FRACTAL PERMEABILITY MODEL FOR POWER-LAW FLUIDS IN FRACTURED POROUS MEDIA WITH ROUGH SURFACES

A novel analytical model is derived based on fractal geometry theory to characterize the permeability of power-law fluids through fractured porous media with fractal asperities on surfaces. The proposed model is expressed as a function of structure parameters of fractured porous media, fractal dimensions for porous matrix and for fracture as well as the index n of power-law fluid behavior. The influences of these parameters on the permeability are analyzed in detail. It is found that the relationship between permeability and roughness exhibits nonlinear characteristics. A higher power-law fluid behavior index significantly affects the reduction rate of permeability with relative roughness. Moreover, permeability is sensitive to the perturbation due to the rate of aperture to length. The proposed fractal model can clearly reveal more physical mechanisms for power-law fluid in fractured porous media than the existing models. Compared with the experimental data available in the literature, the validity of model predictions is verified.

Automated summary

A novel analytical model based on fractal geometry theory is developed to characterize the permeability of power-law fluids in fractured porous media with fractal asperities. The model considers structure parameters of fractured porous media, fractal dimensions for porous matrix and fracture, and the power-law fluid behavior index. The model reveals non-linear characteristics of the relationship between permeability and roughness, and the significant influence of the power-law fluid behavior index on the reduction rate of permeability. The proposed fractal model provides a better understanding of power-law fluid behavior in fractured porous media.