Linear stability of filtration flow of a gas and two immiscible liquids with interfaces in the context of the Forchheimer law

We study the linear stability of the vertical flow that occurs when gas displaces oil from a layer of porous medium using the generalized nonlinear Forchheimer filtration law. We consider the case where areas saturated with oil and gas are separated by a layer of water. The interfaces separating the areas are assumed to be flat at the initial moment. We consider two cases of perturbation evolution. In the first case, only the gas–water interface is perturbed at the initial moment. In the second case, small perturbations of the same amplitude are present on both surfaces. We show that the interaction of perturbations at interfaces depends on the thickness of the water-saturated layer, perturbation wavelength, oil viscosity, pressure gradient, and formation thickness. Calculations demonstrate that perturbations at the oil–water boundary grow much slower than perturbations at the gas–water boundary. We find that there is a critical value of the thickness of the water-saturated layer. If the thickness of the layer is greater than the critical value, then the development of perturbations at the gas–water boundary does not affect the development of perturbations at the water–oil boundary.