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
| PAGE 1 CEA | 10 AVRIL 2012
SEPTEMBER 24 – 28, 2012
WONDER 2012 | Jean-Christophe BENOIT
9 octobre 2012 | PAGE 1 CEA | 10 AVRIL 2012
CEA | SEPTEMBER 24 – 28, 2012 | PAGE 2
9 octobre 2012 | PAGE 2
| PAGE 3 CEA | 10 AVRIL 2012
9 octobre 2012 | PAGE 3 CEA | 10 AVRIL 2012
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.
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)
9 octobre 2012 CEA | SEPTEMBER 24 – 28, 2012 | PAGE 4
1903 1903 1942 1942 1974 1974-
75 2008 2008-
10
CEA | SEPTEMBER 24 – 28, 2012 | PAGE 5
More Safety and more Savings
Nuclear stage impacted Time of cooling Safety Systems of cooling 0.1 second to 8 days Unloading of sub- assemblies from the core 5 to 25 days Road transport 1 to 10 years Reprocessing, Vitrification, Storage 4 to 3000 years Storage 50 to 300 000 years and more
CEA | SEPTEMBER 24 – 28, 2012 | PAGE 6
Validation : Comparison Calculation / Measurements Decay heat (Fission, Fuel pin, core) Isotopic concentrations Predictive : Estimation of the uncertainty
DARWIN PACKAGE
Neutronics
APOLLO ERANOS
Evolution
PEPIN CyRUS Ф σ N DH
| PAGE 7 CEA | 10 AVRIL 2012
9 octobre 2012 | PAGE 7 CEA | 10 AVRIL 2012
CEA | SEPTEMBER 24 – 28, 2012 | PAGE 8
DARWIN PACKAGE
Neutronics
APOLLO ERANOS
Evolution
PEPIN
DARWIN PACKAGE
Neutronics
APOLLO ERANOS
Evolution
PEPIN
Probabilist Code
x1 xn
DH p0 + δp
( )
i i i i p i p i p i i
p p DH p p DH DH p p DH DH p p DH S δ δ / − + = ∂ ∂ =
t
Evolution
CyRUS
n parameters n+1 calculations DETERMINIST STOCHASTIC
CEA | SEPTEMBER 24 – 28, 2012 | PAGE 9
1st order error propagation formula Two assumptions : 1st order formula DH is normally distributed Validated during my PhD
DH p(DH) DH0
σDH = f(σp1, … σpn) ..
( ) (
( ) ( ) ( )
⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ =
n n
p DH p DH n n p DH p DH
S S p p p p S S DH
/ / 1 1 / /
1 1
var , cov var var M O L
Calculation Libraries
CEA | SEPTEMBER 24 – 28, 2012 | PAGE 10
Time Power
1 1
i i i i j j ij ij fi f f i
− =
1 1
i i i j j ij i
− =
N0, δN0
i i i i
N, δN Irradiation Cooling N, δN DH, δDH
CEA | SEPTEMBER 24 – 28, 2012 | PAGE 11
The uncertainty of the decay heat, The contribution of any nuclide to the uncertainty of the decay heat + The reason of this contribution (sensibility or variance), The contribution of any parameter to the uncertainty of the nuclei + The reason of this contribution (sensibility or variance), The number of nuclei to which a parameter contribute significantly to the uncertainty 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).
δDH δNi S(DH/Ni) δDH δpj S(Ni/pj) δNi δpj δN1 δN2 δN3 δDH
| PAGE 12 CEA | 10 AVRIL 2012
9 octobre 2012 | PAGE 12 CEA | 10 AVRIL 2012
CEA | SEPTEMBER 24 – 28, 2012 | PAGE 13
Stable nucleus ≥ 1 % DH 0.1 % ≤ < 1 % 0.01 % ≤ < 0.1 % 99 % DH 369 nuclei 95 % DH
Ba Cs Ce Nd Xe La Pr I Te Rh Ru Mo Tc Y Zr Nb Sr Rb Kr
At least one time between 1 second and 30 years
16 Heavy Nuclides 353 Fission Products
CEA | SEPTEMBER 24 – 28, 2012 | PAGE 14
10 20 30 40 50 60 70 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 Uncertainty of the fission yields (%)
U235 (th) U235 (fast) U238 (fast) PU239 (th) PU239 (fast) PU240 (fast) PU241 (th) PU241 (fast)
CEA | SEPTEMBER 24 – 28, 2012 | PAGE 15
Very well known Only 4 missing uncertainties
5 10 15 20 25 30 1.0E-01 1.0E+01 1.0E+03 1.0E+05 1.0E+07 1.0E+09 1.0E+11 1.0E+13
Half lives (s) Uncertainty of the half lives (%)
20 40 60 80 100 120 140 160 180 200 0 < … < 1 1 < … < 2 2 < … < 3 3 < … < 4 4 < … < 5 5 < … < 6 6 < … < 7 7 < … < 8 8 < … < 9 9 < … < 10
Uncertainty of the half lives (%) Number of nuclei
5 1 2 3 4 6 7 8 9 10
CEA | SEPTEMBER 24 – 28, 2012 | PAGE 16 2 4 6 8 10 12 14 16 18 20 1.0E-01 1.0E+01 1.0E+03 1.0E+05 1.0E+07 1.0E+09 1.0E+11 1.0E+13
Half-lives (s) Uncertainty of the total energy (%)
Known uncertainties Unknown uncertainties
Most of them are well known 75 missing uncertainties
10 20 30 40 50 60 70 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
Uncertainty of the total energy (%) Number of nuclei
20 19 18 17 1 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 2
CEA | SEPTEMBER 24 – 28, 2012 | PAGE 17
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
0.001 0.01 0.1 1 10 100 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Branching Ratio Uncertainty of the branching ratio (%)
Unknown uncertainties Known uncertainties
| PAGE 18 CEA | 10 AVRIL 2012
9 octobre 2012 | PAGE 18 CEA | 10 AVRIL 2012
CEA | SEPTEMBER 24 – 28, 2012 | PAGE 19
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, Why 235U (th) : Widely studied in order to perform an ANS Standard for decay heat Questions : Consistency of the library (value + uncertainty) with the measurements ? 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 ?
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 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) f(t) * Tcool (MeV/fission)
LOTT (1973) DICKENS (1980) JOHANSSON (1987) NGUYEN (1997) DARWIN (JEFF3.1.1)
CEA | SEPTEMBER 24 – 28, 2012 | PAGE 20
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 fission curves fitted from DARWIN/JEFF3.1.1 values and uncertainty from CyRUS, the overall uncertainty must be ± 3 σ :
DICKENS NGUYEN DICKENS LOTT ?
5
7 5
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 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 (seconds) f(t) * Tcool 235U (th) (MeV/fission) LOTT (1973) DICKENS (1980) JOHANSSON (1987) NGUYEN (1997) This work -1sigma This work +1sigma This work -3sigma This work +3sigma
CEA | SEPTEMBER 24 – 28, 2012 | PAGE 21
Range of the uncertainty of the decay heat [2 % ; 5 %] Increase of the uncertainty of the decay heat ↔ Decreasing number of important nuclei + “no correlation” assumption Specific structures appear, Isotopic concentrations are predominant ↔ independent fission yields
1 2 3 4 5 6 1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06 1.0E+07 1.0E+08 1.0E+09
Time (s) Uncertainty of the DH (%)
Independent Fission Yields Half-Lives Energies Total Uncertainty
CEA | SEPTEMBER 24 – 28, 2012 | PAGE 22
0.0 1.0 2.0 3.0 4.0 5.0 6.0 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09
Time (s) Uncertainty of the DH (%)
137mBa 140Ba 132I 144Pr Inc_DH(E) Inc_DH(E(Unknown))
Nuclide δE
143Cs
0.00
136mI
0.00
90Kr
0.00
102Nb
0.00
103Nb
0.00
97Sr
0.00
139Xe
0.00
140Xe
0.00
141Xe
0.00 Nuclide δE
86Br
7.22
87Br
16.53
98Nb
6.62
100Nb
6.62
101Nb
14.59
92Rb
4.38
93Rb
5.36
97Y
12.71
101Zr
10.25 Nuclide δE
144Pr
0.70
137mBa
0.34 Nuclide δE
140Ba
5.07
143Ce
3.09
138Cs
1.19
132I
0.93
133I
2.18
134I
1.15
88Kr
2.84
89Kr
3.11
140La
0.26 Nuclide δE
89Rb
1.91
91Sr
2.16
93Sr
1.87
135Xe
2.64
138Xe
5.22
92Y
1.84
93Y
1.71
94Y
3.87
99Zr
4.68
CEA | SEPTEMBER 24 – 28, 2012 | PAGE 23
DH could benefit from an improvement of those nuclei : 90Rb, 97m,98mY, 99Zr,
97m,100,101,102,102m,103Nb, 104,105,107Mo, 102Tc (JEF/DOC–1413)
Short Half-lives
Half - life NUCLIDES Value (s)
90Rb
158 3.17
97mY
1.17 2.56
98mY
2 10
99Zr
2.2 4.55
97mNb
52.7 3.42
100Nb
1.5 13.33
101Nb
7.1 4.23
102Nb
1.3 15.39
102mNb
4.3 9.30
103Nb
1.5 13.33
102Tc
5.28 2.84
104Mo
60 3.33
105Mo
35.6 4.49
107Mo
3.5 14.29
CEA | SEPTEMBER 24 – 28, 2012 | PAGE 24
Work is done for cooling times greater than 105 seconds → fewer nuclides contribute to the value and the uncertainty of the decay heat.
1 2 3 4 5 6 1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06 1.0E+07 1.0E+08 1.0E+09
Time (seconds) Uncertainty of the DH (%)
Unc_DH 90Y 91Y 95Zr 137mBa 95Nb 144Pr 140La 132I
CEA | SEPTEMBER 24 – 28, 2012 | PAGE 25
Cooling time (s) Ratio of the impact of parameters to the uncertainty of the concentration of the nuclides (%)
132I
Yi(132Te) 58.69 Yi(132Sb) 21.27 Yi(132mSb) 11.56 5,0.105 Yi(132Sn) 8.2
140La
Yi(140Cs) 82.3 Yi(140Xe) 14.26 2,0.106 Yi(140Ba) 3.44
91Y 95Zr
Yi(91Kr) 50.55 Yi(95Sr) 57.18 Yi(91Rb) 47.96 Yi(95Y) 34.17 1,0.107 Yi(91Sr) 1.12 Yi(95Rb) 8.61
95Nb
Yi(95Sr) 57.18 Yi(95Y) 34.17 1,5.107 Yi(95Rb) 8.61
144Pr
Yi(144La) 92.8 5,5.107 Yi(144Ba) 6.9
90Y 137mBa
Yi(90Kr) 64.72 Yi(137Xe) 82.61 Yi(90mRb) 28.24 Yi(137I) 17.03 3,0.108 Yi(90Br) 6.46
Nuclides
Yield δYi (%)
90Kr
4.50E-02 8.13
90mRb
7.17E-03 33.72
91Kr
3.28E-02 15.34
91Rb
2.23E-02 21.97
95Sr
4.67E-02 10.03
95Y
1.18E-02 30.55
132mSb
9.02E-03 18.00
132Sb
1.22E-02 18.00
132Te
1.61E-02 22.70
140Cs
2.11E-02 23.68
144La
8.09E-03 32.14
137Xe
2.73E-02 19.21
CEA | SEPTEMBER 24 – 28, 2012 | PAGE 26
Lots of results (sensitivity, correlation, uncertainty), It is possible to see the propagation of the uncertainties, Validity of a determinist code / Stochastic code, Major contributors to the decay heat uncertainty are listed.
Options to be added (Use cumulative fission yields (Yc) during irradiation when it is possible), Check the impact of neutronics for the propagation during irradiation.
| PAGE 27 CEA | 10 AVRIL 2012
DEN DER SPRC Commissariat à l’énergie atomique et aux énergies alternatives Centre de Cadarache | 13108 St Paul-lès-Durance Cedex
Etablissement public à caractère industriel et commercial | RCS Paris B 775 685 019
9 octobre 2012 | PAGE 27 CEA | 10 AVRIL 2012
CEA | SEPTEMBER 24 – 28, 2012 | PAGE 28
Decay Heat (DH) : Heat produced by radioactivity (after irradiation) Discovery First discovered by P. CURIE, A. LABORDE (1903) in radium salts, Theoretical explanation by E. RUTHERFORD and F. SODDY (1904), Related by G.E.M JAUNCEY (1946) Am. J. Phys. The Early Years of Radioactivity Characterization (Plutonium Project) Build a reactor to produce plutonium → safety Burst Fission Curves BORST, BRADY, DAY & CANNON (1942 – 1943)
9 octobre 2012 | PAGE 28
0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1 10 100 1000 10000 100000 1000000 10000000 Time (s)
235U (th) Energie totale / fission / seconde (MeV/fission)BORST (30 min à 3j) BORST (50j à 100j) BRADY (16j à 324j) DAY & CANNON (1h à 100h) DARWIN/JEFF3.1.1
CEA | SEPTEMBER 24 – 28, 2012 | PAGE 29
Nuclear data are measured or calculated from measurements → Measurement fluctuations are often normally distributed → Nuclear data are normally distributed From the normal distribution, it is easy to link the confidence interval to the standard deviation. Libraries : parameter = mean value + standard deviation
CEA | SEPTEMBER 24 – 28, 2012 | PAGE 30
Link between the variance of the DH and the variance of the parameters : the error propagation formula Two hypotheses : 1st order formula DH is normally distributed Ok (PhD thesis)
DH p(DH) DH0
σDH = f(σp1, … σpn) .. ( )
( ) ( ) ( ) ( )
= ≠ = =
+ =
n i k i n i k k k i p DH p DH n i i p DH
p p corr p p S S p S PR
k i i
1 , 1 / / 1 2 /
, var var var var
Libraries Libraries Calculation Calculation
CEA | SEPTEMBER 24 – 28, 2012 | PAGE 31
Route Moreover Nuclear data : JEFF3.1.1 No correlation
→ →
i N U i N U
n 235 1 235
N0
n
1
N
Equation of evolution during cooling Formula of the decay heat
Data : Yi, λ, br Data : N, λ, E
CEA | SEPTEMBER 24 – 28, 2012 | PAGE 32
50 100 150 200 250 300 1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06 1.0E+07 1.0E+08 1.0E+09 Time (second) Number of nuclei (---) 30% 40% 50% 60% 70% 80% 90% 100% Percentage of the total Decay Heat (o)
>= 0,01% >= 0,1% >= 0,5% >= 1,0% >= 0,01% >= 0,1% >= 0,5% >= 1,0% 99% 95%
99 % DH → 369 nuclei 16 Heavy Nuclides 353 Fission Products
Contribution to the decay heat
R e a c t
: S
i u m F a s t R e a c t
I r r a d i a t i
: 1 y e a r 3 . 1
1 5
n / c m ² / s f a s t s p e c t r u m C
p
i t i
: F i s s i l e a s s e m b l y
CEA | SEPTEMBER 24 – 28, 2012 | PAGE 33
500 1000 1500 2000 2500 3000 10 20 30 40 50 60 70 80 90 100
Time of irradiation (s) Concentration (nb. at.)
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Discrepancy
B (A top of the mass chain) (left) B (B top of the mass chain) (left) Discrepancy (right)
( )
( )
t B F F f F c B F B
B
e N Y t N
λ
λ φ σ
− →
− = ∑ 1
( )
( ) ( ) ( )
t t A B F F f F i A F t B F F f F i B F i A F B
B A B
e e N Y e N Y Y t N
λ λ λ
λ λ φ σ λ φ σ
− − → − → →
− − + − + =
∑ ∑
1
A B F β- Yi
F→A
Yi
F→B Schematic view 1 2 1 2
CEA | SEPTEMBER 24 – 28, 2012 | PAGE 34
1 2 3 4 5 6 7 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09
Time (seconds) Uncertainty of the DH (%)
URANIE/MENDEL CyRUS
CEA | SEPTEMBER 24 – 28, 2012 | PAGE 35
95Zr – 95Nb 97Zr – 97Nb 97mNb – 97Nb 97Zr – 97mNb 135Xe – 135I 91mY – 91Sr 88Rb – 88Kr 92Y – 92Sr 138Xe – 138Cs
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09
Time (seconds) Contribution to the variance of the DH
Variances Covariances