This research presents an approach to accurately simulate flow experiments through a fractured core using experimental, stochastic, and simulation techniques. Very often, a fracture is assumed as a set of smooth parallel plates separated by a constant width. However, the flow characteristics of an actual fracture surface are quite different, affected by tortuosity and the impact of surface roughness. Though several researchers have discussed the effect of friction on flow reduction, their efforts lack corroboration from experimental data and have not converged to form a unified methodology for studying flow on a rough fracture surface. In this study, an integrated methodology involving experimental, stochastic, and numerical simulations that incorporate the fracture roughness and the friction factor is shown to describe flow through single fractures more efficiently. Laboratory experiments were performed to support the study in quantifying the flow contributions from the matrix and the fracture. The results were used to modify the cubic law through reservoir simulations. Observations suggest that the fracture apertures need to be distributed to accurately model the experimental results. The methodology successfully modeled fractured core experiments, which were earlier not possible using the parallel plate approach. A gravity drainage experiment using an X-ray CT scan of a fractured core has also validated the methodology.

Transmissivity (T) and Hydraulic apertures are often calculated from hydraulic test data obtained in fractured rock using analytical solutions such as the Thiem and cubic law equations developed for flow through unconsolidated porous media. These analytical solutions use a variety of simplifying assumptions, which are often violated due to the complex nature of flow through fractured rock systems which introduces error into the calculated hydraulic apertures. A 3-D discrete fracture network numerical model (SMOKER) for flow in dual-permeability media was used to simulate constant-head straddle packer tests to assess the errors in fracture characterization that result from deviations from the Thiem and cubic law assumptions caused by permeable rock matrix, variable aperture fractures, and complex flow patterns. The simulations indicate that SMOKER offers potential as a useful tool for representing non-ideal scenarios of rock and fracture network characteristics to assist in estimates and error analysis in T values and resultant errors in hydraulic aperture. / NSERC: Natural Sciences and Engineering Research Council of Canada

Groundwater inflow is a challenge in construction of tunnels in fractured bedrocks since it affects the safety function of tunnels and leads to potential problems in the surrounding environment, such as subsidence, dropdown of the groundwater table. Quantification of groundwater inflow into the tunnel is also important for design of grouting in the construction of the tunnel. Modelling groundwater flow in fractured bedrocks currently remains a challenge. Commonly used groundwater models are based on continuum assumptions and they do not consider realistic structures of discrete fractures, which leads to high potential uncertainty in prediction of tunnel groundwater inflow. This thesis focuses on prediction of tunnel groundwater inflow, using a discreet fracture-matrix (DFM) model. The DFM model is evaluated and compared with the conventional continuum model based on Darcy’s law. This DFM model considers, in particular, multi-scale heterogeneity, e.g. fracture networks and variable fracture aperture structures. Applying this DFM model, the impact of variable fracture aperture structures on tunnel inflow is investigated through stochastic analysis. The results show that under the same boundary conditions, the traditional continuum model overestimates the inflow compared to the DFM model. The difference in equivalent permeability is 2 to 3 orders of magnitude. The sensitivity analysis shows that the discreet fracture model is sensitive to the variability of fracture aperture. The estimated equivalent permeability values by discreet fracture modelling is in the order of 5×10-6 to 1×10-7 m/s for a fracture density of 1.2 fractures per square meter. This study demonstrates that the DFM represents the more realistic features of fractured rock structures, which is useful and can be used to predict groundwater inflow in fractured rock tunnels. / Grundvatteninflöde är en utmaning vid byggnation av tunnlar i sprucken berggrund eftersom det påverkar tunnlarnas säkerhetsfunktion och leder till potentiella problem i den omgivande miljön, såsom sättningar och Grundvattennivåsänkning. Kvantifiering av grundvatteninflöde till tunneln är också viktig för utformning av injektering i tätning? byggandet av tunneln. Att modellera grundvattenflödet i sprucken berggrund är för närvarande en utmaning. Grundvattenmodeller man normalt använder är baserade på kontinuumantaganden, och de tar inte hänsyn till realistiska strukturer av diskreta sprickor, vilket leder till hög potentiell osäkerhet i uppskattning av tunnelgrundvatteninflöde. Denna avhandling fokuserar på förutsägelse av tunnelinläckage, med hjälp av en diskret sprickmatris (DFM) modell. DFM-modellen utvärderas och jämförs med den konventionella kontinuummodell vilken är baserad på Darcys lag. Denna DFM-modell tar särskilt hänsyn till multi-skala heterogenitet, till exempel spricknätverk och variabla dubbelkolla. Genom att tillämpa denna DFM-modell undersöks effekten av strukturer med variabel spricköppning på grundvatteninflödet genom stokastisk analys. Resultaten visar att under samma randvillkor överskattar den traditionella kontinuummodellen inflödet jämfört med DFM-modellen. Skillnaden i ekvivalent permeabilitet är 2 till 3 storleksordningar. Känslighetsanalysen visar att den diskreta sprickmodellen är känslig möt variationen i spricköppningen. De uppskattade ekvivalenta permeabilitetsvärdena med diskret sprickmodellering är i storleksordningen 5x10-6 till 1x10-7 m/s för en spricktäthet på 1,2 sprickor per kvadratmeter. Denna studie visar att DFM representerar de mer realistiska egenskaperna hos sprickiga bergstrukturer, vilket är användbart och kan användas för att uppskatta grundvatteninflöde i sprickiga bergtunnlar.

A avaliação do risco a contaminação e a escolha de técnicas de remediação de poluentes em aquíferos fraturados depende da quantificação dos fenômenos envolvidos no transporte de solutos. A geometria da fratura, usualmente caracterizada pela abertura, é o principal parâmetro que indiretamente controla o transporte nos aquíferos fraturados. A simplificação mais comum desse problema é assumir que as fraturas são um par de placas planas e paralelas, isto é, com uma abertura constante. No entanto, por causa do limitado número de trabalhos experimentais, não está esclarecida a adequabilidade do uso de uma abertura constante para simular o transporte conservativo em fraturas do Aquífero Serra Geral (ASG), Brasil. O objetivo deste trabalho é avaliar a influência da abertura de uma fratura natural do Aquífero Serra Geral sob o transporte conservativo de solutos. Uma amostra natural de basalto fraturado foi usada em um experimento hidráulico e de transporte de um traçador conservativo (escala de laboratório). O campo de abertura foi medido usando a técnica avançada, de alta resolução e tridimensional, chamada microtomografia computadorizada de raios-X. A concentração de traçador medida foi utilizada para validar uma solução analítica unidimensional da Equação de Advecção-dispersão (ADE). O desemprenho do ajuste da ADE às curvas de passagem experimentais foi avaliado para quatro diferentes tipos de aberturas constantes. Os resultados mostraram que o escoamento de água e o transporte de contaminantes pode ocorrer através de fraturas micrométricas, ocasionando, eventualmente, a contaminação do ASG. A abertura de balanço de massa é a única que pode ser chamada propriamente de \"abertura equivalente\". O uso de aberturas constantes na ADE não permitiu representar completamente o formato das curvas de passagem porque o campo de velocidade não é uniforme e intrinsicamente bidimensional. Portanto, na simulação do transporte deve-se incorporar a heterogeneidade da abertura da fratura. / The contamination risk assessment and the choice of suitable cleanup techniques for pollutants in fractured rock depends on the quantification of the transport phenomena. Fracture geometry often described by the apertures is the major parameter that controls indirectly solute transport in fractured rock. The simplest approach is describing fractures as a pair of smooth parallel plates with constant aperture. However, there is a lack of information about the suitability for using a constant aperture for the conservative solute transport prediction in a single fracture of Serra Geral Aquifer (SGA), Brazil. The aim of this work is to evaluate the effect of aperture variability in a natural single rough-walled fracture of Serra Geral Aquifer on conservative solute transport. A natural core of fractured basalt was used for a hydraulic and tracer tests (laboratory scale). The aperture field was measured using the advanced, high-resolution and tridimensional technique X-ray computed tomography. The measured tracer concentration was validated by means of an analytical solution of the Advection-dispersion Equation (ADE). The ADE fit performance was measured against experimental breakthrough curves for four distinct kind of constant apertures. It was found that water flow and solute transport can take place through micrometric fractures, eventually leading the SGA contamination. Results show that the mass balance aperture is the only appropriate \"equivalent aperture\" for describing solute transport in a single rough-walled fracture. The results showed that ADE is not appropriate for modeling the complete behavior of experimental breakthrough curves because of the dimensional non-uniform velocity field. Therefore, the aperture heterogeneity must be considered in solute transport simulation.

A avaliação do risco a contaminação e a escolha de técnicas de remediação de poluentes em aquíferos fraturados depende da quantificação dos fenômenos envolvidos no transporte de solutos. A geometria da fratura, usualmente caracterizada pela abertura, é o principal parâmetro que indiretamente controla o transporte nos aquíferos fraturados. A simplificação mais comum desse problema é assumir que as fraturas são um par de placas planas e paralelas, isto é, com uma abertura constante. No entanto, por causa do limitado número de trabalhos experimentais, não está esclarecida a adequabilidade do uso de uma abertura constante para simular o transporte conservativo em fraturas do Aquífero Serra Geral (ASG), Brasil. O objetivo deste trabalho é avaliar a influência da abertura de uma fratura natural do Aquífero Serra Geral sob o transporte conservativo de solutos. Uma amostra natural de basalto fraturado foi usada em um experimento hidráulico e de transporte de um traçador conservativo (escala de laboratório). O campo de abertura foi medido usando a técnica avançada, de alta resolução e tridimensional, chamada microtomografia computadorizada de raios-X. A concentração de traçador medida foi utilizada para validar uma solução analítica unidimensional da Equação de Advecção-dispersão (ADE). O desemprenho do ajuste da ADE às curvas de passagem experimentais foi avaliado para quatro diferentes tipos de aberturas constantes. Os resultados mostraram que o escoamento de água e o transporte de contaminantes pode ocorrer através de fraturas micrométricas, ocasionando, eventualmente, a contaminação do ASG. A abertura de balanço de massa é a única que pode ser chamada propriamente de \"abertura equivalente\". O uso de aberturas constantes na ADE não permitiu representar completamente o formato das curvas de passagem porque o campo de velocidade não é uniforme e intrinsicamente bidimensional. Portanto, na simulação do transporte deve-se incorporar a heterogeneidade da abertura da fratura. / The contamination risk assessment and the choice of suitable cleanup techniques for pollutants in fractured rock depends on the quantification of the transport phenomena. Fracture geometry often described by the apertures is the major parameter that controls indirectly solute transport in fractured rock. The simplest approach is describing fractures as a pair of smooth parallel plates with constant aperture. However, there is a lack of information about the suitability for using a constant aperture for the conservative solute transport prediction in a single fracture of Serra Geral Aquifer (SGA), Brazil. The aim of this work is to evaluate the effect of aperture variability in a natural single rough-walled fracture of Serra Geral Aquifer on conservative solute transport. A natural core of fractured basalt was used for a hydraulic and tracer tests (laboratory scale). The aperture field was measured using the advanced, high-resolution and tridimensional technique X-ray computed tomography. The measured tracer concentration was validated by means of an analytical solution of the Advection-dispersion Equation (ADE). The ADE fit performance was measured against experimental breakthrough curves for four distinct kind of constant apertures. It was found that water flow and solute transport can take place through micrometric fractures, eventually leading the SGA contamination. Results show that the mass balance aperture is the only appropriate \"equivalent aperture\" for describing solute transport in a single rough-walled fracture. The results showed that ADE is not appropriate for modeling the complete behavior of experimental breakthrough curves because of the dimensional non-uniform velocity field. Therefore, the aperture heterogeneity must be considered in solute transport simulation.

Le but de cette thèse est d'étudier le transport et le dépôt de particules solides dans les écoulements à travers les fractures. Dans un premier temps, l'écoulement monophasique à travers les fractures est étudié afin d'évaluer la validité de la loi cubique locale comme modèle de l'écoulement. Des canaux à parois sinusoïdales à géométrie variable sont utilisés pour représenter différents types de fractures. Un premier développement analytique montre que l'ouverture hydraulique de la fracture diffère de son ouverture moyenne lorsque la rugosité des parois est élevée. La méthode des éléments finis est ensuite utilisée pour résoudre les équations de continuité et de Navier-Stokes et comparer les solutions numériques aux prédictions théoriques de la loi cubique locale sur une gamme relativement étendue de nombres de Reynolds Re. Pour de faibles Re, typiquement inférieurs à 15, la loi cubique locale décrit raisonnablement l'écoulement, surtout lorsque la rugosité et le déphasage entre les parois sont relativement faibles. Dans un deuxième temps, les écoulements chargés de particules sont étudiés. Une approche analytique est d'abord développée pour montrer comment des particules distribuées dans un écoulement stationnaire et laminaire à travers une fracture peuvent être transportées sur de longues distances ou au contraire se déposer à l'intérieur. Plus précisément, une équation simple décrivant la trajectoire d'une particule est établie. Sur la base de cette équation, il est démontré que, quand l'inertie des particules est négligeable, leur comportement dépend directement de la géométrie de la fracture et d'un nombre adimensionnel W qui relie la vitesse de sédimentation des particules à la vitesse moyenne de l'écoulement. L'équation proposée est vérifiée en comparant ses prédictions à des simulations numériques de suivi de particules prenant en compte l'inertie des particules et résolvent complètement les équations de Navier-Stokes. Il est montré que l'équation est valide lorsque l'inertie du fluide est faible. Des diagrammes de régimes, permettant de prévoir le comportement des particules à travers la fracture sont proposés. Enfin, un appareil expérimental conçu dans le but d'effectuer une évaluation pratique du modèle analytique est présenté et les résultats préliminaires sont discutés. Les résultats expérimentaux préliminaires tendent valider le modèle analytique. De façon plus générale, les résultats obtenus à travers ce travail de thèse font progresser nos connaissances du comportement des petites particules transportées dans les écoulements de fractures. Potentiellement, ce travail devrait permettre d'améliorer notre prévision de la pollution souterraine, et peut avoir des applications dans le développement de nouvelles techniques de filtration de l'eau et de séparation des minéraux / The aim of the present thesis is to study the transport and deposition of small solid particles in fracture flows. First, single-phase fracture ow is investigated in order to assess the validity of the local cubic law for modeling ow in corrugated fractures. Channels with sinusoidal walls having different geometrical properties are considered to represent different fracture geometries. It is analytically shown that the hydraulic aperture of the fracture clearly deviates from its mean aperture when the walls roughness is relatively high. The finite element method is then used to solve the continuity and the Navier-Stokes equations and to simulate fracture ow in order to compare with the theoretical predictions of the local cubic law for Reynolds numbers Re in the range 0.067-67. The results show that for low Re, typically less than 15, the local cubic law can properly describe the fracture ow, especially when the fracture walls have small corrugation amplitudes. For Re higher than 15, the local cubic law can still be valid under the conditions that the fracture presents a low aspect ratio, small corrugation amplitude, and moderate phase lag between its walls. Second, particle-laden flows are studied. An analytical approach has been developed to show how particles sparsely distributed in steady and laminar fracture flows can be transported for long distances or conversely deposited inside the channel. More precisely, a rather simple particle trajectory equation is established. Based on this equation, it is demonstrated that when particles' inertia is negligible, their behavior is characterized by the fracture geometry and by a dimensionless number W that relates the ratio of the particles sedimentation terminal velocity to the ow mean velocity. The proposed particle trajectory equation is verified by comparing its predictions to particle tracking numerical simulations taking into account particle inertia and resolving the full Navier-Stokes equations. The equation is shown to be valid under the conditions that ow inertial effects are limited. Based on this trajectory equation, regime diagrams that can predict the behavior of particles entering closed channel flows are built. These diagrams enable to forecast if the particles entering the channel will be either deposited or transported till the channel outlet. Finally, an experimental apparatus that was designed to have a practical assessment of the analytical model is presented. Preliminary experimental results tend to verify the analytical model. Overall, the work presented in this thesis give new insights on the behavior of small particles in fracture flows, which may improve our prediction and control of underground contamination, and may have applications in the development of new water filtration and mineral separation techniques

Une structure en béton doit assurer des fonctions structurales qui vont au delà de la simple résistance. Dans ce cadre, la fissuration du béton armé joue un rôle primordial sur la durabilité, l'étanchéité et même la sûreté des structures. La structure poreuse du béton rend naturellement possible la pénétration au cours du temps d'espèces délétères. En outre, sous l'effet des chargements mécaniques et des conditions environnementales au sens large, le béton se fissure. Les fissures constituent, elles aussi, des voies préférentielles pour la pénétration de fluides ou d'agents agressifs et ajoutent de manière significative leur contribution à la dégradation des performances structurelles. Dans la thèse une stratégie de modélisation macroscopique probabiliste du couplage entre fissuration et transferts de fluides dans les structures en béton est présentée. Le béton est modélisé comme un milieu poreux saturé d'eau tandis que la fissuration (mécanique) est modélisée au travers d'une approche numérique probabiliste tenant compte de l'hétérogénéité naturelle du matériau et des effets d'échelle qu'elle induit. L'hypothèse physique de base du modèle de fissuration est que chaque élément fini peut être considéré comme représentatif d'un volume de matière hétérogène dont le comportement est géré par son degré d'hétérogénéité, défini comme le rapport entre le volume élémentaire et un volume représentatif de l'hétérogénéité du matériau. Dans la formulation développée, les propriétés mécaniques du matériau sont considérées comme des variables aléatoires (non corrélés) distribuées dans les éléments du maillage selon des distributions statistiques validées expérimentalement. Une approche par analyse inverse permet d'accéder aux paramètres de fonctions de distribution qui, selon les hypothèses du modèle, varient en fonction de la dimension des éléments finis. Le couplage fissuration-transfert est traité de manière faible, sous l'hypothèse d'absence d'interaction entre les deux processus (à savoir que la fissuration de l'élément fini, d'origine mécanique, induit une variation locale de sa perméabilité). L'utilisation d'une loi de Poiseuille modifiée et adaptée expérimentalement selon un protocole développé dans le cadre de la thèse permet de mettre en relation une telle variation avec l'ouverture de fissure et de prendre en compte, de manière macroscopique, les principales causes d'écart entre l'écoulement idéalisé, représenté par la loi de Pouiselle, et l'écoulement dans des fissures réelles. Une approche de type Monte-Carlo permet de valider les résultats des simulations mécaniques et hydriques. Les capacités de la stratégie de modélisation proposée en termes de prédiction des débits d'eau en milieu fissuré sont explorées au travers de la simulation d'essais de perméabilité sous charge sur des éprouvettes cylindriques soumises à du fendage. Ces essais sont utilisés dans le cadre du protocole expérimentale. Une première validation à l'échelle d'un élément structurel multifissuré est presentée. Elle consiste en la simulation d'un essai (récemment proposé dans la littérature) developpé pour l'étude de l'impact de la fissuration sur les propriétés de transfert de tirants en béton armé / Concrete durability is strongly affected by the flow of fluids, gas and pollutants in its porous matrix. The presence of cracks weakens the resistance of concrete porous matrix and constitutes preferential flow paths for aggressive components. In the thesis, a probabilistic numerical modeling strategy for modeling fluids transfers in cracked concrete structures is presented. The concrete is modeled in the framework of water saturated porous media. Its (mechanical) cracking is modeled by means of a macroscopic probabilistic approach, explicitly taking into account material heterogeneity as well as size effects. The main assumption of the model, developed in the frame of the the Finite Element Method, is to consider a finite element volume as a volume of heterogeneous material and to assume that physical mechanisms influencing the cracking processes remain the same whatever the scale of observation. At the scale of the finite element, mechanical properties are then functions of its own volume. To describe the heterogeneity of the material, these mechanical properties are consider as uncorrelated random variables distributed over the finite element mesh. Characteristics of statistical distribution laws are directly depending on the degree of heterogeneity of the finite element (the ratio between its volume and the volume of the coarsest aggregate) and of the quality of the cement paste. An inverse analysis approach allows to find their parameters as functions of the elementary volume. A weak coupling between cracking and fluid transfers is considered, under the assumption of no interaction between the two processes (i.e. the mechanically produced cracking of a finite element induce a local variation of its permeability tensor). An experimentally adapted Pouiseuille law, based on an original experimental protocol, allows to relate this permeability variation to the crack aperture and to macroscopically take into account the influence of crack roughness, aperture variation and tortuosity. A Monte-Carlo like approach is used in order to statistically validate mechanical and hydraulic simulations. The coupling strategy is validated in two phases, both at the scale of a laboratory specimen and at the scale of a multi-cracked structural element

The vast majority of oil and gas reserves are trapped in fractured carbonate reservoirs. Most carbonate reservoirs are naturally fractured, with fractures ranging from millimeter- to kilometer-scale. These fractures create complex flow behaviors which impact reservoir characterization, production performance, and, eventually, total recovery. As we know, bridging the gas from plug to near-wellbore, eventually to field scales, is a persisting challenge in modeling Naturally Fractured Reservoirs (NFRs). This dissertation will focus on assessing the fundamental flow mechanisms in fractured rocks at the plug scale, understanding the governing upscaling parameters, and ultimately, developing fit-for-purpose upscaling tools for field-scale implementation. In this dissertation, we first focus on the upscaling of rock fractures under the laminar flow regime. A novel analytical model is presented by incorporating the effects of normal aperture, roughness, and tortuosity. We then investigate the stress-dependent hydraulic behaviors of rock fractures. A new and generalized theoretical model is derived and verified by a dataset collected from public experimental resources. In addition, an efficient coupled flow-geomechanics algorithm is developed to further validate the proposed analytical model. The physics of matrix-fracture interaction and fluid leakage is modeled by a high-resolution, micro-continuum approach, called extended Darcy-Brinkman-Stokes (DBS) equations. We observe the back-flow phenomena for the first time. Machine learning is then implemented into our traditional upscaling work under complex physics (e.g., initial and Klinkenberg effects). We finally consolidate the lab-scale upscaling tools and scale them up to the field scale. We develop a fully coupled hydro-mechanical model based on the Discrete-Fracture Model (DFM) in fractured reservoirs, in which we incorporate localized effects of fracture roughness at the field-scale.