The stabilization of fingers in a specific oil–water displacement process with capillary pressure has been statistically discussed for a given heterogeneous porous medium. The equation of motion has been solved by a perturbation method. It is shown that the perturbation solution does produce "stable" fingers in one special case corresponding to the investigated problem.

The purpose of this paper is to study the effects of compressibility, rotation, magnetic field, and suspended particles on thermal stability of a layer of visco-elastic Walters' (model B') fluid in porous medium. Using linearized theory and normal mode analysis, dispersion relation has been obtained. In case of stationary convection, it is found that the rotation has stabilizing effect on the system. The magnetic field may have destabilizing effect on the system in the presence of rotation while in the absence of rotation it always has stabilizing effect. The medium permeability has destabilizing effect on the system in the absence of rotation while in the presence of rotation it may have stabilizing effect. The suspended particles and compressibility always have destabilizing effect. Due to vanishing of viscoelastic parameter, the compressible visco-elastic fluid behaves like Newtonian fluid. Graphs have also been plotted to depict the stability characteristics. The viscoelasticity, magnetic field and rotation are found to introduce oscillatory modes into the system which were non-existent in their absence.

In this paper, one special case of oil–water imbibition phenomena in a cracked porous medium of a finite length is analytically discussed. The equation for the linear countercurrent imbibition is a nonlinear differential equation whose solution has been obtained by a perturbation technique. For definiteness, specific results have been used for the relationship between relative permeability and phase saturation) impregnation function, oil–water viscosity ratio, and capillary pressure dependence on phase saturation due to Jones, Bokserman et al., Evgen'ev, and Oroveanu, respectively. An expression for the wetting phase saturation has been derived.

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This paper analytically discusses the phenomenon of instabilities (fingering) which arise frequently in displacement processes through porous media. The underlying assumptions of the investigation are that the two flowing phases are immiscible liquids with a large viscosity difference, the porous medium is homogeneous, and the instabilities are described by their statistical behavior. A mathematical solution of the nonlinear differential system governing fingering has been obtained by using the group-transformation technique of similarity analysis. Finally, an analytical expression for the average cross sectional area occupied by fingers has been derived, and the possibility of finger stabilization is shown under certain specific conditions.