CyRUS : A code dedicated to the calculation and the analysis of the - PowerPoint PPT Presentation

CyRUS : A code dedicated to the calculation and the analysis of the uncertainties of the decay heat WONDER 2012 | Jean-Christophe BENOIT SEPTEMBER 24 – 28, 2012 9 octobre 2012 CEA | 10 AVRIL 2012 CEA | 10 AVRIL 2012 | PAGE 1 | PAGE 1

CONTENTS Chapter 01 : INTRODUCTION Chapter 02 : METHODOLOGY Chapter 03 : NUCLEAR DATA Chapter 04 : RESULTS 9 octobre 2012 CEA | SEPTEMBER 24 – 28, 2012 | PAGE 2 | PAGE 2

INTRODUCTION CEA | 10 AVRIL 2012 CEA | 10 AVRIL 2012 | PAGE 3 | PAGE 3 9 octobre 2012

INTRODUCTION Definition Decay Heat (DH) : Heat produced in a nuclear reactor by the irradiated fuel and structures when the reactor is stopped. It is linked to the α , β , γ radioactivity. An issue for a long time 1900 : First discovered by P. CURIE, A. LABORDE (1903) in radium salts during the early years of radioactivity, Theoretical explanation by E. RUTHERFORD and F. SODDY (1904), 1940 : Characterization (Plutonium Project) in order to safely build a reactor to produce plutonium (BORST, BRADY, DAY & CANNON), 1974 : ANS Standard on decay heat, 1975 : First codes in order to propagate the uncertainties of nuclear data on the decay heat (SCHENTER, SCHIMTTROTH, SPINRAD...) 2008 : MERCI experiment (UOx pin PWR) 2010 : PUIREX during PHENIX Final Tests (whole core of the 350 MWth SFR) 1974 1974- -75 75 2008- 2008 -10 10 1903 1942 1903 1942 9 octobre 2012 CEA | SEPTEMBER 24 – 28, 2012 | PAGE 4

INTRODUCTION Reasons for a more precise calculation More Safety and more Savings Nuclear stage impacted Time of cooling Safety Systems of cooling 0.1 second to 8 days Unloading of sub- 5 to 25 days assemblies from the core Road transport 1 to 10 years Reprocessing, 4 to 3000 years Vitrification, Storage 50 to 300 000 years Storage and more CEA | SEPTEMBER 24 – 28, 2012 | PAGE 5

INTRODUCTION Develop predictive and validated codes Validation : Comparison Calculation / Measurements Decay heat (Fission, Fuel pin, core) Isotopic concentrations DARWIN PACKAGE Neutronics APOLLO ERANOS Ф σ Predictive : Estimation of the uncertainty Evolution PEPIN CyRUS N DH CEA | SEPTEMBER 24 – 28, 2012 | PAGE 6

METHODOLOGY CEA | 10 AVRIL 2012 CEA | 10 AVRIL 2012 | PAGE 7 | PAGE 7 9 octobre 2012

METHODOLOGY DETERMINIST STOCHASTIC DARWIN PACKAGE DARWIN PACKAGE Neutronics Neutronics APOLLO ERANOS APOLLO ERANOS Probabilist Code Evolution Evolution Evolution PEPIN PEPIN CyRUS • m samples of the n parameters n parameters p 0 + δ p n+1 calculations … ∂ 0 ( ) p DH = i S DH / p ∂ i DH p x 1 0 i 0 x n p p ( ) ( ) + δ − • m evolution calculations 0 0 0 p DH p p DH p = i i i i δ DH p 0 i p DH ( ) ( ) S = t var DH S VAR p CEA | SEPTEMBER 24 – 28, 2012 | PAGE 8

METHODOLOGY Detailed Determinist Propagation Method 1st order error propagation formula Libraries ( ) ⎛ ⎞ ⎛ ⎞ var p S ⎜ ⎟ ⎜ ⎟ ) ( ) 1 DH / p 1 ( = ⎜ ⎟ ⎜ ⎟ L O M var DH S S DH / p DH / p ⎜ ⎟ 1 n ⎜ ⎟ ( ) ( ) ⎝ cov p , p var p ⎠ S ⎝ ⎠ 1 n n DH / p Calculation n p(DH) Two assumptions : 1st order formula σ DH = f( σ p1 , … σ pn ) DH is normally distributed .. Validated during my PhD DH DH 0 CEA | SEPTEMBER 24 – 28, 2012 | PAGE 9

METHODOLOGY ∂ − ( ) i 1 ( ) N ( t ) ∑ = σ φ + λ + σ φ − λ + σ φ i N Y N ( t ) N ( t ) ∂ f f fi ij ij j i i i t = j 1 ∂ − i 1 N ( t ) ∑ = λ − λ i N ( t ) N ( t ) ∂ ij j i i t = j 1 ∑ = λ DH ( t ) N ( t ) E i i i i Power N 0 , δ N 0 N, δ N N, δ N DH, δ DH Irradiation Cooling Time CEA | SEPTEMBER 24 – 28, 2012 | PAGE 10

METHODOLOGY Many results δ DH The uncertainty of the decay heat, δ Ni The contribution of any nuclide to the uncertainty of the decay heat δ DH + The reason of this contribution (sensibility or variance), S(DH/Ni) δ pj The contribution of any parameter to the uncertainty of the nuclei δ Ni + The reason of this contribution (sensibility or variance), S(Ni/pj) δ N1 The number of nuclei to which a parameter contribute δ N2 δ pj significantly to the uncertainty δ N3 The possibility to modify the covariance matrix of the parameters and to see the change on the uncertainty of the decay heat quickly (in less than 1 minute). δ DH CEA | SEPTEMBER 24 – 28, 2012 | PAGE 11

NUCLEAR DATA (JEFF3.1.1) CEA | 10 AVRIL 2012 CEA | 10 AVRIL 2012 | PAGE 12 | PAGE 12 9 octobre 2012

NUCLEAR DATA Nd Important nuclei for the Pr Ce calculation of the La Ba decay heat Cs Xe I Te Ru Rh Tc Mo Y Zr Nb Sr Rb Kr At least one time between 1 second and 30 years Stable nucleus ≥ 1 % DH 95 % DH 99 % DH 0.1 % ≤ < 1 % 0.01 % ≤ 369 nuclei < 0.1 % 16 Heavy Nuclides CEA | SEPTEMBER 24 – 28, 2012 | PAGE 13 353 Fission Products

NUCLEAR DATA Independent Fission Yields (JEFF3.1.1, 353 FP) 70 60 Uncertainty of the fission yields (%) 50 40 30 20 U235 (th) U235 (fast) U238 (fast) PU239 (th) 10 PU239 (fast) PU240 (fast) PU241 (th) PU241 (fast) 0 1.E-13 1.E-12 1.E-11 1.E-10 1.E-09 1.E-08 1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 Fission Yields CEA | SEPTEMBER 24 – 28, 2012 | PAGE 14

NUCLEAR DATA Half lives (JEFF3.1.1, 369 nuclei) Very well known 200 Only 4 missing uncertainties 180 30 160 140 Number of nuclei 25 120 Uncertainty of the half lives (%) 100 80 20 60 40 15 20 0 0 1 2 3 5 7 8 9 10 0 < … < 1 1 < … < 2 2 < … < 3 3 < … < 4 4 4 < … < 5 5 < … < 6 6 6 < … < 7 7 < … < 8 8 < … < 9 9 < … < 10 Uncertainty of the half lives (%) 10 5 0 1.0E-01 1.0E+01 1.0E+03 1.0E+05 1.0E+07 1.0E+09 1.0E+11 1.0E+13 CEA | SEPTEMBER 24 – 28, 2012 | PAGE 15 Half lives (s)

NUCLEAR DATA Decay Energies (JEFF3.1.1, 369 nuclei) 70 Most of them are well known 60 75 missing uncertainties 50 20 Number of nuclei 40 Known uncertainties 18 30 Unknown uncertainties Uncertainty of the total energy (%) 16 20 14 10 0 12 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 17 18 19 20 2 Uncertainty of the total energy (%) 10 8 6 4 2 0 1.0E-01 1.0E+01 1.0E+03 1.0E+05 1.0E+07 1.0E+09 1.0E+11 1.0E+13 CEA | SEPTEMBER 24 – 28, 2012 | PAGE 16 Half-lives (s)

NUCLEAR DATA Branching Ratios (JEFF3.1.1) Lots of data are missing (94 known uncertainties and 128 missing) Low impact on the uncertainty of decay heat Low values of branching ratios ↔ High uncertainties High values of branching ratios ↔ low uncertainties 100 Unknown uncertainties Known uncertainties Uncertainty of the branching ratio (%) 10 1 0.1 0.01 0.001 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 CEA | SEPTEMBER 24 – 28, 2012 | PAGE 17 Branching Ratio

RESULTS CEA | 10 AVRIL 2012 CEA | 10 AVRIL 2012 | PAGE 18 | PAGE 18 9 octobre 2012

RESULTS Burst fission curve of 235 U (th) Definition : Heat produced by the fission of one nucleus of a fissionable nuclide. What is it used for ? Validation of nuclear data libraries (no impact of neutronics), Fast calculations of decay heat with fits of several exponentials (ANS Standard), Past : More precise than summation calculations because of missing nuclear data, 1.6 LOTT (1973) DICKENS (1980) 1.4 JOHANSSON (1987) NGUYEN (1997) Why 235 U (th) : DARWIN (JEFF3.1.1) 1.2 Widely studied in order to f(t) * T cool (MeV/fission) 1.0 perform an ANS Standard for 0.8 decay heat 0.6 0.4 Questions : 0.2 Consistency of the library (value + uncertainty) with the measurements ? 0.0 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 Time (s) In case of a use of BFC derived from DARWIN+JEFF3.1.1, what should be the value of the uncertainty of the calculation ¨Parameters of importance for the calculation of the uncertainty of the decay heat ? CEA | SEPTEMBER 24 – 28, 2012 | PAGE 19

RESULTS Comparison between the calculation and the experiments Good consistency of the decay data of JEFF3.1.1, Issue at 1 000 seconds Scientific community seems to rely on DICKENS measurements, LOTT, NGUYEN and JOHANSSON agree perfectly NGUYEN and JOHANSSON (end of the studied range of time), LOTT (beginning of the studied range of time) In the case of a use of burst 1.6 LOTT (1973) fission curves fitted from DICKENS (1980) JOHANSSON (1987) 1.4 DARWIN/JEFF3.1.1 values NGUYEN (1997) This work -1sigma and uncertainty from CyRUS, f(t) * T cool 235 U (th) (MeV/fission) 1.2 This work +1sigma This work -3sigma the overall uncertainty must This work +3sigma 1.0 be ± 3 σ : 0.8 [ ] s ∈ 5 9 %, t 1 ; 2 . 10 0.6 [ ] s 0.4 ∈ 5 7 15 %, t 2 . 10 ; 1 . 10 0.2 DICKENS NGUYEN ? DICKENS LOTT 0.0 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 CEA | SEPTEMBER 24 – 28, 2012 | PAGE 20 Time (seconds)