An Advanced Model for Long-Term Localized Corrosion of Copper
Bibliographic record
Abstract
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 (Cu 2+ ) reduction, and hydrogen (H 2 ) evolution/oxidation) and three irreversible electrochemical reactions (cupric ion reduction, oxygen (O 2 ) reduction, and hydroperoxyl ion (HO 2 - ) 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 (Cu 2 O) 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 Cu 2 O 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.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".