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Uppsala 2013 D. Rochman – 1 / 26
TMC vs. perturbationand other applications
D. Rochman and A.J. Koning
Nuclear Research and Consultancy Group,
NRG, Petten, The Netherlands
Uppsala TMC meeting, April 2013
Contents
Uppsala 2013D. Rochman – 2 / 26
① Short introduction to nuclear data uncertainties② Outcomes of the approach (TMC is one of them)③ TMC vs. perturbation④ Examples for real cases⑤ Fast TMC⑥ Conclusions
All slides can be found at:ftp://ftp.nrg.eu/pub/www/talys/bibrochman/presentation.html.
ftp://ftp.nrg.eu/pub/www/talys/bib_rochman/presentation.html
Introduction to nuclear data uncertainties
Uppsala 2013D. Rochman – 3 / 26
General comments:
uncertainties are not errors (and vice versa),uncertainties should now be given with all data (seems obvious ?),they are related to risks, quality of work, money, perception, fear, safety...
Uncertainty⇌ safety⇌ professionalism
True uncertainties do not exist ! They are the reflection of our knowledge andmethods.
All the above for covariancesThe importance of nuclear data uncertainties should be checked. If believednegligible, please prove it !
Backbone of our methodology: REPRODUCIBILITY
Uppsala 2013D. Rochman – 4 / 26
TALYSnuclear code
T6 softwarepackage
Librarycloning andcomplement Reproducibility
NR
GN
ucle
arsim
ulation
Original nuclear datalibrary TENDL+ covariances
Uncertaintypropagation(fast) TMC
OptimumSearch and find(Petten Method)
TMC: procedure for the random file production
Uppsala 2013D. Rochman – 5 / 26
AutoTalysTASMAN
n TANESinput files
n TALYSinput files
n TARESinput files
n TAFISinput files
TANES TALYS TARES TAFIS
n FissionNeutron Spect.
output files
n TALYSoutput files
n ResonanceParametersoutput files
n ν-baroutput files
TEFAL
1 ENDF file+
covariancesn× ENDFrandom files
TMC for nuclear data uncertainty propagation, what else ?
Uppsala 2013D. Rochman – 6 / 26
© + No covariance matrices (no 2 Gb files)butevery possible cross correlationincluded,
© + No approximationbut true probability distribution,© + Only essential info for an evaluation is stored,© + No perturbation code necessary,only “essential” codes,© + Feedback to model parameters,© + Full reactor core calculation and transient,© + Also applicable to fission yields, thermal scattering, pseudo-fission products, all
isotopes (...just everything),© + Other variants: AREVA (NUDUNA), GRS (XSUSA), CIEMAT (ACAB), PSI
(NUSS), CNRS Grenoble..., based on covariance files,© + Many spin-offs (TENDL covariances, sensitivity, adjustment...)© + QA.
§ - Needs discipline to reproduce,§ - Memory and computer time (not human time),§ - Need mentality change.
2008: Total Monte Carlo (TMC)
Uppsala 2013D. Rochman – 7 / 26
Control of nuclear data (TALYS system)+ processing (NJOY)
+ system simulation (MCNP/ERANOS/CASMO...)
1000times
For each random ENDF file, the benchmark calculation is performed with MCNP. Atthe end of then calculations,n different keff values are obtained.
σ2total = σ2statistics+σ
2nuclear data
Lead Fast Reactor system
keff value
Num
ber
ofco
unts
/bin
s
1.021.011.00
40
30
20
10
0
FitExtreme value
equivalentGaussian
Accelerator Driven System
keff value
Num
ber
ofco
unts
/bin
s
0.980.970.96
50
40
30
20
10
0
Example with 238U: Monte Carlo calculations
Uppsala 2013D. Rochman – 8 / 26
σstand.dev. ≃ 15%
238U(n,inl) at 2 MeV
Cross Section (Barns)
Cou
nts
/chan
nel
3.83.63.43.23.02.8
30
20
10
0
σstand.dev. ≃ 10%
238U(n,γ) at 100 keV
Cross Section (Barns)
Cou
nts
/chan
nel
0.260.230.200.17
30
20
10
0
TALYS238U(n,inl)
Incident Neutron Energy (MeV)
Cro
ssSec
tion
(Bar
ns)
108642
4
3
2
1
TALYS238U(n,γ)
Incident Neutron Energy (MeV)
Cro
ssSec
tion
(Bar
ns)
1.00.1
100
10−1
10−2
Examples with 63Cu(n,2n) and65Cu(n,el)
Uppsala 2013D. Rochman – 9 / 26
n = 10063Cu(n,2n)
Incident Energy (MeV)
Cro
ssse
ctio
n(b
)
2018161412
1.0
0.8
0.6
0.4
0.2
0.0
n = 163Cu(n,2n)
Incident Energy (MeV)
Cro
ssse
ctio
n(b
)
2018161412
1.0
0.8
0.6
0.4
0.2
0.0
Skewness = 0.33
Sigma = 4 mb/Sr
Mean = 22 mb/Sr
cos(θ) = −0.41En = 8 MeV
65Cu(n,el)
Cross section (b/Sr)
Cou
nts
/bin
0.050.040.030.020.01
20
15
10
5
0
En = 8 MeV
65Cu(n,el) (n=100)
cos(θ)
dσ/d
θ(b
/Sr)
0.80.50.2-0.1-0.4-0.7-1.0
101
100
10−1
10−2
Nuclear data: examples in the resonance region
Uppsala 2013D. Rochman – 10 / 26
JEFF-3.1ENDF/B-VII.0
This workExp
50 random 241Pu(n,f)
Incident neutron energy (eV)
Cro
ssse
ctio
n(b
arns)
10010−110−2
104
103
102
101
JEFF-3.1ENDF/B-VII.0
This workExp
50 random 235U(n,f)
Incident neutron energy (eV)
Cro
ssse
ctio
n(b
arns)
4.03.02.01.00.40.1
102
101
TMC versus Perturbation method
Uppsala 2013D. Rochman – 11 / 26
① Obtain uncertainties on large-scale models due to nuclear data uncertainties② Systematic approach, reliable and reproducable
Solution (1): Total Monte Carlo
Control of nuclear data (TALYS)+ simple processing (NJOY)
+ system simulation (MCNP/ERANOS/CASMO...)
1000times
Solution (2): Perturbation method=⇒MCNP+ Perturbation cards+covariance files
TMC versus Perturbation: Results
Uppsala 2013D. Rochman – 12 / 26
Comparison TMC-Perturbation methods for a few keff benchmarks. The ratio in the
last column is ”TMC over Perturbation”.
Total Monte Carlo Perturbation RatioBenchmark Isotopes Uncertainty Uncertainty
due to nuclear due to nuclear
data (pcm) data (pcm)
hst39-6 19F 330 290 1.16hmf7-34 19F 350 290 1.21ict3-132 90Zr 190 150 1.29hmf57-1 208Pb 500 410 1.22pmf2 239Pu 840 720 1.16pmf2 240Pu 790 650 1.21
Results: Details of the TMC-Perturbation methods for239,240Pu keffbenchmarks
Uppsala 2013D. Rochman – 13 / 26
pmf2 239Pu pmf2 240Pu∆keff (pcm) ∆keff (pcm)
TMC Perturbation TMC PerturbationTotal 840 720 790 650MF1 400 - 370 -(n,inl) 170 140 70 50(n,el) 250 240 30 40(n,γ) 100 100 30 30(n,f) 720 660 730 640MF4 20 - 20 -MF5 50 - 30 -MF6 50 - 30 -
Considered data in TMC (or fast TMC)
Uppsala 2013D. Rochman – 14 / 26
Several hundreds of random ENDF files for transport + depletion
• 3 Major actinides:235U, 238U, 239Pu,• Light elements: lighter than oxygen,• 2 Thermal scattering data: H in H2O, D in D2O• All Fission yields (e.g.234,235,236,238U, 239,240,241Pu,237Np, 241,243Am, 243,244Cm),• All Minor actinides (e.g.234,236,237U, 237Np, 238,240,241,242Pu, Am, Cm),• All fission products (e.g. from Ge to Er), and decay data,
(fast) TMC can be applied toanyinput data, propagating uncertainties toanyoutputs
Considered data in TMC (or fast TMC)
Uppsala 2013D. Rochman – 14 / 26
Several hundreds of random ENDF files for transport + depletion
• 3 Major actinides:235U, 238U, 239Pu,• Light elements: lighter than oxygen,• 2 Thermal scattering data: H in H2O, D in D2O• All Fission yields (e.g.234,235,236,238U, 239,240,241Pu,237Np, 241,243Am, 243,244Cm),• All Minor actinides (e.g.234,236,237U, 237Np, 238,240,241,242Pu, Am, Cm),• All fission products (e.g. from Ge to Er), and decay data,
(fast) TMC can be applied toanyinput data, propagating uncertainties toanyoutputs
TMC was already applied to
• criticality-safety, shielding, pincell/assembly burn-up, activation,• PWR, BWR, Gen-IV systems,• UO2, MOX fuels,• MCNP, SERPENT, FISPACT, DRAGON, PANTHER, RELAP-5
Comparison of ∆k∞ for assemblies and full core (SERPENT)
Uppsala 2013D. Rochman – 15 / 26
VVER MOX
VVER UO2
BWR MOX (w Gd)
BWR UO2 (w Gd)
PWR MOX (4 assemblies)
PWR MOX (1 assembly)
PWR UO2 (w Gd)
PWR UO2 (no Gd)
k∞ uncertainty for different assemblies
Burn-up (GWd/tHM)
∆k ∞
1.2
1.0
0.8
0.6
0.4
0.2
0.050403020100
1.2
1.0
0.8
0.6
0.4
0.2
0.0
TMC applied to PWR assembly burn-up calculations with DRAGON
Uppsala 2013D. Rochman – 16 / 26
due to nu-bardue to pointwise xsdue to resonance xs
due to transport data
238U
Burn up (GWd/tHM)
Unce
rtai
nty
onk
eff(%
)
6050403020100
1.0
0.8
0.6
0.4
0.2
0.0
Example of TMC for the impact of the matrix fuel
Uppsala 2013D. Rochman – 17 / 26
1σ Mo data uncertainty
12 % Pu, 88 % Mo (volume)Westinghouse 3 loops type reactor
LWR Inert Matrix Fuel
δT ≃ 35 efpd
Reactivity Swing
Time (efpd)
keff
2000150010005000
1.4
1.3
1.2
1.1
1.0
0.9
0.8
PWR MOX assembly uncertainties
Uppsala 2013D. Rochman – 18 / 26
Fission Products
Fission Yields
H in H2O235U
238U
239Pu
Total
Burn-up (GWd/tHM)
Rel
ativ
e∆
k eff
(%)
50403020100
1.0
0.8
0.6
0.4
0.2
0.0
• 1 MOX assembly surrounded by UO2 assemblies,• Burn-up calculated with SERPENT,• All major nuclear data taken into account.
Effect of H in H 2O for a full core PWR (courtesy of O. Cabellos, UPM,Spain)
Uppsala 2013D. Rochman – 19 / 26
Method: TMC applied to COBAYA (3D multigroup core calculations) + SIMULA(coupled neutronic-thermohydraulics 3D core calculations)
Effect of H in H 2O for a full core PWR (courtesy of O. Cabellos, UPM,Spain)
Uppsala 2013D. Rochman – 20 / 26
Power coeff.
Moderator Temp. coeff.
Boron concentration
H in H2O effect for a PWR full core
Burn-up (GWd/TMU)
Unce
rtai
ntie
s(%
)
8.04.02.01.00.50.20.1
8
4
2
1
Drawbacks of the TMC method
Uppsala 2013D. Rochman – 21 / 26
In TMC:
If we can do a calculation once, we can also doit a 1000 times, each time with a varying data library.
Drawbacks of the TMC method
Uppsala 2013D. Rochman – 21 / 26
In TMC:
If we can do a calculation once, we can also doit a 1000 times, each time with a varying data library.
Well, then uncertainty propagation with TMC takes1000× longer than a singlecalculation...(Each σstatisticsneeds to be small)
Drawbacks of the TMC method
Uppsala 2013D. Rochman – 21 / 26
In TMC:
If we can do a calculation once, we can also doit a 1000 times, each time with a varying data library.
Well, then uncertainty propagation with TMC takes1000× longer than a singlecalculation...(Each σstatisticsneeds to be small)
There is a solution with Monte Carlo codes.
2013: fast TMC method...
Uppsala 2013D. Rochman – 22 / 26
If a single calculation takesm histories (σstatsmall enough),then repeat itn times withm/n histories,random nuclear data and random seeds.
σ2total = σ2statistics+σ
2nuclear datastill holds.
2013: fast TMC method...
Uppsala 2013D. Rochman – 22 / 26
If a single calculation takesm histories (σstatsmall enough),then repeat itn times withm/n histories,random nuclear data and random seeds.
σ2total = σ2statistics+σ
2nuclear datastill holds.
run 0 ENDF/B-VII.1 seed s0 m histories T sec. k± σstat
2013: fast TMC method...
Uppsala 2013D. Rochman – 22 / 26
If a single calculation takesm histories (σstatsmall enough),then repeat itn times withm/n histories,random nuclear data and random seeds.
σ2total = σ2statistics+σ
2nuclear datastill holds.
run 0 ENDF/B-VII.1 seed s0 m histories T sec. k± σstatrun 1 nuclear data 1 seed s1 m/n hist. T/n sec. k1±σ1 ∼ σstat
√n
2013: fast TMC method...
Uppsala 2013D. Rochman – 22 / 26
If a single calculation takesm histories (σstatsmall enough),then repeat itn times withm/n histories,random nuclear data and random seeds.
σ2total = σ2statistics+σ
2nuclear datastill holds.
run 0 ENDF/B-VII.1 seed s0 m histories T sec. k± σstatrun 1 nuclear data 1 seed s1 m/n hist. T/n sec. k1±σ1 ∼ σstat
√n
run 2 nuclear data 2 seed s2 m/n hist. T/n sec. k2±σ2
2013: fast TMC method...
Uppsala 2013D. Rochman – 22 / 26
If a single calculation takesm histories (σstatsmall enough),then repeat itn times withm/n histories,random nuclear data and random seeds.
σ2total = σ2statistics+σ
2nuclear datastill holds.
run 0 ENDF/B-VII.1 seed s0 m histories T sec. k± σstatrun 1 nuclear data 1 seed s1 m/n hist. T/n sec. k1±σ1 ∼ σstat
√n
run 2 nuclear data 2 seed s2 m/n hist. T/n sec. k2±σ2...
......
runn nuclear datan seed sn m/n hist. T/n sec. kn ±σn
2013: fast TMC method...
Uppsala 2013D. Rochman – 22 / 26
If a single calculation takesm histories (σstatsmall enough),then repeat itn times withm/n histories,random nuclear data and random seeds.
σ2total = σ2statistics+σ
2nuclear datastill holds.
run 0 ENDF/B-VII.1 seed s0 m histories T sec. k± σstatrun 1 nuclear data 1 seed s1 m/n hist. T/n sec. k1±σ1 ∼ σstat
√n
run 2 nuclear data 2 seed s2 m/n hist. T/n sec. k2±σ2...
......
runn nuclear datan seed sn m/n hist. T/n sec. kn ±σnn runs T sec.
2013: fast TMC method...
Uppsala 2013D. Rochman – 22 / 26
If a single calculation takesm histories (σstatsmall enough),then repeat itn times withm/n histories,random nuclear data and random seeds.
σ2total = σ2statistics+σ
2nuclear datastill holds.
run 0 ENDF/B-VII.1 seed s0 m histories T sec. k± σstatrun 1 nuclear data 1 seed s1 m/n hist. T/n sec. k1±σ1 ∼ σstat
√n
run 2 nuclear data 2 seed s2 m/n hist. T/n sec. k2±σ2...
......
runn nuclear datan seed sn m/n hist. T/n sec. kn ±σnn runs T sec.
σ2total = 1n−1n
∑i=1
(
ki −k)2
2013: fast TMC method...
Uppsala 2013D. Rochman – 22 / 26
If a single calculation takesm histories (σstatsmall enough),then repeat itn times withm/n histories,random nuclear data and random seeds.
σ2total = σ2statistics+σ
2nuclear datastill holds.
run 0 ENDF/B-VII.1 seed s0 m histories T sec. k± σstatrun 1 nuclear data 1 seed s1 m/n hist. T/n sec. k1±σ1 ∼ σstat
√n
run 2 nuclear data 2 seed s2 m/n hist. T/n sec. k2±σ2...
......
runn nuclear datan seed sn m/n hist. T/n sec. kn ±σnn runs T sec.
σ2total = 1n−1n
∑i=1
(
ki −k)2
σ2statistics = 1nn
∑i=1
σ2i
The fast TMC method
Uppsala 2013D. Rochman – 23 / 26
© as fast as S/U methods (1-2× longer than 1 single calculationwithoutuncertainties),
© tested on criticality & shielding benchmarks, burn-up (keff and inventory),
The fast TMC method
Uppsala 2013D. Rochman – 23 / 26
© as fast as S/U methods (1-2× longer than 1 single calculationwithoutuncertainties),
© tested on criticality & shielding benchmarks, burn-up (keff and inventory),© Example: the Martin-Hoogenboom benchmark (= the Kord SmithChallenge)
MCNP model: 241 fuel assemblies, with 264 fuel pins each
=⇒ 357×357×100 regions (1.26×1.26×3.66 cm3): 12.7 million cells
The fast TMC method
Uppsala 2013D. Rochman – 23 / 26
© as fast as S/U methods (1-2× longer than 1 single calculationwithoutuncertainties),
© tested on criticality & shielding benchmarks, burn-up (keff and inventory),© Example: the Martin-Hoogenboom benchmark (= the Kord SmithChallenge)
MCNP model: 241 fuel assemblies, with 264 fuel pins each
=⇒ 357×357×100 regions (1.26×1.26×3.66 cm3): 12.7 million cellsUncertainty on generated local pin power (tally f7) due to235U, 238U, 239Pu
and H in H2O thermal scattering ineach cell?
Fast TMC method
Uppsala 2013D. Rochman – 24 / 26
1 normal calculation without nuclear data uncertainty takes n = 2×1011 histories(σstatistics= 0.25 % at the center,500 weekson 1 cpu)=⇒ TMC: 500 random runs ofn = 2×1011 histories (500 weeksfor each)=⇒ fast TMC: 500 random runs ofn/500= 4×108 histories (1 weekfor each)
Fast TMC method
Uppsala 2013D. Rochman – 24 / 26
1 normal calculation without nuclear data uncertainty takes n = 2×1011 histories(σstatistics= 0.25 % at the center,500 weekson 1 cpu)=⇒ TMC: 500 random runs ofn = 2×1011 histories (500 weeksfor each)=⇒ fast TMC: 500 random runs ofn/500= 4×108 histories (1 weekfor each)
87654321guidetube
n.a.
y(c
m)
200
150
100
50
0
-50
-100
-150
-200
x (cm)200150100500-50-100-150-200
Nuclear data Uncertainties (%)
mid-height in the core
(2.7 ± 0.2) %
(1.0 ± 0.1) %
Uncertainties due to 235U, 238U, 239Pu and H in H2O
x (cm)
Unce
rtai
nty
onpow
er(%
)
2001000-100-200
10
8
6
4
2
0
Other outcomes of the NRG approach (not detailed here)
Uppsala 2013D. Rochman – 25 / 26
❅ Sensitivity,❅ Nuclear data adjustment,❅ Include fast TMC in Serpent ?
Correlation pmi2 keff-56Fe(n,γ)
Cor
rela
tion
0.1
0.0
-0.1
-0.2
-0.3
-0.4
Exp. dataThis work
ENDF/B-VII.0
56Fe(n,γ)
Incident neutron energy (MeV)
Cro
ssSec
tion
(bar
ns)
2· 1012· 1002· 10−12· 10−22· 10−32· 10−42· 10−52· 10−6
1· 100
1· 10−1
1· 10−2
1· 10−3
1· 10−4
1· 10−5
Conclusions
Uppsala 2013D. Rochman – 26 / 26
➪ (fast) TMC is a powerful tool for uncertainty propagation,➪ All types of nuclear data impact can be assessed,➪ Most direct way to propagate uncertainties,➪ Better QA, better modern use of computers,➪ (fast) TMC is part of global approach to improve transparency and safety of
nuclear simulation
Conclusions
Uppsala 2013D. Rochman – 26 / 26
➪ (fast) TMC is a powerful tool for uncertainty propagation,➪ All types of nuclear data impact can be assessed,➪ Most direct way to propagate uncertainties,➪ Better QA, better modern use of computers,➪ (fast) TMC is part of global approach to improve transparency and safety of
nuclear simulation
TMC: If we can do a calculation once, we can also doit a 1000 times, each time with a varying data library.
Conclusions
Uppsala 2013D. Rochman – 26 / 26
➪ (fast) TMC is a powerful tool for uncertainty propagation,➪ All types of nuclear data impact can be assessed,➪ Most direct way to propagate uncertainties,➪ Better QA, better modern use of computers,➪ (fast) TMC is part of global approach to improve transparency and safety of
nuclear simulation
TMC: If we can do a calculation once, we can also doit a 1000 times, each time with a varying data library.fast TMC:If we can do a calculation once, we can also get
nuclear data uncertainties at the same time
ContentsIntroduction to nuclear data uncertaintiesBackbone of our methodology: REPRODUCIBILITY TMC: procedure for the random file productionTMC for nuclear data uncertainty propagation, what else ?2008: Total Monte Carlo (TMC)Example with 238U: Monte Carlo calculationsExamples with 63Cu(n,2n) and 65Cu(n,el)Nuclear data: examples in the resonance regionTMC versus Perturbation methodTMC versus Perturbation: ResultsResults: Details of the TMC-Perturbation methods for 239,240Pu keff benchmarksConsidered data in TMC (or fast TMC)Comparison of k for assemblies and full core (SERPENT) TMC applied to PWR assembly burn-up calculations with DRAGONExample of TMC for the impact of the matrix fuelPWR MOX assembly uncertaintiesEffect of H in H2O for a full core PWR (courtesy of O. Cabellos, UPM, Spain)Effect of H in H2O for a full core PWR (courtesy of O. Cabellos, UPM, Spain)Drawbacks of the TMC method 2013: fast TMC method...The fast TMC methodFast TMC methodOther outcomes of the NRG approach (not detailed here)Conclusions