# Hydro-Thermal Modeling for Geothermal Energy Extraction from Soultz-sous-Forêts, France

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{−1}making the Soultz-sous-Forêts site ideal for geothermal energy extraction [15]. Figure 1 shows that the temperature around the wellbores of Soultz-sous-Forêts is higher than that of the surrounding region. Free convection along the major faults [16,17,18] is the primary reason causing the increased thermal gradients. For depths greater than 3700 m, the geothermal gradient becomes 10 K/km.

## 2. Methodology

#### 2.1. Reservoir Flow Modeling

^{2}[17] was assigned at the bottom boundary of the domain. All other exterior boundaries of the modeled domain are defined as no flow for both fluid and heat transmission. Because the weather conditions of Soultz are not available, the monthly averaged daily weather fluctuation of Strasbourg, France was used for this study. Strasbourg is approximately 40 km SSE from the Soultz geothermal site. All fractures within the domain are regarded as internal boundaries, implicitly considering the mass and energy exchange between porous media and fractures or fault zones. In the injection well, the diameter of the well is small and can, as a simplification, be represented by a line.

#### 2.2. Wellbore Leakage Modeling

^{−1}K

^{−1}, ${L}_{R}=0.00001$ m

^{−1}, and $\Phi =0.00345$ Km

^{−1}, respectively. Here, ${L}_{R}$ and $\Phi $ accounts for the casing properties, cement properties and their thicknesses.

## 3. Results and Discussions

#### 3.1. Benchmarking

#### 3.2. Validation with Operational Data

_{effective}=T

_{simulation}+ 0.2 × ambient temperature) and (b) 50% impact of ambient temperature (T

_{effective}=T

_{simulation}+ 0.5 × ambient temperature).

#### 3.3. Long-Term Operational Behavior

^{3}/h [40]. Therefore, two scenarios were considered, A and B, for different injection temperatures. For the remaining operational period, scenario A considers four different fluid injection temperatures at the injection wellhead (70, 60, 50 and 40 °C). The fluid injection rates are 13.3 and 11 L/s for GPK-3 and GPK-4, respectively, and the production fluid rate of GPK-2 is 24.3 L/s for the remaining operational period. In Scenario B, the injection rates after 1163 days are 19.6 and 9.7 L/s for GPK-3 and GPK-4, respectively, and the production rate of GPK-2 is 29.3 L/s; the same four injection wellhead temperatures as for scenario A were considered: 70, 60, 50 and 40 °C. These values of the injection and production rates are the operational requirements requested by our industrial partner.

#### 3.4. Uncertainties

#### 3.5. Sensitivity Analysis of Hydrothermal Uncertainties

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Temperature distribution at 2 km depth TVD in the Upper Rhine Graben [19].

**Figure 2.**Geothermal gradient at the Soultz-sous-Forêts site. Here, an anomaly in temperature is observable in the top 3 km section or in the sedimentary layer. We assumed 10 °C temperature at the surface to calculate this geothermal gradient. The initial data up to the depth of 5.1 km is measured alongside GPK-2 by Pribnow and Schellschmidt [25] and further modified by Rolin et al. [13].

**Figure 3.**Geometry for numerical modeling of Soultz-sous-Forêts geothermal site. Elliptic geometries are faults listed in Table 1 (blue color). Open hole sections of the injection wells are denoted by green colors (GPK-3 and GPK-4) whereas open hole section of the production well is denoted by the dark red color (GPK-2). The leakage zone of the production well is denoted by light red whereas the leakage zone of the GPK-3 is shown by the yellow color.

**Figure 6.**Comparison of the numerical solution with the analytical temperature distribution along the fracture length.

**Figure 7.**Injection schedule at (

**a**) GPK-3 and (

**b**) GPK-4 and (

**c**) production schedule at production well GPK-2 for 1163 days of operation from June 2016 to September 2019. Here, the blue lines are the actual injection and production rates. The red dash lines indicate no operation period.

**Figure 8.**Difference between operational data from June 2016 to September 2019 and the data obtained from the numerical model.

**Figure 9.**Comparison between scenarios A and B for (

**a**,

**b**) temperature along the injection well GPK-3, (

**c**,

**d**) temperature along the injection well GPK-4, and (

**e**,

**f**) wellhead temperature at the production well GPK-2.

**Figure 10.**Comparison of temperature distribution (in SI units) in the fractures for scenarios A and B at time (

**a**,

**b**) 0 year, (

**c**,

**d**) 50 years and (

**e**,

**f**) 100 years. Here, $\Delta T$ is the temperature drop in the reservoir from the initial state.

**Figure 11.**Sensitivity analysis for 10 parameters affecting the hydro-thermal processes at Soultz-sous-Forêts for (

**a**) matrix hydraulic conductivity, (

**b**) heat flux from the bottom boundary, (

**c**) matrix specific heat capacity, (

**d**) hydraulic conductivity of faults (here ${K}_{f,0}$ is the fault zone hydraulic conductivity as given in Table 2), (

**e**) porosity of fault zone, (

**f**) leakage contribution to the total fluid flow, (

**g**) matrix porosity, (

**h**) matrix thermal conductivity, (

**i**) fault thickness (here ${F}_{0}$ is the fault thickness as given in Table 2), and (

**j**) thermal conductivity of the fault zone.

Parameter | Unit | Upper Sediment | Buntsandstein | Granite |
---|---|---|---|---|

Hydraulic conductivity | m·s^{−1} | 5 × 10^{−8} | 1 × 10^{−8} | 9 × 10^{−9} |

Specific storage | 1·m^{−1} | 8 × 10^{−7} | 5 × 10^{−7} | 1.75 × 10^{−8} |

Porosity | - | 0.1 | 0.03 | 0.03 |

Thermal conductivity | W·m^{−1}·K^{−1} | 2.8 | 2.5 | 2.5 |

Thermal capacity | J·m^{−3} K^{−1}· | 2 × 10^{6} | 3.2 × 10^{6} | 2.9 × 10^{6} |

Heat production | W·m^{−3} | 5 × 10^{−7} | 5 × 10^{−7} | 3 × 10^{−7} |

**Table 2.**Fault parameters [13].

Parameter | Unit | FZ1800 | FZ2120 | FZ4760 | FZ4770 | FZ4925 |
---|---|---|---|---|---|---|

$\mathrm{Hydraulic}\mathrm{conductivity}({\mathrm{K}}_{\mathrm{f},0}$) | m·s^{−1} | 6.08 × 10^{−6} | 1.7 × 10^{−5} | 0.05 | 2 × 10^{−5} | 6.3 × 10^{−5} |

Specific storage | 1·m^{−1} | 2 × 10^{−6} | 2 × 10^{−6} | 2 × 10^{−6} | 2 × 10^{−6} | 2 × 10^{−6} |

Porosity | - | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 |

Thermal conductivity | W·m^{−1}·K^{−1} | 2.5 | 2.5 | 2.5 | 2.5 | 2.5 |

Thermal capacity | J·m^{−3} K^{−1} | 2.9 × 10^{−6} | 2.9 × 10^{−6} | 2.9 × 10^{−6} | 2.9 × 10^{−6} | 2.9 × 10^{−6} |

$\mathrm{Thickness}({\mathrm{F}}_{0}$) | m | 12 | 15 | 8 | 15 | 1 |

Heat production | W·m^{−3} | 3 × 10^{6} | 3 × 10^{6} | 3 × 10^{6} | 3 × 10^{6} | 3 × 10^{6} |

Transmissivity | m^{2}·s^{−1} | 7.3 × 10^{−5} | 2.55 × 10^{−4} | 0.4 | 3 × 10^{−4} | 6.3 × 10^{−5} |

Parameter | Base Case Value | 1st Assumed Value | 2nd Assumed Value |
---|---|---|---|

Matrix hydraulic conductivity | $9\times {10}^{-9}$ m/s | $0.5\times 9\times {10}^{-9}$ m/s | $2\times 9\times {10}^{-9}$ m/s |

Heat flux from the bottom boundary | 0.07 W/m^{2} | 0.1 W/m^{2} | 0.15 W/m^{2} |

Matrix specific heat capacity | 1115 J/kg/K | 1090 J/kg/K | 1140 J/kg/K |

Hydraulic conductivity of fault zone (see Table 2) | ${K}_{f,0}$ m/s | $0.5{K}_{f,0}$ m/s | $2{K}_{f,0}$ m/s |

Porosity of the fault zone | 0.1 | 0.05 | 0.2 |

Wellbore leakage fraction | 65% | 60% | 70% |

Matrix porosity | 0.03 | 0.01 | 0.05 |

Thermal conductivity of the matrix | 2.5 W/m/K | 2 W/m/K | 3 W/m/K |

Fault thickness (see Table 2) | ${F}_{0}$ m | $0.5{F}_{0}$ m | $2{F}_{0}$ m |

Thermal conductivity of the fault zone | 2.5 W/m/K | 2 W/m/K | 3 W/m/K |

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**MDPI and ACS Style**

Mahmoodpour, S.; Singh, M.; Turan, A.; Bär, K.; Sass, I.
Hydro-Thermal Modeling for Geothermal Energy Extraction from Soultz-sous-Forêts, France. *Geosciences* **2021**, *11*, 464.
https://doi.org/10.3390/geosciences11110464

**AMA Style**

Mahmoodpour S, Singh M, Turan A, Bär K, Sass I.
Hydro-Thermal Modeling for Geothermal Energy Extraction from Soultz-sous-Forêts, France. *Geosciences*. 2021; 11(11):464.
https://doi.org/10.3390/geosciences11110464

**Chicago/Turabian Style**

Mahmoodpour, Saeed, Mrityunjay Singh, Aysegul Turan, Kristian Bär, and Ingo Sass.
2021. "Hydro-Thermal Modeling for Geothermal Energy Extraction from Soultz-sous-Forêts, France" *Geosciences* 11, no. 11: 464.
https://doi.org/10.3390/geosciences11110464