ABSTRACT

A new numerical simulation method for water flow in 2D porous media is proposed. A porous medium is discretized topologically into a discrete branches network. Each branch in the oriented network is defined as a weighted element with a starting node and an ending node. Equivalent hydraulic parameters are derived based on the Darcy's Law. A node law of flow rate and a branch law of pressure are, a unified governing equation for both the inner branches and the boundary branches are introduced from the author's previous researches. Dispersion laws of flow rate is proposed and discussed. Two case studies are analyzed and one of them is compared with analytical solutions. It shows that the proposed topology analysis method (TAM) is effective in analyzing water flow in porous media. The advantage of the proposed TAM is that a continuous porous medium is discretized into a discrete branches network, which is analyzed same as for a discrete fracture network. Solutions of water pressures and flow rates in the discrete branches network are obtained by solving a system of nonhomogeneous linear equations. It is demonstrated with high efficiency and accuracy. The developed method can be extended to analyzing water flow in fractured and porous media in 2D and 3D conditions.

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