Local Volumetric Rate Of Photon Absorption Research Articles

Two-dimensional P1 approximation (P1-2D) for the evaluation of the radiant field in annular and tubular photocatalytic reactors

The local volumetric rate of photon absorption (LVRPA) was formulated by solving the radiative transfer equation (RTE) in two dimensions using the P1 approximation approach (P1-2D) to describe the radiant field in annular and tubular photocatalytic reactors. The radiant sources employed were assumed to be periodic when applying the boundary conditions to facilitate the determination of the integration constants in the RTE solution. Three different systems were considered: S1 and S2 consisted of annular reactors, while S3 consisted of a tubular reactor. Simulations were conducted using commercial TiO2 P25 and anatase TiO2 as photocatalyst models, with their optical properties sourced from the literature. The linear source spherical emission (LSSE), Gaussian emission (GE), and uniform emission (UE) models were used as radiant sources. The LVRPA was found to decrease from the inner to the outer wall of the reactor for S1 and S2, and from the wall to the center of the reactor for S3; it was close to the values obtained using the Monte Carlo (MC) procedure in S2. The overall volumetric rate of photon absorption (OVRPA) increased exponentially with catalyst loading until a point where no significant increase was observed for each reactor. The apparent optical thickness τ App 1 ​formulated was a more reliable optimization parameter than the optical thickness.

A comparative study of metal-sulphide/ZnO for visible-light-induced photocatalysis and the six-flux photon absorption model of an external lamp photoreactor

This study compares the photocatalytic performance of three metal-sulphide/ZnO nanocomposites (Ag2S/ZnO, FeS/ZnO and NiS/ZnO) for degrading tetracycline (TC) under visible light irradiation. The nanocomposites were synthesized using a novel one-pot solid-phase combustion method, analysed by various characterization techniques (XRD, SEM, TEM, BET, FTIR, PL, and UV–vis DRS). Photocatalytic tests revealed significantly higher efficiencies for Ag2S/ZnO (87.50 %), FeS/ZnO (80.53 %) and NiS/ZnO (77.27 %) nanocomposites exhibit much higher photocatalytic efficiency than pure ZnO (42.63 %). The improved performance is attributed to the reduced bandgap energy and suppressed electron-hole (e-/h+) recombination facilitated. This can also be attributed to the photocatalytic inhibition test which confirmed the holes (h+) as the main inhibitor and identified the superoxides (O2•−) radical as the main active specie responsible for the degradation. Additionally, this study innovatively applies the Six Flux radiation absorption-scattering models (SFM) to an external lamp photocatalytic reactor. This approach allows precise determination of reactor parameters and intrinsic reaction kinetics for TC degradation, independent of the radiation field. The TC degradation rate, calculated at 5.6 × 104EinL−1S−1 for every point in the reaction space, shows a half-order dependence on the local volumetric rate of photon absorption (LVRPA) of 142.3 W/m3, at a photon flux of 115.42 W/m2. These findings elucidate the mechanisms behind enhanced visible-light photocatalysis and demonstrate the innovative application of photon absorption and light-scattering models to optimize reactor design and efficiency. This work offers valuable insights for developing advanced photocatalytic systems with improved performance and practical applicability.

Estimation and Optimization of the Radiant Field in Flat Plate Heterogeneous Photoreactors with the P1-approximation of the Radiative Transfer Equation (RTE).

In this work, the P1-approximation of the radiative transfer equation (RTE) was used for the description and optimization of the radiant field in a flat plate photoreactor under solar radiation with three commercial brands of titanium dioxide photocatalysts. The boundary layer of photon absorption (δ_abs), the average volumetric rate of photon absorption (VRPA), and a new apparent optical thickness (ζ_app1) were used as design parameters for optimization. A simple mathematical expression for the calculation of δ_abs also called the best reactor thickness was formulated. For the three catalysts, varying the reactor height (L), it was found a decrease in the local volumetric rate of photon absorption (LVRPA) from the top side until the bottom of the reactor for any value of the catalyst loading (Ccat). It was also observed that when Ccat increases the VRPA increases exponentially until a fixed value where it remains almost constant. With L= 1 cm, the optimum Ccat (Ccatop) was 0.2 g/l in 0.85 cm of thickness, 0.3 g/l in 0.82 cm of thickness, and 0.4 g/l in 0.89 cm of thickness for the photocatalysts Degussa P-25, Aldrich, and Hombitak respectively. The optimum apparent optical thickness (ζ_(app1,op)) was 4.03, 4.62, and 3.7 for the photocatalysts Degussa P-25, Aldrich, and Hombitak respectively. These results are in good agreement with the literature. Results found in this work give predictions on radiation absorption in flat plate photocatalytic reactors with different heights.

Kinetic model of photo-Fenton degradation of paracetamol in an annular reactor: main reaction intermediates and cytotoxicity studies

A kinetic model derived from a simplified reaction sequence is proposed for the photo-Fenton degradation of Paracetamol (PCT), employing an annular photoreactor. The kinetic model explicitly included the effects of radiation absorption on pollutant degradation kinetics through the evaluation of the Local Volumetric Rate of Photon Absorption (LVRPA). Irradiated experiments achieved an average PCT conversion of 99.3% at 5 min of reaction, and a maximum of 69% of mineralization. Conversely, non-irradiated experiments reached an average PCT conversion of 86.6% at 5 min of reaction, and a maximum of 35% of mineralization. Kinetic parameters (k5=5.82×109, k6=3.01×1010,k7=6.01×1010M−1s−1) were estimated employing a nonlinear, multi-parameter regression method, and the validated kinetic model was used to predict temporal variations of the concentrations of HP, PCT, and the main reaction intermediates: hydroquinone (HQ) and 1,4-benzoquinone (BQ). The root mean square error (RMSE) values obtained for HP, PCT, HP, HQ and BQ were 1.16 × 10−2, 7.13 × 10−1, 3.53 × 10−3, 3.05 × 10−3 mM, respectively, showing a good agreement between experimental and predicted data. Moreover, the kinetic model was validated with a new set of experimental tests, confirming its predictive capacity. Beyond the degree of mineralization attained, additional cytotoxicity tests proved that the photo-Fenton process is effective in generating a non-toxic effluent under the operating variables investigated.

Evaluation of a helicoidal flux photoreactor applied in the dicloxacillin degradation by UV-C/H2O2 and UV-A/photo-Fenton including the effect of photon absorption

The efficiency of a helical flow photoreactor in the oxidation of the antibiotic Dicloxacillin as a function of the recirculation flow, the local volumetric rate of photon absorption (LVRPA) and photonic efficiency using oxidation processes based on UV-C/H2O2 and UV-A/photo-Fenton were evaluated in this work. Mathematical modeling of the degradation process and experiments in lab-scale helicoidal reactor were done. Mathematical evaluation was supported in function of photon flux, mass balance and reaction rate law. The LVRPA was calculated by modified Beer-Lambert Equation. The effect of the concentration of hydrogen peroxide and iron (II) on the efficiency of the oxidation of the antibiotic Dicloxacillin was evaluated by means of the photo-Fenton. In 45 min, 100% degradation of dicloxacillin was achieved using 1.5 mM H2O2 and 7.32 μM ferrous ion in the photo-Fenton experiments with the helical flow photoreactor. The optical thickness of the reaction and distribution of energy absorption confirmed the kinetic and photonic efficiency performance. The prediction of the model presented a global error less to 2.4% between experimental and simulated data.

Estimation of the radiation field for CPC photocatalytic reactors using a novel six-flux model in two dimensions (SFM-2D)

In the present work, we introduced a new Six Flux Model in two dimensions (SFM-2D) for the estimation of the local volumetric rate of photon absorption (LVRPA) in polar coordinates. This novel model was applied on a compound parabolic collector (CPC) photocatalytic reactor using the Ray-Tracing Technique (RTT) and Lambert's cosine law. The volumetric rate of photon absorption per unit reactor length (VRPA/H) and overall volumetric rate of photon absorption (OVRPA), calculated with SFM-2D, were compared with SFM-1-DR (diffuse reflectance) and SFM-HG (Henyey-Greenstein).We obtained an analytical solution of the radiant transfer equation (RTE) based on a novel SFM-2D. The most relevant result was a simple algebraic expression from a detailed mathematical development. In addition, we included Lambert's cosine law and the radiation absorption by the fluid to estimate the radiant field in a compound parabolic photoreactor CPC. The numerical results, obtained with simulations, were compared satisfactorily to those reported in previous works at different operating conditions; the global performance of the new model described discrepancies less than 0.5%.

Modeling the photocatalytic oxidation of carboxylic acids on aqueous TiO2 suspensions and on immobilized TiO2-chitosan thin films in different reactor geometries irradiated by UVA or UVC light sources

Photocatalytic reactor models incorporating radiation transport parameters and intrinsic kinetic parameters of photocatalytic decomposition of single-compound and mixtures of oxalic (OA) and formic acid (FA), in both slurry suspensions and immobilized photocatalytic thin films, were validated in two well-mixed annular photoreactors geometries irradiated with either UVA or UVC radiation. The six-flux absorption scattering model (SFM) predicted the radiation field in a titanium dioxide (TiO2 P25) catalyst suspension, the local volumetric rate of photon absorption (LVRPA) at each point of the reactor and, after volumetric integration, the lumped VRPA. The model combining the lumped VRPA, the kinetics models describing the adsorption and photocatalytic decomposition of OA and FA and the material balance of the reacting species was fitted to the experimental results of photocatalytic decomposition of OA and FO in a slurry TiO2 suspension, to determine the OA and FA intrinsic reaction kinetics parameters. Such intrinsic parameters were then used with the average surface rate of photon absorption (SRPA) to model and predict the photocatalytic oxidation of OA and FA on non-porous TiO2–chitosan films immobilized on glass plates immersed in the photoreactor. The models for both slurry suspensions and immobilized photocatalysts predicted the degradation and mineralization of OA and FA and of a mixture of them under diverse experimental conditions. This study demonstrates a systematic methodology for determining intrinsic reaction kinetics rate parameters of water contaminants that can also be used to represent the photocatalytic oxidation of such contaminants in irradiated slurries and in immobilized photocatalytic thin films and in any photoreactor geometry.

Reaction kinetics formulation with explicit radiation absorption effects of the photo-Fenton degradation of paracetamol under natural pH conditions.

The degradation of paracetamol (PCT) in an aqueous medium using the Fenton and photo-Fenton reactions was investigated. The aim of this research was the development of a kinetic model based on a reaction mechanism, which includes two main intermediates of PCT degradation and the local volumetric rate of photon absorption (LVRPA). Ferrioxalate was used as a catalyst and the working pH was adjusted to 5.5 (natural pH). Experimental work was planned through a D-optimal experimental design and performed in a flat plate reactor irradiated by a solar simulator. Hydrogen peroxide (HP) concentration, reaction temperature, and radiation level were the operating parameters. The photo-Fenton reaction allowed to reach a minimum relative PCT concentration of 2.01% compared to 5.04% achieved with Fenton reaction. Moreover, the photo-Fenton system required a 50% shorter reaction time and lower HP concentration than in dark conditions (90 min and 189 mg L-1 vs. 180 min and 334 mg L-1, respectively). The experimental results were used to estimate the kinetic parameters of the proposed kinetic model employing a nonlinear, multi-parameter regression method. The values obtained from the normalized root-mean-square error (14.52, 1.96, 4.36, 13.16, and 8.72 % for PCT, benzoquinone, hydroquinone, HP, and oxalate, respectively) showed a good agreement between the predicted and experimental data.

Comprehensive Kinetics of the Photocatalytic Degradation of Emerging Pollutants in a LED-Assisted Photoreactor. S-Metolachlor as Case Study

Although the potential and beneficial characteristics of photocatalysis in the degradation of a good number of emerging pollutants have been widely studied and demonstrated, process design and scale-up are restrained by the lack of comprehensive models that correctly describe the performance of photocatalytic reactors. Together with the kinetics of degradation reactions, the distribution of the radiation field in heterogeneous photocatalytic systems is essential to the optimum design of the technology. Both the Local Volumetric Rate of Photon Absorption (LVRPA) and the Overall Volumetric Rate of Photon Absorption (OVRPA) help to understand this purpose. This work develops a Six-Flux radiation absorption–scattering model coupled to the Henyey–Greenstein scattering phase function to evaluate the LVRPA profile in a LED-assisted photocatalytic reactor. Moreover, the OVRPA has been calculated and integrated into the kinetic equation, accounting for the influence of the radiation distribution on the reaction rate. The model has been validated with experimental data for the degradation of S-Metolachlor (MTLC), and the set of operating variables that maximize the reactor performance, 0.5 g/L of TiO2 P25 and pH 3, has been determined.

Degradation of bisphenol A by the UV/H2O2 process: a kinetic study.

A theoretical and experimental study of bisphenol A (BPA) degradation by the UV/H2O2 process in water is presented. The effects of the H2O2 concentration and the specific rate of photon emission (EP,0) on BPA degradation were investigated. A kinetic model derived from a reaction sequence was employed to predict BPA and hydrogen peroxide concentrations over time using an annular photochemical reactor in batch recirculation mode. The local volumetric rate of photon absorption (LVRPA) inside the photoreactor was computed using a Line Source with Parallel Plane emission model (LSPP). From the proposed kinetic model and the experimental data, the second order rate constants of the reactions between hydroxyl radicals and the main reacting species (H2O2 and BPA) were estimated applying a nonlinear regression method. A good agreement between the kinetic model and experimental data, for a wide range of operating conditions, was obtained. For BPA, H2O2, and TOC concentrations, the calculated root means square errors (RMSE) were 2.3 × 10- 2, 9.8 × 10- 1, and 9.0 × 10- 2mmolL- 1, respectively. The simplified kinetic model presented in this work can be directly applied to scaling-up and reactor design, since the estimated kinetic constants are independent of the reactor size, shape, and configuration. Further experiments were made by employing low BPA initial concentration (100μgL- 1) in water and real wastewater. A lower degradation rate of BPA was observed in the real wastewater, although the UV/H2O2 process has also been able to completely degrade the target pollutant in less than 1h.

TiO2-rGO photocatalytic degradation of an emerging pollutant: kinetic modelling and determination of intrinsic kinetic parameters

An intrinsic kinetic model, derived from a suggested reaction photo-mechanism and with an explicit dependence on the local volumetric rate of photon absorption (LVRPA), was developed to simulate the photocatalytic degradation of clofibric acid and the main reaction intermediates, with a new titania-reduced graphene oxide nanocomposite (TiO2-rGO), The proposed reaction mechanism takes into account that graphene behaves as an electron acceptor and, therefore, this effect was included in the derivation of the reaction rate expressions and in the parameters estimation of the kinetic model. The photodegradation of clofibric acid was performed in a slurry photoreactor under different irradiation levels and using several loadings of a TiO2-rGO nanocomposite, prepared by hydrothermal method with a 0.5 wt. % of GO. Absorbed radiation profiles inside the photoreactor were obtained by solving the radiation model with the Monte Carlo method. A photocatalyst loading of 100 mg L−1 gave place to the best photodegradation results. Mass balances were proposed for the main pollutant and their main detected intermediates: p-benzoquinone and 4-chlorophenol. The intrinsic kinetic parameters were obtained for the complete (6-parameters) and simplified (5-parameters) models by comparing the experimental and the theoretical concentration values of all the organic compounds detected. The model proved to be able to predict with good accuracy the concentration evolution of clofibric acid, 4-chlorophenol and p-benzoquinone under several photocatalyst concentrations and irradiation levels. Finally, a very good correlation between calculated and experimental values of clofibric acid concentration was obtained with root-mean-square errors below 11%.

Visible-light activation of TiO2 by dye-sensitization for degradation of pharmaceutical compounds

This work reports the improvement in the photon absorption and degradation of acetaminophen (ACF) and diclofenac (DFC) by photosensitizing TiO2 with two types of dyes Eosin Y (Ey) and Rhodamine B (RhB). Experimental tests were carried out in a solar simulator for three hours for different systems and both pollutants. The influences of the TiO2 concentration (100, 200 and 800 mg L−1) and the catalyst–dye ratio (2%, 5% and 10%) were investigated. The degradation of the compounds was higher in the presence of TiO2-Ey compared to the TiO2-RhB and TiO2 for both pharmaceutical compounds, which was attributed to the anionic nature of Ey. DFC total degradation was achieved using 100 mg L−1 of catalyst loading and 10% of catalyst–dye ratio and the highest ACF degradation (71%) was obtained at 800 mg L−1 of catalyst loading and 5% of catalyst–dye ratio. The photon absorption was studied for both dyes using the six-flux absorption scattering model (SFM) for estimating the LVRPA (local volumetric rate of photon absorption). This was done by modifying the apparent optical thickness equation. It was found that the presence of dye in the photocatalytic systems considerably increases the LVRPA. The rate coefficients for the degradation of pharmaceutical compounds in the presence of the organic dyes were also obtained.

Heterogeneous photo-Fenton process using iron-modified regional clays as catalysts: photonic and quantum efficiencies.

A regional raw clay was used as the starting material to prepare iron-pillared clays with different iron contents. The catalytic activity of these materials was tested in the heterogeneous photo-Fenton process, applied to the degradation of 2-chlorophenol chosen as the model pollutant. Different catalyst loads between 0.2 and 1.0gL-1 and pH values between 3.0 and 7.0 were studied. The local volumetric rate of photon absorption (LVRPA) in the reactor was evaluated solving the radiative transfer equation applying the discrete ordinate method and using the optical properties of the catalyst suspensions. The photonic and quantum efficiencies of the 2-chlorophenol degradation depend on both the catalyst load and the iron content of the catalyst. The higher values for these parameters, 0.080molEinstein-1 and 0.152molEinstein-1, respectively, were obtained with 1.0gL-1 of the catalyst with the higher iron content (17.6%). For the mineralization process, photonic and quantum efficiencies depend mainly on the catalyst load. Therefore, it was possible to employ a natural and cheap resource from the region to obtain pillared clay-based catalysts to degrade organic pollutants in water.

Impact of photocatalyst optical properties on the efficiency of solar photocatalytic reactors rationalized by the concepts of initial rate of photon absorption (IRPA) dimensionless boundary layer of photon absorption and apparent optical thickness

The concepts of “initial rate of photon absorption” (IRPA), “dimensionless boundary layer of photon absorption” and “apparent optical thickness (τapp)” are presented to evaluate the radiative transfer phenomena in solar, slurry, planar, photocatalytic reactors. The radiation field produced by suspensions of TiO2 and goethite, two photocatalysts with profoundly different optical properties used in heterogenous photocatalysis and heterogeneous photo-assisted Fenton reactions, was determined by the six-flux radiation absorption-scattering model coupled to the Henyey-Greenstein scattering phase function (SFM-HG). The concept of IRPA, defined by the differentiation at the local volumetric rate of photon absorption (LVRPA) at the reactor window boundary, is proposed as a new approach to determine the impact of catalyst loading and optical properties on the extinction of light inside a photoreactor. The IRPA showed that the extinction of light follows a second order dependency on the photocatalyst concentration while the impact of the optical properties can be expressed by a decoupled function (Ψ function). The Ψ function increased with photocatalyst concentration and approached a maximum at the same optimal photocatalyst concentration determined from the analysis of the total rate of photon absorption (TRPA) in the reactor. The analysis of TRPA and boundary layer of photon absorption redefined here in dimensionless form, as a function of τapp, determined that the most efficient rate of radiation absorption in solar powered planar reactors occurs at τapp = 4.1–4.4, with approximately 10% of the reactor width under darkness. τapp is a similarity dimensionless parameter exclusively derived from the SFM approach, which clusters the effects of photocatalyst loading, reactor dimension and photocatalyst optical properties, providing an ideal parameter for designing and scaling photocatalytic reactors operated with any kind of photocatalytic material.

Photocatalytic Degradation of Commercial Acetaminophen: Evaluation, Modeling, and Scaling-Up of Photoreactors

In this work, the performance of a pilot-scale solar CPC reactor was evaluated for the degradation of commercial acetaminophen, using TiO2 P25 as a catalyst. The statistical Taguchi’s method was used to estimate the combination of initial pH and catalyst load while tackling the variability of the solar radiation intensity under tropical weather conditions through the estimation of the signal-to-noise ratios (S/N) of the controllable variables. Moreover, a kinetic law that included the explicit dependence on the local volumetric rate of photon absorption (LVRPA) was used. The radiant field was estimated by joining the Six Flux Model (SFM) with a solar emission model based on clarity index (KC), whereas the mass balance was coupled to the hydrodynamic equations, corresponding to the turbulent regime. For scaling-up purposes, the ratio of the total area-to-total-pollutant volume (AT/VT) was varied for observing the effect of this parameter on the overall plant performance. The Taguchi’s experimental design results showed that the best combination of initial pH and catalyst load was 9 and 0.6 g L−1, respectively. Also, full-scale plants would require far fewer ratios of AT/VT than for pilot or intermediate-scale ones. This information may be beneficial for reducing assembling costs of photocatalytic reactors scaling-up.

Six-flux absorption-scattering models for photocatalysis under wide-spectrum irradiation sources in annular and flat reactors using catalysts with different optical properties

The photocatalytic oxidation of 2-hydroxybenzoic acid (2-HBA) in an annular tubular reactor (R1) and a flat rectangular open channel reactor (R2), which were irradiated with light sources emitting in the UVB, UVA and visible range of the solar radiation spectrum, and using two photocatalysts, titanium dioxide (TiO2 P25) and Ag-modified TiO2 P25 (Ag@TiO2) was modeled. The local volumetric rate of photon absorption (LVRPA) in the reactors was evaluated by the six-flux absorption scattering model (SFM). The Langmuir-Hinshelwood kinetic model of the degradation of a model contaminant on irradiated aqueous suspensions of TiO2 P25 and Ag@TiO2 was combined with the SFM radiation model and light emission models to determine local reaction rates, and further integrated with the reactors hydrodynamics and material balances to model the degradation of 2-HBA in the photoreactors. The linear source spherical emission (LSSE) and extensive source superficial diffuse emission (ESSDE) models were compared in terms of incident and transmitted photon fluxes through the reactor. It was shown that both LSSE and ESSDE models could be successfully applied for the modeling of annular and flat reactors, considering the emission from tubular fluorescent light sources.Since current research calls for materials with wide absorption in the solar radiation spectrum, spanning from the UV to the visible, therefore, the SFM model was adapted to consider such wide distribution. The optical properties of the photocatalysts were averaged over narrow wavelength ranges of the solar spectrum, wherein the contributions by the UVA, UVB and visible light irradiation to the LVRPA and contaminant degradation rate were separated. The effects of catalyst concentration, liquid velocity profile and the photon flux from different light sources on the 2-HBA degradation rate were explored. The “intrinsic” reaction kinetic constants of 2-HBA photocatalytic oxidation independent of reactor type, catalyst concentration, irradiance levels and hydrodynamic conditions were determined by fitting the experimental data to the model results. It was shown that the model parameters were independent of the type of catalyst used, although the catalyst exhibited significantly different optical properties.

Solar photoreactor design by the photon path length and optimization of the radiant field in a TiO2-based CPC reactor

The photon path length inside the radiant field of a photocatalytic solar reactor (with a compound parabolic collector (CPC)) crossing a slurry fluid with suspended particles of TiO2 was studied. The modeling included three sub-models: a ray-tracing algorithm to determine the boundary conditions in the absorber wall, a boundary layer to calculate the path length of the photon before its extinction and finally, the six-flux scattering-absorption model (SFM) to estimate the absorbed energy profiles. A simple expression for the average of the local volumetric rate of photon absorption (LVRPA) in terms of a reference state was proposed.The recent concept of a radiant boundary layer was extended to CPC reactors, and a new calculation of the photon path length is proposed. We found that a catalyst load higher than the optimum value leads to a shorter photon path length causing a dark zone within the absorber where the catalyst activation does not occur. Optimal conditions for six different commercial TiO2 catalysts were determined. The best catalysts are the Fluka and Fischer catalysts, with 20% of radiant energy absorption over the total irradiated energy. The efficiency is independent of the diameter if the optimal catalyst load is guaranteed. The load-diameter optimal pairs share an absorber optical thickness (τa,opt=13.18 for the Degussa catalyst), which can be used to scale-up the reactor. The path length at maximum photon absorption was 3/4 of the absorber diameter. Reactor diameters of 1–5 cm had optimum catalyst loads of 230–46mg/l. The turbulent regime favors 〈LVRPA〉. The angle between the normal axis to the reactor surface and the sun position may vary up to 10° with minor losses of up to 0.5%.

Coupling the Six Flux Absorption–Scattering Model to the Henyey–Greenstein scattering phase function: Evaluation and optimization of radiation absorption in solar heterogeneous photoreactors

Robust and practical models describing the radiation field in heterogeneous photocatalytic systems, used in emerging environmental, photochemical and renewable energy applications, are fundamental for the further development of these technologies. The six-flux radiation absorption–scattering model (SFM) has shown to be particularly suitable for the modeling of the radiation field in solar pilot-plant photoreactors. In this study, the SFM was coupled to the Henyey–Greenstein (HG) scattering phase function in order to assemble the model with a more accurate description of the scattering phenomenon provided by this phase function. This new version of SFM, named as SFM-HG, was developed through fitting the Local Volumetric Rate of Photon Absorption (LVRPA) determined in a flat photoreactor to the “pseudo-experimental” LVRPA calculated by a Monte Carlo (MC) approach, which included the HG expression. As a result, simple mathematical correlations describing the SFM-HG scattering probabilities as function of the HG scattering parameter were determined. The SFM-HG was validated through a comparison with the MC model predictions of the Total Rate of Photon Absorption (TRPA) in the slab photoreactor. A RMSE% of approximately 5% demonstrated satisfactory agreement between the models. The SFM-HG was further applied to evaluate the impact of selected scattering phase functions on the absorption of radiation in solar photoreactors, operated with commercial TiO2 photocatalyst. The results have established that, the apparent optical thickness, τapp (or τapp,max for tubes) a parameter derived from the SFM approach, is the most appropriate for the design and optimization of photocatalytic reactors. This parameter is insensitive to scattering albedos and phase functions. CPC, tubular and flat-plate photoreactors should be designed with τapp,max=12, τapp,max=7 and τapp=4.5 respectively.

Modeling of a falling-film photocatalytic reactor: Fluid dynamics for turbulent regime

The falling-film photocatalytic reactor is a photochemical device used for several environmental applications due to its simple buildup and its high solar radiation usage. As most of photocatalytic reactors, modeling the falling film photoreactor can be a challenging task. The most difficult aspect of modeling is the photon absorption by the solid catalyst. Nonetheless, modeling the fluid dynamics in turbulent regime of a falling film reactor can also be very demanding. In this work, the eddy viscosity approach was applied for estimating the average velocity profile and the film thickness for turbulent regime. Also, a sensitivity analysis was made for determining how different variables like: flow rate, tilting angle and fluid viscosity, affect to the average velocity profile and the film thickness. As remarkable results, it was found that the flow rate was the most significant operating variable and affects both considered parameters. The model was validated with experimental measurements of the film thickness at three different flow rates. The relative errors between the experimental values and the film thickness values estimated with the model can be considered as plausible, since the maximum was 13.06%. However, regarding to the local volumetric rate of photon absorption (LVRPA) estimation from the calculated and experimental values of the film thickness, the errors were negligible. According to previous works, high flow rates ensure the turbulent regime and therefore, the mass-transfer limitations due to catalyst settling can be avoided; but also with larger film thicknesses can reduce the photon absorption because of longer optical paths. So, the optimization of the photon absorption, based on the film thickness and restricted to the turbulent regime, is a necessary study that can be developed in a future work.

A reaction engineering approach to kinetic analysis of photocatalytic reactions in slurry systems

The knowledge of the rate equation is fundamental for the assessment of the activity of the photocatalytic material and for the study, design and optimization of photocatalytic reactors. In the case of photocatalytic reactions, the local volumetric rate of photon absorption (LVRPA) affects the reaction rate and its inherently uneven distribution within a “slurry” reactor makes complex a correct kinetic analysis. In the present work it is shown which are the critical aspects of the kinetic analysis in slurry reactors and how to carry out photocatalytic experiments to minimize the misinterpretations of the experimental results. In particular, the influence of the type of illumination and of the operating conditions (recirculation flow rate, optical thickness) are studied. For instance, it is shown that the average values of the reaction rate and of the rate of photon absorption give no direct insight on the intrinsic kinetic if the reactor is not uniformly illuminated and the optical thickness is beyond a given value, which is significantly higher than the one usually suggested in literature for a “safe” kinetic analysis. Furthermore, the estimation of the average rate of photon absorption must take into account the backscattering of radiation from the reactor. In any case, the utilization of a proper mathematical model allows carrying out a sound kinetic analysis also in critical situations as those which can arise with an illumination by LEDs.