Effect of Periodic Oscillation on the Interfacial Instability of Two Superposed Fluid Layers in a Fully Saturated Porous Media

We investigate the effect of horizontal periodic oscillation on the interfacial instability of two immiscible and viscous fluids of different densities in a fully saturated porous media. A linear stability analysis of the viscous and time-dependent basic flow leads to a periodic oscillator describing the evolution of the interfacial perturbation amplitude. The horizontal oscillation leads to the occurrence of two types of instability, the Kelvin–Helmholtz’s instability and the parametric resonance. These instabilities appear at the frontier between water and petroleum and have a practical interest in oil reservoir engineering. The results show that, an increase of the oscillation frequency destabilizes the Kelvin–Helmholtz instability and displaces the parametric instability regions toward the short wavelength perturbation. Also, we examine mainly how the other physical parameters of the system affect the instabilities for various permeability and porosity values of the porous medium as well as for relative heights of the two fluid layers.

SINGULAR PERTURBATION SOLUTION OF THE PROBLEM VISCOUS FINGERING PHENOMENON IN MULTIFLUID IMMISCIBLE FLOW

In this paper the phenomenon namely fingering which occurs in the flow problems of oil reservoir engineering has been discussed. The effects arises due to the fingering have been studied by using the Darcy’s law together with different kinds of suitable assumptions and conditions. The problem is then modeled into mathematical form which yields second order partial differential equation. The equation is then solved by using singular perturbation technique together with initial and boundary conditions. The solution is then interpreted in terms of fluid flow terms.