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

Abstract

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 sixflux 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 IntroductionAs an emerging environmental technology, heterogeneous photocatalysis has received increasing attention in recent years. Its promising applications in air and water remediation[1], clean fuels production [2], green products (e.g. self-cleaning surface [3]) and selective 4 synthesis of organic molecules [4] demonstrates great interest in this technology. The underlying basis of every photocatalytic reaction mechanism is the photoactivation of the semiconductor photocatalyst by absorption of photons with energy higher or equal than the catalyst band-gap. The consequent generation of electron-hole pairs produces a chain of reactions that drive simultaneous oxidation and reduction (redox) reactions.The evaluation of the radiation field and of the spatial distribution of radiation absorption in a photoreactor system, commonly described by the local volumetric rate of photon absorption (LVRPA), is therefore a crucial aspect in the development of efficient photocatalytic processes [5].The LVRPA is the photon equivalent to the concentration of reactant species and is always considered in the description of the kinetics of photochemical reactions and in the optimization of the performance of photoreactors. For instance, several methodologies have been proposed for the determination of the optimum catalyst load or reactor thickness which maximize the absorption of radiation [6,7].The estimation of the LVRPA has been a defiant task within the heterogeneous photocatalysis community, as result of the complex nature of the absorption and scattering radiation phenomenon, which in the most rigorous case is modeled by the Radiative Transfer Equation (RTE). The RTE for a medium that does not emit radiation is [8]: where I λ is the photon irradiance at λ wavelength, s is a spatial coordinate, Ω is the directional solid angle, κ λ is the absorption coefficient and σ λ the scattering coefficient. TheΩ → Ω is the scattering phase function representing the probability of a photon to be redirected by scattering from the direction Ω', in surroundings of the position s, into the direction Ω [8]. A trivial solution for the RTE cannot be achieved and a numerical method is always necessary.Although the precise modeling of the LVRPA and a better understanding of the radiationphotocatalyst-operational conditions nexus still remains a challenge, several approaches have been proposed to solve the RTE. The most rigoro...

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“…This result agrees with the influence of the catalyst concentration on the MTLC degradation rate that has been experimentally observed. A similar dependency of OV-RPA with catalyst concentration has been reported for different systems by Acosta-Herazo et al [19], Casado et al [41], Colina-Márquez et al [37], Marugán et al [20] and Tolosana-Moranchel [43,44]. Therefore, this methodology confirms the influence of catalyst concentration on radiation absorption and constitutes a useful tool to describe the light availability inside the reactor.…”

“…Recently, the use of ultraviolet Light-Emitting Diodes (LEDs) as a light source in photocatalytic processes has received increasing attention due to their high efficiency and stability [13,14,17,18]. Thus, modeling the radiation field and the spatial distribution of the radiation absorption inside LEDassisted photocatalytic reactors is a scientific challenge that can contribute to the further development of the technology [19][20][21][22][23].…”

“…Regarding the modeling of heterogeneous photocatalytic reactors, the irradiance distribution inside the reactor can be described with the rigorous solution of the Radiative Transfer Equation (RTE), detailed in the Supplementary Materials [19,23,24]. Romero et al [25] reported the radiation field modeling in an annular photocatalytic reactor based on a system of differential equations.…”

Simulation of Light Propagation in Photochemical Fixed-Bed Reactors Using a BRDF-Based Model

“…Absorption and emission parameters have clear and simple ways of being evaluated, but the picture is slightly more complex for scattering. The majority of models in current use [10][11][12][13][14] were designed to simulate scattering particles with negligible dimensions and random geometries (such as a suspension or a colloid). While this approach suffices to describe most relevant photocatalytic systems, it is clearly inappropriate to simulate larger systems in which the geometry, the size, the position, and the nature of the interacting objects play a significant role, such as packed bed reactors.…”

“…Mathematically, radiation propagation problems are often treated by discrete-ordinate (DOM) 12 , finite volume (FVM) 9,10 or stochastic methods 13,14 . A thorough discussion on these methods can be found elsewhere 15 .…”