Optimal management of oil field development in the Buckley–Leverett model

We consider the problem of two-phase filtering (oil and water) in a horizontal layer of an oil deposit. We propose an asymptotic method for calculating both the filtering process and related optimal control problems, namely the problems of choosing optimal control actions to achieve maximum oil production at a given level of water resource consumption or a minimum water flow rate that provides the level of oil production required by the plan.