A pore-scale understanding of fluid flow underpins the constitutive laws of continuum-scale porous media flow. Porous media flow laws are founded on simplified pore structure such as the classical capillary tube model or the pore-network model, both of which do not include diverging-converging pore geometry in the direction of flow. Therefore, modifications in the fluid flow field due to different pore geometries are not well understood. Thus this may translate to uncertainties on how flow in porous media is predicted in practical applications such as geological sequestration of carbon dioxide, petroleum recovery, and contaminant’s fate in aquifers. To fill this gap, we have investigated the role of a spectrum of diverging-converging pore geometries likely formed due to different grain shapes which may be due to a variety of processes such as weathering, sediment transport, and diagenesis. Our findings describe the physical mechanisms for the failure of Darcy’s Law and the characteristics of Forchheimer Law at increasing Reynolds Number flows. Through fundamental fluid physics, we determined the forces which are most responsible for the continuum-scale porous media hydraulic conductivity (K) or permeability. We show that the pore geometry and the eddies associated therein significantly modify the flow field and the boundary stresses. This has important implications on mineral precipitation-dissolution and microbial growth. We present a new non-dimensional geometric factor β, a metric for diverging-converging pore geometry, which can be used to predict K. This model for K based on β generalizes the original and now widely-used Kozeny (1927) model which was based on straight capillary tubes. Further, in order to better quantify the feasibility of geological CO2 sequestration, we have conducted laboratory fluid flow experiments at reservoir conditions to investigate the controls of media wettability and grain shapes on pore-scale capillary trapping. We present experimental evidence for the snap-off or formation of trapped CO2 ganglion. The total trapping potential is found to be 15% of porosity for a water-wet media. We show that at the pore-scale media wettability and viscous-fingering play a critical role in transport and trapping of CO2. Our investigations clearly show that that in single-phase flow pore geometry significantly modifies pore-scale stresses and impacts continuum-scale flow laws. In two-phase flows, while the media wettability plays a vital role, the mobility ratio of CO2 - brine system significantly controls the CO2 capillary trapping potential- a result which should be taken into consideration while managing CO2 sequestration projects. / text

This thesis is divided into two projects. The first project investigates the dissolution of the Hanford salt cakes, the chemical properties of the effluent and the physical properties such as viscosity of the effluent, the porosity and the permeability of the salt cake bed as the dissolution proceeds. The chemical results are compared to predictions using a thermodynamic model. Physical properties are important because they govern the rate at which the Hanford tanks can be emptied thus facilitating the remediation process. Two simulants were investigated for the dissolution process. The chemical analysis matched with the model predictions for both the simulants. A typical gibbsite layer formation was observed in the chemically complex simulant and experiments were performed to remediate the layer. The second project of this thesis studied the remediation of sodium phosphate dodecahydrate plug using water and sodium carbonate solutions at varying concentrations. A flow loop previously used to study the sodium phosphate dodecahydrate plugging mechanisms, was used to form a plug followed by the addition of water and sodium carbonate solutions. Results indicate that there was a drastic decrease in time to remediate the plug when sodium carbonate solutions were used.

Les écoulements biphasiques en milieux poreux sont généralement accompagnés par des phénomènes d'émulsification d'une phase dans l'autre. Les causes peuvent être nombreuses, de la digitation visqueuse aux instabilités purement capillaires. Cette thèse expérimentale a pour objet l'étude d'un mécanisme particulier d'émulsification de l'huile en milieu poreux, ainsi que le transport des gouttes produites dans des milieux confinés. Dans la première partie de cette thèse, l'instabilité gravito-capillaire de Rayleigh-Taylor est revisitée dans un coin formé entre deux plaques de verre centimétriques. La présence d'un gradient de confinement introduit une force capillaire supplémentaire à cette instabilité canonique, susceptible de stabiliser une couche de liquide suspendue au-dessus du vide. Le seuil de stabilité, les longueurs d'onde caractéristiques et les taux de croissance sont bien modélisés par une analyse de stabilité linéaire de l'interface. La caractérisation de cette force capillaire induite par le gradient de confinement nous amène par la suite à l'étude d'une instabilité purement capillaire se produisant lorsqu'un fluide en mouillage très favorable migre vers les régions les plus confinées d'un coin, occupées initialement par un fluide en mouillage moins favorable. Le gradient de confinement introduit alors une force déstabilisante, aboutissant à l'inversion de la position respective des deux phases. Le liquide le moins mouillant est complètement émulsifié et transporté vers les régions les moins confinées sous la forme de gouttelettes. Une analyse de stabilité linéaire de l'interface permet, là encore, de prédire cette sélection de taille. Les taux de croissance mesurés ne sont en revanche pas en accord avec la modélisation, basée sur la loi de Darcy. Leur valeur suggère une localisation de la dissipation visqueuse dans les lignes de contact déplacées durant le développement de l'instabilité, ainsi que dans les films de lubrification également déposés. Ces dynamiques "non-darciennes" nous ont amenés dans une seconde partie de la thèse à l'étude du transport de gouttes d'huile très visqueuses confinées dans de l'eau en mouillage total. Dans cette configuration, la présence de films de lubrification d'eau entre la goutte et le substrat assure la localisation de la dissipation dans les films peu visqueux, favorisant ainsi la mobilité des gouttes. Nous montrons également que la présence de rugosités sur les parois du confinement induit un ralentissement significatif de la vitesse des gouttes, lié à l'amincissement du film de lubrification par ces rugosités. L'interdépendance subtile entre friction visqueuse à l'avant de la goutte et dans son volume est notamment mise en lumière. Dans une dernière partie, nous étudions l'instabilité capillaire se produisant lorsqu'une goutte binaire d'eau et d'alcool est déposée à la surface d'un bain d'huile. L'évaporation majoritaire de l'alcool à la surface de la goutte induit des variations locales de la tension de surface. Des écoulements interfaciaux de Marangoni se produisent, et aboutissent à la déstabilisation spectaculaire de la goutte en étalement. / Biphasic flows in porous media generally lead to the emulsification of one phase into the other. This may be due to several phenomena, such as viscous fingering or pure capillary instabilities. In this experimental thesis, we study a particular emulsifying phenomenon of oil in a model porous medium, as well as the transport of the produced droplets in confined regions. In the first part of the manuscript, the Rayleigh-Taylor instability is revisited in a wedge formed between two centimetric glass plates. The gradient of confinement leads to a capillary force not present in the canonical Rayleigh-Taylor instability. This new force can stabilize liquid layer above air submitted to gravity. The threshold of the instability, the characteristic wavelength and the growth rate are captured by a linear stability analysis of the interface. This characterization of the confinement-induced capillary force drove us to the study of a pure capillary instability occurring when a wetting liquid migrates toward the most confined regions of a wedge, initially filled with a less wetting liquid. The gradient of confinement generates a destabilizing force, leading to the complete inversion of the position of both phases. The less wetting liquid is fully emulsified and the produced droplets are convected towards the less confined regions. A linear stability analysis of the interface here again predicts the characteristic size of the droplets. However, the measured growth rates are not in agreement with the model, based on the Darcy law. This suggests a localization of viscous dissipation in the contact lines displaced during the development of the instability. Another source of viscous dissipation can be in the deposited lubrication films. Those "non-Darcian" dynamics motivated the second part of this thesis, which focuses on the motion of very viscous and non-wetting droplets confined in water. In this configuration, the lubrication film of water between the drop and the substrate ensures the localization of viscous dissipation in those films of low viscosity. This favors the extremely high mobility of the droplets. We also show that wall roughness may induce a thinning of these lubrication films. We shed light on the intricate coupling between viscous friction at the front of the drop and in its bulk. In a last part of this work, we study the capillary instability occurring when a binary droplet of water and alcohol is deposited at the surface of a vegetable oil bath. The dominant evaporation of alcohol at the surface of the drop induces local variations of surface tension. Interfacial Marangoni flows are thus observed, leading to the spectacular destabilization of the spreading droplet

La modélisation de la migration des hydrocarbures dans les bassins sédimentaires a pour but d'évaluer leur potentiel pétrolier, en localisant et en quantifiant les accumulations d'hydrocarbures au sein des formations géologiques. Dans cette thèse, nous étudions les modèles de migration de type "Darcy" ainsi que des modèles simplifiés de types "ray-tracing" et "invasion percolation"; l'objectif est de mener une analyse critique et de proposer des améliorations tout en fournissant un guide pour une utilisation pertinente sur des cas d'étude.Tout d'abord, nous faisons une revue des mécanismes de la migration depuis l'échelle des pores jusqu'à l'échelle des bassins, puis nous présentons chacun des modèles.Dans le volet suivant, nous proposons deux algorithmes d'invasion percolation : le premier, adapté aux maillages structurés; le second, permettant de mieux prendre en compte les maillages non structurés. Dans un troisième volet, nous nous intéressons à la comparaison entre ces modèles, en nous concentrant sur ceux de types "Darcy" et "invasion percolation". Nous nous focalisons en premier lieu sur les aspects numériques en nous appuyant sur plusieurs cas tests; puis nous effectuons une comparaison formelle en étudiant la limite asymptotique de la solution du modèle de type "Darcy" en temps long. Nous présentons ensuite une série d'applications dont notamment l'étude d'un cas réel 3D en géométrie complexe.Finalement, nous concluons ce travail avec deux articles. Le premier montre une évolution des modèles de type "Darcy" en utilisant la méthode du raffinement local de maillage, avec une illustration sur un cas d'étude du nord du Koweït. Le deuxième synthétise les principaux résultats obtenus concernant les méthodes de "Darcy" et "d'invasion percolation". / Hydrocarbon migration modeling in sedimentary basins aims to localize and to quantify hydrocarbon accumulations in geological formations in order to estimate their petroleum potential. In this thesis, we study “Darcy” migration models and also simplified migration models such as “ray-tracing” and “invasion percolation”; the purpose is to conduct a critical analysis and to offer improvements while providing a guide for a relevant use on case studies.We start by a review of migration mechanisms from the pore scale to the basin scale, then we present each model.In a following part, we propose two invasion percolation algorithms: the first one is suited to structured grids, the second one allows to take better account of unstructured grids.In a third part, we take an interest in the comparison between the different models and particularly between “Darcy” and “invasion percolation” approaches. First we devote our attention to numerical aspects supported by several use cases; then we realize a formal comparison by studying the asymptotic limit of the “Darcy” model large time solution. Afterwards, we present several applications including the study of a 3D real case in complex geometry.Finally, we conclude this work with two articles. The first one shows an evolution of “Darcy” models by using the method of local grid refinement with an illustration on a case study from northern Kuwait. The second one synthesizes the main results on “Darcy” and “invasion percolation” methods.

Liver perfusion can be modelled by Darcy's flow in multiple connected com- partments. The first part of the present thesis shows in detail the existence of a solution to the multi-compartmental model. The flow in each compartment in this model is characterized by a permeability tensor, which is obtained from the geometry of liver vasculature. It turns out that this tensor might be singular, which potentially causes solvability problems. The second part deals with this abnormality in one compartment. By using the theory of degenerate Sobolev spaces, an appropriate weak formulation is defined. Analogues of Poincar'e and traces inequalities in this degenerate setting are proved, which also imply the existence of the weak solutions. In addition, this part justifies another possibil- ity how to deal with degenerate permeability, which is regularizing the tensor by adding a small isotropic permeability to it. In the third part, the aim is to find subdomains of autonomous perfusion with respect to the source positions. This is formulated as a minimization problem and several numerical results are presented. 1