Numerical simulation of planar hydraulic fracture propagation with consideration to transition from turbulence to laminar flow regime

Turbulent flow in fluid-driven fractures exerts important effects on the hydraulic fracture extension, fracture geometry, and proppant transport. Based on linear elastic fracture mechanics, the implicit level set algorithm, laminar flow theory, and turbulent flow theory, this study established planar fracture propagation models of permeable and impermeable reservoirs with consideration the flow regime transition from turbulent to laminar flow when the Reynolds number is larger than the critical Reynolds number. Additionally, the frictional behavior of the fluid in the turbulent flow regime was approximated based on the MDR asymptote and Blasius correlation. The influence of the turbulent flow effect on the hydraulic fracture propagation was theoretically and numerically analyzed. The results reveal that the turbulent flow regime exerts a significant effect within the first few minutes of fracture propagation. Compared with the fully laminar-flow model, the turbulent-laminar flow model predicted a shorter fracture radius, larger maximum fracture width, and fluid net pressure. This indicates that the fracturing process requires greater pumping power than that predicted by the laminar flow models under the influence of turbulent flow to achieve the desired design parameters. Compared with impermeable rock, the turbulent flow in the fracture is enhanced by fluid leak-off. Slickwater can transition from turbulent to laminar flow at a lower critical Reynolds number compared with pure water. The normalized fracture parameters indicate that the fracture radius corresponding to pure water is smaller, and the maximum width of fracture and maximum net pressure are larger than those of slickwater. The threshold time of turbulent flow for different fracture parameters varies depending on the injected fluid properties and reservoir parameters. Our study contributes toward a deeper understanding of the real physical behavior of hydraulic fracture propagation at large injection rates.