Modeling of Iron Removal from Spent Passivation Baths by Ion

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Ind. Eng. Chem. Res. 2009, 48, 7448–7452

Modeling of Iron Removal from Spent Passivation Baths by Ion Exchange in Fixed-Bed Operation Alfredo Ortiz, Inãki Fernańdez-Olmo, Ane Urtiaga, and Inmaculada Ortiz* UniVersidad de Cantabria, Dep. Ingenierıá Quı´mica y Quı´mica Inorgańica, AVda Los Castros s/n 39005 Santander, Cantabria, Spain

In this work the mathematical model that describes the kinetics of the fixed-bed ion exchange iron separation from chromium(III) passivating baths is presented. Passivation is a common step in the zinc electrodeposition galvanic process. The removal of iron species from the passivation baths allows the extention of their life, thus reducing the amount of waste to be managed and the consumption of raw materials. A commercial chelating resin, Purolite S-957, containing sulfonic and phosphonic acid functional groups was employed. Equilibrium experiments, carried out under isothermal conditions at 20 °C, were correlated to the Freundlich equation, with the following parameters KF ) 25 700((mg(n-1)/n L1/n)/kgdry_resin) and n ) 2.45. A simple mathematical model assuming a reversible chemical reaction as the rate-controlling step has been developed to describe the fixed-bed iron removal rate in the media solutions under study. The value of the unknown parameter, the rate coefficient for the forward reaction, kd ) 10 660[(mg(n-1)/n L1/n)/(kgdry_resin h)] was obtained from experimental data of iron uptake employing parameter estimation software. The proposed model offers a satisfactory description of the behavior of the iron loading curves for three different types of real passivation baths under variable feed iron concentration and loading flow rate, using only one estimated parameter. 1. Introduction The electrodeposition of zinc is one of the best and most common methods of improving the corrosion resistance of steel for many applications including components for the automotive industry. In order to enhance the corrosion resistance, chemical passivation products are commonly used after zinc deposition. Formerly used hexavalent chromium passivation is now replaced by Cr(III) based new passivating baths, since it is well documented that Cr(VI) compounds are environmentally and toxicologically hazardous. However, the life of trivalent chromium passivation baths is reduced with respect to hexavalent chromium baths due to the accumulation of iron and zinc impurities resulting from processed parts. While Zn can be removed using a suitable technique of precipitation and filtration, new technologies are needed for the removal of iron, since the iron content in coating baths is restricted to values lower than 30-70 mg/L in order to ensure adequate corrosion resistance. In such a situation, the use of a proper purification system would be highly beneficial, extending the life of baths, thus reducing the amount of waste to be managed and the consumption of raw materials. One of the most promising alternatives for selective iron removal appears to be ion exchange which is considered a best available technology (BAT) for the regeneration of process solutions in the surface treatment of metals, such as acid pickling solutions, chromium electroplating baths, and chromic acid passivation baths.1 Taking into account that trivalent chromium coating baths contain different types of ligands and that iron can form cationic, neutral, and anionic complexes, chelating resins seem to be appropriate to remove iron from this medium. Several chelating resins have been successfully used to remove heavy metals selectively from wastewaters and spent baths (e.g., Chelex 100,2 Lewatit TP-207,3,4 Dowex M4195,5,6 Amberlite IRC748,6 and Purolite S-930,6,7 S-940, and S-9508,9). * To whom correspondence should be addressed. E-mail: ortizi@ unican.es.

Additionally, bifunctional resins which combine chelating groups and conventional acidic groups have been developed.10-12 Thus, Diphonix, a gel-type sulfonated diphosphonic resin was prepared by partially sulfonating microporous divinylbenzenepolystyrene (DVD-PE) beads containing phosphinic acid ligands.11,13 Sulfonic groups enhance the hydrophilicity of the resin resulting in faster overall ion exchange kinetics.14 The rate of uptake of some actinide and transition-metal ions in batch mode by Diphonix resin at trace levels was investigated by Chiarizia et al.15 The authors propose a kinetic model based on a reversible pseudo-first-order chemical reaction, which leads to a rate law formally identical to a kinetic expression based on film-diffusion control; the proposed model leads to a better fitting when it is compared to a rate law based on an intraparticle diffusion controlling step. More recently, Purolite S-957, a sulfonated monophosphonic resin was used for the selective removal of iron ions from three real Cr(III) passivation baths with different iron concentrations.10 The reprocessing of spent passivation baths in plating factories can be performed in fixed-bed columns located close to each zinc plating line. The spent baths can be continuously treated and recirculated, or they can be periodically treated, once the concentration of iron in the passivation solution exceeds a target value. The later operation mode is intended to be applied by a local plating factory; for this purpose, an experimental fixedbed ion exchange study of iron removal from spent Cr(III) passivation baths was performed at laboratory scale. The present study is focused on the modeling of the iron removal from Cr(III) passivation baths using the chelating resin Purolite S-957. A simple model that describes the dynamics of the iron uptake in a fixed-bed column is proposed as a tool to select the size and operating conditions of a full scale column, mainly feed flow rate and iron concentration. This work includes the determination of the equilibrium isotherm parameters and the estimation of the unknown coefficient for the forward reaction, kd.

10.1021/ie900407c CCC: $40.75  2009 American Chemical Society Published on Web 07/02/2009

Ind. Eng. Chem. Res., Vol. 48, No. 15, 2009 Table 1. Chemical Characterization of the Spent Passivation Baths bath type

pH Fe (mg/L) Zn (g/L) Cr (g/L) F- (g/L) Cl- (g/L) NO3- (g/L) SO42- (g/L)

A

B

C

2.05 257-602 2.43 2.21 2.68 6.72 52.9 5.65

1.59 131-342 10 3.52 0.79 7.51 49.5 5.05

1.80 220 11.6 4.21 0.08 0.45 43.9 0.58

2. Experimental Section

plotted against the number of bed volumes (BV) instead of time to get a better understanding of the effect of the feed flow rate on the iron uptake (n° of bed volumes ) flow rate × time/bed volume). The loading flow rate ranged from 1-2.5 L/h, corresponding to a range between 6.7 and 16 BV/h. The regeneration flow rate was around 3-4 BV/h. Since the objective of the operation was to obtain a regenerated bath for reuse in the passivating galvanic process containing less than 50 mg/L of iron, the loading experiments were stopped before exhaustion of the resin bed. 3. Mathematical Model

2.1. Materials. Purolite S-957 is a chelating resin designed for the selective removal of iron from acidic solutions; it is a macroporous cross-linked polymer with phosphonic and sulfonic acid functional groups.16 According to the manufacturer, the maximum iron capacity is 18 g Fe/L wet resin, and the typical particle size of the resin is in the range between 550-750 µm.17 Three different types of spent passivation baths provided by a local plating industry (deployed as A, B, and C), with different initial concentrations of iron, were characterized for Zn, Cr, and Fe concentration by atomic absorption spectrometry (AAS) and for chlorides, sulphates, nitrates, and fluorides by ion chromatography. The iron concentration range in the spent passivation baths was found to fall between 100 and 600 mg/L. The Fe(II) concentration was measured in some samples by visible spectrophotometry, showing that Fe(II) species constitute around 35% of total iron, and Fe(III) species are predominant (65%). The three spent baths come from different suppliers of the galvanic industry, and thus, the chromium concentration and other proprietary chemical characteristics differ from each other. The characterization results are shown in Table 1. The regeneration solution (30 wt % HCl) was prepared by dilution of technical-grade concentrated HCl (37 wt %). 2.2. Experimental Procedure. 2.2.1. Equilibrium Data. Equilibrium experiments were performed using a batch procedure. A fixed mass of wet resin (50 mg approximately) was weighed and introduced into 50 mL polypropylene flasks. A 40 mL portion of the passivation baths with different initial iron concentrations in the range of 65-350 mg/L were transferred into each flask. The bottles were placed onto a magnetic shaker at a speed of 85 rpm at room temperature for 48 h to ensure that equilibrium was reached. The equilibrium capacity of the resin was calculated after measuring the final (equilibrium) iron concentrations of the solution by using the following mass balance equation: eq qjFe )

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V o eq j Fe (C - C ) m Fe

3.1. Equilibrium Relationship. Ion exchange equilibrium is usually described by sorption isotherms. The Freundlich isotherm model has been used in this work to fit the experimental iron equilibrium data in batch mode. qeq ) KF(Ceq)(1/n)

where KF is the Freundlich adsorption equilibrium constant. 3.2. Dynamics of Iron Removal in Fixed Bed Operation. 3.2.1. Mass Balance of the Fixed Bed Column. A material balance on the ion exchange bed results in a partial differential equation which represents the distribution of the iron concentration along the bed length and time.18 ε

∂CFe ∂qjFe ∂2CFe ∂CFe + uL + Fp ) εDL ∂t ∂z ∂t ∂z2

where V is the volume of iron ion solution (L), m, the mass of resin (kg), and CoFe, the initial concentration of iron in the bottle (mg/L). 2.2.2. Fixed-Bed Operation. The fixed-bed experiments were performed in a glass-made cylinder of 250 mL with an inner diameter of 35 mm; the bed volume was approximately 150 mL of wet resin, with a bed length of 157 mm. The column was first rinsed with deionized water. A peristaltic pump was used to feed the passivation bath and the HCl regeneration solution; the loading step was carried out downflow and the regeneration step upflow. Before regeneration, the bed was backwashed with deionized water for cleaning and decompacting the resin bed. During loading runs, samples were taken at given time intervals for iron and pH analysis. Iron loading curves were

(3)

where qjFe is the average iron concentration in the resin. The initial and boundary conditions that apply to eq 3 are: t ) 0 CFe ) 0 z ) 0 DL

∂CFe ) -uL(CFein - CFe) ∂z

z)L

∂CFe )0 ∂z

3.2.2. Transport of Iron from Fluid to Solid Phase. The transport of the iron ions from the fluid bulk phase to the external surface of resin beads results in the accumulation of iron in the solid phase according to eq 4. Fp

(1)

(2)

∂qjFe ) kLap(1 - ε)(CFe - CFes) ∂t

(4)

The initial condition is the following: t ) 0 qjFe ) 0 By considering resin particles as perfect spheres, the surface area per unit volume (ap) is calculated as ap ) 6/dp. Individual liquid-film mass-transfer coefficient in the fixed bed kL can be satisfactorily predicted using the Wilson and Geankoplis correlation that relates the Sherwood number as a function of the Reynolds and Schmidt numbers.19 Sh )

Re ( 1.09 ε )

1/3

Sc1/3

(5)

The diffusion coefficient D for iron ions in the aqueous feed is calculated from equivalent ionic conductivity data measured at

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infinite dilution, obtained from the literature,20 by the NernstEinsten equation:18 D)

( )

RT λ ZF2

(6)

where F is Faraday’s constant and λ the equivalent ionic conductivity. The axial dispersion coefficient, DL, can be obtained from the correlation proposed by Levenspiel21 which can be applied at low Reynolds numbers. DL ) 1.8

uLdp ε

(7)

3.2.3. Ion Exchange Rate. Ion exchange kinetics may be governed by diffusion, convection, electric transference, and chemical reaction or a combination of some of these mechanisms.22 Diffusion inside the resin bead is usually the ratedetermining step.23,24 However, when an ion-exchange process involves chemical reactions such as neutralization and complex formation, the derived rate laws may differ from ordinary ion exchange processes.18,23 When chelating resins are used, the exchange process is slower as compared to conventional ion exchangers, being in general controlled by the kinetics of a chemical reaction.25 The most important reason why chelating resins react slowly, besides the obvious effects of slow chemical reactions of complex formation between the resin chelating groups and certain metal cations and their complex,26 is their low hydrophilicity due to the chelating groups. The overall kinetics can be improved by introducing macroporosity or hydrophilicity through sulfonic groups leading to bifunctional chelating resins.15 The following assumptions have been made to represent the ion exchange rate: (i) relatively fast homogeneous intraparticle diffusion. This hypothesis is based on the macroporosity and bifunctionality of S-957 resin. (ii) a slow chemical reaction involving the dissociation of iron complexes present in passivation baths and formation of new complexes through the coordination of iron ions with the phosphoryl group of the monophosphonic acid in the resin beads. Considering these assumptions, the following reversible chemical reaction has been proposed in the present work to describe the rate of ion exchange: ∂qjFe ) kd(CFes)(1/n) - krqjFe ∂t

(8)

where CFes and qjFe are related by the equilibrium at the solid-liquid interface given by the Freundlich equation (eq 2). n is the exponent of the Freundlich equation, and the direct (kd) and reverse (kr) kinetic constants are related to the adsorption equilibrium constant, KF ) kd/kr. Thus, eq 8 can be expressed as

(

)

∂qjFe 1 ) kd (CFes)(1/n) qj ∂t KF Fe

(9)

Equation 9 has one fitting parameter, kd, while KF and n are the parameters of the Freundlich equilibrium isotherm that will be obtained experimentally. Equations 3, 4, and 9 constitute the proposed mathematical model for the description of the iron uptake curves. This set of differential equations was solved simultaneously using the

Figure 1. Equilibrium isotherm of iron ion onto Purolite S-957 resin at room temperature in a real passivation bath: bath B.

Figure 2. Comparison of predicted and observed iron loading curves for different types of passivation baths and feed iron concentrations: (•) experimental; (-) calculated from the model. Flow rate ) 15.3-17.3 BV/h.

equation-oriented simulation software Aspen Custom Modeler. After solving the system of equations, the time was expressed as number of bed volumes, as indicated in section 2.2. The determination of the parameter kd was performed by using the parameter estimation tool based on the least squares method after minimization of the weighted absolute squared error between the observed and predicted values of the concentration values. 4. Results and Discussion 4.1. Evaluation of Equilibrium Parameters. The main purposes of the equilibrium study were the following: (i) to identify the maximum capacity of the resin for the loading of iron ions and (ii) to determine the isotherm parameters which are required in the proposed kinetic model. The sorption isotherm of iron onto the Purolite S-957 resin is shown in Figure 1, and it was described by the Freundlich model with a satisfactory fitting. Parameters were determined from nonlinear regression of experimental data where the best fitting was obtained for a value of Freundlich equilibrium constant of KF ) 25 700(mg(n-1)/n L1/n)/kgdry_resin and n ) 2.45 getting an R2 ) 0.99. A maximum uptake capacity of 29 g Fe/L wet resin was obtained, which is considerably higher than the value given by the manufacturer.17 4.2. Kinetics of Iron Removal in a Fixed-Bed. Iron loading curves obtained in fixed-bed operation from three passivation baths at different feed iron concentrations ranging from 131 to 602 mg/L are shown in Figure 2. The smooth slope of the experimental curves indicates that the overall ion exchange kinetics is slow. Analysis of the effect of inlet iron concentration and bath type in Figure 2 shows that independent of the type of passivation bath used, the degree of bed saturation is directly proportional to the inlet iron concentration, as would be expected using the same bath.


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The kinetic model has only one fitting parameter, the rate coefficient for the forward ion exchange reaction, kd, which was estimated employing the parameter estimation tool of the software and the experimental data series shown in Figures 2 and 3, obtaining the best fitting value with a 95% confidence interval for kd ) 10660 ( 514[(mg(n-1)/n L1/n)/(kgdry_resin h)]. The standard deviation obtained from the experimental data according to eq 10 was SD ) 24.2.

SD )

Figure 3. Experimental and predicted iron loading curves at different feed flow rates for baths. (a) Type B [CFein ) 131 mg/L]. (b) Type C [CFein ) 220 mg/L ]: (•) experimental; (-) calculated from the model. Table 2. Values of Physical Properties and Parameters Used in the Model parameter ε ) bed voidage Fp ) bed density (kgdry_resin/m3) FL ) liquid density (kg/m3) µL ) liquid viscosity (kg/(m h)) λ ) equivalent ionic conductivity (m2/(mol Ω)) dp ) resin particle diameter (m) D ) molecular diffusion coefficient of iron (m2/h) DL ) axial dispersion coefficient (m2/h) L ) bed length (m) n ) Freundlich coefficient KF ) Freundlich equilibrium constant [(mg(n-1)/n L1/n)/kgdry_resin] kL ) liquid film mass transfer coefficient in the fixed bed (m/h) ap ) surface area per unit volume of particle (m2/m3) a

value 0.5 204 1065.6 3.6 68 5.75 × 10-4 2.6 × 10-6 5.33 × 10-3 0.1575 2.45 25 700 8.18 × 10-2 a 10434.8

kL calculated at a flow rate of 16 BV/h.

Figure 3a and b shows the effect the feed flow rate on the iron uptake in fixed-bed operation for baths B and C at room temperature. The studied flow rates are in the range from 7 to 16 BV/h using a feed concentration of 131 and 220 mg/L of iron. A strong reverse relationship between feed flow rate and iron ion uptake is observed from Figure 3. It should be pointed out that time has been expressed in these figures as number of bed volumes. At high flow rates, the short residence time of the solute in the column does not probably allow the equilibrium to be reached, due to the slow observed ion exchange rate, which is assumed to be controlled by a chemical reaction step. The model developed above determines the outlet iron concentration at different times (or bed volumes) based on different operating conditions, namely, initial iron concentration and flow rate. Table 2 reports a list of properties and parameters used for the simulation, which were either calculated or obtained from the literature.

n

∑ (C

exp

- Csim)2

i)1

N-1

(10)

A reasonable agreement is observed between experimental and calculated iron loading curves, as is shown in Figures 2 and 3. From the observation of Figure 2, it can be concluded that the above-described model can satisfactorily predict the iron removal from the three types of passivation baths by the Purolite S-957 resin when the feed iron concentration changes in a wide range. Thus, the model is able to predict the iron concentration in the exit stream as a function of time at the early stages of the loading curves, which allows to calculate the average concentration of iron in the treated bath, and then to predict the breakthrough condition which is attained, according to the recommendations of the suppliers of the passivations baths, when the average concentration of iron reaches 50 mg/L. Figure 3a and b show that the strong observed effect of the flow rate on the iron removal is satisfactorily described by the proposed dynamic model that assumes kinetic control of a reversible chemical reaction step. This hypothesis is reinforced by the observed effect of temperature on the iron removal shown in our preceding experimental work using the same bath types and resin:10 the early iron uptake heavily improved with increasing the temperature from 25 to 55 °C.10 Thus, considering that even though Purolite S-957 is a macroporous resin which contains sulfonic acid ligands to enhance the access of metal ions into the polymer network due to their high acidity and hydrophilicity, the observed overall kinetics are slow, and taking into account the strong observed effect of temperature on the iron removal rate and the chelating nature of Purolite S-957, a slow chemical reaction step is assumed to be the rate-determining step. 5. Conclusions A dynamic model is presented to describe the performance of the Purolite S-957 resin in fixed-bed operation for the ion exchange separation of iron from spent passivation baths based on chromium(III). The robust model is able to predict the process performance under different operating conditions, i.e.: fluctuating iron concentration in the feed and variable flow rate of the feed stream, and for baths manufactured by different suppliers. Equilibrium experiments, carried out under isothermal conditions at 20 °C were correlated to the Freundlich equation, providing the following parameters KF ) 25 700[(mg(n-1)/n L1/n)/kgdry_resin] and n ) 2.45. The dynamic model assumes a reversible chemical reaction as the controlling rate step. The value of the unknown parameter, the rate coefficient for the forward reaction, kd ) 10 660[(mg(n-1)/n L1/n)/(kgdry_resin h)] was obtained from the fitting of the experimental data of iron uptake to the proposed model. The results found in this work allow us to conclude that this model might be applied to find the appropriate conditions of

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the ion exchange purification of spent passivation baths, constituting an adequate tool for the design and scale up of the operation. Thus, the operational life of Cr(III)-based passivation solutions could be extended, reducing the generation of wastes and minimizing the consumption of raw materials. Nomenclature ap ) surface area per unit volume of particle (m2/m3) CFe ) iron concentration in the liquid phase (mg/L) CFein ) iron concentration in the liquid phase at column inlet (mg/L) CFes ) iron concentration in the liquid phase on the external surface of resin bead (mg/L) dp ) resin particle diameter (m) D ) molecular diffusion coefficient of iron in the bath (m2/h) DL ) axial dispersion coefficient (m2/h) F ) Faraday’s constant (C/mol) kd ) rate coefficient for forward reaction [(mg(n-1)/n L1/n)/(kgdry_resin h)] kL ) liquid film mass transfer coefficient (m/h) kr ) rate coefficient for back reaction (1/h) KF ) Freundlich equilibrium constant [(mg(n-1)/n L1/n)/kgdry_resin] L ) bed length (m) m ) mass of dry resin (kg) n ) Freundlich coefficient qjFe ) average iron concentration in the resin (mg/kgdry_resin) R ) universal gas constant, 8.314 (J/(mol K)) Re ) Reynolds number, FLuLdp/µL Sc ) Schmidt number, µL/(FLD) Sh ) Sherwood number, dpkL/D T ) temperature (K) t ) time (h) uL ) liquid superficial velocity (m/h) V ) volume of iron ion solution (L) Z ) valency of ion z ) distance along column (m) Greek Symbols ε ) bed voidage Fp ) bed density (kgdry_resin/m3) FL ) liquid density (kg/m3) µL) liquid viscosity (kg/(m h)) λ ) equivalent ionic conductivity (m2/(mol Ω))

Acknowledgment This work has been developed within the framework of projects A542/2007/2-11.1 (Ministry of Environment, Spain), CTM2006-0317/TECNO and CTQ2008-00690/PPG funded by the Spanish MEC. Financial aid of the Invesnova Sodercan Programme is also gratefully acknowledged. Literature Cited (1) European Commission Reference Document on Best AVailable Techniques for the Surface Treatment of Metals and Plastics; August 2006. (2) Haas, C. H.; Tare, V. Application of ion exchangers to recovery of metals from semiconductor wastes. React. Polym. 1984, 2, 61–70. (3) Maranõń, E.; Sua´rez, F.; Alonso, F.; Fernańdez, Y.; Sastre, H. Preliminary study of iron removal from hydrochloric pickling liquor by ion exchange. Ind. Eng. Chem. Res. 1999, 38, 2782–2786.

(4) Lasanta, C.; Caro, I.; Pe´rez, L. Theoretical model for ion exchange of iron(III) in chelating resins: application to metal ion removal from wine. Chem. Eng. Sci. 2005, 60, 3477–3486. (5) Diniz, C. V.; Doyle, F. M.; Ciminelli, V. S. T. Effect of pH on the adsorption of selected heavy metal ions from concentrated chloride solutions by the chelating resin Dowex M-4195. Sep. Sci. Technol. 2002, 37 (14), 3169–3185. (6) Mendes, F. D.; Martins, A. H. Selective sorption of nickel and cobalt from sulphate solutions using chelating resins. Int. J. Miner. Process. 2004, 74 (1-4), 359–371. (7) Simpson, C.; Laurie, S. H. Ion exchange studies on zinc-rich waste liquors. Hydrometallurgy 1999, 51 (3), 335–344. (8) Kiefer, R.; Ho¨ll, W. H. Sorption of heavy metals onto selective ionexchange resins with aminophosphonate functional groups. Ind. Eng. Chem. Res. 2001, 40 (21), 4570–4576. (9) Kiefer, R.; Kalinitchev, A. I.; Ho¨ll, W. H. Column performance of ion exchange resins with aminophosphonate functional groups for elimination of heavy metals. React. Funct. Polym. 2007, 67 (12), 1421–1432. (10) Fernańdez-Olmo, I.; Ortiz, A.; Urtiaga, A.; Ortiz, I. Selective iron removal from spent passivation baths by ion exchange. J. Chem. Technol. Biotechnol. 2008, 12, 1616. (11) Chiarizia, R.; Horwitz, E. P.; Alexandratos, S. D.; Gula, M. J. Diphonix resin: a review of its properties and applications. Sep. Sci. Technol. 1997, (1-4), 1–35. (12) Alexandratos, S. D. Ion-Exchange Resins: A Retrospective from Industrial and Engineering Chemistry. Ind. Eng. Chem. Res. 2009, 48, 388– 398. (13) Horwitz, E. P.; Chiarizia, R.; Diamond, H.; Gatrone, R. C.; Alexandratos, S. D.; Trochimzuk, A. Q.; Creek, D. W. Uptake of metalions by a new chelating ion-exchange resin 1. Acid dependencies of actinide ions. SolVent Extr. Ion Exch. 1993, 11, 943–966. (14) Alexandratos, S. D.; Hussain, L. A. Bifunctionality as a means of enhancing complexation kinetics in selective ion exchange resins. Ind. Eng. Chem. Res. 1995, 34, 251–254. (15) Chiarizia, R.; Horwitz, E. P.; Alexandratos, S. D. Uptake of metalions by a new chelating ion-exchange resin 4. Kinetics. SolVent Extr. Ion Exch. 1994, 12, 211–237. (16) McKevitt, B. R. Removal of iron by ion exchange from copper electrowinning electrolyte solutions containing antimony and bismuth. Master Thesis. The University of British Columbia, Nov 2007. (17) Purolite International LTD limited. Purolite ion exchange resins, product information, Nov 2000. (18) Slater, M. J. The Principles of Ion Exchange Technology; Butterworth-Heinemann Ltd.: Woburn, MA, 1991. (19) Rivero, M. J.; Primo, O.; Ortiz, I. Modelling of Cr(VI) removal from polluted groundwaters by ion exchange. J. Chem. Technol. Biotechnol. 2004, 79, 822–829. (20) Chowdiah, V. N.; Foutch, G. L. Binary liquid phase mass transport in mixed-bed ion exchange at low solute concentration. Ind. Eng. Chem. Res. 2003, 42, 1485–1494. (21) Levenspiel, O. Chemical Reaction Engineering, 3rd ed.; John Wiley & Sons: New York, 1999; p 311. (22) Helfferich, F. Models and physical reality in ion-exchange kinetics. React. Polym. 1990, 13, 191–194. (23) Helfferich, F. Ion-exchange kinetics. V. Ion exchange accompanied by reactions. J. Phys. Chem. 1965, 69 (4), 1178–1187. (24) Helfferich, F. Ion Exchange; McGraw-Hill Book Co., Inc.: New York, 1962. (25) Kabay, N.; Demircioglu, M.; Ekinci, H.; Yuksel, M.; Saglam, M.; Akcay, M.; Streat, M. Removal of Metal Pollutants (Cd(II) and Cr(III)) from Phosphoric Acid Solutions by Chelating Resins Containing Phosphonic or Diphosphonic Groups. Ind. Eng. Chem. Res. 1998, 37, 2541–2547. (26) Tare, V.; Karra, B.; Hass, C. N. Kinetics of metal removal by chelating resin from a complex synthetic wastewater. Water Air Soil Pollut. 1984, 22, 429–439.

ReceiVed for reView March 12, 2009 ReVised manuscript receiVed May 26, 2009 Accepted June 14, 2009 IE900407C

Modeling of Iron Removal from Spent Passivation Baths by Ion

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