Metamodels of Chemical System Solvers for Reactive Solute Transport in Engineered Barrier–Steel Canister Interactions in HLW Repositories

Evaluating the long-term behaviour of the engineered barrier system (EBS) in a deep geological repository for high-level radioactive waste (HLW) relies on the application of advanced reactive transport models with a high level of physical and chemical detail. In this context, the EBS comprises the waste canister, the compacted bentonite buffer, and the surrounding concrete liner. In parallel, artificial intelligence and machine learning (ML) techniques are advancing rapidly and are increasingly applied to: (a) speed up numerical computations, (b) handle complex multiscale and multiphysics interactions, and (c) support uncertainty quantification and sensitivity analysis. In this work, we develop metamodels aimed at representing steel canister corrosion processes, the formation of corrosion products, and their interactions with compacted bentonite. These metamodels act as efficient surrogate representations of high-fidelity reactive transport simulations, providing accurate approximations while substantially reducing computational cost.

A metamodel has been developed for a geochemical system with interactions of steel/bentonite and precipitation of corrosion products.  The system includes 3 primary dissolved species (Fe²⁺, H⁺ and O₂aq), 4 aqueous complexes and two minerals (magnetite and goethite). A set of 500.000 data were sampled with a Latin Hyper Cube (LHC) sequence. Batch simulations were performed with CORE^2Dv5 with 3 inputs corresponding to the total concentrations of Fe, H and O₂. Outputs include primary and secondary dissolved species, total dissolved and total precipitated concentrations, magnetite, goethite, pH and Eh. The hybrid metamodel is based on Random Forests for group identification and Gaussian Processes for output predicition. A total of 7 groups were defined based on the presence or absence of minerals and some preselected ranges of Eh and pH (pH ≤ 9 and pH > 9). The metamodel provides excellent results for most of the output variables. Working with log-concentrations improves significantly results for some dissolved and precipitated concentrations. When the metamodel is trained by working with concentrations of dissolved Fe, the validation results show some negative concentrations. On the other hand, when the metamodel is trained by working with the logarithm of the concentrations of dissolved Fe, the predicted validation concentrations are always positive, but the metrics of the validation are slightly worse. The accuracy of the metamodel improves significantly by defining 7 groups with Random Forests. The metamodel shows excellent results for predicting mineral and total precipitated concentrations. The CPU for training the Gaussian process increases significantly with the number of training samples.  Work is in progress to implement the metamodel into CORE^2Dv5 for testing the improvements in CPU time provided by the metamodel.

Acknowledgements: The research leading to these results was funded by ENRESA through Research Contracts within the Work Package ACED of EURAD (European Joint Programme on Radioactive Waste Management of the European Union), HERMES Work Package of EURAD 2 (Grant Agreement No. 101166718), the Spanish Ministry of Science and Innovation Project HERCULES (PID2023-153202OB-I00)  and the Galician Regional Government (Grant Number ED431C 2025/55).