TMC vs. perturbation - Uppsala University · · 2018-03-09TMC vs. perturbation and other applications D. Rochman and A.J. Koning Nuclear Research and Consultancy Group, NRG, Petten,

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


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


TALYSnuclear code

T6 softwarepackage

Librarycloning andcomplement ReproducibilityN

RG

Nuc

le

arsimulation

Original nuclear datalibrary TENDL+ covariances

Uncertaintypropagation(fast) TMC

OptimumSearch and find(Petten Method)

TMC: procedure for the random file production


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× ENDF

random files

TMC for nuclear data uncertainty propagation, what else ?


© + 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)


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 = σ2

statistics+σ2nuclear 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


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)


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) = −0.41

En = 8 MeV65Cu(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


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


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


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


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)


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)


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)


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


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


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


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)


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)


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


In TMC:

If we can do a calculation once, we can also doit a 1000 times, each time with a varying data library.



In TMC:


Well, then uncertainty propagation with TMC takes1000× longer than a singlecalculation...(Each σstatisticsneeds to be small)



In TMC:


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...


If a single calculation takesm histories (σstatsmall enough),then repeat itn times withm/n histories,random nuclear data and random seeds.

σ2total = σ2

statistics+σ2nuclear datastill holds.




σ2total = σ2


run 0 ENDF/B-VII.1 seed s0 m histories T sec. k± σstat




σ2total = σ2



run 1 nuclear data 1 seed s1 m/n hist. T/n sec. k1±σ1 ∼ σstat√

n




σ2total = σ2




nrun 2 nuclear data 2 seed s2 m/n hist. T/n sec. k2±σ2




σ2total = σ2




nrun 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




σ2total = σ2





......


n runs T sec.




σ2total = σ2





......


n runs T sec.

σ2total = 1

n−1

n

∑i=1

(

ki −k)2




σ2total = σ2





......


n runs T sec.

σ2total = 1

n−1

n

∑i=1

(

ki −k)2

σ2statistics = 1

n

n

∑i=1

σ2i

The fast TMC method


© 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



© 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



© 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

Uncertainty on generated local pin power (tally f7) due to235U, 238U, 239Puand H in H2O thermal scattering ineach cell?

Fast TMC method


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


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)


❅ 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


➪ (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



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



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

Documents

TMC vs. perturbation - Uppsala University · · 2018-03-09TMC vs. perturbation and other applications D. Rochman and A.J. Koning Nuclear Research and Consultancy Group, NRG, Petten,