Multiscale Methods for Modeling Fluid Flow Through Naturally Fractured Carbonate Karst Reservoirs

Modeling and numerical simulations of Carbonate Karst reservoirs is a challenging problem due to the presence of vugs and caves which are connected via 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, caves) in a single system of equations. The StokesBrinkman equations also generalize the traditional DarcyStokes 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. Both constant and variable background permeability matrices are considered and the effect the vugs have on the overall permeability is evaluated. Fracture networks connecting isolated vugs are also studied. It is shown that the Stokes-Brinkman equations provide a natural way of modeling realistic reservoir conditions, such as partially filled fractures.