The comparison of discrete ordinate and Monte Carlo methods in solving of the radiation transfer equations in a heterogenous reactor

Photoreactor applications in water and wastewater treatment has been increased in recent years. The simulation of radiation distribution inside the reactors allows the optimization of its operation. The radiation transfer equation (RTE) illustrates the field radiation. We applied the discrete ordinate (DO) method to solve the RTE and computed the local volumetric rate of energy absorption (LVREA) in a photoreactor, consisting of a Ultra Violet (UV) lamp and titanium dioxide Degussa P25 (TiO₂ DP 25) catalyst. First, GAMBIT 2.4.6 was employed to model the reactor in three dimensions. The simulation of the radiation distribution was carried out using FLUENT 14.5 software in the framework of a multiple point source summation (MPSS) model. The robustness of the DO approach was assessed by comparing with the Monte Carlo (MC) method and experimental data. The coefficient of determination (R²) and index of agreement (IA) of DO and experimental data were 0.95 and 0.93, respectively. The DO and MC had a good convergence in the low concentrations of TiO₂ DP 25. In the concentrations between 0.03 g/l to 0.15 g/l, the difference with experimental data increased. In the concentration of 0.15 g/l, and beyond, the both methods and experimental data were in a good agreement.