Modeling of Wastewater Electro-oxidation Processes Part I. General

Ind. Eng. Chem. Res. 2004, 43, 1915-1922

1915

APPLIED CHEMISTRY Modeling of Wastewater Electro-oxidation Processes Part I. General Description and Application to Inactive Electrodes Pablo Can ˜ izares, Jesu ´ s Garcıá-Go´ mez, Justo Lobato, and Manuel A. Rodrigo* Departamento de Ingenierıá Quı´mica, Facultad de Ciencias Quı´micas, Universidad de Castilla-La Mancha, Campus Universitario s/n, 13071 Ciudad Real, Spain

A new mathematical approach to the electrochemical treatment of wastewater polluted with organic materials is presented in this work. This model is based on several assumptions related to the reactor-level description, as well as to the mass-transfer and kinetics characteristics. The assumptions allow an easy-to-use model without adjustable parameters to be obtained. The model is applied to the electrochemical treatment of aqueous wastes containing carboxylic acids (formic, oxalic, and maleic) or phenol, using cells with non-active anodes (boron-doped diamond). Good agreement between the experimental and modeling results is obtained in all cases, which validates the assumptions on which the model is based. Introduction The development of a mathematical model that is consistent with the processes occurring in a physical system is a relevant approach because such a model can confirm the assumptions on which the model is based. In turn, more detailed knowledge of the physical system can be obtained. For this reason, several models have been developed in recent years to describe the electrochemical treatment of wastewater containing organic pollutants. These models represent different methods of describing the physical processes occurring within the reactor, and their validation with experimental data provides support for the assumptions on which they are based. One of the most recent and more relevant models for such processes was proposed by Polcaro et al.,1,2 who developed a model that describes the electrochemical oxidation of aqueous wastes containing chlorophenols in a batch process. The model assumes that the oxidation is mediated by hydroxyl radicals and that the electrochemical cell behaves like a stirred tank reactor. It was also assumed that the oxidation process leads to the sequential formation of quinonic species, aliphatic compounds, and ultimately carbon dioxide. Can˜izares et al.3 introduced a model aimed at explaining the processes occurring in a combined batch oxidation-adsorption reactor containing two anodic materials (stainless steel and activated charcoal). This reactor was designed for the treatment of aqueous wastes containing phenol. The model assumes that oxidation occurs simultaneously on the electrode surface (direct oxidation) and in the bulk solution (oxidation mediated by hydroxyl radicals) but considers the electrochemical cell to behave as a stirred-tank reactor. The sequential oxidation of C4 and C2 carboxylic acids to * To whom correspondence should be addressed. E-mail: [email protected].

yield carbon dioxide is assumed. It is also assumed that some polymer can be formed. The two models described above involve the use of pseudo-first-order kinetic equations, and they were both able to reproduce the experimental results with great accuracy. However, the procedure for the estimation of the model parameters consisted of calculating their values from experimental data obtained in the electrochemical reactor using fitting algorithms. Because the models were not applied to any other situation (e.g., to represent the processes that occur in continuous reactors) and the parameters could not be estimated using data obtained in different circumstances (e.g., on separate batch tests), the validation of these models is not complete, and their underlying assumptions should be treated with caution. On the other hand, Comninellis’ group4-8 developed a model in which the pollution in wastewater is quantified in terms of chemical oxygen demand (COD). In this model, it is assumed that electrochemical reactions occur very close to the electrodes, and the mass-transfer process (quantified by a mass-transfer coefficient) is therefore included. In the description of the model, two types of behavior were considered depending on the value of the limiting current intensity. The reaction was charge-controlled if the applied current intensity was lower than the limiting current intensity. In this case, the decrease in COD with time was linear. Conversely, if the applied current intensity was higher than the limiting current intensity, the process was mass-transfercontrolled. In this case, the decrease in COD with time was exponential. The main advantage of this model is that it does not include any adjustable parameters. Hence, the behavior of the system can be predicted if the experimental conditions (applied current intensity, solution flow rate, and mass-transfer coefficient) are known. The good agreement obtained between the model and experimental data supports the assumptions made in the development of this model.

10.1021/ie0341294 CCC: $27.50 © 2004 American Chemical Society Published on Web 04/01/2004

1916 Ind. Eng. Chem. Res., Vol. 43, No. 9, 2004

Our group has recently proposed a model9,10 to describe the treatmentsusing boron-doped diamond (BDD) electrodessof wastewaters polluted with organics. This model divides the electrochemical reactor into several zones: those close to the electrodes (electrochemical zones) and the bulk zone (chemical zone). In each zone, the concentration is assumed to be the same for all positions and is only time-dependent. Direct reactions can occur in the electrochemical zones, and mediated processes can occur in the chemical zone. The kinetic equation showing the direct oxidation rate depends on the applied current intensity, the masstransfer limitations, and the ease with which compounds present in the system can be oxidized. This model gives good agreement with experimental data, and the only adjustable parameters are the oxidizability factors for the different organic compounds. The existence of these adjustable parameters is the major drawback of this model. However, the low number of assumptions made and the meaningful physical approach mean that this model is representative of the processes occurring in the electrochemical reactor. In the work described here, a new model is proposed that does not contain any adjustable electrochemical parameters. This new model is a modification of that described above and relates the reactivity of the oxidizable compounds to the physical parameters of the electrochemical process. Two different types of behavior are observed depending on the type of anode material used, and the two cases are studied separately. The first part of the work covers the general assumptions made in the model and the modeling of electrochemical treatments using anodes that act only as electron sinks (i.e., non-active electrodes). Mathematical Model General Assumptions. An exhaustive description of the electrochemical treatment of organic-polluted wastewater in which the concentration profile of every compound in the electrochemical cell is calculated is extremely difficult, as it would lead to a mathematical system involving several partial differential equations. This complex situation arises because the concentration of every compound depends on the time and on the distance to the electrode surface. Such a system would not be helpful because of its high degree of complexity, and therefore, in an attempt to achieve a useful model, a number of simplifying assumptions should be made. The first assumption is related to the level of description of the process. The position dependence of the model can be simplified by dividing the electrochemical reactor into three zones: two zones (electrochemical zones) close to the electrodes (anode and cathode) and a third zone corresponding to the bulk solution (chemical zone). In each of these three zones, the concentration of every compound is considered to be independent of position and dependent only on the time. This assumption is valid if the residence time in the electrochemical cell is small, because in this case, the concentration profiles in the flow direction can be assumed to be negligible. The concentration of each compound in the chemical zone is taken as the value measured experimentally. The concentration in each electrochemical zone is assumed to have a value between the concentration at the electrode surface and the concentration in the chemical zone. Hence, the electrochemical reactor is modeled as the combination of several consecutive stirred-tank reactors,

Figure 1. Model of an electrochemical reactor as the combination of three interconnected stirred-tank reactors.

as shown schematically in Figure 1. The volume of each zone can easily be calculated if it is assumed that the thickness of the electrochemical zone is equivalent to the thickness of the Nernst diffusion layer (δ). This assumption is acceptable because direct oxidation and most of the mediated oxidation processes (those with high reaction rates) occur in this zone. The thickness of this zone can be evaluated as a function of the masstransfer coefficient (k) and the diffusivity (D) using the equation

δ)

D k

(1)

The electrode surface area is known, so the volume of each electrochemical zone can easily be calculated by multiplying this area by the thickness δ. The remaining volume of the system corresponds to the volume of the chemical zone. Mass-transport processes between the electrochemical and chemical zones are quantified by assuming that the local exchange rate is proportional to the concentration difference between the two zones. The mass-transfer rate can be calculated from eq 2, where S/i and Si are the concentrations (mol m-3) of component i in the electrochemical and chemical zones, respectively; k (m s-1) is the mass-transfer coefficient; and A (m2) is the specific interfacial area between the electrochemical and chemical zones. The mass-transfer coefficient (k) can be assumed to depend only on the flow rate conditions, because the concentrations of the compounds are low.

ri ) kA(S/i - Si)

(2)

The approach of dividing the electrochemical cell into several zones allows the simplification of the mathematical complexity of the model. Thus, the complex system of partial differential equations (obtained from the mass balance in an unsimplified system) is reduced to an easier-to-solve system of ordinary differential equations. The rate of the electrochemical process, limited by the applied current density (I), is given by eq 3, where F is the Faraday constant.

r)

I F

(3)

Ind. Eng. Chem. Res., Vol. 43, No. 9, 2004 1917

A number of processes can occur at the electrode surface, and therefore, the total current applied must be shared among all of these processes. Thus, a fraction ) corresponds of the applied current intensity (Relectrode i to each process i, and the rate of each process can be calculated from eq 4. From eqs 3 and 4, it is clear that expression 5 must be verified for each electrode.

I ri ) Relectrode F i

(4)

)1 ∑i Relectrode i

(5)

The proportion of electrons involved in a particular electrochemical process (Relectrode ) can easily be related i to measurable parameters, assuming that the difference between the cell potential and the oxidation/reduction potential (Vi) is the driving force in the distribution of electrons. Thus, it can be assumed that the fraction of applied current intensity used in each process depends on both the cell potential (∆Vwork) and the oxidation (or reduction) potential (∆Vi) of each process. The fraction can be calculated using eq 6, where ∆Vwork ) Vwork Vreference and ∆Vi ) Vi - Vreference. In all cases, ∆Vwork must be greater than ∆Vi; otherwise, process i cannot develop.

) Relectrode i

(∆Vwork - ∆Vi)

∑i (∆Vwork - ∆Vi)

(6)

As long as sufficient numbers of molecules of all of the compounds are present in the electrochemical zone, the various molecules will be oxidized/reduced depend. Coning on the relative values of the factors Relectrode i versely, if one of the compounds disappears completely from the electrochemical zone as a result of the oxidafactors must be tion/reduction process, the Relectrode i rearranged to take into account the absence of this compound. The previously proposed kinetic expressions explain the direct electrochemical processes. When the oxidation processes are caused by the oxidants generated at the electrode surface (mediated electrochemical processes), the kinetic processes must be modeled in the same way as typical chemical processes. Chemical reaction modeling can be performed assuming a second-order rate expression depending on the concentrations of the oxidant (Sox) and the organic compound (Si), as shown in eq 7. In this equation, ki is the kinetic constant for process i.

ri ) kiSoxSi

(7)

If the electrogenerated oxidants are very reactive species, the steady-state approximation1,2 can be assumed, and a pseudo-first-order (eq 8) or even pseudozero-order (eq 9) rate expression can be proposed.

ri ) kiSi

(8)

ri ) ki

(9)

Nevertheless, the kinetic expression for a given chemical process must be proposed separately taking into account the experimental performance of this process.

Figure 2. Electrochemical processes considered in the cathodic zone.

Once the cell description and mass-transfer and kinetic considerations have been taken into account, the mass balances of the reaction system provide the resulting model equations. For a typical batch system, the following mass balance equations for the anodic (eq 10) and cathodic (eq 11) electrochemical zones and for the chemical zone (eq 12) can be obtained.

va

dSi,a dt vc

vb

dSi,b dt

n

)

dSi,c dt

I

νji Ranode + kA(Si,b - Si,a) ∑ j F j)1 m

)

(10)

I

νji Rj + kA(Si,b - Si,c) ∑ F j)1

(11) p

) kA(Si,a - Si,b) + kA(Si,c - Si,b) +

νjirj ∑ j)1 (12)

In these equations, νji is the stoichiometric coefficient of compound i in process j, and subscripts a, c, and b represent the anodic, cathodic, and bulk (chemical) zones, respectively. Scheme of Model Processes for Cells with Nonactive Anodes. In the electrochemical treatment of organic-polluted wastewaters, the main processes related to removal of the pollutants involve irreversible oxidative routes. Consequently, the reductive processes are less important, and it can be assumed that, in the cathodic zone (Figure 2), only hydrogen evolution occurs (a). Nevertheless, if some organic compound(s) can be reduced at the cathode, the mass-transfer (b) and reduction (c) processes must be included in the model scheme. When a typical non-active material is employed, the anode acts only as an electron sink. In this particular


Figure 3. Electrochemical processes considered in the anodic zone.

case, the scheme representing the oxidation processes can be explained as shown in Figure 3. The first process that needs to be considered is the mass transfer of the compounds from the bulk zone to the anodic zone (a). The organic compounds can undergo direct oxidation on the electrode surface (b). This process can occur in either one stage or multiple stages, and it proceeds until the final oxidation product is generated (usually carbon dioxide). At the same time, the decomposition of water molecules can lead to the appearance of hydroxyl radicals (c). The formation of this species has been reported in the literature for BDD anodes.11 Hydroxyl radicals are not stable and can cause the formation of other oxidants (ozone, hydrogen peroxide, peroxodisulfate, chlorine, etc.) that can react chemically with the organic matter through mediated oxidation processes (d) or, alternatively, can promote the formation of oxygen (e). If these oxidant compounds reach the bulk zone, it is necessary to take into account their masstransfer process (f) and the oxidation of the organics in the bulk zone (g). Experimental Details Electrochemical Cell. Bulk oxidations of several carboxylic acids (formic, oxalic, and maleic) and phenol aqueous wastes were performed in a one-compartment electrolytic flow cell (Figure 4), using a boron-doped diamond (BDD) anode and a stainless steel (SS) cathode. Both electrodes had a circular form (100 mm in diameter) with an interelectrode gap of 9 mm. The electrolyte was stored in a 500-cm3 glass tank and circulated through the electrolytic cell by a centrifugal pump. A heat exchanger maintained the temperature at the desired set point. Analytical Procedure. The carbon concentration was monitored using a Shimadzu TOC-5050 analyzer.

Figure 4. Experimental setup: (a) bench-scale plant, (b) section of the electrochemical flow cell.

Organic compounds were identified and quantified by liquid chromatography (HPLC). Carboxylic acids were monitored using a Supelcogel H column with a mobile phase of 0.15% phosphoric acid solution at a flow rate of 0.15 cm3 min-1. The UV detector was set at 210 nm. Phenol was monitored using a Nucleosil C18 column with a mobile phase of 40% methanol/60% water at a flow rate of 0.50 cm3 min-1. In this case, the UV detector was set at 270 nm. To confirm the presence of electrogenerated oxidants, I-/I2 assays were performed. This technique can detect and quantify (by titration with thiosulfate) all of the oxidant species capable of oxidizing I- to I2. Preparation of the Diamond Electrode. Borondoped diamond films were provided by CSEM (Neuchaˆtel, Switzerland). These electrodes were produced by the hot filament chemical vapor deposition technique (HF CVD). More details on the production process and the electrode characteristics are provided elsewhere.9,10 Prior to use in galvanostatic electrolysis assays, each electrode was anodically polarized for 30 min with 1 M H2SO4 at 50 mA cm-2 to remove any kind of impurity from its surface. Preparation of the Stainless Steel Electrode. Commercial AISI 304 stainless steel sheets were used as cathodes. This material was sanded and degreased with 2-propanol in an ultrasound bath and cleaned with deionized water. Experimental Procedures. Galvanostatic electrolyses were carried out under a range of experimental


Figure 5. Simplified mechanism for the oxidation of the carboxylic acids studied.9 The carbon oxidation state can be calculated as 4(1 - COD/TOC).

conditions. The wastewaters tested contained 5000 mg of Na2SO4 dm-3 and were polluted with a concentration in the range of 5-20 mM of phenol or a carboxylic acid (formic, oxalic, or maleic). The pH was adjusted by addition of H2SO4 or NaOH. The range of current densities studied was 15-60 mA cm-2. To study the influence of temperature, experiments were carried out in the range from 25 to 60 °C. Determination of Model Parameters. The masstransfer coefficient (k) was measured through a typical limiting-current assay using the redox couple hexacyanoferrate(II)/hexacyanoferrate(III). The thickness of the electrochemical zone was calculated from the values of the mass-transfer coefficient (k) and the diffusivity (D). The diffusivity can be estimated using the WilkeChang expression.12 The oxidation/reduction potentials of each reaction were determined using voltammetric techniques. Results and Discussion The previously described model was used to simulate the electrochemical oxidation, using BDD electrodes, of wastes containing carboxylic acids or phenol.

Anodic Oxidation of Carboxylic-Acid-Containing Aqueous Wastes. Wastewaters containing several carboxylic acids (formic, oxalic, and maleic) were oxidized using a BDD electrode. In all cases, the only product generated was carbon dioxide, and no other intermediates were detected by HPLC. A simplified mechanism for the oxidation of carboxylic acids, which was previously proposed in the literature,9 is shown in Figure 5. This scheme is consistent with the experimental observations and indicates the number of electrons required in each oxidation process. Likewise, to determine the influence of mediated oxidation reactions, a typical I2/I- test was performed on every sample taken during the assays, but the results were negative in all cases. It was therefore concluded that no mediated oxidation processes occurred in the bulk zone. Nevertheless, indirect oxidation reactions mediated by hydroxyl radicals (or other oxidants) might still have occurred in the electrochemical zone, as the I2/I- test does not detect oxidants if the oxidation reactions develop rapidly. As such reactions must take place in a zone very close to the electrode, in this work, they have been considered as direct reactions. The application of the model to the anodic oxidation of carboxylic acids on BDD electrodes is depicted in Figure 6. The organics initially present in the bulk can be transferred to the anodic zone (1) and are oxidized directly on the anode surface to carbon dioxide (2). This carbon dioxide is subsequently transferred to the bulk zone (3). The anodic evolution of oxygen can also take place (4). The process that occurs at the cathode surface is hydrogen evolution (5). The results obtained in several galvanostatic electrolysis assays are shown in Figure 7. These results can be compared with those predicted by the proposed model. Good agreement is obtained in all cases. Coefficient of variation (CV) values for different experimental conditions are reported in Table 1. It can be seen that the mean value of the coefficient of variation is

Figure 6. Sketch representing the processes considered in the modeling of the electro-oxidation of carboxylic-acid-polluted wastewater using BDD anodes.


Figure 8. Simplified mechanism for the oxidation of phenol.10 The carbon oxidation state can be calculated as 4(1 - COD./TOC). Table 1. Experimental Conditions and Coefficient of Variation Values for the Electrochemical Oxidation of Wastewaters Containing Carboxylic Acids experimental conditions run

acid

C0 (mmol dm-3 )

pH

j (mA cm-2)

T (°C)

CV (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

formic formic formic formic formic oxalic oxalic oxalic oxalic oxalic maleic maleic maleic maleic maleic

10 10 20 10 10 10 10 20 10 10 10 10 20 10 10

2 2 2 12 2 2 2 2 12 2 2 2 2 12 2

30 60 30 30 30 30 60 30 30 30 30 60 30 30 30

25 25 25 25 50 25 25 25 25 50 25 25 25 25 50

5.4 5.0 5.7 6.6 3.6 2.8 7.0 5.1 2.0 5.1 2.7 5.9 1.1 2.4 5.2

Table 2. Experimental Conditions and Coefficient of Variation Values for the Electrochemical Oxidation of Wastewaters Containing Phenol experimental conditions Figure 7. Results obtained [simulation (lines) versus experimental data (points)] for three experimental runs: 9 carboxylic acid, b carbon dioxide. (a) Formic acid, j ) 60 mA cm-2, T ) 25 °C, pH ) 2. (b) Oxalic acid, j ) 30 mA cm-2, T ) 25 °C, pH ) 2. (c) Maleic acid, j ) 60 mA cm-2, T ) 25 °C, pH ) 2.

below 5%. These good results indicate that the model is a realistic representation of the physical system. Anodic Oxidation of Phenol-Containing Aqueous Wastes. Phenol-containing aqueous wastes were oxidized using a BDD electrode. The main compounds generated were quinonic products, carboxylic acids, and finally carbon dioxide. Quinones were not detected. A simplified phenol oxidation mechanism previously proposed in the literature10 is represented in Figure 8. The first stage involves aromatic ring opening, which leads to the formation of maleic and oxalic acids. These acids are subsequently oxidized directly to carbon dioxide. This simplified mechanism was used to model the process described here. To determine the influence of mediated oxidation reactions, a typical I2/I- test was also performed, but the results were negative in each case. It was therefore concluded that no mediated

run

C0 (mmol dm-3 )

pH

j (mA cm-2)

T (°C)

CV (%)

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

10 20 5 10 10 10 20 10 20 10 10 5 10 10 10 10 10 10

2 2 2 2 2 2 2 12 12 12 12 12 12 9 5 7 12 2

30 30 30 60 15 30 30 30 30 60 15 30 30 30 30 30 30 30

25 25 25 25 25 60 60 25 25 25 25 25 60 25 25 25 15 15

2.4 2.1 7.8 6.7 5.8 3.5 9.9 2.1 4.0 7.6 2.2 7.2 7.7 2.1 2.8 2.6 2.4 3.9

oxidation processes occurred in the bulk zone. Nevertheless, indirect oxidation reactions mediated by hydroxyl radicals (or other oxidants) might have occurred in the electrochemical zone. Because these reactions


Figure 9. Sketch representing the processes considered in the modeling of the electro-oxidation of phenol-polluted wastewater using BDD anodes.

Figure 10. Results obtained [simulation (lines) versus experimental data (points)] for four experimental runs: [ phenol, 2 maleic acid, 9 oxalic acid, b carbon dioxide. (a) j ) 30 mA cm-2, T ) 25 °C, pH ) 2. (b) j ) 30 mA cm-2, T ) 25 °C, pH ) 12. (c) j ) 30 mA cm-2, T ) 25 °C, pH ) 9. (d) j ) 60 mA cm-2, T ) 25 °C, pH ) 12.

must take place in a zone very close to the electrode, in this work, they have been considered as direct reactions. The model applied to phenol oxidation on BDD electrodes is depicted in Figure 9. Several processes occur at the anode surface. The phenol that is initially present in the bulk can be transferred to the anodic zone

(1), where it is oxidized directly at the anode surface to maleic and oxalic acids (2). These acids can be transferred to the bulk zone (3, 4) or oxidized to carbon dioxide (5, 6). Carbon dioxide reaches the bulk zone (7). Oxygen can also be released (8) simultaneously on the anode surface. Only the reduction reaction of the sup-


porting electrolyte is considered to take place at the cathode surface (9). The results obtained in a number of galvanostatic electrolysis assays are shown in Figure 10. These results are compared with those predicted by the proposed model (Table 2). It can be seen that good agreement is achieved in the majority of cases. The mean value of the coefficient of variation is below 5%. These results indicate that the proposed model is a good representation of the physical system and, together with the results obtained in the carboxylic acid modeling study, can be considered to validate the model. Conclusions An easy-to-use model describing the electrochemical treatment of wastewater polluted with organic materials can be obtained by applying some simplifications related to the reactor-level description and the mass-transfer and kinetics characteristics. The concentration profiles of all model compounds were simplified by assuming that the electrochemical reactor can be represented as three interconnected stirred-tank reactors, which correspond to the two zones close to the electrodes (electrochemical reaction zones) and to the bulk zone (chemical reaction zone). The mass-transfer processes can be modeled with a simple equation depending on the concentration difference between two zones and a masstransfer coefficient. For the modeling of the direct electrochemical processes, an equation based on the applied current and on the oxidation/reduction potentials of the compounds involved in the system can be used. The resulting model has no adjustable parameters. The application of the model to the description of the electrochemical treatment of wastes containing carboxylic acids (formic, oxalic, and maleic) or phenol, using non-active anodes (BDD electrodes), provides good agreement between the experimental and modeling results (average CV < 5%), thus validating the assumptions made in the model for such electrodes. Acknowledgment This work was supported by the MCT (Ministerio de Ciencia y Tecnologıá, Spain) and by the EU (European Union) through Project REN2001-0560.

Literature Cited (1) Polcaro, A. M.; Palmas, S. Electrochemical Oxidation of Chlorophenols. Ind. Eng. Chem. Res. 1997, 36, 1791. (2) Polcaro, A. M.; Palmas, S.; Renoldi, F.; Mascia, M. On the Performance of Ti/SnO2 and Ti/PbO2 Anodes in Electrochemical Degradation of 2-Chlorophenol for Wastewater Treatment. J. Appl. Electrochem. 1999, 29, 147. (3) Can˜izares, P.; Domıńguez, J. A.; Rodrigo, M. A.; Rodrı´guez, J.; Villasenõr, J. Effect of the Current Intensity in the Electrochemical Oxidation of Aqueous Phenol Wastes at an Activated Carbon and Steel Anode. Ind Eng. Chem. Res. 1999, 38, 3779. (4) Panizza, M.; Michaud, P. A.; Cerisola, G.; Comninellis, Ch. Electrochemical Treatment of Wastewaters Containing Organic Pollutants on Boron-Doped Diamond Electrodes: Prediction of Specific Energy Consumption and Required Electrode Area. Electrochem. Commun. 2001, 3, 336. (5) Rodrigo, M. A.; Michaud, P. A.; Duo, I.; Panizza, M.; Cerisola, G.; Comninellis, Ch. Oxidation of 4-Chlorophenol at Boron-Doped Diamond Electrode for Wastewater Treatment. J. Electrochem. Soc. 2001, 148, D60. (6) Gherardini, L.; Michaud, P. A.; Panizza, M.; Comninellis, Ch.; Vatistas, N. Electrochemical Oxidation of 4-Chlorophenol for Wastewater TreatmentsDefinition of Normalized Current Efficiency (Phi). J. Electrochem. Soc. 2001, 148, D78. (7) Iniesta, J.; Michaud, P. A.; Panizza, M.; Cerisola, G.; Aldaz, A.; Comninellis, Ch. Electrochemical Oxidation of Phenol at BoronDoped Diamond Electrode. Electrochim. Acta 2001, 46, 3573. (8) Iniesta, J.; Michaud, P. A.; Panizza, M.; Comninellis, Ch. Electrochemical Oxidation of 3-Methylpyridine at a Boron-Doped Diamond Electrode: Application to Electroorganic Synthesis and Wastewater Treatment. Electrochem. Commun. 2001, 3, 346. (9) Can˜izares, P.; Garcıá-Go´mez, J.; Lobato, J.; Rodrigo, M. A. Electrochemical Oxidation of Aqueous Carboxylic Acid Wastes Using Diamond Thin-Film Electrodes. Ind. Eng. Chem. Res. 2003, 42, 956. (10) Can˜izares, P.; Dıáz, M.; Domıńguez, J. A.; Garcıá-Go´mez, J.; Rodrigo, M. A. Electrochemical Oxidation of Aqueous Phenol Wastes on Synthetic Diamond Thin-Film Electrodes. Ind. Eng. Chem. Res. 2002, 41, 4187. (11) Marselli, B.; Garcıá-Go´mez, J.; Michaud, P. A.; Rodrigo M. A.; Comninellis, Ch. Electrogeneration of Hydroxyl Radicals on Boron-Doped Diamond Electrodes. J. Electrochem. Soc. 2003, 150, D79. (12) Wilke, C. R.; Chang, P. Correlation of Diffusion Coefficients in Dilute Solutions. AIChE J. 1955, 1, 264.

Received for review September 16, 2003 Revised manuscript received January 30, 2004 Accepted February 9, 2004 IE0341294

Modeling of Wastewater Electro-oxidation Processes Part I. General

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