An Advanced Model for Long-Term Localized Corrosion of Copper
Authors: You Chen , Briggs Scott , Orazem Mark E. 
Published: November 2022

The Nuclear Waste Management Organization (NWMO) is responsible for the implementation of the Adaptive Phased Management (APM) plan, the federally-approved plan for the safe long-term management of Canada’s used nuclear fuel.1 Under the APM plan, used nuclear fuel will ultimately be placed within a deep geological repository (DGR) in a suitable host rock formation. Part of evaluating the long-term performance and safety of the repository system is understanding the behavior of the copper-coated container with respect to localized corrosion. Even though localized corrosion is not expected in the DGR design system, there is still a need to develop a mathematical model for localized corrosion of copper.
A 2-D axisymmetric time-dependent model for the localized corrosion of copper was developed using the concept of an Evans droplet.2 The model accounts for three reversible electrochemical reactions on the metal surface (copper dissolution/plating, cuprous ion oxidation (Cu+) /cupric ion (Cu2+) reduction, and hydrogen (H2) evolution/oxidation) and three irreversible electrochemical reactions (cupric ion reduction, oxygen (O2) reduction, and hydroperoxyl ion (HO2
-) reduction). Dissolved cuprous ion reacts in a second chemical step to form the cuprous chloride (CuCl) salt film treated as a diffusion barrier, or it reacts to form the cuprous oxide (Cu2O) film that partially blocked the active area on the metal surface. The model also accounts for fifteen homogeneous reactions involving copper chloride complex, copper hydroxide complex, copper carbonate complex, and superoxide species. The associated equilibrium constants were obtained from PHREEQC thermodynamic software.3

The mathematical model was developed using the finite-element method (COMSOL Multiphysics). The model includes coupled, nonlinear, diffusion equations for ionic species, which include the contribution of migration, local electroneutrality, and homogeneous reactions. The anodic and cathodic regions are not predefined but, instead, are determined by values of local concentration and potential from the simulation results. The growth of nm-scale films was calculated implicitly without using finite-element meshing and surface coverage was expressed in terms of the thickness in units of monolayers. The model also accounted for the effect of porous CuCl film thickness on the surface oxygen concentration and potential applied on electrochemical reactions. The influence of temperature was included on model parameters such as equilibrium rate constant, diffusion coefficient, Henry’s law constant, solubility product constant and kinetic parameters associated with electrochemical reactions. Transient droplet temperature was described by interpolating results from a one-million-year simulation for the temperature change on the used fuel container surface.4 A total of 28 dependent spatial-temporal variables including species’ concentrations, potentials and local corrosion rate were solved in this model.
In the current version of model, two extreme conditions were chosen such that droplet boundary has a faster or slower rate of oxygen decay for an initially air-saturated droplet. The model shows a 10-year time-dependent radial distribution of anodic and cathodic current density, surface coverage of CuCl film and Cu2O film, and localized corrosion rates and depths. It also shows a distribution of pH, potential, and concentrations of dissolved gaseous and ionic species through the entire droplet. Temperature and oxygen concentration is shown to have a strong contribution to the simulation results. Simulations show that the depth of corrosion is almost uniform over the elapsed time simulated and the maximum deviation from the average corrosion depth was less than 0.0004% for slower oxygen decay and less than 0.002% for faster oxygen decay in 10 years.
References

NWMO, “Choosing a Way Forward. The Future Management of Canada’s Used Nuclear Fuel. Final Study,” Nuclear Waste Management Organization, Toronto, Ontario, 2005.

R. Evans, The Corrosion of Metals, E. Arnold & Company, London, 1926.

PHREEQC Version 3, United States Geological Survey, 202, https://www.usgs.gov/software/phreeqc-version-3

Guo, “Thermal response of a Canadian conceptual deep geological repository in crystalline rock and a method to correct the influence of the near-field adiabatic boundary condition”, Engineering Geology, 218 (2017), p50-p62.

Acknowledgement
This work was supported by the Nuclear Waste Management Organization, Canada, under project 2000904.