Population Balance Modeling and Optimization of an Integrated Batch Crystallizer–Wet Mill System for Crystal Size Distribution Control

In this work, the modeling, simulation, and optimization of an integrated batch crystallizer, wet mill system are presented. It is shown that by coupling the external wet mill to the crystallizer it is possible to increase the overall system flexibility, increase the attainable crystal size distribution (CSD), and provide a significantly better distribution shaping control than the crystallizer alone. The population balance modeling approach with appropriate mechanisms is applied for the description of crystal population in both the crystallizer and wet mill. This description generates a system of partial differential-integral equations, which are solved with a high resolution finite volume method, involving calculations on parallel graphical processing unit for improved solution time. In the batch crystallizer, it is assumed that primary nucleation and crystal growth are the key mechanisms, whereas in the wet mill, attrition and fragmentation of crystals occurs. The nucleation and growth rate kinetics are taken from the literature, and a recently developed hydrodynamic model is employed for realistic description of wet mill operation. The simulation results revealed that the simultaneous dynamic optimization of the temperature, circulation flow rate, and wet mill rotation speed improve the process flexibility and lead to considerably better CSDs that can be achieved in crystallizer only configuration. The dynamic optimization also automatically discovered an unexpected optimal integrated system operation, which combines the advantages of in situ seed generation and optimal dynamic seeding. These two features make the system suitable to achieve a significantly higher control on the shape of the CSD than using the crystallization process only, without the need of time-consuming, tailored seed crystal generation and dynamic seed addition.