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All issues Volume 5 (2019) EPJ Nuclear Sci. Technol., 5 (2019) 24 Full HTML
Open Access
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EPJ Nuclear Sci. Technol.
Volume 5, 2019
Article Number 24
Number of page(s) 19
DOI https://doi.org/10.1051/epjn/2019056
Published online 23 December 2019

© A. Rizzo et al., published by EDP Sciences, 2019

Licence Creative CommonsThis is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1 Introduction

Numerous studies report comparisons of calculated (C) and experimental (E) isotopic compositions of used fuels for nuclear data validation purposes. In this work, we have used an experimental database that mainly contains proprietary data obtained from French PWRs fleet. Our database contains 1370 isotopic ratio measurements for UOX and MOX fuels with burnup ranging from 10 GWd/t up to 85 GWd/t. It allows to investigate 45 isotopic ratios for a large number of actinides (U, Np, Pu, Am and Cm) and fission products (Nd, Cs, Sm, Eu, Gd, Ru, Ce, Tc, Mo, Ag and Rh).

Interpretations of post-irradiation experiments (PIEs) of samples irradiated in nuclear power reactors can be performed with the deterministic calculation package DARWIN2.3 [1], which is a calculation tool designed for fuel cycle applications. It solves the Boltzmann and Bateman equations to compute fuel cycle parameters at any irradiation and cooling time. A flow chart of the DARWIN2.3 package for PWR calculations is presented in Figure 1 [1]. DARWIN2.3 includes the APOLLO2 deterministic transport code [2], which provides neutron data to the PEPIN2 depletion solver [3], namely self-shielded cross-sections libraries and multi-group neutron fluxes.

State-of-the-art calculated-to-experimental (C/E-1) ratios obtained with the JEFF-3.1.1 library [4] are summarized in reference [1]. The objectives of the present study are to include most of these C/E-1 ratios in the Integral Data Assimilation procedure of the CONRAD code [5,6] and to provide valuable trends on the nuclear data compiled in the JEFF-3.1.1 library. Guidelines to achieve these objectives and strategies to take into account uncertainties coming from experiments, nuclear data and numerical biases are discussed in references [7–9]. The originality of our approach lies in the use of the AGS code method [10] to generate covariances between the C/E-1 ratios and of the marginalization procedure [11] to propagate uncertainties of “nuisance” parameters. Final results indicate that reliable trends can be obtained for the capture cross sections of some important actinides (235U, 236U, 238Pu, 239Pu, 240Pu, 241Pu, 242Pu, 241Am, 243Am, 245Cm) and fission products (103Rh, 153Eu, 154Eu) as well as for both 238U(n,2n) and 237Np(n,2n) reactions. Meaningful trends can also be obtained for the cumulative fission yields of 144Ce, 133Cs, 137Cs and 106Ru.

The integral data assimilation procedure is presented in Section 2, alongside free and nuisance parameters. Trends obtained on nuclear data are presented in Section 3 and discussed in Section 4.

thumbnail Fig. 1

Flow chart of the DARWIN2.3 package for PWR calculations.

2 Integral Data Assimilation procedure

The Integral Data Assimilation procedure implemented in the CONRAD code [5,6] is based on a two-step calculation scheme. The first step is a least-square fitting procedure, namely the analytic resolution of a standard generalized least-square equation [12], that consists in adjusting model parameters (i.e. nuclear data) on a given set of integral values. The second step is a marginalization procedure designed to propagate nuisance parameter uncertainties after the fitting procedure.

2.1 Governing equations

For a correct use of the Integral Data Assimilation procedure of the CONRAD code, two types of model parameters have to be defined, namely observable and nuisance parameters. The observable parameters are free variables whose values are adjusted during the fitting procedure. The nuisance parameters are fixed model parameters with known uncertainties. Nuisance parameter uncertainties are taken into account via the marginalization technique [11]. The algorithm consists in building a “full” covariance matrix Σ between the observable and nuisance parameters as follows [13]:(1)where(2)and(3)with x being the set of adjusted parameters, M x being the posterior covariance matrix associated to x, θ being the set of nuisance parameters and M θ the corresponding covariance matrix. Matrices G x and G θ contain the partial derivatives of the calculated values with respect to the observable and nuisance parameters:(4) (5)

2.2 Used nuclear fuel data and uncertainties

Integral values included in the fitting procedure are C/E-1 ratios obtained from the interpretation of PIEs with the DARWIN2.3 package [1] using the JEFF-3.1.1 library. Table 1 gives the nuclides for which C/E-1 values are available in the DARWIN2.3 validation suite, as well as the number and the type of fuel rod samples extracted per reactor. Examples of average 〈C/E〉-1 ratios at 40 GWd/t are given in Figure 2. This burnup is representative of the burnup of PWR assemblies at discharge. More information can be found in references [1,14]. According to data reported in Figure 2, the concentrations of the major actinides 235U, 239Pu and 241Pu at 40 GWd/t are accurately calculated for UOX fuels with the JEFF-3.1.1 library. The mean 〈C/E〉-1 ratios are −0.4 ± 3.7%, 0.0 ± 0.8% and −0.8 ± 1.8%, respectively. Average results obtained for MOX fuels remain consistent within the quoted uncertainties, except for the 241Pu/238U ratio. For both types of fuel, the largest C/E–1 ratios are obtained for the curium isotopes. These discrepancies, reaching about −50% for 247Cm in UOX fuels, or discrepancies observed between UOX and MOX fuels, can be explained by using the Integral Data Assimilation procedure of the CONRAD code. The calculated-to-experimental ratios considered in this work share the same sources of systematic uncertainties (parameters p 1 to p 4 detailed in the next paragraph). Therefore, the AGS code method [10] has been used to estimate the covariance matrix M C/E−1 between the C/E-1 values. The originality of the AGS code method is to combine uncorrelated and correlated uncertainties as follows:(6)in which D is a n × n diagonal matrix containing the variances of the uncorrelated uncertainties and S is a n × m rectangular matrix containing the correlated contributions for each of the j ∈ ⟦1, m⟧ sources of uncertainty. No correlation between the experimental isotopic ratios was provided alongside the results of the chemical analyses. Therefore, the covariance matrix D is a diagonal matrix that only contains the experimental uncertainties coming from the measurement process.(7)in which var (C i /E i  − 1) represents the uncertainty associated with the ith experiment. For the S-matrix, four sources of systematic uncertainties are considered:(8)with:(9)

Parameters p 1 and p 2 are related to the fuel and moderator temperatures, respectively. Their contributions Δ1,i and Δ2,i are calculated with DARWIN2.3 from direct perturbations of the parameters, by considering an uncertainty of ±50 °C for the fuel temperature and ±2 °C for the moderator temperature at 1σ. Parameters p 3 and p 4 are numerical scheme-related uncertainties, depending on the use of DARWIN2.3. The former corresponds to the differences that could be obtained between deterministic and Monte-Carlo calculation schemes. It was estimated from pin-cell depletion calculations performed with the deterministic code APOLLO2 and the Monte-Carlo code TRIPOLI-4 [15], with the same filiation chain. The latter corresponds to the differences due to resonant up-scattering effects [16] on fuel inventory calculations. Examples of differences obtained on the calculated isotopic ratios for a UOX fuel (3.7 wt.% 235U) at 40 GWd/t are given in Figure 3. Most of the obtained differences lie below 1%. The comparison of the deterministic and Monte-Carlo calculations schemes indicates that the differences are significant for the curium isotopes and non-negligible for 137Cs. Among the fission products, 137Cs seems to be an isolated case needing more extensive studies. As expected, in the case of the up-scattering effect, non-negligible increases of the concentration of all the actinides are observed. The final correlation matrix between the C/E-1 values reconstructed with the AGS code method (Eq. (6)) is shown in Figure 4. An interesting feature is the correlations between the UOX and MOX fuel data that introduces constraints on the variations of the observable parameters during the fitting procedure.

Table 1

Experimental database used for the validation of the DARWIN2.3 package (grey colour means that a portion or all the samples were analysed, white colour means that no experimental values are available).

thumbnail Fig. 2

Average calculated-to-experimental values (〈C/E〉-1) obtained for UOX and MOX fuels with the DARWIN2.3 package at 40 GWd/t using the JEFF-3.1.1 library.
thumbnail Fig. 3

Differences obtained on the isotopic concentrations (normalized to 238U concentration) on a pin-cell geometry for a 3.7% 235U-enriched UOX fuel at 40 GWd/t between i) in blue: APOLLO2 (AP2) and TRIPOLI-4 depletion calculations (T4), ii) in red: two APOLLO2 depletion calculations, with (AP2-UPS) and without (AP2) resonant up-scattering effects. Error bars represent the statistical uncertainty provided by the TRIPOLI-4 calculations.
thumbnail Fig. 4

Correlation matrix between calculated-to-experimental isotopic ratios used for the assimilation procedure.

2.3 Observable parameters

Isotopic ratios depend on a wide number of nuclear data. Therefore, the CYRUS tool [17] was used, coupled with PEPIN2 depletion solver, to establish an exhaustive list of nuclear data involved in the build-up of actinides and fission products.

The selected set of observable parameters that will be adjusted with the CONRAD code is given in Table 2. It was chosen not to adjust fission cross sections, because it would imply modifying the burnup of the analysed samples. This is incompatible with the fact that the burnup is a fixed parameter for each sample with a known uncertainty of about ±2% (see next section). It was also decided not to fit the decay constants; in our study, decay constants of interest are well known, with quoted uncertainties lesser than 0.6% (see Tab. 3). Eventually, it was chosen not to fit some nuclear data (e.g. fission yields on samarium isotopes, or samarium cross sections) because the number of free parameters was too important with respect to the number of constraints, thus leading to an underdetermined system.

Parameter yc (X,A) indicates the thermal cumulative fission yield of nuclide X for actinide A. For reducing the number of free parameters, the (n,γ) and (n,2n) cross sections are effective cross sections which are averaged over the neutron flux φ(E):(10)

Prior uncertainties for neutron cross sections come from the COMAC-V2.0 covariance matrix database [18,19], developed at CEA Cadarache. For fission yields, they come from the JEFF-3.1.1 library.

Table 2

Fitted parameters, relative prior uncertainty and origin of the uncertainty.

Table 3

Marginalized parameters and associated relative uncertainty (Unc.)

2.4 Nuisance parameters

Nuisance parameters are fixed parameters whose uncertainties are propagated via the marginalization procedure of the CONRAD code (Sect. 2.1). The list of the nuisance parameters introduced in the CONRAD calculation is given in Table 3. It gathers all nuclear data involved in the buildup of nuclides considered, determined with the CYRUS tool, except the ones fitted (see previous section). The cross section uncertainties come from the COMAC-V2.0 database. Uncertainties for the decay data (periods, isomeric ratios and branching ratios) and fission yields are directly taken from the JEFF-3.1.1 library.

Nuisance parameters are not only the nuclear data involved in the build-up of actinides and fission products, but also experimental parameters such as the burnup scaling parameter. The relative uncertainty associated to the latter parameter is close to ±2%.

3 Nuclear data adjustment trends and uncertainties

Nuclear data adjustment trends provided by the Integral Data Assimilation of our used nuclear fuel database are reported in Table 4. Results are listed by ascending order of adjustment coefficient. In particular, those obtained for the europium capture cross sections and cumulative fission yield of 137Cs confirm the results previously reported in references [8,9].

Table 4 also compares the relative uncertainties obtained before and after the marginalization of the nuisance parameters (Sect. 2.4). For most of the posterior values, the fitting uncertainties are lower than 1%. The marginalization provides more realistic uncertainties that allow discussing the quality of some cumulative fission yields and cross sections recommended in the JEFF-3.1.1 library and hence the content of the covariance database COMAC-V2.0.

Table 4

Nuclear data adjustment trends obtained from the Integral Data Assimilation of the C/E-1 values reported in reference [3].

3.1 Cumulative fission yields

Adjustment trends on a few number of cumulative fission yields were extracted from the Integral Data Assimilation of our used nuclear fuel data. This work provide information on the cumulative fission yields of 106Ru, 144Ce, 133Cs and 137Cs for both 235U(n,f) and 239Pu(n,f) reactions with relative uncertainties ranging from 1.3% to 5.7%. These trends can be directly applied to the cumulative fission yields recommended in the JEFF-3.1.1 library. For 235U, adjustment trends reported in Table 4 provide the following results:

y c (144Ce,235U) = 0.0524 ± 0.0018 (3.4%),

y c (133Cs,235U) = 0.0701± 0.0014 (2.0%),

y c (137Cs,235U) = 0.0669 ± 0.0013 (1.9%).

For 239Pu, the following results are obtained:

y c (144Ce,239Pu) = 0.0345 ± 0.0005 (1.3%),

y c (133Cs,239Pu) = 0.0690 ± 0.0021 (3.1%),

y c (137Cs,239Pu) = 0.0654 ± 0.0021 (3.1%),

y c (106Ru,239Pu) = 0.0457 ± 0.0026 (5.7%).

Comparisons with evaluated values and data available in the literature are reported in Section 4.

3.2 Neutron cross sections

Results obtained for the (n,γ) and (n,2n) reactions can be divided in three groups.

  • The first group concerns the reactions for which the adjustment trends remain within the uncertainties obtained after marginalization. This can be observed for six actinides and two fission products: 235U(n,γ), 236U(n,γ), 239Pu(n,γ), 241Pu(n,γ), 244Cm(n,γ), 246Cm(n,γ), 133Cs(n,γ) and 99Tc(n,γ). The case of technetium should be considered with caution because of the large uncertainty obtained (±7.8%). This first group refers to reactions that are correctly described in JEFF-3.1.1 or for which minor corrections are expected.

  • The second group concerns the reactions for which the adjustment trends are higher than the uncertainty obtained after marginalization, while remaining lower than 5%. This is the case of three actinides: 238U(n,2n), 240Pu(n,γ) and 242Pu(n,γ).

  • The third group concerns the reactions for which the adjustment trends are higher than the uncertainty obtained after marginalization and also higher than 5%. Six actinides and three fission products fulfil these conditions: 237Np(n,2n), 241Am(n,γ), 243Am(n,γ), 242Cm(n,γ), 245Cm(n,γ), 247Cm(n,γ), 153Eu(n,γ), 154Eu(n,γ) and 103Rh(n,γ). Results obtained for the 247Cm(n,γ) and 237Np(n,2n) reactions only indicate that such reactions are poorly known. Our used nuclear fuel data cannot provide accurate information to improve them. This latest group provides key information on reactions that have to be corrected in priority for improving significantly the DARWIN2.3 calculations for fuel cycle applications. However, adjustment trends reported in Table 4 need to be interpreted by examining the evolution with the burnup of the posterior calculated-to-experimental ratios provided by CONRAD at the end of the Integral Data Assimilation procedure. 241Am and 243Am are discussed below.

Figures 5 and 6 show the prior and posterior C/E-1 values for the ratio 241Am/238U in UOX and MOX fuels respectively, from 20 GWd/t to 85 GWd/t. The review of the posterior results reveals a slight improvement in average for UOX fuels, while the average C/E discrepancy is slightly degraded for MOX fuels. This result might be explained by the non-negligible dispersion of the calculated-to-experimental values, especially for MOX fuels. Final uncertainties in Table 4 do not reflect the potential inconsistencies between the used nuclear fuel data.

The production chain of 244Cm (Fig. 7) shows that the impact of 243Am capture cross section can be quantified on the calculated-to-experimental ratios of 244Cm/238U. The prior and posterior C/E-1 values for UOX and MOX fuels are reported in Figures 8 and 9. The posterior values are closer to zero in average. However, a dependence of the results with the burnup can be observed. Below approximately 30 GWd/t, the 244Cm/238U ratio is still underestimated. This could be explained by the low amount of 244Cm in the fuel at low burnup, suggesting that the experimental values at low burnup should be considered with caution. Hence, when considering only high burnup data on Figures 8 and 9, for which the 244Cm content becomes more significant, one can observe a slight overestimation of the 244Cm/238U isotopic ratio. This indicates that the increase of the 243Am capture cross section suggested in Table 4 is overcompensating the initial C/E-1 values. In that case, the obtained adjustment trend of +9.4 ± 2.2% should be considered as an upper limit.

thumbnail Fig. 5

Evolution of the calculated-to-experimental discrepancies before and after integral data assimilation for the 241Am/238U isotopic ratio in UOX fuels.
thumbnail Fig. 6

Evolution of the calculated-to-experimental discrepancies before and after integral data assimilation for the 241Am/238U isotopic ratio in MOX fuels.
thumbnail Fig. 7

Production chain of 244Cm.
thumbnail Fig. 8

Evolution of the calculated-to-experimental discrepancies before and after integral data assimilation for the 244Cm/238U isotopic ratio in UOX fuels.
thumbnail Fig. 9

Evolution of the calculated-to-experimental discrepancies before and after integral data assimilation for the 244Cm/238U isotopic ratio in MOX fuels.

3.3 Feedback on the COMAC-V2.0 library

Results reported in Table 4 can be used to assess the quality of the COMAC-V2.0 database: the mean posterior values obtained in this work should presumably remain within the limit of the prior uncertainties provided by COMAC-V2.0, otherwise the latter is underestimated. On the contrary, a prior uncertainty value which is significantly larger than the posterior trend may indicate that the prior uncertainty is overestimated.

When comparing the posterior values with the prior uncertainties, it seems indeed that the prior uncertainties for the capture cross sections of 133Cs, 236U, 242Pu, 244Cm and 246Cm are overestimated. As an example, the COMAC-V2.0 library provides a relative uncertainty for the 242Pu(n,γ) reaction which is close to 12%, while the present study suggests a slight increase of the capture cross section of +3.8 ± 2.8%. On the other hand, the COMAC-V2.0 database seems to underestimate the uncertainties of the 103Rh(n,γ), 241Am(n,γ) and 243Am(n,γ) reactions. This feedback constitutes guidelines for the improvement of the COMAC-V2.0 database.

4 Discussions of the results

Results provided by the Integral Data Assimilation procedure and presented in Section 3 were obtained using the JEFF-3.1.1 library. Since its official release in 2009, numerous validation studies were conducted on this library; furthermore new experimental data and evaluated nuclear data files are now available in the literature. This section compares results obtained in the present work with those reported in the literature and the international libraries in order to draw some recommendations for improving the JEFF library.

4.1 Comparison with results reported in the literature

Some examples of results available in the nuclear data literature for actinides and fission products are highlighted in Tables 5 and 6. We have selected some works that provide nuclear data adjustment trends which are associated to the JEFF-3.1.1 library.

From an integral point of view, many oscillations and activation experiments were carried out in the MINERVE reactor of CEA Cadarache in order to obtain an insight on nuclear data adjustment trends for a large amount of isotopes. OSMOSE [20,21], CERES [22], BUC [23] and MAESTRO [24–26] are programs specifically dedicated to actinides, MOX fuels, fission products and structural materials respectively. PIEs of samples irradiated in thermal spectra (such as the ICARE and SHERWOOD programs carried out in the MELUSINE reactor of CEA Grenoble [27]) and in fast spectra (such as the PROFIL program carried out in the PHENIX reactor of CEA Marcoule [28]) provide integral information similar to used nuclear fuel data, namely isotopic ratios. One must pay attention that the reported C/E-1 values are not adjustment trends on nuclear data. This means that adjustment trends obtained in the present work should compensate the C/E-1 values reported in Tables 5 and 6 (i.e. having opposed signs).

From a microscopic point of view, three time-of-flight experiments carried out in the past years for 242Pu [29], 243Am [30] and 153Eu [31] at the n_TOF and RPI facilities were considered. Resonance parameters extracted from these data provide useful information on the capture resonance integral. For the fission yields, results obtained at the ILL with the Lohengrin spectrometer [32–34] are listed.

From the evaluation point of view, it was chosen to focus on the case of 103Rh, for which a new evaluation has been recently performed at IRSN (Institut de Radioprotection et de Sûreté Nucléaire) with the SAMMY code [35].

In addition to the above-mentioned works, several studies were conducted based on the analyses of integral experiments. Two recent Integral Data Assimilation studies were performed on actinides with the RDN code using criticality-safety benchmarks in association to used nuclear fuel data [36], and integral data provided by the CERES program [22]. Posterior results are reported in Table 5. Finally, a nuclear data trend for the 154Eu(n,γ) reaction has been also obtained from the analysis of used nuclear fuel data [37]. Results are reported in Table 6.

A detailed review of the results listed in Table 5 and 6 leads to three major conclusions.

  • For the cumulative fission yields, trends suggested by our Integral Data Analysis are fully consistent with the ILL results. The agreement between the values remains within the limit of the reported uncertainties, which represents an encouraging result. An exhaustive comparison with a wider number of cumulative fission yields measured in various places could provide good indications about the robustness of our work.

  • For the capture cross sections of the fission products, most of the reported results are also consistent, excepted those related to the 103Rh(n,γ) reaction. The large inconsistencies between the BUC and MAESTRO experiments carried out in the MINERVE reactor justify the replacement of the 103Rh evaluation by a new evaluated nuclear data file, such as the one produced at IRSN [35].

  • The last conclusion concerns the actinides for which the numerous inconsistencies observed between the reported integral data can lead to erroneous conclusions. For some reactions, this confused situation can be clarified with microscopic data, such as recent time-of-flight experiments carried out in the RPI and n_TOF facilities. Examples given in Table 5 and 6 for the 242Pu(n,γ), 243Am(n,γ) and 153Eu(n,γ) reactions provide capture resonance integrals in favor of our Integral Data Assimilation results.

This comparative study indicates that our work provides consistent results for some actinides, fission products and cumulative fission yields; the present set of nuclear data adjustment trends represents a reliable guideline for improving the JEFF library.

Table 5

Comparison of our Integral Data Assimilation results for actinides with results reported in the literature. No data is available for 246Cm(n,γ), 242Cm(n,γ), 237Np(n,2n) and 246Cm(n,γ).

Table 6

Comparison of our Integral Data Assimilation results for fission products with results reported in the literature. I0 and σ0 refers to the capture resonance integral and the thermal capture cross section, respectively.

4.2 Recommended evaluated nuclear data files and resonance parameters

The nuclear data adjustment trends suggested by our Integral Data Assimilation procedure can be used to propose cross section evaluations that could improve calculations related to the fuel cycle. Table 7 gives a list of recommended Evaluated Nuclear Data files or resonance parameters. We only consider capture reactions for which meaningful adjustment trends were obtained. Cumulative fission yields are not discussed because the evaluation process is more complex than the one for cross sections, since it generally relies on an experimental database containing a large number of independent and cumulative fission yield measurements. Adjustment trends obtained on fission yields can nevertheless be used for the validation of the next fission yield evaluation releases.

Two types of recommendations can be distinguished. The first one consists in proposing existing Evaluated Nuclear Data files whose resonance parameters and neutron cross sections fulfil the nuclear data adjustment trends suggested by our study. This is the case for the 236U, 238U, 241Am and 154Eu nuclides. The proposed evaluations come from new or old versions of the JEFF library or from the Japanese library JENDL-4.0. Justifications of these choices are given in Table 7. One can precise that the recommended evaluation for 154Eu capture cross-section relies on a work carried out in [40], which aims at assessing the impact of different nuclear data evaluations on Europium isotopes build-up with the DARWIN package. This study showed that best results are obtained using JEFF-3.0 for 154Eu capture cross section, which exhibits changes on the first resonance parameters that induce a higher thermal capture cross-section compared to JEFF-3.1.1. The second type of recommendations consists in selecting resonance parameters which are not yet available in an official neutron library. Parameters could be retrieved from recent publications [29–31] for 242Pu, 243Am, and 153Eu, and introduced in an Evaluated Nuclear Data file for further validation studies, or they could come from recent resonance analyses for 240Pu and 103Rh. The latter are usually preliminary works that provide encouraging results.

Table 7

Evaluated nuclear data files and new resonance parameters in agreement with the nuclear data adjustment trends provided by our Integral Data Assimilation study.

5 Conclusions

In this paper, comparisons of calculated and experimental isotopic compositions of used nuclear fuels are carried out to provide information on the accuracy of nuclear data from the JEFF-3.1.1 library for fuel cycle applications. The method applied relies on both a fitting algorithm and a marginalization procedure implemented in the CONRAD code.

Final results confirm the accuracy of 235U, 239Pu and 241Pu neutron capture cross sections available in the JEFF-3.1.1 library. Slight increases of +1.2 ± 2.4%, +0.5 ± 2.2% and +1.2 ± 4.2% are respectively suggested, these all remaining within the limit of the quoted uncertainties. Results indicate the good quality of 236U, 244Cm, 246Cm and 133Cs capture cross sections as well, since the adjustment trends obtained remain within the quoted uncertainties. Our study also suggest to slightly increase 238U(n,2n), 240Pu(n,γ) and 242Pu(n,γ), adjustment trends obtained being lower than +5%. Adjustment trends greater than +5% are obtained for 237Np(n,2n), 241Am(n,γ), 243Am(n,γ), 242Cm(n,γ), 245Cm(n,γ), 247Cm(n,γ), 153Eu(n,γ), 154Eu(n,γ) and 103Rh(n,γ).

Meaningful adjustment trends for the cumulative fission yields of 144Ce, 133Cs, 137Cs and 106Ru for the 235U(nth,f) and 239Pu(nth,f) reactions, ranging from −8% to +9% approximately, are also reported.

Comparisons with data from the literature show a good agreement of the adjustment trends obtained on cumulative fission yields with experiments recently conducted at the ILL facility, and show a global agreement of the adjustment trends obtained on neutron cross sections with integral and microscopic experiments carried out in the past. Based on these results, several cross section evaluation are recommended to improve fuel cycle calculations: these evaluations may come from other international libraries or be based on resonance parameters recently measured at time-of-flight facilities. The evaluations recommended in this paper represent a valuable feedback of the fuel cycle applications that can be used for the improvement of the future JEFF library releases and more generally for the improvement of nuclear data.

Acknowledgments

Authors would like to thank Orano for its support and Luiz Leal for providing resourceful information on the 103Rh evaluation. Special acknowledgements go to colleagues from CEA for their valuable help during this work, especially David Bernard, Coralie Carmouze, Vanessa Vallet and Pascal Archier.

References

  1. L. San-Felice et al., Experimental validation of the DARWIN2.3 package for fuel cycle applications, Nucl. Technol. 184, 217 (2013) [CrossRef] [Google Scholar]
  2. A. Santamarina et al., APOLLO2.8: a validated code package for PWR calculations, in Proc. Int. Conf. Advances in Nuclear Fuel Management IV, Hilton Head Island, South Carolina USA, 2009 [Google Scholar]
  3. A. Tsilanizara et al., DARWIN: an evolution code system for a large range of applications, in Proc. Int. Conf. ICRS-9, Tsukuba, Ibakari, Japan, 1999 [Google Scholar]
  4. A. Santamarina et al., The JEFF-3.1.1 Nuclear Data library”, JEFF report, 22, OECD-NEA Data Bank, 2009 [Google Scholar]
  5. C. de Saint Jean et al., Status of CONRAD, a nuclear reaction analysis tool, in Proc. Int. Conf. Nuclear Data for Science and Technology, Nice, France, 2007 [Google Scholar]
  6. P. Archier et al., CONRAD evaluation code: development status and perspectives, in Proc. Int. Conf. Nuclear Data for Science and Technology, New-York, USA, 2013 [Google Scholar]
  7. A. Rizzo et al., Work plan for improving the DARWIN2.3 depleted material balance calculation of nuclides of interest for the fuel cycle, EPJ Web Conf. 146, 09030 (2017) [CrossRef] [Google Scholar]
  8. A. Rizzo et al., Nuclear data Adjustment based on the interpretation of post-irradiation experiments with the DARWIN2.3 package, EPJ Nuclear Sci. Technol. 4, 47 (2018) [Google Scholar]
  9. A. Rizzo et al., Assessment of the 153Eu and 154Eu neutron capture cross sections from the Integral Data Assimilation of used nuclear fuel experiments, Ann. Nucl. Energy 124, 524 (2019) [CrossRef] [Google Scholar]
  10. C. Bastian et al., AGS, a computer code for uncertainty propagation in time-of-flight cross-section data, in Proc. Int. Conf. PHYSOR, Vancouver, Canada, 2006 [Google Scholar]
  11. B. Habert et al., Retroactive generation of covariance matrix of nuclear model parameters using marginalization techniques, Nucl. Sci. Eng. 166, 276 (2010) [CrossRef] [Google Scholar]
  12. G. Noguere et al., Zero variance penalty model for the generation of covariance matrices in integral data assimilation problems, Nucl. Sci. Eng. 172, 164 (2012) [CrossRef] [Google Scholar]
  13. E. Privas et al., Generation of 238U covariance matrices by using the integral data assimilation technique of the CONRAD code, EPJ Web Conf. 106, 04015 (2016) [CrossRef] [Google Scholar]
  14. I.C. Gauld et al., Uncertainties in predicted isotopic compositions for high burnup PWR spent nuclear fuel, U.S. NRC report NUREG/CR-7012, ORNL/TM-2010/41, 2010 [Google Scholar]
  15. E. Brun et al., TRIPOLI-4®, CEA, EDF, and AREVA reference Monte Carlo code, Ann. Nucl. Energy 82, 151 (2015) [CrossRef] [Google Scholar]
  16. M. Ouisloumen et al., A model for neutron scattering off heavy isotopes that accounts for thermal agitation effects, Nucl. Sci. Eng. 107, 189 (1991) [CrossRef] [Google Scholar]
  17. V. Vallet et al., Deterministic approach of the decay heat uncertainty due to JEFF-3.1.1 nuclear data uncertainties with the CYRUS tool and the DARW IN2. 3 depletion code, Proc. Int. Conf. PHYSOR, Kyoto, Japan, 2014 [Google Scholar]
  18. P. Archier et al., COMAC − Nuclear data covariance matrices library for reactor applications, Proc. Int. Conf. PHYSOR, Kyoto, Japan, 2014 [Google Scholar]
  19. N. Terranova, Covariance Evaluation for Nuclear Data of Interest to the Reactivity Loss Estimation of the Jules Horowitz Reactor, Ph.D. thesis report, Bologne University, Italy, 2016 [Google Scholar]
  20. D. Bernard et al., Validation of actinides nuclear cross section using pile-oscillation experiments performed at MINERVE facility, J. Korean Phys. Soc. 59, 1119 (2011) [CrossRef] [Google Scholar]
  21. P. Leconte et al., OSMOSE programme: validation of actinides nuclear data for LWR applications, JEFDOC-1502, OECD NEA Data Bank, 2013 [Google Scholar]
  22. P. Leconte et al., Feedback on 239Pu and 240Pu nuclear data and associated covariances through the CERES integral experiments, J. Nucl. Sci. Technol. 52, 1044 (2015) [CrossRef] [Google Scholar]
  23. A. Gruel et al., Interpretation of fission products oscillations in the MINERVE reactor, from thermal to epithermal spectra, Nucl. Sci. Eng. 169, 229 (2011) [CrossRef] [Google Scholar]
  24. P. Leconte et al., MAESTRO: an ambitious experimental programme for the improvement of nuclear data of structural, detection, moderating, and absorbing materials − first results for natV, 55Mn, 59Co, and 103Rh, in Proc. Int. Conf. ANIMMA, Marseille, France, 2013 [Google Scholar]
  25. P. Leconte et al., Thermal neutron activation experiments on Ag, In, Cs, Eu, V, Mo, Zn, Sn and Zr in the MINERVE facility, EPJ Web Conf. 111, 07001 (2016) [CrossRef] [Google Scholar]
  26. P. Leconte et al., Nuclear data feedback on structural, moderating and absorbing materials through the MAESTRO experimental programme, JEFDOC-1849, OECD NEA Data Bank, 2017 [Google Scholar]
  27. D. Bernard et al., Validation of JEFF-3.1.1 thermal and epithermal induced capture cross sections through MELUSINE experiment analysis, Nucl. Sci. Eng. 179, 302 (2015) [CrossRef] [Google Scholar]
  28. J.-F. Lebrat et al., JEFF-3.1.1 nuclear data validation for sodium fast reactors, J. Nucl. Sci. Technol. 48, 620 (2011) [CrossRef] [Google Scholar]
  29. J. Lerendegui-Marco et al., Radiative neutron capture of 242Pu in the resonance region at the CERN n_TOF-EAR1 facility, Phys. Rev. C 97, 024605 (2018) [CrossRef] [Google Scholar]
  30. E. Mendoza et al., Measurement and analysis of the 243Am neutron capture cross section at the n_TOF facility at CERN, Phys. Rev. C 90, 036608 (2014) [CrossRef] [Google Scholar]
  31. G. Leinweber et al., Europium resonance parameters from neutron capture and transmission measurements in the energy range 0.01-200 eV, Ann. Nucl. Energy 69, 74 (2014) [CrossRef] [Google Scholar]
  32. C. Schmitt et al., Fission yield at different fission-product kinetic energies for thermal-neutron-induced fission on 239Pu, Nucl. Phys. A 940, 21 (1984) [CrossRef] [Google Scholar]
  33. A. Bail, Mesures de rendements isobariques et isotopiques des produits de fission lourds sur le spectrumètre de masse Lohengrin, Ph.D thesis, University of Bordeaux, France, 2009 [Google Scholar]
  34. Y. Gupta et al., Fission fragment yield distribution in the heavy-mass region from the 239Pu(nth, f) reaction, Phys. Rev. C 96, 014608 (2017) [CrossRef] [Google Scholar]
  35. L. Leal et al., Nuclear data evaluation work at IRSN, JEFDOC-1832, OECD NEA Data Bank, 2017 [Google Scholar]
  36. A. Santamarina, D. Bernard et al., Re-estimation of nuclear data and reliable covariances using integral experiments. Application to JEFF3 library, in Proc. Int. Conf. on Mathematicals & Computational methods applied to nuclear science and engineering, Jeju, South Korea, 2017 [Google Scholar]
  37. S.E. Skutnik, Proposed re-evaluation of the 154Eu thermal (n, γ) capture cross-section based on spent fuel nuclear benchmarking studies, Ann. Nucl. Energy 99, 80 (2017) [CrossRef] [Google Scholar]
  38. JEFF-3.3 nuclear data library, available at www.oecd-nea.org/dbdata/JEFF33/ (2018) [Google Scholar]
  39. G. Noguere et al., New resonance parameters shape analysis of the 1st resonance of Pu240 for thermal reactor applications, JEFDOC-1526, OECD NEA Data Bank, 2013 [Google Scholar]
  40. G. Noguere, P.H.L. Doan, Progress report on 154Eu buildup for DARWIN applications, JEFDOC-1592, OECD NEA Data Bank, 2014 [Google Scholar]

Cite this article as: Axel Rizzo, Claire Vaglio-Gaudard, Gilles Noguere, Romain Eschbach, Gabriele Grassi, Julie-Fiona Martin, Feedback from experimental isotopic compositions of used nuclear fuels on neutron cross sections and cumulative fission yields of the JEFF-3.1.1 library by using integral data assimilation, EPJ Nuclear Sci. Technol. 5, 24 (2019)

All Tables

Table 1

Experimental database used for the validation of the DARWIN2.3 package (grey colour means that a portion or all the samples were analysed, white colour means that no experimental values are available).

In the text
Table 2

Fitted parameters, relative prior uncertainty and origin of the uncertainty.

In the text
Table 3

Marginalized parameters and associated relative uncertainty (Unc.)

In the text
Table 4

Nuclear data adjustment trends obtained from the Integral Data Assimilation of the C/E-1 values reported in reference [3].

In the text
Table 5

Comparison of our Integral Data Assimilation results for actinides with results reported in the literature. No data is available for 246Cm(n,γ), 242Cm(n,γ), 237Np(n,2n) and 246Cm(n,γ).

In the text
Table 6

Comparison of our Integral Data Assimilation results for fission products with results reported in the literature. I0 and σ0 refers to the capture resonance integral and the thermal capture cross section, respectively.

In the text
Table 7

Evaluated nuclear data files and new resonance parameters in agreement with the nuclear data adjustment trends provided by our Integral Data Assimilation study.

In the text

All Figures

thumbnail Fig. 1

Flow chart of the DARWIN2.3 package for PWR calculations.
In the text
thumbnail Fig. 2

Average calculated-to-experimental values (〈C/E〉-1) obtained for UOX and MOX fuels with the DARWIN2.3 package at 40 GWd/t using the JEFF-3.1.1 library.
In the text
thumbnail Fig. 3

Differences obtained on the isotopic concentrations (normalized to 238U concentration) on a pin-cell geometry for a 3.7% 235U-enriched UOX fuel at 40 GWd/t between i) in blue: APOLLO2 (AP2) and TRIPOLI-4 depletion calculations (T4), ii) in red: two APOLLO2 depletion calculations, with (AP2-UPS) and without (AP2) resonant up-scattering effects. Error bars represent the statistical uncertainty provided by the TRIPOLI-4 calculations.
In the text
thumbnail Fig. 4

Correlation matrix between calculated-to-experimental isotopic ratios used for the assimilation procedure.
In the text
thumbnail Fig. 5

Evolution of the calculated-to-experimental discrepancies before and after integral data assimilation for the 241Am/238U isotopic ratio in UOX fuels.
In the text
thumbnail Fig. 6

Evolution of the calculated-to-experimental discrepancies before and after integral data assimilation for the 241Am/238U isotopic ratio in MOX fuels.
In the text
thumbnail Fig. 7

Production chain of 244Cm.
In the text
thumbnail Fig. 8

Evolution of the calculated-to-experimental discrepancies before and after integral data assimilation for the 244Cm/238U isotopic ratio in UOX fuels.
In the text
thumbnail Fig. 9

Evolution of the calculated-to-experimental discrepancies before and after integral data assimilation for the 244Cm/238U isotopic ratio in MOX fuels.
In the text

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