Fingering instabilities in vertical miscible displacement flows in porous media

Author:

Manickam O.,Homsy G. M.

Abstract

The fingering instabilities in vertical miscible displacement flows in porous media driven by both viscosity and density contrasts are studied using linear stability analysis and direct numerical simulations. The conditions under which vertical flows are different from horizontal flows are derived. A linear stability analysis of a sharp interface gives an expression for the critical velocity that determines the stability of the flow. It is shown that the critical velocity does not remain 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 depending on the flow velocity, viscosity and density profiles, leading to the potential for ‘reverse’ fingering. As the flow evolves into the nonlinear regime, the strength and location of the stable region changes, which adds to the complexity and richness of finger propagation. The flow is numerically simulated using a Hartley-transform-based spectral method to study the nonlinear evolution of the instabilities. The simulations are validated by comparing to experiments. Miscible displacements with linear density and exponential viscosity dependencies on concentration are simulated to study the effects of stable zones on finger propagation. The growth rates of the mixing zone are parametrically obtained for various injection velocities and viscosity ratios.

Publisher

Cambridge University Press (CUP)

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Reference31 articles.

1. Zimmerman, W. B. & Homsy, G. M. 1992 Three-dimensional viscous fingering: a numerical study.Phys. Fluids A4,1901.

2. Homsy, G. M. 1987 Viscous fingering in porous media.Ann. Rev. Fluid Mech. 19,271.

3. Manickam, O. & Homsy, G. M. 1993 Stability of miscible displacements in porous media with nonmonotonic viscosity profiles.Phys. Fluids A5,1356.

4. Tryggvason, G. & Aref, H. 1983 Numerical experiments on Hele-Shaw flow with a sharp interface.J. Fluid Mech. 136,1.

5. Tan, C. T. 1987 Stability of miscible displacements in porous media.PhD thesis, Stanford University,Stanford.

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