A Parametric Study of Mathematical Model for Long-Term Localized Corrosion of Copper in Canadian Deep Geological Repository
Bibliographic record
Abstract
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 source (direct Gemma or distilled Codex), 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".