An analytical model for permeability of fractal tree-like branched networks composed of converging–diverging capillaries

Abstract

Seepage processes in tree-fractal networks have attracted extensive research, but the results of most of these studies presuppose a constant pore cross section. This research investigates fluid flow in a fractal tree-like branching network composed of five different types of circular cross section pipes and establishes the effective permeability of the network. Furthermore, the effective permeability of the fractal tree-like network is compared with that of a typical parallel channel network, and the effect of structural parameters on the seepage process of the tree-like branching network is systematically investigated. The effective permeability of all pipelines increased sharply with an increase in the internal diameter ratio at first and then decreased. Furthermore, a considerable advantage was seen in the permeability of the fractal tree network over the traditional parallel channel network, with the benefit becoming more noticeable as branching levels increased. The clear physics of the model offers a useful framework for studying seepage processes.