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.

Estimating gene flow across hybrid zones: how reliable are microsatellites?

Due to their high polymorphism, microsatellites have become one of the most valued genetic markers in population biology. We review the first two published studies on hybrid zones of the common shrew based on microsatellites. Both reveal surprisingly high interracial gene flow. It can be shown that these are overestimates. Indeed, in classical population genetics models as F-statistics, mutation is neglected. This constitutes an acceptable assumption as long as migration is higher than mutation. However, in hybrid zones where genetic exchanges can be rare, neglecting mutation will lead to strong overestimates of migration when working with microsatellites which display mutation rates up to 10(-3). As there seems to be no straightforward way to correct for this bias, interracial gene flow estimates based on microsatellites should be taken with caution. This problem should however not conceal the enormous potential of microsatellites to unravel the genetics of hybrid zones.

Quantification of Myocardial Blood Flow in Absolute Terms Using (82)Rb PET Imaging: The RUBY-10 Study.

OBJECTIVES: The purpose of this study was to compare myocardial blood flow (MBF) and myocardial flow reserve (MFR) estimates from rubidium-82 positron emission tomography ((82)Rb PET) data using 10 software packages (SPs) based on 8 tracer kinetic models. BACKGROUND: It is unknown how MBF and MFR values from existing SPs agree for (82)Rb PET. METHODS: Rest and stress (82)Rb PET scans of 48 patients with suspected or known coronary artery disease were analyzed in 10 centers. Each center used 1 of 10 SPs to analyze global and regional MBF using the different kinetic models implemented. Values were considered to agree if they simultaneously had an intraclass correlation coefficient >0.75 and a difference <20% of the median across all programs. RESULTS: The most common model evaluated was the Ottawa Heart Institute 1-tissue compartment model (OHI-1-TCM). MBF values from 7 of 8 SPs implementing this model agreed best. Values from 2 other models (alternative 1-TCM and Axially distributed) also agreed well, with occasional differences. The MBF results from other models (e.g., 2-TCM and retention) were less in agreement with values from OHI-1-TCM. CONCLUSIONS: SPs using the most common kinetic model-OHI-1-TCM-provided consistent results in measuring global and regional MBF values, suggesting that they may be used interchangeably to process data acquired with a common imaging protocol.

Extension of Murray's law using a non-Newtonian model of blood flow.

BACKGROUND: So far, none of the existing methods on Murray's law deal with the non-Newtonian behavior of blood flow although the non-Newtonian approach for blood flow modelling looks more accurate. MODELING: In the present paper, Murray's law which is applicable to an arterial bifurcation, is generalized to a non-Newtonian blood flow model (power-law model). When the vessel size reaches the capillary limitation, blood can be modeled using a non-Newtonian constitutive equation. It is assumed two different constraints in addition to the pumping power: the volume constraint or the surface constraint (related to the internal surface of the vessel). For a seek of generality, the relationships are given for an arbitrary number of daughter vessels. It is shown that for a cost function including the volume constraint, classical Murray's law remains valid (i.e. SigmaR(c) = cste with c = 3 is verified and is independent of n, the dimensionless index in the viscosity equation; R being the radius of the vessel). On the contrary, for a cost function including the surface constraint, different values of c may be calculated depending on the value of n. RESULTS: We find that c varies for blood from 2.42 to 3 depending on the constraint and the fluid properties. For the Newtonian model, the surface constraint leads to c = 2.5. The cost function (based on the surface constraint) can be related to entropy generation, by dividing it by the temperature. CONCLUSION: It is demonstrated that the entropy generated in all the daughter vessels is greater than the entropy generated in the parent vessel. Furthermore, it is shown that the difference of entropy generation between the parent and daughter vessels is smaller for a non-Newtonian fluid than for a Newtonian fluid.

High-performance liquid chromatography of the renal blood flow marker p-aminohippuric acid (PAH) and its metabolite N-acetyl PAH improves PAH clearance measurements.

PAH (N-(4-aminobenzoyl)glycin) clearance measurements have been used for 50 years in clinical research for the determination of renal plasma flow. The quantitation of PAH in plasma or urine is generally performed by colorimetric method after diazotation reaction but the measurements must be corrected for the unspecific residual response observed in blank plasma. We have developed a HPLC method to specifically determine PAH and its metabolite NAc-PAH using a gradient elution ion-pair reversed-phase chromatography with UV detection at 273 and 265 nm, respectively. The separations were performed at room temperature on a ChromCart (125 mmx4 mm I.D.) Nucleosil 100-5 microm C18AB cartridge column, using a gradient elution of MeOH-buffer pH 3.9 1:99-->15:85 over 15 min. The pH 3.9 buffered aqueous solution consisted in a mixture of 375 ml sodium citrate-citric acid solution (21.01 g citric acid and 8.0 g NaOH per liter), added up with 2.7 ml H3PO4 85%, 1.0 g of sodium heptanesulfonate and completed ad 1000 ml with ultrapure water. The N-acetyltransferase activity does not seem to notably affect PAH clearances, although NAc-PAH represents 10.2+/-2.7% of PAH excreted unchanged in 12 healthy subjects. The performance of the HPLC and the colorimetric method have been compared using urine and plasma samples collected from healthy volunteers. Good correlations (r=0.94 and 0.97, for plasma and urine, respectively) are found between the results obtained with both techniques. However, the colorimetric method gives higher concentrations of PAH in urine and lower concentrations in plasma than those determined by HPLC. Hence, both renal (ClR) and systemic (Cls) clearances are systematically higher (35.1 and 17.8%, respectively) with the colorimetric method. The fraction of PAH excreted by the kidney ClR/ClS calculated from HPLC data (n=143) is, as expected, always <1 (mean=0.73+/-0.11), whereas the colorimetric method gives a mean extraction ratio of 0.87+/-0.13 implying some unphysiological values (>1). In conclusion, HPLC not only enables the simultaneous quantitation of PAH and NAc-PAH, but may also provide more accurate and precise PAH clearance measurements.