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SEPARATIONS Solution Crystallization Kinetics of 6-Aminopenicillanic Acid Juliana S. Ferreira,†,‡ Adrie J. J. Straathof,*,† Xiaonan Li,† Marcel Ottens,† Telma T. Franco,‡ and Luuk A. M. van der Wielen† Department of Biotechnology, Delft UniVersity of Technology, Julianalaan 67, 2628 BC Delft, The Netherlands, and School of Chemical Engineering, State UniVersity of Campinas, P.O. Box 6066, 13081-970 Campinas, SP, Brazil
Semisynthetic penicillins, derived from 6-aminopenicillanic acid (APA), constitute an important group of antibiotics. APA is produced by enzymatic hydrolysis of penicillin G (PenG). This study concerns the determination of the crystallization kinetics of APA in the presence of other components that may be present after the PenG hydrolysis, i.e., remaining PenG and the byproduct phenylacetic acid. This evaluation is based on the analyses of growth rate and crystal size distribution, at pH 4 and 5. The results show that the impurities have no significant influence on the APA crystallization, within the range of pH and impurity concentrations evaluated. A mathematical model, based on the population balance, gives a good prediction of the crystallization rate and crystal size distribution with a single set of parameters. Introduction 6-Aminopenicillanic acid (APA) is a key intermediate in the production of many commercial β-lactam antibiotics. It is produced by enzymatic hydrolysis of penicillin G (PenG).1 In the development of new production processes,1-3 reactive crystallization of APA takes place in a multicomponent system where the presence of solutes other than the target product might significantly influence the kinetics of crystallization.4,5 Reactive crystallization may produce sparingly soluble small crystals, which often cause problems in downstream processing, especially in filtration, but also in the treatment of the mother liquor as well in the drying and packing of the crystalline product.6 Usually, crystal growth rates are reduced by impurities. The higher the supersaturation, the weaker the retardation.7-9 Nevertheless, there are few examples of increase in growth rate with increasing impurity concentration in the existing literature.10-12 The current work focuses on the determination of kinetic parameters of APA crystallization from aqueous solution, and on the influence of low concentrations of its precursor PenG, its coproduct phenylacetic acid (PAA), and the solvent butyl acetate (BuAc), which is used for extraction of PAA. Experimental conditions will be restricted to the range pH 4-5 in which a seeded reactive crystallization will be operated,2 with saturating concentrations of BuAc, and concentrations of PenG and PAA of 5-10 mol % of the dissolved APA concentration. Furthermore, a mathematical model will be used based on a population balance for crystals in a specific size class in order to simulate the solute concentration in the liquid phase as a function of time (the desupersaturation curve) and the crystal size distribution (CSD).4
phase as a function of time and the CSD.13 Under the constraints of a constant-volume batch operation and under the assumptions of no agglomeration, no breakage, no death; birth only in the lowest particle class; and size-independent growth, the following simplified equation is obtained:
Theory The population balance for crystals in a specific size class can be used to simulate the solute concentration in the liquid
where Mw is the molar mass of the crystallizing component and V is the vessel volume. The total mass of crystals formed (Mtot) is given by integration over all crystal size classes:
* To whom correspondence should be addressed. E-mail:
[email protected]. † Delft University of Technology. ‡ State University of Campinas.
∂n(t,x) ∂[n(t,x) ∂G(t)] )∂t ∂x
(1)
n is the number of particles (#) per volume per size class in #‚m-4, t is the time, x is the crystal size coordinate, and G is the growth rate. To solve this hyperbolic partial differential equation, boundary and initial conditions are required. The boundary condition at x ) 0 is given by the commonly applied equation
n(t,0) )
J(t) G(t)
(2)
In a unseeded experiment the initial condition at t ) 0 is given by eq 3; otherwise it is given by the size of the seeds.
n(0,x) ) 0
(3)
The desupersaturation curve is obtained by solving the following component mass balance:
M wV
∂C(t) ∂Mtot(t) + )0 ∂t ∂t
Mtot(t) )
∫0∞kVFAPAn(t,x)x3 dx
(4)
(5)
where kV is the crystal shape factor and the crystal density of
10.1021/ie0601652 CCC: $33.50 © 2006 American Chemical Society Published on Web 09/07/2006
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Figure 1. Batch experimental system.
APA is FAPA ) 1.4 × 103 kg m-3. The nucleation rate is described by14
(
J(t) ) J0 exp -
)
B ln(S(t))2
(6)
where B is the nucleation factor. The growth rate is given by14
G(t) ) kg(S(t) - 1)g
(7)
The supersaturation ratio S is the ratio of dissolved concentration C to equilibrium solubility Ceq:
S(t) )
C(t) Ceq
(8)
The parameters in eqs 5-8, i.e., Ceq, kV, kg, and g, are unknown and will be determined to get a complete model. The nucleation parameters will not be evaluated in detail because seeding will be applied. Materials and Methods Materials. KH2PO4 (anhydrous extra pure), 85% H3PO4, 3638% HCl, and 25% NH4OH were from J. T. Baker (Deventer, The Netherlands), and acetonitrile was purchased from Merck (Darmstadt, Germany). PAA and BuAc were purchased from Fluka Chemika (Steinheim, Switzerland). All reagents were of analytical grade. PenG (potassium salt) and APA were kindly provided by DSM, Delft, The Netherlands. Aqueous solutions saturated with BuAc (0.03 w/w) were prepared by mixing Milli-Q water and BuAc in a mass ratio of 1:0.3 and separating both phases using a separation funnel. Determination of the Solubility of APA. To aliquots of 100 mL of BuAc-saturated water in Erlenmeyer flasks, 5.4 g of APA was added. Dependent on the experiment, impurities were added (1 or 10 mM PenG, or 1, 5, or 10 mM PAA). A solution of 2 mol/L NH4OH was used to correct the pH to the intended value. The closed flasks were magnetically agitated at 25 °C for 30 min and left to settle for 30 min. The intervals of 30 min were used after testing the minimum period of time adequate to achieve equilibrium without causing degradation of APA. Liquid samples were filtered through a 0.2 µm cellulose nitrate membrane syringe filter. Subsequently, 4 mL of filtered solution was diluted in 25 mL with Milli-Q water. The concentration of dissolved APA was determined by HPLC analysis.
Crystallization Experiments. The growth rate of APA was determined in a batch crystallizer. The setup is shown in Figure 1. The crystallizer itself consisted of a 2 L cylindrical glass jacketed vessel, stirred by a four-bladed turbine impeller, and provided with three baffles. The refrigeration/heating system kept the temperature constant at 25 °C. The laser probe provided reflection signals that were registered in the computer by LabView software. Supersaturated solutions were prepared by dissolving an aliquot of APA in 600 mL of BuAc-saturated water at room temperature. All APA was dissolved by addition of 25% aqueous NH4OH, and the pH was adjusted to about 6.0 with 37% aqueous HCl. Then, the solution was diluted with water to 2 L, filtered through 0.2 µm cellulose nitrate membrane filters, transferred to a 2 L jacketed vessel at 25 °C, and agitated at 200 rpm. The pH was corrected to pH 4.0 or 5.0 by adding HCl (5 M). The crystallization experiments started by the addition of 1.0 g of seeds. In experiments that were carried out in the presence of PenG, crystals of the impurity were added simultaneously with the seeds, giving a concentration range that varied from 0.55 to 1.13 mM. In the case of PAA, the experiment was carried out by dissolving it in water before adding it to the crystallizer, since PAA takes some time to dissolve completely. Every 30 min a 15 mL sample was taken from the crystallizer using a syringe. Half the sample was filtered through a 0.2 µm cellulose nitrate membrane syringe filter. Subsequently 4 mL of filtered solution was diluted in 25 mL with water and analyzed by HPLC for APA. The remaining part of the sample was used for image analysis. Image Analysis. Samples were taken using a syringe and introduced into a glass cell. Three pictures of crystals in solution were analyzed for size and amount of crystals applying the program Leica Qwin. This procedure was done in triplicate; i.e., for each sample, three mean times and three corresponding mean lengths of the crystals were obtained. The latter were obtained by averaging over n. From a final sample after about 9 h the final CSD was determined. Figure 2 presents some pictures of the crystals that were analyzed. HPLC Analysis. Samples were analyzed for dissolved APA by HPLC (Waters), using a C18-platinum EPS column (particle size 5 µm, pore size 10 nm, column size 4.6 × 250 mm), and UV detection. The mobile phase was 28:72 (v/v) acetonitrile and 0.64 g L-1 aqueous KH2PO4 solution; the pH was adjusted
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Figure 2. Pictures of APA crystals. Experiment at pH 4.0 and CPAA ) 1.13 mM. Figure 5. APA growth rate for pure and impure systems at pH 4.0 and 5.0. Table 1. Crystal Dimensions of APA Obtained after Various Seeded Experiments in the Range pH 4.0-4.2 (pH 5.2 for Experiment 5) expt 1 2 3 4 5 6 7
CPenG (mM)
CPAA (mM)
S0
AR
dp,av (µm)
kv
0 0.55 0 1.13 1.13 0 0
0 0 0.55a 0 0 1.13a 1.13
1.99 1.88 1.85 1.79 1.89 1.93 1.95
1.90 2.09 1.76 2.05 1.80 1.87 1.87
13 ( 10 13 ( 8 14 ( 9 13 ( 11 10 ( 8 15 ( 14 13 ( 16
0.42 0.34 0.48 0.36 0.46 0.43 0.43
1.90
1.91
13.2
0.42
mean a
Figure 3. Solubility of APA at 25 °C (CPenG ) 0, 1.0, and 10 mM). Symbols are experimental values; the line is the best fit to eq 12 for the experiments of CPenG ) 0.
Not dissolved but added as solid.
Finally, the growth rate as a function of supersaturation ratio was obtained from eq 11, the logarithmic form of eq 7
ln G ) ln kg + g ln(S-1)
(11)
Results and Discussion Influence of Impurities on the Solubility of APA. The solubility (Ceq,APA) of pure APA in the range pH 4-5 is shown in Figure 3. From these data the intrinsic solubility of zwitterionic APA was Ceq,APA( ) 12.03 mM according to eq 12, which assumes that the anionic and cationic forms of APA are very soluble and do not limit the total APA solubility Ceq,APA.
Ceq,APA( ) Ceq,APAFAPA(
(12)
FAPA( is the pH-dependent fraction of the zwitterionic APA, which was calculated from Figure 4. Solubility of APA at 25 °C (CPAA ) 0, 1.0, 5.0, and 10 mM). Symbols are experimental values; the line is the same as in Figure 3.
to 2.75 with H3PO4. The flow was 1.0 mL min-1. The elution times of APA, PAA, and PenG were 3.3, 7.7, and 13.9 min, respectively. Growth Rate Determination. The growth rate was obtained from
G)
∆L ∆t
(9)
The supersaturation ratio (S) was determined according to eq 8, where the dissolved APA concentration was determined by HPLC analysis, and the solubility of APA was evaluated using eq 10.
Ceq,APA )
Ceq,APA( FAPA(
(10)
FAPA( )
1 10-pH 10-pKa2 1 + -pK + -pH 10 a1 10
(13)
pKa1 ) 2.5 and pKa2 ) 4.9 are the dissociation constants of APA.15 Thus, the isoelectric point is pH 3.7, for which the minimum solubility is Ceq,APA,pH 3.7 ) 13.55 mM. The solubility values of APA in the literature are different. Mwangi16 reported a value of 16.2 mM as the minimum solubility (at 20 instead of 25 °C), Tavare and Jadhav17 found a value of 12.0 mM, and Rudolph et al.18 reported 10.9 mM. Our value agrees best with the value of 13.8 mM reported by ZareNezhad.19 Note that these authors did not saturate the aqueous phase with BuAc and used different acids and bases to set the pH. Figures 3 and 4 show that the solubility of APA in the range pH 4-5 is not dependent on low concentrations of PenG or PAA, respectively. The error when comparing the experimental data and the solubility given by eq 12 is less than 10% for any experiment.
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Figure 6. Plots of CSD, mass distribution, desupersaturation, and growth rate. S0 ) 1.90; kg ) 4.26 × 10-9 m s-1; g ) 2.0; AR ) 1.91; J0 ) 5 × 106 #‚m-3‚s-1; B ) 2.59. Full lines are model simulations. The green dashed line is the experimental CSD of the seeds. Vertical red dashed lines are averages. Symbols are experimental values at pH 4.0-4.2, for pure APA (spheres), with 1.13 mM PAA impurity (squares), and with 0.55 mM PenG impurity (triangles).
APA Growth Rate. Before analyzing all data of growth as a function of initial supersaturation ratio for pH 4.0 and 5.0, relations of growth rate were obtained as a function of impurity concentration. However, the results showed no statistical difference between the impure and pure systems, except for the experiment characterized by the presence of both PenG and PAA as impurities. For simplicity it was assumed that the latter experiment was an outlier, and all other experimental data were grouped in order to obtain a linear regression as shown in Figure 5. From the analysis of growth rate, the kinetic rate constants were ln kg ) -19.3 ( 0.4 and g ) 2.0 ( 0.35, based on eq 11. This leads to a standard error in the prediction of ln G of 1.2. Thus, the growth rate equation is
G ) (4.26 × 10-9)(S - 1)2.0
(14)
Concerning on the influence of impurities, inhibition of the growth rate has been often reported in the literature.7,9,20 Impurities can change growth rates in different ways.8 Some impurities suppress growth entirely; some may enhance growth. Some impurities can exert an influence at very low concentrations, less than 1 ppm, whereas others need to be present in fairly large amounts before having any effect, as in the current research. Evaluation of Model for APA Crystallization. The aforementioned results allow the calculation of the crystal size distribution using the crystallization model. To be able to check this model, a new series of experiments was performed. The final crystal dimensions are presented in Table 1, in which AR is the aspect ratio of the crystal, thus length/width:
kV )
3 1 2 (A )2
(15)
R
The number-averaged crystal size dp,av increased from 5.2 µm for the seeds to a final value of about 13 µm. The latter value does not depend on the addition of PAA in solid or
dissolved state. A slightly lower crystal size was obtained for experiment 5 at pH 5.2, but it was decided to average all data and to try to model the results with a single set of parameters. The rate constant of growth was used in simulations4 based on eqs 1-8. Nucleation was taken into account in the modeling, based on values of J0 and B from preliminary induction time experiments (not shown but with results on the order of magnitude of those found for ampicillin4). However, nucleation has hardly any impact on the calculations. For example, almost identical values for dp,av were calculated for all J0 values in the range up to 1010 #‚m-3‚s-1. Figure 6 shows the graphs obtained by using the model, including the CSD, mass distribution, desupersaturation, and growth curves. For three typical experiments the values of the desupersaturation and growth rate have been included; these values are of the correct order of magnitude. The numberaveraged size of the crystals according to the model is 12.5 µm, which is in good agreement with the experimental values of Table 1 of about 13 µm. The calculated value of dp,av changed by only 0.1-0.2% when the value of kg in the model was changed by 10%, because faster growth mainly causes the final crystal size to be reached earlier. The mass-based CSD has a bimodal distribution, which is caused by the initial distribution of the seeds, not by nucleation. The deviation between the experimental and simulated desupersaturation curves is partly due to experimental inaccuracies. The pH fluctuated in the range 4.0-4.2 (also within a single experiment), which has a significant impact on the supersaturation. Moreover, at the end of the experiments the supersaturation was 1.2-1.3, whereas the model predicted that equilibrium would be reached. This may be due to degradation products that build up during these long-term experiments. According to a half-life of APA of 120 h,21 about 6% of the APA (1.5 mM) may be degraded after 10 h of crystallization. To obtain a thorough model of the influence of the impurities investigated in this research on the reactive crystallization of APA, a wider investigation would be required including higher concentrations of impurities, especially of PenG. Nevertheless,
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the results of the present study provide enough information to improve the design of APA production processes. Conclusion The kinetic parameters of APA crystallization were determined at pH 4.0 and 5.0. The crystal growth rate strongly depended on the level of supersaturation. A high supersaturation is more easily reached at low pH than at high pH because the solubility of APA is strongly pH dependent in this range. However, a single set of parameters describing growth kinetics could be used. Also, the APA crystal growth rates were not changed by adding PenG and PAA in concentrations of 0.55 and 1.13 mM, at pH 4.0 or 5.0. Acknowledgment The authors gratefully acknowledge the Brazilian government (CNPq and CAPES) for financial support and DSM, Delft, The Netherlands, for donating the chemicals. They are also grateful to Minna Vuolanto from the University of Jyva¨skyla¨ of Finland for assisting in the induction experiments at the Delft University of Technology. Nomenclature AR ) average aspect ratio B ) nucleation factor C ) dissolved concentration, mol/L Ceq ) solubility, mol/L dp,av ) number-averaged crystal size, m FAPA( ) fraction of APA in zwitterionic form G ) crystal growth rate, m s-1 g ) kinetic parameter of growth rate J ) nucleation rate, #‚m-3‚s-1 kg ) growth rate constant, m s-1 kV ) crystal shape factor L ) length crystal, m M ) mass of crystals per volume per size class, kg‚m-4 Mtot ) total mass of crystals formed, kg Mw ) molar mass, kg/mol n ) number of particles per volume per size class, #‚m-4 S ) supersaturation ratio V ) vessel volume, m3 x ) crystal length coordinate, m Greek Symbol FAPA ) crystal density, kg/m-3 Subscripts APA ) 6-aminopenicillanic acid PAA ) phenylacetic acid PenG ) penicillin G 0 ) initial
Literature Cited (1) Van der Wielen, L. A. M.; Ottens, M.; Straathof, A. J. J. In Synthesis of β-lactam antibiotics. Chemistry, biocatalysis and process integration; Bruggink, A., Ed.; Kluwer Academic Publishers: Dordrecht, 2001; pp 150205. (2) Den Hollander, J. L.; Zomerdijk, M.; Straathof, A. J. J.; van der Wielen, L. A. M. Continuous penicillin G hydrolysis in countercurrent waterbutyl acetate biphasic systems. Chem. Eng. Sci. 2002, 57, 1591. (3) Diender, M. B.; Straathof, A. J. J.; van der Does, T.; Ras, C.; Heijnen, J. J. Equilibrium modeling of extractive enzymatic hydrolysis of penicillin G with concomitant 6-aminopenicillanic acid precipitation. Biotechnol. Bioeng. 2002, 78, 395. (4) Ottens, M.; Lebreton, B.; Zomerdijk, M.; Rijkers, M. P. W. M.; Bruinsma, O. S. L.; van der Wielen, L. A. M. Crystallization kinetics of Ampicillin. Ind. Eng. Chem. Res. 2001, 40, 4821. (5) Ottens, M.; Lebreton, B.; Zomerdijk, M.; Rijkers, M. P. W. M.; Bruinsma, O. S. L.; van der Wielen, L. A. M. Impurity effects on the crystallization kinetics of Ampicillin. Ind. Eng. Chem. Res. 2004, 43, 7932. (6) Yang, G.; Louhi-Kultanen, M.; Oinas, P.; Sha, Z.; Kallas, J. The effect of immiscible additives on the batch reactive crystallization of a benzoic acid derivative. J. Chem. Eng. Jpn. 2002, 35, 1140. (7) Klug, D. L. In Handbook of Industrial Crystallization; Myerson, A. S., Ed.; Butterworth-Heinemann: London, 1993; p 65. (8) Mullin, J. W. Crystallization, 3rd ed.; Butterworth-Heinemann: London, 1993. (9) Chianese, A.; Karel, M.; Mazzarotta, B. Crystal growth kinetics of pentaerythritol. Chem. Eng. J. 1995, 58, 215. (10) Sangwal, K. Effect of impurities on the crystal growth processes. Prog. Cryst. Growth Charact. Mater. 1996, 32, 3. (11) Sangwal, K. Effect of impurities on the processes of crystal growth. J. Cryst. Growth 1993, 128, 1236. (12) Sangwal, K.; Mielniczek-Brzo´ska, E. Effect of Fe(III) ions on the growth kinetics of ammonium oxalate monohydrate crystals from aqueous solutions. J. Cryst. Growth 2001, 233, 343. (13) Randolph, A. D.; Larson, M. A. Theory of particulate processes: Analysis and techniques of continuous crystallization; Academic Press: New York, 1971. (14) Tavare, N. S. Industrial Crystallization: Process Simulation Analysis and Design; Plenum Press: New York, 1995; 527 pp. (15) Diender, M. B.; Straathof, A. J. J.; Heijnen, J. J. Predicting enzyme catalyzed reaction equilibria in cosolvent-water mixtures as a function of pH and solvent composition. Biocatal. Biotransform. 1998, 16, 275. (16) Mwangi, S. M. Reactive precipitation of 6-aminopenicillanic acid: Application of a crystallization methodology. Ph.D. Thesis, The Victoria University of Manchester, 1994; 266 pp. (17) Tavare, N. S.; Jadhav, V. K. Solubilities of 6-aminopenicillanic acid and phenoxyacetic acid in hydrotrope solutions. J. Chem. Eng. Data 1996, 41, 1196. (18) Rudolph, E. S. J.; Zomerdijk, M.; Ottens, M.; van der Wielen, L. A. M. Solubilities and partition coefficients of semi-synthetic antibiotics in water + 1-butanol systems. Ind. Eng. Chem. Res. 2001, 40, 398. (19) ZareNezhad, B. Prediction of the solubility of 6APA in aqueous phase and optimum control scheme for batch crystallization process through pH variation. Korean J. Chem. Eng. 2002, 19, 992. (20) Rauls, M.; Bartosch, K.; Kind, M.; Kuch, S.; Lacmann, R.; Mersmann, A. The influence of impurities on crystallization kineticssa case study on ammonium sulfate. J. Cryst. Growth 2000, 213, 116. (21) Ferreira, J. S.; Straathof, A. J. J.; Franco, T. T.; van der Wielen, L. A. M. Activity and stability of immobilized penicillin amidase at low pH values. J. Mol. Catal. B: Enzym. 2004, 27, 29.
ReceiVed for reView February 9, 2006 ReVised manuscript receiVed June 22, 2006 Accepted August 4, 2006 IE0601652
