Scott Briggs

Copper‐coated used fuel containers (UFC) may be exposed to Cl ⁻ ‐containing bentonite pore waters under oxic conditions. A mixed‐potential model has been developed to predict the time dependence of the corrosion potential ( E _CORR ) and corrosion rate of the container as the near‐field environment evolves. Prediction of E _CORR not only provides mechanistic insight into the evolution of uniform corrosion but also allows the assessment of the likelihood of localized corrosion and stress corrosion cracking mechanisms that are contingent on a threshold potential. Both 1‐D and 2‐D axisymmetric versions of the COMSOL‐based model have been validated against experimental measurements of E _CORR of copper electrodes in which the mass transfer coefficient was varied over five orders of magnitude and the O ₂ concentration varied over four orders of magnitude. Good agreement is found between the predicted steady‐state and transient values of E _CORR and those measured experimentally.

This paper presents the development and validation of a mixed‐potential model that couples a bulk radiolysis model to interfacial electrochemical reactions, enabling long‐term prediction of radiation‐induced corrosion of copper‐coated used fuel containers in a deep geological repository. Time‐dependent concentration profiles of molecular radiolysis products were compared between the bulk radiolysis model and the coupled model, highlighting the effects of interfacial reactions on bulk species evolution. Finally, the extent of corrosion from simulations was validated against experimental measurements, demonstrating the capability of the coupled approach to accurately reproduce observed corrosion behaviour on copper systems.

Electrochemical impedance spectroscopy (EIS) is widely used as a nondestructive tool for probing interfacial phenomena, yet interpretation is frequently complicated by electrode-geometry-induced high-frequency phenomena associated with a frequency-dependent complex ohmic impedance. Geometry-induced current and potential distributions strongly influence the impedance response of electrodes subject to faradaic reactions. Classical analyses of disk electrodes show that primary and secondary current distributions generate frequency-dependent capacitive behavior.^1,2 At frequencies above the characteristic faradaic rate, the global impedance exhibits a quasi-constant-phase-element (CPE) character that can be accurately represented using the Havriliak-Negami equation.³ Local impedance calculations further reveal high-frequency capacitive loops arising from local ohmic dispersion. These foundational studies demonstrate that geometry-driven current and potential distributions cannot be neglected when extracting interfacial capacitance or interpreting impedance dispersion.

The concept of Adaptive Phased Management, approved by Canadian federal authorities and implemented by the Nuclear Waste Management Organization, forms a comprehensive strategy for the long-term safe management of used nuclear fuel in Canada. ¹ The used nuclear fuel will ultimately be placed within a container in a deep geological repository (DGR). Current container designs employ steel vessels with a protective copper outer layer, strategically selected to reduce corrosion damage. The copper-coated container may be subjected to various corrosion mechanisms over time as the DGR environment evolves. Specific to this work and in the early aerated environment of the DGR, efflorescing salt impurities present on the container surface may lead to the formation of an Evan’s droplet. To understand the behavior of the copper-coated container with respect to localized corrosion and ensure the effectiveness of this protection strategy, a preliminary two-dimensional axisymmetric time-dependent model for the corrosion of copper under an Evans droplet was developed. ^{2, 3} The mathematical model employs the finite-element method (COMSOL Multiphysics). Some unique features of the model are the inclusion of six heterogeneous and fifteen homogeneous reactions, implicit calculation of nm-scale films, and treatment of the influence of films on surface concentrations and potentials. The model shows the time-dependent localized corrosion rates and depths, calculated for an elapsed time of one hundred years. It also shows time-dependent radial distributions for current density and surface coverage of films. The influence of oxygen conditions and temperature was included, and the model accounted for the influence of films on reaction rate constants. Temperature and oxygen concentration were shown to have a strong contribution to copper corrosion. Preliminary results showed that the corrosion of copper and growth of films in the droplet was almost uniform on the electrode surface. Pitting is normally initiated by localized damage to the oxide film caused by physical cracks or chemical attacks. The evolution process of pits entails formation, growth, and re-passivation. Two methods of simulating pit evolution were developed. First, a unique approach to model pitting was developed in which boundary conditions were modified to define a simulated pit without changing finite-element meshing. Simulations were performed under the assumption that the atmospheric oxygen concentration decreased exponentially with time. The simulated pit was assumed to be created when the oxide film first formed and after it reached its maximum value, representing two extreme conditions for atmospheric oxygen concentration. For both pit formation times, simulations were performed for both small rate constants yielding kinetic control and larger rate constants trending toward oxygen-transport control. ⁴ The pit repassivated for each simulation performed, and the resulting pit depth ranged from 30 nm to 3,560 nm. The largest pit depth was calculated for large rate constants and for pits formed shortly after the oxide film was grown. A second approach for simulating pit evolution accounts for the dynamic growth process by combining the boundary condition method for predefined deep pits with mesh deformation physics. The mesh-deformation approach showed changes within the pit environment. The pH and oxygen concentration within the pit changed before and after pit re-passivation. Boundary-condition-modification and mesh-deformation approaches yield the same answers for repassivation time and resulting pit depth. References NWMO, “Choosing a Way Forward. The Future Management of Canada’s Used Nuclear Fuel. Final Study,” Nuclear Waste Management Organization, Toronto, Ontario, 2005. C. You, S. Briggs, and M. E. Orazem, “Model development methodology for localized corrosion of copper,” Corrosion Science, 222 (2023) 111388. C. You, Y. Chuai, S. Briggs, and M. E. Orazem, “Model for corrosion of copper in a nuclear waste repository,” Corrosion Science, 226 (2024) 111658. Y. Chuai, S. Briggs, and M. E. Orazem, “A Parametric Study of Mathematical Model for Long-Term Localized Corrosion of Copper in Canadian Deep Geological Repository,” ECS Meeting Abstracts, 2024, MA2024-02, 1701. Acknowledgement This work was supported by the Nuclear Waste Management Organization, Canada, under project 2000904.

Copper has been proposed as a container material for the disposal of used nuclear fuel in a number of countries worldwide. The container materials will be subject to various corrosion processes in a deep geological repository, including radiation-induced corrosion (RIC) resulting from the γ-irradiation of the near-field environment. A comprehensive model is being developed to predict the extent of RIC by coupling a radiolysis model to the interfacial electrochemical reactions on the container surface. An important component of the overall model is a radiolysis model to predict the time-dependent concentration of oxidizing and reducing radiolysis products. As a first step in the model development, various radiolysis models have been validated against experimental measurements of the concentrations of dissolved and gaseous radiolysis products. Experimental data are available for pure H₂O- and Cl⁻-containing solutions, with and without a gas headspace. The results from these experiments have been compared with predictions from corresponding radiolysis models, including the effects of the partitioning of gaseous species (O₂ and H₂) at the gas–solution interface. Different reaction schemes for the Cl⁻ radiolysis models are also compared. The validated radiolysis model will then be coupled with interfacial reactions on the copper surface and additional processes related to the presence of bentonite clay in Steps 2 and 3 of the overall model, respectively.

The concept of Adaptive Phased Management, approved by Canadian federal authorities and implemented by the Nuclear Waste Management Organization, forms a comprehensive strategy for the long-term safe management of used nuclear fuel in Canada.¹ The used nuclear fuel will ultimately be placed within a container in a deep geological repository (DGR). Current container designs employ steel vessels with a protective copper outer layer, strategically selected to reduce corrosion damage. The copper-coated container may be subjected to various corrosion mechanisms over time as the DGR environment evolves. Specific to this work and in the early aerated environment of the DGR, efflorescing salt impurities present on the container surface may lead to the formation of an Evan’s droplet. To understand the behavior of the copper-coated container with respect to localized corrosion and ensure the effectiveness of this protection strategy, a preliminary two-dimensional axisymmetric time-dependent model for the corrosion of copper under an Evans droplet was developed.^{2, 3} The mathematical model was developed using the finite-element method (COMSOL Multiphysics). Some unique features of the model are inclusion of six heterogeneous and fifteen homogeneous reactions, implicit calculation of nm-scale films, and treatment of the influence of films on surface concentrations and potentials. The model shows the time-dependent localized corrosion rates and depths, calculated for an elapsed time of ten years. It also shows time-dependent radial distributions for current density and surface coverage of films. The influence of oxygen conditions and temperature was included, and the model accounted for the influence of films on reaction rate constants. Preliminary results show that the corrosion of copper in the Evan’s droplet is almost uniform on the electrode surface. Temperature and oxygen concentration was shown to have a strong contribution to copper corrosion. The current version of the mechanical model has many parameters. Some parameters are obtained from PHREEQC thermodynamic software,⁴ some are selected to yield good results, and some are defined using expert judgement from the literature.While the number of parameters is very large, the impact of each parameter is constrained by the model. A parametric study is necessary to identify reasonable ranges of values and explore different conditions that may lead to localized corrosion of copper. For example, to switch the mechanism from kinetic control to mass-transfer control, the overall rate constants were increased by different orders of magnitude. The influence of both oxide film and salt film on rate constants reduction were also studied. Combining both the blocking effect of films on the copper surface and the control mechanism shift, simulations were completed to study the parameter space. The present work shows that the corrosion rate increased as rate constants were increased, and currents became limited by mass transport of oxygen. References NWMO, “Choosing a Way Forward. The Future Management of Canada’s Used Nuclear Fuel. Final Study,” Nuclear Waste Management Organization, Toronto, Ontario, 2005. C. You, S. Briggs, and M. E. Orazem, “Model Development Methodology for Localized Corrosion of Copper,” Corrosion Science, 222 (2023), 111388. C. You, Y. Chuai, S. Briggs, and M. E. Orazem, “Model for Corrosion of Copper in a Nuclear Waste Repository,” Corrosion Science, 226 (2023), 111658. PHREEQC Version 3, United States Geological Survey, 202, https://www.usgs.gov/software/phreeqc-version-3. Acknowledgement This work was supported by the Nuclear Waste Management Organization, Canada, under project 2000904.

The disposal of high-level radioactive waste (HLW) and spent nuclear fuel (SF) presents a unique challenge for the prediction of the long-term performance of corrodible structures since the HLW/SF canisters are expected, in some cases, to have lifetimes of one million years or longer. Various empirical and deterministic models have been developed over the past 45 years for making predictions of the long-term corrosion behaviour, including models for uniform and localized corrosion, environmentally assisted cracking and microbiologically influenced corrosion. As well as process models focused on specific corrosion mechanisms (described in Part 1 of this review), there is also a need for performance assessment models as part of the overall analysis of the safety of a deep geological repository (DGR). Performance assessment models are often based on simplified or abstracted process models. The manner in which various international waste management programs have predicted the long-term performance of HLW/SF containers with copper, steel, Ni and Ti alloy corrosion barriers is discussed. Performance assessments are repeated periodically during the development and implementation of a DGR, and the corrosion models are constantly updated in light of new mechanistic understanding and/or more information about the deep geological environment. Two examples of how the container performance assessment models evolve over time are also described. Performance assessment models cannot easily be validated, so it is important to build confidence in the long-term predictions using other methods, including natural analogues and large-scale in situ tests and the use of complementary models.

The disposal of high-level radioactive waste (HLW) and spent nuclear fuel (SF) presents a unique challenge for the prediction of the long-term performance of corrodible structures since HLW/SF containers are expected, in some cases, to have lifetimes of one million years or longer. Various empirical and deterministic models have been developed over the past 45 years for making predictions of long-term corrosion behaviour, including models for uniform and localised corrosion, environmentally assisted cracking, microbiologically influenced corrosion, and radiation-induced corrosion. More recently, fracture-mechanics-based approaches have been developed to account for joint mechanical–corrosion degradation modes. Regardless of whether empirical or deterministic models are used, it is essential to be able to demonstrate a thorough mechanistic understanding of the corrosion processes involved. In addition to process models focused on specific corrosion mechanisms, there is also a need for performance-assessment models as part of the overall demonstration of the safety of a deep geological repository. Performance-assessment models are discussed in Part 2 of this review.