Automatic Time Step Control to Resolve Hydromechanically Driven Fault Reactivation, Spontaneous Nucleation, and Seismic Arrest

Han, Zheng; Ren, Guotong; Younis, Rami M.

doi:10.1029/2023WR035626

Title: Automatic Time Step Control to Resolve Hydromechanically Driven Fault Reactivation, Spontaneous Nucleation, and Seismic Arrest

Journal Article · 29 October 2023 · Water Resources Research

DOI: https://doi.org/10.1029/2023WR035626 · OSTI ID:2204060

^[1];

^[2]

The University of Tulsa OK Tulsa USA
The University of Tulsa OK Tulsa USA, Texas A&,M University College Station TX USA

Abstract A physical understanding of the progression from flow‐driven (quasi‐static) poromechanical deformation to dynamic fault rupture is critical to the resilient operations of several engineering systems. These processes are bridged by a progression from fault reactivation to the spontaneous nucleation of unstable sliding. Toward addressing this challenge, novel automatic time step size control methods are developed to enable accurate and efficient simulation of these dynamics and transitions from the first principles. The controllers combine local models for discretization error and Coulomb failure conditions to automatically adjust the time step size across several orders of magnitude. The methods do not require additional empirical or theoretical input and can resolve the pre‐rupture, interseismic, and seismic periods to the allowed accuracy. The computational results reveal that the proposed methods automatically capture the onset of reactivation and nucleation for homogeneous and heterogeneous fields. Hydrodynamic and structural heterogeneity lead to disparate critical nucleation sizes compared to those predicted by theory. The results highlight its potential in predicting induced seismicity in realistic subsurface engineering systems and at practical scales.

View Journal Article

Cite

Export

Save

Research Organization:: Oklahoma State Univ., Stillwater, OK (United States)

Sponsoring Organization:: USDOE; USDOE Office of Fossil Energy (FE)

Grant/Contract Number:: FE0031777

OSTI ID:: 2204060

Journal Information:: Water Resources Research, Journal Name: Water Resources Research Journal Issue: 11 Vol. 59; ISSN 0043-1397

Publisher:: American Geophysical Union (AGU)Copyright Statement

Country of Publication:: United States

Language:: English

References (67)

A finite element method for crack growth without remeshing Mo�s, Nicolas; Dolbow, John; Belytschko, Ted International Journal for Numerical Methods in Engineering, Vol. 46, Issue 1 https://doi.org/10.1002/(sici)1097-0207(19990910)46:1<131::aid-nme726>3.0.co;2-j	journal	September 1999
Generation of large postinjection‐induced seismic events by backflow from dead‐end faults and fractures McClure, Mark W. Geophysical Research Letters, Vol. 42, Issue 16 https://doi.org/10.1002/2015gl065028	journal	August 2015
Rupture propagation behavior and the largest possible earthquake induced by fluid injection into deep reservoirs Gischig, Valentin S. Geophysical Research Letters, Vol. 42, Issue 18 https://doi.org/10.1002/2015gl065072	journal	September 2015
Critical Nucleation Length for Accelerating Frictional Slip Aldam, Michael; Weikamp, Marc; Spatschek, Robert Geophysical Research Letters, Vol. 44, Issue 22 https://doi.org/10.1002/2017gl074939	journal	November 2017
Characterization of nucleation during laboratory earthquakes Latour, S.; Schubnel, A.; Nielsen, S. Geophysical Research Letters, Vol. 40, Issue 19 https://doi.org/10.1002/grl.50974	journal	October 2013
A domain decomposition approach to implementing fault slip in finite-element models of quasi-static and dynamic crustal deformation: FAULT SLIP VIA DOMAIN DECOMPOSITION Aagaard, B. T.; Knepley, M. G.; Williams, C. A. Journal of Geophysical Research: Solid Earth, Vol. 118, Issue 6 https://doi.org/10.1002/jgrb.50217	journal	June 2013
A unified set of single step algorithms. Part 1: General formulation and applications Zienkiewicz, O. C.; Wood, W. L.; Hine, N. W. International Journal for Numerical Methods in Engineering, Vol. 20, Issue 8 https://doi.org/10.1002/nme.1620200814	journal	August 1984
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. International Journal for Numerical Methods in Engineering, Vol. 123, Issue 10 https://doi.org/10.1002/nme.6935	journal	February 2022
Lazy K-Way Linear Combination Kernels for Efficient Runtime Sparse Jacobian Matrix Evaluations in C++ Younis, Rami M.; Tchelepi, Hamdi A. Lecture Notes in Computational Science and Engineering https://doi.org/10.1007/978-3-642-30023-3_30	book	January 2012
Dynamic faulting under rate-dependent friction Cochard, Alain; Madariaga, Ra�l Pure and Applied Geophysics PAGEOPH, Vol. 142, Issue 3-4 https://doi.org/10.1007/bf00876049	journal	January 1994
Localized linear systems for fully implicit simulation of multiphase multicomponent flow in porous media Sheth, Soham; Moncorgé, Arthur; Younis, Rami Computational Geosciences, Vol. 24, Issue 2 https://doi.org/10.1007/s10596-019-09840-9	journal	October 2019
A numerical study of the additive Schwarz preconditioned exact Newton method (ASPEN) as a nonlinear preconditioner for immiscible and compositional porous media flow Klemetsdal, Øystein; Moncorgé, Arthur; Møyner, Olav Computational Geosciences, Vol. 26, Issue 4 https://doi.org/10.1007/s10596-021-10090-x	journal	September 2021
A theory of friction Curnier, A. International Journal of Solids and Structures, Vol. 20, Issue 7 https://doi.org/10.1016/0020-7683(84)90021-0	journal	January 1984
Formulation of Rayleigh damping and its extensions Liu, Man; Gorman, D. G. Computers & Structures, Vol. 57, Issue 2 https://doi.org/10.1016/0045-7949(94)00611-6	journal	October 1995
Numerical simulation of mixed aseismic/seismic fault-slip induced by fluid injection using coupled X-FEM analysis Schwartzkopff, Adam K.; Sainoki, Atsushi; Elsworth, Derek International Journal of Rock Mechanics and Mining Sciences, Vol. 147 https://doi.org/10.1016/J.IJRMMS.2021.104871	journal	November 2021
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
Benchmarking Defmod, an open source FEM code for modeling episodic fault rupture Meng, Chunfang Computers & Geosciences, Vol. 100 https://doi.org/10.1016/j.cageo.2016.11.014	journal	March 2017
A finite element and finite difference mixed approach for modeling fault rupture and ground motion Meng, Chunfang; Wang, Hua Computers & Geosciences, Vol. 113 https://doi.org/10.1016/j.cageo.2018.01.015	journal	April 2018
Stabilized low-order finite elements for frictional contact with the extended finite element method Liu, Fushen; Borja, Ronaldo I. Computer Methods in Applied Mechanics and Engineering, Vol. 199, Issue 37-40 https://doi.org/10.1016/j.cma.2010.03.030	journal	August 2010
Algebraically stabilized Lagrange multiplier method for frictional contact mechanics with hydraulically active fractures Franceschini, Andrea; Castelletto, Nicola; White, Joshua A. Computer Methods in Applied Mechanics and Engineering, Vol. 368 https://doi.org/10.1016/j.cma.2020.113161	journal	August 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
An augmented Lagrangian contact formulation for frictional discontinuities with the extended finite element method Hirmand, M.; Vahab, M.; Khoei, A. R. Finite Elements in Analysis and Design, Vol. 107 https://doi.org/10.1016/j.finel.2015.08.003	journal	December 2015
Adaptive time stepping for fluid-structure interaction solvers Mayr, M.; Wall, W. A.; Gee, M. W. Finite Elements in Analysis and Design, Vol. 141 https://doi.org/10.1016/j.finel.2017.12.002	journal	March 2018
An enriched finite element algorithm for numerical computation of contact friction problems Khoei, A. R.; Nikbakht, M. International Journal of Mechanical Sciences, Vol. 49, Issue 2 https://doi.org/10.1016/j.ijmecsci.2006.08.014	journal	February 2007
Adaptive time-step control for nonlinear fluid–structure interaction Failer, Lukas; Wick, Thomas Journal of Computational Physics, Vol. 366 https://doi.org/10.1016/j.jcp.2018.04.021	journal	August 2018
Nucleation of frictional slip: A yielding or a fracture process? Castellano, Miguel; Lorez, Flavio; Kammer, David S. Journal of the Mechanics and Physics of Solids, Vol. 173 https://doi.org/10.1016/j.jmps.2022.105193	journal	April 2023
Fault reactivation mechanisms and dynamic rupture modelling of depletion-induced seismic events in a Rotliegend gas reservoir Buijze, Loes; van den Bogert, Peter A. J.; Wassing, Brecht B. T. Netherlands Journal of Geosciences, Vol. 96, Issue 5 https://doi.org/10.1017/njg.2017.27	journal	December 2017
Introduction to Adaptive Methods for Differential Equations Eriksson, Kenneth; Estep, Don; Hansbo, Peter Acta Numerica, Vol. 4 https://doi.org/10.1017/s0962492900002531	journal	January 1995
An optimal control approach to a posteriori error estimation in finite element methods Becker, Roland; Rannacher, Rolf Acta Numerica, Vol. 10 https://doi.org/10.1017/s0962492901000010	journal	May 2001
Scaling of the shear rupture process from nucleation to dynamic propagation: Implications of geometric irregularity of the rupturing surfaces Ohnaka, Mitiyasu; Shen, Lin-feng Journal of Geophysical Research: Solid Earth, Vol. 104, Issue B1 https://doi.org/10.1029/1998jb900007	journal	January 1999
Elastodynamic analysis for slow tectonic loading with spontaneous rupture episodes on faults with rate- and state-dependent friction Lapusta, Nadia; Rice, James R.; Ben-Zion, Yehuda Journal of Geophysical Research: Solid Earth, Vol. 105, Issue B10 https://doi.org/10.1029/2000JB900250	journal	October 2000
Hierarchical modeling of flow in naturally fractured formations with multiple length scales Lee, S. H.; Lough, M. F.; Jensen, C. L. Water Resources Research, Vol. 37, Issue 3 https://doi.org/10.1029/2000wr900340	journal	March 2001
Universal nucleation length for slip-weakening rupture instability under nonuniform fault loading: UNIVERSAL NUCLEATION LENGTH Uenishi, Koji; Rice, James R. Journal of Geophysical Research: Solid Earth, Vol. 108, Issue B1 https://doi.org/10.1029/2001jb001681	journal	January 2003
Earthquake nucleation on (aging) rate and state faults: RATE AND STATE EARTHQUAKE NUCLEATION Rubin, A. M.; Ampuero, J. -P. Journal of Geophysical Research: Solid Earth, Vol. 110, Issue B11 https://doi.org/10.1029/2005jb003686	journal	November 2005
Comparison of finite difference and boundary integral solutions to three-dimensional spontaneous rupture Day, Steven M.; Dalguer, Luis A.; Lapusta, Nadia Journal of Geophysical Research, Vol. 110, Issue B12 https://doi.org/10.1029/2005jb003813	journal	January 2005
Earthquake nucleation on rate and state faults – Aging and slip laws Ampuero, Jean-Paul; Rubin, Allan M. Journal of Geophysical Research, Vol. 113, Issue B1 https://doi.org/10.1029/2007jb005082	journal	January 2008
Three-dimensional boundary integral modeling of spontaneous earthquake sequences and aseismic slip Lapusta, Nadia; Liu, Yi Journal of Geophysical Research, Vol. 114, Issue B9 https://doi.org/10.1029/2008JB005934	journal	January 2009
A mechanism for preseismic steady rupture fronts observed in laboratory experiments: MODELING PRESEISMIC STEADY RUPTURE Kaneko, Y.; Ampuero, J. -P. Geophysical Research Letters, Vol. 38, Issue 21 https://doi.org/10.1029/2011gl049953	journal	November 2011
Fully Dynamic Spontaneous Rupture Due to Quasi-Static Pore Pressure and Poroelastic Effects: An Implicit Nonlinear Computational Model of Fluid-Induced Seismic Events Jin, Lei; Zoback, Mark D. Journal of Geophysical Research: Solid Earth, Vol. 123, Issue 11 https://doi.org/10.1029/2018JB015669	journal	November 2018
Nucleation and Arrest of Dynamic Rupture Induced by Reservoir Depletion Buijze, L.; Bogert, P. A. J.; Wassing, B. B. T. Journal of Geophysical Research: Solid Earth, Vol. 124, Issue 4 https://doi.org/10.1029/2018jb016941	journal	April 2019
Stress Perturbation From Aseismic Slip Drives the Seismic Front During Fluid Injection in a Permeable Fault Wynants‐Morel, Nicolas; Cappa, Frédéric; De Barros, Louis Journal of Geophysical Research: Solid Earth, Vol. 125, Issue 7 https://doi.org/10.1029/2019jb019179	journal	July 2020
Initiation of antiplane shear instability under slip dependent friction Campillo, Michel; Ionescu, Ioan R. Journal of Geophysical Research: Solid Earth, Vol. 102, Issue B9 https://doi.org/10.1029/97jb01508	journal	September 1997
Rupture velocity of plane strain shear cracks Andrews, D. J. Journal of Geophysical Research, Vol. 81, Issue 32 https://doi.org/10.1029/jb081i032p05679	journal	November 1976
Preseismic fault slip and earthquake prediction Dieterich, J. H. Journal of Geophysical Research, Vol. 83, Issue B8 https://doi.org/10.1029/jb083ib08p03940	journal	January 1978
Effects of physical fault properties on frictional instabilities produced on simulated faults Okubo, Paul G.; Dieterich, James H. Journal of Geophysical Research: Solid Earth, Vol. 89, Issue B7 https://doi.org/10.1029/jb089ib07p05817	journal	July 1984
Nucleation fronts ignite the interface rupture that initiates frictional motion Gvirtzman, Shahar; Fineberg, Jay Nature Physics, Vol. 17, Issue 9 https://doi.org/10.1038/s41567-021-01299-9	journal	August 2021
A Method of Computation for Structural Dynamics Newmark, Nathan M. Journal of the Engineering Mechanics Division, Vol. 85, Issue 3 https://doi.org/10.1061/jmcea3.0000098	journal	July 1959
Finite Dynamic Model for Infinite Media Lysmer, John; Kuhlemeyer, Roger L. Journal of the Engineering Mechanics Division, Vol. 95, Issue 4 https://doi.org/10.1061/jmcea3.0001144	journal	August 1969
General Theory of Three‐Dimensional Consolidation Biot, Maurice A. Journal of Applied Physics, Vol. 12, Issue 2 https://doi.org/10.1063/1.1712886	journal	February 1941
Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system Mikelić, Andro; Wheeler, Mary F. Journal of Mathematical Physics, Vol. 53, Issue 12 https://doi.org/10.1063/1.4764887	journal	November 2012
Seismic rupture and ground accelerations induced by CO2 injection in the shallow crust: CO2 induced seismic rupture Cappa, Frédéric; Rutqvist, Jonny Geophysical Journal International, Vol. 190, Issue 3 https://doi.org/10.1111/J.1365-246X.2012.05606.X	journal	August 2012
Investigation of injection-induced seismicity using a coupled fluid flow and rate/state friction model McClure, Mark W.; Horne, Roland N. GEOPHYSICS, Vol. 76, Issue 6 https://doi.org/10.1190/geo2011-0064.1	journal	November 2011
Structural dynamic analysis for time response of bars and trusses using the generalized finite element method Torii, André Jacomel; Machado, Roberto Dalledone Latin American Journal of Solids and Structures, Vol. 9, Issue 3 https://doi.org/10.1590/s1679-78252012000300001	journal	June 2012
Mandel's problem revisited Abousleiman, Y.; Cheng, A. H. -D.; Cui, L. Géotechnique, Vol. 46, Issue 2 https://doi.org/10.1680/geot.1996.46.2.187	journal	June 1996
Dataset for Water Resources Research paper #2023WR035626 Han, Zheng Mendeley https://doi.org/10.17632/WHBKSV75PX.1	dataset	January 2023
Initiation of in-plane shear instability under slip-dependent friction Favreau, Pascal; Campillo, Michel; Ionescu, Ioan R. Bulletin of the Seismological Society of America, Vol. 89, Issue 5 https://doi.org/10.1785/bssa0890051280	journal	October 1999
The SCEC/USGS Dynamic Earthquake Rupture Code Verification Exercise Harris, R. A.; Barall, M.; Archuleta, R. Seismological Research Letters, Vol. 80, Issue 1 https://doi.org/10.1785/gssrl.80.1.119	journal	January 2009
Efficient Field-Scale Simulation of Black Oil in a Naturally Fractured Reservoir Through Discrete Fracture Networks and Homogenized Media Li, Liyong; Lee, Seong H. SPE Reservoir Evaluation & Engineering, Vol. 11, Issue 04 https://doi.org/10.2118/103901-PA	journal	August 2008
Parallel Automatically Differentiable Data-Types for Next-Generation Simulator Development Younis, Rami; Aziz, Khalid All Days https://doi.org/10.2118/106493-MS	conference	February 2007
Development of an Efficient Embedded Discrete Fracture Model for 3D Compositional Reservoir Simulation in Fractured Reservoirs Moinfar, Ali; Varavei, Abdoljalil; Sepehrnoori, Kamy SPE Journal, Vol. 19, Issue 02 https://doi.org/10.2118/154246-PA	journal	April 2014
Localized Linear Systems in Sequential Implicit Simulation of Two-Phase Flow and Transport Sheth, Soham M.; Younis, Rami M. SPE Journal, Vol. 22, Issue 05 https://doi.org/10.2118/173320-pa	journal	June 2017
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
High-Resolution Compositional Reservoir Simulation with Dynamic Coarsening and Local Timestepping for Unstructured Grids Klemetsdal, Ø. S.; Møyner, O.; Moncorgé, A. SPE Journal, Vol. 26, Issue 06 https://doi.org/10.2118/203982-pa	journal	September 2021
A Comparison of Techniques for Coupling Porous Flow and Geomechanics Dean, Rick H.; Gai, Xiuli; Stone, Charles M. SPE Journal, Vol. 11, Issue 01 https://doi.org/10.2118/79709-pa	journal	March 2006
Adaptive Galerkin Finite Element Methods for the Wave Equation Bangerth, W.; Geiger, M.; Rannacher, R. Computational Methods in Applied Mathematics, Vol. 10, Issue 1 https://doi.org/10.2478/cmam-2010-0001	journal	January 2010
Mesh refinement and modeling errors in flow simulation Jameson, Anthony; Martinelli, Luigi AIAA Journal, Vol. 36 https://doi.org/10.2514/3.13880	journal	January 1998

Similar Records

Fault steps and the dynamic rupture process: 2-D numerical simulations of a spontaneously propagating shear fracture

Journal Article · 1991 · Geophysical Research Letters (American Geophysical Union); (United States) · OSTI ID:5511848

Harris, R A; Archuleta, R J; Day, S M

Poromechanics of stick-slip frictional sliding and strength recovery on tectonic faults

Journal Article · 2015 · Journal of Geophysical Research. Solid Earth · OSTI ID:1374341

Scuderi, Marco M.; Carpenter, Brett M.; Johnson, Paul A.; +1 more

Hydromechanical Modeling of Fault Rupture in Geologic CO ₂ Sequestration: A Comparison of Two Failure Criteria

Journal Article · 2025 · Geophysical Research Letters · OSTI ID:2566937

Cao, M.; Guglielmi, Y.; Rutqvist, J.; +5 more

Related Subjects

Environmental Sciences & Ecology
Marine & Freshwater Biology
Water Resources

Title: Automatic Time Step Control to Resolve Hydromechanically Driven Fault Reactivation, Spontaneous Nucleation, and Seismic Arrest

Citation Formats

References (67)

Similar Records

Related Subjects