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  1. Analysis of Available Cross-Section Uncertainty Dataand Progress in Defining Uncertainty Methodologies for Inventory Calculations J. Sanz, O. Cabellos, J. Juan, N. García-HerranzUniversidad Nacional de Educación a Distancia (UNED)Universidad Politécnica de Madrid (UPM)Second IP EUROTRANS Internal Training Course on Nuclear Data for Transmutation June 9, 2006

  2. Outline • INTRODUCTION • OBJECTIVES • PART I: ANALYSIS OF AVAILABLE NEUTRON CROSS SECTION UNCERTAINTY DATA FOR INVENTORY CALCULATIONS • PART II: PROGRESS IN UNCERTAINTY METHODOLOGIES • CONCLUSIONS • FUTURE WORK

  3. Introduction • One of the objectives in NUDATRA Domain is to evaluate the impact of nuclear data uncertainties on relevant fuel cycle and repository parameters

  4. Introduction • One of the objectives in NUDATRA Domain is to evaluate the impact of nuclear data uncertainties on relevant fuel cycle and repository parameters • In order to reach these goals three main elements are required: • Cross section uncertainties (Ds) • Computational techniques enable to assess the impact of Ds on the isotopic inventory and other inventory-related responses • List of relevant parameters for the uncertainty evaluation and required target accuracies in those parameters • Our group is mainly involved in steps I and II

  5. Objectives • Review, processing and analysis of the neutron cross-section uncertainty data available in the most recent internationally distributed nuclear data libraries • Result: compilation of the best current available uncertainty data for use in inventory codes (covariance matrices: uncertainties –diagonal values– and their correlations – off-diagonal values –) • Definition of appropriate methodologies to propagate nuclear data uncertainties to the isotopic inventory • Capability to evaluate the impact of cross section uncertainties on the inventory predictions • Applications to EUROTRANS : assess if further improvement of nuclear data is required

  6. PART IAnalysis of available neutron cross- section uncertainty data for inventory calculations I.1 Review and compilation of available cross-section uncertainty data I.2 Processing the uncertainty data for inventory prediction I.3 Analysis of uncertainties: comparison of the previous uncertainty data

  7. I.1 Review of available uncertainty cross-section data • Activation-oriented nuclear data libraries • FENDL UN/A-2.0, EAF2003/UN and the recently released EAF2005 • Included information: Dj,LIBRARY (relative error in the j energy group) • Assumptions: xs within the same energy group are fully correlated; xs in different groups are assumed to be statistically independent no covariances included, covariance matrix diagonal • For non-threshold reactions  3-4 groups • For threshold reactions  1-2 groups • Uncertainty data for all reactions included in the point-wise cross-section library(13,006 in FENDL-2.0, 12,617 in EAF-2003, 62,637 in EAF-2005)

  8. I.1 Review of the nuclear data uncertainties available (cont.) Data covariances for: • General purpose evaluated nuclear data files BROND-2.2 (last updated 1993) CENDL-2.1 (last updated 1995) ENDF/B-VI.8 (october 2001); ENDF/B-VIIb (2005) JEF-2.2 (1993) JEFF-3.0/1 (may 2005) JENDL-3.3 (2002) IRDF90-2.0 (1993); IRDF2002 (2002) Uncertainty information in “covariance files” • Data of interest for inventory calculations: MF33, MF 39 (no data in the libraries), MF40 • Stored values: absolute ( ) or relative covariances ( )  covariance information is still scarce in all major data files

  9. Most covariance matrices correlate only energy intervals of the same reaction and material (SELF) Covariance matrices correlating cross sections for two different reactions of the same material Covariance matrices correlating cross sections for the same reaction of different materials The total covariance matrix for a particular energy-dependent xs is made up of the contribution of single covariance matrices, each one defining a type of correlation

  10. I.1 Review of the nuclear data uncertainties available (cont.) • Since actinides play an important role in ADS studies, we have carried out a more detailed analysis on them. From the 50 neutron-induced cross-sections (on 10 targets) with covariance data: • Most xs (38) have covariance matrices only correlating energy intervals (of the same reaction and material) (SELF) • There are 8 xs correlated with xs of the same reaction type of different materials (for example, in JENDL-3.3, the Pu241(n,fission) is correlated with the U235(n,fission)) • There are 3 xs with covariance matrices correlating different reaction types of different materials (that is the case of U235(n,fission), correlated with U238(n,g) in IRDF90-2.0) • Finally, there are 3 xs with data correlating two different reaction types of the same material (in JENDL-3.3, the U235(n,g) is correlated with U235(n,fission)) Uncertainty information for a few reactions, more detailed uncertainties (energy correlations and correlations among different reactions or different isotopes)

  11. I.1 Review of the nuclear data uncertainties available (cont.) “Home-made” ANL Covariance Matrix • G. Aliberti, G. Palmiotti, M. Salvatores, C. G. Stenberg Transmutation Dedicated Systems: An assessment of Nuclear Data Uncertainty Impact, Nucl. Sci. Eng. 146, 13-50 (2004) • G. Palmiotti, M. Salvatores Proposal for Nuclear Data Covariance Matrix, JEFDOC 1063 Rev.1, January 20 (2005)

  12. 15 energy groups between 19.6 MeV and E(thermal) • Diagonal values given in Aliberti et al.(2004) • Energy correlations given in Palmiotti et al.(2005)(no correlations among isotopes or reaction types) • The same correlations for all isotopes and reactions, under the form of full energy correlation in 5 energy bands: • the region above the threshold of fertile isotope fission cross-sections, and of many inelastic cross-sections, up to 20 MeV • the region of the continuum down to the upper unresolved resonance energy limit • the unresolved resonance energy region • the resolved resonance region • the thermal range

  13. I.2 Processing the uncertainty data for inventory prediction • Covariance data have to be processed into multigroup to be used by an inventory code • Uncertainties in the activation-oriented nuclear data libraries are in a group structure  diagonal covariance matrices are ready for use by the inventory code (cross-sections need to be processed in the same group structure to assure the consistency) • Files MF33 of the general-purpose evaluated data files need to be processed to yield the multigroup covariance matrices. Computational processing tools: • NJOY99.112 (ERRORR/COVR modules) • ERRORRJ-2.1.2 We are able to process covariance data to yield multigroup covariance matrices ready for use by inventory codes (such as ACAB) • Multigroup covariance matrices with energy correlations • Multigroup covariance matrices correlating different isotopes or reaction types In preparation at the NEA Data Bank: they are extracting relevant covariance data from current evaluations in major data files and processing them in the ANL 15-multigroup structure. The derived covariance matrix in called NEA-K Covariance Matrix

  14. Example: 240Pu (n,gamma) from JENDL-3.3 processed by ERRORRJ-2.1.2 in the ANL 15-group structure material mat-mt=(9440,102) grp energy x-sec. rel.s.d. std.dev. 1 2.0000E+07 9.8861E-04 7.5000E-01 7.4146E-04 2 1.9600E+07 9.8861E-04 6.7497E-01 6.6728E-04 3 6.0700E+06 2.6886E-02 4.5694E-01 1.2285E-02 4 2.2300E+06 7.8668E-02 4.5255E-01 3.5601E-02 5 1.3500E+06 1.2688E-01 1.9635E-01 2.4913E-02 6 4.9800E+05 1.9733E-01 5.7960E-02 1.1437E-02 7 1.8300E+05 3.8927E-01 3.5590E-02 1.3854E-02 8 6.7400E+04 6.6387E-01 1.3602E-02 9.0299E-03 9 2.4800E+04 9.7319E-01 1.5024E-02 1.4622E-02 10 9.1200E+03 1.5993E+00 4.5523E-03 7.2805E-03 11 2.0400E+03 3.8849E+00 3.8845E-03 1.5091E-02 12 4.5400E+02 7.1500E+02 6.9444E-04 4.9652E-01 13 2.2600E+01 8.2559E+02 1.7595E-03 1.4526E+00 14 4.0000E+00 8.2559E+02 3.8735E-02 3.1979E+01 15 5.4000E-01 8.2559E+02 4.1812E-03 3.4520E+00 <<< correlation matrix >>> column material mat-mt=(9440,102) vs row material mat-mt=(9440,102) row 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 column-------------------------------------------------------------------------- 1 1000 973 30 0 0 0 0 0 0 0 0 0 0 0 0 2 973 1000 28 0 0 0 0 0 0 0 0 0 0 0 0 3 30 28 1000 925 425 156 94 157 0 0 0 0 0 0 0 4 0 0 925 1000 681 182 137 286 0 0 0 0 0 0 0 5 0 0 425 681 1000 294 106 285 0 0 0 0 0 0 0 6 0 0 156 182 294 1000 807 49 0 0 0 0 0 0 0 7 0 0 94 137 106 807 1000 344 0 0 0 0 0 0 0 8 0 0 157 286 285 49 344 1000 503 148 0 0 0 0 0 9 0 0 0 0 0 0 0 503 1000 674 0 0 0 0 0 10 0 0 0 0 0 0 0 148 674 1000 0 0 0 0 0 11 0 0 0 0 0 0 0 0 0 0 1000 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 0 1000 4 0 2 13 0 0 0 0 0 0 0 0 0 0 0 4 1000 4 10 14 0 0 0 0 0 0 0 0 0 0 0 0 4 1000 530 15 0 0 0 0 0 0 0 0 0 0 0 2 10 530 1000

  15. Example: Covariance 239Pu (n,fission)/235U (n,fission) from JENDL-3.3 processed by ERRORRJ-2.1.2 in the ANL 15-group structure 1st material mat-mt=(9437, 18) vs 2nd material mat-mt=(9228, 18) grp energy 1st x-sec. 2nd x-sec. 1st r.s.d. 2nd r.s.d. 1 2.0000E+07 2.0920E+00 1.5400E+00 1.3734E-02 1.1148E-02 2 1.9600E+07 2.0920E+00 1.5400E+00 5.5090E-03 3.0259E-03 3 6.0700E+06 1.8358E+00 1.1930E+00 5.0920E-03 2.0016E-03 4 2.2300E+06 1.9741E+00 1.2796E+00 5.6020E-03 2.8955E-03 5 1.3500E+06 1.6865E+00 1.1836E+00 5.4778E-03 2.7716E-03 6 4.9800E+05 1.5184E+00 1.2518E+00 6.2445E-03 3.7342E-03 7 1.8300E+05 1.5156E+00 1.5742E+00 7.0030E-03 4.4413E-03 8 6.7400E+04 1.5932E+00 1.9349E+00 1.6937E-02 4.1847E-03 9 2.4800E+04 1.8024E+00 2.5042E+00 6.7252E-02 0.0000E+00 10 9.1200E+03 2.7279E+00 4.2577E+00 4.8178E-02 0.0000E+00 11 2.0400E+03 6.6364E+00 9.3444E+00 4.4939E-03 0.0000E+00 12 4.5400E+02 3.9532E+02 2.2054E+02 5.9599E-04 0.0000E+00 13 2.2600E+01 4.5535E+02 2.5249E+02 4.2970E-03 0.0000E+00 14 4.0000E+00 4.5535E+02 2.5249E+02 1.1932E-02 0.0000E+00 15 5.4000E-01 4.5535E+02 2.5249E+02 1.0917E-01 0.0000E+00 column material mat-mt=(9437, 18) vs row material mat-mt=(9222, 18) row 1 2 3 4 5 6 7 8 9 10 … column------------------------------------------------------- 1 783 170 74 47 40 23 13 6 0 0 … 2 119 536 226 115 102 64 38 19 0 0 … 3 23 116 389 167 148 96 62 35 0 0 … 4 17 65 237 507 292 193 139 94 0 0 … 5 11 50 217 291 495 281 207 139 0 0 … 6 6 37 181 232 342 584 304 209 0 0 … 7 3 23 140 187 276 334 622 285 0 0 … 8 0 1 35 52 77 93 114 228 0 0 … 9 0 0 0 0 0 0 0 0 0 0 … 10 0 0 0 0 0 0 0 0 0 0 … 11 …

  16. I.3 Analysis of uncertainties • Goal: generate an extended ADS uncertainty library made of a compilation of the best current available data to inventory calculations: • EAF-2005/UN(uncertainties for all reactions, variances in a 2/4 groups, no off-diagonal elements) • ENDF covariance files (MF33)(few reactions, more detailed uncertainties, correlations between energy groups, isotopes and reaction types)  to take them if exist; if not • To be consistent  standard cross-sections from the corresponding evaluation • Test: comparison of the multigroup uncertainties obtained after processing data from different sources with a typical ADS neutron flux (ADS concept consists of an 800 MWth fast core cooled by lead-bismuth eutectic in forced convection, E. González et. al., CIEMAT)

  17. I.3 Analysis of uncertainties (cont.) • Comparison of effective uncertainties (1-group) Uncertainties (D %) in actinide (n,g) cross sections • Comparison of uncertainties in a 3-group structure (that used in EAF-2003) Uncertainties in the Pu240(n,g) with the EAF-2003 group structure • Good agreement of the processed uncertainties from the 2 types of uncertainty data sources  Recommendation = ENDF covariance files +EAF/UN + Palmiotti?

  18. PART IIProgress in defining uncertainty methodologies II.1 Main features of the two proposed methodologies to estimate propagation of cross section uncertainties to the isotopic inventory and associated parameters II.2 Application to the actinide inventory of typical ADS irradiated fuel II.3 Effect of the correlation structure on the results

  19. II.1 Methodologies Goal: to analyse how xs uncertainty is transmitted to X • Sensitivity / Uncertainty Analysis • Method based on the first order Taylor series to estimate uncertainty indices for each reaction cross section in a continuous irradiation scenario • 2) Monte Carlo Uncertainty Analysis • To treat the global effect of all cross sections uncertainties in activation calculations, we have proposed an uncertainty analysis methodology based on Monte Carlo random sampling of the cross sections • Assignment of a Probability Density Function (PDF) to each cross section

  20. Sensitivity Analysis Relative error in Xi due to changes in cross-sections Relative error in cross-sections Sensitivity coefficient We solve at the same time the nuclide concentration Xi and the partial derivative

  21. Sensitivity Analysis (cont.)

  22. Monte Carlo Method • Based on a random sampling a PDF is assigned to each sj • Probability distribution of ej ?

  23. . . . Monte Carlo Method (cont.) • We use simultaneous random sampling of all the XS PDFs involved in the problem • From the sample of the random vector s, the matrix A is computed and the vector of nuclide quantities X is obtained • Repeating the sequence, we obtain a sample of isotopic concentration vectors. The statistic estimators of the sample can be estimated • Enables to investigate the global effect of the complete set of Ds on X

  24. II.2 Application Goal: to show the capabilities of ACAB to evaluate uncertainties in the actinide inventory • Reference system • Fuel composition from the transmuter core used in Aliberti et al. (2004) [1] • Neutron flux: 1.944 x 1015 n / cm2 s , ADS typical spectrum <E> = 0.3489 MeV • Irradiation period of 1 year as in [1] • Analysis performed at 15 energy groups, with the structure adopted in [1] • Uncertainty data only for major actinides: 238Pu and 240Pu, 239Pu, 241Pu, 242Pu and minor actinides: 237Np, 241Am and 243Am, 242mAm, 242Cm, 243Cm, 245Cm, 246Cm, 244Cm and reaction types: (fission, capture and n,2n reactions) • Covariance information taken from Aliberti et al.(2004) and Palmiotti et al. (2005): ANL covariance matrices (reference) • Cross section data processed to the required multigroup structure from EAF-2003

  25. II.2 Application (cont.) • Results from Monte Carlo • Inventory of actinides at the end of 1-year irradiation period computed by ACAB • Results for a 1000 history-sampling

  26. Histogram of the 1000 values obtained by Monte Carlo Method

  27. II.2 Application (cont.) • Results from Sensitivity/Uncertainty technique: comparison with Monte Carlo method • Goal of the comparison of both approaches: checking the implementation • Very different (bad implemented) • Similar (well implemented) • Some differences (no linearity for the irradiation time of the example) • Results very similar

  28. II.3 Effect of correlations Significant impact of the covariances in the inventory prediction? How much the xs uncertainty correlations can affect the actinide inventory? where  is a positive parameter between 0 and  (correlation range parameter)  small  high correlations  big  low correlations • We propose an exercise to assess the effect of the covariance structure on the results • Energy range divided in G groups and E1, E2, … EG mean values of each group • We define the correlation rij between the groups with energies Ei and Ej as :

  29. II.3 Effect of correlations (cont.)

  30. Uncertainty values obtained assuming a simple correlation model with a correlation range parameter q = 0.5 very similar to those obtained assuming Palmiotti’s correlation

  31. Conclusions We are able to process any uncertainty information to inventory calculations and the corresponding cross sections. Interest in using the best set of uncertainties currently available: ENDF + EAF/UN + Palmiotti ?? Two methodologies implemented in the inventory code ACAB to estimate nuclear data uncertainty propagation to the isotopic inventory of actinides  appropiated for ADS problems Potential of the Monte Carlo method highlighted Covariance matrices in any arbitrary multigroup structure can be handled by ACAB (at present, only energy correlations taken into account) The effect of the xs correlations are relevant on the actinides

  32. Future Work at UNED / UPM • Generation of an extended ADS/UN library for all the isotopes of interest (not only actinides) to predict the inventory with the best set of uncertainties • Deal with correlations among different isotopes and different reactions • Definition of the reference system in order to perform appropriate tests (potential of Monte Carlo method) • Fuel composition, neutron flux • Follow-up EUROTRANS schedule

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