Numerical Implementation of Mixed-potential Modeling for Copper Corrosion in a Deep Geological Repository Environment

Abstract

Canada’s plan for the long-term management of used nuclear fuel includes a proposed deep geological repository (DGR). A DGR will rely on multiple engineered and natural barriers to contain and isolate the used nuclear fuel for periods in excess of one million years. A key component of the engineered barrier system is a sealed used fuel container (UFC) to house the used nuclear fuel. Understanding the corrosion mechanisms controlling UFC performance, therefore, becomes crucial. While experimental analysis is critical to our mechanistic understanding of corrosion processes, experiments cannot be run for the post-closure timescales of a DGR and associated safety analysis. Hence, numerical modelling plays a role in bridging the gap between experiments and long-term confidence in safety.

A mathematical method is presented with the aim of developing a finite-element model to advance mixed-potential modelling capabilities for UFCs in the DGR . The mixed-potential models include electrochemical reactions at the copper surface and reactions due to the effects of chloride environments, γ-radiation or bentonite geochemistry. The commercial software package COMSOL Multiphysics is used for model development in 1D, 2D axisymmetric or 3 dimensions. Numerical implementation challenges will be presented including the selection of spatial and temporal discretization to ensure stable solutions. For example, challenges associated with fast chemical reaction rates (with characteristic time constants of <<1 s) coupled with 1-million-year model runtimes require careful selection of model timesteps. In addition, some corrosion reaction schemes, and their associated numerical system of equations can be described as stiff where a stiff system is one that requires very small timesteps to accurately compute, even when the solution exhibits little or no change. Solutions include implementing implicit numerical methods that can be applied to stiff systems without the need to use prohibitively small timesteps. A copper corrosion model for radiation induced corrosion (CCM-RIC) is presented including a bulk model with chloride-based radiolysis reactions. In addition, a one-dimensional model is presented with a limited sub-set of reactions but including electrochemical interfacial reactions, a time dependent dose rate and bentonite geochemistry. Both models were successfully implemented in COMSOL Multiphysics.