A probabilistic approach to radiant field modeling in dense particulate systems

Radiant field distribution is an important modeling issue in many systems of practical interest, such as photo-bioreactors for algae growth and heterogeneous photo-catalytic reactors for water detoxification.In this work, a simple radiant field model suitable for dispersed systems showing particle size distributions, is proposed for both dilute and dense two-phase systems. Its main features are: (i) only physical, independently assessable parameters are involved and (ii) its simplicity allows a closed form solution, which makes it suitable for inclusion in a complete photo-reactor model, where also kinetic and fluid dynamic sub-models play a role. A similar model can be derived by making use of concepts developed in the realm of stereology. The resulting equation is similar, yet not identical, to that obtained with the probabilistic approach, due to the fact that in stereology the front plane, or the focus plane, may well cut through particles, a circumstance excluded both in the probabilistic model and in actual photoreactors.The two models are compared with pseudo-experimental data obtained by means of Monte Carlo simulations, and the probabilistic model is found to give rise to the best agreement.