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.

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.

Cadmium-free quantum dots in aqueous solution: potential for fingermark detection, synthesis and an application to the detection of fingermarks in blood on non-porous surfaces

The use of quantum dots (QDs) in the area of fingermark detection is currently receiving a lot of attention in the forensic literature. Most of the research efforts have been devoted to cadmium telluride (CdTe) quantum dots often applied as powders to the surfaces of interests. Both the use of cadmium and the nano size of these particles raise important issues in terms of health and safety. This paper proposes to replace CdTe QDs by zinc sulphide QDs doped with copper (ZnS:Cu) to address these issues. Zinc sulphide-copper doped QDs were successfully synthesized, characterized in terms of size and optical properties and optimized to be applied for the detection of impressions left in blood, where CdTe QDs proved to be efficient. Effectiveness of detection was assessed in comparison with CdTe QDs and Acid Yellow 7 (AY7, an effective blood reagent), using two series of depletive blood fingermarks from four donors prepared on four non-porous substrates, i.e. glass, transparent polypropylene, black polyethylene and aluminium foil. The marks were cut in half and processed separately with both reagents, leading to two comparison series (ZnS:Cu vs. CdTe, and ZnS:Cu vs. AY7). ZnS:Cu proved to be better than AY7 and at least as efficient as CdTe on most substrates. Consequently, copper-doped ZnS QDs constitute a valid substitute for cadmium-based QDs to detect blood marks on non-porous substrates and offer a safer alternative for routine use.

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.

Influence of the implanted pulse generator as reference electrode in finite element model of monopolar deep brain stimulation.

Electrical deep brain stimulation (DBS) is an efficient method to treat movement disorders. Many models of DBS, based mostly on finite elements, have recently been proposed to better understand the interaction between the electrical stimulation and the brain tissues. In monopolar DBS, clinically widely used, the implanted pulse generator (IPG) is used as reference electrode (RE). In this paper, the influence of the RE model of monopolar DBS is investigated. For that purpose, a finite element model of the full electric loop including the head, the neck and the superior chest is used. Head, neck and superior chest are made of simple structures such as parallelepipeds and cylinders. The tissues surrounding the electrode are accurately modelled from data provided by the diffusion tensor magnetic resonance imaging (DT-MRI). Three different configurations of RE are compared with a commonly used model of reduced size. The electrical impedance seen by the DBS system and the potential distribution are computed for each model. Moreover, axons are modelled to compute the area of tissue activated by stimulation. Results show that these indicators are influenced by the surface and position of the RE. The use of a RE model corresponding to the implanted device rather than the usually simplified model leads to an increase of the system impedance (+48%) and a reduction of the area of activated tissue (-15%).

Bilateral deep brain stimulation: the placement of the second electrode is not necessarily less accurate than that of the first one.

BACKGROUND: Deep brain stimulation (DBS) is recognized as an effective treatment for movement disorders. We recently changed our technique, limiting the number of brain penetrations to three per side. OBJECTIVES: The first aim was to evaluate the electrode precision on both sides of surgery since we implemented this surgical technique. The second aim was to analyse whether or not the electrode placement was improved with microrecording and macrostimulation. METHODS: We retrospectively reviewed operation protocols and MRIs of 30 patients who underwent bilateral DBS. For microrecording and macrostimulation, we used three parallel channels of the 'Ben Gun' centred on the MRI-planned target. Pre- and post-operative MRIs were merged. The distance between the planned target and the centre of the implanted electrode artefact was measured. RESULTS: There was no significant difference in targeting precision on both sides of surgery. There was more intra-operative adjustment of the second electrode positioning based on microrecording and macrostimulation, which allowed to significantly approach the MRI-planned target on the medial-lateral axis. CONCLUSION: There was more electrode adjustment needed on the second side, possibly in relation with brain shift. We thus suggest performing a single central track with electrophysiological and clinical assessment, with multidirectional exploration on demand for suboptimal clinical responses.

Bilateral deep brain stimulation : the placement of the second electrode is not necessarily less accurate than that of the first one

Introduction La stimulation cérébrale profonde est reconnue comme étant un traitement efficace des pathologies du mouvement. Nous avons récemment modifié notre technique chirurgicale, en limitant le nombre de pénétrations intracérébrales à trois par hémisphère. Objectif Le premier objectif de cette étude est d'évaluer la précision de l'électrode implantée des deux côtés de la chirurgie, depuis l'implémentation de cette technique chirurgicale. Le deuxième objectif est d'étudier si l'emplacement de l'électrode implantée était amélioré grâce à l'électrophysiologie. Matériel et méthode Il s'agit d'une étude rétrospective reprenant les protocoles opératoires et imageries à résonnance magnétique (IRM) cérébrales de 30 patients ayant subi une stimulation cérébrale profonde bilatérale. Pour l'électrophysiologie, nous avons utilisé trois canules parallèles du « Ben Gun », centrées sur la cible planifiée grâce à l'IRM. Les IRM pré- et post-opératoires ont été fusionnées. La distance entre la cible planifiée et le centre de l'artéfact de l'électrode implantée a été mesurée. Résultats Il n'y a pas eu de différence significative concernant la précision du ciblage des deux côtés (hémisphères) de la chirurgie. Il y a eu plus d'ajustements peropératoires du deuxième côté de la chirurgie, basé sur l'électrophysiologie, ce qui a permis d'approcher de manière significative la cible planifiée grâce à l'IRM, sur l'axe médio- latéral. Conclusion Il y a plus d'ajustements nécessaires de la position de la deuxième électrode, possiblement en lien avec le « brain shift ». Nous suggérons de ce fait d'utiliser une trajectoire d'électrode centrale accompagnée par de l'électrophysiologie, associé à une évaluation clinique. En cas de résultat clinique sub-optimal, nous proposons d'effectuer une exploration multidirectionnelle.