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Machine Learning Prediction of Nitric Acid Extraction Behavior in PUREX Process
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Cite this: ACS Omega 2024, 9, 51, 50357–50366
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https://doi.org/10.1021/acsomega.4c06886
Published December 10, 2024

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Abstract

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Plutonium uranium reduction extraction (PUREX) is a liquid–liquid extraction process used to recover plutonium (Pu) and uranium (U) from irradiated uranium fuel for various nuclear-related applications. Despite extensive efforts, quantitative prediction of liquid–liquid extraction parameters, i.e., distribution ratios and separation factors, of the process remains challenging. Existing thermodynamic models are difficult to develop and often have limited utility due to the complexity of the aqueous feed. Nitric acid is a critical component of the PUREX system, both as a driving force for dissolving irradiated fuels in preprocessing stages, as well as being efficiently extracted by tributyl phosphate (TBP). Models to understand nitric acid’s distribution behavior is therefore a prerequisite to predict actinide extraction. In this work, we compiled a wealth of solvent extraction literature data and built machine learning (ML) models capable of predicting the organic phase nitric acid equilibrium concentration from initial acid and TBP concentrations across a variety of diluents. Our results demonstrate that ML is highly capable of predicting nitric acid extraction behavior in PUREX systems, and the resultant ML-aided response surfaces demonstrate promising progress as an in silico aid for optimizing the design of experiments for future work with the PUREX process.

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Introduction

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The PUREX process is a solvent extraction technology used for the recovery of plutonium (Pu) and uranium (U) from used nuclear fuel. The process relies on the dissolution of used nuclear fuel in concentrated nitric acid; then the dissolved fuel is processed using liquid–liquid extraction (LLE) to recover Pu and U. This PUREX LLE is a well-studied technique that uses tributyl phosphate (TBP) in an alkane diluent to extract Pu and U into the organic phase, where the nitrate ions and TBP form coordinate bonds with the metal ions forming lipophilic complexes. (1) This extraction has been studied extensively over the course of multiple decades and sufficient understanding of the extraction of dissolved fuel components is achieved, as detailed in the wealth of published information. (1−6) Many variations of the PUREX process exist, including coextraction of U and Pu (COEX) and uranium extraction (UREX), amplifying the amount of information available on used fuel reprocessing. (5−7)
Irradiated dissolved fuel contains mostly U, Pu, and a multitude of fission products, making it a complex feed. During nuclear fuel dissolution, nitric acid (HNO3) stabilizes the majority of the reaction constituents. HNO3 facilitates the extraction of Pu and U by TBP, but it also efficiently partitions into the organic phase. Nitric acid also serves as a “salting agent,″ providing nitrate ions that drive the extraction of U and Pu. The understanding of the HNO3 partitioning is important for comprehension of the mechanism of PUREX extraction. This process is typically described, in a slightly simplified manner, by the formation of a 1:1 complex with TBP based on the following chemical equilibrium equation: (8,9)
H++NO3−+TBP―⇌TBP·HNO3―
(1)
where a bar above the chemical compound indicates the complex exists in the organic phase and no bar implies the aqueous phase. This 1:1 extraction of HNO3 by TBP is widely understood to be the primary mechanism for extraction; the 1:2 complex (1 HNO3 + 2 TBP) is also known to form in some circumstances. (10) However, at high HNO3 concentrations a 2:1 acid to TBP complex has been suggested to form as an additional product, as given below: (8)
H++NO3−+TBP·HNO3―⇌TBP·2HNO3―
(2)
Given the complexity of the dissolved fuel composition, it is highly desirable to develop predictive capabilities for the extraction behavior of the dissolved fuel constituents. The PUREX extraction behavior of major constituents in dissolved fuel solution, e.g., HNO3, U, Pu, and zirconium have been sufficiently understood. (11) Several extensive models have been developed; (8,9,12−16) however, they generally require numerous complex input features, such as chemical and redox speciation, as well as thermodynamic details. (8,9,12−16) Additionally, modeling of the minor actinides and other fuel constituents remains challenging.
To develop predictive capabilities while overcoming these constraints, modern data-driven machine learning (ML) approaches can be highly effective. The PUREX process is an attractive system to investigate the use of ML for behavioral prediction in solvent extraction processes due to the large amount of published data available in the open literature. Since the process has been extensively studied and fine-tuned, PUREX data sets also likely offer relatively clean and unbiased data sets, ideal for ML model development. ML excels at modeling nonlinear relationships, feature discovery, and anomaly detection, which are common weaknesses for traditional modeling techniques. In recent years, ML techniques have found successful applications in various fields of nuclear science and technology. For example, ML was useful for evaluating nuclear data, (17) validating and identifying problematic nuclear data, (18,19) and monitoring nuclear energy systems behavior and decision making. (20) ML has also been found to be effective in nuclear forensic applications, (21) nuclear material, (22) and waste research. (23) ML has also been applied to analytical chemistry applications, such as optical spectroscopy, (24) mass spectrometry, (25−27) speciation, (28) and characterization/classification of microstructural features. (29) While ML has seen success with ML-informed safeguards approaches in PUREX reprocessing facilities, (30) it has not yet been explored for predicting PUREX chemical extraction data.
This work aims to build a proof-of-concept for the development of ML predictive capabilities to enhance our understanding and control of the PUREX solvent extraction process. By use of a “phased approach”, the first step is to identify an appropriate model using the extraction of HNO3 by TBP to ensure understanding of this critical component of dissolved used fuel. Initial efforts are focused on the ML prediction of nitric acid partitioning between the aqueous phase and the TBP-based organic phase as precursor knowledge to elucidate the behavior of other fuel constituents. Here, a variety of different ML algorithms are tested and applied to experimental data collected from the literature to develop an ML model for the two-component HNO3-TBP extraction system. A predictive ML model that does not require metal inputs will provide a basic initial understanding of relevant parameter distributions, allowing a general overview of the underlying reactions and capturing important chemical behavior patterns. Our results highlight that the ML model is successful in predicting equilibrium concentration of HNO3 across a variety of diluents using initial HNO3 and TBP concentrations as input features.

Data Set Curation

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The data sets for ML model development were collected from various literature sources, summarized in Table 1, with 368 data points in total extracted. (9,31−37) In all cases, the organic phase containing TBP in a hydrocarbon diluent was contacted in a 1:1 volume ratio with the aqueous phase containing HNO3 in water. All contacts took place at ambient temperature: 20–25 °C. Ochkin et al. (35) and Burns and Hansen. (31) reported using separatory funnels to contact the phases by shaking. Zongcheng et al., (37) Asumussen et al., (9) and Davis et al. (33) reported using centrifuge tubes, however, each employed a different method for combining the phases; Zongcheng et al. (37) shook the tubes inside a thermostated box for 30 min at 25 °C, Asumussen et al. (9) used a vortex mixer for 15 min, and Davis et al. (33) used a high-speed paddle stirrer to achieve a homogeneous mixture for 15 min. Every group centrifuged the samples to achieve separated phases postcontact, with the exception of Davis (36) and Burns and Hanson, (31) who allowed the solutions to settle naturally. Coddinng et al. (32) did not provide specific details regarding the experimental setup beyond that the organic and aqueous phases were combined. All groups titrated the aqueous phase postcontact to determine the acid concentration.
Table 1. Summary of the Data Collected from the Literature for Model Buildinga
AuthorNo. of Data PointsInitial [HNO3]% v/v TBPDiluent
Ochkin et al. (35) (2010)941.0–10.55–30Dodecane
Davis (36) (1962)870.01–9.05–100Amsco 125-82
Zongcheng et al. (37) (1989)430–8.05–100Heptane
Asmussen et al. (9) (2019)201.0–1220–35Dodecane
Burns and Hanson (31) (1964)720.3–10.520–30Kerosene
Davis et al. (33) (1966)410.1–15100None
Coddinng et al. (32) (1958)110.1–6.030Kerosene
a

There were a total of 7 articles, with the extracted data covering a wide range for the % v/v TBP feature and Initial [HNO3] feature. Note that the extracted data was collected across 5 different diluents (including no diluent).

Regarding reported experimental errors, only a few of the groups provided the values of standard deviation among measurements. For example, Davis et al. (33) gave ±1% reproducibility among duplicates for acid concentration between phases and Zongcheng et al. (37) reported a ± 2% deviation for acid concentration reproducibility. Ochkin et al. (35) calculated measurement error via three different methods, comparing the aqueous acid concentration to other results for each % v/v TBP used: for 30% v/v TBP, the uncertainty was 1.7–2.2%; for 12% v/v TBP, it was 1.9–2.7%; and for 5% v/v TBP, it was 3.0%. No other groups reported any experimental errors.
Select extraction isotherms for HNO3 between the aqueous and organic phase at equilibrium obtained from various reports are given in Figure 1. Despite the variations in experimental methods, the data collected by the various groups show relative consistency, as visualized in Figure 1, which can be explained by the fast extraction kinetics. (38) To demonstrate consistency across the reported values, the data were fitted using fifth order polynomials, giving R2 values of 0.9988, 0.9993, and 0.9991 for 5%, 30%, and 100% v/v TBP, respectively (Figure 1a–c). This fitting was only used to visualize the general trends across studies using different experimental techniques and not for any further conclusions. The values reported by Asmussen et al., (9) is the only data set that visually appears to have low consistency (see Figure 1b), with respect to the rest of the extracted data. For this reason, these values were not included in the fitting of the data. The relative consistency across all 368 data points collected from the literature was determined to be sufficient for use with ML, thus providing a reliable database for the model to elucidate the extraction behavior.

Figure 1

Figure 1. Extraction isotherms at 20–25 °C, created from the literature database, denoted by the symbols. Note that the trends present demonstrate that there is no diluent dependency in this data set. The smooth curve represents a polynomial fit within a 98% confidence interval for the fit, used to describe consistency among authors and is otherwise arbitrary. (a) is 5% TBP, (b) is 30% TBP, (c) is 100% TBP, and (d) contains the rest of the data with varying concentrations of TBP.

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Approach

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Machine learning is a data driven approach that consists of training a model from experimental or simulated data. Because the HNO3 concentration values provided in the literature were continuous rather than categorical, regression models were the primary focus within this work. Given our historical data sets, we already had the particular input features and the corresponding outputs for model training, and therefore only used supervised regression techniques. In this work, we focused specifically on five supervised regression models, as implemented in Sci-Kit Learn: (39) multilayer perceptron (MLP), (40) random forest regression (RF), (41) support vector regression (SVR), (42) k-nearest neighbors (KNN), (43) and linear regression (LR) as a baseline. For each model, algorithm hyperparameters were optimized throughout training and testing, and the best performing model was utilized for benchmarking purposes.
The selected model input features were: (1) TBP concentration, (2) the specified diluent, and (3) the initial HNO3 concentration. The output feature was the equilibrium HNO3 concentration within the organic phase (TBP + diluent). Additionally, the diluent input feature was indexed, due to it being a discrete/categorical feature. Water in the organic phase as an output parameter was omitted due to limited available data. To compare performance across all models, several metrics were selected, including R2, mean squared error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE), for each of the train, test, and holdout data sets. (44) For calculating R2, the experimental concentrations are plotted against the values predicted by each model.
After developing initial models with the data set of 368 points collected across 5 different diluents (dodecane, kerosene, heptane, amsco 125-82, and no diluent), it was found that all five of the selected algorithms demonstrated inadequate performance, evidenced by high values for the error metrics as shown in Table 2, even after hyperparameter tuning. This indicated that the influencing factor may occur in the data set preprocessing. We therefore explored the impact of the diluent feature and the initial ordinal encoding on model performance.
Table 2. Metrics for Initial Model Trained on Data with All Diluents, with the Three Input Features of Initial Concentration, Volume TBP, and Diluenta
SubsetTraining SetTest Set
 R2MSEMAEMAPER2MSEMAEMAPE
Metric0.99670.00150.026881.070.99570.00180.0301116.93
a

The multi-layer perceptron model’s metrics are shown here, averaged from 1000 model trainings.

To identify whether the diluent feature was significantly impacting the model’s predictions, permutation feature importance (PFI) (45) was conducted on the data set. Since the R2 value was close to 1.0, using permutation importance was feasible to probe which features were most predictive. The PFI showed that the model was highly independent of the diluent feature relative to the other features. The low PFI score for the diluent feature indicated that it could be safely eliminated from the data set for developing the ML models. Figure 2 displays the results; this same technique can be used when building ML models for more complex data sets with more features.

Figure 2

Figure 2. Permutation feature importance results for initial data set, using the MLP model.

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Models were then trained on the data set with all diluents, with just the two input features of TBP concentration and initial concentration. Additionally, in an effort to assess the generalizability of the model’s performance across each diluent, a holdout set was constructed with representative points from each diluent, by manually selecting 7 points from each diluent set at random. The actual vs prediction plot for this newly structured data set is shown below in Figure 3, for the random forest and MLP models.

Figure 3

Figure 3. Results for two of the best-performing tested models for the full data set with only the 2 input features of initial concentration and vol. TBP. (a) MLP model and (b) random forest model. Note that prediction accuracy is inconsistent across diluents, which can be observed from the difference in accuracies for the different holdout sets.

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Different diluents had noticeably different prediction accuracies and error metrics. For example, for the random forest model, dodecane and kerosene had R2 values >0.98 and MAPE values <10%, while heptane had an R2 value <0.90 and MAPE value >20%, and amsco 125-82 had an R2 value below 0.85 and MAPE value >55%. Since all diluents did not have similar prediction accuracy but the diluent PFI indicated the diluent was not a primary factor, it suggested that the different data sets had other potentially influential factors affecting the results. These could be factors such as temperature, humidity, and extraction efficiency among other confounding variables. This was contrary to our findings from the curation stage of the data set being relatively consistent; it suggested that the small variations for the different diluents were projected when the data was processed by the ML model. Thus, the original data set was reorganized based on diluents with almost identical behavior. With trial and error, it was found that the dodecane and kerosene diluents displayed very similar behavior, which allowed for a combined dodecane + kerosene data set for model development. The other diluents (heptane, amsco 125-82, and no diluent/100% TBP), all displayed noticeably different behaviors, independent of one another.
A reason for this inconsistency could be that the heptane and no diluent data sets were relatively small (∼40 data points each), when compared to the selected dodecane and kerosene diluents (∼90 data points each). This was not the case for the data collected using the amsco 125-82 diluent; however, this data set was still not used due to the issues detailed above. Additionally, only one of the extracted papers used the amsco 125-82 diluent, and the authors provided minimal information about the experimental conditions and error. We discern that this may result in minor inconsistencies with the other extracted data, which the ML modeling projected. Moreover, there could also be greater experimental uncertainties associated with the heptane and no diluent cases due to sampling error. Heptane is very volatile, and concentrations can change during manipulation due to the evaporation of the diluent. In the case of no diluent, undiluted TBP is sufficiently viscous that accurate measurement of the volume can be difficult. As a result, subsequent model training focused primarily on the dodecane + kerosene data set.
Notably, equilibrium water concentration data was not consistently available in our entire data set collected for this study. One hundred seventy-one data points from our data set (33,36,37) included information on the equilibrium organic concentration of water, but none of these data points were considered in the prior mentioned dodecane + kerosene data set used to build the model (all data that included water concentration data used amsco or heptane diluents). We plan to perform deeper datamining to obtain additional data with the water dimension in the future follow-up studies (thus taking it from a HNO3-TBP two-dimensional approach to a HNO3-TBP-H2O three-dimensional approach). For example, potential future approaches to include water in the model would include collecting data that measure water content in the organic phase at equilibrium using a Karl Fischer titration method. The diluent and water (which in most cases was not reported) could potentially have had an interaction that impacted the extraction just enough that the model captures it.

Methods

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The details of the data set organization for the ML modeling are given in Figure 4a. The holdout set consisted of 10 data points from the two diluents. The rest of the data set is then randomly split into training and test sets (70% and 30% of the remaining data, respectively). Training and test sets are randomly resampled for each model training, while the holdout set is always the same to allow for a constant data set to evaluate the models.

Figure 4

Figure 4. (a) Proposed workflow for model building. Training set is used to train the model, while the test set is used to evaluate the model’s performance and then adjust the model’s architecture and parameters as necessary, based on the metrics from the test set. Holdout set is used as a blind test of final model performance, after model is fully trained. (b) Data set organization for model building. 5% of starting data set is held out as the holdout set. The rest is used for building the model with a dedicated training and test set.

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We then train our models using a common machine learning workflow, as shown in Figure 4b. The training set is first used to train the model. Then, the model’s performance is evaluated on the test set, and the resulting test metrics serve as a proxy for the model’s generalization performance on unseen data. Based on these test metrics, the model architecture and parameters are adjusted accordingly to better fit the data points from the training and test sets. This hyperparameter tuning process is done iteratively until the best combination is found. While this approach increases the risk of overfitting, it allowed us to train on more of the training data than would otherwise be possible and was seen as sufficient for the proof-of-concept stage. Models were never exposed to holdout data during training. Once models were fully trained, each was evaluated against the holdout data as a blind test of final model performance.

Results and Discussion

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After combining the data sets for the dodecane and kerosene diluents, all 5 of the selected models were used for training on the combined data set, which contains ∼180 data points in total. The results for the optimized, tested models are displayed in Table 3, with each metric being the average value calculated from 1000 model trainings.
Table 3. Metrics for All Five Models Built on the Dodecane + Kerosene Dataseta
Model (Figure #)Test SetHoldout Set
 R2MSEMAEMAPER2MSEMAEMAPE
MLP (Figure 5)0.99580.00040.016811.45%0.99190.00070.02124.79%
RF (Figure 6)0.99020.00100.020211.44%0.98990.00080.01763.92%
SVR (Figure 7)0.97290.00300.021413.08%0.93890.00500.02584.19%
KNN (Figure 8)0.99100.00100.021039.32%0.99520.00040.01442.97%
LR (Figure 9)0.83410.01760.1085154.99%0.79840.01660.114333.62%
a

Calculated from averaging 1000 model trainings. Results for the test set and holdout set are shown here.

These results demonstrate that the RF and MLP algorithms were the best fit for this data set. This is evident by the high training, testing, and holdout scores that were presented by both algorithms along with the relatively low values for the MSE, MAE, and MAPE for all three subsets, in both cases. High scores and low margins of error generally indicate good performance of the algorithm for the data set being dealt with, in addition to high accuracy and high precision. Specifically, for RF, the holdout set had an average accuracy score (R2 value) of ≥0.98, along with a relatively low average mean absolute percentage error of <4%. For MLP, the holdout set had an average accuracy score (R2 value) of ≥0.99, along with a relatively low average mean absolute percentage error of <5%.
The SVR and KNN models were less performant than the RF and MLP models, although both still significantly outperformed the linear regression. The SVR model demonstrated relatively low error and high R2 for the test set, but its predictions on the holdout set were not as accurate as the predictions made by the RF and MLP models (indicated by the lower R2 value for the holdout set). For the KNN model, its predictions were on-par with the MLP and RF models, albeit with significantly higher error on the test set. Low error is important for ensuring reproducibility and precision. As more experimental data sets become available, additional hyperparameter tuning and retraining may improve these models to perform on-par with the RF and MLP models.
The difference in performance between models is expected due to the fact that different models yield varying results due to their inherent architectural differences. For example, neural networks are composed of interconnected neurons in layers, which learn patterns from data through forward propagation and backpropagation. During the back-propagation stage of the training process, the weights and bias are adjusted during each iteration to decrease the loss function, enabling them to make accurate predictions on unseen data. In comparison, random forests work in an objectively different manner. Random forests are ensemble models that combine multiple decision trees to improve the accuracy and prevent overfitting. Each individual tree outputs a prediction, and the final result is determined by averaging among all of the trees in the forest. In this sense, random forests are like a step function, since each tree in the “forest” works in an independent manner. As a result, certain models are better suited to specific tasks. Here, for example, the architecture of the KNN model and SVR models were not as ideal for the task compared to the architecture of the neural network. The neural network was the more capable of capturing the trends present in the data set.
The most influential hyperparameters for each of the models (excluding the linear model) are summarized here: the MLP model was a relatively narrow network with 6 hidden layers and 40 neurons per layer. We trained for 40 epochs and used the Adam optimizer, ReLU activation, and a learning rate of 0.001. The random forest model had 100 estimators (number of trees), a max depth of 10, and a max features value of 4. For the SVR model, the C value (which is a regularization parameter that helps control the trade-off between the training error and the margin) was 100 and we used an RBF kernel. As for the KNN, we had 5 neighbors and used Manhattan for the distance metric. During our hyperparameter search, these were the hyperparameters we found to perform best for this task.
Below (Figures 5–9) are the actual vs prediction plots for the combined dodecane + kerosene data set (∼180 data points in total) for all five of the tested algorithms. The blue line is the y = x line; the closer the data points are to the blue line, the better the model performed in terms of prediction accuracy.

Figure 5

Figure 5. Experimental vs prediction for multilayer perceptron (MLP) regression model. All subsets were predicted well.

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Figure 6

Figure 6. Experimental vs prediction for random forest (RF) regression model. Some predictions were less precise, but generally accurate predictions.

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Figure 7

Figure 7. Experimental vs prediction for support vector regression (SVR) model. Some predictions errors are apparent, for the test and holdout subsets.

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Figure 8

Figure 8. Experimental vs prediction for k-nearest neighbors (KNN) regression model. Predictions are good though noisy overall.

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Figure 9

Figure 9. Experimental vs prediction for linear regression (LR) model. Performance is poor on all subsets.

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As demonstrated in Figures 5–9, all three data sets (training, testing, and holdout) showed strong, positive correlations for the RF regression and MLP models. As mentioned previously, the KNN and SVR models also displayed encouraging results, albeit not performing as well as RF and MLP.
Also notable is the amount of randomness and noise present in the linear regression plot, which demonstrates that a traditional, standard linear model is not capable of predicting organic nitric acid concentration at equilibrium in this instance. The nonlinear ML algorithms capable of learning nonlinear patterns outperformed the linear regression model in all aspects, which exhibits the superiority of nonlinear machine learning prediction against using a standard linear model for the task.
Figure 10 provides a high-level, simplified visualization detailing the experimental and predicted values for the equilibrium nitric acid concentration in the organic phase for a given range of input values, for the training set and the test set, on the MLP model. The solid black line is the trend line for the actual values, and the values predicted by the model for the three different subsets are scattered in the plot. The ML model is able to successfully capture the nonlinear trends and nuances found in the experimental data set.

Figure 10

Figure 10. Initial concentration vs the organic nitric acid concentration at equilibrium for the training and test set, comparing the experimental values against the values predicted by the model. Results are for the MLP model.

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Generating a response surface using the optimized ML models enables visualization of the optimization landscape, which helps with predictive estimations. The model itself can be used for specific predictions for the nitric acid concentration in the organic phase at equilibrium; these surface plots provide the capability of observing and understanding the general trends and behaviors of the extraction process. This is done by generating numerous linearly spaced values within the given range for the input features (initial concentration and percent volume TBP), and then employing the ML model to predict the corresponding output value (organic nitric acid concentration at equilibrium). Figures 11–14 are the corresponding response surfaces generated using each of the 4 nonlinear models (the linear regression model outputs a hyperplane, due to its linear constraints). Note that the output feature is the z-axis. The extracted experimental values are plotted in orange. With additional data, we anticipate an improvement in the optimized response surface plot.

Figure 11

Figure 11. MLP-employed response surface for the dodecane + kerosene data set.

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Figure 12

Figure 12. Random forest-employed response surface for the dodecane + kerosene data set.

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Figure 13

Figure 13. SVR-employed response surface for the dodecane + kerosene data set.

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Figure 14

Figure 14. KNN-employed response surface for the dodecane + kerosene data set.

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Notably, the only model capable of generating a response surface that correlates well with the data we have is the MLP model, as shown in Figure 11. It generated a smooth surface without any discontinuities, which was not the case for the other models. The RF model generated a step-like function, as shown in Figure 12, since it could not properly correlate the directly proportional relationship between percent volume TBP and nitric acid concentration in the organic phase at equilibrium, when it came to predicting values for the interpolated, synthetic data. Similarly, the KNN model also had major discontinuities (Figure 14), albeit a bit better; however, it was still not the continuous response surface that was expected. The SVR model was particularly intriguing, since outside of the data points it learned its predictions were all relatively linear (Figure 13).
The MLP response surface displays some unique characteristics, such as nonlinearity along the axis with respect to initial concentration, and relative linearity along the axis with respect to volume TBP. It would be plausible to validate the model, particularly these features, by using additional data points with input features not studied here, and comparing the model’s predictions to it. One such data point could be outside of the current axes, which would allow for an assessment of the model’s extrapolation capabilities. Another such point could be between two of the TBP curves (e.g., TBP volume of 22%), which would allow for the assessment of the response surface’s interpolation accuracy.

Conclusion

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This paper explores the application of machine learning for predicting nitric acid extraction behavior in the PUREX process. Our results demonstrate that machine learning models, particularly a multilayer perceptron model, are a viable method for behavior prediction of nitric acid extraction by TBP in the PUREX system. There are some evident signs of preliminary success, based on the current results, which demonstrate prediction capabilities with ≥95% accuracy. Furthermore, ML prediction techniques require minimal a priori knowledge of the system or complex parameter details, making them a valuable alternative to resource-intensive traditional methods.
Data set curation and feature selection was performed through dimensionality reduction, ultimately removing the diluent feature. Models were subsequently trained on the smaller data set that contained only the dodecane + kerosene diluent data. Future work will need to explore the impact of the data set imbalance (i.e., significantly more kerosene and dodecane data than other diluents) on the feature selection, as well as any potential model improvements that may result from this. However, due to constraints such as the outdated nature of amsco 125-82 as a diluent, this may be difficult to carry out. Additionally, future work may deal with data we collect from carrying out our own experimental work or data we receive from simulations, rather than the historical experimental data used here. The workflow will also be re-evaluated in future work, due to the potential risk of overfitting with the current workflow, as discussed earlier; however, no apparent signs of overfitting were observed in this work.
Five different ML model types were trained with subsequent hyperparameter optimization, and the best performing models were compared against one another. The MLP was found to perform the best due to its performance across both evaluation metrics and the robustness of the MLP response surface. The response surface is especially useful, as it can help identify gaps in data sets or system behavior to direct future experimental work.
Ultimately, this work established that ML models can accurately predict the extraction of nitric acid by TBP in a relatively simple system (HNO3-TBP extraction) as a proof-of-concept. Through these efforts, we additionally identified key model features and data set gaps in the literature that require additional experimental work. Future work will focus on extending the models developed here to more complex chemical systems by revisiting the diluent parameter, introducing water as an extractant, and eventually the UO2(NO3)2-HNO3-TBP system.

Author Information

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  • Corresponding Author
  • Authors
    • Sankar V. Harilal - Pacific Northwest National Laboratory, Richland, Washington 99352, United States;  Paul G Allen School of Computer Science, University of Washington, Seattle, Washington 98105, United States;  Orcidhttps://orcid.org/0000-0001-9704-236X
    • Matilda I. Duffy - Pacific Northwest National Laboratory, Richland, Washington 99352, United States
    • Eva Brayfindley - Pacific Northwest National Laboratory, Richland, Washington 99352, United States
    • Tatiana G. Levitskaia - Pacific Northwest National Laboratory, Richland, Washington 99352, United States
    • Elisabeth Moore - Pacific Northwest National Laboratory, Richland, Washington 99352, United States;  Orcidhttps://orcid.org/0000-0002-8463-9252
    • Gregg J. Lumetta - Pacific Northwest National Laboratory, Richland, Washington 99352, United States;  Orcidhttps://orcid.org/0000-0002-0216-8515
    • Brienne N. Seiner - Pacific Northwest National Laboratory, Richland, Washington 99352, United States;  Orcidhttps://orcid.org/0000-0002-5826-2623
  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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Portions of this work were supported by the Office of Defense Nuclear Nonproliferation Research and Development within the U.S. Department of Energy’s National Nuclear Security Administration. This work was also supported in part by the U.S. Department of Energy, Office of Science, Office of Workforce Development for Teachers and Scientists (WDTS) under the Science Undergraduate Laboratory Internships Program (SULI).

References

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  • Abstract

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    Figure 1

    Figure 1. Extraction isotherms at 20–25 °C, created from the literature database, denoted by the symbols. Note that the trends present demonstrate that there is no diluent dependency in this data set. The smooth curve represents a polynomial fit within a 98% confidence interval for the fit, used to describe consistency among authors and is otherwise arbitrary. (a) is 5% TBP, (b) is 30% TBP, (c) is 100% TBP, and (d) contains the rest of the data with varying concentrations of TBP.

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    Figure 2

    Figure 2. Permutation feature importance results for initial data set, using the MLP model.

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    Figure 3

    Figure 3. Results for two of the best-performing tested models for the full data set with only the 2 input features of initial concentration and vol. TBP. (a) MLP model and (b) random forest model. Note that prediction accuracy is inconsistent across diluents, which can be observed from the difference in accuracies for the different holdout sets.

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    Figure 4

    Figure 4. (a) Proposed workflow for model building. Training set is used to train the model, while the test set is used to evaluate the model’s performance and then adjust the model’s architecture and parameters as necessary, based on the metrics from the test set. Holdout set is used as a blind test of final model performance, after model is fully trained. (b) Data set organization for model building. 5% of starting data set is held out as the holdout set. The rest is used for building the model with a dedicated training and test set.

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    Figure 5

    Figure 5. Experimental vs prediction for multilayer perceptron (MLP) regression model. All subsets were predicted well.

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    Figure 6

    Figure 6. Experimental vs prediction for random forest (RF) regression model. Some predictions were less precise, but generally accurate predictions.

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    Figure 7

    Figure 7. Experimental vs prediction for support vector regression (SVR) model. Some predictions errors are apparent, for the test and holdout subsets.

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    Figure 8

    Figure 8. Experimental vs prediction for k-nearest neighbors (KNN) regression model. Predictions are good though noisy overall.

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    Figure 9

    Figure 9. Experimental vs prediction for linear regression (LR) model. Performance is poor on all subsets.

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    Figure 10

    Figure 10. Initial concentration vs the organic nitric acid concentration at equilibrium for the training and test set, comparing the experimental values against the values predicted by the model. Results are for the MLP model.

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    Figure 11

    Figure 11. MLP-employed response surface for the dodecane + kerosene data set.

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    Figure 12

    Figure 12. Random forest-employed response surface for the dodecane + kerosene data set.

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    Figure 13

    Figure 13. SVR-employed response surface for the dodecane + kerosene data set.

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    Figure 14

    Figure 14. KNN-employed response surface for the dodecane + kerosene data set.

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      Mayer, B. P.; Dreyer, M. L.; Prieto Conaway, M. C.; Valdez, C. A.; Corzett, T.; Leif, R.; Williams, A. M. Toward Machine Learning-Driven Mass Spectrometric Identification of Trichothecenes in the Absence of Standard Reference Materials. Anal. Chem 2023, 95, 13064– 13072,  DOI: 10.1021/acs.analchem.3c01474
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      Imasaka, T.; Yoshinaga, K.; Imasaka, T. Machine Learning for Characterizing Biofuels Based on Femtosecond Laser Ionization Mass Spectrometry; Anal. Chem. , 2024. 96, 10193– 10199. DOI: 10.1021/acs.analchem.4c00478
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      Lu, Y.; Li, X.; Yu, L.; Zhang, S.; Wang, D.; Hao, X.; Sun, M.; Wang, S. Machine Learning Algorithms for Intelligent Decision Recognition and Quantification of Cr (III) in Chromium Speciation. Anal. Chem 2023, 95, 18635– 18643,  DOI: 10.1021/acs.analchem.3c04878
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      Pazdernik, K.; LaHaye, N. L.; Artman, C. M.; Zhu, Y. Microstructural Classification of Unirradiated LiAlO2 Pellets by Deep Learning Methods. Comput. Mater. Sci 2020, 181, 109728,  DOI: 10.1016/j.commatsci.2020.109728
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      Shoman, N.; Cipiti, B.; Grimes, T.; Wilson, B.; Gladen, R. Insights from Applied Machine Learning for Safeguarding a PUREX Reprocessing Facility. 2021, SAND2021-9220C.
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      Burns, P.; Hanson, C. Distribution of Nitric Acid Between Tri-n-Butyl Phosphate and Water. J. Appl. Chem 1964, 14, 117– 121,  DOI: 10.1002/jctb.5010140304
      31
      Distribution of nitric acid between tributyl phosphate and water
      Burns, P. E.; Hanson, C.
      Journal of Applied Chemistry (1964), 14 (), 117-21CODEN: JACHAU; ISSN:0021-8871.
      The distribution of HNO3 between H2O and both 20 and 30 vol. % solns. of Bu3PO4 in kerosene at 20 and 25° was studied up to the aq. phase concn. of 10M. An equation is derived to represent the distribution up to aq. phase concns. of 4M.
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      Coddinng, J.; Haas, W.; Heumann, F. Tributyl Phosphate–Hydrocarbon Systems. Organizing equilibrium data. Ind. Eng. Chem 1958, 50, 145– 152,  DOI: 10.1021/ie50578a024
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      Davis Jr, W.; Mrochek, J.; Hardy, C. The System: Tri-n-Butyl Phosphate (TBP)-Nitric Acid-Water-I Activities of TBP in Equilibrium with Aqueous Nitric Acid and Partial Molar Volumes of the Three Components in the TBP Phase. J. Inorg. Nucl. Chem 1966, 28, 2001– 2014,  DOI: 10.1016/0022-1902(66)80292-0
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      Nave, S.; Mandin, C.; Martinet, L.; Berthon, L.; Testard, F.; Madic, C.; Zemb, T. Supramolecular Organisation of Tri-n-Butyl Phosphate in Organic Diluent on Approaching Third Phase Transition. Phys. Chem. Chem. Phys 2004, 6, 799– 808,  DOI: 10.1039/b311702b
      34
      Supramolecular organisation of tri-n-butyl phosphate in organic diluent on approaching third phase transition
      Nave, S.; Mandin, C.; Martinet, L.; Berthon, L.; Testard, F.; Madic, C.; Zemb, Th.
      Physical Chemistry Chemical Physics (2004), 6 (4), 799-808CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      The supramol. organization of org. phases of the extractant tri-Bu phosphate (TBP) in alkane diluents is studied. Effects of extractant and nitric acid concn., temp. and acid nature on third phase formation are presented. The aim is to gain information on the structural aspect of the org. phase just before phase splitting in liq.-liq. extn. Small-angle X-ray and neutron scattering combined to vapor pressure osmometry, tensiometry and cond. are used to characterize these systems. It is shown that org. phases of TBP in equil. with acid solns. are organized in reverse interacting aggregates and that these interactions govern the formation of the third phase. These aggregates disappear at high temps., even in the presence of HNO3, to form regular mol. solns. The shape and size of the aggregates are not modified by varying the acid nature, HNO3 or TBP concns., whereas low temps. and polarizability of the aq. micellar core affect the strength of the interactions. The sticky sphere model proposed by Baxter is used successfully to model the small reverse micelles of the org. TBP phases and quantify their interactions.
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      Davis Jr, W. Thermodynamics of Extraction of Nitric Acid by Tri-n-Butyl Phosphate–Hydrocarbon Diluent Solutions: I. Distribution Studies with TBP in Amsco 125–82 at Intermediate and Low Acidities. Nucl. Sci. Eng 1962, 14, 159– 168,  DOI: 10.13182/NSE62-A28115
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      Zongcheng, L.; Tiezhu, B.; Yuxing, S.; Yigui, L. Determination of the Thermodynamic Equilibrium Constant of the Extraction System HNO3-Tributylphosphate (TBP)-n-C7H16. Fluid Phase Equilib 1989, 46, 281– 293,  DOI: 10.1016/0378-3812(89)80041-X
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      Davis Jr, W. Thermodynamics of Extraction of Nitric Acid by Tri-n-Butyl Phosphate-Hydrocarbon Diluent Solutions: III. Comparison of Literature Data. Nucl. Sci. Eng 1962, 14, 174– 178,  DOI: 10.13182/NSE62-A28117
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      Pedregosa, F.; Varoquaux, G.; Gramfort, A.; Michel, V.; Thirion, B.; Grisel, O.; Blondel, M.; Prettenhofer, P.; Weiss, R.; Dubourg, V. Scikit-learn: Machine Learning in Python. J. Mach. Learn. Res 2011, 12, 2825– 2830
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      Smola, A. J.; Schölkopf, B. A Tutorial on Support Vector Regression. Stat. Comput 2004, 14, 199– 222,  DOI: 10.1023/B:STCO.0000035301.49549.88
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      Botchkarev, A. A New Typology Design of Performance Metrics to Measure Errors in Machine Learning Regression Algorithms. Interdiscip. J. Inf. Knowl. Manage 2019, 14, 045– 076,  DOI: 10.28945/4184
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      Altmann, A.; Toloşi, L.; Sander, O.; Lengauer, T. Permutation Importance: A Corrected Feature Importance Measure. Bioinf 2010, 26, 1340– 1347,  DOI: 10.1093/bioinformatics/btq134
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