Modeling planar hydraulic fractures driven by laminar-to-turbulent fluid flow

The goal of this study is to investigate the effect of turbulent fluid flow on the propagation of planar hydraulic fractures. Modeling a hydraulic fracture includes solving the elasticity equation that ensures the equilibrium of the rock, the fluid volume balance equation, and the fluid flow equation, which are solved together with a propagation condition. In this paper, the influence of turbulent flow is condensed into a single friction factor that influences the fluid flow equation, i.e. the relationship between the fluid flux and the pressure gradient. To capture all possibilities, an approximation for the friction factor, that captures the laminar, the turbulent, and the transitional flows is utilized in this study. Results for the axisymmetric fracture geometry demonstrate that the solution is dominated by turbulent flow at early times and near the source, while transitions to the laminar regime at larger times and close to the fracture tip. In the situation when turbulence dominates, the fracture is shorter and wider, since there is a strong pressure drop in the vicinity of the source, which causes the local fracture width increase. Results for a planar fracture propagating in a three stress layer geometry demonstrate that the turbulence leads to a more circular fracture that promotes height growth through a high stress zone: (C) 2017 Elsevier Ltd. All rights reserved.