Abstract

This paper presents a statistical methodology for a quantified validation of the OCARINa simulation tool, which models the unprotected transient overpower (UTOP) accidents. This validation on CABRI experiments is based on a best-estimate plus uncertainties (BEPU) approach. To achieve this, a general methodology based on recent statistical techniques is developed. In particular, a method for the quantification of multivariate data is applied for the visualization of simulator outputs and their comparison with experiments. Still for validation purposes, a probabilistic indicator is proposed to quantify the degree of agreement between the simulator OCARINa and the experiments, taking into account both experimental uncertainties and those on OCARINa inputs. Going beyond a qualitative validation, this work is of great interest for the verification, validation and uncertainty quantification or evaluation model development and assessment process approaches, which leads to the qualification of scientific calculation tools. Finally, for an in-depth analysis of the influence of uncertain parameters, a sensitivity analysis based on recent dependence measures is also performed. The usefulness of the statistical methodology is demonstrated on CABRI-E7 and CABRI-E12 tests. For each case, the BEPU propagation study is carried out performing 1000 Monte Carlo simulations with the OCARINa tool, with nine uncertain input parameters. The validation indicators provide a quantitative conclusion on the validation of the OCARINa tool on both transients and highlight future efforts to strengthen the demonstration of validation of safety tools. The sensitivity analysis improves the understanding of the OCARINa tool and the underlying UTOP scenario.

References

References
1.
Bertrand
,
F.
,
Marie
,
N.
,
Prulhiere
,
G.
,
Lecerf
,
J.
, and
Seiler
,
J. M.
,
2016
, “
Comparison of the Behavior of Two Core Designs for ASTRID in Case of Severe Accidents
,”
Nucl. Eng. Des.
,
297
, pp.
327
342
.10.1016/j.nucengdes.2015.04.020
2.
Herbreteau
,
K.
,
Marie
,
N.
,
Bertrand
,
F.
,
Seiler
,
J.-M.
, and
Rubiolo
,
P.
,
2018
, “
Sodium-Cooled Fast Reactor Pin Model for Predicting Pin Failure During a Power Excursion
,”
Nucl. Eng. Des.
,
335
, pp.
279
290
.10.1016/j.nucengdes.2018.05.023
3.
Wilson
,
G.
,
2013
, “
Historical Insights in the Development of Best Estimate Plus Uncertainty Safety Analysis
,”
Ann. Nucl. Energy
,
52
(
2
), p.
2
.10.1016/j.anucene.2012.03.002
4.
Boyack
,
B. E.
,
Catton
,
I.
,
Duffey
,
R. B.
,
Griffith
,
P.
,
Katsma
,
K. R.
,
Lellouche
,
G. S.
,
Levy
,
S.
,
Rohatgi
,
U. S.
,
Wilson
,
G. E.
,
Wulff
,
W.
, and
Zuber
,
N.
,
1990
, “
Quantifying Reactor Safety Margins—Part I: An Overview of the Code Scaling, Applicability and Uncertainty Evaluation Methodology
,”
Nucl. Eng. Des.
,
119
(
1
), pp.
1
15
.10.1016/0029-5493(90)90071-5
5.
Waltar
,
A. E.
, and
Reynolds
,
A. B.
,
1981
,
Fast Breeder Reactors
,
Pergamon Press
,
Oxford, UK
.
6.
Lemasson
,
D.
, and
Bertrand
,
F.
,
2014
, “
Simulation With SAS-SFR of a ULOF Transient on ASTRID-Like Core and Analysis of Molten Clad Relocation Dynamics in Heterogeneous Subassemblies With SAS-SFR
,” ICAPP'14, Charlotte, NC.
7.
Kondo
,
S.
,
Morita
,
K.
,
Tobita
,
Y.
,
Kamiyama
,
K.
,
Brear
,
D. J.
, and
Fischer
,
E. A.
,
1996
, “
SIMMER-III: Computer Program for LMFR Core Disruptive Accident Analysis, O-Arai Engineering Center
,” Power Reactor and Nuclear Fuel Development Corporation, Tokyo, Japan, Report No. JNC
TN94002003-071
.https://jopss.jaea.go.jp/pdfdata/JNC-TN9400-2003-071.pdf
8.
Marie
,
N.
,
Marrel
,
A.
,
Seiler
,
J. M.
, and
Bertrand
,
F.
,
2016
, “
Physico-Statistical Approach to Assess the Core Damage Variability Due to a Total Instantaneous Blockage of SFR Fuel Sub-Assembly
,”
Nucl. Eng. Des.
,
297
, pp.
343
353
.10.1016/j.nucengdes.2015.07.012
9.
Droin
,
J.-B.
,
Marie
,
N.
,
Bachrata
,
A.
,
Bertrand
,
F.
,
Merle
,
E.
, and
Seiler
,
J.-M.
,
2017
, “
Physical Tool for Unprotected Loss of Flow Transient Simulations in a Sodium Fast Reactor
,”
Ann. Nucl. Energy
,
106
, pp.
195
210
.10.1016/j.anucene.2017.03.035
10.
Payot
,
F.
,
Serre
,
F.
, and
Suteau
,
C.
,
2017
, “
The SAIGA Experimental Program to Support the ASTRID Core Assessment in Severe Accident Conditions
,”
Proceeding of Fast Reactor Conference (FR17)
,
Yekaterinburg, Russia
,
June 26–29
, Paper No. IAEA-CN245-067.
11.
Philipponneau
,
Y.
,
1992
, “
Thermal Conductivity of (U,Pu)O2-x Mixed Oxide Fuel
,”
J. Nucl. Mater.
,
188
, pp.
194
197
.10.1016/0022-3115(92)90470-6
12.
Lamkin
,
D.
,
1974
, “
Analytical Stress Analysis Solution for a Simplified Model of a Reactor Fuel Element
,”
Ph.D. thesis
,
University of Arizona
,
Tucson, Arizona
. https://inis.iaea.org/search/search.aspx?orig_q=RN:7249287
13.
AFCEN,
2015
, “
Règles de Conception et de Construction Pour les Matériels Mécaniques des Structures à Hautes Températures et des Réacteurs Expérimentaux et à Fusion (RCC-MRx)
,” AFCEN, accessed Oct. 29,
2019
, http://afcen.com/fr/publications/rcc-mrx
14.
Cranga
,
M.
,
Struwe
,
D.
,
Pfrang
,
W.
,
Brear
,
D.
, and
Nonaka
,
N.
,
1990
, “
Transient Material Behaviour in CABRI-I Experiment Failure Under Fully and Semi-Restrained Fuel Pin Conditions
,”
Proceedings of the 1990 International Fast Reactor Safety Meeting, Snowbird, Utah
,
American Nuclear Society, La Grange Park, IL
, Vol.
l
, Aug., p.
421
.
15.
Haessler
,
M.
,
Struwe
,
D.
,
Butland
,
A. T. D.
,
Nonaka
,
N.
,
Sato
,
I.
, and
Papin
,
J.
,
1990
, “
The CABRI-II Programme—Overview on Results
,”
Proceedings of the 1990 International Fast Reactor Safety Meeting
,
Snowbird, Utah, American Nuclear Society, La Grange Park, IL
, Vol.
II
, Aug. 12–16, p.
209
.
16.
Fukano
,
Y.
,
Onoda
,
Y.
,
Sato
,
I.
, and
Charpenel
,
J.
,
2009
, “
Fuel Pin Behavior Under Slow Ramp-Type Transient-Overpower Conditions in the CABRI-FAST Experiments
,”
Proceedings of 13th International Topical Meeting on Nuclear Reactor Thermal Hydraulics
(
NURETH13
),
Kanazawa City, Ishikawa Prefecture, Japan
,
Sept. 27 to Oct. 2
. https://www.researchgate.net/publication/241719299_Fuel_Pin_Behavior_under_Slow-Ramp-type_Transient-Overpower_Conditions_in_the_CABRI-FAST_Experiments
17.
Sato
,
I.
,
Imke
,
U.
,
Pfrang
,
W.
, and
Berne
,
M.
,
1994
, “
Transient Fuel Pin Behaviour and Failure Conditions in CABRI-2 in-Pile Tests
,”
Proceedings of International Topical Meeting on Sodium Cooled Fast Reactor Safety
,
Obninsk, Russia
,
Oct. 3–7
, Vol.
2
, p.
134
.
18.
Papin
,
J.
,
2012
, “
Behavior of Fast Reactor Fuel During Transient and Accident Conditions
,”
Comprehensive Nuclear Materials
,
R.
Konings
, ed.,
Elsevier
,
Amsterdam
, Chap. 2.24.
19.
Manchon
,
X.
,
Bertrand
,
F.
,
Marie
,
N.
,
Lance
,
M.
, and
Schmitt
,
D.
,
2017
, “
Modeling and Analysis of Molten Fuel Vaporization and Expansion for a Sodium Fast Reactor Severe Accident
,”
Nucl. Eng. Des.
,
322
, pp.
522
535
.10.1016/j.nucengdes.2017.07.010
20.
Damblin
,
G.
,
Couplet
,
M.
, and
Iooss
,
B.
,
2013
, “
Numerical Studies of Space Filling Designs: Optimization of Latin Hypercube Samples and Subprojection Properties
,”
J. Simul.
,
7
(
4
), pp.
276
289
.10.1057/jos.2013.16
21.
Parzen
,
E.
,
1962
, “
On Estimation of a Probability Density Function and Mode
,”
Ann. Math. Stat.
,
33
(
3
), pp.
1065
1076
.10.1214/aoms/1177704472
22.
Nanty
,
S.
,
Helbert
,
C.
,
Marrel
,
A.
,
Pérot
,
N.
, and
Prieur
,
C.
,
2017
, “
Uncertainty Quantification for Functional Dependent Random Variables
,”
Comput. Stat.
,
32
(
2
), pp.
559
583
.10.1007/s00180-016-0676-0
23.
Hyndman
,
R. J.
, and
Shang
,
H. L.
,
2010
, “
Rainbow Plots, Bagplots, and Boxplots for Functional Data
,”
J. Comput. Graph. Stat.
,
19
(
1
), pp.
29
45
.10.1198/jcgs.2009.08158
24.
Saltelli
,
A.
,
Chan
,
K.
, and
Scott
,
E. M.
, eds., 2009,
Sensitivity Analysis
(Wiley Series in Probability and Statistics),
Wiley
,
Hoboken, NJ
.
25.
Gretton
,
G.
,
Bousquet
,
O.
,
Smola
,
A.
, and
Scholkopf
,
B.
,
2005
, “
Measuring Statistical Dependence With Hilbert–Schmidt Norms
,”
Proceedings Algorithmic Learning Theory
,
Springer-Verlag, Berlin
, pp.
63
77
.
26.
Iooss
,
B.
, and
Lemaître
,
P.
,
2015
, “
A Review on Global Sensitivity Analysis Methods
,”
Uncertainty Management in Simulation-Optimization of Complex Systems: Algorithms and Applications
, eds.,
Springer
,
Berlin
, pp.
101
122
.
27.
De Lozzo
,
M.
, and
Marrel
,
A.
,
2017
, “
Sensitivity Analysis With Dependence and Variance-Based Measures for Spatio-Temporal Numerical Simulators
,”
Stochastic Environ. Res. Risk Assess.
,
31
(
6
), pp.
1437
1453
.10.1007/s00477-016-1245-3
28.
Da Veiga
,
S.
,
2015
, “
Global Sensitivity Analysis With Dependence Measures
,”
J. Stat. Comput. Simul.
,
85
(
7
), pp.
1283
1305
.10.1080/00949655.2014.945932
29.
De Lozzo
,
M.
, and
Marrel
,
A.
,
2016
, “
New Improvements in the Use of Dependence Measures for Sensitivity Analysis and Screening
,”
J. Stat. Comput. Simul.
,
86
(
15
), pp.
3038
3058
.10.1080/00949655.2016.1149854
30.
Fallet-Fidry
,
G.
,
2012
, “
Contribution à la Modélisation et au Traitement de L'incertain Dans Les Analyses de Risques Multidisciplinaires de Systèmes Industriels: Application à la Source Froide D'une Unité de Production D'énergie
,”
Ph.D. report
,
Université de Lorraine
,
Nancy, France
.
31.
Der Kiuriegan
,
A.
,
2007
, “
Aleatory or Epistemic? Does It Matter?
,”
Special Workshop on Risk Acceptance and Risk Communication
,
Stanford University, Stanford, CA
,
Mar. 26–27
.
32.
Agosti
,
F.
, and
Luzzi
,
L.
,
2007
,
Heat Transfer Correlationsfor Liquid Metal Cooled Fast Reactors: Short Handbook-CESNEF-IN-05-2007, Department of Nuclear Engineering, Politecnico di Milano
,
Milano, Italy
, pp.
1
15
.
33.
Melis
,
J. C.
,
Roche
,
L.
,
Piron
,
J. P.
, and
Truffert
,
J.
,
1992
, “
GERMINAL—A Computer Code for Predicting Fuel Pin Behavior
,”
J. Nucl. Mater.
,
188
, pp.
303
307
.10.1016/0022-3115(92)90488-7
34.
Marrel
,
A.
,
Marie
,
N.
, and
De Lozzo
,
M.
,
2015
, “
Advanced Surrogate Model and Sensitivity Analysis Methods for SFR Accident Assessment
,”
Reliab. Eng. Syst. Saf.
,
138
, pp.
232
241
.10.1016/j.ress.2015.01.019
35.
Le logiciel PHYSURAC
,
1983
, “
Objectifs, Description et Validation, CEA, Rapport CEA-R-5200
,” accessed Oct. 29, 2019, http://www.iaea.org/inis/collection/NCLCollectionStore/_Public/15/001/15001924.pdf
36.
Zio
,
E.
, and
Di Maio
,
F.
,
2008
, “
Bootstrap and Order Statistics for Quantifying Thermal-Hydraulic Code Uncertainties in the Estimation of Safety Margins
,”
Sci. Technol. Nucl. Install.
,
2008
, p.
340164
.
37.
Efron
,
B
, and
Tibshirani
,
R. J.
,
1994
,
An Introduction to the Bootstrap
,
CRC Press
,
Chapman & Hall/CRC Monographs on Statistics and Applied Probability, Boca Raton, FL
.
38.
Hall
,
A. N.
,
1988
, “
Outline of a New Thermodynamic Model of Energetic Fuel-Coolant Interactions
,”
Nucl. Eng. Des.
,
109
(
3
), pp.
407
415
.10.1016/0029-5493(88)90286-5
39.
Natta
,
M.
,
Lauret
,
P.
, and
Moreau
,
J.
,
1993
, “
Accidents de Réactivité Pouvant Affecter Les Réacteurs Super-Phenix et EFR: Rapport CEA/DES/115
,” accessed Oct. 29, 2019, http://www.iaea.org/inis/collection/NCLCollectionStore/_Public/24/054/24054704.pdf
40.
Van Uffelen
,
P.
,
2006
, “
Modelling of Nuclear Fuel Behaviour
,” European Commission Directorate-General Joint Research Centre Institute for Transuranium Elements, Report No. EUR 22321 EN.
41.
Meynaoui
,
A.
,
Marrel
,
A.
, and
Laurent
,
B.
,
2019
, “
New Statistical Methodology for Second Level Global Sensitivity Analysis
,”
SIAM/ASA J. Uncertainty Quantif
.
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