Viscoplastic and pseudoplastic flows through fractal fractures. (October 2022) - Zhu, Jianting
Abstract: A new mathematical model is developed to examine the coupled effects of yield stress, shear-thinning or shear-thickening property and fractal characteristics of fractures on the flow of Herschel–Bulkley fluid through fractal fractures. The flowrate is integrated in a range of fractures that follow a fractal distribution. Increasing the fractal dimension increases the flowrate for both Herschel–Bulkley fluid and Newtonian fluid, but the increase for the Newtonian fluid flow is more significant. The influence of maximum and minimum trace length ratio on the flowrate ratio of the Herschel–Bulkley fluid over the Newtonian fluid is more significant than the fractal dimension. The scaling exponent has very similar effect as maximum and minimum trace length ratio on the flowrate ratio in the fractal fractures. The flowrate ratio drops very quickly with the increasing modified Bingham number. For both shear-thinning and shear-thickening fluids, increasing the pressure head gradient amplifies the effect of the power-law index. Highlights: New solutions of Herschel–Bulkley fluid flow through fractal fractures were developed. Fracture aperture and trace length followed a scaled relationship. Effect of pseudoplasticity and viscoplasticity in fractal fractures was established. Interplay between fractal characteristics and fluid properties was investigated.