The disposal of nuclear waste has far-reaching implications for both the environment and human well-being. To ensure safe storage, transportation, and disposal, vitrification of radioactive materials into waste forms is a crucial step in the waste management process.1,2 Among the critical attributes for successful waste disposal, the chemical durability of waste-bearing glasses stands out as a paramount consideration, given the potential exposure of the disposal to aggressive environments.3 Over the past decades, scientific research has demonstrated that the durability of waste glasses is fundamentally influenced, though not entirely determined, by their chemical compositions. Therefore, understanding the relationship between glass composition and durability performance holds special significance in the context of proper waste disposal.
At the Hanford Tank Waste Treatment and Immobilization Plant (WTP), the immobilized low-activity waste (ILAW) is slated for on-site disposal at the near-surface Integrated Disposal Facility.4 As the ILAW acts as the primary barrier against the release of radionuclides to the biosphere, the Department of Energy (DOE) has mandated two chemical durability-related measurements to characterize the corrosion behavior of candidate ILAW glasses—the product consistency test (PCT)5 and the Vapor Hydration Test (VHT).6 The VHT, in particular, is a hydrothermal corrosion test that leads to partial conversion of the glass into amorphous and crystalline alteration products. The DOE has established specific requirements for measuring the VHT response limit as follows:7
The glass corrosion rate shall be measured using at least a seven (7)-day vapor hydration test run at 200°C as defined in the DOE-concurred upon ILAW Product Compliance Plan. The measured glass alteration rate shall be less than 50 grams/(m2-day). Qualification testing shall include glass samples subjected to representative waste form cooling curves. The vapor hydration test shall be conducted on waste form samples that are representative of the production glass.
In VHT, the rate of conversion is influenced by the coupled rates of glass corrosion and the formation of primarily crystalline zeolite alteration products. The nucleation of zeolite phases in this process is sporadic, leading to a high degree of response variability, particularly during the early stages of conversion (Fig. 1).8 Within the typical 24-day VHT duration, glasses with high alteration rates have usually progressed past the early sporadic phase, while glasses with low alteration rates may still be within the early sporadic phase. Consequently, simple functions used to describe the VHT responses of waste glasses are inaccurate. The high degree of nonlinearity and the variability in zeolite nucleation, coupled with variability in experimental factors, contribute to high bias and uncertainty in VHT response prediction. Jiricka et al. highlighted the significant impacts of surface finish, volume of water, and cutting procedures on the single-time VHT responses, all of which are generally not strictly controlled across different VHT tests.8 As a result of these experimental variations, a relative standard deviation of 63% was observed for the pooled replicated single-time VHT response.9
In real production scenarios, glass property-composition models are utilized to predict the VHT response of glasses during the processing of each waste batch at Hanford's LAW vitrification facility. The use of these models, along with their uncertainty descriptions, is necessary to ensure with sufficient confidence that glasses satisfy the VHT specifications listed in the WTP contract.12 This approach is also used for other glass processing and product quality-related properties.13 Existing VHT response models have met this goal with limited success. In terms of the previous modeling efforts, Vienna et al. first modeled the logarithm VHT response of 58 glasses as a first-order function of composition:14
\(\text{ln}\left(r,\text{g}\frac{{\text{m}}^{2}}{\text{d}}\right)={\sum }_{i=1}^{q}{r}_{i}{g}_{i}\) (Eq. 1)
where r is the VHT rate at 200°C (based on multi-time VHT responses), ri is the ith component coefficient, and gi is the ith component mass fraction in a glass. More recently, partial quadratic mixture (PQM) models were applied to advance the prediction of the VHT response in a similar manner:15 \(\text{ln}\left(d,{\mu }\text{m}\right)={\sum }_{i=1}^{q}{v}_{i}{g}_{i}+\text{Selected}\left\{{\sum }_{i=1}^{q}{v}_{ii}{g}_{i}^{2}+{\sum }_{i=1}^{q-1}{\sum }_{j=i+1}^{q}{v}_{ij}{g}_{i}{g}_{j}...\right\}\) (Eq. 2) where d is the VHT alteration thickness in µm after a 24-day test duration at 200°C, vi is the ith component coefficient, vii is the ith component squared coefficient and vij is the ith and jth component cross-product coefficient. These models demonstrated some success in predicting VHT responses within relatively narrow composition regions but faced high relative uncertainty. For instance, to satisfy the WTP constraint of the VHT rate being 50 g/m2/d with 90% confidence, the predicted rate needed to be below 7.9 g/m2/d.12 Also, the validation performance of the model is unsatisfactory, as shown in Fig. S1. As the composition regions expanded, particularly for the relatively large region of enhanced LAW glasses (EWG),16 the prediction uncertainty increased, and distinct biases emerged. The PQM model by Vienna et al., for instance, over-predicted low VHT responses while under-predicting higher VHT responses (Fig. 2). Vienna et al. also attempted to address this issue using an artificial neural network (ANN) to model VHT response as a function of composition.17 While this model exhibited reduced uncertainty, it did not perform well on validation data, indicating overfitting. Consequently, Vienna et al. did not obtain a suitable model to quantify VHT responses in enhanced ILAW glass data and so developed a logistic regression model to predict pass/fail state of glasses relative to the 50 gm-2d-1 contract limit.18 Therefore, for both research and the design of LAW glasses with enhanced performance, a more robust model is needed to overcome experiential noise and capture the true compositional effects on VHT response.
This study leverages advanced machine learning methods to unveil the distinct effect of different oxides on the durability performance of nuclear waste immobilization glasses. We utilize a dataset comprising VHT alteration rates of more than 600 Hanford LAW glasses, encompassing a wide compositional envelope. Four machine learning methods, including PQM and ANN from previous studies, and two non-parametric approaches, namely, local linear regression (LLR) and Gaussian process regression (GPR), are employed to predict their VHT responses. The non-parametric methods, being more capable of fitting complex relationships without presuming the target function's form, typically offer superior performance.19 Our test results demonstrate that GPR achieves the best overall accuracy and robustness in predicting the VHT response of unseen glass compositions, significantly outperforming the benchmark models. Through detailed interrogation of the GPR model, we decompose the complex relationship between glass composition and VHT response, effectively unveiling the individual effects of the different major oxides. Based on the observations from this study, we further discuss an interesting phenomenon that is generic to machine-learning-based material studies, where a slightly-overfitted model is found to be beneficial for extrapolating a small dataset with a heterogeneous sample distribution.