Linearized Parameter Estimation Methods for Modeled Crystallization Phenomena Using In-Line Measurements and Their Application to Optimization of Partially Seeded Crystallization in Pharmaceutical Processes

In this chapter, we show some parameter estimation methods for modeled crystallization phenomena, and we make comments on the application of the models to optimization of batch cooling crystallization. At first, in Sect. 1 we show linearized parameter estimation methods developed by using in-line measurements with process analytical technologies (PATs). The phenomena occurring in crystallization, such as growth, nucleation, breakage, and agglomeration, are modeled by typical numerical expressions. At the same time, we show the methods for the data acquisition and processing by using in-line measurements. Then, linearized methods and a few non-linear ones for estimation of the model parameters in each phenomenon are developed by using processed in-line data. Next, we show in Sect. 2 how the developed models are applied to the optimization of partially seeded crystallization in pharmaceutical processes. Several seeding policies are discussed to emphasize the importance of partial seeding for pharmaceutical processes. Then, the operating conditions of partially seeded crystallization are optimized, and the process designed optimally is assumed to be implemented. In addition, we show a case study of partially seeded crystallization of l-arginine, and we make a few comments on quality and stability of the crystallization products, with regard to stochastic nucleation.