Determinação de Dados de Equilíbrio Líquido-Vapor para Sistemas Hidrocarbonetos e Desenvolvimento de uma Nova Célula Dinâmica

In the present work are established initially the fundamental relationships of thermodynamics that govern the equilibrium between phases, the models used for the description of the behavior non ideal of the liquid and vapor phases in conditions of low pressures. This work seeks the determination of vapor-liquid equilibrium (VLE) data for a series of multicomponents mixtures of saturated aliphatic hydrocarbons, prepared synthetically starting from substances with analytical degree and the development of a new dynamic cell with circulation of the vapor phase. The apparatus and experimental procedures developed are described and applied for the determination of VLE data. VLE isobarics data were obtained through a Fischer's ebulliometer of circulation of both phases, for the systems pentane + dodecane, heptane + dodecane and decane + dodecane. Using the two new dynamic cells especially projected, of easy operation and low cost, with circulation of the vapor phase, data for the systems heptane + decane + dodecane, acetone + water, tween 20 + dodecane, phenol + water and distillation curves of a gasoline without addictive were measured. Compositions of the equilibrium phases were found by densimetry, chromatography, and total organic carbon analyzer. Calibration curves of density versus composition were prepared from synthetic mixtures and the behavior excess volumes were evaluated. The VLE data obtained experimentally for the hydrocarbon and aqueous systems were submitted to the test of thermodynamic consistency, as well as the obtained from the literature data for another binary systems, mainly in the bank DDB (Dortmund Data Bank), where the Gibbs-Duhem equation is used obtaining a satisfactory data base. The results of the thermodynamic consistency tests for the binary and ternary systems were evaluated in terms of deviations for applications such as model development. Later, those groups of data (tested and approved) were used in the KijPoly program for the determination of the binary kij parameters of the cubic equations of state original Peng-Robinson and with the expanded alpha function. These obtained parameters can be applied for simulation of the reservoirs petroleum conditions and of the several distillation processes found in the petrochemistry industry, through simulators. The two designed dynamic cells used equipments of national technology for the determination Humberto Neves Maia de Oliveira Tese de Doutorado PPGEQ/PRH-ANP 14/UFRN of VLE data were well succeed, demonstrating efficiency and low cost. Multicomponents systems, mixtures of components of different molecular weights and also diluted solutions may be studied in these developed VLE cells

Investigação dos processos hidrossedimentológicos em parcela experimental no semi-árido potiguar

In northeastern semiarid, seasonality on precipitation temporal distribution, high intensity storm events and inadequate management of native vegetation can promote soil erosion. Vegetation removal causes soil surface exposure, reduces soil water storage capacity and can be the source degradation processes. In this context, this approach aims to analyze water and soil erosion processes on a 250 m2 undisturbed experimental plot with native vegetation, slope 2.5% by using 2006 and 2007 monitoring data. The site was instrumented to monitor rainfall, overland flow runoff and erosion by using a 5 m³ tank downstream the plot. Soil erosion monitoring was made by transported sediment and organic matter collection after each event. Field infiltration experiments were made at 16 points randomly distributed within the plot area by using a constant head infiltrometer during drought and rainy seasons, respectively. Infiltration data revealed high spatial and temporal variability. It was observed that during the beginning of the rainy period, 77% of the events showed runoff coefficient less than 0.05. As the rainy season began, soil water increase produced annual species germination. High intensity storms resulted in runoff coefficients varying between 0.33 and 0.42. Once the annual species was established, it was observed that approximately 39% of the events produced no runoff, which reflects an increase on soil water retention capacity caused by the vegetation. A gradual runoff reduction during the rainy season emphasizes the effect of vegetative density increase. Soil erosion observed data allowed to fit an empirical relationship involving soil loss and precipitation height, which was used to analyze the plot installation impact on soil erosion. Observed soil loss in 2006 and 2007 was 230 Kg/ha and 54 Kg/ha, respectively

Produção de forragem verde em sistema hidropônico usando esgoto tratado

In the urban areas of the cities a larger problem of destiny of effluents of the treatment stations is verified due to the junction of the sewages in great volumes. This way the hidroponic cultive becomes important, for your intensive characteristic, as alternative of reuse. This work presents as objective the improvement of the relation hidric-nutritious of the hidroponic cultive of green forage (FVH) using treaty sewage. The production of forage was with corn (Zea mays L.), using double hybrid AG1051, in the experimental field of the Federal University of Rio Grande do Norte (UFRN), in the city of Natal-RN-Brazil. The treated effluent essentially domestic had origin of anaerobic reactor, type decant-digester of two cameras in series followed by anaerobic filters drowned. The hidroponic experimental system was composed of 08 stonemasons, with limited contours for masonry of drained ceramic brick, measuring each one 2,5 meters in length for 1,0 meter of width, with inclination of 4% (m/m) in the longitudinal sense, leveled carefully, in way to not to allow preferential roads in the flow. These dimensions, the useful area of Isow was of 2 square meters. The stonemasons of cultive were waterproof (found and lateral) with plastic canvas of 200 micres of thickness, in the white color. Controlled the entrance and exit of the effluente in the stonemasons, with cycles of 12,68 minutes, it being water of 1,18 minutes. The treatments were constituted of: T1 - 24 hours/day under it waters with flow of 2 L/min; T2 - 12 hours/day under waters with flow of 4 L/min; T3 - 12 hours/day under waters with flow of 2 L/min; and T4 - 16 hours/day under waters with flow of 3 L/min. There were evaluations of the evapotranspirometric demand, of hidroponic system affluent and effluent seeking to characterize and to monitor physical-chemical parameters as: pH, temperature, Electric Conductivity and Fecal Coliforms. This last one was analyzed to the 11 days after isow (DAS) and to the 14 DAS. The others were analyzed daily. I sow it was accomplished in the dates of February 21, 2007, first experiment, and April 10, 2007, second experiment. The density of Isow was of 2 kg of seeds, germinated before 48 hours, for square meter of stonemason. The statistic delineament was it casual entirely with two repetitions, in two experiments. It was applied Tukey test of average to five percent of probability. The cultivation cycle was of 14 DAS with evapotranspirometric demand maximum, reached by T1, of 67,44 mm/day. The analyzed parameters, as mass of green matter - Kg, productivity-Kg/m2 and reason of production of seed FVH/Kg used in Isow, the best result was presented by T1, obtaining value of up to 19,01 Kg/m2 of cultive. Without significant difference, the T4 presented greats values with 16 hours under cycle of water. The Treatments 2 and 3 with 12 hours under cycle of water, they obtained inferior results to the other Treatments. As treatment system, came efficient in the reduction of the salinity. T1 obtained reduction medium maxim of 62,5%, to the 7 DAS, in the amount of salts that enter in the system in they are absorbed in the cultivation. The cultivation FVH acted reducing the microbiologic load. Significant percentile of reduction they were reached, with up to 90,23% of reduction of Units of Colonies (UFC), constituting, like this, the Hidroponic System as good alternative of treatment of effluents of Reactors of high Efficiency

Disponibilidade hídrica potencial em face da distribuição espaço-temporal das precipitações no Estado do Rio Grande do Norte

The state of Rio Grande do Norte, possessor of an extremely irregular regime of rains, has the necessity of enlarge and specify the researches about its own hydro-climatic conditions, to achieve trustworthy results that are able to minimize the adversities imposed by these conditions and make possible the implementation of a better planning in the economic activities and of subsistence that somehow utilize of the multiple uses of hydro resources of the State. This way, the daily values observed from the pluviometric series of 166 posts, with 45 years uninterrupted of historic data, were adjusted to the incomplete gamma function to the determination of the probability of rain in the 36 period of ten days in which the year was divided. To the attainment of the α and β parameters of this function it was applied the method of the maximum verisimilitude allowing, in the end, to analyze the temporal and spatial distribution of the rain in the level of 75% of probability. The values of potential evapo-transpiration were calculated by the Linacre method that, through the SURFER software, were confronted with the dependant rain, obtaining, in this way, the spatialization of the potential hydro availability, which the values can be known to any period of ten days of the year, city and/or region of the state of Rio Grande do Norte. With the identification of the main meteorological systems that act in the State, we sought to better comprehend how this systems interfere, in the irregular regime of rain, in the situations of several clime in the major part of Rio Grande do Norte and in the hydro regional balance. And, finally, with these data in hand and with the generated maps, we verified that space-temporal distribution of the rain and of the potential hydro availability were heterogeneous in the whole State, mainly in the West and Central regions, inserted in potiguar s semi-arid, which, after the period of the rains station, suffers with dry season and length drought during the rest of the year

Caracterização espacial de reservatórios do semiárido em função da qualidade da água através do uso de componentes principais

A região semiárida sofre escassez hídrica. A fim de regularizar a disponibilidade hídrica nos períodos de estiagem, são construídas barragens. No entanto, a qualidade da água armazenada tem sofrido os efeitos do descarte irregular de resíduos no meio ambiente e das atividades antrópicas exercidas nas bacias hidrográficas. A degradação hídrica pode ser constatada a partir do monitoramento dos parâmetros de qualidade da água. Estes dados podem ser analisados através de métodos estatísticos tais como a Análise de Componentes Principais e a análise de agrupamento, que seleciona indivíduos com características semelhantes. O objetivo deste trabalho é realizar oagrupamento dos reservatórios do Rio Grande do Norte, com base nos parâmetros de qualidade da água, para a identificação de grupos homogêneos de reservatórios em termos de fontes de poluição. Serão objeto desse estudo as bacias Piranhas-Açu, Apodi-Mossoró, Trairí, Potengi e Ceará-Mirim. Os parâmetros mercúrio, chumbo, cromo, fósforo total, nitrogênio total e zinco contribuíram para a formação da primeira componente principal, que pode indicar poluição por metais pesados; sólidos totais, DBO, OD e cobre, para a segunda componente, que pode ser indicativo de poluição por matéria orgânica e atividades antrópicas; e clorofila a , cádmio e níquel, para a terceira componente, que pode indicar eutrofização e poluição por metais pesados. De posse das componentes principais se procedeu o agrupamento dos reservatórios, formando-se quatro grupos distintos. Os grupos 1 e 2 são constituídos por reservatórios da Bacia Piranhas-Açu, que apresentou maiores valores de metais pesados. O grupo 3, constituído por reservatórios das bacias Ceará-Mirim, Potengi e Trairí, apresentou maiores valores de DBO e sólidostotais e o grupo 4 é formado por reservatórios da Bacia Apodi-Mossoró. Nas Bacias do Trarí e Piranhas-Açu deve ser coibido o lançamento desordenado de efluentes e fontes de poluição difusas, e implantado um sistema de coleta de esgoto para minimizar a poluição por matéria orgânica

Investigação histórica na formação de professores de matemática: um estudo centrado no conceito de função

In this study we analyzed the development of a teaching experience, involving students with a bachelor s degree in mathematics from UFRN, based on the history of mathematics and mathematical investigations with the aim of contributing to the improvement of the teaching-learning of mathematics. The historical investigation tasks were planned and applied in the classroom, focusing on functional thought. The results obtained during the experience were described and evaluated based on authors who support the assumption of investigation and history as an alternative to the learning of mathematics. We emphasize that the material of analysis consisted of a work diary, audio recordings, questionnaires with testimony of the students involved, and, in addition, the assessment of the teacher of that subject. With regard to the mathematical content, the study was restricted to the concept of function, forms of representation and notation. It was evident that students showed great improvement with regard to the necessary formalization of the mathematical contents which were focused on, and to the active involvement of the students at different stages of the study. We can affirm that the completed study certainly represents significant contributions to an approach in the teaching-learning of functional thought

Formas e função do discurso do outro no gênero monográfico

The present work investigates related discourse in rewriting discursive practices, at monographic works specifically at the theoretical foundation section. Focalizing some discursive strategies of voice management (direct and indirect discourse and modalization voice) we detach the introduction way and function of cited discourse. To do so, it were analyzed eighteen monographic works: nine of them final graduation works and other nine specialization works seeing that each works belonging to the same student, in two different stages, in the period from 2003 in graduation conclusion to 2005 in the end of specialization course. The data reveal that the monographic writer/student emphasizes the use of direct discourse in graduation works while in specialization works there was an emphasis at indirect speech. The analysis the way they introduce cited discourse pointed out that writer/student in graduation course such as specialization student make meaningless constructions when they do not use discendi verbs, they demonstrate difficulties inarticulate citing discourse with cited discourse. In what is related to functions of cited discourse we verify that the student/writer, in both stages or levels give emphasis to the function maintain an assertion, indicating that other s discourse serve mainly as a resource of authority just because that this function reveals the absence of a dialog between student writing and cited discourse. In a general way, the forms of other s discourse claim a form of writing that is found starting from a sequence of cited discourse in what student/writer voice in graduation and specialization comes to text surface just few times, but most of the times, the student takes other s words as they were themselves, every time there is an overlap of author/source

Efeito do exercício físico e estatinas na função muscular em animais com dislipidemia

As estatinas são utilizadas no tratamento das dislipidemias, com grande tolerância; no entanto, vários efeitos colaterais podem surgir, destacando-se miopatia. A prática regular do exercício físico (EF) produz modificações favoráveis no perfil lipídico; entretanto, pode gerar lesões musculares. OBJETIVO: Avaliar o efeito da associação entre exercício físico e estatinas na função muscular, pela análise histológica, em modelo experimental animal com dislipidemia. MÉTODOS: Foram utilizados 80 ratos machos Wistar, distribuídos em oito grupos, incluindo animais submetidos à dieta hipercolesterolêmica (DH), sinvastatina com (G1) e sem (G2) EF; DH e fluvastatina, com (G3) e sem EF (G4); alimentados com ração comercial (RC) na presença (G5) e ausência de (G6) EF; DH submetidos (G7) ou não (G8) a EF. A DH foi administrada por 90 dias, as estatinas e prática de EF em esteira rolante por oito semanas. Os animais foram sacrificados, e o músculo sóleo retirado para análise histológica. Aplicaram-se os testes t de Student pareado e análise multivariada, com nível significante para p < 0,05. RESULTADOS: As principais alterações histológicas encontradas foram fibras de diferentes diâmetros, atróficas, em degeneração, splitting, edema, infiltrado inflamatório. Essas alterações foram observadas em 90% dos animais do grupo G1, 80% do G2, 70% do G3, 30% do G4, 40% do G5 e 30% do G7. Nos grupos G6 e G8 identificaram-se fibras musculares com morfologia preservada. CONCLUSÕES: Na avaliação histológica muscular, a associação entre fluvastatina, sinvastatina e exercício físico acarreta alterações morfológicas com predomínio no uso da sinvastatina, variando de grau leve a grave, no músculo sóleo de ratos, induzidos pelos inibidores da HMG-CoA redutase.

Efeito da técnica de oscilação oral de alta freqüência aplicada em diferentes pressões expiratórias sobre a função autonômica do coração e os parâmetros cardiorrespiratórios

O objetivo deste estudo foi avaliar o efeito da técnica de oscilação oral de alta freqüência (com o aparelho Shaker), aplicada em diferentes pressões expiratórias (PE), sobre a função autonômica e parâmetros cardiorrespiratórios. Foram coletados dados de 20 voluntários jovens saudáveis (21,6±1,3 anos), que permaneceram em repouso inicial por 10 minutos e, em seguida, fizeram três séries de dez expirações no aparelho (com intervalo de descanso de 2 minutos entre as séries) em três diferentes PE - pressão livre (PL), de 10 (P10) e de 20 (P20) cmH2O - permanecendo por mais 10 minutos em repouso final. Os dados foram analisados estatisticamente, com nível de significância de 5%. Após a aplicação da técnica, constatou-se diferença significante nos índices de variabilidade da freqüência cardíaca em PL e um aumento significante na pressão arterial sistólica em P20. Na pressão arterial diastólica, freqüência respiratória e saturação periférica de oxigênio não foram encontradas diferenças antes, durante e após a técnica, nas diferentes PE. A percepção do esforço aumentou significantemente ao longo das séries em PL e P20 e entre P10 e P20 em cada série. A freqüência cardíaca (FC) aumentou e diminuiu em sincronia com os movimentos de inspiração e expiração, respectivamente. Foram observadas modificações na modulação autonômica do coração em PL. A aplicação da técnica nessa população, nas diferentes PE analisadas, promoveu modificações no comportamento da FC, no esforço percebido e, em PL, na modulação autonômica do coração.

Os argumentos transcendentais: kant e o problema de hume

This work whose title is "The transcendental arguments: Kant Andy Hume's problem" has as its main objective to interpret Kant's answer to Hume's problem in the light of the conjunction of the causality and induction themes which is equivalent to skeptical- naturalist reading of the latter. In this sense, this initiative complements the previous treatment seen in our dissertation, where the same issue had been discussed from a merely skeptical reading that Kant got from Hume thought and was only examined causality. Among the specific objectives, we list the following: a) critical philosophy fulfills three basic functions, a founding, one negative and one would argue that the practical use of reason, here named as defensive b) the Kantian solution of Hume's problem in the first critisism would fulfill its founding and negative functions of critique of reason; c) the Kantian treatment of the theme of induction in other criticisms would will fulfill the defense function of critique of reason; d) that the evidence of Kant's answer to Hume's problem are more consistent when will be satisfied these three functions or moments of criticism. The basic structure of the work consists of three parts: the first the genesis of Hume's problem - our intention is to reconstruct Hume's problem, analyzing it from the perspective of two definitions of cause, where the dilution of the first definition in the second match the reduction of psychological knowledge to the probability of following the called naturalization of causal relations; whereas in the second - Legality and Causality - it is stated that when considering Hume in the skeptic-naturalist option, Kant is not entitled to respond by transcendental argument A􀁴B; A⊢B from the second Analogy, evidence that is rooted in the position of contemporary thinkers, such as Strawson and Allison; in third part - Purpose and Induction - admits that Kant responds to Hume on the level of regulative reason use, although the development of this test exceeds the limits of the founding function of criticism. And this is articulated in both the Introduction and Concluding Remarks by meeting the defensive [and negative] function of criticism. In this context, based on the use of so-called transcendental arguments that project throughout the critical trilogy, we provide solution to a recurring issue that recurs at several points in our submission and concerning to the "existence and / or the necessity of empirical causal laws. In this light, our thesis is that transcendental arguments are only an apodictic solution to the Hume s skeptical-naturalist problem when is at stake a practical project in which the interest of reason is ensured, as will, in short, proved in our final considerations

Aspectos dinâmicos da água versus álcool e acetona por técnicas de congelamento

Water still represents, on its critical properties and phase transitions, a problem of current scientific interest, as a consequence of the countless open questions and of the inadequacy of the existent theoretical models, mainly related to the different solid and liquid phases that this substance possesses. For example, there are 13 known crystalline forms of water, and also amorphous phases. One of them, the amorphous ice of very high density (VHDA), was just recently observed. Other example is the anomalous behavior in the macroscopic density, which presents a maximum at the temperature of 277 K. In order to experimentally investigate the behavior of one of the liquid-solid phase transitions, the anomaly in its density and also the metastability, we used three different cooling techniques and, as comparison systems, we made use of the solvents: acetone and ethyl alcohol. The first studied cooling system employ a Peltier plate, a device recently developed, which makes use of small cubes made up of semiconductors to change heat among two surfaces; the second system is a commercial refrigerator, similar to the residential ones. Finally, the liquid nitrogen technique, which is used to refrigerate the samples in a container, in two ways: a very fast and other one, almost static. In those three systems, three Beckers of aluminum were used (with a volume of 80 ml, each), containing water, alcohol and acetone. They were closed and maintained at atmospheric pressure. Inside of each Becker were installed three thermocouples, disposed along the vertical axis of the Beckers, one close to the inferior surface, other to the medium level and the last one close the superior surface. A system of data acquisition was built via virtual instrumentation using as a central equipment a Data-Acquisition board. The temperature data were collected by the three thermocouples in the three Beckers, simultaneously, in function of freezing time. We will present the behavior of temperature versus freezing time for the three substances. The results show the characterization of the transitions of the liquid

Propriedades magnéticas de nanopartículas de ferro em substratos antiferromagnéticos

The effect of finite size on the magnetic properties of ferromagnetic particles systems is a recurrent subject. One of the aspects wide investigated is the superparamagnetic limit where the temperature destroys the magnetic order of ferromagnetic small particles. Above the block temperature the thermal value of the magnetic moment of the particle vanishes, due to thermal fluctuations. The value of the blocking temperature diminishes when the size of the particle is reduced, reflecting the reduction of the anisotropy energy barrier between the uniform states along the uniaxial axis. The increasing demand for high density magnetic media has recently attracted great research interest in periodic arrangements of nanometric ferromagnetics particles, approach in the superparamagnetic limit. An interesting conjecture is the possibility of stabilization of the magnetic order of small ferromagnetic particles (F) by interface coupling with antiferromagnetic (AF) substrate. These F/AF systems may also help to elucidate some details of the effect of exchange bias, because the effect of interface roughness and the paper of domain walls, either in the substrate or the particle, are significantly reduced. We investigate the magnetic phases of small ferromagnetic particles on a antiferromagnetic substrate. We use a self-consistent local field method, incorporating the interface field and the dipole interaction between the spins of the ferromagnetic particle. Our results indicate that increasing the area of the interface favors the formation of the uniform state. Howere above a critical height value appears a state non-uniform is formed where the spins of in the particle s free surface are rotated with respect to the interface spins direction. We discuss the impact of the competition between the dipolar and interface field on the magnetic charge, that controls the field of flux leakage of the particle, and on the format of the hysteresis curves. Our results indicate that the liquid magnetic charge is not a monotonically increasing function of the height of the particle. The exchange bias may display anomalous features, induced for the dipolar field of the spins near the F/AF interface

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

Função de distribuição generalizada aplicada à velocidade de rotação estelar

In the present work we use a Tsallis maximum entropy distribution law to fit the observations of projected rotational velocity measurements of stars in the Pleiades open cluster. This new distribution funtion which generalizes the Ma.xwel1-Boltzmann one is derived from the non-extensivity of the Boltzmann-Gibbs entropy. We also present a oomparison between results from the generalized distribution and the Ma.xwellia.n law, and show that the generalized distribution fits more closely the observational data. In addition, we present a oomparison between the q values of the generalized distribution determined for the V sin i distribution of the main sequence stars (Pleiades) and ones found for the observed distribution of evolved stars (subgiants). We then observe a correlation between the q values and the star evolution stage for a certain range of stel1ar mass

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.