Phase field model of fluid-driven fracture in elastic media: Immersed-fracture formulation and validation with analytical solutions
Abstract
Propagation of fluid-driven fractures plays an important role in natural and engineering processes, including transport of magma in the lithosphere, geologic sequestration of carbon dioxide, and oil and gas recovery from low-permeability formations, among many others. The simulation of fracture propagation poses a computational challenge as a result of the complex physics of fracture and the need to capture disparate length scales. Phase field models represent fractures as a diffuse interface and enjoy the advantage that fracture nucleation, propagation, branching, or twisting can be simulated without ad hoc computational strategies like remeshing or local enrichment of the solution space. Here we propose a new quasi-static phase field formulation for modeling fluid-driven fracturing in elastic media at small strains. The approach fully couples the fluid flow in the fracture (described via the Reynolds lubrication approximation) and the deformation of the surrounding medium. The flow is solved on a lower dimensionality mesh immersed in the elastic medium. This approach leads to accurate coupling of both physics. We assessed the performance of the model extensively by comparing results for the evolution of fracture length, aperture, and fracture fluid pressure against analytical solutions under different fracture propagation regimes. Thus, the excellent performance of themore »
- Authors:
-
[1];
[2];
- Technical Univ. of Madrid, Madrid (Spain). Dept. of Civil Engineering: Hydraulics, Energy, and Environment
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Civil and Environmental Engineering, and Dept. of Earth, Atmospheric and Planetary Sciences
- Technical Univ. of Madrid, Madrid (Spain). Dept. of Civil Engineering: Hydraulics, Energy, and Environment; Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Civil and Environmental Engineering
- Publication Date:
- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Sponsoring Org.:
- Office of Science (SC), Biological and Environmental Research (BER). Earth and Environmental Systems Science Division; The Ministry of Economy, Industry and Competitiveness (MINECO) (Spain); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); José Entrecanales Ibarra Foundation
- OSTI Identifier:
- 1423943
- Grant/Contract Number:
- SC0009297; CTM2014-54312-P; SC0009286; RyC-2012-11704
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Geophysical Research. Solid Earth
- Additional Journal Information:
- Journal Volume: 122; Journal Issue: 4; Journal ID: ISSN 2169-9313
- Publisher:
- American Geophysical Union
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 58 GEOSCIENCES; phase field model; fluid-driven fracturing
Citation Formats
Santillán, David, Juanes, Ruben, and Cueto-Felgueroso, Luis. Phase field model of fluid-driven fracture in elastic media: Immersed-fracture formulation and validation with analytical solutions. United States: N. p., 2017.
Web. doi:10.1002/2016JB013572.
Santillán, David, Juanes, Ruben, & Cueto-Felgueroso, Luis. Phase field model of fluid-driven fracture in elastic media: Immersed-fracture formulation and validation with analytical solutions. United States. https://doi.org/10.1002/2016JB013572
Santillán, David, Juanes, Ruben, and Cueto-Felgueroso, Luis. Thu .
"Phase field model of fluid-driven fracture in elastic media: Immersed-fracture formulation and validation with analytical solutions". United States. https://doi.org/10.1002/2016JB013572. https://www.osti.gov/servlets/purl/1423943.
@article{osti_1423943,
title = {Phase field model of fluid-driven fracture in elastic media: Immersed-fracture formulation and validation with analytical solutions},
author = {Santillán, David and Juanes, Ruben and Cueto-Felgueroso, Luis},
abstractNote = {Propagation of fluid-driven fractures plays an important role in natural and engineering processes, including transport of magma in the lithosphere, geologic sequestration of carbon dioxide, and oil and gas recovery from low-permeability formations, among many others. The simulation of fracture propagation poses a computational challenge as a result of the complex physics of fracture and the need to capture disparate length scales. Phase field models represent fractures as a diffuse interface and enjoy the advantage that fracture nucleation, propagation, branching, or twisting can be simulated without ad hoc computational strategies like remeshing or local enrichment of the solution space. Here we propose a new quasi-static phase field formulation for modeling fluid-driven fracturing in elastic media at small strains. The approach fully couples the fluid flow in the fracture (described via the Reynolds lubrication approximation) and the deformation of the surrounding medium. The flow is solved on a lower dimensionality mesh immersed in the elastic medium. This approach leads to accurate coupling of both physics. We assessed the performance of the model extensively by comparing results for the evolution of fracture length, aperture, and fracture fluid pressure against analytical solutions under different fracture propagation regimes. Thus, the excellent performance of the numerical model in all regimes builds confidence in the applicability of phase field approaches to simulate fluid-driven fracture.},
doi = {10.1002/2016JB013572},
journal = {Journal of Geophysical Research. Solid Earth},
number = 4,
volume = 122,
place = {United States},
year = {Thu Apr 20 00:00:00 EDT 2017},
month = {Thu Apr 20 00:00:00 EDT 2017}
}
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