A dynamic compartment model for spatially heterogeneous reactors: Scalar and Monte-Carlo particle mixing

The coupling of multidimensional population balance models with transport equations is often necessary for the simulation of spatially heterogeneous reactors. Because of numerical intractability, a compromise on both the hydrodynamics and the population description has to be made. In this work, the Monte-Carlo method is used to calculate the local integral source term due to the dispersed phase (isodense particles) and a compartment model is used to describe the fluid motion in the reactor. The number density function n (x, t, xi) is approximated by the number of Monte-Carlo particles per compartment and their movement in the space of compartment uses a stochastic transport algorithm adapted from existing works. The numerical tool is thoroughly and successfully validated in the context of mixing and first order reaction in a 70 L stirred tank equipped with a Rushton turbine. The dynamic method makes use of time resolved CFD simulations to built time dependent flow matrices reflecting the periodic nature of the flow field. The dynamic approach is finally compared to other usual compartment model approaches in terms of complexity, accuracy and rapidity which reveals the benefit of considering the flow unsteadiness within a compartiment model approach for stirred tanks.