Model-based optimization of batch- and continuous crystallization processes

Crystallization is an important separation process, extensively used in most chemical industries and especially in pharmaceutical manufacturing, either as a method of production or as a method of purification or recovery of solids. Typically, crystallization can have a considerable impact on tuning the critical quality attributes (CQAs), such as crystal size and shape distribution (CSSD), purity and polymorphic form, that impact the final product quality performance indicators and inherent end-use properties, along with the downstream processability. Therefore, one of the critical targets in controlled crystallization processes, is to engineer specific properties of the final product. The purpose of this research is to develop systematic computer-aided methodologies for the design of batch and continuous mixed suspension mixed product removal (MSMPR) crystallization processes through the implementation of simulation models and optimization frameworks. By manipulating the critical process parameters (CPPs), the achievable range of CQAs and the feasible design space (FDS) can be identified. Paracetamol in water and potassium dihydrogen phosphate (KDP) in water are considered as the model chemical systems.The studied systems are modeled utilizing single and multi-dimensional population balance models (PBMs). For the batch crystallization systems, single and multi-objective optimization was carried out for the determination of optimal operating trajectories by considering mean crystal size, the distribution s standard deviation and the aspect ratio of the population of crystals, as the CQAs represented in the objective functions. For the continuous crystallization systems, the attainable region theory is employed to identify the performance of multi-stage MSMPRs for various operating conditions and configurations. Multi-objective optimization is also applied to determine a Pareto optimal attainable region with respect to multiple CQAs. By identifying the FDS of a crystallization system, the manufacturing capabilities of the process can be explored, in terms of mode of operation, CPPs, and equipment configurations, that would lead to the selection of optimum operation strategies for the manufacturing of products with desired CQAs under certain manufacturing and supply chain constraints. Nevertheless, developing reliable first principle mathematical models for crystallization processes can be very challenging due to the complexity of the underlying phenomena, inherent to population balance models (PBMs). Therefore, a novel framework for parameter estimability for guaranteed optimal model reliability is also proposed and implemented. Two estimability methods are combined and compared: the first is based on a sequential orthogonalization of the local sensitivity matrix and the second is Sobol, a variance-based global sensitivities technic. The framework provides a systematic way to assess the quality of two nominal sets of parameters: one obtained from prior knowledge and the second obtained by simultaneous identification using global optimization. A multi-dimensional population balance model that accounts for the combined effects of different crystal growth modifiers/ impurities on the crystal size and shape distribution of needle-like crystals was used to validate the methodology. A cut-off value is identified from an incremental least square optimization procedure for both estimability methods, providing the required optimal subset of model parameters. In addition, a model-based design of experiments (MBDoE) methodology approach is also reported to determine the optimal experimental conditions yielding the most informative process data. The implemented methodology showed that, although noisy aspect ratio data were used, the eight most influential and least correlated parameters could be reliably identified out of twenty-three, leading to a crystallization model with enhanced prediction capability. A systematic model-based optimization methodology for the design of crystallization processes under the presence of multiple impurities is also investigated. Supersaturation control and impurity inclusion is combined to evaluate the effect on the product's CQAs. To this end, a morphological PBM is developed for the modelling of the cooling crystallization of pure KDP in aqueous solution, as a model system, under the presence of two competitive crystal growth modifiers/ additives: aluminum sulfate and sodium hexametaphosphate. The effect of the optimal temperature control with and without the additives on the CQAs is presented via utilizing multi-objective optimization. The results indicate that the attainable size and shape attributes, can be considerably enhanced due to advanced operation flexibility. Especially it is shown that the shape of the KDP crystals can be affected even by the presence of small quantity of additives and their morphology can be modified from needle-like to spherical, which is more favourable for processing. In addition, the multi-impurity PBM model is extended by the utilization of a high-resolution finite volume (HR-FV) scheme, instead of the standard method of moments (SMOM), in order for the full reconstruction and dynamic modelling of the crystal size and shape distribution to be enabled. The implemented methodology illustrated the capabilities of utilizing high-fidelity computational models for the investigation of crystallization processes in impure media for process and product design and optimization purposes.