Conservation laws for two-phase filtration models

• Two-phase filtration in porous medium is investigated from group point of view.
• Buckley-Leverett model is considered in detail.
• It is proved that the considered models are nonlinearly self-adjoint.
• New conservation laws and particular solutions are constructed using symmetries.

The paper is devoted to investigation of group properties of a one-dimensional model of two-phase filtration in porous medium. Along with the general model, some of its particular cases widely used in oil-field development are discussed. The Buckley–Leverett model is considered in detail as a particular case of the one-dimensional filtration model. This model is constructed under the assumption that filtration is one-dimensional and horizontally directed, the porous medium is homogeneous and incompressible, the filtering fluids are also incompressible. The model of “chromatic fluid” filtration is also investigated. New conservation laws and particular solutions are constructed using symmetries and nonlinear self-adjointness of the system of equations.