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

The effects of supersaturation, temperature, agitation and seed surface area on secondary nucleation

This work details the estimation of the secondary nucleation kinetics of paracetamol in ethanol solutions for cooling crystallisation processes, by means of isothermal under-seeded batch experiments. A numerical model, incorporating the population balance equation and the method of moments, has been developed to describe the seeding process for a typical cooling crystallisation process, accounting for the primary and secondary nucleation and subsequent crystal growth. Primary nucleation and growth kinetics have been previously evaluated from induction time experiments, and isothermal seeded batch experiments, respectively, allowing the secondary nucleation rate to be evaluated for a wide range of experimental conditions. The experimental technique involved the utilisation of two in-situ Process Analytical Techniques (PAT), with an Focused Beam Reflectance Measurement (FBRM®) utilised to qualitatively indicate the occurrence of secondary nucleation and an Attenuated Total Reflectance - Fourier Transform Infrared (ATRFTIR) probe employed for the online monitoring of solute concentration. Initial Particle Size Distributions (PSD) were used in conjunction with desupersaturation profiles to determine the secondary nucleation rate as a function of supersaturation, temperature and crystal surface area. Furthermore, the effects of agitation rate on the secondary nucleation rate were also investigated. Experimental parameters were compared to the model simulation, with the accuracy of the estimated secondary nucleation kinetics validated by means of the final product PSD and solute concentration

Simultaneous parameter estimation and optimisation of a seeded anti-solvent crystallisation

A population balance incorporating nucleation, growth and agglomeration, solved using quadrature method of moments was coupled with a parameter estimation procedure. The seeded anti-solvent crystallisation of Paracetamol from methanol and water was chosen as the model system. All parameters concerned were regressed from moments calculated using the measured square weighted chord length distribution (CLD) generated by the FBRM. The FBRM and the concentration data are utilised together to obtain experimental moments that reflect the mass of solids in the tank. Using the estimated kinetic parameters, the crystallization model was validated using an additional experiment with a new non linear addition rate. Experimental crystal size distributions measured by laser diffraction are compared to CSDs calculated by the model and found to be in good agreement. No such work exists in the literature using FBRM to model an anti-solvent system which considers agglomeration. Based on the kinetic parameters estimated using the above method, the solution to the optimal anti-solvent addition rate profiles was obtained by applying nonlinear constrained multi-objective free final time formulation optimization on the validated model. These profiles were experimentally tested and CSD were compared with experiments used in the parameter estimation procedure. A 73.3% reduction in batch time was achieved with little impact on the CSD. Analyses of the various conflictions are presented with the aid of a pareto optimal plot to provide the practitioner with increased flexibility