In collaboration with NRG

Transcription

1 COMPARISON OF MONTE CARLO UNCERTAINTY PROPAGATION APPROACHES IN ACTIVATION CALCULATIONS Carlos J. Díez*, O. Cabellos, J.S. Martínez Universidad Politécnica de Madrid (UPM) CCFE (UK), January 24, 2012 In collaboration with NRG *C.J. Díez January 2012, CCFE, UK 1 / 21

2 COMPARISON OF MONTE CARLO UNCERTAINTY PROPAGATION APPROACHES IN ACTIVATION CALCULATIONS ACTIVATION CALCULATIONS Ni Ni,,, N0, dn N eff N ( fiss ) eff N A N dt Ni Ni,, DH i DH i, E,, N i Source of uncertainty: Nuclear Data (ND) Different uncertainty propagation techniques can be used: Sensitivity analysis: Use covariance info Use any library that includes this info First Order Taylor Approximation 2 TV Monte Carlo methods 2 / 21

3 COMPARISON OF MONTE CARLO UNCERTAINTY PROPAGATION APPROACHES IN ACTIVATION CALCULATIONS Monte Carlo Uncertainty Analysis (MC) Treat the global effect of all nuclear data uncertainties Individual global sensitivity coefficients can be calculated Without any approximation Approach 1: Using covariance info on Nuclear Data Libraries (CUP) ND libraries collapsed 1g ACAB Sampling Results Mean values Std. Deviation ACAB Approach 2: Total Monte Carlo (TMC) Sampling Nuclear Model Parameters Random ND libraries 3 / 21 Results

4 COMPARISON OF MONTE CARLO UNCERTAINTY PROPAGATION APPROACHES IN ACTIVATION CALCULATIONS Monte Carlo Uncertainty Analysis (MC) TMC Advantages Disadvantages - No need to choose PDF - Easy to use with black box scheme - Large amount of files needed - To produce more random files needs to run TALYS code - Only uncertainty due to nuclear model parameters?? Using ND libraries with covariance (CUP) Advantages - Only one file is needed - More histories can be produced sampling covariance info - Other nuclear data libraries can be used - Easy to compare with sensitivity analysis Disadvantages - PDF should be chosen - Code to sample should be implemented - Lost of uncertainty info throughout condensing process?? - Large amount of variables to sample 4 / 21

5 COMPARISON OF MONTE CARLO UNCERTAINTY PROPAGATION APPROACHES IN ACTIVATION CALCULATIONS Comparison between CUP and TMC Try to propagate the same uncertainties used in TMC into CUP Use the ND library created by using the X amount of TMC ND libraries Assume a PDF for CUP sampling Method 2: Total Monte Carlo (TMC) Sampling ACAB Results ACAB Results x1000 files Random ND libraries Nuclear Model Parameters Sampling Method 1: CUP Generate COVARIANCE condensing X random libraries ND libraries with COVARIANCE 1 file 5 / 21

6 COMPARISON OF MONTE CARLO UNCERTAINTY PROPAGATION APPROACHES IN ACTIVATION CALCULATIONS Comparison between CUP and TMC ACAB Results x1000 files Random ND libraries How is it done and what kind of info is lost?? Sampling ACAB Results Will same results be obtained?? ND libraries with COVARIANCE 1 file Which pdf should be used?? 6 / 21

7 COMPARISON OF MONTE CARLO UNCERTAINTY PROPAGATION APPROACHES IN ACTIVATION CALCULATIONS FLOWCHARTS CUP TMC EAF-2010 is used as base library and only for one isotope, their XS are changed using TENDL / 21

8 COMPARISON OF MONTE CARLO UNCERTAINTY PROPAGATION APPROACHES IN ACTIVATION CALCULATIONS Reference system for Activation Calculations One of the preliminary conceptual designs of the European Facility for Industrial Transmutation (EFIT) Coolant Pure Lead Thermal Power 400 MWth Fuel (Pu, Am)O2 + MgO Initial mass of actinides tonnes 1,E-03 Constant neutron environment: - neutron flux: 3.12 x 1015 n/cm2 s - average energy <E> = 0.37 MeV Calculations for discharge burn-up: GWd/tHM (778 irradiation days) Normalized Neutron Flux 1,E-04 Initial 400 days 1,E-05 1,E-06 1,E-07 Initial total flux intensity = 2.84E+15 n cm-2s days total flux intensity = 3.12E+15 n cm -2s-1 1,E-08 1,E-09 1,E-06 1,E-05 1,E-04 1,E-03 1,E-02 1,E-01 Eneutron (MeV) 8 / 21 1,E+00 1,E+01 1,E+02

9 COMPARISON OF MONTE CARLO UNCERTAINTY PROPAGATION APPROACHES IN ACTIVATION CALCULATIONS Isotopes studied Mo 98 U235 U238 Pu239 Pu241 Am241 After collapsing to one-group XS-section analysis x1000 files Mean Value Random ND libraries Rel.std.dev Sampling ND libraries with COVARIANCE 1 file Ratios XS1 Mean Value VS Mean Value Rel.std.dev Rel.std.dev XS1000 Mean Value Mean Value Rel.std.dev Rel.std.dev Mean Value Mean Value Rel.std.dev Rel.std.dev 9 / 21

10 Pu239 Cross-section analysis with 700 random files Reaction (n,2n) MT / 21

11 Pu239 Cross-section analysis with 700 random files Reaction (n,f) MT / 21

12 Pu239 Cross-section analysis with 700 random files Reaction (n,g) MT 102 TMC PDF non-normal 12 / 21

13 Pu239 Atoms of Pu239 throughout the burn-up Mean value Rel.std.dev. 20% 13 / 21

14 Pu241 Cross-section analysis with 700 random files Reaction (n,2n) MT / 21

15 Pu241 Cross-section analysis with 700 random files Reaction (n,f) MT / 21

16 Pu241 Cross-section analysis with 700 random files Reaction (n,g) MT / 21

17 Pu241 Atoms of Pu241 throughout the burn-up Mean value Rel.std.dev. 250% 17 / 21

18 Pu241 Cross-correlation between (n,f) and (n,g) in TMC Comparison of the rel.std.dev. Of the number of atoms at the end of burn-up when (n,f) and (n,g) uncertainties are propagated individually and all together Rel.std.dev. TMC CUP All reactions 0.48% 1.14% a. (n,f) 0.73% 0.81% b. (n,g) 0.77% 0.75% Negative correlation 18 / 21

19 Conclusions Not all TENDL-2010 isotope libraries are prepared for being used in TMC and CUP, TENDL-2011 will be the next challenge. Main sources of differences between TMC and CUP Processing the files by NJOY and the PARSER Normal PDF is not always suitable for CUP approach Cross-correlations have to be taken into account in CUP approach Covariance calculation in TMC does not use the mean value (best-value instead) Conclusions for Pu239 - Ratio rel.std.dev. (n,f) TMC/CUP = TMC (n,g) PDF not Normal - No cross-correlations between (n,f) and (n,g) Conclusions for Pu241 - Ratio rel.std.dev. (n,f) TMC/CUP = Ratio rel.std.dev (n,g) TMC/CUP = TMC (n,g) PDF not Normal - Negative cross-correlation between (n,f) and (n,g) Ratio rel.std.dev. Atoms at end of burn-up CUP/TMC = 0.8 Ratio rel.std.dev. Atoms at end of burn-up CUP/TMC = / 21

20 ACKNOWLEDGMENTS - The research leading to these results has received funding from the European Atomic Energy Community s Seventh Framework Programme (FP7/ ) under grant agreement n (FP7-EURATOM-FISSION-2009;Project ANDES/249671) - This work is partially supported by Ministerio de Educación de España (Ministry of Education of Spain) under Ph.D. FPU grant AP for the first author. 20 / 21

21 THANK YOU FOR YOUR ATTENTION!! *C.J. Díez January 2012, CCFE, UK 21 / 21