Process measurements and kinetics of unseeded batch cooling crystallization
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This thesis describes the development of an empirical model of focus beam reflectance measurements (FBRM) and the application of the model to monitoring batch cooling crystallization and extracting information on crystallization kinetics. Batch crystallization is widely used in the fine chemical and pharmaceutical industries to purify and separate solid products. The crystal size distribution (CSD) of the final product greatly influences the product characteristics, such as purity, stability, and bioavailability. It also has a great effect on downstream processing. To achieve a desired CSD of the final product, batch crystallization processes need to be monitored, understood, and controlled. FBRM is a promising technique for in situ determination of the CSD. It is based on scattering of laser light and provides a chord-length distribution (CLD), which is a complex function of crystal geometry. In this thesis, an empirical correlation between CSDs and CLDs is established and applied in place of existing first-principles FBRM models. Built from experimental data, the empirical mapping of CSD and CLD is advantageous in representing some effects that are difficult to quantify by mathematical and physical expressions. The developed model enables computation of the CSD from measured CLDs, which can be followed during the evolution of the crystal population during batch cooling crystallization processes. Paracetamol, a common drug product also known as acetaminophen, is selected as the model compound in this thesis study. The empirical model was first established and verified in a paracetamol-nonsolvent (toluene) slurry, and later applied to the paracetamol-ethanol crystallization system. Complementary to the FBRM measurements, solute concentrations in the liquid phase were determined by in situ infrared spectra, and they were jointly implemented to monitor the crystallization process. The framework of measuring the CSD and the solute concentration allows the estimation of crystallization kinetics, including those for primary nucleation, secondary nucleation, and crystal growth. These parameters were determined simultaneously by fitting the full population balance model to process measurements obtained from multiple unseeded paracetamol-ethanol crystallization runs. The major contributions of this thesis study are (1) providing a novel methodology for using FBRM measurements to estimate CSD; (2) development of an experimental protocol that provided data sets rich in information on crystal growth and primary and secondary nucleation; (3) interpretation of kinetics so that appropriate model parameters could be extracted from fitting population balances to experimental data; (4) identification of the potential importance of secondary nucleation relative to primary nucleation. The protocol and methods developed in this study can be applied to other systems for evaluating and improving batch crystallization processes.