Estimation and Optimization of the Radiant Field in Flat Plate Heterogeneous Photoreactors with the P1-approximation of the Radiative Transfer Equation (RTE).

Abstract

In this work, the P1-approximation of the radiative transfer equation (RTE) was used for the description and optimization of the radiant field in a flat plate photoreactor under solar radiation with three commercial brands of titanium dioxide photocatalysts. The boundary layer of photon absorption (δ_abs), the average volumetric rate of photon absorption (VRPA), and a new apparent optical thickness (ζ_app1) were used as design parameters for optimization. A simple mathematical expression for the calculation of δ_abs also called the best reactor thickness was formulated. For the three catalysts, varying the reactor height (L), it was found a decrease in the local volumetric rate of photon absorption (LVRPA) from the top side until the bottom of the reactor for any value of the catalyst loading (Ccat). It was also observed that when Ccat increases the VRPA increases exponentially until a fixed value where it remains almost constant. With L= 1 cm, the optimum Ccat (Ccatop) was 0.2 g/l in 0.85 cm of thickness, 0.3 g/l in 0.82 cm of thickness, and 0.4 g/l in 0.89 cm of thickness for the photocatalysts Degussa P-25, Aldrich, and Hombitak respectively. The optimum apparent optical thickness (ζ_(app1,op)) was 4.03, 4.62, and 3.7 for the photocatalysts Degussa P-25, Aldrich, and Hombitak respectively. These results are in good agreement with the literature. Results found in this work give predictions on radiation absorption in flat plate photocatalytic reactors with different heights.