A multi-stage multi-component transfer rate morphological population balance model for crystallization processes

A model was proposed for modeling the non-equilibrium crystal growth of single crystals (Y. D. Shu, Y. Li, Y. Zhang, J. J. Liu and X. Z. Wang, CrystEngComm, 2018, 20, 5143–5153). It describes mathematically and digitally the non-equilibrium growth behavior of single crystals using multi-component transfer rate models, as well as considering multi-component phase equilibria, adsorption, orientation and crystallization of individual molecules on crystal faces. In this paper, the model for single crystal growth is extended to modeling a population of crystals in a crystallizer by incorporating it into morphological population balance equations. The resulting modeling approach, i.e. the multi-stage multi-component transfer rate morphological population balance equation (M3PBE) model, is able to predict the spatial and temporal distribution of multi-components inside crystals during the course of crystallization as well as the multi-component composition of the product crystals. The new modeling approach is introduced by reference to a case study of NaNO3 batch cooling crystallization in water.