Mixing rules coupled to a semipredictive kinetic model of the Langmuir-Hinshelwood type were proposed to determine the behavior of the heterogeneous solar photodegradation with TiO2-P25 of multicomponent mixtures at pilot scale. The kinetic expressions were expressed in terms of the effective concentration of total organic carbon
Solar photocatalysis has been implemented and evaluated in the pollutant treatment at pilot scale in heterogeneous reactors using TiO2-P25, among which the following are highlighted: methylene blue [
Scaling of these oxidation processes requires the inclusion of multiple variables that affect the reaction rate such as substrate concentration, catalyst concentration, pH, radiation power, reactor geometry, and the presence of multiple reactive species among others. It is possible to find in several studies the effect of these variables on the process of photocatalytic oxidation of pure components [
Recently, Moulis and Krýsa [
Mueses et al. [
Mazille et al. [
Colina-Márquez et al. [
Research from Gora et al. [
Studies to date on the photocatalytic degradation of mixtures of organic pollutants have not considered explicitly the application of mixing rules, which can facilitate the analysis of the photooxidative behavior of multicomponent systems, having the advantage of allowing the identification of synergistic and antagonistic effects.
This work proposes the implementation of mixing rules to combine the individual kinetic behavior of DCA and 4-CP in a single kinetic expression to predict the global kinetic behavior of the binary mixture. The respective experimental validations were performed in a CPC reactor irradiated with solar light, varying the initial global concentration of the mixture and the proportion of the reagents.
Heterogeneous photocatalytic reaction kinetics can be expressed in a general form as follows [
To apply (
The reaction rate can be represented by (
Equation (
The mineralization process is a multistage process with multiple intermediate species. Using the TOC to analyze the overall performance of the process is a common practice; therefore it is possible to consider the modified reaction model as LH with a reasonable approximation, but in this case it should be applied to a pseudo compound [
The complexity of the degradation pathway of any compound is proportional to the complexity of its chemical structure; therefore it is expected that 4-CP presents the most complex route to complete mineralization than DCA. The reaction mechanism for the 4-CP is based on the electrophilic attack of the aromatic ring caused by adsorbed hydroxyl radicals (the indirect attack) [
Although the reaction mechanisms of the substances used are well known, this model assumes Langmuir-Hinshelwood behavior, without going into details of the reaction mechanism. So, if it use any reaction mechanism, the reaction rate expression can be changed as well as mixing rules.
From (
Those mixing rules may extend to the use of the intrinsic kinetic parameters, since the effects of radiant field may be considered coupled to the “apparent” global constant of reaction rate as an invariant parameter; this means that (
Therefore, when deducing a mixture expression to the contribution
The following assumptions were considered in the formulation of the mixture expressions. (i) The global reaction rate is the sum of the individual kinetics, this applies considering that the hydroxyl radicals generated during the photocatalytic degradation attack the organic matter in a nonselective way [
The first assumption (i) allows establishing an expression to the kinetic constant of the mixture
In this work, we have considered defining the global fraction of TOC for component
From the practical point of view, it is useful to use mass units such as ppm (TOC), considering it is an indirect measure of the mass of the individual compounds and mixtures during the mineralization process. Therefore the molar concentrations of the pollutants were not followed.
On the other hand, to obtain an expression to contribution
Where
Finally, the kinetic expression of the mixture is given by the combination of the mixing rules (
The equation that describes the material balance in a solar heterogeneous photocatalytic reactor that uses this approach and coupling of the mixing rules is the following:
Dichloroacetic acid (Merck, 99.99%), 4-chlorophenol (Merck, 99.99%), and titanium dioxide (Degussa P-25) were used.
Tracking of the substrate concentration was followed using a total carbon analyzer (5050 TOC-VCPHSHIMADZU). The dissolved oxygen was measured with an ORION 083010MD electrode. The pH was measured with a multiparameter (Thermo Scientific Orion 5-Star Plus) using a probe with reference 910500. The UV radiation intensity was monitored using a radiometer (ACADUS 85-PLS, 300–400 nm).
The experiments were carried out in the solar laboratory of the Universidad del Valle (Cali-Colombia). Radiation intensity was set to 30 W/m2 due to the standardization of the experimental time by using
A simplex-lattice
Simplex-lattice
Design points | Proportions | |
---|---|---|
4CP | DCA | |
1 | 1 | 0 |
2 | 2/3 | 1/3 |
3 | 1/3 | 2/3 |
4 | 0 | 1 |
The synthetic preparation of mixtures of DCA and 4-CP was performed using a volume of 100 mL of tap water (to emulate real operating conditions in industrial processing), following the scheme of global concentration given by the adopted experimental design.
The experimental procedure is detailed in Mueses et al. [
The fitting algorithm for obtaining the kinetic parameters was programmed in Matlab 7.0.4 using the
Algorithms of fitting of kinetic parameters and prediction by mixing model.
Applying the algorithm shown in Figure
Initial concentration effect on the initial reaction rate of DCA.
Exponent
Likewise, Figure
Initial concentration effect on the initial reaction rate of 4-CP.
The kinetic expression for DCA coupled to the material balance for the reactor is shown in (
Experimental fitting of the selected model for the DCA: 30 ppm (
According to Figure
Equation (
Experimental fitting of the modified model for 4-CP: 30 ppm (
Using parameters
Kinetic model parameters for the mixture.
Parameter | Value | Unit |
---|---|---|
|
20 | l |
|
51.324 | mg/min |
|
6.625 | mg/min |
|
0.0108590 | l/mg |
|
0.0342685 | l/mg |
|
0.142–0.40 | — |
The prediction results performed at different initial concentrations of the mixture are shown in Figures
Fitting statistical parameters for binary mixtures.
Parameter | Global concentration | |||||
---|---|---|---|---|---|---|
30 ppm | 60 ppm | 120 ppm | ||||
Mix 1 : 2 | Mix 2 : 1 | Mix 1 : 2 | Mix 2 : 1 | Mix 1 : 2 | Mix 2 : 1 | |
|
−0.628 | 0.882 | 0.984 | 0.891 | 0.745 | 0.685 |
|
2.58 | 0.76 | 0.39 | 1.06 | 2.18 | 1.48 |
Solar mineralization of binary mixtures at 30 ppm. Experimental data: Mix 1 : 0 (
Solar mineralization of binary mixtures at 60 ppm. Experimental data: Mix 1 : 0 (
Solar mineralization of binary mixtures at 120 ppm. Experimental data: Mix 1 : 0 (
The highest deviation was obtained in the mixture 1 : 2 (4-CP : DCA), which is shown in Figure
The abovementioned was a deflection of the ideal behavior, which was not considered in the derivation of the proposed model and was likely due to the different interactions between reagents and intermediates. Also it could be caused by the pH decrease that produces positive aspects in the heterogeneous photodegradation of some organic compounds; it modifies the aggregation degree of the catalyst particles, at the same time influencing the molecules adsorption, light scattering and photon absorption, and ions movement among others [
The complexity of the degradation pathways, 4-CP (indirect attack by hydroxyl radicals absorbed), added to the DCA (direct attack by photogenerated holes), suggests a new route of degradation which can only assume that these attacks are still valid for each compound in the mixture.
This seems evident in the accurate prediction made by the proposed mixture model; however the appearance of the synergistic effect is a change or modification of the route of degradation. This could be caused by the occurrence of electrostatic surface charges of the catalyst (electrostatic attraction) caused by a decrease in pH and low concentration of substrate (formation of monolayers).
In general, the results suggest that it is possible to separate the total kinetic effect caused by the mixture, in partial kinetic contributions which are proportional to the concentration of each component in the mixture, as if each reagent was being oxidized independently under the same reaction conditions.
The proposed mixing rules yielded satisfactory results in the prediction of the heterogeneous solar photodegradation of binary mixtures using TiO2-P25. The kinetic behavior of the mixture is the result of individual kinetic contributions which are proportional to the effective concentration of TOC for the component in the mixture. The proposed mixing rules may be used in designing and scaling of multicomponent photocatalytic heterogeneous systems, considering that such rules may be extended to the use of intrinsic kinetic parameters. Also, radiant field effects do not affect the formulation of the mixing rules.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors thank the Vicerectoria de Investigaciones de Universidad del Valle and the Cartagena University for financing this publication. The authors thank COLCIENCIAS for funding doctoral studies.