outline

Analysis of Available Cross-Section Uncertainty Dataand

Progress in Defining Uncertainty Methodologies for Inventory Calculations

J. Sanz, O. Cabellos, J. Juan, J. Sanz, O. Cabellos, J. Juan, N. García-HerranzN. García-Herranz

Universidad Nacional de Educación a Distancia (UNED)Universidad Nacional de Educación a Distancia (UNED)Universidad Politécnica de Madrid (UPM)Universidad Politécnica de Madrid (UPM)

Second IP EUROTRANS Internal Training Course on Nuclear Data for Transmutation

June 9, 2006

2

Outline Outline

INTRODUCTIONINTRODUCTION

OBJECTIVESOBJECTIVES

PART I: PART I: ANALYSIS OF AVAILABLE NEUTRON CROSS ANALYSIS OF AVAILABLE NEUTRON CROSS

SECTION UNCERTAINTY DATASECTION UNCERTAINTY DATA FOR INVENTORY FOR INVENTORY

CALCULATIONS CALCULATIONS

PART II: PART II: PROGRESS IN UNCERTAINTY METHODOLOGIESPROGRESS IN UNCERTAINTY METHODOLOGIES

CONCLUSIONS CONCLUSIONS

FUTURE WORKFUTURE WORK

3

IntroductionIntroduction

One of the objectives in NUDATRA Domain is to evaluate the impact of nuclear data uncertainties on relevant fuel cycle and repository parameters

DOMAIN DM5 NUDATRACoordinator: CIEMAT (Enrique M. González)

WP 5.1 Sensitivity Analysis andValidation of Nuclear Data and Simulation Tools

WP 5.2 Low andIntermediate EnergyNuclear Data Measurements

WP 5.3 Nuclear Data LibrariesEvaluation andLow Inter-mediateEnergy Models

WP 5.4 HighEnergyExperimentsand ModellingCoordinator: UNED (J. Sanz)

T5.1.1 Identification of topics for sensitivity evaluation and development of sensitivity methodologies for the fuelcycle and the repository parameters

T5.1.2 Evaluation of the sensitivities, priority list and table of required accuracies

T5.1.3 Development and validation of simu-ation programs for transmutation plants

T5.1.4 Nuclear data and models validation for the spallation target

T5.1.5 Minor actinide and Pb nuclear data validation in integral experiments

DOMAIN DM5 NUDATRACoordinator: CIEMAT (Enrique M. González)

WP 5.1 Sensitivity Analysis andValidation of Nuclear Data and Simulation Tools

WP 5.2 Low andIntermediate EnergyNuclear Data Measurements

WP 5.3 Nuclear Data LibrariesEvaluation andLow Inter-mediateEnergy Models

WP 5.4 HighEnergyExperimentsand ModellingCoordinator: UNED (J. Sanz)

T5.1.1 Identification of topics for sensitivity evaluation and development of sensitivity methodologies for the fuelcycle and the repository parameters

T5.1.2 Evaluation of the sensitivities, priority list and table of required accuracies

T5.1.3 Development and validation of simu-ation programs for transmutation plants

T5.1.4 Nuclear data and models validation for the spallation target

T5.1.5 Minor actinide and Pb nuclear data validation in integral experiments

4

IntroductionIntroduction

One of the objectives in NUDATRA Domain is to evaluate the impact of nuclear data uncertainties on relevant fuel cycle and repository parameters

In order to reach these goals three main elements are required:

I. Cross section uncertainties ()

II. Computational techniques enable to assess the impact of on the isotopic inventory and other inventory-related responses

III. List of relevant parameters for the uncertainty evaluation and required target accuracies in those parameters

Our group is mainly involved in steps I and II

5

ObjectivesObjectives

I. Review, processing and analysis of the neutron cross-section uncertainty data available in the most recent internationally distributed nuclear data libraries

Result: compilation of the best current available uncertainty data for use in inventory codes (covariance matrices: uncertainties –diagonal values– and their correlations – off-diagonal values –)

II. Definition of appropriate methodologies to propagate nuclear data uncertainties to the isotopic inventory

Capability to evaluate the impact of cross section uncertainties on the inventory predictions

Applications to EUROTRANS : assess if further improvement of nuclear data is required

6

PART IPART I

Analysis of available neutron cross- Analysis of available neutron cross- section uncertainty data for inventory section uncertainty data for inventory

calculationscalculations

I.1 Review and compilation of available cross-section uncertainty data

I.2 Processing the uncertainty data for inventory prediction

I.3 Analysis of uncertainties: comparison of the previous uncertainty data

7

Uncertainty data for all reactions included in the point-wise cross-section library (13,006 in FENDL-2.0, 12,617 in EAF-2003, 62,637 in EAF-2005)

For non-threshold reactions 3-4 groups

For threshold reactions 1-2 groups

Activation-oriented nuclear data libraries

FENDL UN/A-2.0, EAF2003/UN and the recently released EAF2005

Included information: j,LIBRARY (relative error in the j energy group)

Assumptions: xs within the same energy group are fully correlated; xs in different groups are assumed to be statistically independent no covariances included, covariance matrix diagonal

Reaction Energy (eV) j,EXP (%) Covariance matrix (relative)

Pu240 (n,)

1.0E-05-

1.0E-01 3.43

1.0E-01 - 4.0E+03 3.56

4.0E+03 - 2.0E+07 16.67

739988

2140

1035

35873205

1665

528 504228

0

600

1200

1800

2400

3000

3600

Variance range

Nu

mb

er

of

reacti

on

s in

EA

F2003/U

N

var

0.2

0.2

< v

ar

0.4

0.4

< v

ar

0.6

0.6

< v

ar

0.8

0.8

< v

ar

1.

1. <

var

2.

2. <

var

3.

3. <

var

4.

4. <

var

6.

6. <

var

9.

31602911

25502707

1251

425

0

600

1200

1800

2400

3000

3600

Variance range

Nu

mb

er

of

reacti

on

s in

F

EN

DL

UN

/A-2

.0

var

0.6

1

0.6

1 v

ar

< 1

.

1.

var

< 4

.

4.

var

< 5

.76

16

var

16.4

var=

81

I.1 Review of available uncertainty cross-section dataI.1 Review of available uncertainty cross-section data

2E78.2

3E26.1

3E17.1

8

General purpose evaluated nuclear data files

BROND-2.2 (last updated 1993)CENDL-2.1 (last updated 1995)ENDF/B-VI.8 (october 2001); ENDF/B-VIIb (2005)JEF-2.2 (1993)JEFF-3.0/1 (may 2005)JENDL-3.3 (2002)IRDF90-2.0 (1993); IRDF2002 (2002)

I.1 Review of the nuclear data uncertainties available (cont.)I.1 Review of the nuclear data uncertainties available (cont.)

Library# of materials with

covariance data (MF33 and MF40)

# aprox. of xs with covariance

data

BROND-2.2 3 30

CENDL-2.1 9 65

ENDF/B-VI.8 44 400

ENDF/B-VIIb 35 > 200

IRDF90-2.0 37 > 100

IRDF2002 48 > 100

JEF-2.2 15 120

JEFF-3.1 34 350

JENDL-3.3 20 160

Data of interest for inventory calculations: MF33, MF 39 (no data in the libraries), MF40

Stored values: absolute ( ) or relative covariances ( )

Uncertainty information

in “covariance files”

nu(bar) MF31

resonance parameters MF32

reaction cross sections MF33

angular distributions MF34

energy distributions MF35

radionuclide production yields MF39

radionuclide production xs MF40

covariance information is still scarce in all major data files

),cov( YX YXYX /),cov(

Data covariances for:

9

JENDL-3.3MF33 : Reaction Cross Section Covariance Data

Sub-library No. 10

Material (MAT)

Reaction(MT)

Covariance with (MAT, MT)

Reaction(MT)

Covariance with (MAT, MT)

U233

11617102

(n,Total)(n,2n)(n,3n)(n,g)

SELFSELFSELFSELF

U233 (n,fission)

18 (n,fission) SELFU235 (n,fission)U238 (n,fission)Pu239 (n,fission)Pu240 (n,fission)Pu241 (n,fission)

U235

1161737102

(n,Total)(n,2n)(n,3n)(n,4n)(n,g)

SELFSELFSELFSELFSELF

U235 (n,fission)


U238

1161737102

(n,Total)(n,2n)(n,3n) (n,4n)(n,g)



Pu239

11617 37102



18 (n,fission) SELFU233 (n,fission)U235 (n,fission)U238 (n,fission)Pu240 (n,fission)Pu241 (n,fission)

Pu240

11617 37102




Pu241

11617 37102




Most covariance matrices correlate only energy intervals of the same reaction and material (SELF)

Covariance matrices correlating cross sections for two different reactions of the same material

Covariance matrices correlating cross sections for the same reaction of different materials

The total covariance matrix for a particular energy-dependent xs is made up of the contribution of single covariance matrices, each one defining a type of correlation

10


Since actinides play an important role in ADS studies, we have carried out a more detailed analysis on them. From the 50 neutron-induced cross-sections (on 10 targets) with covariance data:

Most xs (38) have covariance matrices only correlating energy intervals (of the

same reaction and material) (SELF)

There are 8 xs correlated with xs of the same reaction type of different materials (for example, in JENDL-3.3, the Pu241(n,fission) is correlated with the U235(n,fission))

There are 3 xs with covariance matrices correlating different reaction types of different materials (that is the case of U235(n,fission), correlated with U238(n,) in IRDF90-2.0)

Finally, there are 3 xs with data correlating two different reaction types of the same material (in JENDL-3.3, the U235(n,) is correlated with U235(n,fission))

Uncertainty information for a few reactions, more detailed uncertainties (energy correlations and correlations among different reactions or different isotopes)

11

“Home-made” ANL Covariance Matrix


G. Aliberti, G. Palmiotti, M. Salvatores, C. G. StenbergTransmutation Dedicated Systems: An assessment of Nuclear Data Uncertainty Impact, Nucl. Sci. Eng. 146, 13-50 (2004)

G. Palmiotti, M. SalvatoresProposal for Nuclear Data Covariance Matrix , JEFDOC 1063 Rev.1, January 20 (2005)

ANL

N. of MAT=42

H (bonded)

B10

Li6-7

C

O

N15

Cr52

Fe56 – 57

Er

Bi

He4

Be9

F19

Al

Na

Si

Ni58

Gd

Zr

Pb

Th232

U233 – 234 – 235 – 236 – 238

Np237

Pu238 – 239 – 240 – 241 – 242

Am241 – 242m – 243

Cm242 – 243 – 244- 245 – 246

12

Energy Group

MeV

1 1.96403E+1

2 6.06531E+0

3 2.23130E+0

4 1.35335E+0

5 4.97871E-1

6 1.83156E-1

7 6.73795E-2

8 2.47875E-2

9 9.11882E-3

10 2.03468E-3

11 4.53999E-4

12 2.26033E-5

13 4.00000E-6

14 5.40000E-7

15 1.00000E-7

1) the region above the threshold of fertile isotope fission cross-sections, and of many inelastic cross-sections, up to 20 MeV

2) the region of the continuum down to the upper unresolved resonance energy limit3) the unresolved resonance energy region4) the resolved resonance region5) the thermal range

15 energy groups between 19.6 MeV and E(thermal)

Diagonal values given in Aliberti et al.(2004)

Energy correlations given in Palmiotti et al.(2005) (no correlations among isotopes or reaction types)

The same correlations for all isotopes and reactions, under the form of full energy correlation in 5 energy bands:

13

I.2 Processing the uncertainty data for inventory predictionI.2 Processing the uncertainty data for inventory prediction

Covariance data have to be processed into multigroup to be used by an inventory code

Uncertainties in the activation-oriented nuclear data libraries are in a group structure diagonal covariance matrices are ready for use by the inventory code (cross-sections need to be processed in the same group structure to assure the consistency)

Files MF33 of the general-purpose evaluated data files need to be processed to yield the multigroup covariance matrices. Computational processing tools:

NJOY99.112 (ERRORR/COVR modules)

ERRORRJ-2.1.2

Multigroup covariance matrices with energy correlations Multigroup covariance matrices correlating different isotopes or reaction types

We are able to process covariance data to yield multigroup covariance matrices ready for use by inventory codes (such as ACAB)

In preparation at the NEA Data Bank: they are extracting relevant covariance data from current evaluations in major data files and processing them in the ANL 15-multigroup structure. The derived covariance matrix in called NEA-K Covariance Matrix

14

material mat-mt=(9440,102) grp energy x-sec. rel.s.d. std.dev. 1 2.0000E+07 9.8861E-04 7.5000E-01 7.4146E-04 2 1.9600E+07 9.8861E-04 6.7497E-01 6.6728E-04 3 6.0700E+06 2.6886E-02 4.5694E-01 1.2285E-02 4 2.2300E+06 7.8668E-02 4.5255E-01 3.5601E-02 5 1.3500E+06 1.2688E-01 1.9635E-01 2.4913E-02 6 4.9800E+05 1.9733E-01 5.7960E-02 1.1437E-02 7 1.8300E+05 3.8927E-01 3.5590E-02 1.3854E-02 8 6.7400E+04 6.6387E-01 1.3602E-02 9.0299E-03 9 2.4800E+04 9.7319E-01 1.5024E-02 1.4622E-02 10 9.1200E+03 1.5993E+00 4.5523E-03 7.2805E-03 11 2.0400E+03 3.8849E+00 3.8845E-03 1.5091E-02 12 4.5400E+02 7.1500E+02 6.9444E-04 4.9652E-01 13 2.2600E+01 8.2559E+02 1.7595E-03 1.4526E+00 14 4.0000E+00 8.2559E+02 3.8735E-02 3.1979E+01 15 5.4000E-01 8.2559E+02 4.1812E-03 3.4520E+00

<<< correlation matrix >>> column material mat-mt=(9440,102) vs row material mat-mt=(9440,102) row 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 column-------------------------------------------------------------------------- 1 1000 973 30 0 0 0 0 0 0 0 0 0 0 0 0 2 973 1000 28 0 0 0 0 0 0 0 0 0 0 0 0 3 30 28 1000 925 425 156 94 157 0 0 0 0 0 0 0 4 0 0 925 1000 681 182 137 286 0 0 0 0 0 0 0 5 0 0 425 681 1000 294 106 285 0 0 0 0 0 0 0 6 0 0 156 182 294 1000 807 49 0 0 0 0 0 0 0 7 0 0 94 137 106 807 1000 344 0 0 0 0 0 0 0 8 0 0 157 286 285 49 344 1000 503 148 0 0 0 0 0 9 0 0 0 0 0 0 0 503 1000 674 0 0 0 0 0 10 0 0 0 0 0 0 0 148 674 1000 0 0 0 0 0 11 0 0 0 0 0 0 0 0 0 0 1000 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 0 1000 4 0 2 13 0 0 0 0 0 0 0 0 0 0 0 4 1000 4 10 14 0 0 0 0 0 0 0 0 0 0 0 0 4 1000 530 15 0 0 0 0 0 0 0 0 0 0 0 2 10 530 1000

Example: 240Pu (n,gamma) from JENDL-3.3 processed by ERRORRJ-2.1.2 in the ANL 15-group structure

15

Example: Covariance 239Pu (n,fission)/235U (n,fission) from JENDL-3.3 processed by ERRORRJ-2.1.2 in the ANL 15-group structure

1st material mat-mt=(9437, 18) vs 2nd material mat-mt=(9228, 18) grp energy 1st x-sec. 2nd x-sec. 1st r.s.d. 2nd r.s.d. 1 2.0000E+07 2.0920E+00 1.5400E+00 1.3734E-02 1.1148E-02 2 1.9600E+07 2.0920E+00 1.5400E+00 5.5090E-03 3.0259E-03 3 6.0700E+06 1.8358E+00 1.1930E+00 5.0920E-03 2.0016E-03 4 2.2300E+06 1.9741E+00 1.2796E+00 5.6020E-03 2.8955E-03 5 1.3500E+06 1.6865E+00 1.1836E+00 5.4778E-03 2.7716E-03 6 4.9800E+05 1.5184E+00 1.2518E+00 6.2445E-03 3.7342E-03 7 1.8300E+05 1.5156E+00 1.5742E+00 7.0030E-03 4.4413E-03 8 6.7400E+04 1.5932E+00 1.9349E+00 1.6937E-02 4.1847E-03 9 2.4800E+04 1.8024E+00 2.5042E+00 6.7252E-02 0.0000E+00 10 9.1200E+03 2.7279E+00 4.2577E+00 4.8178E-02 0.0000E+00 11 2.0400E+03 6.6364E+00 9.3444E+00 4.4939E-03 0.0000E+00 12 4.5400E+02 3.9532E+02 2.2054E+02 5.9599E-04 0.0000E+00 13 2.2600E+01 4.5535E+02 2.5249E+02 4.2970E-03 0.0000E+00 14 4.0000E+00 4.5535E+02 2.5249E+02 1.1932E-02 0.0000E+00 15 5.4000E-01 4.5535E+02 2.5249E+02 1.0917E-01 0.0000E+00

column material mat-mt=(9437, 18) vs row material mat-mt=(9222, 18) row 1 2 3 4 5 6 7 8 9 10 … column------------------------------------------------------- 1 783 170 74 47 40 23 13 6 0 0 … 2 119 536 226 115 102 64 38 19 0 0 … 3 23 116 389 167 148 96 62 35 0 0 … 4 17 65 237 507 292 193 139 94 0 0 … 5 11 50 217 291 495 281 207 139 0 0 … 6 6 37 181 232 342 584 304 209 0 0 … 7 3 23 140 187 276 334 622 285 0 0 … 8 0 1 35 52 77 93 114 228 0 0 … 9 0 0 0 0 0 0 0 0 0 0 … 10 0 0 0 0 0 0 0 0 0 0 … 11 …

16

I.3 Analysis of uncertaintiesI.3 Analysis of uncertainties

1,0E+04

1,0E+05

1,0E+06

1,0E+07

1,0E+08

1,0E+09

1,0E+10

1,0E+11

1,0E+12

1,0E+13

1,0E-01 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

Eneutron (eV)

Ne

utr

on

Flu

x (

n*c

m-2

*s-1

)

Total Flux Intensity = 5.51E+15 n*cm-2*s-1

Average neutron ebergy = 3.49E-01 MeV

(ADS concept consists of an 800 MWth fast core cooled by lead-bismuth eutectic in forced convection, E. González et. al., CIEMAT)

Goal: generate an extended ADS uncertainty library made of a compilation of the best current available data to inventory calculations:

EAF-2005/UN (uncertainties for all reactions, variances in a 2/4 groups, no off-diagonal elements)

ENDF covariance files (MF33) (few reactions, more detailed uncertainties, correlations between energy groups,

isotopes and reaction types) to take them if exist; if not

To be consistent standard cross-sections from the corresponding evaluation

Test: comparison of the multigroup uncertainties obtained after processing data from different sources with a typical ADS neutron flux

17

I.3 Analysis of uncertainties (cont.)I.3 Analysis of uncertainties (cont.)

Comparison of effective uncertainties (1-group)

njni

ji ji ),cov(2

T

iieffi

i

i is the ADS multigroup neutron flux

ni

iT with n the total number of energy groups

),(cov ji is the ENDF multigroup covariance matrix

)4or 3,2(

1

22,

2G

jjEXPj

Isotope FENDL/UN EAF2003/UN ENDF/B-VI

237Np 16.33 16.33 -

238Pu 14.68 14.76 -

239Pu 12.69 12.91 -

240Pu 9.87 9.97 10.87

241Pu 15.92 15.92 -

242Pu 13.08 13.21 -

241Am 25.45 16.30 4.82

242mAm 33.27 16.63 -

243Am 25.01 16.02 -

Uncertainties ( %) in actinide (n,) cross sections

Comparison of uncertainties in a 3-group structure (that used in EAF-2003)

Energy range (eV) Cross sections in 3 groups Covariance matrices in 3 groups (absolute)

Ei Ei+1 EAF-2003 ENDF/B-VI EAF-2003 ENDF/B – VI.R8

4.0E+3 - 2.0E+7 4.05E-1 4.02E-1 4.56E-3 0.00E+0 0.00E+0 2.08E-3 5.28E-4 0.00E+0

1.0E-1 - 4.0E+3 2.79E-1 2.79E-1 0.00E+0 9.88E-5 0.00E+0 5.28E-4 2.35E-3 0.00E+0

1.0E-5 - 1.0E-1 1.09E-5 1.08E-5 0.00E+0 0.00E+0 1.40E-13 0.00E+0 0.00E+0 1.12E-15

Uncertainties in the Pu240(n,) with the EAF-2003 group structure

Good agreement of the processed uncertainties from the 2 types of uncertainty data sources Recommendation = ENDF covariance files + EAF/UN + Palmiotti?

18

PART IIPART II

Progress in defining uncertainty Progress in defining uncertainty methodologiesmethodologies

II.1 Main features of the two proposed methodologies to estimate propagation of cross section uncertainties to the isotopic inventory and associated parameters

II.2 Application to the actinide inventory of typical ADS irradiated fuel

II.3 Effect of the correlation structure on the results

19

1) Sensitivity / Uncertainty Analysis

Method based on the first order Taylor series to estimate uncertainty indices for each reaction cross section in a continuous irradiation scenario

2) Monte Carlo Uncertainty Analysis

To treat the global effect of all cross sections uncertainties in activation calculations, we have proposed an uncertainty analysis methodology based on Monte Carlo random sampling of the cross sections

Assignment of a Probability Density Function (PDF) to each cross section

II.1 Methodologies II.1 Methodologies

AXXdt

d ,..., 21 XXX

,..., 21

Goal: to analyse how xs uncertainty is transmitted to X

,...,ii XX

20

Sensitivity AnalysisSensitivity Analysis

0

0

1 0

0

0

0

01

0

)(

)()(

)()(

)()()(

0

0

j

jjm

j j

i

i

j

i

ii

jj

m

j j

iii

X

XX

XX

XXX

ij j

j

iij

XY

jjj Y

X

AB

A

Y

X

dt

d 0

jj

j

AB

X

Y

X

,

0)0( 0

We solve at the same time the nuclide concentration Xi and the partial derivative

Sensitivity coefficient

ieRelative error in Xi due to changes in cross-sections

Relative error in cross-sections

21

Sensitivity Analysis (cont.)Sensitivity Analysis (cont.)

;0

0

j

jjj

)(

MeVar

imiii

i

T

ii

21

0

0

j

i

i

jij

X;

i

iii

Xe

2222

22

21

21][ mimiiieVar

mimiiie 2211

M)(Var

22

Monte Carlo MethodMonte Carlo Method

j0

0 deviation standard relative:Libraries

j

jjj

),0(log lognormal be toassumed PDF)2

negative! be could , of valueslargeFor ),0()1

0j

j

j

jjjj

N

N

Based on a random sampling a PDF is assigned to each j

Probability distribution of j ?

)(),0(1log

1

10

0

0

smallisifN jjjj

j

j

jj

j

j

23

),0(log

0

20

2

10

1

MN

m

m

We use simultaneous random sampling of all the XS PDFs involved in the problem

From the sample of the random vector , the matrix A is computed and the vector of nuclide quantities X is obtained

Repeating the sequence, we obtain a sample of isotopic concentration vectors. The statistic estimators of the sample can be estimated

Enables to investigate the global effect of the complete set of on X

j

1j

iX...

iX

iX 95iX0iX

mj ...,...,1

ni XXXX ...,...,1

Monte Carlo Method (cont.)Monte Carlo Method (cont.)

24

Reference system

Fuel composition from the transmuter core used in Aliberti et al. (2004) [1]

Neutron flux: 1.944 x 1015 n / cm2 s , ADS typical spectrum <E> = 0.3489 MeV

Irradiation period of 1 year as in [1]

Analysis performed at 15 energy groups, with the structure adopted in [1]

Uncertainty data only for major actinides: 238Pu and 240Pu, 239Pu, 241Pu, 242Pu and minor actinides: 237Np, 241Am and 243Am, 242mAm, 242Cm, 243Cm, 245Cm, 246Cm, 244Cm and reaction types: (fission, capture and n,2n reactions)

Covariance information taken from Aliberti et al.(2004) and Palmiotti et al. (2005): ANL covariance matrices (reference)

Cross section data processed to the required multigroup structure from EAF-2003

II.2 Application II.2 Application

Goal: to show the capabilities of ACAB to evaluate uncertainties in the actinide inventory

25

Results from Monte Carlo

Inventory of actinides at the end of 1-year irradiation period computed by ACAB

Results for a 1000 history-sampling

II.2 ApplicationII.2 Application (cont.) (cont.)

Initial, Xi

×1020

Final, Xf

×1020(Xf -Xi)/Xi

Coefficient of variation of Xf (in %)

No

CorrelationPalmiotti’s Correlation

Pu 238 0,42300 1,23000 1,91 3,6 5,6

Am 241 8,08000 6,93000 -0,14 1,3 2,0

Am 242 0,10900 0,15900 0,46 1,3 2,0

Am 243 5,83000 5,17000 -0,11 0,2 0,3

Cm 242 0,00040 0,39800 974,49 8,7 13,5

Cm 244 2,37000 2,71000 0,14 0,6 0,9

Cm 245 0,31600 0,38500 0,22 2,4 3,6

26

0 1 2 3 4 5 6 7

x 1019

0

20

40

60

80

100

120Cm 242

log Normal (45.1; 0.133)Simulation result

Mean 4.078 x 1019

Std D. 5.430 x 1018

Histogram of the 1000 values obtained by Monte Carlo Method

27

Results from Sensitivity/Uncertainty technique: comparison with Monte Carlo method

Goal of the comparison of both approaches: checking the implementation

Very different (bad implemented)

Similar (well implemented)

Some differences (no linearity for the irradiation time of the example)

Results very similar

II.2 ApplicationII.2 Application (cont.) (cont.)

Coefficients of variation (in %)

Taylor Aprox. Monte Carlo

Pu 238 5,36 5,63

Am 241 1,89 2,01

Am 242 1,95 2,04

Am 243 0,24 0,25

Cm 242 12,9 13,11

Cm 244 0,78 0,85

Cm 245 3,28 3,62

28

where is a positive parameter between 0 and (correlation range parameter) small high correlations

big low correlations

II.3 Effect of correlationsII.3 Effect of correlations

We propose an exercise to assess the effect of the covariance structure on the results

Energy range divided in G groups and E1, E2, … EG mean values of each group

We define the correlation rij between the groups with energies Ei and Ej as :

)log()log( ji EE

ij er

Significant impact of the covariances in the inventory prediction? How much the xs uncertainty correlations can affect the actinide inventory?

29

05,0 50,0

1 ,9 ,8 ,7 ,6 ,5 ,4 ,3 ,2 ,1 ,0

0,125,010,0

)log()log( ji EE

ij er

II.3 Effect of correlations (cont.)II.3 Effect of correlations (cont.)

30

Initial×1020

Final×1020

Coefficient of variation of Xf ( in %)

No Correlation 1 0,5 0,25 0,10 0,05

Palmiotti ´s Correlation

Pu 238 0,42300 1,23000 3,6 4,8 5,9 7,2 8,6 8,9 5,6

Am 241 8,08000 6,93000 1,3 1,7 2,1 2,8 3,2 3,3 2,0

Am 242 0,10900 0,15900 1,3 1,8 2,2 2,7 3,3 3,5 2,0

Am 243 5,83000 5,17000 0,2 0,2 0,2 0,3 0,3 0,3 0,3

Cm 242 0,00040 0,39800 8,7 11,3 14,0 18,0 21,1 21,6 13,5

Cm 244 2,37000 2,71000 0,6 0,8 0,9 0,9 1,1 1,1 0,9

Cm 245 0,31600 0,38500 2,4 3,3 3,8 4,7 5,5 5,6 3,6

Uncertainty values obtained assuming a simple correlation model with a correlation range parameter = 0.5 very similar to those obtained assuming Palmiotti’s correlation

31

We are able to process any uncertainty information to inventory calculations and the corresponding cross sections. Interest in using the best set of uncertainties currently available: ENDF + EAF/UN + Palmiotti ??

Two methodologies implemented in the inventory code ACAB to estimate nuclear data uncertainty propagation to the isotopic inventory of actinides appropiated for ADS problems

Potential of the Monte Carlo method highlighted

Covariance matrices in any arbitrary multigroup structure can be handled by ACAB (at present, only energy correlations taken into account)

The effect of the xs correlations are relevant on the actinides

ConclusionsConclusions

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Generation of an extended ADS/UN library for all the isotopes of interest (not only actinides) to predict the inventory with the best set of uncertainties

Deal with correlations among different isotopes and different reactions

Definition of the reference system in order to perform appropriate tests (potential of Monte Carlo method)

Fuel composition, neutron flux

Follow-up EUROTRANS schedule

Future Work at UNED / UPMFuture Work at UNED / UPM

outline

Documents

nuclear data filesbrond

improvement of nuclear

data of inte

uncertainty evaluation

analysis of uncertainties

inventory calculationsi

inventory predictioni

uncertainties diagonal