(233d) 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.

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).