Two-dimensional P1 approximation (P1-2D) for the Description of the Radiant Field on Cylindrical Solar Photocatalytic Reactors

The local volumetric rate of photon absorption (LVRPA) was formulated by solving the radiative transfer equation (RTE) in polar coordinates with the P1 approximation approach (P1-2D) for the description of the radiant field in cylindrical solar photocatalytic reactors. A general expression of the LVRPA was formulated that can be employed on cylindrical photocatalytic reactors with an incident radiation constant along the reactor length. CPC and tubular photocatalytic reactors were used as reactor models and Lambert's cosine law (irradiance) was considered when using the boundary conditions. Simulations were carried out using the commercial TiO2-P25, its optical properties taken from the literature. The LVRPA was found to decrease exponentially from the reactor wall to its center. literature rate of photon absorption per unit of reactor length (VRPA/H) increased exponentially with the catalyst loading until a value where no significant increase was observed and was found to increase with reactor radius, information that agrees with the literature. The optimum catalyst loading with the CPC reactor was about 0.364 g/L with a reactor radius equal to 1.65 cm similar to that found in the literature when using the six-flux model in two dimensions (SFM-2D). The apparent optical thickness τ_App1 newly formulated with the P1 approximation was introduced for optimization purposes and was found more reliable than the optical thickness τ. This parameter not only removes the dependence of the optimum catalyst loading on the reactor's radius but also its dependence on catalyst albedo. τ_App1 was found about 9.73 and 14.6 for CPC and tubular reactors respectively and provides the optimum catalyst loading and the reactor radius that optimize the radiation absorption inside both reactors.