Needs of reliable nuclear data and covariance matrices for Burnup Credit in JEFF-3 library

Burnup Credit (BUC) is the concept which consists in taking into account credit for the reduction of nuclear spent fuel reactivity due to its burnup. In the case of PWR-MOx spent fuel, studies pointed out that the contribution of the 15 most absorbing, stable and non-volatile fission products selected to the credit is as important as the one of the actinides. In order to get a “best estimate” value of the keff, biases of their inventory calculation and individual reactivity worth should be considered in criticality safety studies. This paper enhances the most penalizing bias towards criticality and highlights possible improvements of nuclear data for the 15 FPs of PWRMOx BUC. Concerning the fuel inventory, trends in function of the burnup can be derived from experimental validation of the DARWIN-2.3 package (using the JEFF3.1.1/SHEM library). Thanks to the BUC oscillation programme of separated FPs in the MINERVE reactor and fully validated scheme PIMS, calculation over experiment ratios can be accurately transposed to tendencies on the FPs integral cross sections.


Introduction
The issue of the acceptability by the Safety Authority of the sub-criticality demonstration of nuclear industrial facilities and applications is based on a criticality-safety study taking into account the most penalizing hypothesis.During the operation, the subcriticality in any situation is guaranteed by the respect of the Under Subcritical Limit for the calculated k eff .
Considering spent fuel management (storage, transportation, reprocessing), the approach using "fresh fuel assumption" results in a significant conservatism in the calculated value of system reactivity.The concept of taking credit for the reduction of the reactivity of spent fuel due to the reduction of net fissile content, build-up of actinides and increase of fission products concentration is referred to as "Burnup Credit" (BUC) [1].Allowing reactivity credit for spent fuel offers many economic incentives.
Recent publications and discussions within the French BUC Working Group highlight the current interest of the BUC of PWR-MOx spent nuclear fuel for transport and storage.On top of that, design studies pointed out that the consideration of full BUC including fission products would enable a load increase in several fuel cycle devices (cask, storage pool).  9Mo, 150 Sm) represent more than a half of the total reactivity credit and 80% of the FPs credit (Table 1. and Fig. 1) [2].In order to get a "best estimate" value of the k eff and to meet USL constraint, calculation biases on FP inventory and individual reactivity worth should be considered in criticality studies [3].

Inventory and individual reactivity worth biases evaluation
In support of BUC studies, a specific experimental programme has been developed at Cadarache Centre in the framework of the CERES CEA-UKAEA co-operation [4], and later within the CEA-AREVA collaboration [5].This BUC programme is in particular composed of two kinds of experiments: 1. Chemical analyses and microprobe measurements of PWR-MOx spent fuel rods to obtain the spent fuel inventory (Actinides and FPs). 2. Reactivity worth measurements of the BUC nuclides by oscillation technique of specific separated-FP samples in the MINERVE reactor.
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Assessment of inventory biases
The BUC calculation route is based on the connection of the depletion code DARWIN [6] and the Criticality-safety Package CRISTAL [7].Concerning the fuel inventory biases, trends in function of the burnup can be derived from the DARWIN-2.3package qualification (using the JEFF-3.1.1 library [8] and the refined SHEM energy mesh).

Post Irradiation Examination database and C/E comparison
15 PWR-MOx fuel rods samples extracted from the French NPPs Saint Laurent and Dampierre were selected, with local burnup from 10 GWd/t HM to 60 GWd/t HM .Considering representative central fuel rods samples reduces the uncertainties due to the environment in the context of nuclear data qualification.For fissile isotopes, the penalized bias is Δ=(C-E)/E -1.65σ and Δ=(C-E)/E +1.65σ for the absorber isotopes.For the metallic FPs, the bias is determined using the impact of cumulative 239 Pu and 241 Pu fission yields, first source of calculation uncertainty on their concentrations.4. Application of the ICFs=1/(1+ Δ) (linear trend for 239 Pu and 241 Pu and unique conservative value for the other isotopes) to the calculated concentrations.

Individual reactivity worth bias
There are not many experimental programs which involve BUC FPs in PWR-MOx spectrum and the access to their results is often restricted.Thanks to the BUC oscillation programme of separated FPs in the MINERVE reactor, calculation over experiment ratios can be accurately transposed to tendencies on the FPs integral cross sections.In 1998, samples of 12 separated FPs and 5 natural elements, Ag, Mo, Nd, Sm, Ru were oscillated in the R1MOX lattice corresponding to a PWR-MOx spectrum in the framework of the BUC experimental program.The introduction of the doped samples at the centre of the MINERVE core creates a flux variation which is detected by a boron chamber linked to a pilot rod.The pilot rod compensates this variation to maintain the critical state and its rotation angle is proportional to the reactivity of the inserted sample.The oscillation technique is well adapted to measure with accuracy low reactivity effects.

Interpretation with the dedicated tool PIMS
To reproduce the experiment by calculation without any numerical bias which could be inappropriately attributed to the nuclear data, a dedicated modular interpretation scheme, PIMS (Pile-Oscillation analysis tool for Improvement of cross Sections), fully validated against stochastic calculations, has been developed at CEA by D. Bernard and P. Leconte [9].PIMS is based on the APOLLO2.8 deterministic code and on the recommendations from the reference SHEM-MOC calculation scheme for Light Water Reactor applications [10] and allow the use of exact perturbation theory to calculate the reactivity variation due to each oscillated sample.The calculation over experiment ratios (Fig. 2) show that, in a PWR-MOx spectrum, the isotopes 109 Ag, 155 Gd, 143 Nd, 149,152 Sm are well predicted with the European JEFF-3.1.1 library.Nevertheless, improvements may be needed in particular for 145 Nd, 133 Cs, 99 Tc and 103 Rh.Concerning these resonant isotopes, we can notice an increase of the observed trends with the spectrum hardness by comparison with the results obtained in the MINERVE PWR-UOx lattice (R1UO2).

Taking into account the individual reactivity worth in criticality-safety study
The individual reactivity worth can be taken into account by the use of k eff penalty terms by means of the Integral Experiment Methodology, based on experiment Representativity with respect of the studied application and on the re-estimation of nuclear data for the assessment of calculation biases and associated uncertainties [11].A preliminary study with the dedicated tool RIB of the CRISTAL criticality-safety package gives a representativity factor r=0.94 of the MINERVE 155  WONDER-2012 nuclear data re-evaluation (rigorous non-linear regression method) [12].Covariance matrices, obtained from ND differential measurements or expert advice, are already available for BUC nuclides : COMAC (COvariance MAtrices from Cadarache) [13], COMMARA, ENDF BVII , SCALE-6, TENDL.However, we will use the MINERVE integral measurements in order to infer realistic JEFF-3.1.1 covariance matrices for BUC FPs.

Conclusion
An important issue of LWR-MOx BUC methodology is the evaluation and the way of taking into account the biases on FPs inventory and individual reactivity worth calculation in criticality-safety studies.In order to support the implementation of such a methodology, specific experimental programs were carried out by CEA.Concerning the fuel inventory biases, trends in function of the burnup can be derived from the DARWIN-2.3package qualification.Thanks to the BUC oscillation program of separated FPs in the MINERVE reactor and the fully validated scheme PIMS, C/E biases can be transposed to tendencies on integral FPs cross sections; the precision of the reactivity worth predicted with JEFF-3.1.1 is highlighted for important BUC FPs : 149 Sm and 155 Gd (< 2%), 143 Nd, 152 Sm, 109 Ag and 153 Eu (< 5%).However, some improvements may be needed to correct the overestimation of 145 Nd, 133 Cs and 103 Rh resonance integral.
The use of the Integral Experiment Methodology confirms the good representativity of the MINERVE experiments for BUC industrial application.On the basis of existing best-estimate covariance matrices and the RDN processing of MINERVE experimental results, missing JEFF-3.1.1 covariances will be derived and introduced in the RIB tool, in order to obtain biases and associated uncertainties in JEFF-3.1.1-basedsafety-criticality calculations.

1 .
Determination of a linear trend of relative Calculation -Experiment discrepancies (C-E)/E in function of the burnup for each isotope using the generalized mean least squares method to take into account the uncertainty level of each point.2. Determination of the total experimental uncertainty 1σ by combination of the various uncertainty components : fuel and coolant/moderator temperatures during irradiation, initial Pu content, measurement uncertainty associated with the chemical assays, local burnup estimation and follow-up uncertainties for sensitive nuclides.It is showed that Actinide and FP ICFs values are mainly driven by the experimental uncertainties, particularly the burnup uncertainty component.3. Penalization of the (C-E)/E bias at each burnup by the one-sided 95% confidence interval.

Fig. 2 .
Fig. 2. Determination of the Isotopic Correction Factor associated with the 239 Pu concentration

Fig. 3 .
Fig. 3. C/E -1 ratios (%) of the BUC FPs in PWR-MOx and PWR-UOx lattices -uncertainty at 2σ (%) Gd worth with respect to FP-BUC poisoning in a PWR-MOx assembly.The use of such a methodology requires the elaboration and introduction in JEFF-3.1.1 evaluation of the missing covariance matrices for actinides and each of the 15 BUC FPs.The actual 235 U covariance matrix associated with the JEFF-3.1.1 has already been derived from targeted clean integral experiments using the RDN process of 03001-p.5

Importance of fission products in PWR-MOx Burnup Credit The
MOx fuel BUC is lower than the one of PWR-UOx fuels because of the conversion factor improvement due to the high 240 Pu content.Studies pointed out that the contribution of the 15 most absorbing, stable and non-volatile fission products selected (BUC-FPs :103Rh, 149 Sm, 155 Gd, 151 Sm, 143 Nd, 133 Cs, 109 Ag, 152 Sm, 153 Eu, 99 Tc, 145 Nd, 101 Ru, 147 Sm,

Table 1 .
PIE database for inventory ICF in PWR-MOx applications Using JEFF-3.1.1,concentrations of actinides and main BUC-FPs are well predicted as shown in

Table 2 .
JEFF-3.1.1 calculation of PIEs in PWR-MOx assemblies