Modeling and numerical simulations of Carbonate karst reservoirs is a challenging problem because of the presence of vugs and caves which are connected through fracture networks at multiple scales. In this paper, we propose a unified approach to this problem by using the Stokes-Brinkman equations which combine both Stokes and Darcy flows. These equations are capable of representing porous media (porous rock) as well as free-flow regions (fractures, vugs, and caves) in a single system of equations. The Stokes-Brinkman equations also generalize the traditional Darcy-Stokes coupling without sacrificing the modeling rigor. Thus, it allows us to use a single set of equations to represent multiphysics phenomena on multiple scales. The local Stokes-Brinkman equations are used to perform accurate scale-up. We present numerical results for permeable rock matrix populated with elliptical vugs and we consider upscaling to two different coarse-scale grids--5×5 and 10×10. Both constant and variable background permeability matrices are considered and the effect the vugs have on the overall permeability is evaluated. The Stokes-Brinkman equations are also used to study several vug/cave configurations which are typical of Tahe oilfield in China.

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