Extended Standing Wave Design Method for Simulated Moving Bed

design that does not consider mass-transfer effects. According to the impurity wave speeds, zone flow rates and switching time are modified to counter...
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Ind. Eng. Chem. Res. 2000, 39, 1993-2005

1993

Extended Standing Wave Design Method for Simulated Moving Bed Chromatography: Linear Systems Yi Xie, Dingjun Wu, Zidu Ma, and N.-H. Linda Wang* School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907-1283

For simulated moving bed (SMB) systems with significant mass-transfer effects, a model-based design method, which requires accurate mass-transfer parameters, was developed previously (Wu et al. Ind. Eng. Chem. Res. 1998, 37, 4023). An extended standing wave design method is developed in this study and tested using computer simulations and pilot-scale SMB experiments for the separation of phenylalanine (phe) and tryptophan (trp). In this method, propagation speeds of impurity waves are estimated from the effluent histories of SMB runs based on a design that does not consider mass-transfer effects. According to the impurity wave speeds, zone flow rates and switching time are modified to counterbalance the mass-transfer effects. The values of the individual mass-transfer parameters are not needed. High-purity (96-99%) and high-yield (96-99%) products are obtained. This method is simpler than the model-based design method and can be applied when mass-transfer parameters are either unknown or inaccurate. Introduction Simulated moving bed (SMB) chromatography is a simulated counter-current process. In a conventional SMB, four or more columns are connected to form a circuit with two inlets (feed and desorbent) and two outlets (extract and raffinate) as shown in Figure 1. The mixture to be separated is continuously loaded into the SMB through the feed port, while the desorbent is introduced through the desorbent port. For a binary mixture, the fast moving component is collected at the raffinate port, whereas the slow moving component is collected at the extract port. The inlet and outlet ports move periodically along the fluid flow direction to catch up with the migrating bands so that the feed mixture is always added in the region where the two migrating bands overlap, whereas pure products are drawn from the regions where the two bands are separated. The port movement results in a simulated counter-current movement of the columns relative to the ports. To achieve high purity and high yield in SMB, complete separation of the two bands is not needed as in batch chromatography. Therefore, SMB has a significantly lower solvent consumption and higher loading per bed volume (or productivity) than batch chromatography. The four ports divide the circuit into four zones in a conventional SMB. Each zone may have a different number of columns (Figure 1). Zones II and III contain the overlapping region of the two migrating bands. These zones are needed for separation and they are called the separation zones.1-3 Zones I and IV are used to recover the extract and raffinate products3 and to prevent cross contamination, which is caused by the fast moving component entering zone I or the slow moving component entering zone IV. For this reason, zones I and IV are called the buffer zones. SMB was first introduced by UOP in 1968,4 and this technique has been applied for large-scale hydrocarbon * To whom all correspondence should be addressed. Tel.: (765) 494-4081. Fax: (765) 494-0805. E-mail: wangn@ ecn.purdue.edu.

Figure 1. Schematic diagram of an SMB system.

purification5 and high-fructose corn syrup purification.6-9 More recently, SMB has attracted significant research interest in biochemical separations and chiral separations.1-2,10-15 In the design of SMB processes, one of the key issues is the determination of the four zone flow rates and switching time, which are defined as the operating parameters in this study. In this paper, “design” refers to the determination of operating parameters for a given SMB unit with fixed column dimensions and number of columns. Many literature methods for SMB design have been reported. In terms of the mathematical models used in the design, literature methods can be classified into (1) the continuous moving bed or true moving bed (CMB or TMB) approach and (2) the dynamic SMB approach. In the CMB approach, the liquid and solid are considered moving continuously in counter-current directions.3,8,14,16-20 In the dynamic SMB approach, beds remain stationary and the periodic port movement is taken into account.2,15,21-27 In terms of mass-transfer effects, literature methods can be classified into (1) equilibrium designs in which masstransfer effects are neglected and (2) nonequilibrium designs in which mass-transfer effects are considered.

10.1021/ie9905052 CCC: $19.00 © 2000 American Chemical Society Published on Web 05/02/2000

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For the equilibrium designs, the operating parameters are obtained by either including a safety margin factor19,28-29 or finding a triangular separation region3,17-18 as explained in the Theory section. For the nonequilibrium designs in the literature, accurate masstransfer parameters are needed to estimate the operating parameters.1,2,13,20,22,26 This study focuses on how to consider mass-transfer effects in a nonequilibrium design without knowledge of individual mass-transfer parameters a priori. For an SMB system without significant mass-transfer effects, the equilibrium design can achieve high purity and high yield.2 However, in many large-scale SMBs, large sorbent particles (compared with those used in HPLC) are used to decrease pressure drop and reduce equipment cost. Mass-transfer effects are dominant in such low-pressure systems, and nonequilibrium designs are needed. Recently, Ma and Wang2 introduced the standing wave analysis method, which can be applied to both equilibrium and nonequilibrium systems. For linear isotherm systems, a set of algebraic equations has been derived to determine the operating parameters for a desired product purity. This design gives the maximum feed flow rate and the minimum desorbent flow rate for a given SMB unit. On the basis of the standing wave analysis, Wu et al.1 developed a systematic modelbased design procedure for binary separations. However, this design method requires accurate individual masstransfer coefficients. In this study, a simple and practical method to find the operating parameters for low-pressure SMB systems is developed. A mixture of two amino acids, phenylalanine (phe) and tryptophan (trp), is used as a model system. In this method, the partition coefficients of the amino acids, the intraparticle voidage, and the interparticle voidage are estimated first and used to design SMB experiments without considering any masstransfer effects. Transient SMB effluent histories are obtained experimentally to estimate the velocities of impurity waves due to overall mass-transfer effects, which include film mass transfer, intraparticle diffusion, and axial dispersion. Finally, the zone flow rates and switching time are modified to counterbalance the masstransfer effects and to improve yield and product purity. Both simulations and experiments are used to show the validity and feasibility of this method. This design method is simpler than the model-based design.1 It is particularly useful when individual mass-transfer coefficients are unavailable or difficult to estimate. The results show that this method works well for binary systems with linear isotherms. Theory and Design Method Standing Wave Analysis. In SMB systems, individual concentration wave velocities with respect to the ports govern the separation. If the flow rates in the four zones are chosen such that the average port velocity is slower than the migration speed of the low-affinity solute and faster than the migration speed of the highaffinity solute, separation occurs.6 Furthermore, if certain adsorption and desorption waves migrate at the same velocity as the average port velocity, they will remain standing on average over a switching period, and high purity and high yield can be assured.2,6,19-20 This concept of “standing waves” is extended in this study to systems of which mass-transfer parameters are either

inaccurate or unknown. The key equations for the standing wave analysis are briefly discussed below, followed by an explanation of the proposed new method. 1. Equilibrium Design (for Systems without Mass-Transfer Effects). For a linear isotherm system without mass-transfer effects, the propagation speeds of the key waves can be calculated from the solute movement theory30 and matched by the port movement velocity. The following equations can be obtained from the standing wave conditions:

v-

uI0 )0 1 + Pδ2

(1)

v-

uII 0 )0 1 + Pδ1

(2)

uIII 0 v)0 1 + Pδ2

(3)

uIV 0 )0 1 + Pδ1

(4)

v-

where the subscripts 1 and 2 stand for the low-affinity solute (phe in this study) and the high-affinity solute (trp in this study), respectively; the superscripts I, II, III, and IV stand for the four zones; u0 is the interstitial velocity; P is the phase ratio, defined as (1 - b)/b, and b is the interstitial bed voidage; δ is defined as p+(1 - p)K, p is the porosity of the particle, and K is the partition coefficient; and v is the average port velocity ()column length/switching time). This set of equations corresponds to the boundary values of all the feasible zone flow rates and port movement velocity that guarantee complete separation. If a volumetric feed flow rate (Ffeed) is given, the following must be satisfied:

Ffeed II ) uIII 0 - u0 bS

(5)

where S is the column cross-sectional area. For a given feed flow rate, one can easily calculate the zone flow rates ()u0bS) and the port velocity (with which the switching time can be obtained) from eqs 1-5. For systems without mass-transfer effects, the zone flow rates and switching time obtained from eqs 1-5 correspond to the special case solutions of Ruthven and Ching6 or Zhong and Guiochon19 by setting the safety margin factor as unity. The solutions of eqs 1-5 also correspond to the special case solutions obtained from the triangle theory,17 in which (1) the mass flow rate of the adsorbed solute 1 along the adsorbent flow direction is set equal to the net mass flow rate of solute 1 along the fluid flow direction in zone II, and (2) the mass flow rate of the adsorbed solute 2 along the adsorbent flow direction is set equal to the net mass flow rate of solute 2 along the fluid flow direction in zone III. If the operating parameters obtained from eqs 1-5 are applied to an SMB system without any masstransfer effects, then the adsorption and desorption concentration waves are square waves (Figure 2a). The adsorption waves of the low-affinity solute (component 1) and the high-affinity solute (component 2) are standing in zones IV and III, respectively, and the desorption waves of component 1 and component 2 are standing

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Figure 2. Comparison of SMB performance based on the standing wave equilibrium design for systems without and with mass-transfer effects. (a) Schematic column profiles based on the standing wave equilibrium design for a system without mass-transfer effects. Concentration is scaled by the individual component concentration in the feed. Dimensionless concentrations in other figures are defined in the same way. (b) and (c) Simulated transient column profiles of trp (b) and phe (c) at mid-cycles for run 1. Cdi , Cei , Cfi, and Cri are the concentrations within the columns near the desorbent, extract, feed, and raffinate ports (i ) 1 for phe and i ) 2 for trp). Curves a, b, c, and d represent respectively the profiles during the 2nd, 6th, 13th, and 200th switching period. (d) and (e) Simulated impurity breakthrough curves in the raffinate (trp) and in the extract (phe) for run 1. Concentrations are averaged over each switching period.

in zones II and I, respectively. In this way, the lowaffinity solute can be drawn from the raffinate port as one pure product, whereas the high-affinity solute can be drawn from the extract port as another pure product. For a system without mass-transfer effects, pure products can be obtained with an SMB of any zone length as long as the pressure limit of the SMB unit is not exceeded. The dimensionless concentrations in all the figures are obtained by dividing the concentrations by the individual feed concentrations, hence providing a convenient way to

observe any dilution effects under different operating conditions. 2. Nonequilibrium Design (for Systems with Mass-Transfer Effects). In practice, large particles are usually used in low-pressure SMB systems and masstransfer effects are significant in such systems. To obtain high purity and high yield, the mass-transfer effects have to be overcome by modification of the zone flow rates and switching time of the equilibrium design. Ma and Wang2 have derived the following equations for

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a binary system with linear isotherms:

Table 1. Column Properties

( ( ( (

) ) ) )

uI0 βI2 Pv2δ22 I v)E + b2 1 + Pδ2 (1 + Pδ2)LI kI2

(6)

βII Pv2δ21 uII 0 1 II )Eb1 + v1 + Pδ1 (1 + Pδ1)LII kII 1

(7)

uIII βIII Pv2δ22 0 2 III v) E + III 1 + Pδ2 (1 + Pδ )LIII b2 k2 2

(8)

βIV Pv2δ21 uIV 0 1 IV ) E + 1 + Pδ1 (1 + Pδ )LIV b1 kIV 1 1

(9)

v-

where L is the zone length; Eb is the axial dispersion coefficient; k is a lumped mass-transfer parameter and is defined as

1 R2 R ) + ki 15pDpi 3kfi

(i ) 1, 2)

(10)

where R is the radius of the resin particle; Dp is the intraparticle diffusivity; kf is the film mass-transfer coefficient. β is the natural logarithm of the ratio of the highest concentration to the lowest concentration of a standing wave in a particular zone (Figure 2b,c):

βI2 ) ln

βII 1

) ln

βIII 2 ) ln

βIV 1

) ln

Ce2

(11)

Cd2 Cf1

(12)

Ce1 Cf2

(13)

Cr2 Cr1

(14)

Cd1

Notice that the individual concentrations are not needed to estimate the β values. Instead, the β values are set in a design according to desired product purities. By assuming that the ratio of Cf2/Cf1 remains the same as IV I III that of the feed and letting βII 1 ) β1 and β2 ) β2 , one can relate β values to purity as follows:

[ ( [ (

βI2 ) βIII 2 ) -ln

)] )]

1 -1 Pr2

(15)

1 1 -1 RF Pr1

(16)

IV βII 1 ) β1 ) -ln RF

where RF is defined as the feed concentration ratio of component 2 to component 1. Pr2 is the purity of component 2 in the extract and Pr1 is the purity of component 1 in the raffinate. Therefore, β is an index of product purity and yield; the larger the β value, the higher the product purity and yield.1-2 If RF equals

LPLC SMB 1 SMB 2

length (cm)

i.d. (cm)

t

b

p

resin size (diameter, µm)

12.3 76.2 68.6

1.5 2.54 2.54

0.714 0.728 0.728

0.370 0.400 0.400

0.546 0.546 0.546

300-425 250-595 250-595

unity, a target purity of 99% for both products will IV 1 III require βII 1 ) β1 ) β2 ) β2 ) 4.6. If the zone length, L, is infinite, or Eb approaches zero and k approaches infinity (i.e., the mass-transfer effects are negligible), then eqs 6-9 reduce to eqs 1-4 (equilibrium design). A comparison of the two sets of equations shows that the nonequilibrium design is a modification of the equilibrium design. In the original nonequilibrium design reported by Ma and Wang,2 accurate mass-transfer parameters (Eb, k) are needed (eqs 6-9). In this study, a new nonequilibrium design method is proposed to modify zone flow rates and switching times to counterbalance masstransfer effects without the individual values of Eb and k as explained below. Overall Mass-Transfer (OMT) Design Method. If the operating parameters for a system with large masstransfer effects are chosen on the basis of the equilibrium design equations (eqs 1-5), low product purity and yield result. This is shown in parts b and c of Figure 2, which are simulated column profiles of phe and trp using the operating parameters obtained from the standing wave equilibrium design (eqs 1-5). The column profiles in Figure 2b,c and other column profiles shown later are recorded at mid-cycle. This simulation and others, which will be shown later, are obtained using a computer program based on a dynamic SMB model.2 The computer program has been benchmarked and validated using the data from sugar separations2,31 and amino acid separations.1 The column properties are listed in Table 1 (SMB 1) and the zone flow rates and switching time are listed in Table 3 (run 1). The numerical parameters and mass-transfer coefficients used in these simulations are listed in Table 2. Eb’s are estimated from the Chung and Wen correlation,32 kf’s are estimated from the Wilson and Geankoplis correlation,33 Dp’s are obtained from the previous study,1 and k’s are estimated from eq 10. The numerical parameters and correlations for mass-transfer coefficients have been reported previously.1 Notice that simulations are used only to validate the design procedure developed in this study. The design itself is independent of the simulation results. As shown in Figure 2d,e, the system reaches cyclic steady state within 3000 min. The last column profiles shown in Figure 2b,c are recorded at the 200th cycle or 6400 min. As shown in Figure 2b,c, the concentration drop between zones II and III decreases with time, but it does not disappear at cyclic steady state. The oscillations in zone II near the feed port occur as a result of a recent port switch. As the feed port advances by one column length downstream, another concentration discontinuity is created downstream, leaving behind the previous discontinuities as the oscillations in zone II. This phenomenon is not unique to this system. It is also found elsewhere in the literature.15,24,26 If there are no mass-transfer effects and the zone flow rates and switching time are determined by the standing wave equilibrium design (eqs 1-5), the impurities will never reach the outlets (Figure 2a) and no impurity

Ind. Eng. Chem. Res., Vol. 39, No. 6, 2000 1997 Table 2. Partition Coefficients (298 K), Mass-Transfer Parameters, and Numerical Simulation Parameters partition coefficients phe 1.61 trp 10.7 mass-transfer parameters run 1

run 2

run 3

run 4

1.76 0.571 1.76 0.571

0.889 0.288 0.889 0.288

phe trp

0.655 0.655

Dp × 0.655 0.655

0.655 0.655

zone I zone II zone III zone IV

1.17 1.15 1.17 1.15

zone I zone II zone III zone IV

1.12 0.524 1.12 0.524

1.73 0.524 1.12 0.322

0.655 0.655

0.655 0.655

1.16 1.15 1.16 1.15

1.17 1.15 1.16 1.14

(Pv2δi2/ki) (cm2/min)a 457 54.0 131 25.8 3.04 7.35 457 54.0 131 26.0 3.04 7.35

129 7.35 131 7.42

104 (cm2/min)

zone I zone II zone III zone IV

212 12.1 212 12.1

k (min-1) 1.17 1.16 1.16 1.14 1.17 1.16 1.15 1.14

numerical parameters axial elements

collocation points

∆t (min)

relative tolerance

200

3

0.002

0.01%

In zones I and III, i ) 2 (trp), whereas in zones II and IV, i ) 1 (phe). a

Table 3. SMB Unit, Design Methods, and Operating Parametersa run 1 SMB 1

run 2

run 3

run 4

SMB Unit SMB 1 SMB 2 SMB 2

Design Method equilibr. OMT equilibr. zone I zone II zone III zone IV

(17)

uII 0 ) -MII v1 + Pδ1

(18)

v-

uIII 0 ) MIII 1 + Pδ2

(19)

v-

uIV 0 ) MIV 1 + Pδ1

(20)

run 4*

(cm2/min)

Eb 3.15 0.966 2.14 0.632

uI0 ) -MI 1 + Pδ2

v-

run 4* b run 4** c SMB 2

SMB 2

OMT

OMT

44.1 14.1 44.1 14.1

Zone Flow Rates (mL/min) 80.3 22.0 27.9 24.0 7.0 12.9 54.0 22.0 27.9 15.6 7.0 12.9

43.4 12.9 27.9 7.9

84.3 23.2 38.2 10.7

32.0

Switching Time (min) 21.8 57.6 36.9

36.9

22.0

a

The feed flow rate is 30 mL/min for runs 1 and 2 and 15 mL/ min for runs 3, 4, 4*, and 4**. b Run 4* followed run 4 after 17 switches (627 min) of run 4. c Run 4** followed run 4 after 17 switches (627 min) of run 4. Run 4** is a virtual experiment done by simulation.

breakthrough will occur. However, when the standing wave equilibrium design is applied to a system with significant mass-transfer effects, the concentration waves of phe and trp are spread, causing the high-affinity (trp) and low-affinity (phe) solutes to appear as impurities in the raffinate and extract, respectively (parts b and c in Figure 2). The impurity concentrations averaged over one switching period increase monotonically with time and then level off at cyclic steady state (Figure 2d,e). The velocities (relative to the ports) of the impurity migration, which is due to mass-transfer effects, can be estimated from the impurity breakthrough curves and used to improve the equilibrium design. Equations 6-9 for the nonequilibrium design can be rewritten as follows:

Observing eqs 17-20, one can find that the M terms, which are related to the mass-transfer parameters, have the units of linear velocity. In the nonequilibrium design, to prevent the impurity waves from reaching the product ports, the average port velocity relative to the standing wave velocities in the absence of mass-transfer effects (which are approximately the wave center velocities in the presence of mass-transfer effects) are increased by MIII and MIV respectively for zones III and IV and decreased by MI and MII respectively for zones I and II. In the standing wave nonequilibrium design reported previously,1,2 the corrections to the equilibrium design are calculated from the individual values of β, P, δ, L, Eb, and k (right-hand side of eqs 6-9). The masstransfer parameters (Eb and k) need to be estimated from fixed-bed chromatography experiments.1 In this study, we propose to estimate the M terms directly from the impurity breakthrough curves of SMB experiments without using the individual mass-transfer coefficients. Once the M terms are known, the zone flow rates and switching time can be recalculated from eqs 5 and 1720. The product purity and yield will increase if the new operating parameters with the corrections for masstransfer effects are applied to the original SMB system. Because this design procedure involves a direct estimation of the overall mass-transfer effects, this method is called the overall mass-transfer (OMT) design method. The key of the OMT design is the estimation of the M terms in eqs 17-20 from an experiment with the zone flow rates and switching time determined from the standing wave equilibrium design (eqs 1-4). To obtain the impurity migration velocities relative to the feed port, the distances and corresponding times are needed. The maximum distance for the high-affinity solute (trp) traveling from the feed port to the raffinate port is LIII. Similarly, the maximum distance for the low-affinity solute (phe) traveling from the feed port to the extract port is LII. The impurity breakthrough time depends on the target impurity level, which is defined as the ratio of the desired impurity concentration to its cyclic steadystate value. For example, if the target impurity level is chosen as 0.5 (Figure 2d,e), then the impurity breakthrough time (tR2 in Figure 2d and tE1 in Figure 2e) is the time corresponding to the impurity concentration which is one-half the concentration at cyclic steady state. From the migration distance and time, the migration velocities (M terms) can be estimated,

MII )

LII tE1

(21)

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MIII )

LIII tR2

(22)

However, MI and MIV cannot be estimated in the same way as MII and MIII. To obtain MI and MIV, the zone length should be taken into account. As discussed previously, if the zone is infinitely long, then the nonequilibrium design equations (eqs 6-9) reduce to the equilibrium design equations (eqs 1-4). This indicates that the zone length affects the corrections to the equilibrium design. The longer the zone length, the smaller the corrections needed. Equations 6-9 provide the theoretical basis for determining MI and MIV. Comparing eq 6 with eq 8, one can find that if βI2 ) βIII 2 , I III Eb2 ) Eb2 , and kI2 ) kIII 2 , then the following relation can be derived:

MI ) MIII

LIII LI

(23)

Following the same reasoning, one can derive the expression for MIV:

M

IV

)

LII MII IV L

(24)

The OMT design procedure can be summarized as follows: 1. Estimate the partition coefficients (Ki) of the system of interest, the bed voidage (b) of the column, and the particle porosity (p). 2. Obtain the zone flow rates and switching times for a given SMB unit and a fixed feed flow rate from the standing wave equilibrium design (eqs 1-5) and run an SMB experiment. 3. Estimate the M terms from the impurity breakthrough curves (eqs 21-24). 4. From the estimated M terms, recalculate the zone flow rates and switching time at the same feed flow rate using eqs 5 and 17-20. In principle, even without accurate mass-transfer parameters, the mass-transfer effects could be reduced by adjusting β in the standing wave nonequilibrium design. However, one could not know how much adjustment in β is needed for a desired product purity. Trial and error will be needed to reach a target purity. By contrast, the OMT design provides a procedure to obtain the exact amount of correction (M terms) to counterbalance the mass-transfer effects. Furthermore, in a production-scale SMB process, the effluent histories at the product ports are usually available. This information can be exploited in the OMT design to improve purity and yield. This method, unlike the model-based design method,1 does not require any fixed-bed chromatography experiments for estimation of mass-transfer parameters. In the aforementioned procedure, the overall masstransfer effects are estimated from the experiments based on the standing wave equilibrium design and this information is used to improve the equilibrium design. In all cases, the zone flow rates and port velocity are increased so that the average port velocity is smaller than the wave velocities in zones I and II but larger than the wave velocities in zones III and IV. If axial dispersion is the dominant mass-transfer mechanism, the overall mass-transfer effects can increase with increasing zone flow rates and several iterations may

be needed to achieve the target purity. However, in many low-pressure systems intraparticle diffusion is usually the controlling mass-transfer mechanism, which is unaffected by changes in zone flow rates. Therefore, the aforementioned design procedure can be applied to such low-pressure SMB systems. Whether axial dispersion or diffusion is dominant can be judged from eqs 6-9. The Eb terms on the right-hand sides are due to axial dispersion effects, whereas the terms including k are mainly due to diffusion effects. According to eq 10, the contribution of film mass transfer to the overall resistance is negligible in this low-pressure system. The values of the diffusion term and the axial dispersion term for the SMB systems studied are compared in Table 2. The diffusion term is at least an order of magnitude higher than the axial dispersion term for each zone in all the experiments. Therefore, diffusion is the dominant mass-transfer mechanism and the corrections to the equilibrium design due to axial dispersion are negligible in the systems studied. Experimental Section Materials. HPLC-grade phenylalanine (phe) and tryptophan (trp) were purchased from Sigma Chemical Co. (St. Louis, MO). Pure ethanol was purchased from McCormick Distilling Co. (Weston, MA). Distilled deionized water (DDW) was obtained through a Milli-Q system by Millipore (Bedford, MA). Blue dextran was also purchased from Sigma Chemical Co. HPLC-grade acetonitrile was purchased from Fisher Scientific (Fairlawn, NJ). REILLEX HP Polymer (PVP) from Reilly Industries Inc. (Indianapolis, IN) was chosen as the sorbent for amino acid separation. Equipment. A Pharmacia (Piscataway, NJ) fast protein liquid chromatography (FPLC) system was used in the low-pressure liquid chromatography (LPLC) experiments. This system consists of two pumps (Pharmacia P-500), a liquid chromatography controller (Pharmacia LCC-500), an injection valve (Pharmacia MV-7), and a fraction collector (Pharmacia Frac-100). Data monitoring and collection were handled by a photodiode array detector (Waters 990) with data collection software. The samples from SMB chromatography were analyzed using HPLC. This HPLC system consists of two pumps (Waters 510), a tunable single wavelength detector (Waters 486), and an injector (Waters U6K). Waters Millenium 2010 software operated in a Windows environment was used for data collection and analysis. A pilot-scale SMB Mini-ADSEP from U.S. Filter (Rockford, IL) was used in all SMB experiments. Because this unit has been described in detail previously,1 only a brief description is given here. The SMB consists of 10 columns. The configuration of the 10 columns is 2-3-3-2, which means there are two columns in zone I, three columns in zone II, three columns in zone III, and two columns in zone IV, respectively. The flow rates of the feed, desorbent, extract, and raffinate streams are controlled by singlepiston positive displacement pumps. The flow rates are highly reproducible and are controlled to within (1%. Procedure. 1. LPLC Column Characterization. An analytical LPLC glass column with an inner diameter of 1.5 cm was used to determine the partition coefficients between the resin and the amino acids. A slurry packing method was used to pack sieved PVP

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resin (diameter 300-425 µm) into the column to achieve a packing length of 12.3 cm. Three bed volumes of pure ethanol were fed into the column at 1 mL/min, followed by washing with 10 bed volumes of DDW. The resin was washed with 5 bed volumes of 0.1 M HCl, followed by 5 bed volumes of 0.1 M NaOH. Finally, DDW was used to elute NaOH. After the resin treatment, the column properties were determined. A pulse of blue dextran was introduced into the column pre-equilibrated with 100% ethanol. From the retention time of the blue dextran pulse, the interparticle voidage of the bed (b) was estimated. The total voidage of the column (t) was obtained from a DDW breakthrough curve from the column pre-equilibrated with 100% ethanol. The resin porosity (p) was then calculated from b and t. 2. Determination of the Partition Coefficients of the Amino Acids. The multifrontal method34 was employed to determine the partition coefficients. The batch equilibrium method was used to check the partition coefficient of trp (see ref 1 for details). In the multifrontal experiments, the LPLC system and the aforementioned analytical column were used. The procedure is as follows: before the multiple breakthroughs, the column was washed and equilibrated with DDW. Then a series of solutions of phe or trp were introduced into the column in a sequence of low to high concentrations. Once the column was saturated, the mobile phase was changed to a more concentrated solution. On the basis of a mass balance, one can calculate the amount of solute adsorbed at equilibrium at each feed concentration. 3. Separation of a Mixture of Phe and Trp by SMB Chromatography. a. HPLC Assay. HPLC was used to determine the concentrations of the samples collected from the extract and the raffinate in SMB experiments. A Waters Nova-Pak C-18 HPLC column was used. The flow rate of the mobile phase (H2O: CH3CN ) 4:1 v/v) was 0.5 mL/min, and the sample injection volume was 5 µL. The column effluent was monitored at the wavelength of 260 nm. The mobile-phase solution was degassed for about 30 min prior to use. The analysis time was about 10 min/sample. The HPLC assay for phe and trp is accurate to within (0.01 mg/mL. b. Operation of SMB. The 10 columns in the SMB were packed with PVP resin (diameter 250-595 µm) using the slurry packing method. DDW was chosen as the desorbent. Before each SMB experiment, the flow rates of the feed, desorbent, and extract pumps were set manually and were checked periodically during the experiment to ensure accuracy. Four SMB experiments were performed. The zone flow rates and switching times of these four runs are listed in Table 3. Samples were collected at the extract and raffinate outlets. During runs 1 and 2 each sample was collected from the extract and the raffinate over an entire switching period (between two switches). The concentration of each sample represents the average concentration over a switching period. For runs 3 and 4, samples (