Explicit-implicit numerical algorithms for porous media multiphase flow problems

The theoretical study on applied problems of oil and gas recovery is based on mathematical models for multiphase fluid flows in porous media. The basic model includes the continuity equation and the Darcy laws for each phase as well as the algebraic expression for the sum of saturations. A numerical algorithm is constructed using the pressure equation. In the present work there are discussed the basic conservation properties for the differential models and the necessity of their fulfillment at the discrete level. Explicit-implicit consistent approximations are constructed for multi-component flows in porous media along with the operator-splitting schemes for compressible media.