Starting pressure head gradient and flow of Bingham plastics through a scaled fractal fracture network

Abstract

In this study, a new approach is developed to determine the starting pressure head gradient and flowrate of a Bingham plastic through a fractal fracture network. The trace length of fracture is assumed to follow a power-law fractal distribution. The aperture of the fracture is related to the trace length by a scaling relationship. Flow in each fracture is treated as rectangular channel-type flow. A dimensionless flowrate ratio is defined by the average fracture flowrate of Bingham plastic over the flowrate of Newtonian fluid in the smallest fracture. The impact of the input parameters that define the fractal characteristics of the network, the pressure head gradient condition and the Bingham plastic properties is quantified and discussed. It is found that the flowrate ratio significantly decreases with the fractal dimension of trace length as the contrast of fracture lengths in the fractal network decreases with the fractal dimension. The flowrate significantly increases with the maximum over minimum trace length ratio in the network. The scaling exponent dramatically enhances the flowrate in the scaled fractal network. The dimensionless flowrate ratio increases with the pressure head gradient in a non-linear fashion. When the Bingham number is small enough, the dimensionless flowrate ratio does not depend on the pressure head gradient. After flows in more fractures have been activated due to the increase in the pressure head gradient, the Bingham plastic flowrate dramatically increases with the pressure head gradient compared to the Newtonian fluid counterpart.