Designing Robust Crystallization Processes in the Presence of Parameter Uncertainty Using Attainable Regions

We consider the influence of uncertainty in crystallization kinetics (i.e., in the nucleation and growth rates) in the context of process design. Specifically, we model continuous and batch crystallization processes using population balance equation models and investigate how the inherent uncertainty in kinetic parameters propagates through the crystallization processes and how it ultimately affects the distribution of process outcomes (yield and mean particle size). We incorporate the effect of uncertainty into the concept of attainable regions, i.e., we exhaustively investigate which combinations of particle size and total residence time (or batch time) can be attained with a certain probability. Avoiding regions of low probability allows the design of robust crystallization processes that can deliver a product with desired specifications, even when the original process was designed using inadequately characterized crystallization kinetics. The concepts presented in this article are illustrated by a case study on the cooling crystallization of paracetamol grown from ethanol as a solvent