A kinetic model for pollutant degradation by the UV/H2O2 system was developed. The model includes the background matrix effect, the reaction intermediate action, and the pH change during time. It was validated for water containing phenol and three different ways of calculating HO° level time-evolution were assumed (non-pseudo-steady, pseudo-steady and simplified pseudo-steady state; denoted as kinetic models A, B and C, respectively). It was found that the kind of assumption considered was not significant for phenol degradation. On the other hand, taking into account the high levels of HO2° formed in the reaction solution compared to HO° concentration (~10–7 M >>>> ~10–14 M), HO2° action in transforming phenol was considered. For this purpose, phenol-HO2° reaction rate constant was calculated and estimated to be 1.6x103 M-1 s-1, resulting in the range of data reported from literature. It was observed that, although including HO2° action allowed slightly improving the kinetic model degree of fit, HO° developed the major role in phenol conversion, due to their high oxidation potential. In this sense, an effective level of HO° can be determined in order to be maintained throughout the UV/H2O2 system reaction time for achieving an efficient pollutant degradation.
- UV/H2O2 process
- matrix background
- kinetic model
- reaction rate constant
Nowadays, one of the major problems associated with the presence of toxic and persistent pollutants in the aquatic environment is the unfeasibility of conventional treatments for the effective removal of those substances [1‐3]. Hence the application of alternative technologies, such as advanced oxidation processes, is needed . Among these techniques, the UV/H2O2 system is included. It consists of the photolysis of hydrogen peroxide (H2O2) by applying ultraviolet (UV) radiation resulting in the generation of hydroxyl radicals (HO°) [5, 6]. This process may be performed at room temperature and pressure, it has no mass transfer problems, it is easy to maintain and operate, no sludge requiring a subsequent treatment and disposal is produced, and it may achieve a complete pollutant mineralization . Therefore, the UV/H2O2 system seems to be a promising alternative for the treatment of water containing toxic and recalcitrant substances. However, this kind of technology can be expensive due to the associated electrical and oxidant costs .
In order to reduce costs and make the process more feasible for industrial applications, the UV/H2O2 system optimization is required  and kinetic models can be considered as functional tools for this purpose. Up to date, several kinetic models have been proposed for describing the UV/H2O2 process and predicting different pollutant removal rates [6–15]. In some of these models [13, 15], the proposed set of ordinary differential equations (ODE) defining the studied pollutant degradation rate can be simplified into a pseudo-first–order kinetic expression, whose solution is an exponential one. In such as models, experimental results are fit to that solution. Subsequently, model predictions agree well with laboratory data. In that kind of models the calculated reaction rate constants for the tested pollutant degradation are apparent reaction rate constants (
On the other hand, there are dynamic kinetic models that try to solve the considered ODE set, for which the values of the mentioned variables are required, increasing the complexity of the kinetic model. In order to solve the proposed ODE set, the pseudo-steady state approximation assumption for reactive intermediates, such as HO°, is invoked by arguing that these chemical species are as transient ones as their concentration can be presumed to be at a pseudo-steady state [10, 12, 14]. In other models [6–15], on the contrary, the non-pseudo-steady state premise in free radical rate expressions for predicting the degradation of the probe compound in a more accurate way is applied. However, although hydroperoxyl radicals (HO2°) are involved in those models, none of them, excluding Huang and Shu  and Liao and Gurol  models, includes HO2° in the target pollutant oxidation final expression. Additionally, some of these models cannot be reproduced unless a conversion factor is included, as demonstrated by Audenaert et al. .
In this sense, the aim of this work was to develop a kinetic model based on the main chemical and photochemical reactions for pollutant degradation in water systems by the UV/H2O2 process taking into account the decomposition of the pollutant through direct photolysis, HO° oxidation, and HO2° and superoxide radical (O2°−) transformation. Furthermore, HO° scavenging effects of carbonate (CO32−), bicarbonate (HCO3−), sulfate (SO42−), and chloride (Cl−) ions were considered. pH changes in the bulk and the detrimental action of the organic matter (OM) and the reaction intermediates in shielding UV and quenching HO° were studied. The influence of the pseudo-steady and non-pseudo-steady state hypothesis for determining HO° concentration-evolution with time was also examined and the second-order HO2° reaction rate constant for the studied pollutant was determined. MATLAB software was used to solve the ODE set that characterizes the current model and the results were validated by using experimental data obtained from the literature for phenol (PHE) degradation by the UV/H2O2 process in a completely mixed batch photoreactor.
2. Experimental model approach
A mathematical model for predicting pollutant degradation and the concentrations of the main species involved in a UV/H2O2 system was developed. The developed model describes radical chain reactions occurring during the UV/H2O2 process in the presence of HO° scavengers and UV-radiation absorbers, such as dissolved organic matter (DOM), anions and reaction intermediate products. Pollutant degradation mechanisms, direct UV photolysis and radical attack by HO°, HO2°, O2°− and other anion radicals (CO3°−, SO4°−, H2ClO°, HClO°, Cl°, and Cl2°−) were included. Additionally, the model incorporates the competitive UV-radiation absorption by H2O2, the parent compound and the DOM in terms of dissolved organic carbon (DOC), as well as the formation and disappearance of intermediate products, also considered as DOC. Moreover, it accounts for the solution pH change due to the mineralization of organic compounds and the formation of acids.
2.1. UV/H2O2 system fundamentals
The UV/H2O2 system initiates with the primary photolysis of H2O2 or HO2−, producing HO° according to Eqs. (1) and (2) [6, 13]. Based on the Beer-Lambert law and quantum yield definition, the reaction rates for H2O2/HO2− direct photodegradation and HO° generation are obtained through Eqs. (3)—(5), respectively.
in which [H2O2], [HO2−], [C], and [DOC] are H2O2, HO2−, contaminant and DOM, in terms of DOC, concentrations, respectively. εH2O2, εHO2–, εC and εDOC (M−1 m−1) are the molar extinction coefficients of H2O2, HO2−, the pollutant and the DOC, respectively. In turn, (mm) is the photoreactor path length and (Ein s−1), the incident UV-light intensity.
In addition to the oxidant photolysis, the target pollutant (C) may interact with the UV-radiation, undergoing degradation and producing reaction intermediates. A fraction of those by-products can be dissolved in the solution . This fraction is denoted as DOC (Eq. (10)) . The reaction rate for the contaminant direct photolysis is obtained through Eq. (11).
Once HO° are produced, they rapidly react with the pollutant of interest, degrading it to form reaction intermediates (Eq. (14)), which subsequently can be attacked by HO° and undergo further degradation to produce final products, such as CO2, H2O, and mineral acids (Eq. (15)) . In this model, intermediate substances were considered as HO° scavengers as well as UV-light absorbers. Additionally, it was assumed that the pH of the solution decreased due to the conversion of the target pollutant, and consequently the reaction intermediates, into carbon dioxide (i.e., H2CO3* in the aqueous phase); although it must be highlighted that not all the DOC is mineralized, since carboxylic acids are also formed during the oxidation process, making the pH of the bulk decreases as well . Under this presumption, Eq. (15) is simplified as Eq. (16). The mass balances for the evolution of the pollutant, the dissolved organic fraction of the formed by-products, HO° and the H2CO3* concentrations with time are shown by Eqs. (17)–(20), respectively.
In the UV/H2O2 system, recombination of HO° can occur to produce H2O2. However, these free radicals can also react with H2O2 and HO2−, particularly when the oxidant is in excess, to produce HO2°. Although HO2° are less reactive than HO° (E° = 0.98 and 2.8 V, respectively) , they can also be involved in pollutant degradation, especially if these radicals are produced in high amounts in the system. Furthermore, HO2° can produce O2°−, which subsequently can participate in pollutant degradation and mineralization . Therefore, the role of these reactive oxygen species was included in the proposed kinetic model.
It is important to note that as the oxidation process develops, the pH of the solution generally goes down, and consequently, some chemical species appear while other species vanish. In order to consider the change of chemical species inside the bulk according to the pH of the solution in the kinetic model, a correction factor (
On the other hand, species commonly present in water, such as DOM and inorganic anions (e.g., CO32−, HCO3−, SO42−, and Cl−, among others) may also have a significant effect because of their ability to absorb UV-light and/or to scavenge HO°. The HO° scavenging effect of matrix constituents drastically limits the oxidation action of HO°, leading to a decrease in the performance of the system .
Taking into account all the mentioned processes and in order to give a more realistic view of what happens in the UV/H2O2 process, the kinetic equation describing pollutant degradation can be expressed as Eq. (21).
where the terms , , , and represent the specific contributions of UV-radiation, the oxidation of HO°, HO2°, O2°− and the formed anion radicals (AR) (including CO3°−, SO4°−, H2ClO°, HClO°, Cl°, and Cl2°−) to the overall pollutant degradation, respectively.
Based on the reactions illustrated in Figures 1 and 2, and the different involved parameters, the mass balances and the corresponding ODE of the species of interest (C, DOC, H2O2, HO2-, HO°, HO2°, O2°−, CO3°−, SO4°−, HClO°−, H2ClO°, HClO°, Cl°, Cl2°−, OH−, H+, H2CO3*, CO32−, HCO3−, HSO4−, SO42−, and Cl−) are summarized in Table 1.
Proposed kinetic model
In the developed kinetic model, three different ways of calculating the evolution of HO° concentration during time were presumed: (a) a non-pseudo-steady or transient state (i.e., the net formation rate of HO° is different from zero); (b) a pseudo-steady state; and (c) a simplified pseudo-steady state; correspondingly denoted as kinetic model A, B, and C.
Considering that the oxidant is in a high level (i.e.,
The initial values of DOC and inorganic anionic species (CO32−, HCO3−, SO42−, Cl−, etc.) are set according to the conditions of the water to be treated.
2.3. Numerical solution of the proposed kinetic models
The ODE system compiled in Table 1 was solved applying MATLAB software and ODE15S function. For simultaneously solving the ODE set of the proposed kinetic models, it was necessary to define several photochemical parameters such as
3. Results and discussion
In order to validate the proposed kinetic models, experimental data for PHE degradation by the UV/H2O2 process were used from Alnaizy and Akgerman  study. These authors conducted a set of experiments in a completely mixed batch cylindrical photoreactor made on Pyrex glass. The used photochemical parameters and the kinetic reaction rate constants of PHE with HO°, O2°−, and CO3°− are presented in Table 2.
|Quantum yield||0.07 mol Ein−1|||
|Molar extinction coefficient||51 600 M−1 m−1|||
|Path length||63.5 mm|
|Incident UV-light intensity (radiation of|
254 nm > 90% and power = 15 W)
|1.516 × 10−6 Ein L−1 s−1|
|Kinetic rate constant phenol-||6.6 × 109 M−1 s−1|||
|Kinetic rate constant phenol-O2°−||5.8 × 103 M−1 s−1|||
|Kinetic rate constant phenol-CO3°−||2.2 × 107 M−1s−1|||
3.1. Assumptions taken into consideration
As stated previously, the developed kinetic models A, B, and C employed the non-pseudo-steady, the pseudo-steady, and the simplified pseudo-steady state assumption, respectively, to estimate HO° concentration. In the proposed models, the impact of UV radiation individually and/or the combined action of H2O2 and UV light (including the effect of HO°, HO2°, O2°−, and CO3°−) on PHE degradation was studied.
A PHE concentration of 2.23 × 10−3 M and a H2O2/PHE ratio of 495 were selected for validating the model. The used PHE solution was prepared by adding the appropriate amount of pollutant solution to deionized water . Therefore, the effect of inorganic anions, excluding HCO3− and CO32− was not taken into account. In this sense, in the PHE degradation rate expression (ODE1) the contribution of inorganic anion radicals, such as SO4°−, H2ClO°, HClO°, Cl°, and Cl2°−, was not studied. It was assumed that the other terms included in ODE1 contributed to pollutant degradation.
As the treated water was deionized, the presence of OM different from the parent compound in the initial solution was neglected ([DOC]0 = 0 M). Hence, the DOC in the solution came from PHE photolysis and free radical (HO°, HO2°, O2°−, and CO3°−) oxidation.
On the other hand, several authors agree that OM reduction by direct photolysis in a UV/H2O2 oxidation process can be neglected [7–9]. That is the reason why this was not included in the proposed kinetic model. However, it is highlighted that the OM is able to absorb UV-light, preventing UV-penetration into the bulk and avoiding H2O2/HO2− and pollutant direct photolysis. Therefore, the detrimental effect of UV-shielding in PHE degradation was taken into consideration. For including this effect in the kinetic model, OM molar extinction coefficient, referred as DOC molar extinction coefficient (ԑDOC), must be previously known. Although this parameter has already been measured [7, 8], its value is not a universal one, since DOM is a complex group of aromatic and aliphatic hydrocarbon structures with attached functional groups [20, 21]. As Alnaizy and Akgerman  did not measure this variable, a mean value from Peuravuori and Pihlaja  study was presumed. This value corresponded to
Additionally, it is widely known that the quantum yield of a compound is dependent on the excitation wavelength and the pH of the solution. For 254 nm, PHE quantum yield in an aqueous solution was found to be in the range of 0.02–0.12 mol Ein−1 at pH 1.6–3.2 . Therefore, an average value (0.07 mol Ein−1) was taken as PHE quantum yield.
Moreover, it is widely recognized that the solution pH decreases as the process proceeds. This variation in the pH can cause difficulties in modeling studies, since the presence of radical species such as HO2°, and O2°−, among other chemical species involved in the oxidation system, is significantly dependent on the pH of the medium. Therefore, to give a more realistic view of what happens inside the reaction medium, H2O2 and HO2− photolysis reactions (Eqs. (1) and (2), correspondingly), as well as reactions expressed in Eqs. (26) and (27) were discriminated in the model according to the solution pH time evolution, as it is simplified in Figure 3. For selecting the suitable reactions with regard to the pH changes over time, previous information about the evolution of the pH during the performance of the process is required. However, in some occasions this is not provided. In this case, the initial pH of the solution was 6.8 . At this pH, one of the predominant species into the bulk was H2O2, since the pKa of the H2O2/HO2− equilibrium is 11.6. Therefore, the photolysis of HO2− was neglected in the model performance (i.e.,
3.2. Kinetic model validation
Initially, the associated ODE sets with model A, B, and C were solved. Parameters
Figure 4 compares the simulation results of the proposed kinetic models A, B, and C with the experimental data for 2.23 × 10−3 M PHE with a H2O2/PHE ratio of 495 and a reaction time of 220 min. The measured and simulated results for PHE direct photolysis alone are also presented. It is observed that more than 90% of the initial PHE concentration was removed after 220 min due to both direct photolysis and indirect degradation (primarily due to HO° attack). The effect of CO3°− could be seen as marginal because of the reduced number of those radicals, in the range of 10−15 M, and the low reaction rate constant with PHE compared to HO°. In addition, it is shown that PHE was not completely removed by direct UV photolysis under the tested photochemical conditions (Table 2), since approximately 50% of the total PHE degradation was attributed to UV photolysis, as it was experimentally determined by Alnaizy and Akgerman . On the other hand, the figure demonstrates that the prediction kinetic model C was in good agreement with the available experimental data with a relative high correlation factor (
Furthermore, Figure 4 clearly presents that the removal rate of the target pollutant was not significantly dependent on the hypothesis assumed to estimate the HO° level (non-pseudo-steady, pseudo-steady and simplified pseudo-steady state assumptions). This could be explained from the relatively low concentration of those reactive species in the solution (with a magnitude order of 10−14 M) when compared to the level of other species involved in the system, such as HO2° and O2°−, whose concentrations were in the range of 10−7 M. The number of HO° remaining in the solution is in concordance with the low final HO° levels found in the literature [24, 25] and even higher than those reported by Ray and Tarr .
In Figure 5, the evolution of the HO°, HO2°, O2°−, DOC and H2CO3* normalized estimated concentrations using the prediction model A is depicted. It is observed that HO2° number increased as the oxidation system proceeded, while O2°− level decreased. Typically, the effect of HO2° and O2°− radicals are neglected in the UV/H2O2 system [6–8, 15, 17, 27, 28] since they are found to be less reactive than HO°, as stated previously. However, when they are produced in a high level, they could also participate in the contaminant oxidation. That is the current case of HO2°, as [HO2°] >>>> [HO°]. Therefore, the contribution of HO2° to PHE degradation should be studied. On the other hand, in this work the action of O2°- in PHE conversion can be omitted since O2°- level decreased with the reaction time, as expected, because of the drop in the pH solution.
Furthermore, generally, there is a drop in the pH of the medium as the system progresses. This is probably due to acidic compound formation, such as carboxylic acids and H2CO3* resulting from pollutant degradation and mineralization. In this study the decrease of the pH in the solution was predicted via DOC conversion and the sole generation of H2CO3* by model A. As presented in Figure 5, DOC generation was progressively increasing as PHE was being degraded up to a certain point (117 min, corresponding to [DOC]max = 2.061 × 10−3 M, and equivalent to ca. 93% of PHE degradation). From this point, DOC started to decrease until [DOC]f = 1.879 × 10−3 M. That breakpoint represented the moment at which PHE was almost completely transformed into by-products. In addition, at this point, PHE mineralization began to be more evident, since H2CO3* level rose approximately in a linear way, up to a final level of 6.493 × 10−14 M, with the subsequent pH decrease. Similarities between the pattern of this DOC profile and that of the formed intermediate curves reported in Alnaizy and Akgerman  research are highlighted.
On the other hand, it is worth noting that HO° level evolution with the reaction time was different when comparing the kinetic prediction model A or B with C. Obviating HO2° contribution to PHE degradation, Figure 6 shows that the highest final HO° level was achieved in the prediction model A, with a maximum HO° concentration equal to 9.435 × 10−14 M. This value was similar to HO° final level in the prediction model B (9.400 × 10−14 M) and different to that of the prediction model C, where HO° final concentration was 4.486 × 10−14 M (ca. 48% lower than the obtained in the kinetic model A or B).
Approximately, in the first 40 min of the process a larger number of HO° in the aqueous medium with the developed kinetic model C was evidenced. Apparently, this amount of HO° was sufficient to degrade about 60% of PHE initial level under the studied experimental conditions. In contrast, models A and B, whose lines are overlapped, produced a lower number of HO° and the theoretical conversion of PHE remained above the experimental data. One possible reason for this discrepancy can be ascribed to DOM and dissolved oxygen positive effects in producing reactive oxygen species (ROS), as HO° , which were not considered. After 40 min of reaction, the HO° level was higher in the kinetic models A and B than in model C. This larger amount of HO° might lead to a faster conversion of the pollutant in comparison with the predicted model C, since the hypothetical depletion curve of PHE was below the measured data. Nevertheless, this rapid pollutant degradation did not occur actually. Therefore, there was an amount of HO° produced in excess that was not reacting with the contaminant. This surplus of HO° could be involved in free radical scavenging reactions. As model A and B consider the detrimental effect of HO° consuming reactions, it is suggested that their kinetic rate constants are higher than those ones used in this paper for these reactions to have a larger weight in the system. Additionally, the contradictory outcome between the actual situation and the theoretical one in the first and second stage of the process can also be attributed to the fact that just a fraction of the concentration of the species involved in the whole kinetic equations of the predicted models was actually reacting. Consequently, the real level of the species implicated in each kinetic reaction should be considered. However, it is rather difficult to determine which amount of the chemical species is exactly involving in each reaction for each time step, especially due to the high reactivity of radicals as the oxidation system progresses. In this context, further studies are required to overcome this limitation.
From these findings, it is suggested that there was an effective level of the formed HO°. Below that level, there was a lack of HO° for an efficient pollutant conversion; and above it, an excessive number of HO° was generated. That HO° effective level could be of relevance for industrial applications in order to be maintained throughout the reaction time, allowing an efficient pollutant degradation.
3.3. Estimation of PHE-HO2° reaction rate constant
In order to study the action of HO2° for pollutant degradation in the UV/H2O2 system, PHE-HO2° rate constant was calculated. For this purpose, the kinetic model A was used and it was estimated through a non-linear least-square objective function. The objective function for minimizing the error between the predicted and the measured data was defined as Eq. (28) .
where and correspond to the evolution of experimental and calculated pollutant concentration, respectively. This expression is a function of PHE-HO2° rate constant. The optimum value for PHE-HO2° second-order rate constant was found to be 1.6 × 103 M−1 s−1, which is consistent with the range of the reported values by Kozmér et al. ((2.7±1.2) × 103 M−1 s−1) . The results of running the new prediction kinetic model A (with and without the contribution of HO2° to pollutant conversion) and the experimental data are presented in Figure 7. The figure shows that the prediction model A with the estimation of PHE-HO2° rate constant was in a stronger agreement with the experimental data (
A kinetic model for studying pollutant degradation by the UV/H2O2 system was developed, including the background matrix effect in scavenging free radicals and shielding UV-light and the reaction intermediate action, as well as the change of the pH as the UV/H2O2 process proceeds. Three different ways for calculating HO° level time evolution were assumed (non-pseudo-steady, pseudo-steady and simplified pseudo-steady state; denoted as kinetic models A, B, and C, respectively). It was found that the assumption of pseudo-steady (simplified or not) or transient state for determining the HO° level evolution with time was not significant in PHE degradation rate due to the relatively low HO° level present into the bulk (~10−14 M). On the other hand, taking into account the high levels of HO2° formed in the reaction solution compared to HO° concentration (~10−7 M >>>> ~10-14 M), HO2° action in transforming PHE was considered. For this purpose, PHE-HO2° reaction rate constant was calculated and estimated to be 1.6 × 103 M−1 s−1, resulting in the range of data reported from literature. It was observed that, although including HO2° action allowed slightly improving the kinetic model degree of fit, HO° developed the major role in PHE conversion, due to their high oxidation potential.
Additionally, it was found that there was an effective level of the HO° formed in solution. Below that level, there was a lack of HO° for an efficient pollutant conversion; and above it, an excessive number of HO° was generated. That HO° effective level calculated from kinetic model C could be of relevance for industrial applications in order to be maintained throughout the reaction time, allowing an efficient pollutant degradation.
In this study, there was an attempt to contemplate a wide range of the chemical reactions involved in the UV/H2O2 process and although high correlation factors were obtained, it is suggested to include the positive effect of the OM and the dissolved oxygen in generating ROS, as well as the effect of other anions naturally present in water bodies, as phosphate and nitrate, for the model to be a more accurate approximation of reality.
This work was financially supported by the Colombian Administrative Department of Science, Technology and Innovation (COLCIENCIAS).