This article discusses a mathematical model of the process of piston displacement of one liquid by another in porous media, with an improved mathematical model of the oil-water filtration process taking into account the mobile boundary of the phase interface. A computational algorithm was developed to determine the main indicators of oil and gas fields, as well as a program for calculating and visualizing the numerical results in graphical form. A computational experiment was conducted to study the distribution of reservoir pressure and the movement of phase boundaries
during flooding.