Technical Papers and Presentations

The study of bentonite erosion mechanisms in fractures is a problem of maximum interest to understand the long-term performance of the engineered barrier in deep geological repositories of spent nuclear fuel. In this context, erosion due to shear by seeping water, sedimentation due to flocculation (chemical erosion), and sedimentation due to gravity have been analyzed for quantifying the mass losses due to the intersecting fractures with low salinity groundwaters.

In this line, the POSKBAR project led by SKB (Sweden) and Posiva (Finland) aimed at quantifying the long-term eroded mass loss from the compacted bentonite buffer in the KBS-3 concept triggered by low salinity groundwater. Based on the formulation developed by Neretnieks et al. (2009), Liu et al. (2009) and Moreno et al. (2010), we implemented a computational framework in COMSOL Multiphysics® accounting for wall friction for the shear resistance exerted by detached flocs at the bentonite-water interface (Pont et al. 2020; Pont and Idiart 2021). A set of three equations corresponding to sodium cation transport, smectite expansion and water flow in a fracture is coupled in a three-dimensional model of a bentonite pellet intersected by a fracture (Figure 1). The prescription of the wall friction term as a boundary force on a moving bentonite-water interface has been implemented with a domain decomposition accounting for two subdomains separated by the rim (Figure 1), which allows segregating the expanding gel from the non-cohesive sol that forms due to the interaction with low salinity groundwater. To track the rim, a moving mesh is used.

The detachment of smectite flocs in sloping fractures is a complex phenomenon. The only addition of gravity and buoyancy forces would not represent the true motion of detached flocs, which is highly affected by drag force. In this sense, a sedimentation model based on the Brinkmann equations (eqs. 1 and 2) has been implemented as ρ ∂t u-∇⋅τ+∇p+ηw ηrel κ^(-1) u = g(ρ-ρw) (1) ∇⋅u =0 (2) with a virtual permeability, κ, derived in eq. 3 from the particle velocity described by eq. 2 (Neretnieks et al., 2017)
κ=(ηrel dp^2)/18 (3) The definition of a correlation between particle aggregate size and fracture aperture is one of the most relevant aspects to be considered in the prediction of the long-term erosion rate in non-horizontal fractures.
dp=dp0 (δ/δ0 )^α (4) In the present work, the calibration process to determine the average particle aggregate diameter for apertures with δ≥δ0 (free sedimentation) is carried out. Besides, the dependence between particle diameter and fracture aperture is assessed for δ<δ_0, since it is crucial for describing the low erosion rates observed in 0.1 mm fractures, where the motion and the size of smectite flocs are strongly constrained by the walls. This can lead to the formation of a secondary gel which might even clog the fracture.

Finally, the numerical model is validated with the simulation of a series of laboratory tests from the literature, covering a relatively wide parametrization in terms of bentonite type, initial dry density, flowrate, fracture slope and aperture.