An improved embedded discrete fracture model and domain connectivity algorithms on 3D unstructured grids

Abstract

Numerical simulation in 3D complex fractured media is challenging as the geometric discretization of porous media and fracture domains is on multiple scales. In this paper, we present an improved embedded discrete fracture model (EDFM) for 3D unstructured non-matching grids, and correspondingly efficient and robust domain connectivity algorithms are developed. Unlike traditional EDFM, improved EDFM is capable to simulate flows on 3D staggered overlapping unstructured matrix and fracture grids. We illustrate flux exchange patterns and formulas of improved EDFM. Two types of domain connectivity are built to assemble hybrid dimensional overlapping grids of matrix and fracture domains to a coupled linear system using finite volume method. Building domain connectivity is an important challenge for 3D hybrid-dimensional unstructured non-matching grids. We classify all points of domain connectivity into three types. A face indexed octree is employed for spatial binary search. Two types of grid adjacency information are used to accelerate the calculation of grid intersection points. Fracture-matrix intersection information is adopted to accelerate fracture-fracture connectivity generation. The performance of the algorithms is tested by 8 cases in different scales and compared with traversal method. Improved EDFM is validated against discrete fracture model and traditional EDFM using a two-phase flow solver. A case with highly complex fracture network is simulated to demonstrate the capacity of improved EDFM in real complex physical problems. The effects of grid type and resolution are also analyzed in this work.