Comparison of Recycle Chromatography and Simulated Moving Bed

Publication Date (Web): July 8, 2009 ... To compare the performances of SMB and recycle batch chromatography, detailed dynamic simulations of each pro...
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Ind. Eng. Chem. Res. 2009, 48, 7724–7732

Comparison of Recycle Chromatography and Simulated Moving Bed for Pseudobinary Separations Ju Weon Lee†,‡ and Phillip C. Wankat*,† School of Chemical Engineering, Purdue UniVersity, 480 Stadium Mall DriVe, West Lafayette, Indiana 47906, ERC for AdVanced Bioseparation Technology, Inha UniVersity, 253 Younghyun-dong, Nam-ku, Incheon 402-751 Republic of Korea

The simulated moving bed (SMB) process has been extensively used in industrial separations for binary and pseudobinary separations. The SMB has been reported to have higher productivity and requires less desorbent than batch chromatography; however, in pseudobinary separations these advantages are dependent on the difference of adsorption behaviors of the nontarget components. In this research, the performance of batch chromatography with a single recycle stream was compared to SMB processes for pseudobinary separations of ternary nucleosides, a model system with competitive Langmuir isotherms. To compare the performances of SMB and recycle batch chromatography, detailed dynamic simulations of each process were performed with optimized operating conditions. The desorbent to feed ratio, D/F, of recycle chromatography was at least 2 times smaller than that of a four-column SMB process for most retained solute separations. For one case of least retained solute separation (2′-deoxycytidine/2′-deoxythymidine/2′-deoxyadenosine), minimum D/F of the four-column SMB process is approximately 15 times larger than that of recycle chromatography. The maximum productivity of recycle chromatography is 1.5-2 times larger than that of the four-column SMB process. When eight columns are used in the four-zone SMB process (two columns per zone), the performance (productivity, D/F, and pressure drop) is improved compared to the four-column SMB. The eight-column SMB has higher maximum productivity, and at the same productivity, it also has lower D/F and lower pressure drop compared to recycle chromatography. However, the recycle chromatography system is simpler and has fewer columns. Introduction Batch chromatographic separation is widely used to isolate target components from a mixture with high purity and yield. However, without recycling, the desorbent is not used efficiently and the product is diluted because a high volumetric ratio of desorbent to feed (D/F) is required. To overcome these deficits, different recycle concepts have been applied to batch chromatography. Seidel-Morgenstern and Guiochon1 studied improving the recovery by recycling insufficiently separated fractions in closed-loop preparative chromatography of low selectivity ( aj).

obtain the cyclic steady-state simulation results for recycle chromatography with two serial batch simulations. Six pseudobinary mixtures composed of three nucleosides were considered to compare recycle chromatography and fourzone SMB processes. Table 1 shows the Langmuir isotherm and mass-transfer parameters of the four nucleosides.11 For most retained or least retained solute separations, three solute systems were chosen to isolate dA or dC, respectively. Selectivity of nontarget solutes varied from 1.30 to 3.74, and selectivity of target solute and neighboring nontarget solute varied from 2.35 to 3.74 (Table 2). The total bed height of recycle chromatography and SMB processes were fixed at 40 cm (40 cm for recycle chromatography, 10 cm each for a 1:1:1:1 configuration of the SMB process, and 5 cm each for a 2:2:2:2 configuration of the SMB process). The feed concentration of each solute was fixed as 5 g/L, which is in the moderately nonlinear isotherm range. The separation criteria (purity and yield of the target component) of SMB processes were chosen to match the corresponding recycle chromatography values that were over 99.8% in all simulations. For the standard model, the mass balance of solutes in a chromatographic column is given by eq 1 (see Table 3). For mass transfer between the mobile phase and the stationary phase, the standard model uses a linear-lumped mass-transfer model for solid film11 (eq 2 in Table 3). The adsorption behaviors of nucleosides follow the competitive Langmuir isotherm model11 (eq 3 in Table 3). For all simulations of recycle chromatography and SMB processes except for Figure 3, this standard model that includes both axial dispersion and mass-transfer resistance was used. Parameters for mass transfer and equilibrium are in Table 1.11 The pressure drop of the column in recycle chromatography and SMB processes was calculated by the BlakeKozeny equation.12 2 ε3 ∆P Dp V) L 150µ (1 - ε)2

(4)

Terms are defined in the Nomenclature. Detailed simulations for recycle chromatography and SMB processes were performed with Aspen Chromatography 2006. A finite element method with biased upwind difference scheme (BUDS) and fixed step-size implicit Euler method for the integration of each node were used to solve the partial differential equations.13 The number of nodes for the space domain was fixed at 4 nodes/cm, and the step-size for the time domain integration was 0.01 mL (time scale step size at a given

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Table 3. Model Equations for Figure 3a models

standardb

mass balance

εT

mass transfer

∂ci ∂qi ∂ci ∂2ci + (1 - εT) +u ) εDe,i 2 ∂t ∂t ∂z ∂z

(1)

∂qi ) apki(q*i - qi) ∂t

isotherm

(2)

q*i )

aici 1+

∑ bc

(3)

j j

j

without mass transferc

εT

∂ci ∂qi ∂ci ∂2ci + (1 - εT) +u ) εDe,i 2 ∂t ∂t ∂z ∂z

(4a)

qi )

none

aici 1+

∑bc

(5a)

j j

j

without axial dispersiond

εT

∂ci ∂qi ∂ci + (1 - εT) +u )0 ∂t ∂t ∂z

(6a)

∂qi ) apki(q*i - qi) ∂t

(7a)

q*i )

aici 1+

∑ bc

(8a)

j j

j

a The standard model is used for all other simulations. Terms are defined in Nomenclature. b Square symbols in Figure 3. c Circle symbols in Figure 3. d Triangle symbols in Figure 3.

Figure 3. Simulation results for productivity and D/F of recycle chromatography versus the mobile-phase flow rate. Solutes are dC, dT, and dA, and the target solute is dA. Open symbols are productivity, and solid symbols are D/F. Squares, circles, and triangles are obtained from the mathematical models in Table 3. Purities of product at the minimum D/F and maximum productivity are listed in Table 4.

flow rate was calculated by dividing 0.01 mL by the flow rate of the mobile phase). To decide the appropriate number of nodes and integration step size, the effect of varying the number of nodes was tested between 2 and 8 nodes/cm and the integration step size was tested between 0.005 and 0.1 mL. Optimization of Recycle Chromatography for Pseudobinary Separations The recycle chromatography system used the optimized recycle method developed for pseudobinary mixtures with linear isotherms.3 Figure 1 shows the migration traces of solutes in the recycle chromatography column and the elution profiles at the column outlet for the optimized condition for most retained solute separation. To overlap the elution bands of nontarget components, one of the separated nontarget components is recycled before or after the feed injection. Normally, a less retained solute has a narrower elution band than a more retained solute when the mass-transfer rate of the less retained solute is lower than or equal to that of the more retained solute (Table 1). Therefore, the less retained nontarget solute was preferred

to be recycled. For example, when the target is the most retained solute, the separated least retained solute (A) was recycled and returned to the column after the feed injection. The injection of recycled A was timed so that A eluted with the intermediate retained solute (B) and the target solute (C) was isolated from the nontarget solutes (Figure 1). Recycling separated nontarget solute reduced desorbent consumption by the recycled amount and the total separation time was shortened because, in a nonlinear competitive system, reused liquid containing nontarget component A helps to desorb solute B. For the least retained solute separation, intermediate retained solute (B) was recycled to elute with the most retained solute (C) and target solute (A) was purified (Figure 2). In this case, because of the wider retention time difference between solutes B and C than between solutes A and B, it is possible to also recycle pure desorbent, which is eluted between the elution bands of the nontarget solutes. However, two recycle streams and tanks are needed to perform this recycle method. In addition, the retention time of the most retained solute is much longer because of the weaker strength of recycled desorbent. By recycling solute B, the elution band of solute B was extended to cover part of the elution band of solute C and solutes B and C were collected together (Figure 2). An iterative numerical method was used to obtain optimum operating conditions for recycle chromatography. The optimized total elution time, the sum of recycle time (tR) and desorbent time (tD), was obtained by matching the simulation results for the rear end of the previously injected most retained solute band and the front end of the newly injected least retained solute band (tr,C - tf,A ) tR + tD, Figures 1 and 2). The optimized feed time (tF) was obtained by matching the simulation results for the rear and front end of the target and neighboring nontarget solute bands (tF ) tf,C - tr,B for most retained solute separation, shown in Figure 1, or tF ) tf,B - tr,A for least retained solute separation, shown in Figure 2). The recycle time and the concentration of each component in the recycle tank can be obtained from the previous simulation. For the calculation of the next operating step, the feed time error (tf,C - tr,B - tF for most retained solute separation or tf,B - tr,A - tF for least retained solute separation) and the elution time error (tr,C - tf,A - tR tD) were considered. Since feed time error and elution time error are dominantly dependent on feed time (tF) and desorbent time (tD), respectively, optimization routines for feed time and

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Table 4. Flow Rates and Simulation Results of Recycle Chromatography for the Separation at the Maximum Productivity and Minimum D/F solute syst

flow rate (mL/min)

dC/dT/dA dG/dT/dA dC/dG/dA dC/dT/dA dG/dT/dA dC/dG/dA

1.196 1.232 1.677 0.308 0.308 0.307

D/F

productivity

purity (%)

yield (%)

18.744 18.685 29.035 8.147 8.016 10.032

99.90 99.94 99.93 99.94 99.94 99.96

99.93 99.88 99.92 99.96 99.93 99.97

2.805 8.623 13.232 1.984 6.440 5.171

99.87 99.88 99.88 99.87 99.89 99.88

99.96 99.96 99.97 99.96 99.96 99.98

(a) Most-Retained Solute Separation max productivity min D/F

12.493 13.794 11.678 6.942 7.620 5.568

(b) Least-Retained Solute Separation max productivity min D/F

dC/dG/dA dC/dG/dT dC/dT/dA dC/dG/dA dC/dG/dT dC/dT/dA

0.929 0.949 1.843 0.508 0.563 0.417

46.355 21.300 24.077 32.826 16.979 11.222

desorbent time can be executed simultaneously. To obtain the front and rear ends of the elution band, two serial batch cycles were simulated and each elution band was obtained for the second batch cycle. For fast and accurate convergence, the last three simulation results of optimization routines were used to obtain the operating conditions of the next simulation by quadratic polynomial interpolation. The following equations were used to obtain the next feed time, and the same method was adopted to obtain the next desorbent time.

{

t+ F,

if |S2tF+ + I2 | e |S2tF + I2 |

tFi+1 ) tF-,

A)

if |S2tF+ + I2 | > |S2tF- + I2 | ,

-B/2A,

if B2 - 4AC e 0

-B + √B2 - 4AC , 2A

S1 - S2 tFi-2

-

tFi

,

tF+ )

tF- )

B ) S1 - A(tFi-2 + tFi-1),

-B - √B2 - 4AC 2A C ) EFi A(tFi )2 - B(tFi )

Sj )

EFi+j-3 - EFi+j-2 tFi+j-3 - tFi+j-2

,

Ij ) EFi+j-3 - SjtFi+j-3

(5)

where EF is the error of the feed time (tf,C - tr,B - tF for most retained solute separation or tf,B - tr,A - tF for least retained solute separation), superscripts i, i - 1, and i - 2 denote the values at the last three iteration steps, and superscript i + 1 denotes the value for next iteration step. To evaluate the convergence of the optimization routine, absolute tolerance for the concentrations of solutes in the recycle tank was 1.0 × 10-4 g/L and relative tolerance for time, |tFi - tFi-1|/tFi , was 1.0 × 10-4. The optimization routine for recycle chromatography converged after 10-20 iterations, and it normally took 3-5 h of calculation time on a Pentium 4 (3.2 GHz) PC. The productivity and D/F of the recycle chromatography is related to the flow rate of the mobile phase at a fixed feed concentration. To explain the occurrence of a minimum D/F, the three mathematical models in Table 3 were solved. Figure 3 shows the changes of productivity and D/F of the recycle chromatography versus the flow rate of the mobile phase for these three models. Purity and yield of the target component are over 99.8%. There are two optimum points for the standard model: One is the maximum productivity which occurs at a high flow rate. The other is the minimum D/F which occurs at a low flow rate. The mathematical models which include mass-transfer resistance between solid and liquid phases (standard and without axial dispersion models) show increased D/F at high flow rates,

and the mathematical models which include the axial dispersion term in the mass balance equation (standard and without mass transfer models) show increased D/F at very low flow rates. In other words, the elution profiles are broadened at high flow rates by the limited mass-transfer rate between the mobile and stationary phases and at low flow rates by axial dispersion.14 If D/F is constant, productivity is proportional to the flow rate of the mobile phase. However, required D/F increases with an increasing rate as a solute band in the column spreads by an increasing flow rate. Eventually, maintaining constant purity with increasing flow rate requires increasing D and reducing F, which reduces productivity. The simulation results for maximum productivity and minimum D/F are presented in Table 4. Approximate Optimization of Simulated Moving Bed Processes Typical four-zone SMB processes use more than four columns because the performance of a four-column four-zone SMB deviates significantly from that of the equivalent TMB process. Because more columns are used in the SMB process, its performance can approach that of the equivalent TMB process. Modification methods such as Varicol,15 Modicon,16 and partial feed17 increase productivity and decrease desorbent consumption when there are few columns. To compare with recycle chromatography, two four-zone SMB processes (one column per zone and two columns per zone) were considered. The main role of zones II and III (above and below the feed) is to separate the mixtures while zone I regenerates adsorbent and zone IV purifies desorbent for recycle. To obtain the optimized operating conditions at a fixed feed flow rate, the flow-rate ratios (ratio of net volumetric flow rate of liquid phase to solid phase) of the equivalent four-zone TMB process were determined from triangle theory.7 These flow-rate ratios are defined as mj )

Qj - εpQS (1 - εp)QS

(6)

where mj is the flow-rate ratio in zone j, Qj and QS are the volumetric flow rates of liquid phase in zone j and of solid phase in TMB, respectively, and εp is the intraparticle void fraction. For “good” separation in zones II and III, the migration velocities of key-separation components (the target component and neighboring nontarget component) were determined. If the absolute velocities of the less retained key-separation component in zone II and the more retained key-separation component in zone III are equal, the internal profiles of key-separation components should move apart with the same velocity. A pair of mII and mIII values which makes the absolute velocity of the

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Figure 4. Changes of optimized D/F for different mIII - mII values (main diagram) obtained from the equal velocity trace on mII - mIII plane (inserted diagram). Solutes are dC, dT, and dA, and the target solute is dA.

less retained key-separation component in zone II equal to the absolute velocity of the more retained key separation component in zone III can be obtained from the following equation:18 mII - (∆qL,II /∆cL,II)max + εT + (1 - εT)(∆qL,II /∆cL,II)max mIII - (∆qM,III /∆cM,III)min )0 εT + (1 - εT)(∆qM,III /∆cM,III)min

(7)

where subscripts L and M represent the less and more retained key-separation components, respectively. Equation 7 was solved by the numerical fixed-point iteration method19 for the competitive Langmuir isotherms. The predicted values of mII and mIII represent an equal Velocity trace. Note that larger differences between mII and mIII will give higher productivity and lower D/F. Figure 4 shows the separation region and the equal velocity trace plotted on the mII-mIII plane for purification of dA. Due to the different mass-transfer rates and axial dispersion coefficients of key-separation components, the operating point on the equal velocity trace is not optimized, but nearly optimal mII and mIII values and good operating conditions can be obtained from the equal velocity trace. Figure 4 also shows D/F values versus mIII - mII for the equal velocity trace. There are upper and lower bounds for mIII - mII to satisfy the separation criteria, purity, and yield of target product. These bounds were obtained from the Aspen Chromatography simulation results and include the mass-transfer effects. When the mIII - mII value is smaller than the minimum, zones I and IV flow rates are too fast to prevent recycling solutes between zone I and IV for the given zone length. When the mIII - mII value is larger than the maximum, zone II and III lengths are not sufficiently long enough to separate the key components because of axial dispersion and mass-transfer resistance. Outside of the permissible range it is impossible to separate key components with the required purity and yield of the target solute. The optimized D/F decreases as the mIII - mII value increases, as shown in Figure 4, and is minimized when mIII - mII is at its maximum. Figure 5 shows the influences of mI and mIV on purity and yield of the target solute, dA, for the dC/dT/dA system. When mI is close to its minimum value calculated from the triangle method9 (mI,min ) 27.7), the most retained solute cannot be perfectly removed from zone I. Since the zone I column is

Figure 5. Simulation results for purity and yield of the target solute versus flow-rate ratios of zone I with constant mIV ()-2) and zone IV with constant mI ()200). Solutes are dC, dT, and dA, and the target is dA. Feed flow rate is 0.0443 mL, mII ) 12.694, and mIII ) 14.396.

moved into zone IV at the next switching time, the yield of the target solute is steeply decreased. However, purity of the target solute is slightly increased as mI moves closer to its minimum because the most retained solute is concentrated as it is recycled from zone I to zone IV. When mIV is close to the maximum value calculated from the triangle method9 (mIV,max ) 2.926), purity of the target solute decreases steeply because of insufficiently regenerated desorbent in zone IV. However, because the purity of nontarget solutes increased slightly, yield of the target solute also slightly increased. A two-step process was used to find approximately optimized operating conditions for a SMB process at a fixed feed flow rate: In the first step, the maximum mIII - mII value was found with sufficiently large mI (∼200) and small mIV (∼-2) values to prevent recycling solutes between zones I and IV. Purity and yield of the target solute is related to the impurity profile at the extract port and the dA profile at the raffinate port, respectively. The maximum mIII - mII value represents the slowest solid phase flow rate (i.e., the longest switching interval in SMB) at a given column length. In the second step, mI and mIV values were optimized while retaining the given target purity and yield of product. Figure 5 shows that for most retained solute separation the purity of the target is dominantly dependent on mI and yield is dominantly dependent on mIV at fixed values of mII and mIII. On the contrary, for the least retained solute separation, purity and yield of the target are dominantly dependent on mIV and mI, respectively. In both cases it is possible to execute the optimization routines for mI and mIV simultaneously. For the optimization of mIII - mII, mI, and mIV the method outlined in eq 5 was used. To evaluate the convergence of optimization routines for zone flow-rate ratios, the absolute tolerance of zone

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flow-rate ratio was set to 10 . To obtain the simulation results of the SMB process at cyclic steady state, the total difference between inflow and outflow was determined at every cycle and the simulation was ended when the absolute value of the total difference was less than 10-6 of inflow. Comparisons of Processes Recycle chromatography and SMB processes with the same total bed height were compared in terms of productivity and D/F. Productivity P and D/F of the recycle chromatography were calculated by the following equations. P)

tFQMCF tCVCεT

D/F )

tD tF

(11)

P)

tC - tR QMCF 1 VCεT D/F - 1 tC

(12a)

This equation for most retained solute purification is P≈ (9)

(10a)

As shown in Figure 1, feed and recycle times for the most retained solute separation are tF ) tf,C - tr,B tR ) tf,B - tf,A

tr,C - tf,B tf,C - tr,B

As shown in eq 11, D/F for most retained solute separation depends on the elution bands of only the key-separation solutes. At the constant flow-rate of the mobile phase and feed concentration of product, productivity is a function of recycle time (tF) and batch time (tC),

(8)

where tF, tC, and tD are the feed, batch, and desorbent times obtained from the simulator results for optimized operating conditions, respectively, QM is the volumetric flow rate of the mobile phase, CF is the feed concentration of the target component, and VC is the column volume. At the optimized operating condition of the recycle chromatography, one batch time can be obtained from the difference between the elution times of the rear end of the most retained solute band and the front end of the least retained solute band (shown in Figures 1and 2). tC - tF ) tR + tD ) tr,C - tf,A

D/F )

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(

Q M CF tf,B - tf,A 1 1VCεT D/F - 1 tr,C - tf,A

)

(12b)

If (tf,B - tf,A) is much smaller than (tr,C - tf,A), and D/F is constant, productivity is almost constant when the least retained solute is changed. For most retained solute separation and the same key-separation solutes (dT and dA), (tf,dT - tf,dG) or (tf,dT - tf,dC) is much smaller than (tr,dA - tf,dG) or (tr,dA - tf,dC). Furthermore, the flow rates of the mobile phase which have the same key-separation solutes are similar to each other (Table 4, dC/dT/dA and dG/dT/dA for most retained solute separation). Consequently, in recycle chromatography for the most retained solute separation of a ternary mixture (aA < aB , aC), productivity and D/F do not change significantly for different least retained solute. For least retained solute purification, eq 9 can be rearranged to D/F )

(tr,C - tf,A) - (tf,C - tf,B) ) tf,B - tr,A (tr,C - tf,C) + (tr,A - tf,A) +1 tf,B - tr,A

(13)

(10c)

D/F for least retained solute purification depends on the bandwidths of the most and least retained solutes. If the keyseparation components are the same, i.e., dC/dG/dA and dC/ dG/dT for least retained solute separation, D/F is strongly dependent on the bandwidth of the most retained solute. The bandwidth of dA is much wider than that of dT because of dA’s small mass-transfer coefficient and long retention time. There-

where tf and tr are the elution times of the front and rear ends of the elution band, respectively, and subscripts A, B, and C represent the least, intermediate, and most retained solutes, respectively. In recycle chromatography, an arbitrary fixed threshold value, 0.5% of the maximum concentration in elution profiles, was used to cut an elution band from outlet concentration profiles. Figure 6 shows the relationship between D/F and productivity for pseudobinary separation by recycle chromatography. For most retained solute separation (Figure 6a), solute systems dC/ dT/dA and dG/dT/dA, which have the same key-separation solutes (dT and dA), have very similar behavior. However, for least retained solute separation (Figure 6b), even though solute systems dC/dG/dA and dC/dG/dT have the same key-separation solutes (dC and dG), the results for productivity and D/F are quite different. This difference can be explained by a characteristic feature of the recycle method. Equation 9 for the most retained solute separation can be rearranged as the following form:

Figure 6. Simulation results for D/F versus productivity in recycle chromatography: (a) Most retained solute separation; (b) least retained solute separation. Purities of product at the minimum D/F and maximum productivity are listed in Table 4.

(10b)

and for the least retained solute separation (Figure 2), feed and recycle times are tF ) tf,B - tr,A tR ) tf,C - tf,B

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Figure 7. Simulation results of D/F and pressure drops versus productivity for recycle chromatography and SMB processes to separate the most retained solute separation. Squares are recycle chromatography, circles are the four-column SMB process, and triangles are the eight-column SMB process.

fore, as shown in Figure 6b, D/F of the dC/dG/dT system is much lower than D/F of dC/dG/dA and productivity of the dC/ dG/dT system is higher than that of dC/dG/dA. When selectivity of the target and neighboring solutes is increased (the dC/dG/ dA system in Figure 6a and the dC/dT/dA system in Figure 6b), D/F is decreased and productivity is increased because of the lengthened feed time and shortened desorbent time. Figures 7 and 8 compare D/F and pressure drop versus productivity curves for recycle chromatography and SMB processes. D/F of the four-column SMB process was at least 2 times larger than D/F of the recycle chromatography for most retained solute purification for all productivity values (Figure 7). For least retained solute purification (dC/dT/dA), the minimum D/F of the four-column SMB process is approximately 15 times larger than the D/F of the recycle chromatography (Figure 8), and the maximum productivity of recycle chromatography is about twice that of the four-column SMB. In addition, the four-column, four-zone SMB process, which has four valve systems between the interconnected columns and three pumps (including the recycle pump, if raffinate and extract streams are controlled by valves), is more complicated than the recycle chromatography, which has two-valve systems at the inlet and outlet of one column, three pumps, and one recycle tank. With two columns per zone in the four-zone SMB (eightcolumn SMB process), mIII - mII of the optimized operating condition is smaller than that of the four-column SMB process. Moreover, mI and mIV are closer to their optimum TMB value than they were for the four-column SMB process. Figure 7 shows that for the most retained solute separation the minimum D/F of the eight-column SMB process (2,2,2,2 configuration) is 1.5-2 times smaller than the minimum D/F of the recycle chromatography, and the maximum productivity of the eight-

Figure 8. Simulation results of D/F and pressure drops versus productivity for recycle chromatography and SMB processes to separate the least retained solute sparation. Squares are recycle chromatography, circles are the fourcolumn SMB process, and triangles are the eight-column SMB process.

column SMB process is larger than the maximum productivity of the recycle chromatography. In the least retained solute

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Table 5. Comparisons of D/F of Recycle Chromatography and Eight-Column SMB Process at the Maximum Productivity of Recycle Chromatography dC/dT/dA a

process

P

dG/dT/dA a

D/F

dC/dG/dA a

P

D/F

P

D/F

18.685 8.162 18.685 19.438

13.794 7.680 4.467 4.464 3.882c

29.035 10.197 29.035 24.107

11.678 5.920 4.224 4.105 3.532c

21.300 16.979 6.768 4.848c

13.232 5.201 13.232 29.170

24.077 11.233 13.036 11.801 9.379c

(a) Most-Retained Solute Separation RCb eight-column SMB

at at at at

RC max P min D/F of RC RC max P min D/F of SMB

at at at at

RC max P min D/F of RC RC max P min D/F of SMB

18.744 8.283 18.744 17.337

TMB

12.493 7.543 4.943 4.872 4.100c

(b) Least-Retained Solute Separation RCb eight-column SMB

2.805 1.894 2.805 -

TMB

46.355 32.826 37.571 15.313c

8.623 6.440 8.623 -

Productivity. b Recycle chromatography. c Obtained from the optimum zone flow-rate ratios calculated from the triangle method, D/Fopt ) (mI,opt mIV,opt)/(mIII,opt - mII,opt). a

separation case, the maximum productivity of the eight-column SMB process is larger than that of the recycle chromatography, but the minimum D/F values are almost identical. In the highproductivity range, D/F of the eight-column SMB process is considerably smaller than D/F for the recycle chromatography. On the other hand, the recycle chromatography system is much simpler than the eight-column SMB process. When many columns are installed in an SMB process, D/F of the SMB process decreases and approaches TMB process performance. Therefore, D/F values obtained from the shortcut method based on the equilibrium theory7911 is the theoretical minimum value with very rapid mass transfer and a large number of columns. Table 5 compares D/F values of recycle chromatography, eight-column SMB, and TMB at the maximum productivity of the recycle chromatography and at minimum D/F values. The D/F values of the eight-column SMB process are close to the minimum D/F obtained from the equilibrium theory. Therefore, a remarkable reduction in D/F is unlikely if more than eight columns are used in the SMB process to separate these pseudobinary mixtures. The pressure drop in the packed column is also an important design parameter. The net pressure drop of SMB processes, the summation of the pressure drop in each column, was compared to the pressure drop of recycle chromatography. For the most retained solute separation (Figure 7), the pressure drop of recycle chromatography is very similar to that of the four-column SMB process even though D/F of the four-column SMB process is larger than D/F of the recycle chromatography. Because D/F for the eight-column SMB is less than D/F of the recycle chromatography, the lower pressure drop of the eight-column SMB is expected. For the least retained solute separation at the same productivity, D/F of the recycle chromatography is between the D/F values of four-column and eight-column SMB processes; as expected the pressure drop of the recycle chromatography is between the pressure drops of the four-column and eight-column SMB processes (Figure 8). The maximum mIII - mII for the eight-column SMB process was larger than that for the four-column SMB process. This means that lower zone flow rates are required in the eight-column SMB process compared to the four-column SMB process at the same feed flow rate. As shown in Figures 7 and 8, pressure drops of the eight-column SMB process are lower than that of the four-

column SMB process at the same productivity (i.e., at the same feed flow rate). Summary For the pseudobinary separation of nucleosides, recycle chromatography composed of one column and one recycle stream was compared to two four-zone SMB processes. In recycle chromatography the separated less retained nontarget component (the least retained solute when the target is the most retained solute or intermediate retained solute when the least retained solute is the target) was recycled to replace solvent and was timed to elute with the other nontarget component. For the most retained solute separation of a ternary mixture (aA < aB , aC), changing the least retained solute has little effect on productivity and D/F. For all pseudobinary separations studied, one-column recycle chromatography has higher productivity and lower D/F than the four-column SMB process, and pressure drops are similar for most retained solute separation. When eight columns were used in a four-zone SMB (2,2,2,2 configuration), D/F of the SMB process approached the ideal minimum D/F of the equivalent TMB process. The eight-column SMB can be operated with lower D/F and higher productivity than the recycle chromatography. However, the onecolumn recycle chromatograph is simpler than both the fourcolumn and eight-column SMB processes. Thus, for pseudobinary separation with competitive Langmuir isotherms, onecolumn recycle chromatography could be better than a fourcolumnfour-zoneSMBprocess.Therefore,recyclechromatography, as well as SMB processes, should be considered for the development of pseudobinary separations, Acknowledgment This work was supported by ERC for Advanced Bioseparation Technology, Inha University, KOSEF, Republic of Korea, and by Purdue University. Nomenclature ai ) Langmuir isotherm parameter of solute i apki ) mass-transfer coefficient of solute i (min-1) bi ) Langmuir isotherm parameter of solute i (L/g) ci ) concentration of solute i in the mobile phase (g/L) CF ) feed concentration of the target component (g/L) De,i ) axial dispersion coefficient of solute i (cm2/min)

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Dp ) particle diameter (µm) EF ) error of feed time (tf,C - tr,B - tF or tf,B - tr,A - tF) (min) L ) column length (cm) mj ) flow-rate ratio in zone j, eq 5 P ) Productivity g of product/L of adsorbent/h, eq 7 ∆P ) pressure drop (psi) qi ) concentration of solute i in the stationary phase (g/L) qi* ) concentration of solute i in the stationary phase at equilibrium with the mobile-phase concentration (g/L) Qj ) volumetric flow rate of liquid phase in zone j (mL/min) QM ) volumetric flow rate of the mobile phase (mL/min) QS ) volumetric flow rate of solid phase (mL/min) tC ) batch time (min) tD ) desorbent time (min) tf ) retention time of front end of elution band (min) tF ) feed time (min) tR ) recycle time (min) tr ) retention time of rear end of elution band (min) u ) interstitial velocity of the mobile phase (cm/min) V ) superficial velocity of the mobile phase (cm/min) VC ) column volume (ml) Greek Symbols ε ) interparticle void fraction of the column εp ) intraparticle void fraction of the column εT ) total void fraction of the column µ ) viscosity of liquid phase (cP)

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ReceiVed for reView January 19, 2009 ReVised manuscript receiVed May 11, 2009 Accepted June 16, 2009 IE900092Y