Detailed population balance modelling of industrial titania synthesis

This thesis presents an efficient and robust detailed population balance framework for simulating aerosol synthesis of structured particles using a stochastic method. This is developed in the context of the industrial titania (TiO2) process to enable extensive numerical characterisation of the pigmentary product. A reactor network model is used to provide a modular treatment of the reactor and account for key features, including multiple reactant injections, and tubular reaction and cooling zones. This approach simplifies the flow field in order to focus computational effort on resolving particle structure using a high-dimensional particle model and its modularity offers flexibility to investigate different configurations. Initial results are presented using a pre-defined temperature profile in the network, and the particulate product is characterised by its property distributions. Numerical performance is studied, highlighting the high computational cost of simulating strong phase-coupling, fast process rates, and broad particle size distributions. A novel hybrid particle model is developed to address these challenges. The hybrid particle model employs a univariate description of small particles and switches to a detailed particle model to resolve morphology of more complicated, aggregate particles. New simulation algorithms are presented to manage interactions between particles of each type. The hybrid model is shown to improve efficiency (resolution versus computational cost) and robustness (sensitivity to numerical parameters), while generating the same solutions and convergence behaviour as earlier models. The reactor model is extended, utilizing the superior numerical performance of the new hybrid particle model to enable inclusion of a system energy balance for more accurate study of a broad range of process conditions, and a more sophisticated particle model to resolve particle geometry. These contributions facilitate the study of particle structure and its sensitivity to reactor design and operational choices, providing insight into how operation affects characteristics of the particles and allowing direct comparison with experimental images of the pigmentary product.This research was supported by the National Research Foundation, Prime Minister's Office, Singapore under its Campus for Research Excellence and Technological Enterprise (CREATE) programme, and by Venator

Complete Reaction Cycle for Methane-to-Methanol Conversion over Cu-SSZ-13: First-Principles Calculations and Microkinetic Modeling

The steadily increasing consumption of natural gas imposes a need to facilitate the handling and distribution of the fuel, which presently is compressed or condensed. Alternatively, reduced volatility and increased tractability are achieved by converting the chemical energy of the main component, methane, into liquid methanol. Previous studies have explored direct methane-to-methanol conversion, but suitable catalysts have not yet been identified. Here, the complete reaction cycle for methane-to-methanol conversion over the Cu-SSZ-13 system is studied using density functional theory. The first step in the reaction cycle is the migration of Cu species along the zeolite framework forming the Cu pair, which is necessary for the adsorption of O2. Methane conversion occurs over the CuOOCu and CuOCu sites, consecutively, after which the system is returned to its initial structure with two separate Cu ions. A density functional theory-based kinetic model shows high activity when water is included in the reaction mechanism, for example, even at very low partial pressures of water, the kinetic model results in a turnover frequency of ∼1 at 450 K. The apparent activation energy from the kinetic model (∼1.1 eV) is close to recent measurements. However, experimental studies always observe very small amounts of methanol compared to formation of more energetically preferred products, for example, CO2. This low selectivity to methanol is not described by the current reaction mechanism as it does not consider formation of other species; however, the results suggest that selectivity, rather than inherent kinetic limitations, is an important target for improving methanol yields from humid systems. Moreover, a closed reaction cycle for the partial oxidation of methane has long been sought, and in achieving this over the Cu-SSZ-13, this study contributes one more step toward identifying a suitable catalyst for direct methane-to-methanol conversion

First-principles-informed energy span and microkinetic analysis of ethanol catalytic conversion to 1,3-butadiene on MgO

Kinetic modeling of single-step catalytic conversion of ethanol to 1,3-butadiene is necessary to inform accurate process design. This paper uses first-principles-informed energy span and microkinetic analysis to explore the reaction free energy landscapes and kinetic limitations of competing reaction pathways on a MgO (100) step-edge. Previous studies suggested mechanisms proceeding via both dehydrogenation and dehydration of ethanol, and highlighted sensitivity to conditions and catalyst composition. Here, we use the energy span concept to characterize the theoretical maximum turnover and degree of turnover frequency control for states in each reaction pathway, finding the dehydration route to be less active for 1,3-butadiene, and suggesting rate-determining states in the dehydrogenation, dehydration, and condensation steps. The influence of temperature on the relative rate contribution of each state is quantified and explained through the varying temperature sensitivity of the free energy landscape. A microkinetic model is developed to explore competition between pathways, interaction with gas-phase species, and surface coverage limitations. This suggests that the turnover may be significantly lower than predicted solely based on energetics. Turnover frequency determining states found to have high surface coverage include adsorbed ethanol and two longer, oxygenated hydrocarbons. The combined energy span and microkinetic analysis permits investigation of a complex system from two perspectives and helps elucidate conflicting observations of rate determining steps and product distribution by considering both energetic and kinetic limitations. The impact of uncertainty in the energy landscape is quantified using a correlated error model. While the range of predictions is large, the average performance and trends are similar

Copper catalysis at operando conditions - bridging the gap between single nanoparticle probing and catalyst-bed-averaging

In catalysis, nanoparticles enable chemical transformations and their structural and chemical fingerprints control activity. To develop understanding of such fingerprints, methods studying catalysts at realistic conditions have proven instrumental. Normally, these methods either probe the catalyst bed with low spatial resolution, thereby averaging out single particle characteristics, or probe an extremely small fraction only, thereby effectively ignoring most of the catalyst. Here, we bridge the gap between these two extremes by introducing highly multiplexed single particle plasmonic nanoimaging of model catalyst beds comprising 1000 nanoparticles, which are integrated in a nanoreactor platform that enables online mass spectroscopy activity measurements. Using the example of CO oxidation over Cu, we reveal how highly local spatial variations in catalyst state dynamics are responsible for contradicting information about catalyst active phase found in the literature, and identify that both surface and bulk oxidation state of a Cu nanoparticle catalyst dynamically mediate its activity

Light-Off in Plasmon-Mediated Photocatalysis

In plasmon-mediated photocatalysis it is of critical importance to differentiate light-induced catalytic reaction rate enhancement channels, which include near-field effects, direct hot carrier injection, and photothermal catalyst heating. In particular, the discrimination of photothermal and hot electron channels is experimentally challenging, and their role is under keen debate. Here we demonstrate using the example of CO oxidation over nanofabricated neat Pd and Au50Pd50 alloy catalysts, how photothermal rate enhancement differs by up to 3 orders of magnitude for the same photon flux, and how this effect is controlled solely by the position of catalyst operation along the light-off curve measured in the dark. This highlights that small fluctuations in reactor temperature or temperature gradients across a sample may dramatically impact global and local photothermal rate enhancement, respectively, and thus control both the balance between different rate enhancement mechanisms and the way strategies to efficiently distinguish between them should be devised

Nanofluidic Trapping of Faceted Colloidal Nanocrystals for Parallel Single-Particle Catalysis

Catalyst activity can depend distinctly on nano -particle size and shape. Therefore, understanding the structure sensitivity of catalytic reactions is of fundamental and technical importance. Experiments with single-particle resolution, where ensemble-averaging is eliminated, are required to study it. Here, we implement the selective trapping of individual spherical, cubic, and octahedral colloidal Au nanocrystals in 100 parallel nanofluidic channels to determine their activity for fluorescein reduction by sodium borohydride using fluorescence microscopy. As the main result, we identify distinct structure sensitivity of the rate-limiting borohydride oxidation step originating from different edge site abundance on the three particle types, as confirmed by first -principles calculations. This advertises nanofluidic reactors for the study of structure-function correlations in catalysis and identifies nanoparticle shape as a key factor in borohydride-mediated catalytic reactions

Study of industrial titania synthesis using a hybrid particle-number and detailed particle model

We apply a hybrid particle model to study synthesis of particulate titania under representative industrial conditions. The hybrid particle model employs a particle-number description for small particles, and resolves complicated particle morphology where required using a detailed particle model. This enables resolution of particle property distributions under fast process dynamics. Robustness is demonstrated in a network of reactors used to simulate the industrial process. The detailed particle model resolves properties of the particles that determine end-product quality and post-processing efficiency, including primary particle size and degree of aggregate cohesion. Sensitivity of these properties to process design choices is quantified, showing that higher temperature injections produce more sintered particles; more frequent injections narrow the geometric standard deviation of primary particle diameter; and chlorine dilution reduces particle size and size variance. Structures of a typical industrial particle are compared visually with simulated particles, illustrating similar aggregate features with slightly larger primary particles.National Research Foundation (NRF)This project is partly funded by the National Research Foundation (NRF), Prime Minister’s Office, Singapore under its Campus for Research Excellence and Technological Enterprise (CREATE) programme. The authors would also like to thank Venator for financial support

Detailed population balance modelling of TiO 2 synthesis in an industrial reactor

This paper uses a network of ideal flow reactors and a detailed population balance model to study the evolution of the size and shape distributions of pigmentary titanium dioxide, formed under industrial synthesis conditions. The industrial reactor has multiple reactant injections, a tubular working zone in which the exothermic reaction is completed, and a cooling zone. A network of continuously stirred tank reactors is used to model variation in composition around the feeds and plug flow reactors with prescribed temperature gradients are used to describe the working and cooling zones. The quality of the industrial product depends on its morphology, and this is influenced by factors including temperature and throughput. In this paper, a multivariate particle model is accommodated using a stochastic method and the particle morphology is characterised in terms of the distributions of primary and aggregate particle diameters, number of primary particles per particle and neck radii of connected primary particles. Increasing temperature or residence time is shown to produce larger particles. Qualitative similarities are highlighted between such findings and previous studies. The throughput studies are also in qualitative agreement with empirical industrial experience. There is scope for extending and improving the current model; however, it is suggested that insights of this type could be used to inform the design and operation of the industrial process.Accepted versio

First-principles-informed energy span and microkinetic analysis of ethanol catalytic conversion to 1,3-butadiene on MgO

Kinetic modeling of single-step catalytic conversion of ethanol to 1,3-butadiene is necessary to inform accurate process design. This paper uses first-principles-informed energy span and microkinetic analysis to explore the reaction free energy landscapes and kinetic limitations of competing reaction pathways on a MgO (100) step-edge. Previous studies suggested mechanisms proceeding via both dehydrogenation and dehydration of ethanol, and highlighted sensitivity to conditions and catalyst composition. Here, we use the energy span concept to characterize the theoretical maximum turnover and degree of turnover frequency control for states in each reaction pathway, finding the dehydration route to be less active for 1,3-butadiene, and suggesting rate-determining states in the dehydrogenation, dehydration, and condensation steps. The influence of temperature on the relative rate contribution of each state is quantified and explained through the varying temperature sensitivity of the free energy landscape. A microkinetic model is developed to explore competition between pathways, interaction with gas-phase species, and surface coverage limitations. This suggests that the turnover may be significantly lower than predicted solely based on energetics. Turnover frequency determining states found to have high surface coverage include adsorbed ethanol and two longer, oxygenated hydrocarbons. The combined energy span and microkinetic analysis permits investigation of a complex system from two perspectives and helps elucidate conflicting observations of rate determining steps and product distribution by considering both energetic and kinetic limitations. The impact of uncertainty in the energy landscape is quantified using a correlated error model. While the range of predictions is large, the average performance and trends are similar

Evidence-Based Dose Planning Aims and Dose Prescription in Image-Guided Brachytherapy Combined With Radiochemotherapy in Locally Advanced Cervical Cancer

The last 2 decades have witnessed the development and broad adoption of image-guided adaptive brachytherapy (IGABT) combined with radiochemotherapy in patients with locally advanced cervical cancer. A variety of brachytherapy techniques and dose/fractionation schedules have been applied, and until recently, there was no strong evidence available for preferring one approach to another. However, large volumes of data have now provided high level clinical evidence for dose-effect relations for both disease and morbidity endpoints. It is therefore now possible to apply evidence based dose planning aims and dose prescription protocols in IGABT for locally advanced cervical cancer. This review gives an overview of targets/organs-at-risk and disease/morbidity endpoints which are relevant in the context of treatment planning and dose prescription in IGABT. The dosimetric and clinical evidence is summarized to support the implementation of dose prescription protocols which include hard and soft constraints for targets and organs at risk