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.