Population Balance: The Auto-Catalytic Nature of Secondary Nucleation in Seeded Batch Crystallizations

ISIC 20 Abstract Submission

Population Balance: The Auto-Catalytic Nature of Secondary Nucleation in Seeded Batch Crystallizations

Rory Tyrrell, Brian De Souza, and Patrick J. Frawley

Synthesis and Solid State Pharmaceutical Centre

Bernal Institute

University of Limerick

Ireland

Existing models for secondary nucleation kinetics predominantly attribute the generation of nuclei to varying forms of particle breakage or attrition during the crystallization process.  However, recent literature has provided new insight into a secondary nucleation mechanism in seeded batch reactions whereby the seed itself serves as a breeding ground for new secondary nuclei to form on its surface (Anwar, et al., 2016; De Souza, et al., 2016).  Furthermore, it has been reported that crystal breakage can be neglected almost entirely in typical crystallization processes as a boundary layer effect between crystals and reactor features, such as impeller blades, effectively protects against any potential breakage events (Tyrrell, et al., 2017).  Through this deeper understanding of the crystallization process, process modelling tools such as the Population Balance (PB) method have become gradually become more accurate as these tools are only as strong as their underlying kinetic expressions.

Presented here is a Finite Volume Method (FVM) for solving the Population Balance equations for growth, secondary nucleation, and associated mass balances (i.e. de-supersaturation).  As the kinetic expressions for growth are known to be relatively well defined, focus is given mostly to the secondary nucleation expressions governing the generation of new nuclei in the early time-scales of the crystallization process.  It is assumed that crystal breakage is a non-issue, and that the process is non-agglomerating.  Therefore, the modelling methodology is focused around developing a kinetic expression describing the surface-nuclei, auto-catalytic mechanism for secondary nucleation proposed in the literature above.

In addition to a new kinetic expression for secondary nucleation, a full description of the formulation for the FVM-PB model is described.  The necessity for high-resolution models is discussed, in combination with flux-limiting methods for managing the associated numerical oscillations typical of higher-order systems.  Furthermore, a critical factor of FVM-PB models, as well as modelling in general, is the requirement for governing conservation laws to be maintained; violation of mass-balances in finite volume schemes with numerical source terms for nucleation can prove to be a challenging problem to surmount and warrants discussion.

References

Anwar, J., Khan, S. & Lindfors, L., 2016. Secondary Crystal Nucleation: Nuclei Breeding Factory Uncovered. Angewandte Chemie, 54(49), pp. 14681 - 14684.

De Souza, B., Cogoni, G., Tyrrell, R. & Frawley, P. J., 2016. Evidence of Crystal Nuclei Breeding in Laboratory Scale Seeded Isothermal Crystallization Experiments. Cryst. Growth Des., 16(6), pp. 3443 - 3453.

Tyrrell, R., De Souza, B. & Frawley, P. J., 2017. Particle Breakage: Limiting Conditions for Crystal-Crystallizer Collisions. Crys. Growth Des. (Under Review).