In this paper we consider the Buckley-Leverett filtration model for a two-phase system (for instance, water oil) in a plane domain of porous media with injection and producing wells. Buckley-Leverett's equations supplemented by the law of conservation of thermal energy. Asymptotic solutions for two-phase flows in porous media are studied. Dimensionless numbers for characterization of these flows are introduced. These numbers we use to construct asymptotic presentations of solutions. We give explicit formulae for the initial terms of this asymptotic which we use for optimal control of oil-field development. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.