SCALING OF FLUID RECOVERY FROM PERCOLATION FRACTALS
We report on the recovery of fluid driven through percolation lattices across a range of scales using a finite difference approximation to the Navier-Stokes equation. This is important in the study of recovery from petroleum reservoirs, in which flow occurs over a wide range of scales, from the microscopic pores right up to the full reservoir. This variation of scale presents difficulties, since flow at the pore level is subject to predominantly viscous effects, whereas at the larger scales the viscous effects may become negligible in comparison with inertial effects. The Navier-Stokes equations may differ greatly with scale. Theoretical rock structures are created using percolation lattices and the flow properties of identical rock structures are then examined as a function of scale. The resultant recovery rates exhibit similarity across scale which would simplify the study of geological reservoir models.