Uncertainty quantification using SCALE 6.2 package and GPT techniques implemented in Serpent 2

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Constance Lamb
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1 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy September 26 th -30 th, 2016 Uncertainty quantification using SCALE 6.2 package and GPT techniques implemented in Serpent 2 Giorgio BAIOCCO Alessandro PETRUZZI Marco CHERUBINI

2 Overview Introduction Codes and methods Test cases Results o UAM Exercise I-1 k eff sensitivity and uncertainty 1 group homogenized XS sensitivity and uncertainty Conclusions and future work 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

Introduction The main objective is to test Monte Carlo code SERPENT-2 in S/U analysis The program is tested on exercises I-1 of UAM benchmark o TMI fuel pin HZP Several cross sections (i.e. elastic & inelastic scattering, fission, capture etc.

3 Introduction The main objective is to test Monte Carlo code SERPENT-2 in S/U analysis The program is tested on exercises I-1 of UAM benchmark o TMI fuel pin HZP Several cross sections (i.e. elastic & inelastic scattering, fission, capture etc.) of several isotopes (i.e. U, U, 16 O and 1 H) are perturbed 2 different cross section covariance libraries are used o 44 groups from SCALE 6.1 o 56 groups from SCALE 6.2 Uncertainty is assessed over different responses o k eff o 1 group s capt, s fiss, S capt and S fiss Results are compared with SCALE/TSUNAMI-1D 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

Codes and methods The effect of a perturbation of a parameter x on the response R is: dr/ dx S R, x / R x Uncertainty can be calculated using the sandwitch

4 Codes and methods The effect of a perturbation of a parameter x on the response R is: dr/ dx S R, x / R x Uncertainty can be calculated using the sandwitch rule: R S Cov x S Var R, x R, x s R Var R 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

Codes and methods SERPENT-2 is a 3D continuous-energy Monte Carlo code for reactor physics calculation In this work a modified version of SERPENT-2 (provided by UC Berkeley), with implemented GPT is

5 Codes and methods SERPENT-2 is a 3D continuous-energy Monte Carlo code for reactor physics calculation In this work a modified version of SERPENT-2 (provided by UC Berkeley), with implemented GPT is used to calculate sensitivity coefficients of different response functions (i.e. k eff, homogenized microscopic and macroscopic cross sections) related to the perturbation of input cross sections. Details about this program can be found in M. Aufiero et al. A collision historybased approach to sensitivity/perturbation calculations in the continuous energy Monte Carlo code SERPENT 2 different cross section covariance libraries are used for uncertainty quantification: o 44 groups from SCALE 6.1 o 56 groups from SCALE 6.2 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

6 Test cases Considered case o TMI pin at HZP 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

7 Test cases Isotopes considered in uncertainty quantification o U- o U- o O-16 o H-1 Perturbed cross sections o (n, elastic) o (n, n ) o (n, fission) o (n, g) o nu-bar o chi-bar 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

8 Test cases Uncertainty quantification k eff 1 group s cap U 1 group s fiss U TMI Pin 1 group s cap U 1 group s fiss U 1 group S cap Fuel 1 group S fiss Fuel 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

9 Results Uncertainty quantification k eff 1 group s cap U 1 group s fiss U TMI Pin 1 group s cap U 1 group s fiss U 1 group S cap Fuel 1 group S fiss Fuel 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

10 Sensitivity coefficient per unit lethargy Results TMI Pin - k eff 9.0E-02 TMI Pin - k eff - U (n,fission) 8.0E E E E E E E E E+00 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 SERPENT 44 groups SCALE groups 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

11 Sensitivity coefficient per unit lethargy Results TMI Pin - k eff 9.0E-02 TMI Pin - k eff - U (n,fission) 8.0E E E E E-02 Integral Values Serpent = ± 2.36E-04 SCALE 6.1 = SCALE 6.2 = E E E E+00 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 SERPENT 44 groups SCALE groups SCALE groups 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

12 Sensitivity coefficient per unit lethargy Results TMI Pin - k eff -5.0E-03 TMI Pin - k eff - U (n,g) 0.0E+00 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E E E E E E E E E-02 SERPENT 44 groups SCALE groups 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

13 Sensitivity coefficient per unit lethargy Results TMI Pin - k eff -5.0E-03 TMI Pin - k eff - U (n,g) 0.0E+00 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E E E E E E E-02 Integral Values Serpent = ± 8.90E-05 SCALE 6.1 = SCALE 6.2 = E E-02 SERPENT 44 groups SCALE groups SCALE groups 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

14 Sensitivity coefficient per unit lethargy Results TMI Pin - k eff 3.5E-01 TMI Pin - k eff - U nubar 3.0E E E E E E E+00 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 SERPENT 44 groups SCALE groups 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

15 Sensitivity coefficient per unit lethargy Results TMI Pin - k eff 3.5E-01 TMI Pin - k eff - U nubar 3.0E E E-01 Integral Values Serpent = ± 5.64E-05 SCALE 6.1 = SCALE 6.2 = E E E E+00 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 SERPENT 44 groups SCALE groups SCALE groups 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

16 Sensitivity coefficient per unit lethargy Results TMI Pin - k eff 1.0E-03 TMI Pin - k eff - U (n,n') 0.0E+00 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E E E E E E E E-03 SERPENT 44 groups SCALE groups 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

17 Sensitivity coefficient per unit lethargy Results TMI Pin - k eff 1.0E-03 TMI Pin - k eff - U (n,n') 0.0E+00 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E E E E E E E-03 Integral Values Serpent = ± 1.74E-04 SCALE 6.1 = SCALE 6.2 = E-03 SERPENT 44 groups SCALE groups SCALE groups 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

18 Sensitivity coefficient per unit lethargy Results TMI Pin - k eff 3.0E-02 TMI Pin - k eff - U (n,fission) 2.5E E E E E E+00 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E E-03 SERPENT 44 groups SCALE groups 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

19 Sensitivity coefficient per unit lethargy Results TMI Pin - k eff 3.0E-02 TMI Pin - k eff - U (n,fission) 2.5E E E-02 Integral Values Serpent = ± 6.42E-05 SCALE 6.1 = SCALE 6.2 = E E E+00 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E E-03 SERPENT 44 groups SCALE groups SCALE groups 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

20 Sensitivity coefficient per unit lethargy Results TMI Pin - k eff TMI Pin - k eff - U (n,g) 0.0E+00 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E E E E E E E-02 SERPENT 44 groups SCALE groups 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

21 Sensitivity coefficient per unit lethargy Results TMI Pin - k eff -2.0E-02 TMI Pin - k eff - U (n,g) 0.0E+00 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E E E E E E-01 Integral Values Serpent = ± 1.08E-04 SCALE 6.1 = SCALE 6.2 = E E E-01 SERPENT 44 groups SCALE groups SCALE groups 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

22 Results TMI Pin - k eff Uncertainty quantification TMI Pin - k eff SERPENT 44 groups SCALE groups SCALE groups Covariance Matrix Relative standard deviation in k eff (pcm) Relative standard deviation in k eff (pcm) Relative standard deviation in k eff (pcm) U nubar U nubar U (n,g) U (n,g) U (n,g) U (n,g) U (n,n ) U (n,n ) U c U c U (n,fiss) U (n,fiss) U nubar U nubar H (n,el) 1 H (n,el) SERPENT 44 groups SCALE groups SCALE groups k eff % Dk/k k eff % Dk/k k eff % Dk/k ± 4E % % % 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

23 Results Uncertainty quantification k eff 1 group s cap U 1 group s fiss U TMI Pin 1 group s cap U 1 group s fiss U 1 group S cap Fuel 1 group S fiss Fuel 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

24 Results Direct and indirect effects Sensitivity coefficients based on the Generalized Perturbation Theory expressions consist of 2 different effects: o Direct effects: due to the perturbation of cross sections appearing directly in the response function o Indirect effects: due to the perturbation of neutron flux (caused by the cross sections perturbation) These effects have been calculated separately with Serpent for the evaluation of the cross sections sensitivity coefficient 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

25 Sensitivity coefficient per unit lethargy Results TMI Pin s capt, U sensitivity to U (n,g) 6.0E E groups 4.0E E E E E E-011.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E E E E-01 Indirect term Direct term Total The indirect term is negative because an increase in the cross-section data enhances the local depression of the neutron flux, causing a decrease of the 1 group s The direct term is positive because an increase in the cross-section data directly increase the 1 group s 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

26 Sensitivity coefficient per unit lethargy Sensitivity coefficient per unit lethargy 3.00E E E E E E E E E E E E E E-01 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E E E E E E E E E E-01 Results TMI Pin s capt, U sensitivity to U (n,g) 44 groups Integral Value Serpent = ± 1.62E-04 SCALE 6.1 = groups 0.00E E E E E E E E E E E E E E-02 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 Integral Value SCALE 6.2 = groups Serpent - Indirect term Serpent - Direct term Serpent - Total SCALE 6.1 SCALE 6.2 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

27 Sensitivity coefficient per unit lethargy Sensitivity coefficient per unit lethargy Results TMI Pin s capt, U sensitivity to U (n,g) 2.5E E groups 1.5E E E-02 Integral Value Serpent = ± 3.31E-04 SCALE 6.1 = E E E E E E E+00 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E E E E E E E groups 0.00E E E E E E E E E E E E E E-02 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 Integral Value SCALE 6.2 = groups Serpent - Indirect term Serpent - Direct term Serpent - Total SCALE 6.1 SCALE 6.2 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

28 Sensitivity coefficient per unit lethargy Sensitivity coefficient per unit lethargy Results TMI Pin s fiss, U sensitivity to U (n,fiss) 3.5E E E E groups Integral Value Serpent = ± 4.31E-04 SCALE 6.1 = E-021.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E E E E E E E E groups 56 groups 1.50E E E E-02 Integral Value SCALE 6.2 = E E-021.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E E E E E E E E E E E E E E E E-01 Serpent - Indirect term Serpent - Direct term Serpent - Total SCALE 6.1 SCALE 6.2 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

29 Sensitivity coefficient per unit lethargy Sensitivity coefficient per unit lethargy Results TMI Pin s fiss, U sensitivity to U (n,fiss) 1.2E E groups 8.0E E E E-01 Integral Value Serpent = ± 5.83E-05 SCALE 6.1 = E E E E E E E+00 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E E E E E E E E groups Integral Value SCALE 6.2 = E E E E E E E E E E E E E E-02 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E groups Serpent - Indirect term Serpent - Direct term Serpent - Total SCALE 6.1 SCALE 6.2 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

30 Results TMI Pin - 1 group s Uncertainty quantification TMI Pin 1 group s s capt, U SERPENT 44 groups SCALE groups SCALE groups s fiss, U SERPENT 44 groups SCALE groups SCALE groups Covariance Matrix RSD (%) RSD (%) RSD (%) U (n,g) U (n,g) 1.284% 1.294% 1.171% Covariance Matrix RSD (%) RSD (%) RSD (%) U (n,n ) U (n,n ) 0.930% 0.918% 0.931% U (n,n ) U (n,n ) 0.962% 0.946% 0.960% U c U c 0.433% 0.430% 0.725% U c U c 0.447% 0.444% 0.750% 1 H (n,el) 1 H (n,el) 0.409% 0.407% 0.241% 1 H (n,el) 1 H (n,el) 0.413% 0.411% 0.215% U (n,g) U (n,g) 0.200% 0.211% 0.216% U (n,fiss) U (n,g) 0.340% 0.340% 0.340% U (n,g) U (n,g) 0.172% 0.172% 0.166% s capt, U SERPENT 44 groups SCALE groups SCALE groups s fiss, U SERPENT 44 groups SCALE groups SCALE groups Covariance Matrix RSD (%) RSD (%) RSD (%) U (n,n ) U (n,n ) 0.919% 0.902% 0.914% Covariance Matrix RSD (%) RSD (%) RSD (%) U (n,n ) U (n,n ) % 3.222% 3.231% U (n,g) U (n,g) 0.844% 0.877% 0.901% U c U c % 2.198% 3.623% U c U c 0.444% 0.437% 0.735% 1 H (n,el) 1 H (n,el) 0.362% 0.361% 0.149% U (n,g) U (n,g) 0.064% 0.065% 0.052% 1 H (n,el) 1 H (n,el) % 0.513% 0.202% U (n,fiss) U (n,fiss) % 0.510% 0.510% U c U c % 0.166% 0.569% 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

31 Results TMI Pin - 1 group s Uncertainty quantification TMI Pin 1 group s SERPENT 44 groups s capt, U ± 4E-05 Total RSD (%) SCALE groups s capt, U Total RSD (%) SCALE groups s capt, U Total RSD (%) % 8.297E % 8.286E % SERPENT 44 groups s fiss, U 3.517E+01 ± 5E-05 Total RSD (%) SCALE groups s fiss, U Total RSD (%) SCALE groups s fiss, U Total RSD (%) % 3.532E % 3.517E % Uncertainty in s fiss, U is big mainly due to the contribution of U (n,n ) and U c SERPENT 44 groups s capt, U 8.136E-01 ± 6E-05 Total RSD (%) SCALE groups s capt, U Total RSD (%) SCALE groups s capt, U Total RSD (%) % 8.350E % 8.266E % SERPENT 44 groups s fiss, U 1.019E-01 ± 7E-05 Total RSD (%) SCALE groups s fiss, U Total RSD (%) SCALE groups s fiss, U Total RSD (%) % 1.010E % 1.008E % 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

32 Results Uncertainty quantification k eff 1 group s cap U 1 group s fiss U TMI Pin 1 group s cap U 1 group s fiss U 1 group S cap Fuel 1 group S fiss Fuel 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

33 Results TMI Pin - 1 group S Uncertainty quantification TMI Pin 1 group S S capt, Fuel SERPENT 44 groups SCALE groups SCALE groups S fiss, Fuel SERPENT 44 groups SCALE groups SCALE groups Covariance Matrix RSD (%) RSD (%) RSD (%) U (n,n ) U (n,n ) 0.919% 0.917% 0.929% Covariance Matrix RSD (%) RSD (%) RSD (%) U (n,n ) U (n,n ) 0.707% 0.702% 0.713% U (n,g) U (n,g) 0.492% 0.516% 0.529% 1 H (n,el) 1 H (n,el) 0.360% 0.359% 0.218% U c U c 0.418% 0.440% 0.740% U c U c 0.293% 0.292% 0.502% U (n,g) U (n,g) 0.403% 0.401% 0.370% U (n,g) U (n,g) 0.185% 0.196% 0.200% 1 H (n,el) 1 H (n,el) 0.375% 0.377% 0.171% U (n,g) U (n,g) 0.160% 0.161% 0.155% SERPENT 44 groups S capt, Fuel 2.720E-02 ± 4E-05 Total RSD (%) SCALE groups S capt, Fuel Total RSD (%) SCALE groups S capt, Fuel Total RSD (%) % 2.759E % 2.740E % SERPENT 44 groups S fiss, Fuel 4.184E-02 ± 4E-05 Total RSD (%) SCALE groups S fiss, Fuel Total RSD (%) SCALE groups S fiss, Fuel Total RSD (%) % 4.199E % 4.182E % 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

34 Conclusions and future work SERPENT-2 GPT and SCALE 6.1 & 6.2 /TSUNAMI1D sensitivity calculations are in good agreement, regarding the TMI HZP pin analysis. In general uncertainty calculations with 44 & 56 groups covariance matrices are in good agreement (single contributions). Some discrepancies can be found in the contributions of U nubar, U & U c and 1 H (n,el), between 44 and 56 groups calculation. This is probably due to some update in the new 56 groups libraries of SCALE 6.2 (check Ds/s). U nubar and U (n,g) are the major contributors in k eff uncertainty. With the used options in SCALE, U (n,g) uncertainty may be slightly overestimated. U (n,n ) has a strong influence on the uncertainty of homogenized cross sections (both in pin and assembly). Also 1 H (n,el) plays an important role. 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

35 Include other sets o HFP o BWR and VVER cases Future work Conclusions and future work Extend the calculation to the fuel assembly and full core (exercises I-2 & I-3) Include other isotopes o Zr o Gd Use the new 56 and 252 groups covariance libraries of SCALE 6.2 with Serpent 2 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

36 Conclusions and future work THANK YOU FOR YOUR ATTENTION! 6th International Serpent User Group Meeting Politecnico di Milano, Milan, Italy - September 26 th - 30 th, /36

SG39 Meeting May 16-17, Update on Continuous Energy Cross Section Adjustment. UC Berkeley / INL collaboration

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