The development, analysis, and implementation of efficient methods to solve algebraic systems of equations are main research directions in the field of numerical simulation and are the focus of this thesis. Due to their lesser demands for computer resources, iterative solution methods are the choice to make, when very large scale simulations have to be performed. To improve their efficiency, iterative methods are combined with proper techniques to accelerate convergence. A general technique to do this is to use a so-called preconditioner. Constructing and analysing various preconditioning methods has been an active field of research already for decades. Special attention is devoted to the class of the so-called optimal order preconditioners, that possess both optimal convergence rate and optimal computational complexity. The preconditioning techniques, proposed and studied in this thesis, utilise the block structure of the underlying matrices, and lead to methods that are of optimal order. In the first part of the thesis, we construct an Algebraic MultiLevel Iteration (AMLI) method for systems arising from discretizations of parabolic problems, using Crouzeix-Raviart finite elements. The developed AMLI method is based on an approximated block factorization of the original system matrix, where the partitioning is associated with a sequence of nested discretization meshes. In the second part of the thesis we develop solution methods for the numerical simulation of multiphase flow problems, modelled by the Cahn-Hilliard (C-H) equation. We consider the discrete C-H problem, obtained via finite element discretization in space and implicit schemes in time. We propose techniques to precondition the Jacobian of the discrete nonlinear system, based on its natural two-by-two block structure. The preconditioners are used in the framework of inexact Newton methods. We develop two nonlinear solution algorithms for the Cahn-Hilliard problem. Both lead to efficient optimal order methods. One of the main advantages of the proposed methods is that they are implemented using available software toolboxes for both sequential and distributed execution. The theoretical analysis of the solution methods presented in this thesis is combined with numerical studies that confirm their efficiency.

Surface energy plays a major role in many phenomena that are important in technological and industrial processes, for example in wetting, grain growth and sintering. In this thesis, such surface-energy driven processes are studied by means of the phase-field method. The phase-field method is often used to model mesoscale microstructural evolution in materials. It is a diffuse interface method, i.e., it considers the surface or phase boundary between two bulk phases to have a non-zero width with a gradual variation in physical properties such as energy density, composition and crystalline structure. Neck formation and coarsening are two important diffusion-controlled features in solid-state sintering and are studied using our multiphase phase-field method. Inclusion of Navier-Stokes equation with surface-tension forces and convective phase-field equations into the model, enables simulation of reactive wetting and liquid-phase sintering. Analysis of a spreading liquid on a surface is investigated and is shown to follow the dynamics of a known hydrodynamic theory. Analysis of important capillary phenomena with wetting and motion of two particles connected by a liquid bridge are studied in view of important parameters such as contact angles and volume ratios between the liquid and solid particles. The interaction between solute atoms and migrating grain boundaries affects the rate of recrystallization and grain growth. The phenomena is studied using a phase-field method with a concentration dependent double-well potential over the phase boundary. We will show that with a simple phase-field model it is possible to model the dynamics of grain-boundary segregation to a stationary boundary as well as solute drag on a moving boundary. Another important issue in phase-field modeling has been to develop an effective coupling of the phase-field and CALPHAD methods. Such coulping makes use of CALPHAD's thermodynamic information with Gibbs energy function in the phase-field method. With the appropriate thermodynamic and kinetic information from CALPHAD databases, the phase-field method can predict mictrostructural evolution in multicomponent multiphase alloys. A phase-field model coupled with a TQ-interface available from Thermo-Calc is developed to study spinodal decomposition in FeCr, FeCrNi and TiC-ZrC alloys. / QC 20100622

Coupled Thermo-Hydro-Mechanical (THM) behavior in geological porous media has been a subject of great interest in many geoengineering disciplines. Many attempts have been made to develop numerical prediction capabilities associated with topics such as the movement of pollutant plumes, gas injection, energy storage, geothermal energy extraction, and safety assessment of repositories for radioactive waste and spent nuclear fuel. This thesis presents a new numerical modeling approach and a new computer code for simulating coupled THM behavior in geological porous media in general, and compacted bentonite clays in particular, as buffer materials in underground radioactive waste repositories. New governing equations were derived according to the theory of mixtures, considering interactions among solid-phase deformation, flows of water and gases, heat transport, and phase change of water. For three-dimensional problems, eight governing equations were formulated to describe the coupled THM processes. A new thermal conductivity model was developed to predict the thermal conductivity of geological porous media as composite mixtures. The proposed model considers the combined effects of solid mineral composition, temperature, liquid saturation degree, porosity and pressure on the effective thermal conductivity of the porous media. The predicted results agree well with the experimental data for MX80 bentonite. A new water retention curve model was developed to predict the suction-saturation behavior of the geological porous media, as a function of suction, effective saturated degree, temperature, porosity, pore-gas pressure, and the rate of saturation degree change with time. The model was verified against experimental data of the FEBEX bentonite, with good agreement between measured and calculated results. A new finite element code (ROLG) was developed for modeling fully coupled thermo-hydro-mechanical processes in geological porous media. The new code was validated against several analytical solutions and experiments, and was applied to simulate the large scale in-situ Canister Retrieval Test (CRT) at Äspö Hard Rock Laboratory, SKB, Sweden, with good agreement between measured and predicted results. The results are useful for performance and safety assessments of radioactive waste repositories. / QC20100720 / THERESA

Integrated theoretical and experimental analysis is carried out in this work to investigate the fundamental failure mechanisms and flow patterns involved in the process of fluid injection into dense granular media. The experimental work is conducted with aqueous glycerin solutions, utilizing a novel setup based on a Hele-Shaw cell filled with dense dry sand. The two dimensional nature of the setup allows direct visualization and imaging analysis of the real-time fluid and grain kinematics. The experimental results reveal that the fluid flow patterns show a transition from simple radial flow to a ramified morphology while the granular media behaviors change from that of rigid porous media to localized failure that lead to development of fluid channels. Based on the failure/flow patterns, four distinct failure/flow regimes can be identified, namely, (i) a simple radial flow regime, (ii) an infiltration-dominated regime, (iii) a grain displacement-dominated regime, and (iv) a viscous fingering-dominated regime. These distinct failure/flow regimes emerge as a result of competition among various energy dissipation mechanisms, namely, viscous dissipation through infiltration, dissipation due to grain displacements, and viscous dissipation through flow in thin channels and can be classified based on the characteristic times associated with fluid injection, hydromechanical coupling and viscoelastoplasticity. The injection process is also analyzed numerically using the discrete element method (DEM) coupled with two fluid flow scheme, a fixed coarse grid scheme based on computational fluid dynamics (CFD) and a pore network modeling scheme. The numerical results from the two complementary methods reproduce phenomena consistent with the experimental observations and justify the concept of associating the displacement regimes with the partition among energy dissipation mechanisms. The research in this work, though fundamental in nature, will have direct impacts on many engineering problems in civil, environmental and petroleum engineering such as ground improvement, environmental remediation and reservoir stimulation.

Gas-Partikel-Stroemungen finden sich in weiten Bereichen der Energie- und Verfahrenstechnik. Beispiele fuer haeu- fig anzutreffende Problemstellungen sind der Transport, die Separation oder die Injektion eines Gemisches aus festen Partikeln und einem Traegergas. Fuer die numerische Simulation solcher disperser Mehr- phasenstroemungen hat sich das Lagrange-Verfahren als besonders geeignet erwiesen. Andererseits stellt die An- wendung dieses Berechnungsverfahrens hoechste Anforderun- gen an die Ressourcen der verwendeten Rechner. Dies gilt im besonderen Masse fuer die Simulation von Stroemungen mit einer moderaten bis hohen Partikelbeladung, in denen die Partikel-Partikel-Kollisionen einen grossen Einfluss auf das Stroemungsverhalten haben. Um das grosse Leistungspotential, das heutige massiv par- allele Hochleistungsrechner bieten, effizient zu nutzen, wurden im Rahmen dieser Arbeit parallele Simulationsalgo- rithmen fuer die numerische Berechnung kollisionsbehafte- ter Gas-Partikel-Stroemungen entwickelt. Die Effizienz dieser Algorithmen wurde anhand verschiedener Testfaelle untersucht. Auf der Grundlage der dabei erzielten Ergeb- nisse wurden Vorschlaege fuer weitere Entwicklungsmoeg- lichkeiten erarbeitet. / Gas-particle-flows can be found widely in the field of energy production and process engineering. Examples for applications of such kind of flows are transport, se- paration or injection of a mixture of solid particles and a gaseous phase. The Lagrangian approach has proved to be a suitable means for the numerical simulation of disperse multiphase flows. On the other hand its application requires a large amount of computational power, especially when flows with a mo- derate or high particle loading are computed and particle- particle collisions have a significant influence on the flow. In order to use efficiently the large computational power that parallel computers provide nowadays, parallel algo- rithms for the numerical simulation of gas-particle flows including particle-particle collisions were developed in the cource of this work. The algorithms' efficiency was investigated considering different test cases. On the basis of the results suggestions for further developments were made.

In this paper we present detailed Euler-Euler Large Eddy Simulations (LES) of dispersed bubbly flow in a rectangular bubble column. The motivation of this study is to investigate potential of this approach for the prediction of bubbly flows, in terms of mean quantities. The set of physical models describing the momentum exchange between the phases was chosen according to previous experiences of the authors. Experimental data, Euler-Lagrange LES and unsteady Euler-Euler Reynolds-Averaged Navier-Stokes model are used for comparison. It was found that the presented modelling combination provides good agreement with experimental data for the mean flow and liquid velocity fluctuations. The energy spectrum made from the resolved velocity from Euler-Euler LES is presented and discussed.

Accurate determination of the pressure losses at the bit is very important for drilling practices in petroleum industry. In the literature, there are several studies on determination of the pressure losses. Major focus is concentrated on single phase drilling fluids, which is far from accurate estimation of pressure losses for multiphase fluids, i.e., fluids including a liquid and a gas phase, at the bit. Some of these models are valid for multiphase fluids, however, they are either valid for very high gas flow rates, or developed using very strong assumptions. This study presents a mathematical model for calculating bit hydraulics for gasified drilling fluids. The theory, which is valid for both sonic (critical) and subsonic (sub-critical) regimes, is based on the solution of the general energy equation for compressible fluid flow. The model is sensitive to changes in internal energy, temperature and compressibility. In addition, the model uses &ldquo / mixture sound velocity&rdquo / approach. A computer program is developed based on the proposed mathematical model. The program calculates pressure drop through a nozzle in subsonic flow region, and suggest flow rate if the calculated pressure drop values is in the sonic flow pressure ranges. The program has been run at reasonable field data. The results of the models have been compared with the results of existing models in the literature. The results show that the pressure losses through the bit can be estimated with a variation less than 9%. Also, it has been observed that bottom hole pressure, velocity of the liquid phase and nozzle size have a strong influence on bit pressure drop.

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-03-12T15:40:08Z No. of bitstreams: 1 DANIELA PASSOS SIMÕES DE ALMEIDA TAVARES - TESE PPGEQ 2016..pdf: 15494076 bytes, checksum: 86040371b4c9f0e560658409f7d3b95d (MD5) / Made available in DSpace on 2018-03-12T15:40:08Z (GMT). No. of bitstreams: 1 DANIELA PASSOS SIMÕES DE ALMEIDA TAVARES - TESE PPGEQ 2016..pdf: 15494076 bytes, checksum: 86040371b4c9f0e560658409f7d3b95d (MD5) Previous issue date: 2016-08-18 / Capes / O vazamento de fluidos tóxicos em tubulações submarinas devido à corrosão, erosão ou falhas na estrutura, geralmente conduzem a danos extensivos à vida marinha, saúde humana e recursos naturais. Quando um vazamento acidental ocorre, uma resposta rápida e adequada é necessária para reduzir as consequências ambientais. Logo, compreender, por exemplo, o comportamento da pluma de óleo vazado possibilita a determinação do percurso da pluma de óleo e a dispersão da mesma na correnteza marítima e, assim, propor técnicas e/ou tecnologias para eliminar ou minimizar os danos causados pelo vazamento. Neste sentido, foi realizado um estudo do comportamento da pluma e sua dispersão, adotando-se uma abordagem Euleriana-Euleriana. Foi utilizado um modelo matemático representativo da fluidodinâmica de uma pluma de óleo originada do vazamento em um riser tipo catenária. Adotou-se um escoamento bifásico (Modelo de Superfície Livre), isotérmico e turbulento (modelo k-ε padrão) para se resolver as equações de conservação de massa e momento linear utilizando ANSYS CFX® v.15. Os resultados dos campos de pressão, velocidade e fração volumétrica, além dos perfis de fração volumétrica possibilitaram a avaliação do comportamento da pluma e de sua dispersão no mar. Observou-se que a pluma atingiu a superfície marítima quando adotado altas velocidades de vazamento de óleo e baixas velocidades da correnteza marítima. Para os casos em que a densidade do óleo é maior, houve espalhamento lateral subsuperfície. Para os casos com maior velocidade do jato de óleo e menor velocidade da água do mar, na chegada do óleo à superfície observou-se que houve espalhamento horizontal a montante e a jusante do sentido de escoamento. A depender das condições de velocidade de vazamento, da correnteza marítima e da diferença de densidade percebeu-se uma tendência da pluma não atingir a superfície marítima. / The leak of toxic fluids in submarine pipes due to corrosion, erosion or failures in the structure, generally lead to extensive damage to marine life, human health and natural resources. When occurs an accidental leak, a quick and adequate response is needed to reduce the environmental consequences. Therefore, understand, for example, the behavior of leaked oil plume enables the determination of the oil plume path and the dispersion of the same in the sea current and like this propose techniques and/or technologies to eliminate or minimize the damage caused by the leak. In this sense, it was proposed a study of the behavior of plume and its dispersion, adopting an EulerianEulerian approach. It was used a representative mathematical model of the fluid dynamics of an oil plume originated from leak at riser in catenary format. It was adopted a two-phase flow (Free Surface Model), isothermal and turbulent (k-ε standard model) to solve the mass and momentum conservation equations using ANSYS CFX® v.15. The results of the pressure, velocity and volumetric fraction fields, and the volumetric fraction profiles allowed the plume behavior assessment and dispersal at sea. Also it was observed that the plume reaches the sea surface when adopted high velocities of oil leak and low velocities of sea current. For the cases in which the oil density is higher, there was lateral subsurface scattering. For the cases with higher velocity of the oil jet and lower velocity of the sea water, in the arrival of the oil to the surface it was observed that there was horizontal scattering upstream and downstream of the direction of flow. Moreover, depending on conditions of the leak velocity, of the sea current and of the density difference was noticed a tendency of the plume not reach the sea surface.

Diversas aplicações industriais envolvem escoamentos multifásicos, como é o caso das operações de produção de petróleo em águas profundas, onde partículas sólidas, como areia ou hidratos, podem estar presentes, dando origem ao escoamento sólido-líquido-gás. O escoamento no padrão golfadas é frequentemente encontrado em linhas de produção de petróleo provocado pela topografia do terreno. É de grande valia para a indústria, a compreensão da dinâmica deste tipo de escoamento para o projeto de linhas de produção de óleo e gás, assim como para o dimensionamento de separadores e equipamentos. Nesse contexto, o presente trabalho experimental caracteriza o escoamento de três fases, gás-sólidolíquido em um tubo horizontal, visando determinar o impacto das partículas sólidas sintéticas (similares aos hidratos de gás) sobre os parâmetros característicos do escoamento em golfadas (velocidade da frente da bolha, frequência de passagem da célula unitária, comprimento da bolha e do pistão). Os testes experimentais foram realizados utilizando partículas sólidas, com massa específica semelhante às partículas de hidratos de gás, dispersas na fase líquida. Partículas sintéticas modelo de polietileno de 0,5 mm de diâmetro e 938 kg/m3 de massa específica foram utilizadas como a fase sólida. Água e ar comprimido foram utilizados como fase líquida e gasosa, respectivamente. A seção de testes compreende uma tubulação de 26 mm de diâmetro interno e 9 m de comprimento. As estruturas do escoamento foram monitoradas por meio de sensores resistivos e uma câmara de alta velocidade. Diversas combinações de velocidades superficiais de líquido e gás, que garantam o padrão intermitente em golfadas, e diferentes concentrações de partículas foram aplicadas nos testes. Os sinais obtidos foram processados e apresentados através de funções densidade de probabilidade (PDF) e valores médios. Estes valores obtidos foram discutidos e comparados com o escoamento bifásico em golfadas líquido-gás para condições semelhantes. Pôde ser observado que as partículas sólidas influenciam positivamente na velocidade da frente da bolha e a frequência, e influenciam negativamente nos comprimentos do pistão e da bolha. / Multiphase flows appear during a large number of industrial operations, as in the case of oil and gas offshore production operations, where solid particles, such as sand and hydrates may occasionally be present in the flow, starting the solid-liquid-gas flow. Slug flow in ducts is a frequently observed flow regime in oil and gas transportation lines. The onset of this kind of flow is due to instabilities generated by irregular pipe topography. Understanding the hydrodynamics of the slug flow is significant in the design of crude oil production lines as well as in the project of equipment involved in oil and gas operations. The present work experimentally characterizes the gas-liquid-solid three-phase flows in a horizontal pipe. The objective here is to determine the role played by solid particles (similar to hydrates) on the characteristic parameters of slug flows, namely the bubble front velocity, unit cell frequency and bubble and liquid slug lengths. Experimental tests with solid particles (whose specific mass are similar to those of the hydrate particles) dispersed in the liquid were carried out. The test section comprised a 26 mm ID, 9 m long transparent acrylic pipe. The flow structures were monitored and measured by means of resistive sensors and a high-speed camera. Several pairs of gas and liquid superficial velocities, for which the slug flow regime was observed, at different solid particle concentration were investigated during the tests. Synthetic standard 0.5 mm diameter polyethylene particles with 938 kg/m3 density constituted the solid phase. Water and compressed air were used as the liquid and gas phase, respectively. The signals captured during the tests were processed and presented in terms of a probability density function (PDF) and averaged values. The experiments and their results are discussed and compared to the two-phase gas-liquid flows at similar conditions. It was observed that solid particles influence positively the bubble front velocity and frequency, and influence negatively the piston and bubble lengths.

[pt] Óleos brutos altamente parafínicos podem causar problemas operacionais significativos, tais como bloqueio de um oleoduto devido à precipitação e deposição de componentes de parafina durante a produção e transporte de petróleo bruto. O custo de gerenciamento da parafina é enorme e aumenta significativamente com o aumento da produção de petróleo em áreas marítimas profundas. Mas estes custos podem ser significativamente reduzidos se a deposição de parafina em dutos puder ser prevista com precisão. Nesta pesquisa, o fenômeno de deposição foi analisado numericamente. O modelo de deslizamento foi utilizado para prever o fluxo multifásico e a deposição de parafina foi determinada a partir de um modelo de convecção. Este modelo previu com precisão as taxas de deposição de escala de laboratório em regime de fluxo laminar e turbulento. A taxa de deposição de parafina apresentou uma boa concordância com os resultados do software comercial OLGA. A comparação com a produção de petróleo de um poço real foi modelado, e bons resultados foram obtidos no impacto da queda de pressão devido à redução da área seção transversal causada pela deposição de parafina progressiva na parede do tubo. Os resultados deste trabalho mostraram uma boa consistência física e um acordo razoável com os dados experimentais e de campo comparados. / [en] Highly waxy crude oils can cause significant operational problems such as blockage of a pipeline due to the precipitation and deposition of select wax components during the production and transportation of the crude oil. The cost of wax management is enormous and rapidly increasing because of increased oil production in deep sea areas. Wax management costs can be significantly reduced if wax deposition in pipeline can be accurately predicted. In this research, the wax deposition phenomenon was numerically investigated. The drift flux model was employed to predict the multiphase flow and the wax deposition was determined based on a convective model. This model accurately predicted the deposition rates for lab scale under laminar and turbulent flows. The wax deposition rate presented a good agreement with the results of commercial software OLGA. A comparison with an existing oil production well was performed, and good results were obtained in the impact in pressure drop due to cross section area reduction caused by progressive wax deposition on the pipe wall. The results of this work showed a good physical consistency and a reasonable agreement with the compared experimental and field data.