On modeling of non-stationary two-phase filtration

Based on the basic mechanics equations of continuous medium, the author's model of non-stationary two-phase oil filtration and water pumped into the reservoir was developed, based on the dependence of the water saturation coefficient on the pressure of water entering the reservoir. The substantiating for applying the proposed dependence was given. To solve the system of non-linear differential equations, the integral relations method was used, which allowed obtaining an approximate analytical solution of the water pressure disturbance distribution in the two-phase filtration area. The radius of the perturbation area (front of the displacement of oil by water) was defined, and the boundaries of the perturbation region were determined for the given boundary conditions at the bottom of the injection well. Examples allowing the quantify assessment the application of the model proposed by the authors were considered.