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NRG Studies on ESFR Oxide Core FeedbackCoefficients: Uncertainty Analyses

(ESFR WP3 T2.1.3)

D. Rochman, A.J. Koning, D.F. DaCruz

and S.C. van der Marck

Nuclear Research and Consultancy Group,

NRG, Petten, The Netherlands

April, 2011

Contents

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① Goals:=⇒ Uncertainties for the ESFR parameters

② Concept for uncertainty propagation:=⇒ Total Monte Carlo (and a perturbation method for sensitivity)

③ SFR Model:=⇒ MCNP ESFR based on the JRC Petten model

④ Nuclear Data:=⇒

238U, 239,240,241,242Pu and 23Na

⑤ Results:=⇒ Void coefficient, keff, βeff and Doppler coefficient

⑥ Conclusions

Goals:

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① Obtain uncertainties on the JRC Petten ESFR model due to nuclear datauncertainties (obtained from H. Tsige-Tamirat, November 2009)

② 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

Concept: TALYS + Monte Carlo = Total Monte Carlo

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ResonanceParameters TARES

Determ.Codes

ENDFGen. purp.

File NJOY MCNP

ExperimentalData

EXFOR TEFAL

Output

ENDF/EAFActiv.File

Proc.codes

FIS-PACT

NuclearModel

Parameters TALYSOtherCodes

TASMAN

+ Covariances

+ Covariances

-keff-Flux-Etc.

+ Covariances

-Activation-Burn-up

+ Covariances

Monte Carlo: 1000 TALYS runs

TMC and Perturbation method

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n TALYSinput files

TALYS

1 ENDF file+

covariances

Perturbationmethod

MCNPinput file TMC n×

ENDFrandom file

NJOY Add perturbation NJOY

Processedcovariances

Processedcross

sections

MCNP input file

+perturbation card

n×Processed

crosssections

MCNP MCNP

Sensitivity

profile n× keffs ± ∆ kstat.

SUSD

∆ knucl.data keff ± ∆ kstat.

keff

±∆ kstat.

±∆ knucl.data

Nuclear data: 239Pu and 238U

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Random 240Pu(n,f)

Incident neutron energy (MeV)

Cro

ssse

ctio

n(b

)

20151050

3.0

2.0

1.0

0.0

Random 239Pu(n,f)

Incident neutron energy (MeV)

Cro

ssse

ctio

n(b

)

20151050

3.0

2.5

2.0

1.5

Random 238U(n,inl)

Incident neutron energy (MeV)

Cro

ssse

ctio

n(b

)

20151050

4.0

3.0

2.0

1.0

0.0

Random 238U(n,γ)

Incident neutron energy (MeV)

Cro

ssse

ctio

n(b

arns)

10110010−1

10−1

10−2

10−3

Nuclear data: examples in the resonance region

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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

Nuclear data: 56Fe and 23Na

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100 random 23Na(n,inl)

Incident neutron energy (MeV)C

ross

sect

ion

(bar

ns)

2015105

1.5

1.2

0.9

0.6

0.3

0.0

100 random 56Fe(n,inl)

Incident neutron energy (MeV)

Cro

ssse

ctio

n(b

arns)

2015105

2.0

1.5

1.0

0.5

0.0

Sensitivities to keff

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Main components: 23Na, 56Fe, Zr, 238U, 239,240PuMost sensitive reactions: 239Pu(n,f) and 238U(n,γ)

238U

235U

240Pu

239Pu

238U

keff sensitivity to (n,γ)

Incident Energy (eV)

Sen

siti

vity

(%/%

)10710610510410310210110−5

0·100

-1·10−4

-2·10−4

238U

235U

240Pu

239Pu

240Pu

238U

239Pu

keff sensitivity to (n,f)

Incident Energy (eV)

Sen

siti

vity

(%/%

)

10710610510410310210110−5

8·10−4

6·10−4

4·10−4

2·10−4

0·100

Results for the ESFR parameters

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The sodium void reactivity (SVR) in units of dollars ($) can be obtained with thefollowing equation :

SVR = k2 − k1k1k2

1βeff

×105, (1)

where the number of delayed neutron βeff (in units of pcm) and the keff values areobtained from the MCNP calculations.k1 corresponds to the core flooded with Na coolant, and k2 to the same corevoided of Na coolant.In both cases the Na coolant present in the axial and radial reflectors is supposedto remain unchanged.

Results for the ESFR parameters

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If we suppose that βeff does not vary with different nuclear data files and that k1and k2 are fully correlated, the uncertainty on the sodium void reactivity can beexpressed as:

∆SVRperturbation =∣

∣

∣

∣

∆k1k21

−∆k2k22

∣

∣

∣

∣

1βeff

×105, (2)

In the case of the TMC method, βeff is also varying.Results on the void coefficient, keff and βeff are presented in the following slide.The change in reactivity per degree of change in the temperature of nuclear fuel(or Doppler coefficient) is calculated from differences in keff obtained at threedifferent temperatures: 1227 C (nominal temperature) ± 200 C.

Results for the ESFR parameters

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Table 1: Uncertainties on the sodium void coefficient (SVR), keff, βeff and Dopplercoefficient due to different nuclear data uncertainties

Coefficient value Uncertainty due tonuclear data

SVR 5.86 $ ' 5 %Non Voided keff 0.98298 ' 100 pcmVoided keff 1.00481 ' 15 pcmβeff 371 pcm < 1 pcmDoppler -0.60 pcm/C ' 7-13 %

The uncertainty obtained for the Doppler coefficient takes into account thestatistical uncertainty coming from the various MCNP calculations, and thelimited number of perturbed calculations from the TMC approach.

Conclusions and Future improvements

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☞ The TMC method was applied to propagate nuclear data uncertainties forthe ESFR model

☞ Main isotopes were considered (239,240,241,242Pu, 238U and 23Na),

☞ Uncertainties have been calculated for the sodium void coefficient, keff, βeffand Doppler coefficient for the ESFR model,

☞ Similar uncertainties were obtained for the Kalimer-600 (see publicationfrom the same authors in the Journal of Nuclear Science and Technology,2011)

ContentsGoals:Concept: TALYS + Monte Carlo = Total Monte Carlo TMC and Perturbation methodNuclear data: 239Pu and 238UNuclear data: examples in the resonance regionNuclear data: 56Fe and 23NaSensitivities to keffResults for the ESFR parametersResults for the ESFR parametersResults for the ESFR parametersConclusions and Future improvements