Simulação de fluxo de fluidos em meios porosos desordenados uma análise de efeito de escala na estimativa da permeabilidade e do coeficiente de arrasto

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.

Elaboração de uma sequência didática sobre os conceitos geométricos preliminares ao estudo da trigonometria

This study is qualitative, including literature search and preparation of teaching materials. Your goal is to report the study of geometric problems of character presented in the application of trigonometry and work on the preparation of detailed activities that help in overcoming these difficulties. For this, we read some papers on teaching and learning of trigonometry in order to identify the difficulties encountered during their journey. Then separate the geometric difficulties of character and prepare a list of geometric content and procedures associated with them. Thus, we can organize a notebook with activities that would address most of these concepts. Finally we present the specification of activities called Activity on introductory concepts to the study of trigonometry

Geometria e arirmética numa visão multicultural: uma experiência pedagógica

This paper aims to build a notebook of activities that can help the teacher of elementary school mathematics. Topics covered are arithmetic and geometry and the activities proposed here were developed aiming print them a multicultural character. We take as a base line developed by Claudia Zaslavsky multiculturalism and reflected in his books "Games and activities worldwide" and "More games and activities worldwide." We structure our work around four themes: the symbol of the Olympic Games, the pyramids of Egypt, the Russian abacus abacus and Chinese. The first two themes allow you to explore basic concepts of geometry while the latter two themes allow us to explore numerical notation and arithmetic operations

Sistemas Nanoestruturados: Heteroestruturas Quasi-Periódicas de Nitretos e Cálculos Ab initio em Polimorfos CaCO3

The physical properties and the excitations spectrum in oxides and semiconductors materials are presented in this work, whose the first part presents a study on the confinement of optical phonons in artificial systems based on III-V nitrides, grown in periodic and quasiperiodic forms. The second part of this work describes the Ab initio calculations which were carried out to obtain the optoeletronic properties of Calcium Oxide (CaO) and Calcium Carbonate (CaCO3) crystals. For periodic and quasi-periodic superlattices, we present some dynamical properties related to confined optical phonons (bulk and surface), obtained through simple theories, such as the dielectric continuous model, and using techniques such as the transfer-matrix method. The localization character of confined optical phonon modes, the magnitude of the bands in the spectrum and the power laws of these structures are presented as functions of the generation number of sequence. The ab initio calculations have been carried out using the CASTEP software (Cambridge Total Sequential Energy Package), and they were based on ultrasoft-like pseudopotentials and Density Functional Theory (DFT). Two di®erent geometry optimizations have been e®ectuated for CaO crystals and CaCO3 polymorphs, according to LDA (local density approximation) and GGA (generalized gradient approximation) approaches, determining several properties, e. g. lattice parameters, bond length, electrons density, energy band structures, electrons density of states, e®ective masses and optical properties, such as dielectric constant, absorption, re°ectivity, conductivity and refractive index. Those results were employed to investigate the confinement of excitons in spherical Si@CaCO3 and CaCO3@SiO2 quantum dots and in calcium carbonate nanoparticles, and were also employed in investigations of the photoluminescence spectra of CaCO3 crystal

Sistema microemulsionado: caracterização e aplicação na indústria de petróleo

Alkyl polyethoxylates are surfactants widely used in vastly different fields, from oil exploitation to pharmaceutical applications. One of the most interesting characteristics of these surfactants is their ability to form micellar systems with specific geometry, the so-called wormlike micelle. In this work, microemulsions with three distinct compositions (C/T = 40 %, 30 % and 25 %) was used with contain UNITOL / butanol / water / xylene, cosurfactant / surfactante (C/S) ratio equal to 0,5. The microemulsion was characterized by dynamic light scattering (DLS), capillary viscometry, torque rheometry and surface tensiometry experiments carried out with systems based on xylene, water, butanol (cosurfactant) and nonaethyleneglycolmonododecyl ether (surfactant), with fixed surfactant:cosurfactant:oil composition (with and without oil phase) and varying the overall concentration of the microemulsion. The results showed that a transition from wormlike micelles to nanodrops was characterized by maximum relative viscosity (depending on how relative viscosity was defined), which was connected to maximum effective diameter, determined by DLS. Surface tension suggested that adsorption at the air water interface had a Langmuir character and that the limiting value of the surfactant surface excess was independent of the presence of cosurfactant and xylene. The results of the solubilization of oil sludge and oil recovery with the microemulsion: C/S = 40%, 30% and 25% proved to be quite effective in solubilization of oil sludge, with the percentage of solubilization (%solubilization) as high as 92.37% and enhanced oil recovery rates up to 90.22% for the point with the highest concentration of active material (surfactant), that is, 40%.

Evolução tectono-estrutural do Campo de Xaréu (Sub-bacia de Mundaú, Bacia do Ceará - NE do Brasil: abordagem multiescala e pluriferramental

The Xaréu Oil Field, located in the center-southern portion of the Mundaú Sub-Basin (eastern portion of the Ceará Basin), is characterized by a main Iramework of NW-trending and NE-dipping faults. The faults in the Xaréu Oil Field, among which the Xaréu Fautt stands out, are arranged according to an extensional-listriclan, rooted on a detachment surface corresponding to the Mundaú Fault, the border fautt of Mundaú Sub-Basin. During the tectonic-structural evolution of the Xaréu Oil Field and the Mundaú Sub-Basin, the Mundaú Fault played a crucial role on the control of the geometry of both compartments. The main carbonatic unit in the Xaréu Oil Field, named the Trairí Member(Paracuru Formation of Late Aptian to Early Albian age), contains the largest oil volume in the field, concentrated in structurally-controlled accumulations. The Trairí Member is composed by a variety of carbonatic rocks (massive, bedded or laminated calcilutites, ostracodites, calcarenites and carbonatic rudites, all of them presenting variable degrees of dolomitization). The carbonatic rocks are interbedded into thick packages of black shales and marls, besides local beds of siliciclastic conglomerates, sandstones, siltnes and argillites. From the spatial association and the genetic relationships between the carbonatic and siliciclastic units, it is possible to group them in three lithofacies associations (Marginal Plain, Ramp and Lacustrine Interior) that, together, were developed in a lacustrine system associated to a marginal sabkha. Structural studies based on drill coresthat sample the Trairí Member in the Xaréu Oil Field allowed to characterize two generations of meso- to microscale structures: the D1 group presents a typical hydroplastic character, being characterized by intra/interstratal to oblique-bedding shear zones. The hydroplastic character related to these structures allowed to infer their development at an early-lithilication stage of the Trairí Member, leading to infer an Early Cretaceous age to them. The second group of structures identified in the drill cores, nominated D2 and ascribed to a Neogene age, presents a strictly brttle character, being typilied by normal faults and slickenfibers of re-crystallized clayminerals, ali olthem displaying variable orientations. Although the present faults in the Xaréu Oil Field (and, consequently, in the Mundaú Sub-Basin) were classically relerred as struetures of essentially normal displacement, the kinematics analysis of the meso-to microscaie D1 struetures in the drill cores led to deline oblique displacements (normal with a clockwise strike-slip component) to these faults, indicating a main tectonic transport to ENE. These oblique movements would be responsible for the installation of a transtensive context in the Mundaú Sub-Basin, as part of the transcurrent to translormant opening of the Atlantic Equatorial Margin. The balancing of four struetural cross-sections ofthe Xaréu Oil Field indicates that the Mundaú Fault was responsible for more than 50% of the total stretching (ß factor) registered during the Early Aptian. At the initial stages of the "rifting", during Early Aptianuntil the Holocene, the Mundaú Sub-Basin (and consequently the Xaréu Oil Fleld) accumulated a total stretching between 1.21 and 1.23; in other words, the crust in this segment of the Atlantic Equatorial Margin was subjeeted to an elongation of about 20%. From estimates of oblique displacements related to the faults, it ws possible to construct diagrams that allow the determination of stretching factors related to these displacements. Using these diagrams and assuming the sense 01 dominant teetonictransport towards ENE, it was possible to calculate the real stretching lactors related to the oblique movement 0 of the faults in the Mundaú Sub-Basin. which reached actual values between 1.28 and 1.42. ln addnion to the tectonic-structural studies in the Xaréu Oil Field, the interpretation of remote sensing products, coupled wnh characterization of terrain analogues in seleeted areas along the northern Ceará State (continental margins of the Ceará and Potiguar basins), provided addnional data and constraints about the teetonic-structural evolution of the oil lield. The work at the analogue sites was particularly effective in the recognition and mapping, in semidetail scale, several generations of struetures originated under a brittle regime. Ali the obtained information (from the Xaréu Oil Field, the remote sensor data and the terrain analogues) were jointly interpreted, culminating with the proposnion of an evolutionary model lor this segment of the Atlantic Equatorial Margin; this model that can be applied to the whole Margin, as well. This segmentof the Atlantic Equatorial Margin was delormedin an early E-W (when considered lhe present-day position of the South American Plate) transcurrent to transform regime with dextral kinematics, started Irom, at least, the Early Aptian, which left its record in several outcrops along the continental margin of the Ceará State and specilically in the Xaréu off Field. The continuous operation of the regime, through the Albian and later periods, led to the definitive separation between the South American and African plates, with the formation of oceanic lithosphere between the two continental blocks, due to the emplacement off spreading centers. This process involved the subsequent transition of the transcurrent to a translorm dextral regime, creating lhe Equatorial Atlantic Oceano With the separation between the South American and African plates already completed and the increasing separation between lhe continental masses, other tecton ic mechanisms began to act during the Cenozoic (even though the Cretaceous tectonic regime lasted until the Neogene), like an E-W compressive stress líeld (related to the spreading olthe oceanic floor along lhe M id-Atlantic Ridge and to the compression of the Andean Chain) effective Irom the Late Cretaceous, and a state of general extension olthe horizontal surface (due to the thermal uplift ofthe central portion of Borborema Province), effective during the Neogene. The overlap of these mechanisms during the Cenozoic led to the imprint of a complex tectonic framework, which apparently influenced the migration and entrapment 01 hydrocarbon in the Ceará Basin

Análises estratigráfica e estrutural da Seção Rifte (Valanginiano ao Barremiano) na área do levantamento sísmico 3D de baixo vermelho, Bacia Potiguar emersa

Baixo Vermelho area, situated on the northern portion of Umbuzeiro Graben (onshore Potiguar Basin), represents a typical example of a rift basin, characterized, in subsurface, by the sedimentary rift sequence, correlated to Pendência Formation (Valanginian-Barremian), and by the Carnaubais fault system. In this context, two main goals, the stratigraphic and the structural analysis, had guided the research. For this purpose, it was used the 3D seismic volume and eight wells located in the study area and adjacencies. The stratigraphic analysis of the Valanginian-Barremian interval was carried through in two distinct phases, 1D and 2D, in which the basic concepts of the sequence stratigraphy had been adapted. In these phases, the individual analysis of each well and the correlation between them, allowed to recognize the main lithofacies, to interpret the effective depositional systems and to identify the genetic units and key-surfaces of chronostratigraphic character. The analyzed lithofacies are represented predominantly by conglomerates, sandstones, siltites and shales, with carbonate rocks and marls occurring subordinately. According to these lithofacies associations, it is possible to interpret the following depositional systems: alluvial fan, fluvio-deltaic and lacustrine depositional systems. The alluvial fan system is mainly composed by conglomerates deposits, which had developed, preferentially in the south portion of the area, being directly associated to Carnaubais fault system. The fluvial-deltaic system, in turn, was mainly developed in the northwest portion of the area, at the flexural edge, being characterized by coarse sandstones with shales and siltites intercalated. On the other hand, the lacustrine system, the most dominant one in the study area, is formed mainly by shales that could occur intercalated with thin layers of fine to very fine sandstones, interpreted as turbidite deposits. The recognized sequence stratigraphy units in the wells are represented by parasequence sets, systems tracts and depositional sequences. The parasequence sets, which are progradational or retrogradational, had been grouped and related to the systems tracts. The predominance of the progradation parasequence sets (general trend with coarsening-upward) characterizes the Regressive Systems Tract, while the occurrence, more frequently, of the retrogradation parasequence sets (general trend with finning-upward) represents the Transgressive System Tract. In the seismic stratigraphic analysis, the lithofacies described in the wells had been related to chaotic, progradational and parallel/subparallel seismic facies, which are associated, frequently, to the alluvial fans, fluvial-deltaic and lacustrine depositional systems, respectively. In this analysis, it was possible to recognize fifteen seismic horizons that correspond to sequence boundaries and to maximum flooding surfaces, which separates Transgressive to Regressive systems tracts. The recognition of transgressive-regressive cycles allowed to identify nine, possibly, 3a order deposicional sequences, related to the tectonic-sedimentary cycles. The structural analysis, in turn, was done at Baixo Vermelho seismic volume, which shows, clearly, the structural complexity printed in the area, mainly related to Carnaubais fault system, acting as an important fault system of the rift edge. This fault system is characterized by a main arrangement of normal faults with trend NE-SO, where Carnaubais Fault represents the maximum expression of these lineations. Carnaubais Fault corresponds to a fault with typically listric geometry, with general trend N70°E, dipping to northwest. It is observed, throughout all the seismic volume, with variations in its surface, which had conditioned, in its evolutive stages, the formation of innumerable structural features that normally are identified in Pendencia Formation. In this unit, part of these features is related to the formation of longitudinal foldings (rollover structures and distentional folding associated), originated by the displacement of the main fault plan, propitiating variations in geometry and thickness of the adjacent layers, which had been deposited at the same time. Other structural features are related to the secondary faultings, which could be synthetic or antithetic to Carnaubais Fault. In a general way, these faults have limited lateral continuity, with listric planar format and, apparently, they play the role of the accomodation of the distentional deformation printed in the area. Thus, the interaction between the stratigraphic and structural analysis, based on an excellent quality of the used data, allowed to get one better agreement on the tectonicsedimentary evolution of the Valanginian-Barremian interval (Pendência Formation) in the studied area

Caracterização macro, meso e microscópica das estruturas frágeis do corpo arenítico conglomerático da região de Santana do Acaraú (CE) e seu embasamento circundante

The structural framework of the sedimentary basins usually plays an important role in oil prospects and reservoirs. Geometry, interconectivity and density of the brittle features developed during basin evolution could change the permo-porous character of the rocks involved in generation, migration and entrapment of fluid flow. Once the structural characterization of the reservois using only sub-surface data is not an easy task, many studies are focused in analogous outcrops trying to understand the main processes by which brittle tectonic is archieved. In the Santana do Acaraú region (Ceará state, NE Brazil) a pack of conglomeratic sandstone (here named CAC) has its geometry controlled mainly by NE trending faults, interpreted as related to reactivation of a precambrian Sobral Pedro II Lineament (LSP-II). Geological mapping of the CAC showed a major NE-SW trending synform developed before its complete lithification during a dextral transpression. This region was then selected to be studied in details in order of constrain the cretaceous deformation and so help the understanding the deformation of the basins along the brazilian equatorial margin. In order to characterize the brittle deformation in different scales, I study some attributes of the fractures and faults such as orientation, density, kinematic, opening, etc., through scanlines in satellite images, outcrops and thin sections. The study of the satellite images showed three main directions of the macrostructures, N-S, NE-SW and E-W. Two of theses features (N-S and E-W) are in aggreement with previous geophysical data. A bimodal pattern of the lineaments in the CAC´s basement rocks has been evidenciated by the NE and NW sets of structures obtained in the meso and microscale data. Besides the main dextral transpression two others later events, developed when the sediments were complety lithified, were recognized in the area. The interplay among theses events is responsible for the compartimentation of the CAC in several blocks along within some structural elements display diferents orientations. Based on the variation in the S0 orientation, the CAC can be subdivided in several domains. Dispite of the variations in orientations of the fractures/faults in the diferents domains, theses features, in the meso and microscopic scale, are concentrated in two sets (based on their trend) in all domains which show similar orientation of the S0 surface. Thus the S0 orientation was used to group the domains in three major sets: i) The first one is that where S0 is E-W oriented: the fractures are oriented mainly NE with the development of a secondary NW trending; ii) S0 trending NE: the fractures are concentrated mainly along the trend NW with a secondary concentration along the NE trend; iii) The third set, where S0 is NS the main fractures are NE and the secondary concentration is NW. Another analized parameter was the fault/fracture length. This attribute was studied in diferent scales trying to detect the upscale relationship. A terrain digital model (TDM) was built with the brittlel elements supperposed. This model enhanced a 3D visualization of the area as well as the spatial distribution of the fault/fractures. Finally, I believe that a better undertanding of the brittle tectonic affecting both CAC and its nearby basement will help the future interpretations of the tectonic envolved in the development of the sedimentary basins of the brazilian equatorial margin and their oil reservoirs and prospects, as for instance the Xaréu field in the Ceará basin, which subsurface data could be correlated with the surface ones