Three‐Dimensional Numerical Modeling of Shear Stimulation of Fractured Reservoirs

Shear dilation based hydraulic stimulations enable exploitation of geothermal energy from reservoirs with inadequate initial permeability. While contributing to enhancing the reservoir's permeability, hydraulic stimulation processes may lead to undesired seismic activity. Here, we present a three dimensional numerical model aiming to increase understanding of this mechanism and its consequences. The fractured reservoir is modeled as a network of explicitly represented large scale fractures immersed in a permeable rock matrix. The numerical formulation is constructed by coupling three physical processes: fluid flow, fracture deformation, and rock matrix deformation. For flow simulations, the discrete fracture matrix model is used, which allows the fluid transport from high permeable conductive fractures to the rock matrix and vice versa. The mechanical behavior of the fractures is modeled using a hyperbolic model with reversible and irreversible deformations. Linear elasticity is assumed for the mechanical deformation and stress alteration of the rock matrix. Fractures are modeled as lower dimensional surfaces embodied in the domain, subjected to specific governing equations for their deformation along the tangential and normal directions. Both the fluid flow and momentum balance equations are approximated by finite volume discretizations. The new numerical model is demonstrated considering a three dimensional fractured formation with a network of 20 explicitly represented fractures. The effects of fluid exchange between fractures and rock matrix on the permeability evolution and the generated seismicity are examined for test cases resembling realistic reservoir conditions.

[1]  Zhixi Chen,et al.  An experimental investigation of hydraulic behaviour of fractures and joints in granitic rock , 2000 .

[2]  J. Dieterich Modeling of rock friction: 1. Experimental results and constitutive equations , 1979 .

[3]  R. Horne,et al.  An embedded fracture modeling framework for simulation of hydraulic fracturing and shear stimulation , 2016, Computational Geosciences.

[4]  Richard E. Goodman,et al.  Methods of Geological Engineering in Discontinuous Rocks , 1975 .

[5]  Eirik Keilegavlen,et al.  Postinjection Normal Closure of Fractures as a Mechanism for Induced Seismicity , 2017, 1705.02986.

[6]  Julian J. Bommer,et al.  Induced seismicity associated with Enhanced Geothermal Systems , 2007 .

[7]  D. J. Andrews,et al.  Bulletin of the Seismological Society of America , 1985 .

[8]  S. Day,et al.  Comparison of finite difference and boundary integral solutions to three‐dimensional spontaneous rupture , 2005 .

[9]  Nick Barton,et al.  Experimental studies of scale effects on the shear behaviour of rock joints , 1981 .

[10]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[11]  P. Wriggers Computational contact mechanics , 2012 .

[12]  H. Takahashi,et al.  Progress toward a stochastic rock mechanics model of engineered geothermal systems , 1996 .

[13]  Jan M. Nordbotten Convergence of a Cell-Centered Finite Volume Discretization for Linear Elasticity , 2015, SIAM J. Numer. Anal..

[14]  R. Horne,et al.  Investigation of injection-induced seismicity using a coupled fluid flow and rate/state friction model , 2011 .

[15]  A. Pitarka,et al.  The SCEC/USGS Dynamic Earthquake Rupture Code Verification Exercise , 2012 .

[16]  A. Ruina Slip instability and state variable friction laws , 1983 .

[17]  Emmanuel Gaucher,et al.  Induced seismicity in geothermal reservoirs: A review of forecasting approaches , 2015 .

[18]  Stein Krogstad,et al.  Open-source MATLAB implementation of consistent discretisations on complex grids , 2012, Computational Geosciences.

[19]  Christophe Geuzaine,et al.  Gmsh: A 3‐D finite element mesh generator with built‐in pre‐ and post‐processing facilities , 2009 .

[20]  B. Berkowitz Characterizing flow and transport in fractured geological media: A review , 2002 .

[21]  M. C. Fehler,et al.  Hydraulic Fracturing of Jointed Formations , 1986 .

[22]  J. Nordbotten,et al.  Finite volume methods for elasticity with weak symmetry , 2015, 1512.01042.

[23]  Reinhard Jung,et al.  A numerical model for fluid injection induced seismicity at Soultz-sous-Forêts , 2010 .

[24]  R. J. Pine,et al.  Downward migration of shearing in jointed rock during hydraulic injections , 1984 .

[25]  N. Barton,et al.  The shear strength of rock joints in theory and practice , 1977 .

[26]  J. Rice Spatio‐temporal complexity of slip on a fault , 1993 .

[27]  Yehuda Ben-Zion,et al.  Earthquake Failure Sequences Along a Cellular Fault Zone in a Three-Dimensional Elastic Solid Containing Asperity and Nonasperity Regions , 1993 .

[28]  P. Dobson,et al.  A 3D hydrogeological and geomechanical model of an Enhanced Geothermal System at The Geysers, California , 2014 .

[29]  Chrystel Dezayes,et al.  3D model of fracture zones at Soultz-sous-Forêts based on geological data, image logs, induced microseismicity and vertical seismic profiles , 2010 .

[30]  Dominique Bruel,et al.  Using the migration of the induced seismicity as a constraint for fractured Hot Dry Rock reservoir modelling , 2007 .

[31]  Markus Häring,et al.  Characterisation of the Basel 1 enhanced geothermal system , 2008 .

[32]  N. Barton,et al.  Strength, deformation and conductivity coupling of rock joints , 1985 .

[33]  Matthew G. Knepley,et al.  A domain decomposition approach to implementing fault slip in finite‐element models of quasi‐static and dynamic crustal deformation , 2013, ArXiv.

[34]  M. F. Lough,et al.  Hierarchical modeling of flow in naturally fractured formations with multiple length scales , 2001 .

[35]  Generation of large postinjection‐induced seismic events by backflow from dead‐end faults and fractures , 2015 .

[36]  Thomas Kohl,et al.  Predictive modeling of reservoir response to hydraulic stimulations at the European EGS site Soultz-sous-Forêts , 2007 .

[37]  Eirik Keilegavlen,et al.  A finite-volume discretization for deformation of fractured media , 2018, Computational Geosciences.

[38]  L. Durlofsky,et al.  An Efficient Discrete-Fracture Model Applicable for General-Purpose Reservoir Simulators , 2004 .

[39]  S. L. Crouch Boundary element methods in solid mechanics: With applications in rock mechanics and geological engineering , 1983 .

[40]  Jan M. Nordbotten,et al.  An efficient multi-point flux approximation method for Discrete Fracture-Matrix simulations , 2012, J. Comput. Phys..

[41]  J. Borggaard,et al.  A Domain Decomposition Approach to POD , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[42]  Mofazzal Hossain,et al.  A shear‐dilation‐based model for evaluation of hydraulically stimulated naturally fractured reservoirs , 2002 .

[43]  Ivar Stefansson,et al.  A Comparison of Two Numerical Models for Flow in Fractured Porous Media and the Impact of Fracture Intersection Cell Removal , 2016 .

[44]  Roland N. Horne,et al.  An investigation of stimulation mechanisms in Enhanced Geothermal Systems , 2014 .

[45]  R. Horne,et al.  Discrete Fracture Network Modeling of Hydraulic Stimulation: Coupling Flow and Geomechanics , 2013 .

[46]  J. A. Ryder Excess shear stress in the assessment of geologically hazardous situations , 1988 .

[47]  C. Cauzzi,et al.  Seismic monitoring and analysis of deep geothermal projects in St Gallen and Basel, Switzerland , 2015 .

[48]  P. Fokker,et al.  Coupled continuum modeling of fracture reactivation and induced seismicity during enhanced geothermal operations , 2014 .

[49]  D. F. Malan,et al.  A viscoplastic discontinuum model of time-dependent fracture and seismicity effects in brittle rock , 1997 .

[50]  Christine Ehlig-Economides,et al.  A fully coupled method to model fracture permeability change in naturally fractured reservoirs , 2011 .

[51]  J. Nordbotten Cell‐centered finite volume discretizations for deformable porous media , 2014 .

[52]  N. Barton,et al.  FUNDAMENTALS OF ROCK JOINT DEFORMATION , 1983 .

[53]  Pierre Henry,et al.  Seismicity triggered by fluid injection–induced aseismic slip , 2015, Science.