Solution of two key issues in arbitrary three-dimensional discrete fracture network flow models

Abstract

Summary It is necessary to consider a great number of arbitrarily developed fractures in applications involving realistic 3-d fracture network flow models of rock masses. In order to model the fluid flow in a complicated arrangement of discrete fracture networks (DFNs), two core issues have to be solved. Firstly, how does one identify the connection relationships between fractures in the 3-d arbitrary fracture network? Secondly, how can one calculate numerically the fluid flow in arbitrarily-shaped 2-d domains? This paper first proposes that the boundaries of all enclosed blocks form flow pathways. All enclosed blocks can be identified using a 3-d block cutting method. The boundaries of the blocks are composed of loops which are formed by intersecting lines between all faces (fractures and other surfaces). Therefore, the connection relationships between fractures can be determined according to the linkages of the loops. Accordingly, the linkages of the finite element nodes between different faces can also be determined. On the other hand, the fluid flow occurring in the fractures can be treated as a 2-d continuous flow within the arbitrarily shaped loops in the fracture’s local coordinates. We propose that these loops can be meshed into triangles using a method of simplex triangulation of the arbitrarily shaped domain. Then, according to the linkages between nodes, the global conductivity matrix can be assembled and the solution of the equations governing flow can be derived. Three cases are used to validate the model. Finally, an analysis is made of a practical engineering example (with 8914 lines of intersection and 4188 loops) which shows that the proposed flow model is practicable and can deal with complicated DFNs.