Sammendrag
Vugs, caves, and fractures can significantly alter the effective permeability of carbonate reservoirs and should be accurately accounted for in a geomodel. Accurate modeling of the interaction between free-flow and porous regions is essential for flow simulation and detailed production engineering calculations. However, flow simulation of such reservoirs is very challenging because of the co-existence of porous and free-flow regions on multiple scales that need to be coupled. Multiscale methods are in concept well-suited for this type of modeling, as they allow varying resolution and provide a systematic procedure for coarsening and refining, though to date they have not been widely applied for problems with both free-flow and porous regions. Our work is a first step to make a uniform multiscale framework, where we develop a multiscale mixed finite-element (MsMFE) method for detailed modeling of vuggy and naturally-fractured reservoirs. The MsMFE method uses a standard Darcy model to approximate pressure and fluxes on a coarse grid, but captures fine-scale effects through basis functions determined from numerical solutions of local Stokes Brinkman flow problems on the underlying fine-scale geocellular grid. The Stokes-Brinkman equations give a unified approach to simulating free-flow and porous regions using a single system of equations, avoid explicit interface modeling, and reduce to Darcy or Stokes flow by appropriate choice of parameters. The local flow problems are set up in a way that forces a unit flow a cross the interface between two coarse blocks, meaning that the corresponding basis functions reduce to the lowest-order Raviart-Thomas basis functions for the special case of Darcy flow in a homogeneous medium. In the general case, the basis functions account for local variations of flow velocity due to subgrid heterogeneities in the porous regions, increased flow velocities resulting from free-flow regions on the subgrid scale, and geometrical effects in t