Impact of yield stress and fractal characteristics on the flow of Bingham fluid through fracture network

Abstract

Flow process of a fluid with yield stress in fractured reservoirs is important in petroleum recovery. In this study, a new approach is proposed to study the combined effect of Bingham fluid properties and fractal characteristics on the flow of a Bingham fluid through a fractal fracture network. Both the aperture and trace length of fractures are distributed according to the power-law fractal distribution with distinct fractal dimensions. The relative effect on the flowrate of Bingham fluid in the network by the Bingham fluid properties and fractal characteristics compared to the Newtonian counterpart is examined. The results demonstrate that the flowrate of Bingham fluid through the network increases quickly with the pressure head gradient since large fractures are first activated which are responsible to quickly increase the Bingham fluid flowrate. The flowrate ratio of the Bingham fluid over Newtonian fluid decreases with the fractal dimension of aperture since the Bingham fluid flowrate decreases with increasing fractal dimension at a faster rate than the Newtonian fluid. A larger ratio of minimum over maximum apertures in the fractal network results in a larger flowrate ratio of the Bingham fluid over Newtonian fluid. The trace length fractal parameters do not affect the flowrate ratio of the Bingham fluid over the Newtonian fluid due to the fact that these parameters affect the actual flowrate for both types of fluid to the same extent.