# 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

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**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