On a Double Porosity Model of Fractured-Porous Reservoirs Based on a Hybrid Flow Function

In this paper, a model of double porosity for a fractured porous medium using a combination of classical and gradient functions of mass transfer between the cracks and porous blocks in a weakly compressible single-phase fluid flow is considered. As compared to the wellknown models, the model with such a mass transfer function allows one to take into account the anisotropic properties of filtration in a more general form. The results of numerical tests for two- and three-dimensional model problems are presented. The computational algorithm is based on a finite element approximation with respect to space and a completely implicit approximation with respect to time.