On the double porosity model of fractured-porous reservoirs based on the hybrid overflow function

The paper considers a model of double porosity for a fractured porous medium using a combination of classical and gradient mass transfer functions among cracks and porous blocks in the case of a flow of a weakly compressible single-phase fluid. As compared to well-known models, 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-dimensional and three-dimensional model problems are presented. The computational algorithm is based on the use of finite element approximation with respect to space and completely implicit approximations with respect to time.