Details
| Original language | English |
|---|---|
| Pages (from-to) | 1530-1555 |
| Number of pages | 26 |
| Journal | Mathematics and Mechanics of Solids |
| Volume | 24 |
| Issue number | 5 |
| Early online date | 13 May 2018 |
| Publication status | Published - May 2019 |
Abstract
In this paper, we present a full phase-field model for a fluid-driven fracture in a nonlinear poroelastic medium. The nonlinearity arises in the Biot equations when the permeability depends on porosity. This extends previous work (see Mikelić et al. Phase-field modeling of a fluid-driven fracture in a poroelastic medium. Comput Geosci 2015; 19: 1171–1195), where a fully coupled system is considered for the pressure, displacement, and phase field. For the extended system, we follow a similar approach: we introduce, for a given pressure, an energy functional, from which we derive the equations for the displacement and phase field. We establish the existence of a solution of the incremental problem through convergence of a finite-dimensional Galerkin approximation. Furthermore, we construct the corresponding Lyapunov functional, which is related to the free energy. Computational results are provided that demonstrate the effectiveness of this approach in treating fluid-driven fracture propagation. Specifically, our numerical findings confirm differences with test cases using the linear Biot equations.
Keywords
- Hydraulic fracturing, nonlinear poroelasticity, phase field
ASJC Scopus subject areas
- Mathematics(all)
- Materials Science(all)
- Engineering(all)
- Mechanics of Materials
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In: Mathematics and Mechanics of Solids, Vol. 24, No. 5, 05.2019, p. 1530-1555.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A monolithic phase-field model of a fluid-driven fracture in a nonlinear poroelastic medium
AU - van Duijn, C. J.
AU - Mikelić, Andro
AU - Wick, Thomas
N1 - Funding Information: The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported in part by the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program ‘‘Investissements d’Avenir’’ (grant number ANR-11-IDEX-0007) operated by the French National Research Agency and by the Darcy Center.
PY - 2019/5
Y1 - 2019/5
N2 - In this paper, we present a full phase-field model for a fluid-driven fracture in a nonlinear poroelastic medium. The nonlinearity arises in the Biot equations when the permeability depends on porosity. This extends previous work (see Mikelić et al. Phase-field modeling of a fluid-driven fracture in a poroelastic medium. Comput Geosci 2015; 19: 1171–1195), where a fully coupled system is considered for the pressure, displacement, and phase field. For the extended system, we follow a similar approach: we introduce, for a given pressure, an energy functional, from which we derive the equations for the displacement and phase field. We establish the existence of a solution of the incremental problem through convergence of a finite-dimensional Galerkin approximation. Furthermore, we construct the corresponding Lyapunov functional, which is related to the free energy. Computational results are provided that demonstrate the effectiveness of this approach in treating fluid-driven fracture propagation. Specifically, our numerical findings confirm differences with test cases using the linear Biot equations.
AB - In this paper, we present a full phase-field model for a fluid-driven fracture in a nonlinear poroelastic medium. The nonlinearity arises in the Biot equations when the permeability depends on porosity. This extends previous work (see Mikelić et al. Phase-field modeling of a fluid-driven fracture in a poroelastic medium. Comput Geosci 2015; 19: 1171–1195), where a fully coupled system is considered for the pressure, displacement, and phase field. For the extended system, we follow a similar approach: we introduce, for a given pressure, an energy functional, from which we derive the equations for the displacement and phase field. We establish the existence of a solution of the incremental problem through convergence of a finite-dimensional Galerkin approximation. Furthermore, we construct the corresponding Lyapunov functional, which is related to the free energy. Computational results are provided that demonstrate the effectiveness of this approach in treating fluid-driven fracture propagation. Specifically, our numerical findings confirm differences with test cases using the linear Biot equations.
KW - Hydraulic fracturing
KW - nonlinear poroelasticity
KW - phase field
UR - http://www.scopus.com/inward/record.url?scp=85060948857&partnerID=8YFLogxK
U2 - 10.1177/1081286518801050
DO - 10.1177/1081286518801050
M3 - Article
AN - SCOPUS:85060948857
VL - 24
SP - 1530
EP - 1555
JO - Mathematics and Mechanics of Solids
JF - Mathematics and Mechanics of Solids
SN - 1081-2865
IS - 5
ER -