Investigating the effects of intersection flow localization in equivalent-continuum-based upscaling of flow in discrete fracture networks

Abstract

Predicting effective permeabilities of fractured rock masses is a crucial component of reservoir modeling. Its often realized with the discrete fracture network (DFN) method, whereby single-phase incompressible fluid flow is modeled in discrete representations of individual fractures in a network. Depending on the overall number of fractures, this can result in high computational costs. Equivalent continuum models (ECMs) provide an alternative approach by subdividing the fracture network into a grid of continuous medium cells, over which hydraulic properties are averaged for fluid flow simulations. While continuum methods have the advantage of lower computational costs and the possibility of including matrix properties, choosing the right cell size to discretize the fracture network into an ECM is crucial to provide accurate flow results and conserve anisotropic flow properties. Whereas several techniques exist to map a fracture network onto a grid of continuum cells, the complexity related to flow in fracture intersections is often ignored. Here, numerical simulations of Stokes flow in simple fracture intersections are utilized to analyze their effect on permeability. It is demonstrated that intersection lineaments oriented parallel to the principal direction of flow increase permeability in a process we term intersection flow localization (IFL). We propose a new method to generate ECMs that includes this effect with a directional pipe flow parameterization: the fracture-and-pipe model. Our approach is compared against an ECM method that does not take IFL into account by performing ECM-based upscaling with a massively parallelized Darcy flow solver capable of representing permeability anisotropy for individual grid cells. While IFL results in an increase in permeability at the local scale of the ECM cell (fracture scale), its effects on network-scale flow are minor. We investigated the effects of IFL for test cases with orthogonal fracture formations for various scales, fracture lengths, hydraulic apertures, and fracture densities. Only for global fracture porosities above 30 % does IFL start to increase the systems permeability. For lower fracture densities, the effects of IFL are smeared out in the upscaling process. However, we noticed a strong dependency of ECM-based upscaling on its grid resolution. Resolution tests suggests that, as long as the cell size is smaller than the minimal fracture length and larger than the maximal hydraulic aperture of the considered fracture network, the resulting effective permeabilities and anisotropies are resolution-independent. Within that range, ECMs are applicable to upscale flow in fracture networks.