The miscible displacement equations provide the mathematical model for simulating the displacement of a mixture of oil and miscible fluid in underground reservoirs during the Enhance Oil Recovery(EOR) process. In this thesis, I propose a stable numerical scheme combining a mixed finite element method and space-time discontinuous Galerkin method for solving miscible displacement equations under low regularity assumption. Convergence of the discrete solution is investigated using a compactness theorem for functions that are discontinuous in space and time. Numerical experiments illustrate that the rate of convergence is improved by using a high order time stepping method. For petroleum engineers, it is essential to compute finely detailed fluid profiles in order to design efficient recovery procedure thereby increase production in the EOR process. The method I propose takes advantage of both high order time approximation and discontinuous Galerkin method in space and is capable of providing accurate numerical solutions to assist in increasing the production rate of the miscible displacement oil recovery process.

Les rejets de matières dangereuses dans l'environnement induisent souvent des pollutions accidentelles des cours d'eau qui s'étendent sur plusieurs kilomètres en aval de la source du rejet. Dans l'objectif de proposer un modèle qui prévoit l'étendue de la pollution, une maquette de cours d'eau est conçue spécifiquement en ce sens à partir d'une étude de similitude pour évaluer la dispersion de polluant en champ lointain et valider le modèle unidimensionnel adopté (Equation d'Advection-Dispersion). Les conclusions issues des études menées à petite et à grande échelle, nous ont amené à développer un modèle permettant de prédire les profils asymétriques dans la zone initiale du champ lointain. L'évaluation des performances du nouveau modèle, basé sur une Gaussienne Modifiée par une Exponentielle, montre une faible divergence des estimations par rapport aux observations. Lors de la validation à l'échelle réelle, les trois paramètres essentiels lors d'une gestion de crise (concentrations maximales, temps d'arrivée du pic et de la pollution) sont estimés respectivement avec un pourcentage d'erreur moyen de 51, 13 et 11 %, ce qui semble acceptable. Finalement, un modèle complet de dispersion est proposé pour évaluer l'étendue d'une dispersion accidentelle dans le champ lointain. Il est composé de l'EMG pour la zone initiale du champ lointain et de l'ADE pour le champ lointain établi. Le passage d'un modèle à une autre se fait à partir d'une distance comprise entre 12 et 50 fois la longueur de mélange. En conclusion, le modèle proposé est adapté à la gestion d'une situation d'urgence par la simplicité de son utilisation et le faible nombre de variables d'entrée nécessaires aux simulations.

Thesis (Doctoral)--Universität Karlsruhe, 2001. / Abstract in German. Hochschulschrift = Thèse/Mémoire. Includes bibliographical references (p. 109-133). Also available via the World Wide Web. http://www.ubka.uni-karlsruhe.de/indexer-vvv/2002/bio-geo/1

Dispersion has been shown to degrade miscibility in miscible displacements by lowering the concentration of the injected solute at the displacement fronts. Dispersion can also improve oil recovery by increasing sweep efficiency. Either way, dispersion is an important factor in understanding miscible displacement performance. Conventionally, dispersion is measured in the laboratory by fitting the solution of one-dimensional convection-dispersion equation (CDE) to the effluent concentration from a core flood. However dispersion is anisotropic and mixing occurs in both longitudinal and transverse directions. This dissertation uses the analytical solution of the two-dimensional CDE to simultaneously determine longitudinal and transverse dispersion. The two-dimensional analytical solution for an instantaneous finite volume source is used to investigate anisotropic mixing in miscible displacements. We conclude that transverse mixing becomes significant with large a concentration gradient in the transverse direction and significant local variation in flow directions owing to heterogeneity. We also utilized simulation models similar to Blackwell's (1962) experiments to determine transverse dispersion. This model coupled with the analytical solution for two-dimensional CDE for continuous injection source is used to determine longitudinal and transverse dispersivity for the flow medium. The validated model is used to investigate the effect of heterogeneity and other first contact miscible (FCM) scaling groups on dispersion. We derive the dimensionless scaling groups that affect FCM displacements and determine their impact on dispersion. Experimental design is used to determine the impact and interactions of significant scaling groups and generate a response surface function for dispersion based on the scaling groups. The level of heterogeneity is found to most significantly impact longitudinal dispersion, while transverse dispersion is most significantly impacted by the dispersion number. Finally, a mathematical procedure is developed to use the estimated dispersivities to determine a-priori the maximum grid-block size to maintain an equivalent level of dispersion between fine-scale and upscaled coarse models. Non-uniform coarsening schemes is recommended and validated for reservoir models with sets of different permeability distributions. Comparable sweep and recovery are observed when the procedure was extended to multi-contact miscible (MCM) displacements. / text

京都大学 / 新制・課程博士 / 博士(理学) / 甲第24390号 / 理博第4889号 / 新制||理||1699(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 大木谷 耕司, 教授 並河 良典, 准教授 竹広 真一 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Physical aging measurements were performed on various polymeric glasses with the overriding goal of developing a better molecular picture of the nonequilibrium glassy state. To this end, aging-induced changes in mechanical properties and in the thermodynamic state (volume and enthalpy) were assessed for two different miscible polymer blends as a function of both composition and aging temperature. This investigation considered the physical aging behavior of blends containing atactic polystyrene (a-PS) and poly(2,6-dimethyl-1,4-phenylene oxide) (PPO) as well as mixtures of poly(methyl methacrylate) (PMMA) and poly(styrene-co-acrylonitrile) (SAN). Substantial attractive chemical interactions are characteristic of a-PS/PPO blends but are absent in PMMA/SAN blends. The distinct nature of interactions for these two blends resulted in differences in the compositional dependence of secondary relaxation intensity, segmental cooperativity which dictates glass formation kinetics, and density (prior to aging). The variation of volume relaxation rate with aging temperature and composition was interpreted based upon these characteristics for the two systems. In addition, a general relationship was uncovered which linked structural relaxation rates for amorphous polymers to their respective segmental relaxation characteristics (glass transition cooperativity or fragility), which in turn are well understood from a molecular standpoint. This work, therefore, established a basis for comprehending glassy state volume and enthalpy relaxation rates based upon molecular characteristics. Developing an understanding of the connection between the evolving thermodynamic state and mechanical property changes fared less well. The fact that the thermodynamic and mechanical properties can have very different relaxation time responses governing their changes in the nonequilibrium glassy state was clearly evident in an extensive study of the physical aging characteristics of an amorphous polyimide material. For some materials, interpretation of mechanical aging behavior was obscured by thermorheological complexity arising due to overlap of a secondary relaxation with the main chain softening dispersion. / Ph. D.

This dissertation discusses results of crystallization kinetic, morphology and scattering studies on miscible semi crystalline blends of poly(pivalolactone)/ poly(vinylidene fluoride)(pPVLIPVF₂) and poly(pivalolactone)/poly(vinylidene fluoride <i>co</i>- tetrafluoroethylene)(95-5) (PPVL/P(VF2-TFE)(95-5)) prepared by solution blending. The spherulitic growth rates of the α-phase PPVL from miscible blends with PVF₂ or P(VF₂- TFE)(95-5) were measured by polarized optical microscopy as a function of blend composition and isothermal crystallization temperature, Tx, between 160°C and 215.5°C. The PPVL weight fraction in the blends ranged from 100 to 10 wt%. Using the Lauritzen-Hoffman kinetic theory of polymer crystal growth, the equilibrium melting temperatures of the α-phase PPVL in both the PPVL/PVF₂ and the PPVL/P(VF₂-TFE)(95-5) blends have been determined, for the first time, directly from the spherulitic growth rate data. Analysis of the composition dependence of the nucleation constant, Kg suggests that the α-phase PPVL crystal/melt lateral interface free energy, Ï , in the blends decreases markedly with increasing PVF₂ or P(VF₂-TFE)(95-5) concentration. / Ph. D.

No estudo da dinâmica de solutos num meio poroso é de suma importância o conhecimento das propriedades do meio e dos líquidos percolantes, bem como de fatores externos. Um fator externo relevante é a temperatura e, nesse sentido, objetivou-se com o presente trabalho a determinação de parâmetros de transporte dos íons potássio e nitrato para diferentes valores de temperatura em experimentos de deslocamento miscível. Os parâmetros avaliados foram o fator de retardamento (R), o coeficiente de difusão/dispersão (D) e a dispersividade (&#955;) e as temperaturas utilizadas foram a ambiente (25&#176;C a 28&#176;C), 40&#176;C e 50&#176;C. Os sais utilizados foram nitrato de potássio e cloreto de potássio, preparados em uma solução composta de 50ppm de nitrato e 2000ppm de potássio e o meio poroso um Latossolo Vermelho Amarelo, textura média. Os resultados obtidos permitiram concluir que a temperatura apresentou influência na velocidade da solução no meio poroso e no coeficiente de dispersão. / In the study of solute dynamics in porous media, it is of extreme importance the knowledge of the medium and transporting liquid properties as well as of external factors as temperature. In this sense, the objective of this work was the determination of parameters for potassium and nitrate ions under different temperatures in miscible displacement experiments, in a sandy loam Oxisol. The evaluated parameters were retardation factor (R) difusion/dispersion coefficient (D) and dispersivity (&#955;), whereas the used temperatures were the prevailing temperature (25&#176;C to 28&#176;C), 40&#176;C and 50&#176;C. The used salts were potassium nitrate and potassium chloride, prepared in a composed solution of 50 ppm of nitrate and 2000 ppm of potassium. From the results, it could be concluded that the temperature showed high influence on soil solution velocity and dispersion coefficient

No estudo da dinâmica de solutos num meio poroso é de suma importância o conhecimento das propriedades do meio e dos líquidos percolantes, bem como de fatores externos. Um fator externo relevante é a temperatura e, nesse sentido, objetivou-se com o presente trabalho a determinação de parâmetros de transporte dos íons potássio e nitrato para diferentes valores de temperatura em experimentos de deslocamento miscível. Os parâmetros avaliados foram o fator de retardamento (R), o coeficiente de difusão/dispersão (D) e a dispersividade (&#955;) e as temperaturas utilizadas foram a ambiente (25&#176;C a 28&#176;C), 40&#176;C e 50&#176;C. Os sais utilizados foram nitrato de potássio e cloreto de potássio, preparados em uma solução composta de 50ppm de nitrato e 2000ppm de potássio e o meio poroso um Latossolo Vermelho Amarelo, textura média. Os resultados obtidos permitiram concluir que a temperatura apresentou influência na velocidade da solução no meio poroso e no coeficiente de dispersão. / In the study of solute dynamics in porous media, it is of extreme importance the knowledge of the medium and transporting liquid properties as well as of external factors as temperature. In this sense, the objective of this work was the determination of parameters for potassium and nitrate ions under different temperatures in miscible displacement experiments, in a sandy loam Oxisol. The evaluated parameters were retardation factor (R) difusion/dispersion coefficient (D) and dispersivity (&#955;), whereas the used temperatures were the prevailing temperature (25&#176;C to 28&#176;C), 40&#176;C and 50&#176;C. The used salts were potassium nitrate and potassium chloride, prepared in a composed solution of 50 ppm of nitrate and 2000 ppm of potassium. From the results, it could be concluded that the temperature showed high influence on soil solution velocity and dispersion coefficient

La dispersion de colorant dans des écoulements newtoniens ou rhéofluidifiants a été étudiée optiquement dans deux fractures modèles rugueuses et transparentes. L'évolution du front de déplacement est analysé en fonction du temps et de la vitesse moyenne $U$ . Pour des rugosités de parois monodisperses et distribuées aléatoirement, l'étalement du front est diffusif ($\Delta x \propto t^{0.5}$) et caractérisé par une dispersivité $l_d$. Aux faibles vitesses, $l_d \simeq$ cst: la dispersion est dominée par les fluctuations spatiales de la vitesse et est amplifiée pour les fluides rhéofluidifiants ; aux vitesses élevées, $l_d$ augmente avec $U$ à cause de la dispersion de Taylor mais plus faiblement pour les fluides rhéofluidifiants. Pour une fracture avec deux parois autoaffines complémentaires décalées perpendiculairement à $U$, des chenaux macroscopiques s'étendent sur toute la longueur de la fracture suivant $U$ : l'épaisseur globale du front augmente alors linéairement avec le temps et plus fortement dans le cas rhéofluidifiant (étalement advectif). La croissance de l'épaisseur locale du front est par contre diffusive et due à la dispersion de Taylor.