Estimating radiant fields in flat heterogeneous photoreactors by the six‐flux model

Abstract

Heterogeneous photoreactor modeling is a task complicated by the integro-differential\ud nature of the Radiation Transfer Equation (RTE) when scattering phenomena are important.\ud In the present work, a novel “Six Flux Model” (SFM) is proposed, which may be\ud regarded as a step forward with respect to the previously proposed “Two Flux Model”\ud (TFM). In order to validate the newly proposed model, Monte Carlo simulations of an\ud indefinite plane-slab photoreactor have been performed. As no simplifying assumptions\ud are involved in this case, the information obtained may be regarded as “pseudoexperimental,”\ud and therefore compared with the predictions of both TFM and SFM\ud models. Results show that the novel SFM is able to closely match the exact solution of the\ud RTE better than the TFM, still retaining the TFM advantage of a simple closed-form\ud solution, that is, ease of use, clearer effect of model parameters, and so forth

Modelling and Simulation of the Radiant Field in an Annular Heterogeneous Photoreactor Using a Four-Flux Model

“…Some of these necessary submodels are (a) radiation emission and incidence, (b) radiation absorption and scattering, (c) photoconversion kinetics, and (d) hydrodynamics [5, 13-15, 17, 18]. These are the result of mass, energy, and momentum balances, as well as radiation distribution and optical characterization of reaction space [6,16,19,20]. These submodels are strongly interlinked.…”

“…According to literature [1,[3][4][5][6][11][12][13][14][15][16], the following different variables are crucial in a photocatalytical process efficiency: (a) catalyst type and concentration, (b) reagent type and concentration, (c) geometry and type of reactor, and (d) characteristics of the radiation inside the photoreactor. Because of the number of variables and the interaction among them, the modeling of this type of processes is expected to be rather useful not only for reactor design but also to achieve a better insight and understanding of the process.…”

“…Also, it is possible to employ analytical simplified methods like the two-flux model (TFM) and the six-flux model (SFM). These models consist of several algebraic equations developed for flat slab geometries [15][16][17]30], which were obtained by solving a system of differential equations with specific boundary conditions, for example, the outer wall of the reactor is opaque. SFM is very accurate for cylindrical geometries [14] in which the space where the reaction occurs, δ, is much smaller than the radius of the reactor,…”

Correlating the photocatalytic activity and the optical properties of LiVMoO6 photocatalyst under the UV and the visible region of the solar radiation spectrum

“…The six-flux model presumes that photons are scattered along the six principal Cartesian directions with respect to the incoming radiation, to which probabilities are assigned (forward, backward, sideward). For considerations due to symmetry, the probability of scattering along any of the four directions of the plane normal to the incoming ray direction is the same [13]. The original SFM [13] was presented for an anisotropic diffuse phase function, and the scattering probabilities were determined from matching the SFM results to Monte Carlo solutions of the RTE.…”

“…The solution of the RTE applied to a suspension of catalyst usually demands complex computational methods. In contrast, simpler but approximate models such as the six-flux absorption-scattering model (SFM) [9,11,[13][14][15] can produce results close to those obtained from the complete solution of the RTE, by a simple analytical estimation of the LVRPA at each position of the reactor. The SFM has shown close agreement with the Monte Carlo simulation of the radiation field in a planar photoreactor.…”