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Little, Sylvia Bandy. "Multiphase flow through porous media." Thesis, Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/11779.
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Booth, Richard J. S. "Miscible flow through porous media." Thesis, University of Oxford, 2008. http://ora.ox.ac.uk/objects/uuid:542d3ec1-2894-4a34-9b93-94bc639720c9.
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This thesis is concerned with the modelling of miscible fluid flow through porous media, with the intended application being the displacement of oil from a reservoir by a solvent with which the oil is miscible. The primary difficulty that we encounter with such modelling is the existence of a fingering instability that arises from the viscosity and the density differences between the oil and solvent. We take as our basic model the Peaceman model, which we derive from first principles as the combination of Darcy’s law with the mass transport of solvent by advection and hydrodynamic dispersion. In the oil industry, advection is usually dominant, so that the Péclet number, Pe, is large. We begin by neglecting the effect of density differences between the two fluids and concentrate only on the viscous fingering instability. A stability analysis and numerical simulations are used to show that the wavelength of the instability is proportional to Pe^−1/2, and hence that a large number of fingers will be formed. We next apply homogenisation theory to investigate the evolution of the average concentration of solvent when the mean flow is one-dimensional, and discuss the rationale behind the Koval model. We then attempt to explain why the mixing zone in which fingering is present grows at the observed rate, which is different from that predicted by a naive version of the Koval model. We associate the shocks that appear in our homogenised model with the tips and roots of the fingers, the tip-regions being modelled by Saffman-Taylor finger solutions. We then extend our model to consider flow through porous media that are heterogeneous at the macroscopic scale, and where the mean flow is not one dimensional. We compare our model with that of Todd & Longstaff and also models for immiscible flow through porous media. Finally, we extend our work to consider miscible displacements in which both density and viscosity differences between the two fluids are relevant.
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Sheng, James Jiaping. "Foamy oil flow in porous media." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq21633.pdf.
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Schechter, David S. "Immiscible flow behaviour in porous media." Thesis, University of Bristol, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.234777.
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GAMA, ROGERIO MARTINS SALDANHA DA. "MODELLING OF FLOW IN POROUS MEDIA." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1985. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=33487@1.
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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOO presente trabalho tem como objetivo a modelagem de escoamentos através de meios porosos, sob o ponto de vista da Teoria Contínua de misturas. O fluido e o sólido, que compõe o meio poroso, são tratados como constituintes contínuos de uma mistura binária, onde não ocorrem reações químicas. Em todas as situações aqui tratadas o fluido é suposto Newtoniano e incompressível, enquanto o meio poroso é rígido, homogêneo e isotrópico. O trabalho pode ser dividido em duas partes principais. Na primeira são modelados escoamentos através de regiões contendo meios porosos saturados e regiões onde só existe o fluido. São discutidas condições de compatibilidade sobre as interfaces, que separam as regiões, e é estabelecido um modelo para escoamentos, nos quais não exista fluxo de massa através das interfaces. A segunda parte trata de escoamentos em meios porosos insaturados, onde é preciso se considerar o efeito de forças capilares. Nesta parte é estabelecido um modelo e são simuladas situações unidimensionais. São estudados vários casos entre eles o enchimento de uma placa porosa, com e sem efeitos de atrito e de forças gravitacionais. A obtenção de resultados, nestes casos, exige a solução numérica de um sistema hiperbólico não-linear de equações diferenciais.
This work aims to a modelling of flow through a porous media based upon the Continuum Theory of Mixtures. The fluid and the solid, which composes the porous media, are assumed as continuous constituent of a binary mixture where chemical reactions do not occur. In all situations here considered, the fluid is assuned Newtonian and incompressíble, while the porous media is rigid, homogeneus and isotropic. This work can be divided in two main parts. In the first one, flows are modelled through regions containing saturated porous media and regions where there is nothing but the fluid. Conditions of compatibility in the interfaces that divide the regions are discussed and a flow modelling is stablished where there are no crosaflow through the interfaces. The second part is concerned with flows in unsaturated porous media, where the effect of capillery pressure is considered. In this Part a model is stablished and unidimensíonal situations are simulated. Several cases are studied and the filling-up of a porous plate is among them, with and without frictíon effect and gravitational forces. The obtainment of results, in such cases, requires the numeric solution of a non-linear hyperbolíc system of differential equations.
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Batycky, Richard Panko. "Inhomogeneous Stokes flow through porous media." Thesis, Massachusetts Institute of Technology, 1995. http://hdl.handle.net/1721.1/36640.
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Sheng, Jopan. "Multiphase immiscible flow through porous media." Diss., Virginia Polytechnic Institute and State University, 1986. http://hdl.handle.net/10919/53630.
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A finite element model is developed for multiphase flow through soil involving three immiscible fluids: namely air, water, and an organic fluid. A variational method is employed for the finite element formulation corresponding to the coupled differential equations governing the flow of the three fluid phase porous medium system with constant air phase pressure. Constitutive relationships for fluid conductivities and saturations as functions of fluid pressures which may be calibrated from two-phase laboratory measurements, are employed in the finite element program. The solution procedure uses iteration by a modified Picard method to handle the nonlinear properties and the backward method for a stable time integration. Laboratory experiments involving soil columns initially saturated with water and displaced by p-cymene (benzene-derivative hydrocarbon) under constant pressure were simulated by the finite element model to validate the numerical model and formulation for constitutive properties. Transient water outflow predicted using independently measured capillary head-saturation data agreed well with observed outflow data. Two-dimensional simulations are presented for eleven hypothetical field cases involving introduction of an organic fluid near the soil surface due to leakage from an underground storage tank. The subsequent transport of the organic fluid in the variably saturated vadose and ground water zones is analysed.Ph. D.
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Woudberg, Sonia. "Laminar flow through isotropic granular porous media." Thesis, Link to the online version, 2006. http://hdl.handle.net/10019/1320.
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Caruana, Albert. "Immiscible flow behaviour within heterogeneous porous media." Thesis, University of London, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.285232.
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Ababou, R. (Rachid). "Three-dimensional flow in random porous media." Thesis, Massachusetts Institute of Technology, 1988. http://hdl.handle.net/1721.1/14675.
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Tambue, Antoine. "Efficient numerical schemes for porous media flow." Thesis, Heriot-Watt University, 2010. http://hdl.handle.net/10399/2389.
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Partial di erential equations (PDEs) are important tools in modeling complex phenomena, and they arise in many physics and engineering applications. Due to the uncertainty in the input data, stochastic partial di erential equations (SPDEs) have become popular as a modelling tool in the last century. As the exact solutions are unknown, developing e cient numerical methods for simulating PDEs and SPDEs is a very important while challenging research topic. In this thesis we develop e cient numerical schemes for deterministic and stochastic porous media ows. More schemes are based on the computing of the matrix exponential functions of the non diagonal matrices, we use new e cient techniques: the real fast L eja points and the Krylov subspace techniques. For the deterministic ow and transport problem, we consider two deterministic exponential integrator schemes: the exponential time di erential stepping of order one (ETD1) and the exponential Euler midpoint (EEM) with nite volume method for discretization in space. We give the time and space convergence proof for the ETD1 scheme and illustrate with simulations in two and three dimensions that the exponential integrators are e - cient and accurate for advection dominated deterministic transport ow in heterogeneous anisotropic porous media compared to standard semi implicit and implicit schemes. For the stochastic ow and transport problem, we consider the general parabolic SPDEs in a Hilbert space, using the nite element method for discretization in space (although nite di erence or nite volume can be used as well). We use a linear functional of the noise and the standard Brownian increments to develop and give convergence proofs of three new e cient and accurate schemes for additive noise, one called the modi ed semi{ implicit Euler-Maruyama scheme and two stochastic exponential integrator schemes, and two stochastic exponential integrator schemes for multiplicative and additive noise. The schemes are applied to two dimensional ow and transport.
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Khayamyan, Shervin. "Transitional and turbulent flow in porous media." Licentiate thesis, Luleå tekniska universitet, Strömningslära och experimentell mekanik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-26476.
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Fluid flow through porous media takes place in many natural processes such as ground water flows, capillary flows in plants and flow in human organs and muscles. It is also of outmost importance to have knowledge of this flow in a number of industrial processes such as paper making, making of fibre boards, composites manufacturing, filtering, forming and sintering of iron ore pellets and drying and impregnation of wood. Despite the significance of porous media flow and the vast amount of work that has been performed to investigate it, knowledge of some fundamentals is missing. Little is, for instance, known about transitional and turbulent flow in porous media on the microscopic level. On a macroscopic level Darcy law is extended to the so called Ergun or Forchheimer Equations when Re becomes larger than about 10 to fit experimental. The actual value depends both on the porous media and how Re is defined. The deviation from Darcy flow can for modest Re be explained by inertia but may, as Re increases, also be attributed to turbulence. The macroscopic way of modelling the transition from inertia dominated to turbulent flow is just to continue with the Forchheimer Equation or possibly some version of it. In any case experimental data yields that, on a macroscopic level, the transition from Darcy flow to inertia dominated and turbulent flow is smooth. To get a better understanding of this process the transition from laminar to turbulent flow in porous media is here studied with a new method. To mimic inter-connected pores, a simplified geometry is studied consisting of a pipe with a relatively large diameter that is split into two parallel pipes with different diameters. This is a pore-doublet set-up and the pressure drop over all pipes is recorded by pressure transducers for different flow rates. Statistical method and frequency analysis are performed to investigate collected data (Papers A and B). Positive skewness of pressure drop fluctuations indicates early stage of presence of turbulent patches in the flow for each pipe. The measured flow distribution and pressure drop fluctuations highlights six distinct flow patterns in the pipe network based on variation in flow regime of each pipe and the level of pressure fluctuations (Paper B). Correlation between the pressure drop between two pipes shows that two parallel pipes follow each other fluctuations much better before both of them become fully turbulent. Some detailed results are that the frequency analysis reveals two different frequency band events in the pipes. The gain factor shows that both frequency band events originate from the larger pipe until the early presence of turbulent patches in the smaller pipe (Paper B). The low frequency fluctuations makes the flow in the pipes to be out of phase while the high frequency band fluctuations try to bring the flow in the pipes back to equilibrium state.Godkänd; 2013; 20130521 (shekha); Tillkännagivande licentiatseminarium 2013-05-29 Nedanstående person kommer att hålla licentiatseminarium för avläggande av teknologie licentiatexamen. Namn: Shervin Khayamyan Ämne: Strömningslära/Fluid Mechanics Uppsats: Transitional and Turbulent Flow in Porous Media Examinator: Professor Staffan Lundström, Institutionen för teknikvetenskap och matematik, Luleå tekniska universitet Diskutant: Professor Carl-Erik Grip, Institutionen för teknikvetenskap och matematik, Luleå tekniska universitet Tid: Onsdag den 19 juni 2013 kl 09.00 Plats: E231, Luleå tekniska universitet
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Alvarez, Martinez José Manuel. "Foam-flow behavior in porous media : effects of flow regime and porous-medium heterogeneity /." Digital version accessible at:, 1998. http://wwwlib.umi.com/cr/utexas/main.
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Stower, G. X. M. "The permeability of regular porous media." Thesis, University of Essex, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.355381.
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Oukili, Hamza. "Flow and transport in complex porous media : particle methods." Thesis, Toulouse, INPT, 2019. http://www.theses.fr/2019INPT0056.
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Les méthodes utilisant des particules ont été largement utilisées pour modéliser les problèmes de transport dans les sols poreux, les aquifères et les réservoirs. Ils réduisent ou évitent certains desproblèmes des méthodes eulériennes, par exemple instabilités, diffusion artificielle excessive, bilan massique et / ou oscillations pouvant conduire à des concentrations négatives. Cette thèsedéveloppe de nouvelles méthodes de particules lagrangiennes pour modéliser les phénomènes d'écoulement et de transport dans des milieux poreux complexes avec des hétérogénéités. Pour ce faire, cette thèse passe d'abord en revue les processus stochastiques et leurs relations avec l'équation (EDP) macroscopique d'Advection-Diffusion ADE. Cette mise en revue permet de trouver les conditions nécessaires à un processus stochastique pour que sa densité de probabilité vérifie l’équation EDP de Fokker-Planck et donc l’ADE. Cependant, l’une de ces conditions est la différentiabilité des coefficients de transport. Il est donc difficile de traiter les discontinuités et les hétérogénéités, en particulier la diffusion et la porosité discontinues. Dans la littérature sur les marches aléatoires de particules, les méthodes précédentes utilisées pour traiter ce problème de discontinuité nécessitaient de petits pas de temps afin de converger vers la solution attendue. Ces restrictions sur le pas de temps conduisent à des algorithmes inefficaces. Dans cette étude, nous proposons une nouvelle approche sans restrictions sur la taille des pas de temps. L’algorithme RWPT (Random Walk Particle Tracking) proposé ici est discret en temps et continu en espace (sans grille). Le nouvel algorithme RWPT est basé sur un pas de temps adaptatif « Stop&Go », combiné à des schémas de réflexion partielle/réfraction, et étendu à trois nouveaux concepts : particules de masse négative ; particules de masse adaptative ; et particules à tête chercheuse ("homing"). Les algorithmes en domaines infinis ont ensuite été généralisés au cas de domaines finis ou semi-infinis. Les conditions aux limites de Dirichlet (concentrations) sont particulièrement difficiles à mettre en œuvre dans les méthodes particulaires. Ainsi, cette thèse propose-t-elle différentes méthodes de mise en œuvre des conditions de Dirichlet avec l'algorithme RWPT utilisé pour traiter les discontinuités. Pour tester les nouveaux schémas RWPT Stop&Go, nous développons des solutions analytiques et semi-analytiques pour la diffusion en présence de multiples interfaces (milieu multicouche discontinu) dans des domaines infinis, semi-infinis et finis avec des conditions limites de Dirichlet. Les résultats montrent que les schémas RWPT Stop&Go proposés correspondent extrêmement bien aux solutions semi-analytiques, même pour des contrastes très forts des coefficients de diffusion et porosités, y compris au voisinage des interfaces. Ensuite, la méthode RWPT est appliquée pour étudier les processus de diffusion à différentes échelles dans des supports composites (systèmes grains/pores 2D). Une condition de flux nul est appliquée localement aux interfaces grain/pore. Au niveau macroscopique, la diffusion se produit dans un milieu homogène avec des paramètres macro-échelle (porosité et coefficients de diffusion effectifs) induits par des méthodes de montée d’échelle à l'aide des moments spatiaux d’ordre 2. L'algorithme RWPT est ensuite appliqué à des géométries plus complexes de grains et pores. Tout d’abord, différentes configurations ou structures micro-échelle sont choisies afin d'obtenir des milieux composites isotropes ayant différentes porosités. Puis, en choisissant des micro-structures allongées, des effets d’anisotropies apparaissent au niveau macroscopique. Les différentes méthodes proposées dans cette thèse pourraient être utilisées pour différents problèmes, chacune ayant ses inconvénients et ses avantages. Les schémas proposés semblent prometteurs dans la perspective d’extensions vers des géométries 3D plus complexesParticle methods have been extensively used for modeling transport problems in porous soils, aquifers, and reservoirs. They reduce or avoid some of the problems of Eulerian methods, e.g. instabilities, excessive artificial diffusion, mass balance, and/or oscillations that could lead to negative concentrations. This thesis develops a new class of gridless Lagrangian particle methods for modeling flow and transport phenomena in complex porous media with heterogeneities and discontinuities. Firstly, stochastic processes are reviewed, in relation to particle positions X(t) and to the corresponding macroscopic Advection-Diffusion Equation (ADE). This review leads to the conditions required for the Probability Density Function (PDF) of X(t) to satisfy the Fokker-Planck equation (and the ADE). However, one of these conditions is the differentiability of transport coefficients: therefore, discontinuities are difficult to treat, particularly discontinuous diffusion D(x) and porosity q(x). In the literature on particle Random Walks, the methods used to handle discontinuous diffusion required excessively small time steps. These restrictions on the time step lead to inefficient algorithms. In this study, we propose a novel approach without restrictions on time step size. The novel RWPT (Random Walk Particle Tracking) algorithms proposed here are discrete in time and continuous in space (gridless). They are based on an adaptive “Stop&Go” time-stepping, combined with partial reflection/refraction schemes, and extended with three new concepts: negative mass particles; adaptive mass particles; and “homing” particles. To test the new Stop&Go RWPT schemes in infinite domains, we develop analytical and semi-analyticalsolutions for diffusion in the presence of multiple interfaces (discontinuous multi-layered medium) in infinite domains. The results show that the proposed Stop&Go RWPT schemes (with adaptive, negative, or homing particles) fit extremely well the semi-analytical solutions, even for very high contrasts for transport properties even in the neighborhood of the interfaces. The schemes provide a correct diffusive solution in only a few macro-steps (macroscopic time steps), with a precision that depends only on the number of particles, and not on the macro-step. The algorithms are then, extended from infinite to semi-infinite and finite domains. Dirichlet conditions are particularly difficult to implement in particle methods. Thus, in this thesis we propose different methods on how to implement Dirichlet boundary conditions with the “discontinuous” RWPT algorithm. This study proposes an algorithm to solve diffusion equations semi-analytically in heterogeneous semi-infinite and finite domains with Dirichlet boundary conditions. The RWPT Dirichlet methods are then checked analytically and verified for various configurations. Finally, the RWPT method is applied for studying diffusion at different scales in 2D composite media (grain/pore systems). A zero-flux condition is assumed locally at the grain/pore interfaces. At the macro-scale, diffusion occurs in an equivalent effective homogeneous medium with macroscopic parameters (porosity and effective diffusion coefficients) obtained from the temporal evolution of second order moments. The RWPT algorithm is then applied to more complex geometries of grains and pores. Different configurations or structures at the micro-scale level will be chosen in order to obtain composite isotropic media at the macro-scale level with different porosities. Then, by choosing elongated micro-structures, anisotropy effects emerge at the macroscopic level. Effective macro-scale properties (porosities, effective diffusion tensors, tortuosities) are calculated using the second order moment. The different methods proposed in this thesis can be used for different problems, since each has its drawbacks and advantages. The schemes proposed seem promising with a view to extensions towards more complex 3D geometries
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Hellström, J. Gunnar I. "Parallel computing of fluid flow through porous media /." Luleå : Luleå University of Technology, 2007. http://epubl.ltu.se/1402-1757/2007/06/.
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Amikiya, Emmanuel Adoliwine. "Flow and reactive transport processes in porous media." Thesis, Stellenbosch : Stellenbosch University, 2013. http://hdl.handle.net/10019.1/85838.
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Thesis (MSc)--Stellenbosch University, 2013.ENGLISH ABSTRACT: Flow and reactive transport of chemical species is a very common phenomenon that occurs in natural and artificial systems. However in this study, the topic is related to acid mine drainage in the South African mining environment. Due to the hazards associated with acid mine drainage, prevention or treatment of mine effluent water before discharging to receiving waters and other environments is a necessity. A new time-dependent mathematical model is developed for a passive treatment method, based on multi-scale modelling of the coupled physico-chemical processes such as diffusion, convection, reactions and filtration, that are involved in the treatment process. The time-dependent model is simulated on a two-dimensional domain using finite volume discretization to obtain chemical species distributions.
AFRIKAANSE OPSOMMING: Vloei en reagerende transport van chemiese spesies is ’n baie algemene verskynsel wat in natuurlike en kunsmatige stelsels plaasvind. In hierdie studie is die onderwerp egter verwant aan suurmyndreinering in die Suid-Afrikaanse mynbou-omgewing. As gevolg van die gevare wat verband hou met suurmyndreinering, is die voorkoming of die behandeling van die afval-mynwater voor dit in opvangswaters en ander omgewings beland ’n noodsaaklikheid. ’n Nuwe tydafhanklike wiskundige model vir ’n passiewe behandelingsmetode is ontwikkel. Dit is gebaseer op die multi-skaal modulering van gekoppelde fisies-chemiese prosesse soos diffusie, konveksie, reaksies en filtrasie, wat by die behandelingsproses betrokke is. Die tydafhanklike model word gesimuleer op ’n twee-dimensionele domein met behulp van eindige volume diskretisasie om die verspreiding van chemiese spesies te bepaal.
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Böttcher, Norbert. "Thermodynamics of porous media: non-linear flow processes." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-137894.
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Numerical modelling of subsurface processes, such as geotechnical, geohydrological or geothermal applications requires a realistic description of fluid parameters in order to obtain plausible results. Particularly for gases, the properties of a fluid strongly depend on the primary variables of the simulated systems, which lead to non-linerarities in the governing equations. This thesis describes the development, evaluation and application of a numerical model for non-isothermal flow processes based on thermodynamic principles. Governing and constitutive equations of this model have been implemented into the open-source scientific FEM simulator OpenGeoSys. The model has been verified by several well-known benchmark tests for heat transport as well as for single- and multiphase flow. To describe physical fluid behaviour, highly accurate thermophysical property correlations of various fluids and fluid mixtures have been utilized. These correlations are functions of density and temperature. Thus, the accuracy of those correlations is strongly depending on the precision of the chosen equation of state (EOS), which provides a relation between the system state variables pressure, temperature, and composition. Complex multi-parameter EOSs reach a higher level of accuracy than general cubic equations, but lead to very expansive computing times. Therefore, a sensitivity analysis has been conducted to investigate the effects of EOS uncertainties on numerical simulation results. The comparison shows, that small differences in the density function may lead to significant discrepancies in the simulation results. Applying a compromise between precision and computational effort, a cubic EOS has been chosen for the simulation of the continuous injection of carbon dioxide into a depleted natural gas reservoir. In this simulation, real fluid behaviour has been considered. Interpreting the simulation results allows prognoses of CO2 propagation velocities and its distribution within the reservoir. These results are helpful and necessary for scheduling real injection strategiesFür die numerische Modellierung von unterirdischen Prozessen, wie z. B. geotechnische, geohydrologische oder geothermische Anwendungen, ist eine möglichst genaue Beschreibung der Parameter der beteiligten Fluide notwendig, um plausible Ergebnisse zu erhalten. Fluideigenschaften, vor allem die Eigenschaften von Gasen, sind stark abhängig von den jeweiligen Primärvariablen der simulierten Prozesse. Dies führt zu Nicht-linearitäten in den prozessbeschreibenden partiellen Differentialgleichungen. In der vorliegenden Arbeit wird die Entwicklung, die Evaluierung und die Anwendung eines numerischen Modells für nicht-isotherme Strömungsprozesse in porösen Medien beschrieben, das auf thermodynamischen Grundlagen beruht. Strömungs-, Transport- und Materialgleichungen wurden in die open-source-Software-Plattform OpenGeoSys implementiert. Das entwickelte Modell wurde mittels verschiedener, namhafter Benchmark-Tests für Wärmetransport sowie für Ein- und Mehrphasenströmung verifiziert. Um physikalisches Fluidverhalten zu beschreiben, wurden hochgenaue Korrelationsfunktionen für mehrere relevante Fluide und deren Gemische verwendet. Diese Korrelationen sind Funktionen der Dichte und der Temperatur. Daher ist deren Genauigkeit von der Präzision der verwendeten Zustandsgleichungen abhängig, welche die Fluiddichte in Relation zu Druck- und Temperaturbedingungen sowie der Zusammensetzung von Gemischen beschreiben. Komplexe Zustandsgleichungen, die mittels einer Vielzahl von Parametern an Realgasverhalten angepasst wurden, erreichen ein viel höheres Maß an Genauigkeit als die einfacheren, kubischen Gleichungen. Andererseits führt deren Komplexität zu sehr langen Rechenzeiten. Um die Wahl einer geeigneten Zustandsgleichung zu vereinfachen, wurde eine Sensitivitätsanalyse durchgeführt, um die Auswirkungen von Unsicherheiten in der Dichtefunktion auf die numerischen Simulationsergebnisse zu untersuchen. Die Analyse ergibt, dass bereits kleine Unterschiede in der Zustandsgleichung zu erheblichen Abweichungen der Simulationsergebnisse untereinander führen können. Als ein Kompromiss zwischen Einfachheit und Rechenaufwand wurde für die Simulation einer enhanced gas recovery-Anwendung eine kubische Zustandsgleichung gewählt. Die Simulation sieht, unter Berücksichtigung des Realgasverhaltens, die kontinuierliche Injektion von CO2 in ein nahezu erschöpftes Erdgasreservoir vor. Die Interpretation der Ergebnisse erlaubt eine Prognose über die Ausbreitungsgeschwindigkeit des CO2 bzw. über dessen Verteilung im Reservoir. Diese Ergebnisse sind für die Planung von realen Injektionsanwendungen notwendig
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Goudie, Jillian M. "Mathematical analysis of fluid flow through porous media." Thesis, University of the West of Scotland, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.283398.
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Phillips, Andrew. "Two phase flow in rapidly rotating porous media." Thesis, University of Nottingham, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.289324.
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Momken, Bahareh. "Fluid flow and deformation in composite porous media /." Full text (PDF) from UMI/Dissertation Abstracts International, 2000. http://wwwlib.umi.com/cr/utexas/fullcit?p3004343.
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Molale, Dimpho Millicent. "A computational evaluation of flow through porous media." Thesis, Link to the online version, 2007. http://hdl.handle.net/10019/686.
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Chaturvedi, Praveen. "Single phase multicomponent flow simulation in porous media." Ann Arbor, Mich. : ProQuest, 2008. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3307176.
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Thesis (Ph.D. in Applied Mathematics)--S.M.U.Title from PDF title page (viewed Mar. 16, 2009). Source: Dissertation Abstracts International, Volume: 69-04, Section: B, page: 2354. Adviser: Zhangxin Chen. Includes bibliographical references.
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SILVA, MARCOS AURELIO CITELI DA. "WATER AND OIL FLOW SIMULATION IN POROUS MEDIA." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2002. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=4779@1.
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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIORMuitos problemas provenientes do mundo real podem ser modelados por sistemas de equações diferenciais parciais (EDP´s). No entanto, as equações resultantes da discretização produzem matrizes grandes e freqüentementes mal condicionadas. Este trabaho implementa o método de elementos finitos mistos para resolver numericamente um sistema de EDP´s oriundo de um modelo de escoamento de fluidos em meios porosos e melhora sua performance usando precondicionadores e processamento paralelo.
Many problems arising from real world can be represented by systems of partial diferential equations (PDE´s). However, the resulting discrete equations produce large and frequently bad conditioned matrices. This work implements the mixed finite element method to numerically solve a system of PDE´s coming from a multiphase flow in porous media model and improve its performance by preconditioners and parallel processing.
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HUERTAS, JACKELINE ROSEMERY C. "NUMERICAL MODELING OF 3D FLOW IN POROUS MEDIA." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2006. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=9948@1.
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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIORSimulações numéricas tendem a simplificar o comportamento de problemas reais, na maioria das vezes pela adoção de um modelo 2D para descrição da resposta hidráulico-mecânica de barragens de terra, escavações, fundações, etc., com base na maior facilidade da construção geométrica de malhas, rapidez de processamento, simplicidade na introdução das condições de contorno, menor dificuldade na obtenção dos parâmetros de engenharia, etc. Entretanto, para certos fenômenos como o fluxo através de barragem em vales estreitos ou no rebaixamento do lençol freático para execução de escavações para construção de fundações, os efeitos tridimensionais podem afetar consideravelmente os resultados obtidos com uma solução simplificada, seja em termos de vazão, cargas, gradientes hidráulicos ou fatores de segurança. Esta dissertação tem como objetivo principal analisar problemas de fluxo, na condição transiente e/ou permanente, considerando solos saturados e parcialmente saturados, em simulações 2D e 3D pelo método dos elementos finitos buscando destacar as principais diferenças entre as respostas obtidas, ressaltando as principais vantagens e dificuldades da realização de uma simulação 3D em relação a uma análise simplificada 2D. Os exemplos numéricos abordados neste trabalho se referem à barragem de terra Macusani, no Peru, à escavação realizada para construção das estruturas da Pequena Central Elétrica Canoa Quebrada - MT e ao rebaixamento do lençol freático para construção das fundações do shopping Brooklin na cidade de São Paulo - SP.
Numerical simulations tend to simplify the behavior of real problems, mainly through the choice of 2D models to describe the hydromechanical responses of earth dams, excavations, foundations, etc., partly because it is easier to construct geometrical meshes, it is simpler to impose the required boundary conditions, the computer calculations are done more rapidly and the estimation of the engineering parameters, either through field or laboratory tests, are less difficulty than it would be if the problem was treated as a complete 3D case. However, for certain phenomena such as the flow of water through dams situated in narrow valleys or the water drawdown in excavations for construction of building foundations, 3D effects can considerably affect the results when compared to a simplified 2D solution, either in terms of quantity of flow, hydraulic heads and gradients, security factors, etc. The main goal of this dissertation is the analysis of flow problems, both in transient and permanent conditions, considering fully saturated or partially saturated soils, employing 2D and 3D numerical models based on the finite element method in order to highlight the main differences between the computed answers, emphasizing the advantages and difficulties of both approaches. The numerical examples studied in this work are the earth dam Macusani, situated in Peru, the excavation carried out for the construction of the structures in the small hydroelectric plant Canoa Quebrada - MT, and groundwater drawdown for the execution of the foundations of the Brooklin shopping mall, in the city of São Paulo - SP.
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Armitage, Paul. "Foam flow through porous media : a micromodel study." Thesis, Imperial College London, 1991. http://hdl.handle.net/10044/1/46650.
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Gray, Farrel. "Simulating flow and reactive transport in porous media." Thesis, Imperial College London, 2016. http://hdl.handle.net/10044/1/51505.
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In this work, we developed and applied computational methods for simulating flow, transport and reactive transport in porous media. This comprised four main components: single-phase flow calculation; chemical transport calculation; the coupling to reaction kinetics at mineral surfaces and resulting structural changes; and the use of parallel and GPU computing to make the calculation practicable on realistic rock geometries. Single phase flow was calculated using the Lattice Boltzmann (LB) method. We used the multi-relaxation-time (MRT) operator for its superior stability and viscosity-independence. A sparse memory approach was employed which improves the efficiency of calculations performed on low-permeability rock pore-space images. We also extended an idea proposed by Skordos in which the lattice Boltzmann densities were transformed to increase the number of floating point bits retained in the calculation. We showed that this enhances the numerical precision of the calculation considerably, where the original paper found no appreciable benefit. We showed how this now permits the 4-byte datatype to be used reliably in slow flowing, heterogeneous domains. The LB algorithm was implemented for the use of parallel GPUs (Graphics Processors) using the MPI (Message Passing Interface) and shown to give strong scaling on a cluster of 24 Tesla K40 GPUs. A study of single phase permeability on micro-CT images of sandstone and carbonate rock pore structures of varying degrees of heterogeneity was carried out. Good agreement with experiment was found for the simpler pore spaces, while discrepancies in the micro-porous samples was attributed to two causes: 1) the exclusion of flow through unresolved micro-porosity and 2) unrepresentative sample sizes used in the simulation. The effect of image resolution and segmentation was studied by comparing single phase permeability computed in 1) scans of the same volume obtained at different voxel sizes, individually segmented and 2) numerically coarsened images from a high resolution segmented image. Numerical coarsening from a high resolution segmented image was found to be much more consistent than 1) and was shown to preserve porosity and permeability down to lower voxel size images unlike the images scanned and segmented at different voxel sizes. Finally, representative elementary volume (REV) was investigated for the rock samples. A statistical method was used in which porosity and permeability were obtained from sub-volumes sampled from the domain. The convergence of these parameters with sub-volume size was used to obtain characteristic length scales and measures of heterogeneity. The image sizes used were found to be unrepresentative for the complex microporous carbonates. Transport curves (propagators) were computed in three different porous media samples of increasing heterogeneity (a bead-pack; sandstone; and carbonate) and found to agree with experiment. Questions about the origins of stagnant transport zones in the microporous carbonate were pursued by investigating the effects of image segmentation. The effects of the image segmentation techniques, in which grey-scale micro-porosity in a scanned pore image is binarised into fluid or mineral, were quantified by computing the fraction of trapped solute (stagnant zones) for segmentations of varying porosity. Physical differences between experiment and calculation were clarified, and we suggest alternative approaches for the treatment of micro-porous rocks. A pore-scale reactive flow model was put together by coupling flow calculation and solute transport methods with changes in pore-structure through chemical kinetics. Convection and diffusion in this model was solved using a finite-volume approach: a second order transport model with a flux limiter function made the model suitable for high Peclet number transport calculations. We also proposed a method for counteracting errors associated with the staircase representation of diagonal surfaces in the Cartesian grid in which exposed grid surfaces are associated with a rescaling factor. First order reaction kinetics were included at mineral surfaces and the dissolution of a sphere was shown to give different dissolution profiles with different dimensionless transport and reaction parameters. The dissolution model was applied to the reaction between HCl acid and calcite mineral under the assumption that products of the reaction could be neglected. An experimental system in which HCl acid was injected through a flow cell containing a calcite block was simulated and the normalised volume of undissolved calcite was compared with the experimental data, as well as resulting morphologies obtained by micro-CT scanning. Good agreement with the experimental dissolution rate was obtained, however some differences in the resulting morphologies were found. This was attributed to neglecting the influence of product ions on the diffusion behaviour of the reactant and was discussed. By obtaining the concentration of H+ reactant on the surface of calcite block, the process could be concluded to be strongly transport-controlled. This enabled the definition of a new effective Damkohler number in terms of the reactant surface concentration which no longer required approximating length scales or separating convection or diffusion rates. Finally, the dissolution of a Ketton carbonate sample was computed. The injection process mirrored that of a strong acid flowing through the pore-space at a given flow rate, and having an intrinsic surface reaction rate with the rock mineral. It was found that the flow rate strongly affected the resulting dissolution pattern, in line with experimental observation. This lead to drastically altered flow properties, including single-phase permeability which was quantified.
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Van, Genabeek Olav (Olav Arnold). "Velocity fluctuations in slow flow through porous media." Thesis, Massachusetts Institute of Technology, 1998. http://hdl.handle.net/1721.1/58059.
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Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences, 1998.Includes bibliographical references (p. 65-70).
In this thesis, I study the spatial statistical properties of slow flow through porous media on the pore scale by a combination of numerical simulation and theoretical arguments. I demonstrate that the flow patterns undergo a transition from swirls to strongly focused and channel-like patterns for decreasing porosities. Not only is the flow in low-porosity media strongly focused, but the flow also possesses long-tailed, non-Gaussian velocity probability density distributions. A main result of our simulations is that the statistics of the flow through a single channel captures the entire flow, insofar as the patterns and probability distributions are concerned. I have constructed a simplified, phenomenological model for the fast part of the flow in random porous media. This model yields the desired exponential velocity distributions. For high porosities, I find that the statistical properties of the velocity fluctuations behave in a similar way as those observed in dilute suspensions flows: the swirls have a power-law dependency on the solid volume fraction, the correlation length is finite and has also a power-law dependency. I demonstrate that this scaling behavior is consistent with the predictions of theories. Finally, I study creeping flow through a single rough walled channel by numerical simulation and present a theory that predicts scale dependency of the permeability for tight fractures.
by Olav van Genabeek.
Ph.D.
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Essiam, Albert K. "Stochastic flow and transport through multifractal porous media." Thesis, Massachusetts Institute of Technology, 2001. http://hdl.handle.net/1721.1/84301.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2001.Includes bibliographical references.
Stochastic theories of flow and transport in aquifers have relied on the linear perturbation approach that is accurate for flow fields with log-conductivity variance cr2 less than unity. Several studies have found that the linear perturbation ignores terms that have significant effects on the spectra of the hydraulic gradient VH and specific discharge q when (Y2 exceeds unity. In this thesis we study flow and transport when the hydraulic conductivity K is an isotropic lognormal multifractal field. Unlike the perturbation approach, results obtained are nonlinear even though several simplifying assumptions are made. The spectral density of F = in (K) for this type of field is SF (k) o kl-D where D is the space dimension. It is found that under this condition, the hydraulic gradient VH and specific discharge q are also multifractal; whose renormalization properties under space contraction involve random scaling and random rotation of the fields. Analytical expressions that are functions of D and the codimension parameter of F, CK 'are obtained for the renormalization properties and marginal distributions of VH and q . Because of the boundary conditions, the fields VH and q are anisotropic at large scales but become isotropic at very small scales. The mean specific flow decreases as the scaling range of F increases, at a rate that is dependent on D and CK. Flow simulations on a plane validate the analytical results. The multifractal properties of VH and q are used to derive their spectral density tensors, the macrodispersivities, and the effective conductivity of the medium. The spectra obtained account for the random rotation of the VH and q at smaller scales. Spectra for VH and q are anisotropic at large scales but become isotropic at small scales.
(cont.) The scale of isotropy depends on D and CK. The linear perturbation approach does not capture this important feature and further gives incorrect amplitudes and power decays of the spectral density tensors. Using the spectra of q the macrodispersivities are computed and compared with results from the linear perturbation approach. Reflecting the properties of the spectral density of q, the macrodispersivities for the nonlinear theory are isotropic at small travel distances and are anisotropic at large travel distances. In the ergodic case when the spatial averages of all fields of interest are close to their ensemble averages, it is found that our expression for effective conductivity Keff corresponds to a formula conjectured by Matheron [1967]. Using the scaling properties of the inverse of the velocity field (also known as slowness), we derive expressions for the first passage time distribution FPTD and mean plume concentration for transport in a multifractal K field. The theoretical results of FPTD for the nonlinear theory are fitted by regression methods to data from field experiments and from numerical simulations and compared with results from the continuous time random walk CTRW and two-phase transport model. Results of the nonlinear theory are found to be more suitable for predicting non-Fickian transport. The CTRW model is more suited for transport in statistically inhomogeneous media. Both the CTRW and two-phase models are suitable for modeling Fickian transport ...
by Albert Essiam.
Ph.D.
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Zhu, Junlin. "Effective properties for flow in heterogeneous porous media." Diss., Virginia Tech, 1990. http://hdl.handle.net/10919/39416.
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Snyder, Kevin P. "Multiphase flow and mass transport through porous media." Thesis, Virginia Tech, 1993. http://hdl.handle.net/10919/40658.
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Hellström, Gunnar. "Parallel computing of fluid flow through porous media." Licentiate thesis, Luleå tekniska universitet, Strömningslära och experimentell mekanik, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-25857.
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Fluid flow through porous media takes place in a variety of technical areas including ground water flow, flow through embankment dams, paper making, composites manufacturing, filtering, drying and sintering of iron ore pellets. When modelling these kinds of flows it is common practice to use averaging techniques rather than computing the detailed flow field in every single pore. This approach is very efficient when averaged quantities are sough for but it is not very convenient for local problems such as forces on particles within an embankment dam and drying of individual iron ore pellets. In this thesis the focus is set on the former and how such forces alter as a function of Reynolds number. Of particular interest are the effects of inertia and turbulence and when they need to be considered. For problem like this a Computational Fluid Dynamics (CFD) approach is well suited since rather complex geometries and flow conditions can be studied by using parallel computing techniques. By using this technique it is also possible to determine at which flow regimes Darcy law is applicable and thus when more elaborate descriptions of the flow like the Forchheimer equation and the Navier-Stokes equations need to be applied. In order to isolate the question above and be able to use advanced models for turbulence a neat geometry is applied being an array of quadratic packed cylinders. To start with the parallel computing capacity of the in-house cluster is scrutinized showing very promising results with up to almost full scalability. Following this study focus is set on the porous media and when inertia-effects need to be taken into account. The significance of this phenomenon turns out to be when Reynolds number is above 10. Then a study in when the flow has to be solved with a full turbulent description has been carried out with the results that as the Reynolds number increases above 100 the significance is clear. In addition a manuscript for a state of the art literature survey is appended.Godkänd; 2007; 20070213 (pafi)
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Humby, Steven John. "Modelling of flow and colloids in porous media." Thesis, University of Surrey, 1999. http://epubs.surrey.ac.uk/844200/.
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Porous media and transport within them play technically important roles in many of our industries. However, classical mean field engineering descriptions used to model the complex interactions between the porous medium and the fluids and colloids within it are not completely satisfactory. The design capability of the engineering community would be greatly enhanced if these models could be more clearly linked to the mesoscopic details of the fluid/suspension/porous solid systems. This would allow cheaper, yet quicker, and more innovative design and optimization of systems involving fluid/suspension flow in porous media. Modern techniques for the explicit mesoscopic modelling of porous media, and fluid and colloid transport within them, have developed to a point where their combination in a single simulation tool can be contemplated. However, at present, no such tool exists. The aim of this study was to design and test a comprehensive simulation tool that could accurately model the transport phenomena of any given fluid and colloidal system within any given porous medium at a mesoscopic level. Lattice gas automata (LGA) modelling techniques for fluid and colloid transport, and the Joshi/Quiblier/Adler (JQA) statistical method for reconstructing porous media, were uniquely combined to achieve this. The results of simulations were compared to measurements obtained using an experimental apparatus. The objectives of the study were to: 1) determine a priori the permeability of porous media, and; 2) simulate deposition phenomena observed experimentally. The study showed that permeabilities predicted using the simulation tool were lower than those determined experimentally. Several causes for this were identified, all of which can be addressed in the short-term. Simulated changes in fluid velocity and particle concentration were found to alter the rate and pattern of deposition in a manner consistent with experimental results. Furthermore, the tool provided a rich description of fundamental physical phenomena at the pore scale level. These preliminary findings indicate that the combination of these models provide the basis for further development leading to a mesoscopic modelling tool capable of predicting fluid and colloid transport in porous media.
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Franc, Jacques. "Two-phase flow properties upscaling in heterogeneous porous media." Phd thesis, Toulouse, INPT, 2018. http://oatao.univ-toulouse.fr/21684/1/FRANC_Jacques.pdf.
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The groundwater specialists and the reservoir engineers share the same interest in simulating multiphase flow in soil with heterogeneous intrinsic properties. They also both face the challenge of going from a well-modeled micrometer scale to the reservoir scale with a controlled loss of information. This upscaling process is indeed worthy to make simulation over an entire reservoir manageable and stochastically repeatable. Two upscaling steps can be defined: one from the micrometer scale to the Darcy scale, and another from the Darcy scale to the reservoir scale. In this thesis, a new second upscaling multiscale algorithm Finite Volume Mixed Hybrid Multiscale Methods (Fv-MHMM) is investigated. Extension to a two-phase flow system is done by weakly and sequentially coupling saturation and pressure via IMPES-like method.
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Birkevold, Jens. "Divergence-free Isogeometric Methods for Flow in Porous Media." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2012. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-19546.
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This thesis is focused on solving the Darcy flow problem using divergence-free isogeometric methods, and comparing these results to the ones obtained using traditional finite element methods with Taylor Hood elements. A short introduction to B-splines is given, and a chapter is also about using repeated knots in the knot vectors to obtain a discontinuous basis for the finite element method. This can be useful when dealing with varying permeabilities.
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Pathak, Mihir Gaurang. "Periodic flow physics in porous media of regenerative cryocoolers." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/49056.
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Pulse tube cryocoolers (PTC) are a class of rugged and high-endurance refrigeration systems that operate without moving parts at their low temperature ends, and are capable of reaching temperatures down to and below 123 K. PTCs are particularly suitable for applications in space, guiding systems, cryosurgery, medicine preservation, superconducting electronics, magnetic resonance imaging, weather observation, and liquefaction of gases. Applications of these cryocoolers span across many industries including defense, aerospace, biomedical, energy, and high tech. Among the challenges facing the PTC research community is the improvement of system efficiency, which is a direct function of the regenerator component performance. A PTC implements the theory of oscillatory compression and expansion of the gas within a closed volume to achieve desired refrigeration. An important deficiency with respect to the state of art models dealing with PTCs is the limited understanding of the hydrodynamic and thermal transport parameters associated with periodic flow of a cryogenic fluid in micro-porous structures. In view of the above, the goals of this investigation include: 1) experimentally measuring and correlating the steady and periodic flow Darcy permeability and Forchheimer’s inertial hydrodynamic parameters for available rare-Earth ErPr regenerator filler; 2) employing a CFD-assisted methodology for the unambiguous quantification of the Darcy permeability and Forchheimer’s inertial hydrodynamic parameters, based on experimentally measured steady and periodic flow pressure drops in porous structures representing recently developed regenerator fillers; and 3) performing a direct numerical pore-level investigation for steady and periodic flows in a generic porous medium in order to elucidate the flow and transport processes, and quantify the solid-fluid hydrodynamic and heat transfer parameters. These hydrodynamic resistances parameters were found to be significantly different for steady and oscillatory flows.
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Reichenberger, Volker. "Numerical simulation of multiphase flow in fractured porous media." [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=970266049.
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Henry, Eric James. "Contaminant induced flow effects in variably-saturated porous media." Diss., The University of Arizona, 2001. http://hdl.handle.net/10150/191256.
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Dissolved organic contaminants that decrease the surface tension of water (surfactants) can have an effect on unsaturated flow through porous media due to the dependence of capillary pressure on surface tension. One and two-dimensional (1D, 2D) laboratory experiments and numerical simulations were conducted to study surfactant-induced unsaturated flow. The 1D experiments investigated differences in surfactant-induced flow as a function of contaminant mobility. The flow in a system contaminated with a high solubility, mobile surfactant, butanol, was much different than in a system contaminated with a sparingly soluble, relatively immobile surfactant, myristyl alcohol (MA). Because surface tension depression caused by MA was confined to the original source zone, the MA system was modeled using a standard unsaturated flow model (HYDRUS-1D) by assigning separate sets of hydraulic functions to the initially clean and source zones. To simulate the butanol system, HYDRUS-1D was modified to incorporate surfactant concentration-dependent changes to the moisture content-pressure head and unsaturated hydraulic conductivity functions. Following the 1D study, a two-dimensional flow cell (2.4 x 1.5 x 0.1 m) was used to investigate the infiltration of a surfactant contaminant plume from a point source on the soil surface, through the vadose zone, and toward a shallow aquifer. Above the top of the capillary fringe the advance of the surfactant solution caused a drainage front that radiated from the point source. Upon reaching the capillary fringe, the drainage front caused a localized depression of the capillary fringe and eventually a new capillary fringe height was established. Horizontal transport of surfactant in the depressed capillary fringe caused the propagation of a wedge-shaped drainage front in the downgradient direction. The numerical model HYDRUS-2D was modified to account for surfactant concentration-dependent effects on the unsaturated hydraulic functions and was successfully used to simulate the surfactant infiltration experiment. The extensive propagation of the drying front and the effect of vadose zone drainage on contaminant breakthrough time demonstrate the potential importance of considering surface tension effects on unsaturated flow and transport in systems containing surface-active organic contaminants or in systems where surfactants are used for remediation of the vadose zone or unconfined aquifers.
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Malcolm, Lorna Taryn. "Multiphase flow in porous media at low interfacial tension." Thesis, University of Oxford, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.362036.
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Mirzaei, Mahsanam. "Dynamic effects on two-phase flow in porous media." Thesis, University of Oxford, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.640167.
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A correct description of multiphase flow behaviour in a porous media involves the determination of various fluid and porous media parameters and, a constitutive relationship among capillary pressure (Pc), saturation (S) and relative permeability (kr). The determination of a Pc-S relationship is difficult because of two effects: (i) presence of heterogeneities in the domain and (ii) the dynamic effects in Pc-S relationships. While the significance of the individual factors has been studied at various scales using different approaches, the combination of the two effects on Pc-S relationships is not well characterised.
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Hellman, Fredrik. "Multiscale and multilevel methods for porous media flow problems." Licentiate thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-262276.
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We consider two problems encountered in simulation of fluid flow through porous media. In macroscopic models based on Darcy's law, the permeability field appears as data. The first problem is that the permeability field generally is not entirely known. We consider forward propagation of uncertainty from the permeability field to a quantity of interest. We focus on computing p-quantiles and failure probabilities of the quantity of interest. We propose and analyze improved standard and multilevel Monte Carlo methods that use computable error bounds for the quantity of interest. We show that substantial reductions in computational costs are possible by the proposed approaches. The second problem is fine scale variations of the permeability field. The permeability often varies on a scale much smaller than that of the computational domain. For standard discretization methods, these fine scale variations need to be resolved by the mesh for the methods to yield accurate solutions. We analyze and prove convergence of a multiscale method based on the Raviart–Thomas finite element. In this approach, a low-dimensional multiscale space based on a coarse mesh is constructed from a set of independent fine scale patch problems. The low-dimensional space can be used to yield accurate solutions without resolving the fine scale.
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Terblanche, Luther. "The prediction of flow through two-dimensional porous media." Thesis, Stellenbosch : University of Stellenbosch, 2006. http://hdl.handle.net/10019.1/1722.
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Thesis (MScEng (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2006.When considering flow through porous media, different flow regimes may be identified. At very small Reynolds numbers the relation between the pressure gradient and the velocity of the fluid is linear. This flow regime ...
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Dyrdahl, Joachim. "Thermal flow in fractured porous media and operator splitting." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2014. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-25927.
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Thermal flow in fractured porous medium is an area of interest for both the oil and the geothermal energy industry. The mathematical model consists of multiple equations, often various conservation laws and constitutive relations. Solving these equations simultaneously is called the fully implicit approach, an alternative is sequential splitting. We investigate and compare these approaches, applied on incompressible and compressible cases of single-phase and two-phase fluid flow. The experiments show that the difference of the solutions between our approaches is small, and that the results from the sequentially split solver are obtained significantly faster than the fully implicit solver scheme.
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Jamiolahmady, Mahmoud. "Mechanistic modelling of gas-condensate flow in porous media." Thesis, Heriot-Watt University, 2001. http://hdl.handle.net/10399/532.
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Huang, Yaduo. "The flow behaviour of xanthan biopolymer in porous media." Thesis, Heriot-Watt University, 1993. http://hdl.handle.net/10399/1456.
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Bristow, Robert Philip. "Micromodels of immiscible two-phase flow in porous media." Thesis, University of Cambridge, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.235763.
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The research is a study on the microscopic scale of the immiscible displacement of oil by water in a porous medium such as sandstone. Of particular interest (with application to the oil industry) are the residual saturation of oil, the permeability to water at residual oil saturation and the maximum trapped blob size. Initially the effects of gravity, surface tension and distribution of pore sizes were studied in a computer simulation of a buoyancy driven, quasi-static invasion. The rock was modelled as a three-dimensional lattice of spherical pores connected by narrow cylindrical throats. With the rock water-wet, the tendency of the surface tension to favour the invasion of smaller pores led to a larger residual oil saturation by pore volume than by pore numbers. Also bourne out were some scaling arguments based on percolation theory for the maximum trapped blob size as a function of the relative strength of buoyancy and surface tension forces. The second part of the research investigated the interaction of viscous and surface tension forces. As this is a much more complicated problem, involving the solution of flow equations, the invasion process was first simulated with exact equations of motion on small networks (up to 10x10), where surface tension effects dominate. From these simulations a simplified set of rules was developed to determine which pore in a locality on the oil-water interface is invaded and how long the invasion takes. These rules include a viscous correction to the dominant surface tension forces. Finally, some theory has been developed for the inclusion of the small-scale analysis into a larger model, allowing a full simulation of the viscous dominated invasion to be performed.
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Kim, Sung-Min. "Numerical investigation on laminar pulsating flow through porous media." Thesis, Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/22601.
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Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2008.Committee Co-Chair: Dr. S. Mostafa Ghiaasiaan; Committee Co-Chair: Dr. S.I. Abdel-Khalik; Committee Member: Dr. Sheldon M. Jeter.
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Petrasch, Jörg. "Multi-scale analyses of reactive flow in porous media." kostenfrei, 2007. http://e-collection.ethbib.ethz.ch/view/eth:29641.
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Jacobs, Bruce Lee. "Effective properties of multiphase flow in heterogeneous porous media." Thesis, Massachusetts Institute of Technology, 1998. http://hdl.handle.net/1721.1/9697.
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Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, February 1999.Includes bibliographical references (leaves 218-224).
The impact of heterogeneity on multiphase fl.ow is explored using a spectral perturbation technique employing a stationary, stochastic representation of the spatial variability of soil properties. A derivation of the system's effective properties - nonwetting phase moisture content, capillary pressure, normalized saturation and permeability - was developed which is not specific as to the form of the permeability dependence on saturation or capillary pressure. This lack of specificity enables evaluation and comparison of effective properties with differing characterization forms. Conventional characterization techniques are employed to parameterize the saturation, capillary pressure, relative permeability relationships and applied to the Cape Cod and Borden aquifers. An approximate solution for the characteristic width of a dense nonaqueous phase liquid (DNAPL) plume or air sparging contributing area is derived to evaluate the sensitivity of system behavior to properties of input processes. Anisotropy is predicted for uniform, vertical flow in the Borden Aquifer consistent with both prior experimental observations and Monte Carlo simulations. Increases of the mean capillary pressure (increasing nonwetting phase saturation) is accompanied by reductions in nonwetting phase anisotropy. Similar levels of anisotropy are not found in the case of the Cape Cod aquifer; the difference is attributed largely to the mean value of the log of the characteristic pressure which is shown to control the rate of return to asymptotic permeability and hence system uniformity. A positive relation between anisotropy and interfacial tension was observed, consistent with prior numerical simulations. Positive dependence of lateral spreading on input fl.ow rate is predicted for Cape Cod Aquifer with reverse response at Borden Aquifer due to capillary pressure dependent anisotropy of Borden Aquifer. The effective permeability for horizontal fl.ow with core scale heterogeneity was found to be velocity dependent with features qualitatively similar to experimental observations and numerical experiments. Application of Leverett scaling as generally implemented in Monte Carlo simulations under represents aquifer hetero geneity and for the Borden Aquifer, van Genuchten characterization reduces system anisotropy by several orders of magnitude. Anisotropy of the effective properties proved to be less sensitive to Leverett scaling if the Brooks-Corey characterization was used due to insensitivity in this case to the variance of the slope parameter.
by Bruce L. Jacobs.
Ph.D.
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Nitsche, Ludwig C. (Ludwig Carlos). "Multiphase flow through spatially periodic models of porous media." Thesis, Massachusetts Institute of Technology, 1989. http://hdl.handle.net/1721.1/111043.
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