Waterflooding involves the injection of water to displace oil from oil and gas reservoirs. Well over 80% of oil reservoirs will undergo waterflooding at some point in their life. It is, therefore, important to understand some key aspects of this process that have hitherto not been well studied. This dissertation investigates the following aspects of waterflooding: (i) the filtration of solids and oil-in-water emulsions in fractured and unfractured injection wells, (ii) the generation and filtration of oil-in-water (O/W) emulsion droplets in the near-well region or in the fracture, (iii) the height-growth and containment of injection-induced fractures, and (iv) the stress reorientation induced by water injection when waterflooding reservoirs. These aspects are investigated as separate physical phenomena, but their impacts are integrated using the platform of a comprehensive waterflooding injection well model. The first phenomenon investigated is filtration in frac-packed injectors. During long-term water injection, solid particles in the injection water may deposit in the proppant pack of frac-packed injectors. Researchers have not fully understood whether particles will travel without plugging the frac-packs or deposit in the near-well area under the high-velocity flow conditions in the proppants. Filtration behavior under frac-pack flow conditions is the most important factor that determines overall injector performance. In this dissertation the filtration of injected solids under these conditions was experimentally studied, and the effect of frac-pack filtration on the injector performance was predicted. The flow of dilute oil droplets in a porous medium under near-well conditions was experimentally investigated. When the porous medium has a residual oil saturation, oil droplets can be generated by viscous forces overcoming entrapping capillary forces. The generated oil droplets will subsequently participate in filtration processes along with injected oil droplets. If this occurs in the near-injector area, the injectivity can severely decline and this may require expensive remediation processes. In this study, prediction of O/W emulsion flow was improved by experimental observations of the rates of generation and filtration of oil droplets. In a larger scale problem, a 3-dimensional model of water-injection-induced fracture was developed to predict the fracture height growth. If a fracture breaches the bounding layers, the sweep efficiency can be significantly impaired and it could have severe environmental consequences (such as contamination of shallower aquifers or the seabed). During long-term water injection, fracture growth can only be simulated properly when the filtration near fractures, thermo-elastic stress changes and reservoir fluid flow behavior are all concurrently calculated. Based on this new model, the impact of reservoir stress conditions, mechanical properties, and injection-water quality on fracture growth was studied. On a reservoir-scale, the stress reorientation caused by injection-production activities during waterflooding was investigated. A new finite-volume multi-phase reservoir simulation with poro- and thermo-elasticity was developed. This model was applied to various waterflooding well patterns, such as five-, nine-spot, line-drive and horizontal well pairs, and the critical geomechanical responses by injection-production activities during waterflooding operations were analyzed. The model can be used to predict the direction of induced fractures, design infill well locations and configurations and optimize the reservoir sweep. Through the use of both experimental observations and numerical models this work has elucidated various physical phenomena affecting fracture growth and injection-well performance. The findings in this dissertation provide critical data and models that help us to more confidently specify injection water quality, the design of pumping and water treatment facilities, and the optimization of well planning. The models developed in this work can be used to substantially improve the predictions of injection well performance and improve reservoir oil recovery by waterflooding. / text

<p> In this thesis, we study the concept of injectivity in equational classes of (universal) algebras and in particular we are concerned with congruence distributive equational classes that have enough injectives. We show that every reasonable equationally complete congruence distributive equational class has enough injectives and we describe them completely. We then examine what equational subclasses of Lattices, Heyting algebras, and pseudo-complemented lattices have enough injectives.</p> / Thesis / Doctor of Philosophy (PhD)

[pt] Este trabalho trata do problema de entupimento de rochas provocado pela injeção de água contendo partículas sólidas. O efeito da redução de permeabilidade e conseqüente perda de injetividade da rocha é analisada através da interpretação de ensaios unidimensionais de fluxo obtidos da literatura e simulados por um programa computacional desenvolvido nesta dissertação. O programa baseia-se no modelo de Pang e Sharma (1994) de perda de injetividade, escolhido dentre um conjunto de modelos pesquisados, e contempla o processo de entupimento devido à formação de camada de filtro interno e/ou externo, onde é introduzido o conceito de tempo de transição. Nesta formulação utilizam-se também dois importantes parâmetros: lambda , definido como coeficiente de filtração, e beta , fator de dano, podendo estes ser determinados por ensaios ou por correlações empíricas. Uma nova teoria de Bredrikovetsky (2001) que sugere o cálculo de ambos parâmetros por dados de pressão também é empregada. Com o objetivo de validar o modelo e o programa, apresenta-se um estudo paramétrico cujas informações podem ser utilizadas na previsão do comportamento de poços injetores. / [en] This work deals with the impairment of rocks subjected to the injection of water with solid particles in suspension. The effect of the permeability reduction and consequent loss in rock injectivity is analyzed by the interpretation of core flow tests, previously reported, and simulated by using a computational program developed for this research. The program is based on the Pang and Sharmas model (1994) for the prediction of injectivity decline, chosen amongst a set of existing models, and contemplates the process of impairment due the formation of an external and/or an internal filter cake, where the concept of transition time is introduced. The formulation also uses two important parameters: lambda, defined as filtration coefficient, and beta, damage factor, which can be determined by test data or empirical correlations. A new theory of Bredrikovetsky (2001) that suggests the calculation of both parameters for pressure data is used. With the objective to validate the model and the program, a parametric study is presented whose information can be used in the prediction of the behavior of the injection wells.

A primeira parte deste trabalho é dedicada ao estudo de sistemas dinâmicos contínuos e discretos bidimensionais com um único ponto de equillíbrio que é do tipo sela hiperbólica. No caso contínuo, obtemos condições sufiientes para que um campo vetorial planar seja topologicamente equivalente à sela linear L(x; y) = (-x; y). No caso em que o campo vetorial é um difeomorfismo local, a injetividade do campo jogará um papel fundamental na obtenção de tal equivalência topológica. Além disto, apresentamos uma descrição das folheações do plano associadas a campos de vetores com uma única singularidade do tipo sela hiperbólica. No âmbito dos sistemas discretos, apresentamos condições para que um difeomorfismo, possuindo uma sela hiperbólica como único ponto fixo, satisfaça as propriedades básicas de um sistema linear com um ponto fixo que é do tipo sela hiperbólica: as quatro separatrizes do ponto fixo se acumulam só no infinito e os iterados dos pontos que não estão nas variedades invariantes deste ponto fixo se acumulam no infinito tanto no passado quanto no futuro. A segunda parte deste texto, se dedica a problemas de injetividade de difeomorfismos locais em \'R POT. n\'. Mais especificamente, obtemos versões fracas da Conjetura Jacobiana Real de Jelonek e de uma Conjetura apresentada por Nollet e Xavier. Ambos problemas estão intimamente ligados à famosa Conjetura Jacobiana, que foi considerada por Smale em 1998 como um dos dezoito problemas matemáticos mais relevantes ainda em aberto / The first part of this work is dedicated to the study of continuous and discrete twodimensional dynamical systems with a unique equilibrium point which is a hyperbolic saddle. In the continuous case, we obtain sufficient conditions for a planar vector field be topologically equivalent to the linear saddle L(x; y) = (-x; y). In the case where the vector field is a local diffeomorphism, the injectivity of the field will play a key role in obtaining such a topological equivalence. Furthermore, we provide a description of foliations of the plane vector fields associated with a unique singularity of hyperbolic saddle type. In the context of discrete systems, we present conditions for a diffeomorphism, possessing a hyperbolic saddle as the single fixed point, to satisfy the basic properties of a linear system with a fixed point of saddle type which is hyperbolic: the four separatrices of the fixed point accumulate only at infinity and iterated the points that are not in invariant manifolds of this fixed point accumulate in infinity in both the past and future. The second part of this text is devoted to problems of injectivity of local diffeomorphisms on \'R POT. n\'. More specifically, we obtain weaker versions of the Jelonek\'s Real Jacobian Conjecture and a Conjecture given by Nollet and Xavier. Both problems are closely linked to the famous Jacobian Conjecture, which was considered by Smale in 1998 as one of eighteen mathematical problems even more important in open

Ce travail est au confluent de la théorie des algèbres d'opérateurs<br />et des probabilités non-commutatives. Nous étudions les propriétés<br />des algèbres de von Neumann, $\Gamma_{q}(H_{\R})$, engendrées par<br />des variables Gaussiennes non-commutatives et $q$-déformées. Ces<br />variables $q$-Gaussiennes sont des opérateurs agissant sur l'espace<br />de Fock $q$-déformé, où sont réalisées les relations de<br />$q$-commutations canoniques.<br /><br />Dans la première partie de ce mémoire, nous établissons des<br />inégalités à coefficients opérateurs de type Khintchine-$L^{\infty}$<br />pour les produits de Wick des algèbres $q$-Gaussiennes. Ces<br />inégalités étendent d'un côté les inégalités scalaires dues à<br />Haagerup dans le cas libre et d'un autre côté les inégalités à<br />coefficients opérateurs, pour les $q$-Gaussiens, dues à Bo\.zejko et<br />Speicher. A l'aide de ces inégalités nous en déduisons que les<br />algèbres $\Gamma_q(H_{\R})$ sont non injectives dès que<br />$\dim_{\R}(H_{\R})\ge 2$.<br /><br />La deuxième partie est dédiée à la construction d'un modèle<br />asymptotique matriciel pour les variables $q$-Gaussiennes.<br />L'existence d'un tel modèle nous permet de prouver que les algèbres<br />$\Gamma_{q}(H_{\R})$ sont QWEP.<br /><br />Chemin faisant, nous traitons également le cas $C^*-$algébrique et<br />étudions diverses généralisations des résultats précédents pour les<br />déformations par opérateur de Yang-Baxter et pour les déformations<br />$q$-Gaussiennes de type $I\!I\!I$.

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.

Polymers play a key role in several EOR processes such as polymer flooding, surfactant-polymer flooding and alkaline-surfactant-polymer flooding due to their critical importance of mobility control in achieving high oil recovery from these processes. Numerical simulators are used to predict the performance of all of these processes and in particular the injection rate of the chemical solutions containing polymer; since the economics is very sensitive to the injection rates. Injection rates are governed by the injection viscosity, thus, it is very important to model the polymer viscosity accurately. For the predictions to be accurate, not only the viscosity model must be accurate, but also the calculation of equivalent shear rate in each gridblock must be accurate because the non-Newtonian viscosity models depend on this shear rate. As the size of the gridblock increases, the calculation of this velocity becomes less numerically accurate, especially close to wells. This research presents improvements in polymer viscosity model. Using the improvements in shear thinning model, the laboratory polymer rheology data was better matched. For the first time, polymer viscosity was modeled for complete range of velocity using the Unified Viscosity Model for published laboratory data. New models were developed for relaxation time, time constant and high shear viscosity during that match. These models were then used to match currently available HPAM polymer's laboratory data and predict its viscosity for various concentrations for full flow velocity range. This research presents the need for injectivity correction when large grid sizes are used. Use of large grid sizes to simulate large reservoir due to computation constraints induces errors in shear rate calculations near the wellbore and underestimate polymer solution viscosity. Underestimated polymer solution viscosities lead to incorrect injectivity calculation. In some cases, depending on the well grid block size, this difference between a fine scale and a coarse simulation could be as much as 100%. This study focuses on minimizing those errors. This methodology although needs some more work, but can be used in accurate predictions of reservoir simulation studies of chemical enhanced oil recovery processes involving polymers. / text

Produced water presents economical and environmental challenges to oil producers. Downhole separation technology is able to separate oil or gas from produced fluid in downhole environment and injects waste water into deeper formations, thus saving energy and reducing waste emission. More than 120 downhole separation systems have been installed worldwide, but only about 60% of the installations achieved success. Most of the failures were due to the injectivity decline under the invasion of impurities in the injected water, such as suspended particles and oil droplets. A reliable model is needed to predict the reaction of reservoir permeability under the invasion of such impurities and serves as a tool to screen appropriate formations for downhole separator installations. / Previous experimental studies on particle-induced permeability damage reveal that high particle concentration, low fluid velocity, large particle size lead to more severe damage. The damage mechanisms are attributed to surface interception, bridging and size exclusion of particles in porous media. While for droplets, the resultant permeability decline is mostly due to surface interception. Empirical correlations with key parameters determined by core flooding data are widely applied to the simulation of permeability decline under invasion of particles and droplets. These correlations are developed based on characteristics of certain rocks and fluids, thus their applications are very restricted. / A more scientific method is to model the flow and capture of particulates at pore level. Reservoir rocks are porous media composed of pores of various sizes. Pore network models employ certain assumptions to imitate real porous media, and have been proved realistic in simulating fluid flow in porous media. In this study, a 2-dimensional square network model is used to simulate capture of particles and droplets in porous media. Pore bodies are represented by globes and pore throats are imitated with capillary tubes. The flow rates in the network are obtained by simultaneously solving mass balance equations at each pore body. The network model is tuned to match the porosity and permeability of a certain rock and serves as the infrastructure where the capture process takes place. / Particles are categorized as Brownian and non-Brownian particles according to size. For Brownian particles, diffusion is dominant and Fick’s law is applied to each pore inside the network to obtain deposition rate. For non-Brownian particles, their trajectories are mainly governed by gravity and drag force acting on them. Besides, the size of each particle is compared with the size of the pore where it is captured to determine the damage mechanism. For particles much smaller than the pore size, surface deposition is dominant and the permeability decline is gradual. For particles with sizes comparable to pore size, bridging and clogging are dominant and the permeability decline is much more severe. / Unlike particles, droplets can not be captured on top of each other. Accordingly, a captureequilibrium theory is proposed. Once the pore surface is covered by droplets, equilibrium is reached and droplets flow freely through porous media without being captured. The simulation on capture of oil droplets reveals that the surface wettability has significant influence on the resultant permeability damage. Most natural reservoirs are neutrally or oil wet. It is thus recommended to apply these surface conditions to future simulations. / The proposed model is validated with test data and reasonably good agreements are obtained. This new mechanistic model provides more insights into the capture process and greatly reduces the dependence on core flooding data.

A primeira parte deste trabalho é dedicada ao estudo de sistemas dinâmicos contínuos e discretos bidimensionais com um único ponto de equillíbrio que é do tipo sela hiperbólica. No caso contínuo, obtemos condições sufiientes para que um campo vetorial planar seja topologicamente equivalente à sela linear L(x; y) = (-x; y). No caso em que o campo vetorial é um difeomorfismo local, a injetividade do campo jogará um papel fundamental na obtenção de tal equivalência topológica. Além disto, apresentamos uma descrição das folheações do plano associadas a campos de vetores com uma única singularidade do tipo sela hiperbólica. No âmbito dos sistemas discretos, apresentamos condições para que um difeomorfismo, possuindo uma sela hiperbólica como único ponto fixo, satisfaça as propriedades básicas de um sistema linear com um ponto fixo que é do tipo sela hiperbólica: as quatro separatrizes do ponto fixo se acumulam só no infinito e os iterados dos pontos que não estão nas variedades invariantes deste ponto fixo se acumulam no infinito tanto no passado quanto no futuro. A segunda parte deste texto, se dedica a problemas de injetividade de difeomorfismos locais em \'R POT. n\'. Mais especificamente, obtemos versões fracas da Conjetura Jacobiana Real de Jelonek e de uma Conjetura apresentada por Nollet e Xavier. Ambos problemas estão intimamente ligados à famosa Conjetura Jacobiana, que foi considerada por Smale em 1998 como um dos dezoito problemas matemáticos mais relevantes ainda em aberto / The first part of this work is dedicated to the study of continuous and discrete twodimensional dynamical systems with a unique equilibrium point which is a hyperbolic saddle. In the continuous case, we obtain sufficient conditions for a planar vector field be topologically equivalent to the linear saddle L(x; y) = (-x; y). In the case where the vector field is a local diffeomorphism, the injectivity of the field will play a key role in obtaining such a topological equivalence. Furthermore, we provide a description of foliations of the plane vector fields associated with a unique singularity of hyperbolic saddle type. In the context of discrete systems, we present conditions for a diffeomorphism, possessing a hyperbolic saddle as the single fixed point, to satisfy the basic properties of a linear system with a fixed point of saddle type which is hyperbolic: the four separatrices of the fixed point accumulate only at infinity and iterated the points that are not in invariant manifolds of this fixed point accumulate in infinity in both the past and future. The second part of this text is devoted to problems of injectivity of local diffeomorphisms on \'R POT. n\'. More specifically, we obtain weaker versions of the Jelonek\'s Real Jacobian Conjecture and a Conjecture given by Nollet and Xavier. Both problems are closely linked to the famous Jacobian Conjecture, which was considered by Smale in 1998 as one of eighteen mathematical problems even more important in open

The goal of this work was to prove the fact, that definable closure of any subclass of cotorsion modules closed under direct sums consists of $\Sigma$-cotorsion modules. The only known proof uses substantially the calculus of derived category, in this work we tried to prove the same, but only by means of a given category of all right $R$-modules and set-theoretic properties of partial orders indexing direct systems of $R$-modules. The main results of this work are proved under additional assumptions on the ring $R$, in particular $\vert R\vert\leq\aleph_{\omega}$ or $\text{dim}(R)<\aleph_{\omega}$. Attempts to give s proof in the same general situation, where the fact is known to hold, was not successful. Powered by TCPDF (www.tcpdf.org)