Spreading due to heterogeneity in two-phase flow

Postprint (published version)

Pore-scale modeling of two-phase flow instabilities in porous media

Les problèmes d'écoulements multiphasiques en média poreux sont d'un grand intérêt pour de nombreuses applications scientifiques et techniques ; comme la séquestration de C02, l'extraction de pétrole et la dépollution des aquifères. La complexité intrinsèque des systèmes multiphasiques et l'hétérogénéité des formations géologiques sur des échelles multiples représentent un challenge majeur pour comprendre et modéliser les déplacements immiscibles dans les milieux poreux. Les descriptions à l'échelle supérieure basées sur la généralisation de l'équation de Darcy sont largement utilisées, mais ces méthodes sont sujettes à limitations pour les écoulements présentant de l'hystérèse. Les avancées récentes en terme de performances computationnelles et le développement de méthodes précises pour caractériser l'espace interstitiel ainsi que la distribution des phases ont favorisé l'utilisation de modèles qui permettent une résolution fine à l'échelle du pore. Ces modèles offrent un aperçu des caractéristiques de l'écoulement qui ne peuvent pas être facilement observées en laboratoire et peuvent être utilisé pour expliquer la différence entre les processus physiques et les modèles à l'échelle macroscopique existants. L'objet premier de la thèse se porte sur la simulation numérique directe : les équations de Navier-Stokes sont résolues dans l'espace interstitiel et la méthode du volume de fluide (VOF) est employée pour suivre l'évolution de l'interface. Dans VOF, la distribution des phases est décrite par une fonction fluide pour l'ensemble du domaine et des conditions aux bords particulières permettent la prise en compte des propriétés de mouillage du milieu poreux. Dans la première partie de la thèse, nous simulons le drainage dans une cellule Hele-Shaw 2D avec des obstacles cylindriques. Nous montrons que l'approche proposée est applicable même pour des ratios de densité et de viscosité très importants et permet de modéliser la transition entre déplacement stable et digitation visqueuse. Nous intéressons ensuite à l'interprétation de la pression capillaire à l'échelle macroscopique. Nous montrons que les techniques basées sur la moyenne spatiale de la pression présentent plusieurs limitations et sont imprécises en présence d'effets visqueux et de piégeage. Au contraire, une définition basée sur l'énergie permet de séparer les contributions capillaires des effets visqueux. La seconde partie de la thèse est consacrée à l'investigation des effets d'inertie associés aux reconfigurations irréversibles du ménisque causé par l'interface des instabilités. Comme prototype pour ces phénomènes, nous étudions d'abord la dynamique d'un ménisque dans un pore angulaire. Nous montrons que, dans un réseau de pores cubiques, les sauts et reconfigurations sont si fréquents que les effets d'inertie mènent à différentes configurations des fluides. A cause de la non-linéarité du problème, la distribution des fluides influence le travail des forces de pression, qui, à son tour, provoque une chute de pression dans la loi de Darcy. Cela suggère que ces phénomènes devraient être pris en compte lorsque que l'on décrit l'écoulement multiphasique en média poreux à l'échelle macroscopique. La dernière partie de la thèse s'attache à démontrer la validité de notre approche par une comparaison avec des expériences en laboratoire : un drainage instable dans un milieu poreux quasi 2D (une cellule Hele-Shaw avec des obstacles cylindriques). Plusieurs simulations sont tournées sous différentes conditions aux bords et en utilisant différents modèles (modèle intégré 2D et modèle 3D) afin de comparer certaines quantités macroscopiques avec les observations au laboratoire correspondantes. Malgré le challenge de modéliser des déplacements instables, où, par définition, de petites perturbations peuvent grandir sans fin, notre approche numérique apporte de résultats satisfaisants pour tous les cas étudiés. - Problems involving multiphase flow in porous media are of great interest in many scientific and engineering applications including Carbon Capture and Storage, oil recovery and groundwater remediation. The intrinsic complexity of multiphase systems and the multi scale heterogeneity of geological formations represent the major challenges to understand and model immiscible displacement in porous media. Upscaled descriptions based on generalization of Darcy's law are widely used, but they are subject to several limitations for flow that exhibit hysteric and history- dependent behaviors. Recent advances in high performance computing and the development of accurate methods to characterize pore space and phase distribution have fostered the use of models that allow sub-pore resolution. These models provide an insight on flow characteristics that cannot be easily achieved by laboratory experiments and can be used to explain the gap between physical processes and existing macro-scale models. We focus on direct numerical simulations: we solve the Navier-Stokes equations for mass and momentum conservation in the pore space and employ the Volume Of Fluid (VOF) method to track the evolution of the interface. In the VOF the distribution of the phases is described by a fluid function (whole-domain formulation) and special boundary conditions account for the wetting properties of the porous medium. In the first part of this thesis we simulate drainage in a 2-D Hele-Shaw cell filled with cylindrical obstacles. We show that the proposed approach can handle very large density and viscosity ratios and it is able to model the transition from stable displacement to viscous fingering. We then focus on the interpretation of the macroscopic capillary pressure showing that pressure average techniques are subject to several limitations and they are not accurate in presence of viscous effects and trapping. On the contrary an energy-based definition allows separating viscous and capillary contributions. In the second part of the thesis we investigate inertia effects associated with abrupt and irreversible reconfigurations of the menisci caused by interface instabilities. As a prototype of these phenomena we first consider the dynamics of a meniscus in an angular pore. We show that in a network of cubic pores, jumps and reconfigurations are so frequent that inertia effects lead to different fluid configurations. Due to the non-linearity of the problem, the distribution of the fluids influences the work done by pressure forces, which is in turn related to the pressure drop in Darcy's law. This suggests that these phenomena should be taken into account when upscaling multiphase flow in porous media. The last part of the thesis is devoted to proving the accuracy of the numerical approach by validation with experiments of unstable primary drainage in a quasi-2D porous medium (i.e., Hele-Shaw cell filled with cylindrical obstacles). We perform simulations under different boundary conditions and using different models (2-D integrated and full 3-D) and we compare several macroscopic quantities with the corresponding experiment. Despite the intrinsic challenges of modeling unstable displacement, where by definition small perturbations can grow without bounds, the numerical method gives satisfactory results for all the cases studied.

Spatiotemporal adaptive multiscale multiphysics simulations of two-phase flow

We present a spatiotemporal adaptive multiscale algorithm, which is based on the Multiscale Finite Volume method. The algorithm offers a very efficient framework to deal with multiphysics problems and to couple regions with different spatial resolution. We employ the method to simulate two-phase flow through porous media. At the fine scale, we consider a pore-scale description of the flow based on the Volume Of Fluid method. In order to construct a global problem that describes the coarse-scale behavior, the equations are averaged numerically with respect to auxiliary control volumes, and a Darcy-like coarse-scale model is obtained. The space adaptivity is based on the idea that a fine-scale description is only required in the front region, whereas the resolution can be coarsened elsewhere. Temporal adaptivity relies on the fact that the fine-scale and the coarse-scale problems can be solved with different temporal resolution (longer time steps can be used at the coarse scale). By simulating drainage under unstable flow conditions, we show that the method is able to capture the coarse-scale behavior outside the front region and to reproduce complex fluid patterns in the front region.

Yeast vacuoles fragment in an asymmetrical two-phase process with distinct protein requirements.

Yeast vacuoles fragment and fuse in response to environmental conditions, such as changes in osmotic conditions or nutrient availability. Here we analyze osmotically induced vacuole fragmentation by time-lapse microscopy. Small fragmentation products originate directly from the large central vacuole. This happens by asymmetrical scission rather than by consecutive equal divisions. Fragmentation occurs in two distinct phases. Initially, vacuoles shrink and generate deep invaginations that leave behind tubular structures in their vicinity. Already this invagination requires the dynamin-like GTPase Vps1p and the vacuolar proton gradient. Invaginations are stabilized by phosphatidylinositol 3-phosphate (PI(3)P) produced by the phosphoinositide 3-kinase complex II. Subsequently, vesicles pinch off from the tips of the tubular structures in a polarized manner, directly generating fragmentation products of the final size. This phase depends on the production of phosphatidylinositol-3,5-bisphosphate and the Fab1 complex. It is accelerated by the PI(3)P- and phosphatidylinositol 3,5-bisphosphate-binding protein Atg18p. Thus vacuoles fragment in two steps with distinct protein and lipid requirements.

Calculations of Boiling Two-Phase Flow Using a Porous Media Model

Boiling two-phase flow and the equations governing the motion of fluid in two-phase flows are discussed in this thesis. Disposition of the governing equations in three-dimensional complex geometries is considered from the perspective of the porous medium concept. The equations governing motion in two-phase flows were formulated, discretized and implemented in a subroutine for pressure-velocity solution utilizing the SIMPLE algorithm modified for two-phase flow. The subroutine was included in PORFLO, which is a three-dimensional 5-equation porous media model developed at VTT by Jaakko Miettinen. The development of two-phase flow and the resulting void fraction distribution was predicted in a geometry resembling a section of BWR fuel bundle in a couple of test cases using PORFLO.

Gas-solid two-phase flow in the riser of circulating fluidized beds: mathematical modelling and numerical simulation

A mathematical model is developed for gas-solids flows in circulating fluidized beds. An Eulerian formulation is followed based on the two-fluids model approach where both the fluid and the particulate phases are treated as a continuum. The physical modelling is discussed, including the formulation of boundary conditions and the description of the numerical methodology. Results of numerical simulation are presented and discussed. The model is validated through comparison to experiment, and simulation is performed to investigate the effects on the flow hydrodynamics of the solids viscosity.

Two-Phase (Solid-Liquid) Flow in Inclined Pipes

This paper presents an experimental research about the behavior of two-phase flows in inclined pipes. The inclination angle varied from 5° to 45° and the slurry solid concentration varied up to 15%. It was concluded that the head losses of the downward sloping pipe flow are always lower than the head losses of the horizontal flow and these are always lower than the head losses of the upward sloping pipe flow, regardless the concentration and inclination angle. It was possible to develop empirical equations to calculate the head losses of the horizontal flow and the upward and downward sloping pipe flows.

Bubble-Bubble Interaction in Horizontal Two-Phase Slug Flow

Modelling of the slug structure requires a new effort on fundamental research. To clarify some aspects of the horizontal slug flow, an experimental study of the behaviour of two isolated bubbles in a single-phase liquid flow was performed. This procedure was adopted to avoid the overlap of different phenomena induced by a train of long bubbles. The experimental facility consists of a 90-m horizontal PVC pipe with internal diameter of 0,053 m. The behaviour of two single air bubbles travelling in a water flow was studied. Focus was given on the influence of the distance between the bubbles on the velocity of the second bubble. This study allows the understanding of the mechanism of overtaking that takes place right after the slug formation and that precedes the coalescence of bubbles in a slug flow. The results show that bubbles placed behind a liquid slug smaller than a critical value move faster than the leading one. Otherwise, they move slower than the leading one.

Detection of Horizontal Two-Phase Flow Patterns Through a Neural Network Model

One of the main problems related to the transport and manipulation of multiphase fluids concerns the existence of characteristic flow patterns and its strong influence on important operation parameters. A good example of this occurs in gas-liquid chemical reactors in which maximum efficiencies can be achieved by maintaining a finely dispersed bubbly flow to maximize the total interfacial area. Thus, the ability to automatically detect flow patterns is of crucial importance, especially for the adequate operation of multiphase systems. This work describes the application of a neural model to process the signals delivered by a direct imaging probe to produce a diagnostic of the corresponding flow pattern. The neural model is constituted of six independent neural modules, each of which trained to detect one of the main horizontal flow patterns, and a last winner-take-all layer responsible for resolving when two or more patterns are simultaneously detected. Experimental signals representing different bubbly, intermittent, annular and stratified flow patterns were used to validate the neural model.

Two-phase flow measurements with spacer grid in a rod bundle geometry

Heat transfer effectiveness in nuclear rod bundles is of great importance to nuclear reactor safety and economics. An important design parameter is the Critical Heat Flux (CHF), which limits the transferred heat from the fuel to the coolant. The CHF is determined by flow behaviour, especially the turbulence created inside the fuel rod bundle. Adiabatic experiments can be used to characterize the flow behaviour separately from the heat transfer phenomena in diabatic flow. To enhance the turbulence, mixing vanes are attached to spacer grids, which hold the rods in place. The vanes either make the flow swirl around a single sub-channel or induce cross-mixing between adjacent sub-channels. In adiabatic two-phase conditions an important phenomenon that can be investigated is the effect of the spacer on canceling the lift force, which collects the small bubbles to the rod surfaces leading to decreased CHF in diabatic conditions and thus limits the reactor power. Computational Fluid Dynamics (CFD) can be used to simulate the flow numerically and to test how different spacer configurations affect the flow. Experimental data is needed to validate and verify the used CFD models. Especially the modeling of turbulence is challenging even for single-phase flow inside the complex sub-channel geometry. In two-phase flow other factors such as bubble dynamics further complicate the modeling. To investigate the spacer grid effect on two-phase flow, and to provide further experimental data for CFD validation, a series of experiments was run on an adiabatic sub-channel flow loop using a duct-type spacer grid with different configurations. Utilizing the wire-mesh sensor technology, the facility gives high resolution experimental data in both time and space. The experimental results indicate that the duct-type spacer grid is less effective in canceling the lift force effect than the egg-crate type spacer tested earlier.

Cassava wastewater (manipueira) treatment using a two-phase anaerobic biodigestor

A two-phase anaerobic biodigestor was employed in order to analyze methane production with different manipueira organic loading rates. The acidogenic phase was carried out in a batch process whereas the methanogenic in an up-flow anaerobic fixed bed reactor with continuous feeding. The organic loading rates varied from 0.33 up to 8.48g of Chemical Demand Oxygen (COD)/L.day. The highest content of methane, 80.9%, was obtained with organic loading rate of 0.33g and the lowest, 56.8%, with 8.48gCOD/L.d. The highest reduction of COD, 88.89%, was obtained with organic loading rate of 2.25g and the lowest, 54.95%, with 8.48gCOD/L.d. From these data it was possible to realize that anaerobic biodigestion can be managed in at least two ways, i.e., for energy production (methane) or for organic loading reduction. The organic loading rate should be calculated as part of the purpose of the treatment to be accomplished.

Molekularbiologische Funktionsanalysen von Thioredoxinen aus Dictyostelium discoideum und Identifizierung neuer Interaktionspartner durch das Two-Hybrid-System

Thioredoxins are small, regulatory proteins with a mass of approximately 12 kDa and a characteristic conserved active center, which is represented in the pentapeptide trp-cys-gly-pro-cys. Up to now it is not possible to present a complete list of thioredoxin interaction partners because there is no predictable sequence in the target enzymes where thioredoxins can interact with. To get closer information about the functions and possible interaction partners of the three thioredoxins from the social soil amoeba Dictyostelium discoideum (DdTrx1 - 3) we have chosen two different strategies. In the first one the thioredoxin levels in the cell should changed by different mutants. But both the antisense technique as well as the creation of knock out mutants were not appropiate strategies in this case. Just an thioredoxin overexpressing mutant results in a developmental phenotype which allows some conclusions for possible functions of the thioredoxin in Dictyostelium discoideum. The second strategie was the two hybrid system where thioredoxin interactions partners can identified systematically. After a screening with a cDNA library from Dictyostelium 13 potential interaction partners could be detected, among them a ribonucleotid reductase, TRFA, two different cytochrome c oxidase subunits, filopodin, three ribosomal proteins, the elongationfactor 1a and the alcohol dehydrogenase from yeast. The verification of the interaction between thioredoxin and these two hybrid clones happened indirectly by a dobble mutant of thioredoxin 1, where the cysteines in the active center were replaced by redox-inactive serins. Further examinations of two choosen candidates resulted that the alcohol dehydrogenase from yeast is a thioredoxin-modululated enzym and that there is an interaction between the elongationfactor 1a and the thioredoxin 1 from Dictyostelium discoideum.