Toward predictive modeling of industrial crystallizers: A compartmental framework for coupling hydrodynamics and population dynamics

Accurate prediction of particle size distribution (PSD) is critical for optimal design of crystallization processes. The interplay between crystallization kinetics and local hydrodynamics complicates predictive process modeling. Computational fluid dynamics (CFD) provides hydrodynamic characterization of the system, which when integrated with population balance equation (PBE) models, leads to a comprehensive representation of the system. Here, we develop a CFD–PBE framework using a compartmental modeling approach, and conduct a systematic evaluation of the impact of hydrodynamics on crystallization processes. CFD simulations of a batch crystallizer provide mean flow field and its turbulence properties, which are mapped onto a coarse-grained structure of well-mixed compartments. PBEs are solved over the compartments, capturing mixing effects on the evolution of the PSD, obtained within few minutes (compared to a few seconds with a perfectly-mixed assumption). Crystallization case studies are conducted to examine mixing effects under varying kinetics, operating conditions, and impeller types. Results show that mixing-driven phenomena are system-specific, and hydrodynamic effects must be considered when transferring insights between systems and scales. The framework is system and geometry-agnostic, and computationally efficient, providing a generalizable approach for scale-up, offering a practical alternative to models that assume perfect mixing.