A Multiscale Mixed Finite-Element Method for Vuggy and Naturally Fractured Reservoirs

Abstract

Summary Vugs, caves, and fractures can alter the effective permeability of carbonate reservoirs significantly and should be accounted for accurately 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 coexistence 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 because they allow varying resolution and provide a systematic procedure for coarsening and refinement. However, to date there are hardly any multiscale methods developed for problems with both free-flow and porous regions. Herein, we develop a multiscale mixed finite-element (MsMFE) method for detailed modeling of vuggy and naturally fractured reservoirs as a first step toward a uniform multiscale, multiphysics framework. The MsMFE method uses a standard Darcy model to approximate pressure and fluxes on a coarse grid, whereas fine-scale effects are captured through basis functions computed numerically by solving 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, they avoid explicit interface modeling, and they reduce to Darcy or Stokes flow in certain parameter limits. In this paper, the MsMFE solutions are compared with finescale 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 fractured reservoirs.