(349f) A Mathematical Model of the Ultrasound-Assisted Crystallization of Aspirin in a Continuous Tubular Reactor

The crystallization of organic nano- and microparticles is significant in all kinds of industries, products, and
applications, such as organic micron-sized crystals of active pharmaceutical ingredients (APIs) and
nanodispersions of coating resins and microcapsules with active ingredients [1]. Currently, only batch
processes are implemented at a sufficiently large scale to meet the market needs, as batch crystallization
has been widely studied. However, the production of particles in batch processes is associated with
problems. The most common limitations in batch reactors are the difficulties in the control of heat
and mass transfer, factors that affect not only the average particle size and particle size distribution
(PSD), but also batch to batch variations. The drawbacks of batch crystallization led researchers and
industry initiatives to explore continuous processing technology, maintaining higher product standards
[2].

As for continuous processes, the most important advantages are their ability to produce particles with
specific particle size and smaller PSD. Additionally, the polymorphism can be controlled [3]. They
produce quantities on demand, minimizing the use of raw materials and equipment. Furthermore, mixing
energy and quantity of solvent could be decreased, and, last but not least, they are capable of being
scaled up [4]. Ultrasound can be used for improving continuous crystallization processes because the
generated bubbles act as a cluster attachment sites, forming finer crystals with low average size and
narrower PSD. However, the nucleation mechanism that takes place during ultrasound is still unclear
[5].

Concerning mathematical modeling, population balance models (PBMs) are used extensively to describe the
crystallization processes because they are available to capture the changes in the number and size of crystals over
time. In case of a tubular reactor, also a spatial PBM that describes the PSD at different axial length position can
be formulated. Impressive advances have been obtained during the previous years in capturing the crystal
production in reactors used for continuous crystallizers (plug flow crystallizers [6] and mixed suspension mixed
product removal (MSMPR) reactors [7]), and batch systems with [8] or without ultrasound [9]. However, there is an
unmet need to investigate novel and high-fidelity mathematical models for scaling-up the continuous crystallization
of APIs under ultrasound. This work proposes the development of the first mathematical model of the
continuous antisolvent crystallization of aspirin in water and ethanol in an experimental plug flow reactor
with ultrasound. Heat generation due to mixing and ultrasound, which increases crystal solubility and
affects the yield of the system subsequently, is also included in the model. Prior to this work, the
population balance model’s growth and nucleation rates in the studied antisolvent system at different
temperatures and antisolvent content were estimated under silent conditions [10]. Global sensitivity
analysis of our ultrasound crystallization system reveals which are the most critical parameters for
capturing the crystal properties, such as the volume based distribution parameters Dv10, 50, and 90, and
the system yield. Dv50 is the median for a volume distribution. Dv10, and Dv90 show the sizes at
which the cummulative volume distribution reaches 10%, and 90%, respectively. Estimation of the
most important model parameters and validation of the model’s predictive capability were successfully
performed for continuous crystallization experiments with different antisolvent volume flowrates and initial
supersaturations.

This work shows that mathematical modeling is undoubtedly useful in order to capture the crystal growth in
continuous crystallizers under the effect of ultrasound and subsequently it will provide insight into the design of new
crystallizers.

References