Flow of power-law fluid through fractal discrete fracture network

Abstract

In this study, a new approach to determine the flowrate of a power-law fluid through a fractal fracture network where fractures are parallel is developed. The aperture and trace length of fracture network can follow separate fractal distributions. The flowrate through the fractal network is determined through mean field approximation from the integration of flowrates in individual fractures over the aperture range of the fractal network. Three dimensionless parameters are defined to investigate the relative effects of a power-law fluid in an individual fracture and in a fractal fracture network. The analytical expression for the ratio of flowrate of power-law fluid over Newtonian fluid is developed. The effects of fractal dimension of aperture, power-law fluid index of fluid and pressure head gradient parameter on the flowrate are analyzed and discussed. The results demonstrate that for a shear-thinning fluid, increase in the fractal dimension of aperture reduces the flowrate ratio of power-law fluid over Newtonian fluid, while the reverse is true for a shear-thickening fluid. A large fractal dimension of aperture amplifies the effect of power-law fluid index of fluid when the pressure head gradient is low. The flowrate ratio of the power-law fluid over Newtonian fluid in the network increases quickly for the shear-thinning fluid and decreases for the shear-thickening fluid with the increase in the pressure head gradient parameter.