Journal
MULTISCALE MODELING & SIMULATION
Volume 13, Issue 1, Pages 367-398Publisher
SIAM PUBLICATIONS
DOI: 10.1137/140967118
Keywords
finite elements; phase field; Biot system; fixed-stress iterative coupling; fracture propagation
Funding
- Conoco Phillips [UTA10-000444]
- StatOil
- J. Tinsley Oden Faculty Fellowship Research Program
- U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences through DOE Modeling and Simulation of coupled complex multiscale subsurface phenomena [DE-FG02-04ER25617, MOD. 010]
- ICES Postdoctoral Fellowship
- Humboldt Foundation
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The recently introduced phase-field approach for pressurized fractures in a porous medium offers various attractive computational features for numerical simulations of cracks such as joining, branching, and nonplanar propagation in possibly heterogeneous media. In this paper, the pressurized phase-field framework is extended to fluid-filled fractures in which the pressure is computed from a generalized parabolic diffraction problem. Here, the phase-field variable is used as an indicator function to combine reservoir and fracture pressure. The resulting three-field framework (elasticity, phase field, pressure) is a multiscale problem that is based on the Biot equations. The proposed numerical solution algorithm iteratively decouples the equations using a fixed-stress splitting. The framework is substantiated with several numerical benchmark tests in two and three dimensions.
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