FINGERING INSTABILITIES IN VERTICAL MISCIBLE DISPLACEMENT FLOWS IN POROUS-MEDIA

The fingering instabilities in vertical miscible displacement flows in porous media driven by both viscosity and density contrasts are studi ed using linear stability analysis and direct numerical simulations. T he conditions under which vertical flows are different from horizontal flows are derived. A linear stability analysis of a sharp interface g ives an expression for the critical Velocity that determines the stabi lity of the flow. It is shown that the critical velocity does not rema in constant but changes as the two fluids disperse into each other. In a diffused profile, the flow can develop a potentially stable region followed downstream by a potentially unstable region or vice versa dep ending on the flow velocity, viscosity and density profiles, leading t o the potential for 'reverse' fingering. As the flow evolves into the nonlinear regime, the strength and location of the stable region chang es, which adds to the complexity and richness of finger propagation. T he flow is numerically simulated using a Hartley-transform-based spect ral method to study the nonlinear evolution of the instabilities. The simulations are validated by comparing to experiments. Miscible displa cements with linear density and exponential viscosity dependencies on concentration are simulated to study the effects of stable zones on fi nger propagation. The growth rates of the mixing zone are parametrical ly obtained for various injection velocities and viscosity ratios.