Simplified Extense Source Model for Photoreactor Analysis and Design”.

Abstract

Most of the research work on photoreactor analysis, modeling, and design published so far relies on two approaches to represent the emission of tubular radiation sources: the line (linear) source models (LSMs) and the extense (three-dimensional) source models (ESMs). It is widely recognized that the ESMs give the more realistic representation of the emission phenomenon so far; however, they are rather difficult to use in some applications, especially when indirect radiation plays a dominant role. On the other hand, LSMs are simpler, and in some cases, mostly when reflected radiation has not been involved, they have been used with success. In this work, the simplified extense model (SEM), systematically derived from the extense source model with voluminal emission (ESVE), is proposed. The SEM retains all of the simplicity of the LSM for the prediction of the direct radiation contribution, while rendering closed mathematical expressions that give a more realistic and often very accurate representation of the reflected radiation inside reflecting cylindrical cavities with elliptical cross sections. The average incident radiation on the reactor surface at the midreactor length as predicted with the SEM never differs by more than 12% of the average value computed with the ESVE. Moreover, for different sets of frequently used parameter values characterizing the shape of the elliptical mirror and the reactor, the compared average values agreed within 5% of the reference value given by the ESVE. Within the same parameter range and for eccentricities of about e = 0.4, nonaveraged values of the incident radiation computed at different points on the external surface of the reactor wall at the midreactor height position using the SEM and the ESVE models agreed remarkably well, to the point that, under certain circumstances, the profiles obtained are not easily distinguishable from one another. The SEM brings together simplicity of implementation with desirable accuracy for a wide set of values of the apparatus parameters used to illustrate the proposal.