This paper is devoted to the study of the Thermo-Hydro-Mechanical (THM) responses of a porous rock with low permeability under thermal loading in the context of deep geological disposal of radioactive waste. To this aim, numerical simulations of a benchmark exercise of a hypothetical high-level radioactive waste (HLW) repository were performed. This benchmark exercise considered as a host formation the Callovo-Oxfordian claystone (COx), which has been selected for a deep geological disposal in France. Within the framework of the DECOVALEX-2019 project, five modelling teams (Andra, LBNL, NWMO, Quintessa, UFZ/BGR) adopted a thermo-poro-elastic approach and proposed different 3D representations of the HLW repository. The differences between the teams consisted mostly in the simplification of the geometrical model and the interpretation of the boundary conditions. Numerical results for temperature, pore pressure, and effective stress evolution in the far field (i.e., at the mid-distance of two HLW cells) were compared between the teams, to quantify the impact of modelling simplifications/assumptions for the assessment of the HLW repository. The THM behaviour of the COx formation in the near field (i.e., excavation damaged zone around the HLW cells) is not the objective of this study. Moreover, plane strain conditions were considered and evaluated in comparison to 3D modelling. Key parameters influencing the THM responses of the HLW repository were assessed by both mono- and multi-parametric analyses. Spatial variability analyses of THM parameters were also carried out to study the influence of the spatial correlation length on the Terzaghi effective stress and to estimate its probability distribution. The conclusions of this study provide reliable numerical techniques for modelling large-scale deep geological disposals and deduce the main behavior of the HLW repository.

The coupled Thermo-Hydro-Mechanical (THM) behavior of the Callovo-Oxfordian claystone (COx) is of great importance for the design and safety calculations of the high-level radioactive waste disposal project in this potential host rock in France. The heat emitted by the waste causes a pore pressure increase within the surrounding rock essentially due to the differential thermal expansion of the pore water and the solid skeleton. The low permeability of the COx and its relative rigidity inhibits the discharge of the induced pressure build-up. Moreover, thermal loading may provoke thermo-mechanical stresses within the formation due to mechanical confinement by the rigidity of the surrounding host rock. An important research program has been conducted by the French National Radioactive Waste Management Agency (Andra) since 2003 in order to investigate the THM response of the COx under thermal loading, through laboratory tests, in-situ experiments, model development and numerical modeling. Within Task E of the DECOVALEX-2019 project, five research teams investigated upscaling THM modeling from a small-scale in-situ experiment (TED) to a full-scale in-situ experiment (ALC). The upscaling modeling started with a verification test to validate the numerical codes. Then, an interpretative modeling of the TED experiment was performed to calibrate the THM parameters of the COx. Finally, the calibrated THM parameters were used for a blind prediction of the ALC experiment. The modeling teams each adopted a thermo-poro-elastic approach which yielded satisfactory results. The blind prediction of the temperature field showed an overestimation of less than 2 °C which was considered acceptable. On the other hand, pore pressure was well predicted only in the direction parallel to the bedding whereas the slow dissipation of the pore pressure in the direction perpendicular to the bedding was not captured by any of the modeling teams – which remains an open question of the present study.

Coupled thermal–hydrological–mechanical (THM) processes in the near field of deep geological repositories can influence several safety features of the engineered and geological barriers. Among those features are: the possibility of damage in the host rock, the time for re-saturation of the bentonite, and the perturbations in the hydraulic regime in both the rock and engineered seals. Within the international cooperative code-validation project DECOVALEX-2015, eight research teams developed models to simulate an in situ heater experiment, called HE-D, in Opalinus Clay at the Mont Terri Underground Research Laboratory in Switzerland. The models were developed from the theory of poroelasticity in order to simulate the coupled THM processes that prevailed during the experiment and thereby to characterize the in situ THM properties of Opalinus Clay. The modelling results for the evolution of temperature, pore water pressure, and deformation at different points are consistent among the research teams and compare favourably with the experimental data in terms of trends and absolute values. The models were able to reproduce the main physical processes of the experiment. In particular, most teams simulated temperature and thermally induced pore water pressure well, including spatial variations caused by inherent anisotropy due to bedding.

In a repository for radioactive waste hosted in a clay formation, hydrogen and other gases may be generated due to the corrosion of metallic materials under anoxic conditions, the radioactive decay of waste and the radiolysis of water. If the gas production rate exceeds the gas diffusion rate within the pores of the clay, a discrete gas phase will form and accumulate until its pressure becomes large enough to exceed the entry pressure of the surrounding material, at which point dilatant, advective flow of gas is expected to occur. The purpose of Task An under DECOVALEX-2019 is to better represent the processes governing the advective movement of gas in both low-permeability argillaceous repository host rocks and clay-based engineered barriers within numerical codes. In this paper special attention is given to the mechanisms controlling gas entry, flow and pathway sealing and their impact on the performance of the engineered clay barrier. Previous work suggests gas flow is accompanied by the creation of dilatant pathways whose properties change temporally and spatially within the medium. Thus, four new types of approaches have been developed: (i) standard two-phase flow models (continuous techniques) incorporating a range of different mechanical deformation behaviours, (ii) enhanced two-phase flow models in which fractures are embedded within a plastic material (continuous techniques) or incorporated into the model using a rigid-body-spring network (discrete approaches), (iii) a single-phase model incorporating a creep damage function in which only gas flow is considered, and (iv) a conceptual approach used to examine the chaotic nature of gas flow. The outputs from these different approaches are compared. This is an essential step as the choice of modelling approach strongly impacts the representation and prediction of gas flow in a future repository. In addition, experience gained through this task is of direct relevance to other clay-based engineering issues where immiscible gas flow is a consideration including hydrocarbon migration, carbon capture and storage, shale gas and landfill design. This paper summarises the outcomes of work in Task A conducted between May 2016 and May 2019 and provides a brief overview of the experimental data and a synthesis of the work of the participating modelling teams.

Process understanding and parameter identification using numerical methods based on experimental findings are key aspects of the international cooperative project DECOVALEX (DEvelopment of COupled models and their VALidation against Experiments http://www.decovalex.org). Comparing the long-term predictions from numerical models against experimental results increases confidence in the site selection and site evaluation process for a radioactive waste repository in deep geological formations. In the present phase of the project, DECOVALEX2015, eight research teams have developed and applied models for simulating the HE-E in situ heater experiment in the Opalinus Clay in the Mont Terri Rock Laboratory in Switzerland. The modelling task was divided into two study stages, related to prediction and interpretation of the experiment. A blind prediction of the HE-E experiment was performed based on calibrated parameter values for both the Opalinus Clay, which were derived from the modelling of another in situ experiment (HE-D experiment in the Mont Terri Rock Laboratory), and calibrated parameters for MX80 granular bentonite and a sand/bentonite mixture, which were derived from modelling of laboratory column tests. After publication of the HE-E experimental data, additional functions for coupled processes were analysed and considered in the different models. Moreover, parameter values were varied to interpret the measured temperature, relative humidity and pore pressure evolution. Generally, the temperature field can be well reproduced and is mainly controlled by thermal conductivity in the heat conduction process; the thermal conductivities of buffer materials and Opalinus Clay strongly depend on the degree of water saturation. The distribution of relative humidity is acceptable as it is reproduced by using both the Richards’ flow model and the multiphase flow model. Important here is to consider the vapour diffusion process. The analysis of the predictive and interpretative modelling confirms that the main processes in the system have been understood at least for the short-term experimental duration and captured using the models developed and associated parameters with respect to the thermal and hydraulic aspects in the high-level nuclear waste disposal in clay formations. The additional experimental results will help to increase confidence in the THM models and in process understanding.

A general description of the mathematical and numerical formulations used in modern numerical reactive transport codes relevant for subsurface environmental simulations is presented. The formulations are followed by short descriptions of commonly used and available subsurface simulators that consider continuum representations of flow, transport, and reactions in porous media. These formulations are applicable to most of the subsurface environmental benchmark problems included in this special issue. The list of codes described briefly here includes PHREEQC, HPx, PHT3D, OpenGeoSys (OGS), HYTEC, ORCHESTRA, TOUGHREACT, eSTOMP, HYDROGEOCHEM, CrunchFlow, MIN3P, and PFLOTRAN. The descriptions include a high-level list of capabilities for each of the codes, along with a selective list of applications that highlight their capabilities and historical development.

For the deep geological disposal of high-level radioactive waste in argillaceous rocks, the heat production of the waste is an important driver for thermal–hydraulic-mechanical (THM)-coupled processes. These THM processes influence the properties and conditions of the near field that in many repository designs contains bentonite as a clay buffer. One task in the DECOVALEX-2015 (DEvelopment of COupled models and their VALidation against Experiments) project was the modelling of a heated bentonite column (Villar et al. in Long-term THM tests reports: THM cells for the HE-E test: update of results until February 2014. Deliverable-no: D2.2-7.3. CIEMAT Technical Report IEMAT/DMA/2G210/03/2014, 2014) in preparation for the in situ heater experiment HE-E at the underground rock laboratory Mont Terri. DECOVALEX is an international cooperative project that focuses on the development and validation of mathematical models for simulating such coupled processes associated with disposal in deep geological repositories. Eight modelling teams developed their own THM-coupled models for the bentonite column experiment, using six different simulation codes. Each of the teams individually calibrated the THM parameters for the bentonite material. The eight resulting parameter sets agree well and allow a satisfactory reproduction of the TH measurements by all models. The modelling results for the evolution of temperature and relative humidity over time at three sensors in the bentonite column are in good agreement between the teams and with the measured data. Also, changes of the temperature due to modifications of the insulation and the adjustment of the heating power during the course of the experiment are well reproduced. The models were thus able to reproduce the main physical processes of the experiment, both for vapour-dominated diffusion during the heating phase and combined liquid and vapour transport during a subsequent heating and hydration phase. Based on the parameter sets, the teams predict a penetration of the water infiltration front in the 48-cm column filled with bentonite pellets to a depth between 25 and 35 cm over the 15,000 h (i.e. over 20 months) of the hydration phase of the experiment.