A numerical study on the viscous fingering instability of immiscible displacement in Hele-Shaw cells

In this thesis, the viscous fingering instability of radial immiscible displacement is analysed numerically using novel mesh-reduction and interface tracking techniques. Using a reduced Hele-Shaw model for the depth averaged lateral flow, viscous fingering instabilities are explored in flow regimes typical of subsurface carbon sequestration involving supercritical CO2 - brine displacements, i.e. with high capillary numbers, low mobility ratios and inhomogeneous permeability/temperature fields. A high accuracy boundary element method (BEM) is implemented for the solution of homogeneous, finite mobility ratio immiscible displacements. Through efficient, explicit tracking of the sharp fluid-fluid interface, classical fingering processes such as spreading, shielding and splitting are analysed in the late stages of finger growth at low mobility ratios and high capillary numbers. Under these conditions, large differences are found compared with previous high or infinite mobility ratio models and critical events such as plume break-off and coalescence are analysed in much greater detail than has previously been attempted. For the solution of inhomogeneous mobility problems, a novel meshless radial basis function-finite collocation method is developed that utilises a dynamic quadtree dataset and local enforcement of interface matching conditions. When coupled with the BEM, the numerical scheme allows the analysis of variable permeability effects and the transition in (de)stabilising mechanisms that occurs when the capillary number is increased with a fixed, spatially varying permeability. Finally, thermo-viscous fingering is explored in the context of immiscible flows, with a detailed mechanistic study presented to explain, for the first time, the immiscible thermo-viscous fingering process