ИСТИНА

We analyze the influence of turbulent flow on the propagation of a radial hydraulic fracture in a permeable reservoir. The fracture is formed in elastic rock against the far-field confining stress due to the injection of a fracturing fluid at a constant volumetric rate. The fracturing fluid is slickwater, a water-based liquid with friction-reducing polymeric additives, which allows decreasing fluid friction in the wellbore and fracture and therefore lower the operational costs. We examine the possibility of the laminar-to-turbulent flow regime transformation inside the fracture channel. The slickwater turbulent flow frictional behavior is governed by the Maximum Drag Reduction asymptote achieved in industrial cases. Carter’s law describes the leak-off process from the fracture into the porous media. For calculating the problem solution, we use a numerical algorithm based on Gauss-Chebyshev quadrature and Barycentric Lagrange interpolation techniques. The advantage and computational efficiency of this approach consist in performing calculations without the explicit numerical implementation of the dominant near-tip asymptotic behavior. We consider solution examples for the problem parameters values relevant to the field application. We show that the turbulent flow has an impact on the fracture geometry during no more than couple minutes from the crack initiation resulting in the shorter radius and larger width at the wellbore than the laminar flow solution provides. However, the turbulent solution is characterized by higher wellbore pressure during tens of minutes, meaning more substantial pump power is required for the injection than otherwise predicted by the solution with the laminar fracture flow. Moreover, the leak-off process prolongs the turbulence influence compared to the impermeable reservoir case. We also convert the problem into dimensionless form and demonstrate that its solution is governed by normalized leak-off and characteristic Reynolds numbers, dimensionless time, and distance from the injection point. We explore the parametric space, determine locations of the limiting solutions corresponding to the dominance of a subset of physical processes to frame the solution in the general case, look at the solution variations and identify zones of the turbulence effects importance.