NUMERICAL ANALYSIS OF THE LEVERETT FUNCTION FORM INFLUENCE FOR THE RAPPOPORT - LEAS EQUATION SOLUTIONS

The article deals with the classical mathematical model of filtration of two immiscible liquids in a non-deformable porous medium taking into account capillary forces. It is the Muskat - Leverett model. The model is based on the experimentally determined functions of water saturation - relative phase permeability and the Leverett’s function of capillary pressure. In the article we study numerically the one-dimensional radial flow with a given flow rate of the mixture. In this case, the Muskat - Leverett model equations are reduced to one quasilinear hyperbolic-parabolic equation for water saturation - Rappoport-Leas equation. The article investigates the influence of the representation of capillary forces in porous media of different structures on the behavior of solutions in the isothermal case.