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Ind. Eng. Chem. Res. 2002, 41, 2504-2511
SMB Operation Strategy-Partial Feed Yifei Zang and Phillip C. Wankat* School of Chemical Engineering, Purdue University, 1283 Chemical Engineering, West Lafayette, Indiana 47907-1283
An operation strategy, partial feed, is developed to increase SMB separation efficiency. With the partial-feed mode of operation, the feed and raffinate flow rates vary with time. The separation of Dextran T6 and raffinose, which have linear isotherms, is modeled with the Aspen Chromatography simulator in a four-zone SMB for both normal-feed and partial-feed operations. Partial-feed operation significantly improved the separation with one column per zone. Either the purity and the recovery or the productivity could be increased. Partial feed introduces two additional degrees of freedom, namely, feed length and feed time. The optimum values for these parameters were determined. The improved separation is explained using local equilibrium theory. Introduction An SMB (simulated moving bed) uses a series of connected packed-bed sections. The intermittent countercurrent movement between the solid and the liquid is simulated either by switching the location of all feed and product withdrawal ports in the direction of fluid flow or by rotating the columns on a carousel. The first commercial SMB was the UOP (Universal Oil Products) Molex process, which was developed in the 1960s to separate paraffins from branched-chain and cyclic hydrocarbons.1,2 The SMB has high productivity and low eluent consumption compared to batch chromatographic separation. Major commodity applications are found in the petroleum industry, the corn wet-milling industry, and the beet sugar industry.3 Recently, there has been an explosion of interest in separating chiral compounds using SMBs.4-7 Most SMB studies in the open literature have used constant flow rates during each switching period. One exception is the study by Kloppenburg and Giles8 in which all flow rates were varied and an optimization method was used to find good operating conditions. Patented processes can be found that vary the flow rate to improve binary separations9 or to develop ternary separations.10 However, these papers8-10 do not explain the physical basis for the improved separation. The research in this paper compares the separation efficiency between “total feed” and “partial feed” by detailed simulations. In total-feed operation, the SMB is fed for the entire switch time, the time span between the switching of port locations (Figure 1a). For partial feed, the SMB is fed during part of the switch time (Figure 1b). Figure 1a and b depicts one column per zone, but both operation methods can have multiple columns per zone. In the partial-feed operation studied in this paper, most variables are maintained constant, such as temperatures, pressures, switch time, etc. The feed flow rate changes from continuous constant flow in total feed to discontinuous pulse flow in partial feed (Figure 2a). Each switch period is divided into three intervals. The flow rates of the desorbent and the extract product are * Corresponding author. Phone: (765) 494-7422. Fax: (765) 494-0805. E-mail:
[email protected].
maintained constant at the same values as in the totalfeed operation. Because of mass balance constraints, the raffinate product’s flow rate changes according to the changes in the feed flow rate (Figure 2b). Although the feed flow rate is changed, the first operating method keeps the feed amount for each switching period the same as in total-feed operation
[(feed flow rate) × tsw]total feed ) [(feed flow rate) × tfeed]partial feed tfeed e tsw (1) In eq 1, tfeed ) tsw/n, (n g 1), and the feed flow rate during tfeed is n times the feed flow rate in the totalfeed process. When n ) 1, partial-feed operation becomes total-feed. Thus, total-feed operation can be considered as a special case of partial feed when tfeed ) tsw. The second operation method uses a larger feed rate for partial-feed operation and is discussed later. Because partial-feed operation is much more constrained than the variable-flow-rate operation, 8-10 it is easier to determine why the separation is improved. Partial-feed operation introduces two additional degrees of freedom: the feed length and the feed time. Feed length refers to the duration of the feed, which is the length of the second interval of each step. Feed time defines the time at which the center of the feed pulse enters the column (Figure 2a). The feed length is expressed as a fraction of the switch time, and the feed time is the time gap from the beginning of each step to the feed center, also expressed as a fraction of the switch time. The operation does not have to be symmetric. The separation efficiency of a partial-feed SMB will depend on the choice of these two parameters. Benchmarking Simulation Software with the Lapidus and Amundson Linear Dispersion Model12 Aspen Chromatography 10.2 was used to simulate the four-zone SMB separation of Dextran T6 (MW ≈ 6000) and raffinose at low concentrations. Because this adsorption system is linear at low concentration,11 the analytical solution developed by Lapidus and Amundson12 was used to check the simulation results. Lapidus and Amundson12 included axial dispersion but assumed very rapid mass transfer so that the solid
10.1021/ie010832l CCC: $22.00 © 2002 American Chemical Society Published on Web 04/19/2002
Ind. Eng. Chem. Res., Vol. 41, No. 10, 2002 2505
Figure 1. Four-zone SMB with one column per zone: (a) total feed, (b) partial feed.
and fluid are in equilibrium. The mass balance equation is13
[
]
1 - e ∂c ∂2c ∂c 1+ K + v - Dap 2 ) 0 e ∂t ∂z ∂z
(2)
where Dap is the apparent diffusion coefficient and K ) q/c is the linear equilibrium constant. For sufficiently long times, the solution for a step input from c ) 0 to c ) cF is12,13
[ ( x )] z-
1 c ) cF 1 - erf 2
vt 1 - e 1+ K e
4Dapt 1 - e 1+ K e
(3)
In linear systems, zone spreading caused by axial dispersion or finite mass-transfer rates is additive.
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Ind. Eng. Chem. Res., Vol. 41, No. 10, 2002 Table 1. System and Operating Parameters d L RP KR KD F keff,R keff,D
System Parameters 1.4 cm 35.625 cma 17.8125 cmb 0.45 0.0011 cm 0.56 0.23 1.0 g/cm3 2.09 × 10-5 cm/s 1.72 × 10-5 cm/s
Operating Parameters concentration of feed cF,i, i ) R, D feed flow rate QF extract flow rate QE desorbent flow rate QD recycle flow rate switching period tsw
0.05 g/cm3 0.0166 cm3/s 0.0233 cm3/s 0.0733 cm3/s 0.0198 cm3/s 463.95 s
a Four-zone SMB with one column per zone. b Four-zone SMB with two columns per zone.
Figure 2. Flow rates at each port: (a) feed rates, (b) raffinate product rates.
Thus, a dispersion model will predict exactly the same result as a complete model that includes axial dispersion and finite mass-transfer rates if the dispersion coefficient is adjusted to an apparent value. Dunnebier et al.14 compared analytical solutions and determined that the apparent axial dispersion coefficient required to obtain identical results is
Dap ) Dax +
v2 k km (1 + k)2
(3a)
where the adjusted mass-transfer resistance is
km )
6keff dPK
(3b)
keff is the effective mass-transfer coefficient
3 ∂q ) keff (c - c*) ∂t RP
(3c)
The axial dispersion coefficient Dax was determined from the Chung and Wen correlation15
Pe )
0.2 0.011 0.48 + Re e e
(3d)
Aspen Chromatography was used to simulate a step input of Dextran T6 solution in one of the chromatography columns used for the SMB (Table 1). The flow rate was 0.0864 cm3/s, the Dextran T6 concentration was 9.6 × 10-3 g/cm 3, the liquid density was 1.0 g/cm3, and the liquid viscosity was 8 × 10-3 g/(cm s). The close agreement between the outlet concentration simulated by Aspen Chromatography and the analytical solution calculated by the Lapidus and Amundson model (Figure 3) provides confidence in the simulation of the columns used to build the SMB simulations. Comparison of Partial-Feed and Total-Feed Operations in Four-Zone SMB with One Column per Zone A four-zone SMB with one column per zone was simulated under both total-feed and partial-feed condi-
Figure 3. Comparison of Aspen Chromatography simulation and Lapidus and Amundsen model12 for step input of Dextran T6.
tions. System and operation parameters are listed in Table 1. Two comparisons of total- and partial-feed SMB systems were done. First, the feed rate was identical for total and partial feed (eq 1). The simulations compared the product purities and recoveries of the two sugars. Partial-feed operation gives higher product purities and recoveries. Operation at Constant Feed Rate. For a four-zone SMB with one column per zone, for the same average feed rate under total-feed and partial-feed operations, the latter shows significant improvements in product purities and recoveries compared with total-feed operation (Table 2). This can also been seen by computing the steady-state concentration profiles (Figure 5a and b). The products are significantly purer (contain less of the unwanted component) and more concentrated in the desired component with partial-feed operation. These results are not totally optimized. For example, with 10% more recycle flow, the simulation shows that both product purities can be increased by about 1%. The reason for the improved separations with partialfeed operation can be explained using local equilibrium theory. This “ideal model”, assumes instant local equilibrium without considering any kinetic mass-transfer
Ind. Eng. Chem. Res., Vol. 41, No. 10, 2002 2507 Table 2. Comparison of Purities and Recoveries in Four-Zone SMB with One Column Per Zone for Systems with Equal Feed Throughput Based on Aspen Chromatography Simulationsa feed span
total feed
from (*tsw) to (*tsw) Qd (L/min) desorbent flow rate Qe (L/min) extract flow rate QF (L/min) 1 (0-tf1) 2 (tf1-tf2) feed 3 (tf2-tsw) flow rate QR (L/min) 1 (0-tf1) 2 (tf1-tf2) raffinate 3 (tf2-tsw) flow rate raffinate prod Dextran T6 raffinose concentration (g/L) extract prod Dextran T6 raffinose concentration (g/L) Dextran T6 recovery (%) raffinose Dextran T6 purity (%) raffinose
0.0 1.0 0.0044 0.0014 0.0010 0.0040 12.18 1.68 0.95 30.82 97.44 86.30 87.88 97.01
a
partial feed 0.2 0.8 0.0044 0.0014 0.0000 0.001 66 0.0000 0.0030 0.004 66 0.0030 12.37 1.31 0.37 31.86 98.96 89.21 90.42 98.85
0.3 0.7 0.0044 0.0014 0.0000 0.002 49 0.0000 0.0030 0.005 49 0.0030 12.42 1.22 0.24 32.11 99.36 89.91 91.06 99.26
0.40 0.60 0.0044 0.0014 0.0000 0.004 98 0.0000 0.0030 0.007 98 0.0030 12.44 1.20 0.17 32.17 99.52 90.08 91.20 99.47
0.10 0.50 0.0044 0.0014 0.0000 0.002 49 0.0000 0.0030 0.005 49 0.0030 12.47 1.68 0.09 30.82 99.76 86.30 88.13 99.71
0.50 0.90 0.0044 0.0014 0.0000 0.002 49 0.0000 0.0030 0.00549 0.0030 12.25 1.01 0.72 32.71 98.00 91.59 92.38 97.85
Productivity ) 3.408 g/(min L), QD,recycle ) 0.001 188 L/min, tsw ) 7.73 min. Table 3. Sensitivity of Product Recoveries and Purities to Changes in the Equilibrium Parameters for Four-Zone, Total-Feed SMB with One Column Per Zone Based on Aspen Chromatography Simulations KD KR raffinate prod conc (g/L) extract prod conc (g/L) recovery (%) purity (%)
Figure 4. Local equilibrium solution in one column of four-zone SMB for total-feed and partial-feed (1/3tsw-2/3tsw) operations.
effect and ignores axial dispersion. The solute velocity ui is related to the interstitial fluid velocity by1,13
ui )
[
vi
]
(1 - b) 1+ Ki b
(4)
for linear systems if a single-porosity model is used. Figure 4 shows the solute movement, or characteristic diagram, within one column of the SMB for one cycle. Only the solute from this single feed step is shown. The flow rates in zones 2-4 are the same for both total-feed (Figure 4a) and partial-feed (Figure 4b) operations. Only zone 1 has a different flow rate. During the partial-feed step, the raffinate product flow rate is increased to keep the flow rate in zone 4 constant. In the total-feed operation, the solute travels with a constant velocity throughout the switch time. Compared with that velocity, in the partial-feed system, the solute velocity is higher during the feed interval and lower when there is no feed. Comparing the solute characteristics for the total-feed and partial-feed systems, we see that, with partial feed, the leading edge of the raffinose does not come as close to the Dextran T6 product (the outlet from zone 1), and the trailing edge of the Dextran T6 is
Dextran T6 raffinose Dextran T6 raffinose Dextran T6 raffinose Dextran T6 raffinose
0.23 0.56 12.2 1.68 0.95 30.8 97.4 86.3 87.9 97.0
0.2185 0.532 12.2 1.73 0.65 30.7 94.9 94.7 87.4 95.6
0.2415 0.532 12.0 1.73 1.40 30.7 89.5 94.7 87.4 95.6
0.2185 0.588 12.2 1.81 0.65 30.5 94.9 94.4 87.1 97.9
0.2415 0.588 12.0 1.81 1.40 30.5 89.5 94.4 86.9 95.6
further from the raffinose product (the outlet from zone 3). When zone spreading caused by dispersion and finite mass-transfer rates is included, the result will be higher-purity products. The use of partial feed does not change the basic inequalities that have to be satisfied for complete separation in an SMB.1,13 Different partial feed strategies show different extents of improvement. The influence of the feed length and feed time are summarized in Figure 6a and b. The shorter the feed duration, the higher the purity and recovery attained (Table 2 and Figure 6a). If the feed length is decreased in Figure 4, the leading edge of the raffinose further departs from the raffinate product, as does the trailing edge of the Dextran T6 from the extract product. Thus, the products are purer. However, decreasing the feed length increases the pressure drop in the column. This concern limits the extent to which the feed length can be decreased. Table 2 and Figure 6b show the influence of feed time. Early feed introduction favors Dextran T6 recovery and raffinose purity, whereas late feed introduction is good for raffinose recovery and Dextran T6 purity. These effects can be explained with Figure 4. An early feed pulse moves the Dextran T6 characteristics further away from the raffinose product and reduces the Dextran T6 impurity in the extract product. Thus, most of the Dextran T6 in the feed is recovered in the raffinate, increasing the Dextran T6 recovery. However, the early feed moves the raffinose characteristics toward the Dextran T6 product and makes the raffinose spend a longer time in the SMB columns, increasing the dispersion compared to that obtained with the late feed. Thus, the raffinose recovery and Dextran T6 product purity
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Ind. Eng. Chem. Res., Vol. 41, No. 10, 2002
Figure 6. Influence of feed parameters on product recoveries and purities based on Aspen Chromatography simulations: (a) feed length (feeds are introduced in the middle of the switch time), (b) feed time (feed lengths are 0.4tsw).
Figure 5. Steady-state axial concentration profiles for four-zone SMB with one column per zone based on Aspen Chromatography simulations: (a) total feed, (b) partial feed.
are reduced. As expected, a late feed time is good for raffinose recovery and Dextran T6 purity and worsens the raffinose purity and Dextran T6 recovery. A compromise is to input the feed near the center of the step (Figure 6b). The sensitivity of the product recoveries and purities to measurement error in the equilibrium parameters was studied. Under total-feed operation, the Henry coefficients were assumed to have (5% error. Because an operator would not know there was an error in the isotherm parameters, the simulations in Table 3 were performed with flow rates that are optimal for the base case. The first column in the table is the base case, and the other four columns give the various combinations of (5% for the K values. The recovery deviation is within 8.4%, while the purity deviation is within 1.4% of the base case. The results show the expected trend of change: the higher the Henry coefficient, the higher the amount of product exiting from extract port; the lower the Henry coefficient, the higher the amount of product exiting from the raffinate port.
Operation at Constant Purity and Recovery. Often, increasing the feed rate, and hence the productivity, is more important than increasing the purities and recoveries. By applying partial-feed operation, the productivity can be increased dramatically while the purities and recoveries obtained with total-feed operation are retained or even improved (Table 4 and Figure 7). Because the adsorbent volumes are constant, the percent productivity increase equals the percent feed increase. For this system, the bottleneck for quality control is the Dextran T6 product purity. When the Dextran T6 purity requirements are satisfied under any partial-feed operation, a higher raffinose product purity is also obtained. The productivity is higher for all of the partial-feed operations than for total-feed operation. As expected, with shorter feed durations, the separation is more complete, which results in a greater productivity improvement (Figure 7a). However, as the feed length is reduced, the improvement is reduced, and eventually, there is no further increase in productivity. The largest improvement is obtained with late feed times (Figure 7b). This occurs because the raffinose does not get close to the Dextran T6 product port and the raffinose dispersion decreases. As mentioned before, the purity of the Dextran T6 is the stricter yardstick. Because the late feed time gives a higher Dextran T6 purity, the productivity can be increased more in this case. The highest productivity increase obtained was 70% for a
Ind. Eng. Chem. Res., Vol. 41, No. 10, 2002 2509 Table 4. Comparison of Productivities in Four-Zone SMB with One Column Per Zone for Systems with Approximately Equal Purities Based on Aspen Chromatography Simulationsa feed span
total feed
from (*tsw) to (*tsw) productivity increase (%) switch time (min) Qd (L/min) desorbent flow rate Qe (L/min) extract flow rate QF (L/min) 1 (0-tf1) 2 (tf1-tf2) feed 3 (tf2-tsw) flow rate QR (L/min) 1 (0-tf1) 2 (tf1-tf2) raffinate 3 (tf2-tsw) flow rate raffinate prod Dextran T6 raffinose concentration (g/L) extract prod Dextran T6 raffinose concentration (g/L) Dextran T6 recovery (%) raffinose Dextran T6 purity (%) raffinose
0.0 1.0 0.00 7.73 0.0044 0.0014 0.0010 0.0040 12.18 1.68 0.95 30.82 97.4 86.5 87.9 97.0
a
partial feed 0.2 0.8 36.00 5.72 0.0060 0.0019 0.0000 0.0023 0.0000 0.0057 0.0080 0.0057 12.37 1.68 0.47 30.88 98.5 88.0 88.0 98.5
0.3 0.7 45.00 5.36 0.0064 0.0020 0.0000 0.0036 0.0000 0.0061 0.0097 0.0061 12.38 1.70 0.25 30.75 99.0 90.5 88.0 99.2
0.40 0.60 45.00 5.36 0.0064 0.0020 0.0000 0.0072 0.0000 0.0061 0.0097 0.0061 12.44 1.69 0.17 30.77 98.9 93.3 88.0 99.4
0.10 0.50 4.00 7.48 0.0045 0.0015 0.0000 0.0026 0.0000 0.0044 0.0069 0.0044 12.52 1.68 0.05 30.32 99.8 90.4 88.2 99.8
0.50 0.90 70.00 4.57 0.0075 0.0024 0.0000 0.0042 0.0000 0.0071 0.0114 0.0071 12.15 1.65 0.87 30.91 96.4 90.8 88.1 97.3
Dextran T6 purity, 87.89% or higher; raffinose purity, 97.03% or higher.
partial feed from 0.5 to 0.9 of the switch time (feed time 0.7 in Figure 7b). Comparison of Partial-Feed and Total-Feed Operations in Four-Zone SMB with Two Columns per Zone Partial-feed operation was also studied for a four-zone SMB with two columns per zone. The top section of Table 5 summarizes the purities and recoveries of the products under total-feed and different partial-feed conditions, operated at the same D/F value (4.4) as the four-zone SMB with one column per zone. The separation efficiency is higher with more columns and a shorter switching period because the approach to true countercurrent operation is closer. Partial feed shows very modest improvement compared to total feed because a four-zone SMB with two columns per zone operates under conditions closer to a true moving bed (TMB) than a four-zone SMB with one column per zone. The total-feed operation separates the two components quite cleanly (Figure 8). The partial-feed operation improves the separation efficiency slightly. The feed length and feed time of the partial-feed operation still affect the separation in the same way. A comparison of Tables 2 and 5 shows that the raffinose product purity can be higher for a partial-feed SMB with one column per zone than for a total-feed SMB with two columns per zone. However, the Dextran T6 purity is higher in the system with two columns per zone. Simulations were also tried with D/F ) 1.4 to determine whether D/F affected the improvement of the partial-feed system. The simulations had the same switch time and same column length as the runs at D/F ) 4.4 (as D/F decreased, the recycle rate was increased). As shown in the bottom section of Table 5, under optimized partial-feed conditions, the Dextran T6 purity can be increased by 0.3% over that obtained under total-feed operation, while the raffinose purity can be increased by 0.1%. Thus, the improvements are small and about the same for both D/F values. Discussion
Figure 7. Influence of feed parameters on productivity based on Aspen Chromatography simulations [productivity ) 3.4 g/(min L) under total-feed operation]: (a) feed length (feeds are introduced in the middle of the switch time), (b) feed time (Feed lengths are 0.4tsw).
An alternative to using partial feed to increase the productivity is to use it to reduce desorbent consump-
tion. If the productivity and the products purities are maintained, the desorbent consumption can be reduced
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Table 5. Comparison of Purities and Recoveries in Four-Zone SMB with Two Columns Per Zone for Systems with Equal Feed Throughput Based on Aspen Chromatography Simulationsa feed span
total feed
from (*tsw) to (*tsw)
0.0 1.0
partial feed 0.2 0.8
0.3 0.7
D/F ) 4.4, QD ) 0.0044 L/min, QD,recycle ) 0.001 188 L/min 0.0014 0.0014 0.0014 Qe (L/min) extract flow rate QF (L/min) 1 (0-tf1) 0.0000 0.0000 2 (tf1-tf2) 0.0010 0.00166 0.0249 feed 3 (tf2-tsw) 0.0000 0.0000 flow rate QR (L/min) 1 (0-tf1) 0.0030 0.0030 2 (tf1-tf2) 0.00399 0.00466 0.00549 raffinate 3 (tf2-tsw) 0.0030 0.0030 flow rate raffinate prod Dextran T6 12.5 12.4 12.4 raffinose 0.37 0.35 0.35 concentration (g/L) extract prod Dextran T6 0.14 0.07 0.065 raffinose 34.5 34.6 34.59 concentration (g/L) Dextran T6 99.4 99.2 99.2 recovery (%) raffinose 96.7 96.9 96.9 Dextran T6 97.1 97.25 97.25 purity (%) raffinose 99.6 99.78 99.81 purity (%) a
D/F ) 1.4, QD ) 0.0014 L/min, QD,recycle ) 0.004 188 L/min Dextran T6 98.5 98.7 98.8 raffinose 91.9 92.0 92.08
0.10 0.50
0.50 0.90
0.0014 0.0000 0.0249 0.0000 0.0030 0.00549 0.0030 12.4 0.41 0.04 34.435 99.3 96.4 96.9 99.9
0.0014 0.0000 0.0249 0.0000 0.0030 0.00549 0.0030 11.9 0.28 0.09 32.487 95.3 91.0 97. 7 99.7
98.7 92.0
98.7 92.0
Productivity ) 3.408 g/(min L), tsw ) 3.865 min.
product purity and recovery are enhanced when the productivity is unchanged. The productivity is improved when the purity is unchanged. Two parameters in partial-feed operations can be adjusted to achieve the desired separation. Decreasing the feed length can increase the quality of both products. Adjustments of the feed time can be used to optimize the SMB for a given product. Acknowledgment This research was partially supported by NSF Grant CTS-9815844 and the Purdue Research Foundation. The assistance of Drs. Andrew Stawarz and Felix Jegede of Aspen Technology is gratefully acknowledged. The comments of the anonymous reviewers were very helpful in improving the paper. Notation
Figure 8. Steady-state axial concentration profile for four-zone SMB with two columns per zone with total-feed operation based on Aspen Chromatography simulations.
by up to 58.8%, corresponding to the productivity increase of 70% in Figure 6b. Partial-feed operation might allow for an inexpensive retrofit of a one column per zone SMB to increase the purities or feed rates. Because the tested system is a dilute system, the isotherms for Dextran T6 and raffinose are both linear. In more concentrated systems, the isotherms will usually become nonlinear. The separation behaviors of linear and nonlinear systems can be quite different, as shock and diffuse waves form in the nonlinear system. However, we believe that partial-feed operation will also result in improved separation with nonlinear systems. Proving this conjecture is the goal of future research. Summary and Conclusions The partial-feed operation strategy increases SMB separation efficiency particularly for a four-zone SMB with one column per zone. Under such operation, both
c ) solute concentration, g/cm3 c* ) equilibrium concentration, g/cm3 dP ) particle diameter, cm Dap ) apparent dispersion coefficient, cm2/s Dax ) axial dispersion coefficient, cm2/s erf ) error function K ) linear equilibrium parameter, K ) (q/c) keff ) effective mass transfer resistance, cm/s, eq 3c k ) capacity factor, k ) ((1 - e)/e)K km ) adjusted mass transfer resistance, 1/s, eq 3b L ) column length, cm Pe ) Peclet number, Pe ) (vdP/Dax) Re ) Reynolds number, Re ) (evdPF/µ) RP ) particle radius, cm t ) time, s tsw ) switch time, s u ) solute velocity, cm/s v ) interstitial fluid velocity, cm/s z ) axial coordinate, cm Definitions productivity (separation rate/efficiency) ) (feed flow rate)/ (adsorbent volume) purity ) (amount of desired component)/(sum of all feed components in the product)
Ind. Eng. Chem. Res., Vol. 41, No. 10, 2002 2511 recovery ) (amount of desired component in its product)/ (amount of this component in the feed) Greek Letters ) void fraction of the bed e ) external void fraction F ) fluid density, g/cm3 FP ) particle density of solid including the fluid in the pores, g/cm3 µ ) viscosity of the fluid, g/(cm s) Subscripts F ) feed i ) component i (i could be raffinose or Dextran T6) 0 ) initial value (at the beginning)
Literature Cited (1) Wankat, P. C. Large-Scale Adsorption and Chromatography; CRC Press: Boca Raton, FL, 1986. (2) Broughton, K. B. Molex: Case History of a Process. Chem. Eng. Prog. 1968, 64, 60. (3) Pynnonen, B. Simulated Moving Bed Processing: Escape from the High-Cost Box. J. Chromatogr. 1998, 827, 149. (4) Francotte, E.; Richer, P.; Mazzotti, M.; Morbidelli, M. Simulated Moving Bed Chromatographic Resolution of a Chiral Antitussive. J. Chromatogr. 1998, 796, 239. (5) Guest, D. W. Evaluation of Simulated Moving Bed Chromatography for Pharmaceutical Process Development. J. Chromatogr. 1997, 760, 159. (6) Nagamatsu, S.; Murazumi, K.; Makino, S. Chiral Separation
of a Pharmaceutical Intermediate by a Simulated Moving Bed Process. J. Chromatogr. 1999, 832, 55. (7) Francotte, E.; Richer, P.; Mazzotti, M.; Morbidelli, M. Simulated Moving Bed Chromatographic Resolution of a Chiral Antitussive. J. Chromatogr. 1998, 796, 239. (8) Kloppenburg, E.; Gilles, E. D. A New Concept for Operating Simulated Moving-Bed Processes. Chem. Eng. Technol. 1999, 22, 10. (9) Kearney, M. M.; Hieb, K. L. Time Variable Simulated Moving Bed Process. U.S. Patent 5,102,553, 1992. (10) Tanimura, M.; Tamura, M. Methods of Separation into Three Components Using a Simulated Moving Bed. U.S. Patent 5,556,546, 1996. (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, 1744. (12) Lapidus, L.; Amundson, N. R. Mathematics of Adsorption in Beds. IV. The Effect of Longitudinal Diffusion in Ion Exchange and Chromatographic Columns. Phys. Chem. 1952, 56, 984. (13) Wankat, P. C. Rate-Controlled Separations; Kluwer: Amsterdam 1990. (14) 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. (15) Chung, S. F.; Wen, C. Y. Longitudinal Dispersion of Liquid Flowing Through Fixed and Fluidized Beds. AIChE J. 1968, 14, 867.
Received for review October 9, 2001 Revised manuscript received February 21, 2002 Accepted March 13, 2002 IE010832L
