Fluid inertia, turbulance, and rate effects in hydraulic fractures

  • Gracie, Robert (University of Waterloo)
  • Gee, Bruce (University of Waterloo)
  • Betancourt Irusta, Nils (University of Waterloo)

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Fluid inertia and rate effects are often important during hydraulic fracturing, yet they are omitted from classical fracture flow models based on the Poiseuille Flow (the cubic law). This presentation will present numerical methods for a recently developed coupled model (GG22) of hydraulic fracturing, which incorporates the effect for fluid inertia, non-parallel fractures, fluid velocity gradients, turbulence, transient flow, and the deformation of a two-dimensional rock mass [1]. Compared to the traditional two-field model (fluid pressure, rock displacement), the GG22 is a three-field model (fluid pressure and velocity, and rock displacement) and so new numerical methods were developed [2]. The governing equation for the GG22, derived from Navier-Stokes, will be explained, the choice of spatial (Finite Element and Volume Methods) and temporal discretization will be discussed for the rock mass and fracture fluid. Strategies (sequential and monolithic) for solving the resulting coupled system of discrete equations will be compared. Techniques to enhance convergence rates and stability will also be touched upon. Lastly, two of illustrative examples will be presented. The first demonstrates the presence of non-Darcian flow in the near-well bore area, with important insights into the relative contributions of turbulence and fluid inertia effects to entrance losses and bottom hole pressure. Lastly, we will demonstrate instances of wave-like fracture-fluid-rock behaviour, not dependent of the inertia of the rock mass - a substantially deviation from the cubic law. Simulations based on the GG22 point towards important implications for the modeling of hydraulic fracturing and the seismic response of faults and natural fractured rock masses.