Resumen de Numerical and statistical analysis of the homogenisation of engineered bentonite barriers in spent nuclear fuel repositories
Ensuring the long-term safety of radioactive waste disposal is an environmental topic of utmost importance that nuclear waste management organisations worldwide are facing today. With regard to long-lived radioactive wastes, such as spent nuclear fuel, there is an international consensus on disposal in deep geological formations, most commonly in mined repositories. In several disposal concepts and facility designs, bentonite-based barriers play a significant role. Bentonite is a naturally occurring clay containing different clay and accessory minerals and is planned to be used in different forms as a buffer and backfill material sealing the disposal and access galleries, shafts and other excavations.
The ability to swell upon water contact, the self-healing capacity, the low permeability, the sorption capacity and the stability over long time scales are all favourable properties making bentonite a suitable barrier material. Many of the characteristics of the barriers depend directly or indirectly on the bentonite density. At initial state, that is, after emplacement of the waste packages, installation of the barriers and closure of the disposal facility, the density distribution within the bentonite barriers is not uniform. This heterogeneity is caused by, for example, the use of different barrier components such as compacted blocks and pellet fills or by the presence of installation gaps unavoidable in the facility design. Density differences present in the buffer surrounding the waste package may have relevant long-term safety implications, for example, in terms of the transfer of decay heat generated by the disposed wastes, shear deformations of the waste packages due to a non-uniform swelling stress evolution and the transport of substances endangering the waste package integrity and, in case the waste package is breached, the release of radionuclides and other harmful substances. However, the swelling of bentonite upon wetting with groundwater leads to a homogenisation of density differences initially present in the system and, thus, will even out differences in related properties of the bentonite barrier.
The process and degree of homogenisation is evaluated as part of the performance assessments carried out to support the safety case used in the licencing of the disposal facility. The Finnish nuclear waste management organisation Posiva has received a construction licence for the planned final disposal facility for spent nuclear fuel ONKALO® located in Olkiluoto, Eurajoki in November 2015 and aims to submit an operating licence application in 2021 in order to begin the disposal activities in the 2020’s (Teollisuuden Voima Oyj, 2020). Hence, the challenge is to work towards the timely implementation of the world’s first final disposal facility for spent nuclear fuel and the presented thesis is targeted at contributing to the solution by addressing the issue of bentonite homogenisation through numerical and statistical analyses.
In particular, this thesis is concerned with the development and qualification of a thermo-hydro-mechanical (THM) model for simulating the homogenisation of bentonite barriers consisting of both compacted blocks and pellet fills. To this end, first a model for compacted bentonite blocks has been developed within the framework of the well-known Barcelona Expansive Model (BExM). Then, the conceptual and mathematical basis of the model has been extended for the application to pellet fills and granular expansive material. Therefore, both the compacted block model and the model for pellet fills and granular material share the same basis and structure. However, particularly noteworthy is the introduction of an additional porosity level representing the void space between individual pellets or granules. As a result, the simulation matches the physical reality of the system more closely, while retaining the number of governing equations, and only slightly increasing the number of required model parameters. The models have been implemented into a simulation software COMSOL Multiphysics® and the resulting numerical code has been named Multiphysics-for-Clay-Barriers (M4CB). A comprehensive programme for testing the model has been carried out including 17 verification and validation exercises covering different features of the model, model geometries, scales, initial configurations and types of boundary conditions. As a result, it can be stated that the model is capable of reproducing the main trends observed in experiments, especially with regard to the homogenisation of initially present density differences.
In addition, a deterministic sensitivity analysis based on experimental designs including 74 simulations in total has been performed in order to identify those parameters related to the developed model, boundary conditions and the repository design that significantly influence the simulation of the homogenisation process. The subject of the analysis has been the buffer design for Loviisa 1 and 2 (LO1-2) type deposition holes at full-scale. For the quantification of the remaining density differences in the buffer, a heterogeneity degree has been defined, which can be interpreted as the normalised average deviation from the theoretically fully homogenised state. It has been found that the elastic stiffness of the inter-pellet pores, the outer gap width, the hydraulic boundary condition (i.e., uniform inflow vs. inflow through a single fracture) and the state function governing the microstructural deformability are the most significant model parameters with respect to the homogenisation.
Next, a statistical model has been developed with the aim to serve as a surrogate for the time-consuming numerical simulations of the homogenisation of the buffer emplaced in LO1-2 type deposition holes. For the development of the surrogate model, in total 500 numerical full-scale simulations with varying parameter value combinations, including those of the deterministic sensitivity analysis, have been carried out. Based on the surrogate model and assigning probability distributions to the different input parameters, a Monte Carlo simulation with 10^6 iterations has been performed. The results indicate that the final heterogeneity degree of the buffer is around 6% on average and that values over 10% are very unlikely. In addition, the probabilistic analysis has confirmed that the final heterogeneity degree of the buffer is especially sensitive to the elastic stiffness of the inter-pellet pores, the outer gap width, the hydraulic boundary condition and the state function. Therefore, measures for effective control of the homogenisation in the buffer should be targeted at these factors.
