Abstract
In this chapter, a novel conceptual model named discrete fracture-vuggy network (DFVN) model, which is assumed to be composed of free flow region (macrovug system) and porous medium region (macrofracture system and porous rock matrix system), has been developed to demonstrate the flow characterization: coupling of free flow and porous media flow. Based on DFVN, the macromathematical model of two-phase coupling flow, including coupling interface conditions, is developed by upscaling micro Navier–Stokes equation through Volume Average Method. Darcy’s law is utilized to describe the flow behavior in the porous medium, while in the free flow region, Navier–Stokes equation is applied. Besides, normal stress and mass continuity conditions, as well as Beavers–Joseph–Saffman boundary condition are added to coupling the two different flow subdomains. The whole mathematical model is solved by upwind Petrov–Galerkin finite element method and the coupling is implemented via alternative solution method. Finally, several numerical cases are given to validate the effectivity and accuracy of the coupling model.
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