Results for Sugar Separations (rBA ) 1.769, rCB ) 2.435, and rBA ) 1.232) for SMB Shown in Figure 7aa

flow rate (mL/min)

purity (%) A

60 300 960 300 300

Feed composition ) 0.25-0.30-0.35-0.10. (Dtotal/F)min ) 26.0, and productivity ) 0.024. b Simulation conditions: L ) 166.67 cm, Dc ) 3.090 cm, e ) 0.4, p ) 0.0, Rp ) 0.001 cm, (D/F)min ) 21, recycle flow rate ) 33.33 mL/min, configuration ) 1-1-1-1. c Simulation conditions: L ) 41.67 cm, D ) 1.382 cm, ) 0.4, c e p ) 0.0, Rp ) 0.001 cm, (D/F)min ) 1.00, recycle flow rate ) 116.667 mL/min, configuration ) 1-1-1-1. a

amount of C and little E, the feed was 25% A, 30% B, 35% C, and 10% E. The SMB systems were simulated with one column per zone. The feed rate was 60 mL/ min, and the switching time was 7.5min. The simulation conditions and results are presented in Table 14. The E product purity could be increased by increasing MC5. Additional simulations were performed for the separation of dextran T9 (A), dextran T6 (B), raffinose (C), and fructose (E) in water (D) using silica gel. Equilibrium and mass-transfer data are given by Ching et al.,16 who reported experimental results for the continuous separation of three carbohydrate mixtures (fructosedextran, raffinose-dextran, and fructose-raffinose) with silica gel as the sorbent and deionized water as the eluent. The equilibrium constants are as follows: Kdextran-T9 ) 0.13, Kdextran-T6 ) 0.23, Kraffinose ) 0.56, and Kfructose ) 0.69. The mass-transfer constants ki (min-1) are kdextran-T9 ) 0.60, kdextran-T6 ) 2.84, kraffinose ) 3.42, and kfructose ) 5.52. The feed composition is 0.25-0.30.35-0.1. The SMB system was first simulated with one

B

C

E

flow rate (mL/min)

A product BC feed E product

72.6301 11.4700 17.7976

Train 1b 26.1549 0.5751 32.6215 44.7022 0.3673 49.9340

0.6399 11.2063 31.9011

60 258 78

B product C product

17.9006 4.6674

Train 2c 53.4709 20.2769 10.2574 66.0400

8.3516 19.0352

258 258

a Both trains have one column per zone. Feed composition ) 0.25-0.30-0.35-0.10. (Dtotal/F)min ) 9.9, and productivity ) 7.18 × 10-4. A ) dextran T9, B ) dextran T6, C ) raffinose, E ) fructose. b Simulation conditions: L ) 406.87 cm, Dc ) 5.060 cm, e ) 0.45, p ) 0.0, Rp ) 0.0011 cm, (D/F)min ) 5.6, recycle flow rate ) 568.91 mL/min. c Simulation conditions: L ) 445.25 cm, Dc ) 5.5215 cm, e ) 0.45, p ) 0.0, Rp ) 0.0011 cm, (D/F)min ) 1.00, recycle flow rate ) 819.49 mL/min.

column per zone and at the minimum D/F values calculated from the local equilibrium theory (Table 15). For this separation, the A-B and B-C separations are of moderate difficulty, and the C-E separation is difficult (eq 15). As expected, the simulations show that the products are not pure. This result agrees qualitatively with equilibrium calculations. To increase the purities of the products, we first increased D/F in train 1. The multipliers used in Table 16 are as follows: (train 1) MA1 ) MB2 ) 0.98, MA3 ) MC4 ) ME5 ) 1.05; (train 2) MB1 ) MC2 ) MB3 ) MC4 ) 1.0. The purities of products A, B, and E improved, whereas the C product purity declined. In additional simulations (not shown), the same multipliers were used, and the number of columns per zone was varied. A 2-2-2-2 system was used for train 2, and 2-2-1-1-2, 2-2-1-2-2, and 2-2-2-2-2 configurations were used for train 1. Compared to the results shown in Table 16, the 2-2-


1-1-2 configuration for train 1 gave the best A, B, and C product purities (93.55% A, 77.39% B, and 73.77% C), but it still gave a low E product purity (48.52% E). The 2-2-1-2-2 configuration improved the E purity to 77.25% but reduced the other product purities (A, 93.23%; B, 71.58%; C, 72.84%). The 2-2-2-2-2 configuration gave all products of lower purity than the 2-2-1-2-2 configuration. The symmetrical SMB system with little A in the feed and a side stream (BC product) above the feed (Figure 7b) was also simulated for the sugar separation with a feed composition of 0.1-0.35-0.3-0.25. The simulation conditions and results are listed in Table 17. Although SMB systems with increased D/F and more columns per zone were not simulated, we expect the results to be similar to but mirror images of the results presented in Tables 15 and 16.

Discussion If mass-transfer rates are reasonably high, the onecascade SMB system for ternary separation shown in Figure 1b is capable of obtaining relatively high purities for all products, particularly when the B-C separation is easy and there is little C in the feed. When RCB is large, this SMB produces a significantly higher B product purity than the TMB. This appears to be the only reported instance in which an SMB is better than a TMB. The reason for the improvement is the chromatographic band movement in the SMB. As expected, the TMB produces purer A and C products. The SMB system in Figure 2b does not produce nearly as pure a B product because there is no chromatographic band separation and because, according to distillation results,10 the wrong phase is withdrawn as the side


Figure 7. Nine-zone SMB for quaternary separation: (a) side stream below feed, (b) side stream above feed.

stream. The TMB would be expected to work better than the SMB for the configuration in Figure 2b because withdrawing the solid phase will minimize component A in the side stream and because there is no chromatographic band separation in the SMB. Local equilibrium theory predicts that the SMB configuration in Figure 3 should provide the same or even better separations than that in Figure 1b. The results from the simulations (Tables 9 and 13 and compare Table 8 to Table 6) show that the A product purities are similar. At the minimum D/F value, the C product in Figure 3 can be purer than that in Figure 1b. As D/F is increased, the purity of the C product in Figure 1b increases rapidly, whereas the purity increase of C for Figure 3 is small. Thus, for larger D/F values, the SMB in Figure 1b is preferable.

It is difficult to obtain high purities for the fourcomponent sugar separation by using the nine-zone SMB system. Therefore, to obtain high-purity products for the separation of dextran T9, dextran T6, raffinose, and fructose, a different SMB design is required.17 The nine-zone SMB system will produce satisfactory product purities for easy separations particularly when there is little of the most strongly adsorbed component in the feed. Conclusions Single-cascade SMB systems for separating ternary mixtures were developed. The proposed five-zone and four-zone single-cascade SMB systems are simpler and will probably have lower costs for the separation of

4860 Ind. Eng. Chem. Res., Vol. 42, No. 20, 2003 Table 16. Simulation Results for Sugar Separations (rBA ) 1.769, rCB ) 2.435, and rBC ) 1.232) for the SMB Shown in Figure 7aa purity (%) A

B

C

E

flow rate (mL/min)


76.1308 7.9496 22.4455

Train 1b 23.3915 0.3057 32.0622 47.6588 0.2506 39.5873

0.1710 12.3294 37.7166

185.916 856.539 258.954

B product C product

12.1057 2.9013

Train 2c 51.2789 21.0936 9.0420 63.1478

15.5218 24.9089

856.539 856.539

Both trains have one column per zone. Feed composition ) 0.25-0.30-0.35-0.10. (Dtotal/F)min ) 34.97, and productivity ) 2.21 × 10-4. A ) dextran T9, B ) dextran T6, C ) raffinose, E ) fructose. b Simulation conditions: L ) 387.497 cm, Dc ) 9.2197 cm, e ) 0.45, p ) 0.0, Rp ) 0.0011 cm, (D/F)min ) 20.69, recycle flow rate ) 1762.82 mL/min. c Simulation conditions: L ) 445.251 cm, Dc ) 10.060 cm, e ) 0.45, p ) 0.0, Rp ) 0.0011 cm, (D/F)min ) 1.00, recycle flow rate ) 2720.633 mL/min. a

Table 17. Simulation Results for Sugar Separations (rBA ) 1.769, rCB ) 2.435, and rBC ) 1.232) for the SMB Shown in Figure 7ba purity (%) A

B

C

E

flow rate (mL/min)


34.4474 11.3445 0.5494

Train 1b 43.1645 1.7281 44.3140 30.8205 0.1746 30.1429

20.6600 13.5210 69.1331

46.154 212.308 60.000

B product C product

15.7007 5.0385

Train 2c 63.5747 11.4238 15.2500 51.8549

9.3008 27.8566

212.308 212.308

a Both trains have one column per zone. Feed composition ) 0.10-0.35-0.30-0.25. (Dtotal/F)min ) 7.85, and productivity ) 2.21 × 10-4. A ) dextran T9, B ) dextran T6, C ) raffinose, E ) fructose. b Simulation conditions: L ) 406.872 cm, Dc ) 4.4379 cm, e ) 0.45, p ) 0.0, Rp ) 0.0011 cm, (D/F)min ) 4.31, recycle flow rate ) 437.622 mL/min. c Simulation conditions: L ) 445.251 cm, Dc ) 5.0087 cm, e ) 0.45, p ) 0.0, Rp ) 0.0011 cm, (D/F)min ) 1.00, recycle flow rate ) 674.355 mL/min.

ternary mixtures than standard SMB systems with eight or more zones.4-7 However, these benefits occur only for easy separations and/or for cases in which the feed contains little of the most strongly adsorbed component. The proposed design can easily use existing SMB technology. A new design for quaternary separations based on the single-cascade SMB was also developed. Acknowledgment This research was partially supported by NSF Grant CTS-0211208 and the ERC for Advanced Bioseparation Technology, KOSEF. Notation AC ) cross-sectional area of the column, cm2 ci ) concentration of species i in the liquid, g/cm3 Ci ) constant for determining the velocity of solute i, eqs 1a and b D ) volumetric flow rate of fresh desorbent, cm3/s Dc ) column diameter, cm F ) volumetric flow rate of the feed, cm3/s KDi ) steric hindrance factor (KDi ) 0 for excluded molecules, and KDi ) 1.0 for molecules that can access all pores) Ki ) qi/ci, linear equilibrium constant, g of adsorbent/m3 of solution

L ) length of each column, cm N ) number of components Mij ) multiplier qi ) amount adsorbed, g of solute/g of adsorbent Rp ) particle radius, cm tp ) product time (Figure 3), s tsw ) switching time, s ui ) velocity of the solute, cm/s uport ) port velocity ) L/tsw, cm/s vj ) interstitial fluid velocity in zone j, cm/s Greek Symbols Rik ) selectivity ) Ki/Kk e ) external porosity p ) particle porosity FB ) bed density, g/cm3 Subscripts A, B, C, i, k ) solutes 1, 2, 3, 4, 5 ) zones in SMB

Literature Cited (1) Mazzotti, M.; Storiti, G.; Morbidelli, M. Optimal Operation of Simulated Moving Bed Units for Nonlinear Chromatographic Separations. J. Chromatogr. 1997, A769, 3. (2) Migliorini, C.; Mazzotti, M.; Morbidelli, M. Robust Design of Countercurrent Adsorption Separation Processes: 5. Nonconstant Selectivity. AIChE J. 2000, 46, 1384. (3) Ruthven, D. M.; Ching, C. B. Countercurrent and Simulated Countercurrent Adsorption Separation Processes. Chem. Eng. Sci. 1989, 44, 1011. (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) Masuda, T.; Sonobe, T.; Matsuda, F.; Horie, M. Process for Fractional Separation of Multi-Component Fluid Mixtures. U.S. Paent 5,198,120, 1993. (6) Mata, V. G.; Rodrigues, A. E. Separation of ternary mixtures by pseudo-simulated moving bed chromatography. J. Chromatogr. A 2001, 939, 23. (7) Wankat, P. C. Simulated Moving Bed Cascades for Ternary Separations. Ind. Eng. Chem. Res. 2001, 40, 6185. (8) Nicoud, R. M. Simulated Moving-Bed Chromatography for Biomolecules. In Handbook of Bioseparations; Ahuja, S., Ed.; Academic Press: San Diego, 2000; pp 475-509. (9) Beste, Y. A.; Arlt, W. Side-Stream Simulated Moving-Bed Chromatography for Multicomponent Separation. Chme. Eng. Technol. 2002, 25, 956. (10) Tedder, D. W.; Rudd, D. F. Parametric Studies in Industrial Distillation: Part 1. Design Comparisons. AIChE J. 1978, 24, 303. (11) Christiansen, A. C.; Skogestad, S.; Lien, K. Complex Distillation Arrangements: Extending the Petlyuk Ideas. Comput. Chem. Eng. 1997, 21, s237. (12) Agrawal, R. Thermally Coupled Distillation with Reduced Number of Intercolumn Vapor Transfers. AIChE J. 2000, 46, 2198. (13) Agrawal, R. Multieffect Distillation for Thermally Coupled Configurations. AIChE J. 2000, 46, 2211. (14) Rong, B.-G.; Kraslawski, A.; Nystro¨m, L. The synthesis of thermally coupled distillation flowsheets for separations of fivecomponent mixtures. Comput. Chem. Eng. 2000, 24, 247. (15) Chung, S. F.; Wen, Y. Longitudinal Dispersion of Liquid Flowing Through Fixed and Fluidized Beds. AIChE J. 1968, 14, 857. (16) 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. (17) Kim, J. K.; Wankat, P. C. Designs of Simulated Moving Bed Cascades for Quaternary Separations. Ind. Eng. Chem. Res., manuscript submitted.

Received for review April 30, 2003 Revised manuscript received July 7, 2003 Accepted July 10, 2003 IE030373J

Single-Cascade Simulated Moving Bed Systems for the Separation of

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