Despite bold steps taken worldwide for the replacement or the reduction of the world’s dependence on fossil fuels, economic and societal realities suggest that a transition to alternative energy forms will be, at best, gradual. It also appears that exploration for new reserves is becoming increasingly more difficult both from a technical and an economic point of view, despite the advent of new technologies. These trends place renewed emphasis on maximizing oil recovery from known fields. In this sense, low-cost and reliable enhanced oil recovery (EOR) methods have a strong role to play. The goal of this dissertation is to explore, using computational simulations, the feasibility of the, so-called, seismic or elastic-wave EOR method, and to provide the mathematical/computational framework under which the method can be systematically assessed, and its feasibility evaluated, on a reservoir-specific basis. A central question is whether elastic waves can generate sufficient motion to increase oil mobility in previously bypassed reservoir zones, and thus lead to increased production rates, and to the recovery of otherwise unexploited oil. To address the many questions surrounding the feasibility of the elastic-wave EOR method, we formulate an inverse source problem, whereby we seek to determine the excitations (wave sources) one needs to prescribe in order to induce an a priori selected maximization mobility outcome to a previously well-characterized reservoir. In the industry’s parlance, we attempt to address questions of the form: how does one shake a reservoir?, or what is the “resonance” frequency of a reservoir?. We discuss first the case of wellbore wave sources, but conclude that surface sources have a better chance of focusing energy to a given reservoir. We, then, discuss a partial-differential-equation-constrained optimization approach for resolving the inverse source problem associated with surface sources, and present a numerical algorithm that robustly provides the necessary excitations that maximize a mobility metric in the reservoir. To this end, we form a Lagrangian encompassing the maximization goal and the underlying physics of the problem, expressed through the side imposition of the governing partial differential equations. We seek to satisfy the first-order optimality conditions, whose vanishing gives rise to a systematic process that, in turn, leads to the prescription of the wave source signals. We explore different (indirect) mobility metrics (kinetic energy or acceleration field maximization), and report numerical experiments under three different settings: (a) targeted formations within one-dimensional multi-layered elastic solids system of semi-infinite extent; (b) targeted formations embedded in a two-dimensional semi-infinite heterogeneous elastic solid medium; and (c) targeted poroelastic formations embedded within elastic heterogeneous surroundings in one dimension. The numerical experiments, employing hypothetical subsurface formation models subjected to, initially unknown, ground surface wave sources, demonstrate that the numerical optimizer leads robustly to optimal loading signals and the illumination of the target formations. Thus, we demonstrate that the theoretical framework for the elastic wave EOR method developed in this dissertation can systematically address the application of the method on a reservoir-specific basis. From an application point of view and based on the numerical experiments reported herein, for shallow reservoirs there is strong promise for increased production. The case of deeper reservoirs can only be addressed with further research that builds on the findings of this work, as we report in the last chapter. / text

Transcapillary exchange is the movement of fluid and molecules through the porous capillary wall, and is important in maintaining homeostasis of bodily tissues. The classical view of this process is that of Starling's hypothesis, in which the forces driving filtration or absorption are the hydrostatic and osmotic pressure differences across the capillary wall. However, experimental evidence has emerged suggesting the importance of the capillary wall ultrastructure, and thus rather than the global differences between capillary and tissue, it is the local difference across a structure lining the capillary wall known as the endothelial glycocalyx that determines filtration. Hu and Weinbaum presented a detailed cellular level microstructural model of this phenomenon which was able to explain some experimental discrepancies. In this Thesis, rather than describing the microstructural details, the capillary wall is treated as a poroelastic material. The assumptions of poroelasticity theory are such that the detailed pore structure is smeared out and replaced by an idealized homogeneous system in which the fluid and solid phases coexist at each point. The advantage of this approach is that the mathematical problem is greatly simplified such that analytical solutions of the governing equations may be obtained. This approach also allows calculation of the stress and strain distribution in the tissue. We depart from classical poroelasticity, however, due to the fact that since there are concentration gradients within the capillary wall, the filtration is driven by both hydrostatic and osmotic pressure gradients. The model predictions for the filtration flux as a function of capillary pressure compares favourably with both experimental observations and the predictions of the microstructural models. An important factor implicated in transcapillary exchange is the endothelial glycocalyx, which was shown experimentally to protect against edema formation. Using our theory in combination with the experimental measurements of glycocalyx thickness and pericapillary space dimension (PSD), we make a quantitative comparison for the excess flow as a result of a deteriorated glycocalyx, which shows reasonably good agreement with the data. Since many of the parameters in the model are difficult to measure, a sensitivity analysis was performed on the most important of these. Finally, since there was variation in the measurements of glycocalyx thickness and PSD, we used probability distributions to represent the data, and performed further calculations to obtain ranges of likely values for the various parameters. This work could find applications in cardiovascular disease, where the glycocalyx is degraded or absent, and in cancer research, where the abnormal vasculature is an impediment to the efficient delivery of anti-cancer drugs.

The effect of coupled thermo-poroelastic behavior on hydraulic fracture propagation is of much interest in geothermal- and petroleum-related geomechanics problems such as wellbore stability and hydraulic fracturing as pore pressure and temperature variations can significantly induce rock deformation, fracture initiation, and propagation. In this dissertation, a two-dimensional (2D) boundary element method (BEM) was developed to simulate the fully coupled thermo-poroelastic fracture propagation process. The influence of pore pressure and temperature changes on the fracture propagation length and path, as well as on stress and pore pressure distribution near wellbores and fractures, was considered in isotropic and homogeneous rock formations. The BEM used in this work consists of the displacement discontinuity (DD) method and the fictitious stress (FS) method. Also, a combined FS-DD numerical model was implemented for the hydraulically or thermally-induced fractures in the vicinity of a wellbore. The linear elastic fracture mechanics (LEFM) theory was adopted to numerically model within the framework of poroelasticity and thermo-poroelasticity theory. For high accuracy of crack tip modeling, a special displacement discontinuity tip element was developed and extended to capture the pore pressure and temperature influence at the tip. For poroelastic fracture propagation, a steadily propagating crack driven by fluid pressure was modeled to find the effect of pore pressure on crack path under the two limiting poroelastic conditions (undrained and drained). The results indicate that the pore pressure diffusion has no influence on the crack growth under the undrained condition because the crack propagation velocity is too fast for the diffusion effect to take place. On the other hand, its influence on the crack path under the drained condition with its low propagation velocity has significance because it induces a change in principal stress direction, resulting in an alteration of fracture orientation. For the thermal fracturing, when the rock around a wellbore and a main fracture is cooled by injecting cold water in a hot reservoir, the rapid decrease in temperature gives rise to thermal stress, which causes a crack to initiate and propagate into the rock matrix. The single and multiple fracture propagation caused by transient cooling in both thermoelastic and poro-thermoelastic rock were numerically modeled. The results of this study indicate that the thermal stresses induced by cooling may exceed the in-situ stress in the reservoir, creating secondary fractures perpendicular to main fracture. Furthermore, the faster cooling rate produces longer crack extension of the secondary thermal fractures. This implies that the faster cooling induces a higher tensile stress zone around the fracture, which tends to produce larger driving forces to make the secondary fractures penetrate deeper into the geothermal reservoir.

In this dissertation we study multiscale methods for slowly varying porous media, fluid and solid coupling, and application to geomechanics. The thesis consists of three closely connected results. We outline them and their relation. First, we derive a homogenization result for Stokes flow in slowly varying porous media. These results are important for homogenization in deformable porous media. Traditionally, these techniques are applied to periodic media, however, in the case of Fluid-Structure Interaction (FSI) slowly varying domains occur naturally. We then develop a computational methodology to compute effective quantities to construct homogenized equations for such media. Next, to extend traditional geomechanics models based primarily on the Biot equations, we use formal two-scale asymptotic techniques to homogenize the fully coupled FSI model. Prior models have assumed trivial pore scale deformation. Using the FSI model as a fine-scale model, we are able to incorporate non-trivial pore scale deformation into the macroscopic equations. The primary challenge here being the fluid and solid equations are represented in different coordinate frames. We reformulate the fluid equation in the fixed undeformed frame. This unified domain formulation is known as the Arbitrary Lagrange-Eulerian (ALE). Finally, we utilize the ALE formulation of the Stokes equations to develop an efficient multiscale finite element method. We use this method to compute the permeability tensor with much less computational cost. We build a dense hierarchy of macro-grids and a corresponding collection of nested approximation spaces. We solve local cell problems at dense macro-grids with low accuracy and use neighboring high accuracy solves to correct. With this method we obtain the same order of accuracy as we would if we computed all the local problems with highest accuracy.

It is perhaps paradoxical that many material properties arise from the absence of material rather than the presence of it. For example, the strength, stiffness, and toughness of a concrete are related to its pore structure. Furthermore, the volume, size distribution, and interconnectivity of porosity is important for understanding permeability, diffusivity, and capillary action occurring in concrete, which are necessary for predicting service lives in aggressive environments. This research advances the state-of-the-art of multiscale characterization of cement-based materials, and uses this characterization information to model the material behavior under competing durability concerns. In the first part of this research, a novel method is proposed to characterize the entrained air void system. In the second and third parts of this research, microstructural characterization is used in tandem with mechanical models to investigate the behavior of cementitious materials when exposed to rapid rates of loading and to cyclic freezing and thawing. First, a novel analytical technique is presented which reconstructs the 3D entrained air void distribution in hardened concrete using 2D image analysis. This method proposes a new spacing factor, which is believed to be more sensitive to microstructural changes than the current spacing factor commonly utilized in practiced, and specified in ASTM C457, as a measure of concrete's ability to resist to damage under cyclic freeze/thaw loading. This has the potential to improve economy by improving the quality of petrographic assessment and reducing the need for more expensive and time-consuming freeze/thaw tests, while also promoting the durability of concrete. Second, quantitative measurements of the sizes, shapes, and spatial arrangements of flaws which are through to drive failure at strain rates above 100/s were obtained in order to model mortar subjected to high strain-rate loading (i.e., extremes in load rate). A micromechanics model was used to study the ways in which flaw geometry and flaw interaction govern damage. A key finding suggests that dynamic strength may be multimodal, with larger flaws shifting the dynamic strength upwards into the highest strength failure mode. Third, a robust theoretical approach, based upon poroelasticity, is presented to further validate the utility of the novel spacing factor proposed this research. The model is truly multiscale, using in its formulation pore size data ranging from the nanoscale to the micro-scale, entrained air data from the micro-scale to the millimeter scale, and infers a representative volume element on the centimeter scale. The results provide an underlying physical basis for the performance of the novel spacing factor. Furthermore, the framework could be used as a forensic tool, or as a tool to optimize the entrained air void system against freeze/thaw damage.

A poroelastic finite element formulation originally derived for modeling porous absorbing material in air is adapted to the problem of acoustic scattering from a poroelastic seafloor with a one-dimensional randomly rough interface. The developed formulation is verified through calculation of the plane wave reflection coefficient for the case of a flat surface and comparison with the well known analytical solution. The scattering strengths are then obtained for two different sets of material properties and roughness parameters using a Monte Carlo approach. These numerical results are compared with those given by three analytic scattering models---perturbation theory, the Kirchhoff approximation, and the small-slope approximation---and from those calculated using two finite element formulations where the sediment is modeled as an acoustic fluid. / text

Manifestations of the tidal force have been known to humanity since an- tiquity. The oldest extant remarks on the origin of the tidal force are in the Natural History of Pliny the Elder. He also left us remarks on periodic changes of water-level in wells. This phenomenon does not necessarily have to be connected to the proximity of seas. As such, it is a subject of research since the end of 19th century. Exploring the mechanisms with which the tidal force affects the groundwater level requires combining the findings of geology and hydrogeology but also the knowledge of hydraulics and geomechanics of porous media and certain understanding of astronomy. This thesis contribu- tes to the knowledge of the mechanism of tidal oscillations in groundwater measured in a borehole near Teplice nad Metují in Police Basin. It utilizes models based on the knowledge of geological and hydrogeological structure of the surroundings of the borehole. It investigates the relation between the physical properties of porous media and the amplitude and phase of the tidal oscillations and presents solutions of the models.

Conventional AVO analysis has been used for the past 4 decades to aid in locating oil and gas reservoirs for extraction. It is, however, not possible to use it to acquire information on the porosity of the rock, the fluid saturation or other important petrophysical parameters. In this thesis, I study the effects of attenuation on seismic waveform signatures, due to wave induced fluid-flow. In the first part of the thesis, 2 models were used to synthetically model the attenuation caused by the wave induced fluid-flow: White's model and the double-porosity dual-permeability (DPDP) model. The parameters used for modeling were both synthetic and acquired from real well data of a known oil field off the coast of Norway. White's model was found to model relatively high attenuation (5%) for intermediately consolidated gas reservoirs while oil saturated intermediately consolidated reservoirs showed such low attenuation (0.3%) that it is easy to say that for the real-world situation it would not be detected. The DPDP model seemed to be able to better describe the attenuation and gave attenuations up to 10% for an intermediately consolidated oil reservoir, but due to lack of parameters from well data it was not sufficiently able to model the real-world situation. The synthetic data, however, show interesting characteristics and it is therefore recommended that more and detailed well parameters be acquired if the research should continue. For the second part, Svenska Petroleum Exploration AB and Det Norske Oljeselskap ASA provided stacked seismic data that were spectrally analyzed for hints of attenuation variation with frequency (using Fourier Transform and Complex Spectral Decomposition). Twelve locations, on the stacked seismic cube, were analyzed; six oil saturated; and six (assumed) water saturated. At each location, a main trace was selected along with the two nearby traces on each side of it (five in total). The Complex Spectral Decomposition method seemed unable to correctly break down the stacked section's signal, which is why Fourier Transform was used for further analysis. The frequency analysis showed a peak at ~30 Hz for both oil and water saturated reservoirs which seems like a characteristic frequency of the source, but that was unfortunately not confirmed and not enough time was available to test the assumption. The Fourier transform seems to show some difference between oil and water saturated traces, but that could well be because of lithological differences and not the pore fluid. It is therefore recommended, if research is to be continued, that 4D seismic data is used to analyze the same location with respect to time. It is also recommended that pre-stack or shot data be used as information is lost in stacked data. / Konventionell AVO-analys har använts under fyra deceniär som ett hjälpmedel för att finna olje- och gasreserver, men tekniken kan även användas för att erhålla information om bergets porositet, vätskemättnaden och andra viktiga petrofysiska parametrar. I denna avhandlingen har jag studerat hur våginducerat vätskeflöde påverkar dämpningen av den seismiska vågformssignaturen. I den första delen av avhandlingen användes två metoder för att syntetisk modellera dämpning orsakad av våginducerat vätskeflöde: "White's modell" och "double-porosity dual-permeability (DPDP) modellen". Både syntetiska parametrar och verkliga parametrar från borrhålsdata från ett känt norskt oljefält användes vid modelleringen. White's modell visade sig modellera relativt kraftig dämpning (5%) för medelstarkt konsoliderade gasreservoarer medan för oljereservoarer med motsvaranda konsolidering dämpningen var så låg (0.3%) att det är uppenbart att i en verklig situation skulle dämpningen inte vara mätbar. DPDP modelleringen verkar vara bättre på att beskriva dämpningen och gav dämpningar upp till 10% för en medelstarkt konsoliderad oljereservoar. Brist på parametrar från borrhålsdata gjorde att det inte var möjligt att på ett tillfredställande sätt modellera en verklig situation.Dock visade syntetisk data intressant karaktäristik och det rekommenderas därför att mer och detaljerade borrhålsparametrar mäts om ytterligare forskning om detta ska genomföras. För den andra delen av avhandlingen har Svenska Petroleum Exploration AB och Det Norske Oljeselskap ASA bidragit med stackad seismisk data som även var spectralanalyserad för indikationer på frekvensberoende dämpningsvariationer (utfört med fouriertransform och komplex spectraldekomposition). Tolv områden på den stackade kuben analyserades; sex oljemättade och sex som antogs vara vattenmättade. I varje område valdes en huvudtracé och de två närmaste tracéerna på vardera sida (totalt fem tracéer). Metoden med komplex spectraldekomposition klarade inte att analysera signalen från den stackade sektionen, varför fouriertransform användes för vidare analys. Frekvensanalysen gav en topp vid ~30 Hz för både olje- och vattenmättade reservoarer vilket tycks vara en karaktäristisk frekvens för källan. Detta kunde tyvärr inte bekräftas och tiden räckte inte till för att testa antagandet. Fouriertransformen tycks visa en viss skillnad mellan olje- och vattenmättade tracéer, men det kan också bero på skillnad i litologin snarare än porvätskan. Där för rekommenderas vid fortsättning på denna forskning att 4D seismisk data används för att analysera samma område men med data från olika tidpunkter. Det rekommenderas även att ostackad eller råa skott-data används eftersom väsentlig information kan försvinna när data stackas. / <p>Advisor present: Dr. Chris Juhlin</p><p>Examiner: Dr. Milovan Urosevic</p><p>Opponent: Álvaro Polín Tornero</p>

[pt] Em operações de perfuração, é importante ter uma estimativa do gradiente de fratura de determinada formação, como o objetivo de poder estimar o máximo peso da lama necessária para a próxima seção da formação rochosa, antes de colocar o revestimento. Por esse motivo, são realizados ensaios de Leak-Off para determinar a máxima pressão que a nova seção do poço pode sustentar sem fraturar ou perder fluido, sendo realizados durante a fase de perfuração do poço, nas formações imediatamente abaixo de cada sapata de revestimento. A finalidade deste estudo é realizar a simulação numérica deste ensaio usando um programa comercial de elementos finitos para calcular a pressão de Leak-Off, considerando a taxa de bombeamento como um dado de entrada do problema e a pressão na parede do poço como uma resposta. O trabalho abordará dois cenários: uma formação rochosa permeável e uma formação rochosa impermeável constituída de rocha de sal. Deste modo, para um estudo de uma análise real de um ensaio de Leak-Off em rocha permeável e rocha impermeável, torna-se necessário a utilização de modelos que considerem poroelasticidade e fluência, respectivamente. Para a caracterização do comportamento da rocha de sal foi usada uma lei de fluência de duplo mecanismo de deformação, que considera apenas os mecanismos de fluência: planar e indefinido. Os modelos estudados foram bidimensionais e analisados sobre a hipótese de deformação plana. A hipótese, de que a pressão de Leak-Off é atingida quando a tensão tangencial efetiva é igual a zero (calculada graficamente), foi considerada. Finalmente, foram simulados alguns casos para verificar os possíveis efeitos da alteração da permeabilidade e influência do fluido de pressurização no cálculo da pressão de Leak-Off em rocha permeável. / [en] In drilling operations, it is important to have an estimate of the fracture gradient of certain formation, in order to being able to estimate the maximum mud weight required for the next section of the rock formation, before casing is placed. For this reason, Leak-Off tests are conducted to determine the maximum pressure that the new section of the well can support without fracturing or losing fluid, being made during the drilling phase of the well in formations immediately below each casing shoe. The purpose this study is to perform the numerical simulation of this test using a commercial finite element program to calculate the Leak-Off pressure, considering the pumping rate as an input data of the problem and pressure at the borehole wall as the answer. The work will address two cases: a permeable rock formation and an impermeable rock formation composed of salt rock. Thus, for studying a real analysis of a Leak-Off test in permeable and impermeable rock, it becomes necessary to use models that consider poroelasticity and creep, respectively. For the characterization of salt rock it was used a creep law of dual mechanism of deformation, which considers only the dislocation creep mechanisms: planar and undefined. The two-dimensional models were studied and analyzed under the assumption of plane strain. The hypothesis that the Leak-Off pressure is reached when the effective tangential stress is zero (estimated graphically), was considered. Finally, some cases were simulated to check the possible effects of changing the permeability and the influence of pressurized fluid in the calculation of Leak-Off pressure in the permeable rock.

La pose d’une Prothèse Totale de Hanche est l’une des chirurgies orthopédiques les plus pratiquées, et représente un enjeu économique et de santé publique majeur. Ainsi, il est essentiel de comprendre le comportement mécanique de l’os et sa réaction à la suite d’une telle chirurgie. La simulation numérique joue un rôle intéressant dans cette perspective, permettant la reproduction et l’analyse de la réponse osseuse aux stimulus externes. L’os est un matériau complexe présentant une structure hiérarchique et poreuse, et une capacité naturelle d’adaptation structurelle grâce à des cellules spécifiques sensibles aux mouvements de fluide. Basé sur ces caractéristiques, un modèle multi-échelle a été développé au cours de cette thèse dans le but de modéliser la réponse de l’os soumis à des sollicitations mécaniques externes. Le modèle développé repose sur la méthode d’homogénéisation pour les structures périodiques basé sur un développement asymptotique. Il simule l’os cortical comme une structure homogène, composé d’une microstructure périodique, d’une porosité de 5%, saturé de fluide interstitiel qui suit dans ce cas la loi de Darcy. La première application du modèle développé est un cas d’étude, consistant en un volume d’os chargé en compression, permettant la détermination d’une raideur poroélastique équivalente. En considérant principalement deux cas extrêmes de conditions aux limites en fluide, l’analyse de la réponse structurelle correspondante permet d’avoir un aperçu de la contribution du fluide dans le comportement mécanique d’un tel matériau, et en particulier de sa raideur équivalente. Ce paramètre est soit réduit (lorsque le fluide peut sortir de la structure), soit augmenté (lorsque le fluide est confiné dans la structure). Pour valider ce modèle, une étude numérique et expérimentale sont proposées. La validation numérique permet l’estimation de la pertinence du modèle en faisant varier certains paramètres d’entrée comme les propriétés matériaux ou les conditions aux limites. Puis, une validation expérimentale est mise en place. En comparaison, des données issues d’un échantillon d’os trabéculaire de hanche mis en compression sont utilisées. La raideur équivalente de l’échantillon est calculée et comparée à celle obtenue expérimentalement. Les courbes obtenues présentent des résultats similaires et permettent d’attester de la validité du modèle compte tenu des circonstances d’essais. Ainsi, le modèle numérique développé, s’inscrit dans l’objectif de fournir un modèle bio-fidèle de l’os, afin de déterminer les paramètres critiques permettant d’avoir une influence sur le remodelage osseux. En prévision de l’élaboration et de la production de nouvelles générations de prothèses, ce modèle numérique d’os présente à la fois le compromis intéressant de la pertinence scientifique sans requérir des ressources numériques excessives, nécessaires à son application en tant qu’outil de prévision pré-opératoire. / Total Hip Arthroplasty is nowadays one of the most performed orthopedic surgery and is representing a major health and economic issue. Thus, it is essential to provide a better understanding of bone mechanical behavior and its reaction to the implantation of a device such as a hip prosthesis. Numerical simulation plays a key role on this challenge, allowing for the reproduction and analysis of the bone response to the external stimuli. Bone is a complex material showing a hierarchical and porous structure, and natural ability to remodel itself thanks to specific cells, which are sensitive to fluid flows. Based on these characteristics, a multiscale numerical model has been developed in order to simulate the bone response under external mechanical solicitations. The developed model relies on the homogenization technique for periodic structures based on an asymptotic expansion. It simulates cortical bone as a homogeneous structure. It is constituted of a porous microstructure with a 5% saturated with bone fluid, which, in the considered conditions, follows the Darcy’s law. The first application of the developed model is a case study, consisting in the loading of a finite volume of bone, allowing for the determination of an equivalent poroelastic stiffness. Focusing on two extreme fluid boundary conditions, the analysis of the corresponding structural response provides an overview of the fluid contribution to the poroelastic behavior, impacting the equivalent stiffness of the considered material. This parameter is either reduced (when the fluid can flow out of the structure) or increased (when the fluid is confined the structure). To validate the developed model, both numerical and experimental validation are proposed. The numerical validation consists in the estimation of the model accuracy when varying parameters such as material properties or boundary conditions. Then, an experimental validation is set up. As a reference case, a previous work on a cubic trabecular bone sample, extracted from a human hip and put under a compressive load, has been used. Increasing the load applied on the top of the bone specimen, the displacement is extracted, allowing the computation of the equivalent strain-stress curve. The equivalent stiffness of the bone specimen, calculated numerically by the developed numerical tool, is then compared with the one from the experiments. A good agreement between the curves attests the validity of the developed numerical model, accounting for both the solid matrix and fluid contributions. The presented poroelastic numerical, is here developed in the perspective of providing a bio-reliable model of bones, to determine the critical parameters that might impact bone remodeling. Towards the design and manufacturing of new generation of prosthesis, this bone model shows both accuracy and ease of computation, which will be required for its application as a preoperative or design tool.