Population balance model-based optimal control of batch crystallisation processes for systematic crystal size distribution design

During recent years crystallisation has found applications in many chemical industries, such as pharmaceutical, petrochemical, micro-electronics and food industries. Crystallisation is a basic step for purification or separation for a large variety of organic, inorganic and pharmaceutical compounds. Most of the product qualities are directly related to the shape of the crystal size distribution (CSD). The main difficulty in batch crystallisation processes is to accomplish a uniform and reproducible CSD. On-line control during the process allows for improved crystalline product quality, shorter process times and reduction or elimination of compromised batches. The actual prediction and estimation of the shape of the distribution at the end of the batch can provide useful information for monitoring or designing the operating curve for the supersaturation controller. Model-based approaches provide consistency of the CSD, can be used for better control and also for product design by reverse engineering the process to achieve the desired CSD and shape. This research presents a novel methodology for solving the population balance equation (PBE) for the estimation of the shape of the crystal size distribution for batch crystallisation processes. The approach combines the quadrature method of moments (QMOM) and the method of characteristics (MOCH), and provides a computationally efficient technique for the reconstruction of the whole crystal size distribution. The technique was used to estimate the kinetic parameters for the size-dependent growth and secondary nucleation, for potash alum-water system using industrial pilot plant data provided by BASF, Chemical Company. The combined technique was also used to estimate the size-dependent dissolution parameters for potash alum-water system, using laboratory scale data. The QMOM-MOCH solution approach is evaluated in a model-based dynamic optimization study, with the aim to obtain the optimal temperature profiles, which drive the system in both the supersaturated and under-saturated region, to achieve desired target CSD. Using growth, dissolution and nucleation parameters the technique was used to optimise the temperature trajectories to obtain bimodal and mono-modal distributions. The technique can serve as a soft sensor for predicting the CSD, or as a computationally efficient algorithm for off-line design or on-line adaptation of operating policies based on knowledge of the full CSD data. Additionally, the PBE model was solved using the method of characteristics under the assumption of constant supersaturation. At constant supersaturation growth is the dominating phenomenon, yielding a simplified analytical expression for the prediction of the CSD. The research presents the new methodology for the systematic design of the setpoint operating curves for supersaturation controlled crystallisation processes, which produces a desired target crystal size distribution (CSD) at the end of the batch. A design parameter, was introduced as a function of the supersaturation and time, and is evaluated for supersaturation controlled processes. Based on the design parameter and the simplified analytical model, the supersaturation setpoint and batch time are determined using an optimisation approach to obtain a target distribution with a desired shape. Two additional methods are also proposed that use the seed in conjunction with the supersaturation setpoint design, and analytical CSD estimator for shaping the product CSD. The first approach designs a seed recipe as a mixture of crystals resulting for example from standard sieve analysis. In this approach the seed was introduced at the beginning of the batch. The second approach introduces the dynamic seeding concept, which allows an easily implementable methodology to achieve complex target CSDs using seed with mono-modal distribution as a process actuator. These methodologies were validated for potassium dichromate-water system. Size-dependent growth kinetic parameters for the potassium dichromate-water system were identified using as experimental setup developed at Loughborough University. The experiments presented in the thesis also illustrates the simultaneous application of in situ Process Analytical Technology (PAT) tools, such as focused beam reflectance measurement (FBRM) for nucleation detection, attenuated total reflection (ATR) UV/Vis spectroscopy for concentration monitoring, as well as the in-line use of a Mastersizer for real-time CSD measurement in the case of the potassium dichromate in water system. The approaches provide a comprehensive framework for model-based dynamic optimisation of crystallisation processes, which combines efficient numerical solution approaches of the PBE with the formulation of novel optimisation problems. The techniques presented include controlled dissolution, simultaneous optimisation of operating policies and seed recipes and dynamic seeding. Simulation and experimental evaluations of the proposed approaches demonstrate the potential of the techniques to provide significant improvement in the current state-of-the-art in crystallisation control

Detailed modelling and optmization of crystallization process

Orientador: Rubens Maciel FilhoTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia QuimicaResumo: O foco de estudo neste trabalho é a cristalização, processo bastante utilizado industrialmente, principalmente na obtenção de produtos de alto valor agregado nas indústrias farmacêuticas e de química fina. Embora seja um processo de clássica utilização, seus mecanismos, sua modelagem e o real controle de sua operação ainda requerem estudos. A tese apresenta discussões e desenvolvimentos na área de modelagem determinística detalhada do processo e sua otimização, tanto por métodos determinísticos quanto estocásticos. A modelagem é discutida detalhadamente e os desenvolvimentos presentes na literatura de métodos numéricos aplicáveis à solução do balanço de população, parte integrante da modelagem, são apresentados com enfoque nos processos de cristalização e nas principais vantagens e desvantagens. Estudos preliminares de melhoria do processo de cristalização em modo batelada operada por resfriamento indicam a necessidade de otimização da política operacional de resfriamento. Uma vez que o método determinístico de otimização de Programação Quadrática Sucessiva se apresenta ineficiente para resolução do problema de otimização, a utilização de Algoritmo Genético, um método estocástico de otimização bastante estabelecido na literatura, é avaliada, para a busca do ótimo global deste processo, em um estudo pioneiro na literatura de aplicação dessa técnica de otimização em processos de cristalização. Uma vez que o uso de Algoritmos Genéticos exige que se executem sucessivas corridas com diferentes valores para os seus parâmetros no intuito de se aumentar a probabilidade de alcance do ótimo global (ou suas cercanias), um procedimento original, geral e relativamente simples é desenvolvido e proposto para detecção do conjunto de parâmetros do algoritmo de influência significativa sobre a resposta de otimização. A metodologia proposta é aplicada a casos de estudo gerais, de complexidades diferentes e se mostra bastante útil nos estudos preliminares via Algoritmo Genético. O procedimento é então aplicado ao problema de otimização da trajetória de resfriamento a ser utilizada em um processo de cristalização em modo batelada. Os resultados obtidos na tese apontam para a dificuldade dos métodos determinísticos de otimização em lidar com problemas de alta dimensionalidade, levando a ótimos locais, enquanto os métodos evolucionários são capazes de se aproximar do ótimo global, sendo, no entanto, de lenta execução. O procedimento desenvolvido para detecção dos parâmetros significativos do Algoritmo Genético é uma contribuição relevante da tese e pode ser aplicado a qualquer problema de otimização, de qualquer complexidade e dimensionalidadeAbstract: This work is focused on crystallization, a process widely used in industry, especially for the production of high added-value particles in pharmaceutical and fine chemistry industries. Although it is a process of established utilization, its mechanisms, modeling and the real control of its operation still require research and study. This thesis presents considerations and developments on the detailed deterministic modeling area and the process optimization with both deterministic and stochastic methods. The modeling is discussed in detail and the literature developed numerical methods for the population balance solution, which is part of the modeling, are presented focusing on crystallization processes and on the main advantages and drawbacks. Preliminary studies on batch cooling crystallization processes improvement drive to the need of cooling operating policy optimization. Since the Sequential Quadratic Programming deterministic method of optimization is inefficient for the optimization problem, the use of Genetic Algorithm (GA), a stochastic optimization method well established in literature, is evaluated in the global optimum search for this process, in a pioneering literature study of GA application in crystallization processes. Since the GA requires that many runs, with different values for its parameters, are executed, in order to increase the probability of global optimum (or its neighborhood) achievement, an original, general and relatively simple procedure for the detection of the parameters set with significant influence on the optimization response is developed and proposed. The proposed methodology is applied to general case studies, with different complexities and is very useful in the preliminary studies via GA. The procedure is, then, applied to the cooling profile optimization problem in a batch cooling optimization process. The results of the study presented in this thesis indicate that the deterministic optimization methods do not deal well with high dimensionality problems, leading to achievement of local optima. The evolutionary methods are able to detect the region of the global optimum but, on the other hand, are not fast codes. The developed procedure for the significant GA parameters detection is a relevant contribution of the thesis and can be applied to any optimization problem (of any complexity and of any dimensionality)DoutoradoDesenvolvimento de Processos QuímicosDoutor em Engenharia Químic

Combining Morphological Population Balances with Face-Specific Growth Kinetics Data to Model and Predict the Crystallization Processes for Ibuprofen

A route map for modeling pharmaceutical manufacturing processes utilizing morphological population balance (MPB) is presented in terms of understanding and controlling particle shape and size for optimizing the efficiency of both the manufacturing process and final properties of the formulated drugs. This is applied to batch cooling crystallization of the pharmaceutical compound ibuprofen from supersaturated ethanolic solutions in which the MPB is combined with the known crystal morphology and associated face-specific growth kinetics (Nguyen et al. CrystEngComm 2014, 16, 4568-4586) to predict the temporal evolution of the shape and size distributions of all crystals. The MPB simulations capture the temporal evolution of the size and shape of ibuprofen crystals and their distributions at each time instance during the crystallization processes. The volume equivalent spherical diameter and crystal size distribution converted from MPB simulation are validated against the experimental studies on the 1 L scale size (Rashid et al. Chem. Eng. Res. Des. 2012, 90, 158-161), confirming the promise of this approach as a powerful simulation, optimization, and control tool for the digital design of precision pharmaceutical processes and products with the desirable properties, with potential applications in crystallization design for personalized medicines

Expanding crystal structure prediction to larger and more flexible molecules of pharmaceutical interest

The use of Crystal Structure Prediction (CSP) studies in the pharmaceutical industry is currently limited by computational cost, which scales badly with molecular size and flexibility. This thesis seeks to develop new methods that would allow to perform CSP studies on larger, more flexible pharmaceutical-like molecules. First, a full CSP workflow was successfully used to predict the crystal structure of a large flexible molecule for the 6th Blind Test and in a joint computational-experimental study of the antihelminthic drug mebendazole. These CSP studies were integrated with three previously published computational analyses of flexible pharmaceuticals and used to benchmark the development of new methods. Successively, knowledge-based conformational information retrieved from the Cambridge Structural Database (CSD) was used to facilitate the generation of candidate crystal structures of these five molecules. Millions of crystal structures were generated at a reduced computational cost, but with an equally effective coverage of the conformational search space, compared to the original CSP efforts. The importance of treating conformational flexibility when optimising search-generated crystal structures was then assessed. This led to using dispersion-corrected density functional tight-binding (DFTB-D) as an intermediate step to minimise all intra- and intermolecular degrees of freedom of several thousands of search-generated crystal structures. DFTB-D reduced the cost of the final lattice energy evaluations by providing better starting points, and results of similar quality to the original CSP studies were obtained after optimising only the intermolecular interactions with a higher quality wave-function. Finally, a CSD survey was performed to determine thresholds that can discriminate the great majority of polymorphs from duplicate determinations. These thresholds and comparison methods were implemented in a Python programme that can be used in CSP studies to perform clustering and to interpret the results more effectively. The prospects for expanding the use of CSP to pharmaceutical development are discussed

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

Population balance model-based optimal control of batch crystallisation processes for systematic crystal size distribution design

During recent years crystallisation has found applications in many chemical industries, such as pharmaceutical, petrochemical, micro-electronics and food industries. Crystallisation is a basic step for purification or separation for a large variety of organic, inorganic and pharmaceutical compounds. Most of the product qualities are directly related to the shape of the crystal size distribution (CSD). The main difficulty in batch crystallisation processes is to accomplish a uniform and reproducible CSD. On-line control during the process allows for improved crystalline product quality, shorter process times and reduction or elimination of compromised batches. The actual prediction and estimation of the shape of the distribution at the end of the batch can provide useful information for monitoring or designing the operating curve for the supersaturation controller. Model-based approaches provide consistency of the CSD, can be used for better control and also for product design by reverse engineering the process to achieve the desired CSD and shape. This research presents a novel methodology for solving the population balance equation (PBE) for the estimation of the shape of the crystal size distribution for batch crystallisation processes. The approach combines the quadrature method of moments (QMOM) and the method of characteristics (MOCH), and provides a computationally efficient technique for the reconstruction of the whole crystal size distribution. The technique was used to estimate the kinetic parameters for the size-dependent growth and secondary nucleation, for potash alum-water system using industrial pilot plant data provided by BASF, Chemical Company. The combined technique was also used to estimate the size-dependent dissolution parameters for potash alum-water system, using laboratory scale data. The QMOM-MOCH solution approach is evaluated in a model-based dynamic optimization study, with the aim to obtain the optimal temperature profiles, which drive the system in both the supersaturated and under-saturated region, to achieve desired target CSD. Using growth, dissolution and nucleation parameters the technique was used to optimise the temperature trajectories to obtain bimodal and mono-modal distributions. The technique can serve as a soft sensor for predicting the CSD, or as a computationally efficient algorithm for off-line design or on-line adaptation of operating policies based on knowledge of the full CSD data. Additionally, the PBE model was solved using the method of characteristics under the assumption of constant supersaturation. At constant supersaturation growth is the dominating phenomenon, yielding a simplified analytical expression for the prediction of the CSD. The research presents the new methodology for the systematic design of the setpoint operating curves for supersaturation controlled crystallisation processes, which produces a desired target crystal size distribution (CSD) at the end of the batch. A design parameter, was introduced as a function of the supersaturation and time, and is evaluated for supersaturation controlled processes. Based on the design parameter and the simplified analytical model, the supersaturation setpoint and batch time are determined using an optimisation approach to obtain a target distribution with a desired shape. Two additional methods are also proposed that use the seed in conjunction with the supersaturation setpoint design, and analytical CSD estimator for shaping the product CSD. The first approach designs a seed recipe as a mixture of crystals resulting for example from standard sieve analysis. In this approach the seed was introduced at the beginning of the batch. The second approach introduces the dynamic seeding concept, which allows an easily implementable methodology to achieve complex target CSDs using seed with mono-modal distribution as a process actuator. These methodologies were validated for potassium dichromate-water system. Size-dependent growth kinetic parameters for the potassium dichromate-water system were identified using as experimental setup developed at Loughborough University. The experiments presented in the thesis also illustrates the simultaneous application of in situ Process Analytical Technology (PAT) tools, such as focused beam reflectance measurement (FBRM) for nucleation detection, attenuated total reflection (ATR) UV/Vis spectroscopy for concentration monitoring, as well as the in-line use of a Mastersizer for real-time CSD measurement in the case of the potassium dichromate in water system. The approaches provide a comprehensive framework for model-based dynamic optimisation of crystallisation processes, which combines efficient numerical solution approaches of the PBE with the formulation of novel optimisation problems. The techniques presented include controlled dissolution, simultaneous optimisation of operating policies and seed recipes and dynamic seeding. Simulation and experimental evaluations of the proposed approaches demonstrate the potential of the techniques to provide significant improvement in the current state-of-the-art in crystallisation control.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Experimental kinetics studies and wavelet-based modelling of a reactive crystallisation system

This thesis has made two significant contributions to the field of reactive crystallisation. First, new data from batch cooling crystallisation and semi-batch reactive crystallisation experiments of mono-ammonium phosphate (MAP) were obtained to describe the key factors that influence crystal nucleation and growth rates, crystal size distribution (CSD), and crystal shape. The second contribution is the development of a numerical scheme for solving the population balance equations, which can be used to describe the evolution of CSD during the crystallisation process. This scheme combines the finite difference method with a wavelet method, and is the first reported application of this approach for crystallisation modelling and simulation.Experiments into the batch cooling crystallisation of MAP were conducted both with and without seed crystals. The effects of key factors such as cooling rate, initial level of supersaturation and seeding technique, including seed concentration and seed size, on the real time supersaturation, final CSD, crystal yield and crystal shape were investigated. It was found that a seed concentration of 20-30% effectively suppressed nucleation. The growth and nucleation rate were estimated by using an isothermal seeded batch approach and their parameters were calculated by non-linear optimisation techniques.The second series of experiments involved the semi-batch reactive crystallisation of MAP. Both single-feed and dual-feed systems were investigated. In the single-feed arrangement, an ammonia solution was fed into a charge of phosphoric acid. In the dual-feed system, phosphoric acid and ammonia solution were fed into a charge of saturated MAP solution. The molar ratio of the reactants, initial supersaturation, presence or absence of seed crystals, initial MAP concentration, reactants’ flow rate, feeding time and stirring speed were varied, and the effects upon the real time supersaturation, final CSD, crystal yield, crystal shape and solution temperature were measured. X-ray diffraction analysis showed that MAP can be produced in both the single-feed and dual-feed arrangements. For the single feed system, the N/P mole ratio controlled the degree of reaction and the CSD of the product. Di-ammonium phosphate (DAP) was not be observed in the single-feed system due to its high solubility. In the dual-feed system, a seeded solution with slow feed addition, moderate stirring speed and a low initial supersaturation provided the most favourable conditions for generating a desirable supersaturation profile, and thus obtaining a product with good CSD and crystal shape.A comparative numerical study was undertaken in order to evaluate the existing numerical schemes for solving the population balance equations (PBE) that describe crystallisation. Several analytical solutions to the PBE were used to benchmark the following numerical schemes: Upwind Finite Difference, Biased Upwind Finite Difference, Orthogonal Collocation with Finite Elements, and Wavelet Orthogonal Collocation. The Wavelet Finite Difference (WFD) method has been applied here for the first time for solving PBE problems. The WFD scheme was adapted to solve the batch cooling and the semi-batch reactive crystallisation models, and the solutions were validated against experimental data that we obtained.In summary, the experimental data provide an improved understanding of MAPreaction and crystallisation mechanisms. The adaptability of the WFD method has beendemonstrated validating the two crystallisation systems, and this should help extendthe application of wavelet-based solutions beyond crystallisation processes and intomore diverse areas of chemical engineering

Generation of realistic white matter substrates with controllable morphology for diffusion MRI simulations

Numerical phantoms have played a key role in the development of diffusion MRI (dMRI) techniques seeking to estimate features of the microscopic structure of tissue by providing a ground truth for simulation experiments against which we can validate and compare techniques. One common limitation of numerical phantoms which represent white matter (WM) is that they oversimplify the true complex morphology of the tissue which has been revealed through ex vivo studies. It is important to try to generate WM numerical phantoms that capture this realistic complexity in order to understand how it impacts the dMRI signal. This thesis presents work towards improving the realism of WM numerical phantoms by generating fibres mimicking natural fibre genesis. A novel phantom generator is presented which was developed over two works, resulting in Contextual Fibre Growth (ConFiG). ConFiG grows fibres one-by-one, following simple rules motivated by real axonal guidance mechanisms. These simple rules enable ConFiG to generate phantoms with tuneable microstructural features by growing fibres while attempting to meet morphological targets such as user-specified density and orientation distribution. We compare ConFiG to the state-of-the-art approach based on packing fibres together by generating phantoms in a range of fibre configurations including crossing fibre bundles and orientation dispersion. Results demonstrate that ConFiG produces phantoms with up to 20% higher densities than the state-of-the-art, particularly in complex configurations with crossing fibres. We additionally show that the microstructural morphology of ConFiG phantoms is comparable to real tissue, producing diameter and orientation distributions close to electron microscopy estimates from real tissue as well as capturing complex fibre cross sections. ConFiG is applied to investigate the intra-axonal diffusivity and probe assumptions in a family of dMRI modelling techniques based on spherical deconvolution (SD), demonstrating that the microscopic variations in fibres’ shapes affects the diffusion within axons. This leads to variations in the per-fibre signal contrary to the assumptions inherent in SD which may have a knock-on effect in popular techniques such as tractography