Um estudo de percolação em barragens de terra, em regimes permanente e transiente, com a aplicação do método de elementos finitos

Este trabalho apresenta um estudo de fluxo de água em barragens de terra, em regimes permanente e transiente, com a utilização do Método de Elementos Finitos. No estudo de fluxo em regime permanente duas formas de abordar o problema são apresentadas e comparadas. A primeira considera, para a discretização da malha de elementos finitos, somente a região saturada, de maneira que a linha freática é obtida através de ajustes desta malha de elementos finitos. A segunda considera toda a região saturada-insaturada, sendo discretizado todo o domínio físico da barragem. A malha de elementos finitos não é modificada ao longo das iterações e a linha freática é obtida por interpolação dentro dos elementos, em função dos valores nodais do potencial de pressões. O desenvolvimento teórico das equações utilizadas para as duas formas de abardagem é apresentado, mostrando onde elas diferem entre si. No estudo de fluxo em regime transiente é utilizado apenas o esquema de malha fixa de elementos finitos.

Sensores de pressão em fibra óptica para o estudo dos fenómenos da percolação da água em solos

Dada a necessidade de obtermos sistemas monitorizados com elevada precisão, de grande durabilidade e resistentes às condições atmosféricas, surgiu a possibilidade de aplicação das fibras ópticas como sensores para monitorização de pressão. Nesse contexto, as fibras “hetero-core” (fibra óptica composta por uma fibra multimodo entre duas fibras ópticas monomodo) e a utilização de lentes GRIN (“GRaded INdex”) em conjunto com superfícies reflectoras permitem a determinação da pressão e são objecto de estudo desta dissertação. Em termos de aplicação, o objectivo principal desta tese de mestrado foi de proporcionar o projecto e desenvolvimentos da medida de pressão em 48 pontos para um tanque de estudo dos fenómenos de percolação da água nos solos e que é pertencente à Secção de Geotecnia do Departamento de Engenharia Civil da Faculdade de Engenharia da Universidade do Porto. Inicialmente, foi caracterizado um sistema contendo uma fibra “hetero-core” à qual foi aplicada uma curvatura, com auxílio de uma carruagem micrométrica. Este sistema permitiu a simulação do mesmo efeito de aplicação de pressão à fibra “hetero-core”. Na configuração seguinte, usou-se um OTDR (“Optical Time Domain Reflectometer”) para visualização e registo das perdas encontradas durante o processo de dobrar e esticar da fibra “hetero-core”. Ao longo deste registo, várias configurações foram testadas até ser encontrada a cabeça sensora com melhor comportamento para monitorizar a pressão. A multiplexagem foi conseguida ao colocar dois sensores em série, sendo cada um deles constituído por uma fibra “hetero-core” colocada no fundo de um tubo de água disposto verticalmente. Com a adição da água no tubo de água, a curvatura na fibra “hetero-core” aumentava, notando-se claramente que as perdas também subiam. Os resultados obtidos nesta configuração foram bastante satisfatórios permitindo a independência entre os dois sensores dispostos em série. Posteriormente, foi testada uma nova configuração sensora, o sensor de fibra óptica para monitorização de pressão foi construído com recurso a uma lente GRIN e uma superfície reflectora. Esta lente, disposta diante de um espelho, permitiu emitir e captar luz de um determinado comprimento de onda devido à reflexão do sinal luminoso no espelho. Com sucessivos incrementos, afastou-se e aproximou-se a lente ao espelho, registando-se e observando-se as perdas de potência obtidas com auxílio do OTDR. Também para esta configuração foi testada a multiplexagem de vários sensores, tendo sido utilizadas as seguintes opções: um acoplador de 2:1; um acoplador 4:1 e um comutador óptico. Verificou-se que a utilização de um comutador óptico é o melhor caso para a monitorização de pressão de múltiplos sensores. A multiplexagem com recurso ao comutador foi possível, uma vez que permitia a medição independente de cada sensor de pressão num determinado tempo. Com este resultado, é possível monitorizar 48 sensores com recurso ao OTDR, multiplexados temporalmente. Toda esta implementação prática da dissertação foi realizada nas instalações da Unidade de Optoelectrónica e Sistemas Electrónicos no INESC Porto, onde foram caracterizados e estudados sensores com diferentes características que poderão ser lidas neste documento. A componente teórica foi efectuada na Universidade da Madeira.

Análise de modelos geológicos utilizando percolação dinâmica

In the present study we elaborated algorithms by using concepts from percolation theory which analyze the connectivity conditions in geological models of petroleum reservoirs. From the petrophysical parameters such as permeability, porosity, transmittivity and others, which may be generated by any statistical process, it is possible to determine the portion of the model with more connected cells, what the interconnected wells are, and the critical path between injector and source wells. This allows to classify the reservoir according to the modeled petrophysical parameters. This also make it possible to determine the percentage of the reservoir to which each well is connected. Generally, the connected regions and the respective minima and/or maxima in the occurrence of the petrophysical parameters studied constitute a good manner to characterize a reservoir volumetrically. Therefore, the algorithms allow to optimize the positioning of wells, offering a preview of the general conditions of the given model s connectivity. The intent is not to evaluate geological models, but to show how to interpret the deposits, how their petrophysical characteristics are spatially distributed, and how the connections between the several parts of the system are resolved, showing their critical paths and backbones. The execution of these algorithms allows us to know the properties of the model s connectivity before the work on reservoir flux simulation is started

Uso de renderização volumétrica e realidade virtual para problemas de percolação na engenharia

In the recovering process of oil, rock heterogeneity has a huge impact on how fluids move in the field, defining how much oil can be recovered. In order to study this variability, percolation theory, which describes phenomena involving geometry and connectivity are the bases, is a very useful model. Result of percolation is tridimensional data and have no physical meaning until visualized in form of images or animations. Although a lot of powerful and sophisticated visualization tools have been developed, they focus on generation of planar 2D images. In order to interpret data as they would be in the real world, virtual reality techniques using stereo images could be used. In this work we propose an interactive and helpful tool, named ZSweepVR, based on virtual reality techniques that allows a better comprehension of volumetric data generated by simulation of dynamic percolation. The developed system has the ability to render images using two different techniques: surface rendering and volume rendering. Surface rendering is accomplished by OpenGL directives and volume rendering is accomplished by the Zsweep direct volume rendering engine. In the case of volumetric rendering, we implemented an algorithm to generate stereo images. We also propose enhancements in the original percolation algorithm in order to get a better performance. We applied our developed tools to a mature field database, obtaining satisfactory results. The use of stereoscopic and volumetric images brought valuable contributions for the interpretation and clustering formation analysis in percolation, what certainly could lead to better decisions about the exploration and recovery process in oil fields

Aplicações da teoria da percolação à modelagem e simulação de reservatórios de petróleo

In this thesis we study some problems related to petroleum reservoirs using methods and concepts of Statistical Physics. The thesis could be divided percolation problem in random multifractal support motivated by its potential application in modelling oil reservoirs. We develped an heterogeneous and anisotropic grid that followin two parts. The first one introduce a study of the percolations a random multifractal distribution of its sites. After, we determine the percolation threshold for this grid, the fractal dimension of the percolating cluster and the critical exponents ß and v. In the second part, we propose an alternative systematic of modelling and simulating oil reservoirs. We introduce a statistical model based in a stochastic formulation do Darcy Law. In this model, the distribution of permeabilities is localy equivalent to the basic model of bond percolation

Percolação convencional, percolação correlacionada e percolação por invasão num suporte multifractal

In this work we have studied the problem of percolation in a multifractal geometric support, in its different versions, and we have analysed the conection between this problem and the standard percolation and also the connection with the critical phenomena formalism. The projection of the multifractal structure into the subjacent regular lattice allows to map the problem of random percolation in the multifractal lattice into the problem of correlated percolation in the regular lattice. Also we have investigated the critical behavior of the invasion percolation model in this type of environment. We have discussed get the finite size effects

Fractais e Percolação na Recuperação de Petróleo

The complex behavior of a wide variety of phenomena that are of interest to physicists, chemists, and engineers has been quantitatively characterized by using the ideas of fractal and multifractal distributions, which correspond in a unique way to the geometrical shape and dynamical properties of the systems under study. In this thesis we present the Space of Fractals and the methods of Hausdorff-Besicovitch, box-counting and Scaling to calculate the fractal dimension of a set. In this Thesis we investigate also percolation phenomena in multifractal objects that are built in a simple way. The central object of our analysis is a multifractal object that we call Qmf . In these objects the multifractality comes directly from the geometric tiling. We identify some differences between percolation in the proposed multifractals and in a regular lattice. There are basically two sources of these differences. The first is related to the coordination number, c, which changes along the multifractal. The second comes from the way the weight of each cell in the multifractal affects the percolation cluster. We use many samples of finite size lattices and draw the histogram of percolating lattices against site occupation probability p. Depending on a parameter, ρ, characterizing the multifractal and the lattice size, L, the histogram can have two peaks. We observe that the probability of occupation at the percolation threshold, pc, for the multifractal is lower than that for the square lattice. We compute the fractal dimension of the percolating cluster and the critical exponent β. Despite the topological differences, we find that the percolation in a multifractal support is in the same universality class as standard percolation. The area and the number of neighbors of the blocks of Qmf show a non-trivial behavior. A general view of the object Qmf shows an anisotropy. The value of pc is a function of ρ which is related to its anisotropy. We investigate the relation between pc and the average number of neighbors of the blocks as well as the anisotropy of Qmf. In this Thesis we study likewise the distribution of shortest paths in percolation systems at the percolation threshold in two dimensions (2D). We study paths from one given point to multiple other points

Fractais e percolação na recuperação de Petróleo

The complex behavior of a wide variety of phenomena that are of interest to physicists, chemists, and engineers has been quantitatively characterized by using the ideas of fractal and multifractal distributions, which correspond in a unique way to the geometrical shape and dynamical properties of the systems under study. In this thesis we present the Space of Fractals and the methods of Hausdorff-Besicovitch, box-counting and Scaling to calculate the fractal dimension of a set. In this Thesis we investigate also percolation phenomena in multifractal objects that are built in a simple way. The central object of our analysis is a multifractal object that we call Qmf . In these objects the multifractality comes directly from the geometric tiling. We identify some differences between percolation in the proposed multifractals and in a regular lattice. There are basically two sources of these differences. The first is related to the coordination number, c, which changes along the multifractal. The second comes from the way the weight of each cell in the multifractal affects the percolation cluster. We use many samples of finite size lattices and draw the histogram of percolating lattices against site occupation probability p. Depending on a parameter, ρ, characterizing the multifractal and the lattice size, L, the histogram can have two peaks. We observe that the probability of occupation at the percolation threshold, pc, for the multifractal is lower than that for the square lattice. We compute the fractal dimension of the percolating cluster and the critical exponent β. Despite the topological differences, we find that the percolation in a multifractal support is in the same universality class as standard percolation. The area and the number of neighbors of the blocks of Qmf show a non-trivial behavior. A general view of the object Qmf shows an anisotropy. The value of pc is a function of ρ which is related to its anisotropy. We investigate the relation between pc and the average number of neighbors of the blocks as well as the anisotropy of Qmf. In this Thesis we study likewise the distribution of shortest paths in percolation systems at the percolation threshold in two dimensions (2D). We study paths from one given point to multiple other points. In oil recovery terminology, the given single point can be mapped to an injection well (injector) and the multiple other points to production wells (producers). In the previously standard case of one injection well and one production well separated by Euclidean distance r, the distribution of shortest paths l, P(l|r), shows a power-law behavior with exponent gl = 2.14 in 2D. Here we analyze the situation of one injector and an array A of producers. Symmetric arrays of producers lead to one peak in the distribution P(l|A), the probability that the shortest path between the injector and any of the producers is l, while the asymmetric configurations lead to several peaks in the distribution. We analyze configurations in which the injector is outside and inside the set of producers. The peak in P(l|A) for the symmetric arrays decays faster than for the standard case. For very long paths all the studied arrays exhibit a power-law behavior with exponent g ∼= gl.

Estudo de sistemas complexos com interações de longo alcance : percolação, redes e tráfego

In this thesis we investigate physical problems which present a high degree of complexity using tools and models of Statistical Mechanics. We give a special attention to systems with long-range interactions, such as one-dimensional long-range bondpercolation, complex networks without metric and vehicular traffic. The flux in linear chain (percolation) with bond between first neighbor only happens if pc = 1, but when we consider long-range interactions , the situation is completely different, i.e., the transitions between the percolating phase and non-percolating phase happens for pc < 1. This kind of transition happens even when the system is diluted ( dilution of sites ). Some of these effects are investigated in this work, for example, the extensivity of the system, the relation between critical properties and the dilution, etc. In particular we show that the dilution does not change the universality of the system. In another work, we analyze the implications of using a power law quality distribution for vertices in the growth dynamics of a network studied by Bianconi and Barabási. It incorporates in the preferential attachment the different ability (fitness) of the nodes to compete for links. Finally, we study the vehicular traffic on road networks when it is submitted to an increasing flux of cars. In this way, we develop two models which enable the analysis of the total flux on each road as well as the flux leaving the system and the behavior of the total number of congested roads

Estudo de propriedades críticas em sistemas complexos: método de procura automática em sistemas tipo Ising e percolação de longo alcance

The new technique for automatic search of the order parameters and critical properties is applied to several well-know physical systems, testing the efficiency of such a procedure, in order to apply it for complex systems in general. The automatic-search method is combined with Monte Carlo simulations, which makes use of a given dynamical rule for the time evolution of the system. In the problems inves¬tigated, the Metropolis and Glauber dynamics produced essentially equivalent results. We present a brief introduction to critical phenomena and phase transitions. We describe the automatic-search method and discuss some previous works, where the method has been applied successfully. We apply the method for the ferromagnetic fsing model, computing the critical fron¬tiers and the magnetization exponent (3 for several geometric lattices. We also apply the method for the site-diluted ferromagnetic Ising model on a square lattice, computing its critical frontier, as well as the magnetization exponent f3 and the susceptibility exponent 7. We verify that the universality class of the system remains unchanged when the site dilution is introduced. We study the problem of long-range bond percolation in a diluted linear chain and discuss the non-extensivity questions inherent to long-range-interaction systems. Finally we present our conclusions and possible extensions of this work

Não-extensividade em percolação por ligações de longo - alcance

A linear chain do not present phase transition at any finite temperature in a one dimensional system considering only first neighbors interaction. An example is the Ising ferromagnet in which his critical temperature lies at zero degree. Analogously, in percolation like disordered geometrical systems, the critical point is given by the critical probability equals to one. However, this situation can be drastically changed if we consider long-range bonds, replacing the probability distribution by a function like . In this kind of distribution the limit α → ∞ corresponds to the usual first neighbor bond case. In the other hand α = 0 corresponds to the well know "molecular field" situation. In this thesis we studied the behavior of Pc as a function of a to the bond percolation specially in d = 1. Our goal was to check a conjecture proposed by Tsallis in the context of his Generalized Statistics (a generalization to the Boltzmann-Gibbs statistics). By this conjecture, the scaling laws that depend with the size of the system N, vary in fact with the quantitie

Análise e comparação entre algoritmos de percolação

In this work, we study and compare two percolation algorithms, one of then elaborated by Elias, and the other one by Newman and Ziff, using theorical tools of algorithms complexity and another algorithm that makes an experimental comparation. This work is divided in three chapters. The first one approaches some necessary definitions and theorems to a more formal mathematical study of percolation. The second presents technics that were used for the estimative calculation of the algorithms complexity, are they: worse case, better case e average case. We use the technique of the worse case to estimate the complexity of both algorithms and thus we can compare them. The last chapter shows several characteristics of each one of the algorithms and through the theoretical estimate of the complexity and the comparison between the execution time of the most important part of each one, we can compare these important algorithms that simulate the percolation.

Um estudo das condições de percolação e estabilidade em barragens de terra mediante métodos geofísicos: caso do dique de Sant Llorenç de Montgai - Espanha

The monitoring of Earth dam makes use of visual inspection and instrumentation to identify and characterize the deterioration that compromises the security of earth dams and associated structures. The visual inspection is subjective and can lead to misinterpretation or omission of important information and, some problems are detected too late. The instrumentation are efficient but certain technical or operational issues can cause restrictions. Thereby, visual inspections and instrumentation can lead to a lack of information. Geophysics offers consolidated, low-cost methods that are non-invasive, non-destructive and low cost. They have a strong potential and can be used assisting instrumentation. In the case that a visual inspection and strumentation does not provide all the necessary information, geophysical methods would provide more complete and relevant information. In order to test these theories, geophysical acquisitions were performed using Georadar (GPR), Electric resistivity, Seismic refraction, and Refraction Microtremor (ReMi) on the dike of the dam in Sant Llorenç de Montgai, located in the province of Lleida, 145 km from Barcelona, Catalonia. The results confirmed that the geophysical methods used each responded satisfactorily to the conditions of the earth dike, the anomalies present and the geological features found, such as alluvium and carbonate and evaporite rocks. It has also been confirmed that these methods, when used in an integrated manner, are able to reduce the ambiguities in individual interpretations. They facilitate improved imaging of the interior dikes and of major geological features, thus inspecting the massif and its foundation. Consequently, the results obtained in this study demonstrated that these geophysical methods are sufficiently effective for inspecting earth dams and they are an important tool in the instrumentation and visual inspection of the security of the dams

Universaidade em sistemas da mecâniaestatística de não equilíbrio com estados absorventes e percolação geográfica

Complex systems have stimulated much interest in the scientific community in the last twenty years. Examples this area are the Domany-Kinzel cellular automaton and Contact Process that are studied in the first chapter this tesis. We determine the critical behavior of these systems using the spontaneous-search method and short-time dynamics (STD). Ours results confirm that the DKCA e CP belong to universality class of Directed Percolation. In the second chapter, we study the particle difusion in two models of stochastic sandpiles. We characterize the difusion through diffusion constant D, definite through in the relation h(x)2i = 2Dt. The results of our simulations, using finite size scalling and STD, show that the diffusion constant can be used to study critical properties. Both models belong to universality class of Conserved Directed Percolation. We also study that the mean-square particle displacement in time, and characterize its dependence on the initial configuration and particle density. In the third chapter, we introduce a computacional model, called Geographic Percolation, to study watersheds, fractals with aplications in various areas of science. In this model, sites of a network are assigned values between 0 and 1 following a given probability distribution, we order this values, keeping always its localization, and search pk site that percolate network. Once we find this site, we remove it from the network, and search for the next that has the network to percole newly. We repeat these steps until the complete occupation of the network. We study the model in 2 and 3 dimension, and compare the bidimensional case with networks form at start real data (Alps e Himalayas)

Estimativa de expoentes críticos em Percolação

In Percolation Theory, functions like the probability that a given site belongs to the infinite cluster, average size of clusters, etc. are described through power laws and critical exponents. This dissertation uses a method called Finite Size Scaling to provide a estimative of those exponents. The dissertation is divided in four parts. The first one briefly presents the main results for Site Percolation Theory for d = 2 dimension. Besides, some important quantities for the determination of the critical exponents and for the phase transistions understanding are defined. The second shows an introduction to the fractal concept, dimension and classification. Concluded the base of our study, in the third part the Scale Theory is mentioned, wich relates critical exponents and the quantities described in Chapter 2. In the last part, through the Finite Size Scaling method, we determine the critical exponents fi and. Based on them, we used the previous Chapter scale relations in order to determine the remaining critical exponents