Mélanger un oxyde de gallium avec une zéolithe H-ZSM-5 donne les mêmes résultats catalytiques en craquage du n-hexane, déshydrogénation du cyclohexane et en aromatisation du propane qu'un catalyseur préparer par échange cationique avec un sel de gallium. En fait, le véritable catalyseur est synthétisé lors du prétraitement sous hydrogène pendant lequel le suboxyde de gallium (Ga2O) issu de la réduction de Ga2O3 réagit avec les sites de Brønsted de la zéolithe pour donner des hydrures de gallium. La réaction de déshydrogénation des alcanes fait intervenir un site catalytique bifonctionnel composé d'un site de Lewis du Ga et d'un site basique généré par l'oxygène de la charpente zéolithique. L'activation du propane se produit sur un hydrure de gallium via un mécanisme de type alkyle. Les aluminosilicates dopés avec Ga sont plus performants que les gallosilicates, ce qui signifie que les espèces de gallium sont plus actives en extra-réseau que dans le réseau de la zéolithe.Le coke généré lors de l'aromatisation du propane est très polyaromatique avec plus de quinze noyaux benzéniques, localisé dans les micropores il s'avère très toxique. La création de mésopores intracristallins sans modifier les propriétés acides de la zéolithe (nombre et force des sites acides) est possible par un traitement alcalin. Leur présence permet de limiter les réactions de transfert d'hydrogène mais est peu efficace pour contrôler la croissance du coke, les mésopores sont mêmes négatifs pour la réaction de déshydrogénation rendant les catalyseurs bifonctionnels hiérarchisés inefficaces en aromatisation du propane ; l'étape cinétiquement limitante pour cette réaction étant la déshydrogénation. / The mixing Ga2O3 with the H-ZSM-5 zeolite yields to the same catalytic performance in n-hexane cracking, cyclohexane dehydrogenation and propane aromatization than a bifunctional catalyst prepared by cationic exchange. The real catalyst appears upon hydrogen pretreatment in which gallium (Ga2O) suboxide that results from Ga2O3 reduction, reacts with the zeolite Brønsted sites to yield to gallium hydrides.The dehydrogenation reaction of alkanes involves a bifunctional catalytic site constituted of a Lewis site (Ga species) and basic site (an oxygen of the zeolite framework). The aluminosilicate catalysts loaded with Ga are more efficient than the gallosilicate catalysts, therefore extraframework gallium species is more active than the framework gallium species.The coke formed during the propane aromatization is very polyaromatic with more than fifteen benzenic rings, is very toxic. The creation of intracrystalline mesopores by alkaline treatment.preserves the acidic properties of the zeolite (number and strength of acidic sites). The mesopores allow limiting the hydrogen transfer reactions but is not very effective for impeding the growth of the coke, the presence of mesopores are even negative for the dehydrogenation reaction making inefficient the hierarchical bifunctional catalysts in propane aromatization; the kinetically limiting step for this reaction being dehydrogenation.

Porous media, including soil, catalysts, rocks, and organic tissue, are ubiquitous in nature, acting as complex environments through which heat, ions, and chemicals travel. Diffusion, often coupled to interfacial reactions, constitutes a fundamental transport process in porous media. It plays an important role in the transport of fertilizer and contaminants in soil, heat conduction in insulators, and natural phenomena such as geological rock transformations and biological signaling and patterning. This thesis aims to enable a deeper understanding of reaction-diffusion processes in porous media by developing a flexible and computationally efficient numerical modeling and simulation workflow. Numerical modeling is required whenever the problem is too complex for mechanistic insight by quantitative experiments or analytical theory. Reaction-diffusion processes in porous media are such a complex problem, as transport is coupled to the intricate pore geometry. In addition, they involve different scales, from microscale tortuous diffusion pathways and local reactions to macroscale gradients, requiring models that resolve multiple scales. Multiscale modeling is, however, challenging due to its large memory requirement and computational cost. In addition, realistic porous media geometries, as can be derived from microscopy images or µCTs, are not parametrizable, requiring algorithmic representation. We address these issues by developing a scalable, multi-GPU accelerated numerical simulation pipeline that enables memory-efficient multiscale modeling of reaction-diffusion processes in realistic, image-based geometries. This pipeline takes volumetric images as input, from which it derives implicit geometry representations using the level-set method. The diffusion domain is discretized in a geometry-adapted, memory-efficient way using distributed sparse block grids. Reaction-diffusion PDEs are solved in the strong form using the finite difference method with scalable multi-GPU acceleration, enabling the simulation in large, highly resolved 3D samples. We demonstrate the versatility of the present pipeline by simulating reaction-diffusion processes in the image-derived 3D geometries of four applications: fertilizer diffusion in soil, heat conduction with surface dissipation in reticulate porous ceramics, fluid-mediated mineral replacement in rocks, and morphogen gradient formation in the extracellular space of a gastrulating zebrafish embryo. The former two are used to benchmark the performance of our pipeline, whereas the latter two address real-world problems from geology and biology, respectively. The geological problem considers a process called dolomitization, which converts calcite into dolomite. Determining the geophysical characteristics of the earth's most abundant rocks, dolomitization plays an important role in engineering and geology. Predicting dolomitization is hampered by the extreme scales involved, as mountain-scale dolomite is produced by ion-scale reactions over millions of years. Using the presented pipeline, we derive rock geometries from µCTs and simulate dolomitization as an inhomogeneous reaction-diffusion process with moving reaction fronts and phase-dependent diffusion. The simulation results show that reaction and diffusion are not sufficient to explain the reaction-front roughness observed experimentally, implying that other processes, such as advection, porosity fingering, or sub-resolution geometric features, such as microcracks in the rock, play an important role in dolomitization. The biological problem, which constitutes the main application of this thesis, is the formation of morphogen gradients during embryonic development. This is a particularly complex problem influenced by several factors, such as dynamically changing tissue geometries, localized sources and sinks, and interaction with molecules of the extracellular matrix (e.g., HSPG). The abundance of factors involved and the coupling between them makes it difficult to quantify how they modulate the gradient individually and collectively. We use the present pipeline to reconstruct realistic extracellular space (ECS) geometries of a zebrafish embryo from a light-sheet microscopy video. In these geometries, we simulate the gradient formation of the morphogen Fgf8a, showing for the first time in realistic embryo geometries that a source-diffusion-degradation mechanism with HSPG binding is sufficient for the spontaneous formation and maintenance of robust long-range morphogen gradients. We further test gradient sensitivity against different source, sink, and HSPG-binding rates and show that the gradient becomes distorted when ECS volume or connectivity in the model changes, demonstrating the importance of considering realistic embryo geometries. In summary, this thesis shows that modeling highly resolved, realistic 3D geometries is computationally feasible using geometry-adapted sparse grids, achieving an 18-fold reduction in memory requirements for the zebrafish model compared to a dense-grid implementation. Multi-CPU/GPU acceleration enables pore-scale simulation of large systems. The pipeline developed in this thesis is fully open-source and versatile, as demonstrated by its application to different kinds of porous media, and we anticipate its future application to other reaction-diffusion problems in porous media, in particular from biology.

Solid oxide fuel cells (SOFCs) are solid-state ceramic cells, typically operating between 1073 K and 1273 K. Because of high operating temperature, SOFCs are mostly applicable in stationary power generation. Among various configurations in which SOFCs exist, the planar configuration of solid oxide fuel cell (SOFC) has the potential to offer high power density due to shorter current path. Moreover, the planar configuration of SOFC is simple to stack and closely resemble the stacking arrangement of polymer electrolyte membrane (PEM) fuel cells. However, due to high operating temperature, there are problems associated with the development and commercialization of planar SOFCs, such as requirement of high temperature gas seals, internal stresses in cell components, and high material and manufacturing costs. Mathematical modeling is an essential tool for the advancement of SOFC technology. Mathematical models can help in gaining insights on the processes occurring inside the fuel cell, and can also aid in the design and optimization of fuel cells by examining the effect of various operating and design conditions on performance. A multi-component and multi-dimensional mathematical model of SOFCs has been developed in this thesis research. One of the novelties of the present model is its treatment of electrodes. An electrode in the present model is treated as two distinct layers referred to as the backing layer and the reaction zone layer. Reaction zone layers are thin layers in the vicinity of the electrolyte layer where electrochemical reactions occur to produce oxide ions, electrons and water vapor. The other important feature of the present model is its flexibility in fuel choice, which implies not only pure hydrogen but also any reformate composition can be used as a fuel. The modified Stefan-Maxwell equations incorporating Knudsen diffusion are used to model multi-component diffusion in the porous backing and reaction zone layers. The coupled governing equations of species, charge and energy along with the constitutive equations in different layers of the cell are solved for numerical solution using the finite volume method and developed code written in the computer language of C++. In addition, the developed numerical model is validated with various experimental data sets published in the open literature. Moreover, it is verified that the electrode in an SOFC can be treated as two distinct layers referred to as the backing layer and the reaction zone layer. The numerical model not only predicts SOFC performance at different operating and design conditions but also provides insight on the phenomena occurring within the fuel cell. In an anode-supported SOFC, the ohmic overpotential is the single largest contributor to the cell potential loss. Also, the cathode and electrolyte overpotentials are not negligible even though their thicknesses are negligible relative to the anode thickness. Moreover, methane reforming and water-gas shift reactions aid in significantly reducing the anode concentration overpotential in the thick anode of an anode-supported SOFC. A worthwhile comparison of performance between anode-supported and self-supported SOFCs reveals that anode-supported design of SOFCs is the potential design for operating at reduced temperatures. A parametric study has also been carried out to investigate the effect of various key operating and design parameters on the performance of an anode-supported SOFC. Reducing the operating temperature below 1073 K results in a significant drop in the performance of an anode-supported SOFC; hence ionic conductivity of the ion-conducting particles in the reaction zone layers and electrolyte needs to be enhanced to operate anode-supported SOFCs below 1073 K. Further, increasing the anode reaction zone layer beyond certain thickness has no significant effect on the performance of an anode-supported SOFC. Moreover, there is a spatial limitation to the transport of oxide ions in the reaction zone layer, thereby reflecting the influence of reaction zone thickness on cell performance.

Solid oxide fuel cells (SOFCs) are solid-state ceramic cells, typically operating between 1073 K and 1273 K. Because of high operating temperature, SOFCs are mostly applicable in stationary power generation. Among various configurations in which SOFCs exist, the planar configuration of solid oxide fuel cell (SOFC) has the potential to offer high power density due to shorter current path. Moreover, the planar configuration of SOFC is simple to stack and closely resemble the stacking arrangement of polymer electrolyte membrane (PEM) fuel cells. However, due to high operating temperature, there are problems associated with the development and commercialization of planar SOFCs, such as requirement of high temperature gas seals, internal stresses in cell components, and high material and manufacturing costs. Mathematical modeling is an essential tool for the advancement of SOFC technology. Mathematical models can help in gaining insights on the processes occurring inside the fuel cell, and can also aid in the design and optimization of fuel cells by examining the effect of various operating and design conditions on performance. A multi-component and multi-dimensional mathematical model of SOFCs has been developed in this thesis research. One of the novelties of the present model is its treatment of electrodes. An electrode in the present model is treated as two distinct layers referred to as the backing layer and the reaction zone layer. Reaction zone layers are thin layers in the vicinity of the electrolyte layer where electrochemical reactions occur to produce oxide ions, electrons and water vapor. The other important feature of the present model is its flexibility in fuel choice, which implies not only pure hydrogen but also any reformate composition can be used as a fuel. The modified Stefan-Maxwell equations incorporating Knudsen diffusion are used to model multi-component diffusion in the porous backing and reaction zone layers. The coupled governing equations of species, charge and energy along with the constitutive equations in different layers of the cell are solved for numerical solution using the finite volume method and developed code written in the computer language of C++. In addition, the developed numerical model is validated with various experimental data sets published in the open literature. Moreover, it is verified that the electrode in an SOFC can be treated as two distinct layers referred to as the backing layer and the reaction zone layer. The numerical model not only predicts SOFC performance at different operating and design conditions but also provides insight on the phenomena occurring within the fuel cell. In an anode-supported SOFC, the ohmic overpotential is the single largest contributor to the cell potential loss. Also, the cathode and electrolyte overpotentials are not negligible even though their thicknesses are negligible relative to the anode thickness. Moreover, methane reforming and water-gas shift reactions aid in significantly reducing the anode concentration overpotential in the thick anode of an anode-supported SOFC. A worthwhile comparison of performance between anode-supported and self-supported SOFCs reveals that anode-supported design of SOFCs is the potential design for operating at reduced temperatures. A parametric study has also been carried out to investigate the effect of various key operating and design parameters on the performance of an anode-supported SOFC. Reducing the operating temperature below 1073 K results in a significant drop in the performance of an anode-supported SOFC; hence ionic conductivity of the ion-conducting particles in the reaction zone layers and electrolyte needs to be enhanced to operate anode-supported SOFCs below 1073 K. Further, increasing the anode reaction zone layer beyond certain thickness has no significant effect on the performance of an anode-supported SOFC. Moreover, there is a spatial limitation to the transport of oxide ions in the reaction zone layer, thereby reflecting the influence of reaction zone thickness on cell performance.