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.

Pecolação em uma rede multifractal

In this work we present the principal fractals, their caracteristics, properties abd their classification, comparing them to Euclidean Geometry Elements. We show the importance of the Fractal Geometry in the analysis of several elements of our society. We emphasize the importance of an appropriate definition of dimension to these objects, because the definition we presently know doesn t see a satisfactory one. As an instrument to obtain these dimentions we present the Method to count boxes, of Hausdorff- Besicovich and the Scale Method. We also study the Percolation Process in the square lattice, comparing it to percolation in the multifractal subject Qmf, where we observe som differences between these two process. We analize the histogram grafic of the percolating lattices versus the site occupation probability p, and other numerical simulations. And finaly, we show that we can estimate the fractal dimension of the percolation cluster and that the percolatin in a multifractal suport is in the same universality class as standard percolation. We observe that the area of the blocks of Qmf is variable, pc is a function of p which is related to the anisotropy of Qmf

Electrical and Optical Properties of Conductive and Transparent ITO@PMMA Nanocomposites

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Remediação de solos contaminados com diesel por lavagem com solução de tensoativos

Combating pollution of soils is a challenge that has concerned researchers from different areas and motivated the search for technologies that aim the recovery of degraded soils. Literature shows numerous processes that have been proposed with the intent of remediating soils contaminated by oils and other by-products of the oil industry, considering that the processes available have, generally, high operating costs, this work proposes a costeffective alternative to the treatment of Diesel-contaminated soils. The washing solutions were prepared using water as aqueous phase, the saponified coconut oil (OCS) as surfactant and n-butanol as co-surfactant. In this study, the soil was characterized by physical and chemical analyses. The study of diesel desorption from the soil was held in bath, using hexane and washing solutions, which had 10 and 20 wt.% active matter (AM - co-surfactant/surfactants) respectively. The study of the influence of active matter concentration and temperature in bath agitated used an experimental planning. The experiment also developed a system of percolation in bed to wash the soil and studied the influence of the concentration of active substance and volume of washing solution using an experimental planning. The optimal times to achieve hexane extraction were 30 and 180 min, while the best results using a 10% AM was 60 min and using a 20% AM was 120 min. The results of the experimental planning on bath showed that the maximum diesel removal was obtained when at a 20 wt.% of AM and under 50 °C, removing 99.92% of the oil. As for experiments in the system of percolation soil bed, the maximum diesel removal was high when the volume of the washing solution was of 5 L and the concentration of 20% AM. This experiment concluded that the concentration of AM and the temperature were vital to bath experiments for diesel removal, while in the system of percolation soil bed only concentration of AM influenced the soil remediation

Investigation about the copper adsorption on the chloropropylsilica gel surface modified with a nanostructured dendrimer DAB-Am-16: an analytical application for determination of copper in different samples

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Avaliação do potencial mutagênico da água do açude de Lucrécia (RN- Brasil): um enfoque na relação saúde e ambiente

The water quality of many reservoirs in the world has been reduced due to percolation of contaminants to water, which can have natural or anthropogenic origin, increasing the level of genotoxic compounds in aquatic ecosystems. This fact has contributed to the reduction of environmental quality, and commitment the health of living beings that inhabit these ecosystems, including the human population. In this backdrop of reduced water quality, is the Lucrecia dam, which is a major surface water reservoirs by volume of semi-arid region of Rio Grande do Norte, and that has shown contamination by heavy metals, cyanobacteria toxic and the natural presence of Radon. The population that use this source has been showing high rates of cancer, popularly associated with the consumption of this water, with a prevalence about three times higher compared to the whole state of Rio Grande do Norte. Based on this, the present study aimed to evaluate the mutagenic potencial of surface water from the Lucrecia dam, using the Micronucleus Test in Tradescantia pallida (Trad-MN) and in human peripheral blood lymphocytes (CBMN) assay, as well as identify the concentrations of some heavy metals in this water. Water samples were collected on a dry season and a rainy season, in two distinct points. Moreover, in order to bring a completely view about the relationship of man-health-environment in this local, through the knowledge of knowing / acting environmental from residents of Lucrecia, and the use and perceptions they have about the dam of your city, a study of Environmental Perception was carried out with local residents. The results obtained for the both micronucleus test, showed significant results for the three points analyzed. The strongest mutagenic effect was observed in the dry season for both assays. Chemical analyses detected an increase of heavy metal levels in different points and season above the maximum allowed by legislation. Regarding the study of Environmental Perception with local residents, it was observed the knowledge of the environment that the residents have, as well as the strong ties and perceptions with the dam of the city. Thus, the combination of these two aspects (the genetic toxicity tests conducted in the dam together with analysis of environmental perception with the residents of Lucrecia) allowed to draw a more complete diagnosis on the local situation

Caracterização geológico-geofísica do meio aqüífero fissural : uma contribuição aos modelos de fluxo e armazenamento de água subterrânea

Northeastern Brazil is mainly formed by crystalline terrains (around 60% in area). Moreover, this region presents a semi-arid climate so that it is periodically subject to drought seasons. Furthermore, ground water quality extracted fromwells usually presents poor quality because of their high salinity contents. Nevertheless, ground water is still a very important source of water for human and animal consumption in this region. Well sitting in hard rocks terrains in Northeastern Brazil offers a mean success index of aboul 60%, given that a successful siting is defined by a well producing at least 0.5 m³/h. This low index reveals lack of knowledga about the true conditions of storage and percolation of ground water in crystalline rocks. Two models for structures storing and producing ground water in crystalline rocks in Northeastem Brazil have been proposed in the literature. The first model,tradnionally used for well sitting since the sixties are controlled by faults or fractures zones. This model is commonly referred, in Brazilian hydrogeological literature, as the "creek-crack" model (riacho-fenda in Portuguese). Sites appearing to present dense drainage network are preferred for water well siting - particularly at points where the drainages cross-cul each other. Field follow up work is usually based only on geological criteria. The second model is the "eluvio-alluvial through" (calha eluvio-aluvionar in Portuguese); it is also described in the literature but it is not yet incorporated in well sitting practice. This model is based on the hypothesis that reclilinear drainages can also be controlled by the folietion of the rock. Eventually, depending upon the degree of weathering, a through-shaped structure filled with sediments (alluvium and regolith) can be developed which can store and water can be produced from. Using severalfield case studies, this Thesis presents a thorough analysis ofthe two above cited models and proposes a new model. The analysis is based on an integrated methodological approach using geophysics and structural geology. Both land (Resitiviy and Ground Penetrating Radar- GPR) and aerogeophysical (magnetics and frequency domain eletromagnetics) surveys were used. Slructural analysis emphasized neolectonic aspects; in general, itwas found that fractures in the E-W direction are relatively open, as compared to fracturas inthe N-S direction, probably because E-W fractures were opened by the neotectonic stress regime in Northeastern Brazil, which is controlled by E-W compression and N-S extension. The riacho-fenda model is valid where drainages are controlled by fractures. The degree of fracturing and associated weathering dictale the hydrogeological potential of the structure. Field work in structural analogues reveals that subvertical fractures show consistent directions both in outcrop and aerophotograph scales. Geophysical surveys reveal subvertical conductive anomalies associated to the fracture network controlling the drainage; one of the borders of the conductive anomaly usually coincide wih the drainage. An aspect of particular importance to the validation of fracture control are the possible presence of relalively deep conductive anomalies wihoul continuation or propagalion to the surface. The conductive nature of lhe anomaly is due to the presence of wealhered rock and sedirnenls (alluvium and/or regolilh) storing ground waler which occur associated to the fracture network. Magnetic surveys are not very sensisnive to these structures.lf soil or covering sedirnents are resislive (> 100 Ohm.m), GPR can ba used to image precisely lhe fracture network. A major limialion of riacho-fenda model, revealed by GPR images, is associated to the fact thal subhorizontal fractures do play a very important role in connecting the fracture network, besides connect shallow recharge zones to relalively deep subvertical frecture zones. Iffractures play just a secondary control on the drainage, however, r/acho-fenda model may have a very limiled validny; in these cases, large portions oflhe drainage do nol coincide wilh frectures and mosl oflhewells localed in lhe drainage surrounding would resull dry. Usually, a secondary conlrol on lhe drainage by Ihefraclure networkcan be revealed only wilh detailed geophysical survey. The calha elClv1o-aluvlonarmodel is valid where drainages are conlrolled by folialion. The degree 01 wealhering 01 lhe lolialion planes dictales lhe hydrogeological polenlial 01 lhe slruclure. Outcrop analysis reveals Ihal lolialion and drainage direclions are parallel and Ihal no Iraclures, orfraclures wilh diflerent directions 01 lhe drainage direclion occur. Geophysical surveys reveal conduclive anomalies in a slab lorm associaled 10 lhe Ihrough 01 lhe wealhered rock and sedimenls (alluvium and/or regolith). Magnelic surveys can ofler a very good conlrol on lolialion direclion. An importanl aspect 10 validale lolialion conlrol are lhe presence 01 conductive anomalies showing shallow and deep portions area which are linked. Illhere is an exlensive soil cover, r/acho-fenda and calha eIClv1o-aluv/onar conlrols can be easily misinlerpreled in lhe absence 01 geophysical conlrol. Certainly, Ihis lacl could explain at leasl a part of lhe failure index in well sitting. The model wealhering sack (bolsllo de Intempertsmo in Portuguese) is proposed to explain cases where a very inlensive wealhering occur over lhe crystalline rock so Ihal a secondary inlerslilial porosity is crealed. The waler is Ihen stored in lhe porous of lhe regolilh in a similar mannerlo sedimentary rocks. A possible example ofthis model was delecled by using land geophysical survey where a relalivelyvery deep isolaled conduclive anomaly, in a slab form, was delected. Iflhis structure does store ground waler, certainly Ihere must be a link 01 lhe deep slructure wilh lhe surface in orderlo provide walerfeeding. This model mighl explain anomalous waler yields as greal as 50 m³/h Ihalsomelimescan occur in crystalline rocks in Northeaslern Brazil

Reavaliação de critérios estruturais na hidrogeologia de terrenos cristalinos, com ênfase na neotectônica e sensoriamento remoto

Hydrogeological prospecting in Northeast Brazil and in other crystalline terrains has been developed on the basis of structural and regional geology concepts that date back to the 50-60 decades and, as such, demand a natural re-evaluation and update. In this kind of terrain, the percolation and accumulation of ground water are controlled by fractures and other types of discontinuities, such as foliations and geological contacts that, through weathering, impart porosity and permeability to the rocks, allowing water flow and storage. Several factors should be considered in the process of locating water wells, as discussed in the literature. Among these, the kind of structures, fracture geometry (including aperture and connectivity) and their geological and chronological context. It is important to correlate fracture systems with the regional neotectonic framework. Fractures at low angle (sub parallel) with the principal stress axis (s1) are those which tend to open (actually they work as tension joints) and, in principle, would present major hydric potential; in the opposite side, fractures at high angle to s1 would behave as closed by a compressional component. Fractures diagonal to the compression and tension axes correspond to shear fractures and, due to their connectivity with second fractures, are also important in terms of hydric potential. Uplift followed by terrain denudation leads to decompression and a general tendency to open (aided by weathering processes) fractures and other rock discontinuities, at different orientations. Low angle fractures, formed in this context, are equally important to increase connectivity, collection of water and recharge of the aquifer systems. In a general way, an opening component (neotectonic or by terrain decompression) and several models to increase fracture connectivity correlate with a greater hydric potential of these structures. Together with parallel research, this thesis addresses models of ground water occurrence in crystalline terrains, either improving well established concepts like the (Riacho-Fenda model), but also stressing other possibilities, like the role of alluvium and paleo-regoliths (the Calha Elúvio-Aluvionar model) and of strongly altered, permo-porous zones placed at variable depths below the present surface, flanking several types of discontinuities, especially interconnected fracture arrays (the Bolsões de Intemperismo model). Different methodological approaches are also discussed in order to improve success rates in the location of water wells in crystalline terrains. In this methodological review, a number of case studies were selected in the eastern domain of the State of Rio Grande do Norte, involving the localities of Santa Cruz, Santo Antônio, Serrinha, Nova Cruz, Montanhas, Lagoa de Pedras and Lagoa Salgada. Besides the neotectonic analysis of brittle structures, this Thesis addresses the validation of remote sensing as a tool for ground water prospecting. Several techniques were tested in order to detect and select areas with higher potential for ground water accumulation, using Landsat 5-TM and RADARSAT images, besides conventional aerial photos. A number of filters were tested to emphasize lineaments in the images, improving their discrimination, to identify areas with higher overburden humidity, which could reflect subsurface water accumulation, as well as alluvium and other sedimentary covers that might act as recharge zones. The work started with a regional analysis with the orbital images, followed by analysis of aerial photos, up to a detailed structural study of rock exposures in the terrain. This last step involved the analysis of outcrops surrounding wells (in a ray of approximately 10 to 100 m) with distinct productivities, including dry examples. At the level required for detail, it was not possible to accomplish a statistical approach using the available well data catalogs, which lack the desired specific information. The methodology worked out in this Thesis must undergo a testing phase through location of new water wells. An increase in the success rates as desired will led to a further consolidation step with wider divulgation of the methodology to private companies and governmental agencies involved in ground water prospecting in crystalline terrains