Hydrodynamic Characterization of Physicochemical Process in Stirred Tanks and Agglomeration Reactors

A short review of the state of the art in experimental and computational fluid dynamics (CFD) characterization of micro-hydrodynamics and physicochemical processes in stirred tanks and agglomeration reactors is presented. Results of experimental and computational studies focusing on classical mixing tanks as well as other innovative reactors with various industrial applications are briefly reviewed. The hydrodynamic characterization techniques as well as the influence of the fluid dynamics on the efficiency of the physicochemical processes have been highlighted including some of the limitations of the reported modeling approach and solution strategy. Finally, the need for specialized CFD codes tailored to the specific needs of fluid-particle reactor design and optimization is advocated to advance research in this field

Multi-scale modeling and optimization for industries with formulated products

[ES] La tesis titulada "Multi-scale Modeling and optimization for Industries with Formulated Products" se centra en el desarrollo de modelos matemáticos y técnicas de optimización para este tipo de productos. Por un lado la tesis se focaliza en modelado de secadores con diferentes metodologías. Primero, se desarrolla un modelo cinético de secado de una una única gota. Luego, se desarrolla un modelo basado en mecánica de fluidos computacional (CFD) para los secadores y el cuál se ha validado a escala industrial. Finalmente, se desarrollan modelos basados en "data-driven" y modelos subrogados para reducir el coste computacional del modelo en CFD sin perder su nivel de detalle. Por otro lado, la tesis tiene una segunda parte donde se focaliza en el desarrollo de modelos de optimización matemática para el tratamiento de residuos y la revalorización del biogás

Modeling, optimization, and sensitivity analysis of a continuous multi-segment crystallizer for production of active pharmaceutical ingredients

We have investigated the simulation-based, steady-state optimization of a new type of crystallizer for the production of pharmaceuticals. The multi-segment, multi-addition plug-flow crystallizer (MSMA-PFC) offers better control over supersaturation in one dimension compared to a batch or stirred-tank crystallizer. Through use of a population balance framework, we have written the governing model equations of population balance and mass balance on the crystallizer segments. The solution of these equations was accomplished through either the method of moments or the finite volume method. The goal was to optimize the performance of the crystallizer with respect to certain quantities, such as maximizing the mean crystal size, minimizing the coefficient of variation, or minimizing the sum of the squared errors when attempting to hit a target distribution. Such optimizations are all highly nonconvex, necessitating the use of the genetic algorithm. Our results for the optimization of a process for crystallizing flufenamic acid showed improvement in crystal size over prior literature results. Through the use of a novel simultaneous design and control (SDC) methodology, we have further optimized the flowrates and crystallizer geometry in tandem.^ We have further investigated the robustness of this process and observe significant sensitivity to error in antisolvent flowrate, as well as the kinetic parameters of crystallization. We have lastly performed a parametric study on the use of the MSMA-PFC for in-situ dissolution of fine crystals back into solution. Fine crystals are a known processing difficulty in drug manufacture, thus motivating the development of a process that can eliminate them efficiently. Prior results for cooling crystallization indicated this to be possible. However, our results show little to no dissolution is used after optimizing the crystallizer, indicating the negative impact of adding pure solvent to the process (reduced concentration via dilution, and decreased residence time) outweighs the positive benefits of dissolving fines. The prior results for cooling crystallization did not possess this coupling between flowrate, residence time, and concentration, thus making fines dissolution significantly more beneficial for that process. We conclude that the success observed in hitting the target distribution has more to do with using multiple segments and having finer control over supersaturation than with the ability to go below solubility. Our results showed that excessive nucleation still overwhelms the MSMA-PFC for in-situ fines dissolution when nucleation is too high

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

Multi-objective optimization and model-based predictive control using state feedback linearization for crystallization

The ongoing Quality-by-Design paradigm shift in the pharmaceutical industry has sparked a new interest in exploring advanced process control techniques to aid the efficient manufacture of high value products. One important process in the manufacturing is crystallization, a key process in purification of active pharmaceutical ingredients (APIs). There has been little crystallization control research in the area of global input/output linearization, otherwise referred to as state-feedback linearization (SFL). The global linearization allows a nonlinear model to be linearized over the whole domain for which the model is valid and can be embedded into a model predictive controller (MPC). MPC allows the control of a process based on a model which captures the physical understanding and constraints, but a widely reported challenge with the SFL technique is the poor ability of explicitly handling the plant constraints, which is not ideal for a highly regulated production environment such as pharmaceutical manufacturing. Therefore, the first purpose of this research is to explore the use of SFL and how it can be applied to controlling batch and continuous MSMPR crystallization processes with the incorporation of plant constraints in the MPC (named SFL-Plant constraints). The contribution made from this research is the exploration of the SFL MPC technique with successful implementation of SFL-Plant constraints. The novelty in this method is that the technique builds on existing SFL-MPC frameworks to incorporate a nonlinear constraints routine which handles plant constraints. The technique is applied on numerous scenarios of batch and continuous mixed suspension mixed product removal (MSMPR) supersaturation control of paracetamol in water, both seeded and unseeded, which all show that the SFL-Plant constraints technique indeed produces feasible control over crystallization subject to constraints imposed by limitations such as heat transfer. The SFL-MPC with SFL-Plant constraints was applied to single-input single-output (SISO) and multiple-input multipleoutput (MIMO) systems, demonstrating consistent success across both schemes of control. It was also determined that the SFL-Plant constraints do increase the computational demand by 2 to 5 times that of the SFL when unconstrained. However, the difference in absolute time is not so significant, typically an MPC which acted on a system each minute required less than 5 seconds of computation time with inclusion of SFL-Plant constraints. This technique 5 presents the opportunity to use the SFL-MPC with real system constraints with little additional computation effort, where otherwise this may have not been possible. A further advancement in this research is the comparison between the SFL-MPC technique to an MPC with a data-driven model - AutoRegression model with eXogenous input (ARX) – which is widely used in industry. An ARX model was identified for batch supersaturation control using a batch crystallization model of paracetamol in isopropyl alcohol (IPA) in gPROMS Formulated Products as the plant, and an ARX model developed in an industrial software for advanced process control – PharmaMV. The ARX-MPC performance was compared with SFL-MPC performance and it was found that although the ARX-MPC performed well when controlling a process which operated around the point the ARX-MPC was initially identified, the capability of tracking the supersaturation profile deteriorated when larger setpoints were targeted. SFL-MPC, on the other hand, saw some deterioration in performance quantified through an increase in output tracking error, but remained robust at tracking a wide range of supersaturation targets, thus outperforming the ARX-MPC for trajectory tracking control. Finally, single-objective and multi-objective optimization of a batch crystallization process is investigated to build on the existing techniques. Two opportunities arose from the literature review. The first was the use of variable-time decision variables in optimization, as it appears all pre-existing crystallization optimization problems to determine the ideal crystallization temperature trajectory for maximising mean-size are constructed of piecewise-constant or piecewise-continuous temperature profiles with a fixed time step. In this research the timestep was added as a decision variable to the optimization problem for each piecewise continuous ramp in the crystallization temperature profile and the results showed that for the maximisation of mean crystal length in a 300-minute batch simulation, when using 10 temperature ramps each of variable length resulted in a 20% larger mean size than that of 10 temperature ramps, each over a fixed time length. The second opportunity was to compare the performance of global evolution based Nondominated Sorting Genetic Algorithm – II (NSGA-II) with a deterministic SQP optimization method and a further hybrid approach utilising first the NSGA-II and then the SQP algorithm. It was found that for batch crystallization optimization, it is possible for the SQP to converge a global solution, and the convergence can be guaranteed in the shortest time with little compromise using the hybrid 6 method if no information is known about the process. The NSGA-II alone required excessive time to reach a solution which is less refined. Finally, a multi-objective optimization problem is formed to assess the ability to gain insight into crystallization operation when there are multiple competing objectives such as maximising the number weighted mean size and minimizing the number weighted coefficient of variation in size. The insight gained from this is that it is more time efficient to perform single-objective optimization on each objective first and then initialize the multi-objective NSGA-II algorithm with the single-objective optimal profiles, because this results in a greatly refined solution in significantly less time than if the NSGA-II algorithm was to run without initialization, the results were approximately 20% better for both mean size and coefficient of variation in 10% of the time with initialization

Experimental and model-based analysis of twin-screw wet granulation in pharmaceutical processes

A shift from batch to continuous processing is challenging but equally rewarding for the pharmaceutical sector. This opportunity for moving beyond traditional batch processing is possible due to a change of attitude in the regulatory environment by the publication of the process analytical technology (PAT) guidance. However, in order to utilise this opportunity, detailed process understanding about the key processes in pharmaceutical manufacturing is required to turn this transformation to the continuous mode into a success. Continuous wet granulation is a crucial part of future continuous manufacturing of solid dosage forms. Continuous high shear wet granulation is performed using a twin-screw granulator (TSG) which is characterised by a modular screw profile including a sequence of different screw elements with various shapes, orientations and functions. A TSG achieves mixing and granulation by a complex interplay between the screw configuration and process settings (e.g. feed rate, screw speed, etc.) to produce granules with certain specifications in a short time. Therefore, a fundamental understanding of these complex phenomena is required to optimise and control this new technology. Analysing the twin-screw wet granulation to a satisfactory degree is only possible when sufficient information on the rheo-kinetic characteristics of the granulation mixture is available. Thus an investigation of residence time distribution (RTD), the solid-liquid mixing, and the resulting granule size distribution (GSD) evolution governed by the field conditions in the TSG contain interesting information about mixing and different granulation rate processes such as aggregation and breakage. For this purpose, a combination of experimental and mathematical techniques/approaches was applied in this work. Additionally, a single placebo formulation based on α-lactose monohydrate was granulated in the experimental studies performed to verify the hypothesis proposed in this work. The characterisation of wetted material transport and mixing inside the confined spaces of the rotating screws was performed by the experimental determination of the residence time distribution at different process conditions and screw configurations using near infrared chemical imaging. The experimental data was later compared with a conceptual model based on classical chemical engineering methods to estimate the parameters of the model and to analyse the effects of changes in number of kneading discs and their stagger angle, screw speed, material throughput and liquid-to-solid ratio (L/S) on RTD. According to this study, increased screw speed resulted in a low mean residence time mean residence time and wider RTD, i.e. more axial mixing. Increasing powder feed rate increased mean residence time by higher throughput force while increasing L/S increased mean residence time by raising the sluggishness or inertia of the material in the barrel. The material transport in the mixing zone(s) of the TSG became more plug-flow like. Thus, an increase in the number of kneading discs reduced the axial mixing in the barrel. In addition, to understand the GSD dynamics as a function of individual screw modules along the TSG barrel, the change in GSD was investigated both experimentally and mathematically. Using a TSG which allows the opening of the barrel, samples from several locations inside the TSG barrel were collected after granulation at different process conditions and screw configurations. A detailed experimental investigation was hence performed to understand the granule size and shape dynamics in the granulator. The experimental data from this study together with the residence time measurements was then used for calibrating a population balance model for each kneading disc module in the twin-screw granulator in order to obtain an improved insight into the role of the kneading discs at certain locations inside the TSG. The study established that the kneading block in the screw configuration acts as a plug-flow zone inside the granulator. It was found that a balance between the throughput force and conveying rate is required to obtain a good axial mixing inside the twin-screw granulator. Also, a high throughput can be achieved by increasing the liquid-solid ratio and screw speed. Furthermore, the study indicated that the first kneading block after wetting caused an increased aggregation rate, which was reduced after the material processing by the second kneading block. In contrast, the breakage rate in the increased successively along the length of the granulator. Such a reversion in physical phenomena indicated potential separation between the granulation regimes, which can be promising for future design and advanced control of the continuous twin-screw granulation process. In another experimental study the transport and mixing (both axial and bulk mixing of solid-liquid) was linked to the GSD of the produced granules. This study demonstrated that insufficient solid-liquid mixing due to inability of the currently used kneading discs is the reason behind the inferior performance of the TSG in terms of yield. It was shown that other factors which support mixing such as higher axial mixing at a high screw speed and a low fill ratio support an increase in the yield. However, more effort is required to explore non-conventional screw elements with modified geometries to find screws which can effectively mix the solid-liquid material. Furthermore, in order to generalise the TSG knowledge, a regime map based approach was applied. Herewith, the scale independent parameters, L/S and specific mechanical energy (SME) were correlated. It was shown that an increasing L/S strongly drives the GSD towards a larger mean granule size. However, an increasing energy input to the system can effectively be used to lower the mean granule size and also narrow the width of the size distribution. Along with this, particle-scale simulations for the characterisation of liquid distribution in the mixing zone of the granulator were performed. It was found that the agglomeration is rather a delayed process which takes place by redistribution of liquid once the excess liquid on the particle surface is transferred to the liquid bridges. Moreover, the transfer of liquid from particle surface to liquid bridges, i.e. initialisation of agglomeration, is most dominant in the intermeshing region of the kneading discs. Besides the major outcomes of this work, i.e. building fundamental knowledge on pharmaceutical twin-screw wet granulation by combining experimental and theoretical approaches to diagnose the transport, mixing and constitutive mechanisms, several gaps and potential research needs were identified as well. As the regulators have opened up to increasingly rely on the science- and risk-based holistic development of pharmaceutical processes and products for commercialisation, the opportunity as well as responsibility lies with academic and industrial partners to develop a systematic framework and scientific approach to utilise this opportunity efficiently

Conceptualisation of an Efficient Particle-Based Simulation of a Twin-Screw Granulator

Discrete Element Method (DEM) simulations have the potential to provide particle-scale understanding of twin-screw granulators. This is difficult to obtain experimentally because of the closed, tightly confined geometry. An essential prerequisite for successful DEM modelling of a twin-screw granulator is making the simulations tractable, i.e., reducing the significant computational cost while retaining the key physics. Four methods are evaluated in this paper to achieve this goal: (i) develop reduced-scale periodic simulations to reduce the number of particles; (ii) further reduce this number by scaling particle sizes appropriately; (iii) adopt an adhesive, elasto-plastic contact model to capture the effect of the liquid binder rather than fluid coupling; (iv) identify the subset of model parameters that are influential for calibration. All DEM simulations considered a GEA ConsiGma™ 1 twin-screw granulator with a 60° rearward configuration for kneading elements. Periodic simulations yielded similar results to a full-scale simulation at significantly reduced computational cost. If the level of cohesion in the contact model is calibrated using laboratory testing, valid results can be obtained without fluid coupling. Friction between granules and the internal surfaces of the granulator is a very influential parameter because the response of this system is dominated by interactions with the geometry