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

Particle size distribution reconstruction: the moment surface method

Numerical simulation of typical chemical engineering processes, such as crystallisation, liquid-liquid extraction, milling and other multi-phase operations in which exist discrete and continuous phases are highly computationally intensive problems. For this reason numerical techniques, such as the Method of Moments (MOM) and Quadrature Method of Moments (QMOM), are utilised to improve the computational efficiency of these simulations. The downside to these approaches is that the simulations only produce the moments of the Particle Size Distribution (PSD), with the actual distribution not preserved. Knowledge of the PSD is very important for many industrial unit operations, particularly in dynamic multi-phase flows in chemical engineering where the composition of the discrete phase(s) evolves in time or space. For example, control of the PSD in crystallisation operations may be required to ensure more efficient downstream operations such as filtration and clarification. Several methods for the reconstruction of a distribution from its respective moments are available in the literature. Typically these techniques are quite computationally expensive. The novel technique presented in this paper involves the pre-calculation of the moments of a pre-defined 2-parameter Probability Density Function (PDF) for a range of values of each parameter. This pre-calculation results in moment surfaces where the surfaces are a function of the two defining parameters. The intersection of constant moment contour lines (termed moment iso-lines) on these surfaces using simulation moment outputs results in the recovery of the defining parameters. Knowledge of the PDF and the total particle count or solids loading allows for the reconstruction of the full PSD. This technique proves to be very efficient which makes it ideal for the reconstruction of large numbers of distributions, for example in transient population balance models or model-based control algorithms, without the need for repeated application of optimisation algorithms

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