Modeling and numerical simulations of fractured vuggy porous media is a challenging problem due to the presence of cavities called macro vugs which are connected via discrete fractures networks. The main difficulty is the co-existence of porous and free-flow region in such media on macro scale. In this study, a novel conceptual discontinuum model i.e. discrete fracture-vug network (DFVN) model has been proposed to this problem.

In DFVN conceptual model, naturally fractured vuggy porous rock masses are considered as a composite porous material, consisting of (1) macro fractures system, (2) porous rock matrix system, and (3) macro vugs system. Macro fractures and vugs are embedded in porous rock, and the isolated vugs are connected via discrete fracture network. We model the fractured vuggy media on macroscopic scale using Navier-Stokes equations within the vugular region, Darcy's law within the porous flow region including porous rock matrix system and macro fractures system, and a Beavers-Joseph-Saffman boundary on the interface between two regions.

A standard Galerkin finite element method is implemetated for the solution of DFVN model. A good match with analytical and numerical solutions for Poiseuille flow in a free/porous channel was achieved, which verified the accuracy of our finite element numerical scheme. Both 2D DFVN models with homogeneous isotropic rock matrix and heterogeneous anisotropic rock matrix are simulated and studied. The numerical results have shown that DFVN model provides a natural way of modeling realistic fluid flow in fractured vuggy porous media.

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