High-fidelity coupled reactive transport models and metamodels of porewater chemistry, solute transport and geochemical evolution interactions in the engineered barrier and the steel canister in a HLW repository

The assessment of the long-term performance of the engineered barrier system (EBS) of a high-level radioactive waste (HLW) deep geological repository requires the use of high-fidelity reactive transport models. The EBS in a HLW repository includes: the canister, the compacted bentonite buffer and the concrete liner.  Artificial intelligence and machine learning methods (ML) are growing at a very fast pace and have been used for: a) Accelerating numerical simulations, b) Addressing multiscale and multiphysics couplings, and c) Uncertainty quantification and sensitivity analyses. Here we present high-fidelity models and ML methods to simulate steel canister corrosion, corrosion products and their interactions with compacted bentonite. Metamodels and surrogate models provide approximate and efficient solutions which emulate the high-fidelity reactive transport simulations and can reduce significantly the CPU times. The high-fidelity model was calibrated with data from the FeMo corrosion test performed by CIEMAT/UAM under isothermal and saturated conditions for 15 years. The FeMo test consists of 6 stainless-steel sinters surrounded by Fe powder emplaced in holes drilled in a FEBEX bentonite block. The bentonite block was hydrated with granitic water through the sinters by using 6 syringes. Two different particle sizes (64 and 450 µm) were used in Fe powder of the FeMo tests. Model results show that pH increases to 9.5 and magnetite is the main corrosion product. Siderite, greenalite and saponite-Mg also precipitate at the Fe powder/bentonite interface. 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), 2 aqueous complexes (OH^- and H₂aq) and magnetite. A set of 5000 data were sampled with a Latin Hyper Cube (LHC) sequence. Batch simulations were performed with CORE^2Dv5 for 5000 data with the following 3 inputs: Fe, H and O₂. Outputs include aqueous primary concentrations, aqueous secondary concentrations, magnetite, pH and Eh. The metamodel is based on Gaussian Processes and Random Forests for defining two groups corresponding to pH > 9 and pH ≤ 9. The metamodel provides excellent results for most of the output variables. Working with log for concentrations of H⁺, OH^- and O₂ improves significantly the results for H and O₂. 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 is significantly improved for pH by defining two groups, one for pH ≤ 9 and another for pH > 9.

Acknowledgements: This research was funded by ENRESA within Work Package ACED of EURAD (Grant Agreement nº 847593), within WP HERMES of EURAD-2 (Grant Agreement nº 101166718) and Project PID2023-153202OB-I00 funded by Spanish Ministry of Science and Innovation  We acknowledge the contributions of CIEMAT and UAM who performed FeMo tests and provided the experimental data.