Hybrid finite volume and Monte Carlo method for solving multi-dimensional population balance equations in crystallization processes

Abstract

A novel hybrid framework that combines our recently proposed event driven constant number Monte Carlo (MC) method and a finite volume discretization scheme is developed to solve population balance equation (PBE) involving nucleation, growth, and breakage events for a batch crystallization process. At each time step, the nucleation and growth terms of the PBE are solved using high resolution finite volume method (HRFV), and then the breakage term is solved using the MC approach. This integrated approach is especially advantageous for solving multi-dimensional PBE involving nucleation, growth, and breakage events. The efficiency of the proposed approach is demonstrated by solving both one-dimensional (1D) and two-dimensional (2D) PBE from published literature. Also, a set of seeded batch cooling crystallization of plate-like pyrazinamide crystals were performed in presence of ultrasound (US) and the proposed hybrid solution scheme was used successfully to model and simulate this system characterised by 2D PBE.