Numerical modelling of crystallisation processes: kinetics to optimization

Crystallisation and precipitation processes are used in the chemical and pharmaceutical industry to produce crystals with desired product properties, such as flow ability, filterability, drying time and bioavailability. These properties are greatly affected by the particle size distribution and control of it is one of the major goals in process design. Model-based design approaches require accurate kinetics and thermodynamic data. The aim of this thesis is twofold: on the one hand, fast and robust characterization methods for the measurement of nucleation and growth kinetics were developed using current process analytical technologies. The second aim of this thesis addresses the implementation of the measured kinetic correlations into a population balance model in order to simulate the influence of process parameters on the final product particle size distribution, thus enabling optimisation of attributes associated with the PSD and other process variable such as time. These simulation tools can be used to develop a better understanding of crystallisation processes and when coupled with carefully designed experiments, the design of crystallisation processes can be executed in a systematic and scientific manner. Two different crystallisation processes were investigated during the course of this work: the anti-solvent crystallisation of paracetamol from methanol-water solutions and the cooling crystallisation of paracetamol from methanol. The majority of the work is concerned with the anti-solvent process, with the final chapter dedicated to the cooling crystallisation. Several methods were employed in this thesis for the estimation of nucleation and growth kinetics, namely independent and simultaneous methods. Firstly, the primary nucleation rate as a function of supersaturation and composition was successfully evaluated using two approaches, namely Meta Stable Zone Width (MSZW) and induction time experiments, using FBRM to detect the particle onset. The theoretical approach of Kubota (2008) was employed to estimate the nucleation kinetics, which accounts for the sensitivity of the nucleation detection technique. This approach is expanded in this work to analyse the induction time for an anti-solvent crystallisation process. The primary nucleation rates were i found to decrease with increasing anti-solvent mass fractions, with the extent of their reduction linked to the gradient of the solubility curve and interfacial tension. Finally, both MSZW and induction time methods have been found to produce similar estimates for the nucleation parameters. The growth kinetics of the same system were measured by combining in situ measured desupersaturation data of seeded batch experiments with population balance modelling. Further process analysis using the process model allowed for a better understanding of the rate determining fundamental mechanisms of the transformation process. Crystal growth rate was found to decrease with increasing water mass fractions. Utilising the growth mechanism it has been postulated that a combination of the solubility gradient and viscosity, are responsible for the reduction in growth rates with increasing antisolvent mass fractions. A population balance incorporating nucleation, growth and agglomeration, solved using the Quadrature Method of Moments was coupled with an integral parameter estimation technique. All parameters concerned were regressed from moments calculated using the measured square weighted chord length distribution (CLD) generated by the FBRM and solute concentration data inferred from ATR-FTIR spectroscopy. Experimental Particle Size Distributions (PSDs) measured by laser diffraction are compared to PSDs calculated by the numerical model and found to be in good agreement. The process models were used for process design and optimization by applying a multi-objective free final time formulation optimization on the validated model. These profiles were experimentally tested and simulated PSDs were compared with PSDs obtained from experiments used in the parameter estimation procedure. A 73.3% reduction in batch time was achieved with little impact on the PSD. As an additional exercise, all the methods presented in the thesis for obtaining growth kinetics are compared in order to access their efficiency in use with population balance models. Finally, the proposed methods for the determination of nucleation and growth kinetics were successfully applied to the cooling crystallisation of paracetamol from methanol. Higher order moments (third and fourth) were shown to be inadequate to estimate nucleation kinetics and due to sampling difficulties and PSD truncation errors, calculation of the lower order moments from the samples was not possible. Parameters estimated previously from antisolvent experiments were tested against the cooling crystallisation experiments and shown to reproduce the experimental PSDs and solute concentration data with significant accuracy. A previously utilised optimisation algorithm was performed on the validated model to obtain the optimal cooling rates to improve selected PSD properties. Based on simulated outputs, various optimisation cases were compared. A 10.6% increase in particle size and 47.5% reduction in process time was achieved with the increase in particle size attributed to agglomeration.