Ind. Eng. Chem. Res. 1998, 37, 4023-4035
4023
Design of Simulated Moving Bed Chromatography for Amino Acid Separations D.-J. Wu, Y. Xie, Z. Ma, and N.-H. L. Wang* School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907-1283
A systematic design method was used to develop a pilot-scale simulated moving bed (SMB) process for the fractionation of two amino acids, tryptophan and phenylalanine. In this method, isotherms were estimated using both frontal chromatography and batch equilibrium methods, and mass-transfer parameters were estimated using frontal chromatography data. SMB experiments were then conducted using the zone flow rates and port velocity calculated from a theoretical analysis without considering mass-transfer effects (an equilibrium design). The estimated parameters were validated with computer simulation and SMB data based on the equilibrium design. A design considering mass-transfer effects (a nonequilibrium design) was then obtained from the standing wave analysis and tested experimentally. The effluent histories at the extract, raffinate, and sampling ports agreed with those from computer simulations. A sensitivity analysis shows that accurate isotherms, intraparticle diffusivities, and bed voidage are important for the SMB design, and the nonequilibrium design is more robust than the equilibrium design. Various column configurations were compared in terms of throughput and desorbent consumption. Introduction Amino acids are important biochemicals for protein synthesis and metabolic regulations. Conventionally, amino acids are separated by means of batch ionexchange chromatography (Dechow, 1989), which is less efficient than simulated moving bed (SMB) chromatography for industrial-scale production. In SMB chromatography, a series of adsorbent columns are connected to form a circuit. The circuit is divided into four zones by two inlet ports (feed and desorbent) and two output ports (extract and raffinate) (Figure 1a). The four ports are periodically moved along the desorbent flow direction to follow the migrating bands and draw pure products. Because part of the desorbent and the unseparated solutes are automatically recycled within the circuit, SMB chromatography can achieve higher yield and lower desorbent consumption than conventional batch chromatography. SMB chromatography has been used for large-scale hydrocarbon purification (Broughton, 1961, 1968) and high fructose corn syrup purification (Barker and Joshi, 1991). Studies on chiral separations and many others have also been reported (Ching et al., 1993; Nicoud et al., 1993; Kusters et al., 1995; Pais et al., 1997; Ruthven and Ching, 1989). A successful design of SMB chromatography depends on the proper selection of the four zone flow rates, the four zone lengths, and the port movement velocity. To achieve separation in SMB, the flow rates in the four zones have to be chosen such that the slow-moving solute moves toward the extract port and stays within zone III and the fast-moving solute moves toward the raffinate port and stays within zone II (Figure 1a). In the literature, the operating parameters are usually derived from the equilibrium theory, assuming negli* To whom correspondence should be addressed. E-mail:
[email protected]. Tel.: (765) 494-4081. Fax: (765) 4940805.
Figure 1. (a) Schematic diagram of a four-zone SMB system. (b) Standing waves for run 2 obtained from simulation. Solid lines, solute 1, phenylalanine; dashed lines, solute 2, tryptophan.
gible mass-transfer resistances (Ruthven and Ching, 1989; Ching et al., 1992; Storti et al., 1989, 1993, 1995; Adachi, 1994; Pais et al., 1997; Zhong and Guiochon, 1996). The resulting design, when applied to a system with significant mass-transfer resistances, cannot guarantee high product purities; it can only serve as an
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4024 Ind. Eng. Chem. Res., Vol. 37, No. 10, 1998
Theory: Standing Wave Design and Simulations
Figure 2. Model-based design for SMB systems.
initial guess for further refinement with iterative numerical simulations. In a recent study by Ma and Wang (1997), a standing wave analysis was developed for the design of continuous moving bed (CMB) systems with linear isotherms. This analysis is based on the idea that there should be four standing concentration waves in CMB to ensure the required product purities (Figure 1b). For linear systems, the analysis gives a set of simple algebraic equations which explicitly link product purities to the four zone flow rates, four zone lengths, switching time, isotherms, and mass-transfer coefficients. If column dimensions, zone lengths, and product purities are given, then the standing wave design gives the maximum feed flow rate and the minimum desorbent flow rate. The goal of this study is to establish a systematic method for SMB process design for linear isotherm systems. The separation of two amino acids, phenylalanine and tryptophan, is used as an example. An efficient model-based design approach (Figure 2) is used to reduce trial and error and a significant number of experiments for process development and scale-up. In this method, a selective resin and an efficient desorbent are first identified from preliminary screening. Adsorption isotherms and intraparticle diffusivities for both solutes are then estimated from batch equilibrium experiments, multiple frontal experiments, and a smallscale pulse test. These intrinsic parameters are used in the standing wave analysis to find proper operating parameters for pilot-scale SMB chromatography. SMB experiments are then carried out to validate the parameters. After validation, the parameters are used in computer simulations to explore various design alternatives. A sensitivity analysis is used to identify the important parameters which control product purities and yield. Our results show that the standing wave analysis can be used successfully to design SMB to obtain high yield and high product purity for the separation of phenylalanine and tryptophan. The experimental effluent histories and time profiles are in close agreement with the simulations based on the isotherms, which are obtained from multiple frontal and batch equilibrium tests, and the mass-transfer parameters obtained from multiple frontal tests. In the pilot-scale SMB system, intraparticle diffusion is the major mass-transfer resistance and has significant effects on product purities. The configurations with either the highest throughput or the lowest desorbent consumption are also found using computer simulations.
For a four-zone CMB system, the standing wave analysis shows that, by proper choices of the four zone flow rates and port switching time, the adsorption wave (front) of the fast-moving solute can remain stationary (or stand) in zone II and the desorption wave (tail) can stand in zone IV (Figure 1b). Similarly, the adsorption wave of the slow-moving solute should stand in zone I and its desorption wave in zone III (Figure 1b). Zones I and IV (the separation zones) are used to achieve partial separation of the two solute bands, while zones II and III (the buffer zones) are used to prevent cross contamination. To keep the required concentration waves stationary, the flow rate in each zone and the port switching velocity can be found for both equilibrium systems (without mass-transfer effects) and nonequilibrium systems (with axial dispersion and masstransfer resistances). The details of the standing wave analysis can be found in a previous paper (Ma and Wang, 1997). Only a brief summary is given below. As shown in the previous paper, these equations originally developed for CMB systems can also be applied for SMB systems with a sufficiently large number of columns. Design Equations under Standing Wave Conditions. (i) Equilibrium Design. There are infinite combinations of zone flow rate and port movement velocity (switching time) which guarantee separation in a given system. Among these, the optimal zone flow rate and port movement velocity that give the highest throughput and the lowest desorbent consumption at a given purity can be found from the standing wave analysis. According to the analysis, the waves of fastmoving solute (solute 1) should stand in zones II and IV, while slow-moving solute (solute 2) should stand in zones I and III (Figure 1b). To achieve the four standing waves, the following equations should be satisfied in equilibrium systems with negligible axial dispersion and other mass-transfer effects:
uI0 ) (1 + Pδ2)ν
(1)
uII 0 ) (1 + Pδ1)ν
(2)
uIII 0 ) (1 + Pδ2)ν
(3)
uIV 0 ) (1 + Pδ1)ν
(4)
Ffeed ) uI0 - uIV 0 bS
(5)
Fdes II ) uIII 0 - u0 bS
(6)
where u0 is the interstitial velocity, ν g 0 is the averaged velocity of port movement along the direction of the desorbent flow, S is the column cross-sectional area and is usually fixed, δi (≡p + (1 - p)ai) is the capacity factor (ai is the partition constant between the adsorbed phase and the liquid phase for solute i at an infinitesimal concentration), P (≡(1 - b)/b) is the bed phase ratio, b is the interstitial bed void fraction, Ffeed is a feed flow rate, and Fdes is a desorbent flow rate. From this set of equations, the four zone flow rates and the port movement velocity can be determined for a given system and a given Ffeed (five equations, eqs 1-5,
Ind. Eng. Chem. Res., Vol. 37, No. 10, 1998 4025 III IV with five unknowns, uI0, uII 0 , u0 , u0 , and ν). As such, eq 6 defines the lowest desorbent flow rate because uII 0 is the highest and uIII 0 is the lowest among all the feasible designs that guarantee separation (Ma and Wang, 1997). Since no mass-transfer effects are present in an equilibrium system, the concentration waves are square waves with infinitely sharp boundaries. Since there is no dispersion, pure products at both output ports can be obtained for any zone length and without any limit on feed flow rate or throughput. Theoretically, the feed flow rate can be as high as the equipment allows. By contrast, for nonequilibrium systems, there exists a maximum feed flow rate that is a function of zone lengths, product purities desired, isotherms, and masstransfer parameters, as explained below. (ii) Nonequilibrium Design. In the model-based design approach, eqs 1-6 are used for an initial design when there is insufficient information about masstransfer parameters or when there is no high-purity requirement. In practice, mass transfer is usually important and cannot be neglected. In systems with significant mass-transfer resistances (nonequilibrium systems), eqs 1-4 have to be modified to take into account the mass-transfer effects. The complete solutions of the linear velocities for the four zones can be found from the following equations (Ma and Wang, 1997):
uIν ≡ (1 + Pδ2)ν - uI0 ) βI2
II uII ν ≡ (1 + Pδ1)ν - u0 )
( (
EIb2 I
+
L
( (
EIII b2
III III uIII ν ≡ (1 + Pδ2)ν - u0 ) -β2
IV IV uIV ν ≡ (1 + Pδ1)ν - u0 ) -β1
KIf2LI
L
EII b1 II β1 II
LIII
EIV b1 LIV
) )
Pν2δ22
+
Pν2δ21 II KII f1L
+
+
(7)
(8)
Pν2δ22
)
III KIII f2 L
Pν2δ21
)
IV KIV f1 L
(9)
(10)
where L is the zone length, Eb is the axial dispersion coefficient, Kf is the lumped mass-transfer coefficient, and β is related to the ratio of the highest concentration to the lowest concentration of the standing wave in the specified zone. βI2, for example, is the natural logarithm of the ratio of the concentration at the feed port to that at the raffinate port for solute 2 (Figure 1b). It is used as an index of product purity and recovery; the higher the concentration ratio, the higher the product purity and recovery. If the product is phenylalanine in the raffinate, the purity is defined as
% purity ≡
(
Craf Phe
raf Craf Phe + CTrp
)
× 100%
(11)
raf where Craf Phe and CTrp are the concentrations at the raffinate port for phenylalanine and tryptophan, respectively. If product purities and column cross-sectional area (S) are specified and a feed flow rate is given, eqs 7-10 and eq 5 can be used to find the four linear velocities and the port movement velocity. These equations define
the standing wave conditions when both Eb and Kf are significant. Also, they define the maximum linear velocities for zones I and II and the minimum linear velocities for zones III and IV for a system with linear isotherms. Any lower velocities in zones I and II and higher velocities in zones III and IV result in better than specified product purities and recoveries. However, such designs will have lower throughput and/or higher desorbent consumption than the standing wave design. To have a physically meaningful solution for ν when I IV I IV KIf1 ) KIV f2 ) Kf, Eb2 ) Eb1 ) Eb, and L ) L , β must satisfy the following condition (Ma and Wang, 1997):
( )(
P(R - 1)2 - 4β
)
R2 + 1 Ffeed 2βEb g 0 (12) + Kf bSL L2
where R ≡ δ2/δ1 is the capacity factor ratio. This equation implies that there is a trade-off between β and Ffeed for a given system. Furthermore, if the capacity factor ratio (R), the phase ratio (P), the zone length (L), the mass-transfer parameters (Kf and Eb), and the product purities (β) are given, eq 12 can be used to calculate the maximum feed flow rate by letting the lefthand side of the equation be zero. Equations 7-10 and eq 5 can then be used to get the operating parameters. These equations can also be used to find either the maximum throughput or the minimum desorbent consumption, which are defined in the following equations:
throughput ) Ffeed/V
(13)
desorbent consumption ) Fdes/FfeedC0i
(14)
where V is the total bed volume and C0i is the concentration of solute i (product) in the feed. In this study, both the total bed volume and C0i are kept constant. The higher the feed flow rate, the higher the throughput. The higher the ratio of desorbent flow rate to feed flow rate, the higher the desorbent consumption. Numerical Simulations. The numerical simulations are performed using an algorithm for SMB systems which has been described in detail elsewhere (Ma and Wang, 1997). A lumped mass-transfer model is employed because linear systems are considered in this study. For linear systems, our recent studies have shown that the lumped model gives essentially the same results as the more detailed porous models (Wu et al., 1998). The lumped model has the advantages of simplicity, fast implementation, and short simulation time. The simulations are used here to validate the intrinsic parameters, to gain fundamental understanding of the effects of various systems and operating parameters, and to find optimal designs. In the lumped model, the following correlation is used to estimate the lumped mass-transfer coefficient Kf (Ma and Wang, 1997):
R2 R 1 ) + Kf 15pDp 3kf
(15)
where R is the sorbent particle radius, Dp is the effective intraparticle diffusivity and can be found from pulse or frontal tests, and kf is the film mass-transfer coefficient and can be found from the correlation of Wilson and Geankoplis (1966). Since kf changes with flow rate, Kf can have a different value at different flow rates. The
4026 Ind. Eng. Chem. Res., Vol. 37, No. 10, 1998 Table 1. Typical Properties for the PVP Resin (from Reilly Industries, Inc.) appearance solubility
white to beige spherical beads insoluble in water, acids, bases, and organic solvents flash point >300 °F BET surface area 60 m2/g total pore area 108 m2/g media pore diameter (volume av) 600 Å bulk density 0.53 g/mL porosity 55.0% loss on drying 53.0% backwashed and settled density 38.5 lb/ft3 true density (wet absolute) 1.07 g/mL void volume 43.0%
Eb in eqs 7-10 and 12 can be estimated from the Chung and Wen correlation (1968) or from experimental data. Experimental Section Materials. HPLC grade acetonitrile was purchased from Fisher Scientific (Fairlawn, NJ). Pure ethanol was purchased from McCormick Distilling Co. (Weston, MA). Ethanol was degassed prior to use by sonicating in a ultrasonic bath from Cole-Parmer Instrument Co. (Vernon Hill, IL). Distilled deionized water (DDW) was obtained through the use of a Milli-Q system by Millipore (Milford, MA). All solvents used were filtered through 0.2-µm Nylon 66 filters that were purchased from Alltech (Deerfield, IL). Blue dextran was purchased from Sigma Chemical Co. (St. Louis, MO). Two amino acids, L-phenylalanine (MW 165) and L-tryptophan (MW 204) with 98% minimum purities (TLC), were also purchased from Sigma Chemical Co. The PVP resin (poly-4-vinylpyridine cross-linked, Reillex HP polymer) used in the experiments was purchased from Reilly Industries, Inc. (Indianapolis, IN). This resin was chosen because it is stable, easily regenerable, and commercially available. Its other properties are listed in Table 1, taken from the manufacturer’s technical information. The batch columns were Omni low-pressure borosilicate glass columns (Alltech, Deerfield, IL) with one fixed end and one adjustable end fitting, allowing for different column lengths. One batch column (PVP-A, 1.5 cm in diameter and 12.3 cm in length) was used for isotherm measurement. Another batch column (PVP-B, 2.54 cm diameter and 43 cm in length) was used for mass-transfer measurement. The 10 SMB columns have equal dimensions (2.54 cm in diameter and 76.2 cm in length). A Waters Nova-Pak C-18 column (60 Å, 4 µm, 3.9 mm × 150 mm) was purchased from Millipore Corp. (Milford, MA) and used to determine the concentrations of both phenylalanine and tryptophan. Instrumentation. The HPLC system consists of two pumps (Waters 510), a tunable single-wavelength detector (Waters 486), and an injector (Waters U6K). Waters Millennium 2010 software operated in a Windows environment was used for data collection and analysis. A Pharmacia (Piscataway, NJ) fast protein liquid chromatography (FPLC) system was used in the batch chromatography. 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 using a photodiode array detector (Waters 990) and accompanying data collection software.
Figure 3. (a) Pilot-scale SMB equipment (Mini ADSEP). (b) Rotary valve for each column.
A pilot-scale SMB unit (Mini ADSEP) was provided gratis by U.S. Filter Co. (Rockford, IL). It consists of 10 stainless steel columns and six single-piston positive displacement pumps (Figure 3a): one for feed, one for desorbent, one for raffinate, one for extract, and two for recycle. Each column has a rotary valve which is connected to the four streams (feed, desorbent, raffinate, extract) as shown in Figure 3b. The SMB pilot is controlled by a central system using the Genesis control software. The feed, desorbent, and extract flow rates are controlled by the pumps. The recycle flow rate and the step time are controlled by the computer. The raffinate flow rate can be adjusted only by adjusting the system pressure balance. Samples can be collected after the raffinate and extract pump. In addition, there is a stationary sampling port located at the outlet of column 5 (Figure 3a). Methods. (i) HPLC Assay. HPLC was used to analyze the collected fractions from both batch and SMB experiments. In this assay, a Waters Nova-Pak C-18
Ind. Eng. Chem. Res., Vol. 37, No. 10, 1998 4027 Table 2. Experimental and Simulation Parameters for Multiple Frontal and Pulse Experiments System Parameters columna
length (cm)
i.d. (cm)
resin diameter (µm)
p (b)
PVP-A PVP-B
12.3 43.0
1.5 2.54
325-400 250-595
0.55 (0.37) 0.55 (0.40)
Mass-Transfer Parameters column PVP-A PVP-B
Eb (cm2/min) 0.100 0.0353
kf (cm/min) 0.123 0.0865
Dp (cm2/min) 10-4
0.655 × 0.655 × 10-4
Kf (min-1) 1.542 1.495
a The small column (PVP-A) was used in isotherm estimation, and the large column (PVP-B) was used to validate the isotherms and mass-transfer parameters obtained from the small column.
column and a premixed mobile phase of H2O/CH3CN (80:20 v/v), at a flow rate 0.5 mL/min, were used. The sample injection volume was 5 µL. The chromatograms were examined at a wavelength of 260 nm using the single-wavelength detector (Waters 486). Prior to analysis, all solvents were degassed for approximately 15 min, and the column was preequilibrated with the mobile phase until a smooth baseline was obtained. The column was washed using acetonitrile after analysis. (ii) Column Preparation. The PVP resin particles as received had a wide range of particle size (from 250 to 595 µm). The resin in the PVP-A column for isotherm measurement had been sieved into particles with diameter from 325 to 400 µm. In the PVP-B column (for validation of mass-transfer parameters and isotherm parameters) and all SMB columns, the resin was used as received. Table 2 lists the parameters of the PVP-A and PVP-B columns. A slurry-packing technique was used to pack all of the columns. The details of the packing procedure and the SMB experiments are explained below. Interparticle porosity was determined from the retention times of 0.5-mL pulses of blue dextran (2.5 g/L in DDW) by using pure ethanol as the mobile phase. Total porosity was determined from pure water breakthrough time. In both cases, the column was preequilibrated with pure ethanol, and the flow rate was 1.0 mL/min. (iii) Isotherm Measurements. As shown in many previous studies, multiple frontal chromatography is an accurate and reliable method for isotherm determination (Ma et al., 1996). In this method, two FPLC pumps were used. One was used to deliver amino acid solution (5 mg/mL phenylalanine or tryptophan in DDW), and the other was used to deliver DDW. The two streams were mixed before entering the column (PVP-A). The column was preequilibrated with DDW. The total flow rate for the two streams was kept constant at 1 mL/ min. Various amino acid compositions were obtained by changing the ratio of the two streams. The ratio was changed only after a concentration plateau appeared at the column outlet. The breakthrough times at different amino acid compositions were found, and their corresponding solid concentrations were calculated from a mass balance equation. The equilibrium adsorption data were fitted by the Langmuir isotherms. For phenylalanine, the multiple frontal method worked very well, as shown in Figure 4a. However, for tryptophan, the breakthrough curves at high concentrations (>2 mg/mL) were asymmetric and did not have stable
Figure 4. (a) Multiple frontal data and simulation result of phenylalanine. Dotted lines are experimental data; solid lines are simulation result. (b) Frontal data of phenylalanine compared with simulation result. Circles are experimental data; solid lines are simulation result.
Figure 5. (a) Multiple frontal data and simulation result of tryptophan. Dotted lines are experimental data; solid lines are simulation result. (b) The first frontal data in Figure 5a compared with simulation result. Circles are experimental data; solid lines are simulation result.
plateaus (Figure 5a). This problem led to uncertainties of isotherm data at high concentrations. For this reason, an independent batch equilibrium method was used to check the results from the multiple frontal method. For the batch equilibrium experiments, a known weight of sorbent and a known volume of solution with a series of different solute concentrations
4028 Ind. Eng. Chem. Res., Vol. 37, No. 10, 1998
were mixed in separate flasks. Both the initial and equilibrium solutions from all the flasks were sampled and analyzed by HPLC. The concentrations of the adsorbed amino acids in different solutions were then calculated from a mass balance. The Langmuir isotherm equation was used to fit these data. (iv) Experiments for Estimation of Mass-Transfer Parameters. The multiple frontal chromatograms (Figures 4 and 5) which were used to obtain the isotherms can also be used to estimate the individual mass-transfer parameters as explained in the Results and Discussion section. Since in SMB pilot experiments the resin particles were not sieved, which is practical in large-scale separation process, the mass-transfer parameters obtained from the small column with a narrow particle size distribution may not apply to columns with a wide particle size distribution. For this reason, additional experiments using a large batch column (PVP-B) were used to confirm the isotherm and mass-transfer parameters obtained from the small column (PVP-A). The large column was first preequilibrated with DDW. A 2-mL pulse of 5 mg/mL phenylalanine in DDW was then injected into the column at 1 mL/min and eluted with DDW at the same flow rate. A pulse test of tryptophan in the large column gave a broad and poorly defined peak (peak width greater than 1000 min), since tryptophan has a much higher affinity than phenylalanine. Instead, a frontal chromatography test in the large column was done. A feed solution of 1 mg/mL tryptophan was pumped into the large column (PVP-B) at a flow rate of 1 mL/min until the breakthrough curve was observed. The pulse and frontal data were compared with the lumped model simulations based on the isotherm and mass-transfer parameters obtained from the small column (PVP-A) as shown in the Results and Discussion section. (v) SMB Experiments. After degassing, the same batch of PVP resin was used for the 10 SMB columns. The entire SMB system was first primed by using water as both the feed and the desorbent. The resin was then packed into each column. After the column was washed with water for more than 4 h, more resin was added into the columns to fill the void space between the column cap and the top of the resin packing. After flow rate calibration, the desired operating parameters (port positions, column temperature, column pressure) were entered into the computer. Experiments were done at room temperature (∼25 °C). Feed and desorbent were continuously pumped into the columns. The feed was a binary mixture of phenylalanine and tryptophan, and the desorbent was DDW. Fractions (about 1 mL) from the sampling port, the raffinate outlet, and the extract outlet were collected at the midcycle time (one cycle is the period between port switching). All the fractions and the feed were analyzed using the HPLC method described above. Between each run, the columns were washed overnight using 15% ethanol in DDW and then washed with DDW to remove the ethanol. The results of two runs are reported below to demonstrate the model-based design approach. The operating parameters for the first run were calculated from the equilibrium design, and those for the second run were calculated from the nonequilibrium design. The column configuration for both runs was 3-2-2-3 (there are 3, 2, 2, and 3 columns in zones I, II, III, and IV, respectively). Other system and operating parameters are summarized in Table 2. A more
Figure 6. Comparison between isotherm data and Langmuir fitting for both phenylalanine and tryptophan. Squares are calculated from phenylalanine multiple frontal data. Circles are calculated from tryptophan batch equilibrium data. Triangles are calculated from tryptophan multiple frontal data (based on the lower bounds and the upper bounds of the plateaus). Solid lines are best-fit Langmuir model result.
detailed explanation of the designs is given in the Theory section. Results and Discussion Parameter Estimation. The bed voidage, particle porosity, adsorption isotherms, and mass-transfer parameters are required for the standing wave analysis. The bed voidage and particle porosity for each of the two columns used in batch chromatography experiments (PVP-A and PVP-B) were estimated from blue dextran pulse tests and breakthrough curves of water, as explained in the Experimental Section. The results are reported in Table 2. (i) Isotherms. After column packing and characterization, multiple frontal chromatograms were obtained for phenylalanine and tryptophan (Figures 4 and 5). The solute solid concentrations (q) at different solute liquid concentrations (C) were calculated from the breakthrough times of the multiple frontal chromatograms and are shown in Figure 6. For phenylalanine, the breakthrough times in the multiple frontal chromatogram are well defined, and each breakthrough time gives a single q at a given C. For tryptophan, the breakthrough curves at high concentrations (>2 mg/mL) did not have well-defined plateau values (Figure 5a), which were likely due to UV detector drift at high absorbance (>1.3). The drift results in a large uncertainty on the calculated q value at a given C as shown in Figure 6, in which the upper bound (4) and the lower bound (3) are connected by the two dashed lines. Since an accurate and reliable isotherm was needed in the SMB design, the tryptophan isotherm was also determined using an independent method, the batch equilibrium method. The results (O) are compared with those obtained from the multiple frontal method in Figure 6. At concentration lower than 2 mg/mL, the two methods gave essentially the same isotherm values. At higher concentrations, the batch equilibrium data fell between the upper bound and the lower bound values obtained from the multiple frontal method. Since the batch isotherm data appeared to be more reliable, the batch data were fitted with the Langmuir isotherm equations to obtain the best-fit parameters (Table 3). For both solutes, the best-fit
Ind. Eng. Chem. Res., Vol. 37, No. 10, 1998 4029 Table 3. Isotherm (298 K), Mass-Transfer, and Numerical Simulation Parameters for Runs 1 and 2 Isotherm Parameters Phe Trp
a
b
1.61 10.73
0.01534 0.16103
Mass-Transfer Parameters Eb (cm2/min) Kf (min-1)
run
zone I
zone II
zone III
zone IV
1 2 1 2
0.864 1.09 1.33 1.35
0.358 0.588 1.24 1.29
0.935 1.18 1.33 1.41
0.352 0.579 1.24 1.30
Numerical Parameters axial elements
collocation points
dt (min)
tolerance
200
3
0.002
0.01%
equation curves and the experimental data (Figure 6) were in close agreement. The fitting equations are
qPhe )
1.61CPhe 1 + 0.01534CPhe + 0.16103CTrp
(16)
qTrp )
10.73CTrp 1 + 0.01534CPhe + 0.16103CTrp
(17)
where Phe and Trp are abbreviations of phenylalanine and tryptophan, respectively. The units for both CPhe and CTrp are mg/mL. q is the amount adsorbed (mg) per solid volume (mL). Since only linear analysis is applied in this study, the solute concentrations should be as low as possible. However, if the concentrations are too low, accurate detection becomes a problem. For this reason, phenylalanine around 2 mg/mL and tryptophan around 1 mg/ mL were used in the SMB experiments. As shown in Figure 6, the deviation from the Langmuir equation was small at these low concentration. (ii) Mass-Transfer Parameters. When solute concentrations are sufficiently low, isotherms are linear, and eq 15 can be applied to calculate the lumped masstransfer coefficient Kf, which is required for the nonequilibrium SMB design and simulations. In this study, kf was estimated from the correlation of Wilson and Geankoplis (1966), and Dp was estimated from the frontal data (Figures 4b and 5b) using the lumped model of Ma and Wang (1997). In the simulation, the axial dispersion coefficient Eb was estimated from the Chung and Wen correlation (1968). By comparing the simulated breakthroughs at different Kf (lumped masstransfer coefficient) values with the experimental data, the best-fit Kf values for phenylalanine and tryptophan were found, and eq 15 was used to calculate the corresponding Dp values (Table 2). Additional experimental and simulation parameters are also listed in Table 2. Simulations of the multiple frontal curves based on the isotherm and Dp values in Table 2 are shown as solid lines in Figures 4a and 5a. They are in close agreement with the multiple frontal data (dotted lines) over a wide concentration range. Simulations of the large column phenylalanine pulse data (Figure 7a) and tryptophan frontal data (Figure 7b) based on the isotherm and Dp values of Table 2 also show good agreement. The small discrepancies in the peak width in Figure 7a could be be due to extracolumn dispersion, which was not taken
Figure 7. Comparison of experimental data and simulation result in the large column (PVP-B). (a) Phenylalanine pulse. Squares are experimental data; solid lines are simulation result. (b)Tryptophan frontal. Circles are experimental data; solid lines are simulation result. Table 4. System and Operating Parameters for Runs 1 and 2 configurationa feed concn (mg/mL) flow rate (mL/min)
switching time (min)
Phe Trp zone I zone II zone III zone IV feed raffinate desorbent extract
run 1
run 2
3-2-2-3 1.95 0.86 25.12 10.19 27.21 10.29 15 14.83 16.92 17.09 43.49
3-2-2-3 2.00 0.93 34.02 16.17 65.82 19.02 15 17.85 49.65 46.79 22.29
a Configuration refers to number of columns in each zone. 3-22-3 means 3 columns in zone I, 2 columns in zone II, 2 columns in zone III, and 3 columns in zone IV. The single-column parameters are 68.6 cm length, 2.54 cm i.d., b ) 0.40.
into account in the simulation. Since the isotherm and Dp values were confirmed with the data from the large column, they were used in the SMB designs and simulations. Equilibrium Design and Experimental Validation of Intrinsic Parameters. To validate the isotherm and mass-transfer parameters obtained from the batch methods, an equilibrium design (run 1) was obtained from the standing wave equations (eqs 1-6) for systems without any mass-transfer effects. A feed flow rate of 15 mL/min was chosen such that this experiment did not require a large amount of feed and desorbent to reach the final cyclic steady state. At this feed flow rate, the operating parameters can be calculated from eqs 1-4. The calculated parameters are shown in Table 4. This simple design is used to provide a set of reasonable flow rates and switching time. According to eqs 1-5, for equilibrium systems with
4030 Ind. Eng. Chem. Res., Vol. 37, No. 10, 1998
Figure 8. Comparison of experimental data and simulation result for the effluent histories in run 1 (equilibrium design). (a) Raffinate. Solid lines are simulation result at midcycle time, and symbols are experimental data. Squares represent phenylalanine, and circles represent tryptophan. (b) Extract. The same legend as (a). The experimental and simulation parameters are listed in Tables 3 and 4.
linear isotherms, the flow rates in zones I and III should be the same, and the flow rates in zones II and IV should also be the same. In run 1, zones I and III have slightly different flow rates because the slight nonlinearity of the tryptophan isotherm was taken into account in the design (Ma et al., 1998). The different feed and desorbent flow rates did not affect the validation since the simulations took into account the effects of the flow rates. The SMB experimental data for this design were then used to validate the isotherm and mass-transfer parameters in Table 3. The experimental effluent histories of both the raffinate and the extract were developed by analyzing the collected samples using the HPLC assay (Figure 8). Since the extracolumn void volume in the SMB system is larger than that for the fixed bed system, the axial dispersion coefficient Eb, which includes the effects of both intracolumn axial dispersion and extracolumn mixing, is expected to be higher than the Eb for the fixed bed experiments. However, according to eqs 7-10, when the zone lengths and capacity factors are sufficiently large, the dispersion effects become negligible compared to intraparticle diffusion effects. In previous studies of sugar purification, Eb was found to have an apparent dependence on interficial velocity u0 (Ma and Wang, 1997; Wooley et al., 1998). To check the validity of eqs 7-10, simulation results based on the Eb values obtained from the Chung and Wen correlation were compared with those based on an empirical correlation of Eb ) 0.5u0. The results are similar as expected from eqs 7-10, indicating that extracolumn dispersion and intracolumn axial dispersion are relatively unimportant in this system.
The small differences between experimental data and predicted values in Figure 8 could be partly due to inaccuracy of the HPLC assay and partly due to the dead volume (about 40-50 mL) in the connecting tubings and pumps as well as the dead volume on top of the resin packing in each column. Before run 1, the SMB columns initially appeared to be fully packed. However, after completion of run 1, which was operated at high zone flow rates for an extended period of time (>900 min), a small void volume appeared on top of the packing. In the simulation, the column length was assumed to be the length measured at the end of run 1, 68.6 cm, instead of the nominal length, 76.2 cm. This assumption gives reasonable agreement between the SMB data and simulated effluent histories (Figure 8). However, since the dead volumes are not considered in the simulation, the actual phenylalanine and tryptophan bands slightly lag behind the simulated bands. This relative shift causes the phenylalanine breakthrough data to lag behind the simulated breakthrough curve (Figure 8a) and the tryptophan breakthrough data to be ahead of the simulated curve (Figure 8b). Since the actual desorption wave of phenylalanine shifts toward the extract port, the phenylalanine (impurity) concentration in the extract is higher than predicted (Figure 8b). The actual tryptophan desorption wave also lags behind slightly, resulting in a slightly higher tryptophan concentration in the raffinate (Figure 8a). The dead volumes affect the migration of tryptophan less than that of phenylalanine because tryptophan has a higher affinity than phenylalanine. The additional retention time due to the dead volumes is relatively small compared to the retention time due to adsorption. Because of significant mass-transfer effects in this system, the equilibrium design did not give high product purities. According to eq 11, the phenylalanine and tryptophan purities at midcycle of the cyclic steady state in run 1 are 91.4% and 85.1%, respectively (Table 5). Since higher purities are usually required for practical applications, a design considering mass-transfer effects (nonequilibrium design) is needed to improve the purities as discussed below. Nonequilibrium Design and Experimental Results. Equations 5-10 of the standing wave analysis take into account mass-transfer effects, and they are the basis for the nonequilibrium design. First, product purities and feed flow rate need to be specified for the nonequilibrium design. Here, the product purities for both phenylalanine and tryptophan are set to be 99.7%. At the required purities, the highest feed flow rate is calculated from eq 12 to be 15.0 mL/min. At this feed flow rate, the operating parameters are then obtained from eqs 7-10 and eq 5 with the same system parameters as run 1. All of the parameters for the nonequilibrium design (run 2) are listed in Tables 3 and 4. The experimental and the simulated effluent histories are shown in Figure 9. The experimental data were obtained at midcycles, and they should fall on the solid lines obtained from the simulation. The data are in close agreement after the cyclic steady state is established. At the cyclic steady state, the extract has almost no phenylalanine, as predicted from the simulation. However, the purity of phenylalanine in the raffinate (96.7%) is slightly less than the predicted value (99.7%) (Table 5). The effluent histories in the initial period ( 1). The migration speed of the high-affinity solute (tryptophan) is more sensitive to inaccurate bed voidage than that of the low-affinity solute (phenylalanine). If an inaccurate b is used in the SMB design, product purities will be lower than expected. In general, the nonequilibrium design is more robust than the equilibrium design. For a fixed total bed volume, the longer the separation zones, the higher the throughput, but also the higher the desorbent consumption. Configurations for the highest throughput or the lowest solvent consumption are found from computer simulations. Acknowledgment This research is supported by grants from NSF (HRD9024174) and the Purdue Research Foundation. The simulated moving bed pilot unit was provided gratis by U.S. Filter (Rockford, IL). Notation C0 ) solute concentration in feed (mg/L) CMB ) continuous moving bed Dp ) pore diffusion coefficient (cm2/min) Eb ) axial dispersion coefficient (cm2/min) F ) volumetric flow rate (mL/min) HPLC ) high-performance liquid chromatography ID ) column diameter (cm) Kd ) size exclusion factor Kf ) lumped mass-transfer coefficient (min-1) L ) zone length (cm) P ) bed phase ratio (1 - b)/b
R ) particle radius (µm) S ) column cross-sectional area (cm2) SMB ) simulated moving bed ST ) switching time V ) total bed volume a ) Langmuir isotherm constant (per solid volume) kf ) film mass-transfer coefficient (cm/min) Phe ) phenylalanine Trp ) tryptophan u0 ) interstitial linear velocity uν ) net interstitial linear velocity with respect to the feed port b ) interparticle void p ) intraparticle porosity R ) capacity factor ratio δ2/δ1 β ) logarithm of concentration ratio δ ) capacity factor p + (1 - p)Ki ν ) solid movement linear velocity I,II, III, IV ) zones 1, 2, 3, and 4, respectively ext ) extract port feed ) feed port raf ) raffinate port des ) desorbent port
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Received for review March 20, 1998 Revised manuscript received July 27, 1998 Accepted July 28, 1998 IE9801711
