Dissertations / Theses on the topic 'Viscous fingering'

We have qualitatively explained the experiments of McCloud and Maher (McCloud and Maher (95)) for the viscous fingering problem in which an anisotropy in the surface tension parameter was imposed by engraving a grid in one of the plates of the Hele-Shaw cell. We saw the need to approach the problem in an analytical form. Therefore we decided to extend solvability theory to incorporate the effect of anisotropy. We have introduced the anisotropy through a moving boundary condition by considering an effective anisotropic surface tension with an anisotropy entering as the simplest cosine term having the right symmetry for a square lattice. We carried out the singular perturbation appropriate for the surface tension parameter assuming the length scale introduced by the anisotropy is small in comparison with the length scale introduced by the surface tension. In this sense, the perturbation can be said to be microscopic. For the case in which the surface tension has a maximum at the finger tip, our theory provides two possible solutions: one corresponding to the solution of the isotropic case and a new solution which, below a threshold of the surface tension parameter, predicts a wider finger than the isotropic solution. Intuitively, we expect the "old" solution, namely the one that does not differ from the isotropic case, to be the selected solution for large values of the surface tension parameter and we expect the new solution to be selected for small values of the surface tension parameter. This was confirmed by dynamical simulations of the interface done by David Jasnow. His simulation predicts that for the case in which the surface tension has a maximum at the finger tip, anisotropy is irrelevant for large values of the surface tension parameter. Furthermore below a threshold in this surface tension parameter, the selected finger width is systematically wider than the corresponding isotropic case. We conclude that our solvability theory together with the dynamic

Viscous fingering occurs when one fluid displaces another fluid of a greater viscosity in a porous medium or a Hele-Shaw cell. Linear stability analysis is used to predict methods of suppressing instability. Then, experiments in which nonlinear growth dominates pattern formation are analysed to explore the nonlinear impact of strategies of suppressing finger growth. Often, chemical treatment fluid is injected into oil reservoirs in order to prevent sand production. This treatment fluid is usually followed by water injection to clean up the well. We explore the potential for viscous instability of the interface between the treatment fluid and the water, and also the treatment fluid and the oil, as a function of the volume of treatment fluid and the injection rate and viscosity ratios of the different fluids. For a given volume of treatment fluid and a given injection rate, we find the optimal viscosity of the treatment fluid to minimise the viscous instability. In the case of axisymmetric injection, the stabilisation associated with the azimuthal stretching of modes leads to a further constraint on the optimisation of the viscosity. In the case of oil production, polymers may be added to the displacing water in order to reduce adverse viscosity gradients. We also explore the case in which these polymers have a time-dependent viscosity, for example through the slow release from encapsulant. We calculate the injection flow rate profile that minimises the final amplitude of instability in both rectilinear and axisymmetric geometries. In a development of the model, we repeat the calculation for a shear-thinning rheology. Finally, experiments are analysed in which the nonlinear growth of viscous fingers develops to test the influence of different injection profiles on the development of instability. Diffusion Limited Aggregation (DLA) simulations are performed for comparison. In all cases, the evolving pattern has a saturation distribution, with an inner zone in which the fingers are static and an outer zone in which the fingers advance and grow. In the very centre of the viscous fingering patterns, there is a small fully-saturated region. In the experiments, the mass distribution in the inner zone varies with radius as a power law which relates to the fractal dimension for the analogue DLA simulations. In the outer region the saturation decreases linearly with radius. The radius of the inner frozen zone is approximately 2/3 of the outer radius in the cases of DLA and -- after a period of evolution -- the viscous fingering experiments. This allows the radial extents of the inner and outer zones to be predicted. The ratio of each radius to the extent of the fully-saturated region is independent of the injection profile and corresponds to values for DLA.

This thesis aims to develop a computer simulation of the process that occurs when one displaces a viscous fluid such as oil by a less viscous one such as water in a porous medium. Chapter 1 outlines the problem and explains why a computer simulation rather than analytical treatment is necessary for the problem. Previous computer simulations of the problem are reviewed and their respective advantages and disadvantages are considered. Chapter 2 introduces the concept of 'simulated annealing', a stochastic computational technique for solving minimisation problems with many variables and this technique is used to make a crude model of the displacement problem. The results from this are considered and the reasons for the model's failure to adequately solve the problem are discussed. In chapter 3, simulated annealing is applied to the simpler problem of the travelling salesman where one has to find the shortest route around a collection of points. The aim of this chapter is to try and find an optimum simulated annealing schedule to minimise the computer time needed to achieve a satisfactory solution. This is successfully accomplished for this particular problem by fitting the relaxation time of the system as a function of temperature to an Arrhenhius type law. But this optimisation is problem specific and it is concluded that the complicated nature of the oil displacement problem effectively precludes treatment by annealing. In chapter 4 a stochastic micro model is developed in which a pressure gradient across the system forces water into oil bearing pores. The pores have varying sizes which represent sizes which represent the varying permeability in a porous medium. A modified Gauss Seidel method is used to solve for the pressure field and an analytic expression for the saturation update is developed. The final chapter, chapter 5, develops the above model further and in particular develops a scheme whereby conservation of fluid is guaranteed. The profiles of the fingering of the water into the oil are studied and it is found that their interface fractal dimension varies monotonically with viscosity ratio.

This thesis focuses on two problems lying within the field of soft condensed matter: the viscous fingering or Saffman-Taylor instability and nematic liquid crystals in confinement. Whenever a low viscosity fluid displaces a high viscosity fluid in a porous medium, for example water pushing oil out of oil reservoirs, the interface between the two fluids is rendered unstable. Viscous fingers develop, grow and compete until a single finger spans all the way from inlet to outlet. Here, using a free energy lattice Boltzmann algorithm, we examine the Saffman-Taylor instability for two different wetting situations: (a) when neither of the two fluids wet the walls of the channel and (b) when the displacing fluids completely wets the walls. We demonstrate that curvature effects in the third dimension, which arise because of the wetting boundary conditions, can lead to a novel suppression of the instability. Recent experiments in microchannels using colloid-polymer mixtures support our findings. In the second part of the thesis we examine nematic liquid crystals confined in wedge-structured geometries. In these systems the final stable configuration of the liquid crystal system is controlled by the complex interplay between confinement, elasticity and surface anchoring. Varying the wedge opening angle this competition leads to a splay to bend transition mediated by a defect in the bulk of the wedge. Using a hybrid lattice Boltzmann algorithm we study the splay-bend transition and compare to recent experiments on {em fd} virus particles in microchannels. Our numerical results, in quantitative agreement with the experiments, enable us to predict the position of the defect as a function of opening angle, and elucidate its role in the change of director structure. This has relevance to novel energy saving, liquid crystal devices which rely on defect motion and pinning to create bistable director configurations.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2012.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 41-42).
Viscous fingering, the hydrodynamic instability that occurs when a lower viscosity fluid displaces a higher viscosity fluid, creates complex patterns in porous media flows. Fundamental facets of the displacement process, such as volumetric sweep and mixing efficiency, depend strongly on the type of pattern created by the uneven front of the less viscous fluid. The interface created from these fingering patterns affects mixing, and therefore understanding how these patterns evolve is of critical importance in applications such as enhanced oil recovery and groundwater remediation. We use a Hele-Shaw cell to study experimentally how changing three parameters the injection rate, the viscosity contrast between the two fluids, and the gap thickness through which the fluid flows -- affects the resulting fingering pattern. The results lead to some basic observations, such as finger widths increasing uniformly with gap thickness, or that increasing the mobility ratio leads to more and narrower fingers. However, this systematic experimental method also uncovered an unexpected trend: non-monotonic finger width behavior with respect to injection rate. This non-monotonicity was observed for all mobility ratios and gap thicknesses, and is summarized in the experimental phase diagram created. To further understand how a viscous fingering pattern evolves over time, we also calculate the interface growth of a pattern over time using image analysis. This analysis shows that the interface moves through three self-similar regimes over time, and suggests that viscous fingering only actively adds interfacial length for a certain period of time in a pattern's growth. Both of these findings impact how much interfacial area a fingering pattern can create, and developing a better understanding of the evolution of miscible viscous fingering patterns is necessary for being able to accurately determine the mixing efficiency of a fingering pattern.
by Jane Chui.
S.M.

Thesis (S.M. in Transportation)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 97-100).
Mixing of two fluids in viscously unstable displacements is far from being fully understood. It is not known how mixing efficiency depends on the viscosity contrast between the fluids, especially for advection-dominated flows (Peclet number Pe > 103). It is well known that when a less viscous fluid displaces a more viscous fluid, the displacement front is unstable and leads to the formation of a pattern known as viscous fingering. However, current simulation technology is unable to cope with large viscosity contrasts (M > 30). We develop a high-resolution simulation approach that is stable for arbitrary viscosity ratios, and we study mixing under different canonical configurations with viscosity contrasts up to M = 400. We explain the observed evolution in degree of mixing through numerical simulation and dimensional analysis. We compute degree of mixing from decay in concentration variance and relate it to the stretching of material interface between the fluids due to fingering. Our analysis predicts the optimum range of viscosity contrast and Peclet number that maximize fluid-fluid interfacial area by balancing the number of fingers with their length before diffusive mixing across the sharp interface takes over. Interesting fingering patterns such as channeling and tip-splitting play an important role in this balancing act which makes degree of mixing a non-monotonic function of viscosity contrast and Peclet number.
by Birendra Jha.
S.M.in Transportation

The removal of artificially and naturally placed oils found in the ground is of paramount concern for environmental reasons and for the extraction of crude oil for energy. While many companies are involved in this soil remediation process, the physics of the underlying problem are not very well understood. We present a mathematical model and analysis of oil extraction in a porous soil based around the injection of water. We first consider a saturation analysis based on conservation of mass between oil and water in a one-dimensional setting and we find that based on certain parameter values, the water-oil interface goes unstable producing viscous finger patterns. We then include the effects of surface tension between oil and water to determine how this affects the growth of such fingers. We conclude that in the limit of small surface tension effects, the results generalize to the original problem, but more importantly, we deduce that there is a scaling which places the formulation into a setting that is invariant with respect to the magnitude of surface tension effects. With this scaling, we notice that the effect of surface tension is to limit the growth of fingers to a maximal wave number and to prevent their formation entirely beyond a certain critical wave number. Finally with the inclusion of temperature, via heated water injection, we see the formation of a dual fingering pattern: one associated with the mass conservation analysis of the oil-water interface and one associated with the conservation of energy across an interface where thermal gradients occur. We see that the thermal gradients across the interface where temperature drops induce unstable viscous patterns with a higher wave number than would occur for an equivalent isothermal interface where there was solely a change in viscosity. The thermal gradients also promote fingering development downstream across the classical viscosity differential driven interface but at the expense of lowering the interfacial velocity. It is interesting to note that the change in saturation that occurs across the energy interface is a result of a pseudo-free boundary created by the thermal problem.

Relative permeability (kr) is a critical input data for any calculation involving multiphase flow in petroleum reservoirs. Normally, kr curves are obtained by performing coreflood experiments as part of SCAL measurements or EOR studies. The results of the experiments are then used to obtain kr values often by either analytical models (e.g. JBN) or history matching techniques. Most of these models are based on the Buckley-Leverett displacement theory and are not applicable to unstable displacements. Therefore, using these models to describe a core flood experiment involving viscous fingering will result in potentially large errors in the estimation of kr curves. This study focused on the estimation of relative permeability curves for unstable experiments, more specifically in unfavourable mobility corefloods with a tendency to develop viscous fingering. Refined 2D coreflood simulations were used to evaluate the effect of viscous fingering in kr estimation methods. The simulations were performed as immiscible corefloods in homogeneous cores using a Black-oil model in a commercial simulator. The first part of this study, describes the methodology used to generate viscous fingering in numerical corefloods. Instability triggering methods were used with high resolution simulation to generate the viscous fingering. This methodology was then used to generate different numerical experiments with viscous fingering formation. In the second part, the currently widely used oil industry approaches for relative permeability estimation (1D history matching and JBN method) were evaluated for cases with unfavourable mobility. The errors were quantified in order to understand the effect of fingering on these methods and the amount of error one can incur when using them for these cases. In the latter part of the thesis, two novel methods are proposed for estimating relative permeabilities for unfavourable mobility coreflood experiments, namely viscous fingering. These methods are based on the proposed model called 'stable equivalent model'. This model proposes a correction to the velocity of the fluids in a coreflood affected by viscous fingering, allowing to account for viscous fingering in relative permeability estimation. The model is used to modify the JBN method and 1D history matching, allowing these methods to tackle viscous instability. The integrity of these techniques was validated against published experimental data and numerical data.

Thesis (M.S. in Mechanical Engineering) Naval Postgraduate School, March 2000.
Thesis advisor(s): Gopinath, Ashok. "March 2000." Includes bibliographical references (p. 49). Also available in print.

In this thesis, the viscous fingering instability of radial immiscible displacement is analysed numerically using novel mesh-reduction and interface tracking techniques. Using a reduced Hele-Shaw model for the depth averaged lateral flow, viscous fingering instabilities are explored in flow regimes typical of subsurface carbon sequestration involving supercritical CO2 - brine displacements, i.e. with high capillary numbers, low mobility ratios and inhomogeneous permeability/temperature fields. A high accuracy boundary element method (BEM) is implemented for the solution of homogeneous, finite mobility ratio immiscible displacements. Through efficient, explicit tracking of the sharp fluid-fluid interface, classical fingering processes such as spreading, shielding and splitting are analysed in the late stages of finger growth at low mobility ratios and high capillary numbers. Under these conditions, large differences are found compared with previous high or infinite mobility ratio models and critical events such as plume break-off and coalescence are analysed in much greater detail than has previously been attempted. For the solution of inhomogeneous mobility problems, a novel meshless radial basis function-finite collocation method is developed that utilises a dynamic quadtree dataset and local enforcement of interface matching conditions. When coupled with the BEM, the numerical scheme allows the analysis of variable permeability effects and the transition in (de)stabilising mechanisms that occurs when the capillary number is increased with a fixed, spatially varying permeability. Finally, thermo-viscous fingering is explored in the context of immiscible flows, with a detailed mechanistic study presented to explain, for the first time, the immiscible thermo-viscous fingering process.

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CNPq; INCT-FCx.
Nesta Tese são empregadas técnicas analíticas e numéricas para investigar o fenômeno de formação de dedos viscosos entre fluidos imiscíveis confinados quando um destes fluidos é um fluido magnético complexo. Diferentes tipos de esquemas geométricos efetivamente bidimensionais foram investigados. Duas situações distintas são tomadas com relação à natureza da amostra de fluido magnético: um fluido newtoniano usual, e um fluido magneto-reológico que apresenta um yield stress dependente da intensidade do campo magnético. Equações governantes adequadas são derivadas para cada um dos casos. Para obter um entendimento analítico dos estágios iniciais da evolução temporal da interface foi empregada uma análise fracamente não-linear de modos acoplados. Este tipo de análise acessa a estabilidade de uma interface inicialmente perturbada e também revela a morfologia dos dedos emergentes. Em algumas circunstâncias soluções estacionárias podem ser encontradas mesmo na ordem não-linear mais baixa. Nesta situação é feita uma comparação de algumas destas soluções com soluções estáticas totalmente não-lineares obtidas através de um formalismo de vortex-sheet na condição de equilíbrio. Em seguida foi desenvolvido um modelo de phase-field aplicado a fluidos magnéticos que é capaz de simular numericamente a dinâmica totalmente não-linear do sistema. O modelo consiste em introduzir uma função auxiliar que reproduz uma interface difusa de espessura finita. Utilizando esta ferramenta também é possível estudar um complexo problema de dedos viscosos de origem biológica: o fluxo de actina como um fluido ativo dentro de um fragmento lamelar.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Civil and Environmental Engineering, September, 2020
Cataloged from student-submitted PDF of thesis.
Includes bibliographical references (pages 131-149).
Flow instabilities arising from differences in temperature, density, or viscosity are commonplace. Viscous fingering is a hydrodynamic instability that occurs when a less viscous fluid displaces a more viscous one. Instead of progressing as a uniform front, the displacing fluid forms fingers that vary in size and shape to form complex patterns. The interface created from these patterns affects mixing between the two fluids, and therefore understanding how these patterns evolve in time is essential in applications such as enhanced oil recovery, bioremediation, and microfluidics. In this Thesis, we experimentally quantify the impact miscible viscous fingering has on mixing. We use a radial Hele-Shaw cell as an analog of radial flows in porous media, and high-resolution fluorescent imaging, to measure the temporal and spatial evolution of the mixing zone. We identify distinct regimes in both the interface length and average thickness of the mixing zone.
We use these results to propose a scaling framework for the growth of the mixing zone, and identify for the first time the competing factors of time-dependent dispersion and fluid-interface stretching from viscous fingering. Although bacteria can be found virtually everywhere viscous fingering occurs, there are no studies on the effects of their presence on the displacement dynamics. In this Thesis, we seek to begin filling this knowledge gap by employing as invading fluid an active suspension of fluorescent motile E. coli, and observing how bacterial motility affects the interface and mixing zone between the two fluids. We start by characterizing how viscous environments affect the rheology of these dense suspensions capable of collective swimming (and therefore effective viscosity reductions) using a Couette rheometer.
Remarkably, we find that for the entire range of solvent viscosities tested (1 to 17 mPa · s), we recover superfluidic regimes, in which the effective suspension viscosity is reduced to near-zero values through collective swimming. We use these experimental results to formulate a constitutive model for the rheology of bacterial superfluids under flow as a function of the bacterial concentration and the solvent viscosity. To visualize the motile bacteria both individually and collectively under viscous fingering conditions, we design and fabricate a mesofluidic Hele-Shaw cell that is large enough to accommodate viscous fingering instabilities and small enough to be used with fluorescent microscopy. Surprisingly, we observe a textured interface between the two fluids, in addition to the larger-scale viscous fingering pattern.
This interface consists of four distinct regions: a monodisperse region near the core of the finger, a filamentous region where bacteria segregate into separate flow paths in the direction of finger movement, a "rafting" region where bacteria aggregate into small groups (or "rafts") near the tip of the finger that then get pushed to the sides of the finger, and a diffuse region where the bacteria organize into a diffuse band at the very edge of the interface. These unexpected observations are a first step towards understanding how the interplay between active suspensions of motile bacteria and fluid-mechanical instabilities, such as viscous fingering, affects overall mixing under these complex flow conditions which are found in both natural and engineered environments.
by Jane Yuen Yung Chui.
Ph. D.
Ph.D. Massachusetts Institute of Technology, Department of Civil and Environmental Engineering

La méthode de Boltzmann sur réseau est une formulation discrète particulière de l'équation de Boltzmann. Depuis ses débuts, il y a trente ans, cette méthode a gagné une certaine popularité, et elle est maintenant utilisée dans presque tous les problèmes habituellement rencontrés en mécanique des fluides notamment pour les écoulements multi-espèces. Dans le cadre de ce travail, une force de friction intermoléculaire est introduite pour modéliser les interactions entre les molécules de différent types causant principalement la diffusion entre les espèces. Les phénomènes de dissipation visqueuse (collision usuelle) et de diffusion moléculaire (force de friction intermoléculaire) sont séparés et peuvent être ajuster indépendamment. Le principal avantage de cette stratégie est sa compatibilité avec des optimisations de la collision usuelle et les opérateurs de collision avancés. Adapter un code mono-espèce pour aboutir à un code multi-espèces est aisé et demande beaucoup moins d’effort comparé aux précédentes tentatives. De plus, il n’ y a pas d’approximation du mélange, chaque espèce a ses propres coefficients de transport pouvant être calculés à l’aide de la théorie cinétique des gaz. En général, la diffusion et la convection sont vus comme deux mécanismes séparés : l’un agissant sur la masse d’une espèce, l’autre sur la quantité de mouvement du mélange. En utilisant une force de friction intermoléculaire, la diffusion et la convection sont couplés par l’intermédiaire la quantité de mouvement de chaque espèce. Les mécanismes de diffusion et de convection sont intimement liés dans de nombreux phénomènes physique tel que la digitation visqueuse.L’instabilité de digitation visqueuse est simulée en considérant dans un milieu poreux deux espèces dans des proportions différentes soit un mélange moins visqueux déplaçant un mélange plus visqueux. Les principaux moteurs de l’instabilité sont la diffusion et le contraste de viscosité entre les espèces. Deux stratégies sont envisagées pour simuler les effets d’un milieu poreux. Les méthodes de rebond partiel et de force de Brinkman bien que basées sur des approches fondamentalement différentes donnent dans notre cas des résultats identiques. Les taux de croissance de l’instabilité calculés à partir de la simulation coïncident avec ceux obtenus à partir d’analyses de stabilité linéaire. L’évolution de la longueur de mélange peut être divisée en deux étapes dominées d’abord par la diffusion puis par la convection. La physique de la digitation visqueuse est ainsi correctement simulée. Toutefois, les effets de diffusion multi-espèces ne sont généralement pas pris en compte lors de la digitation visqueuse de trois espèces et plus. Ces derniers ne sont pas négligeable puisque nous mettons en avant une configuration initialement stable qui se déstabilise. La diffusion inverse entraîne la digitation dont l’impact dépend de la diffusion entre les espèces
The lattice Boltzmann method (LBM) is a specific discrete formulation of the Boltzmann equation. Since its first premises, thirty years ago, this method has gained some popularity and is now applied to almost all standard problems encountered in fluid mechanics including multi-component flows. In this work, we introduce the inter-molecular friction forces to take into account the interaction between molecules of different kinds resulting primarily in diffusion between components. Viscous dissipation (standard collision) and molecular diffusion (inter-molecular friction forces) phenomena are split, and both can be tuned distinctively. The main advantage of this strategy is optimizations of the collision and advanced collision operators are readily compatible. Adapting an existing code from single component to multiple miscible components is straightforward and required much less effort than the large modifications needed from previously available lattice Boltzmann models. Besides, there is no mixture approximation: each species has its own transport coefficients, which can be calculated from the kinetic theory of gases. In general, diffusion and convection are dealt with two separate mechanisms: one acting respectively on the species mass and the other acting on the mixture momentum. By employing an inter-molecular friction force, the diffusion and convection are coupled through the species momentum. Diffusion and convection mechanisms are closely related in several physical phenomena such as in the viscous fingering instability.A simulation of the viscous fingering instability is achieved by considering two species in different proportions in a porous medium: a less viscous mixture displacing a more viscous mixture. The core ingredients of the instability are the diffusion and the viscosity contrast between the components. Two strategies are investigated to mimic the effects of the porous medium. The gray lattice Boltzmann and Brinkman force models, although based on fundamentally different approaches, give in our case equivalent results. For early times, comparisons with linear stability analyses agree well with the growth rate calculated from the simulations. For intermediate times, the evolution of the mixing length can be divided into two stages dominated first by diffusion then by convection, as found in the literature. The whole physics of the viscous fingering is thus accurately simulated. Nevertheless, multi-component diffusion effects are usually not taken into account in the case of viscous fingering with three and more species. These effects are non-negligible as we showcase an initial stable configuration that becomes unstable. The reverse diffusion induces fingering whose impact depends on the diffusion between species

When a less viscous fluid displaces a more viscous fluid inside a quasi-two-dimensional channel, the interface separating the two fluids can become highly unstable and perturbed. By assuming that the more viscous fluid is finite in volume, this thesis uses analytical and computational methods to investigate the effect of two fluid interfaces. The results could have implication in fields such as oil extraction, geology, and advanced manufacturing.

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.

Die vorliegende Arbeit beschreibt eine experimentelle Untersuchung der Schichtbildung von nichtnewtonschen Flüssigkeiten im Tiefdruckverfahren auf nicht saugfähigen Substraten. Das fluiddynamisch bedingte „viscous fingering“ beim Farbspaltungsprozess soll mittels Hydrophobieren der Druckform gehemmt werden. Ziel ist es, möglichst homogene sowie wellenfreie Schichten zu erzeugen. Um ein direkt miteinander vergleichbares Druckergebnis zu erhalten, wird der Druckstoff parallel mit einer unbehandelten und hydrophobierten Form bedruckt. Als Druckstoff werden anstelle von Druckfarbe funktionale Materialien (vorzugsweise PEDOT:PSS) verwendet und variiert, wobei die elektrischen und geometrischen Schichteigenschaften, beispielsweise der elektrische Widerstand und die Rauheit, zur Ermittlung der gesetzten Ziele untersucht wurden. Hiermit und mittels Nutzung einer hydrophobierten Druckform kann eine deutliche Minderung der Wellenbildung (viscous fingering) bei vielen Druckstoffarten beobachtet werden. Die Minderung des viscous fingering im Farbspaltungsprozess und eine nahezu vollständige Leerung der hydrophobierten Tiefdruckform haben einen wesentlichen Nutzwert für den künftigen Einsatz nicht nur für die „gedruckte Elektronik“
In this work is described experimental research about layer forming from non-Newtonian fluids in gravure printing on non-porous substrates. The viscous fingering, caused through fluid dynamics at splitting of printed material should be decreased by hydrophobic-surface modification of gravure printing form. The aim was to print wave-free homogenous layers. To achieve comparable results, modified and pure form were used simultaneously to print the same material. The printed material was mainly PEDOT:PSS and other, which is used in printed electronics. The properties (surface tension, viscosity) of printed materials were varied by additives. Printing conditions were varied too. The characteristic of printed layers were studied: resistivity, roughness, density, etc. The results shows decreasing of waviness, roughness and viscous fingering in final layer through use of hydrophobic gravure printing form, compared to print results with common printing form. This can be applied not only in the field of printed electronics

The Icelandic mantle plume has had a profound influence on the development of the North Atlantic region over its 64 Myr existence. Long-wavelength free-air gravity anomalies and full waveform tomographic studies suggest that the planform of the plume is highly irregular, with up to five fingers of hot asthenosphere radiating away from Iceland beneath the lithospheric plates. Two of these fingers extend beneath the British Isles and southern Scandinavia, where departures from crustal isostatic equilibrium and anomalous uplift have been identified. In this study, the spatial extent of present-day dynamic support associated with the Icelandic plume is investigated using receiver function analysis. Teleseismic events recorded at nine temporary and 59 permanent broadband, three-component seismometer stations are used to calculate 3864 P-to-S crustal receiver functions. The amplitude and arrival time of particular converted phases are assessed, and H-k stacking is applied to estimate bulk crustal properties. Sub-selections of receiver functions are jointly inverted with Rayleigh wave dispersion data to obtain crustal VS profiles at each station. Both inverse- and guided forward modelling techniques are employed, as well as a Bayesian, trans-dimensional algorithm. Moho depths thus obtained are combined with seismic wide-angle and deep reflection data to produce a comprehensive crustal thickness map of northwestern Europe. Moho depth is found to decrease from southeast (37 km) to northwest (26 km) in the British Isles and from northeast (46 km) to southwest (29 km) in Scandinavia, and does not positively correlate with surface elevation. Using an empirical relationship, crustal shear wave velocity profiles are converted to density profiles. Isostatic balances are then used to estimate residual topography at each station, taking into account these novel constraints on crustal density. Areas of significant residual topography are found in the northwestern British Isles (1400 m), southwestern Scandinavia (464 m) and Denmark (620 m), with convective support from the Icelandic plume as its most likely source. Finally, the irregular planform of the Icelandic plume is proposed to be a manifestation of radial viscous fingering due to a Saffman-Taylor instability. This fluid dynamical phenomenon occurs when less viscous fluid is injected into a layer of more viscous fluid. By comparing the thermal and convective characteristics of the plume with experimental and theoretical results, it is shown that viscous fingering could well explain the present-day distribution of plume material.

Au cours de cette thèse, nous avons effectué une étude de l'instabilité de Saffman-Taylor dans les fluides complexes. En particulier, nous avons mené une étude systématique de la relation entre les propriétés rhéologiques de fluides non-newtoniens et la formation de motif, en cellule de Hele-Shaw. Pour cela, nous avons utilisé des fluides modèles ne possédant chacun essentiellement qu'une seule propriété non-newtonienne. Une étude rhéologique a montré que la propriété non-newtonienne dominante d'une solution du polymère rigide Xanthane est la viscosité rhéofluidifiante, qu'une solution du polymère flexible PEO montre des effets élastiques, notamment une contrainte normale élevée, et qu'un gel de polymères possède un seuil d'écoulement. Pour des fluides classiques, la largeur des doigts de Saffman-Taylor est déterminée par le rapport entre les forces visqueuses et les forces capillaires. Dans le cas d'un fluide rhéofluidifiant, les forces visqueuses sont modifiées ce qui entraîne un amincissement des doigts par rapport aux résultats classiques. La modification des contraintes visqueuses par un seuil d'écoulement mène à des structures très ramifiées avec une largeur caractéristique de doigts, fonction de ce seuil. Pour un fluide élastique, la contrainte normale exerce une pression supplémentaire sur le doigt qui s'ajoute aux forces capillaires et qui entraîne un élargissement des doigts. Nous pensons que la connaissance des effets sur l'instabilité des Saffman-Taylor de chacune de ces propriétés, considérée séparément, constitue une base pour l'étude de l'instabilité dans des fluides plus complexes. Les propriétés non-newtoniennes étudiées ici sont parmi les propriétés non-newtoniennes les plus courantes, ce qui devrait permettre de mieux comprendre l'instabilité dans des fluides présentant simultanément plusieurs de ces propriétés non-newtoniennes.

La digitation visqueuse est une instabilité hydrodynamique apparaissant lorsque, dans un milieu poreux, un fluide moins visqueux déplace un fluide plus visqueux. L'objectif de notre thèse est l'étude expérimentale des propriétés des motifs de digitation lorsque l'échantillon de fluide visqueux est de taille finie et lorsqu'une réaction chimique modifie la viscosité dans un milieu poreux modèle, en l'occurrence une cellule de Hele-Shaw. En particulier, notre étude a permis de quantifier la contribution de dispersion et de la digitation visqueuse, l'étalement dans l'espace d'échantillons de taille finie en fonction des paramètres expérimentaux (contraste de viscosité, vitesse de déplacement et taille de l'échantillon). Pour les fluides réactifs, nous analysons la digitation induite par une réaction A + B C dont le produit C est plus visqueux que les réactifs A et B, ceux-ci ayant la même viscosité. Nous mettons en évidence l'effet des concentrations en réactifs, du choix du fluide vecteur et du débit d'injection sur le motif de digitation.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished

En simulation dynamique des réservoirs, un des artéfacts les plus gênants pour la prédiction de production est l’effet de l’orientation du maillage. Bien que celui-ci soit « normal » pour tout schéma numérique, il se trouve amplifié par l’instabilité du modèle physique, ce qui a lieu lorsque le contraste de mobilités entre l’eau (fluide poussant, utilisé dans les procédés de récupération secondaires) et l’huile (fluide poussé, contenant les hydrocarbures) dépasse un certain seuil critique. On parle alors d’écoulements à rapport de mobilités défavorable. Connu depuis longtemps, ce problème a fait l'objet de nombreux travaux dans les années 1980 ayant abouti au schéma dit à neuf points. Actuellement implanté dans PumaFlow, logiciel développé et commercialisé par IFPEN, ce schéma fonctionne relativement bien en maillages carrés et dépend d’un paramètre scalaire dont le réglage varie selon les auteurs sur la base de considérations heuristiques. Dans cette thèse, nous proposons une nouvelle démarche méthodologique afin non seulement d’ajuster ce paramètre libre de manière optimale mais aussi de généraliser le schéma aux maillages rectangulaires. La stratégie que nous préconisons repose sur une analyse d’erreur du problème, à partir de laquelle il est possible de définir une notion d’erreur angulaire et de garantir que le comportement du schéma obtenu soit le « moins anisotrope » possible via une minimisation de son écart par rapport à un comportement idéal. Cette procédure de minimisation est ensuite appliquée à deux autres familles de schémas numériques~ : (1) un schéma multidimensionnel proposé par Kozdon, dans lequel le paramètre libre est une fonction~ ; (2) un autre schéma à neuf points faisant intervenir deux paramètres scalaires. C’est ce dernier qui réduit le mieux l’effet de l’orientation lorsque le rapport des pas de maillage s’éloigne de 1. Enfin, une extension de la méthode à des modèles physiques plus complets est envisagée
In dynamic reservoir simulation, one of the most troublesome artifacts for the prediction of production is the grid orientation effect. Although this normally arises from any numerical scheme, it happens to be amplified by the instability of the physical model, which occurs when the mobility contrast between the water (pushing fluid, used in the processes of secondary recovery) and the oil (pushed fluid, containing the hydrocarbons) exceeds a some critical threshold. We then speak of flows with adverse mobility ratio. This GOE issue has received a lot of attention from the engineers. Numerous works dating back to the 1980s have resulted in the so-called nine-point scheme. Currently implemented in the IFPEN software PumaFlow, this scheme performs relatively well in square meshes and depends on a scalar parameter whose value varies from one author to another, on the grounds of heuristic considerations. In this thesis, we propose a new methodological approach in order not only to optimally adjust this free parameter, but also to extend the scheme to rectangular meshes. The strategy that we advocate is based on an error analysis of the problem, from which it is possible to define a notion of angular error and to guarantee that the behavior of the obtained scheme is the "least anisotropic" possible through a minimization of its deviation from some ideal behavior. This minimization procedure is then applied to two other families of numerical schemes: (1) a multidimensional scheme proposed by Kozdon, in which the free parameter is a function; (2) another nine-point scheme involving two scalar parameters. The latter provides the best results regarding GOE reduction when the ratio of the mesh steps is far away from 1. Finally, an extension of the method to more sophisticated physical models is envisaged

Les mécanismes de fracture dans les matériaux solides ont été activement étudiés. Dans les fluides complexes, les fractures ont déjà été observées et sont jusqu'à présent beaucoup moins bien documentées. Nous avons choisi d'analyser les phénomènes de fracturation dans une classe particulière de fluides complexes : les gels transitoires auto-assemblés. Ces gels, viscoélastiques, possèdent la propriété de s'écouler aux temps longs et de se comporter de manière élastique aux temps courts. Nous avons axé cette thèse autour de trois systèmes modèles : des microémulsions connectées, des solutions de micelles géantes, ainsi qu'un système " hybride " constitué de solutions de micelles de morphologie contrôlable et connectées. Tous ces systèmes, qui sont à l'équilibre thermodynamique, se comportent comme des fluides de Maxwell, néanmoins leurs microstructures sont très différentes. Les microémulsions connectées sont formées de gouttelettes d'huile, stabilisées par des tensioactifs, dispersées dans de l'eau et connectées par des polymères téléchéliques. Les solutions de micelles géantes sont des agrégats allongés et semi-flexibles, enchevêtrés, résultant de l'auto-assemblage de tensioactifs en solution dans l'eau. Enfin, le système de micelles pontées est constitué d'agrégats de tensioactifs dont on peut contrôler la morphologie (sphères -> cylindres -> vers) et qui sont pontés par un polymère téléchélique. Ces trois systèmes ont été étudiés dans une géométrie confinée : une cellule de Hele-Shaw radiale. Elle est constituée de deux plaques de verre séparées par des espaceurs de taille contrôlée (500 µm) et percée d'un trou en son centre permettant l'injection de fluides.Nos expériences consistent en l'injection, à débit contrôlé, d'une huile faiblement visqueuse dans le gel. Le contraste de viscosité entre l'huile injectée et le gel étant important, l'interface huile/gel n'est pas stable. En fonction du débit d'injection d'huile, nous avons observé différents phénomènes. A bas débits d'injection, une instabilité visco-capillaire se développe : l'interface huile/gel se déforme et forme des motifs appelés doigts visqueux. Cette instabilité de Saffman-Taylor est bien connue pour des fluides visqueux. A plus haut débit en revanche, un autre type d'instabilité se développe, d'origine élasto-capillaire : les fractures.Nous avons quantifié les différences entre les deux types d'instabilité. En utilisant des techniques complémentaires, visualisation directe à l'aide d'une caméra rapide et vélocimétrie par corrélation d'images, nous avons montré qu'il existe une discontinuité entre la vitesse de l'interface huile/gel et la vitesse du gel à la pointe de fracture. Cette discontinuité est inexistante dans le cas de la digitation. Nous avons montré que la structure du gel influe sur la transition entre ces deux types d'instabilité. En étudiant les champs de déplacement des microémulsions connectées, nous avons caractérisé les déplacements du gel autour de la pointe, notamment la manière dont l'amplitude des déplacements du gel décroit quand on s'éloigne de la pointe de fracture. Quand la structure du gel peut se réorganiser sous écoulement, nous avons mesuré un signal de biréfringence associé à ces réorganisations. En étudiant ce signal, qui apparait à la pointe d'une fracture, nous avons pu réaliser une première mesure macroscopique de la taille d'une " zone de process ". Nous avons montré que cette zone est d'autant plus grande que la vitesse de la fracture est petite.Lors d'expériences consistant à injecter des solutions de micelles géantes dans elles-mêmes, nous avons découvert l'existence d'une instabilité d'écoulement inconnue jusqu'à aujourd'hui. Elle se caractérise par la perte transitoire de la symétrie radiale de l'écoulement et l'apparition de "branches " biréfringentes se propageant à de très hautes vitesses dans le gel et qui, au final, déforment l'interface air/gel.

Il est important de comprendre les forces motrices qui contrôlent l'écoulement de deux fluides immiscibles dans un milieu poreux. En effet, il existe une large gamme d'applications des écoulements diphasiques en milieux poreux, notamment ceux qui concernent la récupération assistée du pétrole (EOR). Le développement des techniques quantitatives d'imagerie par résonance magnétique (IRM) ouvre de nouvelles possibilités pour étudier et caractériser les flux multiphasiques en milieu poreux. Ce travail s’intéresse précisément à décrire le déplacement de deux fluides immiscibles (eau-huile) au sein d’un milieu poreux en utilisant les techniques d’IRM. Le milieu poreux est initialement saturé d’huile qu’on vient déplacer en injectant de l’eau par le bas, l’huile et l’eau pouvant s’évacuer par le haut. L’objectif général de l’étude est de déterminer le déplacement et la déformation du front (eau-huile) au cours du temps, et de préciser les mécanismes de piégeage des phases. Des expériences sont menées sur deux modèles poreux. L’un mouillant à l’huile consiste en un empilement de petites billes en polystyrène (0,4 mm < dp < 0,6 mm), l’autre mouillant à l’eau est un sable légèrement compacté (0,02 mm < dp < 0,50 mm). Nous avons utilisé un dispositif de micro-imagerie RMN fonctionnant à 14 T (résonance 1H à 600 MHz) pour acquérir des images à haute résolution (0.2 mm) à l’intérieur des milieux poreux au cours du déplacement des deux fluides. Les résultats obtenus ont montré que le profil de saturation en huile est fortement influencé par les propriétés du matériau poreux, telles que la porosité et la perméabilité de l'échantillon, le mouillage des phases, le débit d'injection de l’eau ou encore l’hétérogénéité de la matrice solide. L'influence du débit d’injection d’eau sur la saturation résiduelle en huile a été plus particulièrement étudiée. Les résultats expérimentaux permettent une compréhension fine du déplacement de deux fluides non miscibles pour deux types de milieux poreux, qui se différencient principalement par les effets de la mouillabilité. Dans le même temps, une simulation numérique du déplacement vertical ascendant de l’huile poussée par de l’eau dans une colonne poreuse a été réalisée et les résultats ont été comparés à nos expériences sous IRM
It is important to understand the driving forces that control the flow of two immiscible fluids in a porous medium. Indeed, there is a wide range of applications of two-phase flows in porous media, especially those relating to enhanced oil recovery (EOR). The development of quantitative magnetic resonance imaging (MRI) techniques opens up new possibilities for studying and characterizing multiphase flows in porous media. This work is specifically concerned with describing the displacement of two immiscible fluids (water-oil) in a porous medium using MRI techniques. The porous medium is initially saturated with oil which is displaced by injecting water from below, oil and water can be evacuated from above. The general objective of the study is to determine the displacement and the deformation of the front (water-oil) over time, and to specify the trapping mechanisms of the phases. Experiments are conducted on two porous models. One oil wetting consists of a stack of small polystyrene beads (0.4 mm < dp < 0.6 mm), the other wetting with water is a slightly compacted sand (0.02 mm < dp <0.50 mm). We used a 14 T NMR micro-imaging device (1H resonance at 600 MHz) to acquire high resolution images (0.2 mm) inside the porous media during the movement of the two fluids. The results obtained showed that the oil saturation profile is strongly influenced by the properties of the porous material, such as the porosity and the permeability of the sample, the wetting of the phases, the injection rate of the water or even the heterogeneity of the solid matrix. The influence of the water injection flow rate on the residual saturation of oil has been studied more particularly. The experimental results allow a fine understanding of the displacement of two immiscible fluids for two types of porous media, which mainly differ by the effects of wettability. At the same time, a numerical simulation of the upward vertical displacement of oil pushed by water in a porous column was performed and the results compared to our MRI experiments

Numerical simulation is used to study the effect of different factors on unstable miscible displacement and to clarify the mechanisms of finger growth and interaction. The two-dimensional equations of miscible displacement in a rectangular slab are dedimensionalized and the factors that affect their solution are combined into dimensionless parameters. These parameters are the viscosity ratio, the aspect ratio (ratio of longitudinal to transverse dimension), Peclet numbers for molecular, longitudinal and transverse dispersion and the gravity number. To study the effect of the structure of the porous medium, simulations are performed on different random permeability fields, generated by a statistical method, so that they have a given coefficient of permeability variation and a given correlation length. The concentration equation is solved by an implicit finite element modified method of characteristics, which performs backward characteristic tracking. A mixed finite element method is used for the solution of the pressure equation. The initial number and locations of fingers are dictated by the permeability distribution near the inflow end. The initial number of fingers is reduced by shielding and merging to a smaller number of "active fingers". Large viscosity ratio, aspect ratio, correlation length and coefficient of permeability variation facilitate merging and reduce the number of active fingers. With these parameters fixed, the latter is largely independent of the specific permeability distribution. Growth of individual fingers is approximately linear in time, provided they do not interact with other fingers. Root mean square (RMS) length also grows linearly. The RMS growth rate increases with increasing viscosity ratio and seems to approach an asymptotic value as the viscosity ratio tends to infinity. As the correlation length increases, RMS growth rate passes through a maximum. Large heterogeneity of the medium results in large RMS growth rate; the effect of heterogeneity increases with increasing correlation length. For large gravity numbers, the displacement is dominated by gravity override. In that case a gravity tongue forms and fingering is suppressed. The tongue breaks through early and recovery efficiency after breakthrough is greatly reduced. The effect of gravity weakens as the aspect ratio increases.

博士
長庚大學
機械工程研究所
97
One of the problems encountered in fluid assisted injection molded parts is the gas or water “fingering” phenomenon, in which gas (water) bubbles penetrate non-uniformly into the core of the parts and form finger-shape branches. Severe fingerings can lead to significant reductions in part stiffness. This study investigated the fingering phenomenon in fluid assisted injection molded disk parts. Experiments were carried out on a reciprocating injection molding machine equipped with gas and water injection units. The material used was virgin polypropylene. A disk cavity with two different thicknesses was used for all experiments. The effects of various processing parameters on the fingering were examined. It was found that the melt short shot size and mold temperature were the principal parameters affecting the formation of part fingerings. In addition, the formation mechanism of part fingerings has also been proposed to better understand the formation of part fingerings. It has been shown that the fluid assisted filling process is an unstable system by nature. Any small perturbation by material viscosity or by temperature gradient can trigger the unbalance of gas (water) penetrations in the parts and result in fingerings.

碩士
國立中正大學
物理學系暨研究所
99
The silicon oil is filled in two parallel ITO glass plates and atmospheric gas are injected into the silicon oil layer as a gas bubble. For turning on the plasma, the gas bubble plays the role of gas chamber. We study the beautiful radial evolution of the plasma bubble. By counting the luminescent area of the plasma bubble and the shape of the gas bubble, we classify the evolution of the plasma bubble with three stages. The bubble starts to deform by temperature fluctuation on the boundary which is induced by ion bombandments. We also show how to generate and to control the beautiful radial evolution by changing the experimental parameters in different scales. Thses controlled parameters are find some relations between the wavelength, , of the plasma bubble. In the process of the plasma bubble evolving into the radial fingering plasma bubble, there are bright spots in the fingertips which are observed with microscope and it is found that some microbubble are ejected from the tips. The radial fingering looks like the fractal pattern and the fractal dimension of the fingering plasma bubble is found about 1.74 by sandbox method. i

碩士
國立中央大學
機械工程學系
107
Displacing a more viscous fluid by another less viscous fluid leads to instabilities of the interface between two fluids due to the viscosity contrast. The phenomenon is called viscous fingering. Researchers already found out that linear time-dependent injection rate is able to suppress this phenomenon. Our work here is to take a step further, by applying the scheme in porous media. We consider the radial Hele-Shaw cell and porous media flow, and focus on how wettability may affect the instability suppress. The results in Hele-Shaw cell show that the linear injection flow rate suppress the instabilities effectively for drainage flow, in which a non-wetting fluid displaces a wetting fluid; On the other hand, this scheme doesn’t work for imbibition flow where a wetting fluid displace a non-wetting fluid. This is because the interfacial force caused by the wettability, directs in same the direction as imbibition flow. In porous media, a linear injection rate has little impact on both kinds of flow. Drainage flow tends to flow toward larger pores while imbibition flow most likely flows toward smaller pores, which both induce the onset of instability that is hardly suppressible by the linear flow rates.

碩士
國立中央大學
機械工程學系
107
When low-viscosity fluids displace higher-viscosity fluids, it causes the flow instability of the two-phase interface. This phenomenon is called viscous finger. According to previous studies, time-dependent suction flow rate can inhibit the viscous finger at a low capillary number in the Hele-Shaw cell. This study was to confirm whether this method is equally applicable to porous media. We perform the simulation of radial Hele-Shaw cell to analyze the influence of wettability. The results regarding the Hele-Shaw cell show the linear suction flow rate can indeed suppress finger at low capillary number, and drainage flow performs better than imbibition flow at maintaining the stability of the interface. Regarding porous media flow, little it can suppress finger that we use the linear suction flow rate. Under the influence of capillary pressure for differences pore sizes, drainage flow tends to flow to the larger pores and the imbibition flow tends to flow to the smaller pores. Because the wetting fluid can surround the particles by wetting the particles, imbibition flow has a larger fingering width, and display better displacement rates than drainage flow.

It is estimated that the shallow reservoirs of Ugnu, West Sak and Shraeder Bluff in the North Slope of Alaska hold about 20 billion barrels of heavy oil. The proximity of these reservoirs to the permafrost makes the application of thermal methods for the oil recovery very unattractive. It is feared that the heat from the thermal methods may melt this permafrost leading to subsidence of the unconsolidated sand (Marques 2009; Peyton 1970; Wilson 1972). Thus it is necessary to consider the development of cheap non-thermal methods for the recovery of these heavy oils. This study investigates non-thermal techniques for the recovery of heavy oils. Chemicals such as alkali, surfactant and polymer are used to demonstrate improved recovery over waterflooding for two oils (A:10,000cp and B:330 cp). Chemical screening studies showed that appropriate concentrations of chemicals, such as alkali and surfactant, could generate emulsions with oil A. At low brine salinity oil-in-water (O/W) emulsions were generated whereas water-in-oil (W/O) emulsions were generated at higher salinities. 1D and 2D sand pack floods conducted with alkali surfactant (AS) at different salinities demonstrated an improvement of oil recovery over waterflooding. Low salinity AS flood generated lower pressure drop, but also resulted in lower oil recovery rates. High salinity AS flood generated higher pressure drop, high viscosity emulsions in the system, but resulted in a greater improvement in oil recovery over waterfloods. Polymers can also be used to improve the sweep efficiency over waterflooding. A 100 cp polymer flood improved the oil recovery over waterflood both in 1D and 2D geometry. In 1D geometry 1PV of polymer injection increased the oil recovery from 30% after waterflood to 50% OOIP. The tertiary polymer injection was found to be equally beneficial as the secondary polymer injection. It was also found that the combined application of AS and polymer did not give any major advantage over polymer flood or AS flood alone. Chemical EOR technique was considered for the 330cp oil B. Chemical screening studies showed that microemulsions could be generated in the system when appropriate concentrations of alkali and surfactant were added. Solubilization ratio measurement indicted that the interfacial tension in the system approached ultra-low values of about 10-3 dynes/cm. The selected alkali surfactant system was tested in a sand pack flood. Additionally a partially hydrolyzed polymer was used to provide mobility control to the process. The tertiary injection of ASP (Alkali-Surfactant-Polymer) was able to improve the oil recovery from 60% OOIP after the waterflood to almost 98% OOIP. A simple mathematical model was built around viscous fingering phenomenon to match the experimental oil recoveries and pressure drops during the waterflood. Pseudo oil and water relative permeabilities were calculated from the model, which were then used directly in a reservoir simulator in place of the intrinsic oil-water relative permeabilities. Good agreement with the experimental values was obtained. For history matching the polymer flood of heavy oil, intrinsic oil-water relative permeabilities were found to be adequate. Laboratory data showed that polymer viscosity is dependent on the polymer concentration and the effective brine salinity. Both these effects were taken into account when simulating the polymer flood or the ASP flood. The filtration theory developed by Soo and Radke (1984) was used to simulate the dilute oil-in-water emulsion flow in the porous media when alkali-surfactant flood of the heavy oil was conducted. The generation of emulsion in the porous media is simulated via a reaction between alkali, surfactant, water and heavy oil. The theory developed by Soo and Radke (1984) states that the flowing emulsified oil droplets clog in pore constrictions and on the pore walls, thereby restricting flow. Once captured, there is a negligible particle re-entrainment. The simulator modeled the capture of the emulsion droplets via chemical reaction. Next, the local water relative permeability was reduced as the trapping of the oil droplets will reduce the mobility of the water phase. This entrapment mechanism is responsible for the increase in the pressure drop and improvement in oil recovery. The model is very sensitive to the reaction rate constants and the oil-water relative permeabilities. ASP process for lower viscosity 330 cp oil was modeled using the UTCHEM multiphase-multicomponent simulator developed at the University of Texas at Austin. The simulator can handle the flow of three liquid phases; oil, water and microemulsion. The generation of microemulsion is modeled by the reaction of the crude oil with the chemical species present in the aqueous phase. The experimental phase behavior of alkali and surfactant with the crude oil was modeled using the phase behavior mixing model of the simulator. Oil and water relative permeabilities were enhanced where microemulsion is generated and interfacial tension gets reduced. Experimental oil recovery and pressure drop data were successfully history matched using UTCHEM simulator.
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The flow instability process of viscous fingering has been widely researched for many years but its direct impact on liquid chromatography has not been extensively investigated. More specifically the morphology and flow patterns that the solute plugs experience as they pass through the column at various viscosities. The process of viscous fingering involves a fluid of a lower viscosity penetrating a fluid with a high viscosity. When the viscosity between the two liquids is significantly different the lower viscosity fluid enters the high viscosity fluid in a complex way such that the interface of the two fluids is augmented to resemble a series of fingers. The chromatographic solute plug as two liquid-liquid interfaces and depending on which is more viscous the plug (rear interface – fingers appear to trail plug) or the mobile phase (leading interface – fingers appear to proceed the plug) it will determine at which interface the instability will occur. High viscosity differences between the solute plug and the mobile phase has been linked to poor separations, but small viscosity differences have not been fully evaluated as the chromatographic peaks can maintain a normal distribution. This thesis investigates and describes the phenomena of viscous fingering as it applies to reversed phase high performance liquid chromatography (RP-HPLC) and size exclusion chromatography. Clearly visualising the solute plug as it passes through the liquid chromatography column and the way in which a change of viscosity influences the plug can be monitored using an optical visualisation technique. This technique involves the use of matching the refractive index of the fluid passing through the column to that of the stationary phase (silica based) within a glass column. The mobile phase used was a mixture so that the viscosity could be altered yet the refractive index could be maintained. This optical technique rendered the opaque stationary phase transparent and a coloured solute injected onto the column could be photographed and visual changes due to viscous fingering can be documented. Photographs were used to record the plugs movement along the column, and conventional post-column detection responses (chromatograms) were collected for comparison.

Die vorliegende Arbeit beschreibt eine experimentelle Untersuchung der Schichtbildung von nichtnewtonschen Flüssigkeiten im Tiefdruckverfahren auf nicht saugfähigen Substraten. Das fluiddynamisch bedingte „viscous fingering“ beim Farbspaltungsprozess soll mittels Hydrophobieren der Druckform gehemmt werden. Ziel ist es, möglichst homogene sowie wellenfreie Schichten zu erzeugen. Um ein direkt miteinander vergleichbares Druckergebnis zu erhalten, wird der Druckstoff parallel mit einer unbehandelten und hydrophobierten Form bedruckt. Als Druckstoff werden anstelle von Druckfarbe funktionale Materialien (vorzugsweise PEDOT:PSS) verwendet und variiert, wobei die elektrischen und geometrischen Schichteigenschaften, beispielsweise der elektrische Widerstand und die Rauheit, zur Ermittlung der gesetzten Ziele untersucht wurden. Hiermit und mittels Nutzung einer hydrophobierten Druckform kann eine deutliche Minderung der Wellenbildung (viscous fingering) bei vielen Druckstoffarten beobachtet werden. Die Minderung des viscous fingering im Farbspaltungsprozess und eine nahezu vollständige Leerung der hydrophobierten Tiefdruckform haben einen wesentlichen Nutzwert für den künftigen Einsatz nicht nur für die „gedruckte Elektronik“.
In this work is described experimental research about layer forming from non-Newtonian fluids in gravure printing on non-porous substrates. The viscous fingering, caused through fluid dynamics at splitting of printed material should be decreased by hydrophobic-surface modification of gravure printing form. The aim was to print wave-free homogenous layers. To achieve comparable results, modified and pure form were used simultaneously to print the same material. The printed material was mainly PEDOT:PSS and other, which is used in printed electronics. The properties (surface tension, viscosity) of printed materials were varied by additives. Printing conditions were varied too. The characteristic of printed layers were studied: resistivity, roughness, density, etc. The results shows decreasing of waviness, roughness and viscous fingering in final layer through use of hydrophobic gravure printing form, compared to print results with common printing form. This can be applied not only in the field of printed electronics.

W przyrodzie wiele struktur kształtuje się w trakcie wzrostu. Część z nich zawdzięcza swój kształt niejednorodności budującego je materiału. W wielu jednak przypadkach niepowtarzalny kształt końcowej struktury jest efektem fluktuacji ośrodka, wzmacnianych przez dynamikę wzrostu. Tego typu struktury można obserwować w wielu układach, takich jak: wytrącanie elektrochemiczne, proces wolnego spalania, krystalizacja, czy wzrost włókien i mikrotubuli. Praca Modele sieciowe wzrostu nierównowagowego poświęcona jest dwóm przypadkom wzrostu tego rodzaju - tworzeniu się kanałów w rozpuszczającym się ośrodku porowatym oraz problemowi palców lepkości, polegającym na wypieraniu z układu lepkiej cieczy przez ciecz o mniejszej lepkości. W wielu przypadkach proces wzrostu da się opisać przy pomocy spełniającego równanie Laplace’a, skalarnego pola p(x, t), które można interpretować jako stężenie reagentów lub ciśnienie. Pomimo iż równanie Laplace’a jest liniowe, problem wzrostu staje się nieliniowy z uwagi na warunki brzegowe – front jest niestabilny ze względu na małe zaburzenia. Tak więc, pomimo że w wielu przypadkach podstawowe mechanizmy opisujące proces wzrostu są dobrze znane, silnie nielokalny charakter procesów zachodzących na granicy międzyfazowej sprawia, że opis analityczny zagadnienia nie jest prosty. Dobrze opisane zostały przede wszystkim wczesne fazy wzrostu, kiedy można użyć liniowej analizy stabilności i znaleźć najsilniej wzmacniane długości fal zaburzenia. Głównym tematem pracy są, znacznie gorzej poznane, późniejsze fazy wzrostu, kiedy system wypełniony jest wieloma palczastymi strukturami, które wyewoluowały z początkowych niestabilności. Struktury te oddziałują ze sobą i rywalizują, a także rozszczepiają się tworząc bardziej złożone formy. W przypadku palców lepkości, aby otrzymać układ z wieloma stosunkowo cienkimi palcami, posłużono się prostokątną siecią kanalików, przez które płyną dwie ciecze. W zjawisku rozpuszczania się materiału porowatego szerokość i rodzaj powstających kanałów zależy natomiast bezpośrednio od tzw. liczby Damköhlera – funkcji przepływu, tempa reakcji oraz rozmiarów porów skalnych. W efekcie można dobrać parametry układu tak, by otrzymać liczne, cienkie kanały, rozgałęziające się lub nie. 1 W celu badania układów z cienkimi palcami wykonano eksperymenty mikrofluidyczne palców lepkości we współpracy z Instytutem Chemii Fizycznej PAN. Następnie stworzono opornikowy model numeryczny omawianego problemu. W modelu tym sieć kanalików (porów) przez które płynie płyn traktowana jest jako sieć oporników o zmieniającym się w czasie oporze. W przypadku palców lepkości opór ten zależy od lepkości płynu, który znajduje się w danej chwili w kanaliku, natomiast w przypadku rozpuszczania ośrodka porowatego opór jest malejącą funkcją średnicy kanalików, która rośnie w czasie na skutek rozpuszczania. Dodatkowo, w tym ostatnim przypadku, możliwe jest łączenie się poszczególnych kanalików w jeden, co przekłada się na dynamiczną zmianę topologii sieci oporników. Zarówno w eksperymencie jak i w symulacji numerycznej udało się otrzymać palce o różnej szerokości, w tym również bardzo cienkie, zajmujące szerokość rzędu odległości między kanalikami. W przypadku palców lepkości, a także w przypadku kanałów rozpuszczeniowych znaleziono zależność kształtu palców/kanałów od parametrów układu. W sytuacji, kiedy w układzie rośnie wiele palców ważną rolę odgrywają oddziaływania między nimi. Przede wszystkim oddziaływania te przejawiają się w konkurowaniu o dostępny w układzie przepływ – dłuższe palce ekranują krótszych sąsiadów. W rezultacie w układzie powstaje samopodobna struktura palców o różnej długości, zadanej rozkładem potęgowym. Przeanalizowano i porównano ze sobą rozkłady długości palców lepkości oraz kanałów rozpuszczeniowych otrzymując zbliżone do siebie wyniki. Inny rodzaj oddziaływań pomiędzy palcami to ich wzajemne przyciąganie bądź odpychanie się, które przejawia się ich niesymetrycznym kształtem. W celu opisu tego zjawiska stworzony został uniwersalny model opornikowy, który tłumaczy, jak siła i kierunek oddziaływań zależy od długości palców i od kontrastu ich oporu względem otoczenia. Model ten poprawnie tłumaczy zachowanie zarówno palców lepkości jak i kanałów rozpuszczeniowych. Nowym zjawiskiem zaobserwowanym przy okazji eksperymentów z dwiema cieczami mieszającymi się płynącymi przez sieć kanalików jest odrywanie się głów palców lepkości. Przeanalizowano przyczyny tego zjawiska, a wielkości odrywających się głów powiązane zostały z parametrami układu. W przypadku kanałów rozpuszczeniowych osobnym problemem jest znalezienie optymalnych warunków rozpuszczania, minimalizujących ilość reagenta potrzebnego do przebicia się kanału rozpuszczeniowego przez układ. Zbadano objętość reagenta potrzebną do przebicia jako funkcję parametrów układu znajdując nietrywialną zależność, gdzie poszczególne minima lokalne odpowiadają różnym reżimom rozpuszczania.
The structures of Nature are often shaped by growth processes. Some owe their form to the inhomogeneity of the constitutive matter. Frequently however the unique pattern of a final structure is determined by fluctuations in the medium, amplified by the growth dynamics. Structures of that kind occur in numerous processes, such as: electrochemical deposition, slow combustion, crystallisation, or the growth of fibres and microtubules. The dissertation ‘Network models of non-equilibrium growth’ is devoted to two particular cases: pattern formation in a dissolving porous medium, and the viscous fingering process, where a high-viscosity fluid is displaced by a less viscous one. The growth process in a wide variety of systems may be described in terms of a harmonic scalar field p(x, t), interpreted for instance as a reagent concentration or pressure. Despite the linearity of the Laplace equation, the growth problem becomes non-linear due to the boundary conditions – the front is unstable under small perturbations. Hence, even though the basic mechanisms of growth are well understood, the strongly non-linear character of the processes at the phase boundary makes an analytic description far from being simple. A good description exists for the early stages of growth, where linear stability analysis allows one to find the perturbation modes undergoing strongest amplification. The main focus of the present work are the much less understood later stages of growth, where the system is occupied by multiple finger-like structures evolved from the initial instabilities. These structures interact with each other, compete for growth, and branch into more and more complex forms. In the viscous fingering case, a rectangular lattice of channels hosting a pair of fluids is used to obtain a system featuring numerous relatively thin fingers. In the porous medium dissolution case, the width and type of emerging pattern depends directly on the so-called Damköhler number – a function of the flow, reaction rate and pore size. In effect one may choose the parameters of the system so as to produce numerous thin, fingerlike structures (so called ‘wormholes’), with or without branching. Systems exhibiting thin finger structures have been investigated in a series of microfluidic experiments in collaboration with the Institute of Physical Chemistry PAS. Subsequently, a nu1 merical model has been developed. For the purposes of the latter model, the network of channels (pores) is viewed as a network of resistors whose resistances evolve in time. In the viscous fingering case, the resistance depends on the viscosity of the liquid occupying a given channel; in the porous medium dissolution case, it is a decreasing function of the pore diameter (the diameters grow with time due to dissolution). Furthermore, in the latter case we allow several channels to merge into one, leading to a dynamical evolution of the network topology. Fingers of various widths have been achieved both experimentally and numerically, including extremely thin ones, whose width is of the same order as the channel spacing. The dependence of the finger/wormhole shape on the parameters of the system has been found for both viscous fingering and porous medium dissolution. In presence of several fingers, their interactions play a significant role. Most importantly, they lead the fingers to compete for the available flow, with longer fingers screening their shorter neighbours. This results in a self-similar pattern of fingers whose lengths obey a power-law distribution. The analysis of finger/wormhole lengths for viscous fingering and porous medium dissolution shows that the respective distributions are comparable. There are also attractive and repulsive interactions between the fingers, manifesting themselves in finger shape asymmetry. A universal resistor model has been developed in order to describe this phenomenon, explaining the dependence of interaction strength and direction on the length of the fingers, as well as their resistance relative to the bulk. The model yields correct results for both viscous fingering and porous medium dissolution. In the course of our experiments involving a pair of miscible fluids flowing through a lattice of channels, we have observed a new phenomenon where the heads of the fingers become detached. The causes of this behaviour have been analysed, producing a relation between the size of the detached heads and the parameters of a system. A separate problem in the case of wormhole formation in porous media is to find the optimal conditions for dissolution, minimising the amount of reagent necessary for a wormhole to penetrate the entire system (so-called break-through). We have investigated how the reagent volume needed for break-through varies with the parameters of the system. A non-trivial dependence has been established, with different local minima corresponding to different dissolution regimes.

Understanding flow and transport in porous media is critical as it plays a central role in many biological, natural, and industrial processes. Such processes are not limited to one length or time scale; they occur over a wide span of scales from micron to Kilometers and microseconds to years. While field-scale simulation relies on a continuum description of the flow and transport, one must take into account transport processes occurring on much smaller scales. In doing so, pore-scale modeling is a powerful tool for shedding light on processes at small length and time scales.

In this work, we look into the multi-phase flow and transport through porous media at two different scales, namely pore- and Darcy scales. First, using direct numerical simulations, we study pore-scale Eulerian and Lagrangian statistics. We study the evolution of Lagrangian velocities for uniform injection of particles and numerically verify their relationship with the Eulerian velocity field. We show that for three porous media velocity, probability distributions change over a range of porosities from an exponential distribution to a Gaussian distribution. We thus model this behavior by using a power-exponential function and show that it can accurately represent the velocity distributions. Finally, using fully resolved velocity field and pore-geometry, we show that despite the randomness in the flow and pore space distributions, their two-point correlation functions decay extremely similarly.

Next, we extend our previous study to investigate the effect of viscoelastic fluids on particle dispersion, velocity distributions, and flow resistance in porous media. We show that long-term particle dispersion could not be modulated by using viscoelastic fluids in random porous media. However, flow resistance compared to the Newtonian case goes through three distinct regions depending on the strength of fluid elasticity. We also show that when elastic effects are strong, flow thickens and strongly fluctuates even in the absence of inertial forces.

Next, we focused our attention on flow and transport at the Darcy scale. In particular, we study a tertiary improved oil recovery technique called surfactant-polymer flooding. In this work, which has been done in collaboration with Purdue enhanced oil recovery lab, we aim at modeling coreflood experiments using 1D numerical simulations. To do so, we propose a framework in which various experiments need to be done to quantity surfactant phase behavior, polymer rheology, polymer effects on rock permeability, dispersion, and etc. Then, via a sensitivity study, we further reduce the parameter space of the problem to facilitate the model calibration process. Finally, we propose a multi-stage calibration algorithm in which two critically important parameters, namely peak pressure drop, and cumulative oil recovery factor, are matched with experimental data. To show the predictive capabilities of our framework, we numerically simulate two additional coreflood experiments and show good agreement with experimental data for both of our quantities of interest.

Lastly, we study the unstable displacement of non-aqueous phase liquids (e.g., oil) via a finite-size injection of surfactant-polymer slug in a 2-D domain with homogeneous and heterogeneous permeability fields. Unstable displacement could be detrimental to surfactant-polymer flood and thus is critically important to design it in a way that a piston-like displacement is achieved for maximum recovery. We study the effects of mobility ratio, finite-size length of surfactant-polymer slug, and heterogeneity on the effectiveness of such process by looking into recovery rate and breakthrough and removal times.