A Graph-theoretic Pipe Network Method for water flow simulation in discrete fracture networks: GPNM

• A Graph-theoretic Pipe Network Method is proposed for water flow in fractures.
• A unified governing equation is proposed for fractures and boundaries.
• The physical model and governing equations are graph-theoretically represented.
• No discretization is needed, which saves a lot of computational effort.
• The Graph-theoretic Pipe Network Method (GPNM) is demonstrated with high accuracy.

In order to simulate water flow in discrete fracture networks, a Graph-theoretic Pipe Network Method (GPNM) is proposed. Firstly, identification of water flow pathways is considered and a tree cutting technique is adopted. Then each fracture in a discrete fracture network is treated as a weighted pipe with a starting node and an ending node in an oriented graph. A node law of flow rate and a pipe law of pressure in discrete fracture networks are derived based on the conservation of mass and energy, respectively. Boundaries and fractures are unified with the same form of a unified governing equation. Solutions of water pressures and flow rates in discrete fracture networks are obtained by solving a system of nonhomogeneous linear equations. Since no discretization is needed, GPNM is demonstrated with high efficiency. In addition, a few case studies are implemented and compared with those from analytical solutions or numerical analysis using the software, Universal Distinct Element Code (UDEC). It shows that the proposed Graph-theoretic Pipe Network Method (GPNM) is effective in analyzing water flow in discrete fracture networks. Moreover, GPNM is promising for more engineering applications, and can be used for large scales of water simulation problems with numerous fractures.