ABSTRACT:

The injection of slick-water at the high rates used to fracture unconventional shale-gas reservoirs results in flows that are turbulent - particularly near the wellbore. In this paper we consider the effect of turbulence on the simultaneous propagation of multiple hydraulic fractures that are constrained to evolve in parallel planes. The effect of turbulence is captured using a modification of the Darcy-Weisbach fluid-flow model with an adaptation of Churchill's friction factor approximation to fracture flow geometries that is able to capture the transition from laminar to fully turbulent flow. Since the Reynlods number is proportional to the fracture width, the flow transitions to laminar close to the tip where the fracture width approaches zero. The model used in this paper is therefore able to exploit the multi-scale laminar tip asymptotic behaviour in order to use the Implicit Level Set Scheme (ILSA) to locate the fracture free boundary and to identify the propagation regime. We provide a numerical example for an array of five uniformly distributed planar fractures in which the laminar model exhibits significant stress shadowing while the turbulent model predicts substantially less. This reduction in stress shadowing in the turbulent flow model is due to the significantly larger pressure drop near the well-bore compared to the laminar case that dominates the mutual stress interactions between the fractures in the array.

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