Validation of MVP-II with JENDL-4.0, ENDF/B-VII.1, and JEFF-3.2 through HTC critical experiments

ABSTRACT

In order to validate MVP-II, Haut Taux de Combustion (HTC) experiments were analyzed using a code with relatively new nuclear data libraries, JENDL-4.0, ENDF/B-VII.1, and JEFF-3.2. The effective neutron multiplication factor k_eff values were obtained through analyses of all phases of the HTC experiments. Consequently, the k_eff biases evaluated for each nuclear data library were within 300 pcm. Additionally, microscopic production and capture reaction rates of major actinide isotopes were analyzed to substantiate differences among the libraries for a representative case of Phase 1 of the HTC experiments. The analysis showed that microscopic cross sections of ²³⁸Pu and ²⁴¹Am in JEFF-3.2 were somewhat large compared to those of ENDF/B-VII.1 and JENDL-4.0 for the representative case of Phase 1.

KEYWORDS:

• MVP-II
• JENDL-4.0
• ENDF/B-VII.1
• JEFF-3.2
• HTC

1. Introduction

In the 1980s, a series of the French Haut Taux de Combustion (HTC) critical experiments [1] was conducted at the Apparatus B experimental facility in Valduc with the support of the IRSN and AREVA NC to provide a basis for validation of actinide only burnup credit calculations. In the past, US NRC published a report regarding evaluation using HTC critical experiment data [2]. Here, the applicability of the HTC experiments for burnup credit calculations was confirmed by the sensitivity/uncertainty analysis using the SCALE-5.1 code system [3] using both ENDF/B-V and ENDF/B-VI 238 group cross sections at Oak Ridge National Laboratory and hence, US NRC also recommended the HTC critical experiment data for code validation [4].

A continuous-energy Monte Carlo code MVP-II [5] with JENDL-4.0 [6] has been validated as a tool for criticality safety analysis. Historically, criticality safety analyses for storage, transport, and disposal of spent nuclear fuel were conducted assuming isotopic compositions of unirradiated fuel (i.e. fresh fuel) and the MVP-II with JENDL-4.0 was mainly validated against fresh fuel experiments. When it comes to criticality safety analyses using burnup credit, the MVP-II with JENDL-4.0 should be validated using experimental data that are significantly more applicable to the validation of burnup credit calculation.

In this study, validation of the MVP-II with JENDL-4.0 was carried out with the HTC critical experiment data [1]. In addition, ENDF/B-VII.1 [7] and JEFF-3.2 [8] that were latest recommended evaluated nuclear data files for use in criticality safety analyses were used in order to obtain features of the libraries. As a comprehensive verification of the MVP-II, the HTC critical experiment data were also calculated by SCALE-6.2 [9] with continuous ENDF/B-VII.1 library that was widely used for licensing evaluations.

Since HTC fuel rod contains major actinide isotopes important in burnup credit calculation, microscopic production and capture reaction rates of actinide isotopes were analyzed to substantiate differences between libraries for a representative case of Phase 1.

2. HTC critical experiment

The HTC critical experiments were categorized into four phases to represent fuel and neutron interaction characteristics applicable to fuel handling and rod storage, dissolution in a reprocessing plant, a transportation cask, and pool storage in a Pressurized Water Reactor (PWR) [1]. The HTC fuel rods were specifically manufactured to simulate the compositions of typical pressurized water reactor UO₂ spent fuel initially enriched to 4.5 wt% ²³⁵U and burned to 37.5 GWd/MT. The HTC rods consisted of 1-cm-long pellets contained within a Zircaloy-4 cladding and stuck together by means of a stainless steel spring. The rod diameter corresponds to that of an industrial fuel rod. The fuel stack length was adjusted to the dimensions of the experimental tank, which was 90 cm. The rods were held in place by upper and lower grids placed in a rectangular tank.

2.1. Single array of rods in clean/poisoned water (Phases 1 and 2)

Phase 1 included 18 experiments, which were designed for fuel handling and rod storage. Each configuration involved a single square-pitched array of the HTC rods immersed in clean water. Here, the square pitch varied from 1.3 to 2.3 cm according to test cases. The experimental setup for a typical configuration is depicted in Figure 1. Phase 2 simulated the conditions of the dissolution process in a reprocessing plant and included 41 configurations similar to those of Phase 1, except that the moderator and reflector contained either boron (21 configuration) or gadolinium (20 configuration) in solution with various concentrations: from 0 to 0.6 g/l for boron and from 0 to 0.2 g/l for gadolinium. Here, the square pitch in both the solutions varied from 1.3 to 1.9 cm.

Figure 1. Experimental setups for HTC critical experiment series: Phases 1 and 2 (upper), Phase 3 (center), and Phase 4 (bottom).

S. Shiba: Validation of MVP-II with JENDL-4.0, ENDF/B-VII.1, and JEFF-3.2 through HTC critical experiments.

2.2. Four arrays of rods in clean water with absorbing side panels (Phase 3)

Phase 3 included 26 configurations with a 2 × 2 array of fuel assemblies, each of which was arranged in a 25 × 25 square lattice with a pitch of 1.6 cm. Each array was placed in a basket as shown in Figure 1. In some cases, the arrays were surrounded by either borated steel or Boral or cadmium canisters. The spacing between the assemblies varied from 0 to 14.5 cm, depending on the canister type. The configurations were moderated and reflected by clean water.

2.3. Four arrays of rods in clean water with absorbing side panels and shielding (Phase 4)

Phase 4 included 71 cases similar to the Phase 3 configurations except for the fact that shields were surrounding the 2 × 2 fuel assembly array as shown in Figure 1. This series of experiments is categorized into two parts depending on the shield type: lead and steel screens. For each category, different types of canisters were used, and the water gap between assemblies and the spacing between screens and the outer surfaces of the 2 × 2 fuel assembly array varied. Lead and steel screens have 33 and 38 configurations, respectively.

3. Calculation of k_eff using MVP-II and SCALE-6.2

For each phase of the experimental programs, detailed descriptions of the experiments are given in the HTC reports produced by IRSN [1]. The reports are written in a format similar to that used in the International Handbook of Evaluated Criticality Safety Benchmark Experiments [10]. Using these reports, detailed models of the structures of each experiment were prepared for the calculations. As for the conditions, the number of neutrons per generation was set to 4000, and the number of generations was set to 250, the first 50 of which were omitted from tally estimations. The statistical error (standard deviation) of each calculation is in the order of tens of pcm. From the viewpoint of nuclear data libraries, calculated k_eff values are discussed in the following subsections. Furthermore, as supplementary verification for the k_eff values using the MVP-II with the libraries, the SCALE-6.2 with ENDF/B-VII.1 also calculated k_eff values for all phases.

3.1. Calculation results using MVP-II with the libraries

The calculated k_eff values using MVP-II with the major libraries are described in the following subsections. For each phase of the experiments, averaged k_eff values and standard deviations were listed from Table 1 with the SCALE-6.2 results for comparison.

Table 1. Averaged k_eff values and standard deviations for each phase

Item		MVP-II/JENDL-4.0	MVP-II/ENDF/B-7.1	MVP-II/JEFF-3.2	SCALE-6.2/ENDF/B-VII.1
Phase 1	Average	1.0003	0.9997	0.9981	1.0001
	1σ [-]	0.0008	0.0007	0.0010	0.0007
Phase 2	Average	1.0012	0.9998	0.9990	0.9973
(Gd solution)	1σ [-]	0.0009	0.0011	0.0009	0.0012
Phase 2	Average	1.0009	1.0003	0.9989	1.0003
(Boron solution)	1σ [-]	0.0027	0.0027	0.0028	0.0025
Phase 3	Average	1.0000	0.9993	0.9976	0.9998
	1σ [-]	0.0015	0.0017	0.0015	0.0018
Phase 4	Average	1.0013	0.9997	0.9986	0.9999
(Lead screen)	1σ [-]	0.0018	0.0017	0.0017	0.0017
Phase 4	Average	0.9993	0.9985	0.9972	0.9984
(SS screen)	1σ [-]	0.0018	0.0019	0.0019	0.0019

3.1.1. Phase 1

The averaged k_eff values calculated using the MVP-II with JENDL-4.0 and ENDF/B-VII.1 were in good agreement with the experimental data, with discrepancies less than 50 pcm as shown in Table 1. The MVP-II with JEFF-3.2 slightly underestimated the averaged k_eff value. The calculated k_eff values as a function of fuel rod pitch are described in Figure 2 with the SCALE-6.2 results for comparison. The calculated k_eff values using the libraries were not correlated with fuel rod pitch which corresponds to the neutron spectrum. And the consistent underestimation of k_eff values in JEFF-3.2 should be recognized in criticality analysis.

Figure 2. Calculated k_eff values for Phase 1 as a function of fuel rod pitch.

S. Shiba: Validation of MVP-II with JENDL-4.0, ENDF/B-VII.1, and JEFF-3.2 through HTC critical experiments.

3.1.2. Phase 2

For the experiments with gadolinium solution, the averaged k_eff values using ENDF/B-VII.1 were in good agreement with the experimental data, with discrepancies less than 50 pcm as shown in Table 1. The averaged k_eff values using JEFF-3.2 were slightly underestimated. Those deviations of the averaged k_eff values became larger than those of Phase 1. The calculated k_eff values as a function of fuel rod pitch and gadolinium concentration were described in Figures 3 and 4 with the SCALE-6.2 results for comparison. The k_eff values were correlated with these parameters. In the wider fuel rod pitch, where the neutron spectrum became softer, the k_eff values were slightly overestimated. As the concentration becomes high, the k_eff values gradually declined.

Figure 3. Calculated k_eff values for Phase 2 as a function of fuel rod pitch: Gadolinium (upper) and boron (bottom).

S. Shiba: Validation of MVP-II with JENDL-4.0, ENDF/B-VII.1, and JEFF-3.2 through HTC critical experiments.

Figure 4. Calculated k_eff values for Phase 2 as a function of concentration: Gadolinium (upper) and boron (bottom).

S. Shiba: Validation of MVP-II with JENDL-4.0, ENDF/B-VII.1, and JEFF-3.2 through HTC critical experiments.

For the experiments with boron solution, the averaged k_eff values using JENDL-4.0 and ENDF/B-VII.1 were in good agreement with the experimental data, with discrepancies less than 100 pcm as shown in Table 1. The deviation of calculated k_eff values for each experiment, however, was considerably large and k_eff plots were scattered with varying boron concentration and fuel rod pitch, and no meaningful tendency was observed with the two parameters as shown in Figures 3 and 4. Apparently, this might be caused by experimental uncertainties regarding boron concentration measurements [1,2]. Accordingly, the k_eff values sensitive to the neutron spectrum and concentration may be a concern in criticality analysis.

3.1.3. Phase 3

The averaged k_eff values using JENDL-4.0 and ENDF/B-VII.1 were in good agreement with the experimental data, with discrepancies less than 100 pcm as shown in Table 1. The MVP-II with JEFF-3.2 slightly underestimated the averaged k_eff values. The calculated k_eff values were described in Figure 5 with the SCALE-6.2 results for comparison. As shown in Figure 5, the calculated k_eff values depended on the canister type surrounding each array compared to the results of cases without a canister. The k_eff values for configurations with borated stainless steel and cadmium canisters especially indicated an underestimation trend, whereas the calculated k_eff values for the cases without a canister were similar to those of Phase 1. It was seen that the k_eff values in the configurations corresponding to zero-spacing between canisters (cases 2, 6, and 8) showed erratic behaviors. This tendency suggests some water-filled space between the canisters due to uncertainties in canister positions, which was not taken into account in the calculations. Accordingly, it should be recognized that the calculated k_eff values result in underestimation through the libraries for configurations containing boron and cadmium.

Figure 5. Calculated k_eff values for Phase 3 as a function of case number.

S. Shiba: Validation of MVP-II with JENDL-4.0, ENDF/B-VII.1, and JEFF-3.2 through HTC critical experiments.

3.1.4. Phase 4

The calculated k_eff values for Phase 4 were described in Figure 6 with the SCALE-6.2 results for comparison. In the lead screen cases (upper figure), the MVP-II with JENDL-4.0 overestimated k_eff values as shown in Table 1 and Figure 6. Hence, we might discuss further effects as to lead cross section in JENDL-4.0, and the accuracy of lead cross section of JENDL-4.0 should be reviewed as necessary in criticality analysis. On the other hand, the averaged k_eff value using ENDF/B-VII.1 was in good agreement with the experimental data with discrepancies less than 50 pcm.

Figure 6. Calculated k_eff values for Phase 4 as a function of case number: Lead (upper) and Steel (bottom).

S. Shiba: Validation of MVP-II with JENDL-4.0, ENDF/B-VII.1, and JEFF-3.2 through HTC critical experiments.

For the steel screen cases, the averaged k_eff value using JENDL-4.0 was in good agreement with the experimental data with discrepancies less than 100 pcm as shown in Figure 6 and Table 1. In contrast, the averaged k_eff value using either ENDF/B-VII.1 or JEFF-3.2 had slight underestimation against the experimental data.

3.2. Discussion for validation results

The averaged k_eff values and standard deviations (1σ) in Phases 1–4 were given in Figure 7. Averaged k_eff biases using the MVP-II with the libraries were within 300 pcm. These biases were closely comparable to those of the SCALE-6.2 with ENDF/B-VII.1 and showed similar trends as a function of the parameters as shown in Figures 2–6. Therefore, the MVP-II results were comparable to those with SCALE-6.2.

Figure 7. Averaged biases and standard deviations (1σ) as a function of phase.

S. Shiba: Validation of MVP-II with JENDL-4.0, ENDF/B-VII.1, and JEFF-3.2 through HTC critical experiments.

As further discussion, microscopic production and capture reaction rates for actinide isotopes were analyzed to substantiate differences between the libraries for a representative case of Phase 1. For Phase 1, the reaction rates calculated by the MVP-II with JENDL-4.0 are shown in Figure 8. For ENDF/B-II.1 and JEFF-3.2, the differences from the values of JENDL-4.0 are also shown in Figures 9 and 10. On production reaction rates in JEFF-3.2, the ²³⁸Pu reaction rates were slightly larger than those of JENDL-4.0 and the differences were reduced with the fuel rod pitch as shown in Figure 9. The capture reaction rates of ²³⁸Pu and ²⁴¹Am, regardless of fuel rod pitch, showed 35% and 10% higher values, respectively, compared to those of JENDL-4.0 as shown in Figure 9. Here, these actinide contributions to k_eff are relatively small. These higher capture reaction rates in JEFF-3.2 were also addressed in the past study [11,12]. The study described that the thermal and epithermal capture cross section of ²⁴¹Am and ²³⁸Pu would be relatively larger in JEFF-3.2 in comparison with the other libraries. On the other hand, the differences in production and capture reaction rates between ENDF/B-VII.1 and JENDL-4.0 are less than 2% as shown in Figure 10.

Figure 8. Microscopic production and capture reaction rates of JENDL-4.0 as a function of fuel rod pitch in Phase 1.

S. Shiba: Validation of MVP-II with JENDL-4.0, ENDF/B-VII.1, and JEFF-3.2 through HTC critical experiments.

Figure 9. Difference of microscopic reaction rates as a function of fuel rod pitch in Phase 1. (JEFF-3.2–JENDL-4.0).

Figure 10. Difference of microscopic reaction rates as a function of fuel rod pitch in Phase 1 (ENDF/B-VII.1–JENDL-4.0).

4. Summary and conclusion

The HTC critical experiment data were analyzed by the MVP-II with the libraries and averaged k_eff values through phases were within 150 pcm in JENDL-4.0 and ENDF/B-VII.1 and were within 300 pcm in JEFF-3.2. In comparison with the SCALE-6.2, it was realized that the biases of averaged k_eff values in the MVP-II with JENDL-4.0 were comparable to those of SCALE 6.2. Hence, the MVP-II with JENDL-4.0 was validated using the HTC critical experiment data for the burnup credit criticality calculations.

Microscopic production and capture reaction rates for actinide isotopes were analyzed for a representative case of Phase 1. It indicated that ²³⁸Pu and ²⁴¹Am microscopic capture reaction rates in JEFF-3.2 were ~20% larger than those of JENDL-4.0 for HTC experiment data. On the other hand, the differences in microscopic reaction rates between JENDL-4.0 and ENDF/B-VII.1 were within 2%. Here, since ²³⁸Pu cross section was modified in the update from JEFF-3.2 to JEFF-3.3, HTC experimental data need to be also analyzed by MVP-II with JEFF-3.3.

Acknowledgments

The author acknowledges T. Sakai, T. Nakajima, T. Yamamoto, and F. Nagase at Secretariat of Nuclear Regulation Authority for their very efficient and valuable reviews of the paper. The author also acknowledges numerous partners who have contributed to the code validation.