Bentonite re-saturation: different conceptual models – similar mathematical descriptions
Klaus-Peter Kröhn, 2017. "Bentonite re-saturation: different conceptual models – similar mathematical descriptions", Radioactive Waste Confinement: Clays in Natural and Engineered Barriers, S. Norris, J. Bruno, M. van Geet, E. Verhoef
Download citation file:
Thermohydromechanically (THM) coupled models based on two-phase flow formulations for the hydraulics are presently the most established tools for simulating bentonite re-saturation. Alternatively, the extended vapour diffusion (EVD) model, involving basically diffusion of water vapour and of hydrated water, has been developed specifically for this purpose. These two model concepts are obviously based on entirely different hydraulic processes.
However, applying some acceptable simplifications to the underlying mathematical models leads to an identical formulation for the two approaches that looks formally like Fick’s second law with a saturation-dependent ‘diffusion coefficient’. Concerning the hydraulics, the THM codes hence state a mathematical problem that is similar to the one resulting from the EVD model.
A subsequent quantitative comparison of the two hydraulic approaches requires only the respective diffusion coefficients to be compared. This has been done on the basis of benchmark calculations for two different water-uptake tests with compacted MX-80 at largely the same conditions. Even for variations in temperature and dry density, the resulting diffusion coefficients for the two approaches showed remarkable agreement.
Different physical models have thus led to a similar mathematical problem. The mathematics indicates a diffusion-like process, although the exact nature of this process still remains to be determined.