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dc.contributor.authorNijjer, Japinder Singh
dc.description.abstractThe flow and mixing of fluids in complex porous media is important in a large range of environmental settings, from groundwater flows to the geological storage of carbon dioxide (CO$_2$). This thesis investigates two distinct and fundamental features of such flows; the mixing of miscible fluids of differing viscosity and density in both homogeneous and heterogeneous porous media, and the flow-induced deformation of soft, poroelastic media. In all cases the approach is to combine detailed numerical or experimental observations with simplified mathematical models of the key physical phenomena. Throughout this thesis the results are considered in the context of field-scale CO$_2$ sequestration case studies. In chapter 2, the dynamics of the miscible viscous-fingering instability are investigated. It is found that the dynamics can be divided into three regimes: at early times, the flow is well described by linear stability theory; at intermediate times, the flow is dominated by non-linear finger interactions; and at late times, the flow is composed of an exponentially slowing single-finger exchange-flow. In the course of this study, a critical Péclet number for the instability in the first regime is identified, an improved averaged model for the flow in the second regime is derived and a detailed explanation of the asymptotic fate of the fingering instability in the third regime is provided. In chapters 3 and 4, miscible displacements in layered heterogeneous porous media are studied. Specifically, the combined effects of viscosity and permeability variations are examined. It is found that when the permeability variations are large compared to the viscosity variations or when the injected fluid is more-viscous than the ambient, the interface is hydrodynamically stable and the flow tends to follow the permeability structure imposed. When the injected fluid is less-viscous than the ambient fluid and the viscosity variations are much larger than the permeability variations, the interface is unstable and there is a competition between the evolving wavelength of the viscous fingering and the imposed wavelength of the permeability structure. At intermediate times, depending on the relative magnitude of the viscosity and permeability variations, this competition leads to different dynamics including channelling and fingering. At late times, the dynamics are instead dominated by shear-enhanced (Taylor) dispersion, which asymptotically becomes independent of the viscosity ratio. In chapter 5, miscible displacements are considered in which the injected and ambient fluids have different densities as well as viscosities. A range of different behaviour is observed depending, on the relative importance of viscosity and density variations, including fingering, gravitational slumping and shear-enhanced dispersion. The different dynamical regimes are identified along with their dependence on the governing parameters, and simple reduced-order models for the evolution of the concentration field are derived. The final portion of this thesis (chapter 6) examines the fluid-driven compaction of a deformable porous medium. Experimental studies of water injection into a water-saturated packing of soft hydrogel spheres are presented. Solutions to a one-dimensional axisymmetric model are discussed and comparisons to the experimental results are made. In doing so, particular focus is given to the role of confinement on both the steady-state and transient dynamics of the system.
dc.rightsAll Rights Reserved
dc.subjectporous media
dc.subjectviscous fingering
dc.subjectfluid dynamics
dc.titleFlow and mixing in complex porous media
dc.type.qualificationnameDoctor of Philosophy (PhD)
dc.publisher.institutionUniversity of Cambridge
dc.type.qualificationtitlePhD in Applied Mathematics
cam.supervisorNeufeld, Jerome
cam.supervisorHewitt, Duncan
cam.supervisor.orcidNeufeld, Jerome [0000-0002-3284-5169]

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