One-dimensional six-flux model (SFM-1D) for the description, estimation, and optimization of the radiant field in annular and tubular photocatalytic reactors

Abstract

The goal of this study was to solve the radiative transfer equation in one dimension utilizing the Six-Flux Model technique (SFM-1D) to characterize, estimate, and optimize the radiant field in annular photocatalytic reactors by performing an energy balance in a cylinder's element. The local volumetric rate of photon absorption (LVRPA), a parameter required for the description of the photocatalytic reaction kinetics, was defined. This parameter was defined for two types of reactors with a constant-intensity radiant source located vertically at the center of the first reactor (annular-reactor R1) and outside around the second reactor (tubular-reactor R2). Simulations were made by taking the commercial TiO₂ P25 as the catalyst model with its optical properties taken from other authors. The model was evaluated with Heyney-Greenstein (HG) and diffuse reflectance (DR) phase functions. For reactor R1, the LVRPA decreases from the reactor's inner wall to its outer wall while it decreases from the reactor wall to its center for reactor R2. The volumetric rate of photon absorption per unit of reactor length (VRPA/H) which gives a broader view of the radiation absorption inside the reactor was established. The originality of the present model makes it better than that found in the literature since it was derived from an energy balance and the other was only deduced from the LVRPA formulated on a slab geometry with the SFM approach. The VRPA found in this work differed from that found in the literature by approximately 13.78 % on reactor R1. For both reactors, the VRPA/H was found to increase exponentially with the increase of catalyst loading (Ccat) until reaching a value where no significant increase was observed. The optimum apparent thicknesses were about 4.8 and 10.6 for R1 and R2 respectively using Heyney-Greenstein phase function. The optimum radius for R2 was found in the range of 1-3 cm while for R2, the optimum reaction space thickness was found less than 3 cm and the dimensionless parameter , which was introduced for optimization purposes was found between 0.55 and 0.8.