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.

Multi-phase post-mortem CT angiography: development of a standardized protocol.

The objective of this work was to develop an easily applicable technique and a standardized protocol for high-quality post-mortem angiography. This protocol should (1) increase the radiological interpretation by decreasing artifacts due to the perfusion and by reaching a complete filling of the vascular system and (2) ease and standardize the execution of the examination. To this aim, 45 human corpses were investigated by post-mortem computed tomography (CT) angiography using different perfusion protocols, a modified heart-lung machine and a new contrast agent mixture, specifically developed for post-mortem investigations. The quality of the CT angiographies was evaluated radiologically by observing the filling of the vascular system and assessing the interpretability of the resulting images and by comparing radiological diagnoses to conventional autopsy conclusions. Post-mortem angiography yielded satisfactory results provided that the volumes of the injected contrast agent mixture were high enough to completely fill the vascular system. In order to avoid artifacts due to the post-mortem perfusion, a minimum of three angiographic phases and one native scan had to be performed. These findings were taken into account to develop a protocol for quality post-mortem CT angiography that minimizes the risk of radiological misinterpretation. The proposed protocol is easy applicable in a standardized way and yields high-quality radiologically interpretable visualization of the vascular system in post-mortem investigations.

Hybrid Multiscale Finite Volume method for two-phase flow in porous media

We present a novel hybrid (or multiphysics) algorithm, which couples pore-scale and Darcy descriptions of two-phase flow in porous media. The flow at the pore-scale is described by the Navier?Stokes equations, and the Volume of Fluid (VOF) method is used to model the evolution of the fluid?fluid interface. An extension of the Multiscale Finite Volume (MsFV) method is employed to construct the Darcy-scale problem. First, a set of local interpolators for pressure and velocity is constructed by solving the Navier?Stokes equations; then, a coarse mass-conservation problem is constructed by averaging the pore-scale velocity over the cells of a coarse grid, which act as control volumes; finally, a conservative pore-scale velocity field is reconstructed and used to advect the fluid?fluid interface. The method relies on the localization assumptions used to compute the interpolators (which are quite straightforward extensions of the standard MsFV) and on the postulate that the coarse-scale fluxes are proportional to the coarse-pressure differences. By numerical simulations of two-phase problems, we demonstrate that these assumptions provide hybrid solutions that are in good agreement with reference pore-scale solutions and are able to model the transition from stable to unstable flow regimes. Our hybrid method can naturally take advantage of several adaptive strategies and allows considering pore-scale fluxes only in some regions, while Darcy fluxes are used in the rest of the domain. Moreover, since the method relies on the assumption that the relationship between coarse-scale fluxes and pressure differences is local, it can be used as a numerical tool to investigate the limits of validity of Darcy's law and to understand the link between pore-scale quantities and their corresponding Darcy-scale variables.

Multi-phase postmortem CT angiography: recognizing technique-related artefacts and pitfalls.

BACKGROUND AND PURPOSE: Multi-phase postmortem CT angiography (MPMCTA) is increasingly being recognized as a valuable adjunct medicolegal tool to explore the vascular system. Adequate interpretation, however, requires knowledge about the most common technique-related artefacts. The purpose of this study was to identify and index the possible artefacts related to MPMCTA. MATERIAL AND METHODS: An experienced radiologist blinded to all clinical and forensic data retrospectively reviewed 49 MPMCTAs. Each angiographic phase, i.e. arterial, venous and dynamic, was analysed separately to identify phase-specific artefacts based on location and aspect. RESULTS: Incomplete contrast filling of the cerebral venous system was the most commonly encountered artefact, followed by contrast agent layering in the lumen of the thoracic aorta. Enhancement or so-called oedematization of the digestive system mucosa was also frequently observed. CONCLUSION: All MPMCTA artefacts observed and described here are reproducible and easily identifiable. Knowledge about these artefacts is important to avoid misinterpreting them as pathological findings.

Detection of coronary thrombosis after multi-phase postmortem CT-angiography.

The aim of this study was to compare postmortem angiography-based, autopsy-based and histology-based diagnoses of acute coronary thrombosis in a series of medicolegal cases that underwent postmortem angiographies according to multiphase CT-angiography protocol. Our study included 150 medicolegal cases. All cases underwent native CT-scan, postmortem angiography, complete conventional autopsy and histological examination of the main organs and coronary arteries. In 10 out of the 150 investigated cases, postmortem angiographies revealed coronary arterial luminal filling defects and the absence of collateral vessels, suggesting acute coronary thromboses. Radiological findings were confirmed by autopsy and histological examinations in all cases. In 40 out of 150 cases, angiograms revealed complete or incomplete coronary arterial luminal filling defects and the presence of collateral vessels. Histological examinations did not reveal free-floating or non-adherent thrombi in the coronary arteries in any of these cases. Though postmortem angiography examination has not been well-established for the diagnosis of acute coronary thrombosis, luminal filling defects in coronary arteries suggesting acute thromboses can be observed through angiography and subsequently confirmed by autopsy and histological examinations.

15-OR: Multi-phase postmortem CT angiography of pulmonary embolism: technique-related artefacts or real findings?

Multi-phase postmortem CT angiography (MPMCTA) is recognized as a valuable tool to explore the vascular system, with higher sensitivity than conventional autopsy. However, a limitation is the impossibility to diagnose pulmonary embolism (PE) due to post-mortem blood clots situated in pulmonary arteries. The purpose of this study was to explore an eventual possibility to distinguish between real PE and artefacts mimicking PE. Our study included 416 medico-legal cases. All of them underwent MPMCTA, conventional autopsy and histological examination. We selected cases presenting arterial luminal filling defects in the pulmonary arteries. Their radiological interpretation was confronted to the one of autopsy and histological examination. We also investigated an eventual correlation between artefacts in pulmonary arteries and those in other parts of the vascular system. In 123 cases, filling defects of pulmonary arteries were described during MPMCTA. In 57 cases, this was interpreted as artefact and in 4 cases as suspected PE. In 62 cases only a differential diagnosis was made. Autopsy and histology could clearly identify the artefacts as such. Only one case of real PE was radiologically misinterpreted as artefact. In 6 of the 62 cases with no interpretation a PE was diagnosed. In 3 out of 4 suspected cases, PE was confirmed. We found out that filling defects in pulmonary arteries are nearly always associated to other vascular artefacts. Therefore, we suggest following some rules for radiological interpretation in order to allow a reliable diagnosis of pulmonary embolism after MPMCTA.

A framework for hybrid simulations of two-phase flow in porous media

Rough a global coarse problem. Although these techniques are usually employed for problems in which the fine-scale processes are described by Darcy's law, they can also be applied to pore-scale simulations and used as a mathematical framework for hybrid methods that couples a Darcy and pore scales. In this work, we consider a pore-scale description of fine-scale processes. The Navier-Stokes equations are numerically solved in the pore geometry to compute the velocity field and obtain generalized permeabilities. In the case of two-phase flow, the dynamics of the phase interface is described by the volume of fluid method with the continuum surface force model. The MsFV method is employed to construct an algorithm that couples a Darcy macro-scale description with a pore-scale description at the fine scale. The hybrid simulations results presented are in good agreement with the fine-scale reference solutions. As the reconstruction of the fine-scale details can be done adaptively, the presented method offers a flexible framework for hybrid modeling.

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.

Surgical interventions with fatal outcome: Utility of multi-phase postmortem CT angiography

Cases of fatal outcome after surgical intervention are autopsied to determine the cause of death and to investigate whether medical error caused or contributed to the death. For medico-legal purposes, it is imperative that autopsy findings are documented clearly. Modern imaging techniques such as multi-detector computed tomography (MDCT) and postmortem CT angiography, which is used for vascular system imaging, are useful tools for determining cause of death. The aim of this study was to determine the utility of postmortem CT angiography for the medico-legal death investigation. This study investigated 10 medico-legal cases with a fatal outcome after surgical intervention using multi-phase postmortem whole body CT angiography. A native CT scan was performed as well as three angiographic phases (arterial, venous, and dynamic) using a Virtangio((R)) perfusion device and the oily contrast agent, Angiofil((R)). The results of conventional autopsy were compared to those from the radiological investigations. We also investigated whether the radiological findings affected the final interpretation of cause-of-death. Causes of death were hemorrhagic shock, intracerebral hemorrhage, septic shock, and a combination of hemorrhage and blood aspiration. The diagnoses were made by conventional autopsy as well as by postmortem CT angiography. Hemorrhage played an important role in eight of ten cases. The radiological exam revealed the exact source of bleeding in seven of the eight cases, whereas conventional autopsy localized the source of bleeding only generally in five of the seven cases. In one case, neither conventional autopsy nor CT angiography identified the source of hemorrhage. We conclude that postmortem CT angiography is extremely useful for investigating deaths following surgical interventions. This technique helps document autopsy findings and allows a second examination if it is needed; specifically, it detects and visualizes the sources of hemorrhages in detail, which is often of particular interest in such cases.