Analysis of permeability for the fractal-like tree network by parallel and series models

This work investigates the hydraulic conductivity properties in the fractal-like tree networks between one point and a straight line. The expression for the effective permeability of the networks is derived based on the parallel and series models and the relationship between the effective permeability and the geometry structures of the network is analyzed. It is found the effective permeability after including tortuosity is about 20% lower than that without considering the tortuosity, and the tortuosity effect should be included in analysis of hydraulic conductivity properties in the networks; the effective permeability is very sensitive to the geometrical structures of the network. A comparison of the fractal-like tree network with the traditional parallel net indicates that the fractal-like tree network can provide much higher permeability than that of the traditional parallel net.