On vortex flows of a two-phase fluid in porous media

The results of numerical modeling of the two-phase isothermal motion of immiscible incompressible liquids in porous media taking into account capillary and gravitational forces are presented. The problem is solved by the control volume method in the variables “velocity-saturation”. To solve the equation of hyperbolic type, the scheme WENO of the third order of accuracy in a combination with the Runge-Kutta method is used. It is shown that in the presence of capillary and gravitational forces vortex flows may occur in every phase under certain conditions. In particular, vortex flows arise after infiltration of a heavy liquid into the porous body saturated with easy liquid, and at segregation of liquids in a reservoir if there are inclusions of different permeability in it. It has been found that vortex flows change the configuration of the displacement front. In previous works, the occurrence of vortex flows in porous media has been studied by introducing in the consideration a new desired variable - function of vorticity. In such a statement of the problem, the occurrence of vortex flows in porous media has been studied at the interface of two liquids of different density, on the boundaries of a jump wise change of permeability and in some other cases. In the present work, it is shown that the existence of vorticity in a two-phase flow in porous media can be revealed by performing direct calculations of the velocity field in each phase.