Fractal study on the permeability of power-law fluid in a rough and damaged tree-like branching network

In the field of fractal theory, the study of permeability in tree-like branching networks has always been rather popular. However, most of the studies have been focused on the permeability models of common fluids. In this study, based on fractal theory and the theory of power-law fluid, a fractal model of the permeability of power-law fluid in a damaged tree-like branching network considering roughness is derived. This study discusses the effects of power-law index, roughness level, damage degree, branching layer number, and length ratio on permeability. The results show that the permeability decreases with an increase in the power-law exponent, roughness, damage degree, bifurcation layer number, and length ratio when the diameter ratio is relatively small; on the contrary, with an increase in the diameter ratio and the power-law exponent, the permeability will increase with an increase in the bifurcation layer number; the permeability will decrease with an increase in the bifurcation layer number when the diameter ratio is large and the power-law exponent is small. The proposed model can be used to analyze the permeability of power-law fluid in a rough damaged tree-like branching network.