Model-based optimization of particle size distribution in batch-cooling crystallization of paracetamol

The control objectives of batch crystallization processes are often defined in terms of particle size distribution (PSD), or properties related to the PSD, viz. average particle size, product filterability, dry solids flow properties, etc. To achieve these control objectives, a constrained nonlinear model-based optimization strategy has been adopted. This involves the detailed modeling of batch crystallization including model validation and parameter estimation, on-line monitoring of supersaturation and PSD, and the application of optimization strategies. A deterministic population balance model accounting for solution thermodynamics, crystal growth, and nucleation has been developed. State estimation is achieved by the on-line monitoring of temperature, concentrations in the liquid phase, particle density, and PSD. For this purpose, the focused beam reflectance measurement (FBRM) provides an on-line, in-situ information of crystal size and particle concentration in the form of a chord length distribution (CLD). A method using a three-dimensional geometrical CLD model and an inverse technique based on projections onto convex sets (POCS) has been introduced to calculate PSDs from CLD raw data. These concepts are applied to the batch cooling crystallization of paracetamol in ethanol.