Submitted by Automa??o e Estat?stica (sst@bczm.ufrn.br) on 2016-03-22T19:35:00Z No. of bitstreams: 1 IdervalAlvesBarbosa_TESE.pdf: 5224671 bytes, checksum: 49d3a5c3c3ea197ca03bf98e12e5f60d (MD5) / Approved for entry into archive by Arlan Eloi Leite Silva (eloihistoriador@yahoo.com.br) on 2016-03-28T19:30:07Z (GMT) No. of bitstreams: 1 IdervalAlvesBarbosa_TESE.pdf: 5224671 bytes, checksum: 49d3a5c3c3ea197ca03bf98e12e5f60d (MD5) / Made available in DSpace on 2016-03-28T19:30:07Z (GMT). No. of bitstreams: 1 IdervalAlvesBarbosa_TESE.pdf: 5224671 bytes, checksum: 49d3a5c3c3ea197ca03bf98e12e5f60d (MD5) Previous issue date: 2015-03-25 / Neste trabalho investigamos alguns aspectos do fluxo bidimensional de um fluido viscoso Newtoniano atrav?s de um meio poroso desordenado, modelado por um sistema fractal aleat?rio, semelhante ao tapete de Sierpinski. Este fractal ? formado por obst?culos de diversos tamanhos, cuja fun??o de distribui??o segue uma lei de pot?ncia. Al?m do mais, est?o aleatoriamente dispostos em um canal retangular. O campo de velocidades e outros detalhes da din?mica dos fluidos s?o obtidos resolvendo-se, numericamente, as equa??es de Navier-Stokes e as da continuidade no n?vel de poros, onde ocorre realmente o fluxo de fluidos em meios porosos. Os resultados das simula??es num?ricas permitiram-nos fazer uma an?lise da distribui??o das tens?es de cisalhamento desenvolvidas nas interfaces s?lido-fluido, e encontrar rela??es alg?bricas entre as for?as viscosas ou de atrito e par?metros geom?tricos do modelo, inclusive a sua dimens?o fractal. Com base nos resultados num?ricos propusemos rela??es de escala que envolve os par?metros relevantes do fen?meno, quantificando as fra??es dessas for?as com rela??o ?s classes de tamanhos dos obst?culos. Finalmente, foi poss?vel, tamb?m, fazer infer?ncias sobre as flutua??es na forma da distribui??o das tens?es viscosas desenvolvidas na superf?cie dos obst?culos. / In this work we have investigated some aspects of the two-dimensional flow of a viscous Newtonian fluid through a disordered porous medium modeled by a random fractal system similar to the Sierpinski carpet. This fractal is formed by obstacles of various sizes, whose distribution function follows a power law. They are randomly disposed in a rectangular channel. The velocity field and other details of fluid dynamics are obtained by solving numerically of the Navier-Stokes and continuity equations at the pore level, where occurs actually the flow of fluids in porous media. The results of numerical simulations allowed us to analyze the distribution of shear stresses developed in the solid-fluid interfaces, and find algebraic relations between the viscous forces or of friction with the geometric parameters of the model, including its fractal dimension. Based on the numerical results, we proposed scaling relations involving the relevant parameters of the phenomenon, allowing quantifying the fractions of these forces with respect to size classes of obstacles. Finally, it was also possible to make inferences about the fluctuations in the form of the distribution of viscous stresses developed on the surface of obstacles.

Made available in DSpace on 2014-12-17T14:09:13Z (GMT). No. of bitstreams: 1 AlvaroBN_TESE.pdf: 1929903 bytes, checksum: 92f40cf4d3b6ab5536ad5ad3d2aa192a (MD5) Previous issue date: 2012-02-29 / The present study provides a methodology that gives a predictive character the computer simulations based on detailed models of the geometry of a porous medium. We using the software FLUENT to investigate the flow of a viscous Newtonian fluid through a random fractal medium which simplifies a two-dimensional disordered porous medium representing a petroleum reservoir. This fractal model is formed by obstacles of various sizes, whose size distribution function follows a power law where exponent is defined as the fractal dimension of fractionation Dff of the model characterizing the process of fragmentation these obstacles. They are randomly disposed in a rectangular channel. The modeling process incorporates modern concepts, scaling laws, to analyze the influence of heterogeneity found in the fields of the porosity and of the permeability in such a way as to characterize the medium in terms of their fractal properties. This procedure allows numerically analyze the measurements of permeability k and the drag coefficient Cd proposed relationships, like power law, for these properties on various modeling schemes. The purpose of this research is to study the variability provided by these heterogeneities where the velocity field and other details of viscous fluid dynamics are obtained by solving numerically the continuity and Navier-Stokes equations at pore level and observe how the fractal dimension of fractionation of the model can affect their hydrodynamic properties. This study were considered two classes of models, models with constant porosity, MPC, and models with varying porosity, MPV. The results have allowed us to find numerical relationship between the permeability, drag coefficient and the fractal dimension of fractionation of the medium. Based on these numerical results we have proposed scaling relations and algebraic expressions involving the relevant parameters of the phenomenon. In this study analytical equations were determined for Dff depending on the geometrical parameters of the models. We also found a relation between the permeability and the drag coefficient which is inversely proportional to one another. As for the difference in behavior it is most striking in the classes of models MPV. That is, the fact that the porosity vary in these models is an additional factor that plays a significant role in flow analysis. Finally, the results proved satisfactory and consistent, which demonstrates the effectiveness of the referred methodology for all applications analyzed in this study. / O presente trabalho proporciona uma metodologia que d? um car?ter preditivo ?s simula??es computacionais baseadas em modelos detalhados da geometria porosa de um meio. N?s utilizando o software FLUENT para investigar o escoamento de um fluido newtoniano viscoso atrav?s de um meio fractal aleat?rio que simplifica um meio poroso desordenado bidimensional representando um reservat?rio de petr?leo. Este modelo fractal ? formado por obst?culos de diversos tamanhos, cuja fun??o de distribui??o segue uma lei de pot?ncia, onde o expoente ? definido como sendo a dimens?o fractal de fracionamento Dff do modelo e caracteriza o processo de fragmenta??o desses obst?culos. Eles s?o aleatoriamente dispostos em um canal retangular. O processo de modelagem incorpora conceitos modernos, leis de escala, para analisar a influ?ncia das heterogeneidades encontradas nos campos da porosidade e da permeabilidade de tal maneira que se possa caracterizar o meio em fun??o de suas propriedades fractais. Este procedimento permite analisar numericamente as medidas da permeabilidade k e do coeficiente de arrasto Cd propondo rela??es, tipo lei de pot?ncia, para essas propriedades sobre v?rios esquemas de modelagem. O prop?sito desta pesquisa ? estudar a variabilidade proporcionada por estas heterogeneidades onde o campo de velocidade e outros detalhes da din?mica dos fluidos viscosos s?o obtidos resolvendo numericamente as equa??es da continuidade e de Navier-Stokes no n?vel de poros e observar como a dimens?o fractal de fracionamento do modelo pode afetar as suas propriedades hidrodin?micas. Neste estudo foram consideradas duas classes de modelos, modelos com porosidade constante, MPC, e modelos com porosidade vari?vel, MPV. Os resultados permitiram-nos encontrar rela??es num?ricas entre a permeabilidade, coeficiente de arrasto e os par?metros geom?tricos do modelo. Com base nestes resultados num?ricos propusemos rela??es de escala envolvendo os par?metros relevantes do fen?meno. Nesta pesquisa foram determinadas equa??es anal?ticas para Dff em fun??o dos par?metros geom?tricos dos modelos. Constatamos tamb?m uma rela??o entre a permeabilidade e o coeficiente de arrasto onde uma ? inversamente proporcional ? outra. Quanto ? diferen?a de comportamento ela ? mais marcante nas classes de modelos MPV. Isto ?, o fato da porosidade variar nestes modelos constitui um fator adicional que desempenha um papel significativo na an?lise de fluxo. Finalmente, os resultados encontrados se mostraram consistentes e satisfat?rios, o que demonstra a efic?cia da referida metodologia para todas as aplica??es analisadas nesta pesquisa.