Numerical modelling of cooling crystallisation: process kinetics to optimisation

The research detailed in this dissertation expands the field of knowledge in the area of numerical modelling of cooling crystallisation processes in stirred vessels. The paracetamol and ethanol solution system was chosen as the model system, which represents a typical Active Pharmaceutical Ingredient (API) cooling crystallisation process. This solution system exhibits three competing crystallisation mechanisms of primary nucleation, secondary nucleation and crystal growth. The primary nucleation rate as a function of absolute supersaturation was successfully evaluated using two approaches, namely Meta-Stable Zone Width (MSZW) and induction time experiments. The induction time was observed to be independent of the solution temperature, a novel finding, as suggested by Kubota's theory. The growth kinetics of paracetamol in ethanol solutions, were evaluated by means of isothermal seeded batch experiments. The growth kinetics of paracetamol crystals were evaluated in isolation, with the growth rate assumed to be size independent, using a method previously suggested by Schöll et al. (2007a) which was modified for cooling crystallisation processes. The technique utilises a combination of in-situ Process Analytical Technologies (PAT), ex-situ analysis methods and population balance modelling to determine growth kinetics of the solute crystals. A quantitative approach to the evaluation of the minimum seed loading was employed, to ensure negligible nucleation occurred. Initial Particle Size Distributions (PSDs) were used in conjunction with desupersaturation profiles to determine the growth rate as a function of temperature and supersaturation. The secondary nucleation kinetics were determined in a similar manner, by means of isothermal under-seeded batch experiments. In this case, insufficient seed loadings were employed, so that nucleation and growth of secondary nuclei contributed significantly to the mass of the final product. With knowledge of the primary nucleation and crystal growth kinetics, the secondary nucleation kinetics were evaluated in isolation for a wide range of experimental conditions. The Method of Moments (MOM) approach was utilised to solve the population balance equation. However, this method does not conserve the actual PSD, with a reconstruction technique required to produce the PSD from its respective moments. A recently suggested (Hutton et al. 2012) PSD reconstruction method, involving the generation of moment surfaces as a function of the distribution parameters was employed in this thesis. A wide range of conditions for supersaturation, solution temperature and cooling mode were employed to evaluate the robustness of the nucleation (both primary and secondary) and growth rate kinetics. The numerical model was subsequently employed to optimise the temperature cooling profile for certain process objectives, such as improved product PSD, with reduced fine particles. Experimental validation of optimised processes were conducted to verify simulated improvements to the final crystallised product, which served to further validate the estimated process kinetics. Finally, the MOM and Method of Classes (MOC) approaches to modelling crystallisers were compared. The outputs of the numerical model developed in this thesis were compared to a commercially available crystallisation modelling software gCRYSTAL®, which employed the MOC approach, comparing corresponding simulated concentrations, final yields and PSDs. The effects of impeller type, material and blade width on the measured secondary nucleation rate were also investigated in a qualitative manner. A significant finding from this work was the major quantifiable effects of impeller material, in particular stainless steel, on the secondary nucleation kinetics. In combination with a different mixing regime, this effect largely explained the observed differences in the secondary nucleation kinetics measured in this thesis and the available literature data. Finally, a novel method which allows for the rapid and accurate calibration of the ATR-FTIR spectral data for the prediction of dissolved solution concentration, was also outlined and verified using the paracetamol and ethanol solution system.