Local 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%.

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.

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 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

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.

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.

Photocatalytic decomposition of chloroform in a fully irradiated heterogeneous photoreactor using titanium oxide particulate suspensions

The photocatalytic decomposition of HCCl 3 was studied in a fully irradiated photoreactor (FIP) by varying the concentrations of (a) chloroform, (b) dissolved oxygen and (c) titania, as well as (d) the local volumetric rate of energy absorption (LVREA). Fully irradiated conditions are achievable when all the particles along the light path ‘see the photons’. In order to compute the VREA (average value of the LVREA), the radiative transfer equation (RTE) was applied to the reactor and solved using a simplified radiation model. Model parameters, i.e., optical properties, as well as the boundary condition for the RTE were obtained experimentally. Initial rate data of the chloroform decomposition showed that, within the studied range of process variables and under fully irradiated conditions: (1) The reaction rate is of first order with respect to [HCCl 3], zero order with respect to [O 2] and about one-half-order with respect to the LVREA inside the reactor and (2): The effects due to catalyst concentration are fully accounted for within the LVREA dependence.

SELECTIVITY STUDIES IN THE PHOTOCHLORINATION OF METHANE II: EFFECT OF THE RADIATION SOURCE OUTPUT POWER AND OUTPUT SPECTRAL DISTRIBUTION

The effect of the output power and output spectral distribution of the radiation energy fed to a photoreactor upon the reaction yield and selectivities is studied both theoretically and experimentally. The study aims at the analysis of these influences in a series reaction such as the photochlorination of methane where methylene chloride and eventually chloroform are the most valuable products. The computational model employed has been verified for a group of selected conditions by means of bench-sale experiments. It is found that the chlorine conversion shows the expected square root dependence with respect to the Local Volumetric Rate of Energy Absorption (LVREA). This dependence, in a first approximation, can also be assigned to the effect of the radiation source output power upon yield. It is also found that by manipulating the amount of radiation power fed to the reactor it is possible to ascertain the operating conditions favoring the production of predetermined intermediate products (e.g., methylene chloride or chloroform). It is concluded that the use of customized lamps especially designed for each particular product on the basis of feasible changes in the characteristics of the existing radiation sources will favor a selective and more economical production of some of the stable intermediates, i.e., lamp design is an important feature in any optimal process design.

A cylindrical photoreactor irradiated from the bottom—II. Models for the local volumetric rate of energy absorption with polychromatic radiation and their evaluation

This study of the radiation field generated in a cylindrical photoreactor irradiated from the bottom presents the theoretical foundations of a method for the experimental verification of three different radiation models. The expressions representing the local volumetric rate of energy absorption (LVREA) were formulated and applied to the prediction of the rate of an actinometric reaction. This reaction takes place inside a microreactor operated in a batch recycling system with polychromatic radiation. The values obtained portray the same behaviour as that of the energy densities calculated previously (Part I), thus becoming a valid, accurate method for the experimental measurement of the absolute values of the radiation field that are sought after (volumetric rate of energy absorption). The proposed approach is able to produce quasi-point values of the absolute values of the VREA at the microreactor as an excellent approximation to the absolute values of the LVREA (local measurements). The present work also points out the qualitative and quantitative discrepancies of the results predicted by the line models when compared with those of the extense source model with volumetric emission.

Photosensitized reactions in an annular continuous photoreactor

The process of energy emission by a lamp of finite spatial dimensions is considered, and a general expression for the local volumetric rate of energy absorption (L.V.R.E.A.) is given under the assumptions of no reflection and of negligible scattering and emission phenomena in the absorbing medium. When a reaction is occurring in the absorbing medium, L.V.R.E.A. can be easily computed if the reaction is a photosensitized one. In this case profiles of L.V.R.E.A., computed in an annular photoreactor solving the equations which govern rigorously the phenomenon, can differ in a relevant way from those computed assuming a radial model for the emission by the same lamp, the difference being mainly dependent, for a given radial geometry, on the reactor length and on the value of the optical thickness of the absorbing medium. Photosensitized reactions of order 0 and 1 with respect to the reactant concentration were studied for different values of the optical thickness, of Damkoheler and Peclet numbers. In particular the effects of variations of Pe number on the conversion were taken into consideration and the results were explained on the basis of physical and mathematical arguments.