Fundamentals of Population Balance Based Crystallization Process Modeling

Crystallization is ubiquitous in pharmaceutical manufacturing as a means of separation and purification. The pharmaceutical industry is currently going through a paradigm shift from batch to continuous manufacturing due to its various benefits such as improved product consistency, improved productivity, ease of scale up, efficient use of physical space and reduction in energy consumption. Crystallization is a key unit operation in a continuous manufacturing process since in addition to being a critical purification step it also defines the critical properties of the particulate products. In silico evaluation and design of crystallization systems can significantly reduce process development time and allow the understanding and defining of the optimal operating space. While significant progress has been made to date, this chapter is primarily focused on presenting the basic concepts of modeling and simulation of the two continuous crystallizer platforms – mixed suspension mixed product removal (MSMPR) crystallizer and plug flow crystallizer (PFC). Starting from the fundamental concepts of the crystallization process, modeling of the various sub processes such as nucleation, growth, aggregation and breakage are discussed. Then, the population balance model for the continuous crystallizer platforms are discussed along with the numerical techniques that can be used to solve the model equations. Finally, a few case studies are presented including cooling and antisolvent crystallizations, as well as crystallization of polymorphic and enantiomeric systems.