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Nuclear data uncertainty propagation fora Sodium Fast Reactor

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

and S.C. van der Marck

Nuclear Research and Consultancy Group,

NRG, Petten, The Netherlands

April, 2010

Contents

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① Goals:=⇒ Uncertainties on an SFR parameters

② Concept for uncertainty propagation:=⇒ Total Monte Carlo and Perturbation methods

③ SFR Model:=⇒ Kalimer-600 and MCNP

④ Nuclear Data:=⇒

235,238U, 239,240Pu, 23Na, 56Fe, 90Zr

⑤ Results:=⇒ Void coefficient and keff

⑥ Conclusions and Future Studies

Goals:

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① Obtain uncertainties on an SFR model due to nuclear data uncertainties

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 TMC

+ Covariances

+ Covariances

-keff-Flux-Etc.

+ Covariances

-Activation-Burn-up

+ Covariances

Monte Carlo: 1000 runs of all codes

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

Kalimer model and MCNP

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Simplified full core model of the Kalimer-600 (one single fuel zone for freshfuel) & Equilibrium reactor core with 4-batches,Fuel type: metal alloy U-TRU-10 %Zr, isotopic vector provided by KAERI.238U: 83 %, 239Pu: 10 %, 240Pu: 5 %, 241Pu: 1 %

-100 -50 0 50 100

-100

-50

050

100

9

10

8

0

8

10

9

11

8

10

8

11

2

10

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10

6

8

11

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11

9

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8

9

9

11

11

9

10

9

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8

10

8

9

11

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10

8

8

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9

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8

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8

1110

9

6 9

9

11

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8 11

11/21/08 13:12:47KALIMER-600 1/6 full core / U-TRU-10Zr metallic fuel / equilibrium core BOCprobid = 11/21/08 13:11:15basis: XY( 1.000000, 0.000000, 0.000000)( 0.000000, 1.000000, 0.000000)origin:( 101.12, 83.37, 0.00)extent = ( 116.18, 116.18)cell labels are material numbers

.

-100

-50

050

100

-100-50050100

11/21/08 13:12:59

KALIMER-600 1/6 full core /

U-TRU-10Zr metallic fuel /

equilibrium core BOC

probid = 11/21/08 13:11:15

basis: XY

( 1.000000, 0.000000, 0.000000)

( 0.000000, 1.000000, 0.000000)

origin:

( 101.12, 83.37, 0.00)

extent = ( 116.18, 116.18)

.

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 on void coefficient SVR =k2−k1k1k2

1βeff

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Reduced Chi-square=0.215

SVR= 8.02510± 0.55092 $

Kalimer void coefficient (23Na)

Void coefficient value ($)

Num

ber

ofco

unts

/bin

s

9.38.77.97.36.7

20

15

10

5

0<Skewness>

Sample number

Updat

edsk

ewnes

s

8006004002000

0.0

-0.1

-0.2

-0.3

-0.4

< σ >

Updat

edunce

rtai

nty

($)

0.6

0.5

0.4

0.3

< void coefficient >

Sodium Fast Reactor (Kalimer-600)

Updat

edSV

R($

)

8.5

8.3

8.1

7.9

Uncertainty on the void coefficient due to nuclear data using the TMCand perturbation methods

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Isotope Varied Uncertainty MethodNuclear data on SVR

23Na all ' 6 % TMC238U (n,inl)+(n,γ) ' 2 % Pert.239Pu (n,f) +(n,γ) ' 2 % Pert.239Pu all ' 2.5 % TMC240Pu (n,f) +(n,γ) ' 0.1 % Pert.56Fe (n,inl) ' 0.1 % Pert.90Zr (n,inl)+(n,γ) < 0.1 % Pert.

Uncertainty on keff due to nuclear data using the TMC andperturbation methods

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Isotope Varied Uncertainty MethodNucl. data. on keff (pcm)

238U (n,γ) 1000 Pert.239Pu all 800 TMC239Pu (n,f) 700 Pert.240Pu (n,f) 600 Pert.238U (n,inl) 300 Pert239Pu (n,γ) 260 Pert.23Na all 130 TMC241Pu (n,f) 120 Pert.56Fe (n,inl) 100 Pert.

Conclusions and Future improvements

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☞ Two methods were applied to propagate nuclear data uncertainties for aKalimer model

☞ Main isotopes were considered (239,240Pu, 235,238U, 23Na, 56Fe, 90Zr)

☞ Results in agreement with previous studies (SG-26) for initial targetaccuracies

☛ Better evaluation work is necessary to meet final target accuracies

☛ Consider all nuclear data with the TMC method

☛ Obtain uncertainty on burn-up (isotope content at the end of cycle)