Influence of viscosity contrast on buoyantly unstable miscible fluids in porous media

TL;DR

This study investigates how viscosity contrast affects the stability of buoyantly unstable miscible fluids in porous media, revealing conditions for delaying or stabilizing the interface through linear stability analysis and numerical simulations.

Contribution

It introduces an initial value approach for linear stability analysis and provides a phase diagram identifying stability regimes based on viscosity contrast and displacement velocity.

Findings

Viscosity contrast delays the onset of instability.

Proper viscosity contrast and injection velocity can fully stabilize the interface.

Results from DNS agree with linear stability analysis.

Abstract

The influence of viscosity contrast on buoyantly unstable miscible fluids in a porous medium is investigated through a linear stability analysis (LSA) as well as direct numerical simulations (DNS). The linear stability method implemented in this paper is based on an initial value approach, which helps to capture the onset of instability more accurately than the quasi-steady state analysis. In the absence of displacement, we show that viscosity contrast delays the onset of instability in buoyantly unstable miscible fluids. Further, it is observed that suitably choosing the viscosity contrast and injection velocity a gravitationally unstable miscible interface can be stabilized completely. Through LSA we draw a phase diagram, which shows three distinct stability regions in a parameter space spanned by the displacement velocity and the viscosity contrast. DNS are performed corresponding to parameters from each regime and the results obtained are in accordance with the linear stability results. Moreover, the conversion from a dimensionless formulation to the other and its essence to compare between two different type of flow problems associated with each dimensionless formulation are discussed.