Abstract
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 simulations 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 conceptually well-suited for this type of modeling as they allow varying resolution and provide a systematic procedure for coarsening and refinement. However, to date there are hardly no multiscale methods developed for problems with both free-flow and porous regions. Our work is a first step to make a uniform multiscale framework in which 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 choices of parameters. In the paper, the MsMFE solutions are compared with fine-scale Stokes--Brinkman solutions for test cases including both short- and long-range fractures. The results demonstrate how fine-scale flow in fracture networks can be represented within a coarse-scale Darcy flow model by using multiscale elements computed solving the Stokes--Brinkman equations. The results indicate that the MsMFE method is a promising path toward direct simulation of highly detailed geocellular models of vuggy and naturally-fract