Photocatalytic Oxidation of Phenol: Reaction ... - ACS Publications

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Photocatalytic Oxidation of Phenol: Reaction Network, Kinetic Modeling, and Parameter Estimation Aaron Ortiz-Gomez,† Benito Serrano-Rosales,‡ Miguel Salaices,§ and Hugo de Lasa*,† Faculty of Engineering, Chemical Reactor Engineering Centre, The UniVesity of Western Ontario, London, Ontario N6A5B8, Canada; Chemical Engineering Department, UniVersidad Autonoma de Zacatecas, Zacatecas, Me´ xico; and Electric Research Institute, CuernaVaca, Morelos, Me´ xico

The photocatalytic degradation of phenol and other phenolic compounds can follow different pathways depending on the reaction conditions. It is found that the photocatalytic oxidation of phenol is faster in acidic pHs with an optimum pH value of 3.2. On the basis of experimental data, it is concluded that the photocatalytic oxidation of phenol, ortho-dihydroxybenzene (o-DHB), para-dihydroxybenzene (p-DHB), and 1,4-benzoquinone (1,4-BQ) can all be described with a series-parallel reaction scheme. The present study reports a detailed reaction network incorporating possible reaction steps based on data obtained for the oxidation of phenol and its three aromatic intermediates. Four carboxylic acids (fumaric acid, maleic acid, oxalic acid, and formic acid) are detected as intermediates in the photocatalytic oxidation of phenol, o-DHB, p-DHB, and 1,4-BQ, suggesting that, in the oxidation of any phenolic compounds, these acids are part of the oxidation breakdown of more complex molecules. Additionally, two kinetic models are proposed with different degrees of complexity. A first model (KM#1) contains enhancements to that proposed by Salaices et al. (Chem. Eng. Sci. 2004, 59, 3) and helps predict the formation and disappearance of aromatic compounds only. In a second kinetic model (KM#2), a lumped acid concentration and CO2 formation are incorporated to account for the formation and disappearance of carboxylic acids as well as for the overall rate of mineralization. Both models provide a very good fit of the experimental data and work for a wide range of phenol concentrations (20-50 ppm C in phenol). Parameters estimates with statistical indicators for both models are also reported in this study. 1. Introduction Heterogeneous photocatalysis has emerged as a viable alternative process to tackle the widely spread problem of air and water waste streams contaminated with hazardous pollutants. Photocatalysis has, therefore, been the subject of extensive research over the last decades.1 Its greatest advantage is that most organic pollutants can be completely mineralized to CO2 and mineral acids. Phenol has been extensively used as a model compound to both understand the photocatalytic reaction mechanisms and test the performance of various photocatalytic processes. Phenol itself is a contaminant prevalent in wastewater streams from different manufacturing processes (ref 2 and references therein) and is resistant to conventional water treatments. Moreover, phenol and other hydroxylated contaminants (e.g., para-dihydroxybenzene) have been linked to serious medical conditions such as leukemia3 and severe failures in human organs.4 Thus, its complete removal from waste streams is of utmost importance to minimize human exposure to this pollutant and similar contaminants. Given that the photocatalytic oxidation of phenol occurs via hydroxyl radical attack, some other hydroxylated aromatic compounds are produced as intermediates, which can be equally harmful as the parent species. Various authors report the formation of ortho- and para-dihydroxybenzene, as well as 1,2,3-trihydroxybenze.5 Other studies show that 1,2,4-trihydroxybenze and 1,4-benzoquinone are also produced during phenol oxidation over TiO2,6,7 while other authors report only * To whom correspondence should be addressed. E-mail: hdelasa@ eng.uwo.ca. Phone: 519-6612144. Fax: 519-8502931. † The Univesity of Western Ontario. ‡ Universidad Autonoma de Zacatecas. § Electric Research Institute.

the formation of para-dihydroxybenzene and 1,4-benzoquinone in the oxidation of phenol in aqueous solutions.8,16 The above-mentioned studies were performed under different reaction conditions and in different reactor setups. Thus, the formation and concentration of reaction intermediates greatly depend on the conditions at which the reaction takes place, with the pH of the reacting media playing a major role in the formation of oxidation intermediates. Salaices et al.,9 for instance, report the formation of significant amounts of paraand ortho-dihydroxybenzene at a pH of 4, while the latter was not formed at a pH of 7. Moreover, ortho-dihydroxybenzene was not detected when the catalyst was changed from Degussa to Hombikat UV-100. Also, 1,2,4-trihydroxybenze and 1,4benzoquione were identified in most experiments, with their concentrations not varying significantly from run to run. The above results confirm that the extent to which an intermediate is produced will depend mainly on the reaction conditions. Furthermore, the reaction conditions affect not only the intermediate distribution but also the overall mineralization rate of the pollutant. The pH of the solution is an important variable that has shown a major effect on the rate of disappearance and mineralization of various compounds. From the data obtained in the literature, it can be inferred that there is a strong relationship between pH, adsorption of substrate on catalyst surface, and rate of reaction. Studies with organic dyes10 showed that, as the capability of a molecule to adsorb on the catalyst surface increases, its reaction rate increases as well. Conversely, other studies with azo dyes11 found no relationship between the adsorption rate and the reaction rate. Moreover, optimum pH values are reported over a wide range for the oxidation of various chemical species. For instance, some studies report an optimum pH of 9-10 for the oxidation of CHCl3,12 while others state an optimum pH of 3 for the oxidation of 3-chlorophenol.13

10.1021/ie0611960 CCC: $37.00 © 2007 American Chemical Society Published on Web 04/05/2007

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For phenol in particular, some studies show optimum pH values of 6.5,8,14 while others find optimum values of 47,9 and 3.19 Therefore, it can be concluded that optimum pH values will be dictated by various factors, such as substrate adsorption capability, substrate chemical structure, and its reaction rate. This inevitably has to be evaluated experimentally for each molecule, given that every species may behave in a different manner vis-a-vis adsorption and reaction, and generalizations cannot be made. In this regard, it is our view that further clarifications for optimum pH values for phenol degradation are necessary. Another important aspect that has not been fully addressed is the identification and quantification of short-chain acidic compounds derived from aromatic oxidations upon the aromatic ring cleavage. Some carboxylic acids were identified in the oxidations of complex aromatic molecules. Maleic acid, for instance, was detected in the photocatalytic oxidation of biphenyl compounds,20 1,2,4-trihydroxybenzene,15 1,2-dimethoxybezene,23 and acid orange 7.25 Other acids such as muconic acid have also been identified in photocatalytic oxidations of biphenyls,20 as well as succinic and malonic acids from the oxidation of polycarboxylic benzoic acids.28 Therefore, it might be expected that these or similar acids are produced during the photocatalytic oxidation of phenol and its oxidation intermediates. With the only exception of a recent publication of our research group,24 none of these or other acids has been reported as direct byproducts of phenol oxidation. In this respect, studies have only dealt with the photocatalytic oxidation of various acids, such as maleic acid,26,29 oxalic acid,27 and formic acid,30 as model compounds but not directly as oxidation intermediates of more complex molecules. A complete identification and quantification of aromatic and carboxylic acid intermediates in the oxidation of phenol will allow the development of a comprehensive reaction scheme and, thus, the development of a complete and detailed kinetic model that incorporates most of the oxidation intermediates. While few contributions propose kinetic models for the photocatalytic oxidation of phenol and other phenolic compounds,14,16 kinetic modeling is based mainly on the initial rates of reaction only. Such kinetic models fail to account for the formation of the different reaction intermediates, which may play an important role in the overall mineralization rate. More recently, Salaices et al.9 developed a series-parallel kinetic model based on some identified aromatic intermediates. This model was applied to a wide range of conditions of pH, phenol concentration, and catalyst type. In this kinetic model, however, some steps were stated as hypothetical and no carboxylic acids were accounted for. An objective of this study is, therefore, to provide further understanding of the complex reaction pathways of the photocatalytic oxidation of phenol by identifying as many reaction intermediates as possible, including both aromatic compounds and carboxylic acids. This is accomplished at reaction conditions where the reaction rate was the highest possible in the slurry Photo-CREC reactor employed for this study. While there is a considerable effort to find new photocatalytic reactors in which the catalyst is supported instead of being suspended to avoid catalyst loss or to facilitate its separation from the slurry, it is well-established by now that slurry reactors provide more certainty of the photocatalyst load used in a given experiment and of the extent of its irradiation.10,17,21 Hence, the slurry PhotoCREC is considered as a tool of choice for understanding photocatalytic oxidation pathways. Another important goal is to develop a kinetic model that involves all detectable species including aromatic and short-

Figure 1. Photocatalytic reactor and additional accessories used in the experimental work for this study.

chain carboxylic acids. Two kinetic models with different degrees of complexity are considered. One model considers the rate of formation and disappearance of aromatic species only. The second model predicts the rate of formation and disappearance of aromatics and short-chain carboxylic acids, as well as the formation of CO2. Both kinetic models are developed and validated using experimental data and statistical parameter estimation techniques. 2. Experimental Methods 2.1. Reaction Setup. The experimental setup used in this study is shown in Figure 1. It is composed of a slurry-annular photocatalytic reactor (1), a mixing tank (2), and a pump (3). The entire system operates in the batch mode. The reacting media is first fed into the mixing tank and then pumped to the upper entrance of the reactor. After passing through the reactor annular section, the reacting media goes back to the mixing tank. A sampling port and an air supply are placed in the mixing tank. Additional details of this setup can be found in the paper by Salaices et al..9 2.2. Reactants. The following reactants were used as received from suppliers without any further treatment: phenol (Sigma GC, lot 32k1460), TiO2 P25 (Degussa, lot 1611), catechol (oDHB, EM lot 41157123), hydroquinone (p-DHB, Aldrich, lot 11929KN), 1,4-benzoquinone (98%, Aldrich, lot 00816CG), 1,2,4-benzentriol (99%, Aldrich, lot 03527LU), fumaric acid (99%, Aldrich, lot 07918BC), maleic acid (99%, Fluka, lot 63180), oxalic acid (99%, Aldrich, lot 16527MC), and formic acid (96%, Sigma-Aldrich, lot 12026KD). H2SO4 was used in all experiments to control the pH of the reacting media. Table 1 shows all chemical species used in the present study with their corresponding acronyms that will be used throughout this paper. Their CAS numbers are included as well. 2.3. Analytical Techniques. The analyses of aromatic components were performed in a 1525 Binary Waters highperformance liquid chromatograph (HPLC) with a 2487 dual absorbance detector using a Symmetry C18 column and a mobile phase of methanol (HPLC grade, EMD, lot 45115) and water at a ratio of 67/33% v/v. Carboxylic acids analyses were performed using the same HPLC system with an Atlantis dC18 column and mobile phase of 20 mM of NaH2PO4 (Fluka, lot 1172656) at pH 2.7. pH was monitored with a Corning 430 pH meter. For most experiments, the total organic carbon (TOC) was also analyzed using a Shimadzu 5050 TOC analyzer equipped with a NDIR detector coupled with autosampler ASI 5000.

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Table 1. Names and Acronyms Employed in the Text and Chemical Structure of Chemical Species Involved in the Present Study

The identification of both aromatic and carboxylic intermediates was performed, comparing the retention times of model reactants with those of the reaction intermediates detected in the samples. Additionally, comparisons with spectra provided in catalogues from column manufacturers were made to corroborate the identification of reaction intermediates. 2.4. Experimental Procedure. For each experiment, a predefined amount of reactant was weighed and dissolved in 50 mL of water. It was then added to a known volume of water, whose pH had been previously adjusted to the desired value using an H2SO4 solution. A reference sample was taken. Next, the photocatalyst TiO2, which had been previously dissolved in 100 mL and stirred for 10 min, was added to the mixture. The timer was started at this moment. More H2SO4 solution was added if needed to adjust the pH to the desired value, and more water was then added to make up to 6 L in total. The reactants were allowed to be in contact with the catalyst for 30 min or more before the UV lamp was turned on. During this period of time, henceforth referred to as the dark period, the reacting media was pumped around the system at a rate of 16 L/min and the air flowrate was set to 6 L/min, which provided the necessary oxygen for the reaction and prevented the catalyst from settling in the mixing tank. After this period, the lamp was turned on and the timer was reset to zero to start measuring the reaction time. All other operating conditions (air flowrate, reacting media flowrate, and catalyst weight ) 0.14 g/L) were kept constant, except for the pH, which was not adjusted after the reaction started. All experiments were carried out at room temperature (30 ( 1 °C). Samples were taken at different time intervals to track the concentration of the reactants and the intermediates. Each sample was filtered using poly(tetrafluoroethylene) PTFE filters (20 mm, Mandel) before being analyzed. 3. Results and Discussion 3.1. Kinetic Modeling of the Mineralization of Phenol and its Intermediates. A series of experiments was performed with phenol as a model compound to find the optimum value of pH that maximized the rate of oxidation. Then different experiments were carried out to identify major intermediates at an optimum value of pH. Once they were clearly identified and quantified, new experiments with those species were performed using them as model compounds to both identify their corresponding intermediates and elucidate the full reaction scheme. 3.1.1. Photocatalytic Oxidation of Phenol. The first set of experiments was developed to find the optimum value of pH in the reacting system. Various authors have reported optimum

Figure 2. Concentration profiles of phenol and its major aromatic intermediates: (a) 20 ppm C and (b) 30 ppm C. TOC profile is in a scale six times higher than that shown on y-axis.

values of pH over a wide range for the photocatalytic conversion of several organic species.9,12,13,19 In these runs, different amounts of an acidic solution were added to the reacting media to adjust the initial pH to a predefined value. An amount of phenol was weighed to have a concentration of 20 ppm of carbon in phenol (henceforth ppm of carbon in phenol or in any other reactant will be represented as ppm C). The changes in phenol concentration with time were monitored by taking samples at different time intervals. After a series of repeats, the rate of disappearance of phenol was found to be higher at a pH of 3.2. This value is consistent with other studies reporting optimum pH values of 3,19 3.5,22 and 4.9 In the tests for this study, all other values gave slower reaction rates. Hence, the remaining experiments were performed with an initial pH of 3.2 ((0.05). The next set of runs was performed to identify and quantify the major reaction intermediates. In all experiments with phenol as the model compound, three major aromatic intermediates were detected: ortho-dihydroxybenzene (o-DHB), para-dihydroxybenzene (p-DHB), and 1,4-benzoquinone (1,4-BQ). All of these species were identified in previous studies.5-9,19 Of these, o-DHB was the intermediate with a higher concentration, followed by p-DHB with a significant concentration. 1,4-BQ, however, was observed in very small amounts only. For all tests with phenol at these conditions, the following carboxylic acids were also identified: maleic acid (MeAc), fumaric acid (FuAc), oxalic acid (OxAc), and formic acid (FoAc). Their concentrations were, however, considerably smaller than the ones of other aromatic intermediate species. The changes in phenol and aromatic intermediates concentrations resulting from phenol photoconversion at different irradiation times and for different initial phenol concentrations (20 and 30 ppm C in phenol) are reported in parts a and b of Figure 2.


Figure 4. Series-parallel reaction scheme for the photocatalytic oxidation of phenol involving all detected species.

Figure 3. Concentration profiles of phenol oxidation intermediates: carboxylic acids (a) FuAc and MeAc and (b) OxAc and FoAc; 20 ppm C in phenol.

Figure 3 displays the concentration profiles of (a) MeAc and FuAc and (b) OxAc and FoAc. One should notice that the maxima of the concentration profiles of carboxylic acids do not coincide exactly with the maxima of the concentration profiles of the aromatic intermediate species. From the results above, it can be noticed that, as soon as the photocatalytic reaction is initiated, aromatic intermediates are detected in small amounts. Note also that there is an immediate reduction in the TOC content from the early stages of the reaction, which can be attributed to complete mineralization. This phenomenon was observed in all experiments developed in this study and also reported by Salaices et al..9 This means that phenol is quickly hydroxylated via hydroxyl radical attack to form mainly o-DHB and p-DHB. Furthermore, phenol can also undergo simultaneous complete oxidation, being quickly mineralized to CO2. This can be explained given that adsorbed phenol molecules on TiO2 are subject to variable interaction with hydroxyl radicals. In some cases, associated with regions of low irradiation, only one step of photoconversion can occur, while in others many concurrent photoconversion steps take place, leading to complete phenol mineralization and CO2 formation. Moreover, it can be observed that the formed carboxylic acids are detected from the very beginning of the reaction. Thus, the origin of these acid molecules can also be traced to the nonuniform distribution of hydroxyl radicals on the TiO2 surface, where either phenol or aromatic intermediates can be quickly oxidized, forming carboxylic acids. Therefore, this confirms the fact that, since the early stages of the photocatalytic reaction, phenol is oxidized, undergoing ring aromatic cleavage and formation of carboxylic acids and CO2. In this regard, one should make the distinction between reaction mechanism and observable kinetic rate network, likely

the result of the disparity of hydroxyl radical concentrations on the photocatalyst surface sites. It is understood that, for phenol to be completely oxidized, it must undergo a series of successive partial oxidative mechanistic steps, producing first some intermediates such as o-DHB or p-DHB. These species are subsequently oxidized, producing short-chain carboxylic acids upon the aromatic ring cleavage. The acids can be further oxidized until complete mineralization is achieved and CO2 is formed. However, given that all intermediates are detected from the very beginning of the reaction, one can argue that the measurable kinetic steps result from a combination of several quick mechanistic elementary steps and occur to different extents with carboxylic acids and even CO2 being produced from the start of the photocatalytic reaction. Thus, if one considers the photoconversion of phenol, the observable effect is that phenol produces all kinds of intermediate species from the early stages of the reaction, regardless of the mechanistic pathway followed to produce such intermediates. These observations validate the series-parallel reaction scheme first introduced by Salaices et al..9 All the steps described above are summarized in the reaction scheme shown in Figure 4, with such a scheme being based on all observable species. 3.1.2. Photocatalytic Oxidation of ortho-Dihydroxybenzene (o-DHB). In order to obtain a more detailed photocatalytic reaction scheme, a separate series of experiments was performed using o-DHB as the model reactant. This helped to determine the reaction steps in which this chemical species participates and to evaluate how this model compound behaves as a model pollutant in a photocatalytic process. In the oxidation of o-DHB, the p-DHB and 1,4-BQ species were the only identified aromatic intermediates, although 1,4-BQ was present in small quantities. In all the experiments developed with o-DHB, the same carboxylic acids, FuAc, MeAc, FoAc, and OxAc, were also detected as in the photocatalytic oxidation of phenol. Figure 5 shows the concentration profile for the photocatalytic oxidation of o-DHB and its aromatic intermediates, as well as the TOC profile. The concentration profiles of carboxylic acids are reported in parts a and b of Figure 6. One can notice in parts a and b of Figure 6 that the maxima of carboxylic acids are slightly displaced toward the last stages of the photoconversion. It can also be observed that the oxidation of o-DHB follows a similar pattern to that of phenol. That is, all intermediates, aromatic compounds and carboxylic acids, are detected from the very beginning of the reaction. This shows that some o-DHB molecules are also completely and quickly oxidized to CO2, as proven by the early decrease in the TOC concentration. Likewise, some o-DHB molecules are partially

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Figure 7. Series-parallel reaction scheme for the photocatalytic oxidation of ortho-dihydroxybenzene involving all detected species. Figure 5. Concentration profiles of ortho-dihydroxybenzene and its major aromatic intermediates; 20 ppm C in o-DHB. TOC profile is in a scale six times higher than that shown on y-axis.

Figure 8. Concentration profiles of para-dihydroxybenzene and its major aromatic intermediates; 20 ppm C in p-DHB. TOC profile is in a scale six times higher than that shown on y-axis.

Figure 6. Concentration profile of ortho-dihydroxybenzene oxidation intermediates: carboxylic acids (a) FuAc and MeAc and (b) OxAc and FoAc; 20 ppm C in o-DHB.

oxidized to carboxylic acids. These results confirm that the oxidation of o-DHB can also be represented with a seriesparallel reaction scheme, as shown in Figure 7. 3.1.3. Photocatalytic Oxidation of para-Dihydroxybenzene (p-DHB). Similar experiments to those of o-DHB were performed using p-DHB as the model pollutant. Figure 8 reports the concentration profiles for the photocatalytic oxidation of p-DHB and its intermediates, as well as the TOC profile. In this case, 1,4-BQ and 1,2,4-THB were the only aromatic intermediate species identified. 1,2,4-THB was detected in

extremely small concentrations only. The formation of 1,2,4THB from p-DHB has been reported in previous studies.15 Carboxylic acids FuAc, MeAc, FoAc, and FoAc were also identified in these experiments (see Figure 9). Of the two aromatic intermediates 1,2,4-THB and 1,4-BQ, 1,4-BQ was present in the solution even before the photocatalytic reaction was initiated. Figure 8 shows that, during the dark period, the actual concentration of p-DHB was lower than the expected initial concentration. This difference was equivalent to the concentration of 1,4-BQ, suggesting that p-DHB forms 1,4-BQ even before the photocatalytic reaction starts. However, as soon as the lamp is turned on, the 1,4-BQ immediately disappears and the concentration of p-DHB increases almost in the same magnitude of the 1,4-BQ reduction, suggesting that, in a photocatalytic reaction, 1,4-BQ has a great tendency to form first p-DHB instead of producing directly carboxylic acids. Regarding the oxidation of p-DHB, one can notice that a similar kinetic rate network to the one for phenol and o-DHB can be developed for this model pollutant. In this case as well, all intermediates, including both aromatic compounds and carboxylic acids, are detected from the initial reaction stages. Even more, one can also notice that some p-DHB molecules are quickly oxidized to CO2, whereas some others are only partially oxidized to carboxylic acids. Hence, it can be concluded that the photocatalytic oxidation of p-DHB can also be represented with a series-parallel reaction scheme. This scheme is reported in Figure 10.


Figure 11. Concentration profiles of 1,4-benzoquinone and its major aromatic intermediates; 20 ppm ppm C in 1,4-BQ. TOC profile is in a scale six times higher than that shown on y-axis.

Figure 9. Concentration profile of para-dihydroxybenzene oxidation intermediates: carboxylic acids (a) FuAc and MeAc and (b) OxAc and FoAc; 20 ppm C in p-DHB.

Figure 10. Series-parallel reaction scheme for the photocatalytic oxidation of para-dihydroxybenzene involving all detected species.

3.1.4. Photocatalytic Oxidation of 1,4-Benzoquinone (1,4BQ). Similar experiments to those carried out for o-DHB and p-DHB were performed using 1,4-BQ as the model pollutant under the same reaction conditions. It was found that, in the photocatalytic oxidation of 1,4-BQ, the p-DHB and 1,2,4-THB were the only identified aromatic intermediates, although 1,2,4THB was detected in trace amounts only. The carboxylic acids, FuAc, MeAc, FoAc, and OxAc, were observed as intermediates. Note that these acids are the same intermediates observed in the oxidations of phenol, o-DHB, and p-DHB. Figure 11 reports the changes of 1,4-BQ, p-DHB, and TOC concentrations, whereas parts a and b of Figure 12 present the profiles of the carboxylic acids.

Figure 12. Concentration profiles of 1,4-benzoquinone oxidation intermediates: carboxylic acids (a) FuAc and MeAc and (b) OxAc and FoAc; 20 ppm C in 1,4-BQ.

In this case, an interesting phenomenon was observed: the 1,4-BQ was depleted during the first few minutes of the photoreaction while the concentration of p-DHB increased almost in the same magnitude of the decrease of 1,4-BQ concentration. This suggests a quick reduction of 1,4-BQ into p-DHB. Even more, one can also observe (refer to Figure 11) that, during the dark period, the concentration of 1,4-BQ is slightly lower than the expected concentration and that p-DHB is present before the photocatalytic reaction was started. One can notice as well that this phenomenon is similar to that observed during the p-DHB oxidation, where some 1,4-BQ was

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Figure 13. Series-parallel reaction scheme for the photocatalytic oxidation of 1,4-benzoquinone involving all detected species.

detected prior to the photocatalytic reaction period. The 1,4BQ in this case was depleted very quickly after the photoreaction was initiated. This confirms that, during the dark period, a reaction takes place between 1,4-BQ and p-DHB. This can be attributed to interphotoconversion between these species due to their sensitivity to the visible light impinging upon the reacting media before the photoreaction starts. It is expected that visible light might promote the reduction of 1,4-BQ into p-DBH. In addition, the fast reduction of 1,4-BQ into p-DHB during the photocatalytic reaction can be explained, considering that there is a large concentration of the reducing species promoting the reduction of 1,4-BQ into p-DHB. The reducing agents, in this case, outnumber the oxidizing species (which are consumed in other oxidation steps), promoting the reverse reaction of p-DHB into 1,4-BQ, thus displacing the product distribution toward the formation of p-DHB. This leads to a quick reduction of 1,4-BQ into p-DHB. Previous studies19 have suggested that p-DHB is oxidized to 1,4-BQ, with the latter species being considered as a precursor of the aromatic ring opening. However, these results show that, in the case of a photocatalytic reaction, 1,4-BQ is primarily reduced with the photogenerated electron to produce p-DHB. A similar phenomenon was also reported in other studies.15 From the results described above, it can also be concluded that the photocatalytic oxidation of 1,4-BQ can be represented with a series-parallel model in the same manner as was done for the other model pollutants such as phenol, p-DHB, and o-DHB. Figure 13 presents the proposed series-parallel reaction network for 1,4-BQ. 3.1.5. Overall Series-Parallel Reaction Scheme. All reaction networks described in the previous sections for the photocatalytic oxidation of phenol, o-DHB, p-DHB, and 1,4BQ were developed considering the observable chemical species detected in the liquid phase during the irradiation period. An overall reaction scheme for the photocatalytic oxidation of phenol can then be established, considering the individual photocatalytic conversions of phenol, o-DHB, p-DHB, and 1,4BQ as model pollutants and their corresponding intermediates species. This overall reaction network consistently incorporates all reaction steps that are proven applicable for the various aromatic pollutants considered. This kinetic reaction scheme is developed under the assumption that all chemical species follow the same behavior when they are modeled either as a model pollutant or as an intermediate. For instance, o-DHB is produced in phenol oxidation as an intermediate, and when o-DHB is used as a model pollutant, it produces some p-DHB. Therefore, it is assumed that when

o-DHB is an intermediate, it will also produce p-DHB. That means that, regardless of a compound being an intermediate or model pollutant, it is expected to produce the same intermediates, assuming all reaction conditions are kept the same. While there might always be some extent of competition among different species for catalyst active sites, it is expected that this difference will not alter the overall reaction behavior of chemical species. All the steps for the formation and disappearance of all chemical species in the oxidation of phenol are reported in Figure 14. The proposed reaction network incorporates all new experimental observations presented in this study. The main contributions and clarifications in the proposed reaction network compared with that presented in a previous study9 include the following: (i) The photoconversion of phenol, o-DHB, p-DHB, and 1,4-BQ leads to formation of the same carboxylic acids, FuAc, MeAc, OxAc, and FoAc. (ii) The interconversion of 1,4BQ and p-DHB is a reversible reaction step displaced toward p-DHB during the photocatalytic reaction. (iii) The 1,2,4-THB is only formed from p-DHB at the reaction conditions used in this study. (iv) The step for the formation 1,2,4-THB from phenol is established as a possible step given that 1,2,4-THB was not detected during the oxidation of phenol but only in the oxidation of p-DHB (see (iii)). 1,2,4-THB might be formed from phenol directly, but at to an undetectable level. (v) There is an addition of a reaction step stating the formation of p-DHB from o-DHB. (vi) There is the removal of a reaction step relating the formation of 1,4-BQ directly from phenol. This change was proposed considering that the chemical structure of the 1,4BQ suggests it is formed from p-DHB. The experimental evidence shows that it is formed from p-DHB in low amounts, however. 3.2. Kinetic Modeling. For the overall series-parallel reaction scheme, a set of differential equations can be developed to describe the rates of formation and disappearance of phenol and all its aromatic and carboxylic intermediates. It is wellaccepted in the literature that photocatalytic reactions occur on the catalyst surface; therefore, the rates of formation and disappearance of all components can be modeled using a Langmuir-Hinshelwood (LH) type equation, which takes into account the adsorption of the reactants on the catalyst surface as well as the kinetic reaction constants. The general form of a LH equation for this system is given by31

ri )

kki KAi Ci (1)

n

1+

∑ j)1

KAj Cj

where ri is the rate of reaction of component i in M/(gcat min), kki is the kinetic constant for component i in M/(gcat min), and KAi is the adsorption constant for component i in L/M. j is a subscript to denote each component in the denominator term, while n is the number of chemical species. In addition, considering that the system in which the experiments were carried out operates in batch mode and that it has a low spacetime, a balance equation for each component i can also be expressed as follows,

V dCi ) ri W dt

(2)

where V is the volume of the reactor in L, W is the weight of the catalyst in g, and t is the time in min. By equating eqs 1


Figure 14. Overall series-parallel reaction scheme for the photocatalytic oxidation of phenol. The dashed arrow represents a possible step not proven experimentally.

and 2, the general form for the rates of reaction for each chemical species is obtained:

dCi

)

dt

W k A ki Ki Ci V n

1+

KAj Cj ∑ j)1

dt

(4)

n

1+

∑ j)1

KAj Cj

VCST + VPFR VPFR

pDHB pDHB

(6)

kPhfAc ) kPhfFoAc + kPhfOxAc + kPhfMeAc + kPhfFuAc

(7)

and the last term in the denominator involves all the adsorptions terms for all carboxylic acids and is defined as

All kinetic constants in eq 4 represent apparent constants. The intrinsic kinetic constant can be calculated using the following relationship:32

kIi )

oDHB oDHB

A K14-BQ C14-BQ + KAAcCAc

where kPhfAc is a lumped kinetic constant involving all the kinetic constants for the production of acids from phenol and is given by

kiCi

)

dCPh -(kPhfAc + kPhfoDHB + kPhfpDHB + kPhfCO2)CPh ) dt 1 + KA C + K A C + KA C + Ph Ph

(3)

By letting ki ) (W/V)kki KAi , eq 3 can be simplified to

dCi

First for phenol, the rate of reaction is given by

(5)

Thus, developing one equation with the form of eq 4 for each of the observable components one can obtain a set of differential equations to represent the photocatalytic oxidation of phenol. One should notice, however, that, in the following kinetic modeling, the 1,2,4-THB intermediate considered in Figure 14 was omitted in the analysis, given it was not detected directly in the oxidation of phenol. Thus, 1,2,4-THB formation and consumption steps are not accounted for in the upcoming rate equations.

KAAcCAc ) KAFoAcCFoAc + KAOxAcCOxAc + KAMeAcCMeAc + KAFuAcCFuAc (8) Similar equations can be written for each intermediate. For o-DHB, the rate of reaction is given by

kPhfoDHBCPh - (koDHBfpDHB + koDHBfAc + dCoDHB ) dt 1 + KA C + K A C + KA C + Ph Ph

oDHB oDHB

pDHB pDHB

koDHBfCO2)CoDHB A K14-BQ C14-BQ + KAAcCAc

(9)

where koDHBfAc is also a lumped constant involving all the kinetic constants for the production of acids from o-DHB and

7402


is given by

koDHBfAc ) koDHBfFoAc + koDHBfOxAc + koDHBfMeAc + koDHBfFuAc (10)

For a system modeled with a set of ODEs, the mathematical representation of the model is given by33

dC B(t) ) f(C B(t),u b,k B); C B(t0) ) C B0 dt

(16)

y(t) ) AC(t)

(17)

The equation describing the rate of reaction of p-DHB can be written as follows:

dCpDHB ) dt kPhfpDHBCPh + koDHBfpDHBCoDHB + k14-BQfpDHBCBQ A A 1 + KAPhCPh + KoDHB CoDHB + KpDHB CpDHB +

(kpDHBfTHB + kpDHBfAc + kpDHBfBQ)CpDHB A K14-BQ C14-BQ + KAAcCAc

(11)

For 1,4-BQ, the rate of reaction is written as

dC14-BQ kpDHBfBQCpDHB - (k14-BQfpDHB + ) dt 1 + KA C + K A C + KA C Ph Ph

oDHB oDHB

pDHB pDHB

k14-BQfAc + k14-BQfCO2)CBQ A K14-BQ C14-BQ + KAAcCAc

+ (12)

N

SSR )

In eqs 11 and 12, kpDHBfAc and k14-BQfAc are given by equations analogous to eq 10. Given that all carboxylic acids are present in small amounts, they can be lumped in just one concentration. By defining the following relationships,

CAc ) CFoAc + COxAc + CMeAc + CFuAc

where B k ) [k1, k2, ..., kp]T is a p-dimensional vector of parameters whose numerical values are unknown; C B ) [C1, C2, ..., Cn]T is an n-dimensional vector of state variables; C B0 ) [C10, C20, ..., Cn0]T is an n-dimensional vector of initial conditions for the state variables; b u ) [u1, u2, ..., ur]T is an r-dimensional vector of set or measured variables; f ) [f1, f2, ..., fn]T is an n-dimensional vector of known form (differential equations); b y ) [y1, y2, ..., ym]T is an m-dimensional output vector, i.e., the set of variables that are measured experimentally; and A is the m × n observation matrix which indicates the state variables that are measured experimentally. The parameters of the proposed model are estimated by minimizing the least-squares (LS) objective function, defined as the sum of the squares of the residuals. For ODEs, the objective function is given by

(13)

[yˆ - b y (tt,k B)]T[yˆ - b y (tt,k B)] ∑ i)1

where [yˆ - b y(tt,k B)] is the residuals for the ith measurement, defined as the difference between the measured value, yˆ , and the calculated value using the model and the estimated parameters, b y(tt,k B). For the estimation of parameters using experimental data for more than one experiment, the objective function becomes

and

NE

SSR )

kAcfCO2CAc ) kFoAcfCO2CFoAc + kOxAcfCO2COxAc + kMeAcfCO2CMeAc + kFuAcfCO2CFuAc (14) the rate equation for the lumped carboxylic acids can be written as

dCAc kPhfAcCPh + koDHBfAcCoDHB + kpDHBfAcCpDHB + ) dt 1 + KA C + K A C + KA C + Ph Ph

oDHB oDHB

pDHB pDHB

k14-BQfAcC14-BQ - kAcfCO2CAc A K14-BQ C14-BQ + KAAcCAc

(15)

where kPhfAc, koDHBfAc, kpDHBfAc, and k14-BQfAc are the same constants involved in the previous equations and are defined by equations like eq 10. 3.3. Parameter Estimation. Once the mathematical model, a set of ordinary differential equations (ODEs) that describe the chemical reaction network, was developed, the next step is the validation of such a model. This is performed through the estimation of the parameters involved in all equations using the experimental data. The mathematical model with the best parameter estimates can be used to predict the behavior of a system where that model is assumed to describe the process. Given that the ODE system describing the process cannot be solved analytically, the problem is to estimate the parameters using a different algorithm that calls for the iterative integration of the ODEs set and the minimization of an objective function for parameter estimation.33

(18)

N

[yˆ - b y (tt,k B]T[yˆ - b y (tt,k B)] ∑ ∑ j)1 i)1

(19)

where NE is the number of experiments. For the estimation of the parameters in our system, two builtin MATLAB subroutines were used: lsqcurVefit for the minimization of the objective function and ode45 for the numerical integration of the differential equations. 3.3.1. Constrained Relationships for the Estimation of Parameters. The analysis of the set of equations reveals that there are two important relationships that must be established before all parameters are estimated simultaneously. These are the relationship between koDHBfpDHB and (koDHBfAc + koDHBfCO2) and the relationship between k14-BQfpDHB and kpDHBf14-BQ, given that these relationships might affect the parameter estimation in the entire system if they are not clearly defined beforehand. Bearing in mind that the estimation of parameters is based on the minimization of an objective function, if these relationships are not constrained, the minimization could lead to unfeasible solutions or solutions that do not fully represent the phenomena. For instance, the solver may converge to a solution where koDHBfpDHB is much larger than (koDHBfAc + koDHBfCO2) and could still be a minimum of the objective function. However, from the sole o-DHB reaction, it is clear that o-DHB forms p-DHB in low amounts with most of the o-DHB being converted into acids and CO2. Thus, a very large koDHBfpDHB would not be a feasible solution, despite the fact that it might lead to a lower value of the objective function. 3.3.1.1. Constrained Relationship 1: Analysis of o-DHB Reaction. As previously stated, it was found that the photo-


Figure 15. Reaction scheme for the photocatalytic oxidation of orthodihydroxybenzene; 20 ppm C in o-DHB.

Figure 17. Reaction scheme for the photocatalytic oxidation of paradihydroxybenzene and 1,4-benzoquinone. Table 2. Estimated Parameters for the Photocatalytic Oxidation of ortho-Dihydroxybenzene

koDHBfCO2 (1/sec) koDHBfpDHB (1/sec) A A KoDHB , KpDHB (1/µM) R ) koDHBfCO2/koDHBfpDHB

Figure 16. Experimental and estimated concentration profiles for the photocatalytic oxidation of ortho-dihydroxybenzene; 20 ppm C in o-DHB.

conversion of o-DHB produces p-DHB and 1,4-BQ as intermediates and CO2 + H2O as final products. The concentration of 1,4-BQ in this case was rather small; therefore, neglecting this component in the estimation of parameters will not affect the outcome of the results. For this reaction, a ratio of the kinetic constants between koDHBfpDHB and (koDHBfAc + koDHBfCO2) needs to be determined given that there is a relationship between the fraction of o-DHB that produces p-DHB and the fraction that produces carboxylic acids and CO2. To do this, a set of two differential equations is established based on the sole reaction of o-DHB, whose reaction network is reported in Figure 15. In this case, it is considered that o-DHB directly produces CO2 and H2O, so (koDHBfAc + koDHBfCO2) is reduced to koDHBfCO2, given that CO2 is the final product. The schematic representation is presented in Figure 15.

dCoDHB -(koDHBfpDHB + koDHBfCO2)CoDHB ) dt 1 + KA C + KA C oDHB oDHB

CI 5.0E-04 1.0E-04 4.28E-02

that might arise otherwise. If this relationship is not constrained, the solver may converge to a solution where koDHBfpDHB is much larger than koDHBfCO2, which is not possible given o-DHB produces only small amounts of p-DHB. 3.3.1.2. Constrained Relationship 2: Analysis of 1,4-BQ S pDHB Reaction. The next step in the kinetic modeling parameter analysis is to consider the photoconversion of p-DHB and 1,4-BQ. It was observed that, during these reactions, 1,4BQ forms p-DHB at a very high rate. If the sole reaction between these two components is considered, a mechanism like that shown in Figure 17 can be developed. In this case, 1,2,4THB is neglected, as its concentration remains extremely small in all cases. Again, it was assumed that both chemical species produce CO2 and H2O directly, so (kpDHBfAc + kpDHBfCO2) is reduced to kpDHBfCO2. Likewise (k14-BQfAc + k14-BQfCO2) is reduced to k14-BQfCO2. The proposed reaction network is schematically represented in Figure 17. On the basis of this reaction network, a new set of two differential equations was considered to estimate the forward and reverse kinetic constants of the reaction 1,4-BQ S pDHB and to evaluate their significance in the overall mechanism. In this case, the following two differential equations were adopted:

dCpDHB ) dt -(kpDHBf14-BQ + kpDHBfCO2)CpDHB + k14-BQfpDHBC14-BQ A A 1 + KpDHB CpDHB + K14-BQ C14-BQ

(22) (20)

pDHB pDHB

dCpDHB koDHBfpDHBCoDHB - kpDHBfCO2CpDHB (21) ) dt 1 + KA C + KA C oDHB oDHB

estimate 6.19E-04 1.49E-04 5.22E-02 4.15

pDHB pDHB

Figure 16 shows experimental concentration profiles of o-DHB and the estimated profiles using eqs 20 and 21 for the photocatalytic oxidation of 20 ppm C in o-DHB. The values of the estimated parameters are presented in Table 2. From these results, a ratio R of koDHBfpDHB to koDHBfCO2 can be established to later constrain the estimation of parameters in the overall system. This constraint helps avoid reaching unfeasible solutions

dC14-BQ ) dt kpDHBf14-BQCpDHB - (k14-BQfpDHB + k14-BQfCO2)C14-BQ A A 1 + KpDHB CpDHB + K14-BQ C14-BQ

(23) Figure 18 reports the concentration profile of p-DHB and 1,4-BQ and the estimated profiles using eqs 22 and 23 for the photocatalytic oxidation of 1,4-BQ. The values of the estimated parameters are presented in Table 3. These results show that the reverse reaction kinetic constant k14-BQfpDHB is extremely large compared to the forward reaction kinetic constant,

7404


Figure 19. Schematic representation of reaction network for kinetic model no. 1 (KM#1)

Figure 18. Experimental and predicted concentration profiles of the photocatalytic oxidation of 1,4-benzoquinone; 20 ppm C in 1,4-BQ. Table 3. Estimated Parameters for the Photocatalytic Oxidation of 1,4-Benzoquinone

kpDHBf1,4-BQ (1/sec) k14-BQfpDHB (1/sec) kpDHBfCO2 (1/sec) k14-BQfCO2 (1/sec) KBQA14-, KDHB Ap (1/µM)

estimate

CI

4.36E-14 2.70E-3 1.72E-04 2.82E-14 8.3E-03

1.01E-04 1.9E-03 1.0E-04 9.00E-04 5.2E-03

kpDHBf14-BQ. Similar results were obtained for different 1,4BQ and p-DHB concentrations. Even more, the estimated value is much lower than its CI. Thus, this kinetic constant is statistically insignificant and should be dropped from the kinetic model altogether. Hence, it can be assumed then that, in all cases, the production of 1,4-BQ from p-DHB will be extremely small. Moreover, only in cases where there is some 1,4-BQ at the beginning of the reaction, it will immediately be converted to p-DHB once the photocatalytic reaction is initiated, and the step considering the formation of p-DHB from 1,4-BQ has to be included. However, if the concentration of 1,4-BQ at the beginning of the reaction is negligible, all terms involving 1,4BQ concentrations and their related constants can be safely omitted from the kinetic models since 1,4-BQ is not be formed in significant amounts. 3.3.2. Parameter Estimation for Simplified Kinetic Models. The ODEs set resulting from the kinetic modeling of the proposed reaction network is a system with a large number of variables and parameters with a high degree of correlation. Thus, the estimation of these parameters brings about numerical issues that can only be overcome when considering various scenarios to reduce their number and extent of correlation. First, and as observed from the experimental results for all photocatalytic reactions, there are many intermediate species. Some of them are produced in very low amounts nonetheless. Thus, if their corresponding concentrations and related constants are dropped from the entire system, this will not affect the estimation of parameters related to the major and detectable intermediates species, that is, those observed in larger and significant amounts. Also, small concentrations can be lumped in single terms to further simplify the model and lessen the computational burden. These strategies can lead to various models if different appropriate assumptions are considered. 3.3.2.1. Kinetic Model No. 1 (KM#1): Aromatics Only. A first proposed model considers that those aromatic intermediates produced in low amounts can be neglected and that all remaining aromatics are converted directly into CO2 and water

(e.g., carboxylic acids are neglected). A schematic representation of this reaction network is reported in Figure 19. This proposed model could then be considered under the following assumptions: (1) The concentration and related constants of 1,4-BQ, 1,2,4THB, and all carboxylic acids are neglected. (2)There is an immediate conversion of phenol to CO2, as demonstrated from the TOC profile; thus, the constant kPhfCO2 is kept. (3)The ratio R is included in the model to constrain the ratio of o-DHB producing p-DHB and CO2, as described earlier in this study. The resulting differential equation set is as follows,

-(kPhfCO2 + kPhfoDHB + kPhfpDHB)CPh dCPh ) dt 1 + KA C + K A C + KA C Ph Ph

oDHB oDHB

[(

pDHB pDHB

(24)

) ]

koDHBfCO2 + koDHBfCO2 CoDHB dCoDHB kPhfoDHBCPh R ) dt 1 + KA C + K A C + KA C Ph Ph

oDHB oDHB

pDHB pDHB

(25) dCpDHB ) dt koDHBfCO2 CoDHB - kpDHBfCO2CpDHB R (26) A A 1 + KAPhCPh + KoDHB CoDHB + KpDHB CpDHB

kPhfpDHBCPh +

The results for the oxidation of 30 ppm C in phenol are reported in Figure 20. This estimation was performed with the additional assumption that the adsorption constants for o-DHB and p-DHB, A A KoDHB and KpDHB , are equal. One can certainly notice that the fit of the KM#1 model is very good. Similar results were obtained for a wide range of phenol concentrations (20, 30, 40, and 50 ppm). The parameter estimates along with the CI intervals for this case are presented in Table 4. The results for the estimation of parameters using the data of three different concentrations (20, 30, and 40 ppm C in phenol) are shown in Figure 21. Note that this model provides a good fit of the experimental data. The estimated parameters and their corresponding CI for this case are presented in Table 5.


Figure 20. Experimental and predicted profiles of phenol, ortho-dihydroxybenzene, and para-dihydroxybenzen using KM#1 for the photocatalytic oxidation of 30 ppm C in Ph. Table 4. Estimated Parameters with KM#1 for the Photocatalytic Oxidation of 30 ppm C in Phenol

kPhfCO2 (1/sec) kPhfoDHB (1/sec) kPhfpDHB (1/sec) koDHBfCO2 (1/sec) kpDHBfCO2 (1/sec) KAPh (1/µM) A A KoDHB , KpDHB (1/µM)

estimate

CI

1.45E-04 3.34E-04 2.24E-04 4.55E-04 5.10E-04 1.05E-02 2.96E-02

8.91E-05 1.58E-04 1.06E-04 2.10E-04 2.28E-04 0.61E-02 1.76E-02

When the adsorption constants of o-DHB and p-DHB, A A KoDHB and KpDHB , respectively, are not constrained to be equal and are evaluated independently, the model fitting does not improve significantly, but it does affect the CI estimations as they become larger with the number of parameters to be evaluated. Table 6 presents the estimated parameters when A A the adsorption constants KoDHB and KpDHB are evaluated independently. One can also notice that the parameter estimates as reported in Table 6 are very similar to the case when the adsorption constants are considered to be equal. Note also that the A A and KpDHB have the same value in adsorption constants KoDHB this last case, even though they were evaluated independently. However, when they are assumed to be equal (Table 5), their CIs are narrower than when they are calculated separately, despite converging to the same value (Table 6). Therefore, it is A A to be equal to KpDHB is a good concluded that assuming KoDHB approximation that provides a better estimation of the parameters without compromising the quality of the fitting. 3.3.2.2. Kinetic Model No. 2 (KM#2): Lumped Acids and CO2 Production. The previous model considers only the oxidation of the major aromatic intermediates. As shown in the previous section, when most of the major intermediates have been depleted, there is still a substantial concentration of other remaining organic intermediates, as the TOC profile shows. Therefore, it is of particular interest to calculate and predict the times for total mineralization, an effect that has not been considered in most models presented in other studies. Also, with TOC measurements, it is possible to approximate the amount of CO2 produced along the course of the reaction. In this new series-parallel model, the formation and disappearance of carboxylic acids as well as the production of CO2 are incorporated.

Figure 21. Experimental and predicted profiles of phenol, ortho-dihydroxybenzene, and para-dihydroxybenzene using KM#1 for the photocatalytic oxidation of phenol. Simultaneous parameter evaluation of 20, 30, and 40 ppm C in phenol. Table 5. Estimated Parameters with KM#1 for the Photocatalytic Oxidation of Phenol; Simultaneous Parameter Evaluation for 20, 30, and 40 ppm C in Phenol

kPhfCO2 (1/sec) kPhfoDHB (1/sec) kPhfpDHB (1/sec) koDHBfCO2 (1/sec) kpDHBfCO2 (1/sec) KAPh (1/µM) A A KoDHB , KpDHB (1/µM)

estimate

CI

1.14E-04 3.90E-04 2.49E-04 5.03E-04 5.39E-04 1.03E-02 3.78E-02

1.01E-04 2.46E-04 1.58E-04 3.16E-04 3.31E-04 0.80E-02 2.82E-02

Table 6. Estimated Parameters with KM#1 for the Photocatalytic Oxidation of Phenol; Simultaneous Parameter Evaluation of 20, 30, and 40 ppm C in Phenol Using Three Adsorption Constants.

kPhfCO2 (1/sec) kPhfoDHB (1/sec) kPhfpDHB (1/sec) koDHBfCO2 (1/sec) kpDHBfCO2 (1/sec) KAPh (1/µM) A KoDHB (1/µM) A KpDHB (1/µM)

estimate

CI

1.14E-04 3.90E-04 2.49E-04 5.03E-04 5.39E-04 1.03E-02 3.78E-02 3.78E-02

1.02E-04 2.74E-04 1.76E-04 3.62E-04 3.90E-04 0.93E-02 7.06E-02 10.24E-02

The representation of the experimental data with this new approach allows one to infer important information that can be applied for the estimation of parameters in this new model. When the summation of the organic carbon due to the detected aromatic components (OCAR) is compared with the TOC, it is observed that, as the reaction proceeds, both profiles divert from one another, as shown in Figure 22. The difference between these lines is employed to represent the amount of organic carbon contained in the carboxylic acids (OCAC). Therefore, OCAC can be calculated by subtracting OCAR from TOC. If this amount is considered as a lumped concentration, a new kinetic model can be developed using this information. Concerning these findings, one can notice that the OCAC profile, also shown in Figure 22, increases with time, reaching a maximum in the last stage of the reaction; once it reaches the maximum, it decreases very rapidly. This new lumped concentration helps model this sudden change in those profiles. By including the concentration of the acids in the model, it will be possible to approximate the end of the mineralization given that, once the concentration of the lumped acids goes to zero, the pollutant photoconversion reaction reaches the final CO2 product.

7406


Figure 25. Reaction scheme obtained after testing various scenarios based on the original scheme used to develop the kinetic model KM#2.

Figure 22. Comparison between OCAR and TOC for 30 ppm C in phenol. TOC and CO2 profiles are in a different scale (six times higher than that shown on y-axis).

Figure 26. Experimental and predicted profiles of Ph, o-DHB, and p-DHB using reduced-KM#2 for the photocatalytic oxidation of 20 ppm C in Ph. Figure 23. Schematic representation of reaction network for kinetic model no. 2 (KM#2).

where nA is the number of aromatics. Thus, the difference between TOC and OCAR is the organic carbon due to carboxylic acids

OCAc ) TOC - OCAR

(28)

The amount of CO2 produced during the course of the reaction is approximated with the difference between the initial concentration of total organic carbon and the concentration of TOC at any given time, as expressed in the following equation,

COProd ) [TOC0] - [TOC] 2

Figure 24. Experimental and predicted profiles of phenol, o-DHB, and p-DHB using KM#2 for the photocatalytic oxidation of 30 ppm C in phenol.

Therefore, a number of relationships can be applied. The sum of all organic carbon (OC) in aromatics is given by nA

OCAR )

CAromatics ∑ i)1

(27)

(29)

where CO2Prod is the amount of carbon associated with CO2 and [TOC0] is the initial amount of TOC. The CO2Prod profile is also shown in Figure 22. In Figure 22, both TOC and CO2Prod profiles are reported in µmol/L and are shown in a different scale for ease of comparison. The scale is six times higher than that shown on the y-axis. A summary of the main assumptions for this model can be reported as follows: (1) 1,4-BQ and 1,2,4-THB terms are neglected. (2) All carboxylic acids are lumped in one term. (3) All aromatic intermediates produce both carboxylic acids and CO2 during the reaction.

Ind. Eng. Chem. Res., Vol. 46, No. 23, 2007 7407 Table 7. Estimated Parameters with Reduced-KM#2 for the Photocatalytic Oxidation of 20 ppm C in Phenol

kPhfCO2 (1/min) kPhfoDHB (1/min) kPhfpDHB (1/min) koDHBfLuAc (1/min) kpDHBfCO2 (1/min) kLuAcfCO2 (1/min) A A KAPh, KoDHB , KpDHB (1/µM)

estimate

CI

3.10E-04 5.17E-04 4.75E-04 4.05E-04 7.99E-04 6.45E-04 3.56E-02

1.53E-04 2.54E-04 3.19E-04 1.49E-04 5.13E-04 1.53E-04 2.11E-02

(4) The amount of CO2 produced is incorporated in the model. CO2 is not adsorbed onto the catalyst surface, and its concentration is considered to be cumulative throughout the course of the reaction. Figure 23 shows a schematic representation of this new reaction network. The resulting equations for this new proposed reaction scheme are the following:

dCPh ) dt -(kPhfLuAc + kPhfoDHB + kPhfpDHB + kPhfCO2)CPh A A 1 + KAPhCPh + KoDHB CoDHB + KpDHB CpDHB + KALuAcCLuAc (30)

dCoDHB kPhfoDHBCPh - [koDHBfpDHB + koDHBfLuAc + ) dt 1 + KA C + K A C + KA C + Ph Ph

oDHB oDHB

pDHB pDHB

]

koDHBfCO2 CoDHB KALuAcCLuAc dCpDHB kPhfpDHBCPh +koDHBfpDHB CoDHB ) dt 1 + KA C + K A C + KA C Ph Ph

oDHB oDHB

+

pDHB pDHB

(kpDHBfLuAc + kpDHBfCO2)CpDHB KALuAcCLuAc kPhfLuAcCPh + koDHBfLuAcCoDHB + dCLuAc ) dt 1 + KA C + K A C + KA C Ph Ph

oDHB oDHB

pDHB pDHB

KALuAcCLuAc

dt

)

(32)

+

kpDHBfLuAcCpDHB - kLuAcfCO2CLuAc

dCCO2

(31)

(33)

kPhfCO2CPh + koDHBfCO2CoDHB + A A 1 + KAPhCPh + KoDHB CoDHB + KpDHB CpDHB +

kLuAcfCO2CLuAc KALuAcCLuAc

(34)

Figure 24 reports the experimental and predicted concentration profiles using KM#2 for the photocatalytic oxidation of 30 ppm C in phenol. One can conclude that the proposed model describes the experimental data very well. However, because of the very complex nature of the mathematical model involved, some of the parameters are not significant and can be dropped from the model. Moreover, there is a high degree of correlation,

Figure 27. Experimental and predicted profiles of phenol, o-DHB, and p-DHB using reduced-KM#2 for the photocatalytic oxidation of phenol. Simultaneous parameter evaluation for 20, 30, and 40 ppm C in phenol. Table 8. Estimated Parameters with Reduced-KM#2 for the Photocatalytic Oxidation of Phenol; Simultaneous Parameter Evaluation of 20, 30, and 40 ppm C in Phenol.

kPhfCO2 (1/min) kPhfoDHB (1/min) kPhfpDHB (1/min) koDHBfLuAc (1/min) kpDHBfCO2 (1/min) kLuAcfCO2 (1/min) A A , KpDHB (1/µM) KAPh, KoDHB

estimate

CI

3.93E-04 5.72E-03 6.19E-04 3.70E-04 8.53E-03 2.48E-04 4.22E-02

2.17E-04 3.33E-04 4.07E-04 1.86E-04 5.46E-04 1.84E-04 2.48E-02

especially because of the large number of parameters in the denominator (adsorption constants). Hence, dropping some of the kinetic constants and assuming equal adsorption constants for some of the chemical species can lead to several simplified model variations. In this respect, various possibilities were tested to obtain a kinetic model that could help describe the experimental data over a wide range of concentrations with narrower CI. The model that provided the best estimates with the narrowest CI was obtained from the reaction scheme presented in Figure 25. The results obtained with the simplified KM#2 are shown in Figure 26. One should notice that the concentration profile of CO2 is reported in a different scale for ease of comparison (CO2 concentration is six times higher). Regarding the model, one can observe that the fitting of the model is indeed very good. The statistically meaningful estimated parameters for this example are presented in Table 7. In this case, it was assumed that the adsorption constants for phenol, o-DHB, and p-HB were A A ) KoDHB ). All other combinations led to equal (KAPh ) KpDHB similar solutions with very wide CIs. The results using the simplified KM#2 for the estimation of parameters using the data of three different concentrations (20, 30, and 40 ppm C in phenol) are reported in Figure 27. It can be observed that the proposed model provides a good fit of the experimental data. The estimated parameters and their corresponding CIs for this case are reported in Table 8. Thus, it can be concluded that both KM#1 and KM#2 work well for a single concentration or for a wide range of concentrations, proving the usefulness of such models in the prediction of formation and disappearance of the model reactant and its oxidation intermediates in a photocatalytic reaction.

7408


4. Conclusions From the present study, the following conclusions can be drawn: (1) The photocatalytic oxidation of phenol is faster in acidic pHs with an optimum pH value of 3.2, which is consistent with those reported in the literature. All other values of pH gave slower oxidation rates. (2) At reaction conditions, three major aromatic intermediates were identified in the photocatalytic oxidation of phenol: o-DHB, p-DHB, and 1,4-BQ. (3) On the basis of experimental data, it is observed that photocatalytic oxidations of phenol, o-DHB, p-DHB, and 1,4BQ can be described with series-parallel reaction schemes. (4) A detailed and refined reaction network for the photocatalytic oxidation of phenol is reported. This network incorporates all possible reaction steps based on the experimental data obtained for the oxidation of phenol and all aromatic species detected as reaction intermediates. (5) All four carboxylic acids, FuAc, MeAc, OxAc, and FoAc, were detected as intermediates in the photocatalytic oxidation of phenol, o-DHB, p-DHB, and 1,4-BQ, suggesting that, in the oxidation of any phenolic compounds, these acids will be part of the oxidation breakdown of more complex molecules. Their concentrations varied depending on the parent species, but all of them are clearly identified in all experiments. (6) The refined kinetic model is developed to predict the rate of reaction of phenol and its major aromatic intermediates. The ratio (R) of the fraction of o-DHB that is converted into p-DHB to the fraction that is directly converted into acids and CO2 was incorporated in the kinetic model originally presented by Salaices et al.9 The resulting model provides very good and statistically meaningful fitting. (7) It was found that 1,4-BQ is reduced at a very high rate to form p-DHB during a photocatalytic reaction. The kinetic constants for this reversible reaction reveal that p-DHB produces 1,4-BQ in very small amounts while 1,4-BQ produces p-DHB very rapidly, thus favoring the formation of p-DHB along the irradiation period. (8) A second kinetic model (KM#2) is considered in which a lumped acid concentration and CO2 formation are incorporated. This model helps predict the formation and disappearance of aromatic intermediates, carboxylic acids, and CO2 along the course of the photocatalytic reaction. It provides a very good fit of the experimental data and works very well for a wide range of phenol concentrations (20-50 ppm C in phenol). Acknowledgment The authors are very grateful to the Consejo Nacional de Ciencia y Tecnologıá in Mexico (CONACyT) for the scholarship granted to A.O.-G to pursue his Ph.D. studies at the University of Western Ontario. The authors also acknowledge the financial support of the Natural Sciences and Engineering Research Council of Canada. Nomenclature

T ) transpose V ) volume, L VCST ) volume of CST, L VPFR ) volume of PFR, L b u ) vector of measured variables W ) weight of catalyst, gcat yˆ ) vector of experimental observations b y ) vector of predicted values Parameters k ) apparent kinetic constant kI ) intrinsic kinetic constant kk ) kinetic constant, M/(gcat min) KA ) adsorption constant, 1/M B k ) vector of parameters Subscripts 0 ) evaluated at initial conditions 1,2,4-THB ) 1,2,4-trihydroxybenzene 1,4-BQ ) 1,4-benzoquinone Ac ) carboxylic acids CO2 ) carbon dioxide CST ) continuous stirred tank E ) number of experiments FoAc ) formic acid FuAc ) fumaric acid i ) chemical species j ) chemical species LuAc ) lumped acid concentration MeAc ) maleic acid OxAc ) oxalic acid oDHB ) ortho-dihydroxybenzene pDHB ) para-dihydroxybenzene Ph ) phenol PFR ) plug-flow reactor Acronyms 1,4-BQ ) 1,4-benzoquinone 1,2,3-THB ) 1,2,3-trihydroxybenzene 1,2,4-THB ) 1,2,4-trihydroxybenzene CI ) confidence intervals CO2Prod ) amount of CO2 produced HPLC ) high-performance liquid chromatography KM#1 ) kinetic model #1 KM#2 ) kinetic model #2 o-DHB ) ortho-dihydroxybenzene OCAc ) organic carbon due to carboxylic acids OCAR ) organic carbon due to aromatic species p-DHB ) para-dihydroxybenzene ppm C ) parts per million of carbon Photo-CREC ) chemical reactor designed at the Chemical Reaction Engineering Centre SSR ) squared sum of residuals TOC ) total organic carbon TiO2 ) titanium dioxide UV ) ultraviolet

Variables C ) pollutant concentration, µM C B ) vector of concentrations C B0 ) vector of initial concentrations nA ) number of aromatic species N ) experiment number ri ) rate of reaction, mol/(gcat min) t ) time, min

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ReceiVed for reView September 13, 2006 ReVised manuscript receiVed December 5, 2006 Accepted December 5, 2006 IE0611960

Photocatalytic Oxidation of Phenol: Reaction ... - ACS Publications

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