Ind. Eng. Chem. Res. 2008, 47, 9601–9610
9601
Optimized Design of Recycle Chromatography for Separation of a Single Component from a Ternary Mixture Ju Weon Lee†,‡ and Phillip C. Wankat*,† School of Chemical Engineering, Purdue UniVersity, Forney Hall of Chemical Engineering, 480 Stadium Mall DriVe, West Lafayette, Indiana 47906-2100 and ERC for AdVanced Bioseparation Technology, Inha UniVersity, 253 Younghyun-dong, Nam-ku, Incheon 402-751, Republic of Korea
Recycle chromatographic systems were designed to isolate one component from a ternary mixture. Since the concentrations of the dilute ternary mixtures studied (phenols, amino acids, and benzenes) were all in the linear range of isotherms, the Lapidus-Amundson equation was used to predict the broadening of elution bands caused by axial dispersion and mass-transfer resistance. Optimum operating conditions were designed to isolate the target solutes with over 99% purity and yield. Compared to complete ternary separation, recycle chromatography for separation of a single component required significantly less solvent and had higher productivity. For the amino acid system the optimum column length and mobile-phase velocity which had maximum productivity were determined with different sizes of adsorbent particle. When large particles were used, longer columns and faster mobile-phase velocities were needed to obtain maximum productivity as compared with small particle sizes. Introduction Chromatographic separation processes are generally used to isolate target solutes with high purity in a wide range of fields, such as biological and pharmaceutical industries. For binary separation it is well known that the simulated moving bed (SMB) process is more efficient than batch chromatography and pseudobinary separation, such as xylenes.1,2 However, the SMB process is natural only for binary separation, such as chiral separations. Extending the SMB to ternary or multicomponent separations has generated considerable interest.3-5 Single-loop SMB processes can be operated as pseudobinary systems for multicomponent separation if the target component is the most or least retained in a selected adsorbent.6 Unfortunately, unless the unwanted solutes have very similar adsorption isotherms, solvent use is high in these applications. Recycle chromatography has been adapted to binary separations as an analogue of SMB.7-10 Recently, SMB3 and recycle chromatography11,12 systems have been developed for recovery of only the middle component of ternary mixtures. In many recycle chromatographic separations inline detectors or offline analytical tools were used to fractionate the pure desorbent for recycle.13-17 This recycle depends on the column efficiency, which controls the elution band broadening. In batch chromatography the next feed time is decided by the migration velocity difference of the least and most retained solutes and the broadened width of the elution band. The ends of each elution band are also important in developing criteria for the operating conditions of recycle chromatography. The analytical solution reported by Lapidus and Amundson18 for linear isotherms, local equilibrium, and axial dispersion is convenient for calculation. This solution was extended to cases with masstransfer resistance and axial dispersion by Dunnebier et al.19 In this work, recycle chromatography methods were developed for cases where only one component of a ternary mixture is valuable. The target solute can be the intermediate retained * To whom correspondence should be addressed. Tel.: 765-494-0814. E-mail:
[email protected]. † Purdue University. ‡ Inha University.
solute, the least retained solute, or the most retained solute. Three ternary mixtures (phenols, amino acids, and benzene derivatives) were studied. The operating conditions were determined by estimation of the elution band based on the Lapidus-Amundson equation. The optimum operating conditions were determined by maximizing the productivity. For the amino acid system, with a maximum pressure drop of 100 psi, the optimum column length and the mobile-phase velocity were investigated with different adsorbent particle sizes. Design Method for Recycle Chromatography Design with Lapidus-Amundson Solution. In batch chromatography the wave velocity can be derived from a simple wave equation which does not include the mass-transfer resistance and axial dispersion.20 However, zone spreading caused by a combination of mass-transfer resistance and axial dispersion also needs to be estimated for the elution band. Lapidus and Amundson18 developed an elegant solution for the dispersion equation for linear isotherms.
Figure 1. Illustration of the adsorption breakthrough curve predicted by the Lapidus-Amundson equation.
10.1021/ie800583p CCC: $40.75 2008 American Chemical Society Published on Web 10/28/2008
9602 Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008
Figure 2. Schematic of the recycle chromatography apparatus.
Figure 3. Migration traces of the solutes to isolate the intermediate retained solute B. Solid, dashed, and dotted lines are the migration traces of solute A, solute B, and solute C, respectively.
The mass balance of solute in the chromatographic column is ∂ci ∂2ci ∂ci (1 - ) ∂qi + + u ) De,i 2 ∂t ∂t ∂z ∂z
(1)
where is the void fraction of the column, ci is the concentration of solute i in the mobile phase, qi is the concentration of solute i in the stationary phase, u is the interstitial velocity of the mobile phase, and De,i is the axial dispersion coefficient for solute i. For mass transfer between the mobile and stationary phase, it is common to use a linear lumped mass-transfer model ∂qi ) apkeff,i(ci - c*i ) (2) ∂t where apkeff,i is the mass-transfer coefficient of solute i, ap is 6/Dp for spherical particles, and ci* is the concentration of solute i in the liquid film. Lapidus and Amundson solved these equations for linear isotherms and local equilibrium (apkeff,i is very large).18 For long columns the result is ci(z, t) )
{ [
cF,i 1 - erf 2
z - uS,it
√4Dap,iuS,it ⁄ u
]}
(3)
u (4) 1-∈ Ki 1+ ∈ where cF,i is the concentration of solute i in the feed, uS,i is the wave velocity of solute i, Dap,i is the apparent axial dispersion uS,i )
Figure 4. Migration traces of the solutes to isolate the least retained solute A (a) and most retained solute C (b). Solid, dashed, and dotted lines are the migration traces of solute A, solute B, and solute C, respectively.
coefficient of solute i, and Ki is the partition coefficient of solute i. This solution predicts a symmetric sigmoidal curve for concentration versus distance z when the time t is constant. Because the apparent axial dispersion coefficient can be related to the mass-transfer resistance and the real axial dispersion coefficient, this solution can be used for cases where local equilibrium is not attained. The axial dispersion was estimated by the Chung and Wen correlation21 1 Pe ) (0.2 + 0.011Re0.48)
(5)
where Pe is the Peclet number and Re is the Reynolds number. With a design criterion that maximum pressure drop is 100 psi, the optimum column length was calculated with different particle sizes. It is well known that the column efficiency increases if the adsorbent has a smaller particle size. The apparent dispersion coefficient can be estimated from either of the following two relations19 Dap ) Dap ) De +
Lu 2Nap
k u2K 1- K , k) aPkeff (1 + k)2
(6a) (6b)
where De is the axial dispersion coefficient, k is the retention factor, and Nap is the apparent theoretical plate number, which can be determined from experiments. The end of the elution band in a chromatographic column can be estimated by the tangential line at the inflection point
Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 9603 Table 1. System Parameters and Properties of Mixtures (a) phenols:23phenol (A), 2-phenylethanol (B), and 3-phenyl-1-propanol (C)
(b) amino acids:24glycine (A), L-phenylalanine (B), and L-tryptophan (C)
(c) benzene derivatives: acetophenone (A), toluene (B), and p-xylene (C)
25 cm 0.46 cm 0.54 10 µm Nap,A ) 3500 Nap,B ) 4000 Nap,C ) 6000 KA ) 2.15 KB ) 3.61 KC ) 6.85
120 cm 1.1 cm 0.70 422.5 µm aPkeff,A ) 1000 /min, Dax,A ) 0.217 cm2/min aPkeff,B ) 2.758 /min, Dax,B ) 0.217 cm2/min aPkeff,C ) 4.204 /min, Dax,C ) 0.217 cm2/min KA ) 0.116 KB ) 1.134 KC ) 5.968 CA ) 0.544 g/L CB ) 0.970 g/L CC ) 0.408 g/L 1.0 mL/min
15 cm 0.46 cm 0.65 5 µm Nap,A ) 6241 Nap,B ) 9957 Nap,C ) 11115 KA ) 1.09 KB ) 3.59 KC ) 5.62
length of column (L) column diameter (d) voidage () particle diameter (DP) mass transfer/dispersion partition coefficient feed concentration
5 g/L flow rate of the mobile phase
0.5 mL/min
5 g/L 0.5 mL/min
Table 2. Calculated Elution Times of Front and Rear of Elution Bands Obtained from Eq 5 solute A systems phenols amino acids benzenes a
solute B
solute C
front end [min] L/uSa [min] rear end [min] front end [min] L/uSa [min] rear end [min] front end [min] L/uSa [min] rear end [min] 12.18 74.11 4.99
12.71 83.80 5.15
13.26 94.75 5.32
17.58 99.97 9.31
18.29 118.62 9.54
19.03 140.76 9.79
29.69 222.32 12.80
30.67 284.01 13.11
31.68 362.81 13.43
Retention time of the solute.
Figure 5. Changes of productivity and D/F as a function of feed time for isolation of the intermediate retained solute in the phenol system.
(Figure 1). In this case, the end of the elution band is located at about 0.6% of the feed concentration on the curve obtained from the Lapidus-Amundson equation. The ends of the elution band based on the Lapidus-Amundson solution are Za,i(t) ) uS,it +
4πDap,iuS,it , Zd,i(t) ) uS,it u
4πDap,iuS,it u (7)
where Za,i and Zd,i are the axial distance of the elution band of solute i in the adsorption and desorption breakthrough curves, respectively. From this equation, the elution time of front and rear bands are tf,i )
[
]
√πDap,i ⁄ u + L - √πDap,i ⁄ u , √uS,i √πDap,i ⁄ u + L + √πDap,i ⁄ u tr,i ) √uS,i
[
2
]
where L is the column length and tf,i and tr,i are the elution times of the front and rear bands of solute i, respectively. These equations allow easy estimation of the broadening of the elution band at the column outlet. Figure 2 shows a schematic diagram of the recycle chromatography system. A recycled solution is stored in the tanks. It is assumed that the tank is well mixed and the concentration of the solute is homogeneous. All of the tanks were initially empty until recycled liquid filled the tanks during the first cycle. The recycle streams were sent to the feed stream after the second cycle. All simulations were continued until the concentrations of the solutes in the recycle tanks reached a cyclic steady state. A maximum cycle count of 30 cycles was allowed. Isolation of Intermediate Retained Solute. The feed solute band is broadened by the difference between tr and tf. The recyclable pure desorbent and unseparated solutes are calculated based on the following design criteria for recycle chromatography to isolate the intermediate retained solute. First, the intermediate retained solute (B) has to be eluted separately from the least retained (A) or most retained (C) solutes. Second, pure desorbent or unseparated solutes can be recycled as a desorbent or as feed, respectively. The range of feed times can be divided as follows: when tf,B - tr,A is less than tf,C - tr,B 0 e tF < tf,B - tr,A
(9a)
tf,B - tr,A e tF < Min(tf,C - tr,B, tr,C - tr,A - tr,B + tf,A) (9b) Min(tf,C - tr,B, tr,C - tr,A - tr,B + tf,A) e tF < tr,C - tr,A - Min(tr,A - tf,A, tr,C - tf,C) (9c) when tf,B - tr,A is greater than tf,C - tr,B 0 e tF < tf,C - tr,B
(10a)
tf,C - tr,B e tF < Min(tf,B - tr,A, tf,C - tf,A - tr,C + tf,B) (10b) Min(tf,B - tr,A, tf,C - tf,A - tr,C + tf,B) e tF < tf,C - tf,A - Min(tr,A - tf,A, tr,C - tf,C) (10c)
2
(8)
where tF is the feed time. In the ranges delineated by eqs 9a and 10a, solute B is fully isolated from the other solutes, solutes A and C elute together, and recycled eluent is solute free. In
9604 Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 Table 3. Optimized Operating Conditions and Results of Recycle Chromatography To Isolate Solute B feed stream tCycle [min]
tF [min]
product stream tD [min]
tDR [min]
tA/C [min]
tB [min]
purity [%]
yield [%]
11.27-17.58 222.32-99.97 4.99-0.82
17.58-4.92 99.97-145.98 1.50-4.99
99.91 99.66 99.84
99.94 99.43 99.86
11.27-17.58 222.32-99.97 5.67-1.50
5.50-11.27 176.30v222.32 1.50-4.99
99.92 99.89 99.82
99.95 99.85 99.87
pure desorbent recycle phenol system amino acid system benzene system
18.42 268.06 7.81
0-4.32 0-5.22 0-3.02
4.32-18.42 5.22-268.06 3.02-7.81
phenol system amino acid system benzene system
18.42 268.06 7.81
0-10.67 0-81.55 0-3.69
10.70-18.42 81.55-268.06 3.69-7.81
4.92-11.27 145.98-222.32 0.82-1.50 feed recycle 17.58-5.50 99.97-176.30 4.99-5.67
concentrations of solutes decrease. When tf,B - tr,A is less than tf,C - tr,B, the cycle time is tCycle ) tr,C - tr,A
(11a)
when tf,B - tr,A is greater than tf,C - tr,B tCycle ) tf,C - tf,A
(11b)
where tCycle is the cycle time. The cycle time of recycle chromatography is constant for isolation of the intermediate retained solute because solute A from the next feed step is eluted with solute C from the current feed step. Figure 3 shows the trace of the solutes in the column described by eqs 7-11a. Isolation of the Least or Most Retained Solute. To isolate the least or most retained solute, the least retained solute from the current feed step should not overlap with the most retained solute from the previous feed step. In these cases, one undesired solute is recycled until it is eluted with the other undesired solute. The decision of which solute to recycle depends on the broadening of the elution bands. To decrease D/F, the solute that spreads less should be recycled to overlap the other solute. The optimum feed time for isolation of solute A is tF,Opt ) tf,B - tr,A
(12a)
while for isolation of solute C tF,Opt ) tf,C - tr,B
(12b)
If the feed time is greater than tF,Opt, the target solute will be eluted with the other solute. To maintain recovery of the target solute, this unseparated target solute is recycled to the feed stream. Because recycling to the feed causes the feed time to increase with a constant amount of desorbent, the cycle time increases proportionally. tC ) tF + tr,C - tf,A Figure 6. Changes of productivity and D/F as a function of feed time for isolation of the least retained solute (a) and most retained solute (b) in the phenol system.
this range there is no recycle of feed (unseparated solutes), and the concentrations of solutes in the column inlet are exactly the same as in the feed. In the ranges listed in eqs 9b and 10b, part of the solute B elution band overlaps with the closer eluted solute (A or C). Therefore, there are two different recycle streams: one is pure desorbent which is the same as eqs 9a and 10a, and the other is unseparated solutes. The concentrations of solutes in the inlet of the column decrease as the amount of recycled feed solution (unseparated solutes) increases. However, the cycle time (time difference between two feeds) is constant due to the alternation between pure desorbent and unseparated solutes. In the ranges listed in eqs 9c and 10c, there is only one recycle stream which contains unseparated solutes because the solute B elution band overlaps with farther eluted solute (solute C or A). Therefore, as the feed time increases, the inlet
(13)
where tr,C - tf,A is the minimum desorbent feed time to separate solute A from the current feed step and solute C from the previous feed step. Figure 4a illustrates the migration traces of solutes when solute A is the target and solute B is recycled, and Figure 4b illustrates the migration traces of solutes when solute C is the target and solute A is recycled. Complete Ternary Separation. As a comparison with purification of only one solute, we also studied complete ternary separations. To separate all components in a ternary mixture, the optimum feed time is the minimum of eqs 12a and 12b and the feed time cannot be greater the maximum of eqs 12a and 12b. There should be no elution of overlapped solutes. If there is elution of overlapped solutes, it should be recycled to the feed stream because all the components are targets. Effect of Column Length and Mobile-Phase Velocity. Productivity and D/F are closely related to the particle size of adsorbent and the linear velocity of the liquid phase due to the different band broadening rates of the solutes caused by axial
Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 9605 Table 4. Optimized Operating Conditions and Results of Recycle Chromatography To Isolate Solute A feed stream
phenol system amino acid system benzene system
product stream
tCycle [min]
tF [min]
tBR [min]
tD [min]
tBR [min]
tB/C [min]
tA [min]
purity [%]
yield [%]
23.82 293.92 12.42
0-4.32 0-5.22 0-3.99
4.32-16.44 5.22-127.57 3.99-7.48
16.44-23.82 127.57-293.92 7.48-12.42
17.58-5.87 99.97-222.32 9.31-0.38
5.87-12.18 222.32-74.11 0.38-4.99
12.18-17.58 74.11-99.97 4.99-9.31
99.89 99.05 99.84
99.97 99.84 99.96
Table 5. Optimized Operating Conditions and Results of Recycle Chromatography To Isolate Solute C feed stream
phenol system amino acid system benzene system
product stream
tCycle [min]
tF [min]
tAR [min]
tD [min]
tAR [min]
tA/B [min]
tC [min]
purity [%]
yield [%]
30.17 370.25 11.45
0-10.67 0-81.55 0-3.02
10.67-16.07 81.55-107.41 3.02-7.33
16.07-30.17 107.41-370.25 7.33-11.45
12.18-17.58 74.11-99.97 4.99-9.31
17.58-29.69 99.97-222.32 9.31-1.35
29.69-12.18 222.32-74.11 1.35-4.99
99.97 99.92 99.79
99.98 99.91 99.92
dispersion and kinetic resistance. We estimated the optimum flow rate of the mobile phase with given column length owing to the elution band estimated by eq 8. Therefore, the column length is one of the design parameters of the chromatography process along with the flow rate. However, the column length is restricted by the pressure capacity of the pump and structural limitations. To estimate the pressure drop, the Blake-Kozeny equation was used22 2
3 ∆P Dp (14) L 150µ (1 - )2 where V is the superficial velocity, ∆P is the pressure drop, Dp is the diameter of the adsorbent particle, and µ is the viscosity of the fluid. V)
Results and Discussion Table 1 shows the system parameters and properties for the three ternary mixtures studied. The original data for the phenol23
Figure 7. Changes of productivity and D/F as a function of the feed time for the complete ternary separation in the phenol system.
and benzene derivative mixtures were obtained with highperformance columns. Feed concentrations were selected so that all systems were within the linear range of the isotherms. Since the apparent theoretical plate numbers were given, eq 6a was used to estimate Dap. For the amino acid24 separation system the axial dispersion coefficients were estimated from the Chung and Wen correlation, eq 5, and the apparent dispersion coefficients were estimated from eq 6b. In the phenol and amino acid separation system solute B is eluted closer to solute A than to solute C. In the benzene derivative system solute B is eluted closer to solute C. To decide the optimized operating conditions the elapsed times of both the front and the rear ends of the solute band were calculated by eq 5. Table 2 shows the calculated elapsed times of front and rear ends of the elution bands and the retention time of solute calculated by the wave velocity, uS. If the feed time is long enough, the product concentration forms a plateau at the feed concentration and the width of the mass-transfer zone (see Figure 1) becomes constant. Even if the feed time is not long enough, the mass-transfer zone is still approximately constant if there is little product dilution. As shown in Table 2, the difference between tr,A and tf,B is smaller than the difference between tr,B and tf,C in the phenol and amino acid systems, while the difference between tr,A and tf,B is bigger than the difference between tr,B and tf,C in the benzene derivative system. The elution bandwidths of amino acids were much wider than the other systems because a large particle size adsorbent was used (see Table 1). Isolation of Intermediate Retained Solute. For isolation of the intermediate retained solute the next feed time was adjusted to cause overlap of the less and more retained solutes. At a specified purity, the operating condition which has the lowest D/F and highest productivity is the optimum operating condition. Figure 5 shows the effects of feed time for the phenol system. All other systems showed similar trends. As the feed time increased, D/F decreased and the productivity increased until the feed time reached 4.32 min () tf,B - tr,A). Productivity and D/F were not changed in the range from 4.32 to 10.67 min ()
Table 6. Optimized Operating Conditions and Results of Recycle Chromatography to Separate All Components feed stream tCycle [min] tF [min] phenol system amino acid system benzene system
product stream
tD [min]
tDR [min] 23.35-5.87
tA [min]
tB [min]
23.82
0-4.32
4.32-23.82
293.92
0-5.22
5.22-293.92 145.98-222.32 74.11-99.97 99.97-145.98 145.98-222.32
11.45
0-3.02
3.02-11.45
8.33-9.31
12.18-17.58 17.58-23.35
tC [min]
4.99-8.33
9.31-1.35
5.87-12.18
1.35-4.99
purity yield (A/B/C) [%] (A/B/C) [%] 99.90 99.95 99.96 99.06 99.80 99.20 99.90 99.90 99.80
99.95 99.94 99.93 99.55 99.43 99.44 99.88 99.86 99.86
9606 Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 Table 7. Comparisons of Batch and Recycle Chromatography optimized D/F
target solute solute A solute B solute C all
system
batch
recycle
reduced DCa [%]
productivity [g/mL-h]
phenol amino acid benzene phenol amino acid benzene phenol amino acid benzene phenol amino acid benzene
4.51 55.34 2.11 3.26 50.38 1.59 1.83 3.54 2.80 4.51 55.34 2.80
1.71 31.89 1.24 1.80 35.75 1.37 1.32 3.22 1.37 3.04 40.71 2.47
62.1 42.4 31.1 44.8 29.0 14.1 27.7 9.0 51.2 32.6 26.4 11.5
6.55 5.08b 19.32 8.47 9.93b 23.23 12.77 47.28b 15.85 19.64 17.95b 47.54
DC is desorbent consumption, and reduced DC [%] ) (DCBatch - DCRecycle)/DCBatch × 100. adsorbent-h]. a
b
The unit of productivity is [g of product/L of
Table 8. Effect of Adsorbent Particle Size on Productivity and D/F for Amino Acid System with Constant Column Dimensions and Feed Conditions (see Table 1) solute A
solute B
solute C
complete separation
particle size [µm]
pressure drop, ∆P/∆P422.5
(D/F)/(D/F)422.5
P/P422.5
(D/F)/(D/F)422.5
P/P422.5
(D/F)/(D/F)422.5
P/P422.5
(D/F)/(D/F)422.5
P/P422.5
422.5 200 100 50 25
1.0 4.5 17.9 71.4 285.6
1.00 0.44 0.32 0.27 0.25
1.00 2.18 2.88 3.32 3.61
1.00 0.45 0.34 0.30 0.28
1.00 2.13 2.77 3.17 3.42
1.00 0.89 0.84 0.82 0.81
1.00 1.09 1.14 1.17 1.18
1.00 0.44 0.33 0.28 0.26
1.00 2.18 2.88 3.32 3.61
tf,C - tr,B) even though the feed time increased because the excess material was recycled to the feed stream and the cycle time was constant. As shown in eq 9c, the feed time cannot be over tf,C - tr,A ) 16.43 because the periods of the B and A/C products shrink to zero and the period of feed recycle expands to the cycle time (see Figure 3). From 4.32 to 10.67 min of the
Figure 8. Changes of productivity and D/F as flow rate changes (amino acid mixture, Dp ) 50 µm, L ) 300 cm).
feed time the system has minimum D/F and maximum productivity. When the feed time is 4.32 min, only pure desorbent is recycled to the desorbent stream, and only unseparated solutes are recycled to the feed stream when the feed time is 10.67 min. In these two cases, only one recycle tank is required but between these two feed times two recycle tanks are required to collect pure desorbent and unseparated solutes separately. Table 3 shows the optimized operating conditions and results of the recycle chromatography to isolate solute B for each system. As shown Table 3a and 3b, the two different recycle methods had the same cycle time and solute B was separated with over 99% purity and yield. In the amino acid system the feed time is quite small compared to the cycle time and the products were diluted much more than for the other systems. However, solute B was separated with over 99% purity and yield. The threshold value (0.609% of feed concentration) which is used to determine the bandwidth is enough to obtain 99% purity and yield in the amino acid system. Obviously different purities and yields can be obtained by adjusting the threshold value. Isolation of the Least or Most Retained Solutes. Figure 6a shows the changes in D/F and productivity according to the increase of the feed time to isolate solute A (the least retained solute) in the phenol system. Up to 4.32 min () tf,B - tr,A) of feed time the tendencies of D/F and the productivity were similar to Figure 5. However, after 4.32 min, the productivity decreased as the feed time increased because the cycle time also increased as the feed time increased. For isolation of solute C (more retained solute), the productivity also decreased after the feed time was over 10.67 min () tf,C - tr,B), as shown in Figure 6b. In the recycle stream of these two cases one of the undesired solutes was recycled to be eluted with the other. However, after the optimum feed time unseparated target solute should also be recycled to the feed stream. Thus, two different recycle tanks were required. Tables 4 and 5 show the optimized operating conditions and results to isolate solutes A and C, respectively. For all systems, target solutes were separated with over 99% purity and yield.
Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 9607
Figure 9. Changes of productivity, D/F, and pressure drop at the optimum operating condition for each column length (amino acid mixture, Dp ) 50 µm): (a) isolation of solute A, (b) isolation of solute B, (c) isolation of solute C, and (d) complete ternary separation. Table 9. Comparisons of Optimum Design Parameters for Different Adsorbent Particle Sizes for Amino Acid System Dp [µm]
L [cm]
V [cm/min]
L/V [min]
VL/Dp2 ( × 10-6) [1/min]
D/F
Productivity [g/L-h]
∆P [psi]
Feed throughput [mL/min]
19.0 19.0 19.1 19.1 19.1
0.0263 0.0263 0.0264 0.0265 0.0266
94.0 94.3 94.7 95.1 95.5
0.333 0.668 1.34 2.02 2.70
0.0475 0.0476 0.0478 0.0479 0.0481
93.8 94.0 94.5 94.9 95.3
0.270 0.540 1.08 1.63 2.18
0.0862 0.0863 0.0863 0.0863 0.0864
101.5 101.5 101.5 101.6 101.6
1.05 2.09 4.19 6.28 8.38
0.0927 0.0930 0.0934 0.0938 0.0941
94.0 94.3 94.7 95.1 95.5
0.265 0.532 1.07 1.61 2.15
solute A 50 100 200 300 400
300 600 1200 1800 2400
7.02 14.1 28.3 42.6 57.0
42.7 42.6 42.4 42.3 42.1
0.842 0.846 0.849 0.852 0.855
50 100 200 300 400
300 600 1200 1800 2400
7.00 14.0 28.2 42.5 56.9
42.8 42.7 42.5 42.3 42.2
0.841 0.843 0.847 0.850 0.854
50 100 200 300 400
300 600 1200 1800 2400
7.58 15.2 30.3 45.5 60.7
39.6 39.6 39.6 39.6 39.6
0.909 0.910 0.910 0.910 0.910
50 100 200 300 400
300 600 1200 1800 2400
7.02 14.1 28.3 42.6 57.0
42.7 42.6 42.4 42.3 42.1
0.842 0.845 0.849 0.852 0.855
solute B 23.7 23.7 23.7 23.8 23.8 solute C 5.88 5.88 5.88 5.88 5.88 all solute
Complete Ternary Separation. Figure 7 shows the changes in D/F and productivity according to the increase of the feed time to separate all three components in the phenol system. After the optimum feed time (4.32 min) D/F increased as the feed time increased because the unseparated solutes A and B were recycled to the feed stream. The decrease in
24.1 24.2 24.2 24.2 24.2
productivity and increase in D/F changed steeply after the feed time was greater than 10.69 min because the unseparated solutes B and C also had to be recycled to feed stream. In the optimum operating condition all components were separated with greater than 99% purity and yield as shown in Table 6. The maximum feed time for separation of all
9608 Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 Table 10. Comparisons of Productivity, D/F, and Pressure Drop for Different Particle Sizes for the Amino Acid System (L ) 300 cm) Dp [µm]
V [cm/min]
50 100 200 300 400
7.02 6.58 5.97 5.48 5.08
50 100 200 300 400
7.58 7.56 7.52 7.48 7.44
a
(D/F)/(D/F)50 solute A 1.00 1.03 (1.12)a 1.08 (1.35)a 1.13 (1.61)a 1.20 (1.94)a solute C 1.00 1.01 (1.01)a 1.02 (1.03)a 1.04 (1.05)a 1.05 (1.07)a
P/P50
∆P/∆P50
V [cm/min]
1.00 0.90 (0.90)a 0.77 (0.76)a 0.66 (0.63)a 0.58 (0.53)a
1.00 0.234 0.053 0.022 0.011
7.00 6.56 5.93 5.46 5.06
1.00 0.99 (0.99)a 0.97 (0.97)a 0.95 (0.95)a 0.94 (0.94)a
1.00 0.249 0.062 0.027 0.015
7.02 6.58 5.97 5.48 5.08
(D/F)/(D/F)50
P/P50
solute B 1.00 1.00 1.02 (1.10)a 0.91 (0.91)a 1.05 (1.31)a 0.78 (0.76)a 1.10 (1.55)a 0.68 (0.65)a 1.15 (1.86)a 0.59 (0.54)a complete separation 1.00 1.00 1.02 (1.11)a 0.90 (0.90)a 1.08 (1.33)a 0.77 (0.75)a 1.13 (1.59)a 0.66 (0.63)a 1.19 (1.91)a 0.58 (0.53)a
∆P/∆P50 1.000 0.234 0.053 0.022 0.011 1.000 0.234 0.053 0.022 0.011
Ratios at the same linear velocity as used for the 50 µm particle size.
components was the same as the maximum feed time for isolation of solute B, and it is impossible to recycle any solutes to reduce desorbent consumption. Comparisons with Batch Chromatography. With linear isotherms recycle chromatography does not increase the feed throughput compared with batch chromatography; thus, both batch and recycle chromatograph have the same productivity. However, recycle chromatography significantly decreases desorbent consumption. Table 7 shows the optimized D/F and productivity of batch and recycle chromatography. For isolation of solute B undesired solutes were eluted together by adjusting the next feed time. Thus, the recycled amount is determined by the difference of (tr,A - tf,B) and (tr,B - tf,C). As expected, the reduction in desorbent consumption of the benzene system is lower than the other systems. When the target solute is eluted far from other solutes (solute C in the phenol and amino acid system and solute A in the benzene system), most of the undesired solutes were already eluted together because their retention times were close to each other. Therefore, the reduced desorbent consumption by recycle chromatography was smaller than the other cases (isolation of solute A in the phenol and amino acid system and isolation of solute C in the benzene system). Scale-up of Recycle Chromatography. In the scale-up of chromatography processes a larger adsorbent particle size is used to decrease the cost and pressure drop. The traditional scale-up method uses the same linear velocity of the mobile phase as in the small-scale unit.25 Table 8 shows the effect of the adsorbent particle size on the productivity and D/F for the amino acid system. The column dimensions and feed conditions are constant as described in Table 1. As the adsorbent particle size becomes smaller, productivity increased and D/F decreased. When a 25 µm diameter adsorbent (16.9 times smaller than 422.5 µm) was used, desorbent consumption decreased about 75% and the productivity increased about 3.5 times in three cases (solute A, solute B, and complete separation). However, eq 14 shows that the pressure drop increases in inverse proportion to the square of the particle diameter. Therefore, scale up in this form can be expensive if the pressure becomes very high. Figure 8 shows the changes of productivity and D/F as the flow rate of the mobile phase is changed for a constant particle diameter. Note that a mobile-phase flow rate of 1.0 mL/min used for Tables 1-8 is not optimized. For scale up of the amino acid system two design criteria were considered. First, the maximum pressure drop was set to 100 psi. Figure 9 shows the changes in productivity, D/F, and pressure drop as the column length is changed when 50 µm adsorbent was used. For each column length a different optimum flow rate of the mobile phase was determined based on the highest productivity. The D/F decreased and produc-
tivity increased as the column length increased, but the pressure drop increased. According to the design criterion of a maximum pressure drop of 100 psi, the optimum column length for 50 µm particle size was approximately 300 cm for all design cases. Other particle sizes had similar trends. Table 9 shows the optimum design parameters with different sizes of adsorbent. For all design cases (purification of A, B, C, or ternary) the optimum column lengths and flow rates were almost the same at the same particle size. According to the Blake-Kozeny equation, the pressure drop is constant if VL/Dp2 is constant. However, each particle size and column length has different optimum flow rates. The optimum column length was proportionally longer as the particle size was increased. The optimum design for each particle size gives almost identical D/F and productivity values. In addition, the ratios, L/V (column holdup time) and VL/Dp2 were constant for the optimum designs for each type of separation. These two ratios can be useful to decide the flow rate and column length in different particle size systems. Commonly, productivity and desorbent consumption deteriorate when large adsorbent particles are used. However, if it is possible to build the optimum column length and operate at the optimum flow rate, systems with large particle sizes can obtain the same productivity and D/F as compared with small particles. However, the column cost can become prohibitive since the length may be excessive. The second design criterion considered is using a column with constant dimensions. As shown in Table 9 the optimum column length for 400 µm diameter adsorbent was 24 m. However, it would be difficult and expensive to build this system. Commonly, the lengths of commercial chromatography columns are not over 12 m, and usually they are shorter than this.26 The design criterion of the column length was set to 300 cm, which is the optimum column length for 50 µm particles. Table 10 shows the ratios of the productivity, D/F, and pressure drop based on the 50 µm particle size data. The optimum flow rates of the mobile phase decreased and the pressure drop decreased by approximately 100 times as the particle size increased from 50 to 400 µm. However, productivity and D/F deteriorated just 40% and 20%, respectively. For the 400 µm particle size at the optimum flow rate productivity increased by 10% and D/F decreased by 60% compared with the values required at the same flow rate as the 50 µm particles for purification of A, B, and all three solutes. For solute C the productivity and D/F values were changed less than 5%, even though the particle size changed from 50 to 400 µm. This phenomenon was also observed in Table 8. Solute C is easily
Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 9609
separated from solutes A and B. Therefore, the feed time is long because zone spreading has little effect on productivity and D/F. Summary The design method based on the Lapidus-Amundson solution can determine the optimum operating conditions for recycle chromatography to isolate one valuable solute in a ternary mixture. In this study, one valuable component (the least retained solute, intermediate retained solute, and most retained solute) was isolated from three ternary mixtures: phenols, amino acids, and benzene derivatives. The target solute was isolated with over 99% purity and yield. For isolation of intermediate retained solute, desorbent recycle or feed recycle of unseparated solutes can be used in the optimum range of the feed period. In this optimum range the two recycle methods give the same productivity and D/F. For purification of the least or most retained solute, there was only one optimum recycle operation that caused one undesired solute to overlap the other undesired solute elution. With linear isotherms, recycle chromatography decreases desorbent use but does not increase productivity compared to batch operation. The broadening of the elution bands was determined by the column length, linear velocity of the mobile phase, and effective dispersion coefficients which depended on the adsorbent particle size. For the amino acid system the optimized column length and flow rate of the mobile phase were determined with various adsorbent particle sizes. With fixed column length and particle size there was an optimum flow rate of the mobile phase which provided maximum productivity. When the maximum pressure drop was specified, all optimum design parameters obtained from the different particle sizes had constant ratios of L/V and VL/Dp2. These ratios can be used to determine the column length and flow rate for different adsorbent particle sizes. With large particle sizes faster flow rates and longer column lengths were needed to obtain the same productivity and D/F as small particle sizes. Acknowledgment This work was supported by the Center for Advanced Bioseparation Technology at Inha University, KOSEF, Republic of Korea. Nomenclature apkeff,i ) mass-transfer coefficient of solute i [1/min] ci ) concentration of solute i in the mobile phase [g/L] ci* ) concentration of solute i in the liquid film [g/L] cF,i ) concentration of solute i in feed solution [g/L] Dap,i ) apparent axial dispersion coefficient of solute i [cm2/min] De,i ) effective axial dispersion of solute i [cm2/min] Dp ) diameter of the adsorbent particle [µm] D/F ) ratio of the fresh pure desorbent and fresh feed solution volume in one cycle time k ) retention factor K ) partition coefficient L ) column length [cm] Nap ) apparent theoretical plate number P ) productivity [g/mL-h] Pe ) Peclet number () uDp/De) ∆P ) pressure drop [psi] qi ) concentration of solute i in the stationary phase [g/L] Re ) Reynolds number () DpVF/µ) tA ) time interval while solute A is produced [min]
tA/C ) time interval while solutes A/C are produced [min] tA/B ) time interval while solutes A/B are produced [min] tAR ) time interval while solute A is collected to recycle or recycled solute A is fed to the column [min] tB ) time interval while solute B is produced [min] tB/C ) time interval while solutes B/C are produced [min] tBR ) time interval while solute B is collected to recycle or recycled solute B is fed to the column [min] tC ) time interval while solute C is produced [min] tCycle ) cycle time [min] tD ) time interval while the desorbent is fed to the column [min] tDR ) time interval while the desorbent is collected to recycle [min] tF ) time interval while the feed solution is fed to the column [min] tFR ) time interval while the unseparated solute is collected to recycle [min] tf,i ) elution times of front bands of solute i [min] tr,i ) elution times of rear bands of solute i [min] u ) interstitial velocity of the mobile phase [cm/min] uS,i ) wave velocity of solute i [cm/min] V ) superficial velocity [cm/min] Za,i ) axial distance of elution band of solute i in the adsorption breakthrough curve [cm] Zd,i ) axial distance of elution band of solute i in the desorption breakthrough curve [cm] ) void fraction of the column µ ) viscosity of the fluid phase [cP]
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ReceiVed for reView April 11, 2008 ReVised manuscript receiVed August 13, 2008 Accepted September 5, 2008 IE800583P
