The design and evaluation of hydraulic fracturing jobs is critical for efficient production from shale oil and gas fields. The efficiency of a fracturing job depends on the interaction between hydraulic (induced) and naturally occurring discrete fractures. A rigorous fracture propagation model is therefore necessary to predict fracture growth pattern in a heterogeneous, anisotropic poroelastic medium. The propped fracture length and aperture is dependent on the poroelastic behavior of rock matrix and proppants under consideration. Additionally, we need to account for complex reservoir geometries and features including non-planar fractures, faults and barriers. A long-term production assessment of these reservoirs therefore requires a coupled reservoir-fracture flow and geo-mechanics model which takes into account above considerations. In this report, we present updates for the phase field fracture propagation and the coupled flow and geomechanics model developments for fractured poroelastic reservoirs.
Two phase field fracture propagation models were developed: (1) pressurized and (2) fluid-filled models. The pressurized approach assumes fracture pressure distribution is known a priori (given) and increases linearly with time. The fluid-filled approach, on the other hand, solves a coupled flow problem for the reservoir and fracture domains to determine pressure distribution along the fracture. The latter approach is an active area of research to determine the significance of coupled flow and poro-mechanics on crack growth. The fracture pressure is then assumed to be in equilibrium with the normal component of the reservoir stresses at the fracture interface for both approaches. A brittle fracture theory, as originally presented by Griffith, is invoked along with its underlying assumptions to determine a fracture growth rate and failure criterion.
A substantial research effort is being directed to address the modeling and computational challenges involved herein. Three different numerical solution algorithms were developed to solve the coupled system differing in the treatment of an irreversible crack growth criterion: (1) simple penalization (2) augmented Lagrangian and (3) primal-dual active set method. The active set approach has faster Newton iteration convergence rates and is therefore the method of choice for 3D simulations. A detailed study describing each of these algorithms and the associated numerical results can be found in ICES Reports 13-15, 13-25 and 14-27. The fracture propagation models using phase field approach have the following advantages:
- The models are easy to implement and use fixed-grid topology. This avoids remeshing required to resolve an exact fracture location.
- The fracture nucleation, propagation, kinking, and path are intrinsically determined. This reduces computational cost associated with post-processing of quantities such as stress intensity factors when compared to the widely used displacement discontinuity methods.
- The models can handle joining and branching of multiple fractures without requiring tracking of fracture interfaces.
- Crack growth in heterogeneous media does not require special treatment. Furthermore, the fracture aperture can be calculated using the phase-field function.
This work is published in the following papers:
Mikelić, Andro, Mary F. Wheeler, and Thomas Wick. “A phase field approach to the fluid filled fracture surrounded by a poroelastic medium.“ ICES Preprint 13-15, Jun 2013, link
Wheeler, M. F., T. Wick, and W. Wollner. “An augmented-Lagrangian method for the phase-field approach for pressurized fractures.” Computer Methods in Applied Mechanics and Engineering 271 (2014): 69-85.
Mikelić, Andro, Mary F. Wheeler, and Thomas Wick. “A quasi-static phase-field approach to pressurized fractures.” Nonlinearity 28, no. 5 (2015): 1371-1399
Heister, Timo, Mary F. Wheeler, and Thomas Wick. “A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach.” Computer Methods in Applied Mechanics and Engineering 290 (2015): 466-495
Wick, Thomas, Sanghyun Lee, and Mary F. Wheeler. “3D Phase-Field for Pressurized Fracture Propagation in Heterogeneous Media.”, ECCOMAS and IACM Coupled Problems, San Servolo, Venice/Italy, May 18-20 2015