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Ndjaka, Ange. "THERMOPHYSICAL PROCESSES AND REACTIVE TRANSPORT MECHANISMS INDUCED BY CO2 INJECTION IN DEEP SALINE AQUIFERS". Electronic Thesis or Diss., Pau, 2022. http://www.theses.fr/2022PAUU3003.
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Le stockage du CO2 dans les aquifères salins profonds a été reconnu comme l'une des voies les plus prometteuses pour atténuer les émissions atmosphériques de CO2 et répondre ainsi aux enjeux du changement climatique. Cependant, l’injection du CO2 dans le milieu poreux perturbe considérablement son équilibre thermodynamique. La zone proche du puits d’injection est particulièrement impactée avec une forte réactivité géochimique associée à d’intenses échanges thermiques. Cela a un impact majeur sur l’injectivité du réservoir et l’intégrité du stockage. A ces effets s’ajoute une complexité supplémentaire liée à la présence de deux phases non miscibles : la saumure et le CO2. Ces effets conduisent à des processus Thermo-Hydro-Mécaniques-Chimiques (THMC) fortement couplés, dont les interprétations ne sont pas encore abouties ni formellement implémentées dans les modèles numériques.Ce travail de thèse, associant des mesures expérimentales et des modélisations numériques, porte sur l’étude du couplage entre les gradients thermiques et les processus diffusifs de transport réactif se déroulant dans les aquifères salins, notamment dans la zone proche du puits d’injection. Nous avons étudié les échanges entre une phase froide CO2 anhydre qui s’écoule dans des zones de forte perméabilité, et une phase aqueuse salée chaude piégée dans la porosité de la roche. La stratégie de l'étude commence par une approche simple en milieu libre sans flux de CO2 afin d'étudier la réactivité des solutions salines de différentes compositions chimiques et d’évaluer l'impact d'un gradient thermique sur ce réseau réactionnel.Nous avons développé une cellule expérimentale permettant de superposer 2 à 3 couches de solution de concentration et composition chimique différentes. L’analyse de la lumière diffusée par les fluctuations de non-équilibre de la concentration et de la température permet de remonter aux coefficients de diffusion des sels dans l’eau. Nos résultats sont en bon accord avec les valeurs de la littérature. Pour ce qui est de l’étude du transport réactif diffusif, l’analyse du contraste des images a permis de mettre en évidence le fait que la précipitation de minéral, par mise en contact de deux couches aqueuses de sels réactifs, s’accompagne d’une instabilité convective qui s’estompe dans le temps. La modélisation numérique des résultats expérimentaux avec PHREEQC par une approche de diffusion multi-espèce hétérogène permet de rendre compte des instabilités convectives. Différents gradients de température ont été appliqués au système réactif, tout en conservant une température moyenne de 25 °C. Les observations expérimentales et les interprétations numériques montrent que le gradient de température n'a pas d’influence significative sur le comportement du système.Ensuite, nous avons étudié numériquement le processus de dessiccation (évaporation de l’eau) à l’interface entre une saumure piégée dans la porosité de la roche et du CO2 circulant dans une structure porale drainante, simulant les conditions de l’aquifère du Dogger du bassin parisien. Un modèle couplant l’évaporation de l’eau dans le flux de CO2 et la diffusion multi-espèces hétérogène des sels prévoit l’apparition d’un assemblage minéral au niveau du front d’évaporation, principalement composé d’halite et d’anhydrite. La modélisation de ce phénomène à l’échelle du réservoir nécessite la prise en compte de la vitesse d’évaporation en fonction du taux d’injection du CO2 et de l’évolution de la porosité au niveau de l’interface.Ce travail de thèse a permis de mettre en évidence plusieurs phénomènes physico-chimiques, thermo-physiques et de transport diffusif aux interfaces de phase. Ce qui ouvre de nouvelles perspectives d’amélioration des approches numériques et de modélisation à grande échelle notamment du proche puits d’injection du CO2 et des réservoirs de stockage géologique et soutenir les futurs développements industriels et technologiques pour la transition écologiqueCO2 storage in deep saline aquifers has been recognised as one of the most promising ways to mitigate atmospheric CO2 emissions and thus respond to the challenges of climate change. However, the injection of CO2 into the porous medium considerabely disturbs its thermodynamic equilibrium. The near-well injection zone is particularly impacted with a strong geochemical reactivity associated with intense heat exchanges. This has a major impact on injectivity of the reservoir and the integrity of the storage. In addition to these effects, there is the added complexity of the presence of two immiscible phases: brine (wetting fluid) and CO2 (non-wetting fluid). These effects lead to highly coupled Thermo-Hydro-Mechanical-Chemical (THMC) processes, whose interpretations have not yet been completed nor formally implemented into the numerical models.This thesis work, combining experimental measurements and numerical modelling, focuses on the study of the coupling between the thermal gradients and the diffusive reactive transport processes taking place in the deep saline aquifers, particularly in the near-well injection zone. We studied the exchanges between a cold anhydrous CO2 phase flowing in high permeability zones, and a hot salty aqueous phase trapped in the porosity of the rock. The strategy of the study starts with a simple approach in a free medium without CO2 flow, in order to study the reactivity of saline solutions of different chemical compositions, and to evaluate the impact of a thermal gradient on this reaction network.We have developed an experimental cell that allow to superimpose 2 to 3 layers of solution of different concentration and chemical composition. The analysis of the light scattered by the non-equilibrium fluctuations of concentration and temperature allows to obtain the diffusion coefficients of salts in water. Our results are in good agreement with literature values. Regarding the study of diffusive reactive transport, the analysis of the contrast of the images allowed us to highlight the fact that the precipitation of minerals, obtained by superimposing two aqueous layers of reactive, is accompanied by a convective instability that fades with time. Numerical modelling of the experimental results with PHREEQC using a heterogeneous multicomponent diffusion approach has allowed us to account for these convective instabilities. Different temperature gradients were applied to the reactive system, while keeping a mean temperature of 25 °C. The experimental observations and numerical interpretations swhow that the temperature gradient has no significant influence on the behaviour of the system. Subsequently, we numerically studied the desiccation process (evaporation of water) at the interface between a brine trapped in the rock porosity and the CO2 flowing in a draining pore structure, simulating the conditions of the Dogger aquifer of the Paris basin. A model coupling the evaporation of water in the CO2 stream and the heterogeneous multicomponent diffusion of salts predicts the appearance of a mineral assemblage at the evaporation front, mainly composed by halite and anhydrite. Modelling this phenomenon at the reservoir scale would requires taking into account the evaporation rate as a function of the CO2 injection rate and the change in porosity at the interface.This thesis work has made it possible to highlight several physicochemical, thermophysical and diffusive transport phenomena at phase interfaces. This opens up new perspectives for improving numerical approaches and large-scale modelling, in particular of near-well injection of CO2 and geological storage reservoirs, and supports future industrial developments and technologies for the ecological transition
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Seigneur, Nicolas. "A coupled experimental, numerical and statistical homogenization approach towards an accurate feedback relationship between porosity and diffusive properties of model cementitious materials in the field of reactive transport modelling". Doctoral thesis, Universite Libre de Bruxelles, 2016. https://dipot.ulb.ac.be/dspace/bitstream/2013/237928/3/TDM.pdf.
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Au vu de leurs différentes propriétés, les matériaux cimentaires sont largement considérés dans les différents projets de gestion de déchets radioactifs. Leurs propriétés mécaniques, leurs faibles coefficients de transport ainsi que leur capacité à fixer les principaux radionucléides sont les principaux avantages qui en font un des meilleurs choix pour la conception des barrières ouvragées.Pour les études de sûreté, leur durabilité est capitale. Au cours de la vie d’un tel dépôt,via l’infiltration d’eau ou les interfaces chimiquement agressives avec les argiles, les différents matériaux vont subir des perturbations physicochimiques qui vont altérer leurs structures et potentiellement compromettre leurs fonctions de sûreté. L’étendue de ces perturbations, fondamentale pour l’étude de sûreté, est contrôlée par les propriétés de transport de ces matériaux.Pour modéliser proprement ces phénomènes, il faut pouvoir coupler les évolutions géochimiques des matériaux tout en évaluant le transport à travers ceux-ci. C’est le but de différents codes de transport réactif, qui utilisent une loi de rétroaction pour modifier les propriétés de transport lors d’une modification de microstructure. Le problème est qu’il n’existe pas de loi de rétroaction adaptée aux matériaux cimentaires, qui possèdent une structure poreuse complexe du nanomètre jusqu’à plusieurs micromètres. En général, des lois empiriques de type Archie sont utilisées. Toutefois, même l’utilisation de lois plus sophistiquées ne permet pas de reproduire sensiblement les évolutions liées à la structure porale. Cette loi de rétroaction est probablement la principale raison pour laquelle les résultats de simulation ont du mal à reproduire lesrésultats expérimentaux. Le but de cette thèse est de proposer une meilleure loi de rétroaction et de l’intégrer dans un code de transport réactif.Pour ce faire, trois approches complémentaires ont été mises en oeuvre. La première, expérimentale,consiste en la réalisation des matériaux cimentaires les plus simples possibles :des phases C-S-H pures et une pâte de ciment modèle. Ces matériaux sont ensuite caractérisés finement :leurs propriétés de transport sont évaluées et une description fine de leur microstructure est obtenue. L’approche expérimentale consiste ensuite en la dégradation (par lixiviation et carbonatation sous eau) de la pâte de ciment modèle, afin de comprendre l’impact de ces dégradations sur la microstructure et les propriétés de transport.La deuxième partie, numérique, consiste en l’obtention d’un volume élémentaire représentatif de la pâte de ciment modèle, basée sur les caractérisations expérimentales. Différentes analyses de sensibilité et de propriétés de transport permettent de comprendre les liens entre les différents paramètres et les propriétés effectives. Ensuite, l’approche numérique modélise les dégradations.Ces approches numériques démontrent pourquoi les approches empiriques fonctionnent dans certains cas, et pas dans d’autres.La dernière partie dédiée à la modélisation mathématique développe une approche d’homogénéisation statistique de la diffusion, basée sur une description du phénomène à l’échelle du pore. Cette étude met en évidence des paramètres clés qui contrôlent les propriétés effectives de diffusion.C’est ce pour quoi il est démontré que cette approche, en plus d’être très adaptée aux matériaux cimentaires, est applicable à un large spectre de microstructures. Les paramètres mis en évidences ont intrinsèquement sensibles aux propriétés de percolation et de connectivités de la structure poreuse, qui sont centrales pour la compréhension des propriétés effectives de transport ainsi que l’impact des dégradations. La finalité de la thèse consiste en le couplage de ces différentes approches et en l’incorporation de celles-ci dans un code de transport réactif. Les résultats obtenus en utilisant différentes lois de rétroaction sont comparés entre eux. L’utilisation de lois de rétroaction basée sur l’étude tri-dimensionnelle de la microstructure améliore la comparaison aux résultats expérimentaux.Doctorat en Sciences de l'ingénieur et technologie
info:eu-repo/semantics/nonPublished
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Morgado, Lopes André. "Reactive transport through nanoporous materials". Thesis, Aix-Marseille, 2018. http://www.theses.fr/2018AIXM0560/document.
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Le but de cette thèse est d’étudier le comportement des asphaltènes dans des condition de hydrotraitement, y compris les propriétés de transport et d’adsorption. La chromatographie d'exclusion stérique inverse (ISEC) ainsi que la spectroscopie d'impédance sont utilisées pour déterminer des paramètres topologiques de solides poreux d’alumine (porosité, taille de pores, tortuosité). Des coefficients de diffusion effectifs de polystyrènes de différentes tailles sont aussi étudiés par chromatographie liquide en conditions non-adsorbantes: les molécules de petites tailles pénètrent plus profondément dans le milieu poreux donc elles prennent plus de temps pour traverser la colonne, tandis que les molécules ayant une taille supérieure à la taille du pore ne sondent que la macroporosité. Avec l'utilisation des méthodes dynamique et «peak parking», il est possible de modéliser le transport des molécules de différentes tailles, et cela aidera à prédire le comportement de molécules d’une taille quelconque. Les colonnes ont été assemblées au laboratoire à partir de poudres et de monolithes d’alumine. Les caractéristiques d'adsorption des asphaltènes modèles sont déterminées et comparées avec une fraction d’asphaltènes extraite d’un brut. Un phénomène de dimérisation ainsi qu’une très forte adsorption sur la surface de l’alumine sont observés avec la molécule modèle. La méthode dynamique a été utilisée avec des colonnes courtes dans des conditions de saturation. Une influence apparente du débit dans l’importance et le mécanisme d’adsorption a pu être constatéeThis work aims to study the complex behaviors of asphaltenes within the hydrotreatment catalytic porous system including transport properties and adsorption. Inverse size-exclusion chromatography (ISEC) and impedance spectroscopy are used to determine the topological characteristics of different alumina porous solids (porosity, pore size, tortuosity). The effective diffusion coefficient of polystyrenes of different sizes was studied via chromatography in non-adsorbing conditions. Elution peaks are used to determine the effect of molecule size on the accessible pore volume and the transport properties therein: molecules of relatively small sizes penetrate further into the porous medium, thus taking more time to navigate the chromatographic setup, while larger molecules traverse much faster, through the macroporosity. The liquid chromatography technique is divided in two different methods. Both methods yield diffusion coefficient values which are modelled, predicting the behavior of molecules of any size. Columns were assembled manually from alumina powders or monoliths. A synthesized asphaltene model molecule was used and its adsorption behavior was determined and compared to an asphaltene fraction recovered from crude oil. The asphaltene model molecule shows a dimerization behavior as well as extremely strong interactions with the alumina surface. Dynamic method was attempted in short alumina columns at saturation conditions and an apparent influence of the flow rate on the extent and mechanics of adsorption was observed
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Pfeifer, Peter y Chen Hou. "Diffusion-Reaction in space-filling networks". Universitätsbibliothek Leipzig, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-184563.
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Kaganovskii, Yuri, Andrey A. Lipovskii, Emma Mogilko, Valentina Zhurikhina y Michael Rosenbluh. "Kinetics of bulk nano-clustering in silver-doped glasses during reactive hydrogen diffusion". Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-193695.
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Agliari, Elena, Raffaella Burioni, Davide Cassi y Franco M. Neri. "Autocatalytic reaction-diffusion processes in restricted geometries". Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-192966.
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Kuzovkov, Vladimir, Guntars Zvejnieks, Olaf Kortlüke y Niessen Wolfgang von. "Forced oscillations in self-oscillating surface reaction models". Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-195406.
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Kosztolowicz, Tadeusz y Katarzyna D. Lewandowska. "Subdiffusive reaction front in the enamel caries process". Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-196978.
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Starting with the equation describing subdiffusion associated with chemical reactions for one-static reactant, we show that the reaction front X f evolves in time as x f ~ t α/2 with α < 1. The equation is applied to the carious lesion which is caused by the chemical reactions of diffusing acid molecules or pure hydrogen ions with static hydroxyapatite in the tooth enamel. Comparing our theoretical results with the already published experimental ones, we conclude that in some cases the transport process of the acids in the tooth enamel appears to be subdiffusive and should be described by the subdiffusion-reaction equation with the fractional time derivative.
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Sinder, Michael, Zeev Burshtein y Joshua Pelleg. "Reaction fronts and ambipolar chemical diffusion in oxide crystals". Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-198684.
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Agliari, Elena, Raffaella Burioni, Davide Cassi y Franco M. Neri. "Autocatalytic reaction-diffusion processes in restricted geometries". Diffusion fundamentals 7 (2007) 1, S. 1-8, 2007. https://ul.qucosa.de/id/qucosa%3A14157.
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Titze, Tobias, Christian Chmelik, Dirk Enke, Roger Gläser, Jens Kullmann, Jörg Kärger, Lutz Prager y Jens Weitkamp. "Exploring diffusion and reaction in nanoporous catalysts by IR micro-imaging". Universitätsbibliothek Leipzig, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-183231.
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Kisilevich, Slava, Misha Sinder, Joshua Pelleg y Vladimir Sokolovsky. "Irreversible A + B → 0 reaction – diffusion process with initially separated reactants". Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-193402.
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Friedel, Frank, Frank Janowski, Thomas Hahn y Dirk Enke. "Transport properties of catalyst supports derived from a catalytic test reaction". Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-196501.
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Larisch, Wolfgang. "4 Coupled compartments – an analytical solution for diffusion and reaction kinetics". Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-198373.
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NASSI, Marianna. "Reactive transport of pollutants in porous media". Doctoral thesis, Università degli studi di Ferrara, 2012. http://hdl.handle.net/11392/2389259.
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Accidental or deliberate crude oil spills have been, and still continue to be, a significant source of environmental pollution, and pose a serious environmental problem, due to the possibility of air, water and soil contamination. Chlorinated volatile organic compounds (VOCs), such as 1,1-dichloroethylene (DCE) and aromatic hydrocarbons, BTEX (benzene, toluene, ethyl benzene and xylene) constitute a significant fraction of hazardous air and water pollution. Human beings are exposed to elevated levels of a wide spectrum of VOCs, many of which have been found to be toxic and potentially carcinogenic. Removal of these organic contaminants from water and wastewater has been achieved using several treatment technologies, such as advanced oxidation processes, air stripping, reverse osmosis, ultrafiltration and adsorption.
Adsorption processes can be successfully used when contaminants are not amenable to fast biological degradation. Permeable Reactive Barriers (PRB) are one of the most promising passive treatment technologies, due to their effectiveness regarding various contaminants, and their low cost compared to other in situ technologies. Typical PRB configuration consists in a permeable treatment zone placed vertically to the flow path of groundwater, which contains reactive material that immobilises or decomposes the contaminants by adsorption as the groundwater flows through it.
PRBs are installed as permanent, semi-permanent, or replaceable units. A wide variety of pollutants are degraded, precipitated, sorbed or exchanged in the reactive zone, including chlorinated solvents, heavy metals, radionuclides and other organic and inorganic species.
Conventional permeable reactive barriers for the decontamination of water are based on systems which most widely use Granular Activated Carbon (GAC).
GAC has been shown to be only slightly effective in treating water containing very soluble compounds, such as oxygenated organics, or low molecular weight compounds, such as DCE and vinyl chloride (VC). However, their use for the removal of organic contaminants in water and wastewater applications can be complicated by the presence of dissolved natural organic matter in the water stream being treated, which can decrease the removal efficiency of GAC. When activated carbon is saturated, it has to be regenerated or renewed, which is rather an expensive operation. The adsorbed molecules are then released and still have to be destroyed by thermal treatments. Moreover, this additional treatment also degrades the activated carbon adsorption properties in the long term [1]. Zero-valent iron (ZVI), which directly degrades several contaminants, appears to be ineffective too, both on irreducible compounds such as DCE and chlorobenzenes as well as on hydrocarbons. Furthermore, when ZVI is used, it causes a reduction in the permeability of the barrier due to encrustations or precipitation of minerals which derive from the reactions between the ions of the oxidised metal and the substances contained in the groundwater [1-2]. Therefore, when operating with a barrier based on metallic iron alone, the chemical reduction reaction of the reducible compounds can require from 1 to 2 days. In this case, it is only the thickness of the iron which can ensure the time necessary for completing the reactions and large quantities are required to guarantee the complete decontamination of the groundwater.
Recently, high-silica zeolites were shown to be more effective than activated carbon or ZVI in removing certain organics from water [3-4].
The selection of zeolites from among the large variety of adsorbent materials is based on their stability and efficiency properties.
To date, the adsorption mechanisms of zeolites in gas phase systems have been widely investigated. On the contrary, studies and applications on organic pollutants adsorption in microporous zeolitic materials from aqueous media have been relatively scarce. Adsorption from gas phase systems can significantly differ from that observed from the corresponding aqueous solutions, due to the highly polar nature of water molecules. In literature, it has been reported that water plays a very important role in the diffusion of hydrocarbons in the zeolite pore system. In particular, large amounts of co-adsorbed water molecules block the migration of host molecules such as alkanes and olefins, thus reducing the adsorption capacity of zeolites, especially at low adsorbate concentrations. As a consequence, water acts as a screen between the cationic sites of the zeolite and the hydrocarbon molecules (screening effect) and reduces both the sorption volume (steric effect) and the aperture of the zeolite windows (blocking effect). On the contrary, small amounts of co-adsorbed water lower the extent of specific adsorption without significant blocking effects. However, as mentioned above, this research on hydrocarbon adsorption has also mainly been focused on single components from air matrices, whereas there are few studies involving aqueous dilute solutions. Nonetheless, in most environmental applications, these pollutants are present as very dilute aqueous solution mixtures.
The work developed in the present thesis is part of a wider project whose purpose is to study the interaction and mobility of groundwater pollutants adsorbed in zeolite pores, in order to improve the efficiency of permeable reactive barriers. This project involves Ferrara and Bologna Universities with the financial support of the ENI and the scientific support of Dr. Roberto Bagatin of the research centre of Novara. Several techniques were employed such as X ray diffraction, gas chromatography, IR spectroscopy, thermal analyses, as well as computational studies.
In this thesis, combined diffractometric, thermogravimetric and gas chromatographic techniques were employed to study the adsorption process in order to: 1) investigate the adsorptive properties of these hydrophobic synthetic zeolites; 2) characterise their structure after the adsorption of selected contaminants (1-2 dichloroethane, tert-butyl methyl ether and toluene); 3) localise the organic species in the zeolite channel system; 4) probe the interactions between organic molecules and framework oxygen atoms; 5) compare the adsorption data for a mixture of these contaminants with concentrations in the ppb and ppm range; 6) characterise the kinetic of the adsorption processes.
In particular, the thermodynamic and kinetic of the adsorption processes of contaminants on hydrophobic zeolites were obtained by using complementary, batch, linear and non-linear chromatography and thermogravimetry techniques. Batch and non-linear chromatography were mainly used to measure the adsorption isotherms for the compounds of interest. The adsorption isotherm is useful in representing the capacity of a zeolite to adsorb organics from waste, and in providing description of the functional dependence of capacity on the concentration of pollutants. Experimental determination of the isotherm allows to evaluate the feasibility of adsorption for treatment, to select a zeolite, and to estimate adsorbent dosage requirements. Moreover, it is possible to evaluate the adsorption energy distribution of the process from isotherm parameters. Batch and linear chromatography, instead, were employed to investigate the kinetic of the adsorption. Kinetics deals with changes in chemical properties in time and is especially concerned with the rate of changes and plays a fundamental role in determining the proper time contact for the removal of pollutant components from wastewater. In addition, an original theoretical model able to give information regarding the kinetic and the thermodynamic constants of systems in which both reactions and adsorption processes occur simultaneously was developed. To investigate the adsorption mechanism, diffraction techniques were employed to localize the organics adsorbed into the zeolite structure. The information gathered by this latter investigation – in cooperation with the Earth Science Department UNIFE - allows to define the interactions between organic molecules and zeolite framework. Finally, adsorption on mesoporous materials was investigated. It is well known that water is contaminated by different classes of substances, and zeolites are mainly suitable for molecules with dimensions comparable to that of their pores. However, many compounds belonging to the class of emergent contaminants have large molecular dimensions, and in such cases mesoporous materials can be more efficient than zeolites. To accomplish this task MCM-41 and HMS were synthesized and characterised – this work was carried out at the ‘Institut Charles Gerhardt (ICG), Matériaux Avancés pour la Catalyse et la Santé (MACS)’ at Montpellier (France) with the supervision of Prof. Francesco di Renzo and Dr. Anne Galarneau – and then the adsorption of acid perfluorooctanoic onto these mesoporous materials was performed.
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Titze, Tobias, Christian Chmelik, Jens Kullmann, Lutz Prager, Erich Miersemann, Roger Gläser, Dirk Enke, Jens Weitkamp y Jörg Kärger. "Monitoring the interplay between diffusion and reaction during catalytic conversion in nanoporous materials". Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-198723.
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Frömberg, Daniela. "Reaction Kinetics under Anomalous Diffusion". Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2011. http://dx.doi.org/10.18452/16374.
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Die vorliegende Arbeit befasst sich mit der Verallgemeinerung von Reaktions-Diffusions-Systemen auf Subdiffusion. Die subdiffusive Dynamik auf mesoskopischer Skala wurde mittels Continuous-Time Random Walks mit breiten Wartezeitverteilungen modelliert. Die Reaktion findet auf mikroskopischer Skala, d.h. während der Wartezeiten, statt und unterliegt dem Massenwirkungsgesetz. Die resultierenden Integro-Differentialgleichungen weisen im Integralkern des Transportterms eine Abhängigkeit von der Reaktion auf. Im Falle der Degradation A->0 wurde ein allgemeiner Ausdruck für die Lösungen beliebiger Dirichlet-Randwertprobleme hergeleitet. Die Annahme, dass die Reaktion dem Massenwirkungsgesetz unterliegt, ist eine entscheidende Voraussetzung für die Existenz stationärer Profile unter Subdiffusion. Eine nichtlineare Reaktion stellt die irreversible autokatalytische Reaktion A+B->2A unter Subdiffusion dar. Es wurde ein Analogon zur Fisher-Kolmogorov-Petrovskii-Piscounov-Gleichung (FKPP) aufgestellt und die resultierenden propagierenden Fronten untersucht. Numerische Simulationen legten die Existenz zweier Regimes nahe, die sowohl mittels eines Crossover-Argumentes als auch durch analytische Berechnungen untersucht wurden. Das erste Regime ist charakterisiert durch eine Front, deren Breite und Geschwindigkeit sich mit der Zeit verringert. Das zweite, fluktuationsdominierte Regime liegt nicht im Geltungsbereich der kontinuierlichen Gleichung und weist eine stärkere Abnahme der Frontgeschwindigkeit sowie eine atomar scharf definierte Front auf. Ein anderes Szenario, bei dem eine Spezies A in ein mit immobilen B-Partikeln besetztes Medium hineindiffundiert und gemäß dem Schema A+B->(inert) reagiert, wurde ebenfalls betrachtet. Diese Anordnung wurde näherungsweise als ein Randwertproblem mit einem beweglichen Rand (Stefan-Problem) formuliert. Die analytisch gewonnenen Ergebnisse bzgl. der Position des beweglichen Randes wurden durch numerische Simulationen untermauert.The present work studies the generalization of reaction-diffusion schemes to subdiffusion. The subdiffusive dynamics was modelled by means of continuous-time random walks on a mesoscopic scale with a heavy-tailed waiting time pdf lacking the first moment. The reaction was assumed to take place on a microscopic scale, i.e. during the waiting times, obeying the mass action law. The resultant equations are of integro-differential form, and the reaction explicitly affects the transport term. The long ranged memory of the subdiffusion kernel is modified by a factor accounting for the reaction of particles during the waiting times. The degradation A->0 was considered and a general expression for the solution to arbitrary Dirichlet Boundary Value Problems was derived. For stationary solutions to exist in reaction-subdiffusion, the assumption of reactions according to classical rate kinetics is essential. As an example for a nonlinear reaction-subdiffusion system, the irreversible autocatalytic reaction A+B->2A under subdiffusion is considered. A subdiffusive analogue of the classical Fisher-Kolmogorov-Petrovskii-Piscounov (FKPP) equation was derived and the resultant propagating fronts were studied. Two different regimes were detected in numerical simulations, and were discussed using both crossover arguments and analytic calculations. The first regime is characterized by a decaying front velocity and width. The fluctuation dominated regime is not within the scope of the continuous description. The velocity of the front decays faster in time than in the continuous regime, and the front is atomically sharp. Another setup where reactants A penetrate a medium initially filled with immobile reactants B and react according to the scheme A+B->(inert) was also considered. This problem was approximately described in terms of a moving boundary problem (Stefan-problem). The theoretical predictions concerning the moving boundary were corroborated by numerical simulations.
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Stallmach, Frank y Sven Crone. "Analytical model for extrapolation of experimental NMR diffusion studies to reaction conditions for formulated catalyst particles". Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-196682.
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Sinder, Michael, Zeev Burshtein y Joshua Pelleg. "Reaction fronts and ambipolar chemical diffusion in oxide crystals". Diffusion fundamentals 24 (2015) 50, S. 1, 2015. https://ul.qucosa.de/id/qucosa%3A14569.
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Singare, Pravin U. "Ion-Isotopic exchange reaction kinetics in characterization of anion exchange resins Dowex 550A LC and Indion-820". Universitätsbibliothek Leipzig, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-184151.
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The present paper involves application of nondestructive radioactive tracer technique in characterization of Dowex 550A LC and Indion-820 anion exchange resins. The characterization study was based on kinetic of exchange reactions between inactive iodide/bromide ions on the resins with radioactive iodide/bromide ions in the solution. During iodide exchange reaction performed at a constant temperature of 40.00C, using 1.000 g of ion exchange resins and labeled iodide ion solution of concentration 0.003 mol/L, for Dowex 550A LC resin the specific reaction rate and initial rate of ion exchange was 0.271 min-1 and 0.141 mmol/min respectively, while the amount of iodide ions exchanged was 0.522 mmol, and log Kd was calculated to be 12.1. The above values calculated for Dowex 550A LC resin was higher than the respective values of 0.108, 0.330, 0.036 and 6.0 as obtained for Indion-820 resins. Similar results were obtained for the two resins during bromide exchange reactions, thereby indicating superior performance of Dowex 550A LC resin over Indion-820 resins.
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Kuzovkov, Vladimir, Guntars Zvejnieks, Olaf Kortlüke y Niessen Wolfgang von. "Forced oscillations in self-oscillating surface reaction models". Diffusion fundamentals 2 (2005) 27, S. 1-2, 2005. https://ul.qucosa.de/id/qucosa%3A14357.
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Kosztolowicz, Tadeusz y Katarzyna D. Lewandowska. "Subdiffusive reaction front in the enamel caries process". Diffusion fundamentals 2 (2005) 124, S. 1-2, 2005. https://ul.qucosa.de/id/qucosa%3A14466.
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Starting with the equation describing subdiffusion associated with chemical reactions for one-static reactant, we show that the reaction front X f evolves in time as x f ~ t α/2 with α < 1. The equation is applied to the carious lesion which is caused by the chemical reactions of diffusing acid molecules or pure hydrogen ions with static hydroxyapatite in the tooth enamel. Comparing our theoretical results with the already published experimental ones, we conclude that in some cases the transport process of the acids in the tooth enamel appears to be subdiffusive and should be described by the subdiffusion-reaction equation with the fractional time derivative.
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Al-Naji, Majd, Michael Goepel, Anca Roibu y Roger Gläser. "Reduction of p-Nitrophenol to p-Aminophenol over supported monometallic catalysts as a model reaction for mass-transfer investigations". Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-197993.
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Titze, Tobias, Christian Chmelik, Jens Kullmann, Lutz Prager, Erich Miersemann, Roger Gläser, Dirk Enke, Jens Weitkamp y Jörg Kärger. "Monitoring the interplay between diffusion and reaction during catalytic conversion in nanoporous materials: Monitoring the interplay between diffusion and reaction during catalyticconversion in nanoporous materials". Diffusion fundamentals 24 (2015) 53, S. 1, 2015. https://ul.qucosa.de/id/qucosa%3A14572.
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Larisch, Wolfgang. "4 Coupled compartments – an analytical solution for diffusion and reaction kinetics". Diffusion fundamentals 24 (2015) 32, S. 1, 2015. https://ul.qucosa.de/id/qucosa%3A13497.
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Titze, Tobias, Christian Chmelik, Dirk Enke, Roger Gläser, Jens Kullmann, Jörg Kärger, Lutz Prager y Jens Weitkamp. "Exploring diffusion and reaction in nanoporous catalysts by IR micro-imaging". Diffusion fundamentals 20 (2013) 58, S. 1-2, 2013. https://ul.qucosa.de/id/qucosa%3A13635.
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Pfeifer, Peter y Chen Hou. "Diffusion-Reaction in space-filling networks: oxygen transport in the lung". Diffusion fundamentals 16 (2011) 5, S. 1-2, 2011. https://ul.qucosa.de/id/qucosa%3A13732.
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Friedel, Frank, Frank Janowski, Thomas Hahn y Dirk Enke. "Transport properties of catalyst supports derived from a catalytic test reaction". Diffusion fundamentals 2 (2005) 92, S. 1-2, 2005. https://ul.qucosa.de/id/qucosa%3A14427.
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Wolf, Leah Michelle. "A field study of non-reactive transport behavior and evaluation of diffusion mediated processes". Thesis, The University of Arizona, 2003. http://etd.library.arizona.edu/etd/GetFileServlet?file=file:///data1/pdf/etd/azu_etd_hy0264_sip1_w.pdf&type=application/pdf.
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Kaganovskii, Yuri, Andrey A. Lipovskii, Emma Mogilko, Valentina Zhurikhina y Michael Rosenbluh. "Kinetics of bulk nano-clustering in silver-doped glasses during reactive hydrogen diffusion: Kinetics of bulk nano-clustering in silver-doped glasses duringreactive hydrogen diffusion". Diffusion fundamentals 6 (2007) 42, S. 1-2, 2007. https://ul.qucosa.de/id/qucosa%3A13168.
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Kisilevich, Slava, Misha Sinder, Joshua Pelleg y Vladimir Sokolovsky. "Irreversible A + B → 0 reaction – diffusion process with initially separated reactants: exponential temporal asymptotics". Diffusion fundamentals 6 (2007) 23, S. 1-2, 2007. https://ul.qucosa.de/id/qucosa%3A14197.
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McKinley, Michael Scott. "Higher-order boundary condition perturbation methods in transport and diffusion theory". Diss., Georgia Institute of Technology, 2000. http://hdl.handle.net/1853/16034.
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Ilas, Danut. "Coarse mesh transport theory model for heterogeneous systems". Diss., Georgia Institute of Technology, 2001. http://hdl.handle.net/1853/16089.
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Al-Naji, Majd, Michael Goepel, Anca Roibu y Roger Gläser. "Reduction of p-Nitrophenol to p-Aminophenol over supported monometallic catalysts as a model reaction for mass-transfer investigations: Reduction of p-Nitrophenol to p-Aminophenol over supportedmonometallic catalysts as a model reaction for mass-transferinvestigations". Diffusion fundamentals 24 (2015) 2, S. 1, 2015. https://ul.qucosa.de/id/qucosa%3A14515.
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Rasouli, Pejman. "On the role of multicomponent diffusion and electrochemical migration for reactive transport in porous media". Thesis, University of British Columbia, 2016. http://hdl.handle.net/2429/59956.
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In multicomponent solutions, electrostatic coupling between charged species leads to a process called “electromigration”. Neglecting electromigration results in a charge imbalance and an incomplete and unrealistic description of mass transfer. Although not commonly considered in reactive transport codes, electromigration can strongly affect mass transport processes and can explain unexpected behaviors such as uphill diffusion or isotope fractionation. Including electrostatic coupling in reactive transport codes enables simulation of problems involving mass transport by advection and diffusion, electromigration and geochemical reactions, such as electrokinetic remediation and the geobattery concept associated with buried ore bodies. There are generally two methods for coupling charge and mass continuities. The first method is based on the null-current approach which assumes negligible electric current transmission. The second method considers explicit coupling of mass and electric fluxes. In this study both methods are investigated and their implications for reactive transport are examined.
To this end, MIN3P, a fully coupled 3D reactive transport code, was extended by integrating the Nernst-Planck and Gauss-Ampère equations. The implementation of the Nernst-Planck equations was verified by inter-comparison with other existing reactive transport codes based on a set of benchmark problems. At the same time, these benchmark problems illustrate the effect of electric coupling during multicomponent diffusion and electrochemical migration.
By explicit coupling of the Nernst-Planck and Gauss-Ampère equations, MIN3P was further enhanced to simulate electrokinetic remediation and the resulting code was tested for desalination problems. In addition, scenario and sensitivity analysis were used to investigate the potential for spontaneous exsolution of gases in response to gas generation at the electrodes of electrokinetic remediation systems.
Finally, a process-based model linking surface-measureable self-potential signals to electrochemical transport and geochemical reactions associated with buried metallic bodies was developed. The enhanced code provides a reactive transport modeling framework for process-based forward modeling of self-potential signals and associated geochemical signatures of buried ore bodies and allows a quantitative investigation of the “geobattery concept”. The code was tested based on published data from a laboratory experiment involving a buried iron bar and used to evaluate the geobattery concept based on an illustrative example of a buried ore body.Applied Science, Faculty of
Earth, Ocean and Atmospheric Sciences, Department of
Graduate
36
Stallmach, Frank y Sven Crone. "Analytical model for extrapolation of experimental NMR diffusion studies to reaction conditions for formulated catalyst particles". Diffusion fundamentals 2 (2005) 105, S. 1-2, 2005. https://ul.qucosa.de/id/qucosa%3A14443.
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Gurevich, Svetlana V. "Lateral self-organization in nonlinear transport systems described by reaction diffusion equations". [S.l.] : [s.n.], 2007. http://deposit.ddb.de/cgi-bin/dokserv?idn=983706921.
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Singare, Pravin U. "Ion-Isotopic exchange reaction kinetics in characterization of anion exchange resins Dowex 550A LC and Indion-820". Diffusion fundamentals 19 (2013) 4, S. 1-21, 2013. https://ul.qucosa.de/id/qucosa%3A13706.
Texto completoResumen
The present paper involves application of nondestructive radioactive tracer technique in characterization of Dowex 550A LC and Indion-820 anion exchange resins. The characterization study was based on kinetic of exchange reactions between inactive iodide/bromide ions on the resins with radioactive iodide/bromide ions in the solution. During iodide exchange reaction performed at a constant temperature of 40.00C, using 1.000 g of ion exchange resins and labeled iodide ion solution of concentration 0.003 mol/L, for Dowex 550A LC resin the specific reaction rate and initial rate of ion exchange was 0.271 min-1 and 0.141 mmol/min respectively, while the amount of iodide ions exchanged was 0.522 mmol, and log Kd was calculated to be 12.1. The above values calculated for Dowex 550A LC resin was higher than the respective values of 0.108, 0.330, 0.036 and 6.0 as obtained for Indion-820 resins. Similar results were obtained for the two resins during bromide exchange reactions, thereby indicating superior performance of Dowex 550A LC resin over Indion-820 resins.
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Hernandez, Velazquez Hector Alonso. "Numerical stabilization for multidimensional coupled convection-diffusion-reaction equations: Applications to continuum dislocation transport". Doctoral thesis, Universite Libre de Bruxelles, 2017. https://dipot.ulb.ac.be/dspace/bitstream/2013/257833/6/contratHH.pdf.
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Partial differential equations having diffusive, convective and reactive terms appear naturally in the modeling of a large variety of processes of practical interest in several branches of science such as biology, chemistry, economics, physics, physiology and materials science. Moreover, in some instances several species or components interact with each other requiring to solve strongly coupled systems of convection-diffusion-reaction equations. Of special interest for us is the numerical treatment of the advection dominated continuum dislocation transport equations used to describe the plastic behavior of crystalline materials.Analytical solutions for such equations are extremely scarce and practically limited to linear equations with homogeneous coefficients and simple initial and boundary conditions. Therefore, resorting to numerical approximations is the most affordable and often the only viable strategy to deal with such models. However, when classical numerical methods are used to approximate the solutions of such equations, even in the simplest one dimensional case in the steady state regime for a single equation, instabilities in the form of node to node spurious oscillations are found when the convective or reactive terms dominate over the diffusive term.To address such issues, stabilization techniques have been developed over the years in order to handle such transport equations by numerical means, overcoming the stability difficulties. However, such stabilization techniques are most often suited for particular problems. For instance the Streamline Upwind Petrov-Galerkin method, to name only one of the most well-known, successfully eliminates spurious oscillations for single advection-diffusion equations when its advective form is discretized, but have been shown useless if the divergence form is used instead. Additionally, no extensive work has been carried out for systems of coupled equations. The reason for this immaturity is the lack of a maximum principle when going from a single transport equation towards systems of coupled equations.The main aim of this work is to present a stabilization technique for systems of coupled multidimensional convection-diffusion-reaction equations based on coefficient perturbations. These perturbations are optimally chosen in such a way that certain compatibility conditions analogous to a maximum principle are satisfied. Once the computed perturbations are injected in the classical Bubnov-Galerkin finite element method, they provide smooth and stable numerical approximations.Such a stabilization technique is first developed for the single one-dimensional convection-diffusion-reaction equation. Rigorous proof of its effectiveness in rendering unconditionally stable numerical approximations with respect to the space discretization is provided for the convection-diffusion case via the fulfillment of the discrete maximum principle. It is also demonstrated and confirmed by numerical assessments that the stabilized solution is consistent with the discretized partial differential equation, since it converges to the classical Bubnov-Galerkin solution if the mesh Peclet number is small enough. The corresponding proofs for the diffusion-reaction and the general convection-diffusion-reaction cases can be obtained in a similar manner. Furthermore, it is demonstrated that this stabilization technique is applicable irrespective of whether the advective or the divergence form is used for the spatial discretization, making it highly flexible and general. Subsequently the stabilization technique is extended to the one-dimensional multiple equations case by using the superposition principle, a well-known strategy used when solving non-homogeneous second order ordinary differential equations. Finally, the stabilization technique is applied to mutually perpendicular spatial dimensions in order to deal with multidimensional problems.Applications to several prototypical linear coupled systems of partial differential equations, of interest in several scientific disciplines, are presented. Subsequently the stabilization technique is applied to the continuum dislocation transport equations, involving their non-linearity, their strongly coupled character and the special boundary conditions used in this context; a combination of additional difficulties which most traditional stabilization techniques are unable to deal with. The proposed stabilization scheme has been successfully applied to these equations. Its effectiveness in stabilizing the classical Bubnov-Galerkin scheme and being consistent with the discretized partial differential equation are both demonstrated in the numerical simulations performed. Such effectiveness remains unaffected when different types of dislocation transport models with constant or variable length scales are used.These results allow envisioning the use of the developed technique for simulating systems of strongly coupled convection-diffusion-reaction equations with an affordable computational effort. In particular, the above mentioned crystal plasticity models can now be handled with reasonable computation times without the use of extraordinary computational power, but still being able to render accurate and physically meaningful numerical approximations.Doctorat en Sciences de l'ingénieur et technologie
info:eu-repo/semantics/nonPublished
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Hellander, Andreas. "Multiscale Stochastic Simulation of Reaction-Transport Processes : Applications in Molecular Systems Biology". Doctoral thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-152098.
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Quantitative descriptions of reaction kinetics formulated at the stochastic mesoscopic level are frequently used to study various aspects of regulation and control in models of cellular control systems. For this type of systems, numerical simulation offers a variety of challenges caused by the high dimensionality of the problem and the multiscale properties often displayed by the biochemical model. In this thesis I have studied several aspects of stochastic simulation of both well-stirred and spatially heterogenous systems. In the well-stirred case, a hybrid method is proposed that reduces the dimension and stiffness of a model. We also demonstrate how both a high performance implementation and a variance reduction technique based on quasi-Monte Carlo can reduce the computational cost to estimate the probability density of the system. In the spatially dependent case, the use of unstructured, tetrahedral meshes to sample realizations of the stochastic process is proposed. Using such meshes, we then extend the reaction-diffusion framework to incorporate active transport of cellular cargo in a seamless manner. Finally, two multilevel methods for spatial stochastic simulation are considered. One of them is a space-time adaptive method combining exact stochastic, approximate stochastic and macroscopic modeling levels to reduce the simualation cost. The other method blends together mesoscale and microscale simulation methods to locally increase modeling resolution.eSSENCE
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Ayodele, Segun Gideon [Verfasser]. "Lattice Boltzmann Modeling of Advection-Diffusion-Reaction Equations in Non-equilibrium Transport Processes / Segun Gideon Ayodele". Aachen : Shaker, 2013. http://d-nb.info/1050344170/34.
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Ramm, Beatrice [Verfasser] y F. Ulrich [Akademischer Betreuer] Hartl. "Self-organization and molecular transport by a biological reaction-diffusion system / Beatrice Ramm ; Betreuer: F. Ulrich Hartl". München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2020. http://d-nb.info/1227839855/34.
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ORCIL, KERVAJAN LOUISIANE. "Etude de l'influence des cinetiques d'echange sur les processus de transport dans les electrolytes". Paris 6, 1987. http://www.theses.fr/1987PA066561.
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Faurel, Michaël. "Conception et mise en place d'expériences de diffusion de l'eau et de solutés dans des milieux poreux modèles d'argiles gonflantes". Thesis, Poitiers, 2012. http://www.theses.fr/2012POIT2320/document.
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La plupart des données existantes de diffusion d'eau et de solutés sont obtenues pour des roches argileuses extrêmement complexes ou des échantillons en apparence plus simples préparés à base d'argiles gonflantes sodiques de type smectite. Ces dernières pouvant présenter des organisations très variables et encore mal comprises (phase gel-floc-suspension stable) en conditions saturées, il reste très difficile de contraindre les modèles à double milieu (eau porale ou interfoliaire) parfois avancés pour interpréter des expériences de diffusion. Un système modèle d'argiles gonflantes reflétant réellement un double milieu a pu être obtenu à partir de trois fractions granulométriques d'une vermiculite-Na. Celles-ci ne présentent pas de phase gel en conditions saturées mais des particules bien définies dont la morphologie et l'organisation ont pu être caractérisées. Un dispositif de diffusion a été développé afin d'étudier la diffusion de HDO et Br- pour ces différentes fractions en fonction de la porosité. L'avantage majeur de ce dispositif est de pouvoir préparer des échantillons par sédimentation analysables en tomographie de rayons-X afin de valider leur homogénéité organisationnelle ; hypothèse considérée dans les modélisations. Les résultats obtenus démontrent que cette nouvelle voie de préparation conduit à des échantillons plus homogènes par rapport aux méthodes classiques. Les premières perspectives quant à l'utilisation de ces doubles milieux modèles se dégagent à travers les premiers résultats de diffusion obtenus puisque leurs caractéristiques géométriques parfaitement contrôlées peuvent permettre de pondérer l'impact des différents processus de transport potentielsMost of existing data on diffusion of water and solutes were obtained either on extremely complex clayey rocks or on seemingly more simple samples prepared from sodium-saturated swelling clay minerals, namely smectites. Because these latter can exhibit in water-saturated conditions various organizations not yet fully understood (gel phase-floc-stable suspension), it is still difficult to constrain dual-porosity media modeling (pore or interlayer water) sometimes considered for interpreting results from diffusion experiments. A model system for swelling clay minerals, mimicking a true dual-porosity medium, was obtained by using three size fractions of a Na-vermiculite. These fractions do not exhibit gel-like behavior in water-saturated conditions but rather well defined particles, whose morphology and organization have been characterized. An experimental set-up was designed for the investigation of HDO and Br- diffusion in these size-fractions as a function of porosity. The main advantage of this set up is that it allows assessing for the organizational homogeneity of a sample prepared by sedimentation process through X-ray tomography measurements, an assumption considered for diffusion modeling. The obtained results showed that this new method for sample preparation leads to more homogeneous samples as compared to classical procedures. The first perspectives concerning the use of these dual-porosity model systems are drawn from the first diffusion results obtained, as the well-controlled geometrical characteristics of these model systems successfully help in balancing the contribution of the different potential transport processes
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Pöschke, Patrick. "Influence of Molecular Diffusion on the Transport of Passive Tracers in 2D Laminar Flows". Doctoral thesis, Humboldt-Universität zu Berlin, 2018. http://dx.doi.org/10.18452/19526.
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In dieser Arbeit betrachten wir das Strömungs-Diffusions-(Reaktions)-Problem für
passive Markerteilchen, die in zweidimensionalen laminaren Strömungsmustern mit
geringem thermischem Rauschen gelöst sind. Der deterministische Fluss umfasst Zellen
in Form von Quadraten oder Katzenaugen. In ihnen tritt Rotationsbewegung auf.
Einige der Strömungen bestehen aus wellenförmigen Bereichen mit gerader Vorwärtsbewegung.
Alle Systeme sind entweder periodisch oder durch Wände begrenzt. Eine
untersuchte Familie von Strömungen interpoliert kontinuierlich zwischen Reihen von
Wirbeln und Scherflüssen. Wir analysieren zahlreiche numerische Simulationen, die
bisherige theoretische Vorhersagen bestätigen und neue Phänomene offenbaren. Ohne
Rauschen sind die Teilchen in einzelnen Bestandteilen des Flusses für immer gefangen.
Durch Hinzufügen von schwachem thermischen Rauschen wird die normale Diffusion
für lange Zeiten stark verstärkt und führt zu verschiedenen Diffusionsarten für
mittlere Zeiten. Mit Continuous-Time-Random-Walk-Modellen leiten wir analytische
Ausdrücke in Übereinstimmung mit den numerischen Ergebnissen her, die je nach
Parametern, Anfangsbedingungen und Alterungszeiten von subdiffusiver bis superballistischer
anomaler Diffusion für mittlere Zeiten reichen. Wir sehen deutlich, dass
einige der früheren Vorhersagen nur für Teilchen gelten, die an der Separatrix des
Flusses starten - der einzige Fall, der in der Vergangenheit ausführlich betrachtet wurde
- und dass das System zu vollkommen anderem Verhalten in anderen Situationen
führen kann, einschließlich einem Schwingenden beim Start im Zentrum einesWirbels
nach einer gewissen Alterungszeit. Darüber hinaus enthüllen die Simulationen, dass
Teilchenreaktionen dort häufiger auftreten, wo sich die Geschwindigkeit der Strömung
stark ändert, was dazu führt, dass langsame Teilchen von schnelleren getroffen werden,
die ihnen folgen.
Die umfangreichen numerischen Simulationen, die für diese Arbeit durchgeführt
wurden, mussten jetzt durchgeführt werden, da wir die Rechenleistung dafür besitzen.In this thesis, we consider the advection-diffusion-(reaction) problem for passive tracer particles suspended in two-dimensional laminar flow patterns with small thermal noise. The deterministic flow comprises cells in the shape of either squares or cat’s eyes. Rotational motion occurs inside them. Some of the flows consist of sinusoidal regions of straight forward motion. All systems are either periodic or are bounded by walls. One examined family of flows continuously interpolates between arrays of eddies and shear flows. We analyse extensive numerical simulations, which confirm previous theoretical predictions as well as reveal new phenomena. Without noise, particles are trapped forever in single building blocks of the flow. Adding small thermal noise, leads to largely enhanced normal diffusion for long times and several kinds of diffusion for intermediate times. Using continuous time random walk models, we derive analytical expressions in accordance with numerical results, ranging from subdiffusive to superballistic anomalous diffusion for intermediate times depending on parameters, initial conditions and aging time. We clearly see, that some of the previous predictions are only true for particles starting at the separatrix of the flow - the only case considered in depth in the past - and that the system might show a vastly different behavior in other situations, including an oscillatory one, when starting in the center of an eddy after a certain aging time. Furthermore, simulations reveal that particle reactions occur more frequently at positions where the velocity of the flow changes the most, resulting in slow particles being hit by faster ones following them. The extensive numerical simulations performed for this thesis had to be done now that we have the computational means to do so. Machines are powerful tools in order to gain a deeper and more detailed insight into the dynamics of many complicated dynamical and stochastic systems.
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Ramasomanana, Fanilo Heninkaja. "Modélisation du transport réactif dans les eaux souterraines : généralisation des méthodes ELLAM : (Eulerian-Lagrangian Localized Adjoint Method)". Thesis, Strasbourg, 2012. http://www.theses.fr/2012STRAH001/document.
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Le devenir des polluants dans les sols constitue un enjeu environnemental majeur. Dans ce travail, nous apportons une contribution à quelques méthodes numériques pour la simulation de l’écoulement et du transfert de polluants en milieu poreux variablement saturés. La propagation d’un contaminant dans les milieux souterrains dépend en premier lieu des caractéristiques de l’écoulement qui le transporte. Dans la première partie de ce travail, nous présentons la méthode des éléments finis mixtes hybrides pour la résolution de l’équation de Richards. Une procédure de condensation de la masse est proposée pour éviter l’apparition d’oscillations non physiques, notamment lors de la simulation de problèmes d’infiltration dans un milieu initialement sec.Dans la deuxième partie de ce travail, la méthode ELLAM (Eulerian-Lagrangian Localized Adjoint Method) est utilisée pour la modélisation du transport réactif en milieux fortement hétérogènes. En effet, les résultats obtenus pour le transport linéaire, décrit par l’équation d’advection-dispersion, avec les ELLAM sont très encourageants. La méthode ELLAM permet (i) de s’affranchir des contraintes de discrétisations spatiale ettemporelle imposées avec les méthodes eulériennes classiques, (ii) de conserver la masse et (iii) de traiter toutes les conditions aux limites. Par ailleurs, nous proposons une nouvelle formulation des ELLAM (C_ELLAM) permettant d’éviter les oscillations numériques et de limiter la diffusion numérique générées parla formulation standard.Dans la dernière partie, le code de calcul élaboré avec la formulation C_ELLAM est utilisé pour la caractérisation de la macrodispersion dans les milieux hétérogènes. Pour ce faire, il est indispensable de disposer d’outils de simulation précis et efficaces car cette étude est basée sur une méthode Monte Carlo nécessitant la réalisation d’un très grand nombre de simulations sur des grilles de calcul de l’ordre du million de mailles. Les résultats obtenus sont comparés avec une étude antérieure basée sur le Random WalkParticle MethodThe fate of contaminants in soils is a major environmental challenge. In this work, we develop efficient and reliable numerical tools for simulation of water flow and distribution prediction of pollutants in variably saturated porous media. In the first part of this document, the mixed hybrid finite element method is presented for solving Richard’s equation. A mass lumping technique is proposed to avoid unphysical oscillations when sharp infiltration fronts are simulated. In the second part of this work, the Eulerian Lagrangian Localized Adjoint Method (ELLAM) is used for modeling reactive transport in highly heterogeneous domains. Solute transport is described mathematically by the advection-dispersion and results obtained with ELLAM are very encouraging. ELLAM allows (i)overcoming spatial and time discretizations constraints imposed by classical Eulerian method, (ii)conserving mass and (iii) treating general boundary conditions naturally in the formulation. Moreover, we introduce a new ELLAM scheme (C_ELLAM) which avoid unphysical oscillations and reduce the numerical dispersion generated by the standard formulation.In the last part of this document, the C_ELLAM scheme is used to characterize the macrodispersion of a nonreactive solute in heterogeneous domains. This study is based on Monte Carlo simulations andtherefore requires highly efficient simulators. Our results are compared with previous work using Random Walk Particle Method to solve the advection-dispersion equation
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Godongwana, Buntu. "Effect of nutrient momentum and mass transport on membrane gradostat reactor efficiency". Thesis, Cape Peninsula University of Technology, 2016. http://hdl.handle.net/20.500.11838/2149.
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Thesis submitted in fulfilment of the requirements for the degree Doctor technologiae (engineering: chemical) In the faculty of engineering at the cape peninsula university of technologySince the first uses of hollow-fiber membrane bioreactors (MBR’s) to immobilize whole cells were reported in the early 1970’s, this technology has been used in as wide ranging applications as enzyme production to bone tissue engineering. The potential of these devices in industrial applications is often diminished by the large diffusional resistances of the membranes. Currently, there are no analytical studies on the performance of the MBR which account for both convective and diffusive transport. The purpose of this study was to quantify the efficiency of a biocatalytic membrane reactor used for the production of enzymes. This was done by developing exact solutions of the concentration and velocity profiles in the different regions of the membrane bioreactor (MBR). The emphasis of this study was on the influence of radial convective flows, which have generally been neglected in previous analytical studies. The efficiency of the MBR was measured by means of the effectiveness factor. An analytical model for substrate concentration profiles in the lumen of the MBR was developed. The model was based on the solution of the Navier-Stokes equations and Darcy’s law for velocity profiles, and the convective-diffusion equation for the solute concentration profiles. The model allowed for the evaluation of the influence of both hydrodynamic and mass transfer operating parameters on the performance of the MBR. These parameters include the fraction retentate, the transmembrane pressure, the membrane hydraulic permeability, the Reynolds number, the axial and radial Peclet numbers, and the dimensions of the MBR. The significant findings on the hydrodynamic studies were on the influence of the fraction retentate. In the dead-end mode it was found that there was increased radial convective flow, and hence more solute contact with the enzymes/biofilm immobilised on the surface of the membrane. The improved solute-biofilm contact however was only limited to the entrance half of the MBR. In the closed shell mode there was uniform distribution of solute, however, radial convective flows were significantly reduced. The developed model therefore allowed for the evaluation of an optimum fraction retentate value, where both the distribution of solutes and radial convective flows could be maximised.
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Wadi, Hicham. "Géométrie globale du transport dans l'espace des phases (Systèmes à deux degrés de liberté) : application à l'étude de la réactivité chimique". Université Joseph Fourier (Grenoble), 1997. http://www.theses.fr/1997GRE10239.
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Le cadre de cette these est strictement celui des systemes hamiltoniens a deux degres de liberte, invariants par renversement du temps. Notre resultat principal est d'etre parvenus a construire des sections de poincare globalement transverses au flot. A partir de ces sections il devient possible d'analyser d'une maniere globale l'organisation geometrique des trajectoires dans l'espace des phases. Notre construction repose essentiellement sur le concept de pods (periodic orbit dividing surface) ; il s'agit de trajectoires periodiques dont la trace sur l'espace des configurations ne dessine pas de boucles. Nous montrons que ces pods generalisent aux systemes a 2d les idees de puits et de barrieres de potentiel. Bien que de multiples applications soient a priori envisageables, nous nous sommes exclusivement penches sur le cas des reactions chimiques de la forme : ab + c abc a + bc a partir de nos sections globales, nous avons developpe une methode generale pour d'ecrire et analyser la dynamique de ces reactions ; en particulier afin d'obtenir des moyennes d'observables et les probabilites de reaction. Quant au chaos de diffusion, nous avons pu en donner une interpretation totalement nouvelle (le theoreme des enroulements), mais surtout, nous avons montre qu'il n'y a pas lieu de le distinguer du chaos dit borne.
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Alshammari, Abdullah A. A. M. F. "Mathematical modelling of oxygen transport in skeletal and cardiac muscles". Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:65a34cb0-ef00-44c9-a04d-4147844c76ac.
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Understanding and characterising the diffusive transport of capillary oxygen and nutrients in striated muscles is key to assessing angiogenesis and investigating the efficacy of experimental and therapeutic interventions for numerous pathological conditions, such as chronic ischaemia. In articular, the influence of both muscle tissue and microvascular heterogeneities on capillary oxygen supply is poorly understood. The objective of this thesis is to develop mathematical and computational modelling frameworks for the purpose of extending and generalising the current use of histology in estimating the regions of tissue supplied by individual capillaries to facilitate the exploration of functional capillary oxygen supply in striated muscles. In particular, we aim to investigate the balance between local capillary supply of oxygen and oxygen demand in the presence of various anatomical and functional heterogeneities, by capturing tissue details from histological imaging and estimating or predicting regions of capillary supply. Our computational method throughout is based on a finite element framework that captures the anatomical details of tissue cross sections. In Chapter 1 we introduce the problem. In Chapter 2 we develop a theoretical model to describe oxygen transport from capillaries to uniform muscle tissues (e.g. cardiac muscle). Transport is then explored in terms of oxygen levels and capillary supply regions. In Chapter 3 we extend this modelling framework to explore the influence of the surrounding tissue by accounting for the spatial anisotropies of fibre oxygen demand and diffusivity and the heterogeneity in fibre size and shape, as exemplified by mixed muscle tissues (e.g. skeletal muscle). We additionally explore the effects of diffusion through the interstitium, facilitated--diffusion by myoglobin, and Michaelis--Menten kinetics of tissue oxygen consumption. In Chapter 4, a further extension is pursued to account for intracellular heterogeneities in mitochondrial distribution and diffusive parameters. As a demonstration of the potential of the models derived in Chapters 2--4, in Chapter 5 we simulate oxygen transport in myocardial tissue biopsies from rats with either impaired angiogenesis or impaired arteriolar perfusion. Quantitative predictions are made to help explain and support experimental measurements of cardiac performance and metabolism. In the final chapter we summarize the main results and indicate directions for further work.
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Mahfoudhi, Imed. "Problèmes inverses de sources dans des équations de transport à coefficients variables". Phd thesis, INSA de Rouen, 2013. http://tel.archives-ouvertes.fr/tel-00975168.
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Cette thèse porte sur l'étude de quelques questions liées à l'identifiabilité et l'identification d'un problème inverse non-linéaire de source. Il s'agit de l'identification d'une source ponctuelle dépendante du temps constituant le second membre d'une équation de type advection-dispersion-réaction à coefficients variables. Dans le cas monodimensionnel, la souplesse du modèle stationnaire nous a permis de développer des réponses théoriques concernant le nombre des capteurs nécessaires et leurs emplacements permettant d'identifier la source recherchée d'une façon unique. Ces résultats nous ont beaucoup aidés à définir la ligne de conduite à suivre afin d'apporter des réponses similaires pour le modèle transitoire. Quant au modèle bidimensionnel transitoire, en utilisant quelques résultats de nulle contrôlabilité frontière et des mesures de l'état sur la frontière sortie et de son flux sur la frontière entrée du domaine étudié, nous avons établi un théorème d'identifiabilité et une méthode d'identification permettant de localiser les deux coordonnées de la position de la source recherchée comme étant l'unique solution d'un système non-linéaire de deux équations, et de transformer l'identification de sa fonction de débit en la résolution d'un problème de déconvolution. La dernière partie de cette thèse discute la difficulté principale rencontrée dans ce genre de problèmes inverses à savoir la non identifiabilité d'une source dans sa forme abstraite, propose une alternative permettant de surmonter cette difficulté dans le cas particulier où le but est d'identifier le temps limite à partir duquel la source impliquée a cessé d'émettre, et donc ouvre la porte sur de nouveaux horizons.