Efficient co-solution of time step size and independent state in simulations of fluid-driven fracture propagation with embedded meshes

Ren, Guotong; Younis, Rami M.

doi:10.1002/nme.6935

Title: Efficient co-solution of time step size and independent state in simulations of fluid-driven fracture propagation with embedded meshes

Journal Article · 29 January 2022 · International Journal for Numerical Methods in Engineering

DOI: https://doi.org/10.1002/nme.6935 · OSTI ID:1976368

Ren, Guotong ^[1]; Younis, Rami M. ^[2]

University of Tulsa, Tulsa, OK (United States); OSTI
University of Tulsa, Tulsa, OK (United States)

Here we present an efficient time-continuation scheme for fluid-driven fracture propagation problems in the extended finite element method framework. The approach applies a monolithic solution strategy to a fully coupled and implicit approximation of hydro-mechanical systems in conjunction with simultaneous linear elastic propagation of multiple fractures. At the end of each time step, the process ensures that the weakest fracture tip is in an equilibrium propagation regime. Furthermore, the solution process provides an initialization procedure for the newly created fracture spaces and an a priori estimate of the stress intensity factor growth rate, improving simulation robustness, and efficiency. The solution process is validated using the Kristianovich-Geertsma-de Klerk analytical solution under the toughness- and viscosity-dominated regimes. It is also extended to and demonstrated on problems with multiple fractures undergoing simultaneous propagation with stress shadow interactions. Numerical examples demonstrate that the solution process can reduce the required computational cost by one order of magnitude compared to other existing methods.

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Research Organization:: Oklahoma State University, Stillwater, OK (United States); University of Tulsa, Tulsa, OK (United States)

Sponsoring Organization:: TU Future Reservoir Simulation Systems & Technology (FuRSST); USDOE; USDOE Office of Fossil Energy (FE)

Grant/Contract Number:: FE0031777

OSTI ID:: 1976368

Journal Information:: International Journal for Numerical Methods in Engineering, Journal Name: International Journal for Numerical Methods in Engineering Journal Issue: 10 Vol. 123; ISSN 0029-5981

Publisher:: WileyCopyright Statement

Country of Publication:: United States

Language:: English

References (36)

A finite element approach to the simulation of hydraulic fractures with lag: FINITE ELEMENT APPROACH TO HYDRAULIC FRACTURES WITH LAG Hunsweck, Michael J.; Shen, Yongxing; Lew, Adrian J. International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 37, Issue 9 https://doi.org/10.1002/nag.1131	journal	February 2012
An explicitly coupled hydro-geomechanical model for simulating hydraulic fracturing in arbitrary discrete fracture networks: FULLY COUPLED MODEL FOR HYDRO-FRACTURING IN ARBITRARY FRACTURE NETWORKS Fu, Pengcheng; Johnson, Scott M.; Carrigan, Charles R. International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 37, Issue 14 https://doi.org/10.1002/nag.2135	journal	August 2012
Simulation of non-planar three-dimensional hydraulic fracture propagation: SIMULATION OF NON-PLANAR 3D HYDRAULIC FRACTURE PROPAGATION Gupta, P.; Duarte, C. A. International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 38, Issue 13 https://doi.org/10.1002/nag.2305	journal	June 2014
A fully coupled method for massively parallel simulation of hydraulically driven fractures in 3-dimensions: FULLY COUPLED PARALLEL SIMULATION OF HYDRAULIC FRACTURES IN 3-D Settgast, Randolph R.; Fu, Pengcheng; Walsh, Stuart D. C. International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 41, Issue 5 https://doi.org/10.1002/nag.2557	journal	September 2016
A stabilized extended finite element framework for hydraulic fracturing simulations: STABILIZED XFEM FOR HYDRAULIC FRACTURE SIMULATIONS Liu, Fushen; Gordon, Peter; Meier, Holger International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 41, Issue 5 https://doi.org/10.1002/nag.2565	journal	September 2016
Coupled hydromechanical-fracture simulations of nonplanar three-dimensional hydraulic fracture propagation Gupta, P.; Duarte, C. A. International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 42, Issue 1 https://doi.org/10.1002/nag.2719	journal	August 2017
Numerical modeling of fracturing in permeable rocks via a micromechanical continuum model Eghbalian, Mahdad; Wan, Richard; Pouragha, Mehdi International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 43, Issue 10 https://doi.org/10.1002/nag.2940	journal	April 2019
Improved algorithms for generalized finite element simulations of three‐dimensional hydraulic fracture propagation Shauer, Nathan; Duarte, Carlos Armando International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 43, Issue 18 https://doi.org/10.1002/nag.2977	journal	October 2019
Modeling hydraulic fracture propagation in permeable media with an embedded strong discontinuity approach Liu, Fushen International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 44, Issue 12 https://doi.org/10.1002/nag.3080	journal	May 2020
An improved crack tracking algorithm with self‐correction ability of the crack path and its application in a continuum damage model Yun, Kumchol; Kim, Tae‐Jong; Jang, Paek San International Journal for Numerical Methods in Engineering, Vol. 117, Issue 2 https://doi.org/10.1002/nme.5955	journal	September 2018
Coupled poromechanics‐damage mechanics modeling of fracturing during injection in brittle rocks Bubshait, Ahmed; Jha, Birendra International Journal for Numerical Methods in Engineering, Vol. 121, Issue 2 https://doi.org/10.1002/nme.6208	journal	October 2019
Fully coupled simulation of multiple hydraulic fractures to propagate simultaneously from a perforated horizontal wellbore Zeng, Qinglei; Liu, Zhanli; Wang, Tao Computational Mechanics, Vol. 61, Issue 1-2 https://doi.org/10.1007/s00466-017-1412-5	journal	May 2017
The application of the dual boundary element method to the analysis of cracked stiffened panels Salgado, N. K.; Aliabadi, M. H. Engineering Fracture Mechanics, Vol. 54, Issue 1 https://doi.org/10.1016/0013-7944(95)00111-5	journal	May 1996
An improved projection-based embedded discrete fracture model (pEDFM) for multiphase flow in fractured reservoirs Jiang, Jiamin; Younis, Rami M. Advances in Water Resources, Vol. 109 https://doi.org/10.1016/j.advwatres.2017.09.017	journal	November 2017
A Model for coupled geomechanics and multiphase flow in fractured porous media using embedded meshes Ren, Guotong; Jiang, Jiamin; Younis, Rami M. Advances in Water Resources, Vol. 122 https://doi.org/10.1016/j.advwatres.2018.09.017	journal	December 2018
An implicit level set method for modeling hydraulically driven fractures Peirce, Anthony; Detournay, Emmanuel Computer Methods in Applied Mechanics and Engineering, Vol. 197, Issue 33-40 https://doi.org/10.1016/j.cma.2008.01.013	journal	June 2008
A scalable 3D fracture and fragmentation algorithm based on a hybrid, discontinuous Galerkin, cohesive element method Radovitzky, R.; Seagraves, A.; Tupek, M. Computer Methods in Applied Mechanics and Engineering, Vol. 200, Issue 1-4 https://doi.org/10.1016/j.cma.2010.08.014	journal	January 2011
Coupling schemes for modeling hydraulic fracture propagation using the XFEM Gordeliy, Elizaveta; Peirce, Anthony Computer Methods in Applied Mechanics and Engineering, Vol. 253 https://doi.org/10.1016/j.cma.2012.08.017	journal	January 2013
A combined XFEM–damage mechanics approach for concrete crack propagation Roth, Simon-Nicolas; Léger, Pierre; Soulaïmani, Azzeddine Computer Methods in Applied Mechanics and Engineering, Vol. 283 https://doi.org/10.1016/j.cma.2014.10.043	journal	January 2015
Pressure and fluid-driven fracture propagation in porous media using an adaptive finite element phase field model Lee, Sanghyun; Wheeler, Mary F.; Wick, Thomas Computer Methods in Applied Mechanics and Engineering, Vol. 305 https://doi.org/10.1016/j.cma.2016.02.037	journal	June 2016
A J -integral-based arc-length solver for brittle and ductile crack propagation in finite deformation-finite strain hyperelastic solids with an application to graphene kirigami Barbieri, Ettore; Ongaro, Federica; Pugno, Nicola Maria Computer Methods in Applied Mechanics and Engineering, Vol. 315 https://doi.org/10.1016/j.cma.2016.10.043	journal	March 2017
A variational phase-field model for hydraulic fracturing in porous media Chukwudozie, Chukwudi; Bourdin, Blaise; Yoshioka, Keita Computer Methods in Applied Mechanics and Engineering, Vol. 347 https://doi.org/10.1016/j.cma.2018.12.037	journal	April 2019
A fully-coupled computational framework for large-scale simulation of fluid-driven fracture propagation on parallel computers Giovanardi, Bianca; Serebrinsky, Santiago; Radovitzky, Raúl Computer Methods in Applied Mechanics and Engineering, Vol. 372 https://doi.org/10.1016/j.cma.2020.113365	journal	December 2020
An integrated numerical model for coupled poro-hydro-mechanics and fracture propagation using embedded meshes Ren, Guotong; Younis, Rami M. Computer Methods in Applied Mechanics and Engineering, Vol. 376 https://doi.org/10.1016/j.cma.2020.113606	journal	April 2021
A parallel staggered hydraulic fracture simulator incorporating fluid lag Smilovich, Damián; Radovitzky, Raúl; Dvorkin, Eduardo Computer Methods in Applied Mechanics and Engineering, Vol. 384 https://doi.org/10.1016/j.cma.2021.114003	journal	October 2021
An arc-length method for controlled cohesive crack propagation using high-order XFEM and Irwin’s crack closure integral Wang, Yongxiang; Waisman, Haim Engineering Fracture Mechanics, Vol. 199 https://doi.org/10.1016/j.engfracmech.2018.05.018	journal	August 2018
On the moving boundary conditions for a hydraulic fracture Detournay, Emmanuel; Peirce, Anthony International Journal of Engineering Science, Vol. 84 https://doi.org/10.1016/j.ijengsci.2014.06.010	journal	November 2014
Geohydromechanical processes in the Excavation Damaged Zone in crystalline rock, rock salt, and indurated and plastic clays—in the context of radioactive waste disposal Tsang, Chin-Fu; Bernier, F.; Davies, C. International Journal of Rock Mechanics and Mining Sciences, Vol. 42, Issue 1 https://doi.org/10.1016/j.ijrmms.2004.08.003	journal	January 2005
Geomechanical behavior of the reservoir and caprock system at the In Salah CO2 storage project White, J. A.; Chiaramonte, L.; Ezzedine, S. Proceedings of the National Academy of Sciences, Vol. 111, Issue 24 https://doi.org/10.1073/pnas.1316465111	journal	May 2014
Branching of hydraulic cracks enabling permeability of gas or oil shale with closed natural fractures Rahimi-Aghdam, Saeed; Chau, Viet-Tuan; Lee, Hyunjin Proceedings of the National Academy of Sciences, Vol. 116, Issue 5 https://doi.org/10.1073/pnas.1818529116	journal	January 2019
Transport phenomena Bird, R. Byron Applied Mechanics Reviews, Vol. 55, Issue 1 https://doi.org/10.1115/1.1424298	journal	January 2002
Why Fracking Works Bažant, Zdeněk P.; Salviato, Marco; Chau, Viet T. Journal of Applied Mechanics, Vol. 81, Issue 10 https://doi.org/10.1115/1.4028192	journal	August 2014
Adaptively Localized Continuation-Newton Method—Nonlinear Solvers That Converge All the Time Younis, R. M. . M.; Tchelepi, H. A. . A.; Aziz, K. . SPE Journal, Vol. 15, Issue 02 https://doi.org/10.2118/119147-PA	journal	December 2009
Predictions of the Growth of Multiple Interacting Hydraulic Fractures in Three Dimensions Castonguay, Stephen T.; Mear, Mark E.; Dean, Rick H. SPE Annual Technical Conference and Exhibition https://doi.org/10.2118/166259-MS	conference	September 2013
Hybrid Coupled Discrete-Fracture/Matrix and Multicontinuum Models for Unconventional-Reservoir Simulation Jiang, Jiamin; Younis, Rami M. SPE Journal, Vol. 21, Issue 03 https://doi.org/10.2118/178430-PA	journal	June 2016
History Matching an Unconventional Reservoir with a Complex Fracture Network Liu, Zhe; Reynolds, Albert C. SPE Reservoir Simulation Conference, Day 2 Thu, April 11, 2019 https://doi.org/10.2118/193921-MS	conference	April 2019

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42 ENGINEERING
97 MATHEMATICS AND COMPUTING
elasticity
extended finite element method
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nonlinear solvers
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Title: Efficient co-solution of time step size and independent state in simulations of fluid-driven fracture propagation with embedded meshes

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