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.
Papers presented to the 12th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Costa de Sol, Spain on 11-13 July 2016.