Statistical properties for two-dimensional fluid flow in percolation porous media

We study the statistical properties of fluid flows in percolation porous media at very low Reynolds number by numerical simulations for 20,000 different configurations. It is shown that there are some important differences between fluid flows in macroscopically homogeneous and fractal porous media. For fluid flows in macroscopically homogeneous media, the pressure is definite, but the velocity is random and depends on the structural details of porous media. The permeability k for fluid flows in fractal changes with the size L as k∼L−α where α≈1.0, not approaching the constant expected from Darcy's law. The statistical distribution of pressure in fractal is independent of the size L and can be approximated by a function of the triangular shape.