Phase field method for quasi-static hydro-fracture in porous media under stress boundary condition considering the effect of initial stress field

authored by: Shuwei Zhou, Xiaoying Zhuang, Timon Rabczuk
Abstract: Phase field model (PFM) is an efficient fracture modeling method and has high potential for hydraulic fracturing (HF). However, the current PFMs in HF do not consider well the effect of in-situ stress field and the numerical examples of porous media with stress boundary conditions were rarely presented. The main reason is that if the remote stress is applied on the boundaries of the calculation domain, there will be relatively large deformation induced on these stress boundaries, which is not consistent with the engineering observations. To eliminate this limitation, this paper proposes a new phase field method to describe quasi-static hydraulic fracture propagation in porous media subjected to stress boundary conditions, and the new method is more in line with engineering practice. A new energy functional, which considers the effect of initial in-situ stress field, is established and then it is used to achieve the governing equations for the displacement and phase fields through the variational approach. Biot poroelasticity theory is used to couple the fluid pressure field and the displacement field while the phase field is used for determining the fluid properties from the intact domain to the fully broken domain. In addition, we present several 2D and 3D examples to show the effects of in-situ stress on hydraulic fracture propagation. The numerical examples indicate that under stress boundary condition our approach obtains correct displacement distribution and it is capable of capturing complex hydraulic fracture growth patterns.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Tongji University
Ton Duc Thang University
Bauhaus-Universität Weimar
Type: Article
Journal: Theoretical and Applied Fracture Mechanics
Volume: 107
ISSN: 0167-8442
Publication date: 06.2020
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Materials Science(all), Condensed Matter Physics, Mechanical Engineering, Applied Mathematics
Electronic version(s): https://doi.org/10.1016/j.tafmec.2020.102523 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{8533d258a41e43e88f6219d9cea59556,
title = "Phase field method for quasi-static hydro-fracture in porous media under stress boundary condition considering the effect of initial stress field",
abstract = "Phase field model (PFM) is an efficient fracture modeling method and has high potential for hydraulic fracturing (HF). However, the current PFMs in HF do not consider well the effect of in-situ stress field and the numerical examples of porous media with stress boundary conditions were rarely presented. The main reason is that if the remote stress is applied on the boundaries of the calculation domain, there will be relatively large deformation induced on these stress boundaries, which is not consistent with the engineering observations. To eliminate this limitation, this paper proposes a new phase field method to describe quasi-static hydraulic fracture propagation in porous media subjected to stress boundary conditions, and the new method is more in line with engineering practice. A new energy functional, which considers the effect of initial in-situ stress field, is established and then it is used to achieve the governing equations for the displacement and phase fields through the variational approach. Biot poroelasticity theory is used to couple the fluid pressure field and the displacement field while the phase field is used for determining the fluid properties from the intact domain to the fully broken domain. In addition, we present several 2D and 3D examples to show the effects of in-situ stress on hydraulic fracture propagation. The numerical examples indicate that under stress boundary condition our approach obtains correct displacement distribution and it is capable of capturing complex hydraulic fracture growth patterns.",
keywords = "Hydraulic fracture, In-situ stress, Phase field model, Porous media, Staggered scheme, Stress boundary",
author = "Shuwei Zhou and Xiaoying Zhuang and Timon Rabczuk",
note = "Funding Information: The authors gratefully acknowledge financial support provided by Deutsche Forschungsgemein-schaft (DFG ZH 459/3-1), and RISE-project BESTOFRAC (734370). ",
year = "2020",
month = jun,
doi = "10.1016/j.tafmec.2020.102523",
language = "English",
volume = "107",
journal = "Theoretical and Applied Fracture Mechanics",
issn = "0167-8442",
publisher = "Elsevier",
}