# Hydraulic Stimulation of Geothermal Reservoirs: Numerical Simulation of Induced Seismicity and Thermal Decline

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Thermo-Hydro-Mechanical 3D Model of Fault Reactivation

#### 2.2. Flow and Heat Transport along Faults

#### 2.3. Frictional Strength of Faults

#### 2.4. Model Description and Parameters

## 3. Results

#### 3.1. Fault Reactivation and Injection Design

#### 3.2. Seismic Rupture and Earthquake Magnitude

#### 3.3. Permeability Enhancement

#### 3.4. Long-Term Operation and Thermal Decline

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Colglazier, W. Sustainable development agenda: 2030. Science
**2015**, 349, 1048–1050. [Google Scholar] [CrossRef] [PubMed] - Mahbaz, S.; Dehghani-Sanij, A.; Dusseault, M.; Nathwani, J. Enhanced and integrated geothermal systems for sustainable development of Canada’s northern communities. Sustain. Energy Technol. Assess.
**2020**, 37, 100565. [Google Scholar] [CrossRef] - MIT Energy Initiative. The Future of Geothermal Energy: Impact of Enhanced Geothermal Systems (EGS) on the United States in the 21st Century; Massachusetts Institute of Technology: Cambridge, MA, USA, 2006. [Google Scholar]
- Kinney, C.; Dehghani-Sanij, A.; Mahbaz, S.; Dusseault, M.; Nathwani, J.; Fraser, R. Geothermal Energy for Sustainable Food Production in Canada’s Remote Northern Communities. Energies
**2019**, 12, 4058. [Google Scholar] [CrossRef] - Soltani, M.; Moradi-Kashkooli, F.; Dehghani-Sanij, A.; Nokhosteen, A.; Ahmadi-Joughi, A.; Gharali, K.; Mahbaz, S.; Dusseault, M. A comprehensive review of geothermal energy evolution and development. Int. J. Green Energy
**2019**, 16, 971–1009. [Google Scholar] [CrossRef] - Andrés, S.; Santillán, D.; Mosquera, J.; Cueto-Felgueroso, L. Thermo-Poroelastic Analysis of Induced Seismicity at the Basel Enhanced Geothermal System. Sustainability
**2019**, 11, 6904. [Google Scholar] [CrossRef] - Santillan, D.; Mosquera, J.; Cueto-Felgueroso, L. Fluid-driven fracture propagation in heterogeneous media: Probability distributions of fracture trajectories. Phys. Rev. E
**2017**, 96, 053002. [Google Scholar] [CrossRef] - Santillán, D.; Juanes, R.; Cueto-Felgueroso, L. Phase field model of hydraulic fracturing in poroelastic media: Fracture propagation, arrest, and branching under fluid injection and extraction. J. Geophys. Res. Solid Earth
**2018**, 123, 2127–2155. [Google Scholar] [CrossRef] - Rinaldi, A.; Rutqvist, J.; Sonnenthal, E.; Cladouhos, T. Coupled THM Modeling of Hydroshearing Stimulation in Tight Fractured Volcanic Rock. Transp. Porous Med.
**2014**, 108, 131–150. [Google Scholar] [CrossRef] - Rinaldi, A.; Rutqvist, J. Joint opening or hydroshearing? Analyzing a fracture zone stimulation at Fenton Hill. Geothermics
**2019**, 77, 83–98. [Google Scholar] [CrossRef] - Giardini, D. Geothermal quake risks must be faced. Nature
**2009**, 462, 848–849. [Google Scholar] [CrossRef] - Schultz, R.; Skoumal, R.; Brudzinski, M.; Eaton, D.; Baptie, B.; Ellsworth, W. Hydraulic Fracturing-Induced Seismicity. Rev. Geophys.
**2020**, 58, e2019RG000695. [Google Scholar] [CrossRef] - Parker, R. The Rosemanowes HDR project 1983–1991. Geothermics
**1999**, 28, 603–615. [Google Scholar] [CrossRef] - Pine, R.; Batchelor, A. Downward migration of shearing in jointed rock during hydraulic injections. Int. J. Rock. Mech. Min. Sci. Geomech. Abstr.
**1984**, 21, 249–263. [Google Scholar] [CrossRef] - Häring, M.; Hopkirk, R. The Swiss Deep Heat Mining Project-The Basel Exploration Drilling. GHC Bull.
**2002**, 23, 31–33. [Google Scholar] - Häring, M.; Schanz, U.; Ladner, F.; Dyer, B. Characterisation of the Basel 1 enhanced geothermal system. Geothermics
**2008**, 37, 469–495. [Google Scholar] [CrossRef] - Baisch, S.; Vörös, R.; Weidler, R.; Wyborn, D. Investigation of Fault Mechanisms during Geothermal Reservoir Stimulation Experiments in the Cooper Basin, Australia. Bull. Seismol. Soc. Am.
**2009**, 99, 148–158. [Google Scholar] [CrossRef] - Ellsworth, W.; Giardini, D.; Townend, J.; Ge, S.; Shimamoto, T. Triggering of the Pohang, Korea, Earthquake (M
_{w}5.5) by Enhanced Geothermal System Stimulation. Seismol. Res. Lett.**2019**, 90, 1844–1858. [Google Scholar] [CrossRef] - Chang, K.; Yoon, H.; Kim, Y.; Lee, M. Operational and geological controls of coupled poroelastic stressing and pore-pressure accumulation along faults: Induced earthquakes in Pohang, South Korea. Sci. Rep.
**2020**, 10, 2073. [Google Scholar] [CrossRef] - Ziagos, J.; Phillips, B.; Boyd, L.; Jelacic, A.; Stillman, G.; Hass, E. A Technology Roadmap for Strategic Development of Enhanced Geothermal Systems. In Proceedings of the 38th Workshop on Geothermal Reservoir Engineering, Stanford, CA, USA, 11–13 February 2013. [Google Scholar]
- Minetto, R.; Montanari, D.; Planès, T.; Bonini, M.; Ventisette, C.; Antunes, V.; Lupi, M. Tectonic and Anthropogenic Microseismic Activity While Drilling Toward Supercritical Conditions in the Larderello-Travale Geothermal Field, Italy. J. Geophys. Res. Solid Earth
**2020**, 125, e2019JB018618. [Google Scholar] [CrossRef] - Bagagli, M.; Kissling, E.; Piccinini, D.; Saccorotti, G. Local earthquake tomography of the Larderello-Travale geothermal field. Geothermics
**2020**, 83, 101731. [Google Scholar] [CrossRef] - Rutqvist, J.; Jeanne, P.; Dobson, P.; Garcia, J.; Hartline, C.; Hutchings, L.; Singh, A.; Vasco, D.; Walters, M. The Northwest Geysers EGS Demonstration Project, California—Part2: Modeling and interpretation. Geothermics
**2016**, 63, 120–138. [Google Scholar] [CrossRef] - Garcia, J.; Hartline, C.; Walters, M.; Wright, M.; Rutqvist, J.; Dobson, P.; Jeanne, P. The Northwest Geysers EGS Demonstration Project, California—Part 1: Characterization and reservoir response to injection. Geothermics
**2016**, 63, 97–119. [Google Scholar] [CrossRef] - Kim, K.; Ree, J.; Kim, Y.; Kim, S.; Kang, S.; Seo, W. Assessing whether the 2017 M
_{w}5.4 Pohang earthquake in South Korea was an induced event. Science**2018**, 360, 1007–1009. [Google Scholar] [CrossRef] [PubMed] - Grigoli, F.; Cesca, S.; Rinaldi, A.; Manconi, A.; López-Comino, J.; Clinton, J.; Westaway, R.; Cauzzi, C.; Dahm, T.; Wiemer, S. The November 2017 M
_{w}5.5 Pohang earthquake: A possible case of induced seismicity in South Korea. Science**2018**, 360, 1003–1006. [Google Scholar] [CrossRef] - Hubbert, M.; Rubey, W. Role of fluid pressure in mechanics of overthrust faulting I. Mechanics of fluid-filled porous solids and its application to overthrust faulting. Geol. Soc. Am. Bull.
**1959**, 70, 115–166. [Google Scholar] - Pampillón, P.; Santillán, D.; Mosquera, J.; Cueto-Felgueroso, L. Geomechanical Constraints on Hydro-Seismicity: Tidal Forcing and Reservoir Operation. Water
**2020**, 12, 2724. [Google Scholar] [CrossRef] - Pampillón, P.; Santillán, D.; Mosquera, J.; Cueto-Felgueroso, L. Dynamic and Quasi-Dynamic Modeling of Injection-Induced Earthquakes in Poroelastic Media. J. Geophys. Res. Solid Earth
**2018**, 123, 5730–5759. [Google Scholar] [CrossRef] - National Research Council. Induced Seismicity Potential in Energy Technologies; The National Academies Press: Washington, DC, USA, 2013. [Google Scholar]
- Ellsworth, W. Injection-Induced Earthquakes. Science
**2013**, 341, 1225942. [Google Scholar] [CrossRef] - Brodsky, E.; Lajoie, L. Anthropogenic Seismicity Rates and Operational Parameters at the Salton Sea Geothermal Field. Science
**2013**, 341, 543–546. [Google Scholar] [CrossRef] - Buijze, L.; van Bijsterveldt, L.; Cremer, H.; Paap, B.; Veldkamp, H.; Wassing, B.; van Wees, J.; van Yperen, J.; ter Heege, J.; Jaarsma, B. Review of induced seismicity in geothermal systems worldwide and implications for geothermal systems in the Netherlands. Neth. J. Geosci.
**2019**, 98, E13. [Google Scholar] [CrossRef] - Horton, S. Disposal of hydrofracking waste fluid by injection into subsurface aquifers triggers earthquake swarm in central Arkansas with potential for damaging earthquake. Seismol. Res. Lett.
**2012**, 83, 250–260. [Google Scholar] [CrossRef] - Juanes, R.; Hager, B.; Herzog, H. No geologic evidence that seismicity causes fault leakage that would render large-scale carbon capture and storage unsuccessful. Proc. Natl. Acad. Sci. USA
**2012**, 109, E3623. [Google Scholar] [CrossRef] [PubMed] - Vilarrasa, V.; Carrera, J. Geologic carbon storage is unlikely to trigger large earthquakes and reactivate faults through which CO
_{2}could leak. Proc. Natl. Acad. Sci. USA**2015**, 112, 5938–5943. [Google Scholar] [CrossRef] [PubMed] - White, J.; Foxall, W. Assessing induced seismicity risk at CO
_{2}storage projects: Recent progress and remaining challenges. Int. J. Greenh. Gas Control**2016**, 49, 413–424. [Google Scholar] [CrossRef] - Vilarrasa, V.; De Simone, S.; Carrera, J.; Villaseñor, A. Unraveling the causes of the seismicity induced by underground gas storage at Castor, Spain. Geophys. Res. Lett.
**2021**, 48, e2020GL092038. [Google Scholar] [CrossRef] - Weingarten, M.; Ge, S.; Godt, J.; Bekins, B.; Rubinstein, J. High-rate injection is associated with the increase in U.S. mid-continent seismicity. Science
**2015**, 348, 1336–1340. [Google Scholar] [CrossRef] [PubMed] - Shirzaei, M.; Ellsworth, W.; Tiampo, K.; González, P.; Manga, M. Surface uplift and time-dependent seismic hazard due to fluid injection in eastern Texas. Science
**2016**, 353, 1416–1419. [Google Scholar] [CrossRef] - McComas, K.; Lu, H.; Keranen, K.; Furtney, M.; Song, H. Public perceptions and acceptance of induced earthquakes related to energy development. Energy Policy
**2016**, 99, 27–32. [Google Scholar] [CrossRef] - Mignan, A.; Karvounis, D.; Broccardo, M.; Wiemer, S.; Giardini, D. Including seismic risk mitigation measures into the Levelized Cost of Electricity in enhanced geothermal systems for optimal siting. Appl. Energy
**2019**, 238, 831–850. [Google Scholar] [CrossRef] - Lee, K.; Ellsworth, W.; Giardini, D.; Townend, J.; Ge, S.; Shimamoto, T.; Yeo, I.; Kang, T.; Rhie, J.; Sheen, D.; et al. Managing injection-induced seismic risks. Science
**2019**, 364, 730–732. [Google Scholar] [CrossRef] - McGarr, A. Maximum magnitude earthquakes induced by fluid injection. J. Geophys. Res. Solid Earth
**2014**, 119, 1008–1019. [Google Scholar] [CrossRef] - Scholz, C. The Mechanics of Earthquakes and Faulting; Cambridge University Press: Cambridge, UK, 2002. [Google Scholar]
- Charlety, J.; Cuenot, N.; Dorbath, L.; Dorbath, C.; Haessler, H.; Frogneux, M. Large earthquakes during hydraulic stimulations at the geothermal site of Soultz-sous-Forêts. Int. J. Rock. Mech. Min. Sci.
**2007**, 44, 1091–1105. [Google Scholar] [CrossRef] - Deichmann, N.; Giardini, D. Earthquakes Induced by the Stimulation of an Enhanced Geothermal System below Basel (Switzerland). Seismol. Res. Lett.
**2009**, 80, 784–798. [Google Scholar] [CrossRef] - De Simone, S.; Carrera, J.; Vilarrasa, V. Superposition approach to understand triggering mechanisms of post-injection induced seismicity. Geothermics
**2017**, 70, 85–97. [Google Scholar] [CrossRef] - Rutqvist, J.; Birkholzer, J.; Tsang, C.F. Coupled reservoir-geomechanical analysis of the potential for tensile and shear failure associated with CO
_{2}injection in multilayered reservoir-caprock systems. Int. J. Rock. Mech. Min. Sci.**2008**, 45, 132–143. [Google Scholar] [CrossRef] - De Simone, S.; Vilarrasa, V.; Carrera, J.; Alcolea, A.; Meier, P. Thermal coupling may control mechanical stability of geothermal reservoirs during cold water injection. Phys. Chem. Earth
**2013**, 64, 117–126. [Google Scholar] [CrossRef] - Vilarrasa, V.; Olivella, S.; Carrera, J.; Rutqvist, J. Long term impacts of cold CO
_{2}injection on the caprock integrity. Int. J. Greenh. Gas Control**2014**, 24, 1–13. [Google Scholar] [CrossRef] - Jacquey, A.; Cacace, M.; Blöcher, G.; Watanabe, N.; Huenges, E.; Scheck-Wenderoth, M. Thermo-poroelastic numerical modelling for enhanced geothermal system performance: Case study of the Groß Schönebeck reservoir. Tectonophysics
**2016**, 684, 119–130. [Google Scholar] [CrossRef] - Rice, J. Heating and weakening of faults during earthquake slip. J. Geophys. Res.
**2006**, 111, B05311. [Google Scholar] [CrossRef] - Dieterich, J.; Linker, F. Fault stability under conditions of variable normal stress. Geophys. Res. Lett.
**1992**, 19, 1691–1694. [Google Scholar] [CrossRef] - Kilgore, B.; Beeler, N.; Lozos, J.; Oglesby, D. Rock friction under variable normal stress. J. Geophys. Res. Solid Earth
**2017**, 122, 7042–7075. [Google Scholar] [CrossRef] - Dieterich, J. Modeling of rock friction: 1. Experimental results and constitutive equations. J. Geophys. Res.
**1979**, 84, 2161–2168. [Google Scholar] [CrossRef] - Linker, F.; Dieterich, J. Effects of variable normal stress on rock friction: Observations and constitutive equations. J. Geophys. Res.
**1992**, 97, 4923–4940. [Google Scholar] [CrossRef] - Wyss, R.; Link, K. Actual Developments in Deep Geothermal Energy in Switzerland. In Proceedings of the World Geothermal Congress 2015, Melbourne, Australia, 19–25 April 2015. [Google Scholar]
- Meier, P.; Alcolea Rodríguez, A.; Bethmann, F. Lessons Learned from Basel: New EGS Projects in Switzerland Using Multistage Stimulation and a Probabilistic Traffic Light System for the Reduction of Seismic Risk. In Proceedings of the World Geothermal Congress 2015, Melbourne, Australia, 19–25 April 2015. [Google Scholar]
- Gischig, V.; Wiemer, S. A stochastic model for induced seismicity based on non-linear pressure diffusion and irreversible permeability enhancement. Geophys. J. Int.
**2013**, 194, 1229–1249. [Google Scholar] [CrossRef] - Mena, B.; Wiemer, S.; Bachmann, C. Building Robust Models to Forecast the Induced Seismicity Related to Geothermal Reservoir Enhancement. Bull. Seismol. Soc. Am.
**2013**, 103, 383–393. [Google Scholar] [CrossRef] - Catalli, F.; Rinaldi, A.; Gischig, V.; Nespoli, M.; Wiemer, S. The importance of earthquake interactions for injection-induced seismicity: Retrospective modeling of the Basel Enhanced Geothermal System. Geophys. Res. Lett.
**2016**, 43, 4992–4999. [Google Scholar] [CrossRef] - Andrés, S.; Santillán, D.; Mosquera, J.; Cueto-Felgueroso, L. Delayed weakening and reactivation of rate-and-state faults driven by pressure changes due to fluid injection. J. Geophys. Res. Solid Earth
**2019**, 124, 11917–11937. [Google Scholar] [CrossRef] - Ungemach, P.; Antics, M. The Road Ahead Toward Sustainable Geothermal Development in Europe. In Proceedings of the World Geothermal Congress 2010, Bali, Indonesia, 25–29 April 2010. [Google Scholar]
- Gholizadeh Doonechaly, N.; Abdel Azim, R.; Rahman, S. Evaluation of recoverable energy potential from enhanced geothermal systems: A sensitivity analysis in a poro-thermo-elastic framework. Geofluids
**2016**, 16, 384–395. [Google Scholar] [CrossRef] - Liu, G.; Zhou, C.; Rao, Z.; Liao, S. Impacts of fracture network geometries on numerical simulation and performance prediction of enhanced geothermal systems. Renew. Energy
**2021**, 171, 492–504. [Google Scholar] [CrossRef] - Wu, X.; Yu, L.; Hassan, N.; Ma, W.; Liu, G. Evaluation and optimization of heat extraction in enhanced geothermal system via failure area percentage. Renew. Energy
**2021**, 169, 204–220. [Google Scholar] [CrossRef] - Biot, M. General Theory of Three-Dimensional Consolidation. J. Appl. Phys.
**1941**, 12, 155–164. [Google Scholar] [CrossRef] - Rice, J.; Cleary, M. Some basic stress diffusion solutions for fluid-saturated elastic porous media with compressible constituents. Rev. Geophys.
**1976**, 14, 227–241. [Google Scholar] [CrossRef] - Cueto-Felgueroso, L.; Santillán, D.; Mosquera, J. Stick-slip dynamics of flow-induced seismicity on rate and state faults. Geophys. Res. Lett.
**2017**, 44, 4098–4106. [Google Scholar] [CrossRef] - Cueto-Felgueroso, L.; Vila, C.; Santillán, D.; Mosquera, J. Numerical Modeling of Injection-Induced Earthquakes Using Laboratory-Derived Friction Laws. Water Resour. Res.
**2018**, 54, 9833–9859. [Google Scholar] [CrossRef] - Fourier, J. Théorie Analytique de la Chaleur; Chez Firmin Didot Pére et Fils: Paris, France, 1822. [Google Scholar]
- Andrés, S.; Dentz, M.; Cueto-Felgueroso, L. Multirate mass transfer approach for double-porosity poroelasticity in fractured media. Water Resour. Res.
**2021**, 57, e2021WR029804. [Google Scholar] [CrossRef] - Jha, B.; Juanes, R. Coupled multiphase flow and poromechanics: A computational model of pore pressure effects on fault slip and earthquake triggering. Water Resour. Res.
**2014**, 50, 3776–3808. [Google Scholar] [CrossRef] - Bowden, F.; Tabor, D. The Friction and Lubrication of Solids I; Clarendon Press: London, UK, 1950. [Google Scholar]
- Baumberger, T.; Caroli, C. Solid friction from stick-slip down to pinning and aging. Adv. Phys.
**2006**, 55, 279–348. [Google Scholar] [CrossRef] - Barber, J. Multiscale Surfaces and Amontons’ Law of Friction. Tribol. Lett.
**2013**, 49, 539–543. [Google Scholar] [CrossRef] - Ruina, A. Slip instability and state variable friction laws. J. Geophys. Res.
**1983**, 88, 10359–10370. [Google Scholar] [CrossRef] - Tal, Y.; Hager, B.; Ampuero, J. The Effects of Fault Roughness on the Earthquake Nucleation Process. J. Geophys. Res. Solid Earth
**2018**, 123, 437–456. [Google Scholar] [CrossRef] - Rice, J.; Lapusta, N.; Ranjith, K. Rate and state dependent friction and the stability of sliding between elastically deformable solids. J. Mech. Phys. Solids
**2001**, 49, 1865–1898. [Google Scholar] [CrossRef] - Putelat, T.; Dawes, J.; Willis, J. On the microphysical foundations of rate-and-state friction. J. Mech. Phys. Solids
**2011**, 59, 1062–1075. [Google Scholar] [CrossRef] - Hong, T.; Marone, C. Effects of normal stress perturbations on the frictional properties of simulated faults. Geochem. Geophys. Geosyst.
**2005**, 6, Q03012. [Google Scholar] [CrossRef] - Perfettini, H.; Molinari, A. A micromechanical model of rate and state friction: 2. Effect of shear and normal stress changes. J. Geophys. Res. Solid Earth
**2017**, 122, 2638–2652. [Google Scholar] - Rathbun, A.; Marone, C. Symmetry and the critical slip distance in rate and state friction laws. J. Geophys. Res. Solid Earth
**2013**, 118, 3728–3741. [Google Scholar] [CrossRef] - Bhattacharya, P.; Rubin, A.; Bayart, E.; Savage, H.; Marone, C. Critical evaluation of state evolution laws in rate and state friction: Fitting large velocity steps in simulated fault gouge with time-, slip-, and stress-dependent constitutive laws. J. Geophys. Res. Solid Earth
**2015**, 120, 6365–6385. [Google Scholar] [CrossRef] - Perfettini, H.; Schmittbuhl, J.; Rice, J.; Cocco, M. Frictional response induced by time-dependent fluctuations of the normal loading. J. Geophys. Res.
**2001**, 106, 13455–13472. [Google Scholar] [CrossRef] - Hanks, T.; Kanamori, H. A moment magnitude scale. J. Geophys. Res.
**1979**, 84, 2348–2350. [Google Scholar] [CrossRef] - Norbeck, J.; McClure, M.; Horne, R. Field observations at the Fenton Hill enhanced geothermal system test site support mixed-mechanism stimulation. Geothermics
**2018**, 74, 135–149. [Google Scholar] [CrossRef] - Cacace, M.; Jacquey, A. Flexible parallel implicit modelling of coupled thermal-hydraulic-mechanical processes in fractured rocks. Solid Earth
**2017**, 8, 921–941. [Google Scholar] [CrossRef] - COMSOL. COMSOL Multiphysics Structural Mechanics Module User’s Guide v5.2a; COMSOL: Stockholm, Sweden, 2016. [Google Scholar]
- Clark, C.; Harto, C.; Sullivan, J.; Wang, M. Water Use in the Development and Operation of Geothermal Power Plants; Agronne National Laboratory, U.S. Department of Energy: Lemont, IL, USA, 2011.
- Gischig, V.; Preisig, G. Hydro-Fracturing Versus Hydro-Shearing: A Critical Assessment of Two Distinct Reservoir Estimulation Mechanisms. In Proceedings of the 13th International Congress of Rock Mechanics, Montreal, QC, Canada, 10–13 May 2015. [Google Scholar]
- Deichmann, N.; Kraft, T.; Evans, K. Identification of faults activated during the stimulation of the Basel geothermal project from cluster analysis and focal mechanisms of the larger magnitude events. Geothermics
**2014**, 52, 84–97. [Google Scholar] [CrossRef] - Alghannam, M.; Juanes, R. Understanding rate effects in injection-induced earthquakes. Nat. Commun.
**2020**, 11, 3053. [Google Scholar] [CrossRef] [PubMed] - Riahi, A.; Damjanac, B. Numerical Study of Hydro-Shearing in Geothermal Reservoirs with a Pre-Existing Discrete Fracture Network. In Proceedings of the 38th Workshop on Geothermal Reservoir Engineering, Stanford, CA, USA, 11–13 February 2013. [Google Scholar]
- Ye, Z.; Ghassemi, A. Injection-Induced Shear Slip and Permeability Enhancement in Granite Fractures. J. Geophys. Res. Solid Earth
**2018**, 123, 9009–9032. [Google Scholar] [CrossRef] - Liu, R.; Huang, N.; Jiang, Y.; Jing, H.; Li, B.; Xia, Y. Effect of Shear Displacement on the Directivity of Permeability in 3D Self-Affine Fractal Fractures. Geofluids
**2018**, 2018, 9813846. [Google Scholar] [CrossRef] - Gehne, S.; Benson, P. Permeability enhancement through hydraulic fracturing: Laboratory measurements combining a 3D printed jacket and pore fluid over-pressure. Sci. Rep.
**2019**, 9, 12573. [Google Scholar] [CrossRef] - McDermott, C.; Randriamanjatosoa, A.; Tenzer, H.; Kolditz, O. Simulation of heat extraction from crystalline rocks: The influence of coupled processes on differential reservoir cooling. Geothermics
**2006**, 35, 321–344. [Google Scholar] [CrossRef] - Koh, J.; Roshan, H.; Rahman, S. A numerical study on the long term thermo-poroelastic effects of cold water injection into naturally fractured geothermal reservoirs. Comput. Geotech.
**2011**, 38, 669–682. [Google Scholar] [CrossRef] - De Simone, S.; Pinier, B.; Bour, O.; Davy, P. A particle-tracking formulation of advective–diffusive heat transport in deformable fracture networks. Comput. Geotech.
**2021**, 603, 127157. [Google Scholar] [CrossRef]

**Figure 1.**Scheme of the 2D Basel EGS model. We show the model domain, a 5 km${}^{2}$ square with a strike-slip fault of 2 km length oriented 10${}^{\circ}$ with respect to the x-axis. The domain is a horizontal section of the reservoir located at 4800 m depth, with an injection well of 5 m radius located at 50 m from the midpoint of the fault. The figure also includes the boundary conditions applied: tectonic stresses, hydrostatic pore pressure, and natural temperature on NE and SE boundaries; normal displacements, thermal transport, and fluid flow impeded on NW and SW boundaries.

**Figure 2.**Optimization of the injection protocol for the Basel geothermal reservoir, based on fault reactivation predicted by the model. In panel (

**a**), we show the conducted injection protocol in Basel-1 well in 2006 (solid line) and the one with a constant flow rate equal to 22.4 l/s (dashed line). In panel (

**b**), we plot the change in friction variables with time on the fault control point, so when mobilized friction $\tau /|{\sigma}^{\prime}|$ (green line) equals the friction coefficient $\mu $ (blue line), the fault reactivates. This occurs for the injection protocol registered in 2006 but not for the injection at constant flow rate. In panel (

**c**) we include a phased injection protocol designed to avoid fault reactivation, which consists of a series of 11 injections at a constant flow rate for 5 days. In panel (

**d**), we show the change with time in the dimensionless Coulomb failure function, $CFF/|{\sigma}^{\prime}|$, on the fault control point. For the phased protocol, reactivation would occur at 56 days (continuous line), while for the injection at a constant flow rate, the reactivation occurs at 31.6 days (dashed line). In panel (

**e**), we represent an optimized injection protocol that avoids fault reactivation. The dashed line shows the constant flow rate required to inject the same volume in the same duration. The change in the dimensionless Coulomb failure function, $CFF/|{\sigma}^{\prime}|$, with time for both injection protocols is depicted (

**f**). The fault reactivates after 31.5 days of injection when water is injected at a constant flow rate, whereas the fault does not reactivate with the optimized protocol.

**Figure 3.**Results of the pore pressure increase (

**a**) and the temperature increase (

**b**) around the injection well at the moment of fault reactivation in the model. We show how the cooling caused by the injection has hardly spread around the well, contrary to what happens with the pressure, which spreads to areas further away from the well.

**Figure 4.**Results of the seismic rupture for the Basel EGS reservoir. We show the results for the injection protocol registered in 2006 (Figure 4b). In panel (

**a**), we represent the evolution of the pore pressure along the fault during the rupture. The fronts of undrained pressures spread to both sides of the fault almost symmetrically. In panel (

**b**), we show the results of the slip velocity for the same time steps. In panel (

**c**), we plot the results of the relative slip between the walls of the fault at the same time steps. We compute the seismic moment and estimate the earthquake magnitude with the relative slip between the walls of the fault.

**Figure 5.**Changes in permeability on the fault zone at several time steps during the rupture. In panel (

**a**), we show the fault permeability ${k}_{fr}$ for several time steps. In panel (

**b**), we plot the value of the coefficient ${k}_{T,fr}$ that controls the transversal flow on the fault.

**Figure 6.**Evolution of the temperature in the reservoir for a long-term operation scenario. We show the simulated injection and production scheme, so the injection flow rate is 100 l/s at 70 °C and the production flow rate is 84 l/s. We include temperature results for 5, 10, and 30 years, showing that heat transport initially occurs by advection in the vicinity of the fault and later extends to wider areas around the injection well.

**Figure 7.**Averaged temperature at the extraction well for different fault apertures. The dashed line shows the usual threshold of water temperature to produce electric energy. This threshold is reached sooner or later depending on the fault aperture.

**Table 1.**Summary of Basel EGS reservoir model parameters, taken from [6].

Parameter | Value | Unit | Description |
---|---|---|---|

E | 20 | GPa | Young modulus of the rock |

$\nu $ | 0.25 | – | Poisson ratio of the rock |

$\rho $ | 2700 | kg/m${}^{3}$ | Rock density |

${\sigma}_{y}$ | 86 | MPa | Maximum principal stress |

${\sigma}_{x}$ | 195 | MPa | Minimum principal stress |

${\rho}_{f}$ | 1000 | kg/m${}^{3}$ | Fluid density |

${\eta}_{f}$ | 0.00024 | Pa·s | Fluid viscosity |

${\chi}_{f}$ | 4 × 10${}^{-10}$ | Pa${}^{-1}$ | Fluid compressibility |

k | 10${}^{-15}$ | m${}^{2}$ | Porous matrix permeability |

$\varphi $ | 0.1 | – | Porosity |

${\kappa}_{s}$ | 2.4 | W/(m·K) | Solid thermal conductivity |

${\kappa}_{f}$ | 0.6 | W/(m·K) | Fluid thermal conductivity |

${c}_{s}$ | 800 | J/(kg·K) | Solid heat capacity |

${c}_{f}$ | 4200 | J/(kg·K) | Fluid heat capacity |

T${}_{0}$ | 473.15 | K | Natural temperature |

${\alpha}_{B}$ | 1 | – | Biot coefficient |

${\alpha}_{T}$ | 8 × 10${}^{-6}$ | K${}^{-1}$ | Thermal expansion coefficient |

${\mu}_{0}$ | 0.55 | – | Friction coefficient |

a | 0.005 | – | Direct effect parameter |

b | 0.03 | – | Friction evolution parameter |

${D}_{c}$ | 0.0007 | m | Characteristic slip distance |

${V}^{*}$ | 10${}^{-9}$ | m/s | Reference slip velocity |

$\alpha $ | 0.2 | – | Linker–Dieterich stressing rate coefficient |

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**MDPI and ACS Style**

Andrés, S.; Santillán, D.; Mosquera, J.C.; Cueto-Felgueroso, L. Hydraulic Stimulation of Geothermal Reservoirs: Numerical Simulation of Induced Seismicity and Thermal Decline. *Water* **2022**, *14*, 3697.
https://doi.org/10.3390/w14223697

**AMA Style**

Andrés S, Santillán D, Mosquera JC, Cueto-Felgueroso L. Hydraulic Stimulation of Geothermal Reservoirs: Numerical Simulation of Induced Seismicity and Thermal Decline. *Water*. 2022; 14(22):3697.
https://doi.org/10.3390/w14223697

**Chicago/Turabian Style**

Andrés, Sandro, David Santillán, Juan Carlos Mosquera, and Luis Cueto-Felgueroso. 2022. "Hydraulic Stimulation of Geothermal Reservoirs: Numerical Simulation of Induced Seismicity and Thermal Decline" *Water* 14, no. 22: 3697.
https://doi.org/10.3390/w14223697