The objective of this study was to characterize non-wetting fluid in multi-phase systems comprising a range of fluid and porous medium properties. Synchrotron X-ray microtomography was used to obtain high-resolution, three-dimensional images of fluids in natural porous media. Images were processed to obtain quantitative measurements of fluid distribution, morphology, and interfacial area. Column-flooding experiments were conducted with four enhanced-solubilization (ES) solutions to examine their impact on entrapped organic liquid. Mobilization caused a change in organic-liquid morphology and distribution for most experiments. The effect of ES-solution flooding on fluid-fluid interfacial area was similar to that of water flooding. Organic-liquid mobilization was observed at total trapping numbers that were smaller than expected. This was attributed to pore-scale mobilization of blobs that were re-trapped prior to being eluted from the column. Pore-scale mobilization was also observed during water-flooding experiments for which trapping numbers varied over several orders of magnitude. Water-flooding and surfactant-flooding experiments were compared to investigate the impact of interfacial tension, viscosity, and fluid velocity on entrapped organic liquid. For similar total trapping numbers, flooding at larger velocities appeared to have a greater effect on the distribution of non-wetting blobs than lowering interfacial tension or increasing the viscosity of the wetting fluid. The fluid-normalized interfacial area was generally independent of the total trapping number. Finally, the impact of fluid type on the interfacial area between different pairs of non-wetting fluids was investigated during drainage and imbibition in four natural porous media. Interfacial areas were similar among all fluid pairs for a given porous medium. They were also similar for drainage and imbibition conditions. The maximum specific interfacial area (A(m)) was determined to quantify the magnitude of interfacial area associated with a given porous medium. The value of A(m) was larger for the media with smaller median grain diameters. Therefore, physical properties of the porous medium appear to have a greater influence on the magnitude of specific total interfacial area for a given saturation than fluid properties or wetting-phase history.

Cette étude est consacrée au développement d'outils numériques basés sur la Transformée de Fourier Rapide (TFR) en vue de la détermination des propriétés effectives des structures périodiques. La première partie est dédiée aux matériaux composites. Au premier chapitre, on présente et on compare les différentes méthodes de résolution basée sur la TFR dans le contexte linéaire. Au second chapitre on propose une approche à deux échelles, pour la détermination du comportement des composites non linéaires. La méthode couple, les techniques de résolution basées sur la TFR à l'échelle locale, une méthode d'interpolation multidimensionnelle du potentiel des déformations à l'échelle macroscopique. L'approche présente de nombreux avantages faces aux approches existantes. D'une part, elle ne nécessite aucune approximation et d'autre part, elle est parfaitement séquentielle puisqu'elle ne nécessite pas de traiter simultanément les deux échelles. La loi de comportement macroscopique obtenue a été ensuite implémentée dans un code de calcul par éléments finis. Des illustrations dans le cas d'un problème de flexion sont proposées. La deuxième partie du travail est dédiée à la formulation d'un outil numérique pour la détermination de la perméabilité des milieux poreux saturés. Au chapitre trois, on présente la démarche dans le cas des écoulements en régime quasi-statique. La méthode de résolution repose sur une formulation en contrainte du itératif basée sur la TFR, mieux adaptée pour traiter le cas des contrastes infinis. Deux extensions de cette méthode sont proposées au quatrième chapitre. La première concerne la prise en compte des effets de glissement sur la paroi de la matrice poreux. La méthodologie employée repose sur le concept d'interphase et d'interface équivalente, introduite dans le contexte de l'élasticité des composites et adaptée ici au cas des milieux poreux. Enfin, on présente l'extension de la méthode au cas des écoulements en régime dynamique. Pour cela, on propose un nouveau schéma itératif pour la prise en compte des effets d'origine inertiel / This study is devoted to developing numerical tools based on Fast Fourier Transform (FFT) for determining the effective properties of periodic structures. The first part is devoted to composite materials. In the first chapter, we present and we compare the different FFT-based methods in the context of linear composites. In the second chapter, we propose a two-scale approach for determining the behavior of nonlinear composites. The method uses both FFT-based iterative schemes at the local scale and a multidimensional interpolation of the strain potential at the macroscopic scale. This approach has many advantages over existing ones. Firstly, it requires no approximations for the determination of the macroscopic response. Moreover, it is sequential in the sense that it is not required to process both scales simultaneously. The macroscopic constitutive law has been derived and implemented in a finite element code. Some illustrations in the case of a beam bending are proposed. The second part of the work is dedicated to the formulation of a numerical tool for determining the permeability of saturated porous media. In chapter three, we present the approach in the context of quasi-static flows. To solve the problem we propose a FFT stress-based iterative scheme, better suited to handle the case of infinite contrasts. Two extensions of this method are proposed in the fourth chapter. The first concerns the slip effects which occurs at the interface between solid and fluid. The methodology use the concept of interface and the equivalent interphase, initially introduced in the context of elastic composites and adapted here to the case of porous media. Finally, we present the extension of the method in the dynamic context. We propose a new iterative scheme for taking into account the presence of inertial terms

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

The primary objective of this research is to develop a mathematical framework that could be used to model or predict the rate of fluid absorption and release in fibrous sheets made up of solid or porous fibers. In the first step, a two-scale two-phase modeling methodology is developed for studying fluid release from saturated/unsaturated thin fibrous media made up of solid fibers when brought in contact with a moving solid surface. Our macroscale model is based on the Richards’ equation for two-phase fluid transport in porous media. The required constitutive relationships, capillary pressure and relative permeability as functions of the medium’s saturation, are obtained through microscale modeling. Here, a mass convection boundary condition is considered to model the fluid transport at the boundary in contact with the target surface. The mass convection coefficient plays a significant role in determining the release rate of fluid. Moreover the release rate depends on the properties of the fluid, fibrous sheet, the target surface as well as the speed of the relative motion, and remains to be determined experimentally. Obtaining functional relationships for relative permeability and capillary pressure is only possible through experimentation or expensive microscale simulations, and needs to be repeated for different media having different fiber diameters, thicknesses, or porosities. In this concern, we conducted series of 3-D microscale simulations in order to investigate the effect of the aforementioned parameters on the relative permeability and capillary pressure of fibrous porous sheets. The results of our parameter study are utilized to develop general expressions for kr(S) and Pc(S). Furthermore, these general expressions can be easily included in macroscale fluid transport equations to predict the rate of fluid release from partially saturated fibrous sheets in a time and cost-effective manner. Moreover, the ability of the model has been extended to simulate the radial spreading of liquids in thin fibrous sheets. By simulating different fibrous sheets with identical parameters but different in-plane fiber orientations has revealed that the rate of fluid spread increases with increasing the in-plane alignment of the fibers. Additionally, we have developed a semi-analytical modeling approach that can be used to predict the fluid absorption and release characteristics of multi-layered composite fabric made up of porous (swelling) and soild (non-swelling) fibrous sheets. The sheets capillary pressure and relative permeability are obtained via a combination of numerical simulations and experiment. In particular, the capillary pressure for swelling media is obtained via height rise experiments. The relative permeability expressions are obtained from the analytical expressions previously developed with the 3-D microscale simulations, which are also in agreement with experimental correlations from the literature. To extend the ability of the model, we have developed a diffusion-controlled boundary treatment to simulate fluid release from partially-saturated fabrics onto surfaces with different hydrophilicy. Using a custom made test rig, experimental data is obtained for the release of liquid from partially saturated PET and Rayon nonwoven sheets at different speeds, and on two different surfaces. It is demonstrated that the new semi-empirical model redeveloped in this work can predict the rate of fluid release from wet nonwoven sheets as a function of time.

A superhydrophobic coating can be produced using a hydrophobic material textured with surface roughness on the micro-/nano-scale. Such a coating on the outside of a submersible body may result in reduced skin-friction drag due to a trapped layer of air in the coating. However, this layer may become unstable when subjected to elevated hydrostatic pressures, and a coating’s performance is compromised beyond a certain threshold (critical pressure). This thesis presents a numerical model for predicting the pressure tolerances of superhydrophobic coatings comprised of randomly deposited hydrophobic particles or fibers. We have also derived a set of force-balance-based analytical equations for predicting critical pressure in surfaces with ordered roughness, and compared our numerical model against it, observing reasonable agreement. The numerical model was then applied in a large parameter study, predicting critical pressure for coatings with a given set of microstructure properties.

Cette étude présente la mise au point de mesures de porosité et de vitesse d’écoulement faites par IRM dans des colonnes de billes de verre et de polymère de différentes granulométries saturées en eau. L’avantage des billes en polymère est qu’elles ne contiennent pas d’éléments ferro ou paramagnétiques, contrairement aux billes de verre qui perturbent le champ magnétique créant des artéfacts sur les images IRM. La séquence d’IRM utilisée pour l’étude des écoulements en milieu poreux a été préalablement paramétrée à l’aide d’une étude sur un écoulement de Poiseuille. Deux situations ont été examinées : d’une part, l’observation des écoulements interstitiels entre les billes permet de minimiser les effets de volume partiel et de faciliter la correction du phénomène de repliement de phase. D’autre part, la mesure de vitesses moyennes (Darcy) nécessite d’utiliser simultanément les images de vitesse et les images de porosité. Dans ce cas, il est préférable d’ajuster la puissance des gradients d’encodage de vitesse de façon à éviter tout phénomène de repliement de phase. La géométrie du dispositif utilisé a permis une comparaison rigoureuse des mesures de débit de façon intrinsèque uniquement par IRM (débit en milieu poreux et dans l’espace annulaire) et aussi à partir de la mesure directe du débit (pesée). / This study presents the development of measurement of porosity and velocity of flow made by MRI in packed beds with glass and polymer beads of various size saturated in water. The advantage of polymer beads is that they do not contain elements ferro or paramagnetics, contrary to the glass beads which disrupt the magnetic field creating artifacts on the MRI images. The calibration of the MRI velocity measurements was achieved from Poiseuille flow in a tube at different flow rates. Two situations were examined: first, the observation of interstitial flows between the beads minimizes partial volume effects and facilitates the correction of the phenomenon of phase aliasing. On the other hand, the measurement of average interstitial velocity (Darcy) requires using simultaneous velocity image and porosity image. In this case, it is preferable to adjust the strength of magnetic field gradient in the velocimetry sequence in a way to avoid any phase aliasing. The geometry of the flow cell was chosen to enable comparison by the MRI method between volume flow rates of water in the porous media and in the outer annulus.

L'écoulement des fluides complexes à l'échelle micrométrique est une problématique qui intéresse notamment la récupération assistée du pétrole. Ici, les fluides sont des solutions de polymères et de tensioactifs capables de s'auto-assembler en micelles géantes. Nous étudions ces écoulements au sein d'outils microfluidiques fabriqués en résine SU-8 selon un protocole développé pendant cette thèse. Nous avons réalisé des expériences de drainage d'huile en milieux poreux et montré que la rhéofluidification et le glissement promeuvent le phénomène de digitation pendant l'invasion. Nos expériences montrent que ces solutions peuvent être élastiquement turbulentes à de faibles nombre de Reynolds. Ces instabilités de vitesse ont des conséquences sur la rhéologie locale du fluide dans un simple canal droit et sont une source de dissipation additionnelle dans des géométries plus complexes. / The flow of complex fluids in confined geometries is an issue of interest notably in the field of oil recovery. In this work, the fluids are polymer solutions of high molecular weight and surfactant solutions enable to form wormlike micelles. We study the flow in microfluidic devices made-up with Su-8 resin following a protocol that has been set during this PhD. We carried out experiences of oil drainage in porous media and show that shear-thinning and slippage are propoting the fingering during the invasion. our experiences also show that these solutions can be turbulent at low reynods numbers. These instabilities have consequences on the local rheology in a simple straight channel and are source of additional dissipation in more complex geometries.

Dans cette thèse, nous proposons un modèle pour le calcul des écoulements le long des failles. Ce modèle, baptisé modèle double interface permet de traiter deux difficultés majeures rencontrées lors de la modélisation des failles. Tout d'abord, l'utilisation d'un modèle interface, dans lequel les failles sont représentées par des éléments de dimension inférieure permet de s'affranchir du problème d'échelle spatiale. Ensuite, l'utilisation de deux interfaces pour représenter chaque faille permet de traiter naturellement les maillages non-conformes apparaissant dans ce type de problème. Les questions de failles non-planes et de réseaux de failles sont aussi abordées. Ce modèle est validé numériquement sur différents cas tests académiques et un cas synthétique inspiré du stockage du CO2 a aussi été réalisé. Finalement, une étude théorique a été menée afin de confirmer mathématiquement l'approche retenue. / In this thesis, we are interested in the modelisation of fluid flow along conductive faults. This model, so-called double interface model tackles two majors difficulties encountered when modelising faults. First of all, the use of an interface model, in which the faults are represented by lower dimension elements allows to treat the problem of space scale. Then, the use of two interfaces to modelise each fault allows to handle quite naturally the non-matching grid problem arising from this kind of problem. The question of non-planar fault and fault networks is also addressed. This model is then validated on several academic test cases and a synthetic case inspire by CO2 storage is also performed. Finally, a theoric study is also conducted in order to validate our approach.

This thesis is concerned with developing porous materials from tyre shred residue and polyurethane binder for acoustic absorption and thermal insulation applications. The resultant materials contains a high proportion of open, interconnected cells that are able to absorb incident sound waves through viscous friction, inertia effects and thermal energy exchanges. The materials developed are also able to insulate against heat by suppressing the convection of heat and reduced conductivity of the fluid locked in the large proportion of close-cell pores. The acoustic absorption performance of a porous media is controlled by the number of open cells and pore size distribution. Therefore, this work also investigates the use of catalysts and surfactants to modify the pore structure and studies the influence of the various components in the chemical formulations used to produce these porous materials. An optimum type and amounts of catalyst are selected to obtain a high chemical conversion and a short expanding time for the bubble growth phase. The surfactant is used to reduce the surface tension and achieve a homogenous mixing between the solid particulates tyre shred residue, the water, the catalyst and the binder. It is found that all of the components significantly affect the resultant materials structure and its morphology. The results show that the catalyst has a particularly strong effect on the pore structure and the ensuing thermal and acoustical properties. In this research, the properties of the porous materials developed are characterized using standard experimental techniques and the acoustic and thermal insulation performance underpinned using theoretical models. The important observation from this research is that a new class of recycled materials with pore stratification has been developed. It is shown that the pore stratification can have a positive effect on the acoustic absorption in a broadband frequency range. The control of reaction time in the foaming process is a key function that leads to a gradual change in the pore size distribution, porosity, flow resistivity and tortuosity which vary as a function of sample depth. It is shown that the Pade approximation is a suitable model to study the acoustic behaviour of these materials. A good agreement between the measured data and the model was attained.

Ce travail porte sur l’étude de la propagation de décharges couronnes impulsionnelles à pression atmosphérique dans les milieux poreux et/ou alvéolaires. Face à la complexité des phénomènes mis en jeu, liés aux interactions entre la décharge et les surfaces du matériau qui la confine, nous proposons l’étude de décharges confinées par des structures élémentaires. L’étude du confinement radial des décharges, assuré par un large panel de capillaires, a été réalisée. Des diagnostics électriques et optiques de pointe permettent d’étudier la propagation de la décharge au sein des différents capillaires. La corrélation entre ces diagnostics a même permis des mesures de vitesse de propagation au sein de capillaires opaques. Les résultats montrent que la propagation de la décharge dépend grandement de la géométrie des capillaires et des paramètres électriques de génération de la décharge. Dans le cas de sections carrées ou rectangulaires, les arêtes induisent un renforcement local du champ qui attire la décharge. Dans le cas de capillaires cylindriques, le diamètre interne est le paramètre crucial qui détermine aussi bien la structure de la décharge que sa vitesse de propagation. Quelle que soit la nature du capillaire, la propagation présente alors une vitesse optimale à tout autre paramètre constant pour une valeur donnée du diamètre interne. Dans le cas du verre, la vitesse est maximale pour un diamètre interne de 200 µm. L’épaisseur et la permittivité diélectrique du capillaire possèdent également une influence sur la propagation de la décharge radialement confinée. Ainsi, diminuer l’épaisseur ou la permittivité diélectrique engendre une accélération de la décharge. Si l’épaisseur est très faible, la décharge peut même se déconfiner pour se propager à l’extérieur du capillaire. Une étude spectroscopique complémentaire montre que la réduction du diamètre de confinement implique une augmentation de la température du plasma, ce qui pourrait contribuer à l’obtention de ce profil de vitesse en fonction du diamètre de confinement. L’étude du confinement axial des décharges a ensuite été réalisée en insérant des membranes de différentes natures et caractéristiques, perpendiculairement à l’axe pointe plan. Les résultats montrent que la décharge présente une propagation en trois étapes : pointe/membrane, radialement au voisinage de la membrane, puis membrane/plan. Dans cette étude, nous avons mis en évidence l’importance du critère poreux ou non de la membrane. Dans le cas poreux, la propagation de la décharge dans l’ensemble du gap est continue, même pour des pores de l’ordre de la dizaine de µm. Dans le cas non poreux, la propagation est discontinue, et il est nécessaire pour assurer la propagation dans l’ensemble du gap qu’un ré-allumage ait lieu de l’autre côté de la membrane. Après l’instant de l’impact sur la membrane, la décharge marque un arrêt qui correspond à la réorganisation des charges et à la restructuration du champ électrique dans le gap. Elle se propage ensuite radialement au voisinage de la membrane en plusieurs fronts d’ionisation. Si les conditions de claquage sont réunies dans le volume membrane/plan, alors un ré-allumage apparaît à partir de la membrane pour atteindre le plan. L’étude de ces ré-allumages semble montrer l’importance de la position de la membrane au sein de l’espace inter-électrodes et de la dynamique des charges aux surfaces de la membrane. Plus on diminue la distance membrane/plan, plus il est facile d’en observer. Nous montrons également que la diminution de la permittivité diélectrique de la membrane ou l’augmentation de son épaisseur, semble augmenter la probabilité de ces ré-allumages. Dans le cas poreux, nous avons également mis en évidence l’influence de la taille des pores de la membrane sur l’ensemble des étapes de propagation. Lorsque la porosité est inférieure à 100 µm la propagation de la décharge est ralentie du fait de la difficulté de la décharge à traverser directement le matériau. / This study is an attempt to understand the mechanisms involved in the propagation of pulsed corona discharges at atmospheric pressure inside porous and/or alveolar media. Due to the complexity of these phenomena which hardly depends on plasma/surface interactions, the study was focused first on the propagation inside basic structures of confinement, before doing it in more complex media, such as monolithic cordierites or foams. Therefore, capillaries have been used to radially confine the discharge propagation. Thanks to highly resolved optical and current diagnostics, we succeed in describing precisely the propagation. A correlation of these diagnostics allowed us to measure propagation velocity inside opaque media. Results show that geometry is the key parameter which both governs the discharge structure and the propagation velocity. Electrical parameters of the discharge ignition have a great role in the propagation also. In case of square and rectangular capillaries, the local electric field enhancement due to edges attracts the discharge. In case of round capillaries, the internal diameter becomes the key parameter which governs the pattern of the discharge and its velocity. Whatever the kind of capillary used, the velocity of propagation shows an optimal value for a given internal diameter, at all others parameters constants. In case of glass capillaries, this maximum value is obtained for a 200 µm internal diameter. Parameters such as wall thickness or dielectric permittivity have also an influence on the propagation velocity. The decrease of the thickness or the dielectric permittivity implies an increase of the propagation velocity. If the thickness is small enough, we observe that the discharge is able to propagate outside the tube. A complementary spectroscopic study of that kind of discharge shows that the plasma temperature depends on the internal diameter, and warming observed for smallest internal diameters could contribute to the internal diameter/velocity of propagation relation. The study of the axial confinement of the propagation of the discharge has been made thanks to different kinds of dielectric membranes, perpendicularly inserted between the electrodes. Results show that the propagation of the discharge is a three step process: tip to membrane propagation, radial propagation near the membrane surfaces, and membrane to plane propagation under specific conditions. The porous feature of the membrane has a key role in the propagation. In case of porous membranes, the whole propagation in the gap is continuous, even for the smallest porosities under investigations (~10µm). In case of non porous films, the propagation by three step processes is no more continuous, and the propagation in the entire gap needs a re-ignition of the discharge on the other side of the membrane. After its impact on the membrane, the discharge stops on the dielectric while the charges and the electric field are self reorganized. Then a radial propagation of several ionization waves starts near the membrane surface. If the disruptive voltage is reached behind the obstacle, a re-ignition could occur in the membrane/plane gap and reach the cathode. Investigation on these reignition conditions shows that the key parameters seem to be the position of the membrane inside the gap and the dynamics of the surface charges on the membrane. Closer is the membrane to the plane, higher is the probability of seeing re-ignitions. Results also show that the decrease of the dielectric permittivity or the increase of the membrane thickness leads to more re-ignition events. In case of porous membrane, the pore size is the main parameter which will influence the propagation. When the pore size is below 100 µm, the discharge propagation is slower due to the discharge difficulties to penetrate totally inside the material.