A GENERAL STABILITY ANALYSIS FOR IMMISCIBLE VISCOUS DISPLACEMENT IN A POROUS-MEDIUM

A perturbation of an immiscible displacement process causes relative motion of the two fluids involved. At the macroscopic scale such relative motions are considered to propagate throughout the porous medium in the form of fluid waves. A description of these waves is given on surfaces of constant saturation in a similar fashion to the description of a surface wave propagating on the interface between two fluids. In the porous medium, however, the wave propagation is not restricted to the surface of constant saturation and as a result one obtains a wave equation that is both dissipative diffusive. A stability analysis is also considered for the immiscible displacement process.