A Computational Model of Fluid Filtration in Fractured Porous Media

This paper discusses a computational 3D dual porosity model of two-phase incompressible fluid filtration in a fractured-porous medium. The conservation laws are formulated in integral form, and for their spatial approximation a combination of a mixed finite element method to determine the total flow and pressure velocities and a finite volume method to determine the saturations in the porous blocks and in the fractures are used. The equations for saturations are approximated with an explicit upwind scheme to eliminate nonphysical oscillations. The model under consideration includes injection and production wells with given total flow rates. For the total velocities and pressures, a Neumann problem is formulated, for which a condition of unique solvability is used and a method for solving it without additional conditions is proposed. For the explicit upwind scheme used for solving the equations for saturations, a weak maximum principle is established, which is illustrated by computational experiments.