Understanding the physics of water evaporation from saline porous media is important in many processes such as soil salinity, terrestrial ecosystem functioning, vegetation and crop production, biological activities in vadose zone, and CO2 sequestration. Precipitation of salt is one of the possible outcomes of the evaporation process from saline porous media which may either enhance or interrupt the desired process depending on the localization and pattern of the precipitated salt. In the present study X-ray micro tomography was used to study the 3D dynamics and patterns of salt deposition in drying porous media under different boundary conditions and the effects of salt concentration, particle size distribution and shape of grains on the precipitation patterns and dynamics at pore-scale have been investigated. Evaporation process from porous media involves preferential invasion of large pores on the surface while the fine pores remain saturated serving as the evaporation sites to supply the evaporative demand. This results in increasing salt concentration in fine pores during evaporation. Precipitation starts when salt concentration exceeds the solubility limit in the preferential evaporation sites. At the early stages, the precipitation rate increases with time until all evaporation sites at the surface reach the solubility limit and turn into the precipitation sites. This is followed by a constant rate of precipitation proportional to the evaporation rate. We show that the formation of salt crust at the surface does not immediately interrupt the evaporation process due to the porous nature of the precipitated salt investigated using the scanning electron microscopy. Also, our results confirmed the formation of discrete efflorescence at the surface of porous media due to the presence of pores with different sizes. Distribution of these fine pores on the surface directly influences the patterns of salt precipitation and thickness of the salt crust such that in the media with more fine pores, precipitated salt forms a thinner crust as the solute transferred to the surface is distributed among more evaporation sites. In contrast, in the media with fewer evaporation sites at the surface the salt crust will be more discrete but thicker. A simple equation is also proposed to estimate the evolution if the thickness of the salt crust on the surface of porous media. Our results provide new insights regarding the physics of salt precipitation and its complex dynamics in porous media during evaporation.

Up-to-date methods of numerical modelling of random fields were applied to investigate some features of solute transport in saturated porous media with stochastic hydraulic conductivity. The paper describes numerical experiments which were performed and presents the first results.

La thèse concerne trois problématiques indépendantes : le transport dissipatif dans des milieux hétérogènes; échange de masse entre un réservoir de gaz et aquifère ; ségrégation compositionnelle. Le point commun entre les problèmes traités sont les processus irréversibles de redistribution de la composition chimique. Le premier chapitre est consacré à la déduction, en accord avec les principes de la thermodynamique, d’un modèle généralisé de transport simultané de matière et de chaleur. Le chapitre 2 est consacré à l’étude de diffusion multi-compositionnelle dans un milieu hétérogène. Cette étude vise une application aux phénomènes de transport dans les réservoirs des hydrocarbures qui, d’une part, sont le siège de divers des processus de transport (plusieurs composants + chaleur) en interaction (processus croisés au sens d’Onsager) et, d’autre part, sont anisotropes pour les processus de transport étudiés. Le chapitre 3 est consacré à l’étude du processus de balayage d’un réservoir par une nappe aquifère. Le chapitre 4 est consacré au développement d’un code « éléments finis » conçu pour résoudre le même problème que dans le chapitre 3, mais dans une approche moins idéalisée. Le chapitre 5 est consacré à l’étude de la convection forcée dans un réservoir avec des champs de gravité et de température non colinéaires. Cette convection est une des composantes du processus de séparation thermo-gravitationnelle des espèces chimiques qui peut avoir lieu dans les réservoirs souterrains / The thesis concerns three independent subject areas: the dissipative transport in heterogeneous geological media; a transport problem in an underground gas reservoir; compositional segregation in reservoirs. The common point of all examined problems is the irreversible redistribution of chemical composition of a fluid in the reservoirs. The first chapter is devoted to development of a microscopic model of simultaneous mass and heat transfer in agreement with thermodynamic principles. The second chapter is dedicated to study of multi-component diffusion in a heterogeneous medium. This study aims an application to transport phenomena in hydrocarbon reservoirs characterized firstly by diversity of transported substances (several components + heat) and their interaction (in Onsager’s meaning) and secondly by anisotropy of medium where they take place. The third chapter is dedicated to analytical study of underground gas storage sweeping due to gas dissolution in aquifer. In the fourth chapter the same problem (gas sweeping) was studied numerically in a less idealized approach using finite element method. The fifth chapter is dedicated to study of forced convection taking place in the reservoirs where the temperature gradient and gravity force are not collinear. This convection represents an element of the thermo-gravitational component segregation employed in industry (thermo-gravitational columns) and can take place in underground reservoirs

Foram estudados dois sistemas referentes à células a combustível de membrana de troca protônica através de modelos computacionais. Um protótipo de célula foi utilizado para o estudo da dinâmica de fluidos, tendo sido utilizados resultados cedidos para a validação da formulação do escoamento e posterior quantificação da contribuição do mesmo no transporte de espécies nos meios porosos. Este mesmo sistema foi explorado quanto à geometria dos canais de escoamento, sendo possível estabelecer uma hierarquia de perda por sobrepotencial de concentração em função da estequiometria do reagente. Obteve-se que, para as estequiometrias recomendadas em uma célula real, os melhores desempenhos seriam atingidos por geometrias de serpentina simples e serpentina dupla, ou tripla, para o ânodo e cátodo, respectivamente. Uma célula completa também fora estudada, sendo comparada a resultados experimentais obtidos localmente. Foi observado que o modelo utilizado apresenta boa concordância com os aspectos globais do dispositivo real, enquanto que os aspectos locais são largamente mal representados pelo modelo computacional. Este modelo também fora utilizado para quantificar a contribuição do transporte convectivo na distribuição de reagentes, corroborando e estendendo os estudos realizados com o protótipo de célula. Em suma, são sugeridas as possibilidades e desafios de se utilizar modelos computacionais para células a combustível e sistemas similares, neste caso estabelecendo a conexão entre um protótipo e um dispositivo real. / Two systems related to proton-exchange membrane fuel cells were studied through computational models. A cell prototype was used to study fluid dynamics, where the fluid flow formulation was validated against provided experimental results, being later used to quantify its contribution to species transport in the porous media. This same systems was explored regarding its flow channel geometry, where it was possible to establish a hierarchy relative to the concentration overpotential loss as a function of the reactant stoichiometry. It was obtained that, for the recommended stoichiometries for a real cell, the best performance would be attained by a single serpentine and a double, or triple, serpentine geometries for the anode and cathode, respectively. A full cell was also studied, being compared against experimental results obtained locally. It was observed that the model shows good agreement with the global aspects of the real device, while the local aspects are widely misrepresented. This model was also used to quantify the contribution of convection to reactant distribution, corroborating and extending the studies performed with the cell prototype. In all, the possibilities and challenges concerning the use of computational models with fuel cells and similar systems are suggested, particularly by establishing the connection between a prototype and a real device.

Foram estudados dois sistemas referentes à células a combustível de membrana de troca protônica através de modelos computacionais. Um protótipo de célula foi utilizado para o estudo da dinâmica de fluidos, tendo sido utilizados resultados cedidos para a validação da formulação do escoamento e posterior quantificação da contribuição do mesmo no transporte de espécies nos meios porosos. Este mesmo sistema foi explorado quanto à geometria dos canais de escoamento, sendo possível estabelecer uma hierarquia de perda por sobrepotencial de concentração em função da estequiometria do reagente. Obteve-se que, para as estequiometrias recomendadas em uma célula real, os melhores desempenhos seriam atingidos por geometrias de serpentina simples e serpentina dupla, ou tripla, para o ânodo e cátodo, respectivamente. Uma célula completa também fora estudada, sendo comparada a resultados experimentais obtidos localmente. Foi observado que o modelo utilizado apresenta boa concordância com os aspectos globais do dispositivo real, enquanto que os aspectos locais são largamente mal representados pelo modelo computacional. Este modelo também fora utilizado para quantificar a contribuição do transporte convectivo na distribuição de reagentes, corroborando e estendendo os estudos realizados com o protótipo de célula. Em suma, são sugeridas as possibilidades e desafios de se utilizar modelos computacionais para células a combustível e sistemas similares, neste caso estabelecendo a conexão entre um protótipo e um dispositivo real. / Two systems related to proton-exchange membrane fuel cells were studied through computational models. A cell prototype was used to study fluid dynamics, where the fluid flow formulation was validated against provided experimental results, being later used to quantify its contribution to species transport in the porous media. This same systems was explored regarding its flow channel geometry, where it was possible to establish a hierarchy relative to the concentration overpotential loss as a function of the reactant stoichiometry. It was obtained that, for the recommended stoichiometries for a real cell, the best performance would be attained by a single serpentine and a double, or triple, serpentine geometries for the anode and cathode, respectively. A full cell was also studied, being compared against experimental results obtained locally. It was observed that the model shows good agreement with the global aspects of the real device, while the local aspects are widely misrepresented. This model was also used to quantify the contribution of convection to reactant distribution, corroborating and extending the studies performed with the cell prototype. In all, the possibilities and challenges concerning the use of computational models with fuel cells and similar systems are suggested, particularly by establishing the connection between a prototype and a real device.

La liquéfaction des sols s'observe lors de forts séismes dans des zones saturées en eau et peut causer un enfoncemenl des bâtiments dans le sol. On propose ici un nouveau modèle qui explique de nombreux cas de liquéfaction incompris jusque là. Un modèle analytique de milieu granulaire a été conçu avec une sphère modélisant un bâtiment. Le milieu est soumis à une oscillation horizontale et on caractérise l'état liquéfié par l'amplitude d'enfoncement de la sphère. On suppose que la liquéfaction a lieu lorsque la secousse permet aux grains du milieu de glisser les uns sur les autres. La fenêtre d'accélération permettant ce glissement dépend de la hauteur d'eau dans le milieu, du coefficient de frottement et de la densité du matériau. Les expériences et les simulations numériques réalisées confirment nos prédictions précédentes, caractérisent la micromécanique des milieux liquéfiés, expliquent la vitesse de pénétration de la sphère et ouvrent des pistes pour l'étude des sables mouvants. / Sail liquefaction happens during important earthquakes in water-saturated zones and can make the buildings sink in the soil. A new model explaining many occurences of liquefaction we cannot understand yet is presented in this paper. A new analytical model of granular medium, with a sphere representing a building, has been developed. A horizontal oscillation is applied on the medium. The penetration rate of the sphere then caracterizes the liquefaction state of the modeled soil. We suppose that liquefaction happens when the shaking makes the grains slide against one another. The interval of acceleration allowing this sliding depends on the water height in the medium, on the friction coefficient and on the material density. Experiments and numerical simulations have been carried out. They confirmed our previous predictions, they caracterize the micromecanics of liquefied media, they explain the penetration speed of the sphere and they suggest perspectives to study quicksands.

L'ingénierie tissulaire intervient pour restaurer le tissu osseux. Parmi les traitements possibles, l'utilisation d'un bioréacteur à perfusion permet l'amplification in vitro de cellules souches ou osseuses prélevées chez le patient avant réimplantation. La contrainte de cisaillement générée par l'écoulement stimule mécaniquement les cellules et amplifie la production tissulaire. Cette technique souffre cependant de sa conception empirique et doit à présent être optimisée. L'objectif de cette thèse est l'étude et la modélisation de la croissance tissulaire et de la prolifération cellulaire à l'échelle du bioréacteur. En particulier, il s'agit de comprendre l'impact de l'écoulement sur la formation du tissu. Pour cela, une double approche de modélisation et d'expérimentation a été adoptée. Des expériences de culture cellulaire ont permis de mettre au jour la prolifération préférentielle des cellules près des parois du bioréacteur comme conséquence de l'hétérogénéité du support, et l'évolution de la morphologie du tissu. Un modèle prédisant le devenir des cellules ainsi que la croissance tissulaire à l'échelle du bioréacteur est proposé. L'aspect multi-échelles du problème est pris en considération et les procédures d'homogénéisation sont menées à bien grâce à la méthode de prise de moyenne volumique. / Bone tissue engineering aims at restoring bone tissues. Among the possible treatments, the use of a perfusion bioreactor allows the amplification in vitro of the patient bone or stem cells prior to implantation. The advantage of using such bioreactors is two-fold: in addition to greatly improving species transport, tissue production is enhanced. Although promising, this technique suffers from its empirical conception and now needs to be optimized. The purpose of this thesis is to study and model tissue growth and cell proliferation under a fluid flow of culture medium at the scale of the bioreactor. In particular, we wish to understand the impact of fluid flow on tissue formation. To this end, a double approach of experimentation and modeling has been adopted. Cell culture experiments in a perfusion bioreactor highlighted the preferential cell proliferation in the parietal region as a consequence of the heterogeneity of the scaffold, and the evolution of the tissue morphology. A model for predicting the cell's fate along with tissue growth at the scale of the bioreactor is proposed. The hierarchy of the system is considered and the upscaling procedures are carried out with the Volume Averaging Method.

L'étude décrite dans cette thèse porte sur l'injection ponctuelle d'une solution saline au sein d'une cellule dite de Hele-Shaw, afin de caractériser le comportement dispersif d'un polluant en milieu poreux. L'approche expérimentale employée est basée sur l'implémentation originale d'un dispositif de Fluorescence Induite par Laser (LIF) dans la cellule. La mise en place d'un protocole de mesure efficace permet de mener une analyse quantitative des résultats expérimentaux. En outre, en appliquant la méthode des moments, il est possible de caractériser avec précision le comportement dispersif de la zone de mélange de la solution injectée. Parallèlement aux expériences, à l'aide du code numérique FRIPE, les injections ont été simulées numériquement. L'analyse quantitative a été appliquée à ces dernières. Une comparaison poussée des résultats expérimentaux et numériques a donc été effectuée, du point de vue qualitatif mais aussi sur l'expression de la dispersion du panache de la zone de mélange de la solution / The study described in this thesis is about punctual injection of a saline solution inside a "Hele-Shaw cell" in order to characterize the dispersive behavior of a pollutant in porous media. The chosen experimental approach is based on the setup of an original Laser Induced Fluorescence (LIF) in the Hele-Shaw cell. The setting of the experimental apparatus allows quantitative data reduction of the experimental results. Moreover the "Moments Method" studied precisely the solution mixing dispersive behavior. Using the numerical code FRIPE the same injections have been simulated. The same quantitative data reductions have been applied to the numerical results. This led to an extensive comparison of the numerical and the experimental results, qualitatively but also of the dispersion in the mixing area of the injected solution

Random fields are frequently used in computational simulations of real-life processes. In particular, in this work they are used in modeling of flow and transport in porous media. Porous media as they arise in geological formations are intrinsically deterministic but there is significant uncertainty involved in determination of their properties such as permeability, porosity and diffusivity. In many situations description of properties of the porous media is aided by a limited number of observations at fixed points. These observations constrain the randomness of the field and lead to conditional simulations. In this work we propose a method of simulating the random fields which respect the observed data. An advantage of our method is that in the case that additional data becomes available it can be easily incorporated into subsequent representations. The proposed method is based on infinite series representations of random fields. We provide truncation error estimates which bound the discrepancy between the truncated series and the random field. We additionally provide the expansions for some processes that have not yet appeared in the literature. There are several approaches to efficient numerical computations for partial differential equations with random parameters. In this work we compare the solutions of flow and transport equations obtained by conditional simulations with Monte Carlo (MC) and stochastic collocation (SC) methods. Due to its simplicity MC method is one of the most popular methods used for the solution of stochastic equations. However, it is computationally expensive. The SC method is functionally similar to the MC method but it provides the faster convergence of the statistical moments of the solutions through the use of the carefully chosen collocation points at which the flow and transport equations are solved. We show that for both methods the conditioning on measurements helps to reduce the uncertainty of the solutions of the flow and transport equations. This especially holds in the neighborhood of the conditioning points. Conditioning reduces the variances of solutions helping to quantify the uncertainty in the output of the flow and transport equations. / Graduation date: 2013

Cette thèse se propose d'examiner les phénomènes de transport dans des milieux poreux colonisés par des biofilms. Ces communautés sessiles se développent dans les sols ou les roches souterraines, ou dans la zone hyporhéique des rivières et peuvent influencer significativement le transport de masse et de quantité de mouvement. Les biofilms modifient également très largement la spéciation chimique des éléments présents dans le milieu, menant à la biodégradation de nombreux polluants. Par conséquent, ces systèmes ont reçu une attention considérable en ingénierie environnementale. Pourtant, la recherche dans ce domaine a été très fortement limitée par notre incapacité à (1) observer directement les microorganismes dans des milieux poreux opaques réels et (2) prendre en compte la complexité multi-échelles des différents phénomènes. Cette thèse présente des avancées théoriques et expérimentales permettant de surmonter ces deux difficultés. Une nouvelle stratégie, basée sur la microtomographie à rayons X assistée par ordinateur, a été utilisée pour obtenir des images en trois dimensions de la distribution spatiale du biofilm dans la structure poreuse. Ces informations topologiques peuvent être utilisées pour étudier la réponse de l'entité biologique à différents paramètres physiques, chimiques et biologiques à l'échelle du pore. De plus, ces images sont obtenues sur des volumes relativement importants et peuvent donc être utilisées pour étudier l'influence du biofilm sur le transport de solutés à plus grande échelle. Pour cela, les problèmes aux conditions limites décrivant le transport de matière à l'échelle du pore peuvent être moyennés en volume pour obtenir des équations homogénéisées à l'échelle de Darcy. Différents modèles, ainsi que leurs domaines de validité, sont présentés dans les cas réactifs et non-réactifs. Cette thèse se base sur la technique de prise de moyenne volumique, en conjonction avec des analyses utilisant les moments spatiaux, pour présenter une théorie complète de transport macroscopique ainsi qu'une analyse détaillée des relations entre les différents modèles, tout particulièrement entre les modèles à une et deux équations. Une décomposition non standard en terme de moyenne plus perturbation est présentée dans le but d'obtenir un modèle à une équation dans le cas du transport multiphasique avec des taux de réactions linéaires en fonction de la concentration. Finalement, la connexion entre l'analyse théorique et l'imagerie en trois dimensions est établie. Cette thèse illustre aussi brièvement comment la perméabilité peut être calculée numériquement en résolvant des problèmes de fermeture à partir des images en trois dimensions. / This dissertation examines transport phenomena within porous media colonized by biofilms. These sessile communities of microbes can develop within subsurface soils or rocks, or the riverine hyporheic zone and can induce substantial modification to mass and momentum transport dynamics. Biofilms also extensively alter the chemical speciation within freshwater ecosystems, leading to the biodegradation of many pollutants. Consequently, such systems have received a considerable amount of attention from the ecological engineering point of view. Yet, research has been severely limited by our incapacity to (1) directly observe the microorganisms within real opaque porous structures and (2) assess for the complex multiple-scale behavior of the phenomena. This thesis presents theoretical and experimental breakthroughs that can be used to overcome these two difficulties. An innovative strategy, based on X-ray computed microtomography, is devised to obtain three-dimensional images of the spatial distribution of biofilms within porous structures. This topological information can be used to study the response of the biological entity to various physical, chemical and biological parameters at the pore-scale. In addition, these images are obtained from relatively large volumes and, hence, can also be used to determine the influence of biofilms on the solute transport on a larger scale. For this purpose, the boundary-value-problems that describe the pore-scale mass transport are volume averaged to obtain homogenized Darcy-scale equations. Various models, along with their domains of validity, are presented in the cases of passive and reactive transport. This thesis uses the volume averaging technique, in conjunction with spatial moments analyses, to provide a comprehensive macrotransport theory as well as a thorough study of the relationship between the different models, especially between the two-equation and one-equation models. A non-standard average plus perturbation decomposition is also presented to obtain a one-equation model in the case of multiphasic transport with linear reaction rates. Eventually, the connection between the three-dimensional images and the theoretical multiple-scale analysis is established. This thesis also briefly illustrates how the permeability can be calculated numerically by solving the so-called closure problems from the three-dimensional X-ray images.