Upscaled Model for Mixed Dimensional Coupled Flow Problem in Fractured Porous Media Using Non-local Multicontinuum (NLMC) Method

Abstract

In this paper, we consider a mixed dimensional discrete fracture model with highly conductive fractures. Mathematically the problem is described by a coupled system of equations consisting a d - dimensional equation for flow in porous matrix and a (d-1) - dimensional equation for fracture networks with a specific exchange term for coupling them. For the numerical solution on the fine grid, we construct unstructured mesh that is conforming with fracture surface and use the finite element approximation. Fine grid approximation typically leads to very large systems of equations since it resolves the fracture networks, and therefore some multiscale methods or upscaling methods should be applied. The main contribution of this paper is that we propose a new upscaled model using Non-local multi-continuum (NLMC) method and construct an effective coarse grid approximation. The upscaled model has only one additional coarse degree of freedom (DOF) for each fracture network. We will present results of the numerical simulations using our proposed upscaling method to illustrate its performance.