Stochastic modeling of nonisothermal antisolvent crystallization processes

In this Thesis a stochastic approach to model antisolvent crystallization processes is addressed. The motivations to choice a stochastic approach instead of a population balance modeling has been developed to find a simple and an alternative way to describe the evolution of the Crystal Size Distribution (CSD), without consider complex thermodynamic and kinetic aspects of the process. An important parameter to consider in crystallization process is the shape of the CSD (in terms of variance) and the mean size of crystals in order to optimize the filtering of the final product and then increase the production. The crystallization processes considered in this Thesis are the antisolvent crystallization processes used in particular when the solute is weakly temperature-sensitive and then a second solvent, properly called antisolvent, is added in the solution favoring the crystallization of the solute. In antisolvent crystallization processes it is important the consumption of the second solvent added, in particular, optimizing the feed-rate and coupling the process in synergy with cooling crystallization in order to improve the production and the quality of the desired product. The stochastic approach used in this Thesis is based on the Fokker Plank Equation (FPE), which has allowed finding an analytical solution of the model, with some assumptions, and obtaining an analytical model able to describe the evolution of the mean size of crystals and the variance of the CSD. This analytical solution has leaded to develop an analytical relationship between the evolution in time of the first two stochastic moments of the FPE, such as mean and variance, and the manipulated variables, such as antisolvent feed-rate and temperature, obtaining as a result a map showing the asymptotic moments obtainable within a certain range of operating conditions. This Thesis also analyzes the physical-chemical aspects of the antisolvent crystallization processes, including the temperature effects, finding a strong influence onto the nucleation and growth rate of crystals due by the hydrogen bond strength between solventantisolvent molecules despite of the molecular interaction in a solvated system.The physical-chemical consideration concerning the antisolvent crystallization processes allowed to better understand the influence of the second solvent added, consequently optimizing the choice for the proper antisolvent to use with a proper feed-rate and temperature profile, minimizing the energy consumptions, in order to obtain the desired product. The stochastic model and the physical-chemical considerations have been validated with experimental data performed in a laboratory scale crystallizer. The experimental samples have been analyzed using an optical microscope and then the images taken have been manually processed in order to obtain the experimental CSDs

A Model-based Framework to Control the Crystal Size Distribution

Crystallization is an old unit operation in the industry which is widely used as a separation process due to its ability to produce highly valued chemical with high purity. Despite the long history of batch crystallization, industry still relies on rule of- thumb techniques for their crystallization processes. Thus, any method to improve the products characteristics such as size and morphology will be highly valued. Advances in robustness and accuracy of automated in situ sensors give the possibility to move towards an engineering based approach by implementing the real-time monitoring and control of the process. The research undertaken here investigates the development of an advanced framework for the operation of crystallization processes. This project builds upon the synergy among the research teams at LSU and at the University of Cagliari. The proposed methodology comprises of exploiting an advanced model to simulate the process, On-line implementation of the image-based approach within a feedback loop in a completely automated feedback fashion and implementation of model-free control technology. In situ measurement of crystals’ size distribution by using image-based technique and wavelet-fractal algorithm is implemented in a real-time environment for inferring the particles characteristics captured at different time of the experiment. This technique is becoming increasingly more attractive due to availability of high speed imaging devices and powerful computers at reasonable costs and the adaptability to real time application. The process is modelled by means of a stochastic approach. This is an alternative method to the traditional population balance which leads to a more straightforward model that can be solved analytically and obtain the CSD over time. The simplicity of the model gives the possibility to properly implement an automatic control strategy

Stochastic modeling of nonisothermal antisolvent crystallization processes

In this Thesis a stochastic approach to model antisolvent crystallization processes is addressed. The motivations to choice a stochastic approach instead of a population balance modeling has been developed to find a simple and an alternative way to describe the evolution of the Crystal Size Distribution (CSD), without consider complex thermodynamic and kinetic aspects of the process. An important parameter to consider in crystallization process is the shape of the CSD (in terms of variance) and the mean size of crystals in order to optimize the filtering of the final product and then increase the production. The crystallization processes considered in this Thesis are the antisolvent crystallization processes used in particular when the solute is weakly temperature-sensitive and then a second solvent, properly called antisolvent, is added in the solution favoring the crystallization of the solute. In antisolvent crystallization processes it is important the consumption of the second solvent added, in particular, optimizing the feed-rate and coupling the process in synergy with cooling crystallization in order to improve the production and the quality of the desired product. The stochastic approach used in this Thesis is based on the Fokker Plank Equation (FPE), which has allowed finding an analytical solution of the model, with some assumptions, and obtaining an analytical model able to describe the evolution of the mean size of crystals and the variance of the CSD. This analytical solution has leaded to develop an analytical relationship between the evolution in time of the first two stochastic moments of the FPE, such as mean and variance, and the manipulated variables, such as antisolvent feed-rate and temperature, obtaining as a result a map showing the asymptotic moments obtainable within a certain range of operating conditions. This Thesis also analyzes the physical-chemical aspects of the antisolvent crystallization processes, including the temperature effects, finding a strong influence onto the nucleation and growth rate of crystals due by the hydrogen bond strength between solventantisolvent molecules despite of the molecular interaction in a solvated system.The physical-chemical consideration concerning the antisolvent crystallization processes allowed to better understand the influence of the second solvent added, consequently optimizing the choice for the proper antisolvent to use with a proper feed-rate and temperature profile, minimizing the energy consumptions, in order to obtain the desired product. The stochastic model and the physical-chemical considerations have been validated with experimental data performed in a laboratory scale crystallizer. The experimental samples have been analyzed using an optical microscope and then the images taken have been manually processed in order to obtain the experimental CSDs

A Model-Centric Framework for Advanced Operation of Crystallization Processes

Crystallization is the main physical separation process in many chemical industries. It is an old unit operation which can separate solids of high purity from liquids, and is widely applied in the production of food, pharmaceuticals, and fine chemicals. While industries in crystallization operation quite rely on rule-of-thumb techniques to fulfill their requirement, the move towards a scientific- and technological- based approach is becoming more important as it provides a mechanism for driving crystallization processes optimally and in more depth without increasing costs. Optimal operation of industrial crystallizers is a prerequisite these days for achieving the stringent requirements of the consumer-driven manufacturing. To achieve this, a generic and flexible model centric framework is developed for the advanced operation of crystallization processes. The framework deploys the modern software environment combined with the design of a state-of-the-art 1-L crystallization laboratory facility. The emphasis is on developing an economically and practically feasible implementation which can be applied for the optimal operation of various crystallization systems by pharmaceutical industries. The key developments in the framework have occurred in three broad categories: i. Modeling: Using an advanced modeling tool is intended for accurate representation of the behavior of the physical system. This is the cornerstone of any simulation, optimization or model-based control approach. ii. Monitoring: Applying a novel image-based technique for online characterization of the particulate processes. This is a promising method for direct tracking of particle size and size distribution with high adaptability for real-time application iii. Control: Proposing numerous model-based strategies for advanced control of the crystallization system. These strategies enable us to investigate the role of model complexity on real-time control design. Furthermore, the effect of model imperfections, process uncertainty and decision variables on optimal operation of the process can be evaluated. Overall, results from this work presents a robust platform for further research in the area of crystal engineering. Most of the developments described will pave the way for future set of activities being targeted towards extending and adapting advanced modeling, monitoring and control concepts for different crystallization processes

A thermodynamic framework for the modeling and optimization of crystallization processes

Crystallization is a widely used chemical engineering separation unit operation process. Since this technique can produce high purity products it is used for the industrial production of many chemical compounds, such as pharmaceuticals, agrochemicals, and fine chemicals. The production of these products is a multi-million dollar industry. Any methods to improve the production of these products would be highly valued. Thus, the main objective of this work is to target model-based optimal strategies for crystallization operations specifically targeting crystal size and crystal size distribution (CSD). In particular, take the knowledge gained and translate it into an economically and practically feasible implementation that is utilizable by the pharmaceutical industry. To achieve this, a comprehensive crystallization modeling framework is developed. This framework predicts the CSD while taking into account temperature, seeding variables, and antisolvent feed rates. In addition, this framework takes into account the recent proliferation of predictive thermodynamic solubility models. These solubility models have the potential to greatly reduce the need for experimental data, thus, improving the crystallization model’s predictive ability. Finally, these crystallization models are implemented into the gPROMS modeling software and are used for model-based optimization. The crystallization modeling framework is developed for several different scenarios. One framework consists of a full thermodynamic crystallization model for potassium chloride. This modeling framework when combined with model-based optimization is proven to be superior to heuristic methods. Another framework, which utilizes several different predictive thermodynamic solubility models, evaluates their use to predict crystallization behavior and to determine optimal operating conditions, cooling profiles, and antisolvent feed profiles. It is shown that these models can be used to determine optimal operating conditions and cooling profiles, but they are not sufficiently accurate to be used to determine optimal antisolvent feed profiles. The last crystallization framework is developed for the non-isothermal antisolvent crystallization of sodium chloride. This framework shows that for systems whose solute solubility is relatively independent of temperature, adding temperature control as a second degree of freedom is beneficial. In particular, it allows for the production of crystal mean sizes unattainable at other temperatures, and for the joint control of particle mean size and dispersion

Modeling microalgae cell mass distributions using the Fokker-Planck equation

The modeling of the cell mass distribution for microalgae growth processes is addressed using the Fokker-Planck equation for a stochastic logistic growth model of a single cell. Relations between the proposed model and the classical Droop model used for mass-balance based modeling of the algae growth are established. The proposed model is evaluated using experimentally obtained cell mass distribution data for the microalgae Chlamydomonas reinhardtti showing a good correspondence between measurements and model predictions. The obtained model is considerably simpler in comparison to cell mass population balance models used so far to describe the temporal behavior of the cell mass distribution

Intensification of a workflow for particle engineering and crystallisation process development

Crystallisation is a fundamental aspect of chemical and pharmaceutical manufacturing to ensure high purity, bio-availability and desirable physical attributes of quality products. In this thesis, a comprehensive workflow was designed to enhance the efficiency of crystallisation process development through the utilisation of digital tools. This research aims to integrate existing knowledge in crystallisation thermodynamics and kinetics and quality by design (QbD) principles into a unified framework. To develop and test the workflow’s approach, two case studies were conducted involving the crystallisation of lamivudine and aspirin. These studies served as foundational experiments to first develop the workflow and second validate the individual components and the logical flow of the workflow. Data collected was inclusive of solubility, morphological characteristics, particle size, kinetic properties, and solid forms in a time and material-reductive way. The two case studies highlighted a need for a more intelligent experimental planning and optimisation tool, particularly when contrasted with conventional methodologies. To address this requirement, an Adaptive Bayesian Optimisation (AdBO) tool was developed and applied to the crystallisation processes of lamivudine and aspirin. This acceleration of the workflow demonstrated significant advantages when compared to traditional grid search and design of experiment (DoE) optimisation approaches. Subsequently, the generalisability of the workflow was validated by applying it to five additional active pharmaceutical ingredient (API) case studies, ibuprofen, ascorbic acid, salicylic acid, benzoic acid and D-mannitol. This evaluation, across a broader chemical scope, demonstrated the versatility and robustness of the workflows approach. In contrast to conventional industrial research and development methods, which typically operate on a scale exceeding 100 mL, consume substantial time resources, and necessitate a large workforce, our workflow was integrated into an industrial pharmaceutical facility. This integration enabled the systematic validation of the workflow across various stirring methods, crystallisation modes, and vessel sizes, ultimately leading to the design of a robust hybrid antisolvent-cooling crystallisation process. This thesis provides a comprehensive framework for the optimisation of crystallisation processes, leveraging digital tools to streamline experimentation, enhance efficiency and promote consistency. This is impactful to the wider community as the workflow and digital tools developed can seamlessly be integrated into existing chemical and pharmaceutical research to yield efficiencies. The generalisability shown by this work also allows for the expansion of similar work packages into areas outside of chemical and pharmaceutical manufacturing.Crystallisation is a fundamental aspect of chemical and pharmaceutical manufacturing to ensure high purity, bio-availability and desirable physical attributes of quality products. In this thesis, a comprehensive workflow was designed to enhance the efficiency of crystallisation process development through the utilisation of digital tools. This research aims to integrate existing knowledge in crystallisation thermodynamics and kinetics and quality by design (QbD) principles into a unified framework. To develop and test the workflow’s approach, two case studies were conducted involving the crystallisation of lamivudine and aspirin. These studies served as foundational experiments to first develop the workflow and second validate the individual components and the logical flow of the workflow. Data collected was inclusive of solubility, morphological characteristics, particle size, kinetic properties, and solid forms in a time and material-reductive way. The two case studies highlighted a need for a more intelligent experimental planning and optimisation tool, particularly when contrasted with conventional methodologies. To address this requirement, an Adaptive Bayesian Optimisation (AdBO) tool was developed and applied to the crystallisation processes of lamivudine and aspirin. This acceleration of the workflow demonstrated significant advantages when compared to traditional grid search and design of experiment (DoE) optimisation approaches. Subsequently, the generalisability of the workflow was validated by applying it to five additional active pharmaceutical ingredient (API) case studies, ibuprofen, ascorbic acid, salicylic acid, benzoic acid and D-mannitol. This evaluation, across a broader chemical scope, demonstrated the versatility and robustness of the workflows approach. In contrast to conventional industrial research and development methods, which typically operate on a scale exceeding 100 mL, consume substantial time resources, and necessitate a large workforce, our workflow was integrated into an industrial pharmaceutical facility. This integration enabled the systematic validation of the workflow across various stirring methods, crystallisation modes, and vessel sizes, ultimately leading to the design of a robust hybrid antisolvent-cooling crystallisation process. This thesis provides a comprehensive framework for the optimisation of crystallisation processes, leveraging digital tools to streamline experimentation, enhance efficiency and promote consistency. This is impactful to the wider community as the workflow and digital tools developed can seamlessly be integrated into existing chemical and pharmaceutical research to yield efficiencies. The generalisability shown by this work also allows for the expansion of similar work packages into areas outside of chemical and pharmaceutical manufacturing

Measurement, modelling, and closed-loop control of crystal shape distribution: Literature review and future perspectives

Crystal morphology is known to be of great importance to the end-use properties of crystal products, and to affect down-stream processing such as filtration and drying. However, it has been previously regarded as too challenging to achieve automatic closed-loop control. Previous work has focused on controlling the crystal size distribution, where the size of a crystal is often defined as the diameter of a sphere that has the same volume as the crystal. This paper reviews the new advances in morphological population balance models for modelling and simulating the crystal shape distribution (CShD), measuring and estimating crystal facet growth kinetics, and two- and three-dimensional imaging for on-line characterisation of the crystal morphology and CShD. A framework is presented that integrates the various components to achieve the ultimate objective of model-based closed-loop control of the CShD. The knowledge gaps and challenges that require further research are also identified

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