Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 509-541 |
| Seitenumfang | 33 |
| Fachzeitschrift | Computer Methods in Applied Mechanics and Engineering |
| Jahrgang | 312 |
| Publikationsstatus | Veröffentlicht - 1 Dez. 2016 |
| Extern publiziert | Ja |
Abstract
In this paper we present a phase field model for proppant-filled fractures in a poroelastic medium. The formulation of the coupled system involves four unknowns: displacements, phase field, pressure, and proppant concentration. The two-field displacement phase-field system is solved fully-coupled and accounts for crack irreversibility. This solution is then coupled to the pressure equation via a fixed-stress iteration. The pressure is obtained by using a diffraction equation where the phase-field variable serves as an indicator function that distinguishes between the fracture and the reservoir. The transport of the proppant in the fracture is modeled by using a power-law fluid system. The numerical discretization in space is based on Galerkin finite elements for displacements and phase-field, and an enriched Galerkin method is applied for the pressure equation in order to obtain local mass conservation. The concentration is solved with cell-centered finite elements. Nonlinear equations are treated with Newton's method. Our developments are substantiated with several numerical examples in two and three dimensions.
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in: Computer Methods in Applied Mechanics and Engineering, Jahrgang 312, 01.12.2016, S. 509-541.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Phase-field modeling of proppant-filled fractures in a poroelastic medium
AU - Lee, Sanghyun
AU - Mikelić, Andro
AU - Wheeler, Mary F.
AU - Wick, Thomas
N1 - Funding Information: All the authors wish to acknowledge partial support by Department of Energy National Energy Technology Laboratory grant DE-FE0023314 , Aramco grant UTA 11-000320 , and Statoil grant STNO-4502931834 . A. Mikelić would like to thank the Institute for Computational Engineering and Science (ICES), UT Austin for hospitality during his visits in February and June 2015. T. Wick was partially supported by the Austrian Academy of Sciences , the Institute for Computational Engineering and Sciences JT Oden fellowship , and the Center for Subsurface Modeling at UT Austin. Funding Information: All the authors wish to acknowledge partial support by Department of Energy National Energy Technology Laboratory grant DE-FE0023314, Aramco grant UTA 11-000320, and Statoil grant STNO-4502931834. A. Mikeli? would like to thank the Institute for Computational Engineering and Science (ICES), UT Austin for hospitality during his visits in February and June 2015. T. Wick was partially supported by the Austrian Academy of Sciences, the Institute for Computational Engineering and Sciences JT Oden fellowship, and the Center for Subsurface Modeling at UT Austin. Publisher Copyright: © 2016 Elsevier B.V. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2016/12/1
Y1 - 2016/12/1
N2 - In this paper we present a phase field model for proppant-filled fractures in a poroelastic medium. The formulation of the coupled system involves four unknowns: displacements, phase field, pressure, and proppant concentration. The two-field displacement phase-field system is solved fully-coupled and accounts for crack irreversibility. This solution is then coupled to the pressure equation via a fixed-stress iteration. The pressure is obtained by using a diffraction equation where the phase-field variable serves as an indicator function that distinguishes between the fracture and the reservoir. The transport of the proppant in the fracture is modeled by using a power-law fluid system. The numerical discretization in space is based on Galerkin finite elements for displacements and phase-field, and an enriched Galerkin method is applied for the pressure equation in order to obtain local mass conservation. The concentration is solved with cell-centered finite elements. Nonlinear equations are treated with Newton's method. Our developments are substantiated with several numerical examples in two and three dimensions.
AB - In this paper we present a phase field model for proppant-filled fractures in a poroelastic medium. The formulation of the coupled system involves four unknowns: displacements, phase field, pressure, and proppant concentration. The two-field displacement phase-field system is solved fully-coupled and accounts for crack irreversibility. This solution is then coupled to the pressure equation via a fixed-stress iteration. The pressure is obtained by using a diffraction equation where the phase-field variable serves as an indicator function that distinguishes between the fracture and the reservoir. The transport of the proppant in the fracture is modeled by using a power-law fluid system. The numerical discretization in space is based on Galerkin finite elements for displacements and phase-field, and an enriched Galerkin method is applied for the pressure equation in order to obtain local mass conservation. The concentration is solved with cell-centered finite elements. Nonlinear equations are treated with Newton's method. Our developments are substantiated with several numerical examples in two and three dimensions.
KW - Hydraulic fracturing
KW - Phase field fracture
KW - Proppant transport
KW - Quasi-Newtonian flow model
UR - http://www.scopus.com/inward/record.url?scp=84959934283&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2016.02.008
DO - 10.1016/j.cma.2016.02.008
M3 - Article
AN - SCOPUS:84959934283
VL - 312
SP - 509
EP - 541
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
ER -