One-Column Chromatograph with Recycle Analogous to Simulated

Because the analogue would be useful in short campaigns, a start-up analysis was performed for both a linear system of dextran ... A shutdown analysis...
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Ind. Eng. Chem. Res. 2004, 43, 5291-5299

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One-Column Chromatograph with Recycle Analogous to Simulated Moving Bed Adsorbers: Analysis and Applications Nadia Abunasser and Phillip C. Wankat* School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907-2050

A single chromatography column with tanks (the “analogue”) can be made analogous to a simulated moving bed (SMB) configuration with the appropriate recycle pattern. The analogues and the corresponding SMBs were simulated using Aspen Chromatography. Typically, the analogue produces a lower purity product because of mixing in the tanks. For the linear system of dextran T6-fructose, the use of a large number of tanks to approach plug flow improved the separation in the analogue so that it asymptotically approached the SMB separation. Because the analogue would be useful in short campaigns, a start-up analysis was performed for both a linear system of dextran T6-fructose and the nonlinear system of binaphthol enantiomers. Correct start-up conditions can reduce the time needed to reach steady state by 50%. A shutdown analysis for the linear system was also performed, and several strategies were suggested that reduce the time and amount of desorbent used during shutdown. The concept of the one-column analogue was successfully applied to various three-zone SMB configurations for the linear system of dextran T6-raffinose and to the VARICOL process for the dextran T6-fructose system. Introduction Simulated moving bed (SMB) chromatography has become a widely used separation method. Its beginnings can be traced back to the Shanks system for leaching in 1841.1 The modern applications in adsorption and chromatography were first developed and commercialized by UOP in the 1960s.2-4 Since then, the SMB has been used to separate materials such as hydrocarbons,2-4 sugars,5-8 and pharmaceuticals.9 The SMB simulates the countercurrent movement of the solid adsorbent and the fluid in a true moving bed. It does this through intermittent switching of the inlet and outlet ports. The most commonly used SMB is the four-zone SMB (Figure 1). Zone 1 purifies the fast component (less strongly adsorbed), zone 2 purifies the slow component (more strongly adsorbed), zone 3 desorbs the slow component, and zone 4 purifies the desorbent for recycle. Since the introduction of the SMB, new configurations such as the three-zone SMB7,10 have been designed. Although the three-zone SMB does not have the fourth zone for desorbent purification, some desorbent can be recycled with proper timing.10 One of the most recent modifications to the standard four-zone SMB is the VARICOL system, which uses an asynchronous shift in the inlet and outlet ports.11-13 It has been shown to achieve higher purities than the standard four-zone SMB for several systems.11-13 While SMB processes can produce high purities with a minimal amount of desorbent, it is a complex system and all of the columns must be packed identically. This will cause problems when a plant is operating campaigns if the next campaign requires a different sorbent. A simpler, more flexible, one-column recycle chromato* To whom correspondence should be addressed. Tel.: (765) 494-7422. Fax: (765) 494-0805. E-mail: wankat@ecn. purdue.edu.

Figure 1. Complete cycle for a four-zone SMB with one column per zone.

graphic analogue to the SMB (called the analogue) was introduced previously.14 This system consists of one column with several tanks to hold recycle fluids. The analogue can be designed by studying one column of any SMB through a complete cycle and then replacing the other columns with tanks of the appropriate volume. For a four-zone SMB with one column per zone, a complete cycle is shown in Figure 1 within the envelope enclosed by the dotted line. The analogue would consist of one column and four well-mixed tanks (Figure 2). For an SMB with two columns per zone, it would consist of one column and eight tanks and so on.14 The analogue is designed to ensure that the productivity is equal to that of the SMB, where

productivity )

F no._columns × AcLcol

10.1021/ie0400346 CCC: $27.50 © 2004 American Chemical Society Published on Web 07/16/2004

(1)

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Figure 3. Purities of the analogue to a four-zone SMB with one column per zone at D/F ) 4.15 versus the number of tanks used. Figure 2. One-column analogue to a four-zone SMB with one column per zone. Reprinted with permission from ref 14. Copyright 2003 American Chemical Society.

The solute velocities for the design of both the SMB and the analogue are also identical. For a linear system, the design equations based on the local equilibrium theory are14,15

smaller tanks such that the total volume remained the same. Thus,

volume of each tank replacing tank 1 ) [(V1 - Vraff)tsw]/n (4a) volume of each tank replacing tank 2 ) [V2tsw]/n (4b)

uB1,new) M1uport, M1 e 1

(2a)

volume of each tank replacing tank 3 ) [(V3 - Vextr)tsw]/n (4c)

uA2,new ) M2uport, M2 g 1

(2b)

volume of each tank replacing tank 4 ) [V4tsw]/n (4d)

uB3,new ) M3uport, M3 g 1

(2c)

uA4,new ) M4uport, M4 e 1

(2d)

usi )

vi 1 - e 1+ FsKi e

[ ]

(3)

The purities obtained with the analogue are lower than those obtained with an SMB because of mixing in the tanks.14 This design was also successfully applied to the partial feed SMB configurations.14,16 In this paper the analogue concept is further developed and applied to additional SMB systems, including three-zone SMB and VARICOL systems.

and n is the number of smaller tanks each of the tanks is split into. Also, to retain the concentration profile, these tanks are emptied in the same order as they were filled. Other terms are defined in the Notation section. The commercially available software, Aspen Chromatography, version 12.1, was used to simulate the analogue for the linear system of dextran T6 and fructose.7,14 Runs were performed using 4, 8, 16, 20, and 28 tanks at D/F ) 4.15 for a one-column analogue to a fourzone SMB with one column per zone. The operating conditions are identical with those in Tables 1 and 4 of ref 14. Figure 3 shows the product purities versus the number of tanks used as well as the SMB purities. As the number of tanks increased, the purities also increased and approached the SMB purities. As the number of tanks used in each step increased, plug flow was approached and therefore the profile in the column was more accurately retained in the storage tanks. This analysis shows that, with the correct configuration, the purities in the analogue approach those of the SMB. Because a total of 28 tanks is 7 per step, it is unlikely that more than seven tanks per step will improve the separation significantly in any configuration of the analogue.

Tank Mixing

Two-Column Analogue to a Four-Zone SMB

It was shown in the previous work14 that mixing in the tanks is what causes the separation in the onecolumn analogue (Figure 2) to be worse than that achieved in the corresponding SMB (Figure 1). To try to reduce the effect of mixing, plug-flow tanks, i.e., unmixed tanks, could be used instead of well-mixed tanks. To achieve the effect of plug flow, the tanks in the one-column analogue were divided into several

As an alternative to using plug-flow tanks, a twocolumn analogue was tried. For a four-zone SMB with one column per zone, the two-column analogue is designed by simultaneously studying two columns for a complete cycle (solid envelope in Figure 1). The other columns are then replaced with tanks to form the analogue (Figure 4). In this analogue, the tanks feed only column 2 and tanks are only filled from column 1. This design ensures that the SMB and the two-column

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be split into several smaller tanks so that the concentration profile was partially retained.14 Start-up Analysis

Figure 4. Complete cycle for a two-column analogue to a fourzone SMB. Table 1. Comparison of the Results for the Linear System of Dextran T6 and Fructose raffinate extract (% dextran T6) (% fructose) D/F ) 1

four-zone SMB14 one-column analogue14 two-column analogue D/F ) 2.05 four-zone SMB14 one-column analogue14 two-column analogue

82.27 73.76 76.98 92.26 82.32 86.48

86.94 77.20 79.57 95.14 84.56 86.93

analogue have the same productivies. Equations 1-3 are also used to design this analogue. The two-column analogue was studied for both a linear system (dextran T6 and fructose)7,14 and a nonlinear system (binaphthol enantiomers).14,17,18 Simulations were performed on the commercially available software Aspen Chromatography, version 12.1. The linear system was simulated at two desorbent-to-feed ratios (D/F), 1.0 and 2.05, while the nonlinear system was studied at D/F ) 6.47. The operating conditions are identical with those used for the one-column analogue in Tables 1, 3, and 4 of ref 14. The results and system comparisons for the linear system can be found in Table 1. The results show that for both D/F values the purities achieved in the twocolumn analogue were higher than those achieved in the one-column analogue. However, they still are quite a bit lower that the SMB purities. If one compares the outlet concentration profiles for both columns 1 and 2 of the two-column analogue (Figure 5a,b) at steady state to those of the one-column analogue (Figure 5c), there is an obvious similarity between the outlet profile of column 2 (Figure 5b) and that of the one-column analogue (Figure 5c). Both of these concentration profiles have “shoulders”. This results from column saturation because of feeding from tanks that are at constant concentrations. The concentration profile exiting column 1 of the two-column analogue (Figure 5c) is much smoother. This occurs because this column is being fed a concentration profile from column 2 instead of a constant concentration from a tank. This effect causes the separation to improve when compared to that of the one-column analogue while still being worse than that of the SMB. Similar results were found for the nonlinear isotherms (Table 2). The extremely low extract purities for the analogues occur because of mixing. The solute velocities in the nonlinear systems are a function of concentration, and because a constant concentration was being fed into column 2, the velocities were no longer optimized, which leads to poor separation. To improve this purity, one or more of the tanks used could

Because the analogue may be used for relatively short campaigns, start-up can be an important factor in the operation. For this reason, a start-up analysis was performed for the one-column analogue for both linear and nonlinear systems. For the linear system of dextran T6 and fructose, the analysis was performed for the onecolumn analogue to a four-zone SMB with one column per zone at two D/F values, 1.0 and 6.33, while for the nonlinear system of binaphthol enantiomers, the analysis was performed for a one-column analogue to a fourzone SMB with two columns per zone at D/F ) 6.47. The operating conditions are again given in Tables 1, 3, and 4 of ref 14. The approaches used here are similar to that of Xie et al.19 used for the start-up of SMBs. They did an SMB simulation to cyclic steady state and then determined faster approaches to the same cyclic steady state. In all cases simulations were run until the cyclic steady state was achieved. The criterion for the cyclic steady state over the course of a complete cycle was

(mass of component i in - mass component i out)/ mass of component i in e 0.0005 (5) The steady-state values for the tank concentrations and column concentration profiles were then recorded. For the linear system, three different start-up approaches were used. The first approach is the standard procedure of starting with a clean column and tanks containing pure desorbent. In both of the new start-up cases, it was assumed that pure dextran T6 and fructose were available. This is different from the approach used by Xie et al.,19 who assumed that only feed and desorbent were available. The key to start-up in the second approach is the very low concentration in the column at the beginning of step 4 (Figure 6a). The simulation was started with a clean column and the tank concentrations at steady-state values achieved in the original run; however, the column was started in step 4 instead of step 1. The third approach approximately matched the concentration profile in the column at steady state in step 1. Figure 6b shows the steady-state concentration profile in the column at the beginning of step 1 for D/F ) 1.0. It can be seen that about 70% of the column is saturated with dextran T6 at 40 g/L and fructose at 14.9 g/L. Using a feed concentration of 40 g/L of dextran T6 and 14.9 g/L of fructose, the concentration profile in Figure 7 was achieved. The tank concentrations were then set at the steady-state values, and the simulation was run until steady state. This same procedure was used for D/F ) 6.33. The results for the six start-up runs for the linear system are given in Table 3. Run 1 refers to the initial run using a clean column and tanks filled with desorbent only, starting in step 1; run 2 refers to a clean column with tank concentrations at steady-state values, starting in step 4; and run 3 refers to a column with an approximate steady-state concentration profile with tanks at steady-state concentrations, starting in step 1.

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Figure 5. Steady-state concentration profiles exiting for analogues at D/F ) 1.0 for the dextran T6-fructose system: (a) exiting column 1 of a two-column analogue; (b) exiting column 2 of a two-column analogue; (c) exiting column of a one-column analogue. Table 2. Comparison of the Results for the Nonlinear System of Binaphthol Enantiomers

D/F ) 6.47

four-zone SMB14 one-column analogue14 two-column analogue

raffinate (% A)

extract (% B)

89.26 76.02 77.98

86.76 54.39 55.19

From the results, it is clear that the runs starting with the column concentration profiles as close as possible to the steady-state values reached steady state the quickest. This procedure saved 16.9-17.6 h in

process time (57.5-60%) during which the product would not meet specifications. For the nonlinear system, start-up analysis was performed for a one-column analogue to a four-zone SMB with two columns per zone at D/F ) 6.47 with feed concentrations of 10 g/L for both of the components. Three approaches were also used for this system. The procedure for runs 1 and 3 are identical with those used for the linear system. The feed concentrations used to set up the axial concentration profile in run 3 were 6.8 g/L for the fast component and 3.0 g/L for the slower component. The actual time needed to set up this profile

Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004 5295 Table 3. Number of Cycles Needed To Reach Cyclic Steady State for the Different Start-up Conditions for the Analogue to a Four-Zone SMB with One Column per Zone for the Linear System of Dextran T6 and Fructose D/F

run

no. of cycles to reach cyclic steady state

process time to reach steady state (min)

1.0 1.0 1.0 6.33 6.33 6.33

1 2 3 1 2 3

40 27 17 40 23 16

1760 1188 748 1760 1012 704

Table 4. Number of Cycles Needed To Reach Cyclic Steady State for the Different Start-up Conditions for the Analogue to a Four-Zone SMB with Two Columns per Zone for the Nonlinear System of Binaphthol Enantiomers D/F

run

no. of cycles to reach steady state

process time to reach steady state (min)

6.47 6.47 6.47

1 2 3

80 30 15

1984 744 372

number of cycles needed to reach steady state (81% for run 3 compared to run 1). Shutdown Analysis

Figure 6. Axial concentration profile in the one-column analogue at D/F ) 1.0 for the dextran T6-fructose system: (a) at cyclic steady state at the beginning of step 4; (b) at cyclic steady state at the beginning of step 1; (c) built up in the one-column analogue after feeding column 1 with adjusted feed (run 3 at D/F ) 1.0 in Table 3).

Figure 7. Shutdown cycle for the analogue to a four-zone, one column per zone SMB.

was also longer than the calculated time; it took approximately 24 min using the feed flow rate. The one-column analogue to a four-zone SMB with two columns per zone had the lowest concentrations in step 6. Therefore, in run 2 the simulation started in step 6 with a clean column and tanks at the previously found steady-state values of the solute concentrations. The results for the nonlinear system are given in Table 4. The improved start-up methods greatly reduce the

Shutdown of the analogue can also be an important issue in its operation in campaigns. There are several strategies that can be used to successfully shut down the analogue. In all cases, it would be possible to directly mix the contents of tank 1 (Figure 2) with the raffinate product and tank 3 (Figure 2) with the extract product. Therefore, the only tanks that would need to be dealt with are tanks 2 and 4. As in the case of start-up, the fact that the column is the cleanest at the beginning of step 4 will be used to make the shutdown process as quick as possible. For all of the shutdown strategies discussed, the cycle will be stopped at the beginning of step 4 and tanks 1 and 3 will be mixed with the products. There are two advantages to this: first, the column is the cleanest it can be during the cycle, and second, tank 4 will have a very small amount of material in it at the beginning of this step and therefore there will be less material to clean out of the system. If it is not necessary for all of the feed to be separated into products, then the shutdown process is quite simple. The column can be cleaned out with pure desorbent, and the material exiting during this process can be mixed with tank 2, as can the heel remaining in tank 4. This material can then be stored until the next campaign, when it could be mixed with the feed. For the linear sugars system (dextran T6-fructose) operating at D/F ) 1.0, the amount of desorbent used would be approximately 670 cm3 or about 12.6 column void volumes. Approximately 100 min is required to clean the column. If all of the feed must be separated into products, then there are several strategies that can be used. The simplest is replacing the feed tank with a desorbent tank, filling tanks 3 and 4 with desorbent, and then running the same cycle as before until the column and tanks are clean. Unfortunately, this method uses a very large amount of desorbent and is time-consuming. For the dextran T6-fructose system operating at D/F ) 1.0, it will take 73.3 h and use 6126 cm3 or 116 column void

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volumes of desorbent to reduce the concentration in the column and tanks to the order of 10-5 g/L. A quicker, more efficient method is to use the shutdown cycle shown in Figure 7. In this cycle, tanks 1, 3, and 4 are disconnected, and the contents of the heel remaining in tank 4 is mixed with tank 2. There will be three steps through which the contents of tank 2 will be separated. The flow rate in the column is constant throughout the cycle (flow rate of column 2 in the original cycle), and the step time is equal to the switching time of the original cycle. For the sugars system at D/F ) 1.0, the concentration in tank 2 at the beginning of the shutdown procedure is 38.96 g/L of dextran T6 and 38.04 g/L of fructose (after mixing in the contents of tank 4). After 25 cycles, or 825 min, the concentration in the column is on the order of 10-6 g/L and the average purity of the material mixed with the raffinate was 75.4% dextran T6 and that mixed with the extract was 70.21% fructose (the original cycle gave 73.5% dextran T6 in the raffinate and 73.78% fructose in the extract). The amount of desorbent used for this procedure was 3374 cm3 or 63.6 column void volumes. At the end of the process, tank 2 contained 1.72 g/L of dextran T6 and 3.6 × 10-4 g/L of fructose, or 99.9% dextran T6, and therefore could be mixed with the raffinate product. This approach reduced the desorbent use by 44.9% and the time required by 81.24% compared to operating the analogue with desorbent instead of feed. These same strategies were applied to higher D/F values, and similar results were obtained. Therefore, the results can be generalized in that using the cycle in Figure 7 will use less desorbent than the direct method of replacing the feed with desorbent. Analogue to Three-Zone SMB Configurations After the analogue was successfully applied to the four-zone SMB, a logical step is to apply it to other SMB configurations. One of the configurations of interest is the three-zone SMB. The original three-zone SMB7 (Figure 8a) has no desorbent recycle. The zones in this SMB have the same function as the corresponding zones in the four-zone SMB (Figure 3), with the exception that there is no zone where the desorbent would be regenerated (zone 4 in the four-zone SMB). To achieve separation in the three-zone SMB, the following inequalities must be satisfied:10

uA1, uA2 > uport

(6a)

uB3 > uport > uB1, uB3

(6b)

In general, the four-zone SMB gives higher purities and uses less desorbent than the standard three-zone SMB.7 The three-zone SMB can be improved with partial feed, where the feed is not fed for the whole switching time, and with selective withdrawal of the raffinate, where relatively pure desorbent exiting zone 1 is recycled.10 With the correct balance between the partial feed and selective withdrawal, the three-zone SMB with one column per zone (Figure 8b) can give purities as high and possibly higher than those achieved with a four-zone SMB with one column per zone. The analogue was applied to the standard three-zone SMB at D/F ) 5.6, a three-zone SMB with only selective withdrawal (D/F ) 4.7) and a three-zone SMB with both partial feed and selective withdrawal (D/F ) 2.5). The

Figure 8. Three-zone SMB: (a) original design;7 (b) with partial feed and selective withdrawal.10

analogue to Figure 8a requires a minimum of two tanks (Figure 9a). Figure 9b shows the analogue for a threezone SMB with selective withdrawal and partial feed (Figure 8b). It should be noted that steps 6 and 7 in Figure 9b are not identical. The flow rate exiting tank 1 is higher in step 7 because the feed would be added to the SMB in that step. The flow rates in and out of the tanks can be calculated using simple mass balances. This design of the analogue ensures that the flow rates and therefore the productivity of the analogue match those of the corresponding SMB. The separation simulated was the linear system of dextran T6 and raffinose.7,10 The simulation conditions and system properties can be found in Tables 1 and 3 in ref 10. All of the SMBs studied and therefore all of the analogues were designed such that the productivity is kept constant. The results from the various runs are in Table 5. As in the case of the four-zone SMB, the purities obtained with the analogue were lower that those obtained with the SMB. This decrease in purity is again attributed to the mixing in the tanks. In our previous work,14 the advantage of the partial feed was lost in the standard analogue design unless the tank that is mixed with the feed was split into more than one tank. A run for the analogue of the three-zone SMB with both partial feed and selective withdrawal was performed in which tank 2 was divided into two smaller tanks. Comparison of the analogue runs in Table 5 shows the advantage of selective withdrawal and partial feed, particularly when additional tanks are used. VARICOL and Its Analogue The next SMB configuration studied was VARICOL operation. This operation is relatively new, and its main characteristic is the asynchronous shift in the inlet and

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Figure 9. Three-zone analogues: (a) analogue to the original three-zone SMB; (b) analogue to the three-zone SMB with partial feed and selective withdrawal. Table 5. Product Purities for the Various Three-Zone SMBs and Their Corresponding Analogues standard three-zone SMB10 analogue to standard three-zone SMB, two tanks analogue to standard three-zone SMB, three tanks (tank 2 split in half) three-zone SMB with selective withdrawal10 analogue to three-zone SMB with selective withdrawal, three tanks analogue to three-zone SMB with selective withdrawal, four tanks (tank 2 split in half) three-zone SMB with selective withdrawal and partial feed10 analogue to three-zone SMB with partial feed and partial withdrawal, three tanks analogue to three-zone SMB with partial feed and partial withdrawal, four tanks (tank 2 split in half)

D/F

raffinate (%)

extract (%)

5.6 5.6 5.6 4.7 4.7 4.7

98.75 79.36 81.22 98.75 78.72 80.64

92.02 91.94 93.20 92.02 91.23 92.62

2.5 2.5

99.84 83.38

98.08 91.86

2.5

85.54

94.52

outlet ports.11-13 That is, the number of columns in each zone is not constant throughout the switching time. For this study, a VARICOL system was set up for the linear system of dextran T6-fructose using five columns where both zones 1 and 2 (Figure 10) will contain two columns for a fraction of the switching time.13 All systems were assumed to have zero dead volume. VARICOL may be set up using eqs 1-3. The fraction of the switching time for which each of these zones had two columns was studied at D/F ) 1.0. Simulation conditions are given in Table 1 of ref 14. The design that gave the highest purity index was chosen for the analogue analysis. The purity index is defined as

purity index ) (% dextran in raffinate + % fructose in extract)/2 (7) The results from SMB and VARICOL runs at D/F ) 1.0 are given in Table 6. For the system chosen for separation in this study, it was found that VARICOL using five columns was slightly better than the SMBs with five columns. The VARICOL design that gave the highest purity index was when zones 1 and 2 each had two columns for approximately half of the switching time.

Figure 10. Five-column VARICOL system.

The VARICOL design with two columns in zone 1 for half of the time was chosen for the analogue study (Figure 11). Simulations were run for D/F values of 1.0

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Figure 11. Analogue to the five-column VARICOL system. Table 6. Purity Indexes for the Various Five-Column SMB and VARICOL Designs at D/F ) 1.0 system

purity index

SMB (2, 1, 1, 1) SMB (1, 2, 1, 1) VARICOL with two columns in zone 1 for 0.25tsw VARICOL with two columns in zone 1 for 0.33tsw VARICOL with two columns in zone 1 for 0.5tsw VARICOL with two columns in zone 1 for 0.75tsw

88.03 87.56 88.10 88.26 88.42 87.84

Table 7. Simulation Conditions for VARICOL at D/F ) 2.94a value L d e

units

37.5 2.0 0.45

cm cm m3 void/ m3 bed 0.0011 cm 670 kg/m3 1000 kg/m3 8e-4 Pa‚s 2.84 1/min

rp Fs Fl µ kmap (dextran T6) kmap 5.52 (fructose) tsw 11

adsorbent particle radius bed density liquid density liquid viscosity constant mass-transfer coefficient

1/min

constant mass-transfer coefficient

min

switching time for a four-zone SMB with one column per zone and its analogue feed concentration for both solutes feed flow rate for all configurations desorbent flow rate for all configurations raffinate flow rate for all configurations extract flow rate for all configurations recycle flow rate for SMBs

cF feed rate desorbent

50 1.33 3.91

g/L cm3/min cm3/min

raffinate

2.63

cm3/min

extract

2.61

cm3/min

recycle

5.58

cm3/min

a

description column length diameter of column interparticle voidage

Two columns in zones 1 and 2 for half of the switching time.

and 2.94. Design conditions at D/F ) 2.94 are listed in Table 7. Table 8 shows the simulation results for both D/F values for VARICOL, standard SMBs, and their analogues. For both D/F values, the purity index of VARICOL is slightly higher than either of the SMB configurations. When the analogue was constructed with only five tanks, the purity index of the analogue to VARICOL was lower for both D/F values than either of the SMB configurations. The advantage of VARICOL was lost because the concentration profiles were lost in the tanks because of mixing. As in previous cases, the solution was to split some of the tanks. In the case of VARICOL, splitting tanks 1 and 2 was sufficient to increase the

Table 8. Purity Indexes for VARICOL, SMBs, and Their Analoguesa purity index system

D/F ) 1.0

D/F ) 2.94

VARICOL analogue to VARICOL, five tanks analogue to VARICOL, seven tanks SMB (2, 1, 1, 1) analogue to SMB (2, 1, 1, 1), five tanks analogue to SMB (2, 1, 1, 1), seven tanks SMB (1, 2, 1, 1) analogue to SMB (1, 2, 1, 1), five tanks analogue to SMB (1, 2, 1, 1), seven tanks

88.42 78.26 80.95 88.03 78.56 80.02 87.56 78.45 80.23

98.55 89.68 92.5 98.52 90.4 92.3 96.34 88.8 91.14

a VARICOL and VARICOL analogues have two columns in zones 1 and 2 for half of the switching time.

purity index. These two tanks were chosen because they are the tanks that are mixed with the feed, and it has been found that those tanks tend to have the largest effect on the separation.14 It can be seen from Table 8 that the analogues to VARICOL with seven tanks give higher purity indexes than the analogues of the SMBs with seven tanks. Also, the difference in the purity indexes between VARICOL and its analogue are about the same as the differences between the SMBs and their analogues. Discussion and Conclusions The analogue concept is very versatile and can be applied to many different SMB configurations. In this work, we have shown that dividing the tanks into a number of smaller tanks makes the purities of the onecolumn analogue to a four-zone SMB with one column per zone almost identical with that of the SMB. A similar effect could be achieved by using plug-flow tanks. The new two-column analogue had purities between the one-column analogue and the SMB. Mixing occurring in the tanks of the two-column analogue remained a major factor in lowering the purities of the product streams. Therefore, it would probably be preferable to use one column and multiple tanks (or plug-flow tanks) rather than two columns and multiple tanks. Optimizing the start-up conditions for the analogue greatly reduces the time needed to reach steady state. Because this analogue should be useful for short campaigns, start-up will probably be a major factor in the design. Performing a start-up analysis using computer

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simulation to find the optimal start-up conditions can greatly reduce the period when off-spec product is produced. Also, using the correct shutdown procedure will reduce the time and amount of desorbent needed to clean out the system. The analogue is probably more stable than the SMB. One problem that arises in the SMB is the difference in purities when switching occurs. That is, if the columns are not identically packed, this affects the separation when the columns are switched. This is not a factor in the analogue because there is only one column. Also, if the SMB columns are not identically packed, the pressure drop and/or flow rates in each zone will vary when switching occurs. Because there is only one column, the analogue will more stable than the SMB to these fluctuations. The versatility of the concept of the analogue was further shown by its application to two other SMB configurations. The analogue to a three-zone SMB with partial feed and selective withdrawal gave purities that approached those of the corresponding three-zone SMB. When applied to the VARICOL system, it was possible to design the analogue so that it retained the slight increase in the purity index over the analogues to traditional SMBs. This was achieved by splitting two of the tanks in half. Because the application of the analogue concept to several SMB configurations has been successful, it can be concluded that this concept can be applied to the other SMB configurations used for binary separations. While the basic design of the analogue (one tank for every column) may not always give the best separation, these tanks either can be split into several smaller tanks or can be replaced by plug-flow tanks. Acknowledgment This research was partially supported by NSF Grants CTS-9815844 and CTS-0211208. The assistance of Dr. Andrew Stawarz of Aspen Technology is gratefully acknowledged. The help received from Dr. Yifei Zang on the three-zone SMB section is also gratefully acknowledged. Notation e ) external void fraction F ) density (kg/m3) Ac ) cross-sectional area of the column (cm2) D ) desorbent volumetric flow rate (cm3/min) F ) feed volumetric flow rate (cm3/min) Ki ) linear equilibrium parameter Lcol ) length of the column (cm) tF,1 ) time at which feed begins in the partial feed (min) tF,2 ) time at which feed ends in the partial feed (min) tS,1 ) time at which feed port switch occurs in VARICOL (min) tsw ) switch time (min) tw1 ) time at which raffinate withdrawal begins in selective withdrawal (min) uport) Lcol/tsw (cm/min) usi ) solute velocity of component s in zone i (cm/min)

vi ) interstitial velocity (cm/min) Vi ) volumetric flow rate in zone i Vraff ) volumetric flow rate of raffinate (cm3/min) Vextr ) volumetric flow rate of extract (cm3/min)

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Received for review January 23, 2004 Revised manuscript received May 28, 2004 Accepted June 9, 2004 IE0400346