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.

Influence of the temperature and type of salt on the phase equilibrium of peg 1500 + potassium phosphate and peg 1500 + sodium citrate aqueous two-phase systems

The present work analyzed the effect of the temperature and type of salt on the phase equilibrium of aqueous two-phase systems (ATPS) formed by poly (ethylene glycol) (PEG) 1500 + potassium phosphate, from (278.15 to 318.15) K, and PEG 1500 + sodium citrate, from (278.15 to 298.15) K. The rise of the temperature normally increased the slope of the tie line (STL). With respect to the influence of the type of salt, sodium citrate showed better capability to induce phase separation, when compared to potassium phosphate.

Can affinity interactions influence the partitioning of glucose-6-phosphate dehydrogenase in two-phase aqueous micellar systems?

In this work, we provide an investigation of the role and strength of affinity interactions on the partitioning of the glucose-6-phosphate dehydrogenase in aqueous two-phase micellar systems. These systems are constituted of micellar surfactant solutions and offer both hydrophobic and hydrophilic environments, providing selectivity to biomolecules. We studied G6PD partitioning in systems composed of the nonionic surfactants, separately, in the presence and absence of affinity ligands. We observed that G6PD partitions to the micelle-poor phase, owing to the strength of excluded-volume interactions in these systems that drive the protein to the micelle-poor phase, where there is more free volume available.

Partition of proteases from Lentinus citrinus DPUA 1535 by the Peg/Phosphate Aqueous Two-Phase System

A full two-level factorial design was employed to study the influence of PEG molar mass (MM PEG), PEG concentration (C PEG) and phosphate concentration (C PHOSPH) on proteases partition by Lentinus citrinus DPUA 1535 in a PEG/phosphate aqueous two-phase system (ATPS). For all ATPS studied, proteases partitioned for the top phase and the best proteases extraction condition was obtained with MM PEG = 6000 g mol-1, C PEG = 17.5% (w/w) and C PHOSPH = 25% (w/w) with (1.1) purification factor and (151%) activity yield. Findings reported here demonstrate a practical strategy that serves as a first step for proteases purification from crude extract by L. citrinus.

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.

Biotransformations of water insoluble substrates in aqueous, two-phase and encapsulated systems /

The biotransformation of water insoluble substrates by mammalian and bacterial cells has been problematic, since these whole cell reactions are primarily performed in an aqueous environment The implementation of a twophase or encapsulated system has the advantages of providing a low water system along with the physiological environment the cells require to sustain themselves. Encapsulation of mammalian cells by formation of polyamide capsules via interfacial polymerization illustrated that the cells could not survive this type of encapsulation process. Biotransformation of the steroid spironolactone [3] by human kidney carcinoma cells was performed in a substrate-encapsulated system, yielding canrenone [4] in 70% yield. Encapsulation of nitrile-metabolizing Rhodococcus rhodochrous cells using a polyamide membrane yielded leaky capsules, but biotransformation of 2-(4- chlorophenyl)-3-methylbutyronitrile (CPIN) [6] in a free cell system yielded CPIN amide [7] in 40% yield and 94% ee. A two-phase biotransformation of CPIN consisting of a 5:1 ratio of tris buffer, pH 7.2 to octane respectively, gave CPIN acid [8] in 30% yield and 97% ee. It was concluded that Rhodococcus rhodochrous ATCC 17895 contained a nonselective nitrile hydratase and a highly selective amidase enzyme.

On the generation mechanisms of short-scale unbalanced modes in rotating two-layer flows with vertical shear

We report on the results of a laboratory investigation using a rotating two-layer annulus experiment, which exhibits both large-scale vortical modes and short-scale divergent modes. A sophisticated visualization method allows us to observe the flow at very high spatial and temporal resolution. The balanced long-wavelength modes appear only when the Froude number is supercritical (i.e. $F\,{>}\,F_\mathrm{critical}\,{\equiv}\, \upi^2/2$), and are therefore consistent with generation by a baroclinic instability. The unbalanced short-wavelength modes appear locally in every single baroclinically unstable flow, providing perhaps the first direct experimental evidence that all evolving vortical flows will tend to emit freely propagating inertia–gravity waves. The short-wavelength modes also appear in certain baroclinically stable flows. We infer the generation mechanisms of the short-scale waves, both for the baro-clinically unstable case in which they co-exist with a large-scale wave, and for the baroclinically stable case in which they exist alone. The two possible mechanisms considered are spontaneous adjustment of the large-scale flow, and Kelvin–Helmholtz shear instability. Short modes in the baroclinically stable regime are generated only when the Richardson number is subcritical (i.e. $\hbox{\it Ri}\,{<}\,\hbox{\it Ri}_\mathrm{critical}\,{\equiv}\, 1$), and are therefore consistent with generation by a Kelvin–Helmholtz instability. We calculate five indicators of short-wave generation in the baroclinically unstable regime, using data from a quasi-geostrophic numerical model of the annulus. There is excellent agreement between the spatial locations of short-wave emission observed in the laboratory, and regions in which the model Lighthill/Ford inertia–gravity wave source term is large. We infer that the short waves in the baroclinically unstable fluid are freely propagating inertia–gravity waves generated by spontaneous adjustment of the large-scale flow.