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Proceedings of ICAPP ‘12 Chicago, USA, June 24-28, 2012
Paper 12136
APPLICATION OF THE JENDL-4.0 NUCLEAR DATA SET FOR UNCERTAINTY ANALYSIS OF THE PROTOTYPE FBR MONJU
P. TAMAGNO Institut National des Sciences et Techniques Nucléaires
INSTN - Point courrier n°35 Centre CEA de Saclay
F-91191 Gif-sur-Yvette Cedex FRANCE [email protected]
W. F. G. Van ROOIJEN, T. TAKEDA
Research Institute of Nuclear Engineering University of Fukui
T910-8507 Fukui-ken, Fukui-shi Bunkyo 3-9-1 JAPAN
[email protected] ; [email protected]
M. KONOMURA Japan Atomic Energy Agency
FBR Plant Engineering Center 919-1279 Fukui-ken, Tsuruga-shi
Shiraki 1 JAPAN [email protected]
Abstract – This paper deals with uncertainty analysis of the Monju reactor using JENDL-4.0 and the ERANOS code1. In 2010 the Japan Atomic Energy Agency – JAEA – released the JENDL-4.0 nuclear data set. This new evaluation contains improved values of cross-sections and emphasizes accurate covariance matrices. Also in 2010, JAEA restarted the sodium-cooled fast reactor prototype Monju after about 15 years of shutdown. The long shutdown time resulted in a build-up of 241Am by natural decay from the initially loaded 241Pu. As well as improved covariance matrices, JENDL-4.0 is announced to contain improved data for minor actinides2. The choice of Monju reactor as an application of the new evaluation seems then even more relevant. The uncertainty analysis requires the determination of sensitivity coefficients. The well-established ERANOS code was chosen because of its integrated modules that allow users to perform sensitivity and uncertainty analysis. A JENDL-4.0 cross-sections library is not available for ERANOS. Therefor a cross-sections library had to be made from the original ENDF files for the ECCO cell code (part of ERANOS). For confirmation of the newly made library, calculations of a benchmark core were performed. These calculations used the MZA and MZB benchmarks3 and showed consistent results with other libraries. Calculations for the Monju reactor were performed using hexagonal 3D geometry and PN transport theory. However, the ERANOS sensitivity modules cannot use the resulting fluxes, as these modules require finite differences based fluxes, obtained from RZ SN-transport or 3D diffusion calculations. The corresponding geometrical models have been made and the results verified with Monju restart experimental data4. Uncertainty analysis was performed using the RZ model. JENDL-4.0 uncertainty analysis showed a significant reduction of the uncertainty related to the fission cross-section of 239Pu along with an increase of the uncertainty related to the capture cross-section of 238U compared with the previous JENDL-3.3 version. Covariance data recently added in JENDL-4.0 for 241Am appears to have a non-negligible contribution.
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Paper 12136
I. INTRODUCTION In nuclear engineering calculations, errors are
strongly penalizing because the resulting uncertainties induce extra safety margins, which reduce the operating flexibility. Reducing such margins is therefor a financially attractive objective for the nuclear reactors designer and the utility. After Monju's long shutdown periode due to secondary circuit sodium leakage, the build-up of 241Am made the 2010 restart a valuable full size experiment in the areas of reactor physics, nuclear data and modeling.
The uncertainties are calculated from covariance
matrices contained in the same evaluation files used to produce cross-sections libraries that are used in nuclear codes. Before explaining how to process evaluation files in order to make cross-sections libraries for ECCO, it is useful to recall the processing scheme of deterministic codes. The explanations given here are brief. More detailed explanations are available in standard text books5. Most of the codes used in nuclear engineering are deterministic because they provide accurate results with short calculation times. All these codes solve an equation – such as the Boltzmann equation or the diffusion equation – in which the unknown is a function. As codes use a numerical approach, they cannot handle continuous variables and then have either to discretise the phase space (energy, space, time, angle, etc.) or to decompose the unknown function into a (truncated) series of basic trial functions. The code solves then either a discretized set of equations or the coefficients of the expansion functions. For example, these expansion functions can be Legendre polynomials, spherical harmonics, etc. There are then different kinds of numerical schemes that can be used: finite differences, finite elements or nodal methods. For a full core calculation with explicit modeling of all core features, the number of unknowns far exceeds the current computer capabilities. This is why intermediate models have to be made and why full core calculations have to be divided into different steps. Most commonly, the following steps are used:
1. The cross-sections processing: Starting from the evaluated data files, reconstruct point-wise cross-sections from nuclear parameters and make multi-group cross-sections. This step is done once for each isotope contained in an evaluation. It provides a cross-sections library, which is specific to the evaluation and that can be used, for a given nuclear code, in several situations i.e. for different reactor cores.
2. The cell calculation: The cell calculation consists usually on modeling a representative part of a domain: an assembly with pellets, cladding, coolant, etc. This calculation is usually made in two dimensions. It uses symmetries of the assembly, calculates the flux in the cell, and then homogenizes the cell cross-sections over space. It can also reduce the energy group structure into a simpler one.
3. The core calculation: The core calculation step uses the homogenized cross-sections from the previous
1
step along with the core loading pattern to calculate the flux using either transport or diffusion theory.
II. CREATION OF A CROSS-SECTIONS LIBRARY FOR ECCO
II.A. Cross-section Processing
In the present work, we need to produce a cross-sections library for the cell code ECCO. The process is described in Ref. 6, which provides useful information along with scripts that can be used to process evaluation files. The process is shown in Fig. 1 and can be described as follows:
• ENDF files7: These are the files made by evaluators considering quantum mechanical models and experimental measurements. They contain data such as evaluated cross-sections but also scattering law data, radioactive decay data and fission yield data, mass, etc.
• NJOY8: This processing code reconstructs tabulated point-wise cross-sections. Then it calculates multi-group cross-sections. The process is repeated for several temperatures from 293.6 K to 2973.6 K. NJOY calculates also angular distributions and fission spectra.
• CALENDF9: This code calculates several cross-sections and prepares probability tables for specific use in ECCO, more detailed explanation about probability tables are available in Ref. 9. These probability tables are used in the ECCO cell code of ERANOS which uses the Pij and the subgroup method10. The probability tables give an accurate description of the cross-sections, especially in the Unresolved Resonance Range.
• MERGE is used to merge the output data from NJOY and CALENDF into a single GENDF* file and run tests to check the consistency. By default, cross-sections from NJOY are replaced by CALENDF cross-sections when available. It is possible to manually instruct MERGE to prefer NJOY cross-sections instead of those from CALENDF for certain user-defined energy groups.
• GECCO: This final step adds to the previous GENDF* file some useful data such as mass, disintegration constant or energy reactions. The program also compares the sum of partial cross-sections to the total cross-section and converts the file into the ECCO-library format.
Fig. 1. Processing ENDF-6 files into an ECCO library
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Proceedings of ICAPP ‘12 Chicago, USA, June 24-28, 2012
This process has to be done for all JENDL-4.0 isotopes required for Monju modeling. In order to process the ENDF files properly it has been necessary to slightly modify MERGE and CALENDF. In rare cases, it was decided to modify ENDF files themselves in order to get rid of processing defaults concerning some inelastic cross-sections as illustrated later. II.B. Verification of the Library Processing
To make sure that the processing was correctly done, test calculations were performed and comparisons were made with references libraries. Our institute has three ECCO libraries processed by CEA which have been used as a reference for validation for the following evaluations: JEF-2.2, JEFF-3.1 and JENDL-3.3. Calculations have been done for the infinite multiplication factor (k∞) for several important isotopes using the CEA "reference" libraries (CEA) and the libraries that we created (UF). The results are shown in Fig. 2.
(a) k∞ for 239Pu
(b) k∞ for 235U
(c) k∞ for 240Pu
(d) k∞ for 241Am Fig. 2. k∞ calculation for several actinides from several
evaluations using ECCO in 1968 energy groups
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Paper 12136
Rater large differences are found between the CEA and UF libraries based on JEF-2.2. The difference is assumed to be caused by the use of different subversions of JEF-2.2. The relevant comparisons are then between JENDL-3.3 and JEFF-3.1 libraries. For those libraries the relative differences of k∞ between CEA and UF range from 10-7 to 4.10-4. The differences between evaluations are much larger, usually hundreds times larger than differences between the CEA and UF libraries. It was assumed these results were good enough to use the newly generated libraries for reactor analysis.
II.C Remaining Uncertainties • Even if verifications shown in section II.B give credit to the library, here are discussed some surprising microscopic features. As can be seen in Fig. 2c, no k∞ for 240Pu can be calculated for JENDL-3.3. This problem also occurs in the CEA version and was left as is. • 235U from the JENDL-4.0 data set (Fig. 2b) shows a much larger reactivity than the other evaluations. This is not an immediate source of concern. In fact, it is reported that JENDL-4.0 "improves underestimations for low-enriched uranium systems observed in the JENDL-3.3 results"2. • Comparison between NJOY and CALENDF cross-sections revealed that for some isotopes and some resonances large differences occur. This situation is illustrated in Fig. 3 in the case of 48Ti for JENDL-4.0, but this behavior has been observed for several other isotopes as well. This phenomenon is caused by NJOY and CALENDF not interpreting the resonances parameters given in the ENDF file with the same formalism. ENDF files contain resonances parameters, the treatment of which can be done using several possible formalisms. Point-wise cross-section values are also given and can be summed, or not, with the cross-section reconstructed from the resonance parameters. The formalism of the resonances parameters is recommended by the evaluators and included in the ENDF file. However, CALENDF can chose to use a self-determined formalism in order to be as accurate as possible.
Fig. 3. JENDL-4.0, 48 Ti: Cross-sections reconstruction with Multi-Level Breit-Wigner and Reich-Moore formalism
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Proceedings of ICAPP ‘12 Chicago, USA, June 24-28, 2012
Paper 12136
This results in such large differences in this case. A comparison with the JANIS data viewer showed that the CALENDF cross-sections for 48Ti in JENDL-4.0 are close to the JEFF-3.1.1 cross-sections of 48Ti in JANIS. At the same time, the NJOY result in Fig. 3 for 48Ti in JENDL-4.0 is close to the values cited in JANIS for JENDL-3.3 and ENDF/B-VII.0. After consultation with cross-sections experts at CEA and JAEA, the issue of 48Ti remains as yet unresolved. JAEA announced that the 48Ti cross-sections should be reviewed.
The formalism used by CALENDF may yield
negative cross-sections in rare cases. In such case cross-sections are manually replaced by the corresponding NJOY cross-sections. Such replacement of CALENDF cross-sections erases the corresponding probability tables. The number of negative cross-sections is small and concern only cross-sections where the corresponding NJOY values are close to zero. • It was also necessary to enforce CALENDF to use the evaluator formalism for 238U in the JENDL-3.3 evaluation otherwise it triggers inconsistencies and a high reactivity overestimation in the flux calculations. • A final correction had to be applied to some JENDL-3.3 ENDF files (for 238U and 239Pu) in order to make CALENDF and NJOY results consistent. This issue is illustrated in Fig. 4. The difference occurs in the Unresolved Resonances Range, the cross-section calculated by CALENDF is about twice larger than the NJOY value for the inelastic reaction. In this range CALENDF sums the cross-sections reconstructed from the resonance parameters and the point-wise values contained in the ENDF file. This issue is discussed in more details in Appendix D.3.3 of the ENDF-6 Format Manual7. This problem has also been observed for some isotopes in the JEFF-3.1 library but resulted in a much smaller impact in the core calculations that were performed to verify the libraries.
Fig. 4. JENDL-3.3 238U inelastic cross-section calculated by CALENDF and NJOY
This process leads to the completion of a 1968-
groups ECCO library. For many applications it is useful
167
to have a 33-groups library. This library is obtained by condensation of the previous library using a weighting flux. This flux is obtained from a sodium-cooled fast reactor cell calculation performed in 1968 groups. Three options are available for this condensation and strongly impact the final calculation. The option named 'MIXED_WEIGHTING' was chosen because it resulted in a better consistency with CEA libraries and is used in the ERANOS standard procedures. Cell k∞ tests showed that this option gives the best agreement between 1968 groups and 33 groups calculations. III. ECCO LIBRARY VERIFICATION WITH MZA/MZB
The process described in section II led to operational
cross-sections libraries usable for core calculation. MZA/MZB benchmarks3 were used to verify the libraries with real core measurements. The verification is done by effective multiplication factor (keff) comparisons. There are two major modules in ERANOS to perform a core calculation using transport theory: VARIANT that uses the nodal method in XYZ or Hexagonal-Z geometry and BISTRO that uses the SN method in RZ geometry. MZA was modeled with both modules and confirmed the consistency between the 3D XYZ and the 2D RZ modeling. Therefor MZB/3 was only modeled in RZ geometry. Some minor isotopes are not present in the 1968-group CEA libraries (JENDL-3.3 and JEFF-3.1) and these have been removed from the core models.
The fuel cell calculation was performed using ECCO
in 1968 groups. The reference calculation scheme given in the ECCO documentation10 involves a 33 groups calculation, but preliminary results showed that the condensation option evoked in section II yields large differences in a core calculation. Thus only the 1968-group library was used for the fuel cell calculations. For non-fuel cells, sub-critical calculations were performed with the 33-groups library because it is too time consuming to perform all calculations in 1968 groups.
The core calculation with VARIANT is performed
using a P3 flux angular development in 33 energy groups. The RZ model is taken from the benchmark specifications3. BISTRO was used with the fine S16 SYMETRIQUE angular mesh. The results of the calculations of MZA and MZB are shown in Table I and II and Fig. 5 and 6. As a correction had to be applied for inelastic reaction in the JENDL-3.3 library as discussed in section II, results without this correction are explicitly shown in Fig. 5 and 6. Comparison with Monte-Carlo calculation is presented; the values are taken from the benchmark documentation3. GMVP value for MZB/3 core is taken from Ref. 11.
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Proceedings of ICAPP ‘12 Chicago, USA, June 24-28, 2012
Paper 12136
€
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TABLE I
MZA reactivity calculation
kC −1kC
.105
JEF-2.2 JENDL-3.3 JEFF-3.1 JENDL-4.0
CEA 1343 1571 2174 - VARIANT
UF 1758 1693 2201 1907
CEA 1444 1676 2273 - BISTRO
UF 1853 1793 2302 1958
Monte-Carlo 1225 922 1373 - Experimental value (kE )
960 ± 160
TABLE II
MZB/3 reactivity calculation
kC −1kC
.105 JEF-2.2 JENDL-3.3 JEFF-3.1 JENDL-4.0
CEA -512 -271 390 - BISTRO
UF 10 -158 416 -135
Monte-Carlo 685 499 878 -
Experimental value (kE ) 438 ± 100
Fig. 5. Reactivity calculation for ZEBRA MZA core
16
Fig. 6. Reactivity calculation for ZEBRA MZB/3 core
Even if the calculated reactivity do not agree to the experimental values and Monte-Carlo calculations, our libraries match perfectly the CEA libraries for JEFF-3.1 as well as for JENDL-3.3 when no inelastic correction is applied. Differences involve more the modeling than the libraries and are likely to be due to ECCO settings, for which many options are possible. Differences with the benchmark values are larger for MZA. This may be due to missing isotopes, reducing the internal capture and increasing the reactivity. The MZA XYZ and RZ geometry calculations are consistent, giving credit to the MZB results that are only calculated in RZ geometry. It is concluded that our libraries give consistent results. The results are good enough to consider using these newly made libraries for core calculation test on Monju.
IV. APPLICATION TO MONJU
Collecting data about Monju and modeling its full core required intensive efforts due to strict disclosure rules and scarcity of detailed information related to the core composition. Information given here are from publicly available documentation (Ref. 12…15). The modeled core corresponds to the Monju restart core in May 2010. As the experiment was done as a zero power test, no temperature profile is required.
Public information is nevertheless not complete enough to provide accurate descriptions and thus some assumptions had to be made about the exact fuel composition. These hypotheses are not reported here. The model was tested with several available libraries. It was also a full size test for the new JENDL-4.0 libraries. These tests were performed using the VARIANT and the BISTRO modules of ERANOS with mostly the same settings than for the benchmark calculations from section III, VARIANT flux order being now P5. The results are shown in Fig. 7.
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Proceedings of ICAPP ‘12 Chicago, USA, June 24-28, 2012
Paper 12136
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In these calculations CEA and UF libraries give small
differences: less than 10-4. The remaining differences between CEA libraries and UF libraries are likely to be due to numerical processing. However, differences between “CEA” and “UF” results are very small compared with the differences observed between evaluations.
The difference between JAEA and UF calculations indicated in Fig. 8 are possibly due to the accuracy of the composition and differences in codes; for example, JAEA values are obtained in 70 groups, using diffusion theory with corrections. But the difference is also likely to be due to fuel burn-up resulting from the 40% power test in 1994-1995, which has not been considered for the model presented here.
The JENDL-4.0 library and the Monju model being verified it is possible to use the dedicated ERANOS sensitivity and uncertainty modules.
V. SENSITIVITY COEFFICIENTS CALCULATION Once the Monju core model is verified, calculation of
the sensitivity coefficients is done in a straightforward way using a dedicated module in ERANOS. Eq. (1) and Eq. (2) define the parameters used here to display the sensitivity coefficients. In these equations, i stands for the isotope, r the reaction, g the energy group and S the corresponding sensitivity coefficient. Fig. 8 and 9 show respectively the parameters defined in Eq. (1), and Eq (2).
Xi,r =Si,r,g
g∑
Si,r,gg∑⏐
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⏐
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Xg,r =Si,r,g
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These sensitivity profiles have been calculated using JENDL-3.3 and JENDL-4.0 but no significant differences were observed. This is expected because the sensitivity
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VI. UNCERTAINTY ANALYSIS VI.A Correlation Matrices Processing
Sensitivity coefficients are not the only required data to perform uncertainty analysis. Estimated errors on the cross-sections and errors interdependence data have to be included in the calculation. These data are formalized in the covariance matrices and contained in the original ENDF files. The covariance matrices are extracted form the ENDF files using NJOY and processed regarding the energy group structure and calculation intended to be performed. Here the process was done in 15 and 33 energy groups.
The following discussion requires an understanding of the treatment of cross-sections in ERANOS. To optimize the use of resources, only the minimum number of cross-sections sets is used in the flux calculations8. This means for example that all reactions involving disappearance of the incoming neutron are summed into a
0
Proceedings of ICAPP ‘12 Chicago, USA, June 24-28, 2012
Paper 12136
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single cross-sections set named CAPTURE. In the same way cross-sections for which more than one neutron is released (e.g. (n,2n)) are summed into a set named NxN. INELASTIC is defined as the sum of all reactions where only one neutron is emitted expect the elastic reaction. The ELASTIC and FISSION sets correspond to the standard definitions. Hereafter these sets are named computational sets of cross-sections. Three matrices are used along with these sets corresponding to the elastic reaction, inelastic reactions and the NxN reaction in which data about multiplicity of emitted neutrons is stored. Another set NU contains the averaged number of emitted neutrons per fission (υ).
In the ERANOS module, uncertainty calculation is performed for the six sets: CAPTURE, ELASTIC, FISSION, INELASTIC, NxN and NU. Uncertainty on the fission spectrum is not considered because unlike the other sets, normalization issues have to be considered. In the ENDF files, covariance data are given for physical reactions. For example, (n,α) is a physical reaction but is only a part of the computational CAPTURE set. Therefor covariance data from the ENDF files have to be treated to reflect the uncertainty on the ERANOS sets. This process is based on the following method. Definitions and details can be found in Ref. 8 (ERRORR section).
Here X and Y stand for two of the ERANOS computational set x (resp. y) is one of the physical cross-sections that is a part of X (resp. Y). A computational set is defined by: σX = σx
x∈X∑ (3)
Covariance between two computational parameters is given by: cov σX ,σY( )= cov σx,σy( )
y∈Y∑
x∈X∑ (4)
Correlation between two computational parameters is given by:
corr σX ,σY( )=cov σX ,σY( )
cov σX ,σX( ).cov σY ,σY( )( )1/ 2
(5)
Standard deviation of a computational parameter is given by:
Δ σX( )= cov σX ,σX( )( )1/ 2
(6) There are several possibilities to input the covariance
data into ERANOS. Here it was chosen to use the AMER-format reading module. The covariance matrices produced by NJOY are treated to correspond to ERANOS sets covariance matrices and turned into correlation matrices and standard deviation vectors using Eq. (5) and (6). The ERANOS AMER-format reading module was slightly modified to be able to read 33-groups correlation files.
VI.B Uncertainty calculation
Uncertainty analysis can then be performed using the sensitivity coefficients. Some features have to be pointed.
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Not all of the isotopes used for the Monju modeling have covariance data. Total uncertainty calculation is reported in table III. Results of uncertainty calculation can be seen for JENDL-3.3 (respectively JENDL-4.0) in Fig.10 (respectively Fig. 11).
TABLE III
Monju criticality total uncertainty
on keff JENDL-3.3 JENDL-4.0
15 groups 0.00797 0.00813
33 groups 0.00813 0.00823
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Fig. 11. Total uncertainty structure: JENDL-4.0 / 33 groups
The choice between the two groups structures have a small influence on the total calculated uncertainty and the structure of the uncertainty remains similar. Results showed in Fig. 10 and 11 are from 33 groups calculations.
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VI.C Uncertainty Analysis VI.C.1 Total Uncertainty
It can be seen from Fig. 10, 11 and 12 that the total uncertainty calculated using the JENDL-3.3 data is mostly due to 239Pu-fission whereas it is mostly due to 238U-capture when using JENDL-4.0 data. It can also be noted that several isotopes are included in the JENDL-4.0 data but not in the JENDL-3.3 data although the added uncertainty is sizable. For example, 241Am-capture stands for a non-negligible part of the JENDL-4.0 total uncertainty. For most of the isotopes present in both evaluations, the effect of the updates and re-evaluations is mainly a slight increase in the uncertainty. But the dramatic reduction of the uncertainty due to 239Pu-fission counterbalances mostly these increases and the contribution of the addition of covariance for the new isotopes.
Fig. 12. Isotopes contribution to Monju criticality uncertainty
VI.C.2 Fission Uncertainty Fig. 13 shows a comparison in the fission
contribution between the JENDL-3.3 and JENDL-4.0 evaluations. Explanations of the evaluation results differences can be found it the ENDF original files.
Fig. 13. Fission contribution to Monju criticality uncertainty • The major change is for 239Pu and is due to updates from Ref. 16 to Ref. 17. These updates or re-evaluations are shown on correlation matrices (Fig. 14) and standard deviations (Fig 15). These figures show that the changes in the correlation data goes along with standard deviations reduction, mainly between 2keV and 50keV where the reactivity is highly sensitive to the fission cross-section as shown in Fig. 9 , the reduction between 0.1eV and 40eV being with small effect. This explains the significant reduction in the uncertainty related to 239Pu–fission. The
168
other sources of changes can be considered with a similar approach.
(a) JENDL-3.3 version
(b) JENDL-4.0 version Fig. 14. Correlation matrices for 239Pu – Fission (33 groups)
Fig. 15. Standard deviation of 239Pu – Fission (33 groups)
• For 238U: Data from Ref. 16 was updated using data from Ref. 17 and Ref. 18. Below 400keV, standard deviation was highly reset up to 80%.
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Proceedings of ICAPP ‘12 Chicago, USA, June 24-28, 2012
Paper 12136
• For 240Pu: Data from Ref. 16 was updated using data from Ref. 18 and Ref. 19. Covariance data was added between 9keV and 40keV, which explains the increase of uncertainty. • For 241Pu: Data from Ref. 16 was updated using Ref. 19 and Ref. 20. Standard deviation was raised up between 4eV and 450eV. VI.C.3 Capture Uncertainty
Fig. 16 shows a comparison in the capture
contribution between the JENDL-3.3 and JENDL-4.0 evaluations. Main changes are: • For 238U: The dramatic change is due to the 10% error re-estimation below 20keV, where data from JENDL-3.3 were replaced. • For 240Pu: Data from Ref. 21 was updated using Ref. 22. Here also covariance data was added between 9keV and 40keV. • For 241Pu: Data from Ref. 21 was updated using Ref. 19 and Ref. 22. • For 23Na: Data from Ref. 17 was re-estimated by considering the difference between evaluated and measured data by standard deviation was reduced between 8eV and 15keV.
Fig. 16. Capture contribution to Monju criticality uncertainty VI.C.4 Inelastic Uncertainty
Fig. 17 shows a comparison in the inelastic
contribution between the JENDL-3.3 and JENDL-4.0 evaluations. Change is mainly due to 238U, 56Fe and 23Na. • For 238U: It is not possible from the ENDF files to determine where the update comes from. The variance was increased especially between 40keV and 1MeV.
Fig. 17. Inelastic contribution to Monju criticality uncertainty
• For 56Fe and 23Na: Variances from Ref. 17 for the inelastic cross-sections were revised by considering the
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spread of experimental data. This was mainly above 6MeV for 56Fe and below 6MeV for 23Na. VI.C.5 Elastic, Nu, (n,xn) Uncertainties
The elastic and (n,xn) cross-sections and the υ
parameter do not stand for a significant part of the total uncertainty. The corresponding results are nevertheless given in Fig. 18, 19 and 20 for respectively the elastic, (n,xn) and υ.
Fig. 18. Elastic contribution to Monju criticality uncertainty
Fig. 19. (n,xn) contribution to Monju criticality uncertainty
Fig. 20. υ contribution to Monju criticality uncertainty
VII. CONCLUSIONS
A new cross-sections library for ERANOS based on the JENDL-4.0 evaluation has been successfully produced. The library was tested and compared with others codes and other libraries on two benchmarks: MZA and MZB and showed good results on criticality calculation.
This library was tested on the Monju 2010 restart core and showed significant improvement compared with previous evaluations. The library can be expected to become a useful tool for various applications.
Sensitivity analysis was performed and showed the relative importance of isotopes and reactions in a core criticality calculation.
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The uncertainty analysis revealed effective changes in covariance data between the JENDL-4.0 and the former JENDL-3.3. Major improvements have been observed for 239Pu-fission. A significant uncertainty has been brought by the newly included isotopes such as 241Am and by re-evaluation of 238U-capture covariance data. An increase of the uncertainty was also shown for 23Na-inelastic, 56Fe-inelastic, 240Pu-fission and 241Pu-fission due to re-evaluation of covariance data. The results can now be used to identify the next improvement possibilities for cross-sections evaluation.
ACKNOWLEDGMENTS The authors would like to thank J.-C. Sublet and O.
Bouland (CEA, DEN/DER/SPRC) and P. Ribon (CEA, DEN/DM2S/SERMA) for their help in the ENDF files processing; G. Noguere (CEA/DEN/DER/LEPh) and G. Rimpault (CEA/DEN/DER/SPRC) for their help to process covariance matrices; Japan Atomic Energy Agency for making the internship of Pierre Tamagno possible in the scope of his MSc thesis at INSTN; the European Nuclear Educational Network (ENEN) and Electricité De France (EDF) for their financial support to the study.
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