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Interfacial Tension and Phase Behavior of Oil/Aqueous Systems with Applications to Enhanced Oil RecoveryJaeyub Chung (9511022) 16 December 2020 (has links)
Chemical enhanced oil recovery (cEOR) aims to increase the oil recovery of mature oil fields, using aqueous solutions of surfactants and polymers, to mobilize trapped oil and maintain production. The interfacial tensions (IFTs) between the injected aqueous solution, the oil droplets in reservoirs, and other possible phases formed (e.g., a “middle phase” microemulsion) are important for designing and assessing a chemical formulation. Ultralow IFTs, less than 10<sup>-2</sup> mN·m<sup>-1</sup>, are needed to increase the capillary number and help mobilize trapped oil droplets. Despite this fact, phase behavior tests have received more attention than IFTs for designing and evaluating surfactant formulations that result in high oil recovery efficiencies, because incorporating reliable IFTs into such evaluation process is avoided due to difficulties in obtaining reliable values. Hence, the main thrusts of this dissertation are to: (a) develop robust IFT measurement protocols for obtaining reliable IFTs regardless of the complexity of water and oil phase constituents and (b) improve the existing surfactant polymer formulation evaluation and screening processes by successfully incorporating the IFT as one of the critical parameters.<br>First, two robust tensiometry protocols using the known emerging bubble method (EBM) and the spinning bubble method (SBM) were demonstrated, for determining accurately equilibrium surface tensions (ESTs) and equilibrium IFTs (EIFTs). The protocols are used for measuring the dynamic surface tensions (DSTs), determining the steady state values, and establishing the stability of the steady state values by applying small surface area perturbations by monitoring the ST or IFT relaxation behavior. The perturbations were applied by abruptly expanding or compressing surface areas by changing the bubble sizes with an automated dispenser for the EBM, and by altering the rotation frequency of the spinning tube for the SBM. Such robust tension measurement protocols were applied for Triton X-100 aqueous solutions at a fixed concentration above its critical micelle concentration (CMC). The EST value of the model solution was 31.5 ± 0.1 mN·m<sup>-1</sup> with the EBM and 30.8 ± 0.2 mN·m<sup>-1</sup> with the SBM. These protocols provide robust criteria for establishing the EST values.<br>Second, the EIFTs of a commercial single chain anionic surfactant solution in a synthetic brine against a crude oil from an active reservoir were determined with the new protocol described earlier. The commercial surfactant used here has an oligopropoxy group between a hydrophobic chain and a sulfate head group. The synthetic brine has 9,700 ppm of total dissolved salts, which are a mixture of sodium chloride (NaCl), potassium chloride (KCl), manganese (II) chloride tetrahydrate (MnCl<sub>2</sub>·4H<sub>2</sub>O), magnesium (II) chloride hexahydrate (MgCl<sub>2</sub>·6H<sub>2</sub>O), barium chloride dihydrate (BaCl<sub>2</sub>·2H<sub>2</sub>O), sodium sulfate decahydrate (Na<sub>2</sub>SO<sub>4</sub>·10H<sub>2</sub>O), sodium bicarbonate (NaHCO<sub>3</sub>), and calcium chloride dihydrate (CaCl<sub>2</sub>·2H<sub>2</sub>O). The DSTs curves of the surfactant concentrations from 0.1 ppm to 10,000 ppm by weight had a simple adsorption/desorption equilibrium at air/water surface with surfactant diffusion from bulk aqueous phase. Such a mechanism was also observed from the tension relaxation behavior after area perturbations for the oil/water interfaces while DIFT measurements. The CMC of the commercial surfactant was determined to be 12 ppm in water and 1 ppm in the synthetic brine used. From the initial tension reduction curves from DST and DIFT measurements, the equilibrium timescales were shorter with brine than with water, because the adsorbed surfactant on the oil/water interfaces were partitioned into oil phases. For both DST and DIFT results suggest that the adsorbed surfactant layer at interfaces were typical adsorbed soluble monolayers.<br>Third, the phase and rheological behavior of a commercial anionic surfactant in water and in brine are important for large scale applications. A phase map of the surfactant at 25 °C at full range of surfactant concentration was obtained. The supramolecular structures of the various phases were characterized by dynamic light scattering (DLS), cryogenic transmission electron microscopy (cryo-TEM), conductimetry, densitometry, and x-ray scattering. The identified phases evolved as the surfactant concentration was increased; they were a micellar solution phase, a hexagonal liquid crystalline phase, and a lamellar liquid crystalline phase. In addition, the characterization results provided detailed information about supramolecular structure parameters such as micellar sizes and their aggregation numbers, and liquid crystal spacings. The phase and rheological behavior trends identified here were of great importance because the trend was similar to that of single chain monoisomeric surfactant. Thus, this study provides a potential universality of phase behavior trends of surfactant-water systems despite of the multicomponent nature of surfactants.<br>Fourth, the EIFTs of the pre-equilibrated mixtures of surfactant, brine, and oil were determined and compared to the EIFTs prior to pre-equilibration, in order to systematically identify the most relevant IFT for oil recovery. The EIFT between surfactant solutions and oil without any pre-equilibration prior to tension measurements is defined as the un-pre-equilibrated EIFT (EIFT<sub>up</sub>). The EIFT between oil and water phases after the pre-equilibration of surfactant, brine, and oil is defined as pre-equilibrated EIFT (EIFT<sub>p</sub>). The EIFT<sub>p</sub>’s were generally higher than EIFT<sub>up</sub>’s. In addition, the effects of three mixing methods and the water-to-oil volume ratio (WOR) on the EIFT<sub>p</sub> were evaluated. Out of three mixing methods, (A) mild mixing, (B) magnetic stirring, and (C) shaking vigorously by hand, method C produced mixtures which are the closest to the equilibrium state. The mixtures produced by method C had the largest decrease of the surfactant concentration during pre-equilibration due to the surfactant partitioning into oil phases. Moreover, the WOR affects the EIFT<sub>p</sub> significantly due to the preferential partitioning of surfactant components into oil phases. More specifically, the WOR and the EIFT<sub>p</sub> were found to be inversely correlated, because the amount of partitioned surfactant increased as the oil volume fraction increased. The EIFT<sub>p</sub>’s were different from the EIFT<sub>up</sub>’s at the same total surfactant concentrations in the aqueous layer evidently because of preferential partitioning of the various surfactant components.<br>Finally, the effect of surfactant losses due to adsorption into the rock surface on the pre-equilibrated EIFT (EIFT<sub>p</sub>) were evaluated to improve surfactant formulation protocols. Here, five types of EIFTs were identified, along with robust protocols for determining them. These are: (I) the un-pre-equilibrated equilibrium IFT (EIFT<sub>up</sub>); (II) the un-pre-equilibrated EIFTs in the presence of rock (EIFT<sub>up,rock</sub>); (III) the pre-equilibrated EIFTs (EIFT<sub>p</sub>) in the presence of oil; (IV) the pre-equilibrated EIFT in the presence of rock and oil (EIFT<sub>p,rock</sub>); and (V) the effluent EIFT (EIFT<sub>eff</sub>). The EIFT<sub>up</sub> is the EIFT of the aqueous surfactant/brine solution against an oil drop without any pre-equilibration. The EIFT<sub>up,rock</sub> is the EIFT between an oil drop and the surfactant solution after pre-equilibration with a rock sample to account for adsorption losses. The EIFT<sub>p</sub> is the EIFT between the pre-equilibrated water and the oil phases from surfactant/brine/oil mixtures. The EIFT<sub>p,rock</sub> is the EIFT between the pre-equilibrated water and the oil phases from surfactant/brine/oil/rock mixtures. The EIFT<sub>eff</sub> is the EIFT from an effluent sample mixture of a laboratory-scale core flood test. Among the five types of EIFTs, the EIFT<sub>p,rock</sub> was found to be the most important for the highest oil recovery performance in core flood tests, because it captures the most important surfactant partition processes, the partitioning to the oil phase and the partitioning by adsorption on the rock surface. Among three surfactant formulations tested with core flood experiments, the one with the lowest EIFT<sub>p,rock</sub> (~0.01 mN·m<sup>-1</sup>) had the highest oil recovery ratio (78%), and the one with the highest EIFT<sub>p,rock</sub> (~0.2 mN·m<sup>-1</sup>) had the lowest oil recovery ratio (55%). The other EIFTs correlated less with the oil recovery performance. Identifying surfactant formulations that have low or ultralow EIFTs, especially ultralow EIFT<sub>p,rock</sub>’s, are critical for screening formulations appropriate for core flood tests and target field applications, and for predicting oil recovery performance. These works are a significant contribution for improving (a) the surfactant formulation evaluation protocols, and (b) the utilization of reliable IFTs and phase behavior test protocols for oil recovery and many other surfactant and colloid sciences applications.<br>
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IIoT-based Instrumentation and Control System for a Lateral Micro-drilling Robot Using Machine Fault Diagnosis and Failure PrognosisJose A. Solorio Cervantes (11191893) 11 October 2023 (has links)
<p dir="ltr">This project aimed to develop an instrumentation and control system for a micro-drilling robot based on Industrial Internet of Things (IIoT) technologies. The automation system integrated IIoT technological tools to create a robust automation system capable of being used in drilling operations. The system incorporated industrial-grade sensors, which carried out direct measurements of the critical variables of the process. The indirect variables relevant to the control of the robot were calculated from the measured parameters. The system also considered the telemetry architecture necessary to reliably transmit data from the down-the-hole (DTH) robot to a receiver on the surface. Telemetry was based on wireless communication through long-range radio frequency (LoRa). The system developed had models based on Artificial Intelligence (AI) and Machine Learning (ML) for determining the mode of operation, detecting changes in the process, and changes in drilling variables in critical hydraulic components for the drilling process. Algorithms based on AI and ML models also allowed the user to make better decisions based on the variables' correlation to optimize the drilling process (e.g., dynamic change of flow, pressure, and RPMs based on automatic rock identification). A user interface (UI) was developed, and digital tools to perform data analysis were implemented. Safety assessment in all robot systems (e.g., electrical, hardware, software) was contemplated as a critical design component. The result of this research project provides innovative micro-drilling robots with the necessary technological tools to optimize the drilling process. The system made drilling more efficient, reliable, and safe, providing diagnostic and prognostic tools that allowed planning maintenance based on the actual health of the devices. The system that was developed was tested in a test bench under controlled conditions within a laboratory to characterize the system and collect data that allowed ML models' development, training, validation, and testing. The prototype of a micro-drilling robot installed on the test bench served as a case study to assess the implemented models' reliability and the proposed telemetry.</p>
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Simulação do escoamento miscível decorrente da injeção de ácido em um meio poroso com dissolução parcial do meio / Flow simulation of the acid injection in porous media with partial dissolution of the porous mediaLucimá Barros da Rocha 28 September 2007 (has links)
Formulamos um modelo simplificado para o estudo do processo de injeção de solvente em reservatórios de petróleo, onde o fluido injetado (um ácido) tem a capacidade de dissolver parcialmente a matriz sólida. Como hipóteses principais, consideramos que o solvente e o soluto (componente químico que constitui o meio poroso) são espécies totalmente miscíveis, a viscosidade da mistura solvente + soluto não varia com a concentração de soluto, há significativa transferência de massa entre as fases e a permeabilidade do meio poroso varia linearmente com a porosidade. O modelo é formado por duas Equações Diferenciais Parciais, uma do tipo Convecção-Difusão a outra é do tipo Convecção-Reação. Para resolução numérica, desenvolvemos uma metodologia que denominamos de EPEC (Explícita Porosidade e Explícita Concentração). Tal metodologia se baseia em um limitador de fluxo do tipo TVD e em diferenças finitas centradas de segunda ordem. Em adição, o EPEC emprega uma técnica de separação de operadores. Deste modo, em cada passo de tempo, realizamos inicialmente o cálculo explícito da porosidade seguido do cálculo explícito da concentração do solvente. Assim, obtemos um desacoplamento natural das equações que
descrevem o problema. Resultados de simulações são apresentados para um meio poroso bidimensional, após sessenta dias de injeção de solvente. / We formulate a simplified Model to study the process of solvent injection in petroleum Reservoir, where the injected fluid (an acid) can partially dissolve a solid matrix. As prime hypotheses, we considered that solvent an soluble component are completely mixed, the viscosity of the fluid does not vary with the concentration of the soluble component, theres significant transfer of mass between the parts and, the permeability of media porous changes linearly with porosity. The model is formed by two Partial Differential Equation, one is convection-diffusion type and another is a convection-reaction type. The Numerical Resolution weve developed a method called EPEC (Explicit Porosity Explicit Concentration). Such methodology is based upon a Limiting of Flow of TVD type and, used Centered Finite Differences of second order. In addition, the EPEC use a operators separation technique. This way, every time, first we clearly calculate the porosity and then the concentration of solvent is calculated. Thus we obtain a natural decoupling of the equations that describe the problem. Simulation results are presented to a two dimensional media porous after sixty days of solvent injection.
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Simulação numérica do escoamento bifásico em meios porosos heterogêneos empregando uma formulação semi-implícita, imitadores de fluxo e o método dos volumes finitos / Numerical simulation of two-phase flow in heterogeneous porous media applying a semi-implicit formulation, flux limiter and finite volume methodJulhane Alice Thomas Schulz 31 March 2009 (has links)
Neste trabalho apresentamos um esquema numérico para a simulação computacional de escoamentos bifásicos, água-óleo, em reservatórios de petróleo. O modelo matemático consiste em um sistema de equações diferenciais parciais não-linear nas incógnitas velocidade, pressão e saturação. Uma quebra de operadores a dois níveis possibilita uma maior eficiência ao método permitindo que a velocidade, fornecida pelo problema de velocidade-pressão, seja atualizada somente para determinados intervalos de tempo associados ao problema de transporte advectivo-difusivo em termos da saturação. O método dos volumes finitos é empregado na resolução numérica do problema de velocidade-pressão e do transporte de massa por advecção e difusão. Na solução do problema de transporte de massa utilizamos limitadores de fluxo na aproximação dos termos advectivos e diferenças centradas para os termos difusivos. O nosso simulador foi validado a partir de confrontações dos seus resultados com as soluções teóricas conhecidas para os problemas unidimensionais, equações de Burgers e de Buckley-Leverett, e com outros resultados numéricos em se tratando do escoamento bifásico água-óleo bidimensional em meios porosos heterogêneos. / A new numerical method is proposed for the solution of two-phase flow problem in petroleum reservoirs. The two-phase (water and oil) flow problem is governed by a pressure-velocity equation coupled to a saturation equation. For computational eficiency an operator spliting technique is used; distinct time steps can be used for the computation of transport and pressure-velocity problems. The finite volume method is used in the numerical solution of the velocity-pressure and mass transport problems. A flux limiter is used for the numerical discretization of the advective terms while centered schemes are employed for the diffusion terms in the mass transport problem. In the validation of our numerical method we compared numerical and theoretical solutions for one dimensional problems, Burgers and Buckley-Leverett equations, and compared our numerical results to others, in the case of oil-water flows in two dimensions for an heterogeneous porous media.
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Um novo algoritmo, naturalmente paralelizável, para o cálculo de permeabilidades equivalentes em reservatórios / A new algorithm, of course parallelization, for the calculation of equivalent permeabilities in reservoirsClovis Antonio da Silva 27 February 2008 (has links)
Conselho Nacional de Desenvolvimento Científico e Tecnológico / Neste trabalho é apresentado um novo procedimento numérico para o upscaling de permeabilidade utilizando condições de contorno periódicas. Este procedimento combina decomposição de domínio com elementos finitos mistos na discretização do problema local de pressão-velocidade necessário para se encontrar as permeabilidades equivalentes. / A new numerical method is proposed for the permeabilities upscaling take into consideration periodic boundary conditions. This method combines domain decomposition with mixed finite elements in discretization of the local problem of pressure-velocity necessary to meet the equivalent permeabilities.
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Simulação do escoamento miscível decorrente da injeção de ácido em um meio poroso com dissolução parcial do meio / Flow simulation of the acid injection in porous media with partial dissolution of the porous mediaLucimá Barros da Rocha 28 September 2007 (has links)
Formulamos um modelo simplificado para o estudo do processo de injeção de solvente em reservatórios de petróleo, onde o fluido injetado (um ácido) tem a capacidade de dissolver parcialmente a matriz sólida. Como hipóteses principais, consideramos que o solvente e o soluto (componente químico que constitui o meio poroso) são espécies totalmente miscíveis, a viscosidade da mistura solvente + soluto não varia com a concentração de soluto, há significativa transferência de massa entre as fases e a permeabilidade do meio poroso varia linearmente com a porosidade. O modelo é formado por duas Equações Diferenciais Parciais, uma do tipo Convecção-Difusão a outra é do tipo Convecção-Reação. Para resolução numérica, desenvolvemos uma metodologia que denominamos de EPEC (Explícita Porosidade e Explícita Concentração). Tal metodologia se baseia em um limitador de fluxo do tipo TVD e em diferenças finitas centradas de segunda ordem. Em adição, o EPEC emprega uma técnica de separação de operadores. Deste modo, em cada passo de tempo, realizamos inicialmente o cálculo explícito da porosidade seguido do cálculo explícito da concentração do solvente. Assim, obtemos um desacoplamento natural das equações que
descrevem o problema. Resultados de simulações são apresentados para um meio poroso bidimensional, após sessenta dias de injeção de solvente. / We formulate a simplified Model to study the process of solvent injection in petroleum Reservoir, where the injected fluid (an acid) can partially dissolve a solid matrix. As prime hypotheses, we considered that solvent an soluble component are completely mixed, the viscosity of the fluid does not vary with the concentration of the soluble component, theres significant transfer of mass between the parts and, the permeability of media porous changes linearly with porosity. The model is formed by two Partial Differential Equation, one is convection-diffusion type and another is a convection-reaction type. The Numerical Resolution weve developed a method called EPEC (Explicit Porosity Explicit Concentration). Such methodology is based upon a Limiting of Flow of TVD type and, used Centered Finite Differences of second order. In addition, the EPEC use a operators separation technique. This way, every time, first we clearly calculate the porosity and then the concentration of solvent is calculated. Thus we obtain a natural decoupling of the equations that describe the problem. Simulation results are presented to a two dimensional media porous after sixty days of solvent injection.
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Simulação numérica do escoamento bifásico em meios porosos heterogêneos empregando uma formulação semi-implícita, imitadores de fluxo e o método dos volumes finitos / Numerical simulation of two-phase flow in heterogeneous porous media applying a semi-implicit formulation, flux limiter and finite volume methodJulhane Alice Thomas Schulz 31 March 2009 (has links)
Neste trabalho apresentamos um esquema numérico para a simulação computacional de escoamentos bifásicos, água-óleo, em reservatórios de petróleo. O modelo matemático consiste em um sistema de equações diferenciais parciais não-linear nas incógnitas velocidade, pressão e saturação. Uma quebra de operadores a dois níveis possibilita uma maior eficiência ao método permitindo que a velocidade, fornecida pelo problema de velocidade-pressão, seja atualizada somente para determinados intervalos de tempo associados ao problema de transporte advectivo-difusivo em termos da saturação. O método dos volumes finitos é empregado na resolução numérica do problema de velocidade-pressão e do transporte de massa por advecção e difusão. Na solução do problema de transporte de massa utilizamos limitadores de fluxo na aproximação dos termos advectivos e diferenças centradas para os termos difusivos. O nosso simulador foi validado a partir de confrontações dos seus resultados com as soluções teóricas conhecidas para os problemas unidimensionais, equações de Burgers e de Buckley-Leverett, e com outros resultados numéricos em se tratando do escoamento bifásico água-óleo bidimensional em meios porosos heterogêneos. / A new numerical method is proposed for the solution of two-phase flow problem in petroleum reservoirs. The two-phase (water and oil) flow problem is governed by a pressure-velocity equation coupled to a saturation equation. For computational eficiency an operator spliting technique is used; distinct time steps can be used for the computation of transport and pressure-velocity problems. The finite volume method is used in the numerical solution of the velocity-pressure and mass transport problems. A flux limiter is used for the numerical discretization of the advective terms while centered schemes are employed for the diffusion terms in the mass transport problem. In the validation of our numerical method we compared numerical and theoretical solutions for one dimensional problems, Burgers and Buckley-Leverett equations, and compared our numerical results to others, in the case of oil-water flows in two dimensions for an heterogeneous porous media.
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Um novo algoritmo, naturalmente paralelizável, para o cálculo de permeabilidades equivalentes em reservatórios / A new algorithm, of course parallelization, for the calculation of equivalent permeabilities in reservoirsClovis Antonio da Silva 27 February 2008 (has links)
Conselho Nacional de Desenvolvimento Científico e Tecnológico / Neste trabalho é apresentado um novo procedimento numérico para o upscaling de permeabilidade utilizando condições de contorno periódicas. Este procedimento combina decomposição de domínio com elementos finitos mistos na discretização do problema local de pressão-velocidade necessário para se encontrar as permeabilidades equivalentes. / A new numerical method is proposed for the permeabilities upscaling take into consideration periodic boundary conditions. This method combines domain decomposition with mixed finite elements in discretization of the local problem of pressure-velocity necessary to meet the equivalent permeabilities.
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Smart Sensing System for a Lateral Micro Drilling RobotJose Alejandro Solorio Cervantes (11191893) 28 July 2021 (has links)
The oil and gas industry
faces a lack of compact drilling devices capable of performing horizontal
drilling maneuvers in depleted or abandoned wells in order to enhance oil
recovery. The purpose of this project was to design and develop a smart sensing
system that can be later implemented in compact drilling devices used to
perform horizontal drilling to enhance oil recovery in wells. A smart sensor is
the combination of a sensing element (sensor) and a microprocessor. Hence, a
smart sensing system is an arrangement that consists of different sensors,
where one or more have smart capabilities. The sensing system was built and
tested in a laboratory setting. For this, a test bench was used as a case study
to simulate the operation from a micro-drilling device. The smart sensing
system integrated the sensors essential for the direct operational measurements
required for the robot. The focus was on selecting reliable and sturdy
components that can handle the operation Down the Hole (DTH) on the final
lateral micro-drilling robot. The sensing system's recorded data was sent to a
microcontroller, where it was processed and then presented visually to the
operator through a User Interface (UI) developed in a cloud-based framework.
The information was filtered, processed, and sent to a controller that executed
commands and sent signals to the test bench’s actuators. The smart sensing
system included novel modules and sensors suitable for the operation in a harsh
environment such as the one faced in the drilling process. Furthermore, it was
designed as an independent, flexible module that can be implemented in test
benches with different settings and early robotic prototypes. The outcome of
this project was a sensing system able to provide robotic drilling devices with
flexibility while providing accurate and reliable measurements during their
operation.
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Modelagem computacional de escoamentos com duas e três fases em reservatórios petrolíferos heterogêneos / Computational modeling of two and three-phase flow in heterogeneous petroleum reservoirsGrazione de Souza 21 February 2008 (has links)
Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro / Considera-se neste trabalho um modelo matemático para escoamentos com duas e três fases em reservatórios petrolíferos e a modelagem computacional do sistema de equações governantes para a sua solução numérica. Os fluidos são imiscíveis e incompressíveis e as heterogeneidades da rocha reservatório são modeladas estocasticamente. Além disso, é modelado o fenômeno de histerese para a fase óleo via funções de permeabilidades relativas. No caso de escoamentos trifásicos água-óleo-gás a escolha de expressões gerais para as funções de permeabilidades relativas pode levar à perda de hiperbolicidade estrita e, desta maneira, à existência de uma região elíptica ou de pontos umbílicos para o sistema não linear de leis de conservação hiperbólicas que descreve o transporte convectivo das fases fluidas. Como conseqüência, a perda de hiperbolicidade estrita pode levar à existência de choques não clássicos (também chamados de choques transicionais ou choques subcompressivos) nas soluções de escoamentos trifásicos, de difícil simulação numérica. Indica-se um método numérico com passo de tempo fracionário, baseado
em uma técnica de decomposição de operadores, para a solução numérica do sistema governante de equações diferenciais parciais que modela o escoamento bifásico água-óleo imiscível
em reservatórios de petróleo heterogêneos. Um simulador numérico bifásico água-óleo eficiente desenvolvido pelo grupo de pesquisa no qual o autor está inserido foi modificado com
sucesso para incorporar a histerese sob as hipóteses consideradas. Os resultados numéricos obtidos para este caso indicam fortes evidências que o método proposto pode ser estendido para o caso trifásico água-óleo-gás. A técnica de decomposição de operadores em dois níveis permite o uso de passos de tempo distintos para os quatro problemas definidos pelo procedimento de decomposição: convecção, difusão, pressão-velocidade e relaxação para histerese. O problema de transporte convectivo (hiperbólico) das fases fluidas é aproximado por um esquema central de diferenças finitas explícito, conservativo, não oscilatório e de segunda ordem. Este
esquema é combinado com elementos finitos mistos, localmente conservativos, para a aproximação dos problemas de transporte difusivo (parabólico) e de pressão-velocidade (elíptico).
O operador temporal associado ao problema parabólico de difusão é resolvido fazendo-se uso de uma estratégia implícita de solução (Backward Euler). Uma equação diferencial ordinária
é resolvida (analiticamente) para a relaxação relacionada à histerese. Resultados numéricos para o problema bifásico água-óleo em uma dimensão espacial em concordância com resultados semi-analíticos disponíveis na literatura foram reproduzidos e novos resultados em meios heterogêneos, em duas dimensões espaciais, são apresentados e a extensão desta técnica para o caso de problemas trifásicos água-óleo-gás é proposta. / We consider in this work a mathematical model for two- and three-phase flow problems in petroleum reservoirs and the computational modeling of the governing equations for its numerical solution. We consider two- (water-oil) and three-phase (water-gas-oil) incompressible, immiscible flow problems and the reservoir rock is considered to be heterogeneous. In our model, we also take into account the hysteresis effects in the oil relative permeability functions.
In the case of three-phase flow, the choice of general expressions for the relative permeability functions may lead to the loss of strict hyperbolicity and, therefore, to the existence of an elliptic region or umbilic points for the system of nonlinear hyperbolic conservation laws describing the convective transport of the fluid phases. As a consequence, the loss of hyperbolicity may lead to the existence of nonclassical shocks (also called transitional shocks or undercompressive shocks) in three-phase flow solutions. We present a new, accurate fractional time-step method based on an operator splitting technique for the numerical solution of a system of partial differential
equations modeling two-phase, immiscible water-oil flow problems in heterogeneous petroleum reservoirs. An efficient two-phase water-oil numerical simulator developed by our
research group was sucessfuly extended to take into account hysteresis effects under the hypotesis previously annouced. The numerical results obtained by the procedure proposed indicate
numerical evidence the method at hand can be extended for the case of related three-phase water-gas-oil flow problems. A two-level operator splitting technique allows for the use of distinct time steps for the four problems defined by the splitting procedure: convection, diffusion, pressure-velocity and relaxation for hysteresis. The convective transport (hyperbolic) of the fluid phases is approximated by a high resolution, nonoscillatory, second-order, conservative central difference scheme in the convection step. This scheme is combined with locally conservative mixed finite elements for the numerical solution of the diffusive transport (parabolic) and the pressure-velocity (elliptic) problems. The time discretization of the parabolic problem is performed by means of the implicit Backward Euler method. An ordinary diferential equation
is solved (analytically) for the relaxation related to hysteresis. Two-phase water-oil numerical results in one space dimensional, in which are in a very good agreement with semi-analitycal
results available in the literature, were computationaly reproduced and new numerical results in two dimensional heterogeneous media are also presented and the extension of this technique to the case of three-phase water-oil-gas flows problems is proposed.
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