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1. Introduction
Nuclear material accountancy plays a crucial role in verifying special nuclear materials (SNMs) within the framework of safeguards for nuclear non-proliferation. To quantify SNMs (e.g., U and Pu) in unknown nuclear material samples, such as spent nuclear fuels (SNFs), destructive assay (DA) which examines small sample masses has been utilized due to its outstanding precision. However, the substantial time and cost associated with DA analysis present a practical challenge making it advisable to minimize the number of DA samples.
Pyro-processing, a dry-type reprocessing technology, enhances the environmental and economic sustainability of treating SNFs while maintaining robust proliferation resistance. In contrast to wet-type reprocessing, which uses aqueous solutions wherein nuclear materials can be homogeneously dissolved, pyro-processing requires DA analysis of solid-state particle samples. If DA samples (~several grams) are simply extracted from the entire SNF assembly (≈500 kg) following mechanical de-cladding, substantial deviations in SNM concentrations may occur among DA samples due to the intrinsic non-uniformity of burn-up across the SNF matrix [1].
To address this, a low-temperature oxidation, known as ‘voloxidation’, is typically employed to pulverize SNFs post-decladding, as illustrated in Fig. 1 [2,3]. Ensuring appropriate mixing of the resultant powder prior to input material accounting is essential for verifying the representativeness of DA samples, thereby mitigating the risk of significant under- or over-estimations of the characteristics of the original material. Consequently, an effective homogenization process is critical, with careful consideration given to estimating sampling uncertainty (denoted as ‘homogeneity’) [4]. Here, heterogeneity corresponds to the variance in estimated Pu concentration prior to DA sampling, directly influencing the uncertainty of input material accounting.
Fig. 1
Simplified scheme of the procedural steps from SNF assembly through to the electrolytic reduction process in pyro-processing.
Several prior studies have explored the homogenization process for SNFs within the context of pyro-processing. One study described mixing the entirety of materials (~500 kg) from the SNF assembly, though it did not address the resulting sampling or accounting uncertainties in detail [5]. Another study proposed a double-stage homogenization process using two types of mixers (a Tumbler and a Nauta mixer, with capacities of 75 kg and 10 kg, respectively) designed with considerations for remote control and maintenance [4].
The latter study provided a thorough analysis of Pu sampling uncertainty (referred to as ‘Pu heterogeneity’) across various parameters, demonstrating that the process achieved Pu accounting uncertainty below 1% under specified conditions [4]. However, challenges remain with the double-stage process. It relied on the grab sampling method, which necessitated relatively large sampling quantities due to limited homogenization effectiveness and reproducibility. Consequently, voloxidation was required for the entire SNF mass before the sampling and homogenization stages. Additionally, materials unaccounted for (MUF) could be impacted by potential hold-ups in multiple instruments and their uses due to adhesive and cohesive fine particles (< 45 μm) that are sensitive to air conditioning properties [6,7].
In this study, a simulative estimation of Pu accounting uncertainty was performed based on the principles of representative sampling for homogenization in the headend process of pyro-processing. Representative sampling, widely applied in the pharmaceutical industry, employs tools such as the rotary riffler for effective sampling and powder mixing [8]. The rotary riffler functions by rotating a sample distributor, dividing materials uniformly into multiple containers through centrifugal force to yield homogeneous subsamples. This method was anticipated to achieve a low heterogeneity even with smaller sample quantities and larger particle sizes.
With the foundational mechanism of representative sampling via the rotary riffler in mind, particle sampling was computationally simulated using Python code. This study focused on processing relatively large particles (≥ 1,000 μm) and small sample quantities (≤ 5 kg) for sampling and homogenization, in contrast to previous studies. Based on the axial and radial Pu concentration distributions, heterogeneity was estimated under various preconditions, including particle size, sample mass, and de-cladding efficiency [4,9]. The resulting Pu accounting uncertainty was calculated by considering additional variables, revealing that representative sampling is an effective approach for the head-end process of pyro-processing.
2. Research Method
2.1 Head-end Process With Representative Sampling
Fig. 2 illustrates the conceptual head-end process incorporating representative sampling. The SNF assembly first undergoes mechanical de-cladding, separating it into hulls and approximately 450 kg of residual materials. Subsequently, a sieving process is applied to isolate finer particles (< 45 μm). From the remaining larger particles, a sub-sample weighing a few kilograms is selected via representative sampling (using a rotary riffler) and then subjected to voloxidation, which converts it into a fine powder. This powdered form is utilized to extract DA samples, enabling precise analytical measurements. Due to the extensive pulverization achieved by voloxidation, the sampling uncertainty associated with these DA samples is expected to be negligible, as it consists of numerous finely divided particles.
Fig. 2
Schematic of the conceptual head-end process for input material accounting using representative sampling.
In this study, the simulation assumed ideal conditions for representative sampling using a rotary riffler. However, experimental validation in a hot-cell environment would require additional considerations in order to suppose a rotary riffler to be utilizable. The specifications and structural features of a rotary riffler, such as capacity, rotational speed, material compatibility, and ability to handle specific particle sizes, must be carefully considered. Furthermore, remote operability via machinery manipulators (robotic arms) and ease of maintenance are critical factors to ensure reliable and reproducible sampling under hot-cell conditions.
2.2 Pu Concentration
To calculate Pu accounting uncertainty for the SNF assembly, axial and radial burn-up profiles were first prepared, as illustrated in Fig. 3. These were based on the results of gamma scanning [9] at 30 mm intervals along the total 3,780 mm of rod length and RAdial power and burnup Prediction by following fission Isotope Distribution in the pellet (RAPID) program [10,11]. According to the burn-up profiles, the axial and radial distributions of Pu concentration were established and subsequently applied in the particle sampling phase, which will be discussed in Section 2.3.
Fig. 3
Axial and radial Pu concentration distributions based on each burn-up profile obtained through gamma scanning and calculation using the RAPID program [4]. Adapted from C. Lee et al. (2022), J. Nucl. Fuel Cycle Waste Technol., under the terms of the Creative Commons CC BY-NC 3.0 license.
Gamma scanning indicated that axial burn-up reaches saturation along the initial 600 mm of the rod height, so Pu concentration was assumed symmetric at both ends of this 600 mm segment. For the intermediate region, Pu concentration was approximated to match that observed at 600 mm. The RAPID program, developed to predict radial distributions of power, burn-up, and fissionable nuclide densities [10,11], provided radial distribution data aligned with each axial point. The initial fuel quality was specified as 4.5wt% with a density of 10.44 g∙cc⁻1 and a pellet diameter of 8.19 mm. Given the sharp change in burn-up near the radial edge of the fuel rod, data points were densely allocated close to the radius of 4.095 mm. Consequently, Pu concentration distribution was assumed symmetric around the center of the fuel rod (radius = 0 mm, height = 1,890 mm).
2.3 Particle Sampling
Representative sampling based on a rotary riffler was simulated using Python code. The theoretical and empirical foundations of representative sampling are detailed in prior studies by Idaho National Laboratory [12,13]. For the simulation, each sample was assumed to comprise spherical particles of a single size, with the number of particles per sample calculated according to specified particle sizes and sample masses, as outlined in Table 1. Particle sizes ranged from 1,000 to 5,000 μm in diameter, increasing at 1,000 μm intervals, for each sample mass of 1.0, 2.5, and 5.0 kg.
Table 1
Number of particles based on particle size (1,000–5,000 μm) for varying sample masses (1.0, 2.5, and 5.0 kg)
| Particle Size (μm) | 1.0 kg (#particles) | 2.5 kg (#particles) | 5.0 kg (#particles) |
|---|---|---|---|
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|
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| 5,000 | 1,393 | 3,484 | 6,967 |
| 4,000 | 2,722 | 6,804 | 13,608 |
| 3,000 | 6,451 | 16,128 | 32,257 |
| 2,000 | 21,773 | 54,433 | 108,867 |
| 1,000 | 174,187 | 435,467 | 870,933 |
The Pu concentration for each particle was determined based on its specific location, with particle positions randomly sampled within the 3-dimensional (x, y, z) geometry of an SNF rod. For each sampled location, the corresponding Pu concentration was assigned according to the axial and radial burn-up profiles. For example, simulating a 5.0 kg sample composed of 5,000 μm particles required a total of 6,967 location samples. By calculating the average Pu concentration across these samples, and repeating the sampling process 2,500 times for each specified combination of particle size and sample mass, a distribution of average Pu concentrations was obtained for statistical analysis. Note that Pu concentrations for intermediate locations were interpolated due to the discrete nature of the Pu concentration data. Each combination of particle and sample conditions was tested under varying mechanical de-cladding efficiencies of 1.0 (100%), 0.95 (95%), and 0.90 (90%). Fig. 4 presents the distribution of average Pu concentrations for a 5 kg sample of 1,000 μm particles, assuming 100% mechanical de-cladding efficiency.
Fig. 4
Distribution of average Pu concentrations for a 5 kg sample comprising 870,933 particles with a diameter of 1,000 μm, assuming a mechanical de-cladding efficiency of 100%.
2.4 Pu Accounting Uncertainty
Various parameters influence the resulting Pu accounting uncertainty, as illustrated in Fig. 5. In general, heterogeneity decreases with increasing sample mass and decreasing particle size, as the latter leads to a larger number of particles within the sample. The performance of sampling devices can be qualitatively assessed based on the resulting heterogeneity. The distribution of Pu concentration was incorporated into the estimation of Pu heterogeneity under specific preconditions. As outlined in Equation (1), Pu heterogeneity is defined as the relative Pu mass deviation (σm) normalized by the sample mass (m). The Pu mass deviation was calculated by multiplying the sample mass by the standard deviation of the average Pu concentrations (σconc).
Fig. 5
Various parameters influencing Pu accounting uncertainty in relation to sampling and homogenization processes for input material accountancy in the head-end process.
Pu accounting uncertainty was calculated by combining random and systematic uncertainties from both bulk (σBulk) and DA (σDA) components with Pu heterogeneity through the root sum of squares, as shown in Equation (2) [4]. The uncertainties associated with the bulk and DA components are referred to as the international target values (ITV) for measurement uncertainties in safeguarding nuclear materials by the IAEA [14]. The ITV values indicate that uncertainties in both components are sufficiently low to avoid significantly impacting Pu accounting uncertainty. Therefore, achieving Pu heterogeneity below 1% during the homogenization stage is recommended. With sufficiently low Pu heterogeneity, fewer DA samples would be required, reducing the time and cost associated with the process.
3. Results and Discussion
Pu heterogeneity was calculated based on the simulated average Pu concentration distributions, derived from 2,500 repetitions of the sampling procedure under specified preconditions (particle size, sample mass, and de-cladding efficiency). Fig. 6 presents Pu heterogeneity values according to particle size (1,000–5,000 μm) for varying sample masses (1.0, 2.5, and 5.0 kg) and de-cladding efficiencies (A: 1.0, B: 0.95, and C: 0.90).
Fig. 6
Pu heterogeneity as a function of particle size (1,000–5,000 μm) for sample masses of 1.0, 2.5, and 5.0 kg, at varying mechanical de-cladding efficiencies (A: 1.0, B: 0.95, C: 0.90).
As anticipated, higher Pu heterogeneity values were observed with larger particle sizes, smaller sample masses, and higher de-cladding efficiencies. For different decladding efficiencies, this trend is visually evident in Fig. 7. The effect arises because higher Pu concentrations are typically present near the edge of the radius of an SNF rod; at high mechanical de-cladding efficiencies, this region is sufficiently introduced into the sample, resulting in greater dispersion in Pu concentration and subsequently increasing Pu heterogeneity.
Fig. 7
Pu heterogeneity as a function of particle size (1,000–5,000 μm) for mechanical de-cladding efficiencies (mdE) of 1.0, 0.95, and 0.90 at a 1.0 kg sample mass.
In most conditions, Pu heterogeneity was below 1%, except in cases involving 5,000 μm particle size, 1.0 kg sample mass, and 1.0 de-cladding efficiency. Given the potential additional contributions from bulk and DA components, Pu accounting uncertainty is expected to exceed 1% in such cases. In practical terms, the application of representative sampling to the head-end process is expected to enhance the safeguardability of pyro-processing. This is attributed to its anticipated demonstration of effective homogenization performance while allowing a relatively simplified process. Additionally, it is expected to minimize the impact of fine powder hold-up, further contributing to the robustness of the process.
Table 2 summarizes the random and systematic uncertainties for each bulk and DA component [14]. For the bulk component, random and systematic uncertainties were each set at 0.2% for mass ranges (0–20 kg) when assuming an electronic balance (EBAL) measurement, yielding an ITV value of 0.2828% via the root sum of squares. For the DA component, random and systematic uncertainties were set at 0.3% each, based on the use of isotope dilution mass spectrometry (IDMS) for plutonium mass fraction measurement in hot cell conditions, resulting in an ITV value of 0.4243% through the same calculation.
Table 2
Random and systematic uncertainties for each bulk and DA component, and corresponding ITV values [14]
| Bulk uncertainty | DA uncertainty | ||
|---|---|---|---|
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|
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| Random uncertainty | Systematic uncertainty | Random uncertainty | Systematic uncertainty |
|
|
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| 2.000×10⁻3 | 2.000×10⁻3 | 3.000×10⁻3 | 3.000×10⁻3 |
| ITV (EBAL) | 2.828×10⁻3 | ITV (IDMS) | 4.243×10⁻3 |
Table 3 displays the resultant Pu accounting uncertainties for various particle sizes and sample masses at different mechanical de-cladding efficiencies (mdE). Overall, Pu accounting uncertainties remained below 1%, with one exception (5,000 μm particle size, 1.0 kg sample mass, and 1.0 mdE), where the value was marginally higher. It was determined that achieving a Pu accounting uncertainty below 1% is feasible with a particle size of 4,000 μm for a 1.0 kg sample mass or with a 2.5 kg sample mass of 5,000 μm particles, even at 100% mdE. This study thereby confirms the effectiveness of representative sampling in achieving highprecision Pu accounting in SNFs, alleviating challenges associated with homogenization, and reducing time and cost burdens.
Table 3
Absolute Pu accounting uncertainties calculated for various particle sizes, sample masses, and mechanical de-cladding efficiencies (mdE)
| Sample Mass | ||||
|---|---|---|---|---|
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|
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| Particle size (<m) | 1.0 kg | 2.5 kg | 5.0 kg | |
|
|
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| mdE (1.0) | 5,000 | 1.173×10−2 | 8.472×10−3 | 7.003×10−3 |
| 4,000 | 9.231×10−3 | 6.944×10−3 | 6.137×10−3 | |
| 3,000 | 7.136×10−3 | 6.006×10−3 | 5.572×10−3 | |
| 2,000 | 5.778×10−3 | 5.381×10−3 | 5.236×10−3 | |
| 1,000 | 5.189×10−3 | 5.133×10−3 | 5.117×10−3 | |
|
|
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| mdE (0.95) | 5,000 | 7.238×10−3 | 6.092×10−3 | 5.607×10−3 |
| 4,000 | 6.314×10−3 | 5.657×10−3 | 5.379×10−3 | |
| 3,000 | 5.656×10−3 | 5.334×10−3 | 5.212×10−3 | |
| 2,000 | 5.264×10−3 | 5.170×10−3 | 5.135×10−3 | |
| 1,000 | 5.121×10−3 | 5.107×10−3 | 5.104×10−3 | |
|
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| mdE (0.90) | 5,000 | 6.375×10−3 | 5.633×10−3 | 5.382×10−3 |
| 4,000 | 5.797×10−3 | 5.391×10−3 | 5.243×10−3 | |
| 3,000 | 5.407×10−3 | 5.220×10−3 | 5.159×10−3 | |
| 2,000 | 5.186×10−3 | 5.137×10−3 | 5.117×10−3 | |
| 1,000 | 5.111×10−3 | 5.104×10−3 | 5.101×10−3 | |
4. Conclusion
In this study, representative sampling method using a rotary riffler was evaluated to ensure reliable plutonium (Pu) accountancy in the head-end process of pyro-processing for spent nuclear fuel (SNF). The research highlighted the benefits of representative sampling, a technique widely used in the pharmaceutical industry, for homogenizing solid-state materials like those found in pyro-processing. Simulations indicated that this approach could achieve Pu heterogeneity at less than 1% with larger particle sizes (≥ 1,000 μm) and smaller sample masses (≤ 5 kg) compared to the previous studies, meeting the requirements for nuclear material accountancy.
The results presented that Pu heterogeneity is influenced by particle size, sample mass, and mechanical de-cladding efficiency (mdE). Larger particles and smaller sample masses resulted in higher heterogeneity values, especially at maximum mdE. Despite this, it was shown that even with a minimal sample mass of 1 kg, Pu accounting uncertainties could be kept under 1% while using particles of approximately 4,000 μm, provided the mdE is maintained at 1.0. This suggests that the rotary riffler-based approach offers a significant advantage in homogenizing solid-state samples from SNFs with reasonably low time and cost by DA analysis.
Overall, the study appears the applicability of representative sampling for Pu accountancy at the head-end process of pyro-processing, achieving a balance between sampling precision and operational efficiency. The methodology not only meets the requirements of nuclear safeguards but also minimizes the sample quantity and associated procedures. Future work should explore the experimental validation of these findings to enhance the robustness of the sampling strategy under various operational conditions.
