5268
Ind. Eng. Chem. Res. 2003, 42, 5268-5279
One-Column Chromatograph with Recycle Analogous to a Four-Zone Simulated Moving Bed Nadia Abunasser and Phillip C. Wankat* School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907-2100
Y.-S. Kim and Yoon Mo Koo ERC for Advanced Bioseparation Technology, Inha University, Incheon 402-751, Korea
A one-column chromatograph with recycle analogous to a four-zone simulated moving bed (SMB), called “the analogue”, was developed for binary separations. The analogue has one chromatography column connected to a number of tanks equal to the number of steps in the SMB cycle. For example, the analogue to a four-zone SMB with two columns per zone would have eight tanks. The analogue’s simple design gives it great flexibility. The analogues and corresponding SMBs were simulated using Aspen Chromatography (v 11.1) for the separation of dextran T6fructose and dextran T6-raffinose mixtures, which are linear systems, and for the separation of binaphthol enantiomers, which is a nonlinear system. Because of mixing in the tanks, lower purities were obtained with the analogue than with the SMB at equal productivities and desorbent to feed, D/F, values. Therefore, dividing the tanks into several smaller tanks increased the product purities. By increasing D/F from 1.0 to 2.6 (for one column per zone) or to 2.3 (for two columns per zone), the analogue achieved the same purities as the SMB. These increases in D/F are significantly less than the increased amounts of desorbent and adsorbent required for a chromatograph without recycle to obtain the same purity as an SMB. Introduction Large-scale liquid chromatography including simulated moving beds (SMBs) has proven to be an indispensable tool in the separation of materials in industries ranging from petrochemicals to pharmaceuticals. An early use of this technology can be traced back to the Manhattan project.1 In the 1940s, gradient elution using activated carbon was used to separate carotene, xanthophylls, and chlorophyll.2 Then, in the 1950s, a largescale elution liquid chromatograph was developed by Sun Oil Co. as the Arosorb process for the separation of aromatics from alkyl hydrocarbons.3 Elution is the most commonly used mode of chromatography. In this mode, a pulse of feed is followed by solvent.4 Unfortunately, to prevent overlapping of the solute concentration profiles, excess solvent might be required to obtain high product purities. One method used to improve product purities is to recycle the impure portion of the outlet stream. In the simplest case, the outlet stream is divided into three sections, the two product streams and the recycle containing the overlap. The recycled material can be added back into the system before, after, or with the feed step. To further improve the separation, the recycle stream can be subdivided into several fractions that are then recycled separately, reducing the amount of mixing and therefore retaining more of the separation achieved before the recycle.1,4,5 An alternative method of improving separation is to use a true moving bed adsorber. In this system, the solid and fluid move countercurrently in the column. However, movement of solid countercurrent to liquid in a * To whom correspondence should be addressed. Phone: 765-494-7422. Fax: 765-494-0805. E-mail: wankat@ ecn.purdue.edu.
true moving bed with minimal axial mixing is a technical challenge that has yet to be solved. This problem is avoided if the solid is held stationary and the liquid ports are switched, as in a simulated moving bed (SMB).6,7 The most commonly used SMB configuration is the four-zone SMB (Figure 1). Universal Oil Products (UOP) first commercialized an SMB for the fractionation of two solutes by adsorption.6-8 SMBs are also used to separate petrochemicals,6-8 as well as solutions of sugars,9-12 proteins and amino acids 13,14 and chiral compounds.14-17 Although an SMB can achieve higher purities than a simple elution chromatograph, with much less adsorbent and desorbent,18,19 it is a much more complex device. Equipment costs are high, especially if highpressure chromatographic columns are used.17 In addition, standard SMB units are relatively inflexible for multiproduct plants that use a series of campaigns. Because the packing in a separation column needs to be changed for every new product, every column in an SMB needs to be emptied and repacked when products are switched. Before startup, the columns must be checked to show that they are essentially identical. For these reasons a simpler, more flexible, and less expensive alternative to the SMB that produces product that is almost as pure as that obtained from SMBs is proposed. This system, “a one-column recycle chromatographic analogue to simulated moving bed adsorption”, is referred to here as “the analogue”. The analogue proposed here is a single chromatographic column with a number of tanks that allow for recycling in a manner that mimics SMB operation. The analogue was developed by studying the same column in the SMB through a complete cycle and then replacing the remaining columns with tanks to provide the
10.1021/ie030283e CCC: $25.00 © 2003 American Chemical Society Published on Web 08/29/2003
Ind. Eng. Chem. Res., Vol. 42, No. 21, 2003 5269
Figure 1. Complete cycle for a four-zone SMB with one column per zone.
column. In the first step, the feed and the contents of tank 2 are inputted into the column, product P1 (raffinate) is withdrawn, and tank 1 is filled. In the second step, tank 3 feeds into the column, which then fills tank 2. Then, in the third step, fresh desorbent and the contents of tank 4 are fed into the column, while the product P2 (extract) is withdrawn, and tank 3 is filled. In the final step of the cycle, the contents of tank 1 are fed into the column, and tank 4 is filled. For a fourzone SMB with two columns per zone (Figure 3), the basic analogue would consist of one column and eight tanks (Figure 4) and so on. Simulations
Figure 2. Complete cycle for an analogue to a four-zone SMB with one column per zone.
necessary recycle streams while keeping the productivity constant. Productivity is defined as
productivity ) (feed volume/time)/ (total adsorbent volume) (1a) productivity )
F NAcLcol
Aspen Chromatography 11.1 was used to simulate both the SMBs and the analogues. The SMB unit is built into the software. The analogue was built using the various units available in the chromatography portion of the software. Additional details of the simulations are given in Abunasser.20 The separations studied were two linear systems, dextran T6-fructose, and raffinosedextran T6, plus the nonlinear binaphthol enantiomer system. The physical parameters used for these systems are listed in Tables 1-3. A lumped parameter linear driving force model was used for mass transfer
(1b)
where N is the number of columns, Ac is the crosssectional area of a column, and Lcol is the column length. Figure 1 shows a complete cycle of a four-zone SMB with one column per zone. The rectangle shows the column that is isolated to form the analogue (Figure 2). For this configuration, the basic analogue has four tanks and one
∂q ji ) kmaP(ci - c/i ) ∂t
(2)
The flow rates and column dimensions for the linear systems were calculated using the local equilibrium model and the solute movement theory for the single porosity model.19,25,26 The solute velocity is given by
5270 Ind. Eng. Chem. Res., Vol. 42, No. 21, 2003 Table 1. Physical Properties and Column Specifications for Fructose-Dextran T6 System,11 D/F ) 1. Base Cases for SMB and One-Column Analogue value L d e
37.5 2.0 0.45
units
rp Fs Fl m kmap (dextran T6) km a p (fructose) tsw
0.0011 670 1000 8 × 10-4 2.84
cm cm m3 of void/ (m3 of bed) cm kg/m3 kg/m3 Pa‚s 1/min
5.52
1/min
11
min
tsw
5.5
min
cF
50
g/L
feed rate
2.69
cm3/min
desorbent
2.69
cm3/min
raffinate
2.69
cm3/min
extract
2.69
cm3/min
recycle
5.58
cm3/min
description
value
column length column diameter interparticle voidage adsorbent particle radius bed density liquid density liquid viscosity constant mass-transfer coefficient constant mass-transfer coefficient switch time for four-zone SMB with one column per zone and its analogue switch time for four-zone SMB with two columns 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
Table 2. Physical Properties and Column Specifications for Dextran T6-Raffinose System,11,25 Partial-Feed SMB and Corresponding Total-Feed SMB value
units
L d e
35.625 1.4 0.45
rp Fs Fl m kmap (dextran T6) kmap (raffinose) tsw
0.0011 670 1000 8 × 10-4 0.057
cm cm (m3 of void)/ (m3 of bed) cm kg/m3 kg/m3 Pa‚s 1/s
0.0469
1/s
7.73
min
Table 3. Simulation Conditions for the SMBs with One and Two Columns Per Zone and Their Analogues for the Binaphthol System15,26 at D/F ) 6.47
description column length column diameter interparticle voidage
cF
50.0
g/L
feed rate desorbent
0.0010 0.0044
L/min L/min
raffinate extract
0.0040 0.0014
L/min L/min
recycle feed time feed flow rate raffinate raffinate
0.001 188 (0.4-0.6)tsw 0.004 98 0.003 0.007 98
L/min
adsorbent particle radius bed density liquid density liquid viscosity constant mass-transfer coefficient constant mass-transfer coefficient switch time for four-zone SMB with one column per zone and its analogue feed concentration for both solutes feed flow rate for total feed desorbent flow rate for all configurations raffinate flow rate for total feed extract flow rate for all configurations recycle flow rate for SMB
L/min L/min L/min
feed flow rate for partial feed raffinate flow rate without feed raffinate flow rate with feed
vi usi ) 1 - e 1+ FsKi e
( )
(3)
For separation to occur, the solute velocities of components A and B in the SMB in Figure 1 must satisfy the following equations
uB1,new ) M1uport, M1 e 1
(4a)
uA2,new ) M2uport, M2 g 1
(4b)
units
L
21.0
cm
d
2.6
cm
L
21.0
cm
d
2.4
cm
e
0.4
rp Fs Fl m kmap (A) kmap (B) tsw
1.6 × 10-3 1000 600 0.876 0.5 0.5 6.2
(m3 of void)/ (m3 of bed) cm kg/m3 kg/m3 cP 1/s 1/s min
tsw
3.1
min
tsw
11
min
tsw
5.5
min
feed rate desorbent raffinate extract recycle feed rate desorbent raffinate extract recycle
3.64 23.55 7.68 19.51 21.79 3.64 21.45 9.09 16.0 35.38
cm3/min cm3/min cm3/min cm3/min cm3/min cm3/min cm3/min cm3/min cm3/min cm3/min
description height of adsorbent layer at D/F ) 6.47 internal diameter of adsorbent layer at D/F ) 6.47 height of adsorbent layer at D/F ) 5.9 internal diameter of adsorbent layer at D/F ) 5.9 interparticle voidage adsorbent particle radius bed density liquid density liquid viscosity constant mass-transfer coefficient constant mass-transfer coefficient switch time for four-zone SMB with one column per zone and its analogue at D/F ) 6.47 switch time for four-zone SMB with two columns per zone and its analogue at D/F ) 6.47 switch time for four-zone SMB with one column per zone and its analogue at D/F ) 5.9 switch time for four-zone SMB with two columns per zone and its analogue at D/F ) 5.9 feed flow rate at D/F ) 6.47 desorbent flow rate at D/F ) 6.47 raffinate flow rate at D/F ) 6.47 extract flow rate at D/F ) 6.47 recycle flow rate at D/F ) 6.47 feed flow rate at D/F ) 5.9 desorbent flow rate at D/F ) 5.9 raffinate flow rate at D/F ) 5.9 extract flow rate at D/F ) 5.9 recycle flow rate at D/F ) 5.9
uB3,new ) M3uport, M3 g 1
(4c)
uA4,new ) M4uport, M4 e 1
(4d)
where the port velocity is
uport ) lport/tport
(5)
and the Mi are multipliers used to convert inequalities into equalities. An alternative method is to use the “triangle theory”,21-24 which is mathematically equivalent for linear systems. To achieve the thermodynamic minimum of desorbent-to-feed ratio (D/F) ) 1, the multipliers M1, M2, M3, and M4 are set equal to 1.0. The flow rates and column dimensions for this case, D/F ) 1, are listed in Table 1, and the velocities in each zone for the other D/F values studied are given in Table 4. The volumes of the tanks and the flow rates in and out of them in the various steps are calculated using simple mass balances.20 Results for Linear Systems The dextran T6-fructose system has linear isotherms11
dextran T6: q ) 0.23c
(6a)
fructose: q ) 0.69c
(6b)
The SMB and analogue have the same productivities, which varied from 0.0195 min-1 for D/F ) 1 to 0.0016 min-1 for D/F ) 6.33. The results for both the SMB with one column per zone and the analogue for this configuration are shown in Figure 5. As expected, the purities
Ind. Eng. Chem. Res., Vol. 42, No. 21, 2003 5271
Figure 3. Complete cycle for a four-zone SMB with two columns per zone. Table 4. Velocities in the Different Zones for the Dextran T6-Fructose System for Figures 4 and 6-9 D/F
v1 (cm/min)
v2 (cm/min)
v3 (cm/min)
v4 (cm/min)
1.0 2.05 3.015 4.03 4.15 6.33
6.28 5.91 5.84 5.72 5.59 5.56
6.28 4.65 4.89 4.96 4.85 5.03
6.28 6.69 6.91 6.91 6.98 7.23
6.28 4.10 4.04 3.84 3.89 3.84
achieved with the analogue were lower than those achieved with the SMB in all cases. This can be attributed to the loss of separation due to mixing in the tanks as opposed to retaining concentration profiles in the columns. The purities increased with increasing D/F for both systems. The difference between the SMB purity and the analogue purity decreases as the SMB purity increases. For example, at D/F ) 1.0, the difference is 8.5 percentage points for the raffinate products and 9.7 for the extract, whereas at D/F ) 6.33, the difference is 7.96 for the raffinate and 7.44 for the extract.
From Figure 5, one can also determine the increase in D/F needed in the analogue to achieve the same purity as obtained with the SMB for D/F ) 1. The horizontal line in Figure 4 shows that D/F ) 2.6 is needed for the analogue to give the same extract purity as an SMB at D/F ) 1.0 when both systems have the same productivity. To support our hypothesis that mixing is the reason the purities from the analogue were lower that those from the SMB, additional recycle tanks were added. In the first round of simulations, five tanks instead of four were used, where one of the tanks in each simulation was replaced by two tanks with volumes equal to onehalf that of the original tank. The tanks were emptied in the order in which they were filled. The simulation with five tanks that gave the highest purity was the one where tank 2 (Figure 2) was replaced by two tanks (Figure 6). In the next round of simulations, six tanks were used. In these simulations, tank 2 was always divided into at least two tanks. Four simulations were run in which one of the remaining tanks was replaced
5272 Ind. Eng. Chem. Res., Vol. 42, No. 21, 2003
Figure 4. One-column analogue to a four-zone SMB with two columns per zone.
Figure 5. Product purities for a four-zone SMB with one column per zone and its analogue versus D/F for the dextran T6-fructose system.
by two tanks in three of the simulations and tank 2 was replaced by three tanks in the fourth. The highest purities were obtained when tanks 2 and 3 were both
divided into two tanks. A simulation with eight tanks was run with two tanks replacing each of the four tanks, and then simulations were run with nine tanks. The highest purity obtained with nine tanks was with tank 2 divided into three tanks and the other tanks divided into two each. All of these simulations were run at D/F ) 4.15. The results for the optimum configuration of tanks are shown in Figure 7. As expected, the analogue approaches the SMB as more tanks are used. This analysis also suggests that the use of a plug-flow tank in place of multiple well-mixed tanks might improve the separation; however, the amount of this improvement is still to be determined. Figures 8 and 9 show the concentration profiles being fed into the tanks at cyclic steady state for analogues to a four-zone SMB with one column per zone with four tanks and eight tanks, respectively. The horizontal lines are the average concentrations for each tank, which are the concentrations fed to the analogue in the next cycle and are also the average product concentrations (tanks 1 and 3). First, note that the profile in Figure 9 is much smoother than that in Figure 8 (there are “shoulders” in Figure 8). We can also see that the concentrations of the desired products in the raffinate (tank 1 in Figure
Figure 6. One-column analogue to a four-zone SMB with one column per zone using five tanks.
Ind. Eng. Chem. Res., Vol. 42, No. 21, 2003 5273
column length and the switch time were one-half the corresponding values for the one-column-per-zone systems to keep the productivies constant for the two cases. The results for an SMB with two columns per zone and its analogue can be seen in Figure 10. All product purities increase with increasing D/F. The difference between the analogue purities and the SMB purities decreased with increasing SMB purity. This is especially visible in the case of the extract stream. A D/F value of 2.3 is needed for the analogue to give the same extract purity as an SMB with D/F )1.0 when the two systems have the same productivity. It was also found that, to achieve a purity of about 99% in the extract, the analogue to an SMB with two columns per zone required D/F ) 19.6. Partial Feed SMB Figure 7. Purities of product streams for the analogue to a fourzone SMB with one column per zone at D/F ) 4.15 versus the optimum distributions of the number of tanks used for the dextran T6-fructose system.
8, tanks 1a and 1b in Figure 9) and the extract (tank 3 in Figure 8, tanks 3a and 3b in Figure 9) increased, and the concentration of the undesired product decreased when more tanks are used. With only four tanks, the analogue gave purities of 80.09% for the raffinate and 88.7% for the extract, whereas with eight tanks, the purities increased to 93.8 and 93.9%, respectively. SMBs with two columns per zone and their analogues were also studied. For these simulations, both the
In partial-feed SMBs,25 unlike total-feed systems, in which the product and feed flow rates and the flow rates in every zone are constant, the feed and raffinate flow rates vary with time. During each switch period, a partial-feed approach introduces feed for a fraction of the switch time. When feed is introduced, the raffinate flow rate is increased while all other stream flow rates remain constant. The average amount of feed introduced in a partial-feed system is the same as or greater than that in the total-feed configuration. This setup increases the efficiency of the SMB separation, especially for an SMB with one column per zone, and leads to an enhancement of product purity and recovery with
Figure 8. Concentration profile exiting the analogue to a four-zone SMB with one column per zone and entering the tanks at cyclic steady state for D/F ) 4.15 using four tanks for the dextran T6-fructose system.
5274 Ind. Eng. Chem. Res., Vol. 42, No. 21, 2003
Figure 9. Concentration profile exiting the analogue to a four-zone SMB with one column per zone and entering the tanks at cyclic steady state for D/F ) 4.15 using eight tanks for the dextran T6-fructose system. Table 5. Purities for SMBs and Corresponding Analogues for Total-Feed and Partial-Feed Strategies purity (%) raffinate extract SMB with total feed25 SMB with partial feed25 analogue to total-feed SMB with four tanks analogue to partial-feed SMB with four tanks analogue to total-feed SMB with six tanks analogue to partial-feed SMB with six tanks
Figure 10. Product purities for a four-zone SMB with two columns per zone and its analogue versus the D/F for the dextran T6-fructose system.
constant productivity, compared to the results obtained with a standard four-zone SMB.25 The first step of the analogue was divided into three sections (Figure 11). The system considered here also followed linear isotherms11,25
dextran T6: q ) 0.23c
(7a)
raffinose: q ) 0.59c
(7b)
87.88 91.2 78.54 78.12 81.91 83.85
97.01 99.47 89.85 89.55 92.45 96.09
The physical properties and column specifications are in Table 2. When the analogues to the partial-feed SMB and the corresponding total-feed SMB were set up using four tanks, the purities in the two cases were approximately equal, with the total-feed results being slightly higher (Table 5). This was a surprise, as the partial-feed SMB has significantly higher purities then the standard SMB.25 Apparently, the mixing that occurs in the analogue caused the lower purities for the partialfeed system. To reduce the effect of the mixing, tank 2 (refer to Figure 11) was divided into three tanks (Figure 12), each with a volume equal to one-third of the original tank volume. Each of these tanks was emptied during one of the three parts of the feed step (no feed, feed, no feed), and the tanks were filled in the same order. This procedure significantly reduced the mixing, and the partial-feed analogue with six tanks gave higher purities than the total-feed analogue with six tanks (Table 5).
Ind. Eng. Chem. Res., Vol. 42, No. 21, 2003 5275
Figure 11. One-column analogue to a four-zone SMB with one column per zone with partial feed using four tanks.
Figure 12. One-column analogue to a four-zone SMB with one column per zone with partial feed using six tanks.
Results for Nonlinear System
Table 6. Purities for Four-Zone SMB with One Column Per Zone and Its Analogue for the Binaphthol System
The equilibrium data for the nonlinear binaphthol enantiomer system fit the following isotherms14
q)
2.69cA 0.10cA + (8a) 1 + 0.0336cA + 0.0466cB 1 + cA + 3cB
q)
3.73cA 0.30cA + (8b) 1 + 0.03362cA + 0.0466cB 1 + cA + 3cB
Simulations were run at two feed concentrations: 2.9 g/L (for both A and B), representing the linear portion of the isotherm, and 10 g/L (for both A and B), representing the nonlinear portion. Other operating conditions are listed in Table 3. Two D/F values were used: D/F ) 5.9 for the linear portion and D/F of 6.4 for the nonlinear portion.26 The results for the onecolumn-per-zone SMB and its analogue at the two concentrations are presented in Table 6. Note that the analogue (Figure 2) purity for the feed concentration of 10 g/L at D/F ) 6.4 is very low, 54.9%. When the simulation was run for an analogue with five tanks (Figure 6), all purities increased considerably (Table 6). The concentration profiles for the analogues in Figures 2 and 4 are shown in Figures 13 and 14, respectively. The profiles from the analogue in Figure 2 (Figure 13) are shifted to the right compared to those from the analogue in Figure 4 (Figure 14), resulting in the poor separation for the four-tank analogue. This shift is
purity (%) raffinate extract SMB (cF ) 2.9, D/F ) 5.9) analogue (cF ) 2.9, D/F ) 5.9) using four tanks analogue (cF ) 2.9, D/F ) 5.9) using five tanks SMB (cF ) 10, D/F ) 6.4) analogue (cF ) 10, D/F ) 6.4) using four tanks analogue (cF ) 10, D/F ) 6.4) using five tanks
89.9 80.08 81.32 89.26 76.02 83.74
86.87 72.52 74.17 86.76 54.89 78.25
caused by the combination of mixing and the concentration dependence of the solute velocities for nonlinear isotherms. Simulations were also run for the system with feed concentrations of 2.9 g/L at D/F ) 5.9 and 10 g/L at D/F ) 6.4 for a four-zone SMB with two columns per zone and its analogue (Figure 4). The results obtained (Table 7) are typical of the results obtained from the other systems studied. The purities of the SMBs with two columns per zone are higher than the purities of the SMBs with one column per zone, and the analogues with two columns per zone gave lower purities than the corresponding SMBs. Discussion The analogue proposed here has several advantages compared to currently used chromatographic separation techniques. These include the simple design and corresponding flexibility in use. The analogue could be used
5276 Ind. Eng. Chem. Res., Vol. 42, No. 21, 2003
Figure 13. Concentration profile exiting the analogue to a four-zone SMB with one column per zone and entering the tanks at cyclic steady state for the binaphthol system using cF ) 10 g/L at D/F ) 6.4 using four tanks. Table 7. Purities for Four-Zone SMB with Two Columns Per Zone and Its Analogue for the Binaphthol System purity (%) SMB (cF ) 2.9, D/F ) 5.9) analogue (cF ) 2.9, D/F ) 5.9) SMB (cF ) 10, D/F ) 6.4) analogue (cF ) 10, D/F ) 6.4)
raffinate
extract
96.58 88.5 94.40 87.63
95.43 82.38 94.51 85.21
as a chromatograph performing multicomponent separations and then as an analogue to an SMB performing binary separations. Because only one column has to be repacked, switching from one binary system to another is easier than with an SMB. Considering the results presented, the most obvious characteristic of the analogue is that it gives lower purities than the corresponding SMB columns. As mentioned earlier, this result is due to the mixing occurring in the tanks as opposed to the retention of concentration profiles in the SMB. The simulations for the analogues to the one-column-per-zone SMB at D/F ) 4.15 using more than four tanks (Figure 7) support this statement. In these simulations, as the number of tanks increased, so did the product purities. Dividing the tanks into two or more smaller tanks retained more of the concentration profile. Tank 2 (see Figures 2, 6, and 11) has the largest effect on the purities of the products. The effects of splitting tank 2 can be explained from Figure 15, which shows the concentration profiles in each column of a four-zone, onecolumn-per-zone SMB at the end of the switching period. In the next step, column 1 will become column 2. Therefore, at the beginning of the switch time, column 2 (Figure 15) will have a concentration profile with a high concentration of dextran T6 at the top (150 cm)
and a low concentration at the bottom. The fructose concentration is low at the top of the column and high at the bottom. Thus, at the beginning of the switch time, the material being mixed with the feed (at the top of column 2) will have a high concentration of dextran T6 and a low concentration of fructose. Toward the end of the switch time, there will be a higher concentration of fructose and a lower concentration of dextran T6 being mixed with the feed. Thus, more of the faster-moving dextran T6 enters the column earlier and exits earlier. Because the fructose enters at high concentrations toward the end of the switch time, most of it does not reach the top of the column before the ports are switched. This leads to higher raffinate and extract product purities because more of the dextran T6 exits in the raffinate. In the case of the analogue, this profile is lost when all of the material that exits column 2 is mixed in tank 2; therefore, for the duration of the switch time, the concentration of the stream mixed with the feed is about 25.5 g/L dextran T6 and 20.0 g/L fructose (Figure 8) (about 55% dextran T6-45% fructose). Because more of the fructose is being fed earlier, it exits earlier and lowers the purity of the raffinate. Also, because not all of the dextran exits the column, there is more to be carried into the next steps and out in the extract product, lowering its purity. The tank volumes used in these simulations are relatively small because adsorption is relatively weak (small isotherm parameters); however, if the isotherm parameters were higher, breakthrough would take longer, and the tank volumes would increase.20 Table 8 shows pairs of arbitrarily chosen isotherm parameters, the value of ui/v, and the ratio between the tank volume and the column volume at D/F ) 1.0. With strong
Ind. Eng. Chem. Res., Vol. 42, No. 21, 2003 5277
Figure 14. Concentration profile exiting the analogue to a four-zone SMB with one column per zone and entering the tanks at cyclic steady state for the binaphthol system using cF ) 10 g/L at D/F ) 6.4 using five tanks.
Figure 15. Cyclic-steady-state column profiles for a four-zone SMB with one column per zone at D/F ) 4.15 at the end of a switch time for the dextran T6-fructose system. In the next step, column 1 will become column 2 and so on.
adsorption (large parameters), the tank volumes can become large multiples of the column volume. Thus, the
analogue might not be an economical design for strongly adsorbed solutes.
5278 Ind. Eng. Chem. Res., Vol. 42, No. 21, 2003 Table 8. Ratio between the Column Volume and the Tank Volume for an Analogue to a One-Column-per-Zone SMB for Different Values of Linear Isotherm Parameters at D/F ) 1 KA
KB
uA/v
uB/v
Vt/Vcol
0.23 0.5 0.8 1.5 2 4 10 40
0.69 1 1.2 2.5 3 5 20 50
0.78 0.62 0.51 0.35 0.29 0.17 0.076 0.02
0.54 0.45 0.40 0.25 0.21 0.14 0.04 0.016
0.57 0.72 0.88 1.27 1.54 2.63 5.91 22.3
For simple elution chromatographic columns to match purities achieved using SMBs, the amounts of desorbent and adsorbent are orders of magnitude higher than the amounts used in the SMB.18,27 However, the results of this research show that the analogues, which are recycle chromatographic columns, can reach moderate SMB purities with an increase in D/F of less than 3 with the same productivity, and with an increase in D/F of about a factor of 5 to achieve the very high purities (99.0% and above) for the linear dextran T6-fructose system. The basic analogue (Figure 2) provides no advantage for partial-feed versus total-feed operation because of mixing. One of the reasons the partial-feed SMB gives higher purities than the total-feed SMB is that the feed enters the column when the concentrations of the dextran T6 and raffinose exiting column 2 are about equal. At the beginning of the switching period, when the concentration of dextran T6 is higher than the concentration of the raffinose, and at the end of the switching period, when the raffinose concentration is significantly higher, the effluent from column 2 is partially separated and thus should not be mixed with the feed. Because the concentrations in tank 2 are approximately 50-50%, this partial separation is lost in the basic analogue design. Dividing tank 2 into two tanks would probably solve this problem; however, the three steps in the partial-feed process make using three tanks easier (Figure 11). For the binaphthol system, as expected, the simulations in the linear region of the isotherms followed the same trends as with the previous linear systems studied. The analogue to the SMB with one column per zone with four tanks (Figure 2) for cF ) 10 g/L (nonlinear region) and a D/F value of 6.4 gave a reasonable value for the raffinate purity, but the extract purity was very low. Upon comparing the concentration profiles exiting the column for the analogue with four tanks (Figure 13) to that with five tanks (Figure 14), one sees a shift in the profile to the right in the case with four tanks such that the concentration overlaps are in the steps where the products are withdrawn. In a nonlinear system, the velocities of the diffuse wave and the shock waves are dependent on the concentration. In the SMB, the solute velocities are changing throughout the switch time, because the concentrations of the material being fed change. For the analogue with one tank per switching period, the concentrations being fed are constant throughout the switch time. Thus, one would expect the SMB and analogue to have different profile shapes. The analogue can be made closer to the SMB by reducing the mixing by adding more tanks. The need for a fifth tank in the case of nonlinear systems might depend heavily on the type of isotherm, switch time, and column specifications.
These nonlinear systems were also studied for a fourzone SMB with two columns per zone and its analogue. The results for both the linear and nonlinear portions of the isotherms seemed to be typical of the results achieved for the dextran T6-fructose system. The effect of the mixing was not as prominent in the nonlinear portion for the two-column-per-zone SMB as it was in the one-column-per-zone SMB because there are automatically more tanks with two columns per zone. Conclusions The analogue proposed here is an inexpensive and flexible alternative to elution chromatography and the SMB that can, with the correct recycle, achieve relatively high purities. The SMB clearly has advantages if very high purities are required. The analogue will have advantages when frequent changes in adsorbent are required. The analogue can be applied to many different SMB configurations if additional tanks are used. This research has also shown that recycle chromatographs can achieve the same purities as an SMB with only a modest increase in the desorbent-to-feed ratio. Acknowledgment This research was partially supported by NSF grant CTS-9815844. The assistance of Dr. Andrew Stawarz of Aspen Technology is gratefully acknowledged. Discussions with Oliver Ludemann-Hombouger were very helpful in clarifying the need for flexible equipment. Notation aP ) surface-to-volume ratio (1/m) c ) concentration (g/L) cF ) feed concentration (g/L) c* ) equilibrium concentration (g/L) D ) desorbent flow rate (cm3/min) F ) feed flow rate (cm3/min) Ki ) linear equilibrium parameter (L/g of solute) km ) - coefficient (cm2/s) Mi ) multiplier for linear system analysis q ) amount of solute adsorbed (g/g of solute) t ) time (min) tsw ) switch time (min) uport ) port velocity (cm/min) us ) solute velocity (cm/min) ush ) shock wave velocity (cm/min) vi ) interstitial velocity (cm/min) e ) interparticle voidage Fs ) solid density (g/cm3)
Literature Cited (1) Wankat, P. C. Large-Scale Adsorption and Chromatography, 2; CRC Press: Boca Raton, FL, 1986 (2) Shearon, W. H.; Gee, O. F. Carotene and Chlorophyll Commercial Chromatographic Production. Ind. Eng. Chem. 1949, 42, 218. (3) Harper, J. I.; Olse, J. L.; Shuman, F. R. The Arosorb Process. Chem Eng. Prog. 1952, 48, 276. (4) Hill, D. A. Alternative Modes of Operation of Chromatography Columns in the Process Situation. Process Scale Liquid Chromatography; VCH: 1995; pp 71-80. (5) Crary, J. R.; Cain-Janicki, K.; Wijayaratne, R. External Recycle Chromatography: A Practical Method for Preparative Purifications. J. Chromatogr. 1989, 462, 85-94. (6) Broughton, D. B.; Carson, D. B. The Molex Process. Pet. Refin. 1959, 38, 130.
Ind. Eng. Chem. Res., Vol. 42, No. 21, 2003 5279 (7) Broughton, D. B.; Neuzil, R. W.; Pharis, J. M.; Brearley, C. S. The Parex Process for Recovering Paraxylene. Chem. Eng. Prog. 1970, 66, 70. (8) Broughton, D. B. Production-Scale Adsorptive Separations of Liquid Mixture by Simulated Moving Bed Technology. Sep. Technol. 1984, 19, 723. (9) Azevedo, D. C. S.; Rodrigues, A. Fructose-Glucose Separation in an SMB Pilot Unit: Modeling, Simulation, Design, and Operation. AIChE J. 2001, 47, 2042-2051. (10) Dunnebier, G.; Weirich, I.; Klatt, K.-U. Computationally Efficient Dynamic Modeling and Simulation of Simulated Moving Bed Chromatographic Processes with Linear Isotherms. Chem. Eng. Sci. 1998, 53, 2537-2546. (11) 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, 17441750. (12) 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, 1-7. (13) Wu, D.; Xie, Y.; Ma, Z.; Wang, N.-H. L. Design of Simulated Moving Bed Chromatography for Amino Acid Separation. Ind. Eng. Chem. Res. 1998, 37, 4023-4035. (14) Pais, L.; Loureiro, J. M.; Rodrigues, A. Modeling Strategies for Enantiomers Separation by SMB Chromatography. AIChE J. 1998, 44, 561-596. (15) da Silva, E. A. B.; de Souza, A. A. U.; Souza, S. M. A.; Guelli, U. The Use of Simulated Moving Bed in Chromatographic Separation: Study of the SMB Configuration. Sep. Technol. 2002, 37, 1489-1504. (16) Denet, F.; Hauck, W.; Nicoud, R. M.; Di Giovanni, O.; Mazzotti, M.; Jaubert, J. N.; Morbidelli, M. Enantioseparation through Supercritical Fluid Simulated Moving Bed (SF-SMB) Chromatography. Ind. Eng. Chem. Res. 2001, 40, 4603-4609. (17) Ludemann-Hombourger, O.; Bailly, M.; Nicoud, R. M. Design of a Simulated Moving Bed: Optimal Particle Size of the Stationary Phase. Sep. Technol. 2002, 35, 1285-1305.
(18) Strube, J.; Schmidt-Traub, H. Dynamic Simulation of Simulated-Moving-Bed Chromatographic Processes. Comput. Chem. Eng. 1998, 22, 1309-1317. (19) Wankat, P. C. Rate-Controlled Separations; Kluwer: Amsterdam, 1990. (20) Abunasser, N. One-Column Chromatograph with Recycle that is Analogous to a Four-Zone SMB. M.S. Thesis, Purdue University, West Lafayette, IN, 2002. (21) Mazzotii, M.; Storti, G.; Morbidelli, M. Optimal Operation of Simulated Moving Bed Units for Nonlinear Chromatographic Simulations. J. Chromatogr. A 1997, 769, 3-24. (22) Mazzotti, M.; Storti, G.; Morbidelli, M. Robust Design of Countercurrent Adsorption Separation Processes: 2. Multicomponent Systems. AIChE J. 1994, 40, 1825. (23) Mazzotti, M.; Storti, G.; Morbidelli, M. Robust Design of Countercurrent Adsorption Separation Processes: 3. Nonstoichiometric Systems. AIChE J. 1996, 42, 2784-2796. (24) Mazzotti, M.; Storti, G.; Morbidelli, M. Robust Design of Countercurrent Adsorption Separation Processes: 4. Desorbent in the Feed. AIChE J. 1997, 43, 64-72. (25) Zang, Y.; Wankat, P. C. SMB Operation StrategysPartial Feed. Ind. Eng. Chem. Res. 2002, 41, 2504-2511. (26) Wankat, P. C.; Kim, J.-K. Architecture and Scaling of Simulated Moving Bed Systems. In Proceedings of the 3rd International Symposium on Bioseparation; ERC for Advanced Bioseparation Technology: Seoul, Korea, 2002. (27) Pynnonen, B. Simulated Moving Bed Processes: Escape from the High-Cost Box. J. Chromatogr. A 1998, 827, 143-160.
Received for review April 4, 2003 Revised manuscript received July 9, 2003 Accepted July 10, 2003 IE030283E
