A Mathematical Model for Localized Corrosion of Copper Under a Droplet

Abstract

The Nuclear Waste Management Organization (NWMO) is responsible for the implementation of Adaptive Phased Management (APM), 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 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. The Canadian Deep Geological Repository (DGR) system does not lend itself to passivation of the copper surface, owing to the nature of copper and the environment, so conventional pitting corrosion is not expected. However, the system will transition from dry to wet conditions, and there is a possibility that deliquescent species may be present on the container surface, which may produce different localized environments, and as a result, localized corrosion damage.A 2-D axisymmetric time-dependent model for localized corrosion is being developed using the concept of an Evans droplet,2 in which the metal is covered by a drop of electrolyte. The model considers the aerobic, unsaturated conditions likely to be found at early times in a deep geological repository.3 In the present work, sodium chloride was chosen as the supporting electrolyte and the concentration of oxygen in the solution at the droplet boundary was assumed to be in equilibrium with the oxygen in the surrounding air. The electrochemical reactions proposed for the copper metal surface include oxygen (O2) reduction and copper dissolution through a sequence of steps in which copper chloride is an adsorbed intermediate that reacts in a second chemical step to form cuprous chloride (CuCl2 -). The model accounts for the homogeneous oxidation of cuprous chloride to form cupric ion (Cu2+), and Cu2+ introduced a cathodic reaction to form CuCl2 -. Hydrolysis of both Cu(I) and Cu(II) to form precipitates is also considered in the current model.The mathematical model is developed using the finite-element method (COMSOL Multiphysics). The mathematical approach is similar to that developed by Chang et al.4 for corrosion of iron under a droplet or under a deposit. The model includes coupled, nonlinear, diffusion equations for ionic species, which include the contribution of migration, local electroneutrality, homogeneous reactions, and formation of precipitates. One of the unique approaches taken in this work is that the anodic and cathodic regions are not predefined but are rather determined by values of local concentration and potential from the simulation results. While in its preliminary stages, the model shows a time-dependent radial distribution of anodic and cathodic current, fractional coverage of the CuCl adsorbed intermediate, and dissolved oxygen concentration.References NWMO, “Choosing a Way Forward. The Future Management of Canada’s Used Nuclear Fuel. Final Study,” Nuclear Waste Management Organization, Toronto, Ontario, 2005.U. R. Evans, The Corrosion of Metals, E. Arnold & Company, London, 1926.F. King, M. Kolar, P. Maak, “Reactive-transport model for the prediction of the uniform corrosion behavior of copper used fuel containers,” Journal of Nuclear Materials 379 (2008) 133-141.Y.-C. Chang, R. Woollam, and M. E. Orazem, "Mathematical Models for Under-Deposit Corrosion: 1. Aerated Media,'' Journal of The Electrochemical Society, 161 (2014), C321-C329. AcknowledgementThis work was supported by the Nuclear Waste Management Organization, Canada, under project 2000904.