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Two-phase flow occurs during the production of oil and gas in the wellbores. Modeling this phenomenon is important for monitoring well productivity and designing surface facilities. Since the transient time period in the wellbore is usually shorter than reservoir time steps, stabilized flow is assumed in the wellbore. As such, semi-steady state models are used for modeling wellbore flow dynamics. However, in the case that flow variations happen in a short period of time (i.e., a gas kick during drilling) the use of a transient two-phase model is crucial. Over the last few years, a number of numerical and analytical wellbore simulators have been developed to mimic wellbore-reservoir interaction. However, some issues still remain a concern in these studies. The main issues surrounding a comprehensive wellbore model consist of fluid property calculations, such as black-oil or compositional models, governing equations, such as mechanistic or correlation-based models, effect of temperature variation and non-isothermal assumption, and methods for coupling the wellbore to the reservoir. In most cases, only standalone wellbore models for blackoil have been used to simulate reservoir and wellbore dynamic interactions. Those models are based on simplified assumptions that lead to an unrealistic estimation of pressure and temperature distributions inside the well. In addition, most reservoir simulators use rough estimates for the perforation pressure as a coupling condition between the wellbore and the reservoir, neglecting pressure drops in the horizontal section. In this study, we present an implementation of a compositional, pseudo steady-state, non-isothermal, coupled wellbore-reservoir simulator for fluid flow in wellbores with a vertical section and a horizontal section embedded on the producing reservoir. In addition, we present the implementation of a pseudo-compositional, fully implicit, transient two-fluid model for two-phase flow in wellbores. In this model, we solve gas/liquid mass balance, gas/liquid momentum balance, and two-phase energy equations in order to obtain the five primary variables: liquid velocity, gas velocity, pressure, holdup and temperature. In our simulation, we compared stratified, bubbly, intermittent flow effects on pressure and temperature distributions in either a transient or steady-state condition. We found that flow geometry variation in different regimes can significantly affect the flow parameters. We also observed that there are significant differences in flow rate prediction between a coupled wellbore-reservoir simulator and a stand-alone reservoir simulator, at the early stages of production. The outcome of this research leads to a more accurate and reliable simulation of multiphase flow in the wellbore, which can be applied to surface facility design, well performance optimization, and wellbore damage estimation. / text

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Gas-liquid, two-phase flow is encountered in a wide variety of industrial equipment. A few examples are steam generators, condensers, oil and gas pipelines, and various components of nuclear reactors. Slug flow is one of the most common and complex flow patterns and it occurs over a broad range of gas and liquid flow rates. In vertical tubes, most of the gas is located in large, bullet-shaped bubbles (Taylor bubbles) which occupy most of the pipe cross section and move with a relatively constant velocity. The objectives of this work are to increase our understanding of slug flow in vertical tubes, to provide reliable data for validation of numerical models developed to predict the behaviour of slug flow, to interpret the behaviour of Taylor bubbles based on knowledge of the velocity field, and to determine the shape of the Taylor bubbles rising in stagnant and upward flowing liquid under various experimental conditions. To achieve these objectives, an experimental facility was designed and constructed to provide instantaneous two-dimensional (2-D) velocity field measurements using particle image velocimetry (PIV) around Taylor bubbles rising in a vertical 25 mm tube containing stagnant or upward moving liquids at Reynolds number based on the superficial liquid velocity (ReL = 250 to 17,800). The working fluids were filtered tap water and mixtures of glycerol and water (µ = 0.0010, 0.0050 and 0.043 Pa•s) and air. Mean axial and radial velocity profiles, axial turbulence intensity profiles, velocity vectors, and streamlines are presented for Taylor bubbles rising in stagnant and upward flowing liquids. The measurements were validated by a mass balance around the nose of the bubble. In stagnant liquids, the size of the primary recirculation zone in the near wake of the Taylor bubble depends on the inverse viscosity. For low viscosity liquid, the length of the primary recirculation zone is 1.23D (D is the tube diameter), for the intermediate viscosity it is 1.2D, and for the high viscosity it is 0.68D. Based on the velocity measurements, the minimum stable liquid slug length (the minimum distance needed to re-establish a fully-developed velocity distribution in the liquid in front of the trailing Taylor bubble) for stagnant cases was found to be in the range of 2~12D. In the flowing liquid, the flow structure of the wake depends on the relative motion between the two phases and the liquid viscosity. The wake is turbulent in all cases except at high viscosity where the wake is transitional. In general, the length of the primary recirculation zone increases with increasing liquid flow rate. For low viscosity cases, in a frame of reference moving at the bubble velocity, the length of the recirculation zone is 1.73D for ReL =9,200 and become essentially constant at 1.90D for ReL ≥ 13,600. For the intermediate viscosity, the length of the recirculation zone is 1.22D for ReL = 1,500. The length of the recirculation zone is increased to 1.34D for ReL = 3,900. For the high viscosity, the length of the recirculation region is elongated to 1.4D for ReL = 260. As the liquid flow rate increases the oscillations of the bottom surface increase and the number of small bubbles shed from the bubble bottom increases. The liquid slug minimum stable length for turbulent upward flowing liquid is around 12D. For laminar flow, the minimum stable length is 10D for ReL = 260 (high viscosity) and > 28D for ReL=1,500 (intermediate viscosity) and depends on the wake flow pattern and the liquid flow rate.

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Mathematical models possible to simulate are of great importance in order to make successful projects in the aircraft manufacturing industry. An aircraft fuel system is very complex, containing pipes, tanks, orifices, valves and pumps. The principal of this thesis is using the tool Easy5, which no longer is considered reliable enough in terms of development and support. This thesis tries to evaluate the Modelica language as a possible alternative to Easy5. To make this evaluation, the components concerned in the fuel library in Easy5 are implemented to the Modelica language. Small hydraulic systems are built up in Dymola, and verified against Easy5 through simulation with high accuracy. A model of the fuel system of an unmanned aerial vehicle (UAV) is built from the implemented Modelica components to examine how Dymola manage a large model. The simulation made in Dymola was considerably more time efficient than the one made in Easy5, in the range of minutes instead of hours. Thus, much time can be saved if Dymola is used instead of Easy5. Finally, the components in the fuel library handle a two phase flow of fuel and air. Modeling a two phase flow is not trivial and discontinuous mass flow and pressure values are also implemented and discussed. / För att driva framgångsrika projekt inom flygindustrin är det av stor vikt att ha matematiska modeller som kan simuleras. Ett bränslesystem till ett flygplan kan ses som ett komplext system bestående av bl.a. rör, tankar, ventiler och pumpar. För närvarande använder uppdragsgivaren till detta examensarbete modeller till dessa komponenter i verktyget Easy5, vars framtid anses osäker med avseende på nyutveckling och support. Syftet med detta examensarbete är därför att utvärdera modelleringsspråket Modelica som möjligt alternativ till Easy5. För att kunna göra en utvärdering implementeras berörda komponenter i Modelica med utgångspunkt från Easy5s bränslebibliotek. Mindre hydrauliska system skapas i verktyget Dymola, och dessa verifieras mot Easy5 genom simuleringar. Simuleringsresultaten visar på hög överensstämmelse mellan de båda verktygen. För att undersöka hur verktyget Dymola hanterar en stor modell skapas bränslesystemet till ett obemannat flygplan (UAV) utifrån de implementerade Modelicakomponenterna. Resultat tyder på att simuleringstiden kan kortas betydligt om Dymola används gentemot Easy5; storleksordningen minuter istället för timmar. Avslutningsvis hanterar komponenterna i bränslebiblioteket ett massflöde av både bränsle och luft. Att modellera ett 2-fasflöde stöter på vissa simuleringstekniska komplikationer i form av diskontinuerliga massflöden och tryck, vilket visas och diskuteras.

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