Determinação de dados de equilíbrio líquido-vapor a altas pressões para sistemas de hidrocarbonetos assimétricos

Crude oil is a complex liquid mixture of organic and inorganic compounds that are dominated by hydrocarbons. It is a mixture of alkanes from the simplest to more complex aromatic compounds that are present derivatives such as gasoline, diesel, alcohol, kerosene, naphtha, etc.. These derivatives are extracted from any oil, however, only with a very high quality, in other words, when the content of hydrocarbons of low molecular weight is high means that production of these compounds is feasible. The American Petroleum Institute (API) developed a classification system for the various types of oil. In Brazil, the quality of most of the oil taken from wells is very low, so it is necessary to generate new technology to develop best practices for refining in order to produce petroleum products of higher commercial value. Therefore, it is necessary to study the thermodynamic equilibrium properties of its derivative compounds of interest. This dissertation aims to determine vapor-liquid equilibrium (VLE) data for the systems Phenilcyclohexane - CO2, and Cyclohexane - Phenilcyclohexane - CO2 at high pressure and temperatures between 30 to 70oC. Furthermore, comparisons between measured VLE experimental data from this work and from the literature in relation to the Peng- Robinson molecular thermodynamic model, using a simulation program SPECS IVCSEP v5.60 and two adjustable interaction parameters, have been performed for modeling and simulation purposes. Finally, the developed apparatus for determination of phase equilibrium data at high pressures is presented

Caracterização de água produzida na indústria de petróleo para fins de descarte e otimização do processo de separação óleo/água

The oil industry has several segments that can impact the environment. Among these, produced water which has been highlight in the environmental problem because of the great volume generated and its toxic composition. Those waters are the major source of waste in the oil industry. The composition of the produced water is strongly dependent on the production field. A good example is the wastewater produced on a Petrobras operating unit of Rio Grande do Norte and Ceará (UO-RNCE). A single effluent treatment station (ETS) of this unit receives effluent from 48 wells (onshore and offshore), which leads a large fluctuations in the water quality that can become a complicating factor for future treatment processes. The present work aims to realize a diagnosis of a sample of produced water from the OU - RNCE in compliance to certain physical and physico-chemical parameters (chloride concentration, conductivity, dissolved oxygen, pH, TOG (oil & grease), nitrate concentration, turbidity, salinity and temperature). The analysis of the effluent is accomplished by means of a MP TROLL 9500 Multiparameter probe, a TOG/TPH Infracal from Wilks Enterprise Corp. - Model HATR - T (TOG) and a MD-31 condutivimeter of Digimed. Results were analyzed by univariated and multivariated analysis (principal component analysis) associated statistical control charts. The multivariate analysis showed a negative correlation between dissolved oxygen and turbidity (-0.55) and positive correlations between salinity and chloride (1), conductivity, chloride and salinity (0.70). Multivariated analysis showed there are seven principal components which can explain the variability of the parameters. The variables, salinity, conductivity and chloride were the most important variables, with, higher sampling variance. Statistical control charts have helped to establish a general trend between the physical and chemical evaluated parameters

Modelagem da transferência de massa na remoção do óleo da água produzida por flotação em coluna com uso de tensoativos de origem vegetal

The treatment of oil produced water and its implications are continually under investigation and several questions are related to this subject. In the Northeast Region Brazil, the onshore reservoirs are, in its majority, mature oil fields with high production of water. As this oil produced water has high levels of oil, it cannot be directly discarded into the environment because it represents a risk for contamination of soil, water, and groundwater, or even may cause harm to living bodies. Currently, polyelectrolytes that promote the coalescence of the oil droplets are used to remove the dispersed oil phase, enhancing the effectiveness of the flotation process. The non-biodegradability and high cost of polyelectrolytes are limiting factors for its application. On this context, it is necessary to develop studies for the search of more environmentally friendly products to apply in the flotation process. In this work it is proposed the modeling of the flotation process, in a glass column, using surfactants derived from vegetal oils to replace the polyelectrolytes, as well as to obtain a model that represents the experimental data. In addition, it was made a comparative study between the models described in the literature and the one developed in this research. The obtained results showed that the developed model presented high correlation coefficients when fitting the experimental data (R2 > 0.98), thus proving its efficiency in modeling the experimental data.

Nano emulsões aplicadas a recuperação avançada de petróleo

A exploração de petróleo está a cada dia em circunstâncias mais adversas, no que diz respeito à profundidade dos poços como também, em relação à fluidez do óleo. Os reservatórios de descobertas recentes não possuem energia própria para produzir ou os métodos convencionais não são eficientes para fazer com que esses reservatórios tenham uma vida útil elevada, devido a alterações das propriedades físico-químicas, como por exemplo a viscosidade, que torna o deslocamento do óleo pelos poros do reservatório até a superfície cada vez mais complexo. O presente trabalho tem como objetivo estudar a preparação, caracterização e a utilização de nanoemulsões obtidas a partir de sistemas microemulsionados, com e sem a presença de polímero. Esses sistemas foram aplicados como método químico de recuperação de petróleo, com o intuito de obter maior eficiência de volume de óleo deslocado. O interesse por esse tipo de sistema existe devido a sua baixa tensão superficial, o pequeno tamanho de gotícula e, principalmente, pelo baixo percentual de matéria ativa presente em sua composição. Os ensaios realizados para caracterizar esses sistemas foram: aspecto físico, medidas de tamanho de gotícula, índice de polidispersão, tensão superficial, pH e condutividade. Ensaios de reologia e de adsorção dos sistemas foram realizados com o objetivo de avaliar sua influencia na recuperação de petróleo. Os ensaios de recuperação foram realizados em um equipamento que simula as condições de um reservatório de petróleo, utilizando plugs de rocha arenito Botucatu. Esses plugs foram saturados com salmoura (KCl 2%) e com petróleo proveniente da Bacia Potiguar do campo de Ubarana. Após essas etapas foi realizada a recuperação convencional utilizando a salmoura e, por último, foi injetada, a nanoemulsão, como método de recuperação avançada. Os sistemas obtidos variaram de 0% à 0,4% de polímero. Os ensaios de tamanhos de partícula obtiveram como resultado uma variação de 9,22 a 14,8 nm, caracterizando que as nanoemulsões estão dentro da faixa de tamanho inerente a esse tipo de sistema. Para ensaios de tensão superficial os valores foram na faixa de 33,6 a 39,7 dynas/cm, valores semelhantes à microemulsões e bem abaixo da tensão superficial da água. Os resultados obtidos para os valores de pH e condutividade se mantiveram estáveis ao longo do tempo de armazenamento, essa avaliação indica estabilidade das nanoemulsões estudadas. O teste de recuperação avançada utilizando nanoemulsão com baixo percentual de matéria ativa obteve como resultado de eficiência de deslocamento 39,4%. Porém esse valor foi crescente, de acordo com o aumento do percentual de polímero na nanomeulsão. Os resultados de eficiência de deslocamento de petróleo estão diretamente relacionados com o aumento da viscosidade das nanoemulsões. A nanoemulsão V (0,4% polímero) é o sistema mais viscoso dentre os analisados, e obteve o maior percentual de óleo deslocado (76,7%), resultando na maior eficiência de deslocamento total (90%). Esse estudo mostrou o potencial de sistemas nanoemulsionados, com e sem polímeros, na recuperação avançada de petróleo. Eles apresentam algumas vantagens com relação a outros métodos de recuperação avançada, como: o baixo percentual de matéria ativa, baixo índice de adsorção do polímero, dissolvido em nanoemulsão, na rocha e alta eficiência de recuperação

Levantamento e avaliação de critérios para a ampliação de escala da produção de biossurfactantes utilizando melaço como substrato

Biosurfactants are amphiphilic molecules synthesized by microorganisms such as bacteria, yeast or filamented fungi cultivated in various carbon sources among sucrose and hydrocarbons. These molecules are composed by a hydrophilic and hydrophobic part. They operate mostly at interfaces of fluids of different polarities. Because of this characteristic, they are potentially employed in numerous industries, such as the textile, medical, cosmetics, food and mainly in the petrochemical ones. Therefore industry has interest in developing new biosurfactant production processes in high scale, in order to become them economically competitive when compared to synthetic biosurfactants. This work aims to evaluate the biosurfactant production applying a non-conventional substrate sugar cane molasses proceeding from the sugar industry thus reducing the production costs. The strain identified as AP029/GLIIA, isolated from oil wells in Rio Grande do Norte state and used in these experiments belongs to the culture collection of Antibiotics Department of UFPE. The fermentation were carried out using different conditions according to a factorial planning 24 with duplicate at center point, in which the studied factors were molasse concentration, nitrate concentration, agitation and aeration ratio. The experiments were performed in a shaker at 38ºC of temperature. Samples were withdrawn in regular periods of time of up to 72 hours of fermentation in order to analyze substrate consumption, cellular concentration, superficial tension, critical micelle dilution (CMD-1 e CMD-2) as well as extracelullar protein production. The results showed a production of 3,480 g/L of biomass, a reduction of 41% on superficial tension, 67% of substrate consumption and 0,2805 g/L of extracellular protein

Estudo da recuperação de óleo por drenagem gravitacional assistida por injeção de vapor

Steam assisted gravity drainage process (SAGD) involves two parallel horizontal wells located in a same vertical plane, where the top well is used as steam injector and the bottom well as producer. The dominant force in this process is gravitational. This improved oil recovery method has been demonstrated to be economically viable in commercial projects of oil recovery for heavy and extra heavy oil, but it is not yet implemented in Brazil. The study of this technology in reservoirs with characteristics of regional basins is necessary in order to analyze if this process can be used, minimizing the steam rate demand and improving the process profitability. In this study, a homogeneous reservoir was modeled with characteristics of Brazilian Northeast reservoirs. Simulations were accomplished with STARS , a commercial software from Computer Modelling Group, which is used to simulate improved oil recovery process in oil reservoirs. In this work, a steam optimization was accomplished in reservoirs with different physical characteristics and in different cases, through a technical-economic analysis. It was also studied a semi-continuous steam injection or with injection stops. Results showed that it is possible to use a simplified equation of the net present value, which incorporates earnings and expenses on oil production and expenses in steam requirement, in order to optimize steam rate and obtaining a higher net present value in the process. It was observed that SAGD process can be or not profitable depending on reservoirs characteristics. It was also obtained that steam demand can still be reduced injecting in a non continuous form, alternating steam injection with stops at several time intervals. The optimization of these intervals allowed to minimize heat losses and to improve oil recovery

Uso da tecnologia de troca iônica no tratamento de águas contaminadas com Nitrato do Aqüífero Dunas-Barreiras, Natal/RN-Brasil

The city of Natal comprises an area of about 170 km² (65,63 squares miles). The Dunas-Barreiras Aquifer is the most important reservoir of the coastal basin of RN. It is being responsible for the water supplying of about 70% of the population, however, due to the sewage disposal system by cesspools and drains, it is presently affected in a great extent by nitrates contamination. Thus, the present work proposes to research the utilization of contaminated water by nitrates of this fountainhead and find cost of the potable water through the ionic exchange technology. This technology consists in the removal of mineral salts by the exchange of cations for one ion of hydrogen (H+), through the passage of water by cationic resin bed and, secondly, by the exchange of the anions for hydroxyl ions (OH-) through a anionic resin bed. The obtained results have showed the waters derived from fountains, big water holes and shallow wells were microbiologically contaminated, while the waters derived from deep wells (above 70 m 76,58 yards) were free of contamination. Thus, only these ones are suitable to the use of ionic technology. The experiments were conducted with the resin IMAC-HP-555 such as kinetic, thermodynamic, and adsorption by fixed bed studies, being obtained several project variables for the experimental column, as follow: work temperature of 25oC; resin maximum capacity maximum e mean of adsorption ==0,01692 g NO3-1/g R e 0,0110 g NO3-1/g R, respectively. On the experimental column were performed breakthrough tests which pointed for an average ideal average speed of work of 13.2 m / h, with an average efficiency of 45% of adsorption, an optimal concentration of NaCl desorption of 8%, and an ideal desorption time of 80 minutes for the equilibrium conditions of water from the Dunas-Barreiras aquifer. Scale projection for ion-exchange column for denitrification, for these variables, using a computer modeling programme, to project the column of ion exchange ROREX-420/2000, obtained a cost for the drinking water denitrified by this system of R$ 0,16 / m3

Estudo da cristalização de parafinas em sistemas solventes/tensoativos/água

The WAT is the temperature at the beginning of the appearance of wax crystals. At this temperature the first wax crystals are formed by the cooling systems paraffin / solvents. Paraffins are composed of a mixture of saturated hydrocarbons of high molecular weight. The removal of petroleum from wells and the production lines means a surcharge on produced oil, thus solubilize these deposits formed due to modifications of thermodynamics has been a constant challenge for companies of oil exploration. This study combines the paraffin solubilization by microemulsion systems, the determination of WAT systems paraffin / solvent and performance of surfactant in reducing the crystallization. We used the methods: rheological and the photoelectric signal, validating the latter which was developed to optimize the data obtained due to sensitivity of the equipment used. Methods developed for description of wax precipitation are often in poor agreement with the experimental data, they tend to underestimate the amount of wax at temperatures below the turbidity point. The Won method and the Ideal solution method were applied to the WAT data obtained in solvent systems, best represented by the second interaction of Won method using the solvents naphtha, hexane and LCO. It was observed that the results obtained by WAT photoelectric signal when compared with the viscosity occur in advance, demonstrating the greatest sensitivity of the method developed. The ionic surfactant reduced the viscosity of the solvent systems as it acted modifying the crystalline structure and, consequently, the pour point. The curves show that the WAT experimental data is, in general, closer to the modeling performed by the method of Won than to the one performed by the ideal solution method, because this method underestimates the curve predicting the onset of paraffin hydrocarbons crystallization temperature. This occurs because the actual temperature measured was the crystallization temperature and the method proposes the fusion temperature measurement.

Avaliação da Qualidade da Água do rio Pitimbu

The Pitimbu River Basin is concern reason, therefore this is one of the mains freshwater sources for the Natal city supplying. The Pitimbu waters river flow into Jiqui pond, as the main supplier of this, that supplies 16% of Natal population and there is a bigger importance despite the supplying of a parcel of Natal city made joining underground waters with the water proceeding from the Jiqui pond, being used for dilution waters of contaminated wells with nitrate. Even with the importance of the Pitimbu, there is a strong pressure of occupation of its edge according to a critical urban growth, becoming the situation worse and increasing the necessity of management of the use and occupation of the ground and keeping the control of the prompt pollution, as punctual as diffuse. There are many studies about Pitimbu River Basin, however they summarize themselves to some months or even in a few years. This work, that gathers these information, increasing the amplitude and making possible an evaluation of the attitude of the water in a period extended for an evaluation of values of variable quality of water referring to the standards, that usually happens about the variable frequency distribution, central tendency and measures of dispersion, as the coefficient of variation, coefficient of skewness and the coefficient of determination of certain variable on another one. This work to evaluates the quality conditions of the Pitimbu river waters by analyzing thirty five (35) variables Physical, chemical and biological in eight (8) points of water course since 1993 to 2007. Given this situation, all knowledge about the waters quality conditions obtained in this work, is a strong subsidy for management of use and ground occupation, considering the river basin as territorial unit of management, and as the water is public good domain, being a priority human use, It is necessary to guarantee to current and the future generations available water resources in appropriate standards of quality as the established standard and identifying possible reasons of pollution through statistics analysis

Avaliação das barragens subterrâneas no regime de um curso d água na região do semi-árido do RN

The Serido is a region of northeastern Brazil highlighted by its problems related to water scarcity because of its semi-arid region, large rates of evaporation and rainfall irregular and scarce. Thus, the underground dams, become a strategically important resource with a simple and inexpensive technique for storage of water. They act in a positive way in the development of inland cities that suffer from drought, because in addition to exercise a great improvement in the social role of these families, can enjoy the type of soil (silt) and provides water for both irrigation and for human consumption throughout the year. Is therefore essential to its monitoring and studies to assess its effectiveness in accordance with its purposes, along with their wells Amazons, as can occur in conditions of physical degradation, chemical and microbiological appropriate, according to the Ordinance No 518/04 Ministry of Health, however, the proposed work aims to analyze the underground dams in the municipality of Sierra Negra North-RN (semi-arid region) as to their uses and their influences on the quality and quantity of water in periods of drought and rain. Analyzing monthly these parameters: determination of pH, conductivity, calcium, magnesium, sodium, potassium, chloride, sulfate, RAS (sodium adsorption ratio), turbidity, total iron, nitrite, nitrate, total dissolved solids (STD), bicarbonate (HCO3), fecal coliform and pesticides compared to the standards allowed by the Ordinance in force for quality for human consumption. While at the risk of salinity and sodicity on the model proposed by the United Salinity Laboratory (USSL). Although efficient, it was found that results varied annually on water quality which may influence their specific uses, whether or irrigation water supply in the city

Controle sanitário e ambiental de um projeto de reúso em um complexo de prédios corporativos

The study that resulted in this dissertation was developed at OU RNCE PETROBRAS, in Natal, which implemented a project of rational use and reuse of water, including use of wastewater from a Sewage Treatment Plant (STP) already in place, diluted with water from own wells for irrigation of green area of the building complex corporate enterprise. Establish a methodology that can serve as guidelines for future projects controlled reuse of water like this was the objective of this research. Been proposed, implemented and evaluated three instruments of sanitary and environmental control: 1) adaptation of sewage treatment plant and quality control of the treated effluent 2) analysis of soil-nutrient interaction in the irrigated area, 3) knowledge of the local hydrogeology, especially with regard to the direction of flow of the aquifer and location of collection wells of Companhia de Águas e Esgotos do Rio Grande do Norte (CAERN) situated in the surroundings. These instruments have proven sufficient and appropriate to ensure the levels of sanitary and environmental control proposed and studied, which were: a) control of water quality off the STP and the output of the irrigation reservoir, b) control of water quality sub surface soil and assessment of progress on soil composition, c) assessment of water quality in the aquifer. For this, we must: 1) establishing the monitoring plan of the STP and its effluent quality sampling points and defining the parameters of analysis, improve the functioning of that identifying the adequacy of flow and screening as the main factors of operational control, and increase the efficiency of the station to a relatively low cost, using additional filters, 2) propose, implement and adapt simple collectors to assess the quality of water percolating into the soil of the irrigated area, 3) determine the direction of groundwater flow in the area study and select the wells for monitoring of the aquifer.

Simulação numérica do fluxo hídrico subterrâneo na bacia hidrográfica do Rio Pitimbu RN

Urban centers in Pitimbu Watershed use significant groundwater sources for public supply. Therefore, studies in Dunas Barreiras aquifer are relevant to expand knowledge about it and help manage water resources in the region. An essential tool for this management is the numerical modeling of groundwater flow. In this work, we developed a groundwater flow model for Pitimbu Watershed, using the Visual Modflow, version 2.7.1., which uses finite difference method for solving the govern equation of the dynamics of groundwater flow. We carried out the numerical simulation of steady-state model for the entire region of the basin. The model was built in the geographical, geomorphological and hydrogeological study of the area, which defined the boundary conditions and the parameters required for the numerical calculation. Owing to unavailability of current data based on monitoring of the aquifer it was not possible to calibrate the model. However, the simulation results showed that the overall water balance approached zero, therefore satisfying the equation for the three-dimensional behavior of the head water in steady state. Variations in aquifer recharge data were made to verify the impact of this contribution on the water balance of the system, especially in the scenario in which recharge due to drains and sinks was removed. According to the results generated by Visual Modflow occurred significantly hydraulic head lowering, ranging from 16,4 to 82 feet of drawdown. With the results obtained, it can be said that modeling is performed as a valid tool for the management of water resources in Pitimbu River Basin, and to support new studies

Caracterização e avaliação do macro sistema urbano de distribuição de água de Natal RN

The aim of this study is to characterize and evaluate the Macro System of Regional Water Distribution Natal North (RNN) and Southern Regional Natal (RNS), covering 35% and 65% respectively of the Natal-RN City. The terms of the quality and quantity of water (surface and groundwater) were also evaluated in order to adjust the parameters that contribute to proper distribution and control in water reserves. The methodology of the work took place from collecting volumetric data of production capacity and distribution of the two treatment plants for Regional as well as the flow rates of wells. Yet the quantitative capacity of reservation, distribution and consumption of the main reservoirs, population numbers and consumption of members neighborhoods were collected. Data were tabulated and used in computational simulator EPANET to diagnose possible through the water balance, the offers and demands on the water supply system in the neighborhoods of the capital, linking them to specific distribution points. We also evaluated the wells in the levels of nitrate in water consumed. As a result it was found that some neighborhoods in the South Regional Natal, was ranked as critical supply situation: City of Hope, Lagoa Nova and Nova Descoberta, where demand exceeds supply. While in most Northern Regional Natal present deficiency in the supply system as: Lagoa Azul, the Parque dos Coqueiros, igapó, Amarante and Salinas. The rates of nitrate in the city were significant, but manageable with corrective and preventive measures. The averages were 12 mg /l-N in Candelária, 10 mg/l-N in Lagoa Nova, 9 mg/l-N in Satelite, 20 mg/l-N in Gramore and 15 mg/l-N in N. Sra. Apresentação. Therefore proper distribution of water abstracted and implementation of quality control ensures the supply required by the system, associated with preservation of Water Resources of the Metropolitan Region of Natal

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.