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

Flotação por ar dissolvido na clarificação de águas com baixa turbidez utilizando sulfato de alumínio e sementes de Moringa oleifera como coagulantes

This work aims to investigate the process of Dissolved air Flotation (DAF) for clarifying water samples with low turbidity using aluminum sulphate and Moringa oleifera seeds as coagulants. The experimental procedure was carried out in a bench scale flotation unit. The influences on the pre-treatment conditions (coagulant dosage and flocculation time) and flotation parameters (superficial application rate and recirculation rate) were evaluated considering the efficiency of the process. The efficiency was evaluated by determining the turbidity of the untreated and treated water samples. The results obtained showed that turbidity reduction can be obtained very efficiently by using DAF and the latter coagulant in low turbidity water. Using aluminum sulphate in pH´s 5.0 and 6.0 better efficiencies were obtained with low concentrations (15 mg/L), achieving values of 92% of turbidity reduction. In the case of use of Moringa oleifera better efficiencies of reduction of turbidity were reported when using a concentration of 50 mg/L in all range of pH´s, achieving 86% of reduction. The zeta potential was also determined, in an attempt to aid comprehension of the coagulation mechanisms involved. The coagulation mechanisms with Moringa oleifera seeds were shown to be adsorption and charge neutralization, as well as adsorption and bridging. Concerning aluminum sulphate, the predominant mechanisms are adsorption and charge neutralization and enmeshment in a precipitate. The results indicate that for low turbidity water, Moringa oleifera seeds could potentially be a viable substitute for aluminum sulphate

Avaliação do comportamento de fluidos micelares na recuperação avançada de petróleo

In heavy oil fields there is a great difficulty of the oil to flow from the reservoir to the well, making its production more difficult and with high cost. Most of the original volumes of oil found in the world are considered unrecoverable by the use of the current methods. The injection of micellar solutions has a direct action in the oil interfacial properties, resulting in an enhanced oil recovery. The objective of this research was the study and selection of micellar solutions with ability to decrease the interfacial interactions between fluids and reservoir formation, increasing oil production. The selected micellar solutions were obtained using commercial surfactants and surfactants synthesized in laboratory, based on the intrinsic properties of these molecules, to use in the enhanced oil recovery. Petroleum Reservoirs were simulated using sandstone plugs from Botucatu formation. Experiments with conventional and enhanced oil recovery techniques were accomplished. The obtained results showed that all micellar solutions were able to enhance oil recovery, and the micellar solution prepared with a SB anionic surfactant, at 2% KCl solution, showed the best recovery factor. It was also accomplished an economic analysis with the SB surfactant solution. With the injection of 20% porous volume of micellar solution, followed by brine injection, the increment in petroleum recovery can reach 81% recovery factor in the 3rd porous volume injected. The increment in the total cost by the addition of surfactant to the injection water represents R$ 7.50/ton of injected fluid

Desenvolvimento de tensoativos e sistemas microemulsionados para recuperação de petróleo

The high concentration of residual oil is one of the greatest problems found in petroleum mature fields. In these reservoirs, different enhanced oil recovery methods (EOR) can be used, highlighting the microemulsion injection. The microemulsion has showed to be efficient in petroleum recovery due to its ability to promote an efficient displacement of the petroleum, acting directly in the residual oil. In this way, this research has as objective the study of microemulsion systems obtained using a commercial surfactant (TP), determining microemulsion thermal stabilities and selecting points inside the pseudoternary phases diagram, evaluating its efficiencies and choosing the best system, that has the following composition: TP as surfactant (S), isopropyl alcohol as co-surfactant (C), kerosene as oil phase, water as aqueous phase, C/S ratio = 1, and 5% sodium p-toluenesulfonate as hydrotope; being observed the following parameters for the selection of the best pseudoternary phases diagram: C/S ratio, co-surfactant nature and addition of hydrotope to the system. The efficiency in petroleum recovery was obtained using two sandstone formation systems: Assu and Botucatu. The study of thermal stabilities showed that as the concentration of active matter in the system increased, the thermal stability also increased. The best thermal stability was obtained using point F (79.56 0C). The system that presented the best recovery percentile between the three selected (3) was composed by: 70% C/S, 2% kerosene and 28% water, with 94% of total recovery efficiency and 60% with microemulsion injection, using the Botucatu formation, that in a general way presented greater efficiencies as compared with the Assu one (81.3% of total recovery efficiency and 38.3% with microemulsion injection)

Estudo da viabilidade da destilação solar para polimento de águas produzidas de petróleo

This work study of solar distillation feasibility in effluent of petroleum industry: produced water, making possible your reuse for irrigation of oleaginous cultures or fodder crops or in steam generation, as well the transport phenomena involved. The methodology for development of this project was to characterize the effluent to be treated and to accomplish physical and chemical analysis in the distilled, to build distillation equipment, concomitant operation of both equipments and implementation of data processing and economical evaluation. The methodology used for all parameters is outlined in APHA (1998) and sampling of the type compound. The feeding of distillation equipment was performed with treated effluent from UTPF of Guamaré. The temperature was monitored throughout the distillers and during the time of operation. The distillers feed occur, as a rule, for sifon. The distillers were operated by a period of 17 months between July 2007 and February 2009, in which 40 experiments were performed. The radiation and temperature datas were acquired in the INPE s site and the temperature inside of the distillers was registered by DATALOGGER Novus. The rates of condensation (mL / min) were determined by measuring of the flow in a graduate test tube of 10 mL and a chronometer. We used two simple solar effect distillers of passive type with different angles in coverage: 20 ° and 45 °. The results obtained in this study and the relevant discussions are divided into six topics: sample characterization and quality of distilled; construction of distillers; operation (data, temperature profile), climatic aspects, treatment of data and economical analysis. Results obtained can be inferred that: the energy loss by the adoption of vessel glass was not significant, however, complicates the logistics of maintenance the equipment on a large scale. In the other hand, the surface of the tub with a glass shield on the equipment deterioration, both devices showed similar performance, so there is not justified for use of equipment 450. With regard to the climatological study it was verified that the Natal city presents monthly medium radiation varying in a range between 350 and 600 W/m2, and medium of wind speed of 5 m / s. The medium humidity is around 70% and rainfall is very small. The regime of the system is transient and although it has been treated as a stationary system shows that the model accurately represents the distillers system's 20 degrees. The quality of the distilled with regard to the parameters evaluated in this study is consistent with the Class 3 waters of CONAMA (Resolution 357). Therefore we can conclude that solar distillation has viability for treat oilfield produced water when considered the technical and environmental aspects, although it is not economically viable

Recuperação e purificação de proteínas do soro de queijo tipo coalho usando cromatografia de troca iônica e interação hidrofóbica em leito na forma expandida

Expanded Bed Adsorption plays an important role in the downstream processing mainly for reducing costs as well as steps besides could handling cells homogenates or fermentation broth. In this work Expanded Bed Adsorption was used to recover and purify whey proteins from coalho cheese manufacture using Streamline DEAE and Streamline SP both ionic resins as well as a hydrophobic resin Streamline Phenyl. A column of 2.6 cm inner diameter with 30 cm in height was coupled to a peristaltic pump. Hydrodynamics study was carried out with the three resins using Tris-HCl buffer in concentration of 30, 50 and 70 mM, with pH ranging from 7.0 to 8.0. In this case, assays of the expansion degree as well as Residence Time Distribution (RTD) were carried out. For the recovery and purification steps, a whey sample of 200 mL, was submitted to a column with 25mL of resin previously equilibrated with Tris/HCl (50 mM, pH 7.0) using a expanded bed. After washing, elution was carried out according the technique used. For ionic adsorption elution was carried out using 100 mL of Tris/HCl (50 mM, pH 7.0 in 1M NaCl). For Hydrophobyc interaction elution was carried out using Tris/HCl (50 mM, pH 7.0). Adsorption runs were carried out using the three resins as well as theirs combination. Results showed that for hydrodynamics studies a linear fit was observed for the three resins with a correlation coefficient (R2) about 0.9. In this case, Streamline Phenyl showed highest expansion degree reaching an expansion degree (H0/H) of 2.2. Bed porosity was of 0.7 when both resins Streamline DEAE and Streamline SP were used with StremLine Phenyl showing the highest bed porosity about 0.75. The number of theorical plates were 109, 41.5 and 17.8 and the axial dipersion coefficient (Daxial) were 0.5, 1.4 and 3.7 x 10-6 m2/s, for Streamline DEAE, Streamline SP and Streamline Phenyl, respectively. Whey proteins were adsorved fastly for the three resins with equilibrium reached in 10 minutes. Breakthrough curves showed that most of proteins stays in flowthrough as well as washing steps with 84, 77 and 96%, for Streamline DEAE, Streamline SP and Streamline Phenyl, respectively. It was observed protein peaks during elution for the three resins used. According to these peaks were identified 6 protein bands that could probably be albumin (69 KDa), lactoferrin (76 KDa), lactoperoxidase (89 KDa), β-lactoglobulin (18,3 KDa) e α-lactoalbumin (14 KDa), as well as the dimer of beta-lactoglobulin. The combined system compound for the elution of Streamline DEAE applied to the Streamline SP showed the best purification of whey proteins, mainly of the α-lactoalbumina

Recuperação e purificação de ramnolipídeos produzidos por pseudomonas aeruginosa P029-GVIIA utilizando melaço de cana como substrato

Biosurfactants are molecules produced by microorganisms mainly bacteria as Pseudomonas and Bacillus. Among the biosurfactants, rhamnolipids play an important role due to their tensoactive as well as emulsifying properties. Besides can be produced in a well consolidated way the production costs of biosurfactants are quite expansive mainly if downstream processing is goning to be considered. Actually, attention has been given to identification of biosurfactants as well as optimization of its fermentative processes including downstream ones. This work deals with the development of strategies to recovery and purification of rhamnolipids produced by Pseudomonas aeruginosa P029-GVIIA using sugar-cane molasses as substrate. Broth free of cells was used in order to investigate the best strategies to recovery and purification produced by this system. Between the studied acids (HCl and H2SO4) for the acid precipitation step, HCl was the best one as has been showed by the experimental design 24. Extraction has been carried out using petroleum ether and quantification has been done using the thioglycolic acid method. Adsorption studies were carried out with activated carbon in a batch mode using a 24 experimental design as well as combined with an hydrophobic resin Streamline Phenyl aiming to separate the produced biosurfactant. Biosurfactant partial identification was carried out using High Performance Liquid Chromatography (HPLC). Experiments in batch mode showed that adsorption has been controlled mainly by pH and temperature. It was observed a reduction of 41.4% for the liquid phase and the solid phase it was possible to adsorb up to 15 mg of rhamnolipd/g of activated carbon. The kinetics of adsorption has been well fitted to a pseudo-first order reaction with velocity constant (k1) of 1.93 x 10-2 min-1. Experiments in packed bed ranging concentration on eluent (acetone) has been shown the highest recovery factor of 98% when pure acetone has been used. The combined effect if using activated carbon with an hydrophobic resin Streamline Phenyl has been shown successful for the rhamnolipids purification. It has been possible to purify a fraction of the crude broth with 98% of purity when the eluted of activated carbon packed bed was used with pure acetone

Aplicação de tensoativos não iônicos na recuperação de fluidos de perfuração poliméricos

The drilling fluid used to assist in the drilling operation of oil wells, accumulates solids inherent in the formation as it is circulated in the well, interfering in the fluid performance during operation. It is discarded after use. The disposal of these fluids causes one of the most difficult environmental problems in the world. This study aims to promote liquid phase separation of drilling fluids, which have circulated in oil wells, and enable this recovered liquid to formulate a new fluid. For this, non-ionic surfactants were used in order to select the best outcome in phase separation. Five real water-based drilling fluids were utilized, which were collected directly from the fields of drilling oil wells, classified as polymeric fluids. The methodology used consisted in combining the fluid with surfactant and then subjecting it to a process of centrifugation or decantation. The decantating tests were scheduled through experimental planning 23 and 32, using as variables the percentage (%) of surfactant utilized and the stirring time in minutes. The surfactants used were ethoxylated nonylphenol and lauryl alcohol ethoxylated with different degrees of ethoxylation. Phase separation was monitored first by tests of stability, and subsequently by the height of the interface in beakers of 100 mL. The results showed that from the surfactants studied, the lauryl alcohol ethoxylated with 3 ethoxylation units has been the most effective in the phase separation process of the drilling fluids tested. The statistical tool used was of great industrial value regarding the programming phase separation in drilling fluids. In conclusion, the liquid phase separated using surfactant can be reused for a new formulation of drilling fluid with similar properties of a new fluid, assuring its efficiency. And in the resulting analysis it is also suggested that the adsorption is the mechanism that leads the phase separation, with surfactant adsorbing in the active solids

Influência das águas da Bacia Hidrográfica Pirangi na balneabilidade das praias de Pirangi, nos municípios de Nísia Floresta e Parnamirim Rio Grande do Norte, Brasil

The Pirangi beach is located in the eastern coastline of Rio Grande do Norte state, in the municipality of Parnamirim and Nísia Floresta. In it flow into Pirangi Watershed (PW), whose water receives large amounts of pollutants, mainly domestic and industrial sewage from districts where pass the rivers that consist it, compromising, thus, the bathing water quality of the Pirangi beach. Bearing in mind the importance of water sanitary quality to ensure an environment that no present risk to the bathers s health, this work had as main objective to assess the influence of the PW s waters in the bathing water quality of the Pirangi beaches. To that end, were made collections of water in the beaches and in the rivers with the intention of quantify the fecal contamination indicators thermotolerant coliforms and enterococci, to then classify the conditions of bathing water quality according with the CONAMA Resolution number 274 of 2000. For the purposes greater knowledge about the health conditions of the Beaches Pirangi and about the influence the PW s waters exert on it, was done parallely to the study of the water quality, an investigation of the sand sanitary quality. Furthermore, it was made an evaluation of the PW s Water Quality through Water Quality Index (WQI). Starting from the results obtained in the research present was possible to verify, among other aspects, that the entry of the PW s waters in the Pirangi beaches exerts direct influence in the bathing water quality of the same ones, being the North Pirangi beach (point tracking PA-02) the most influenced. There was noticed also a significant reduction in the conditions of bathing water quality of the beaches in the rainy season. However, the precariousness do sewerage system of the Natal metropolitan region and the absence of a right system of treatment an final disposal of domestic sewage and industrial are the main factors responsi le for deterioration of the PW s Water Quality, and as a consequence, compromising the bathing water quality of the Pirangi beaches

Estudo de manejo de águas pluviais urbanas na cidade Natal-Rio Grande do Norte

Urban stormwater can be considered as potential water resources as well as problems for the proper functioning of the manifold activities of the city, resulting from inappropriate use and occupation of the soil, usually due to poor planning of the occupation of the development areas, with little care for the environmental aspects of the drainage of surface runoff. As a basic premise, we must seek mechanisms to preserve the natural flow in all stages of development of an urban area, preserving the soil infiltration capacity in the scale of the urban area, comprising the mechanisms of natural drainage, and noting preserving natural areas of dynamic water courses, both in the main channel and in the secondary. They are challenges for a sustainable urban development in a harmonious coexistence of modern developmental, which are consistent with the authoritative economic environmental and social quality. Integrated studies involving the quantity and quality of rainwater are absolutely necessary to achieve understanding and obtaining appropriate technologies, involving both aspects of the drainage problems and aspects of use of water when subjected to an adequate management of surface runoff , for example, the accumulation of these reservoirs in detention with the possibility of use for other purposes. The purpose of this study aims to develop a computer model, adjusted to prevailing conditions of an experimental urban watershed in order to enable the implementation of management practices for water resources, hydrological simulations of quantity and, in a preliminary way, the quality of stormwater that flow to a pond located at the downstream end of the basin. To this end, we used in parallel with the distributed model SWMM data raised the basin with the highest possible resolution to allow the simulation of diffuse loads, heterogeneous characteristics of the basin both in terms of hydrological and hydraulic parameters on the use and occupation soil. The parallel work should improve the degree of understanding of the phenomena simulated in the basin as well as the activity of the calibration models, and this is supported by monitoring data acquired during the duration of the project MAPLU (Urban Stormwater Management) belonging to the network PROSAB (Research Program in Basic Sanitation) in the years 2006 to 2008

Otimização do Uso das Águas da Barragem Santa Cruz-RN

The semiarid potiguar presents a quite discrepant. It is a region with one of the highest rates of artificial lake the world, but the policy of building dams to mitigate the problem of water scarcity does not solve, given that they have not demonstrated the ability to ensure supply human priority during periods of great drought and fail to solve the widespread demand existent in the semiarid. This work aims to present the optimal allocation of water, according to multiple uses and limited availability of water resources in the reservoir, from the simulation of the operation of the same, with the application of techniques to support decision making and performance evaluation alternatives for water use. The reservoir of Santa Cruz, the second largest reservoir of RN with storage capacity of approximately 600 million cubic meters, located about 20 km from the town of Apodi in RN, was conceived as a way to promote economic development in the region as well as the water supply of nearby towns. The techniques used are the simulation model of network flow ACQUANET and also the set of performance indicators. The results showed that the container has the capacity to serve up to 3,83m3/s flow required by existing uses, without any compromising the same. However, it was also observed that all anticipated future demands are implemented it will generate failures in meeting some uses

Recuperação de fósforo por cristalização de estruvita

This study investigated the influence of the molar ratio, the phosphorus initial concentration, the mixture gradient, mixing time, pH and the secondary nucleation on struvite s crystallization in synthetic water in batch reactors. The study was divided into two stages. The first investigated struvite s crystallization at different Mg:N:P molar ratios and at different initial concentrations of magnesium, nitrogen and phosphorus. It was also evaluated the importance of secondary nucleation on the struvite s crystallization. In the second, five parameters were tested to evaluate their influence on the struvite s crystallization, which were: Mg:N:P molar ratio, initial concentration of phosphate, mixing time, mixture gradient and pH. The best conditions for struvite s crystallization were: Mg:N:P = 1,3:1:1 molar ratio; mixture gradient = 60 rpm, pH = 10.0, mixing time = 5 minutes and high initial concentrations of the constituent ions of struvite. Furthermore, the use of struvite crystals as seed influenced positively on the struvite s crystallization

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.