The oil production from well fractured carbonate reservoirs is a considerable part of the total oil production in the world. The petroleum resource base in naturally fractured reservoirs is estimated to be in the range of billions of barrels in the U.S and in addition, a multibillion- barrel international oil resource base exists in naturally fractured reservoirs. Gravity drainage is important in some of oil recovery processes, either acting as the driving force in processes using horizontal wells or altering the displacement patterns during water-flooding, chemical flooding, CO2 flooding and other EOR methods. The gravity drainage process has a major effect on oil recovery from oil reservoirs. Gravity drainage driven oil production in naturally fractured and other complex reservoirs falls into two regimes: the balk flow regime and the film flow regime. Oil recovery by gravity drainage in a fractured reservoir strongly depends on the capillary height of the porous medium. Capillarity and gravity forces are usually the major driving forces in fractured reservoirs. This PhD thesis consists of two main parts namely: 1) Experimental works on gravity drainage, and 2) Modeling and simulation of the gravity drainage processes using COMSOL® software. An appropriate design of experiment (DOE) method was selected to find the most important parameters contributing in gravity drainage and then conduct the experiments in a useful as well as economic manner. A two-dimensional experimental setup was employed to investigate free fall gravity drainage (FFGD) and controlled gravity drainage (CGD) using unconsolidated glass beads fractured porous media having various fractures configurations. Flow visualization measurements were carried out. Following the flow visualization experiments, parametric sensitivity analysis was performed considering the effects of different system parameters such as fracture aperture, matrix height, permeability, and fluid properties on the dependent variables including drainage rate, critical pumping rate, maximum drainage rate, recovery factor and so on. These experiments enabled us to capture some aspects of the recovery mechanism and the flow communication between matrix block and fracture during gravity drainage. After analyzing the experimental data for the FFGD test runs, it was found that the rate of liquid flowing from matrix to fracture is proportional to the difference of liquid levels in the matrix and in the fracture. In addition, the characteristic rate and the maximum liquid drainage rate from the fractured models were determined for such a stable gravity-dominated process. The experiments showed that the presence of fracture is more influential in lower matrix permeability systems. For a given fracture-matrix system with different initial liquid saturation conditions, it was seen that the production history can be correlated by plotting the fraction of recoverable liquid as a function of time. Furthermore, the recovery factor can be correlated using dimensionless numbers such as the Bond number and the dimensionless time. For the controlled gravity drainage (CGD) test runs conducted, the experimental results indicated that higher pumping rates cause a higher difference between the liquid levels in the fracture and in the matrix, thus the gas breakthrough happens sooner. Moreover, it was found that as long as the porous medium is drained with a constant liquid pumping rate but lower than critical rate, the height difference between the G-L interfaces in matrix and fracture remains constant. In this study, a new concept of “Critical Pumping Rate” (CPR) was defined at which each particular porous medium has recovery factor equal to the recovery factor for higher rates just before gas breakthrough. The difference between liquid levels in fracture and matrix remains unchanged at rates higher than CPR. Known this particular withdrawal rate, there are two main advantages, namely: 1) choosing a pumping rate lower than it to drain the reservoir without getting gas breakthrough; and 2) understanding the physics of pumping behaviour from fractured media and extending the concept to the real cases. In addition, the maximum liquid pumping rate from each physical model was studied and it was found that the rate depends strongly on the storage capacity of the fractures, petrophysical properties of each model as well as physical properties of test fluids. The critical rate, maximum rate, recovery factor at gas breakthrough and difference of gas liquid interface positions in matrix and fracture were correlated by dimensionless numbers such as Bond number, Capillary, and the ratio of permeabilities. Linear regression correlations presented in this study can predict production history and flow behaviour in the fractured porous media for a wide range of dimensionless numbers. The COMSOL® software was used to numerically simulate the gravity drainage processes in the two-dimensional flow experiments for fractured porous media. The parameters of the model were based on theory, as well as on the results of the two-dimensional gravity drainage experiments. The simulation results for the gravity drainage processes compared favourably with the experimental results, as a good match between the numerical solution and the experimental data was found. The simulation model developed provides a basis for further modeling of gravity drainage process in more complicated porous media.

The oil production from well fractured carbonate reservoirs is a considerable part of the total oil production in the world. The petroleum resource base in naturally fractured reservoirs is estimated to be in the range of billions of barrels in the U.S and in addition, a multibillion- barrel international oil resource base exists in naturally fractured reservoirs. Gravity drainage is important in some of oil recovery processes, either acting as the driving force in processes using horizontal wells or altering the displacement patterns during water-flooding, chemical flooding, CO2 flooding and other EOR methods. The gravity drainage process has a major effect on oil recovery from oil reservoirs. Gravity drainage driven oil production in naturally fractured and other complex reservoirs falls into two regimes: the balk flow regime and the film flow regime. Oil recovery by gravity drainage in a fractured reservoir strongly depends on the capillary height of the porous medium. Capillarity and gravity forces are usually the major driving forces in fractured reservoirs. This PhD thesis consists of two main parts namely: 1) Experimental works on gravity drainage, and 2) Modeling and simulation of the gravity drainage processes using COMSOL® software. An appropriate design of experiment (DOE) method was selected to find the most important parameters contributing in gravity drainage and then conduct the experiments in a useful as well as economic manner. A two-dimensional experimental setup was employed to investigate free fall gravity drainage (FFGD) and controlled gravity drainage (CGD) using unconsolidated glass beads fractured porous media having various fractures configurations. Flow visualization measurements were carried out. Following the flow visualization experiments, parametric sensitivity analysis was performed considering the effects of different system parameters such as fracture aperture, matrix height, permeability, and fluid properties on the dependent variables including drainage rate, critical pumping rate, maximum drainage rate, recovery factor and so on. These experiments enabled us to capture some aspects of the recovery mechanism and the flow communication between matrix block and fracture during gravity drainage. After analyzing the experimental data for the FFGD test runs, it was found that the rate of liquid flowing from matrix to fracture is proportional to the difference of liquid levels in the matrix and in the fracture. In addition, the characteristic rate and the maximum liquid drainage rate from the fractured models were determined for such a stable gravity-dominated process. The experiments showed that the presence of fracture is more influential in lower matrix permeability systems. For a given fracture-matrix system with different initial liquid saturation conditions, it was seen that the production history can be correlated by plotting the fraction of recoverable liquid as a function of time. Furthermore, the recovery factor can be correlated using dimensionless numbers such as the Bond number and the dimensionless time. For the controlled gravity drainage (CGD) test runs conducted, the experimental results indicated that higher pumping rates cause a higher difference between the liquid levels in the fracture and in the matrix, thus the gas breakthrough happens sooner. Moreover, it was found that as long as the porous medium is drained with a constant liquid pumping rate but lower than critical rate, the height difference between the G-L interfaces in matrix and fracture remains constant. In this study, a new concept of “Critical Pumping Rate” (CPR) was defined at which each particular porous medium has recovery factor equal to the recovery factor for higher rates just before gas breakthrough. The difference between liquid levels in fracture and matrix remains unchanged at rates higher than CPR. Known this particular withdrawal rate, there are two main advantages, namely: 1) choosing a pumping rate lower than it to drain the reservoir without getting gas breakthrough; and 2) understanding the physics of pumping behaviour from fractured media and extending the concept to the real cases. In addition, the maximum liquid pumping rate from each physical model was studied and it was found that the rate depends strongly on the storage capacity of the fractures, petrophysical properties of each model as well as physical properties of test fluids. The critical rate, maximum rate, recovery factor at gas breakthrough and difference of gas liquid interface positions in matrix and fracture were correlated by dimensionless numbers such as Bond number, Capillary, and the ratio of permeabilities. Linear regression correlations presented in this study can predict production history and flow behaviour in the fractured porous media for a wide range of dimensionless numbers. The COMSOL® software was used to numerically simulate the gravity drainage processes in the two-dimensional flow experiments for fractured porous media. The parameters of the model were based on theory, as well as on the results of the two-dimensional gravity drainage experiments. The simulation results for the gravity drainage processes compared favourably with the experimental results, as a good match between the numerical solution and the experimental data was found. The simulation model developed provides a basis for further modeling of gravity drainage process in more complicated porous media.

No description available.

Pore scale interaction between matrix and fracture during miscible and immiscible CO2 injection was studied experimentally using visual models. Initially, visualization experiments were conducted on 2-D glass bead packed models by injecting n-heptane (solvent) displacing different kinds of processed oil. The focus was on the displacement patterns and solvent breakthrough controlled by matrix-fracture interaction and the pore scale behaviour of solvent-oil interaction for different fracture and injection conditions (rate, vertical vs. horizontal injection) as well as oil viscosity. Besides the visual investigation, effluent was also analyzed to calculate the solvent cut and oil recovery. Next, the process was modeled numerically using a commercial compositional simulator and the saturation distribution in the matrix was matched to the experimental data. The key parameters in the matching process were the effective diffusion coefficients and the longitudinal and transverse dispersivities. The diffusion coefficients were specified for each fluid and dispersivities were assigned into grid blocks separately for the fracture and the matrix. Finally, glass etched microfluidic models were used to investigate pore scale interaction between the matrix and the fracture. The models were prepared by etching homogeneous and heterogeneous micro scale pore patterns on glass sheets bonded together and then saturated with colored n-decane as the oleic phase. CO2 was injected at miscible and immiscible conditions. The focus was on visual pore scale analysis of miscibility, breakthrough of CO2 and oil/CO2 transfer between the matrix and the fracture under different miscibility, injection rate and wettability conditions. / Petroleum Engineering

[pt] Esse trabalho apresenta um modelo numérico para a análise de processos acoplados de efeitos mecânicos e escoamento bifásico em meios porosos fraturados, com a utilização de diferentes métodos numéricos combinados (Elementos finitos contínuos e descontínuos), e utilizando uma mesma malha de elementos finitos para representar uma célula de modelo de simulação de reservatório. As descontinuidades são inseridas na malha como elementos de nós duplicados colapsados. Empregam-se procedimentos numéricos desenvolvidos em dois grupos distintos. Um primeiro grupo de simulações trata de um procedimento numérico de escoamento bifásico, com ênfase à obtenção de um balanço de volumes verdadeiramente conservativo. Nesta fase, avalia-se uma formulação numérica que emprega um processo em três etapas: o método dos elementos finitos (EF), para a aproximação da equação da pressão; intermediariamente, utiliza-se o método de Raviart-Thomas de mais baixa ordem para aproximação da velocidade; e a aproximação da equação da saturação pelo método dos elementos finitos descontínuos (MEFD), que utiliza um limitador de inclinação multidimensional de modo a evitar oscilações na reconstrução dos dados de saturação. Para fins de validação da formulação desenvolvida, comparam-se os resultados obtidos com simulações utilizando o Método do Volumes Finitos (VF). O segundo grupo de simulações trata de acoplar o módulo mecânico (em EF) ao simulador de escoamento bifásico, de modo que a variação do estado de tensões, decorrente da explotação, seja considerada nas simulações. Essa análise permite uma melhor representação do fenômeno estudado além de proporcionar melhores resultados quanto à chegada da água nos poços produtores, afetando a produtividade do modelo. / [en] This work presents a numerical model for the analysis of coupled processes of mechanical effects and two-phase flow in fractured porous media using different numerical methods (continuous and discontinuous finite elements), and using the same finite element mesh to represent a cell of reservoir simulation model. The discontinuities are inserted into the mesh as elements of collapsed duplicate nodes. Numerical procedures developed in two distinct groups are used. A first group of simulations deals with a numerical two-phase flow procedure, with special emphasis on obtaining a truly conservative volume balance. At this stage, a numerical formulation using a three-step process is evaluated: The Finite Element Method (EF), for the approximation of the pressure equation; the lower order of Raviart-Thomas method is used to velocity approximation; and the approximation of the saturation equation by the discontinuous finite element method (MEFD), using a multidimensional slope limiter in order to avoid oscillations in the reconstruction of the saturation data. For the validation of the developed formulation, the results obtained are compared with simulations using the Finite Volume Method (VF), with focus on the analysis of the conservation of volumes. The second group of simulations couple the mechanical module (in EF) to twophase flow computer program, so the variation of the stress state, due to exploitation, is considered in the simulations. This analysis allows a better representation of the phenomenon. In addition to providing better results regarding the arrival of water in the producing wells, affecting the productivity of the model.

Le but de cette thèse est de développer et d’analyser les méthodes Hybrides d’Ordre Élevé (HHO: Hybrid High-Order, en anglais) pour des problèmes d’interfaces. Nous nous intéressons à deux types d’interfaces (i) les interfaces diffuses, et (ii) les interfaces traitées comme frontières internes du domaine computationnel. La première moitié de ce manuscrit est consacrée aux interfaces diffuses, et plus précisément aux célèbres équations de Cahn–Hilliard qui modélisent le processus de séparation de phase par lequel les deux composants d’un fluide binaire se séparent pour former des domaines purs en chaque composant. Dans la deuxième moitié, nous considérons des modèles à dimension hybride pour la simulation d’écoulements de Darcy et de transports passifs en milieu poreux fracturé, dans lequel la fracture est considérée comme un hyperplan (d’où le terme hybride) qui traverse le domaine computationnel. / The purpose of this Ph.D. thesis is to design and analyse Hybrid High-Order (HHO) methods on some interface problems. By interface, we mean (i) diffuse interface, and (ii) interface as an immersed boundary. The first half of this manuscrit is dedicated to diffuse interface, more precisely we consider the so called Cahn–Hilliard problem that models the process of phase separation, by which the two components of a binary fluid spontaneously separate and form domains pure in each component. In the second half, we deal with the interface as an immersed boundary and consider a hybrid dimensional model for the simulation of Darcy flows and passive transport in fractured porous media, in which the fracture is considered as an hyperplane that crosses our domain of interest.

Cette thèse est consacrée à l'étude mathématique d'un problème inverse en hydrogéologie : le but est d'identifier des fractures en milieu poreux, connaissant des mesures de l'écoulement dans le sous-sol. Le nombre, la localisation et les paramètres physiques des fractures sont recherchés. Ce problème est formulé comme la minimisation au sens des moindres carrés d'une fonctionnelle évaluant l'écart entre les mesures et les résultats du modèle direct. L'écoulement est celui d'un fluide monophasique incompressible (loi de Darcy). Un modèle traitant les fractures comme des interfaces est utilisé. Le problème direct est le modèle de fracture discrétisé par la méthode des éléments finis mixtes hybrides.Pour résoudre ce problème inverse, un nouvel algorithme itératif a été développé, basé sur l’utilisation d’indicateurs de fractures mis au point pendant la thèse. Ces indicateurs donnent une information au premier ordre concernant l'effet de l'ajout d'une nouvelle fracture. Comme ces indicateurs sont peu coûteux, un grand nombre de configurations de fractures sont testées à chaque itération. L’algorithme a été programmé, validé puis testé numériquement dans des situations variées, en utilisant des mesures synthétiques. Il donne des résultats très satisfaisants, bien que ce problème soit réputé difficile.Enfin, l’étude de l’identifiabilité du problème inverse a été amorcée. Pour un modèle simplifié de fractures (failles très perméables, cas le plus courant dans le sous-sol), on a montré que le problème. / This PhD is dedicated to the mathematical study of an inverse problem in hydrogeology: the goal is to identify fractures in porous medium, knowing measurements of the underground flow. The number, the location and the physical parameters of the fracture are looked for. This problem is formulated as the least squares minimization of a function evaluating the misfit between measurements and the result of the direct model. We used a model describing the flow of a monophasic incompressible fluid (Darcy's law), in a porous medium containing some fractures represented by interfaces. The direct problem is the fracture model discretized by the mixed hybrid finite element method. To solve this inverse problem, we developed an iterative algorithm, which is based on the use of fracture indicators that have been developed durig the thesis. These indicators give a first order information concerning the effect of the addition of a new fracture. As these indicators are inexpensive, a large number of configurations of new fractures is tested at each iteration. The algorithm was programmed, validated and tested numerically in various situations, using synthetic measurements. It gives very satisfactory results, although this problem is considered difficult. Finally, an early study of identifiability of the inverse problem of fractures in porous medium has been achieved. It allowed to prove the identifiability for a simplified model (very permeable faults, which is common in the underground). The question of identifiability for the full fracture model remains open.

[pt] Meios porosos fraturados estão presentes em diferentes tipos de formações geológicas, como os maciços rochosos e os reservatórios de petróleo e gás. A modelagem adequada dos sistemas de fraturas presentes nesses meios é de grande relevância para o desenvolvimento de estratégias de exploração e produção dessas formações. Isso porque os processos de fluxo de fluido são fortemente influenciados pelas características dos sistemas de fraturas. Nesse contexto, diversas abordagens têm sido desenvolvidas para a modelagem desses problemas utilizando representações explícitas e implícitas para as fraturas. A representação explícita usando modelos de fraturas discretas fornece resultados precisos, mas possui um custo computacional elevado e apresenta dificuldades na construção de modelos mais complexos. Por outro lado, modelos de representação implícita, como o de dupla porosidade/dupla permeabilidade, são muito atrativos por incorporarem o efeito das fraturas nas simulações sem a necessidade de representá-las no modelo. No entanto, esses modelos são adequados para problemas envolvendo fraturas pequenas e conectadas, possuindo aplicabilidade limitada para representar fraturas principais de maior escala que podem dominar o fluxo. Assim, este trabalho apresenta algumas das abordagens disponíveis para a representação de formações porosas fraturadas. Diferentes cenários foram estudados para avaliar pontos fortes e limitações de cada método em diferentes aplicações. Além disso, uma nova formulação foi proposta para representar o efeito de fraturas isoladas, que se demonstrou eficiente em modelos com considerável número de fraturas. / [en] Fractured porous media are present in different types of geological formations as rock masses and oil and gas reservoirs. The proper modelling of the fractured systems present in these media is of high relevance to the development of production and exploitation strategies of these formations. This is because the fluid flow processes are strongly influenced by the fractured systems characteristics. In this context, several approaches have been developed to model these problems using explicit and implicit representations to fractures. The explicit representation using discrete fracture models provides accurate results, but has a high computational cost and exhibits difficulties to construct more complex models. On the other hand, implicit representation models, as the dual porosity/dual permeability, are very attractive because they incorporate the effect of fractures to simulations without the need to represent them explicitly in the models. However, these models are suitable to problems with small and connected fractures, and have limited capability to represent major fractures of larger scale that can dominate the flow. Therefore, this work shows some of the available approaches to represent fractured porous formations. Moreover, a new formulation was proposed to represent the effect of isolated fractures, which proved to be efficient in models with considerable number of fractures.

[pt] Este trabalho apresenta o desenvolvimento/montagem de um sistema computacional para análise de fluxo em meios porosos, meios fraturados, porosos fraturados e em combinações destes meios, considerando regime permanente ou transiente, sob condições saturadas e não saturadas. O sistema consiste de quatro programas, três programas de funções específicas interligadas por rotinas de programação feitas na linguagem Cmaismais e o quarto é um visualizador de resultados. O FracGen 3D (Telles, 2006) gera fraturas ou famílias de fraturas de forma determinística ou probabilística. O programa ICEM CFD v.14 divide o domínio de interesse em sub-dominios, através da geração de malha de elementos finitos. O programa FTPF-3D (Telles, 2006) utiliza o método de elementos finitos para discretizar as equações governantes no espaço e em diferenças finitas no tempo, e para resolver a não linearidade, utiliza o método iterativo de Picard ou o método iterativo BFGS e finalmente O Pos3D é o responsável pela visualização dos resultados. Neste trabalho foram desenvolvidos cinco exemplos, dois deles para a validação deste procedimento, e três aplicados a um talude típico do Rio de Janeiro, os quais incluem fraturas verticais e juntas de alívio. Estes casos estudados verificam a influência das fraturas nos meios porosos em termos de carga de pressão, totais e campo de velocidades, para a verificação do comportamento hidráulico dos maciços e de eventuais instabilidades. / [en] This work presents the development/assembly of a computational system for flow analysis in porous media, fractured and fractured porous media and in combination of both media, considering steady or transient states under saturated and unsaturated conditions. The system comprehends four computational programs, three of them of specific functions interconnected by Cplusplus programing routines and the last program is an output viewer. FracGen 3D program (Telles, 2006) generates fractures or fracture families in a determinist or probabilistic way. ICEM CFD v.14 program divides the interest domain in sub-domains by means of the element finite mesh generation. FTPF-3D program (Telles, 2006) uses the element finite method to discretize the governing equations in the space domain and the difference finite method for the time domain and for solving the nonlinearity is used the iterative Picard or BFGS method, so that, finally, Pos3D viewer program is answerable by visualization of the results. In the present dissertation five examples were developed, two of them for the validation of this procedure and the three others applied to a typical slope in Rio de Janeiro, which include vertical fractures and relief joints on their slopes. All those studied cases evaluate the influence of the fractures on porous media in terms of pressure and total heads and velocity fields for verifying of the hydraulic behavior of solid masses and eventual instabilities.

[pt] O rebaixamento e controle das águas subterrâneas são atividades implementadas e monitoradas de forma contínua ao longo da vida dos projetos de mineração subterrânea ou a céu aberto. A implementação apropriada e eficiente destas atividades depende de estudos hidrogeológicos de grande porte, que permitem avaliar os sistemas de controle mais adequados. A procura da eficiência técnico-econômica destes processos demanda análises numéricas de fluxo tridimensionais de toda a região em estudo, caracterizada por profundas e complexas estratificações de materiais permeáveis abaixo do lençol freático, como normalmente abrangem projetos de mineração, onde as soluções analíticas não podem mais ser aplicadas. O presente trabalho de pesquisa contribui na melhor compreensão das formulações numéricas que representam o comportamento do fluxo subterrâneo, através de dois estudos de caso, o primeiro em uma mina subterrânea e segundo em uma mina superficial. No caso da mina subterrânea foram incorporadas feições cársticas através de elementos discretos 1D dentro de um modelo tridimensional de elementos finitos com o intuito de representar caminhos preferenciais de fluxo. Foram discutidas as vantagens de incorporar tais feições de forma explicita, quantificando o fluxo que passam por estas, que alimentam à mina através de conexões diretas com um rio adjacente. Estes elementos discretos permitem uma representação mais realista do meio hidrogeológico e ao mesmo tempo, uma avaliação mais aprimorada dos efeitos no comportamento do fluxo subterrâneo devido à impermeabilização superficial do rio, como a solução mais coerente para este problema de infiltração. Também foi elaborado um modelo hidrogeológico conceitual para representar o comportamento hidrogeológico de uma mina a céu aberto, desenvolvendo uma sistemática de uso adequado das condições de contorno e de restrição, a calibração deste modelo e a verificação de diferentes cenários de fluxo, como resultado da incorporação das diferentes técnicas de controle das águas avaliadas em regime transiente, que abrange poços de bombeamento, paredes cut-off assim como ponteiras filtrantes e drenos horizontais. As diferentes técnicas modeladas mostraram resultados satisfatórios, sendo que arranjos de várias técnicas, configuradas de forma localizada, resultam ser mais recomendáveis e eficientes para tratar problemas particulares. / [en] Dewatering and groundwater control are activities continuously implemented and monitored throughout the duration of underground mining or open pit projects. The proper and efficient implementation of these activities depends on large hydrogeological studies, for assessing the most appropriate control systems. The demand for technical and economic efficiency of these processes requires three-dimensional flow numerical analysis of the entire study area, characterized by deep and complex stratifications of permeable materials below the water table, as usually cover mining projects, where analytical solutions cannot be applied. The present research contributes to a better understanding of the numerical formulations that represent the behavior of groundwater flow via two case studies—the first in an underground mine and the second in a surface mine. In the case of the underground mine, 1D discrete elements were incorporated within a finite-three dimensional model in order to represent preferential flow paths. The advantages of incorporating such features explicitly to quantify the flow passing through them, that feed the mine through direct connections with an adjacent river, were discussed. The use of discrete elements allows for a more realistic representation of the hydrogeological environment and, at the same time, a more refined assessment of the effects on the behavior of groundwater flow due to surface sealing of the river, as the most coherent solution to this infiltration problem. Furthermore, a conceptual hidrogeologic model representing the hydrogeological behavior of an open pit mine was created, developing a system of the appropriate use of boundary and constraint conditions, calibrating the model and verifying different flow scenarios, as a result of the incorporation of different water control techniques assessed in transient regime, such as covering pumping wells, cut-off walls as well as wellpoints and horizontal drains. The different techniques modeled showed satisfactory results, with various arrangements of techniques configured in a localized form resulting in the most desirable and efficient treatments for particular problems.