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Études numérique et expérimentales du mélange en milieux poreux 2D et 3D

Abstract : Solute mixing in porous media flows plays a central role in driving chemical reactions in a number of subsurface applications, including contaminant transport and remediation, subsurface energy storage and extraction, and CO2 sequestration. We study the mechanisms of solute mixing, in particular how the pore scale flow topology is related to the mixing dynamics of conservative solutes, with a particular emphasis on the possible emergence of chaotic mixing processes in three-dimensional (3D) porous media. To do so, we perform numerical computations or experimental measurements of the flow velocities and temporal evolution of the concentration fields, and characterize fluid deformation and mixing at the pore scale. This PhD work consists of three main studies. In the first study, we experimentally characterize mixing in a fluid flowing through a two-dimensional (2D) porous medium built by lithography. We measure the velocity distributions from Particle Tracking Velocimetry (PTV). The time evolution of the separation distance between two particles is analyzed to characterize the Lagrangian deformation dynamics. In parallel we perform conservative transport experiments with the same porous media, and quantify the temporal evolution of the mean concentration gradient, which is a measure of the mixing rate. From these experimental results we obtain the first experimental pore scale validation of the lamella mixing theory, which relates the fluid deformation properties to the mixing dynamics. In the second study, we investigate the conditions of emergence of chaotic mixing in the flow through 3D ordered granular porous media. In these periodic cubic crystalline packings (Simple Cubic - SC - and Body-Centered Cubic - BCC) of spheres, we are able to perform highly resolved computations of the 3D Stokes flow. Using custom-developed numerical tools to measure the Lagrangian deformation from the computed velocity fields, we uncover the existence of a rich array of Lagrangian deformation dynamics in these 3D media, depending on the flow orientation. When the flow direction is not normal to one of the reflection symmetry planes of the crystalline lattice, we find that the Lagrangian deformation dynamics follow an exponential law, which indicates chaotic advection. This chaotic behavior is controlled by a mechanism akin to the baker's transformation: fluid particles traveling around a solid grain along different paths end up either separated by, or on the same side of, a virtual surface projecting from the grain surface and called a manifold. Multiple such manifolds exist within the flow, and the way they intersect controls the nature of mixing (that is, either non-chaotic or chaotic), and the strength of chaos. We show in particular that the magnitude of the Lyapunov exponent (a measure of the vigor of chaos) is controlled by the spatial frequency of transverse connections between the manifolds (called heteroclinic intersections). We thus demonstrate that the conventional 2D picture of the mechanisms of mixing may not be adapted for natural porous media because that picture imposes topological constraints which cannot account for these important 3D mechanisms. The third study has two objectives: (i) provide experimental evidence of the chaotic nature of pore scale advection/mixing, both by visualizing the manifolds and by obtaining a quantitative estimate of the Lyapunov exponent; and (ii) assess if the results obtained numerically in ordered packings of spheres extend to random packings, which are closer to natural porous media. The experiment features a random packing of glass beads rendered transparent by optical index-matching between the fluid and solid grains. We use Laser Induced Fluorescence (LIF) to detect the manifolds, and PTV techniques to measure flow velocities and subsequently quantify Lyapunov exponent. The first experimental results are promising.
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Régis Turuban. Études numérique et expérimentales du mélange en milieux poreux 2D et 3D. Mécanique des fluides [physics.class-ph]. Université Rennes 1, 2017. Français. ⟨NNT : 2017REN1S051⟩. ⟨tel-01686457⟩

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