Mathematical Models of Fluid Flow in Fractured-Porous Media

The problem of mathematical modeling of multiphase flow is closely linked with the problems of the development of oil and gas reservoirs. Big part of the world's oil reserves is located in fields with fracture-porous type collectors. Our presentation deals with mathematical modelling of the processes such reservoirs. This work presents some of the results obtained recently in the framework of the project, funded by the Russian Science Foundation. This is a whole complex computing tasks include, as a direct implementation of the model multiphase fluid flow in heterogeneous fractured porous media. in the presence of injection and production wells with access to the permafrost zone, and a number of auxiliary tasks: modeling of filtration gas combustion, the problem of constructing the new generation of efficient numerical algorithms. Here we present some results on incompressible fluid flow in heterogeneous fractured porous media. We deal with two approaches: direct description of cracks using detail meshes and double porosity models, based on G.I. Barenblatt’s approach (see, for example, G.I. Barenblatt, V.M. Entov, V.M. Ryzhik, 1984). In the last case we consider single phase and two-phase fluids separately. For two-phase fluid some new model of mass transfer between cracks and porous blocks is proposed.