Numerical simulation of high viscosity oil displacement by water following non-linear filtration law

The non-linear filtration law with a limiting gradient of two immiscible fluids (oil and water) into a flat warp-free layer exploited by horizontal and vertical wells is investigated. The method for numerical determination of pressure and oil saturation and the corresponding difference analogues are considered. The analysis of high viscosity oil displacement by water in the five-point waterflooding element for three types of heterogeneity (zonal, with spline-interpolation application, and laminated) is carried out. The influence of the displacement limiting gradient on the basic technological characteristics of non-Newtonian oil production is studied. The results of the mathematical simulation show that the front movement at the initial stage of displacement is close to circular. The movement of non-Newtonian oil after the displacing fluid breakthrough into the producing well occurs mainly in a narrow area close to the straight current line connecting the producing and pressure wells. The dynamics of the current oil recovery coefficient depends on the properties of the displaced fluid, absolute permeability distribution in the filtration area, and set of limitations to exploitation of the operating producing and pressure wells.