# Thermo-Poroelastic Analysis of Induced Seismicity at the Basel Enhanced Geothermal System

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Frictional Strength and Resistance of Faults

#### Rate-and-State Models for Interfaces

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

#### 2.3. Case Study: The Deep Heat Mining Project in Basel, Switzerland

#### 2.4. The Basel 3D Model

## 3. Results and Discussion

#### 3.1. Calibration

#### 3.2. Fault Reactivation

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Scheme of the 3D Basel EGS model. In (

**a**) we show the domain that is a 1.5 km${}^{3}$ cube with the fault plane oriented 10$\xb0$ with respect to the x-axis and dip 80$\xb0$ to the SW. The domain is located between 4050 and 5550 m depth, while the injection section of the Basel-1 well extends from 4629 to 5000 m depth. In (

**b**) we plot the injection protocol (left vertical axis) and injection pressure (right vertical axis) measured at the Basel-1 well, obtained from [56].

**Figure 2.**3D finite element mesh and mechanical boundary conditions applied. At the exterior boundaries with no stresses applied, we impede the displacement in its normal direction.

**Figure 3.**3D model calibration results. In (

**a**) we show the injection flow rate pattern used in the model (red line) that is similar to the real injection protocol from the Basel-1 data (blue line). In (

**b**) we plot the computed injection pressure (red line) and the values measured in 2006 (blue line).

**Figure 4.**3D model results at the horizontal reference plane. In (

**a**) (left) we show the reference plane inside the model, the fault plane, and the injection well. The increase of pore pressure (right) in that plane shows the results of the pore pressure increase caused by the injection at the instant of fault reactivation (among 26 MPa). In (

**b**) we display the increment of temperature due to the injection at the reference plane, with an inset that zooms the surroundings of the injection well and shows that the temperature diffusion is much slower than pressure propagation. In (

**c**) we show the results of the pore pressure increase at the fault plane. The vertical axis of the image corresponds to the maximum slope line of the fault plane and the horizontal axis corresponds to a horizontal direction in the 3D model deviated 10$\xb0$ with respect to the x-axis.

**Figure 5.**3D model results on the fault plane 5.5 days after the onset of injection (the instant of fault reactivation). We display the increase in Coulomb Failure Function on the fault plane due to the injection $\Delta CFF$ = $\Delta \left(\mu \right|{\sigma}^{\prime}|-\tau )$ = $CFF\left(t\right)-CFF(t=0)$. The results show the fault weakening (red color, $\Delta CFF$ < 0) due to the injection of cold water.

**Figure 6.**Display of 3D model results at the 2D fault plane 5.5 days after the injection starting (the instant of fault reactivation). In (

**a**) we show the effective normal stress $|{\sigma}^{\prime}|$ (positive values of effective normal stresses are compressive). In (

**b**) we display the modulus of the shear stress $\tau $, in (

**c**) the friction coefficient $\mu $ obtained from the rate-and-state equations, and in (

**d**) the Coulomb Failure Function $CFF$.

**Figure 7.**Evolution of the friction variables at the fault control point. The blue line represents the evolution of the friction coefficient $\mu $ as derived from the rate-and-state equations. The green line plots the evolution of the ratio $\tau /|{\sigma}^{\prime}|$. The slopes of both curves are related to the different flow-rate levels of the injection protocol.

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 |

$Tec{t}_{max}$ | 1.6 | – | High tectonic ratio |

$Tec{t}_{min}$ | 0.7 | – | Low tectonic ratio |

${\sigma}_{h}$ | ${\sigma}_{v}\xb7$Tect | MPa | Confinement 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 media 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${}_{amb}$ | 293.15 | K | Ambient temperature |

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

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

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

c | 0 | MPa | Contact cohesion |

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 velocity |

$\alpha $ | 0.2 | – | Linker-Dieterich normal stress coefficient |

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**MDPI and ACS Style**

Andrés, S.; Santillán, D.; Mosquera, J.C.; Cueto-Felgueroso, L.
Thermo-Poroelastic Analysis of Induced Seismicity at the Basel Enhanced Geothermal System. *Sustainability* **2019**, *11*, 6904.
https://doi.org/10.3390/su11246904

**AMA Style**

Andrés S, Santillán D, Mosquera JC, Cueto-Felgueroso L.
Thermo-Poroelastic Analysis of Induced Seismicity at the Basel Enhanced Geothermal System. *Sustainability*. 2019; 11(24):6904.
https://doi.org/10.3390/su11246904

**Chicago/Turabian Style**

Andrés, Sandro, David Santillán, Juan Carlos Mosquera, and Luis Cueto-Felgueroso.
2019. "Thermo-Poroelastic Analysis of Induced Seismicity at the Basel Enhanced Geothermal System" *Sustainability* 11, no. 24: 6904.
https://doi.org/10.3390/su11246904