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Rock Mechanics is Meeting the Challenge of Geo-Energies
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ScienceDirect Procedia Engineering 191 (2017) 1104 – 1107
Symposium of the International Society for Rock Mechanics
Rock Mechanics is Meeting the Challenge of Geo-Energies F.L. Pellet* Mines Paristech, PSL Research University, Geosciences and Geoengineering Department, 35 rue Saint Honoré, Fontainebleau, 77300, France
Abstract The exploitation of geo-energies often leads to difficulties that rock mechanics helps to overcome. These essentially consist of instability problems caused by changes in the state of stress, associated pore pressures, and temperature. Besides the classical near field problem of wellbore stability, the changes can impact a larger scale, triggering earthquakes and inducing seismicity. In this paper the current approaches envisaged to tackle these problems are briefly reviewed and discussed. Some extensions that have been made possible thanks to the combination of new numerical techniques will be outlined. © 2017 2017The TheAuthors. Authors. Published by Elsevier Ltd.is an open access article under the CC BY-NC-ND license © Published by Elsevier Ltd. This Peer-review under responsibility of the organizing committee of EUROCK 2017. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of EUROCK 2017 Keywords: Enhanced Geothermal System; hydraulic fracturing; numerical modelling
1. Introduction The term geo-energy could be defined as the set of energy sources that the Earth produces. As in physical science where all is Energy or Matter, this would include fossil fuels such as coal, oil, gas or organic matter (wood) which is nowadays classified as unconventional geo-resources. In fact, the neologism “geo-energy” is mostly devoted to the energy that has been created from the temperature of the Earth and which is used to heat or to produce electricity. This is the case for geothermal energy [1]; the exploitation of geothermal energy was considered a long time ago [2], but it has only taken off in the last twenty years. The main reason is the urgent need to limit emissions of greenhouse gases and the lure of a renewable resource [3].
* Corresponding author. Tel.: +33-1-6469-4928; fax: +33-1-6469-4894. E-mail address: [email protected]
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of EUROCK 2017
doi:10.1016/j.proeng.2017.05.284
F.L. Pellet / Procedia Engineering 191 (2017) 1104 – 1107
1105
Despite the fact that many other issues could be related to Geo-energies, such as energy storage by compressed air for instance, this paper will be limited to rock mechanics problems associated with Enhanced Geothermal Systems. 2. Enhanced Geothermal System (EGS) 2.1. Principle and brief history The principle of a geothermal installation can be schematically represented by two boreholes. From the first borehole the injected cold water circulates into the rock mass and is heated up in contact with the hot rock. This hot water is then extracted in the second borehole and treated to remove energy. Later, this cooled water is re-injected in the first borehole. The effectiveness and the efficiency of the system depends on the existence or the formation of a sufficient exchange surface in the hot dry rock formation, between the two boreholes. The exploitation of geothermal energy is challenging especially for installations at great depth. The most obvious risk is to induce seismicity by changing the pore pressure within the rock mass due to water injection and pumping. This was the case for instance, in the city of Basel (Switzerland) where the operations triggered a 3.4 magnitude earthquake in 2006 [4]. Other incidents could occur such as that which happened in Stauffen (Germany) where drilling through an anhydrite layer provoked water losses which caused the gypsum rock to transform. The consequent expansion caused the development of major upheavals of the ground surface, which caused serious damage to existing buildings [5]. A deep geothermal installation is most often performed in geological formations of the Paleozoic era – i.e. in igneous or plutonic rocks. The design of the facility requires the fullest possible knowledge of the existing network of discontinuities as well as the initial state of stress, which is often anisotropic due to tectonic thrusts [6]. The natural intrinsic permeability of a rock mass is, most of the time, not high enough to profitably produce energy. Consequently, hydraulic fracturing is often performed to increase the permeability by generating new fractures. This technique was used in particular in Fenton Hill (USA) in 1975 [7]. However, the problem that may be encountered is that the induced fractures do not have the expected geometry, in terms of orientation and extension; they do not always connect the 2 geothermal wells effectively [8]. 2.2. Hydraulic fracturing In principle hydraulic fracturing consists of injecting a pressurized fluid into the borehole at the depth where it is desired to create a fracture. Whenever the pressure exceeds the tensile strength of the rock, a break will occur. A crack is therefore created in the opening mode (Mode I) and propagates in a direction that will tend to align with the major principal stress orientation [9], [10], [11]. To maintain sufficient flow by preventing the crack closure when the hydraulic pressure is released, a proppant - which consists of hard granular material - is then introduced into the crack. Given the uncertainties on the intensity and the direction of the initial principal stress, added to the uncertainties on the position, the orientation and the extension of existing discontinuities, the trajectories of newly created cracks are difficult to predict and require special numerical techniques which will be evoked hereafter. 2.3. Hydro Thermo Mechanical couplings The coupling between the mechanical stresses and the internal hydraulic pressures is, for obvious reasons, essential. Within the rock medium the nature of the voids is dissimilar because long cracks cohabit with pores of the rock matrix. This has led some researchers to suggest double porosity models to make the computation more accurate [12], [13]. In the case of igneous rock formations, which are suitable for Enhanced Geothermal Systems, the rock matrix porosity can often be neglected, because it is extremely low in regards to cracks porosity. Therefore, the classical approach based on poro-mechanics and Darcy’s law might sometimes be insufficient and alternative approaches have to be considered [14]. Indeed, fracture permeability evolution in time has to be accounted for, as over the life
1106
F.L. Pellet / Procedia Engineering 191 (2017) 1104 – 1107
span of the installation, fluid-rock chemical interaction can lead to an increase in permeability due to dissolution or a decrease related to precipitation [15]. This could greatly affect the duration of the installation serviceability. Besides the hydro-mechanical coupling, the effect of temperature is also very important. Indeed the differential temperature between extracted and re-injected water may be close to 1000 Celsius. This can lead to thermal microcracking - especially in the vicinity of the borehole wall - which will create a Damage Zone around the borehole that could impair the energy exploitation [16]. All these considerations make it necessary to promote multi-physics approaches in a comprehensive manner. 2.4. Induced seismicity and fault reactivation Changes in pore pressure lead to changes in the effective stress regime and possible rock material failure. The latter may result in fault reactivation [17] which will generate seismicity that has to be limited according to the operating regulations. Additionally, rock fracturing - which occurs in a brittle manner - is accompanied by sonic wave generation. It is relatively easy to measure acoustic emissions during a small scale loading test in the lab [18], [19], but it is much more difficult to relate this to on site recorded seismicity with hydraulic fracturing [20]. Indeed, wave propagation through a heterogeneous and possibly anisotropic damaged geological formation is difficult to model. Therefore, in this context, a carefully instrumented site is essential [21]. The connection of the newly created fractures to the existing fractures network is also a concern which outlines, once again, the need of a perfect knowledge of the geological context. 3. Numerical modeling Numerical modeling of the entire geothermal exploitation process formally requires a Thermo-Hydro-Mechanics approach, which accounts for the dynamic problem to simulate the seismicity [22]. To date, a few approaches have been developed to tackle this problem. They mostly consist of a mix of the Finite Element Method with a Discrete Element Approach known as FDEM [23]. Most of the time, cohesive elements are used. This means that the fracture trajectory has to be inferred prior to the calculation. This is a major limitation which leads to the use of different methods such as the eXtended Finite Element Method (XFEM). In this method, crack initiation and propagation are determined based on Fracture Mechanics theory [24]. Today this method still exhibits some limitations, mostly related to the merging or the crossing of cracks. 4. Conclusion Rock mechanics can significantly improve the understanding of any anthropogenic changes made in the rock crust, especially for the exploitation of geo-energy. Besides the classical data on petrophysical and mechanical properties of rock formations, a good knowledge of the existing fracture networks is required, along with an accurate comprehension of the initial tectonic stresses. Enhanced Geothermal Systems utilize Thermo-Hydro Mechanical couplings; however, an understanding of the mechanical behavior is required to account for the development of fractures and therefore, the use of fracture mechanics appears necessary. Additionally, the dynamic response of the system must also to be accounted for, as any seismicity due to earthquakes will lead to detrimental effects. All these considerations make the numerical modeling quite complicated. Even if, for the moment, no method is capable of modelling the whole exploitation process of EGS, recent advances lead us to think that the appropriate tools, combining different numerical techniques, will soon be operational.
F.L. Pellet / Procedia Engineering 191 (2017) 1104 – 1107
1107
References [1] D. Banks, An Introduction to Thermogeology: Ground Source Heating and Cooling, New York, N.Y., John Wiley, 2012. [2] W.E. Grasseley, Geothermal energy: geology and hydrology, In Renewable Energy Systems, Kaltschmitt et al. Eds, Berlin, Germany, Springer, 2013, pp. 761–771. [3] F.L. Pellet, Rock mechanics’ contribution to environmental geotechnics, Environmental Geotechnics, 3 (3) (2016) 140. [4] T. Terakawa, S.A. Miller, N. Deichmann, High fluid pressure and triggered earthquakes in the enhanced geothermal system in Basel, Switzerland, Journal of Geophysical Research 117 (2012) B07305. [5] I. Sass, U. Burbaum, Damage to the historic town of Staufen (Germany) caused by geothermal drillings through anhydrite-bearing formations, Acta Carsologica 39 (2010) 233–245. [6] D. Bruel, Modelling heat extraction from forced fluid flow through stimulated fractured rock masses: evaluation of the soultz-sous-forets site potential , Geothermics 24 (3) (1995) 439–450. [7] M.C. Fehler, Stress control of seismicity patterns observed during hydraulic fracturing experiments at the Fenton Hill hot dry rock geothermal energy site, New Mexico, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 26 (1989) 211–218. [8] T.M. Hunt, Geothermal field and reservoir monitoring: In Renewable Energy Systems, Kaltschmitt et al. Eds, Berlin, Germany, Springer, vol 1, 2013, pp. 783–803. [9] O. Stephansson, J.A. Hudson, L. Jing, Coupled Thermo-Hydro-Mechanical-Chemical Processes in Geo-Systems. Fundamentals, Modelling, Experiments and Applications, Elsevier Geo-Engineering Book series, vol. 2, Amsterdam, The Netherlands: Elsevier Scientific, 2004. [10] A.P.S. Selvadurai, B.M. Singh, On the expansion of a penny-shaped crack by a rigid circular disc inclusion, International Journal of Fracture 25 (1) (1984) pp. 69–77. [11] A.P.S. Selvadurai, Normal stress-induced permeability hysteresis of a fracture in a granite cylinder, Special Issue on Crustal Permeability, Geofluids 15 (2015) 37–47. [12] R. Gelet, B. Loret, N. Khalili, Borehole stability analysis in a thermoporoelastic dual-porosity medium, International Journal of Rock Mechanics and Mining Sciences 50 (2012) 65–76. [13] N. Khalili, A.P.S. Selvadurai, A fully coupled constitutive model for thermo-hydro-mechanical analysis in elastic media with double porosity, Geophysical Research Letters 30 (24) (2003) SDE 7-1–SDE 7-5. [14] M. Bai, J.C. Roegiers, Fluid flow and heat flow in deformable fractured porous media, International Journal of Engineering Sciences 32 (1994) 1615–1633. [15] T.J. Massart, A.P.S. Selvadurai, Computational modelling of crack-induced permeability evolution in granite with dilatant cracks, International Journal of Rock Mechanics and Mining Sciences 70 (2014) 593–604. [16] Y. Wang, E. Papamichos, Thermal effects on fluid flow and hydraulic fracturing from wellbores and cavities in low permeability formations, International Journal on Numerical and Analytical Methods in Geomechanics 23 (1999) 1819–1834. [17] P. Dublanchet, P., Bernard, P., Favreau, Interactions and triggering in a 3-D rate-and-state asperity model, Journal of Geophysical Research: Solid Earth 118 (5) (2013) 2225–2245. [18] M. Keshavarz, V.K. Dang, K. Amini Hosseini, F.L. Pellet, AE thresholds and compressive strength of different crystalline rocks subjected to static and dynamic loadings, Proc. 1st International Conference on Rock Dynamics and Applications, Lausanne, Switzerland, 2013, pp 213–218. [19] M. Keshavarz, F.L. Pellet, B. Loret, Damage and changes in mechanical properties of a gabbro thermally loaded up to 1000 °C, Pure and Applied Geophysics 167 (2010) 1511–1523. [20] E.L. Majer, R. Baria,M. Stark, et al., Induced seismicity associated with enhanced geothermal systems, Geothermics 36 (2007) 185–222. [21] D. Bruel, Using the migration of the induced seismicity as a constraint for fractured Hot Dry Rock reservoir modelling, International Journal of Rock Mechanics and Mining Sciences,44 (2007) 1106–1117. [22] A. Lisjak, Q. Liu, Q. Zhao, O.K. Mahabadi, G. Grasselli, Numerical simulation of acoustic emission in brittle rocks by two-dimensional finite-discrete element analysis, Geophysical Journal International 195 (1) (2013) 423–443. [23] M. Haddad, K. Sepehrnoori, Simulation of hydraulic fracturing in quasi-brittle shale formations using characterized cohesive layer: Stimulation controlling factors, Journal of Unconventional Oil and Gas Resources 9 (2015) 65–83. [24] M. Faivre, B. Paul, F. Golfier, R. Giot, P. Massin, D. Colombo, 2D coupled HM-XFEM modeling with cohesive zone model and applications to fluid-driven fracture network, Engineering Fracture Mechanics 159 (2016) 115–143.
ScienceDirect Procedia Engineering 191 (2017) 1104 – 1107
Symposium of the International Society for Rock Mechanics
Rock Mechanics is Meeting the Challenge of Geo-Energies F.L. Pellet* Mines Paristech, PSL Research University, Geosciences and Geoengineering Department, 35 rue Saint Honoré, Fontainebleau, 77300, France
Abstract The exploitation of geo-energies often leads to difficulties that rock mechanics helps to overcome. These essentially consist of instability problems caused by changes in the state of stress, associated pore pressures, and temperature. Besides the classical near field problem of wellbore stability, the changes can impact a larger scale, triggering earthquakes and inducing seismicity. In this paper the current approaches envisaged to tackle these problems are briefly reviewed and discussed. Some extensions that have been made possible thanks to the combination of new numerical techniques will be outlined. © 2017 2017The TheAuthors. Authors. Published by Elsevier Ltd.is an open access article under the CC BY-NC-ND license © Published by Elsevier Ltd. This Peer-review under responsibility of the organizing committee of EUROCK 2017. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of EUROCK 2017 Keywords: Enhanced Geothermal System; hydraulic fracturing; numerical modelling
1. Introduction The term geo-energy could be defined as the set of energy sources that the Earth produces. As in physical science where all is Energy or Matter, this would include fossil fuels such as coal, oil, gas or organic matter (wood) which is nowadays classified as unconventional geo-resources. In fact, the neologism “geo-energy” is mostly devoted to the energy that has been created from the temperature of the Earth and which is used to heat or to produce electricity. This is the case for geothermal energy [1]; the exploitation of geothermal energy was considered a long time ago [2], but it has only taken off in the last twenty years. The main reason is the urgent need to limit emissions of greenhouse gases and the lure of a renewable resource [3].
* Corresponding author. Tel.: +33-1-6469-4928; fax: +33-1-6469-4894. E-mail address: [email protected]
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of EUROCK 2017
doi:10.1016/j.proeng.2017.05.284
F.L. Pellet / Procedia Engineering 191 (2017) 1104 – 1107
1105
Despite the fact that many other issues could be related to Geo-energies, such as energy storage by compressed air for instance, this paper will be limited to rock mechanics problems associated with Enhanced Geothermal Systems. 2. Enhanced Geothermal System (EGS) 2.1. Principle and brief history The principle of a geothermal installation can be schematically represented by two boreholes. From the first borehole the injected cold water circulates into the rock mass and is heated up in contact with the hot rock. This hot water is then extracted in the second borehole and treated to remove energy. Later, this cooled water is re-injected in the first borehole. The effectiveness and the efficiency of the system depends on the existence or the formation of a sufficient exchange surface in the hot dry rock formation, between the two boreholes. The exploitation of geothermal energy is challenging especially for installations at great depth. The most obvious risk is to induce seismicity by changing the pore pressure within the rock mass due to water injection and pumping. This was the case for instance, in the city of Basel (Switzerland) where the operations triggered a 3.4 magnitude earthquake in 2006 [4]. Other incidents could occur such as that which happened in Stauffen (Germany) where drilling through an anhydrite layer provoked water losses which caused the gypsum rock to transform. The consequent expansion caused the development of major upheavals of the ground surface, which caused serious damage to existing buildings [5]. A deep geothermal installation is most often performed in geological formations of the Paleozoic era – i.e. in igneous or plutonic rocks. The design of the facility requires the fullest possible knowledge of the existing network of discontinuities as well as the initial state of stress, which is often anisotropic due to tectonic thrusts [6]. The natural intrinsic permeability of a rock mass is, most of the time, not high enough to profitably produce energy. Consequently, hydraulic fracturing is often performed to increase the permeability by generating new fractures. This technique was used in particular in Fenton Hill (USA) in 1975 [7]. However, the problem that may be encountered is that the induced fractures do not have the expected geometry, in terms of orientation and extension; they do not always connect the 2 geothermal wells effectively [8]. 2.2. Hydraulic fracturing In principle hydraulic fracturing consists of injecting a pressurized fluid into the borehole at the depth where it is desired to create a fracture. Whenever the pressure exceeds the tensile strength of the rock, a break will occur. A crack is therefore created in the opening mode (Mode I) and propagates in a direction that will tend to align with the major principal stress orientation [9], [10], [11]. To maintain sufficient flow by preventing the crack closure when the hydraulic pressure is released, a proppant - which consists of hard granular material - is then introduced into the crack. Given the uncertainties on the intensity and the direction of the initial principal stress, added to the uncertainties on the position, the orientation and the extension of existing discontinuities, the trajectories of newly created cracks are difficult to predict and require special numerical techniques which will be evoked hereafter. 2.3. Hydro Thermo Mechanical couplings The coupling between the mechanical stresses and the internal hydraulic pressures is, for obvious reasons, essential. Within the rock medium the nature of the voids is dissimilar because long cracks cohabit with pores of the rock matrix. This has led some researchers to suggest double porosity models to make the computation more accurate [12], [13]. In the case of igneous rock formations, which are suitable for Enhanced Geothermal Systems, the rock matrix porosity can often be neglected, because it is extremely low in regards to cracks porosity. Therefore, the classical approach based on poro-mechanics and Darcy’s law might sometimes be insufficient and alternative approaches have to be considered [14]. Indeed, fracture permeability evolution in time has to be accounted for, as over the life
1106
F.L. Pellet / Procedia Engineering 191 (2017) 1104 – 1107
span of the installation, fluid-rock chemical interaction can lead to an increase in permeability due to dissolution or a decrease related to precipitation [15]. This could greatly affect the duration of the installation serviceability. Besides the hydro-mechanical coupling, the effect of temperature is also very important. Indeed the differential temperature between extracted and re-injected water may be close to 1000 Celsius. This can lead to thermal microcracking - especially in the vicinity of the borehole wall - which will create a Damage Zone around the borehole that could impair the energy exploitation [16]. All these considerations make it necessary to promote multi-physics approaches in a comprehensive manner. 2.4. Induced seismicity and fault reactivation Changes in pore pressure lead to changes in the effective stress regime and possible rock material failure. The latter may result in fault reactivation [17] which will generate seismicity that has to be limited according to the operating regulations. Additionally, rock fracturing - which occurs in a brittle manner - is accompanied by sonic wave generation. It is relatively easy to measure acoustic emissions during a small scale loading test in the lab [18], [19], but it is much more difficult to relate this to on site recorded seismicity with hydraulic fracturing [20]. Indeed, wave propagation through a heterogeneous and possibly anisotropic damaged geological formation is difficult to model. Therefore, in this context, a carefully instrumented site is essential [21]. The connection of the newly created fractures to the existing fractures network is also a concern which outlines, once again, the need of a perfect knowledge of the geological context. 3. Numerical modeling Numerical modeling of the entire geothermal exploitation process formally requires a Thermo-Hydro-Mechanics approach, which accounts for the dynamic problem to simulate the seismicity [22]. To date, a few approaches have been developed to tackle this problem. They mostly consist of a mix of the Finite Element Method with a Discrete Element Approach known as FDEM [23]. Most of the time, cohesive elements are used. This means that the fracture trajectory has to be inferred prior to the calculation. This is a major limitation which leads to the use of different methods such as the eXtended Finite Element Method (XFEM). In this method, crack initiation and propagation are determined based on Fracture Mechanics theory [24]. Today this method still exhibits some limitations, mostly related to the merging or the crossing of cracks. 4. Conclusion Rock mechanics can significantly improve the understanding of any anthropogenic changes made in the rock crust, especially for the exploitation of geo-energy. Besides the classical data on petrophysical and mechanical properties of rock formations, a good knowledge of the existing fracture networks is required, along with an accurate comprehension of the initial tectonic stresses. Enhanced Geothermal Systems utilize Thermo-Hydro Mechanical couplings; however, an understanding of the mechanical behavior is required to account for the development of fractures and therefore, the use of fracture mechanics appears necessary. Additionally, the dynamic response of the system must also to be accounted for, as any seismicity due to earthquakes will lead to detrimental effects. All these considerations make the numerical modeling quite complicated. Even if, for the moment, no method is capable of modelling the whole exploitation process of EGS, recent advances lead us to think that the appropriate tools, combining different numerical techniques, will soon be operational.
F.L. Pellet / Procedia Engineering 191 (2017) 1104 – 1107
1107
References [1] D. Banks, An Introduction to Thermogeology: Ground Source Heating and Cooling, New York, N.Y., John Wiley, 2012. [2] W.E. Grasseley, Geothermal energy: geology and hydrology, In Renewable Energy Systems, Kaltschmitt et al. Eds, Berlin, Germany, Springer, 2013, pp. 761–771. [3] F.L. Pellet, Rock mechanics’ contribution to environmental geotechnics, Environmental Geotechnics, 3 (3) (2016) 140. [4] T. Terakawa, S.A. Miller, N. Deichmann, High fluid pressure and triggered earthquakes in the enhanced geothermal system in Basel, Switzerland, Journal of Geophysical Research 117 (2012) B07305. [5] I. Sass, U. Burbaum, Damage to the historic town of Staufen (Germany) caused by geothermal drillings through anhydrite-bearing formations, Acta Carsologica 39 (2010) 233–245. [6] D. Bruel, Modelling heat extraction from forced fluid flow through stimulated fractured rock masses: evaluation of the soultz-sous-forets site potential , Geothermics 24 (3) (1995) 439–450. [7] M.C. Fehler, Stress control of seismicity patterns observed during hydraulic fracturing experiments at the Fenton Hill hot dry rock geothermal energy site, New Mexico, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 26 (1989) 211–218. [8] T.M. Hunt, Geothermal field and reservoir monitoring: In Renewable Energy Systems, Kaltschmitt et al. Eds, Berlin, Germany, Springer, vol 1, 2013, pp. 783–803. [9] O. Stephansson, J.A. Hudson, L. Jing, Coupled Thermo-Hydro-Mechanical-Chemical Processes in Geo-Systems. Fundamentals, Modelling, Experiments and Applications, Elsevier Geo-Engineering Book series, vol. 2, Amsterdam, The Netherlands: Elsevier Scientific, 2004. [10] A.P.S. Selvadurai, B.M. Singh, On the expansion of a penny-shaped crack by a rigid circular disc inclusion, International Journal of Fracture 25 (1) (1984) pp. 69–77. [11] A.P.S. Selvadurai, Normal stress-induced permeability hysteresis of a fracture in a granite cylinder, Special Issue on Crustal Permeability, Geofluids 15 (2015) 37–47. [12] R. Gelet, B. Loret, N. Khalili, Borehole stability analysis in a thermoporoelastic dual-porosity medium, International Journal of Rock Mechanics and Mining Sciences 50 (2012) 65–76. [13] N. Khalili, A.P.S. Selvadurai, A fully coupled constitutive model for thermo-hydro-mechanical analysis in elastic media with double porosity, Geophysical Research Letters 30 (24) (2003) SDE 7-1–SDE 7-5. [14] M. Bai, J.C. Roegiers, Fluid flow and heat flow in deformable fractured porous media, International Journal of Engineering Sciences 32 (1994) 1615–1633. [15] T.J. Massart, A.P.S. Selvadurai, Computational modelling of crack-induced permeability evolution in granite with dilatant cracks, International Journal of Rock Mechanics and Mining Sciences 70 (2014) 593–604. [16] Y. Wang, E. Papamichos, Thermal effects on fluid flow and hydraulic fracturing from wellbores and cavities in low permeability formations, International Journal on Numerical and Analytical Methods in Geomechanics 23 (1999) 1819–1834. [17] P. Dublanchet, P., Bernard, P., Favreau, Interactions and triggering in a 3-D rate-and-state asperity model, Journal of Geophysical Research: Solid Earth 118 (5) (2013) 2225–2245. [18] M. Keshavarz, V.K. Dang, K. Amini Hosseini, F.L. Pellet, AE thresholds and compressive strength of different crystalline rocks subjected to static and dynamic loadings, Proc. 1st International Conference on Rock Dynamics and Applications, Lausanne, Switzerland, 2013, pp 213–218. [19] M. Keshavarz, F.L. Pellet, B. Loret, Damage and changes in mechanical properties of a gabbro thermally loaded up to 1000 °C, Pure and Applied Geophysics 167 (2010) 1511–1523. [20] E.L. Majer, R. Baria,M. Stark, et al., Induced seismicity associated with enhanced geothermal systems, Geothermics 36 (2007) 185–222. [21] D. Bruel, Using the migration of the induced seismicity as a constraint for fractured Hot Dry Rock reservoir modelling, International Journal of Rock Mechanics and Mining Sciences,44 (2007) 1106–1117. [22] A. Lisjak, Q. Liu, Q. Zhao, O.K. Mahabadi, G. Grasselli, Numerical simulation of acoustic emission in brittle rocks by two-dimensional finite-discrete element analysis, Geophysical Journal International 195 (1) (2013) 423–443. [23] M. Haddad, K. Sepehrnoori, Simulation of hydraulic fracturing in quasi-brittle shale formations using characterized cohesive layer: Stimulation controlling factors, Journal of Unconventional Oil and Gas Resources 9 (2015) 65–83. [24] M. Faivre, B. Paul, F. Golfier, R. Giot, P. Massin, D. Colombo, 2D coupled HM-XFEM modeling with cohesive zone model and applications to fluid-driven fracture network, Engineering Fracture Mechanics 159 (2016) 115–143.