Upscaled discrete fracture matrix model (UDFM): an octree-refined continuum representation of fractured porous media

Abstract

We develop a computational geometry-based upscaling approach to accurately capture the dynamic processes occurring within and between subsurface fracture networks and the surrounding porous matrix named the Upscaled Discrete Fracture Matrix model (UDFM). Fracture attributes (orientations and apertures) are upscaled and combined with matrix attributes (permeability and porosity) into properties of an unstructured spatially variable Delaunay tetrahedral continuum mesh. The resolution of the mesh depends on proximity to the fractures to preserve the geometric and topological integrity of the underlying fracture network as well as increasing the accuracy of gradients in the dynamics between the fractures and matrix. The UDFM Delaunay mesh and its dual Voronoi mesh can be used in existing multiphysics simulators for flow, solute/heat mass transport, and geomechanics, thereby eliminating the need for the additional development of numerical methods to couple processes in fracture/matrix systems. The model is verified by comparing flow, transport, and coupled heat-mass flow simulations on the provided meshes against analytical and numerical benchmarks. We also provide an additional example to demonstrate the applicability of the UDFM to complex heteregenous fractured media. Overall, the UDFM is accurate in all of the cases considered here and presents an attractive alternative to other modeling strategies that require novel numerical methods or multi-dimensional meshes.