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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
371

Estudo experimental sobre bomba centrífuga operando com fluido viscoso e escoamento bifásico gás-líquido / Experimental study of centrifugal pump handling viscous fluid and two-phase flow

Paternost, Guilherme Miranda 22 August 2018 (has links)
Orientador: Antonio Carlos Bannwart / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica e Instituto de Geociências / Made available in DSpace on 2018-08-22T07:33:01Z (GMT). No. of bitstreams: 1 Paternost_GuilhermeMiranda_M.pdf: 4957872 bytes, checksum: 34efcf3e5536aa84d89fa2b289df6cee (MD5) Previous issue date: 2013 / Resumo: O bombeio centrífugo submerso (BCS) é o segundo método de elevação artificial mais utilizado em poços de petróleo no mundo. Nestes poços, o equipamento está sujeito à influência de fluidos viscosos e à presença de gás livre, os quais impactam significativamente seu desempenho já que este é resultado da dinâmica de fluidos nos impelidores e difusores da bomba. Historicamente, devido ao escoamento de gás e de fluidos viscosos se tratarem de situações distintas, as maiorias dos estudos realizados analisam estes fenômenos separadamente vistos a complexidade e particularidades existentes de cada. O objetivo deste trabalho é a realização de um estudo experimental de avaliação do desempenho de uma bomba centrífuga sob os dois fenômenos, onde foi mensurado o impacto e a interação das principais variáveis que afetam seu desempenho. Para isto, foi construída uma bancada experimental constando de uma bomba centrífuga do tipo voluta, permitindo medir seu desempenho com água e fluido viscoso juntamente com os efeitos de fração de vazio, diâmetro de bolha e pressão de entrada. Foi também avaliada uma proposta existente de mapeamento do comportamento de uma bomba centrífuga operando com escoamento monofásico em função de números adimensionais que traduzem os efeitos combinados da viscosidade e da rotação. Foram sugeridas modificações e correlações baseadas nesta proposta e seus resultados comparados aos dados experimentais obtidos / Abstract: The Electrical Submersible Pumping (ESP) is the second most commonly used artificial lift method worldwide, being responsible for the highest amount of total fluids produced (oil and water). In wells using this method, the equipment may be subjected to viscous fluids and free gas flow, both affecting pump performance since it is a result of the fluid dynamics inside its impellers and diffusers. Generally, since the presence of free gas and liquid viscosity are independent phenomena, most studies so far have examined their effect separately due to their complexity. The purpose of this experimental study is to take another step towards understanding the performance of a centrifugal pump under these two phenomena, measuring the impact of the main variables involved. A testing rig consisting of a centrifugal pump of volute type was built, where its performance was measured with the varying effects of viscosity, void fraction and rotational speed / Mestrado / Explotação / Mestre em Ciências e Engenharia de Petróleo
372

Efeito da vazão nas curvas de permeabilidade relativa em regime transiente / Flow rate effect on transient relative permeability curves

Domínguez, Lucía García, 1988- 02 October 2015 (has links)
Orientador: Rosângela Barros Zanoni Lopes Moreno / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica e Instituto de Geociências / Made available in DSpace on 2018-08-28T12:56:20Z (GMT). No. of bitstreams: 1 Dominguez_LuciaGarcia_M.pdf: 8169227 bytes, checksum: 3b6d0e210f4dc8a2db3d9f8b9f93f6c0 (MD5) Previous issue date: 2015 / Resumo: A capacidade de armazenamento de hidrocarbonetos no reservatório depende do tipo de rocha e da estrutura dos poros. Uma das propriedades rocha-fluido mais estudadas é a permeabilidade relativa, ou seja, a medida da resistência ao escoamento que um fluido apresenta na presença de outro. A permeabilidade relativa é essencial para a avaliação dos processos de recuperação de hidrocarbonetos e previsão do escoamento multifásico de fluidos através do reservatório. A permeabilidade relativa depende de outros parâmetros que têm sido estudados por especialistas durante os últimos anos, como saturação dos fluidos, molhabilidade, tensão interfacial, estrutura porosa, temperatura, heterogeneidades e vazão de deslocamento. Em relação ao efeito da vazão de deslocamento na permeabilidade relativa, muitas pesquisas têm sido realizadas sem conseguir um acordo. Por tanto, a principal motivação deste estudo é a falta de conformidade na literatura. O foco do trabalho é encontrar se existe dependência da permeabilidade relativa com a vazão e avaliar este efeito em óleos de diferentes viscosidades. Foram realizados quinze testes de deslocamento em regime transiente a temperatura e vazão constantes. Os experimentos de laboratório foram executados com três plugues, cortados a partir de uma amostra única de rocha carbonática e saturados com três óleos de viscosidades diferentes, respetivamente. Foram utilizadas três vazões diferentes para cada amostra, que correspondem aos valores mínimo, máximo e intermediário de acordo o critério de dos Santos et al (1997) que visa balancear as forças viscosas, capilares e gravitacionais. Estas vazões foram variadas começando pela maior e diminuindo até a menor e posteriormente revertendo o ciclo, para observar se a sequência seguida influencia nos resultados. A análise dos resultados foi realizada mediante o método de Johnson-Bossler-Naumann para calcular as permeabilidades relativas ao óleo e à água. Sob as condições dos testes realizados, observou-se que as saturações e permeabilidades dos pontos terminais bem como as curvas de permeabilidade relativa, dependem da vazão. Além disso, pode-se observar que as variações foram diferentes dependendo da viscosidade do óleo utilizado. Deste modo, o óleo de menor viscosidade sempre se comportou de modo contrário ao de maior viscosidade e a mistura dos outros dois teve um comportamento intermediário. Este comportamento tem sido atribuído, nos óleos mais viscosos, a um aumento no ângulo de contato e consequente diminuição do número capilar em resposta à vazão mais elevada. Já nos óleos menos viscosos, a vazão não altera significativamente o ângulo de contato e, portanto, o número capilar aumenta com a vazão. Estas diferenças na variação do número capilar, dependendo do óleo utilizado, podem gerar as tendências diferentes nos resultados e explicar o desacordo na literatura / Abstract: The storability of hydrocarbons in the reservoir is dependent upon the rock formation and the pore structures. One of the main important rock-fluid property is the relative permeability, a measure of the flow resistance of one fluid in the presence of another one into the rock. Relative permeability depends on other parameters which have been studied by researchers during the years like fluid properties and saturation, wettability, interfacial tension, porous structure, temperature, heterogeneity and flow rate. Many researchers have focused on flow rate influence in relative permeability curves without obtaining agreement. Therefore, the main motivation for this study is the lack of conformity in the literature. The focus of the work is to find whether there is dependence of relative permeability with the flow and evaluate this effect in oils of different viscosities. Fifteen transient displacement tests were performed at constant temperature and flow rate. The laboratory experiments were performed with three plugs, cut from a single sample of carbonate rock and saturated with three fluids of different viscosities, respectively. Three different flow rates were used for each sample, corresponding to the minimum, maximum and intermediate according to dos Santos et al criterion (1997) which aims to balance the viscous, capillary and gravitational forces. These flow rates were varied starting with the largest and decreasing to the smallest, and subsequently reversing the cycle, to see if the next sequence influences the results. Experimental results were analyzed using JBN method (Johnson-Bossler-Naumann) to calculate oil and water relative permeability curves. Under the studied circumstances, it was observed that the end point saturations and permeabilities and the relative permeability curves depend on the flow rate. Moreover, variations were different depending on the viscosity of the oil used. Thus, the lower viscosity oil will always behave in a contrary manner to the higher viscosity and the mixture of the other two had an intermediate performance. This behavior has been attributed, for more viscous oils, to an increment in contact angle and thus diminution in the capillary number in response to the higher flow. Nevertheless in lower viscous oils, the flow rate does not alter significantly the contact angle and thus the capillary number increases with flow rate. These differences in the variation of the capillary number depending on the oil used may generate the differences on the results trends and explain the disagreement in the literature / Mestrado / Reservatórios e Gestão / Mestra em Ciências e Engenharia de Petróleo
373

Representação de superfícies livres utilizando partição da unidade implícita no sistema Freeflow / Free surface representation on freeflow using partition of unity implicits

Luis Felipe da Costa Ladeira 13 June 2011 (has links)
Este trabalho consiste em introduzir uma nova abordagem de representação de superfície no ambiente de simulação Freeflow2D. Consiste em usar Partição da Unidade Implícita para estimar da superfície a geometria, normais e curvatura. Procurando se valer das vantagens de métodos do tipo meshless (sem malha) conservando no entanto a malha Lagrangiana, no interesse de manter o fácil acesso de vizinhança, inserção e eliminação de pontos / The objective of this work is to introduce a new approache of surface representation within the Freeflow system. It consists of using implicit functions by means of Partition of Unit Implicit to estimate surface geometry, normals and curvature. Aiming at the advantages of meshless methods of surface representation whilst keeping the Lagrangian mesh in order to preserve ease of access of geometric vicinity, particle insertion and removal
374

Phase noise reduction in a multiphase oscillator

Alberts, Antonie Craig January 2017 (has links)
Oscillators are ubiquitous to radio frequency circuits, where frequency translations and channel selection play a central role in the analogue communications channel. Oscillators also form part of digital systems as a time reference. Typical heterodyne receivers require an intermediate frequency channel. The associated oscillators and variable filters can only be centred perfectly at a single frequency, and degrade performance at the boundaries of the channel. These circuits also require image-rejecting filters and phase-locked loops in order to enable down-conversion. The penalties for these components are increased circuit area and power consumption. A direct down-conversion circuit will reduce the number of components in the system. A requirement added by the structural change is a passive sub-harmonic mixer. Quadrature oscillators may be achieved by cross-coupling two nominally identical LC differential voltage-controlled oscillators. Because of the widespread use of voltage-controlled oscillators in wireless communication systems, the development of comprehensive nonlinear analysis is pertinent in theory and applications. A key characteristic that defines the performance of an oscillator is the phase noise measurement. The voltage-controlled oscillator is also a key component in phase-locked loops, as it contributes to most of the out-of-band phase noise, as well as a significant portion of in-band noise. Current state-of-the-art modulation techniques, implemented at 60 GHz, such as quadrature amplitude modulation, and orthogonal frequency domain multiplexing, require phase noise specifications superior to 90 dBc/Hz at a 1 MHz offset. It has been shown that owing to the timing of the current injection, the Colpitts oscillator tends to outperform other oscillator structures in terms of phase noise performance. The Colpitts oscillator has a major flaw in that the start-up gain must be relatively high in comparison to the cross-coupled oscillator. The oscillation amplitude cannot be extended as in the cross-coupled case. The oscillator’s bias current generally limits the oscillation amplitude. The phase noise is defined by a stochastic differential equation, which can be used to predict the system’s phase noise performance. The characteristics of the oscillator can then be defined using the trajectory. The model projects the noise components of the oscillator onto the trajectory, and then translates the noise into the resulting phase and amplitude shift. The phase noise performance of an oscillator may be improved by altering the shape of the trajectory. The trajectory of the oscillator is separated into slow and fast transients. Improving the shape of the oscillator’s slow manifold may improve its phase noise performance, and improving the loaded quality factor of the tank circuit may be shown to directly improve upon close-in phase noise. The approach followed describes oscillator behaviour from a circuit-level analysis. The derived equations do not have a closed form solution, but are reformulated using harmonic balance techniques to yield approximate solutions. The results from this closed form approximation are very close to both the numerical solutions of the differential equations, as well as the Simulation Program with Integrated Circuit Emphasis solutions for the same circuits. The derived equations are able to predict the amplitude and frequency in the single-phase example accurately, and are extended to provide a numerical platform for defining the amplitude and frequency of a multiphase oscillator. The analysis identifies various circuit components that influence the oscillator’s phase noise performance. A circuit-level modification is then identified, enabling the decoupling of some of the factors and their interactions. This study demonstrates that the phase noise performance of a Colpitts oscillator may be significantly improved by making the proposed changes to the oscillator. The oscillator’s figure of merit is improved even further. When a given oscillator is set at its optimum phase noise level, the collector current will account for approximately 85% of the phase noise; with the approach in this work, the average collector current is reduced and phase noise performance is improved. The key focus of the work was to identify circuit level changes to an oscillator’s structure that could be improved or changed to achieve better phase noise performance. The objective was not to improve passive components, but rather to identify how the noise-to-phase noise transfer function could be improved. The work successfully determines what can be altered in an oscillator that will yield improved phase noise performance by altering the phase noise transfer function. / The concept is introduced on a differential oscillator and then extended to the multiphase oscillator. The impulse sensitivity function of the modified multiphase oscillator is improved by altering the typical feedback structure of the oscillator. The multiphase oscillator in this work is improved from -106 dBc/Hz to -113 dBc/Hz when considering the phase noise contribution from the tank circuits’ bias current alone. This is achieved by uniquely altering the feedback method of the oscillator. This change alters the noise-to-phase noise properties of the oscillator, reducing phase noise. The improvement in the phase noise does not account for further improvements the modification would incorporate in the oscillator’s limit cycle. For a given tank circuit, supply current and voltage, compared to an optimised Colpitts oscillator, the modifications to the feedback structure proposed in this work would further improve the figure of merit by 9 dB. This is not considering the change in the power consumption, which would yield a further improvement in the figure of merit by 7 dB. This is achieved by relaxing the required start-up current of the oscillator and effecting an improvement in the impulse sensitivity function. Future research could include further modelling of the phase shift in the feedback network, including the transmission lines in the feedback networks using the harmonic balance technique in a numerical form. The feedback technique can also be modified to be applicable to single and differential oscillators. / Dissertation (MEng)--University of Pretoria, 2017. / National Research Foundation / The Department of Science and Technology, South Africa / GEW Technologies (Pty) Ltd / Electrical, Electronic and Computer Engineering / MEng / Unrestricted
375

Additively Manufactured Conformal Microwave Sensors for Applications in Oil Industry

Karimi, Muhammad Akram 11 1900 (has links)
Depleting oil reserves and fluctuating oil prices have necessitated to increase the efficiency of oil production process. This thesis is focused on developing low-cost sensors, which can increase oil production efficiency through real-time monitoring of oil wells and help in safe transport of oil products from the wells to the refineries. Produced fluid from an oil well is a complex mixture of oil, water and gases, which needs to be quantified for various strategic and operational decisions. For many years, test separators have been used to separate oil, water and gases into three separate streams and then to analyse them individually. However, test separators are being replaced by multiphase flow meters (MPFM) which can analyse the complex mixture of oil, water and gas without separating it. However, existing MPFMs are either intrusive or require fluid mixing before the sensing stage. In contrast to existing techniques, first part of this thesis presents a microwave sensor, which can measure water fraction in oil in a non-intrusive way without requiring it to be mixed. Gas fraction sensing can also be performed using the same microwave sensor, which is an on-going work. The sensor operates on dielectric measurement principles and comprises a microstrip T-resonator that has been optimized for a 3D pipe surface. Certain locations on an oil field have limited available space, for which we have also presented a compact version of the microwave water-fraction sensor in this thesis. In this version, metallic housing of the sensor has been used to function as a ground plane for the coaxially located spiral resonator. This housing also protects the sensor from environmental effects. In addition to the efficient production of oil, its safe transport is also a concern for the industry. It is physically impossible to inspect a network of thousands of kilometres of pipelines manually. The existing leak detectors suffer from low sensitivity, high false alarms and dependence on environmental effects. In the last part of this thesis, we present a flexible ringresonator based leak detector, which can be clamped at vulnerable locations along the pipeline for early leak detection.
376

The Modified-Multiphase Boost Converter: Combined Inductors and Capacitors Topology

Eldredge, Zachary L 01 June 2018 (has links)
In this work, a modified boost converter design has been implemented in a multiphase configuration with a condensed topology. The modified aspect of the design has already been proven to drastically reduce input current ripple by about 40% in a single-phase implementation. By placing two modified boost converters in parallel with interleaving main switches (multiphase), the input inductors and modified capacitors of the modified topology can be reduced to just one of each, lowering the number of components, size, and cost. Additionally, multiphase DC/DC converters lower input/output voltage and current ripples while delivering more power compared to single-phase converters. By combining the modified and multiphase benefits, this thesis creates a topology with low ripple and noise while providing high power capability. This thesis covers the analysis, simulation, hardware implementation, and testing of the Modified-Multiphase Boost Converter as well as an equivalent Standard-Multiphase Boost Converter for comparison. Simulation and hardware test results exhibited a 9% input current ripple reduction with the Modified-Multiphase design, presenting a high-power converter with considerable input noise reduction. Keywords: dc/dc, boost, multiphase, interleave, modified, power, ripple
377

CFD analýza tepelného zatížení trubkovnice / CFD analysis of thermal stress of a tubesheet

Vince, Tomáš January 2021 (has links)
This diploma thesis focuses on the phenomena of multiphase flow in a steam generator as a one of probable causes of tubes and tubesheet weld cracking. In the first part of the work, a research was carried out focusing on the boiling and the phenomenon of two-phase flow in technical applications, its characteristics and properties. The thesis continuous with an overview of available numerical multiphase models in the ANSYS Fluent 2021 R1 and a research of previously published works focused on two-phase flow with the presence of boiling. The research is followed by a description of the particular boiler, which is part of the nitric acid production plant in the chemical company DUSLO, a.s., its operating conditions and a more detailed description of the issue that is being addressed in this thesis. The second part of the work continuous with a description of the computational model, including a description of the geometry of the model and used simplifications, the computational mesh and the description of boundary conditions. Important part is the description of calculation setting of steady-state and transient CFD simulations in ANSYS Fluent. Finally, the results of the two-phase flow calculation are presented and then discussed in the conclusions.
378

Propagation d'une onde de choc dans un liquide aéré : modélisation et application aux rideaux de bulles / Propagation of shock waves in bubbly liquids : modelling and application to the bubble curtain problem

Grandjean, Hervé 24 October 2012 (has links)
L'objectif de ces travaux est de déterminer l'atténuation des effets d'une explosion sous-marine par un rideau de bulles. Dans ce cadre, une modélisation de la propagation d'un chocdans les liquides à bulles a été développée, basée sur une technique de transition d'échelles.Cette méthode permet la formulation de modèles continus de liquides aérés, dont la mise enoeuvre est aisée et rapide. Nous avons d'abord développé une modélisation pour des liquidesdiphasiques au sein desquels les bulles sont régulièrement réparties dans l'espace, avant deproposer une extension de ce modèle au cas des liquides à bulles présentant des hétérogénéitésde porosité sous la forme d'amas sphériques de bulles. Un modèle de fragmentation des bulleslors du passage du choc a également été développé, basé sur une analyse linéaire de stabilitédes bulles. L'étude a permis d'établir un critère prédictif de fission et de déterminer le nombrede fragments associés. L'ensemble des modélisations proposées a fait l'objet de comparaisonsavec des résultats expérimentaux issus de la littérature. La concordance entre résultats d'essaiset résultats issus de la modélisation démontre les capacités prédictives de l'approche proposée.Cette modélisation a enfin été appliquée au cas de rideaux de bulles soumis à une explosionsous-marine. Une étude de sensibilité sur les paramètres physiques du rideau a été menée, eta permis de confirmer les tendances expérimentales : sous certaines conditions, la dispositiond'un rideau de bulles sous l'eau permet de diminuer de façon très conséquente l'énergie duchoc transmis en aval du rideau. / The present work deals with the modelling of shock wave propagation in bubbly liquids, inorder to assess the damping of underwater explosion by bubble curtains. The modelling is basedon a scale transition technique, which allows to formulate efficient continuum models of bubblyliquids. A modelling of homogeneous bubbly liquids has first been proposed, then extended tothe case of liquids with spherical bubble clusters. A modelling of bubble fragmentation duringshock propagation has also been developed, based on a stability analysis of the bubbles. Thisstudy enables us to establish a criterion for bubble fission and to determine the numberof fragments. The accuracy of the proposed models has been assessed through comparisonwith experimental data of the literature. The agreement between numerical and experimentalresults proves the predictive capabilities of the whole approach. The modelling has then beenapplied to the mitigation of UNDEX-induced shock wave by bubble curtain. A sensitive studyabout physical parameters of the curtain has been performed, and confirms the experimentaltendencies : the use of a bubble curtain can dissipate a significant part of the shock energy.
379

Suspensions turbulentes de particules de tailles finies : dynamique, modification collective de l'écoulement turbulent / Finite size particles suspensions in a turbulent flow : dynamic, flow modifications and collectives effects

Cisse, Mamadou 10 April 2015 (has links)
Les travaux numériques et expérimentaux de cette thèse contribuent à une meilleure compréhension de la dynamique de grosses particules dans un écoulement turbulent. Un premier volet m’a permis de quantifier leur mouvement relatif au fluide, ainsi que leur influence locale sur l’écoulement turbulent. Dans un second volet, j'ai trouvé que l'effet collectif des particules est d'atténuer l’amplitude des fluctuations turbulentes. En revanche, celles-ci n’ont pas d’influence sur les propriétés statistiques fines de l’écoulement. Aussi, ces mesures suggèrent l’existence d’une transition de phase dans les grandes échelles de l’écoulement au-delà d’un seuil critique du nombre de particules. / The numerical and experimental work of this thesis contribute to a better understanding of the dynamics of large particles in a turbulent flow. The first part allowed me to quantify their relative motion to the flow and their local influence on the surrounding flow. In a second part, I found that the collective effect of particles is to reduce the amplitude of turbulent fluctuations. In revanche, they have no influence on the fine statistical properties of the flow. Also, these measurements suggest the existence of a phase transition in the larger scales of the flow beyond a critical threshold of the number of particles.
380

Développement d'un modèle numérique pour l'écoulement triphasique de fluides incompressibles / Numerical modeling of three-phase incompressible flow with gravity effects using the global pressure formulation

Schneider, Lauriane 18 February 2015 (has links)
La modélisation des hydrosystèmes souterrains est devenue un outil crucial dans la gestion des ressources d'eaux souterraines ainsi que pour la surveillance des sites contaminés. L'objectif de ce travail de thèse est de modéliser l'écoulement d'une phase non-aqueuse liquide dense (DNAPL) dans les sols, et de développer un code pour la simulation des écoulements triphasiques de fluides incompressibles en milieux poreux. Le modèle mathématique pour les écoulements multiphasiques de fluides en milieux poreux est généralement constitué d'une équation de pression et de deux équations de saturation. Notre approche est fondée sur une formulation en pression globale : elle permet un découplage partiel des équations de pression et de saturations, et elle est plus efficace en termes de résolution numérique. Le nouveau modèle est discrétisé selon un schéma IMPES. Dans ce travail de thèse, la méthode des Eléments Finis Discontinus de Galerkine est combinée à un schéma de Godunov généralisé pour la résolution de la partie convective de l'équation de saturation. Un écoulement diphasique non miscible avec effets gravitaires importants et sans capillarité a été simulé. Une analyse fonctionnelle démontre que le profil de saturation de la phase non-aqueuse entrante dépend essentiellement du rapport de la vitesse totale sur la différence de densité entre la phase non aqueuse et l'eau. Le code développé a permis de simuler un drainage gravitaire à grande échelle. Enfin, un modèle numérique non-linéaire d'écoulement triphasique de fluides utilisant la Méthode des Lignes est introduit. Les causes d'oscillations instables du système en zone elliptique sont examinées. Des méthodes de relaxation et la construction d'un modèle de perméabilités relatives vérifiant la condition de Différentielle Totale sont envisagées. / Numerical simulation has become a crucial tool in addressing water-resource management and other environmental problems such as polluted sites monitoring. The aim of this work is to model the flow of a dense non aqueous phase liquid (DNAPL) in the subsurface by developing a numerical code to simulate three-phase (DNAPL, water, and gas), incompressible flow in porous media. The mathematical model for multiphase flow in porous media is generally composed of a system of one pressure and two saturation equations. Our approach is based on a global pressure model : it leads to a partial decoupling of the pressure and the saturation equation and is more efficient from the computational point of view. The new model is discretized by a Mixed Hybrid Finite Elements Method (MHFEM), Discontinuous Galerkin Finite Elements (DGFEM), IMPES resolution method. In this work, the DGFEM scheme is combined with a generalised Godunov scheme to solve the convective part of the saturation equation. An immiscible two-phase flow with predominant gravity effects and whithout capillary effects has been modelled. It has been shown that the saturation profile of a displacing non-aqueous phase liquid (NAPL) in an initially water-saturated porous medium depends strongly on the ratio between the total specific discharge and the density difference between the NAPL and water. The 2D-code enabled a simulation of a large-scale gravity drainage. Finally, a non-linear three-phase 1D flow formulation using Method of Lines (MOL) has been introduced. Unstable oscillatory behavior of the system when the initial state are in the elliptic region of the ternary diagram is examined. Non-equilibrium formulation and construction of relative permeability model satisfying the Total-Differential are foreseen.

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