Capturing Thermal and Hydrodynamic Heterogeneity in Polymorphic Crystallization Scale-Up via Physics-Inspired Multicompartmental Population Balance Models

Abstract

Abstract

Abstract Scaling up crystallization processes is notoriously difficult for polymorphic systems, where spatial heterogeneities in temperature and hydrodynamics dictate nucleation, growth, agglomeration, and solid-form selection. Conventional population balance models (PBMs) generally assume perfect mixing and uniform thermal conditions─assumptions that fail at industrial scales. Conversely, fully coupled Computational Fluid Dynamics-Population Balance Equation (CFD-PBE) approaches are often computationally prohibitive for iterative design optimization. In this work, we develop a physics-inspired multicompartment PBM to account for hydrodynamic and thermal heterogeneity with high computational efficiency. The crystallizer is partitioned into dynamically connected compartments that represent key sources of heterogeneity with clear physical meaning─such as wall regions, free-surface effects, impeller zones, and bulk fluid regions─guided by short-time CFD simulations. CFD-derived intercompartment fluxes, turbulent energy dissipation rates, and wall-induced thermal effects are incorporated into a compartmental thermal model coupled with the PBM. Case studies on enantiotropic p-aminobenzoic acid and monotropic l-glutamic acid demonstrate that spatial temperature gradients and energy-dissipation-dependent kinetics reshape predicted crystal size distributions and predicted polymorphic outcomes, even when predicted bulk concentration appears uniform. This framework bridges the gap between well-mixed PBMs and fully coupled CFD-PBE, enabling robust digital design and scale-up for complex polymorphic systems.