Ind. Eng. Chem. Res. 2000, 39, 4365-4369
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Kinetic and Equilibrium Study of the Enantioseparation of Fenoprofen in a Batch Setup C. B. Ching,†,‡ W. Arlt,§,| M. Lisso,*,†,⊥,# and G. Wozny*,⊥,X Department of Chemical and Environmental Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 0511, Singapore, and Institute of Process and Plant Design, Technical University of Berlin, Sekr. TK 15 and KWT 9, Strasse des 17 Juni 135, D-10623 Berlin, Germany
The bed voidage, axial dispersion, and kinetic and isotherm parameters for the chromatographic enantioseparation of racemic Fenoprofen, using cellulose ester as the chiral stationary phase and 2-propanol/hexane/acetyl alcohol as the mobile phase, were evaluated by moment analyses on the basis of equilibrium theory and the linear driving force model. The peak-fitting method was used to identify the coefficients of the competitive Langmuir isotherm for both enantiomers. For this reason and for the validation of the model parameters, a simulation program was developed. The simulated results describe the experimental data well. On the basis of the isotherm parameters and the equilibrium theory, the process region for the simulated moving bed (SMB) process was identified. Changes of the process region will be discussed by considering fluctuations in the feed concentration and uncertainties in the determined capacity factor. 1. Introduction Because of the strict regulation by governments and pressure from the public and academic organizations, there is a need to develop optically pure drugs.1 For this several methods are available, one of them being highperformance liquid chromatography (HPLC).2 Fenoprofen is a commonly used drug in its racemic form, which works as a nonnarcotic analgesic.3 For a safer and more effective drug, it is better to separate the enantiomers before use. Enantioseparation of racemic Fenoprofen using a chiral adsorbent, cellulose ester (Daicel, Chiracel OJ), has been demonstrated using an analytical column.4 In this study, a preparative column was employed for the separation of Fenoprofen, using hexane and 2-propanol with a small amount of acetyl alcohol (AcOH) as the mobile phase. Chiracel OJ was employed as a stationary phase. The preparative chiral column was characterized by the bed voidage and the axial dispersion coefficient. The adsorption process was described by the kinetics of mass transfer and the parameters of the isotherm. The method of moments was used to analyze the experimental data. A competitive Langmuir model was used to describe the behavior of both components of the isomer. An amount of 1 mg/mL of each enantiomer was injected at different flow rates to identify the capacity factors and the Langmuir competitive coefficients by using the peakfitting method.5 * To whom correspondence should be addressed. † National University of Singapore, where the work was conducted. ‡ E-mail:
[email protected]. § Technical University of Berlin, Sekr. TK 5. | E-mail:
[email protected]. ⊥ Technical University of Berlin, Sekr. KWT 9. # Present address: Technical University of Berlin, Sekr. KWT 9. E-mail:
[email protected]. Phone: +49-30-314-26904. Fax: +49-30-314-26915. X E-mail:
[email protected]. Phone: +4930-314-26900. Fax: +49-30-314-26915.
For the peak-fitting method and to check the validity of the isotherm parameters, a simulation program was developed, using the parameters obtained from the model. Further the experimental data of the injection of three different concentrations of Fenoprofen were compared with the simulation results. In conclusion the isotherm parameters were used to predict the operating triangle for the SMB process in the m2-m3 plane.6-9 Here fluctuations in the feed concentration model were taken into account to determine their effects on the operating triangle. 2. Theoretical Section The mass balance equation for each component using the equilibrium-dispersive model in the mobile phase can be written as eq 1.9 Further, the linear driving force
u
∂c ∂c ∂2c ∂q + +F ) Dax 2 ∂z ∂t ∂t ∂z
(1)
(LDF) model was used to describe the adsorption process (eq 2). The Langmuir and competitive Langmuir iso-
∂q ) kf(q* - q) ∂t
(2)
therm models were chosen for modeling the isotherms (eqs 3 and 4) under the assumption of the same
qi* ) qi* )
(
(
)
Kici , with i ) 1, 2 1 + bici
)
(3)
Kici , with i ) 1, 2; j ) 1, 2; i * j 1 + bici + bjcj (4)
saturation concentration qs for both isomers (eq 5). For
Ki ) qsbi
(5)
an infinitely small amount of the injected component,
10.1021/ie990219q CCC: $19.00 © 2000 American Chemical Society Published on Web 09/23/2000
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Ind. Eng. Chem. Res., Vol. 39, No. 11, 2000
the competitive Langmuir coefficients bi can be neglected; hence, the capacity factor Ki corresponds to Henry’s coefficient for a linear isotherm. For the simulation the corresponding boundary and initial conditions for eqs 1 and 2 are given by eqs 6-10. The feed to a
c(z,t)0) ) q(z,t)0) ) 0 Dax
(6)
∂2 c (z)0,t)0) ) -u[c(z)0-,t) - c(z)0+,t)] (7) 2 ∂z ∂c (z)L,t)0) ) 0 ∂z
(8)
column was represented as a square pulse (eqs 9 and 10).
c(z)0-,t) ) cT c(z)0-,t) ) 0
∀ 0 e t e tT
(9)
∀ t g tT
(10)
2.1. Moment Analysis. The method of moments were used to determine the hydrodynamic characteristic of the column. This moment is well proofed and commonly accepted.10-12 A linear isotherm model is valid for a small amount of the injected enantiomer and an infinitely fast kinetics of adsorption-desorption. This leads in combination with the method of moments to an expression for the retention time (eq 11). The height
L tR,i ) [1 + FKi] u
(11)
equivalent to a theoretical plate (HETP) was calculated with eq 12 and the axial dispersion coefficient with eq
HETP )
[
2Dax F 1 1+ + 2uF u K ikf Ki
]
-2
(12)
13. This expression is valid for samples that enter the porous medium without adsorption under the circumstances of a high mass-transfer coefficient and the neglect of the molecular diffusion coefficient.12 Hence,
Dax ) Dax,coeffu
(13)
HETP is a constant value independent of the velocity (eq 14). This result correlates with the right side of a
HETP ) 2Dax,coeff
(14)
Van Deemter plot without adsorption. 2.2. Determination of the Process Plane for the SMB Process. Because of the complexity of a SMB plant, a systematic approach to determine the right process conditions is necessary. Several procedures can be found in the literature for an optimal design of the SMB process.12-14 In this paper the latest suggestion was used, based on the equilibrium theory model, which takes into account the nonlinearity of the adsorption isotherm while it neglects the effect of axial mixing and masstransfer resistance.6 This method has provided a very useful tool to determine the process parameters of countercurrent separation units, because in many ap-
plications the unit behavior is mostly determined by the properties of the adsorption equilibrium.6-9 3. Experimental Setup 3.1. Material and Equipment. Fenoprofen was purchased from Aldrich (Milwaukee, WI). The solvents hexane, 2-propanol, and AcOH came from J. T. Baker (Phillipsburg, NJ). The pure isomers were prepared by sample collection behind the column (see below). 1,3,5Tri-tert-butylbenzene (TTBB) was purchased from Aldrich (Milwaukee, WI). The experiments were carried out using a single-column liquid chromatographic system. A Chiracel OJ column (1 × 25 cm, Daicel Chemical Ind.) with the stationary phase cellulose ester was used. The room temperature was constant at 21 °C. The HPLC system consisted of an eluent reservoir, a series 200 HPLC pump (Perkin-Elmer), an injection valve from Agilent Technologies (Cotati, CA), and a Waters 486 tunable UV detector set at 245 nm. The UV detector was connected with a PC by a tunable amplifier for the data acquisition. The HPLC pump moved the degassed solvent from the eluent reservoir through the injection valve, the column, and the UV detector to a waste collector. 3.2. Experimental Procedures. A mixture of hexane/2-propanol/AcOH (9:1:0.05) was used as a mobile phase in all experiments. TTBB and Fenoprofen were dissolved separately in the mobile phase, which was first degassed in an ultrasonic bath for 20 min. An ultrasonic bath was also used to support the dissolution of Fenoprofen in the above eluent, which was filtered afterward. The solubility of Fenoprofen was limited to no more than 4.4 mg/mL for the racemic mixture. The TTBB experiments and the single enantiomer experiments were performed with a concentration of 1.0 mg/mL to determine the features of the column and the parameters of the isotherm. Flow rates of 1-4 mL/min were chosen for the above experiments. Tracers of Fenoprofen with total concentrations of 2, 3.9, and 4.2 mg/mL at a flow rate of 4 mL/min were performed to compare the experimental data with the simulation results and to validate the model. 4. Results and Discussion The maximum possible total concentration of Fenoprofen in the solvent was limited to no more than 4.4 mg/mL. That was the most limiting factor to receive experimental data over a wide range of concentrations, despite the fact that nonlinear behavior was observed in the experimental results. As a result, the competitive Langmuir isotherm model might not fit the equilibrium behavior over the whole theoretical range of the concentration, but it will describe the realistic range of the equilibrium sufficiently up to the solubility limit. 4.1. Determination of the Porosity and the Axial Dispersion. A total porosity of 0.702, an external porosity of 0.458, and an axial dispersion coefficient of 0.0025 cm was determined as a result of TTBB experiments. 4.2. Determination of the Linear Capacity Factor and the Mass-Transfer Coefficient. The retention time data for both enantiomers of Fenoprofen were plotted against the inverse interstitial velocity in Figure 1). Hence, the capacity factors were found to be 3.9 for the (R)-(+) isomer and 3.1 for the (S)-(-) isomer. Plots of HETP against the interstitial velocity for the single isomers increase linearly with velocity. The
Ind. Eng. Chem. Res., Vol. 39, No. 11, 2000 4367 Table 1. Initial Values for the Peak-Fitting Method initial value
model parameter
Figure 1. Plot of the first moments of the two enantiomers of Fenoprofen versus the inverse interstitial velocity.
capacity factor [(S)-(-) isomer] capacity factor [(R)-(+) isomer] competitive parameters [(S)-(-) isomer] competitive parameters [(R)-(+) isomer] overall mass-transfer coefficient [(S)-(-) isomer] overall mass-transfer coefficient [(R)-(+) isomer]
3.1 3.9 0.05 mL/mg 0.05 mL/mg 452 min-1 314 min-1
Table 2. Determined Values Based on the Peak-Fitting Method model parameter
Figure 2. Plot of HETP of the two enantiomers of Fenoprofen versus the interstitial velocity.
capacity factor [(S)-(-) isomer] capacity factor [(R)-(+) isomer] competitive parameters [(S)-(-) isomer] competitive parameters [(R)-(+) isomer] overall mass-transfer coefficient [(S)-(-) isomer] overall mass-transfer coefficient [(R)-(+) isomer]
determined value 3.29 4.105 0.0669 mL/mg 0.0835 mL/mg 2880 min-1 2383 min-1
Table 3. Experimental Setups of the Overall Feed Concentration at a Constant Flow Rate of 4 mL/min
Figure 3. Comparison of the simulated and experimental band profiles for the single (S)-(-) enantiomer experiments at a flow rate of 4 mL/min.
Figure 4. Comparison of the simulated and experimental band profiles for the single (R)-(+) isomer at a flow rate of 4 mL/min.
overall mass-transfer coefficients were found to be 314 and 452 min-1 for (R)-(+)- and (S)-(-)-Fenoprofen based on eq 7 and Figure 2. The eluted profiles (Figures 3 and 4 of the single isomers showed competitive behavior despite the low injected tracer concentration of 1 mg/mL. Consequently, the assumptions of independence of both parameters and linearity of the isotherm are simplifications. Hence, the calculated values for the capacity factors and the mass transfer are initial values for the peak-fitting method. 4.3. Simulation and Peak-Fitting Method. The peak-fitting method was used to tune the parameters of the LDF model and to determine the parameters of the adsorption isotherm. This method is less timeconsuming than other methods. Disadvantageous is the lower accuracy of the results because the parameter cannot be determined independently. Therefore, the
overall feed conc of Fenoprofen
Figure
2 mL/min 3.8 mL/min 4.2 mL/min
7 8 9
effect of mass-transfer resistance may be covered by parameters of the isotherm. Nevertheless, it is a fast and simple method to find a valid range of the isotherm parameters especially under time critical circumstances, as is usually the case in the industrial environment. The developed simulation tool for the peak-fitting method was programmed in Fortran. Therefore, the partial differential equation (PDE) systems in eqs 1-10 were solved by the well-known techniques of orthogonal collocation.15 The initial guesses for the overall mass-transfer coefficient and the capacity factors were based on the above-described experimental results. The initial values of the competitive parameters in the Langmuir isotherm were chosen empirically (Table 1). The peak-fitting method5 was used to tune the model parameters based on experimental results of the single isomer at different flow rates. Therefore, the Langmuir isotherm (eq 3) was implemented in the model. The retention time of the peak maximum and the shape of the profile were used to determine the right set of parameters (Table 2). The comparison between the experimental and simulation results can be seen in Figures 3 and 4 for the single isomer experiments. Experiments with different feed concentrations of Fenoprofen (Table 3) were carried out at constant flow rates of 4 mL/min for the verification of the model parameters (Figures 5-7). The comparison between the experimental and simulation results leads to the following conclusions:
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Ind. Eng. Chem. Res., Vol. 39, No. 11, 2000
Figure 5. Comparison of the simulated and experimental band profiles for Fenoprofen with a tracer concentration of CT+ ) CT- ) 1 mg/mL.
Figure 8. Effects of uncertainties in the determination of the capacity factor on the location of the process triangle in the m2m3 plane. Table 4. Parameter Combinations by Considering Fluctuations in the Feed Concentration and Uncertainties in the Capacity Factor
Figure 6. Comparison of the simulated and experimental band profiles for Fenoprofen with a tracer concentration of CT+ ) CT- ) 1.95 mg/mL.
Figure 7. Comparison of the simulated and experimental band profiles for Fenoprofen with a tracer concentration of CT+ ) CT- ) 2.2 mg/mL.
feed conc [mg/mL]
capacity factor
triangle in Figure 8
3.4 4.4 3.4 4.4
3.29/4.105 3.29/4.105 3.1/3.9 3.1/3.9
1 2 3 4
5.1. SMB Set Up by Uncertainties of the Isotherm Parameters. Because of the lower exactness of the peak-fitting method, it is probable that the real capacity factors are in a range between the linear capacity factor and the determined capacity factors. Hence, it is useful to take into consideration the range of the capacity factors to determine an average range of the different triangles (Figure 8). That was done for two different feed concentrations of 3.4 and 4.4 mg/mL of the isomer (Table 4). The starting point for further optimizations of the process should be selected inside the average area of the triangles for the same feed concentration as that in Figure 8. Therefore, rigorous simulations of the whole SMB process or experiments can be used. 6. Conclusion
(a) The peak maximum corresponds well in all figures by using the same concentration for the normalization of the first and second peaks. (b) With an increase of the feed concentration, differences between the simulation results and the experimental data can be seen for the second peak. In summary the isotherm parameters for this particular system for the separation of Fenoprofen were evaluated with the peak-fitting method. This is a very fast method to estimate the range of the isotherm parameters. Disadvantageous, the following points have to taken into consideration critically: (i) The limited solubility of Fenoprofen in the solvent leads to a limited accuracy of the determined equilibrium data. (ii) With the chosen method, it was not possible to evaluate all parameters independently, especially the mass-transfer resistance and the isotherm parameters. 5. Setup of the SMB Process Conditions The model parameters to describe the separation of Fenoprofen in a batch column corresponded sufficiently. In the following paragraph the SMB setup will be discussed. Therefore, the lower exactness of the isotherm parameters will be considered. A four-section SMB plant will be considered to determine the process triangle in a m2-m3 plane. The details of the method are well-known.6-9
In this study, the overall mass-transfer coefficient, the axial dispersion, and the bed voidage of a Chiracel OJ column were determined by applying the method of moments. Further parameters of the adsorption isotherm and the mass transfer for the separation of Fenoprofen were determined by using the peak-fitting method. The chiral stationary phase exhibits a greater affinity to the R enantiomer of Fenoprofen than to the S enantiomer. The magnitude of the overall masstransfer coefficient shows that the mass transfer on the chiral column is relatively fast in reference to the limitations of the peak fitting. The advantages and limits of these methods for the determination of the isotherm parameters of Fenoprofen were discussed. A simulation program was developed to use the peakfitting method and to validate the parameters of the model at different process conditions. The changes of the process triangle in the m2-m3 process plane of a SMB process were discussed under the assumptions of uncertainties of the capacity factor for both enantiomers and two different feed concentrations. Acknowledgment We gratefully acknowledge financial support of DAAD. Nomenclature c ) concentration in the liquid phase [mg/mL]
Ind. Eng. Chem. Res., Vol. 39, No. 11, 2000 4369 b ) competitive coefficient of the Langmuir and competitive Langmuir isotherm models [mg/mL] Dax ) axial dispersion [cm2/min] Dax,coeff ) axial dispersion coefficient [cm] F ) phase ratio equation, (1 - )/ HETP ) height equivalent to a theoretical plate [cm] K ) capacity factor of the Langmuir and competitive Langmuir isotherm models and Henry’s coefficient in the linear isotherm model kf ) coefficient of the LDF model [min-1] L ) length of the column [cm] q ) concentration in the solid phase [mg/mL] q* ) equilibrium concentration in the solid phase [mg/mL] qs ) saturation concentration in the solid phase [mg/mL] t ) time [min] tR ) retention time [min] u ) interstitial velocity [cm/min] z ) axial coordinate of a column [cm] Greek Letters ) external porosity t ) total porosity Subscripts i ) component i j ) component j T ) tracer T+ ) tracer of the (R)-(+) enantiomer T- ) tracer of the (S)-(-) enantiomer
(3) The Merck Index, 11th ed.; Merck & Co. Inc.: New York, 1989. (4) Ueji, M.; Tomizawa, C. J. Pest. Sci. 1986, 11, 447. (5) Dose, E. V.; Jacobson, St.; Guiochon, G. Determination of Isotherms from Chromatographic Peak Shapes. Anal. Chem. 1991, 63, 833-839. (6) Storti, G.; Masi, M.; Carra` S.; Morbidelli, M. Optimal Design of Multicomponent Adsorption Separation Processes Involving Nonlinear Equilibria. Chem. Eng. Sci. 1989, 44, 1329. (7) Storti, G.; Mazotti, M.; Morbidelli, M.; Carra`, S. Robust Design of Binary Countercurrent Adsorption Separation Processes. AIChE J. 1993, 3, 471. (8) Mazotti, M.; Storti, G.; Morbidelli, M. Robust Design of Binary Countercurrent Adsorption Separation Processes: 2. Multicomponent Systems. AIChE J. 1994, 11, 1825. (9) Mazotti, M.; Storti, G.; Morbidelli, M. Optimal Operation of Simulated Moving Bed Units for Nonlinear Chromatographic Separations. J. Chromatogr. A 1997, 769, 3. (10) Kucera, E. J. Contribution to the Theory of Chromatography Linear Non-Equilibrium Elution Chromatography. J. Chromatogr. A 1965, 19, 237. (11) Suzuki, M. Adsorption Engineering; ISBN 0-444-98802-5; Elsevier: Amsterdam, The Netherlands, 1990; p 179. (12) Ruthven, D. M. Principles of Adsorption and Adsorption Processes; ISBN 0-471-86606-7; Wiley: New York, 1984. (13) Yamamoto, S.; Nakanishi, K.; Matsumo, R. Ion-Exchange Chromatography of Proteins; Marcel Dekker: New York, 1988. (14) Ching, C. B.; Ruthven, D. M.; Hidajat, K. Experimental Study of a Simulated Counter-Current Adsorption SystemsIII. Sorbex Operation. Chem. Eng. Sci. 1985, 40, 1411. (15) Madsen, N. K.; Sincovec, R. F. Trans. Math. Software 1979, 5, 326.
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Received for review March 25, 1999 Revised manuscript received August 2, 1999 Accepted June 16, 2000 IE990219Q
