Topology analysis method for water flows in 2D discrete fracture networks

摘要

A new 2D numerical simulation method for water flows in discrete fracture networks is proposed. Firstly, hydraulic analysis of a single fracture is carried out. Each fracture in a discrete fracture network is treated as a weighted branch with a start node and an end node in a directed network. Node and branch laws of water flow in discrete fracture networks are derived based on the conservation of mass and energy. The topology theory is applied in order to search the subways of water flow, and to calculate water pressures and flow rate in each branch of a weighted, directed and connected path. Identification of water flow pathways and tree cutting are considered in the developed method. An example is analyzed. It shows that the proposed topology analysis method (TAM) is effective in analyzing water flow in discrete fracture networks. The advantages of TAM include: 1) Boundaries and fractures are unified with the same form of governing equation, which makes it possible to obtain water flows in a network analytically; so TAM is actually an efficient analytical method for analyzing water flows in discrete fracture networks; 2) Solutions of water pressures and flow rates in discrete fracture networks are obtained by solving a system of nonhomogeneous linear equations; 3) Results demonstrate that the developed method is effective and promising for more complex applications and engineering purpose.