# Thermo-Hydro-Mechanical Coupled Modeling of In-Situ Behavior of the Full-Scale Heating Test in the Callovo-Oxfordian Claystone

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## Abstract

**:**

## 1. Introduction

## 2. Description of the ALC1604 Experiment

## 3. Numerical Method

#### 3.1. Governing Equations

#### 3.1.1. Hydraulic Processes

#### 3.1.2. Thermal Processes

#### 3.1.3. Mechanical Processes

#### 3.2. Numerical Coupling Method

## 4. Model Setup

#### 4.1. Conceptual Model, Geometry, and Spatial Discretization

#### 4.2. Initial and Boundary Conditions

#### 4.3. Model Parameters

^{−20}m

^{2}and 1.0 × 10

^{−20}m

^{2}, respectively. These values are based on the back-analysis of the field measured pore pressure evolution during the ALC1604 experiment test [5]. The values of porosity and permeability at zero stress are calculated from Equations (15) and (16) based on the current stress conditions. Moreover, the field excavation induces damage and fracturing around the gallery or tunnel (see Figure 8), which is named as excavation damage zone (EDZ) [35]. The EDZ has significant effects on fluid flow and transport properties in the low permeability COx claystone [5,36]. In our model, the artificial EDZ of 0.5 m thick around the ALC1604 cell is simply considered by increasing permeability to 1.0 × 10

^{−15}m

^{2}[4]. The specific heat capacity of the solid particles is 800 J/kg/K [4,5]. The values of thermal conductivity parallel and vertical to the bedding are estimated at approximately 2.1 W/m/K and 1.3 W/m/K, respectively [4,5]. In addition, the ALC1604 cell is modeled as a porous medium, while with high porosity of 0.99 and high permeability of 1.0 × 10

^{−15}m

^{2}, respectively [19].

#### 4.4. Operation Stages

## 5. Results and Discussion

#### 5.1. Thermal Response

#### 5.2. Hydraulic Response

^{−20}m

^{2}) means the excess pore pressure cannot dissipate rapidly. This promotes the significant growth of the excess pore pressure in the COx formation. As a result, the formation water continues to flow into the cell induced by pressure gradient in the excavation and heating stages, resulting in increased water saturation in the cell (Figure 13).

#### 5.3. Mechanical Response

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

${M}^{\kappa}$ | Mass accumulation of component $\kappa $, kg/m^{3} |

${F}^{\kappa}$ | Mass flux of component $\kappa $, kg/(m^{2}·s) |

${q}^{\kappa}$ | Sink/source of component $\kappa $, kg/(m^{3}·s) |

${M}^{\theta}$ | Energy accumulation, J/m^{3} |

${F}^{\theta}$ | Energy flux, J/(m^{2}·s) |

${q}^{\theta}$ | Sink/source of heat, J/(m^{3}·s) |

$t$ | Time, s |

$\varphi $ | Porosity |

${\varphi}_{r}$ | Residual porosity with high stress |

${\varphi}_{0}$ | Porosity at aero stress |

${S}_{\beta}$ | Saturation of phase $\beta $ |

${\rho}_{\beta}$ | Density of phase $\beta $, kg/m^{3} |

${X}_{\beta}^{\kappa}$ | Mass fraction of component $\kappa $ in phase $\beta $ |

${J}_{\beta}^{\kappa}$ | Mass diffusion of component $\kappa $ in phase $\beta $, kg/(m^{2}·s) |

$k$ | Permeability, m^{2} |

${k}_{0}$ | Permeability at zero stress, m^{2} |

${k}_{r\beta}$ | Relative permeability of phase $\beta $ |

${\mu}_{\beta}$ | Viscosity of phase $\beta $, Pa·s |

${P}_{\beta}$ | Pressure of phase $\beta $, Pa |

${P}_{c}$ | Capillary pressure, Pa |

$g$ | Gravitational acceleration vector, m/s^{2} |

$b$ | Klinkenberg factor, Pa |

${\tau}_{\beta}$ | Medium tortuosity of phase $\beta $ |

${D}_{\beta}^{\kappa}$ | Molecular diffusion coefficient of component $\kappa $ in phase $\beta $, m^{2}/s |

${\rho}_{R}$ | Density of rock grain, kg/m^{3} |

${C}_{R}$ | Specific heat of rock grain, J/(kg·°C) |

$T$ | Temperature, °C |

${U}_{\beta}$ | Internal energy of phase $\beta $, J/kg |

${Q}_{d}$ | Hydrate reaction heat, J |

${\lambda}_{\theta}$ | Average thermal conductivity, W/(m·K) |

${h}_{\beta}$ | Specific enthalpy of phase $\beta $, J/kg |

$\beta $ | Phase, $\beta =A,G$ is aqueous and gasous, respectively |

$\kappa $ | Component, $\kappa =w,i,d$ is water, salt and air, respectively |

$\mathsf{\sigma}$ | Total stress, Pa |

${\sigma}^{\prime}$ | Effective stress, Pa |

${\sigma}_{m}^{\prime}$ | The mean effective stress, Pa |

$\mathsf{\epsilon}$ | Strain |

$w$ | Displacement, m |

$E$ | Elastic modulus, Pa |

$G$ | Shear modulus, Pa |

$K$ | Bulk modulus, Pa |

$\upsilon $ | Poisson’s ratio |

${\alpha}_{\mathrm{B}}$ | Biot coefficient |

${\beta}_{T}$ | Linear thermal expansion coefficient, 1/°C |

$F$ | Body force, Pa |

$a$ | The experimental coefficient for porosity changes |

$b$ | The experimental coefficient for permeability changes |

$D$ | The given rock functions |

$tr$ | The transpose of a tensor |

$\mathsf{\Delta}$ | The increment operator |

## References

- Kim, J.S.; Kwon, S.K.; Sanchez, M.; Cho, G.C. Geological storage of high level nuclear waste. KSCE J. Civ. Eng.
**2011**, 15, 721–737. [Google Scholar] [CrossRef] - Murshed, M.; Saboori, B.; Madaleno, M.; Wang, H.; Doğan, B. Exploring the nexuses between nuclear energy, renewable energy, and carbon dioxide emissions: The role of economic complexity in the G7 countries. Renew. Energy
**2022**, 190, 664–674. [Google Scholar] [CrossRef] - Çakar, N.D.; Erdoğan, S.; Gedikli, A.; Öncü, M.A. Nuclear energy consumption, nuclear fusion reactors and environmental quality: The case of G7 countries. Nucl. Eng. Technol.
**2022**, 54, 1301–1311. [Google Scholar] [CrossRef] - Bumbieler, F.; Plua, C.; Tourchi, S.; Minh-Ngoc, V.; Vaunat, J.; Gens, A.; Armand, G. Feasibility of constructing a full-scale radioactive high-level waste disposal cell and characterization of its thermo-hydro-mechanical behavior. Int. J. Rock Mech. Min. Sci.
**2021**, 137, 104555. [Google Scholar] [CrossRef] - Tourchi, S.; Vaunat, J.; Gens, A.; Bumbieler, F.; Vu, M.N.; Armand, G. A full-scale in situ heating test in Callovo-Oxfordian claystone: Observations, analysis and interpretation. Comput. Geotech.
**2021**, 133, 104045. [Google Scholar] [CrossRef] - Lee, C.; Lee, J.; Park, S.; Kwon, S.; Cho, W.-J.; Kim, G.Y. Numerical analysis of coupled thermo-hydro-mechanical behavior in single-and multi-layer repository concepts for high-level radioactive waste disposal. Tunn. Undergr. Space Technol.
**2020**, 103, 103452. [Google Scholar] [CrossRef] - Armand, G.; Bumbieler, F.; Conil, N.; de la Vaissiere, R.; Bosgiraud, J.M.; Vu, M.N. Main outcomes from in situ thermo-hydro-mechanical experiments programme to demonstrate feasibility of radioactive high-level waste disposal in the Callovo-Oxfordian claystone. J. Rock Mech. Geotech. Eng.
**2017**, 9, 415–427. [Google Scholar] [CrossRef] - Jia, Y.; Bian, H.B.; Duveau, G.; Su, K.; Shao, J.F. Numerical modelling of in situ behaviour of the Callovo-Oxfordian argillite subjected to the thermal loading. Eng. Geol.
**2009**, 109, 262–272. [Google Scholar] [CrossRef] - Carter, J.; Luptak, A.; Gastelum, J.; Stockman, C.; Miller, A. Fuel Cycle Potential Waste Inventory for Disposition; U.S. Department of Energy, Office of Used Fuel Disposition: Washington, DC, USA, 2012.
- Wang, W.; Shao, H.; Nagel, T.; Kolditz, O. Analysis of coupled thermal-hydro-mechanical processes during small scale in situ heater experiment in Callovo-Oxfordian clay rock introducing a failure-index permeability model. Int. J. Rock Mech. Min. Sci.
**2021**, 142, 104683. [Google Scholar] [CrossRef] - Armand, G.; Conil, N.; Talandier, J.; Seyedi, D.M. Fundamental aspects of the hydromechanical behaviour of Callovo-Oxfordian claystone: From experimental studies to model calibration and validation. Comput. Geotech.
**2017**, 85, 277–286. [Google Scholar] [CrossRef] - Conil, N.; Vitel, M.; Plua, C.; Vu, M.N.; Seyedi, D.; Armand, G. In Situ Investigation of the THM Behavior of the Callovo-Oxfordian Claystone. Rock Mech. Rock Eng.
**2020**, 53, 2747–2769. [Google Scholar] [CrossRef] - Ma, Y.-S.; Chen, W.-Z.; Yu, H.-D.; Gong, Z.; Li, X.-L. Variation of the hydraulic conductivity of Boom Clay under various thermal-hydro-mechanical conditions. Eng. Geol.
**2016**, 212, 35–43. [Google Scholar] [CrossRef][Green Version] - Ma, Y.-S.; Chen, W.-Z.; Gong, Z.; Yu, H.-D.; Li, F.-F.; Li, X.-L. Coupled thermo-hydro-mechanical anisotropy characteristics of clay Based on the ATLAS III in situ heating test. Rock Soil Mech.
**2018**, 39, 426–436. [Google Scholar] [CrossRef] - Chen, W.Z.; Ma, Y.S.; Yu, H.D.; Li, F.F.; Li, X.L.; Sillen, X. Effects of temperature and thermally-induced microstructure change on hydraulic conductivity of Boom Clay. J. Rock Mech. Geotech. Eng.
**2017**, 9, 383–395. [Google Scholar] [CrossRef] - Mueller, H.R.; Garitte, B.; Vogt, T.; Kohler, S.; Sakaki, T.; Weber, H.; Spillmann, T.; Hertrich, M.; Becker, J.K.; Giroud, N.; et al. Implementation of the full-scale emplacement (FE) experiment at the Mont Terri rock laboratory. Swiss J. Geosci.
**2017**, 110, 287–306. [Google Scholar] [CrossRef][Green Version] - Marschall, P.; Giger, S.; De la Vassiere, R.; Shao, H.; Leung, H.; Nussbaum, C.; Trick, T.; Lanyon, B.; Senger, R.; Lisjak, A.; et al. Hydro-mechanical evolution of the EDZ as transport path for radionuclides and gas: Insights from the Mont Terri rock laboratory (Switzerland). Swiss J. Geosci.
**2017**, 110, 173–194. [Google Scholar] [CrossRef] - Bossart, P.; Jaeggi, D.; Nussbaum, C. Experiments on thermo-hydro-mechanical behaviour of Opalinus Clay at Mont Terri rock laboratory, Switzerland. J. Rock Mech. Geotech. Eng.
**2017**, 9, 502–510. [Google Scholar] [CrossRef] - Seyedi, D.M.; Plúa, C.; Vitel, M.; Armand, G.; Rutqvist, J.; Birkholzer, J.; Xu, H.; Guo, R.; Thatcher, K.E.; Bond, A.E.; et al. Upscaling THM modeling from small-scale to full-scale in-situ experiments in the Callovo-Oxfordian claystone. Int. J. Rock Mech. Min. Sci.
**2021**, 144, 104582. [Google Scholar] [CrossRef] - Xu, H.; Rutqvist, J.; Plúa, C.; Armand, G.; Birkholzer, J. Modeling of thermal pressurization in tight claystone using sequential THM coupling: Benchmarking and validation against in-situ heating experiments in COx claystone. Tunn. Undergr. Space Technol.
**2020**, 103, 103428. [Google Scholar] [CrossRef] - Plúa, C.; Vu, M.N.; Armand, G.; Rutqvist, J.; Kolditz, O. A reliable numerical analysis for large-scale modelling of a high-level radioactive waste repository in the Callovo-Oxfordian claystone. Int. J. Rock Mech. Min. Sci.
**2021**, 140, 104574. [Google Scholar] [CrossRef] - Pruess, K.; Oldenburg, C.M.; Moridis, G.J. TOUGH2 User’s Guide Version 2; Lawrence Berkeley National Lab. (LBNL): Berkeley, CA, USA, 1999; 204p. [Google Scholar]
- Wileveau, Y.; Cornet, F.H.; Desroches, J.; Blumling, P. Complete in situ stress determination in an argillite sedimentary formation. Phys. Chem. Earth
**2007**, 32, 866–878. [Google Scholar] [CrossRef] - Lei, H.; Xu, T.; Jin, G. TOUGH2Biot-A simulator for coupled thermal-hydrodynamic-mechanical processes in subsurface flow systems: Application to CO
_{2}geological storage and geothermal development. Comput. Geosci.**2015**, 77, 8–19. [Google Scholar] [CrossRef] - Klinkenberg, L.J. The Permeability of Porous Media To Liquids and Gases. In Proceedings of the Drilling and Production Practice, New York, NY, USA, 1 January 1941; pp. 200–213. [Google Scholar]
- Moridis, G.J. User’s Manual for the Hydrate v1.5 Option of TOUGH+ v1.5: A Code for the Simulation of System Behavior in Hydrate-Bearing Geologic Media; Lawrence Berkeley National Lab. (LBNL): Berkeley, CA, USA, 2014. [Google Scholar]
- Stauffer, P.H.; Vrugt, J.A.; Turin, H.J.; Gable, C.W.; Soll, W.E. Untangling Diffusion from Advection in Unsaturated Porous Media: Experimental Data, Modeling, and Parameter Uncertainty. Vadose Zone J.
**2009**, 8, 510–522. [Google Scholar] [CrossRef][Green Version] - Stauffer, P.H.; Lewis, K.C.; Stein, J.S.; Travis, B.J.; Lichtner, P.; Zyvoloski, G. Joule–Thomson Effects on the Flow of Liquid Water. Transp. Porous Media
**2014**, 105, 471–485. [Google Scholar] [CrossRef] - Jin, G.; Lei, H.; Xu, T.; Xin, X.; Yuan, Y.; Xia, Y.; Juo, J. Simulated geomechanical responses to marine methane hydrate recovery using horizontal wells in the Shenhu area, South China Sea. Mar. Pet. Geol.
**2018**, 92, 424–436. [Google Scholar] [CrossRef] - Rutqvist, J.; Moridis, G.J. Numerical Studies on the Geomechanical Stability of Hydrate-Bearing Sediments. Spe J.
**2009**, 14, 267–282. [Google Scholar] [CrossRef] - Rutqvist, J.; Wu, Y.S.; Tsang, C.F.; Bodvarsson, G. A modeling approach for analysis of coupled multiphase fluid flow, heat transfer, and deformation in fractured porous rock. Int. J. Rock Mech. Min. Sci.
**2002**, 39, 429–442. [Google Scholar] [CrossRef] - Leverett, M.C. Capillary Behaviour in Porous Solids. Trans. AIME
**1941**, 142, 151–169. [Google Scholar] [CrossRef] - Yuan, Y.; Xu, T.; Jin, C.; Zhu, H.; Gong, Y.; Wang, F. Multiphase flow and mechanical behaviors induced by gas production from clayey-silt hydrate reservoirs using horizontal well. J. Clean. Prod.
**2021**, 328, 129578. [Google Scholar] [CrossRef] - Robinet, J.C.; Paul, S.; Coelho, D.; Parneix, J.C.; Pret, D.; Sammartino, S.; Boller, E.; Altmann, S. Effects of mineral distribution at mesoscopic scale on solute diffusion in a clay-rich rock: Example of the Callovo-Oxfordian mudstone (Bure, France). Water Resour. Res.
**2012**, 48, 5554. [Google Scholar] [CrossRef] - Tsang, C.F.; Bernier, F.; Davies, C. Geohydromechanical processes in the Excavation Damaged Zone in crystalline rock, rock salt, and indurated and plastic clays—In the context of radioactive waste disposal. Int. J. Rock Mech. Min. Sci.
**2005**, 42, 109–125. [Google Scholar] [CrossRef] - Armand, G.; Leveau, F.; Nussbaum, C. Geometry and Properties of the Excavation-Induced Fractures at the Meuse/Haute-Marne URL Drifts. Rock Mech. Rock Eng.
**2014**, 47, 21–41. [Google Scholar] [CrossRef] - Moridis, G.J.; Freeman, C.M. The RealGas and RealGasH2O options of the TOUGH+ code for the simulation of coupled fluid and heat flow in tight/shale gas systems. Comput. Geosci.
**2014**, 65, 56–71. [Google Scholar] [CrossRef][Green Version] - Mánica, M.; Gens, A.; Vaunat, J.; Ruiz, D.F. A time-dependent anisotropic model for argillaceous rocks. Application to an underground excavation in Callovo-Oxfordian claystone. Comput. Geotech.
**2017**, 85, 341–350. [Google Scholar] [CrossRef]

**Figure 3.**Locations of monitor boreholes and observation points around the ALC1604 cell. Reprinted from [5] with permission from Elsevier.

**Figure 4.**Longitudinal view of the ALC1604 cell. Reprinted from [5] with permission from Elsevier.

**Figure 7.**(

**a**) The numerical grids used in the 2D simulation and (

**b**) the distribution of monitoring boreholes surrounding the Heater 3.

**Figure 8.**The observed fractures around the micro-tunnel in COx claystone induced by excavation. Reprinted from [5] with permission from Elsevier.

**Figure 9.**Casing temperature evolution obtained by numerical simulation in comparison with the measurements.

**Figure 10.**Comparison of temperature evolution between the measurements and numerical results at sensors in three monitoring boreholes.

**Figure 11.**Spatial distributions of model predicted temperatures at (

**a**) 496.5 days, (

**b**) 938.5 days, (

**c**) 1668.5 days, (

**d**) 2763.5 days, (

**e**) 3128.5 days, and (

**f**) 4588.5 days.

**Figure 12.**Comparison of pore pressure evolution between the measurements and numerical results at sensors in three monitoring boreholes.

**Figure 14.**Spatial distributions of model predicted pore pressure at (

**a**) 496.5 days, (

**b**) 938.5 days, (

**c**) 1668.5 days, (

**d**) 2763.5 days, (

**e**) 3128.5 days, and (

**f**) 4588.5 days.

**Figure 15.**Temporal evolutions of the total stresses (${\sigma}_{1}$ and ${\sigma}_{3}$) and effective stresses (${\sigma}_{1}^{\prime}$ and ${\sigma}_{3}^{\prime}$) at (

**a**) 1.0 m and (

**b**) 5.0 m away from the ALC1604 cell along the bedding direction.

**Figure 16.**Spatial distributions of model predicted effective stress in Z direction at (

**a**) 496.5 days, (

**b**) 938.5 days, (

**c**) 1668.5 days, (

**d**) 2763.5 days, (

**e**) 3128.5 days, and (

**f**) 4588.5 days.

**Figure 17.**Temporal evolution of vertical deformation at the top of the ALC1604 cell, and also shows spatial distributions of vertical deformation after (

**a**) excavation, (

**b**) heating, and (

**c**) cooling stage.

**Figure 18.**Spatial distributions of model predicted porosity at (

**a**) 938.5 days, (

**b**) 2763.5 days, (

**c**) 4588.5 days, and permeability at (

**d**) 938.5 days, (

**e**) 2763.5 days, and (

**f**) 4588.5 days.

**Table 1.**The main petrophysical, hydraulic, and thermal parameters of the COx claystone used in the simulations.

Properties | Parameters | Orientation * | Value | Reference |
---|---|---|---|---|

Petrophysical | Density (kg/m^{3}) | 2700 | [5,19] | |

Porosity (−) | 17.3% | [5,7,19] | ||

Residual porosity (−) | 0.9% | [31] | ||

Porosity at zero stress (−) | 26.9% | |||

Specific heat capacity of solid (J/kg/K) | 800 | [4,5] | ||

Solid compressibility (1/Pa) | 2.5 × 10^{−5} | [4,5] | ||

Hydraulic | Intrinsic permeability (m^{2}) | Parallel | 2.0 × 10^{−20} | [5] |

Perpendicular | 1.0 × 10^{−20} | [5] | ||

Permeability at zero stress (m^{2}) | Parallel | 2.0 × 10^{−}^{18} | ||

Perpendicular | 1.0 × 10^{−}^{18} | |||

Intrinsic permeability of EDZ (m^{2}) | Parallel | 2.0 × 10^{−15} | [4] | |

Perpendicular | 1.0 × 10^{−15} | [4] | ||

Biot’s coefficient (−) | 0.6 | [4,5] | ||

Klinkenberg factor (Pa) | 73,830.6 | [37] | ||

Thermal | Linear thermal expansion coefficient (1/K) | 1.4 × 10^{−5} | [4,5] | |

Thermal conductivity (W/m/K) | Parallel | 2.1 | [4,5] | |

Perpendicular | 1.3 | [4,5] | ||

Geothermal gradient (°C/m) | 0.04 | [19] |

Parameters | Value | Reference |
---|---|---|

Young’s modulus (MPa) | 5200 | [5,38] |

Poisson’s ratio (−) | 0.25 | [5,38] |

Friction angle (°) | 22.0 | [5,38] |

Cohesion (MPa) | 3.55 | [5,38] |

Exponent for Equation (15), a (1/Pa) | −5.0 × 10^{−8} | [31] |

Exponent for Equation (16), b (−) | 22.2 | [31] |

**Table 3.**Stages of in-situ test at the ALC1604 cell. Reprinted from [5] with permission from Elsevier.

Stage | Program | Date | Duration |
---|---|---|---|

1 | Microtunnel excavation | 23 October 2012 → 31 October 2012 | 2.5 days |

2 | Boreholes/instrumentation | 31 October 2012 → 30 January 2013 | 94 days |

3 | Heating test (30 W/m) | 30 January 2013 → 15 February 2013 | 16 days |

4 | Cooling | 15 February 2013 → 18 April 2013 | 61 days |

5 | Main heating stage (220 W/m) | 18 April 2013 → 6 February 2019 | 2120 days |

6 | First cooling phase (200 W/m) | 6 February 2019 → 8 April 2019 | 61 days |

7 | Second cooling phase (167 W/m) | 8 April 2019 → 11 June 2019 | 64 days |

8 | Final cooling phase (0 W/m) | 11 June 2019 → 4 August 2025 | ~6 years |

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**MDPI and ACS Style**

Yuan, Y.; Xu, T.; Gherardi, F.; Lei, H. Thermo-Hydro-Mechanical Coupled Modeling of In-Situ Behavior of the Full-Scale Heating Test in the Callovo-Oxfordian Claystone. *Energies* **2022**, *15*, 4089.
https://doi.org/10.3390/en15114089

**AMA Style**

Yuan Y, Xu T, Gherardi F, Lei H. Thermo-Hydro-Mechanical Coupled Modeling of In-Situ Behavior of the Full-Scale Heating Test in the Callovo-Oxfordian Claystone. *Energies*. 2022; 15(11):4089.
https://doi.org/10.3390/en15114089

**Chicago/Turabian Style**

Yuan, Yilong, Tianfu Xu, Fabrizio Gherardi, and Hongwu Lei. 2022. "Thermo-Hydro-Mechanical Coupled Modeling of In-Situ Behavior of the Full-Scale Heating Test in the Callovo-Oxfordian Claystone" *Energies* 15, no. 11: 4089.
https://doi.org/10.3390/en15114089