Details
| Original language | English |
|---|---|
| Pages (from-to) | 367-398 |
| Number of pages | 32 |
| Journal | Multiscale Modeling and Simulation |
| Volume | 13 |
| Issue number | 1 |
| Publication status | Published - 2015 |
| Externally published | Yes |
Abstract
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.
Keywords
- Biot system, Finite elements, Fixed-stress iterative coupling, Fracture propagation, Phase field
ASJC Scopus subject areas
- Chemistry(all)
- Mathematics(all)
- Modelling and Simulation
- Environmental Science(all)
- Ecological Modelling
- Physics and Astronomy(all)
- Computer Science(all)
- Computer Science Applications
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In: Multiscale Modeling and Simulation, Vol. 13, No. 1, 2015, p. 367-398.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A phase-field method for propagating fluid-filled fractures coupled to a surrounding porous medium
AU - Mikelić, Andro
AU - Wheeler, Mary F.
AU - Wick, Thomas
N1 - Publisher Copyright: © 2015 Society for Industrial and Applied Mathematics. Copyright: Copyright 2015 Elsevier B.V., All rights reserved.
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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.
KW - Biot system
KW - Finite elements
KW - Fixed-stress iterative coupling
KW - Fracture propagation
KW - Phase field
UR - http://www.scopus.com/inward/record.url?scp=84925146233&partnerID=8YFLogxK
U2 - 10.1137/140967118
DO - 10.1137/140967118
M3 - Article
AN - SCOPUS:84925146233
VL - 13
SP - 367
EP - 398
JO - Multiscale Modeling and Simulation
JF - Multiscale Modeling and Simulation
SN - 1540-3459
IS - 1
ER -