Dans un contexte de réduction internationale des émissions de gaz à effet de serre, les techniques de Captage Transport et Stockage de ce{CO2} (CTSC) apparaissent comme une solution à moyen terme particulièrement efficace. En effet, les capacités de stockage géologique pourraient s'élever jusqu'à plusieurs millions de tonnes de ce{CO2} injectées par an, soit une réduction substantielle des émissions atmosphériques de ce gaz. Une des cibles privilégiées pour la mise en place de cette solution sont les aquifères salins profonds. Ces aquifères sont des formations géologiques contenant une saumure dont la salinité est souvent supérieure à celle de la mer la rendant impropre à la consommation. Cependant, cette technique fait face à de nombreux défis technologiques; en particulier la précipitation des sels, dissous dans l'eau présente initialement dans l'aquifère cible, suite à son évaporation par le ce{CO2} injecté. Les conséquences de cette précipitation sont multiples, mais la plus importante est une modification de l'injectivité, c'est-à-dire des capacités d'injection. La connaissance de l'influence de la précipitation sur l'injectivité est particulièrement importante tant au niveau de l'efficacité du stockage et de l'injection qu'au niveau de la sécurité et de la durabilité du stockage. Le but de ces travaux de thèse est de comparer l'importance relative des phénomènes négatif (colmatage) et positif (fracturation) consécutifs à l'injection de ce{CO2} et à la précipitation des sels. Au vu des nombreux résultats de simulations et de modélisation dans la littérature décrivant le colmatage de la porosité, il a été décidé de porter l'accent sur les effets mécaniques de la cristallisation des sels et la possible déformation de la roche mère. Une modélisation macroscopique et microscopique, tenant compte de deux modes possibles d'évaporation induits par la distribution spatiale de l'eau résiduelle a donc été développée afin de prédire le comportement mécanique d'un matériau poreux soumis à un assèchement par injection de ce{CO2}. Les résultats montrent que la pression de cristallisation consécutive à la croissance d'un cristal en milieu confiné peut atteindre des valeurs susceptibles localement de dépasser la résistance mécanique du matériau, soulignant ainsi l'importance de ces phénomènes dans le comportement mécanique global de l'aquifère. Sur le plan expérimental, les travaux ont porté sur l'utilisation d'un nouveau prototype de percolation réactive afin de reproduire le comportement d'une carotte de roche soumise à l'injection et ainsi obtenir l'évolution des perméabilités dans des conditions similaires à celle d'un aquifère / In a context of international reduction of greenhouse gases emissions, CCS (ce{CO2} Capture and Storage) appears as a particularly interesting midterm solution. Indeed, geological storage capacities may raise to several millions of tons of ce{CO2} injected per year, allowing to reduce substantially the atmospheric emissions of this gas. One of the most interesting targets for the development of this solution are the deep saline aquifers. These aquifers are geological formations containing brine whose salinity is often higher than sea water's, making it unsuitable for human consumption. However, this solution has to cope with numerous technical issues, and in particular, the precipitation of salt initially dissolved in the aquifer brine. Consequences of this precipitation are multiple, but the most important is the modification of the injectivity i.e. the injection capacity. Knowledge of the influence of the precipitation on the injectivity is particularly important for both the storage efficiency and the storage security and durability. The aim of this PhD work is to compare the relative importance of negative (clogging) and positive (fracturing) phenomena following ce{CO2} injection and salt precipitation. Because of the numerous simulations and modelling results in the literature describing the clogging of the porosity, it has been decided to focus on the mechanical effects of the salt crystallization and the possible deformation of the host rock. A macroscopic and microscopic modelling has then been developed, taking into account two possible modes of evaporation induced by the spatial distribution of residual water, in order to predict the behavior of a porous material subjected to the drying by carbon dioxide injection. Results show that crystallization pressure created by the growth of a crystal in a confined medium can reach values susceptible to locally exceed the mechanic resistance of the host rock, highlighting the importance of these phenomena in the global mechanical behavior of the aquifer. At the experimental level, the study of a rock core submitted to the injection of supercritical carbon dioxide has been proceeded on a new reactive percolation prototype in order to obtain the evolution of permeabilities in conditions similar to these of a deep saline aquifer

In this note, we consider an inverse problem in a jump diffusion model. Using characteristic functions we prove the injectivity of the forward operator mapping the five parameters determining the model to the density function of the return distribution.

[pt] A injeção de água como método de recuperação de petróleo é usualmente utilizada devido à sua eficiência em recuperar óleo que encontra-se recluso no reservatório. Um teste de injetividade consiste basicamente em injetar uma fase (água ou gás) continuamente, por um determinado período de tempo, em um reservatório saturado de óleo. A partir da análise do comportamento da pressão no poço, esse procedimento tem por finalidade estimar, além do volume de óleo recuperável, parâmetros do reservatório, tais como permeabilidade, efeito de película, entre outros. Na atualidade, na literatura são encontrados estudos relativos a um único período de injeção (e um único período de fall-off) em reservatórios multicamadas e estudos relativos a reservatórios de camada única considerando vazão de injeção variável. Em vista disto, este trabalho tem como objetivo propor uma solução analítica aproximada para o comportamento da pressão em um reservatório multicamadas considerando um esquema de múltiplas vazões. A acurácia da solução proposta foi avaliada a partir da comparação com um simulador numérico de diferenças finitas em diferentes cenários. Os resultados exprimem uma considerável consonância entre os dados fornecidos pelo simulador numérico e o modelo proposto. / [en] The water injection is usually used as an oil recovery method due to its efficiency in recovering oil that is trapped in the reservoir. An injectivity test basically consists of continuously injecting a phase (water or gas), for a certain period of time, into an oil-saturated reservoir. From the analysis of the wellbore pressure behavior, this procedure aims to estimate, in addition to the volume of recoverable oil, parameters of the reservoir, such as permeability, film effect, among others. Nowadays, in the literature are found studies referring to a single injection period (and a single fall-off period) in multilayer reservoirs and studies referring to a single layer reservoirs considering variable injection flow-rates. In this context, this work aims to propose an approximate analytical solution for the pressure behavior in a multilayer reservoir considering a scheme of multiple flow-rates. The accuracy of the proposed solution was evaluated by comparison to a commercial finite difference-based flow simulator in different scenarios. The results express a considerable agreement between the data provided by the numerical simulator and the proposed model.

Neste texto é feita uma discussão sobre alguns resultados que fornecem condições suficientes para que um difeomorfismo local, do espaço euclideano n-dimensional nele próprio, seja injetivo. Dentro deste cenário, são exploradas as contribuições destes resultados na tentativa de solucionar conhecidas conjecturas no meio científico como a Conjectura Jacobiana e a Conjectura de Ponto Fixo. Do ponto de vista dinâmico, existem relações entre injetividade global e estabilidade assintótica global. Neste sentido, os resultados também são contextualizados com respeito a importantes conjecturas de estabilidade assintótica: Conjectura de Markus-Yamabe e o Problema de LaSalle / We present some results which give suficient conditions for a local diffeomorphism from the n-dimensional Euclidean space into itself be globally injective. Within this context, we consider some partial results addressed to solve the well known Fixed Point Conjecture and Jacobian Conjecture. From the dynamical point of view, there are connections between global injectivity and global asymptotic stability. In this way, we present a solution of the Markus-Yamabe Conjecture and of the LaSalle Problem

We describe some classical results on global injectivity of local dieomorphism on Euclidian spaces. This is not exhaustive, and it does not purport to be a complete history, it simply describes some useful results in injectivity. The first part describes some results related to the Qualitative Theory of Diferential Equations, and presents a characterization of global injectivity on planar applications by using the existence of an isochronous global center. The Global Asymptotic Stability Problem is also described. The second part describes the so called Palais-Smale condition. / Se dan algunos teoremas que garantizan la inyectividad global de los difeomorsmos locales en espacios euclidanos. De momento el trabajo no es aun exaustivo, ni pretende serlo, simplemente se describe algunos resultados utiles en la teoría del estudio de las aplicaciones inyectivas. La primera parte describe algunos resultados relacionados con la teoría cualitativa de las ecuaciones diferenciales, y presenta una caracterización de la inyectividad global de aplicaciones en el plano por medio de la existencia de un centro global isócrono. También se presenta el problema de la estabilidada sintóotica global. La segunda parte describe la "condicion de Palais Smale".

Neste texto é feita uma discussão sobre alguns resultados que fornecem condições suficientes para que um difeomorfismo local, do espaço euclideano n-dimensional nele próprio, seja injetivo. Dentro deste cenário, são exploradas as contribuições destes resultados na tentativa de solucionar conhecidas conjecturas no meio científico como a Conjectura Jacobiana e a Conjectura de Ponto Fixo. Do ponto de vista dinâmico, existem relações entre injetividade global e estabilidade assintótica global. Neste sentido, os resultados também são contextualizados com respeito a importantes conjecturas de estabilidade assintótica: Conjectura de Markus-Yamabe e o Problema de LaSalle / We present some results which give suficient conditions for a local diffeomorphism from the n-dimensional Euclidean space into itself be globally injective. Within this context, we consider some partial results addressed to solve the well known Fixed Point Conjecture and Jacobian Conjecture. From the dynamical point of view, there are connections between global injectivity and global asymptotic stability. In this way, we present a solution of the Markus-Yamabe Conjecture and of the LaSalle Problem

[pt] O teste de injetividade consiste em injetar uma fase, usualmente água, em um reservatório de óleo para coletar informações sobre ele. Conhecer os parâmetros do reservatório pode ser valioso para melhorar a produção de óleo. Muitos estudos têm sido apresentados a respeito do comportamento da pressão em reservatórios multicamadas sob escoamento de fluxo monofásico e, também, durante os testes de injetividade. No entanto, uma solução analítica para o comportamento da pressão em reservatórios de múltiplas camadas durante os testes de injetividade é bem conhecida apenas quando o fluxo cruzado de formação não é considerado. Portanto, o presente trabalho apresenta um modelo analítico no espaço de Laplace para reservatórios radialmente compostos multicamadas considerando o fluxo cruzado de formação sob fluxo monofásico e, então, para reservatórios multicamadas com fluxo cruzado de formação sob fluxo bifásico. A precisão da solução proposta foi verificada através da comparação com um simulador numérico de fluxo. Os resultados fornecidos pelo modelo analítico e pelos dados numéricos foram consistentemente semelhantes. Além disso, os dados obtidos pela solução analítica foram utilizados para estimar a permeabilidade equivalente do reservatório. Os valores calculados apresentaram uma aproximação satisfatória para todos os casos. / [en] The injectivity test consists of injecting a phase, usually water, into an oil reservoir in order to collect information about it. Knowing these reservoir s parameters can be valuable in order to improve oil production. Many studies have been presented regarding the behavior of pressure in multilayered reservoirs under single phase fluid flow and, also, during injectivity tests. However, an analytical solution for pressure behavior in multilayered reservoirs during injectivity tests is well known only when the formation crossflow is not considered. Therefore, the present work attempts to develop an analytical model in the Laplace space for multilayered radially composite reservoirs with formation crossflow under single phase fluid flow, and then, for multilayered reservoirs with formation crossflow under two phase fluid flow. The accuracy of the proposed solution was verified by comparison with a finite difference flow simulator. The results provided by the analytical model and by the numerical data were consistently similar. Furthermore, the data obtained by the analytical solution was used to estimate the reservoir s equivalent permeability. Calculated values presented a satisfactory accuracy for all cases.

[pt] O ES-MDA tem sido usado amplamente no que diz respeito a problemas inversos de reservatórios de petróleo, usando a estatística bayesiana como cerne. Propriedades importantes como a permeabilidade, raio da zona de skin e permeabilidade da zona de skin, são estimadas a partir de dados de histórico de reservatório usando esse método baseado em conjuntos. Nessa tese, a pressão medida no poço durante um teste de injetividade foi calculada usando uma abordagem analítica de um reservatório multicamadas, com zona de skin, usando a Transformada de Laplace. O algoritmo de Stehfest foi usado para inverter os dados para o campo real. Além disso, ao usarmos essa abordagem, conseguimos obter facilmente a vazão em cada camada como um novo dado a ser considerado no ES-MDA, enriquecendo a estimativa dos dados desejados. Por usarmos a vazão e a pressão como dados de entrada no ES-MDA, é de suma importância que a diferença de ordens de grandezas não influencie em nossas estimativas e por isso optou-se por usar o ES-MDA na forma adimensional. Visando uma maior precisão de nossas estimativas, usou-se um algoritmo de otimização dos fatores de inflação do ES-MDA. / [en] The ES-MDA has been extensively used concerning inverse problems of oil reservoirs, using Bayesian statistics as the core. Important properties such as permeability, skin zone radius, and skin zone permeability are estimated from historical reservoir data using this set-based method. In this thesis, the pressure measured at the well during an injectivity test was calculated using an analytical approach of a multilayer reservoir, with skin zone, using the Laplace Transform. Stehfest s algorithm was used to invert the data to the real field. Furthermore, using this approach, we were able to easily obtain the flow rate in each layer as new data to be considered in the ES-MDA, enriching the estimation of the targeted data. As we use flow rate and pressure as input data in the ES-MDA, it is important to assure that the difference in orders of magnitude does not influence our estimates. For this reason, we chose to use the ES-MDA in the dimensionless form. Aiming at a greater precision of our estimates, we used an algorithm to optimize the ES-MDA inflation factors.

Le polymer flooding est une des techniques de récupération assistée des hydrocarbures (RAH) ; elle consiste à injecter une solution de polymères de forte masse moléculaire afin de déplacer plus efficacement le pétrole emprisonné dans la roche. Cependant, une limite importante de cette technique est la possible dégradation mécanique des polymères au cours de l'injection et dans le réservoir, due à une scission des chaînes macromoléculaires induite par l’écoulement. Ce travail de thèse a pour objectif de mieux comprendre les mécanismes et scénarios de scission, mais aussi leur impact sur le procédé de polymer flooding. Nous nous sommes intéressés au seuil de dégradation mécanique de solutions de poly(oxyde d’éthylène) et de de polyacrylamide partiellement hydrolysé, pour différents régimes de concentration (solutions diluées et semi-diluées) en régime laminaire et inertiel, et pour des solvants de différentes qualités. L’étude de la dégradation mécanique des solutions et de leur impact sur les propriétés rhéologiques a été menée à l’aide de différents dispositifs de dégradation et de différents rhéomètres, dont un dispositif microfluidique en élongation ; ces techniques de mesure ont été combinées à des mesures de distribution de masses moléculaires par chromatographie d’exclusion stérique couplée à la diffusion de lumière. L’étude montre en premier lieu qu’une composante élongationnelle est indispensable pour dégrader les chaînes macromoléculaires en solution. Les résultats mettent aussi clairement en évidence que les mécanismes de dégradation sont très différents en régime dilué et semi-dilué. En régime dilué, la dégradation mécanique des solutions de polymères est indépendante du régime d’écoulement et affecte préférentiellement les macromolécules de fortes masses, avec une scission en milieu de chaîne. En revanche, en régime semi-dilué, la dégradation mécanique dépend du régime de l’écoulement : en écoulement laminaire, la dégradation est gouvernée par le réseau d’enchevêtrements et la scission des chaînes est aléatoire, tandis qu’en régime inertiel, les chaînes se dégradent comme en régime dilué, avec le même scénario de scission en milieu de chaîne. Par ailleurs, les résultats montrent que les propriétés rhéologiques en élongation peuvent être très fortement impactées par la dégradation mécanique. Enfin, les résultats de l’étude préliminaire des propriétés d’injectivité dans un milieu poreux d’une solution de polymère semi-diluée faiblement dégradée montrent que la dégradation mécanique améliore l’injectivité du polymère aux abords du puits. / Polymer flooding is a technique used in enhanced oil recovery; it consists in injecting high molecular weight polymer solutions in order improve oil sweep efficiency in the reservoir. However, polymer flooding is challenged by possible mechanical degradation of polymer solutions during injection and in the reservoir, due to the flow induced scission of macromolecules. This work aims at better understanding the scission mechanisms and scenarios, but also their impact on polymer flooding. We investigated the onset of mechanical degradation of poly(ethylene oxide) and partially hydrolysed polyacrylamide solutions, for different concentration regimes (dilute and semi-dilute regimes), under laminar or inertial conditions, but also under good or bad solvent conditions. The study of mechanical degradation of polymer solutions and their impact on the rheological properties was performed using different degradation devices and different rheometers, including a microfluidic extensional device; these investigation techniques were combined with measurements of the molecular weight distributions using size exclusion chromatography coupled with light scattering experiments. The study first shows that an extensional component is needed to get a mechanical degradation of polymer chains. The results also clearly show that the degradation mechanisms are very different in dilute and semi-dilute regime. In dilute regime, the mechanical degradation of polymer solutions does not dependent on flow regime and mainly affects the macromolecules with high molecular weights, with a mid-chain scission scenario. On the other hand, in semi-dilute regime, mechanical degradation depends on flow regime: in laminar flows, degradation is governed by the entanglement network and chain scission is random, whereas in inertial flows, chain degradation is similar to that observed in dilute regime, with the same mid-chain scission scenario. Besides, the results show that the extensional rheological properties can be very strongly affected by mechanical degradation. At last, the results of a preliminary study of the injectivity of a slightly degraded semi-dilute polymer solution in porous media show that mechanical degradation improves polymer injectivity near the wellbore.

Der Grenzwert kleiner Deformationen in Anwesenheit eines gegebenen Risses wird in drei verschiedenen kontinuumsmechanischen Modellen betrachtet. Erstens wird für rein statische Elastizität mit finiter Spannung im Grenzwert kleiner Belastung bewiesen, dass die Nebenbedingung globaler Injektivität im Sinne der Gamma-Konvergenz eine lokale Nichtdurchdringungsbedingung auf dem Riss ergibt. Zweitens wird Deformationsplastizität mit finiten Spannungen und multiplikativer Zerlegung des Spannungstensors behandelt und die Gamma-Konvergenz zu linearisierter Deformationsplastizität mit Rissbedingungen gezeigt. Drittens wird die ratenunabhängige Evolution der Elastoplastizität betrachtet mit einer allgemeineren Klasse globaler Injektivitätsbedingungen für den finiten Fall. Hierbei wird einerseits die evolutionäre Gamma-Konvergenz unter Vernachlässigung der Nebenbedinung gezeigt, andererseits eine Vermutung aufgestellt, unter deren Voraussetzung die evolutionäre Gamma-Konvergenz auch mit Rissbedingungen gilt. / The small-deformation limit in presence of a given crack is considered in three distinct continuummechanical models. First, a purely static finite-strain elasticity model is considered in the limit of small loading, where the constraint of global injectivity is shown to converge in the sense of Gamma-convergence to a local constraint of non-interpenetration along the crack. Second, finitestrain deformation plasticity based on the multiplicative decomposition of the strain tensor is shown to Gamma-converge to linearized deformation elastoplasticity with crack conditions. Third, the rate-independent evolution of elastoplasticity is considered with a generalized class of global injectivity constraints for the finite-strain model. On the one hand, neglecting the constraints the evolutionary Gamma-converge to linearized elastoplasticity is proven. On the other hand, a conjecture is made, subject to which the evolutionary Gamma-convergence with constraints still holds.