The modeling of conventional reactors based on first principles usually requires the solution of the momentum, thermal energy and multicomponent mass conservation equations. In the case of photocatalytic reactors, the equation of radiative transfer must be considered. This equation can be solved independently of the thermal energy equation since thermal effects are usually negligible for photocatalytic processes. Therefore, the main interest of this chapter will be focused on the evaluation of the radiation absorption and its effect on the kinetics of the photocatalytic reaction.

The evaluation of the photon absorption rate is schematically exemplified in Figure 14.1.¹  Firstly, expressions of the reaction rates for each one of the reacting species are required for the mass balances. As it is known, one of the reaction steps is initiated by radiation absorption (irradiated step). Then, the formulation of the local volumetric rate of photon absorption (LVRPA) or the local surface rate of photon absorption (LSRPA) is needed to evaluate the rate of the irradiated step (Section 14.2). In turn, to calculate the LVRPA or LSRPA, the radiative transfer equation (RTE) and the constitutive equations for radiation absorption, emission and scattering are required (Section 14.3). Boundary conditions to solve the RTE can be considered taking into account different possibilities: emission models developed for tubular lamps (with voluminal or superficial emission), photocatalytic reactions initiated by solar radiation (direct and diffuse components) and actinometric reactions employed to assess the radiation flux incident on the reactor window (Section 14.4). Specific numerical methods should subsequently be applied to solve the RTE in the reaction space for absorbing and scattering media (Section 14.5).