| High flow rate, water-driven hydraulic fractures are increasingly popular in the oil and gas industry. The high injection rate and low fluid viscosity associated with these treatments leads to high Reynolds numbers. While there is some recent recognition of the growing need to extend the classical hydraulic fracture models beyond the laminar flow regime, there is little understanding of the impact of turbulent flow on hydraulic fracture growth nor are there existing solutions for simplified geometries that can provide benchmarks for numerical simulators and means for rapid estimation of hydraulic fracture dimensions.;Thus motivated, the goal of this research is to quantify the impact of replacing laminar flow with turbulent flow in HF by developing a benchmark solutions for classical HF crack propagation geometries. This study therefore is comprised of 3 main parts, each associated with a particular geometry (plane strain, blade-shaped, and radial). Each geometry brings its own challenges and a need to adopt a solution method suited to these challenges.;The noteworthy contributions of this work begin with providing a complete suite of benchmarks for simplified but practically-relevant geometries that can be used to estimate fracture dimensions and to benchmark more general numerical simulators. Secondly, this study provides a new numerical approach to HF simulation including laminar, turbulent, and laminar-turbulent transition regimes. Thirdly, this investigation demonstrates the evolution of turbulent-laminar regime in a radial HF, which has implications also for the overall behavior and evolution in more general planar fracture growth geometries. Fourthly, this study has identified that the transition range of fluid regime from turbulent-to-laminar fluid flow is relatively small and practically, it will often suffice to approximate the HF growth using the asymptotic solutions obtained from either the laminar or turbulent solution. |
