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Over the previous summer I studied mixing of a passive tracer by flow in a straight cylindrical pipe, under the supervision of prof. Bernoff. The mixing process can be thought of as the successive action of advection by the fluid flow and diffusion modeled by random walks. With this method we were able to distinguish three different regimes. For short times, diffusion is more relevant than advection and we observed a Gaussian longitudinal distribution of the concentration. In an intermediate regime, advection by the shear is dominant over longitudinal diffusion and we observed a distinctively asymmetric distribution which spread much faster than would be expected by the action of diffusion alone. Finally when the tracer had completely mixed across the pipe’s cross- section, we recovered the classical Taylor regime with a longitudinal Gaussian distribution. In each regime we have analytical prediction of tracer distribution, confirmed by numerical calculation. The object of this thesis is to extend our results to curved pipes; we will start by considering curved planar pipes and helical pipes. We will try to determine if mixing in these geometries displays the same three distinctive regimes of mixing. The pipe’s curvature introduces a secondary flow in the form of a transverse recirculation with a dipolar form, discovered by Dean (1928). We believe this transverse flow should enhance mixing, which explains why curved pipes are used in cooling systems and other situations where heat exchange is relevant. Our object is to first understand existing analytical approximations to the flow in a curved pipe due to Dean and others and then to study analytically and numerically the spread of a passive scalar in these flows.

Universiẗat, Diss., 2003--Bremen.

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Os óleos lubrificantes utilizados nos diferenciais de veículos comerciais, do tipo SAE 90 API GL-5, sob condições extremas de trabalho, para o qual o diferencial não foi projetado, por exemplo (estradas com má conservação, excesso de carga, eixo não apropriado para determinados usos, etc.) se degradam, impossibilitando a identificação do tipo de óleo lubrificante, aplicado originalmente e dificultando a avaliação correta em um processo de garantia ou de assistência técnica. A adição de\"tracer\" (substância organometálica) ao óleo lubrificante do diferencial, desde que o mesmo seja estável em condições extremas de trabalho, pode indicar qual a sua formulação. O estudo da estabilidade do \"tracer\" no óleo é feito utilizando o aparelho de quatro esferas, no qual a propriedade antidesgaste é avaliada através de um ensaio força do de degradação do óleo lubrificante, onde se medem o desgaste da calota da esfera, a rugosidade e a temperatura gerada durante o ensaio. A propriedade de extrema pressão do óleo lubrificante é avaliada pelo ensaio de extrema pressão DIN 51350. Em ambos os casos, são adicionadas proporções variadas de \"tracer\" e comparados os resultados dos mesmos, com aqueles obtidos anteriormente sem a sua utilização. / The used oil in differential of commercial vehicles, like type SAE 90 API GL-5, in extreme work conditions - for which the differential was not projected (for example highways with bad conservation, load excess, axis not adapted for certain uses, etc.) - degrades and cease the condition to identify the type of oil (formulation) originally applied, eliminating the correct evaluation in a warranty process, or the technical attendance. The \"tracer\" addition (substance organometallic) to the lubricant oil at the differential - since it is stable to extreme work conditions - can indicate the type of used formulation. The study of the \"tracer\" stability in the oil is made with the four-ball-device, in which the property is evaluated, through a forced test of the lubricant oil degradation, on which is measured the wear from the concave sphere, roughness and the temperature, generated during the test. The property to extreme pressure of the lubricant oil (formulation) is evaluated by the extreme pressure test accordingly to DIN 51350. In both cases varied \"tracer\" proportions are added and the results compared with the same ones obtained previously without the \"tracer\".

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Os óleos lubrificantes utilizados nos diferenciais de veículos comerciais, do tipo SAE 90 API GL-5, sob condições extremas de trabalho, para o qual o diferencial não foi projetado, por exemplo (estradas com má conservação, excesso de carga, eixo não apropriado para determinados usos, etc.) se degradam, impossibilitando a identificação do tipo de óleo lubrificante, aplicado originalmente e dificultando a avaliação correta em um processo de garantia ou de assistência técnica. A adição de\"tracer\" (substância organometálica) ao óleo lubrificante do diferencial, desde que o mesmo seja estável em condições extremas de trabalho, pode indicar qual a sua formulação. O estudo da estabilidade do \"tracer\" no óleo é feito utilizando o aparelho de quatro esferas, no qual a propriedade antidesgaste é avaliada através de um ensaio força do de degradação do óleo lubrificante, onde se medem o desgaste da calota da esfera, a rugosidade e a temperatura gerada durante o ensaio. A propriedade de extrema pressão do óleo lubrificante é avaliada pelo ensaio de extrema pressão DIN 51350. Em ambos os casos, são adicionadas proporções variadas de \"tracer\" e comparados os resultados dos mesmos, com aqueles obtidos anteriormente sem a sua utilização. / The used oil in differential of commercial vehicles, like type SAE 90 API GL-5, in extreme work conditions - for which the differential was not projected (for example highways with bad conservation, load excess, axis not adapted for certain uses, etc.) - degrades and cease the condition to identify the type of oil (formulation) originally applied, eliminating the correct evaluation in a warranty process, or the technical attendance. The \"tracer\" addition (substance organometallic) to the lubricant oil at the differential - since it is stable to extreme work conditions - can indicate the type of used formulation. The study of the \"tracer\" stability in the oil is made with the four-ball-device, in which the property is evaluated, through a forced test of the lubricant oil degradation, on which is measured the wear from the concave sphere, roughness and the temperature, generated during the test. The property to extreme pressure of the lubricant oil (formulation) is evaluated by the extreme pressure test accordingly to DIN 51350. In both cases varied \"tracer\" proportions are added and the results compared with the same ones obtained previously without the \"tracer\".

In the quest for production optimization from established resources, there is a continual interest in secondary and tertiary recovery methods. The success of these enhanced recovery methods, however, rely to a large extent on a sound understanding of fluid dynamics and migration paths in the reservoir. To this end, several approaches to reservoir characterization have been put to test with varying degrees of success. The unique ability of tracers to provide direct information on preferential fluid flow paths in the reservoir, and the sensitivity of partitioning tracers to fluid saturation distribution has highlighted the prospects of a detailed reservoir characterization through interwell tracer tests. In a broad sense, analysis of interwell tracer tests fall into two categories, analytical and inverse modeling. While most of the analytical methods are laden with limiting assumptions, the method of moments boasts rigorous formulation and accurate estimates of swept volume and average saturation of bypassed oil. The inverse modeling infers permeability and saturation distribution by matching the tracer response. An extremely effective approach to the inverse modeling methods computes sensitivities based on streamlines. The accurate modeling of tracer flow requires accounting for complex phenomena such as transverse dispersion. Also, it is sometimes desired to model pertinent tracer components through compositional simulation. This necessitates the inclusion of a physical dispersion tensor and, hence, the well established finite difference formulation. In this work, we have coupled the finite difference and streamline simulation techniques for the inversion-based reservoir characterization to take advantage of the robustness of the finite difference formulation and computational efficiency of streamline simulation. We have also extended the formalism of the inversion technique for fluid distribution estimation to scenarios with mobile oil saturations and have attempted integrating the analytical and inverse-modeling techniques to facilitate detailed reservoir characterization. We have demonstrated the feasibility of our approach on both synthetic and field cases.