A finite element approach to the simulation of hydraulic fractures with lag

Abstract

SUMMARYWe presented a finite-element-based algorithm to simulate plane-strain, straight hydraulic fractures in an impermeable elastic medium. The algorithm acCOllllts for the nonlinear coupling between the fluid pressure and the crack opening and separately tracks the evolution of the crack tip and the fluid front. It therefore allows the existence of a fluid lag. The fluid front is advanced explicitly in time, but an implicit strategy is needed for the crack tip to guarantee the satisfaction of Griffith's criterion at each time step. We enforced the coupling between the fluid and the rock by simultaneously solving for the pressure field in the fluid and the crack opening at each time step. We provided verification of our algorithm by performing sample simulations and comparing them with two known similarity solutions.

Numerical methods for hydraulic fracture propagation: A review of recent trends

“…Note that linear elastic fracture mechanics model also simplifies when the fracture path is predetermined, reducing the complexity of finding the fracture front within a priori known planes (Hunsweck et al, 2013;Golovin et al, 2015).…”

The XFEM with an Explicit-Implicit Crack Description for Hydraulic Fracture Problems

“…The boundary condition of zero displacement at infinity is approximated by a finite body and standard finite elements and a local mesh refinement in the area close to the crack interface. Computational evidence of the validity of approximating the infinite medium with a finite block is provided in [13]. The results are scaled to dimensionless quantities in the viscosity scaling.…”

“…The results are scaled to dimensionless quantities in the viscosity scaling. For a detailed description of the scaling for the pressure Π, the opening Ω and the crack length γ see the original publication [13]. The domain and the explicit interface are meshed independently with 5000 and 3000 elements, respectively.…”

An embedded fracture modeling framework for simulation of hydraulic fracturing and shear stimulation

“…Previous work has been done in the area of developing models that apply adaptive grid refinement as fractures propagate [12,33]. This requires a significant level of computational overhead, and the numerical results have been observed to be grid-dependent.…”