Control of displacement front in a model of immiscible two-phase flow in porous media

For the Buckley–Leverett equation describing the flow of two immiscible fluids in porous media, an exact parametric representation of the solution is constructed with the help of the Backlund transformation. As a result, the advance of the displacement front can be controlled to a high degree of accuracy. The method is illustrated using an example of a typical oil well with actual parameters.