Spherical seepage model of Bingham fluid in rough and low-permeability porous media

Based on the microstructure of porous media that exhibits statistical self-similarity fractal features, this paper investigates the radial flow characteristics of non-Newtonian fluids within rough porous media. The analytical equation of permeability and starting pressure gradient of Bingham fluid in low permeability rough porous media are established. It is found that the relative roughness is inversely proportional to the permeability and proportional to the starting pressure gradient. In addition, it is also found that the permeability of low permeability porous media decreases spherically with the increase of radial distance and curvature fractal dimension, and increases with the increase of pore area fractal dimension and porosity. Furthermore, the staring pressure gradient is directly proportional to the radial distance, yield stress and curvature fractal dimension. By comparing the model in this paper with the existing experimental data, the correctness and rationality of the spherical seepage fractal model are effectively verified.