This study provides information to design heterogeneous photocatalytic solar reactors with flat plate geometry used in treatment of effluents and conversion of biomass to hydrogen. The concept of boundary layer of photon absorption taking into account the efficient absorption of radiant energy was introduced; this concept can be understood as the reactor thickness measured from the irradiated surface where 99% of total energy is absorbed. Its thickness and the volumetric rate of photons absorption (VRPA) were used as design parameters to determine (i) reactor thickness, (ii) maximum absorbed radiant energy, and (iii) the optimal catalyst concentration. Six different commercial brands of titanium dioxide were studied: Evonik-Degussa P-25, Aldrich, Merck, Hombikat, Fluka, and Fisher. The local volumetric rate of photon absorption (LVRPA) inside the reactor was described using six-flux absorption-scattering model (SFM) applied to solar radiation. The radiation field and the boundary layer thickness of photon absorption were simulated with absorption and dispersion effects of catalysts in water at different catalyst loadings. The relationship between catalyst loading and reactor thickness that maximizes the absorption of radiant energy was obtained for each catalyst by apparent optical thickness. The optimum concentration of photocatalyst Degussa P-25 was 0.2 g/l in 0.86 cm of thickness, and for photocatalyst Aldrich it was 0.3 g/l in 0.80 cm of thickness.
Heterogeneous photocatalysis based on TiO2 and modified photocatalysts is widely used in energetic and environmental applications, including water and air purification systems [
A clean route for hydrogen production has been proposed by photogenerated electrons at the conduction band from reduction of water in the absence of oxygen and oxidation of waste biomass using solar energy [
Regarding the mineralization of organic contaminants, Turchi and Ollis proposed a path based on the generation of oxidizing species (Table
Heterogeneous photocatalysis reaction scheme based on semiconductor TiO2, extracted from Turchi and Ollis [
Activation |
|
(1) |
Adsorption |
|
(2a) |
|
(2b) | |
|
(3) | |
|
(4) | |
Recombination |
|
(5) |
Hole trapping |
|
(6a) |
|
(6b) | |
|
(7) | |
Electron trapping |
|
(8a) |
|
(8b) | |
Hydroxyl attack | ||
Case I |
|
(9) |
Case II |
|
(10) |
Case III |
|
(11) |
Case IV |
|
(12) |
The above mentioned applications present a trend towards the use of solar energy as a sustainable source of energy, development of efficient reactors geometries, and scale-up of reactors. Therefore, rigorous methodologies have been developed for design and optimization of photoreactors based on scientific knowledge of the photocatalytic process [
The rigorous description of photoreactor requires (i) radiation field, (ii) hydrodynamic field, and (iii) mass balance with kinetic expression whose parameters should be independent of photon absorption. The study of the radiation field provides optimal design information such as reactor geometry, catalyst selection, catalyst loading, and dimensions of the reactor [
The variable most employed to quantify the spatial distribution of radiant energy absorbed within the reactor is the local volumetric rate of photon absorption (LVRPA); it depends on the geometry, radiation source, loading, and type of photocatalyst, in some cases on the pollutant if this presents absorption of radiant energy. A rigorous approach to determine the LVRPA is the solution of the radiative transfer equation (RTE), by the discrete ordinate method (DOM), which requires spatial, directional, and spectral discretizations inside the reactor [
A useful approach is the six-flux absorption-scattering model (SFM); it has been applied to different geometries: compound parabolic collector (CPC) photoreactors [
Flat plate reactors are scalable, and these can be used with solar radiation, so they are very attractive and also provide an excellent configuration for efficient excitation of the semiconductor photocatalyst TiO2 [
In this study, design parameters of a flat plate photoreactor with photocatalysts based on TiO2 and solar radiation were analyzed in terms of absorption of photons. For mathematical convenience, the variable
This paper proposes a new concept for heterogeneous photocatalytic reactor design, which allows us to determine the best thickness. Figure
Boundary layer of photon absorption in a double flat plate reactor irradiated onto upper plate.
The region where there is a gradient of energy absorption has been called “boundary layer of photon absorption,” and its thickness
This design parameter is similar to the apparent optical thickness used for sizing of annular reactors and CPCs [
VRPA is defined as an average value of LVRPA in the whole volume. For a flat plate reactor the VRPA is expressed as [
VRPA and boundary layer thickness presented above are design parameters of photoreactors and their calculations require a model of radiant field, which quantify LVRPA within the reactor.
The radiation field of a reactor with incident solar radiation was modeled by six-flux absorption-scattering model (SFM) [
The parameters of (
Extinction coefficient
Scattering albedo requires a correction
To obtain the new parameter, boundary layer thickness of photon absorption
The SFM parameters that are independent of the catalyst concentration are shown in Table
Average optical properties of commercial photocatalysts based on titanium dioxide under solar radiation.
Catalyst |
|
|
|
|
|
---|---|---|---|---|---|
Aldrich | 3.73 | 2.43 | 3.98 | 0.94 | 0.84 |
Degussa | 5.42 | 2.87 | 5.71 | 0.95 | 0.87 |
Merck | 2.97 | 2.68 | 3.24 | 0.92 | 0.81 |
Hombikat | 2.52 | 1.17 | 2.64 | 0.96 | 0.88 |
Fischer | 1.60 | 2.65 | 1.86 | 0.86 | 0.72 |
Fluka | 1.64 | 2.89 | 1.92 | 0.85 | 0.71 |
The values reported here disagree with those reported by [
Figure
Profile of energy absorption rate (
The
The change of
Finally, the distance from the surface (
To validate the SFM in a flat plate reactor, the model was run against rigorous solution of RTE proposed by [
Figure
Design parameters of a flat plate solar photoreactor for different commercial brands of TiO2 as a function of its loading. VRPA/
For all catalysts, a catalyst loading less than 0.2 g/l has low rate of photon absorption; from 0.2 to 0.4 g/l there are high values of
From
The catalyst Aldrich has a maximum VRPA 7% higher than the one presented by the catalyst Degussa. A similar trend was reported for polychromatic radiation using UV lamps, where the catalyst Aldrich is 19% more efficient than Degussa P-25 [
For all catalysts and loadings lower than 0.1 g/l, the absorption of photons occurs in the entire thickness of the reactor (1 cm), but the VRPA has small values. Catalyst loadings between 0.1 and 0.2 g/l employ the entire thickness of the reactor with approximately zero values of the LVRPA at the bottom of the reactor and begin to show a boundary layer of photon absorption thinner than 1 cm, due to some form of saturation between photon transport and the catalyst amount to absorb them.
For catalyst loading higher than 0.2 g/l, different boundary layer thicknesses of absorption can be seen. Catalysts with higher coefficient of photon extinction have a thinner boundary layer because the energy is quickly extinguished as it travels through the fluid.
However, Hombikat catalyst has the largest boundary layer of photon absorption, despite having an intermediate value of extinction coefficient; this is due to its low absorption coefficient
Profile of boundary layer thickness of photon absorption represents the best conditions of design. A point above this curve presents a dark layer inside reactor, while a point below it presents VRPA less than the maximum possible.
Figure
To design a photoreactor using a specific catalyst, for example, Degussa P-25 (point line), the
Optimum catalyst loading, maximum energy absorbed, and design thickness of flat plate reactor under solar radiation.
Catalyst | Loading (g/L) |
|
Suggested thickness of the reactor (cm) |
---|---|---|---|
Degussa P-25 | 0.2 | 0.42 | 0.86 |
Aldrich | 0.3 | 0.45 | 0.80 |
Merck | 0.3 | 0.49 | 0.85 |
Hombikat | 0.4 | 0.40 | 0.90 |
Fisher | 0.4 | 0.56 | 0.88 |
Fluka | 0.4 | 0.57 | 0.86 |
The optimum catalyst loading was calculated for catalysts water system; this increases in systems where there is absorption of radiant energy by substrate. Other authors have reported optimum values of catalyst loading similar to those reported in this paper. Brandi et al. report a loading close to 0.3 g/l based on the simulation of photon absorption for Aldrich and Degussa catalysts with radiation from UV lamps in a flat plate reactor [
Experimental researches developed at the solar platform from Almeria obtained an optimal loading of Degussa P-25 in a plate flat solar reactor equal to 0.2 g/l [
Different geometries are not comparable; however, the reported values of optimum catalyst loading have proved to be very similar in different reactors. An example of this result is the work made by Colina-Márquez and coworkers. They found optimum catalyst loadings from 0.17 to 0.4 g/l for catalysts with scattering albedo between 0.75 and 0.95 in a CPC solar reactor and catalyst loadings between 0.2 and 0.6 g/l for a tubular reactor [
For thicknesses not near 1 cm, it is recommended to use the design parameter called apparent optical thickness
Reactor design information presented in this paper is useful to determine the optimum catalyst loading, the optimal thickness of reactor, and the radiant energy absorbed. In addition, it eliminates the need of statistical analysis of experiment design which involves considerable consumption of time and resources [
This study has presented a new parameter for selection of thickness of a flat plate reactor called boundary layer thickness of photon absorption
The parameter was evaluated for TiO2 semiconductors Degussa P-25, Aldrich, Merck, Hombikat, Fluka, and Fisher, as a function of reactor thickness, catalyst loading, and the maximum amount of energy absorbed getting optimal operating conditions in the catalyst loading.
SFM parameter, dimensionless
SFM parameter, dimensionless
Catalyst concentration,
Objective function,
Thickness, cm
Emission spectrum of radiation source, Einstein
Flux of radiation at surface, Einstein
Local volumetric rate of photon absorption, Einstein
Probability of backward scattering, dimensionless
Probability of forward scattering, dimensionless
Probability of side scattering, dimensionless
Auxiliary coordinate in the photon flux direction, cm
Cartesian coordinate, cm
Cartesian coordinate, cm
Cartesian coordinate, cm.
Specific extinction coefficient,
SFM parameter, dimensionless
Boundary layer thickness of photon absorption, cm
Specific absorption coefficient,
Radiation wavelength, nm
Mean free path of photons, cm
Extinction length, cm
Specific scattering coefficient,
Optical thickness, dimensionless
Apparent optical thickness, dimensionless
Scattering albedo, dimensionless
Scattering albedo corrected, adimensional.
Corrected
Maximum
Minimum
Reactor
Irradiated surface
Bottom of reactor.
Spectral.
Specific.
Average value.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors are grateful to Universidad del Valle for the financial support to produce this work and to Colciencias for the financial support during their Ph.D. studies. M. A. Mueses thanks Universidad de Cartagena for the financial support. Finally, the authors thank Fernando Otálvaro for the English revision.