Slickwater hydraulic fracture propagation: near-tip and radial geometry solutions

We quantify the importance of turbulent flow on the propagation of hydraulic fractures (HF) accounting for the addition of friction reducing agents to the fracturing fluid (slickwater fluid). The addition in small quantities of a high molecular weight polymer in water is sufficient to drastically reduce friction of turbulent flow. The maximum drag reduction (MDR) asymptote is always reached during industrial like injections. The energy required for pumping is thus drastically reduced, allowing to perform high volume high rate hydraulic fracturing operations at a reasonable cost. We investigate the propagation of a hydraulic fracture propagating in an elastic impermeable homogeneous solid under a constant (and possibly very high) injection rate accounting for laminar and turbulent flow conditions with or without the addition of friction reducers. We solve the near-tip HF problem and estimate the extent of the laminar boundary layer near the fracture tip as function of a tip Reynolds number for slickwater. We obtain different propagation scalings and transition time-scales. This allows to easily quantify the growth of a radial HF from the early-time turbulent regime(s) to the late-time laminar regimes. Depending on the material and injection parameters, some propagation regimes may actually be bypassed. We derive both accurate and approximate solutions for the growth of radial HF in the different limiting flow regimes (turbulent smooth, rough, MDR) for the zero fracture toughness limit (corresponding to the early stage of propagation of a radial HF). We also investigate numerically the transition(s) between the early time MDR regime to the late time laminar regimes (viscosity and toughness) for slickwater fluid. Our results indicate that the effect of turbulent flow on high rate slickwater HF propagation is limited and matters only at early time (at most to the first minutes for industrial hydraulic fracturing operations).