Stimulation of gas or oil shales by hydraulic fracturing requires injecting water at a very high rate into kilometre-long boreholes, in order to induce sufficient fracture width to place the proppant. Since such high rate of injection implies flow in the turbulent regime, heavy-molecular-weight polymers are added to water to reduce drag and thus drastically lessen the energy required for pumping. Lecampion & Zia (J. Fluid Mech., vol. 880, 2019, pp. 514-550) explore via modelling how the rheology of slickwater-water with a small amount of drag-reducing agents-affects the propagation of a hydraulic fracture. Theoretical models in combination with scaling arguments and numerical simulations indicate that flow in a radial fracture is inherently laminar, with the turbulent regime restricted at most to the first few minutes of injection, for plausible values of rock and fluid parameters and the injection rate.
- lubrication theory
- turbulent transition