Abstract
In applications involving the injection of a fluid in a porous medium to displace another fluid, a main objective is the maximization of the displacement efficiency. Displacement fronts moving in porous media are subjected to hydrodynamic instability when a liquid of low viscosity displaces a high-viscosity liquid and consequently finger-like structure forms along the interface. This finger instability is usually undesirable in technical applications and natural filtration processes. We discuss the external periodic forcing as one of the promising ways to control the instability and perform numerical simulation of an initially spherical drop in a porous media under vertical vibrations. The drop is a favorable object to study since in this case one can observe the effect of vibrations on fluid interface domains inclined by different angles with respect to vibration axis. It is shown that under vibrations small-scale perturbations of interface are suppressed and in the case of vibrations of large enough intensity the drop becomes stable. The stability criterion is derived.
Highlights
In the framework of the conventional Darcy model a planar displacement front in a porous medium was found to be unstable if the displacing fluid has lower viscosity than the displaced one [2]
The problem of the extraction of the retained oil is a topical one, since the solution of this problem could noticeably increase the recovery efficiency. Another example is the production of titanium [11], according to the technology the producing magnesium drops of molten magnesium have to be extracted from a porous titanium sponge saturated with liquid magnesium chloride
Numerical modeling of the liquid drop dynamics in porous medium saturated by the other liquid under gravity has been carried out
Summary
In the framework of the conventional Darcy model a planar displacement front in a porous medium was found to be unstable if the displacing fluid has lower viscosity than the displaced one [2]. This finger pattern is observed in different technical applications and natural filtration processes, for instance oil and gas production [2, 9, 20], geological CO2 storage [5, 7], development of low-temperature polymerelectrolyte fuel cells [24], water seepage [6], and ink spreading [1] This instability is usually undesirable and in the present paper we analyze the use of vibrations to control the stability of fluid-fluid interface in a porous medium. In the present paper the numerical simulation of liquid drop dynamics in a porous medium under gravity is performed and the effect of modulation of external forcing is analyzed.
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