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.

Seismic attenuation and velocity dispersion in heterogeneous partially saturated porous rocks

Using a numerical approach, we explore wave-induced fluid flow effects in partially saturated porous rocks in which the gas-water saturation patterns are governed by mesoscopic heterogeneities associated with the dry frame properties. The link between the dry frame properties and the gas saturation is defined by the assumption of capillary pressure equilibrium, which in the presence of heterogeneity implies that neighbouring regions can exhibit different levels of saturation. To determine the equivalent attenuation and phase velocity of the synthetic rock samples considered in this study, we apply a numerical upscaling procedure, which permits to take into account mesoscopic heterogeneities associated with the dry frame properties as well as spatially continuous variations of the pore fluid properties. The multiscale nature of the fluid saturation is taken into account by locally computing the physical properties of an effective fluid, which are then used for the larger-scale simulations. We consider two sets of numerical experiments to analyse such effects in heterogeneous partially saturated porous media, where the saturation field is determined by variations in porosity and clay content, respectively. In both cases we also evaluate the seismic responses of corresponding binary, patchy-type saturation patterns. Our results indicate that significant attenuation and modest velocity dispersion effects take place in this kind of media for both binary patchy-type and spatially continuous gas saturation patterns and in particular in the presence of relatively small amounts of gas. The numerical experiments also show that the nature of the gas distribution patterns is a critical parameter controlling the seismic responses of these environments, since attenuation and velocity dispersion effects are much more significant and occur over a broader saturation range for binary patchy-type gas-water distributions. This analysis therefore suggests that the physical mechanisms governing partial saturation should be accounted for when analysing seismic data in a poroelastic framework. In this context, heterogeneities associated with the dry frame properties, which do not play important roles in wave-induced fluid flow processes per se, should be taken into account since they may determine the kind of gas distribution pattern taking place in the porous rock.

Self-potentials in partially saturated media: the importance of explicit modeling of electrode effects

Self-potential (SP) data are of interest to vadose zone hydrology because of their direct sensitivity to water flow and ionic transport. There is unfortunately little consensus in the literature about how to best model SP data under partially saturated conditions, and different approaches (often supported by one laboratory data set alone) have been proposed. We argue that this lack of agreement can largely be traced to electrode effects that have not been properly taken into account. A series of drainage and imbibition experiments were considered in which we found that previously proposed approaches to remove electrode effects were unlikely to provide adequate corrections. Instead, we explicitly modeled the electrode effects together with classical SP contributions using a flow and transport model. The simulated data agreed overall with the observed SP signals and allowed decomposing the different signal contributions to analyze them separately. After reviewing other published experimental data, we suggest that most of them include electrode effects that have not been properly taken into account. Our results suggest that previously presented SP theory works well when considering the modeling uncertainties presently associated with electrode effects. Additional work is warranted to not only develop suitable electrodes for laboratory experiments but also to assure that associated electrode effects that appear inevitable in longer term experiments are predictable, so that they can be incorporated into the modeling framework.

Simulation of surface waves in porous media

We present a novel numerical algorithm for the simulation of seismic wave propagation in porous media, which is particularly suitable for the accurate modelling of surface wave-type phenomena. The differential equations of motion are based on Biot's theory of poro-elasticity and solved with a pseudospectral approach using Fourier and Chebyshev methods to compute the spatial derivatives along the horizontal and vertical directions, respectively. The time solver is a splitting algorithm that accounts for the stiffness of the differential equations. Due to the Chebyshev operator the grid spacing in the vertical direction is non-uniform and characterized by a denser spatial sampling in the vicinity of interfaces, which allows for a numerically stable and accurate evaluation of higher order surface wave modes. We stretch the grid in the vertical direction to increase the minimum grid spacing and reduce the computational cost. The free-surface boundary conditions are implemented with a characteristics approach, where the characteristic variables are evaluated at zero viscosity. The same procedure is used to model seismic wave propagation at the interface between a fluid and porous medium. In this case, each medium is represented by a different grid and the two grids are combined through a domain-decomposition method. This wavefield decomposition method accounts for the discontinuity of variables and is crucial for an accurate interface treatment. We simulate seismic wave propagation with open-pore and sealed-pore boundary conditions and verify the validity and accuracy of the algorithm by comparing the numerical simulations to analytical solutions based on zero viscosity obtained with the Cagniard-de Hoop method. Finally, we illustrate the suitability of our algorithm for more complex models of porous media involving viscous pore fluids and strongly heterogeneous distributions of the elastic and hydraulic material properties.

Comment on "Streaming potential dependence on water-content in Fontainebleau sand" by V. Allegre, L. Jouniaux, F. Lehmann and P. Sailhac

Allegre et al. recently presented new experimental data regarding the dependence of the streaming potential coupling coefficient with the saturation of the water phase. Such experiments are important to model the self-potential response associated with the flow of water in the vadose zone and the electroseismic/seismoelectric conversions in unsaturated porous media. However, the approach used to interpret the data is questionable and the conclusions reached by Allegre et al. likely incorrect

A stable and 40Ar/39Ar isotope study of a major thrust in the Helvetic nappes (Swiss Alps) - Evidence for fluid-flow and constraints on nappe kinematics

Stable isotope and Ar-40/Ar-39 measurements,were made on samples associated with a major tectonic discontinuity in the Helvetic Alps, the basal thrust of the Diablerets nappe (external zone of the Alpine Belt) in order to determine both the importance of fluids in this thrust zone and the timing of thrusting. A systematic decrease in the delta(18)O values (up to 6 parts per thousand) of calcite, quartz, and white mica exists within a 10- to 70-m-wide zone over a distance of 37 km along the thrust, and they become more pronounced toward the root of the nappe. A similar decrease in the delta(13)C values of calcite is observed only in the deepest sections (up to 3 parts per thousand). The delta D-SMOW (SMOW = standard mean ocean water) values of white mica are -54 parts per thousand +/- 8 parts per thousand (n = 22) and are independent of the distance from the thrust. These variations are interpreted to reflect syntectonic solution reprecipitation during fluid passage along the thrust. The calculated delta(18)O and delta D values (versus SMOW) for the fluid in equilibrium with the analyzed minerals is 12 parts per thousand to 16 parts per thousand and -30 parts per thousand to +5 parts per thousand, respectively, for assumed temperatures of 250 to 450 degrees C. The isotopic and structural data are consistent with fluids derived from the deep-seated roots of the Helvetic nappes where large volumes of Mesozoic sediments were metamorphosed to the amphibolite facies, It is suggested that connate and metamorphic waters, overpressured by rapid tectonic burial in a subductive system escaped by upward infiltration along moderately dipping pathways until they reached the main shear zone at the base of the moving pile, where they were channeled toward the surface, This model also explains the mechanism by which large amounts of fluid were removed from the Mesozoic sediments during Alpine metamorphism. White mica Ar-49/Ar-39 ages vary from 27 Ma far from the Diablerets thrust to 15 Ma along the thrust. An older component is observed in micas far from the thrust, interpreted as a detrital signature, and indicates that regional metamorphic temperatures were less than about 350 degrees C. The;plateau and near plateau ages nearest the thrust are consistent with either neocrystallization of white mica or argon loss by recrystallization during thrusting, which may have been enhanced in the zones of highest fluid flow. The 15 Ma Ar-40/Ar-39 age plateau measured on white mica sampled exactly on the thrust surface dates the end of both fluid flow and tectonic transport.

Ambient vertical flow in long-screen wells: a case study in the Fontainebleau Sands Aquifer (France)

A tritium (H-3) profile was constructed in a long-screened well (LSW) of the Fontainebleau Sands Aquifer (France), and the data were combined with temperature logs to gain insight into the potential effects of the ambient vertical flow (AVF) of water through the well on the natural aquifer stratification. AVF is commonly taken into account in wells located in fracture aquifers or intercepting two different aquifers with distinct hydraulic heads. However, due to the vertical hydraulic gradient of the flow lines intercepted by wells, AVF of groundwater is a common process within any type of aquifer. The detection of 3H in the deeper parts of the studied well ( approximate depth 50m), where H-3-free groundwater is expected, indicates that shallow young water is being transported downwards through the well itself. The temperature logs show a nearly zero gradient with depth, far below the mean geothermal gradient in sedimentary basins. The results show that the age distribution of groundwater samples might be biased in relation to the age distribution in the surroundings of the well. The use of environmental tracers to investigate aquifer properties, particularly in LSWs, is then limited by the effects of the AVF of water that naturally occurs through the well.

Study of gene flow through a hybrid zone in the common shrew (Sorex araneus) using microsatellites

The common shrew (Sorer araneus) is subdivided into several chromosomal races. As hybrid zones between them have been characterized, this organism is of particular interest in studying the role of chromosomes in speciation. Six microsatellite loci were used to evaluate the level of gene how in the S. araneus hybrid zone between the Cordon and Valais races. Most of these loci were very polymorphic, the total number of alleles detected per locus ranging from 3 to 20. Using Mantel tests, we showed that the effect of rivers as barriers to gene flow is less important at this sampling scale. The effect of the chromosomal race is of particular importantance in diminishing gene flow.

Oligoclonal expansions in the CD8(+)CD28(-) T cells largely explain the shorter telomeres detected in this subset: analysis by flow FISH.

We have previously reported that CD8(+)CD28(-) T cells have relatively shorter telomeres compared with CD8(+)CD28(+) T cells. Oligoclonal expansion is a common feature of CD8(+) T cells in human peripheral blood, and these expansions predominantly occur in the CD57(+)/CD28(-) population. We studied the telomere length in subsets of CD8(+) T cells using quantitative fluorescence in situ hybridization and flow cytometry (flow FISH). Our results confirm that CD8(+)CD28(-) T cells have shorter telomeres as compared with their CD28(+) counterpart cells. In addition, the oligoclonally expanded cells within the CD8(+)CD28(-) T cell subset generally have even shorter telomeres than the CD28(-) subset as a whole. We conclude that the presence of clonal expansions in the CD8(+)CD28(-) T cell population largely explain the shorter telomeres in this subset. These clonally expanded CD8(+)CD28(-) T cells generally have characteristics of terminally differentiated effector cells. Nevertheless, there is considerable individual variation in the degree of telomere shortening in these cells, which may reflect host genetic factors as well as the type and timing of the antigenic exposure.

Using flow cytometry for in situ monitoring of antimicrobial compound production in the biocontrol bacterium Pseudomonas fluorescens CHA0.

Pseudomonas fluorescens strain CHA0 is able to protect plants against a variety of pathogens, notably by producing the two antimicrobial compounds 2,4-diacetylphloroglucinol (DAPG) and pyoluteorin (PLT). The regulation of the expression of these compounds is affected by many biotic factors, such as fungal pathogens, rhizosphere bacteria as well as plant species. Therefore, the influence of some plant phenolic compounds on the expression of DAPG and PLT biosynthetic genes has been tested using GFP-based reporter, monitored by standard fluometry and flow cytometry. In situ experiments were also performed with cucumber plants. We found that several plant metabolites such as IAA and umbelliferone are able to modify significantly the expression of DAPG and PLT. The use of flow cytometry with autofluorescents proteins seems to be a promising method to study rhizobacteria-plant interactions.

Fluid flow through the sedimentary cover in northern Switzerland recorded by calcite-celestite veins (Oftringen borehole, Olten)

Abundant veins filled by calcite, celestite and pyrite were found in the core of a 719 m deep borehole drilled in Oftringen near Olten, located in the north-western Molasse basin, close to the thrust of the Folded Jura. Host rocks are calcareous marl, argillaceous limestone and limestone of the Dogger and Malm. The delta O-18 values of vein calcite are lower than in host rock carbonate and, together with microthermometric data from fluid inclusions in vein calcite, indicate precipitation from a seawater-dominated fluid at average temperatures of 56-68A degrees C. Such temperatures were reached at the time of maximum burial of the sedimentary pile in the late Miocene. The depth profile of delta C-13 and Sr-87/Sr-86 values and Sr content of both whole-rock carbonate and vein calcite show marked trends towards negative delta C-13, high Sr-87/Sr-86, and low Sr content in the uppermost 50-150 m of the Jurassic profile (upper Oxfordian). The Sr-87/Sr-86 of vein minerals is generally higher than that of host rock carbonate, up to very high values corresponding to Burdigalian seawater (Upper Marine Molasse, Miocene), which represents the last marine incursion in the region. No evidence for internally derived radiogenic Sr (clay minerals) has been found and so an external source is required. S and O isotope composition of vein celestite and pyrite can be explained by bacterial reduction of Miocene seawater sulphate. The available data set suggests the vein mineralization precipitated from descending Burdigalian seawater and not from a fluid originating in the underlying Triassic evaporites.