Dissertations / Theses on the topic 'Capillary number'

Complex interactions in porous media play an important role on many industrial and geotechnical applications, such as groundwater treatment, porous catalysts, carbon geosequestration, and oil recovery. Rate-dependent wetting effects are of great significance in understanding the multiphase behaviours of porous media thus further throw light on engineering solutions to the above problems. In this thesis, a modified smoothed particle hydrodynamics (SPH) model is applied to simulate (1) the contact angle dynamics and (2) stretching of liquid bridge at meso-scale. This SPH model adopted an inter-particle force formulation with short-range repulsive force and long-range attractive force to take into account single-phase and multiphase interactions. Particularly, a newly-introduced viscous force is imposed at the liquid-solid interface to capture the rate-dependent behaviours of contact angle without prescribing additional arbitrary condition or force. After identification of model parameters, the rate-dependent contact angle behaviours are studied for both wetting and dewetting phenomena. By analysing the contact angle results of fluid at triple-line region with different moving speeds, the dynamic contact angles and corresponding capillary numbers can be correlated by power law functions. The derived correlation and constants are compared with different forms of empirical power law functions and the results are satisfactory. Moreover, we investigated the properties of stretching liquid bridges, including shape evolution, liquid transfer ratio and flow condition under dynamic loading. Different stretching rates are applied, and the shapes of liquid bridge at same breakup distance is presented. By differentiating the wettability of top and bottom substrates, the liquid transfer ratio regarding wettability difference and substrate moving speed is studied.

This thesis describes a new dynamic network model for imbibition which is based on a physically realistic description of the complex dynamics of corner film flow, swelling and snap-off. The model shows that film flow is a capillary driven non-linear diffusive process and that the competition between snapoff and frontal displacements is rate dependent and results in rate dependent relative permeabilities and residual saturations. In contrast to previously published models in which length scales for snap-off are either specified a priori or calculated assuming steady-state film flow and constant film conductivities, in the present model, snap-off arises as a natural consequence of the fully transient nature of film flow and swelling. The network model is used to analyse the complex interaction between displacement rate, contact angle, aspect ratio and pore and throat shape on relative permeability and residual saturation. Computed relative permeabilities and residual saturations are compared with laboratory measurements reported in the literature. It is concluded that the magnitude of the rate effect on imbibition relative permeabilities and residual saturations for a particular rock microstructure and wettability condition depends largely on the pore-throat aspect ratio. Higher aspect ratios result in stronger rate effects than do smaller aspect ratios.

The productivity of most gas condensate wells is reduced significantly due to condensate banking when the bottom hole pressure falls below the dew point. The liquid drop-out in these very high rate gas wells may lead to low recovery problems. The most important parameter for determining condensate well productivity is the effective gas permeability in the near wellbore region, where very high velocities can occur. An understanding of the characteristics of the high-velocity gas-condensate flow and relative permeability data is necessary for accurate forecast of well productivity. In order to tackle this goal, a series of two-phase drainage relative permeability measurements on a moderate permeability North Marmara &ndash
1 gas well carbonate core plug sample, using a simple synthetic binary retrograde condensate fluid sample were conducted under reservoir conditions which corresponded to near miscible conditions. As a fluid system, the model of methanol/n-hexane system was used as a binary model that exhibits a critical point at ambient conditions. The interfacial tension by means of temperature and the flow rate were varied in the laboratory measurements. The laboratory experiments were repeated for the same conditions of interfacial tension and flow rate at immobile water saturation to observe the influence of brine saturation in gas condensate systems. The laboratory experiment results show a clear trend from the immiscible relative permeability to miscible relative permeability lines with decreasing interfacial tension and increasing velocity. So that, if the interfacial tension is high and the flow velocity is low, the relative permeability functions clearly curved, whereas the relative permeability curves straighten as a linear at lower values of the interfacial tension and higher values of the flow velocity. The presence of the immobile brine saturation in the porous medium shows the same shape of behavior for relative permeability curves with a small difference that is the initial wetting phase saturations in the relative permeability curve shifts to the left in the presence of immobile water saturation. A simple new mathematical model is developed to compute the gas and condensate relative permeabilities as a function of the three-parameter. It is called as condensate number
NK so that the new model is more sensitivity to temperature that represents implicitly the effect of interfacial tension. The new model generated the results were in good agreement with the literature data and the laboratory test results. Additionally, the end point relative permeability data and residual saturations satisfactorily correlate with literature data. The proposed model has fairly good fitness results for the condensate relative permeability curves compared to that of gas case. This model, with typical parameters for gas condensates, can be used to describe the relative permeability behavior and to run a compositional simulation study of a single well to better understand the productivity of the field.

Optimizing proppant pack conductivity and proppant-transport and -deposition patterns in a hydraulic fracture is of critical importance to sustain effective and economical production of petroleum hydrocarbons. In this research, a numerical modeling approach, combining the discrete element method (DEM) with the lattice Boltzmann (LB) simulation, was developed to provide fundamental insights into the factors regulating the interactions between reservoir depletion, proppant-particle compaction and movement, single-/multiphase flows and non-Darcy flows in a hydraulic fracture, and fracture conductivity evolution from a partial-monolayer proppant concentration to a multilayer proppant concentration. The potential effects of mixed proppants of different sizes and types on the fracture conductivity were also investigated. The simulation results demonstrate that a proppant pack with a smaller diameter coefficient of variation (COV), defined as the ratio of standard deviation of diameter to mean diameter, provides better support to the fracture; the relative permeability of oil was more sensitive to changes in geometry and stress; when effective stress increased continuously, oil relative permeability increased nonmonotonically; the combination of high diameter COV and high effective stress leads to a larger pressure drop and consequently a stronger non-Darcy flow effect. The study of proppant mixtures shows that mixing of similar proppant sizes (mesh-size-20/40) has less influence on the overall fracture conductivity than mixing a very fine mesh size (mesh-size-100); selection of proppant type is more important than proppant size selection when a proppant mixture is used. Increasing larger-size proppant composition in the proppant mixture helps maintain fracture conductivity when the mixture contains lower-strength proppants. These findings have important implications to the optimization of proppant placement, completion design, and well production. In the hydraulic-mechanical rock-proppant system, a fundamental understanding of multiphase flow in the formation rock is critical in achieving sustainable long-term productivity within a reservoir. Specifically, the interactions between the critical dimensionless numbers associated with multiphase flow, including contact angle, viscosity ratio, and capillary number (Ca), were investigated using X-ray micro computed tomography (micro-CT) scanning and LB modeling. The primary novel finding of this study is that the viscosity ratio affects the rate of change of the relative permeability curves for both phases when the contact angle changes continuously. Simulation results also indicate that the change in non-wetting fluid relative permeability was larger when the flow direction was switched from vertical to horizontal, which indicated that there was stronger anisotropy in larger pore networks that were primarily occupied by the non-wetting fluid. This study advances the fundamental understanding of the multiphysics processes associated with multiphase flow in geologic materials and provides insight into upscaling methodologies that account for the influence of pore-scale processes in core- and larger-scale modeling frameworks. During reservoir depletion processes, reservoir formation damage is an issue that will affect the reservoir productivity and various phases in fluid recovery. Invasion of formation fine particles into the proppant pack can affect the proppant pack permeability, leading to potential conductivity loss. The combined DEM-LB numerical framework was used to evaluate the role of proppant particle size heterogeneity (variation in proppant particle diameter) and effective stress on the migration of detached fine particles in a proppant supported fracture. Simulation results demonstrate that a critical fine particle size exists: when a particle diameter is larger or smaller than this size, the deposition rate increases; the transport of smaller fines is dominated by Brownian motion, whereas the migration of larger fines is dominated by interception and gravitational settling; this study also indicates that proppant packs with a more heterogeneous particle-diameter distribution provide better fines control. The findings of this study shed lights on the relationship between changing pore geometries, fluid flow, and fine particle migration through a propped hydraulic fracture during the reservoir depletion process.
Doctor of Philosophy

The goal of submitted thesis is to perform a computer simulation of bubble creation in T-channel. In the first section of the paper, the theoretical applications of microfluidic bubble, micromachines and droplet formation are described. In the second part of the text, author uses cross flowing method for simulation od bubble creation. Furthermore, several settings in computer simulation software Fluent are mentioned. In addition, the influence of velocity at the T-channel inlet on surface tension and on bubble length is presented.

L'injection de tensioactifs est une méthode très appliquée dans le domaine de la récupération améliorée des hydrocarbures. Cependant, son efficacité repose sur la capacité de ces agents chimiques à mobiliser l'huile résiduelle en diminuant la tension interfaciale entre l'huile et l'eau. Des modèles à l'échelle du réservoir calculent l'efficacité de la récupération d'huile résiduelle par injection de solutions contenant des tensioactifs. Les mécanismes physiques pris en compte dans les modélisations font intervenir la physico-chimie du système roche-fluide et une courbe globale donnant la saturation résiduelle en huile en fonction du nombre capillaire (courbe de désaturation capillaire). Cette donnée est majeure dans le calcul de l'efficacité de récupération d'huile par injection de solutions de tensioactifs. En effet la mobilisation de l'huile résiduelle laissée en place après injection d'eau n'est possible qu'en augmentant considérablement le nombre capillaire. La prédiction de l'efficacité d'un procédé chimique de récupération passe par la compréhension, à l'échelle du pore, du processus de mobilisation des ganglions d'huile suivant la structure poreuse et le nombre capillaire. L'objet de cette thèse est de caractériser la récupération d'huile tertiaire en fonction du nombre capillaire dans diverses roches mouillables à l'eau. Ces courbes permettront de quantifier l'effet de la microstructure, les hétérogénéités du milieu poreux et diverses propriétés pétrophysiques sur la récupération d'huile. Cette thèse permettra aussi de caractériser les différents mécanismes d'action de tensioactifs sur la mobilisation d'huile résiduelle dans le milieu poreux. L'expérimentation par tomographie RX est utilisée. La tomographie RX permettra de caractériser les courbes de désaturation capillaire à l'échelle de Darcy et visualiser localement le déplacement d'huile résiduelle à travers les milieux poreux. Des essais d'écoulement diphasique sous micro-CT permettront d'observer in-situ et d'étudier les interfaces eau/huile et leurs évolutions en 3D au sein du milieu poreux en fonction du nombre capillaire.

Thesis (Ph. D.)--Ohio State University, 2004.
Title from first page of PDF file. Document formatted into pages; contains xv, 145 p. : ill. (some col.). Advisors: David L. Tomasko and L. James Lee, Dept. of Chemical Engineering. Includes bibliographical references (p. 135-145).

Ce travail porte sur l'étude théorique des interfaces entre deux fluides visqueux, soumis à un écoulement de Couette plan. Dans cette situation hors d'équilibre, les fluctuations thermiques de l'interface sont modifiées en raison du couplage par le cisaillement entre les effets visqueux et les effets de tension. Comme c'est le cas pour d'autres systèmes de matière molle (par exemple, les phases lamellaires), le cisaillement peut alors amplifier ou amortir les déformations interfaciales. On s'intéresse tout d'abord à la dynamique des fluctuations interfaciales. On montre que ces dernières vérifient une équation stochastique non-linéaire, dont la solution est contrôlée par un paramètre sans dimension qui contient toute l'information sur le système. La résolution à faible taux de cisaillement révèle que le déplacement quadratique moyen des fluctuations thermiques diminue avec l'écoulement, conformément aux observations expérimentales et numériques. Ensuite, on étudie l'influence des effets inertiels sur la stabilité de l'écoulement, dans le régime des fortes viscosités et des faibles tensions. Ce régime des grands nombres capillaires n'a été que très peu étudié, mais trouve sa pertinence par exemple dans les mélanges biphasiques de colloïdes et de polymères. Des critères de stabilité simples sont mis en évidence. Finalement, on réalise une étude numérique des propriétés des fluctuations interfaciales à grand cisaillement. Bien que les effets visqueux soient dominants, il en ressort une phénoménologie similaire à certains modèles de turbulence.

This thesis deals with the dynamics of a thin liquid film falling down a heated plate. The heating yields surface tension gradients that induce thermocapillary stresses on the free surface, thus affecting the stability and the evolution of the film. Accounting for the coherence of the flow due to viscosity, two main approaches that reduce the dimensionality of the original problem are usually considered depending on the flow rate (as measured by the Reynolds number): the `long wave' asymptotic expansion for small Reynolds numbers and the `integral boundary layer' approximation for moderate Reynolds numbers. The former suffers from singularities and the latter from incorrectness of the instability threshold for the occurrence of hydrodynamic waves. Thus, the aim of this thesis is twofold: in a first part, we define quantitatively the validity of the `long wave' evolution equation (Benney equation) for the film thickness h including the thermocapillary effect; and in a second part, we improve the `integral boundary layer' approach by combining a gradient expansion to a weighted residual method.

In the first part, we further investigate the Benney equation in its validity domain in the case of periodically inhomogeneous heating in the streamwise direction. It induces steady-state deformations of the free surface with increased transfer rate in regions where the film is thinner, and also in average. The inhomogeneities of the heating also modify the nature of travelling wave solutions at moderate temperature gradients and allows for suppressing wave motion at larger ones.

Moreover, large temperature gradients (for instance positive ones) in the streamwise direction produce large local film thickening that may in turn become unstable with respect to transverse disturbances such that the flow may organize in rivulet-like structures. The mechanism of such instability is elucidated via an energy analysis. The main features of the rivulet pattern are described experimentally and recovered by direct numerical simulations.

In the second part, various models are obtained, which are valid for larger Reynolds numbers than the Benney equation and account for second-order viscous and inertial effects. We then elaborate a strategy to select the optimal model in terms of linear stability properties and existence of nonlinear solutions (solitary waves), for the widest possible range of parameters. This model -- called reduced model -- is a system of three coupled evolution equations for the local film thickness h, the local flow rate q and the surface temperature Ts. Solutions of this model indicate that the interaction of the hydrodynamic and thermocapillary modes is non-trivial, especially in the region of large-amplitude solitary waves.

Finally, the three-dimensional evolution of the solutions of the reduced model in the presence of periodic forcing and noise compares favourably with available experimental data in isothermal conditions and with direct numerical simulations in non-isothermal conditions.

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Cette thèse analyse la dynamique d'un film mince s'écoulant le long d'une paroi chauffée. Le chauffage crée des gradients de tension superficielle qui induisent des tensions thermocapillaires à la surface libre, altérant ainsi la stabilité et l'évolution du film. Grâce à la cohérence de l'écoulement assurée par la viscosité, deux approches permettant de réduire la dimensionnalité du problème original sont habituellement considérées suivant le débit (mesuré par le nombre de Reynolds): l'approximation asymptotique dite `longues ondes' pour les faibles nombres de Reynolds et l'approximation `intégrale couche limite' pour les nombres de Reynolds modérés. Cependant, la première approximation souffre de singularités et la dernière de prédictions imprécises du seuil de stabilité des ondes hydrodynamiques à la surface du film. Le but de cette thèse est donc double: dans une première partie, il s'agit de déterminer, de manière quantitative, la validité de l'équation d'évolution `longues ondes' (ou équation de Benney) pour l'épaisseur du film h, en y incluant l'effet thermocapillaire; et dans une seconde partie, il s'agit d'améliorer l'approche `intégrale couche limite' en combinant un développement en gradients avec une méthode aux résidus pondérés.

Dans la première partie, nous étudions l'équation de Benney, dans son domaine de validité, dans le cas d'un chauffage inhomogène et périodique dans la direction de l'écoulement. Cela induit des déformations permanentes de la surface libre avec un accroissement du transfert de chaleur dans les régions où le film est plus mince, mais aussi en moyenne. Un chauffage inhomogène modifie également la nature des solutions d'ondes progressives pour des gradients de températures modérés et conduit même à leur suppression pour des gradients de températures plus importants. De plus, ceux-ci, lorsqu'ils sont par exemple positifs le long de l'écoulement, produisent des épaississements localisés du film qui peuvent à leur tour devenir instables par rapport à des perturbations suivant la direction transverse à l'écoulement. Ce dernier s'organise alors sous forme d'une structure en rivulets. Le mécanisme de cette instabilité est élucidé via une analyse énergétique des perturbations. Les principales caractéristiques des structures en rivulets sont décrites expérimentalement et retrouvées par l'intermédiaire de simulations numériques.

Dans la seconde partie, nous dérivons une famille de modèles valables pour des nombres de Reynolds plus grands que l'équation de Benney, qui prennent en compte les effets visqueux et inertiels du second ordre. Nous élaborons ensuite une stratégie pour sélectionner le modèle optimal en fonction de ses propriétés de stabilité linéaire et de l'existence de solutions non-linéaires (ondes solitaires), et ce pour la gamme de paramètres la plus large possible. Ce modèle -- appelé modèle réduit -- est un système de trois équations d'évolution couplées pour l'épaisseur locale de film h, le débit local q et la température de surface Ts. Les solutions de ce modèle indiquent que l'interaction des modes hydrodynamiques et thermocapillaires n'est pas triviale, spécialement dans le domaine des ondes solitaires de grande amplitude. Finalement, l'évolution tri-dimensionnelle des solutions du modèle réduit en présence d'un forçage périodique ou d'un bruit se compare favorablement aux données expérimentales disponibles en conditions isothermes, ainsi qu'aux simulations numériques directes en conditions non-isothermes

Doctorat en sciences appliquées
info:eu-repo/semantics/nonPublished

碩士
臺灣大學
機械工程學研究所
96
The present study is aimed at investigating theoretically the dip-coating processes. Based on the appropriate scaling analysis, three flow regimes are defined; they are the low-capillary number flows, the viscocapillary flows, and the high-capillary number flows. The whole flow domain is further decomposed into three regions with specific flow characteristics; they are Region I, the constant-thickness region, Region II, the nearly one-dimensional dynamic region, and Region III, the static region. Numerical calculations using the fifth-order Runge-Kutta- Fehlberg method are needed for the dynamic region, which is then matched smoothly to Region I and III to give the solution for the whole flow domain. The results indicate that the liquid film is reduced when the gravity effect becomes important or the value of To increases. Thus, in micro-gravity environment, a larger distance is necessary to attain a uniform thickness of coating material on the substrate when the dip-coating process is applied. In addition, with stronger surface tension or a smaller value of Ca the free surface of the liquid film becomes more concave and, consequently, the length of the liquid film before reaching the constant-thickness region, L, increases.

碩士
高雄醫學大學
臨床醫學研究所
100
論文英文摘要 Alpha-thalassemia is one of the most common autosomal recessive disorders in the world and characterized by a microcytic hypochromic anemia. Alpha-thalassemia has a high prevalence rate in Southeast Asia area including Taiwan with a rate of 5%. A majority of the genetic defects of α-thalassemia are deletions of the α-globin genes. Normal individuals have four functioning α-globin genes and are defined as αα/αα. According to the defects of the α-globin, the clinical phenotypes of α-thalassemia could be divided into four groups. Individuals with loss of one α-globin gene (-α/αα) have 3 functional α-globin genes. Loss of one gene constitutes a silent carrier state without any clinical symptoms. Alpha thalassemia trait occurs with loss of two α-globin genes, namely -α/-α, --/αα. Such individuals are characterized with mild to moderate microcytic anemia. Individuals with hemoglobin (Hb) H disease show deletions of three α-globin genes. Such individuals are characterized with more severe anemia and splenomegaly. Lastly, the loss of four α-globin genes causes Hb Barts hydrops in individuals, which result in intrauterine death. The initial laboratory examinations for the diagnosis of α-thalassemia include a complete blood cell count, red cell indices, iron status and hemoglobin electrophoresis. To identify the copy number of α-globin genes in α-thalassemia, we developed a novel method using multiplex polymerase chain reaction (PCR) in combination with the CE analysis. Total 66 α-thalassemia patients with α-globin gene deletions including 6 with -α3.7 and 4 -α4.2 types of one-gene deletion, 27 with Southeast Asia type (- -SEA), 16 Filipino (- -FIL) type, 5 Thai (- -THAI) types of two-gene deletions, 7 Hb H disease with three-gene deletions, and 1 Hb Barts hydrops fetalis with four-gene deletions were included in this study. 46 normal controls were also obtained at Kaohsiung Medical University Hospital. The copy number ratios of HBA1/KRIT1, HBA2/KRIT1, HBA1/CYBB and HBA2/CYBB were around 2/2, 2/2, 2/1 and 2/1 in normal male individuals, and around 2/2, 2/2, 2/2 and 2/2 in normal female individuals. The copy number ratios of HBA1/KRIT1, HBA2/KRIT1, HBA1/CYBB and HBA2/CYBB were around 2/2, 1/2, 2/1 and 1/1 in male patients, and around 2/2, 1/2, 2/2 and 1/2 in female patients with a genotype of one α-globin-gene deletion, -α/αα, α-thalassemia. The copy number ratios of HBA1/KRIT1, HBA2/KRIT1, HBA1/CYBB and HBA2/CYBB were around 1/2, 0/2, 1/2 and 0/2 in male patients, and around 1/2, 1/2, 1/2 and 1/2 in female patients with a genotype of two α-globin-gene deletions, --/αα, α-thalassemia. The copy number ratios of HBA1/KRIT1, HBA2/KRIT1, HBA1/CYBB and HBA2/CYBB were around 1/2, 0/2, 1/1 and 0/1 in patients and around 1/2, 0/2, 1/2 and 0/2 in female patients with a genotype of three α-globin-gene deletions, --/-α, α-thalassemia. There is no HBA1 and HBA2 copy number detection in a fetus with a four α-globin-gene deletions, --/--, hemoglobin Barts hydrops fetalis α-thalassemia. In the present study, we established a rapid and efficient method to measure the copy number of two α-globin genes, HBA1 and HBA2, in α-thalassemia patients, determine low level of maternal DNA contamination in the fetus specimen for prenatal diagnosis and defect of rare multiplicated α-globin genes in the individuals. The proposed method provides a rapid detection of the common α-globin gene deletions. Sixty-six α-thalassemia patients and 46 normal controls were included in the present study. The obtained results showed good correlation with those obtained by gap PCR. Moreover, a low amount of maternal cell contamination in the fetus specimen for the prenatal diagnosis of hemoglobin Barts hydrops fetalis as well as the rare multiplicated α-globin genes can be identified using this method.

Multiphase flows abound in nature and enterprises. Our daily interactions with fluids - washing, drinking, and cooking, for example - occur at a free surface and within the realm of multiphase flows. The applications of multiphase flows within the context of emulsions, which are caused by mixing two immiscible fluids, have been of interest since the nineteenth century: compartmentalizing one fluid in another is particularly of interest in applications in pharmaceutical, materials, microfluidics, chemical, and biological engineering. Even more control in compartmentalization and delivery can be obtained through the usage of double emulsions, which are emulsions of smaller drops (i.e., inner drop) within larger drops (i.e., outer drop). The goal of this work is to understand the dynamic behavior of compound drops in confined flow at low Reynolds numbers. These behaviors include the migration patterns, limit cycles, and equilibrium locations in confined flows such as channel flows.

Firstly, we look at non-concentric compound drops that are subject to simple shear flows. The eccentricity in the inner drop is either within the place of shear, normal to the plane of shear, or mixed. We show unreported motions that persist throughout time regardless of the initial eccentricity, given that the deformations of the inner and outer drops are small. Understanding the temporal dynamics of compound drops within the simple shear flow, one of the simplest background flows that may be imposed, allows us to probe at the dynamics of more complicated background flows.

Secondly, we look at the lateral migration of compound drops in a Poiseuille flow. Depending on the initial condition, we show that there are multiple equilibria. We also show that the majority of initial configurations results in the compound drop with symmetry about the short wall direction. We then show the time it takes for the interfaces to merge if a given initial configuration does not reach the aforementioned symmetry.

Thirdly, while the different equilibria of compound drops offer some positional differences at different radii ratio, we show that the lift force profiles at non-equilibrium locations offer distinctly different results for compound drops with different radii ratio. We then look at how this effect is greater than changes that arise due to viscosity ratio changes, and offer insights on what may create such a change in the lift force profile.