Ind. Eng. Chem. Res. 2002, 41, 5789-5793
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Intrinsic Kinetic Parameters of Clavulanic Acid Adsorption by Ion-Exchange Chromatography Marlei Barboza,† Renata M. R. G. Almeida,‡ and Carlos O. Hokka*,‡ Department of Chemical Engineering, UFSCar-Federal University of Sa˜ o Carlos, Via Washington Luiz, km 235, C. Postal 676, CEP 13565-905 Sa˜ o Carlos, SP, Brazil, and Department of Chemical Engineering, UNAERP-University of Ribeira˜ o Preto, Avenida Costa´ bile Romano 2201, C. Postal 98, CEP 14096-380 Ribeira˜ o Preto, SP, Brazil
This paper reports on an evaluation of the intrinsic kinetic parameters of the specific sorption of clavulanic acid (CA) by ion-exchange chromatography. The first step of this work was to determine the diffusivity of CA in the pores of a resin, using a model based on diffusion with instantaneous adsorption. However, the adsorption rate step was found to affect the adsorption process. A mathematical kinetic model for the adsorption and desorption of CA was, therefore, proposed considering both kinetics and diffusion. Intrinsic kinetic parameters were obtained using the same experimental data utilized in determining diffusivity. In this case, the adsorption rate was considered to be the process-limiting factor. Tests were carried out in a 200 mL stirring tank, with the initial solution at pH ) 7.0 and the temperature maintained at 10 °C. The results showed that both the reaction rate and mass-transfer limitation have to be taken into account in the analysis of CA adsorption by ion-exchange resins. Introduction The β-lactam family is the most important of all antibiotic groups, constituting the greatest part of the multibillion-dollar worldwide antibiotic market. Approximately 60% of the total worldwide production of antibiotics is of the β-lactam type.1 Bacterial resistance is one of the greatest hindrances to the use of chemotherapeutic agents and antibiotics and the control of infectious diseases. Clavulanic acid (CA) is a β-lactam antibiotic produced by a filamentous bacterium (actinomycete) named Streptomyces clavuligerus. CA covers a broad antibacterial spectrum, but its level of activity is relatively low. It is, however, a potent inhibitor of the β-lactamases produced by strains of some pathogenic microorganisms resistant to β-lactam antibiotics. These enzymes are able to catalyze the hydrolysis of molecules containing a β-lactam ring. CA can block this resistance; as a result, in the presence of low concentrations of CA, many of these β-lactamaseproducing organisms are rendered almost as sensitive to penicillins and cephalosporins now commercially available as non-β-lactamase-producing strains.2 The combination of CA with amoxycillin is currently the most successful example of the use of a β-lactam antibiotic sensitive to β-lactamase together with an inhibitor of these enzymes.3 The isolation of CA from fermentative broth is performed in a series of steps. At the end of fermentation, the broth is first clarified by filtration or centrifugation. The most important step, primary extraction from clarified broth, is based on several two-phase separation methods. One of these methods is the direct extraction of the filtrate with an organic solvent, producing an * Corresponding author. E-mail:
[email protected]. Telephone: (+55 16) 260-8264. † UNAERP-University of Ribeira˜o Preto. Telephone: (+55 16) 603-6789. ‡ UFSCar-Federal University of Sa˜o Carlos.
organic phase containing CA, which is subsequently isolated. An alternative process, to avoid the use of solvent, consists of chromatographic adsorption techniques with nonionic or ionic adsorbers. This technique has developed rapidly in recent decades, mainly since the introduction of synthetic adsorbers.4 Adsorption techniques can be used in several steps of the separation and purification of antibiotics. One type is ion-exchange adsorption, which involves electrostatic attraction of ionic components to sites on the adsorbent surface with opposite charge. However, CA is a compound that has no strongly hydrophobic group and exhibits low chemical stability. These characteristics are responsible for the low recuperation levels of CA during purification. An investigation of the use of Amberlite XAD resins in the purification of CA from fermentative broth was carried out by Mayer et al.5 Preliminary studies had shown a very weak interaction between CA and the nonpolar surface of these resins, as a consequence of the chemical structure of this antibiotic. A new system based on ion-pair formation was developed. In this system, the XAD matrixes were tested in combination with water-soluble quaternary ammonium salts to form ion pairs with the acid group of the CA molecule. Comparative tests were run, using the ion-pairing system, the traditional anion-exchanger Amberlite IRA 400, in its original chloride form. The authors concluded that the ion-pair system was a viable alternative for the purification of CA. The resin Amberlite XAD-4 with the quaternary ammonium salts displayed a better performance than the ion-exchange Amberlite IRA 400. However, the system proposed by these authors increases the cost of the purification process, owing to the use of quaternary ammonium salts. In the work reported herein, adsorption isotherms were determined and kinetic studies were made to verify the mass-transfer effects on the overall kinetics, taking into account mass-transfer and kinetic limitations. A model of the CA adsorption process, including these
10.1021/ie0201361 CCC: $22.00 © 2002 American Chemical Society Published on Web 10/17/2002
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Ind. Eng. Chem. Res., Vol. 41, No. 23, 2002
phenomena, is proposed and analyzed. The adsorption of biomolecules is usually considered to be a masstransfer-limited (external and internal diffusion) process. Materials and Methods Adsorbate. CA was obtained from a mixture of SiO2/ potassium clavulanate (1:1) that was kindly provided by Gist Brocades, Delft, The Netherlands. Preparation of the Stationary Phase. The stationary phase was the anion-exchanger Amberlite IRA 400, kindly supplied by Rohm and Haas. This resin can be regenerated with NaCl (chloride cycle). When it is regenerated with NaCl, it is possible to remove only anions, such as SO4-2, NO3-, and PO4-3, that are capable of removing the chloride from these matrixes. In this work, the resin was pretreated with 10% (w/v) NaCl to work with the chloride cycle; the resin was then washed several times with deionized water to eliminate the excess ions. Analytical Methods. The CA concentrations were determined by high-performance liquid chromatography (HPLC), as described by Foulstone and Reading.6 An HPLC device with a photodiode array detector (Waters 996 PDA) was utilized with a reversed-phase column (C-18 µ-Bondapak 3.9 × 300 mm). The HPLC equipment was operated at 28 °C, with a flow rate of 2.5 mL/min, and was calibrated against solutions of the pharmaceutical product “Clavulin” (tablets containing 125 mg of potassium clavulanate and 500 mg of amoxycillin), produced by SmithKline Beecham Laborato´rios Ltda., Rio de Janeiro, Brazil. The mobile phase was composed of a 0.1 M KH2PO4 buffer solution containing 6% of methanol and phosphoric acid, which puts the pH at 3.2. Determination of the Adsorption Isotherm. The adsorption isotherm run was carried out in a shaker at 10 °C until adsorption equilibrium was attained. Different concentrations were obtained by diluting the sample in deionized water, and two glasses containing 5 mL of a CA solution and 0.25 g of the stationary phase (wet basis) were used for each concentration. The initial and final concentrations were analyzed by HPLC, as described above. The Langmuir model was utilized to describe the equilibrium behavior. Batch Runs. The experiments to study the adsorption and desorption kinetics of CA in IRA 400 resin were carried out in a 200 mL isothermic glass stirring vessel. The vessel contained 100 mL of a CA solution and 5.0 g of ion-exchanger resin (wet basis). Samples were withdrawn periodically, and the antibiotic concentrations were determined.
where k1 and k2 are the intrinsic rate constants, Ci is the antibiotic concentration in the solution at any position inside the resin, qi is the antibiotic concentration adsorbed at a specific site of the resin, and qm is the maximum adsorption capacity of the resin. At adsorption equilibrium
q* )
qmC* KD + C*
(2)
where q* is the equilibrium concentration in the solid phase (gCA/gres), C* is the corresponding equilibrium concentration in the liquid phase, qm is the maximum capacity of the resin, and KD is the dissociation constant ()k2/k1). The proposed model is based on ideal surfaces and predicts that the adsorption surface is energetically ideal. Thus, eq 2 is the Langmuir equilibrium model. Mathematical Modeling for the Adsorption Step in a Stirred Tank Reactor. Let us assume that Vs is the volume of adsorber immersed in a volume V1 of liquid with CA dissolved at an initial concentration C0, contained in a perfectly stirred reactor. The solute (CA) diffuses into the resin particles and is adsorbed until equilibrium is reached. In the formulation of the model, it is assumed that the resin particles are spherical; CA diffusion in the solid particles follows Fick’s law; diffusion is in the r direction only; adsorption takes place under isothermal conditions. The adsorbed CA is assumed to be in equilibrium with that in the pore fluid at each radial position within the particle. The following conservation equations and boundary conditions are used to describe the CA uptake kinetics for spherical particles of radius R in a closed batch system. Based on the above assumptions, the adsorption process in a constant-volume stirred tank can described by eq 3:
dCb 3 Vs )k (C - Cs) dt R Vl s b
(3)
where Cb is the bulk and Cs is the surface of the solid concentration of CA. The initial condition for eq 3 is
t ) 0 f Cb ) C0
(4)
The differential material balance inside the solid particles, where adsorption takes place on the porous surface, is
(
)
1 - p ∂2Ci 2 ∂Ci ∂Ci + rq ) Def 2 ∂t r ∂r p ∂r
(5)
If the equilibrium at the surface is considered, this equation can be reduced to
Mathematical Model The kinetic behaviors of CA adsorption on the resin are described as follows. Kinetic Model. CA adsorption on the resin:
[
]
(
)
∂qi ∂Ci ∂2Ci 2 ∂Ci ) Def p + (1 - p) + ∂Ci ∂t r ∂r ∂r2
(6)
(resin)+Cl- + CA- {\ } complex + Clk
The initial and boundary conditions associated with the diffusion process inside the solid particles are respectively
The rate expressions for the intrinsic kinetic model may be written as follows:
t ) 0 f Ci ) qi ) 0
k1
2
rq ) k1Ci(qm - qi) - k2qi
(1)
r)Rf
∂Ci ks (C - Cs) ) ∂r pDef b
(7) (8)
Ind. Eng. Chem. Res., Vol. 41, No. 23, 2002 5791
r)0f
∂Ci )0 ∂r
(9)
The diffusion equation inside the particles was discretized and solved by the method of orthogonal collocation, where the boundary condition referring to the film resistance was used as a collocation point.7 To integrate the two differential equations, the code DASSL was used.8 To determine the effective diffusion coefficient (Def) and the film coefficient (ks), the Nedler and Mead9 method for parameter optimization was utilized, with the simultaneous numerical solution of the set of differential equations. Optimization was performed by the least-squares method algorithm to minimize the objective function defined by eq 10: N
Φ)
∑1 (Cb - Cexp)2
(10)
When the values of Φi in the simplex vortexes and their mean values Φ h i satisfied the inequality (11), the optimization was considered complete
(
m
)
∑1 (Φi - Φh i)2 m+1
1/2
3.0 mass-transfer limitation. The values found indicate that both steps should be considered. Determination of the Intrinsic Kinetic Parameters Figures 3 and 4 show typical graphs comparing the experimental and calculated values of the CA adsorption data. The first adjustment was made considering the balance on the surface of the resin (eq 6), a consideration that allows the transport parameters Def and ks to be determined. Once these data were obtained, eqs 1 and 5 were used to determine the intrinsic kinetic parameters (k1 and k2). Table 2 shows the results of the intrinsic parameters. The results given in Table 1 demonstrate that the adsorption and mass-transfer steps limit the process. The purely intrinsic kinetic
Ind. Eng. Chem. Res., Vol. 41, No. 23, 2002 5793 Table 2. Intrinsic Parameters Obtained with Nonlinear Adjustment k1 k1 (L g-1 min-1) k2 k′1 k′2 kR run (L g-1 min-1) (min-1) (L g-1 min-1) (min-1) (min-1) (from eq 18) 1 2 3 4 5
1.10 1.10 1.10 1.13 1.13
0.043 0.043 0.043 0.045 0.045
0.89 0.24 0.32 0.46 0.46
0.035 0.010 0.013 0.018 0.018
1.34 0.64 0.70 0.99 0.94
1.27 0.61 0.68 0.95 0.91
Table 3. Effectiveness Factor and Thiele Modulus for Each Run run
φ
η
run
φ
η
1 2 3
0.31 0.36 0.37
0.95 0.93 0.93
4 5
0.44 0.37
0.90 0.93
model (which does not take into account the effective diffusivity of eq 1) was evaluated, and the intrinsic kinetic constants (k1 and k2) were compared with the model that considers the diffusivity (eqs 1 and 5). The value of the k′1 (purely intrinsic model according eq 1) parameter was found to be lower than that of the k1 parameter obtained from the adjustment of eqs 1 and 5 (intrinsic-diffusive model). Diffusion coefficient values were found. Also, the initial bulk CA concentration seemed to affect Def. The same phenomena were observed by Mayer et al.10 Probably a dead core in the particles, whose size depends on the external concentration, affects the R2/Def ratio that appears in the model. Furthermore, in the Thiele modulus (eq 23) and effectiveness factor, in eq 24, this ratio is present. Based on the experimental data and eq 20, it was possible to determine kR and, thus, to estimate the k1 value in eq 18. The results reveal that k1 obtained by eq 18 is much lower than that obtained, considering the intrinsic-diffusive model of eqs 1 and 5. This fact emphasizes the consideration that reaction kinetics and mass-transfer limitation should be considered. The Thiele modulus (φ) can be calculated using the kR value, as shown below:
φ)
x
R 3
kR Def
(23)
The effectiveness factor can be calculated by eq 24.
η)
1 1 1 φ tanh 3φ 3φ
(
)
(24)
These values are given in Table 3. According to these results, both mass transfer and the adsorption step are limiting factors to be considered in the analysis of this process. The intrinsic parameters calculated are highly representative of the process studied here. The transport coefficient of external film mass transfer was constant in every run, probably because of the fact that the conditions under which the runs were carried out did not limit the process, a fact that is not coherent with the simplex optimization method. Dif-
fusive resistance to mass transfer through the boundary layer film of the spherical resin particles was negligible, a phenomenon that is reflected in the large Biot values obtained in the process. Conclusions An analysis of the results presented herein leads us to conclude that the mass-transfer limitations and the adsorption step must be taken into account to analyze the process. The results clearly demonstrated that the model proposed to simulate the adsorption step (through eqs 1 and 5), considering the adsorption kinetics, equilibrium data, and mass-transfer limitations, fitted the experimental data very well, providing valuable information for further process optimization. Acknowledgment The authors gratefully acknowledge the financial support of the Brazilian research funding institution FAPESP (Projects 99/07693-2, 99/03279-7, and 98/ 11596-0). Literature Cited (1) Ghosh, A. C.; Bora, M. M.; Dutta, N. N. Development in liquid membrane separation of beta-lactam antibiotics. Bioseparation 1996, 6, 91-105. (2) Brown, A. G.; Butterworth, D.; Cole, M.; Hanscomb, G.; Hood, J. D.; Reading, C.; Rolinson, G. N. Naturally ocurring β-lactam inhibitors with antibacterial activity. J. Antibiot. 1976, 29, 668-669. (3) Mayer, A. F.; Deckwer, W. D. Simultaneous production and decomposition of clavulanic acid during streptomyces clavuligerus cultivation. Appl. Microbiol. Biotechnol. 1996, 45, 41-46. (4) Butterworth, D. In Clavulanic acid: properties, biosynthesis and fermentation. Biotechnology of Industrial Antibiotcs; Vandamme, E. J., Ed.; Marcel Dekker: New York, 1984; Vol. 6; pp 225-235. (5) Mayer, A. F.; Anspach, F. B.; Deckwer, W. D. Purification of clavulanic acid by ion-pairing systems. Bioseparation 1996, 6, 25-39. (6) Foulstone, M.; Reading, C. Assay of amoxycillin and clavulanic acid, the components of augmentin, in biological fluids with high-performance liquid chromatography. Antimicrob. Agents Chemother. 1982, 22, 753-762. (7) Villadsen, J.; Michelsen, M. L. Solution of Differential Equation Models by Polynomial Approximation; Prentice Hall: Englewood Cliffs, NJ, 1978. (8) Petzold, L. Differential Algebraic System Solver (DASSL) Subroutine; Computing and Mathematics Research Division, Lawrence Livermore National Laboratory: Livermore, CA, 1989. (9) Nedler, J. A.; Mead, R. A. Simplex method for function minimization. Comput. J. 1965, 7, 308-315. (10) Mayer, A. F.; Hartmann, R.; Deckwer, W. D. Diffusivities of clavulanic acid in porous sorption systems with ion-pairing. Chem. Eng. Sci. 1997, 52, 4561-4568.
Received for review February 11, 2002 Revised manuscript received August 20, 2002 Accepted August 21, 2002 IE0201361
