A Mathematical Model for Gas Migration In Natural and Engineered Barriers for Radioactive Waste Disposal

Abstract

This work provides a comprehensive assessment into the processes governing two-phase flow in a swelling geomaterial under critical gas pressures whereby the material strength of the soil may be exceeded and for which dilation and dilation-controlled gas flow is expected to occur. The author first provides background on the importance of understanding such processes in the safe geological disposal of radioactive waste. This is followed by a review of experimental studies to describe mechanisms of gas migration processes through natural (host rock formations) and engineered barrier materials, and an evaluation of existing studies that have attempted to numerically model multi-phase flow in expansive soils. Finally, the author provides a literary synthesis of the hydraulic and mechanical behaviour of bentonite clays observed in laboratory experiments under saturated and unsaturated conditions. The novel contribution of this work is then presented through a series of articles. The author first develops a fully-coupled hydro-mechanical (HM) mathematical model for advective-diffusive visco-capillary controlled two-phase flow through a geomaterial and applies it to simulate a 1-dimensional (1D) flow problem using the Finite Element Method (FEM) commercial code COMSOL Multiphysics®. The model results are compared to experimental data and although several key-features of the experimental results were realized, additional flow mechanisms would be necessary to achieve complete gas breakthrough of the sample. In the second article, a verification study is performed, whereby analytical solutions for a 1D steady-state and 1D transient gas flow problem under constant volume boundary conditions were derived. Successful verification of the numerical model was completed by comparing the pore-gas pressure evolution and stress evolution to that of the results of the analytical solution, which showed near-perfect agreement. Building upon the authors original mathematical model, an investigation of enhanced processes and characteristics which may be contributing to dilation-controlled gas flow were conducted. These processes included the introduction of material heterogeneity, consideration of the Klinkenberg “slip flow” effect, and the presence of a swelling strain, and were applied to simulate the same 1D flow problem. The results showed significant improvement over the previous work, including observing complete breakthrough and matching experimental stress evolution. However, the results showed a high degree of gas saturation within the sample and a plug outflow behavior, which were not characteristic of dilation-controlled gas flow. To further improve the mathematical model, the author conducted a detailed investigation of the highly coupled relationship between mechanical deformation and flow. This included assessing the effect of plasticity, damage, and non-localization to dilation-controlled gas flow, while incorporating the knowledge gained from previous studies. These advanced mathematical models were applied to numerically simulate 1D flow and a 3D spherical flow under constant boundary conditions. Some results demonstrated very good agreement with experimental data and provide further understanding of the processes involved. The collection of this research provides much needed insight into the possible mechanisms controlling two-phase flow and the capability of continuum models to do so. The intent of this research is to expand the literature further and provide a few steps closer in the development of a robust numerical model that can be used to support long-term safety assessments for radioactive waste disposal, by correctly capturing major features of two-phase flow.