Volumetric Rate Of Energy Absorption Research Articles

The comparison of discrete ordinate and Monte Carlo methods in solving of the radiation transfer equations in a heterogenous reactor

Photoreactor applications in water and wastewater treatment has been increased in recent years. The simulation of radiation distribution inside the reactors allows the optimization of its operation. The radiation transfer equation (RTE) illustrates the field radiation. We applied the Discrete Ordinate (DO) method to solve the RTE and computed the local volumetric rate of energy absorption (LVREA) in a photoreactor, consisting of a Ultra Violet (UV) lamp and titanium dioxide Degussa P25 (TiO 2 DP 25) catalyst. First, GAMBIT 2.4.6 was employed to model the reactor in three dimensions. The simulation of the radiation distribution was carried out using FLUENT 14.5 software in the framework of a multiple point source summation (MPSS) model. The robustness of the DO approach was assessed by comparing with the Monte Carlo (MC) method and experimental data. The coefficient of determination (R 2 ) and index of agreement (IA) of DO and experimental data were 0.95 and 0.93, respectively. The DO and MC had a good convergence in the low concentrations of TiO 2 DP 25. In the concentrations between 0.03 g/l to 0.15 g/l, the difference with experimental data increased. In the concentration of 0.15 g/l, and beyond, the both methods and experimental data were in a good agreement.

Monte Carlo simulation of the light distribution in an annular slurry bubble column photocatalytic reactor

Slurry bubble column photocatalytic reactors have been used for photocatalytic wastewater treatment. In order to design and optimize these reactors, the light distribution needs to be determined. In this work, the light distribution in a slurry bubble column photocatalytic reactor was simulated using the Monte Carlo model. The model was validated using total transmitted radiation (TTR) measurements. The validated model was then used to determine the local volumetric rate of energy absorption (LVREA) and volumetric rate of energy (VREA) profiles. Very good agreement was achieved between experimental and simulated TTR values at different catalyst loadings using a Henyey-Greenstein scattering parameter of 0.84. The Monte Carlo model was more accurate than the six-flux model. From an analysis of the LVREA profiles, the light distribution along the radial coordinate was found to be highly non-uniform. Using the VREA, the optimum catalyst loading was estimated to be 0.4g/L. Bubbles were observed to slightly decrease the TTR while slightly increasing the light absorption especially at low catalyst loadings; therefore, bubble simulation could be neglected without significant loss of accuracy. This work highlights the accuracy and utility of Monte Carlo simulation for determining the light distribution in an annular slurry bubble column photocatalytic reactor.

Validity of the Six-Flux model for photoreactors

In the literature for photocatalytic reaction modeling engineering, several simplified schemes applicable to ambient temperature radiative transfer for scattering media are available. A popular strategy is the Six-Flux method because it is simple and is not computer time demanding but its accuracy is not always explicit. In the present work we assess the accuracy of low order methods, including six flux case, by solving the radiative transfer equation in dimensionless form within a cubic enclosure, for i) a collimated beam and ii) a diffuse beam. Radiation enters the cube through a square window centered on one face and with an area one quarter the area of the face. The simulation considers fully absorbing walls, and isotropic scattering. The deviations of simplified models based on Discrete Ordinate or Finite Volume schemes, are compared to the mesh independent solution. The results indicate that for a collimated beam boundary condition the Six-Flux model and more refined models are moderate. The error of the total rate of energy absorbed (TREA) and that of the local volumetric rate of energy absorption (LVREA) with respect to a mesh independent solution are below 5% and 22% respectively. In contrast, it is found that for diffuse boundary conditions the Six-Flux model is very inaccurate since the corresponding errors are larger than 120%.

Optical fluence modelling for ultraviolet light emitting diode-based water treatment systems

This work presents a validated optical fluence rate model optimised for ultraviolet light-emitting diodes (UV-LEDs), which allow a very wide range of emission wavelengths and source geometries to be used in water treatment units. The model is based on a Monte Carlo approach, in which an incremental ray-tracing algorithm is used to calculate the local volumetric rate of energy absorption and subsequently convert it to the local fluence rate distribution for an UV-LED water treatment chamber of arbitrary design. The model includes contributions from optical reflections and scattering by treatment chamber walls and from scattering due to particulates and/or microorganisms. The model successfully predicts optical fluence rates in point-of-use water treatment units, as verified using biodosimetry with MS-2 bacteriophage at a UV-LED emission wavelength of 254 nm. The effects of chamber geometry are also modelled effectively and are consistent with the inactivation data for E. coli at 254 nm. The data indicate that this model is suitable for application in the design and optimisation of UV-LED-based water treatment systems.

Influence of light absorption rate by Nannochloropsis oculata on triglyceride production during nitrogen starvation.

This study aims to understand the role of light transfer in triglyceride fatty-acid (TG-FA) cell content and productivity from microalgae during nitrogen starvation. Large amounts of TG-FA can be produced via nitrogen starvation of microalgae in photobioreactors exposed to intense light. First, spectral absorption and scattering cross-sections of N. oculata were measured at different times during nitrogen starvation. They were used to relate the mean volumetric rate of energy absorption (MVREA) per unit mass of microalgae to the TG-FA productivity and cell content. TG-FA productivity correlated with the MVREA and reached a maximum for MVREA of 13 μmol hν/gs. This indicated that TG-FA synthesis was limited by the photon absorption rate in the PBR. A minimum MVREA of 13 μmol hν/gs was also necessary at the onset of nitrogen starvation to trigger large accumulation of TG-FA in cells. These results will be instrumental in defining protocols for TG-FA production in scaled-up photobioreactors.

CFD simulation of a pilot scale slurry photocatalytic reactor and design of multiple-lamp reactors

The hydrodynamics behaviour and radiation transport occurring inside a pilot-scale slurry photocatalytic reactor (treating real shower water) with large diameter was investigated using computational fluid dynamics (CFD). The multiphase flow system was solved using a granular Eulerian model while the solution of the radiative transport equation (RTE) was solved using the finite volume based discrete ordinate model (DOM). Multiphase simulation showed recirculation zones caused by the high slurry inlet velocity. Due to the rapid attenuation of light occurring radially within the reactor, regions of varying reaction orders exist, i.e., half order reaction close to the lamp and first order reaction further from the lamp, as the incident radiation goes below a certain value. A rate equation relating pollutant degradation to the rate occurring in the half and first order reaction regions (in terms of local volumetric rate of energy absorption – LVREA) was proposed. Using a value of 225Wm−2 as the minimum incident light intensity at which half order reactions take place, a Pearson correlation of 0.88 between simulated and experimental data indicated that the proposed model satisfactorily described the experimental observations. Next, simulations performed with a system of multiple lamps (2 and 4 lamps) at different geometrical arrangements (i.e. with the lamps separated by the distance Xlamp) showed that within the range of catalyst concentration investigated, the maximum potential increases in reaction rate was 56% and 123% when using 2 and 4 lamps (at optimum lamp arrangement) respectively, as compared to using one lamp. The increase in reaction rate occurred due to the maximisation of incident radiation contours at which first order reactions take place. The optimum lamp separation was dependent on the catalyst concentration in the wastewater and decreased with increasing catalyst concentration.

Quantum yield with platinum modified TiO2 photocatalyst for hydrogen production

The present study reports quantum yields for hydrogen production using a Pt modified titanium dioxide (DP25) photocatalyst in a slurry medium, under near-UV irradiation. The photocatalyst was prepared using the incipient wetness impregnation method. The modified photocatalyst exhibited a reduced energy band of 2.73eV upon Pt addition. Experiments were performed in a Photo CREC Water II Reactor. This unit allows the establishment of macroscopic radiation balances. These irradiation balances showed a maximum LVREA (local volumetric rate of energy absorption) of 0.15g/L. Regarding hydrogen formation via H radicals, the addition of a 2vol.% ethanol scavenger allowed achieving significant amounts of hydrogen free of oxygen. It was noticed that the rate of hydrogen formation in the presence of ethanol is a function of the pH of the water solution. It was also observed that the calculated 7.8% quantum efficiency showed good degree of photon utilization and confirmed the value of the Pt modified TiO2 photocatalyst and Photo CREC Water II Unit set up for hydrogen production, via water splitting.

Light intensity distribution in multi-lamp photocatalytic reactors

A computational fluid dynamics approach has been used to investigate the effect of lamp separation (Xlamp) on the radiation intensity distribution in a multiple-lamp photocatalytic reactor. The optical parameters (absorption and scattering coefficients) of Aeroxide® P25 titanium dioxide (TiO2) were determined by performing experiments using a single lamp system. Since the optical properties are wavelength dependent, the range of wavelength from the UV lamp was divided into 4 bands, and optical properties in each of the bands were determined by matching the experimental observations with simulated values. Simulations were then carried on multiple-lamp (2 and 4 lamps) photoreactors as a function of lamp separation and catalyst loadings. In case of 2-lamp system, the maximum local volumetric rate of energy absorption (〈LVREA〉) occurred at Xlamp=40mm, and it was independent of the catalyst loading. With 4 lamps however, optimum Xlamp was dependent on the catalyst loading. At low loads (up to Wcat=0.06gL−1), the optimum Xlamp was 80mm but as the catalyst concentration increased, the value of the optimum lamp separation decreased considerably, with 30mm for Wcat=0.07gL−1 and decreasing further as the concentration further increased. Because of the high absorption coefficient of the catalyst, the wall emissivity had a negligible effect on the 〈LVREA〉 for both configurations, even when the lamps were close to the wall. Finally, in both cases, the optimum lamp separation was independent of the lamp emissive power.

TiO 2 absorption and scattering coefficients using Monte Carlo method and macroscopic balances in a photo-CREC unit

The radiation field inside photocatalytic reactors can be predicted by solving the Radiative Transfer Equation (RTE). From the solution of the RTE, the Local Volumetric Rate of Energy Absorption ( LVREA) can also be obtained. This LVREA is an important parameter in photocatalytic reactor design, energy efficiency assessments and kinetic studies of photocatalytic reactions. However, when solving the RTE, two optical parameters are needed: (1) the absorption and scattering coefficients and (2) the phase function. In the present study, the Monte Carlo (MC) method along with an optimization technique is shown to be effective in predicting the wavelength-averaged absorption and scattering coefficients for three different TiO 2 powders. To accomplish this, the LVREA and the transmitted radiation ( P t ) in a Photo-CREC annular photoreactor have to be determined using a macroscopic balance. The optimized coefficients are calculated ensuring that they comply with a number of physical constrains, falling in between bounds established via independent criteria. The optimization technique is demonstrated by finding the absorption and scattering coefficients for three different semiconductors that best fit the experimental values from the macroscopic balance minimizing the least-squared error of objective functions for the LVREA and P t . The proposed approach is a general and promising one, not being restricted to reactors of concentric geometry, specific semiconductors and/or particular photocatalytic reactor unit scale.

Photoreactor design and CFD modelling of a UV/H2O2 process for distillery wastewater treatment

AbstractA pseudo‐kinetic model for the treatment of a distillery wastewater by the ultraviolet irradiation and hydrogen peroxide process in a continuous tubular photoreactor is developed. There is a scarcity of information on modelling of organic degradation rates based on chemical oxygen demand (COD) and total organic carbon (TOC) in advanced oxidation technologies (AOTs). In this study, the COD and TOC are used as surrogate parameters to design a photoreactor instead of individual concentrations of species. The rate constants for the reaction between COD and TOC with hydroxyl radicals were determined to be 4.9 × 109 and 5.0 × 106 M−1 s−1, respectively. A laminar flow model was simulated to estimate the velocity and residence time of the medium in a cylindrical photoreactor. The model was validated by the experimental data published in the open literature for different concentrations of H2O2 (1, 10, and 100 mM), COD (589, 709, and 850 mg O2 L−1), and TOC (190, 200, and 192 mg C L−1). The optimal value of the inlet hydrogen peroxide concentration was predicted to be 400 mg L−1. Axial and radial concentration distributions of species in the photoreactor were also obtained. At different photoreactor radii (from 50 to 200 mm), the values of radial local volumetric rate of energy absorption (LVREA) were estimated. It was found that a higher LVREA was achieved in the photoreactor space at smaller radii. © 2011 Canadian Society for Chemical Engineering

Performance evaluation of P-1 model in a photocatalytic reactor

The P-1 model which allows to numerically solve the radiation transport equation (RTE) was used to predict the light intensity in an annular photocatalytic reactor. Experimental results on light intensity distribution in a photoreactor were used to validate the P-1 model and a good agreement was obtained. The effect of absorption coefficient, scattering coefficient, wall reflectivity and phase function parameter was investigated on the relative local light intensity. The light intensity decreased rather sharply with the increase in the absorption coefficient, but slightly decreased with the increase in the scattering coefficient. The local volumetric rate of energy absorption (LVREA) increased with the catalyst loading in the region r < 0.06 m and the opposite trend was obtained beyond this region. However, the wall reflectivity had very little effect on the light intensity at high catalyst loading. Furthermore, the light intensity is not much influenced by the phase function parameter.

Light Intensity Distribution in a Dual-Lamp Photoreactor

Photochemical and photocatalytic reactors are being widely used in the wastewater treatment and water/air purification. One of the popular reactor configurations for water purification is the multiple lamp tubular reactor. The efficiency of purification in a photoreactor is determined by the distribution of UV radiation within the tubular space. In this study, the light intensity distribution in a two-lamp photoreactor has been evaluated using a finite volume scheme (which is essentially a variant of the discrete ordinate model). The irradiated space was divided into a number of finite volumes and angles (directional discretisation). Simulations were performed for both homogenous and heterogenous (with titania catalyst) reactors. Contours of incident radiation and local volumetric rate of energy absorption were plotted and analysed. Model predictions were used to assess the effect of catalyst loading on the light intensity distribution inside various reactor configurations. The optimum value of the distance between lamps in a 2-lamp photoreactor was found to be dependent on the optical properties of the photocatalyst used. Model predictions were found to match-well qualitatively with the published data from the literature.

Light distribution field in catalyst suspensions within an annular photoreactor

In photochemistry, an accurate description of the radiation field is important for successful modeling and subsequent design of a photocatalytic reactor, since the radiation field determines the local volumetric rate of energy absorption, which in turn controls the photocatalytic reaction rate. However, scattering by catalyst particles present in water causes the photon energy to be redistributed and the light field in a heterogeneous photoreactor is consequently difficult to evaluate. Light field in a heterogeneous photoreactor is determined by selected optical properties of the catalyst particle, such as scattering and absorption coefficients. However, so far there has been no direct experimental method to measure these two values. In addition, these two coefficients alone are not sufficient to describe the effect of catalyst on the light field in a catalyst suspension. A third optical property of scattering mode, which gives the spatial distribution of the scattering directions, has been found to be important in parallel light field. In this study, a new light model along with the optical properties of two commercially available titanium dioxide (TiO 2) catalysts was used to determine the light field in a test annular photoreactor for different concentrations of suspended TiO 2. Chemical actinometry was used to measure the light intensity inside the reactor. The scattering mode of the catalysts was determined by fitting experimental data with the model predictions. It was found that the optical properties of the catalyst change significantly at different catalyst concentrations. This suggests that the application of universal optical properties of a catalyst may not be suitable for the determination of light field for a large range of catalyst concentrations.

Light intensity distribution in a photocatalytic reactor using finite volume

AbstractA conservative variant of discrete ordinate model was used to solve the radiation transport equation. The model prediction was used to assess the effect of wall reflectivity, catalyst loading, and phase function parameter on the light intensity distribution in an annular heterogeneous photocatalytic reactor. For relatively low catalyst loadings, the wall reflectivity strongly influenced the light intensity distribution. However, for an optically thick medium, the wall reflectivity had very little or no effect. The volume‐average light intensity distribution decreased rather sharply with the catalyst loading and an opposite trend was obtained for the local volumetric rate of energy absorption (LVREA). However, after the initial sharp increase, the LVREA appeared independent of catalyst loading. For nonreflecting reactor walls, phase function parameter did not show much influence. However, for the specularly reflecting reactor walls and optically thin mediums, a moderate dependency on the phase function parameter was observed. 2004 American Institute of Chemical Engineers AIChE J, 50:1273–1288, 2004

Evaluation of Three Different Lamp Emission Models Using Novel Application of Potassium Ferrioxalate Actinometry

The application of advanced oxidation processes using hydroxyl radicals in the degradation of organic contaminants from various waste streams has become increasingly popular over the last 2 decades. The relationship between the local volumetric rate of energy absorption in a photoreactor and the rate of photodegradation of organics is essential in scaling up photoreactors to treat large volumes of air and water. Thus, it is very important that the light intensity in a photoreactor is evaluated correctly. In this research, local light intensities as a function of both radius and longitudinal axis in a test photoreactor for the treatment of air were measured using chemical actinometry and compared with the simulated data using three radiation models. A good agreement exists between the experimental data and the model predictions, and no model exhibits a clear advantage over others. The line source with diffused emission model shows the best overall performance among the three models with regard to computational time, simplicity, and accuracy.

Modeling and experimental verification of radiative transfer of a flat‐plate photoreactor with immobilized photocatalyst

AbstractA cost‐effective design of photocatalytic reactor needs efficient contact of the polluted substance with the solid catalyst while uniformly irradiating the solid catalyst with light. In the present paper, an immobilized photocatalyst comprising TiO2 coated on Pyrex‐glass‐coils (abbreviated hereafter as TGC) was developed, and a flat‐plate photocatalytic reactor packed with TGC was designed. The reactor has some advantages such as low pressure drop, intensification of mass transfer; relatively uniform distribution of light radiation; high ratio of illuminated catalyst surface area to volume, and is flexible enough for large‐scale application. The radiation intensity distribution and the two‐flux model parameters were measured, and the two‐flux model was solved numerically. The experimental values were compared with the theoretical predictions. Good agreement was obtained with a maximum deviation about 10%. Finally, the two‐flux model described the radiation intensity distribution and local volumetric rate of energy absorption in the flat‐plate reactor packed with TGC.© 2002 Society of Chemical Industry

Two-dimensional heterogeneous model for a reticulated-foam photocatalytic reactor

A 2-D heterogeneous convection reaction model for a gas–solid lamp-in-tube annular photocatalytic reactor is presented. The catalyst (TiO2) is supported on a reticulated-foam monolithic structure placed in the annular space between the UV lamp and the reactor wall. Mass balances for individual species are coupled through the reaction-rate expression that appears in the boundary condition at the fluid–solid interface in heterogeneous catalytic reactor models. The heterogeneous reaction rate is modeled using semiempirical Langmuir-Hinshelwood-Hougen-Watson (LHHW) kinetics with adsorption constants for various species. The local volumetric rate of energy absorption (LVREA) term in the rate expression was computed using a 3-D polychromatic radiation-field model. The overall system of nonlinear partial differential equations was solved using a combination of the Crank-Nicolson method and the globally convergent Newton-Raphson method. The apparent, average quantum yield in the LHHW kinetic rate form is the single adjustable parameter in the model. Isopropanol (IPA) was chosen as the test contaminant to conduct experimental performance measurements for model validation. Model-predicted radial and axial profiles for bulk and surface concentration reveal that the extent to which mass transport influences the operation of a photocatalytic reactor is determined largely by the local magnitude of the LVREA. Similitude in the scale-up of an annular lamp-in-tube heterogeneous photocatalytic reactor is achieved only when the dimensionless radial radiation profile, as well as corresponding magnitudes of a geometric number, the Peclet number, the Stanton number, and the photocatalytic analog of the Damkohler number, are identical.

Rigorous model and experimental verification of the radiation field in a flat-plate solar collector simulator employed for photocatalytic reactions

In any kinetically controlled photocatalytic process the catalyst activation is always a photochemical act that depends upon the local value of the volumetric rate of energy absorption (LVREA). In a heterogeneous photocatalytic reaction, a precise evaluation of the LVREA can be obtained when the spatial and directional distributions of radiation intensities are known. With this purpose, a mathematical model of the radiation field inside a flat-plate heterogeneous reactor (a solar simulator) has been developed. The solid–liquid reactor is irradiated by two tubular UV lamps with the aid of two parabolic reflectors. Since titanium dioxide suspensions absorb and scatter radiation the model accounts for both effects. Resorting to information about the lamp and reflector characteristics, the catalyst optical properties and concentration, as well as the reactor dimensions and wall reactor properties, the solution of the mathematical model (a two-dimensional–two-directional model) provides a detailed description of the spatial and angular directional distributions of radiation intensities inside the reactor. Using this information, it is possible to precisely calculate the rate of absorbed radiation energy at each point inside the reactor. This is one of the key variables for reactor design and/or scale-up purposes. The radiation distribution inside the reactor was verified by computing forwardly transmitted and backwardly scattered radiation fluxes coming out of the reaction space through the glass reactor walls. These radiation fluxes were compared with experimental measurements made with a UV radiometer and good agreement was obtained; when no fouling was present and considering low catalyst loading to obtain measurable radiation fluxes, the maximum observed error was 12%. The predicted inlet boundary condition was also verified with actinometry and the error was smaller than 14% For this reactor configuration, when the radiation absorption performance is the only factor under consideration, it was found that Aldrich titania is more efficient than the Degussa P 25 variety.

Monte Carlo simulation of the radiation field in a reticulated foam photocatalytic reactor

AbstractThe 3‐D polychromatic radiation field for an annular packed‐bed photocatalytic reactor using alumina reticulated foams as a monolithic catalyst support was simulated using Monte Carlo methodology. Two distinct methods were used for simulating photon transport: (1) a “spatial” approach that tracks the flight of a photon in a predetermined reticulate structure; (2) a “temporal” approach that generates the random porous structure of the reticulate as the photon flies into it. The two approaches yield almost identical results, although the temporal approach is far more efficient computationally. Simulations for the integral axially‐averaged radial ultraviolet (UV) light profiles agree closely with experimental measurements for titania‐coated 10, 20 and 30 PPI alumina reticulates and near UV lamps. The simulations reveal that the local volumetric rate of energy absorption (LVREA) in the reticulate and the magnitude of the LVREA gradient both increase with decreasing reticulate pore size.

Simplified Modeling of Radiant Fields in Heterogeneous Photoreactors. 1. Case of Zero Reflectance

A strongly simplified model is proposed for the estimation of the radiant flow field, and related quantities such as the local volumetric rate of energy absorption, in heterogeneous photoreactors. The model is based on the assumption that a photon carrying energy greater than that of the catalyst band gap, when interacting with a catalyst particle, is invariably absorbed. The model equations allow, for simple geometries, analytical integral solutions to be obtained. These have the advantage of giving an immediate grasp on how the main physical parameters affect the radiation field: an important feature especially for engineering purposes. The case developed here is that of a plane slab, for both monosized catalyst particles and particles with size distributions. Notably, as no adjustable parameters are used, fully predictive results can be obtained. The model predictions are successfully compared with the results of original experimental tests, therefore leading to model validation. In Part 2 of this paper, another model is developed in which the assumption of zero reflectance of the particles is removed, yet allowing analytical solutions to be obtained. One of the key features of the two models is that their predictions bound the real behavior of irradiated photoreactors, as shown in the papers. Therefore, although only approximate solutions are obtained from each of the two models, the real behavior can be better approximated by some sort of interpolation between the two solutions and, what is more important, confidence limits for the final solution are obtained.