Simplified modeling of radiant fields in heterogeneous photoreactors .1. Case of zero reflectance

A strongly simplified model is proposed for the estimation of the radiant flow field, and related quantities such as the local volumetric rate of energy absorption, in heterogeneous photoreactors. The model is based on the assumption that a photon carrying energy greater than that of the catalyst band gap, when interacting with a catalyst particle, is invariably absorbed. The model equations allow, for simple geometries, analytical integral solutions to be obtained. These have the advantage of giving an immediate grasp on how the main physical parameters affect the radiation field: an important feature especially for engineering purposes. The case developed here is that of a plane slab, for both monosized catalyst particles and particles with size distributions. Notably, as no adjustable parameters are used, fully predictive results can be obtained. The model predictions are successfully compared with the results of original experimental tests, therefore leading to model validation. In Part 2 of this paper, another model is developed in which the assumption of zero reflectance of the particles is removed, yet allowing analytical solutions to be obtained, One of the key features of the two models is that their predictions bound the real behavior of irradiated photoreactors, as shown in the papers. Therefore, although only approximate solutions are obtained from each of the two models, the real behavior can be better approximated by some sort af interpolation between the two solutions and, what is more important, confidence limits for the final solution are obtained.