Coupled process modelling with applications to radionuclide storage and disposal

Abstract

Radioactive waste repositories, designed in accordance with the current UK concept, would be required to provide containment for thousands of years beneath hundreds of metres of rock. The physical processes, both geological and other processes, that might lead to migration of radionuclides are slow in comparison to human timescales — it is impractical to make an experiment of the whole system and so these systems are typically investigated through the use of numerical models. Predictive models are based on combinations of: assumptions, mathematical formulations and parameter values derived from experimental observations. The Ventilation Experiment in the Opalinus Clay at Mont Terri, Switzerland, was designed to involve geological and other physical processes that would be active during the excavation and construction phases of a repository, and with consequences for the repository performance during the operational phase. The experiment consisted of a 10m long tunnel of 1:3m diameter through which air of known relative humidity was circulated in order to force drying and re-saturation through the tunnel wall. Two such cycles over four years have been observed via installed instrumentation. Several numerical models have been constructed of the ventilation experiment by different international teams under the decovalex project using different approaches for cross-validation. Through participation in this project, a 1D model using Richards’ Equation was developed that effectively reproduces the hydrodynamic, mechanical and conservative mass transport results. During the course of developing that model, many other domains, meshes, formulations and software versions were investigated. Now that the field scale Ventilation Experiment can be reproduced with numerical models, the findings (assumptions, formulations, parameter values, computational methods and software) would be transferable to other argillaceous formations to enable predictive modelling of similar scenarios and contribute to the safe disposal of nuclear waste and other problems involving similar geological processes. Work of this type fills the gap between laboratory scale experiments and regional scale modelling of geological systems. The gap is especially wide for low-permeability formations because the size and time-scale limitations effect the ability to make direct observations and measurements. Two particular problems were also addressed in this work: that of the use relative permeability functions and also the computational treatment of the physical interface between the tunnel domain and the rock domain. A sensitive component in many models of unsaturated flow through porous media and covering a wide variety of applications, including reservoir engineering, is the representation of permeability at an unsaturated point (kx) as a scaling of the saturated permeability (ksat) by introducing some function of the pressure head, or saturation as the relative permeability (krel) in the relation kx = ksatkrel. The choice of the particular function and its parameter values adds little to our understanding of the physical parameters. A solution is proposed to the second problem, of how to computationally represent, implement and manage the interface between two physical (i.e. spatial) domains. The scheme maps every part of the boundary of one domain onto the corresponding part of the boundary of the other domain, storing the state variables in shared memory and converting between physical components.