NEA Burn-up Credit Criticality Safety Benchmark

Annals of Nuclear Energy 87 (2016) 48–57

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Review calculations for the OECD/NEA Burn-up Credit Criticality Safety Benchmark José J. Herrero a,⇑, Alexander Vasiliev a, Marco Pecchia a, Hakim Ferroukhi a, Stefano Caruso b a b

Laboratory for Reactor Physics and Systems Behavior, Paul Scherrer Institut (PSI), 5232 Villigen PSI, Switzerland National Cooperative for the Disposal of Radioactive Waste (NAGRA), Hardstrasse 73, 5430 Wettingen, Switzerland

a r t i c l e

i n f o

Article history: Received 11 June 2015 Received in revised form 16 August 2015 Accepted 17 August 2015

Keywords: Burn-up credit MCNP6 SERPENT2 CINDER Waste disposal Criticality safety

a b s t r a c t A calculation methodology for criticality safety evaluations related to medium term dry storage, e.g. interim storage, and long term waste disposal, e.g. deep geological repository, is under development at PSI. In that sense, the performance of present decay and criticality safety codes has to be evaluated for this kind of applications, with code to code, and data to data, comparison as a very first step. In this article, the Burn-up Credit Criticality Safety Benchmark Phase VII organized by OECD/NEA has been employed to evaluate decay calculations results for the codes CINDER and SERPENT2. The computed isotopic compositions have then been used for the assessment of the criticality calculations with MCNP6 and SERPENT2, while employing the most recent available cross sections libraries from ENDF/B-VII.1, JEFF-3.2 and TENDL-2014. Results show overall a good agreement for all the options listed, while differences are pointed out and their origin is discussed. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction The Swiss National Cooperative for the Disposal of Radioactive Waste (NAGRA) plans to submit a general license application for the site of a deep geological repository for the disposal of spent fuel and high-level waste by 2022. One of the requirements to be accomplished for the design of the repository is the safety of the installations (encapsulation facility and repository) from the point of view of a possible criticality excursion on the time span when the concentration of actinides in the fuel is supposed to lead to the formation of a critical mass. In this article, the Burn-up Credit Criticality Safety Benchmark Phase VII organized by the Expert Group on Burn-up Credit Criticality Safety of the OECD/NEA Working Party on Nuclear Criticality Safety (Radulescu and Wagner, 2012) has been employed to evaluate decay calculations performances for the codes CINDER 1.05 and SERPENT2. The decay data was taken from ENDF/B-VII.1 or JEFF-3.1.1 for SERPENT2, and from ENDF/B-VI.2 in the CINDER data library. The different results are compared in the article. After evaluation of the decay calculations, the set of isotopic compositions computed with SERPENT2 and the ENDF/B-VII.1

⇑ Corresponding author. Tel.: +41 56 310 2802; fax: +41 56 310 2327. E-mail address: [email protected] (J.J. Herrero). http://dx.doi.org/10.1016/j.anucene.2015.08.014 0306-4549/Ó 2015 Elsevier Ltd. All rights reserved.

decay library have then been used for the assessment of the criticality calculations with the Monte Carlo codes MCNP6 and SERPENT2, employing the most recent cross sections libraries ENDF/ B-VII.1, JEFF-3.2 and TENDL-2014. Results show overall a good agreement for all the options listed, differences from one result to another are pointed out and the reasons for such deviations are discussed in the article.

2. Burn-up credit Phase VII benchmark specification The objective of the benchmark was ‘‘to study the ability of the computer codes and the associated nuclear data to predict spent fuel isotopic compositions and k-eff values in a cask configuration over the time duration relevant to SNF disposal” (Radulescu and Wagner, 2012). Participants performed decay and criticality calculations at 30 post-irradiation time steps, out to one million years. Although isotopes important to public dose were also considered, here the attention is focused on the criticality results and therefore only the isotopes considered for these calculations will be compared. Also the fresh fuel composition k-eff values were reported. From all the participants’ results, an averaged value for each compared quantity (with 4 significant digits) together with its standard deviation was included in the final report. These average

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values will be used for the comparison to our results. The initial discharge composition is representative of a PWR assembly with an initial enrichment of 4.5 w/0 of U-235 and 50 GWd/MTU burnup. The k-eff values will be computed taking credit only for actinides (11 isotopes) or for actinides plus fission products (19 additional isotopes), and including the O-16 (stable) present in the compositions. The isotopes considered for each type of calculation are listed in Tables 1 and 2. The cask is loaded with 21 intact standard 17  17 fuel assemblies, all the dimensions for the fuel pins and the guide tubes are described in the final report (Radulescu and Wagner, 2012). The assemblies are situated in a borated stainless steel basket inside a stainless steel (SS304) cask forming an array. The cask is flooded with water and the temperature of the cask is supposed to be 293 K. All the material compositions are given and the isotopic compositions for each metallic species were taken from an IUPAC Technical Report (Berglund and Wieser, 2011) when needed.

has shown to be fast and accurate (Pusa, 2013) when coupled to the transport solution for core burn-up calculations. More recently, the effect of the order of approximation in the calculation of the coefficients of the rational function was studied in connection with the use of very large time steps in decay calculations (Pusa, 2014), it indicates a limit to the time step to be used with the present approximation order. The code can be instructed to run only the decay calculation without predictor/corrector transport calculations in between. In this case, the classical Transmutation Trajectory Analysis (TTA) or linear chains method is activated internally (Isotalo, 2013), this is the same method used by CINDER and the differences with this code should then come only from the decay data employed. In practice, the code was also instructed to use the CRAM to compare both algorithms, and no differences were encountered between both methods. Unlike CINDER, here the user can choose the ENDF decay data library to be employed, which permits to investigate the effect of using different sources of data. Thus, the decay libraries from the ENDF/B-VII.1 evaluation and the JEFF-3.1.1 evaluation, including the spontaneous fission yields files, were employed in the decay calculations. The differences between the solutions from both libraries were minor as reported in next sections.

3. Methodology

3.2. Criticality codes

3.1. Decay codes

Given the geometry to be modelled and the possible complexity in the material composition and distribution when more realistic configurations could be considered; and also to allow the possibility of using continuous energy and the most up to date cross sections libraries; Monte Carlo neutron transport codes have been chosen for these calculations. Among them, MCNP6 and SERPENT2 were studied as candidates. MCNP-6.1 (Goorley et al., 2013) was released by merging together the MCNP5 and MCNPX codes. Its extensive validation and large number of users ensure constant development and improvement, MCNP is an important reference code for criticality calculations. SERPENT2 is a neutron transport code directed towards calculation of models typical of reactor physics problems (Leppänen, 2007), version 2 is beta testing. A main difference with MCNP6 is that it is based on the Woodcock delta-tracking method instead of the track-length estimator (Leppänen, 2010).

Table 1 Actinides only burn-up credit nuclides. U-233 Pu-239

U-234 Pu-240

U-235 Pu-241

U-236 Pu-242

U-238 Am-241

Pu-238

Two codes have been considered during the decay calculations, CINDER 1.05 and the decay module inside SERPENT2. The characteristics of these codes should facilitate also a future coupling to the fuel burn-up sequence for the Swiss power plants and the sensitivity and uncertainty analysis methodologies under development. 3.1.1. CINDER 1.05 CINDER 1.05 is the latest version of CINDER available from the OECD/NEA Databank, it was compiled with the highest precision available. CINDER’s method of resolution is based on the linearization of the Markov chains plus an automatic procedure to simplify the chains depth depending on a user given accuracy parameter (Wilson et al., 2008). The decay data used by CINDER cannot be easily changed and it is based on ENDF/B-VI.2, plus other sources when ENDF/B values were not available. For the benchmark, two calculations were performed; one including only the original time positions whose results were included in the benchmark; another one halving these time steps by including intermediate points in the original time mesh. The results showed deviations in term of relative errors below 10 3, so the method is quite independent on the time step. Also, some sensitivity study to the error tolerance for the convergence parameters was performed. In summary, default parameters can be considered adequate. 3.1.2. SERPENT2 SERPENT2 comes with a decay calculation module used in principle for burn-up calculations. The default decay calculation in SERPENT uses ‘‘an advanced matrix exponential solution based on the Chebyshev Rational Approximation Method (CRAM)”, which

3.3. Nuclear data The nuclear parameters employed in the calculations are as important as the codes benchmarked. In this case, three distributions have been considered: ENDF/B-VII.1, JEFF-3.2 and TENDL2014. In this way, it is expected to obtain at least a first estimation of the agreement of these libraries for waste disposal problems. 3.3.1. ENDF/B The decay and neutron cross sections library files of version VII.1 (Chadwick et al., 2011) have been obtained through two paths. One is the data coming directly bounded to the MCNP6 distribution which includes neutron cross sections in ACE format, and the decay data contained in the CINDER data file (which is from ENDF/B-VI.2 mainly). The other way is through the files posted in

Table 2 Actinides plus fission products burn-up credit nuclides. U-233 Pu-242 Nd-143

U-234 Am-241 Nd-145

U-235 Am-242m Sm-147

U-236 Am-243 Sm-149

U-238 Mo-95 Sm-150

Np-237 Tc-99 Sm-151

Pu-238 Ru-101 Sm-152

Pu-239 Rh-103 Eu-151

Pu-240 Ag-109 Eu-153

Pu-241 Cs-133 Gd-155

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the American National Nuclear Data Center (NNDC), in ACE format for the neutron cross section. Also decay data and the fission yields were obtained from the NNDC, only these were used in the calculations, and MCNP6 cross sections were preferred. The data accompanying MCNP6 included for the first time thermal scattering data processed in continuous energy, which has been used in the calculations with MCNP6 for the hydrogen in water. The discrete energy version was used with SERPENT2. In practice, it has been checked that the k-eff from both descriptions is similar. 3.3.2. JEFF Very recently, the latest neutron data from the JEFF evaluation was released on version 3.2 (Cabellos, 2014). These data only includes thermal scattering libraries for hydrogen in water. Finally, the decay data and fission yields are those from the JEFF-3.1.1 release (Kellett et al., 2009). 3.3.3. TENDL The TALYS based (Koning and Rochman, 2012) evaluated nuclear data library (TENDL) released a new version in late 2014, the approach used here to generate the neutron cross sections is, in principle, independent from ENDF/B or JEFF evaluations. In that sense, this library could be a good indicator for possible needs of review in the evaluated nuclear data, although the results should always be considered cautiously. It can be also useful for the application of stochastic methods for uncertainty propagation in the future. This distribution does not include decay data, and it also does not include the thermal scattering S(a,b) data, the data from ENDF/B-VII.1 were taken instead. 4. Results 4.1. Decay calculations The study starts with a code to code comparison to identify discrepancies, then same method and different libraries, and then proceed with a comparison to the average benchmark results with the results selected as reference. We advance that the results from SERPENT2 using the decay data from ENDF/B-VII.1 (labelled S_E71ref) have been taken as the reference values. These will be shown reliable and they will be used for the comparison to the benchmark average values and later for the criticality calculations. SERPENT2 results with and without including the spontaneous fission yields information produced the same concentrations, with discrepancies below 0.1% for all cases. To have an idea of the impact of such deviation, we used the sensitivities of k-eff to the total cross sections of each isotope reported in the benchmark from TSUNAMI calculations and contrasted to a separate publication from ACAB plus MCNP5 results (Cabellos et al., 2010; Radulescu and Wagner, 2012). For the isotope with the highest relative sensitivity of around 0.425 (Dk/k)/(DN/N) at the end of the 1 million years, which is U-235, considering k-eff equals approximately 0.75 and a relative change in concentration DN/N of 0.001, the Dk results in around 32 pcm. On the other hand, for the highest k-eff position at the beginning of 0.85, and the highest sensitivity possible from Pu239, the obtained Dk would be about 12 pcm for a DN/N of 0.001. These deviations are lower than the Monte Carlo statistical uncertainty band of our calculations. 4.1.1. Comparison between CINDER and SERPENT2 The comparison of the results from CINDER 1.05 calculations using ENDF/B-VI.2 with the values from SERPENT2 using the

Table 3 Relative error (CINDER-S_E71ref/S_E71ref) (%) of isotopic concentrations.

0 1 2 5 10 20 40 60 80 100 120 150 200 300 500 1000 2000 5000 8000 10000 15000 20000 25000 30000 40000 45000 50000 100000 500000 1000000

Gd155 0.00 -0.14 -0.14 -0.11 -0.07 -0.03 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

U 233 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.16 0.16 0.16 0.17 0.17 0.18 0.18 0.19 0.19 0.19 0.19 0.19 0.19 0.19 0.19 0.19 0.18 0.17 0.14

U 234 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.01 0.01 0.01 0.02 0.10 0.13

Np237 0.00 0.00 0.00 0.00 0.00 -0.01 -0.02 -0.02 -0.03 -0.03 -0.03 -0.03 -0.02 -0.02 -0.02 -0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.01 -0.03 -0.06

Pu240 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.02 0.02 0.03 0.05 0.06 0.08 0.09 0.12 0.14 0.16 0.31 0.00 0.00

Pu241 0.00 0.02 0.04 0.10 0.20 0.40 0.81 1.22 1.63 2.04 2.45 3.05 3.84 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Am241 0.00 -0.21 -0.26 -0.30 -0.29 -0.23 -0.12 -0.06 -0.02 0.00 0.01 0.02 0.02 0.02 0.03 0.05 0.09 0.16 0.04 0.03 0.02 0.02 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

ENDF/B-VII.1 data (S_E71ref) in Table 3 shows good agreement, only differences larger than 0.1% are reported. In the table, some errors suddenly fall to zero while they are increasing, this is because a threshold on the error calculation has been setup. Whenever the isotope density falls below 10 9 at/b/cm the error is set to 0.0, in order to prevent the computing of very high relative errors for isotope concentrations which would be totally negligible in the criticality calculations. Pu-241 half-life in CINDER data file is 4.5284  108 s, while in ENDF/B-VII.1 data is 4.509581  108 s, which agrees with the higher concentration encountered in CINDER results. As a consequence, the appearance of Am-241 from Pu-241 is delayed in this case. The Gd-155 initial difference comes from different decay constants in both sets of data for Eu-155; its half-life in CINDER is larger, so the appearance of Gd-155 is slightly delayed. The method used by both CINDER and SERPENT2 was the TTA for these calculations. Nevertheless, SERPENT2 results using the CRAM were equal, despite of the published problem with the order approximation for large time steps mentioned before (Pusa, 2014). 4.1.2. Comparison between ENDF/B-VII.1 and JEFF-3.1.1 data Calculations employing ENDF/B-VII.1 (E71) and JEFF-3.1.1 (J311) evaluations with SERPENT2 were also compared. Table 4 includes the relative differences in percentage between both, and only the isotopes with differences above 0.1% are included. The reasons for the deviation on Tc-99, Sm-149, Pu-241, and Am-243 are given in the next sections. 4.1.2.1. Technetium 99 decay constant. A growing discrepancy between JEFF and ENDF/B results was observed for Tc-99. This isotope is not bred by any parent in this case. The half-life in JEFF3.1.1 is 214000 ± 8000 y, and in ENDF/B-VII.1 is 211105 ± 1200 y. This agrees with higher concentrations after decay computed with JEFF data. ENDF/B-VII.1 data is considered here as the reference because of the lower uncertainties in the decay constants.

J.J. Herrero et al. / Annals of Nuclear Energy 87 (2016) 48–57 Table 4 Relative error (J311-E71/E71) (%) of isotopic concentrations.

0 1 2 5 10 20 40 60 80 100 120 150 200 300 500 1000 2000 5000 8000 10000 15000 20000 25000 30000 40000 45000 50000 100000 500000 1000000

Tc99 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.02 0.04 0.04 0.07 0.09 0.11 0.13 0.18 0.20 0.22 0.45 2.25 4.54

Sm149 0.00 -0.54 -0.54 -0.54 -0.54 -0.54 -0.54 -0.54 -0.54 -0.54 -0.54 -0.54 -0.54 -0.54 -0.54 -0.54 -0.54 -0.54 -0.54 -0.54 -0.54 -0.54 -0.54 -0.54 -0.54 -0.54 -0.54 -0.54 -0.54 -0.54

U233 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.16 0.16 0.16 0.16 0.17 0.18 0.18 0.19 0.19 0.19 0.19 0.19 0.19 0.19 0.19 0.19 0.19 0.19 0.17

Np237 0.00 0.00 0.00 0.00 0.00 -0.01 -0.02 -0.02 -0.02 -0.02 -0.02 -0.03 -0.03 -0.02 -0.02 -0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.01 -0.03 -0.06

Pu238 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Pu240 0.00 0.00 0.00 0.00 0.01 0.01 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.01 0.02 0.03 0.05 0.06 0.08 0.09 0.12 0.14 0.15 0.30 0.00 0.00

Pu241 Am241 Am243 0.00 0.00 0.00 0.01 -0.14 0.00 0.03 -0.18 0.00 0.07 -0.20 0.00 0.14 -0.19 0.00 0.27 -0.15 0.00 0.54 -0.08 0.00 0.82 -0.04 0.00 1.09 -0.01 0.00 1.36 0.00 0.00 1.64 0.01 0.00 2.04 0.02 0.00 2.57 0.02 0.00 0.00 0.03 0.00 0.00 0.04 0.00 0.00 0.08 -0.01 0.00 0.16 -0.01 0.00 0.30 -0.03 0.00 0.07 -0.05 0.00 0.05 -0.07 0.00 0.05 -0.10 0.00 0.05 -0.13 0.00 0.00 -0.17 0.00 0.00 -0.20 0.00 0.00 -0.27 0.00 0.00 -0.30 0.00 0.00 -0.33 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Considering the Mo-99 ? Tc-99 decay chain, Fig. 1 shows the relative differences resulting from analytical calculations performed with the data from JEFF and ENDF/B for that chain, and also the same differences computed with SERPENT2. The agreement is quite exact, indicating that the discrepancy does not come from the method but from the data. 4.1.2.2. Americium 243 decay constant. The differences can be explained also here by the half-life (JEFF half-life is approximately 7365.0 ± 21.9 y and ENDF/B value is 7370.1 ± 15.0 y), but it is not so clear which one is more accurate, although the uncertainty in ENDF decay constant is half of the uncertainty in JEFF decay constant. Considering the chain Pu-243 ? Am-243, the differences in Am-243 concentrations obtained with SERPENT2 using JEFF and ENDF/B values from Table 4 are compared with the differences resulting from analytical calculations performed with the data from both distributions. Again the differences in the data explain the discrepancy, as shown in Fig. 1. 4.1.2.3. Samarium 149 production. Samarium 149 is stable, however a deviation is observed between the results from JEFF and ENDF/B data. The deviation appears in the first decay year, remaining constant over the full time range. The reason is that Sm-149 is considered stable in ENDF/B, but it is radioactive in JEFF with a T1/2 of 2  1015 years. This is several orders of magnitude higher than the next value of its parent Pm-149 which is 2.21 days. Comparing the linear system values in the TTA method of solution used in SERPENT2, it was found that the matrix condition was very poor for the problem with the JEFF coefficient for the Samarium included. A change was introduced to nullify decay constants lower than 10 19 s, which in practice makes the Samarium isotope to be considered as stable, as its decay constant of order 10 23 s. After this change, the relative errors between JEFF and ENDF/B remain as in Table 4 except that the discrepancy for Sm-149 disappears.

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4.1.2.4. Plutonium 241 decay constant. Noticeable relative differences for the computed Pu-241 concentration were found between the different results for its decay. The values obtained with SERPENT2 and the JEFF-3.1.1 decay data yield final concentrations higher than the final concentrations employing ENDF/B-VII.1 decay data, as shown in Table 4. The parent nuclide for Pu-241 is Cm-245, its half-life of 8500 years is much longer than the 100 years it takes the Pu-241 to disappear, and the values of the decay constant for this isotope are the same in both evaluations. Therefore, the reason for the difference in the computed values must be found elsewhere. In particular, it can be observed that the half-life of Pu-241 in JEFF3.1.1 is 14.33 ± 0.04 y, and the value in ENDF/B-VII.1 is 14.290 ± 0.006 y. So Pu-241 will decay faster using ENDF/B data which coincides with the calculations. To conclude this explanation, one should pay attention to the accompanying uncertainties. The values are consistent as the nominal value of each evaluation is inside the uncertainty band of the other. And as the lowest uncertainty is on the value from ENDF/ B-VII.1, these library results are chosen here as reference. 4.1.3. Comparison to benchmark average Finally, the SERPENT2 solution with the ENDF/B-VII.1 data (S_E71ref) was chosen to compare to the benchmark average (bench) results averaged from all the participants’ values. Table 5 illustrates all deviations which are negligible except for few cases, which gives confidence on our solution. From this comparison, the higher deviations are observed for U234, Pu-241, Am-241 and Am-242 m, however these differences would not have a noticeable impact on the criticality results attending to the available sensitivities. These differences were not further investigated as it can become difficult to track their origin from the average of the participants. Furthermore, there is clear disagreement among the participants’ results for these isotopes; the deviations encountered are inside the standard deviations of the benchmark results, except for Pu-241 where they are slightly higher in this comparison. 4.2. Criticality calculations The criticality calculations were performed for all the cross sections libraries and codes combinations available using the isotopic compositions from the SERPENT2 calculation with ENDF/B-VII.1 decay data. Each run used 50 inactive cycles and 400 active cycles, with 50,000 histories per cycle. All the cases were run in parallel with OpenMP with both codes. In the SERPENT inputs, the initial fission source was setup at every fuel pin position in the lattice. In the MCNP6 inputs, for the cases computed with the spent fuel compositions for increasing decay periods, the initial fission source was taken from the converged problem computed with the previous composition, except for the fresh fuel case. The initial spent fuel case already used the fresh fuel case fission source as the starting source. Before comparing k-eff values along the decay period, the values for the fresh fuel problem as specified in the benchmark are also provided in Table 6. The execution times using 16 threads on 8 cores Intel Xeon E5-2670 @ 2.60 GHz were approximately of 450 s for MCNP6 (beta version 6.1.1b) and 240 s for SERPENT2 (version 2.1.22). The results for the fresh fuel calculation between MCNP6 and SERPENT2 show good agreement; SERPENT2 seems to compute consistently lower reactivities but the uncertainty bands still overlap. As a further check, the difference between the results computed with MCNP6 and SERPENT2 for all the time positions, the three cross sections libraries considered, and the actinides only

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Fig. 1. Comparison on the relative deviation (J311-E71/E71) in the compositions computed with different nuclear data libraries using SERPENT2 and analytical solution.

Table 5 Relative error (S_E71ref-bench/bench) (%) of isotopic concentrations.

0 1 2 5 10 20 40 60 80 100 120 150 200 300 500 1000 2000 5000 8000 10000 15000 20000 25000 30000 40000 45000 50000 100000 500000 1000000

Tc99 Sm151 Eu151 Gd155 U233 U234 0.00 0.00 -0.01 0.00 0.00 0.00 0.01 0.00 -0.30 0.34 0.00 0.00 0.01 0.00 -0.31 0.33 0.00 0.00 0.01 0.01 -0.36 0.26 0.00 0.01 0.01 0.02 -0.36 0.19 0.00 0.00 0.00 0.04 -0.34 0.07 0.00 0.01 0.00 0.09 -0.30 0.02 0.00 0.01 0.01 0.13 -0.28 0.01 0.00 0.01 0.00 0.17 -0.27 0.00 0.00 0.01 0.01 0.21 -0.24 0.00 0.00 -0.01 0.00 0.26 -0.22 0.00 0.00 0.03 0.01 0.32 -0.20 0.00 -0.59 0.03 0.00 0.42 -0.16 0.00 -0.59 0.04 0.00 0.65 -0.09 0.00 -0.67 0.03 0.00 1.08 -0.03 0.00 -0.55 0.00 0.00 0.00 0.00 0.00 -0.43 -0.01 0.00 0.00 0.01 0.00 -0.37 0.03 0.00 0.00 0.01 0.00 -0.35 0.02 -0.01 0.00 0.01 0.00 -0.32 0.01 -0.01 0.00 0.01 0.00 -0.31 -0.02 -0.02 0.00 0.01 0.00 -0.34 0.03 -0.01 0.00 0.01 0.00 -0.32 0.03 -0.03 0.00 0.01 0.00 -0.28 0.05 -0.04 0.00 0.01 0.00 -0.27 0.08 -0.03 0.00 0.01 0.00 -0.24 0.06 -0.05 0.00 0.01 0.00 -0.23 0.08 -0.05 0.00 0.01 0.00 -0.17 0.11 -0.09 0.00 0.01 0.00 -0.21 0.18 -0.53 0.00 0.01 0.00 -0.15 1.33 -1.03 0.00 0.01 0.00 -0.11 3.86

Table 6 k-Eff values for fresh fuel calculation with MCNP6 and SERPENT2. ENDF/B-VII.1

JEFF-3.2

TENDL-2014

MCNP6

k-eff 2r

1.15000 0.00036

1.15044 0.00034

1.15128 0.00034

SERPENT2

k-eff 2r

1.14970 0.00032

1.14996 0.00032

1.15092 0.00032

set of isotopes is plot in Fig. 2. We show the difference together with its 2r standard deviation supposing no correlation in both Monte Carlo results. Now it is more apparent that no clear bias

Np237 -0.01 0.02 0.01 0.00 0.01 0.03 0.02 0.01 0.01 0.04 0.02 -0.34 -0.31 -0.26 -0.23 -0.17 -0.16 -0.15 -0.15 -0.16 -0.16 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.02 0.05

Pu238 0.00 0.00 0.00 0.00 0.00 -0.01 -0.01 -0.01 0.00 -0.01 0.00 -0.02 -0.04 -0.03 -0.07 -0.30 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Pu241 0.01 -0.02 -0.05 -0.11 -0.24 -0.48 -0.91 -1.36 -1.78 -2.27 -2.74 -3.37 -4.24 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Pu242 -0.03 -0.02 -0.02 -0.02 -0.02 -0.02 -0.02 -0.02 -0.02 -0.02 -0.02 -0.02 0.02 0.01 -0.01 0.01 -0.01 -0.02 0.02 -0.02 -0.03 -0.03 -0.02 -0.01 -0.01 -0.03 -0.04 -0.03 -0.25 -0.51

Am241 Am242m 0.00 0.00 0.25 0.00 0.31 -0.01 0.37 -0.02 0.35 -0.03 0.27 -0.04 0.15 -0.10 0.08 -0.14 0.02 -0.20 -0.01 -0.24 -0.01 -0.28 -0.02 -0.37 -0.02 -0.50 -0.02 -0.79 0.01 -1.32 0.03 0.00 -0.02 0.00 0.12 0.00 0.51 0.00 0.95 0.00 2.82 0.00 2.80 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

exists between both codes. It is decided to use SERPENT2 results for the rest of comparisons and plots; results from MCNP6 were also computed showing always a similar behavior. Only deviations on the results from different cross sections libraries larger than 50 pcm will be attempted to be explained, as the ±50 pcm band belongs clearly to the stochastic uncertainty. 4.2.1. Comparison to benchmark average Fig. 3 shows the evolution of k-eff as computed with SERPENT2 (S2) for the three cross sections libraries considered. The results include the 2r uncertainty bands from the Monte Carlo result which are not noticeable. Also the benchmark average value is pic-

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Fig. 2. Difference in k-eff value and its standard deviation from the results computed with MCNP6 and SERPENT2 for each of the cross sections libraries and actinides only.

Fig. 3. k-Eff computed with SERPENT2 and the three libraries and benchmark average using actinides only composition.

Fig. 4. k-Eff difference with the benchmark average for the three libraries computed with SERPENT2 and actinides only composition.

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Fig. 5. k-Eff computed with SERPENT2 and the three libraries and benchmark average using actinides plus fission products composition.

Fig. 6. k-Eff difference with the benchmark average for the three libraries using Am-241 data from ENDF/B-VII.1 computed with SERPENT2 and actinides only composition.

tured for comparison together with its 2r deviation as computed from all participants’ results. From this figure, the results for the first decades and after 1000 years are all within the standard deviation band of the benchmark averaged results. While, in the period around 100 years, there exists a discrepancy between the average benchmark value and the results from JEFF-3.2 (J32) and TENDL-2014 (T14) which is outside the deviation band covered by the previous benchmark results, indicating some notable change has happened in the library distributions, next section discusses that change. The reactivity deviation from the benchmark’s average is plot in Fig. 4 together with the uncertainty bands. The parabolic shape of the deviation around 100 years is clear. The following calculations included also the isotopes indicated in the benchmark for the actinides plus fission products set of isotopes. The evolution of the effective neutron multiplication factor with this set shows a similar trend as the calculations including actinides only, but k-eff reaches lower values due to the poisoning effect of the fission products as shown in Fig. 5. Also very impor-

tant is the fact that the increase in k-eff after 100 years is very much reduced by the fission products effect, which would be very convenient from the point of view of the safety analysis. As in the case with actinides only in the composition, apart from the slight deviations of the results from one library to the others, it appears the same discrepancy around 100 years. 4.2.2. Effect of Americium 241 on the deviations The observed deviation of the results for the three libraries at around 100 years are of about the same magnitude but in the inverse direction for TENDL-2014 cross sections which yield a higher k-eff value, and for JEFF-3.2 which yield a lower k-eff value. Am-241 reaches its peak concentration exactly in this same period after 100 years of cool-down and the concentration takes also a parabolic shape as the k-eff deviation does; besides the sensitivity of k-eff to this isotope is notable in this period. With this in mind, we have executed the same calculations forcing to use the Am-241 cross sections in the ACE library file from ENDF/B-VII.1. Fig. 6 shows the new differences with the bench-

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Fig. 7. k-Eff differences with ENDF/B-VII.1 for different JEFF-3.2 isotopes substituted in the actinides only composition.

Fig. 8. k-Eff differences with ENDF/B-VII.1 for different TENDL-2014 isotopes substituted in the actinides only composition.

mark results including the uncertainty bands, now zero deviation from the benchmark average results is included inside the bands for all the cases. The cross section value for Am-241 has been updated from JEFF3.1.2 to JEFF-3.2, and now it is slightly higher than the ENDF/BVII.1 value in agreement with a lower k-eff computed. On the contrary, the value from TENDL-2014 is lower than the other two as the higher k-eff computed also reproduces. The value of Am-241 has been updated based on experiments with MOX fuel to improve the agreement with the measurements (Noguere et al., 2012), and in this sense we should consider the JEFF-3.2 results as more accurate. Then, the deviation of TENDL2014 at 100 years could amount for 1000 pcm, and the deviation of ENDF/B-VII.1 would be around 500 pcm. In any case, after using the same data for the Am-241, all the three nominal values are inside the Monte Carlo uncertainty bands associated to each other, and a final statement on what distribution is the most accurate will not be made as the cross sections uncertainty bands could not be further checked.

4.2.3. Effect of actinides and fission products nuclear data library distributions in the computed k-eff In order to study the impact of other isotopes cross sections differences in the libraries, it is now more meaningful to evaluate the difference between the libraries and put aside the benchmark average. The results from SERPENT2 with ENDF/B-VII.1 data have been taken as reference for next comparisons arbitrarily. The calculations are ENDF/B-VII.1 based but the ACE file of one isotope is changed in turn by the JEFF-3.2 or the TENDL-2014 version to see the deviation caused in k-eff for the different compositions in the one million years period. If these deviations are greater than 50 pcm which is the width of the stochastic uncertainty, then the deviation source must be found in the nuclear data; deviations inside that band are not presented. To help identify the tendencies, a local polynomial regression fitting is applied to the deviation values using the 2r standard deviation of the differences as weight, zero degree polynomials or local constant fitting, and a span value of 0.06 which implies 4 nearest neighbors are considered in the averaging. The fitting is

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Fig. 9. k-Eff differences with ENDF/B-VII.1 for different JEFF-3.2 isotopes substituted in the actinides plus fission products composition.

Fig. 10. k-Eff differences with ENDF/B-VII.1 for different TENDL-2014 isotopes substituted in the actinides plus fission products composition.

obtained with R (R Development Core Team, 2010). The values are chosen to smooth the Monte Carlo oscillations without losing the physical meaning. First, the actinides only case has been computed. For the JEFF3.2 library the differences are in Fig. 7, where, apart from Am241, also Pu-238 and Pu-239 produce a higher k-eff value than ENDF/B-VII.1 above 100 pcm each, while Pu-240 introduces a 100 pcm reduction, also Pu-241 and U-236 introduce slight deviations. Of course, the impact of these deviations usually vanishes when the isotopes’ concentration in the spent fuel decreases. For the actinides from TENDL-2014 the results are summarized in Fig. 8; apart from the Am-241, the isotope Pu-241 induces a 300 pcm higher k-eff disappearing after 100 years. Pu-240 gives a 100 pcm lower k-eff, and U-234 and U-236 could be inducing a higher k-eff. Afterwards, the deviations for the additional isotopes in Table 2 are computed in the actinides plus fission products case. For the nuclear data from JEFF-3.2, Fig. 9 points to Sm-149 as a main contributor to a higher k-eff, also Nd-143 and Np-237 would increase k-eff value, while Eu-151 would reduce k-eff.

The results from TENDL-2014 fission products in Fig. 10 show Eu-153 as unique responsible of a lower k-eff value than the ENDF/B-VII.1 cross sections, while the rest of isotopes resulted in deviations inside the uncertainty band. 5. Conclusions In summary, SERPENT2 and CINDER 1.05 are good candidates for future calculations, although the decay data used by CINDER 1.05 is outdated. Also the decay data from JEFF-3.1.1 is adequate when compared to ENDF/B-VII.1, but the latest could be preferred because of the lower uncertainties. Another base of comparison should consider the accuracy of the decay heat information for a possible future use which was not included in this study. For criticality calculations, MCNP6 and SERPENT2 showed to be both valid candidates. Regarding to the cross sections data, latest updates in Am-241 are quite discrepant and since they impact the results at larger extent over the first hundreds years, further improvements seem to be necessary.

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A systematic comparison of ENDF/B-VII.1 cross sections data for each isotope with JEFF-3.2 and TENDL-2014 showed that:  JEFF-3.2 actinides cross sections are more conservative (yield a higher k-eff) when clearly discrepant, except for Pu-240.  JEFF-3.2 fission products and minor actinides cross sections are also more conservative, except for Eu-151.  TENDL-2014 actinides cross sections are less conservative than ENDF/B-VII.1 for Am-241 and Pu-240, and more conservative for Pu-241.  TENDL-2014 fission products cross sections are less conservative for Eu-153. A final decision about the preferred criticality code and cross sections data set cannot be taken by solely looking into this benchmark analysis. Real applications need to be considered with a broad fuel assembly spectrum, i.e. MOX and BWR fuels with different burn-up distributions. Additionally, a validation stage comparing calculation results to experimental measurements will be needed to support the level of accuracy in the results. At the moment, separate validation for burnup calculations (Grimm et al., 2014) and for Monte Carlo criticality safety evaluation results (Kolbe et al., 2008; Pecchia et al., 2014) are also the subject of our work. As for the cross sections distributions, propagation of cross section uncertainties would be needed to carry out a fair comparison. Nevertheless, the main isotopes causing deviations between the results were assessed and attention will be devoted to their uncertainties in future works. Acknowledgment This work has been partially funded by NAGRA, the Swiss organization for waste management. References Berglund, M., Wieser, M.E., 2011. Isotopic compositions of the elements 2009 (IUPAC Technical Report). Pure Appl. Chem. 83, 397–410. http://dx.doi.org/ 10.1351/PAC-REP-10-06-02.

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