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Multiscale Mixed Finite Elements for the Stokes-Brinkman Equations


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. 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, and are thus well suited for modelling vuggy and naturally-fractured media.   Multiscale methods enable 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.  Here, we present a multiphysics version of the multiscale mixed finite-element (MsMFE) method that 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 local flow problems are set up in a way that forces a unit flow across 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 the case of non-square blocks.   We present simulation results for some idealized test cases inc


Academic lecture





  • SINTEF Digital / Mathematics and Cybernetics

Presented at

Challenges of Porous Media and Inaugural Meeting of the International Society for Porous Media (Interpore)


Kaiserslautern, Germany


11.03.2009 - 14.03.2009



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