PERCOLATION CHARACTERISTICS OF POWER-LAW FLUID IN THE FRACTAL TREE-LIKE BIFURCATION NETWORKS WITH ROUGH SURFACES

In order to study the seepage characteristics of power-law fluids in the fractal tree-like bifurcation networks with rough surfaces based on fractal theory, the shape factor of rough surfaces is treated as the randomly distributed cones. According to the generalized Darcy's law and the constitutive equation of power-law fluids, the fully-developed laminar and incompressible flow of power-law fluids in rough pipelines is explored, and the velocity graduation and flow rate expressions of fluids in rough pipelines are obtained. Then, the fractal model for the permeability of power-law fluid in the tree-like bifurcation network with rough surfaces is proposed, and the total flow rate, total pressure drop, and permeability of power-law fluid in the tree bifurcation network with rough surfaces are derived. The relative increase in pressure and the relative decrease in permeability are also obtained. Finally, the analytical expression for the permeability of power-law fluids is analyzed. It can be seen that the permeability of a rough tree-like bifurcation network is inversely proportional to relative roughness, length ratio, bifurcation angle, etc., and directly proportional to the power-law index and diameter ratio. At the same time, the predicted values of the model are compared with existing models, proving the correctness and rationality of the model.