Transcription

1 This article was originally published in a journal published by Elsevier, and the attached copy is provided by Elsevier for the author s benefit and for the benefit of the author s institution, for non-commercial research and educational use including without limitation use in instruction at your institution, sending it to specific colleagues that you know, and providing a copy to your institution s administrator. All other uses, reproduction and distribution, including without limitation commercial reprints, selling or licensing copies or access, or posting on open internet sites, your personal or institution s website or repository, are prohibited. For exceptions, permission may be sought for such use through Elsevier s permissions site at:

2 Separation and Purification Technology 49 (2006) Minimizing the environmental impact of the regeneration process of an ion exchange bed charged with transition metals Abstract José L. Valverde, Antonio De Lucas, Manuel Carmona, Juan P. Pérez, Marcela González, Juan F. Rodríguez Department of Chemical Engineering, University of Castilla-La Mancha, Avda. de Camilo José Cela s/n, Ciudad Real, Spain Received 9 May 2005; received in revised form 12 September 2005; accepted 18 September 2005 A transport mathematical model to describe the performance of ion exchange processes in fixed beds, to use the regeneration curves as a tool to optimize the regeneration process was developed. The model is based on both the Nernst Planck equation and the mass action law. This model allowed to obtain the optimum amount of regenerant agent to be used, regardless the system considered. Therefore, it would be possible to minimize the final waste volume and maximize the recovered bed capacity without any additional consumption of regenerant agent. The results obtained allowed to conclude that the sodium chloride is better regenerant agent than chlorhydric acid for strong acid resins, because it requires a lower amount of equivalents to reach the same regeneration level and is cheaper. Finally, the concentration of regenerant agent required for copper elution is less than that required for the other ions (Cd 2+ and Zn 2+ ). These results were found to agree with the affinity of the resin Elsevier B.V. All rights reserved. Keywords: Ion exchange; Kinetics; Mass transfer; Diffusion; Nernst Planck; Fixed resin bed; Regeneration 1. Introduction The presence of hazardous ions in aqueous waste streams is an important environmental problem. Basic metals such as aluminum, cadmium, chromium, copper, iron, lead, mercury, nickel and zinc have been classified as the 10 metals of primary importance for recovery from industrial waste streams [1]. The ion exchange in some cases is the most economic and effective technique to remove these types of ions from wastewaters. Pollutant ions present in the stream are replaced by non-contaminant ions released from the ion exchanger. Once the capacity of the ion exchanger has been spent by entering ions uptake, it must be regenerated with a highly concentrated regenerant agent, in order to restore the initial ionic form and continue again with the removal process [2,3]. To minimize the final pollutant volume and the regeneration costs are the main concerns of ion exchange users. During decades several groups contributed to a deep understanding of ion exchange in fixed beds [4 6]. Klein [7] presents an interesting review about the operation of cycling fixed bed Corresponding author. Tel.: ; fax: address: juan.rromero@uclm.es (J.F. Rodríguez). operations based in his own experience in ion exchange process and regeneration. From that time not very much theoretical effort has been done for a deep understanding of regeneration process in ion exchange in order to minimize the amount of effluent generated in the regeneration process. According to Strydom and Frederick [8], the regeneration process can be optimized by analyzing concentration profiles of the different ions in the regenerant stream. The efficiency of the regeneration process is generally evaluated in terms of the restoration of the exchange capacity of the resin. Ion exchange operation does not utilize the total capacity of the resin for exchange because of a complete regeneration may require excessive time and material. Up to date, the study of the regeneration process continues to be empirical and dependent on the resin type and the ions to be considered. Although, some experimental efforts have been done to systematize the regeneration process [9], the general rules remain being quite empirical and have not been summarized in a unique text. Some authors have used the same amount of regenerant agent regardless the involved system. Strydom and Frederick [8] used 4 wt% NaOH as the regenerant agent for strong base and weak base anion exchangers in the upward and downward direction, respectively, at 49 C. Korngold [10] used 2N HCl as the regenerant agent to release /$ see front matter 2005 Elsevier B.V. All rights reserved. doi: /j.seppur

3 168 J.L. Valverde et al. / Separation and Purification Technology 49 (2006) Nomenclature C A, CA s concentration of species A in the solution phase at equilibrium (eq/m 3 ) C A0 initial concentration of species A (eq/m 3 ) C T total ionic concentration in solution (eq/m 3 ) D A intraparticle diffusion coefficient of species A (m 2 /s) D x axial dispersion coefficient F flow rate (m 3 /s) I Faraday constant K AB equilibrium constant (Eq. (12)) K L film mass transfer coefficient N A flux of ion A (eq/(m 2 s)) q total solid-phase capacity (eq/m 3 ) q A solid-phase concentration of species A (eq/m 3 ) qa s concentration of species A at the solid resin surface (eq/m 3 ) r radial position in the particle (m) R perfect gas constant R p particle radius (m) Re Reynolds number Sc Schmidt number t time (s) T temperature (K) u superficial velocity (m/s) x position along the bed length z j electrochemical valence of the ion j (j = A and B) Greek letters ε b porosity of the resin bed φ electric potential µ viscosity of solvent (kg/(m s)) ρ density of solvent (kg/m 3 ) divalent iron from a macroporous weak acid cation exchange resin. Tenório and Espinosa [11] used 2 wt% H 2 SO 4 as the regenerant agent for cationic resins and 4 wt% NaOH for the anionic. Bahowick et al. [12] employed 15.8 wt% NaCl as the regenerant agent to remove hexavalent chrome from Purolite A- 600 resin. For Amberlite IR-120, supplier recommends to use HCl solutions from 4 to 6 wt% or a 10 wt% NaOH as regenerant agents. Most of the manufacturers propose general methods of regeneration for water softening. Any case, a compromise between economical cost and the environmental impact has to be reached. In this case, the minimization of effluent volume is especially important due to the polluting capability of these waste streams. To avoid the application of empirical procedures in the prediction of the regeneration of fixed beds capacity, some mathematical efforts have been carried out. Kataoka et al. [13] developed a model whose application is only constrained to irreversible systems; the model proposed by Erickson and Howard [14] did not take into account the influence of axial dispersion. It is well known that the regeneration of beds saturated with systems with favourable isotherms is mainly controlled by equilibrium and a very simple mathematical treatment would be enough to predict the approximated concentration profiles in the regeneration effluent. Any case, it is clear that for an accurate optimized design of the ion exchange process, one must be able to predict the regeneration effluent concentration history. Thus, it is necessary to know not only the basic equilibrium parameters but also the kinetic parameters of the charged resin with respect to the regenerant agent. In previous papers [15,16], models for measuring monovalent and heterovalent cations intraparticle diffusivities in geliform ion exchange resins by the zero-length-column (ZLC) technique were developed. The model described ion fluxes using Nernst Planck equations and equilibrium using ideal mass action law, and included the resistance to mass transfer both in the particle and in the film. The model took into account the influence of the electric field caused by the differences in the mobilities of counterions on the ion exchange rate. Differences between uptake and elution kinetics for a given system and the dependence of the exchange rate with the concentration of each counterion can be predicted [17]. External mass transfer resistance also affects the ion exchange rate and can be the controlling step at low solution concentrations [18,19]. On the contrary, at high solution concentrations, intraparticle diffusional resistance is usually the controlling step [20]. The main objectives of the present study are as follows: (i) To develop a generalized mathematical model for heterovalent systems to describe the performance of ion exchange process in fixed beds. The model includes the resistance to mass transfer in the film and inside the particle, a thermodynamic constant to describe the ion exchange equilibrium at the particle surface, and the effect of the electric field. (ii) To use the regeneration curves as a tool to optimize the regeneration process. (iii) To optimize the concentration of regenerant agent in order to minimize waste volume. 2. Mathematical model A complex mathematical model including the effect of film and internal mass transfer resistances, Nernst Planck equations to describe ion fluxes and equilibrium using ideal mass action law has been developed. A simpler solution based in equilibrium theory [21] could be used but this type of model does not take account the intraparticle diffusional resistance which is the controlling step at high solution concentrations regeneration conditions and the theoretical curves obtained would present a certain delay with respect to the dispersive breakthrough curves experimentally obtained. Thus, the complex model will allow us to confirm the validity of the equilibrium and kinetic parameters obtained in previous works [16,22] and quantify exactly the amount of eluted ion in each moment of the regeneration to relate it with the efficacy of the regenerant solution. Model equations have been derived including the followings simplifying assumptions:

4 J.L. Valverde et al. / Separation and Purification Technology 49 (2006) (i) The whole resin is treated as a quasi-homogeneous phase. Resin beads are assumed to be completely spherical in shape with no appreciable volume changes during the ion exchange process. (ii) The effects of pressure gradients and activity are neglected. (iii) Co-ion concentration in the ion exchanger is negligible. (iv) Ion intraparticle diffusivities do not depend on particle concentration. An isothermal ion exchange process between an ion A z A + presaturating the resin and an ion B z B + entering the resin particle, can be described by the following general equation: z B (Resin za A) + z A B z B z A (Resin zb B) + z B A z A (1) Applying the Nernst Planck equation, the flux of ion in the solid phase, expressed in terms of the concentration gradient, are given by: [ ] qj N j = D j r z I φ jq j (j = A and B) (2) RT r The conditions of electroneutrality and no net electric current are described as follows: N A + N B = 0 (3) q A + q B = q (4) The term corresponding to the electric field for solid phase in Eq. (2), can be eliminated, so: I φ RT r = (D A D B ) qa r q A (D B z B D A z A ) D B z B q (5) The general equation corresponding to the flux of ion A in the solid phase, expressed in terms of the concentration gradient, is then: { (DA D B )[q A (z B z A ) z B q } ] qa N A = q A (D B z B D A z A ) D B z B q (6) r The mass balance in the resin particle is: q A = 1 t r 2 r (r2 N A ) (7) Deriving Eq. (7), one gets: q A = 2 t r [N A] r [N A] (8) It is possible to assume that the concentration profiles will be symmetric about the center. Consequently, flux across the center does not exist and the initial and boundary conditions will be: r = 0; dq A dr = 0 (9) c t = 0; q A = q ; C A = C A0 = C T (10) r = R p ; N A r=rp = K L (C s A C A) (11) Ion exchange equilibrium can be reproduced by applying the mass action law: ( ) 1 qs za A q (C s K AB = A C T z A ) z B ( q s ) zn (12) A q [(1 C s A ) C T z A ] z A Introducing the flux equation (6), Eq. (8) becomes: q A = 2 [ t r (DA D B )[q A (z B z A ) z B q ] ] q A q A (D B z B D A z A ) D B z B q r r [N A] (13) The gradients are approximated by finite differences [23], where N A takes different values depending on the resin position. According to the boundary conditions, r [N A] at the surface is transformed in gradients respect to r using Eqs. (6) and (11). Inside the particle, this gradient is obtained by deriving Eq. (6). In this way, the ion exchange model is reduced to a stiff system of ordinary differential equations. The mass balance in a differential length of the fixed bed is: C A = u C A t ε b x D 2 C A x x q A ε b t (14) r=rp being: q A = 3 (N A )(1 ε b ) (15) t R p and N A is defined by Eq. (6). Initial and boundary conditions for the regeneration of the bed are: t = 0; 0 <x bed length; C A = C A0 ; (16) t 0; x = 0; C A = 0; (17) Axial dispersion coefficient, D x, can be defined by the following equation [24]: [ D x = 2uR ( )( ) ] p ρRp u (18) ε b µ ε b ε b To describe the mass transfer through the external film, the following relation [13] is used: K L = u [ ] 1 1/3 1.85Re 2/3 Sc 2/3 εb (19) ε b where u is the superficial velocity, Sc the Schmidt number and Re is the Reynolds number both defined as Sc = µ ρ D f (20) and Re = ρ 2R pu (21) µ(1 ε b ) Partial differential equations (13) and (14) are transformed in a system of (n +1)l ordinary differential equations, n being ε b

5 170 J.L. Valverde et al. / Separation and Purification Technology 49 (2006) Fig. 1. Theoretical regeneration curves calculated from the model here developed. Influence of the flow, F (C T = N; D A = m 2 /s; D B = m 2 /s; K AB = 5.36; z A =1; z B = 2; bed length = 0.6 m; bed diameter = m; R p = m; q = 1450 eq/m 3 ; T = 298 K). the number of nodes inside the particle, and l is the number of nodes along the length of the resin bed. The Rosenbrock method [25] was used to integrate numerically the stiff set of ordinary differential equations due to the few steps of integration required to achieve the solution and its stability, although in this case the solutions for the regeneration curves are of dispersive wave type. A Fortran 6.0 application was developed for solving this model. With the aim of checking the performance of the model, different simulations of the regeneration theoretical curves under different conditions were carried out. As example, Fig. 1 shows the elution curves for the ion A at different input flows. As was expected, when the flow increases, a faster elution is achieved, since the quantity of ions fed to the bed is higher. Likewise, it is observed as the slope of the regeneration curve diminishes when flow does. 3. Experimental 3.1. Chemical Zinc, copper and cadmium nitrates PRS grade (99%), and nitric acid 65% (w/w) PA grade, were supplied by Panreac. Demineralized water with a conductivity value lower than 5 S/cm was used. The cationic resin Amberlite IR-120, supplied by Rohm and Haas, was used as the ion exchanger. Parameters of the fixed bed are summarized in Table 1. Table 1 Parameters of the fixed bed Parameter Resin Amberlite IR-120 Resin bed porosity 0.33 Length of the resin bed (m) Radius of the resin bed (m) Average particle diameter (m) Weight of dry resin in the bed (g) 5160 Volume of resin in the bed (m 3 ) Fig. 2. Schematic diagram of the pilot plant used in this research. (1) Principal drum; (2) wash water drum; (3) regenerant solution drum; (4) centrifugal pump; (5) rotameter; (6) fixed bed containing the ion exchange resin; (7) conductivity cell; (8) conductivity meter; (9) computer; (10) control panel Procedure Charge and regeneration cycles were carried out in an ion exchange pilot plant. The experimental system is shown schematically in Fig. 2. The metal concentration of the effluent was measured by AAS. The resin bed was aged by three successive processes of load and regeneration. The flows and concentrations used in this work correspond to those recommended by the suppliers in their specification sheets. Once the bed was completely saturated with the transition metal ion, the bed was expanded by washing with water in a counter current flow. The regeneration of the resin bed was carried out turning back the resin bed to the primitive state, whatever Na + or H + form. All the experiments were carried out at 25 C. The ions under study were Cu 2+,Cd 2+ and Zn 2+. As regenerant agents, NaCl and HCl were used. Table 2 summarizes experimental conditions. 4. Results and discussion Test runs with different nodes inside the particle and along the bed were performed in order to choose the optimal values Table 2 Experimental conditions in the regeneration of Amberlite IR-120 fixed bed Regenerant agent Regenerant concentration (wt%) Cation initially in the resin Flow rate (m 3 /s) NaCl 4 Copper NaCl 6 Copper NaCl 16 Copper NaCl 24 Copper HCl 6 Copper NaCl 8.9 Cadmium NaCl 7.8 Zinc T = 298 K. Resin initially loaded with copper, cadmium and zinc.

6 J.L. Valverde et al. / Separation and Purification Technology 49 (2006) Fig. 3. Experimental and theoretical regeneration curves of a fixed bed consisting of Amberlite IR-120 loaded with copper, cadmium and zinc at T = 298 K. Copper: NaCl 6%; F = 6 BV/h; cadmium: NaCl 8.9%; F = 5.7 BV/h; zinc: NaCl 7.8%; F = 6.3 BV/h. for efficient and accurate computing. This way, 6 nodes inside the particle and 60 along the bed were used. As can be seen in Fig. 3, the developed model fits very well the experimental performance of the metal loaded resin regeneration. The standard average difference between experimental and theoretical curves is lower than 10% in all the cases. The computational time to simulate an experiment took less that half an hour. The equilibrium constants for Eq. (12) have been obtained using the thermodynamic equilibrium data reported by Valverde et al. [22]. First, the equilibrium curves at 298 K were calculated and after that the data obtained were fitted to Eq. (12) to obtain the ideal equilibrium constant of the systems at 298 K shown in Table 3. The values of the diffusion coefficients in the resin Amberlite IR-120 used were reported by Valverde et al. [16] (D Cu = m 2 /s, D Cd = m 2 /s and D Zn = m 2 /s). The sodium ion diffusion coefficient was obtained by Rodriguez et al. [15] (D Na = m 2 /s). As can be observed, the model is able to reproduce the regeneration curves for different systems using the equilibrium and diffusion coefficients calculated in the mentioned previous works. These results would also allow conclude that this model might be applied to find the optimal regeneration conditions of fixed bed of resins without additional experimental treatment whenever an optimal condition exists. The knowledge of an optimal regeneration condition is very important, since the concentration of the regenerant agent has a high impact over the final cost of the regeneration process. From this point of view, several experiments were carried out using Table 3 Ion exchange equilibrium constants for the resin Amberlite IR-120 at 298 K (from ref. [22]) System K AB Est. dev. (%) Na + /Cu Na + /Cd Na + /Zn Fig. 4. Influence of the concentration of sodium chloride solution on the level of regeneration for a fixed bed consisting of resin Amberlite IR-120 in Cu form. F = 5.7 BV/h; T = 298 K. a resin bed charged with copper and different concentrations of regenerant agent. As can be seen in Fig. 4, the regeneration level achieved for the resin bed charged with copper depends on the concentration of the regenerant agent, raising this level with the concentration. A regeneration level higher than 97% can be obtained after 4 bed volumes (BV) using concentrations of the regenerant agent between 6 and 24 wt%. On the other hand, the lowest concentration of the regenerant agent studied would require additional volume in order to reach a useful regeneration degree. In other words as the external concentration increases the charged metal is less retained due to the electroselectivity effect and the efficiency increases. However, this effect reduces at high concentration and the and for that reason the regeneration efficiency of the solutions above the 6% is almost the same. If a regeneration level of 100% is not required, any concentration of regenerant agent over 6% is not necessary. To define a specific regeneration degree is necessary to know the environmental regulations of the place in which the installation is to be located. Anyway, the complete regeneration (100%) is not economically and industrially recommended. At NaCl concentrations of 6 wt% the regeneration degree shifts from 80 to 99 wt% when the bed volumes go from 2 to 5. An increase in the regeneration level implies an increase of costs. Smaller reagent dosages lead to a reduction of the operational capacity of the bed and a big volume of residuals. The effectiveness of the regeneration process using different concentrations of sodium chloride was evaluated. It was defined as the ratio between the number of equivalents of the ion eluted and the number of equivalents of the regenerant ion fed (in percentage). The efficacy of the regenerant solutions was of 30.93, 9.47 and 6.02% for the concentrations of 6, 16 and 24% of NaCl, respectively. This effectiveness was calculated taking as reference the same regeneration level (98 99%). According to that, the optimal concentration of NaCl is about 6 wt%. Nevertheless, the regeneration of strong acid

7 172 J.L. Valverde et al. / Separation and Purification Technology 49 (2006) Zn 2+ ). These results were found agreed with the affinity of the resin. Acknowledgement Fig. 5. Influence of the regenerant agent on the level of regeneration of a bed consisting of resin Amberlite IR-120 in Cu form. F = 5.7 BV/h; T = 298 K. resins can be carried out by chlorhydric acid solutions. In order to compare regenerant agents, an experience was carried out using a 6 wt% of a HCl solution corresponding to the optimum achieved with NaCl solutions. The results are shown in Fig. 5. Both regenerant agents allow to achieve the same regeneration degree for 7 BV consumed. However, the 6 wt% sodium chloride solution seems to be the optimal agent, because when the acid is used, the amount of equivalents of H + spent was 62.72% higher than the amount of Na + needed. Furthermore, sodium chloride is cheaper, less corrosive and safe to handle. The optimal regenerant agent concentration found in the regeneration of the resin in the zinc and cadmium forms by applying the theoretical model were about 7.8 and 8.9 wt%, respectively. These differences can be attributed to the different values of both the equilibrium constants and the diffusion coefficients (Table 3). Thus, Cu 2+, the ion less preferred by the resin, is the ion that required the lower concentration of the regenerant agent. 5. Conclusions The regeneration curves of the systems here considered have been predicted by using a model based on both the Nernst Planck equation and the mass action law. This model also allowed to obtain the optimum amount of regenerant agent to be used, regardless the system considered. Therefore, it would be possible to minimize the final waste volume and maximize the recovered bed capacity without any additional consumption of regenerant agent. According to the results, a regeneration level close to 100% is impractical since it would require a higher amount of regenerant. The results here obtained allowed to conclude that the sodium chloride is better regenerant agent than chlorhydric acid for strong acid resins, because it requires less amount of equivalents to reach the same regeneration level and is cheaper. Finally, the concentration of regenerant agent required for copper elution is less than that required for the other ions (Cd 2+ and We gratefully acknowledge the fellowship awarded to Marcela González by the A.E.C.I. References [1] J.W. Patterson, Metal Speciation Separation and Recovery, Lewis Publishers, Chelsea, MI, [2] K. Frederick, Countercurrent regeneration: principles and applications, Ultrapure Water (1996) [3] C.A. Sauer, Characteristics of strong-acid cation exchangers. 1. Optimization of regeneration, Desalination 51 (1984) [4] J.A. Dodds, D. Tondeur, Design of cyclic fixed-bed ion-exchange operations. 1. Predictive method applied to a simple softening cycle, Chem. Eng. Sci. 27 (6) (1972) [5] J.A. Dodds, D. Tondeur, Design of cyclic fixed-bed ion-exchange operations. 2. Effects of changes in total concentration, Chem. Eng. Sci. 27 (12) (1972) [6] J.A. Dodds, D. Tondeur, Design of cyclic fixed-bed ion-exchange operations. 3. Softening solutions containing Na +,Mg 2+,Ca 2+, Chem. Eng. Sci. 29 (2) (1974) [7] G. Klein, Design and development of cycling operations, in: A. Rodrigues, D. Tondeur (Eds.), Percolation Processes: Theory and Applications, Sijthoff & Noordhoff, Alphen aan den Rijn, [8] C. Strydom, C. Frederick, The use of regeneration profiles as a tool to optimize the performance of demineralization water treatment plants, Water SA 29 (4) (2003) [9] C. Costa, A. Rodrigues, Design of cyclic fixed-bed adsorption processes. II. Regeneration and cyclic operation, AIChE J. 31 (1985) [10] E. Korngold, Iron removal from tap water by cation exchanger, Desalination 94 (1994) [11] J. Tenorio, D. Espinosa, Treatment of chromium plating process effluents with ion exchange resins, Waste Manage. 21 (2001) [12] S. Bahowick, D. Dobie, G. Kumamoto, Ion-Exchange Resin for Removing Hexavalent Chromium from Ground Water at Treatment Facility C: Data on Removal Capacity, Regeneration Efficiency, and Operation, Lawrence Livermore Nat l Laboratory, [13] T. Kataoka, H. Yoshida, T. Yamada, Liquid-phase mass transfer in ion exchange based on the hydraulic radius model, J. Chem. Eng. Jpn. 2 (1973) 172. [14] K. Erickson, F. Howard, fixed bed ion exchange with differing ionic mobilities and nonlinear equilibria: ethylene diamine dihydrochlride and ammonium chloride system, Ind. Eng. Chem. Fundam. 18 (1979) [15] J.F. Rodriguez, J.L. Valverde, A. Rodrigues, Measurements of effective self-diffusion coefficients in a gel-type cation exchanger by the zero-length-column method, Ind. Eng. Chem. Res. 37 (1998) [16] J.L. Valverde, A. De Lucas, M. Carmona, M. González, J.F. Rodríguez, A generalized model for the measurement of effective diffusion coefficients of heterovalent ions in ion exchangers by the zero-length column method, Chem. Eng. Sci. 59 (2004) [17] V. Chowdiah, G.L. Foutch, A kinetic model for cationic-exchange-resin regeneration, Ind. Eng. Chem. Res. 34 (1995) [18] G. Kraaijeveld, J.A. Wesselingh, The kinetics of film-diffusion-limited ion exchange, Chem. Eng. Sci. 48 (1993) [19] M.J. Slater, The Principles of Ion Exchange Technology, Butterworth- Heinemann, Oxford, [20] F. Helfferich, Ion exchange kinetics. III: experimental test of the theory of particle-diffusion controlled ion exchange, J. Phys. Chem. 66 (1962)

8 J.L. Valverde et al. / Separation and Purification Technology 49 (2006) [21] D. Tondeur, M. Bailly, in: A. Rodrigues (Ed.), Design Methods for Ion Exchange Processes Based on the Equilibrium Theory in Ion Exchnage: Science and Technology, Martinus Nijhoff Publishers, Dordrech, The Netherlands, [22] J.L. Valverde, A. De Lucas, M. González, J.F. Rodríguez, Equilibrium data for the exchange of Cu 2+,Cd 2+, and Zn 2+ ions for Na + on the cationic exchange Amberlite IR-120, J. Chem. Eng. Data 46 (2001) [23] B.A. Finlayson, Nonlinear Analysis in Chemical Engineering, McGraw- Hill, New York, [24] J.B. Butt, Reaction Kinetics and Reactor Design, first ed. Prentice-Hall, Englewood Cliffs, NJ, USA, 1980, p [25] W. Press, B.P. Flannery, S.A. Teukolsky, W.T. Wetterling, Numerical Recipes in Fortran, second ed., Cambridge University Press, USA, 1992.