A new system of kinetic equations is suggested to describe pressure distribution in the reservoir porous medium in the course of oil recovery. The equation system accounts the reservoir characteristics and boundary conditions together with the distribution of injection and production wells. The system solution provides the time-dependent evolution of the reservoir pressure in every site of the reservoir modelling lattice. The Dynamic Percolation Invasion with Trapping model [6,7] is adjusted for the heterogeneous case when the reservoir local characteristics are time- and recovery technology-dependent. The special software is created to simulate and visualize the oil recovery process in 3D. Simulation results are verified in numerous laboratory experiments with sand tanks and in a test field.