Linear stability analysis of time-dependent immiscible flow displacements in porous media

Abstract

Flow displacements in porous media are encountered in a wide variety of fields, in particular in the energy and environmental sectors. Such flows are prone to a hydrodynamic instability that develops as a result of differences in the physical properties of the different fluids, namely their viscosity and/or density. A simple and inexpensive way to attenuate the instabilities is to implement time-dependent injection schemes. In this study, flows in radial two- dimensional homogeneous porous media are modelled. A low-viscosity fluid is injected radially at the centre of the cell to displace a more viscous one. The model equations are developed and a linear stability analysis is carried out. Different time-dependent velocity profiles are considered and the effects of different flow parameters are analysed and compared with the corresponding constant injection velocity flows. For consistency, the comparisons are conducted on the basis that all injection schemes including the constant one, result in the same total amount of injected fluid. Qualitative analyses are conducted using different measures of the growth of the instability and are used to determine the changes induced by the time-dependent injections. These changes in the flow dynamics can be used to control the degree of mixing between the two fluids and to optimize a variety of flow displacements in porous media.