SENSITIVITY TO NUCLEAR DATA AND UNCERTAINTY ANALYSIS: THE EXPERIENCE OF VENUS2 OECD/NEA BENCHMARKS. A.BIDAUD, I. KODELI, V.MASTRANGELO, E.SARTORI IPN Orsay CNAM PARIS OECD/NEA Data Bank, Issy les moulineaux
One certainty about nuclear data : they are not the «good» one ----JEFF-30 MATERIAL 600 -----INCIDENT NEUTRON DATA ------ENDF-6 FORMAT ***************************** JEFF-3.0 ************************* DATA TAKEN FROM :- ENDF/B-VI.3 (DIST-SEP91 REV1-JUL91)
Geometry Mesh size Nuclear Data Geometry Temperatures Sensitivity and Uncertainty Code System Mesh + input generation BOT3P Adjoint and direct calculation DORT Nuclear Data Geometry, densities Temperatures Energy group structure multigroup cross-section set production Partial Cross Section Covariance matrices production NJOY Sensitivity and uncertainty calculation SUSD3D
VENUS 2 Benchmark Zero power Thermal Water reactor in SCK*CEN (Belgium) Partial MOX fuelled Axial and radial pin power distribution measurements are available Deterministic and Monte-Carlo calculations are compared Most recent data libraries were used
Cross section preparation 199 group library based on VITAMIN-B6 fine group library processed with SCALE4.4 18 group library processed by RESMOD code, provided by W. Zwermann(GRS) 2D and 3D calculations with both library Impact of Buckling factor on 2D results
Calculation Kinf or keff Participant's average UO2 3,3% Cell 1,40642 1,40646 UO2 4,0% Cell 1,33735 1,33769 MOX Cell 1,25469 1,25737 3D 199g core 0,99466 3D 18g Core 1,0052 1,00122 1,15 1,1 1,05 C/E 1 0,95 0,9 0,85 UO2 3/0 UO2 4/0 MOX 2/2,7 SCALE199g ZWERMAN 18g C/E=1
material H1 B10 O16 (n,gamma) (n,alpha) (n,gamma) 2D zwermann -3,86E-02-4,35E-02-2,05E-05 3D zwermann -4,63E-02-4,27E-02-2,21E-05 2D 199g -3,98E-02-3,18E-02-2,10E-05 3D 199g -5,41E-02-3,28E-02-2,49E-05 material U235 U238 Pu239 reaction (n,gamma) fission Nu total (n,gamma) fission Nu total (n,gamma) fission Nu total 2D zwermann -1,05E-01 3,21E-01 8,06E-01-1,75E+00 5,74E-02 7,97E-02-3,25E-02 5,39E-02 1,15E-01 3D zwermann -1,04E-01 3,23E-01 8,06E-01-1,70E+00 5,73E-02 7,91E-02-3,25E-02 5,41E-02 1,15E-01 2D 199g -1,09E-01 3,45E-01 8,38E-01-1,66E+00 4,00E-02 6,12E-02-2,79E-02 4,87E-02 1,00E-01 3D 199g -1,16E-01 3,10E-01 8,36E-01-1,73E+00 4,13E-02 6,21E-02-3,03E-02 4,57E-02 1,02E-01
2D-3D Comparison 3D allows axial reflector explicit model =>more H2O atoms in the 3D model! Mat. Reaction 2D 3D(Volume corrected) H-1 Elastic 3.37E-1 3.74E-1 (3.55E-1) (n,γ) -3.86E-2-4.63E-2 (-3.84E-2) O-16 Elastic 3.59E-2 5.11E-2 (4.69E-2) (n,γ) -6.54E3-6.45E-3 (-6.40E-3)
Buckling Effect Material reaction 2D 199g critical B2 H1 (n,gamma) -3,98E-02-3,93E-02 B10 (n,alpha) -3,18E-02-3,59E-02 O16 (n,gamma) -2,10E-05-2,08E-05 (n,gamma) -1,09E-01-1,09E-01 U235 fission 3,45E-01 3,47E-01 Nu total 8,38E-01 8,40E-01 (n,gamma) -1,66E+00-1,67E+00 U238 fission 4,00E-02 4,09E-02 Nu total 6,12E-02 6,26E-02 (n,gamma) -2,79E-02-2,69E-02 Pu239 fission 4,87E-02 4,79E-02 Nu total 1,00E-01 9,78E-02 No real impact but for boron =>Strong impact of self shielding effect
Sensitivity profile 5,00E-01 Sensitivity per Unit Lethargy 0,00E+00-5,00E-01-1,00E+00-1,50E+00-2,00E+00 U238 capture 18g U238 capture 199g -10*(H1 elas) -2,50E+00 1,E-05 1,E-03 1,E-01 1,E+01 1,E+03 1,E+05 1,E+07 1,E+09 Energy
5% underestimation on fission rates == 15% underestimation in sensitivity 3,50E-02 3,00E-02 Sensitivity per Unit Lethargy 2,50E-02 2,00E-02 1,50E-02 1,00E-02 5,00E-03 Pu 239 fission 18g Pu 239 fission 199g 0,00E+00 1,E-05 1,E-03 1,E-01 1,E+01 1,E+03 1,E+05 1,E+07 1,E+09 Energy
Impact of Boron macrocell calculation 7,0E+03 6,0E+03 5,0E+03 4,0E+03 3,0E+03 2,0E+03 1,0E+03 without self shielding with selfshielding 0,0E+00 1,0E-05 1,0E-04 1,0E-03 1,0E-02 1,0E-01 1,0E+00 0,00E+00-2,00E-03-4,00E-03-6,00E-03-8,00E-03-1,00E-02-1,20E-02-1,40E-02 2D 18g 2D 199g 2D 18g corrected -1,60E-02 1,E-05 1,E-03 1,E-01 1,E+01 1,E+03 1,E+05
Covariances matrices : U238 capture σ/σ vs. E for 238 U(n,γ) 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 10-3 10-1 10 1 10 3 10 5 10 7 Correlation Matrix Linear Axes: Rel. Standard Dev. (%) Logarithmic Axes: Energy (ev) 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 10-3 10-1 10 1 10 3 10 5 10 7 σ/σ vs. E for 238 U(n,γ) 50 40 30 20 10 σ/σ vs. E for 238 U(n,γ) 0 10-3 10-1 10 1 10 3 10 5 10 7 Correlation Matrix 0 10-3 10-1 10 1 10 3 10 5 10 7 Linear Axes: Rel. Standard Dev. (%) Logarithmic Axes: Energy (ev) 10 20 30 40 50 σ/σ vs. E for 238 U(n,γ) 1.0 0.8 0.6 0.4 0.2 0.0-1.0-0.8-0.6-0.4-0.2 0.0 1.0 0.8 0.6 0.4 0.2 0.0-1.0-0.8-0.6-0.4-0.2 0.0
Uncertainties based on various covariance data Uncertainty Uncertainty Material reaction Sensitivity (%/%) JENDL 3.2 (pcm) IRDF-90 (pcm) B10 (n,alpha) -4,35E-02 20 7 (n,gamma) -1,05E-01 88 _ U235 fission 3,21E-01 74 60 Nu total 8,06E-01 211 _ (n,gamma) -1,75E+00 3012 625 U238 fission 5,74E-02 29 31 Nu total 7,97E-02 68 _ (n,gamma) -3,25E-02 168 _ Pu239 fission 5,39E-02 129 14 Nu total 1,15E-01 6 _ Total (pcm) 3050 628
Conclusions (1) Our multidimentional tests shows that : Sensitivities to fuel isotopes are not much sensitive to geometrical modelisation Errors on reaction rates due to cross section preparation impacts the sensitivities For some isotopes with strong self-shielding, the partial cross sections needed for sensitivity analysis done with NJOY bodarenko s method can be inacurrate.
Conclusions (2) Total uncertainty is about 1% which is larger than participant results spread. U238 first resonances are responsible for a very large part of it. Neutron yelds are the second source of uncertainties. Analysis results are limited by poor nuclear data uncertainty information (lack of covariance matrices in evaluated files).