Nuclear Safety
NEA/CSNI/R(2022)9
March 2024
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NEA Leak Rate Benchmark
Final ReportNEA/CSNI/R(2022)9  1
Nuclear Energy Agency

NEA/CSNI/R(2022)9
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12 March 2024

NUCLEAR ENERGY AGENCYCOMMITTEE ON THE SAFETY OF NUCLEAR INSTALLATIONSNEA Leak Rate Benchmark Final Report

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NEA LEAK RATE BENCHMARK FINAL REPORT
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COMMITTEE ON THE SAFETY OF NUCLEAR INSTALLATIONS (CSNI)The Committee on the Safety of Nuclear Installations (CSNI) addresses Nuclear Energy Agency (NEA)
programmes and activities that support maintaining and advancing the scientific and technical knowledge
base of the safety of nuclear installations.
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between organisations, which can contribute, from their respective backgrounds in research, development
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and safety R&D programmes of various sizes in order to keep all member countries involved in and abreastof developments in technical safety matters.
The Committee reviews the state of knowledge on important topics of nuclear safety science andtechniques and of safety assessments, and ensures that operating experience is appropriately accounted forin its activities. It initiates and conducts programmes identified by these reviews and assessments in order
to confirm safety, overcome discrepancies, develop improvements and reach consensus on technical issuesof common interest. It promotes the co-ordination of work in different member countries that serve tomaintain and enhance competence in nuclear safety matters, including the establishment of joint
undertakings (e.g. joint research and data projects), and assists in the feedback of the results to participatingorganisations. The Committee ensures that valuable end-products of the technical reviews and analyses areprovided to members in a timely manner, and made publicly available when appropriate, to support broader
nuclear safety.
The Committee focuses primarily on the safety aspects of existing power reactors, other nuclear
installations and new power reactors; it also considers the safety implications of scientific and technicaldevelopments of future reactor technologies and designs. Further, the scope for the Committee includes
human and organisational research activities and technical developments that affect nuclear safety.

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Acknowledgements
This collaborative project and its final report were enabled and improved by several
participants of the Nuclear Energy Agency (NEA) Committee on the Safety of Nuclear
Installations (CSNI) Working Group on Integrity and Ageing of Components andStructures (WGIAGE). The recommendations of Jürgen Sievers (Gesellschaft für Anlagenund Reaktorsicherheit [GRS]), Robert Tregoning (Nuclear Regulatory Commission[NRC]) and Klaus Germerdonk (Eidgenössisches Nuklearsicherheitsinspektorat [ENSI])
during the initiation and design of the benchmark are appreciated. Also, the support of the
WGIAGE metal subgroup, the main group and the NEA Secretariat are acknowledged.
Special thanks go to the Materials Testing Institute (MPA) of the University of Stuttgart
for sharing selected experimental results as benchmark analysis cases. The benchmark itself
was co-ordinated by Klaus Heckmann (GRS) and Fabian Silber (MPA).
The main benchmark participants who contributed their analyses and documented theirapproaches were P K Singh (Bhabha Atomic Research Centre [BARC]), Klaus Heckmann
and Jens Arndt (GRS), Sun Ye Kang ( Korea Electric Power Corporation Engineering andConstruction [KEPCO E&C]), Yong-Beum Kim and Yeji Kim (Korea Institute of Nuclear
Safety [KINS]), Peter Dillström (KIWA), Robert Tregoning and Jay Wallace (UnitedStates Nuclear Regulatory Commission [NRC]), Richard Bass and Paul Williams(Oakridge Consulting International [OCI]), Gaojun Mao and Markus Niffenegger (PaulSherrer Institute [PSI]), Xinjian Duan and Yifan Huang (SNC), Valdimir Krhounek andPavel Samohyl (ÚJV). Their efforts are gratefully appreciated.
Besides the co-ordinators, the present report was compiled and finalised by Jens Arndt andNicole Brückner (GRS).

Leading authors
Klaus HECKMANN

Gesellschaft für Anlagen- und Reaktorsicherheit,
Germany

Contributors
Robert TREGONING

Chair of the Metal Subgroup, WGIAGE

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Table of contents
List of abbreviations and acronyms ................................................................................................... 10
1. Introduction and background ........................................................................................................ 15
2. Leak rate assessment: compendium of methods ........................................................................... 16
2.1. Introduction................................................................................................................................. 16
2.2. Leak opening computation.......................................................................................................... 16
2.2.1. Ductile Fracture Handbook, GE/EPRI method or Zahoor method ...................................... 17
2.2.2. GE/EPRI elastic.................................................................................................................... 19
2.2.3. GRS-PB method ................................................................................................................... 19
2.2.4. LBB.ENG2 method .............................................................................................................. 19
2.2.5. Tada-Paris method................................................................................................................ 20
2.2.6. WRC method ........................................................................................................................ 21
2.2.7. xLPR COD module .............................................................................................................. 222.3. Leak morphology and flow resistance consideration .................................................................. 22
2.3.1. Inlet pressure loss ................................................................................................................. 22
2.3.2. Roughness and morphology parameters............................................................................... 22
2.3.3. Friction factor ....................................................................................................................... 23
2.3.4. Measurement of integral flow resistance.............................................................................. 24
2.4. Fluid mechanical modelling........................................................................................................ 25
2.4.1. Abdollahian-Chexal model................................................................................................... 25
2.4.2. ATHLET-CDR model .......................................................................................................... 26
2.4.3. Burnell model ....................................................................................................................... 27
2.4.4. Henry-Fauske model ............................................................................................................ 27
2.4.5. Metastable jet model ............................................................................................................ 29
2.4.6. Modified Bernoulli model or Zaloudek model..................................................................... 29
2.4.7. Pana model ........................................................................................................................... 30
2.5. Software ...................................................................................................................................... 30
2.5.1. ANSYS CFX ........................................................................................................................ 30
2.5.2. ExcelSQUIRT ...................................................................................................................... 31
2.5.3. LEAKH ................................................................................................................................ 32
2.5.4. LEAPOR .............................................................................................................................. 32
2.5.5. LOCI .................................................................................................................................... 33
2.5.6. PICEP and SI-PICEP ........................................................................................................... 34
2.5.7. SCALE ................................................................................................................................. 35
2.5.8. SQUIRT ............................................................................................................................... 35
2.5.9. WinLeck ............................................................................................................................... 35
2.6. Regulatory perspective................................................................................................................ 36
3. First benchmark phase.................................................................................................................... 37
3.1. Exercise set ................................................................................................................................. 37
3.1.1. Artificial slit ......................................................................................................................... 37
3.1.2. Fatigue crack ........................................................................................................................ 38
3.1.3. Real event ............................................................................................................................. 39
3.1.4. LBB sensitivity analysis ....................................................................................................... 40
3.2. Computation................................................................................................................................ 41
3.2.1. BARC ................................................................................................................................... 41
3.2.2. GRS ...................................................................................................................................... 41

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3.2.3. KEPCO E&C........................................................................................................................ 43
3.2.4. KINS .................................................................................................................................... 45
3.2.5. KIWA ................................................................................................................................... 47
3.2.6. NRC...................................................................................................................................... 50
3.2.7. OCI ....................................................................................................................................... 52
3.2.8. PSI ........................................................................................................................................ 59
3.2.9. SNC ...................................................................................................................................... 61
3.2.10. UJV .................................................................................................................................... 63
3.3. Comparison ................................................................................................................................. 65
3.3.1. Artificial slit ......................................................................................................................... 65
3.3.2. Fatigue crack ........................................................................................................................ 68
3.3.3. Real event ............................................................................................................................. 70
3.3.4. LBB sensitivity..................................................................................................................... 71
4. Second benchmark phase................................................................................................................ 75
4.1. Exercise set ................................................................................................................................. 75
4.1.1. Blind calculation of artificial slit .......................................................................................... 75
4.1.2. Blind calculation of fatigue crack ........................................................................................ 76
4.1.3. Blind calculation of real event analysis ................................................................................ 76
4.1.4. LBB sensitivity analysis ....................................................................................................... 77
4.1.5. Steam generator tube leak analysis ...................................................................................... 79
4.2. Computation................................................................................................................................ 79
4.2.1. BARC ................................................................................................................................... 80
4.2.2. GRS ...................................................................................................................................... 80
4.2.3. KINS .................................................................................................................................... 82
4.2.4. KIWA ................................................................................................................................... 84
4.2.5. NRC...................................................................................................................................... 88
4.2.6. OCI ....................................................................................................................................... 91
4.2.7. PSI ........................................................................................................................................ 92
4.2.8. SNC ...................................................................................................................................... 95
4.3. Comparison ................................................................................................................................. 97
4.3.1. Blind artificial slit case ......................................................................................................... 97
4.3.2. Blind fatigue crack case ....................................................................................................... 98
4.3.3. Blind real event case .......................................................................................................... 101
4.3.4. LBB sensitivity case ........................................................................................................... 103
4.3.5. Steam generator tube leak case .......................................................................................... 104
5. Conclusions and recommendations for further work ................................................................ 107
References .......................................................................................................................................... 109
Appendix ............................................................................................................................................ 112

List of tables
Table 2.1 Elastic coefficients for the GE/EPRI method, from [5].
Table 2.2 h2 values for 15.51 MPa pressure in combination with bending from [5]Table 2.3 Coefficients for the LBB.ENG2 method, from [7]Table 3.1 Phase 1 artificial slit specification
Table 3.2 Phase 1 artificial slit fluid conditions and measured leak rates
Table 3.3 Phase 1 fatigue crack specification
Table 3.4 Phase 1 fatigue crack fluid conditions and measured leak rates

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Table 3.5 Phase 1 real event case specification
Table 3.6 Phase 1 LBB sensitivity study pipe specification
Table 3.7 Phase 1 LBB sensitivity study leak specification
Table 3.8 GRS results of the artificial slit case
Table 3.9 GRS results of the fatigue crack
Table 3.10 GRS result of the real event analysis
Table 3.11 Result of the LBB sensitivity analysis
Table 3.12 Results of the artificial slit case calculated by KEPCO E&C
Table 3.13 Results of the fatigue crack calculated by KEPCO E&C
Table 3.14 Result of the real event analysis evaluated by KEPCO E&C
Table 3.15 Result of the LBB sensitivity analysis by KEPCO E&C
Table 3.16 Results of the artificial slit case calculated by KINS
Table 3.17 Results of the fatigue crack calculated by KINS
Table 3.18 Result of the real event analysis evaluated by KINS
Table 3.19 Result of the LBB sensitivity analysis by KINS
Table 3.20 KIWA results of the artificial slit case
Table 3.21 KIWA results of the fatigue crack
Table 3.22 NRC results of the artificial slit case
Table 3.23 NRC results of the fatigue crack
Table 3.24 NRC result of the real event analysis
Table 3.25 NRC result of the LBB sensitivity analysis
Table 3.26 Morphology parameters as a function of damage mechanism
Table 3.27 OCI results for the artificial slit case using LOCI™
Table 3.28 OCI results for the fatigue crack case using LOCI™
Table 3.29 OCI results for the real event case using LOCI™
Table 3.30 OCI results of the LBB sensitivity analysis
Table 3.31 PSI results of the artificial slit case
Table 3.32 PSI results of the fatigue crack
Table 3.33 PSI result of the real event analysis
Table 3.34 Result of the LBB sensitivity analysis
Table 3.35 SNC results of the artificial slit case
Table 3.36 SNC results of the fatigue crack
Table 3.37 SNC result of the real event analysis
Table 3.38 SNC result of the LBB sensitivity analysis
Table 3.39 ÚJV results of the artificial slit case
Table 3.40 ÚJV results of the fatigue crack
Table 3.41 ÚJV results of the real event analysis
Table 3.42 ÚJV results of the LBB sensitivity analysis
Table 4.1 Exercise sheet for the blind calculation of artificial slit
Table 4.2 Pressure and temperature variation of the blind artificial slit case
Table 4.3 Exercise sheet for the blind calculation of fatigue crack
Table 4.4 Pressure and temperature variation for the blind calculation of fatigue crack
Table 4.5 Exercise sheet for the blind calculation of real event
Table 4.6 Exercise sheet for the LBB sensitivity analysis
Table 4.7 Bending moment and resulting crack opening for the LBB sensitivity analysis
Table 4.8 Exercise sheet for the SGT analysis
Table 4.9 Pressure and temperature variation for the SGT analysis
Table 4.10 BARC results of the artificial slit case
Table 4.11 BARC results of the fatigue crack case
Table 4.12 GRS’ result of the LBB sensitivity analysis
Table 4.13 GRS’ result of the SGT analysis
Table 4.14 Results of the artificial slit case calculated by KINS
Table 4.15 Results of the fatigue crack estimated by KINS
Table 4.16 Result of the real event analysis calculated by KINS
Table 4.17 Result of the LBB sensitivity analysis estimated by KINS
Table 4.18 Result of the SGT analysis by KINS
Table 4.19 KIWA results of the artificial slit blind case
Table 4.20 KIWA results of the fatigue crack blind case
Table 4.21 KIWA’s results for the steam generator tube leak specimen
Table 4.22 NRC results for the blind artificial slit case

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Table 4.23 NRC results for the blind calculation of fatigue crack
Table 4.24 NRC exercise sheet for the blind calculation of real event
Table 4.25 NRC result of the LBB sensitivity analysis
Table 4.26 NRC result of the SGT analysis
Table 4.27 OCI results for blind artificial slit case
Table 4.28 OCI Results for blind fatigue crack case
Table 4.29 OCI Results for blind real event case
Table 4.30 OCI Results for blind LBB sensitivity case
Table 4.31 OCI results for blind SGT case
Table 4.32 PSI’ results of the blind artificial slit case
Table 4.33 PSI’ results of the blind fatigue crack
Table 4.34 PSI’ result of the real event analysis
Table 4.35 PSI’ result of the LBB sensitivity analysis
Table 4.36 PSI’ result of the SGT analysis
Table 4.37 SNC results of the blind artificial slit case
Table 4.38 SNC results of the blind fatigue crack
Table 4.39 SNC result of the real event analysis
Table 4.40 SNC result of the LBB sensitivity analysis
Table 4.41 SNC result of the SGT analysis

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List of figures
Figure 2.1 Geometrical characterisation of idealised cracks in cylindrical pipes
Figure 2.2 User Interface of LEAPOR-SA
Figure 2.3 User Interface for LOCI™ (under development)
Figure 2.4 Interface of the WinLeck code
Figure 3.1 KIWA results of the artificial slit case, sensitivity analysis using different COD
Figure 3.2 KIWA results of the real event analysis, sensitivity analysis using different global bending stresses
Figure 3.3 KIWA results of the LBB sensitive study, sensitivity analysis using different crack lengths
Figure 3.4 Artificial slit case LOCI™ solutions from Henry-Fauske and modified Bernoulli models.
Figure 3.5 Fatigue crack case solutions from the Henry-Fauske and modified Bernoulli models.
Figure 3.6 Transition model in LOCI™ – flow regime definitions.
Figure 3.7 Primary contributors to total pressure drop with local Rz = 114 m.
Figure 3.8 Primary contributors to total pressure drop with local Rz = 17 m
Figure 3.9 Left: Comparison of the calculated leak rates (coloured) with the reference (black). Right: The test conditionsin the pT-diagram of water.
Figure 3.10 Analysis results for the artificial slit with emphasis on the leak geometry.
Figure 3.11 Influence of friction modelling to the leak rate computation
Figure 3.12 Evaluation of flow models in the artificial slit exercise
Figure 3.13 Phase 1 fatigue crack result
Figure 3.14 Resistance classification for fatigue crack exercise
Figure 3.15 Flow model analysis for fatigue crack case
Figure 3.16 Phase 1 real event
Figure 3.17 Phase 1 real event: COD analysis by method
Figure 3.18 Phase 1 LBB Sensitivity study crack opening displacement as a function of full crack length
Figure 3.19 Friction factor as a function of the crack opening displacement
Figure 3.20 Mass flow rate as a function of crack opening displacement
Figure 4.1 KIWA results of the artificial slit blind case, with a sensitivity analysis using different local
roughness (1-22 m)
Figure 4.2 KIWA results of the fatigue crack blind case, with a sensitivity analysis using different local
roughness (1-40 m) and predefined data within ExcelSQUIRTFigure 4.3 KIWA results of the LBB sensitivity study, using elastic COD estimates
Figure 4.4 KIWA results of the LBB sensitivity study, using elastic-plastic COD estimates
Figure 4.5 KIWA’s results for the steam generator tube leak specimen
Figure 4.6 PSI result for bending moment and COD
Figure 4.7 Result comparison for the blind artificial slit case.
Figure 4.8 Comparison of flow model influence in the artificial slit case (blind contributions)Figure 4.9 Comparison of non-blind contributions for the artificial slit case
Figure 4.10 Result comparison of the blind fatigue crack case.

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NEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  9Figure 4.11 Characterisation of friction and pressure loss in the blind fatigue crack case
Figure 4.12 The blind fatigue crack case by applied flow model
Figure 4.13 Comparison of non-blind analyses of the fatigue crack
Figure 4.14 COD as a function of the full crack length in the blind real event case; the different choices of the effective
pipe radius (not indicated) are a reason for vertical scattering.
Figure 4.15 Leak rate as a function of the leak opening area
Figure 4.16 Result comparison of the blind real event case
Figure 4.17 Results comparison of non-blind analyses of the real event case
Figure 4.18 Result comparison for the LBB sensitivity case.
Figure 4.19 LBB sensitivity case by COD model
Figure 4.20 Result comparison for the steam generator tube leak case.
Figure 4.21 Steam generator tube leak case analysed by model.
Figure A.1 FSI test rig
Figure A.2 First benchmark phase artificial slit specimen (left) and fatigue crack specimen (right).
Figure A.3 Second benchmark phase specimens: Artificial slit (left), fatigue crack (centre), and a detail of the thin
specimen for steam generator tube leak testing (right).

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List of abbreviations and acronyms
AEA

Atomic Energy Authority (United Kingdom)

ASME

American Society of Mechanical Engineers

B&PV

Boiler and Pressure Vessel

BfE

Bundesamt für kerntechnische Entsorgungssicherheit (Federal
Office for the Safety of Nuclear Management, Germany)

BPVC

Boiler and Pressure Vessel CodeCAPS

CSNI Activity Proposal Sheet

CDR

Critical discharge rate

CF

Corrosion fatigue

CFD

Computational fluid dynamic

CFP

Crack face pressure

COA

Crack opening area

COD

Crack opening displacement

CPS

Computer program services

CSNI

Committee on the Safety of Nuclear Installations (NEA)

EPRI

Electric Power Research Institute (United States)

FEA

Finite Element Analysis

FSI

Fluid-structure-interaction

GUI

Graphical User Interface

HEM

Homogeneous equilibrium model

IAEA

International Atomic Energy Agency

ID

Inside diameter

IGSCC

Intergranular stress corrosion cracking

LBB

Leak-before-break

LEAPOR

Leak Analysis of Piping – Oak Ridge

MERIT

Maximizing Enhancements in Risk-Informed Technology

MW

Mid-wall

NEA

Nuclear Energy Agency

NRC

Nuclear Regulatory Commission (United States)

OD

Outside diameter

OECD

Organisation for Economic Co-operation and Development

ORNL

Oak Ridge National Laboratory (United States)

PWSCC

Primary water stress corrosion cracking
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QA

Quality assurance

SCALE

Slit and Crack Analysis for Leak Estimation

SIA

Structural Integrity Associates, Inc.

SQA

Software Quality Assurance

WGIAGE

Working Group on Integrity and Ageing of Components andStructures (NEA)WRC

Welding Research Council

xLPR

Extremely Low Probability of Rupture

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Executive summary
BackgroundIn the piping and components of nuclear power plants, degradation mechanisms may leadto wall-penetrating defects that may cause water to leak to the containment. One important
aspect of these leaks is that they offer an opportunity to rapidly detect the defects and takecountermeasures, which is part of the leak-before-break concept (LBB).
In assessing the consequences of a leak, it is important to estimate the mass flow rate
through a defect. This encouraged the development of models to predict and compute themass flow rates through leaks and also several experimental tests for the validation of thesemodels.
The activity presented in this report was approved by the Nuclear Energy Agency (NEA)
Committee on the Safety of Nuclear Installations (CSNI) in December 2018 (as recordedin the “Summary Record of the 64th Meeting of the Committee on the Safety of Nuclear
Installations” [NEA/SEN/SIN(2018)3] [not publicly available]). The benchmark was
conducted under the metal subgroup of the NEA Working Group on Integrity and Ageingof Components and Structures (WGIAGE). This report was approved by the CSNI on 30
May 2022 and prepared for publication by the NEA Secretariat.
Objective
The objective of this study is to compare leak rate computation practices and the applied
tools and software solutions. Leak rate prediction is an important aspect of the leak-beforebreak assessment, as assessing the detectability of leaks requires an appropriate
understanding of a fluid’s flow through wall-penetrating cracks. In this context, the defects
are postulated, and inevitable uncertainties concerning the exact geometric shape of defects
are present. Therefore, the attainable accuracy of a leak rate prediction is fundamentally
limited, so that complex three-dimensional numerical fluid simulations for leak flow are
rare, and one-dimensional simulations are primarily used. However, the determination of
the geometric shape and the influence of the surface morphology are also important aspectsof the leak rate computation.
Work performed
Participants from ten organisations representing eight countries contributed analysis results
to this comparative benchmark study. The participants described their individual
approaches, applied tools, underlying methods and input data settings. The reporting ofintermediate results within the analysis, if applicable and available, supported theinterpretation and discussion of the results comparison. Besides the mass flow rate, thecrack opening displacement was also determined for specific tasks.
Besides the actual cases, the analysis documentation and the comparison, this report also
contains a compendium of methods. This compendium summarises the individual
approaches for leak opening, morphology and flow resistance, and the fluid mechanicalmodelling, which are combined by the different participants in modular ways to predictleak flow rates. The compendium shows the conceptual differences in the different
approaches and demonstrates that there is a variety of approaches that can be combined indifferent ways. The detailed descriptions of the individual model ingredients allow for an
efficient comparison of the participants’ approaches in the analysis cases.
The benchmark comprises two phases. The first phase involved open computation, i.e. themeasured leak rates were communicated to the participants together with the actual leaksetup. This initial phase made possible a common understanding of case descriptions and

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analysis requirements in order to avoid misinterpretations and unclear specifications. The
second phase involved blind analysis cases, cases where the measured leak rate value was
not communicated to the participants. In the comparison of open and blind analysis cases,
the obtained accuracy was similar.
Both phases started with the analysis of specimen tests measured at the Materials Testing
Institute at the University of Stuttgart, Germany. In these laboratory tests, the flow rate ofwater under different stagnation conditions through artificial slits and fatigue cracks wasmeasured.
Results and their significanceThe analysis results show that the individual approaches can accurately predict the flow
through these specimens, even for the blind analysis cases. Moreover, the methodologicalsurvey made it possible to group the results by assumptions concerning morphology/flow
resistance and the applied flow model, which shows that participants applying similar
models with different implementations obtain the same results.
Following a recommendation of the WGIAGE metal subgroup, the benchmark study also
proposed one open and one blind analysis of an actual leak incident in an operating nuclear
power plant. The analysis of these incidents confirmed that the uncertainties in a real leakcase are much larger than in a laboratory test with controlled conditions, and it was
expected that the assessment would give an estimate of a range of plausible values. In fact,
the guesses and estimates by the participants in the leak assessment were consistent, andthe estimated range of possible flow rates through a leak was in accordance with thenecessary assumptions. It was found that the reported leak rate of one case could not be
explained by the leak finding and the operational conditions, as all computational
assessments underpredicted the reported leak rate. While being conservative with respect
to the leak-before-break assessment, this finding shows that the validation of leak rateassessment methods with real leak incidents should be considered more intensively in the
future in order to check if this is a singular finding and to assess the suitability of leak ratecomputation approaches for leaks in actual operating plants.
The parallel leak-before-break (LBB) benchmark study motivated the investigation of
specific cases related to the LBB assessment and allowed a study of the details of leak ratecomputations for exercises from the LBB benchmark. The two sensitivity studies involved
investigating specific assumptions in the leak rate computation and the influence of thedifferent model approaches.
As an additional analysis case, a thin laboratory specimen inspired by steam generator tube
leaks was also included in the analysis. This made it possible to assess also the suitabilityof different methods for the computation of leak flow through thin-walled specimens.
Conclusions and recommendations: the lessons learnt from the benchmark• Leak rate tests under controlled conditions can be reproduced well by the available
methods and tools. Differences between the computations and the measurements,
as well as differences between different approaches, are satisfyingly small.
• Uncertainties in a real leak case are much larger than in a laboratory test with
controlled conditions. Validation of leak rate assessment methods with real leakincidents should be considered more intensively in the future.
• The approach of documenting the individual models and tools showed that the leakrate computation can be a transparent combination of assumptions andcomputational models, instead of being a result of black box-like software.
Finally, it should be stated that the benchmark profited from the parallel activities of the
LBB benchmark and the probabilistic fracture mechanics benchmark. In both activities,
NEA LEAK RATE BENCHMARK FINAL REPORT14  NEA/CSNI/R(2022)9
leak rate assessment is a part of the analysis, and the present methodological survey andcomparison helps with the interpretation of submitted results in the two adjoining activities.

NEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  15

1. Introduction and backgroundIn the piping and components of nuclear power plants, degradation mechanisms may leadto wall-penetrating defects that cause a loss of the medium – in many cases it is coolingwater leaking to the containment. These leaks are key events because they offer theopportunity to rapidly detect the defect and take countermeasures, which is a part of theleak-before-break concept (LBB). However, leaks are of course also a source of concern
with respect to the loss of coolant from the coolant loop and with respect to damage to theexterior side, such as internal flooding, jet damage and pipe whip, and radiation release.
To assess the consequences of a leak, it is important to estimate the mass flow rate througha defect. This leak rate computation is a key part of the discussion of the aforementioned
scenarios, and the result of this computation has an impact on the assessment of the safety
relevance. This motivated the development of models to predict and compute the mass flow
rates through leaks, as well as experimental tests for the validation of these models. Also,
software products have emerged which facilitate the computation.
Due to the increasing importance of the LBB approach, the reliability of leak rateassessments is a key topic. This motivated the CSNI to address once again the question ofleak rate computation practices, after a similar benchmark study in the 1990s focused on
LBB concepts, and as another benchmark study on probabilistic fracture mechanics was
about to start. In 2019, the metals subgroup of the Working Group on Integrity and Ageingof Components and Structures (WGIAGE) discussed a CSNI Activity Proposal Sheet(CAPS) on leak rate computation. While the activity is based on laboratory tests at the
University of Stuttgart, the metals subgroup members commented on the CAPS, which led
to an extension of the scope of the work.
This report is organised as follows. In Chapter 2, a compendium of methods summarises
all the approaches that have been applied to the leak rate benchmark problems. The twophases of the benchmark are presented in Chapters 3 and 4; both show the exercise set, thecomputation documentation and the result synopsis in consecutive subsections. The reportconcludes with Chapter 5, which contains recommendations for future work.

NEA LEAK RATE BENCHMARK FINAL REPORT16  NEA/CSNI/R(2022)9

2. Leak rate assessment: compendium of methods

2.1. Introduction
For the computation of leak flow rates, different aspects have to be considered that
influence the final assessment. According to the investigation [1], these aspects can besorted into three categories:
a. the cross section of the leakb. the consideration of the morphology of the leak and the resulting fluid-dynamical
resistancec. the fluid motion together with the evaporation.
In each of these aspects, different approaches can be used for computation, which gives
rise to a potentially high number of model combinations. This chapter is intended to providea reference for the different models and assumptions applied within this benchmark. This
short presentation is given in Sections 2.2, 2.3, and 2.4 for the leak opening, the flow
resistance, and the fluid modelling, respectively. In Section 2.5, the software tools applied
within this benchmark activity are presented. Section 2.6 is dedicated to regulatory aspectsof specific models in codes and standards.

2.2. Leak opening computation
This part of the compendium gives a comprehensive summary of the methods applied by
the different participants. The survey aims to present all approaches in a unified
nomenclature. Crack opening displacement (COD) computations are required in thebenchmark for through-thickness cracks in cylindrical pipes; the relevant geometricalproperties for the characterisation are shown in Figure 2.1.

Figure 2.1. Geometrical characterisation of idealised cracks in cylindrical pipes

The computation involves the crack opening stresses, which give rise to a finite crosssection area A enabling a leakage flow. The typical situations are interior pressure p and,for circumferential cracks, bending moment 𝑀. The nominal stresses (in absence of a crack
and in the limit of 𝑡 ≪ 𝑟𝑚 ) in these situations can be derived analytically.
NEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  17

𝑟𝑖2
𝑀
𝑟𝑚
𝑀
𝜎𝑎 = 22 𝑝 + 𝐽 𝑟𝑒 cos 𝜑 ≈ 2𝑡 𝑝 + 𝐽 𝑟𝑒 cos 𝜑𝑟𝑒 − 𝑟𝑖𝑧𝑧(1)

The moment of inertia is defined as 𝐽𝑧 = (𝑟𝑒4 − 𝑟𝑖4 )𝜋/4), and 𝜑 is the angle measured fromthe maximal bending. As the crack opening stresses act perpendicular to the orientation,
the axial stresses 𝜎𝑎 are relevant for circumferential cracks, while the circumferential
stresses 𝜎𝑐 are relevant for axial cracks.
𝑟𝑖2𝑟𝑚
𝜎𝑐 = 2 2
2𝑝 ≈ 𝑡 𝑝𝑟𝑒 − 𝑟𝑖(2)

From these formulas, it is clear that the membrane stress acting on the crack faces is amultiple of the interior pressure. In case of leak flow, the space within the crack faces isalso filled with pressurised fluids, thus a crack face pressure should be considered.
However, the pressure is decreasing along the radial co-ordinate, typically between fullpressure and saturation pressure for critical two-phase flow (see also Section 2.4.6), or
between full pressure and ambient pressure for subcritical flow (less relevant for nuclear
application).
Common characteristics of the pipe material are the elastic modulus 𝐸, the Poisson number
𝜈, the yield stress 𝜎𝑦 , and the ultimate stress 𝜎𝑢 . The parametrisation of the stress-strain
curve with a Ramberg-Osgood formula is also useful.
𝜖(𝜎) = 𝜖0 [𝜎𝜎 𝑛+𝛼 ( ) ]
𝜎0
𝜎0

(3)

The determination of the cross section 𝐴 (also called crack opening area [COA]) is astandard fracture mechanical problem which computes the displacements of the crack faces
under consideration of material properties, loads and crack tip effects. The state of the art
for this task is the use of elastic-plastic Finite Element Analysis (FEA), which can lead tothe most accurate results. However, a number of analytical formulations for COA and COD
have been proposed for standard situations. The methods applied in the benchmark are
discussed in the following subsections.

2.2.1. Ductile Fracture Handbook, GE/EPRI method or Zahoor method
The GE/EPRI method for COD computation is based on references [2] and [3]. It is anapproximative elastic-plastic approach for materials obeying a Ramberg-Osgood stressstrain behaviour. The COD can be written as the sum of an elastic and a plastic part.
𝐶𝑂𝐷 = 𝐶𝑂𝐷𝑒𝑙 + 𝐶𝑂𝐷𝑝𝑙(4)

The elastic crack opening is computed by the 𝑉1 function and the elastic material properties,
together with the geometrical properties. For pure pressure loads (interior pressure 𝑝), theelastic contribution reads as follows.
𝐶𝑂𝐷𝑒𝑙 =NEA LEAK RATE BENCHMARK FINAL REPORT

2𝑎𝛾 𝑟𝑚 𝑝𝑉1 ( , )
𝜋𝑟𝑡
𝜋 𝑡 𝐸

(5)

18  NEA/CSNI/R(2022)9
The elastic part for pure bending loads (bending moment 𝑀) uses the same 𝑉1 function andalso the moment of intertia 𝐼.
𝐶𝑂𝐷𝑒𝑙 =

4𝑎𝑟
𝛾 𝑟𝑚 𝑀
𝑉1 ( , )
𝐼
𝜋 𝑡 𝐸

(6)

The 𝑉1 function depends on the ratio of pipe radius to wall thickness, and the angle of thecrack γ/π just gives the fraction of the crack on the full circumference. The 𝑉1 value iscomputed by FEA; the values from [5] are summarised in Table 2.1.

Table 2.1. Elastic coefficients for the GE/EPRI method, from [5].
𝛾/𝜋

𝑟𝑚 /𝑡

1/16
1/8
1/4
1/2

5

10

20

1.234
1.388
2.008
5.331

1.206
1.480
2.379
7.165

1.111
1.482
3.079
11.585The plastic part is available either for pressure or for bending – while the linear-elastic
solutions for separate loads can be superposed, this is not possible in the strict sense by thebasic GE/EPRI method as proposed in [3]. The plastic part due to pressure p is based on
the ℎ2 function.
𝑎𝑟 𝑝 𝑛
𝐶𝑂𝐷𝑝𝑙 = 𝛼 𝜖0 ℎ2 ( , 𝑛, ) ( )
𝑏
𝑡 𝑝0

(7)

The plastic part in presence of a bending moment 𝑀 is similar, with another ℎ2 function
for this load case.
𝑎𝑟 𝑀 𝑛
𝐶𝑂𝐷𝑝𝑙 = 𝛼 𝜖0 ℎ2 ( , 𝑛, ) ( )
𝑏
𝑡 𝑀0

(8)

An extension of the method is the consideration of a ℎ2 -function for combined pressure
and bending load – while the linear terms can be superposed, the plastic COD for combined
loading requires its own ℎ2 function.[5] proposes to consider a constant PWR-like pressure
and compute the plastic COD with a ℎ2 function for variable bending in the presence of
this pressure. The ℎ2 -coefficients for this load are summarised in Table 2.2.

Table 2.2. h2 values for 15.51 MPa pressure in combination with bending from [5]
1/16
1/8

𝛾/𝜋
5
5

𝑟𝑚 /𝑡
6.851
6.182

𝑛=2
7.115
5.918

𝑛=3
7.232
5.312

𝑛=3
6.979
4.766

𝑛=7

𝑛 = 10
6.153
3.580

1/16
1/8
1/16
1/8

10
10
20
20

6.973
6.888
7.561
8.375

7.460
6.868
8.292
8.705

8.108
6.844
10.92410.3838.923
6.181
14.07812.4799.009
6.578
15.81313.051

An extension to axial through-wall cracks under pressure loads is proposed in [37], wherean adjusted 𝑉- and ℎ2 -function is derived.

NEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  19

2.2.2. GE/EPRI elastic
This method is based on [2] and [3] as described in Section 2.2.1. It can also be used byskipping the plastic part of the model, thus by only considering equations (5) and (6). Since
this approach does not require the numerical tables of the full GE/EPRI method, it istechnically much simpler. However, its validity is restricted to smaller loadings.

2.2.3. GRS-PB method
The GRS-PB method [4] is a generalisation of the Wüthrich assessment [6] which allows
computing the COA under combined membrane stress and bending loads. It is constructed
as an underestimating approach for the conservative underestimation of the leak area in an
LBB assessment. It is based on the elastic opening area of a crack in a plate under a stress𝜎.
𝐴elastic
plate = 2 𝜋

𝜎 2
𝑐
𝐸′

(9)

In this equation, E' is the modulus of elasticity E for plane stress state, and 𝐸/(1 − 𝜈 2 ) for
plane strain. The bulging function 𝛼(𝜆) is used to map the solution to a cylindrical structure.
4

𝛼 (𝜆𝑠 =

√12(1 − 𝜈 2 )𝑐√𝑟𝑚 𝑡

1 + 0.1𝜆𝑠 + 0.16 𝜆2𝑠)= {√1 + 0.177𝜆2𝑠

axial crack
circumferential(10)

The shell parameter 𝜆𝑠 is a dimension-less quantity depending on the geometry of the pipe
and the crack. The idea of the GRS-PB approach to modify this formulation by Wüthrich
is to replace the stress 𝜎 with an equivalent of the bending stress.
𝐴GRS-PB = 𝛼(𝜆𝑠 ) {2𝜋𝜎𝑝 𝑐 2 𝑀𝜋
𝑐4
𝑐6
𝑐8
2
+
[2𝑟𝑐
−
+
−
]}
𝐸′
𝐽𝑧 𝐸 ′
4𝑟 96𝑟 3 4608𝑟 5(11)This method proposed to avoid an overestimation of the bending stress, which would beagainst the underestimating philosophy of conservative leak rate computation within LBB
assessment.

2.2.4. LBB.ENG2 method
The LBB.ENG2 method [5] considers elastic-plastic material properties and a combinationof pressure load with a bending moment. It shares the elastic COD with the GE/EPRI
approach (see Section 2.2.1), but the plastic COD is computed differently (while also
relying on the Ramberg-Osgood plasticity description). Approach [7] is applied in thefollowing.

𝐶𝑂𝐷𝑝𝑙 =𝜎 𝑛−1
𝛼𝜖0 ( 𝜎𝑇 )𝛾
+ 𝑟𝑚 (1 + sin ) 𝜙𝑝𝑙
𝛾 2
sin 𝛾
2
1 − 𝜋 − 𝜋 sin−1 20

In this formulation, 𝜙𝑝𝑙 is the plastic rotation in the presence of a crack.

NEA LEAK RATE BENCHMARK FINAL REPORT(12)20  NEA/CSNI/R(2022)9𝑛−1

𝜙𝑝𝑙 = [𝜋]𝛾
4 cos 2 − 2 sin 𝛾2+𝑛 𝑛𝑛2√𝜋 Γ ( 2 ) 𝛼 𝐼𝐵 (𝛾)
𝑀
(
)
(
)
3+𝑛
𝐸𝜎0𝑛−1 𝜋𝑟𝑚2 𝑡
4 Γ( 2 )(13)

The integral 𝐼𝐵 can be computed analytically with the scheme of [7], Appendix A.
3

𝛾 2
𝛾 3
𝐼𝐵 (𝛾) = 2 𝛾 [1 + 8 ( ) 𝐼𝐵1 + ( ) (𝐼𝐵2 + 𝐼𝐵3 )]
𝜋
𝜋
2

(14)

With six additional auxiliary quantities AB, BB, CB, IB1, IB2 and IB3, the rotation can becomputed explicitly.
𝑟
𝑡

𝑗

𝑟

𝑗

𝑟
𝑡

𝑗

𝐴𝐵

=

∑3𝑗=0 𝑎𝐵,𝑗 ( 𝑚 )𝐵𝐵=∑3𝑗=0 𝑏𝐵,𝑗 ( 𝑚 )
𝑡

𝐶𝐵

=

∑3𝑗=0 𝑐𝐵,𝑗 ( 𝑚 )𝐼𝐵1=

𝐴𝐵 𝐵𝐵 𝛾 𝐶𝐵 𝛾 2
+
+
( )
7
9 𝜋 11 𝜋

𝐼𝐵2

=

2 𝐴2𝐵
2𝐴 𝐵 𝛾
4𝐴 𝐶 +2𝐵2 𝛾 2+ 3𝐵 𝐵 𝜋 + 𝐵 𝐵7 𝐵 (𝜋)
5

𝐼𝐵3

=

𝐵𝐵 𝐶𝐵 𝛾 3
2𝐶𝐵2 𝛾 4
(
)
+
(𝜋)
2
𝜋
9

(15)

The numerical values of the polynomial coefficients of AB, BB and CB in this approach aresummarised in Table 2.3.

Table 2.3. Coefficients for the LBB.ENG2 method, from [7]
𝑗
𝑎𝐵,𝑗
𝑏𝐵,𝑗
𝑐𝐵,𝑗

0
-3.26543
11.36322-3.18609

1
1.52784-3.91412
3.847632-0.072698
0.18619-0.18304

30.0016011-0.004099
0.00403

This formulation of the LBB.ENG2 method (note that 𝐼𝐵 differs in [5]) is a closed form forthe combination of pressure and bending loads for Ramberg-Osgood plasticity.

2.2.5. Tada-Paris method
The Tada-Paris method [8] allows computing the COD under pressure load. The computed
areas are purely elastic.
𝐴 =2𝜋𝑟𝑚 𝑡 𝜎𝑐
𝐺 (𝜆 𝑇𝑃 =
)
′
𝐸
√𝑟𝑚 𝑡

(16)

NEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  21

For circumferential cracks, the stress is obtained by 𝜎 circ = 𝑝𝑟𝑚 /(2𝑡), and the function
𝐺(𝜆 𝑇𝑃 ) is computed as follows.
𝐺 circ (𝜆𝑇𝑃 ) = {𝜆2𝑇𝑃 + 0.16 𝜆4𝑇𝑃
0.02 + 0.81 𝜆2𝑇𝑃 + 0.3 𝜆3𝑇𝑃 + 0.03 𝜆4𝑇𝑃

0 < 𝜆 𝑇𝑃 ≤ 1
1 ≤ 𝜆 𝑇𝑃 ≤ 5(17)

For axial cracks the stress is 𝜎 axial = 2 𝜎 circ, and the 𝐺-function is defined as follows.

𝐺 axial (𝜆𝑇𝑃 ) = {𝜆2𝑇𝑃 + 0.625 𝜆4𝑇𝑃
0.14 + 0.36 𝜆2𝑇𝑃 + 0.72 𝜆3𝑇𝑃 + 0.405 𝜆4𝑇𝑃

0 < 𝜆 𝑇𝑃 ≤ 1
1 ≤ 𝜆 𝑇𝑃 ≤ 5(18)

Note that the formulas of the stresses can be generalised as shown in equation (2).

2.2.6. WRC method
The method proposed by the Welding Research Council (WRC) [9] for computing starts
also from a crack in an infinite plate under homogeneous load and corrections. The COA
is given as follows.
ID/OD 𝑟𝑖

𝐴ID/OD = 𝐴elastic
plate [∑ 𝜎𝑖 𝐻𝑖𝑖( , 𝜆𝑠 )] 𝛾(𝐿𝑟 )𝑡(19)

The elastic plate solution under uniaxial load is similar to equation (9), but the uncorrected
elastic modulus 𝐸 is used instead of 𝐸′.
𝐴elastic
plate = 2 𝜋

𝜎 2
𝑐
𝐸

(20)

The solution is mapped to a pipe by multiplying it with a 𝐻-function. This 𝐻-function
depends on the actual load, the 𝑟𝑖 /𝑡-ratio, and the shell parameter 𝜆. This approach also
allows to give separate 𝐻-functions for the inner and outer side (ID/OD) of the pipe wall.
For circumferential cracks, tables of 𝐻 are given in [9] for three loads (constant load, linear
stress variation through the wall, and bending moment), for seven 𝑟𝑖 /𝑡-ratios, nine 𝜆𝑠 values, and for the inner and outer side. For axial cracks, the load states are constant load,
linear stress variation and bending moment.
The last term is the plastic correction factor, which corrects the elastic approach and also
considers biaxiality effects.
𝛾(𝐿𝑟 ) = 1.008 − 0.33015 𝐿2𝑟 + 5.53696 𝐿4𝑟 − 3.96974 𝐿6𝑟 + 2.00844 𝐿8𝑟(21)

The load ratio 𝐿𝑟 is computed by consideration of the biaxiality influence factor and thematerial’s yield stress 𝜎𝑌 .
𝐿𝑟 = 𝐹 (𝐵 =NEA LEAK RATE BENCHMARK FINAL REPORT

𝜎∥ 𝜎⊥
)
𝜎⊥ 𝜎𝑌

(22)

22  NEA/CSNI/R(2022)9
The symbol 𝜎⊥ denotes the stress component perpendicular to the crack face, i.e. the crack
opening stress, and 𝜎∥ the orthogonal stress tensor component. 𝐹(𝐵) is given for values of
𝐵 between 0 and 2 in [9].

2.2.7. xLPR COD module
The circumferential crack xLPR COD module that provides elastic-plastic COD solutions
is based on [23] and [24] for use in the Extremely Low Probability of Rupture (xLPR)
programme [34]. It provides elastic-plastic COD solutions for circumferential cracks for
simultaneously applied axial and crack face pressure with an applied bending moment. The
axial crack COD module is based on [36] and [37].

2.3. Leak morphology and flow resistance consideration
Classically, the leak morphology (surface structure characteristics) is considered to enter
the leak computation via flow resistance. According to custom surface characterisation
approaches, the flow resistance has several contributions: form loss associated with theentrance into the leak channel, frictional pressure losses due to flow along the rough crack
faces, as well as pressure losses due to bends in the flow path and effects of cross sectionchanges. A total flow resistance can be defined as the sum of the individual parts.
𝜁total = 𝜁in + 𝜁friction + 𝜁bends + 𝜁cross-section(23)

Since many leak flow models (see Section 2.4) are unidimensional and have origins in pipe
flow, the concepts are very similar to engineering approaches for piping system analysis.

2.3.1. Inlet pressure loss
The entrance resistance 𝜁in is associated with form pressure loss at the entrance into theleak. This is related to the flow along the more or less sharp edge and the reduction of theeffective cross section via the contraction of the flow (vena contracta). Anothercharacterisation of this is the discharge coefficient 𝑐𝑑 , which is the cross section fraction
relative to the full leak cross section. Based on incompressible flow, 𝜁in and 𝑐𝑑 are often
related to each other as follows.
𝜁in =

1
−1
𝑐𝑑2

(24)

For crack-like leaks, the value of the discharge coefficient typically ranges from 0.62 to
0.95 [11]; a value of 𝜁𝑖𝑛 = 0.5 is also a common choice [10][20].

2.3.2. Roughness and morphology parameters
The surface of a crack-like leak created by a damage mechanism is irregular and rough,while the roughness of a known leak geometry can be measured (the roughness parameter
𝑅𝑧 is often used).
When the COD is varying, the irregularities in the crack faces can either play a role asbendings in the flow path, or as surface roughness. This feature is considered by the
improved morphology model [14]. This approach defines global values of roughness, andNEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  23

if the two crack faces are close enough to each other, this global roughness plays the roleof bendings, while the local roughness is the effective surface roughness 𝜇eff .
𝐶𝑂𝐷
< 0.1
𝜇𝐺
𝜇𝐺 − 𝜇𝐿 𝐶𝑂𝐷
𝐶𝑂𝐷(− 0.1) 0.1 << 10
𝜇eff = 𝜇𝐿 +
9.9
𝜇𝐺
𝜇𝐺
𝐶𝑂𝐷
𝜇𝐺
> 10
{
𝜇𝐺
𝜇𝐿

(25)

The number of turns is computed analogously as an effective number 𝑛𝑒𝑓𝑓 depending on
the COD, a local number 𝑛𝐿 and a global number 𝑛𝐺 .
𝐶𝑂𝐷
< 0.1
𝜇𝐺
𝑛𝐿 𝐶𝑂𝐷
𝐶𝑂𝐷− 0.1) 0.1 << 10𝑛eff = 𝑛𝐿 − (
11 𝜇𝐺
𝜇𝐺
𝐶𝑂𝐷
0.1 𝑛𝐿
> 10
{
𝜇𝐺
𝑛𝐿

(26)

As cracks found in service are usually not ideally straight, a correction parameter 𝐾
characterising the actual leak flow path divided by the pipe wall thickness is introduced.
𝐶𝑂𝐷
< 0.1
𝜇𝐺
𝐾𝐺+𝐿 − 𝐾𝐺 𝐶𝑂𝐷
𝐶𝑂𝐷(− 0.1) 0.1 << 10
𝐾eff = 𝐾𝐺+𝐿 −
9.9
𝜇𝐺
𝜇𝐺
𝐶𝑂𝐷
𝐾𝐺
> 10
{
𝜇𝐺
𝐾𝐺+𝐿

(27)

The morphology parameters 𝜇𝐿 , 𝜇𝐺 , 𝑛𝐿 , 𝐾𝐺+𝐿 and 𝐾𝐺 are specific to a damage mechanism,
and recommendations for specific parameters exist.

2.3.3. Friction factor
The frictional pressure loss is an important part for many applications, and also this origin
dates back to the analysis of rough pipes. The frictional resistance is proportional to thelength of the leak channel 𝐿 = 𝐾𝑒𝑓𝑓 𝑡, with the Darcy-Weissbach friction factor 𝜆.
𝜆, 𝑑ℎ 𝜆𝐿
𝜆(𝑧)
𝑑𝑧 =
𝑑
0 𝑑ℎ (𝑧)𝑐𝑜𝑛𝑠𝑡. ℎ𝐿𝜁frcition = ∫(28)

The ratio 𝐿/𝑑ℎ is the hydraulic relative length of the leak, where 𝐿 is just the wall thickness
in the simplest case.

Nikuradse
The classical relation for 𝜆 was derived for sand-rough pipes in the form of the Nikuradse
friction relation [16].

NEA LEAK RATE BENCHMARK FINAL REPORT24  NEA/CSNI/R(2022)9

𝜆 = [ 3.39 log10 (2−2𝑑ℎ) − 0.866 ]
2 𝑅𝑧

(29)

The Darcy-Weissbach friction factor 𝜆 depends in this model on the roughness 𝑅𝑧 = 𝜇eff ,a natural generalisation of the parameter 𝑘 of sand grain sizes in the analysis of rough pipes.

John et al.
The approach for the relation between the friction factor and the surface roughness of theflow channel proposed by [10] is based on the evaluation of laboratory tests with rough slit
samples and fatigue cracks.
−2𝑑ℎ
𝜆 = [ 2 log10 () + 1.74 ]
2 𝑅𝑧

(30)

This friction relation has a steeper increase of the friction factor in the regime of narrowcracks than the Nikuradse Karman friction factor – note that it diverges for very narrowcracks, which in turn leads to an infinite flow resistance.

Paul et al.
The approach proposed in [11] uses the formula of John et al. [10] for narrow slits, and the
Nikuradse relation for wider slits.
𝜆Nikuradse
𝜆=
{

𝜆John

𝑑ℎ
≥ 50
2 𝑅𝑧
𝑑ℎ
if
< 50
2 𝑅𝑧
if

(31)

This considers the fact that John et al. focused on narrow, rough slits, and their relation isless accurate for wide smooth geometries, where the classical results from pipe flow are
more representative. Instead of an inverse relative roughness value 𝑑ℎ /2𝑅𝑧 of 50 as theborder between the two definitions, a value of 55.48 might also be imposed.

KTA 3206
The safety standard KTA 3206 [20] is guided by the philosophy of a conservative
underestimation of the leakage rate. One key element of this approach is the conservative
overestimation of the friction factor. The safety standard proposes its own friction factor
relation for this purpose.
1
3 𝑑ℎ −2𝜆 = min (2, [log10 ()] )2
2 2 𝑅𝑧(32)This relation is valid for 𝑑ℎ /2𝑅𝑧 > 1. In contrast to the other friction factor relations, it is
not a best-estimate approach, but can be used for the underprediction of the leak rate.

2.3.4. Measurement of integral flow resistanceInstead of deriving the friction factor of a laboratory test from the roughness by an empirical
relation, it is also possible to measure the single-phase flow resistance. This measured flow
resistance value can be assumed in the two-phase flow computations as well. Of course,
NEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  25

this procedure is restricted to the laboratory tests where the flow resistance was measured.
According to the Bernoulli equation for an incompressible fluid of density 𝜌, the flow
resistance 𝜁 of a leak is related to the mass flow rate 𝑚 at a defined pressure drop Δ𝑝.
𝜁 = 2 𝜌 Δ𝑝

𝐶𝑂𝐴2
−1
𝑚̇2

(33)

COA denotes the cross section of the leak. The use of the single-phase flow resistance for
two-phase leak flow is a way to reduce uncertainties in the leak assessment for laboratory
tests.

2.4. Fluid mechanical modelling
After the determination of the leak geometry and the characterisation of the resistance dueto the morphology, the fluid mechanical analysis is required to predict the mass flowrate 𝑚. For single-phase incompressible fluid flow (such as cold water, in good
approximation), the flow rate through a cross section 𝐴 can be computed using the
Bernoulli equation.
2𝜌(𝑝0 − 𝑝𝑒𝑥𝑡 )𝑚̇ = 𝐴 √1+𝜁

(34)

In this study, some of the fluid tests are in this regime, but others (and possibly the most
relevant) have hot pressurised water in the stagnation volume, where evaporation would
occur. This violates the assumption of single-phase incompressible fluid and gives rise to
the more complex models discussed in the following subsections.
These models are defined with a common nomenclature, where the mass density is denotedas 𝜌, the specific enthalpy is denoted as ℎ, the specific volume as 𝑣 = 1/𝜌, and the specificentropy as 𝑠. The indices (like 𝜌𝐿 , 𝜌𝐺 ) indicate the liquid in gaseous/vapour phase,respectively. Mixture quantities also occur, which use the void fraction 𝛼.
𝜌̅ = 𝜌𝐿 (1 − 𝛼) + 𝜌𝐺 𝛼

(35)

The (local) velocity is denoted as w. It is also convenient to define the mass flux density
𝐺 = 𝑚̇/𝐴, which is also related to the velocity by 𝑤 = 𝐺/𝜌.

2.4.1. Abdollahian-Chexal model
The Abdollahian-Chexal model [15] is constructed as an approximative scheme avoiding
numerical complications of iterative solutions. It is based on the assumption that thepressure drops to the saturation pressure, and resistance occurs due to the friction factor 𝜆and entrance losses described by the discharge coefficient 𝑐𝑑 .
𝑚̇ = 𝐴

NEA LEAK RATE BENCHMARK FINAL REPORT

2𝜌(𝑝0 − 𝑝𝑠𝑎𝑡 )√𝐿 𝑣
𝑣𝑚 + 𝑣𝑚 𝜆 + 20
𝑑ℎ 𝑐𝑑

(36)

26  NEA/CSNI/R(2022)9
While 𝑣0 denotes the specific volume upstream, the average specific volume 𝑣𝑚 is basedon the mean pressure 𝑝̅ = [𝑝0 + 𝑝𝑠𝑎𝑡 (𝑇0 )]/2.
𝑣𝑚 = 𝑣𝐿 (𝑝̅ ) + 𝛼(𝑝̅ ) [𝑣𝐺 (𝑝̅ ) − 𝑣𝐿 (𝑝̅ )](37)

The remaining parameter, the quality 𝛼 at the average pressure 𝑝̅ , is computed assuming
the isenthalpic changes, 𝛼(𝑝̅ ) = [ℎ0 − ℎ𝐹 (𝑝̅ )]/ℎ𝐹𝐺 (𝑝̅ ). This model is an iteration-free
approximation based on the estimate of the exit pressure and a simple correction of thefluid density.

2.4.2. ATHLET-CDR model
Thermal-hydraulical system codes are possible computation tools for two-phase flow
through slit-like leaks. Within this benchmark, the thermal-hydraulic code ATHLET with
the included critical discharge rate (CDR) model [1] was applied. The CDR model is basedon the evolution of the mass fraction of liquid and vapour phase with time 𝑡 and flow pathdistance 𝑧. Together with the mixture energy and the mixture momentum, four equations
define the CDR model (gravitational influences are neglected in the following).
𝑑𝑑(𝜌𝐿 (1 − 𝛼)𝐴) + (𝜌𝐿 (1 − 𝛼)𝑤𝐴) = −𝜓𝐴
𝑑𝑡
𝑑𝑧

(38)

𝑑
𝑑
(𝜌𝐺 𝛼𝐴) + (𝜌𝐺 𝛼𝑤𝐴) = 𝜓𝐴
𝑑𝑡
𝑑𝑧

(39)

𝑑
𝜌
𝑑𝐴 𝑑
𝜌
̅̅̅̅ + 𝑤 2 − 𝑝) 𝐴) + 𝑝
̅̅̅̅ 𝑤 + 𝑤 3 − 𝑝) 𝐴) = 𝑞 ∗ 𝐴+ ((𝜌ℎ
((𝜌ℎ
𝑑𝑡
2
𝑑𝑡 𝑑𝑧
2
𝑑
𝑑
𝑑𝐴
(𝜌̅ 𝑤𝐴) + ((𝑝 + 𝜌̅ 𝑤 2 )𝐴) − 𝑝= −𝑅 ∗ 𝐴
𝑑𝑡
𝑑𝑧
𝑑𝑧

(40)

(41)

In this equation system, 𝑅 ∗ denotes the (friction-influenced) pressure loss per length, and𝑞 ∗ the power density relevant for the energy balance, and 𝜓 the mass transfer rate between
the states. For stationary conditions, the time-dependence can be dropped out, and theequation system can be written as a matrix equation.
𝐶̂

𝑑
𝒖=𝒓
𝑑𝑧

(42)

The 4-vector 𝒖 reads (𝑝, 𝑇, 𝑤, 𝛼). In the case of critical flow, the criticality at the exit plane
implies a boundary condition at 𝑧 = 𝐿 for the eigenvalues 𝜆𝐶𝑖 of the system.
∃𝑗 𝜆𝑗𝐶 = 0 ∧ 𝜆𝐶𝑖 > 0 ∀ 𝑖 ≠ 𝑗(43)With this boundary condition, the matrix equation (42) can be solved numerically. It is
worth noting that the CDR model is a complex and accurate model, but relies intrinsicallyon critical flow conditions – it is not constructed for the (often simpler) case of subcritical

NEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  27

flow, where an appropriate continuation has to be chosen (e.g. the Bernoulli equation forcold water flow).

2.4.3. Burnell model
The Burnell model [12][18] is a model for short orifices for leak flow, which is the reason
why it assumes only a very small amount of evaporation. The mechanism which is
supposed to prevent evaporation is the surface tension. The model is formulated as a singlephase flow equation of a fluid of density 𝜌, undergoing a pressure drop from the upstream
condition to a value (1 − 𝐶)𝑝𝑠𝑎𝑡 , slightly below the saturation pressure.
𝑚̇ = 𝑐𝑑 𝐴 √2𝜌[𝑝0 − (1 − 𝐶)𝑝𝑠𝑎𝑡 ](44)

The coefficient 𝐶 is determined for one saturation pressure and corrected by a simple
relation for the variation of the surface tension.
𝐶(𝑝𝑠𝑎𝑡 ) = 𝐾

𝛾(𝑝𝑠𝑎𝑡 )

(45)

𝑟𝑒𝑓

𝛾(𝑝𝑠𝑎𝑡 )𝑟𝑒𝑓

𝑟𝑒𝑓

The values of 𝐾 = 0.264 for 𝑝𝑠𝑎𝑡 = 175 psia and 𝐾 = 0.284 for 𝑝𝑠𝑎𝑡 = 200 psia are usedin [18].

2.4.4. Henry-Fauske model
A classical approach for the computation of evaporating liquid flow is the formulation ofHenry and Fauske [13][38]. It is a class of models that share a common basis, as discussed
in [11][14][15]; the notable extension to the original formulation is the consideration offriction effects. The key equation for the mass flow rate is the critical mass flow rate 𝐺.
𝐺=

1
𝑥𝑣𝐺
𝑑𝑥
− (𝑣𝐺 − 𝑣𝐿 )𝑁 𝐸
𝛾𝑝𝑐
𝑑𝑝

(46)

This model uses a phenomenological vapour generation rate, representing the delayed
evaporation in a fast-flowing fluid discharge, while the equilibrium steam quality 𝑥𝐸 canbe derived from the stagnation entropy 𝑠0 and the specific entropy of both phases.
𝑥𝐸 =𝑠0 − 𝑠𝐿
𝑠𝐺 − 𝑠𝐿(47)

The factor 𝑁 denotes the correction factor for the non-equilibrium evaporation, which
depends on the steam quality 𝑥𝐸 itself.
𝑁(𝑥𝐸 ) = {20 𝑥𝐸 if 𝑥𝐸 < 0.05
1 or 1.2 if 𝑥𝐸 ≥ 0.05

(48)

The pressure at the exit at critical mass flux 𝑝𝑐 is a result of different contributions to thepressure drop Δ𝑝𝑡𝑜𝑡𝑎𝑙 = (𝑝0 − 𝑝𝑒𝑥𝑖𝑡 ) and is itself a function of the mass flow rate 𝐺.

NEA LEAK RATE BENCHMARK FINAL REPORT28  NEA/CSNI/R(2022)9

𝑝𝑐 = 𝑝0 − Δ𝑝in − Δ𝑝friction − Δ𝑝acc − Δ𝑝area − Δ𝑝𝑡𝑜𝑟𝑡(49)

The term Δ𝑝in is the pressure loss at the entrance in the leak which is associated withentrance effects. It is expressed in terms of the discharge coefficient 𝑐𝑑 , and depends on themass flux through the entrance (where the density is 𝜌0 and the cross section area is 𝐴0 ).
Δ𝑝in =

2
𝑚̇2 1
𝐺𝑒𝑥𝑖𝑡
𝐴2𝑒𝑥𝑖𝑡=𝐴2𝑖𝑛 𝜌0 2 𝑐𝑑2 2 𝑐𝑑 𝜌0 𝐴20(50)

The frictional pressure drop Δ𝑝friction is a function of the friction factor 𝜆 (see equation(28)), which simplifies for the assumption of constant values of 𝐺, 𝑥 and 𝑣𝐺 (using
averages).
Δ𝑝friction = 𝜆 (𝐿𝐺2[(1 − 𝑥)𝑣𝐿 + 𝑥𝑣𝐺 ]
− 12)
𝑑ℎ
2

(51)

Alternatively, and especially in case of variations of the cross section 𝐴 along the flow path,the frictional pressure loss can also be computed by the following expression.
Δ𝑝friction = 𝜆𝐺 2 𝐴2𝑒𝑥𝑖𝑡𝐿[6 𝑣0 + ( − 12) [(1 − 𝑥)𝑣𝐿 + 𝑥𝑣𝐺 ]]2
2 𝐴𝑒𝑣𝑎𝑝𝑑ℎ(52)

In this equation, 𝑥 denotes the isenthalpic vapour quality at the average pressure. In thecase of short leaks with 𝐿/𝑑ℎ < 12, the frictional pressure drop is instead computed by thefollowing equation.
Δ𝑝friction = 𝜆𝐺 2 𝐴2𝑒𝑥𝑖𝑡
12 𝜌0
2 𝐴𝑒𝑣𝑎𝑝 𝐴0(53)

The acceleration pressure drop Δ𝑝acc is associated with the acceleration of the fluid due tothe decreasing density induced by the phase transition (vapourisation).
Δ𝑝acc = 𝐺𝑐2

𝐴𝑒𝑥𝑖𝑡 𝐴𝑒𝑥𝑖𝑡(ℎ)(ℎ)[(1 − 𝑥𝑒𝑥𝑖𝑡 ) 𝑣𝑡ℎ𝑟,𝑠𝑎𝑡,𝐿 + 𝑥𝑒𝑥𝑖𝑡 𝑣𝑡ℎ𝑟,𝑠𝑎𝑡,𝐺 − 𝑣0 ]𝐴𝑒𝑣𝑎𝑝 𝐴0

(54)

(ℎ)

In this expression, 𝑥𝑒𝑥𝑖𝑡 denotes the isenthalpic equilibrium vapour quality at the crack exit
plane, and 𝑣𝑡ℎ𝑟,𝑠𝑎𝑡,𝐿 and 𝑣𝑡ℎ𝑟,𝑠𝑎𝑡,𝐺 denote the specific volume at the throat of saturated
liquid and vapour, respectively. Under certain simplifying assumptions, and a constantcross section, the pressure drop can also be computed as follows.
Δ𝑝acc = 𝐺 2 𝑥𝑐 (𝑣𝐺 − 𝑣𝐿 )(55)

For cross section changes (from the interior side 𝐴𝑖 to the exterior side 𝐴𝑒 ), the additionalterm Δ𝑝area arises.

NEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  29
2
Gexit
𝐴2𝑒
𝐴2𝑐
Δ𝑝area =[𝑣𝐿 (1 − 2 ) + 𝑥(𝑣𝐺 − 𝑣𝐿 ) (1 − 2 )]
2
𝐴𝑖
𝐴𝑖

(56)

An alternative formulation is given in terms of the interpolated area at the start ofevaporation 𝑧 = 12𝑑ℎ , which is denoted 𝐴𝑒𝑣𝑎𝑝 .
Δ𝑝area =22
Gexit
𝑣0 𝐴2𝑒𝑥𝑖𝑡 𝐴2𝑒𝑥𝑖𝑡
𝐺𝑒𝑥𝑖𝑡
𝐴2[1 − 𝑥 𝑣𝐹 (𝑝̅ ) + 𝑥𝑣𝐺 (𝑝̅ )][1 − 2𝑒𝑥𝑖𝑡 ][ 2− 2 ]+
2
2
𝐴𝑒𝑣𝑎𝑝
𝐴0
𝐴𝑒𝑣𝑎𝑝

(57)

In the latter equation 𝑝̅ denotes the average pressure between the section past the entrance
and the exit. The steam quality to be used here is the isenthalpic vapour quality at thisaverage pressure, determined by the following equation (in which Δℎ is the latent heat ofevaporation).
𝑥 (ℎ) =ℎ𝐿 (𝑝0 , 𝑇0 ) − ℎ𝐹,𝑠𝑎𝑡 (𝑝̅ )𝛥ℎ(𝑝̅ )

(58)

The tortuosity pressure loss Δ𝑝𝑡𝑜𝑟𝑡 is a function of the crack face morphology, more
precisely of the number of turns 𝑛𝑡 . This number can also be given in terms of the turndensity per length 𝜂𝑡 , where 𝑛𝑡 = 𝜂𝑡 𝐿𝑒𝑓𝑓 .
𝐺 2 𝐴𝑒𝑥𝑖𝑡
Δ𝑝tort =𝑛[1 − 𝑥 𝑣𝐹 (𝑝̅ ) + 𝑥𝑣𝐺 (𝑝̅ )]2 𝑡 𝐴𝑒𝑣𝑎𝑝(59)

The combination of equations (46) and (49) has to be solved, either iteratively or bynumerical root finding, in order to find the critical pressure 𝑝𝑐 and the CDR 𝐺𝑐 . Comparedto other approaches, the solution of a differential equation is avoided by the averaging
strategy in the contributions to the pressure drop.

2.4.5. Metastable jet model
The metastable jet model [17] is an approach for the flow through short orifices, where no
evaporation occurs and a jet of metastable liquid water forms. It is a single-phase
compressible fluid equation without consideration of friction.
𝑚̇ = 𝐴 𝑐𝑑 𝜌𝑀𝐿 (𝑝𝑒𝑥𝑡 ) √2[ℎ(𝑝0 ) − ℎ𝑀𝐿 (𝑝𝑒𝑥𝑡 )](60)

In this equation, ℎ𝑀𝐿 and 𝜌𝑀𝐿 denote the specific enthalpy of the metastable fluid and its
mass density, respectively.

2.4.6. Modified Bernoulli model or Zaloudek model
The modified Bernoulli equation is a simple estimation scheme for leak flow rates at
sufficient subcooling [18][19][20]. This approach is based on the observation that thethermodynamic conditions at the exit plane are on the saturation line. A guess for thissaturation condition is the saturation pressure at the stagnation temperature 𝑝𝑠𝑎𝑡 (𝑇0 ). Whenthe density reduction is neglected, the mass flow rate can be written as a Bernoulli equation(like equation (34)) with modified exterior pressure.

NEA LEAK RATE BENCHMARK FINAL REPORT30  NEA/CSNI/R(2022)92𝜌(𝑝0 − 𝑝𝑠𝑎𝑡 )𝑚̇ = 𝐴 √1+𝜁

(61)

This simplification works very well for large subcooling (i.e. large pressure or temperature
difference to saturation conditions) but fails for small subcooling (where it is very
underpredicting) and cold water conditions (where the saturation pressure is below theexterior pressure).

2.4.7. Pana model
The Pana model [21] describes the unidimensional flow through a leak by modelling theflow between defined check points. This description concentrates on the subcooledstagnation conditions. The check points are indicated by the index ‘1’ for a location
downstream of the entrance region, and the index ‘2’ by the exit plane. The mass flow tolocation ‘1’ is modelled by the Moody model by an isentropic pressure drop from 𝑝0 to 𝑝1 .

𝐺Moody (𝑘, 𝑝1 ) = √2 (ℎ0 − (1 − 𝑥)ℎ𝐿 − 𝑥 ℎ𝐺 )1−𝑥[𝑥 𝑣𝐺 + 𝑘(1 − 𝑥)𝑣𝐹 ]2 (𝑥 + 2 )𝑘(62)

The thermodynamic properties are to be taken at location ‘1’: the parameter 𝑘 is used for
maximisation, 𝐺(𝑝1 ) = max𝑘 𝐺(𝑘, 𝑝1 ). The pressure drop from 𝑝1 to 𝑝2 is governed by theflow resistance 𝜁, which is an implicit relation of 𝑝2 (𝑝1 ).
𝜕𝑣(𝑝)
)
𝜕𝑝 𝑠
𝑑𝑝
𝐺 2 𝑣(𝑝)𝑝2 1 + 𝐺

𝜁 = −2 ∫
𝑝1

2

(

(63)

The Pana model is solved by maximising 𝐺Moody by the parameter 𝑘, and by maximising
this result by the variation of 𝑝1 , under the side condition of 𝑝2 (𝑝1 ) > 𝑝𝑒𝑥 .
𝐺Pana (𝑝0 , 𝑠0 , 𝜁, 𝑝𝑒𝑥 ) = max [max 𝐺Moody (𝑘, 𝑝1 )]
𝑝1𝑘𝑝2 (𝑝1 )>𝑝𝑒𝑥(64)

This approach can be used for critical mass flow as well as for subcritical discharge rates
since the side condition acts directly in the iteration scheme. It is possible to solve
equation (64) numerically with two nested optimisers.

2.5. Software
The previous sections show that the different parts of leak flow rate prediction require
numerical computation of at least moderate complexity, and thus the methods were
implemented in computer programs for reliable application of the approaches. This section
presents the different software tools that were used in the benchmark activity.

2.5.1. ANSYS CFX
ANSYS-CFX is a general purpose commercial computational fluid dynamic software. It is
used to simulate the behaviour of systems involving fluid flow, heat transfer and otherrelated physical processes. ANSYS-CFX works by solving the equations of fluid flow over
NEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  31

a region of interest, with specified conditions on the boundary of that region. ANSYS CFX
is stemmed from the programme CFX-4, (formerly known as Flow3D) which was
originally developed by the United Kingdom Atomic Energy Authority (AEA). In 2003,
just prior to the release of CFX-5.6, ANSYS Inc. of Canonsburg, PA, acquired the CFX
division from AEA Technology.
The set of Navier-Stokes equations are used to describe the processes of momentum, heatand mass transfer. These partial differential equations are discretised and solved
numerically. A single-phase or multiphase approach is used for the leak rate analysis.
Detailed physical models can be referred to the ANSYS CFX theory manual [22]. The finite
volume technique is adopted in ANSYS CFX. In this technique, the region of interest isdivided into small sub-regions, so-called control volumes. The equations are discretised
and solved iteratively for each control volume. As a result, an approximation of the valueof each variable at specific points throughout the domain can be obtained. In this way, one
derives a full picture of the behaviour of the flow. Additional code features include:•

steady-state and transient flows;•

laminar and turbulent flows;•

subsonic, transonic and supersonic flows;•heat transfer and thermal radiation;•buoyancy;•

non-Newtonian flows;•transport of non-reacting scalar components;•

multiphase flows;•

combustion;•flows in multiple frames of reference;•

particle tracking.

Full licence of the software needs to be purchased from ANSYS Inc. For purpose of study,
the software can be downloaded on the ANSYS website with a free student licence for a
problem size limit of 512K cells/nodes. ANSYS CFX is in compliance with 10CFR50,
Appendix B, and has been approved for use at Candu Energy Inc.

2.5.2. ExcelSQUIRT
ExcelSQUIRT is a derivative of the SQUIRT software (see Section 2.5.8); both are owned
and maintained by Battelle. It provides leak rate computation functionalities by separatetabs of an Excel spreadsheet.
The LeakRate tab calculates the leak rate for a given pipe geometry and set of thermalhydraulic conditions (temperature and pressure). The CrackSize tab calculates the leakage
crack size for a prescribed leakage detection limit, pipe geometry, loading conditions(moment and pressure), and thermal-hydraulic conditions. The crack type (e.g. corrosion
fatigue [CF], intergranular stress corrosion cracking [IGSCC], primary water stresscorrosion cracking [PWSCC ]) and crack shape (rectangle, diamond, elliptical) are definedon the Info tab of the spreadsheet.
The Leak Rate code used in the software is that which is used in the latest version of ProLOCA. It is derived from Version 2.1.3 of SQUIRT with some modification to improve
convergence. The COD calculations are based on the Pro-LOCA version of the COD
NEA LEAK RATE BENCHMARK FINAL REPORT32  NEA/CSNI/R(2022)9
routine which was updated to improve the COD calculation under combined bending andtension. Details of this model can be found in [23], [24] and [25].

2.5.3. LeakH
The code LeakH was developed by ÚJV. Its main purpose is to be implemented into
BASLBB code performing automatic LBB evaluation. The code is also used for evaluating
effects induced by a postulated pipe break.
The mathematical model used in the LeakH code consists of few simple thermodynamic
laws. One of the most important parts of the code are tables of water and steam properties.
The tables contain a set of equations precisely describing the properties of water and steam
according to [26].
Entrance parameters of leaking coolant can be up to 100 MPa and 800°C. These values arewithin the validity of the tables of water and steam properties. The model includes entrance
loss pressure, crack surface friction influence and changes of crack areas through the wall
thickness. Changes of flow direction in the crack of about 45° and 90° are also considered.
Calculations are performed using the following simplifying assumptions:
1. Flow is assumed to be one-dimensional.
2. In two-phase region the flow is considered to be homogeneous, i.e. slip between
phases is not considered.
3. Heat exchange with the environment is not considered.
4. Changes of area in the direction of flow are linear.
5. Flow is in steady state and input parameters do not vary in time.
The code was prepared in agreement with a quality assurance (QA), and its validation was
performed based on comparison with PICEP (see Section 2.5.6) and measurement on an
experimental device (pipe about 100 mm, primary circuit condition, artificial crack).
Detailed information can be found in the code’s user manual.
The code is available in ÚJV. It can be sold in this form based on negotiation with thecustomer (typically as a subroutine to be implemented into another code). It was sold to the
Ignalina Nuclear Power Plant.

2.5.4. LEAPOR
LEAPOR (Leak Analysis of Piping – Oak Ridge) was developed at Oak Ridge National
Laboratory (ORNL) as the module for performing leak rate calculations in the xLPR
(Extremely Low Probability of Rupture) Version 2 (V2) probabilistic fracture mechanics
code [34], jointly developed by the US Nuclear Regulatory Commission (USNRC) and theElectric Power Research Institute (EPRI), Inc. LEAPOR was developed using the thermohydraulic models employed in the SQUIRT leak rate code (see Section 2.5.8) [11] [14].
LEAPOR employs a four-regime model that was originally developed under the MERIT(Maximising Enhancements in Risk-Informed Technology) Programme [35] to represent
the spectrum of leak rates from tight cracks to orifice flow, where the boundaries of eachregime are defined by a ratio of the effective flow path length to the hydraulic diameter.
As one of a number of modules in the xLPR project, the LEAPOR code was required to bea Software Quality Assurance (SQA) auditable application, fulfilling the software workpractice requirements of ASME NQA 1-2008 (including Addenda 2009) Quality
Assurance Requirements for Nuclear Facility Applications. The code structure must be
designed to be maintainable for current and future needs. “Code maintainability” refers to

NEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  33

how easily a software system can be changed to add new features, modify existing features,find and fix bugs, and/or improve performance. Additionally, the xLPR Project SQA planstated that the “source code components (source code and documentation) must be
evaluated for correctness, consistency, completeness, accuracy, readability, andtestability”. These requirements were driven by the need to provide proven mechanisms for
managing increasing and evolving complexity throughout the life cycle of the application.
Further details about the theory and modelling decisions in LEAPOR and validation withexperimental data can be found in [39].
LEAPOR‐SA has the same capabilities and uses the same code as LEAPOR andincorporates a Graphical User Interface (GUI) to facilitate standalone applications outsideof xLPR V2. The LEAPOR‐SA GUI was written by the NRC staff. It provides a userfriendly method of entering the necessary parameters needed to calculate leak rates using
LEAPOR‐SA. The GUI is programmed in Fortran. As shown in Figure 2.2, operation
parameters (i.e. numerical values for geometry, pressure, and temperature), crack
parameters (i.e. crack shape including ellipse, rectangular as well as diamond and crack
surface toughness type containing IGSCC, PWSCC base metal and weld metal, CF anduser input) and crack size are needed. A two‐dimensional table of crack lengths (2c) and
CODs will be generated and the leak rate will be calculated for each 2c‐COD pair. Herethe 2c values are at the mid‐wall (MW) location and the crack is assumed to be ideal (i.e. thecrack angle at the MW, inside diameter [ID], and outside diameter [OD] locations areequal). The COD at the ID and OD are assumed to be equal. Error checking is performed
prior to the computation to ensure valid inputs have been entered.

Figure 2.2. User Interface of LEAPOR-SA

2.5.5. LOCIThe LOCI™ code is under development by OCI. LOCI™ is a new leakage code [40] being
implemented within a modular and layered architectural software design that takes
advantage of the object-oriented features and constructs available in the Fortran 2003

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standard. Employing the LEAPOR1 code (see Section 2.5.4) as a baseline prototype,
LOCI™ includes, in addition to the best-estimate Henry-Fauske leakage-rate model (seeSection 2.4.4) inherited from LEAPOR, four conservative leakage-rate models from theGerman safety standard KTA 3206 [20]. LOCI™ also includes three leakage-area COD
models, specifically the GE/EPRI, KTA 3206 linear-elastic, and KTA 3206 elastic-plastic
models.
In the context of an LBB assessment where emphasis is placed on the detection of small
leakage rates, the distinction between conservative and best-estimate models becomes very
important. This classification can provide guidance on where these models can beappropriately applied in terms of understanding margins and uncertainties. A conservative
leakage-rate model is required to consistently underestimate the actual leakage rate and istypically applied in deterministic procedures, e.g. the deterministic approach in the German
standard KTA 3206. A best-estimate leakage-rate model places greater emphasis on
predictive accuracy. In a probabilistic framework, the model’s estimated solutions canserve as a measure of central tendency (mean, median, or mode) for a prescribed statistical
distribution characterising the uncertainties in the leakage-rate predictions. As noted above,
LOCI™ provides both best-estimate and conservative leakage-area and leakage-rate
models.
Also inherited from LEAPOR, LOCI™ contains a database of morphology parameters as
a function of damage mechanism. The default values from this database can be consideredin addition to user-input values in all analysis cases. A user interface for LOCI™ iscurrently under development by OCI (see Figure 2.3).

Figure 2.3. User Interface for LOCI™ (under development)

2.5.6. PICEP and SI-PICEPThe PICEP code is a computer code developed by EPRI for the leak rate assessment [27].
The PICEP calculates the flow through a crack in a pipe. PICEP uses the simplified
1

Note that the OCI developer (Dr. Paul T. Williams) for LOCI™, before his retirement from ORNL,
was the lead developer for the LEAPOR code.

NEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  35

engineering approach for elastic-plastic fracture analysis for finding the COD and COA.
Fluid calculation options include single and two-phase flow as well as allowance for
friction.
Later, Structural Integrity Associates, Inc. (SIA) developed the SI-PICEP code reflecting
nuclear quality assurance from PICEP. The SI-PICEP is subject to formal quality assurance
following SIA assurance procedures, which are in compliance with the requirements of
10CFR50, Appendix B, 10CFR21, and ANSI/ASME NQA-1-1989, 1994, and 2008/2009A
and meets the applicable portions of ANSI N45.2.

2.5.7. SCALEThe SCALE code calculates crack opening parameters using the Tada-Paris model (seeSection 2.2.5) for circumferential through-wall cracks and the Zahoor model (seeSection 2.2.1) for axial through-wall cracks. It utilises a number of models for leak rateestimation. These models are of two categories. The Burnell (see Section 2.4.3) andZaloudek (see Section 2.4.6) models are for subcooled flow leakage. These arehomogeneous non-equilibrium models based on liquid-vapour surface tension and purely
empirical. The model development is based on experimental verification and validation.
These models do not consider any flow losses in terms of morphological roughness, thoughroughness is used in most leak flow estimation models. The losses can only be taken into
account by means of a discharge coefficient. For critical flow, the throat pressure is not
explicitly calculated. The other types of models are Henry’s non-equilibrium andHomogenous Frozen (see Section 2.4.4). These are also homogenous non-equilibrium
models; however, they consider critical flow based on stagnation and throat pressure. The
relations between these two pressures (stagnation and throat) are through flow losses.
Consequently, these models make provision for the consideration of morphologicalfriction, form and turning losses. The SCALE code checks for the existence of the inertial
and critical flow regimes.

2.5.8. SQUIRTThe SQUIRT (Seepage Quantification of Upsets In Reactor Tubes) computer code wasdeveloped as a tool for leak rate estimation, combining thermal-hydraulic and crack
opening area models [11]. While the crack opening is based on the GE/EPRI method (seeSection 2.2.1), the fluid-dynamical model is an implementation of the Henry-Fauske model(see Section 2.4.4). The friction factor approach is also carefully addressed; its
implementation became a standard reference (described in Section 2.3.3.3).
SQUIRT led to the development of ExcelSQUIRT (see Section 2.5.2) and LEAPOR (seeSection 2.5.4). It was widely distributed due to its availability through the NEA computer
program services (CPS).

2.5.9. WinLeck
The WinLeck code was developed by GRS in the framework of several research projects
since the mid-1990s. The code is designed for leak rate computation, mainly for watersteam-leaks, though it can also be used for gas/air leaks. The computational models in thecode were validated by allowing the processing of many experimental data points and asystematic model validation matrix. The code is designed to support leak-before-breakassessments.
Multiple models were implemented into WinLeck for the leak opening (GE/EPRI method,
Section 2.2.1, GRS-PB method, Section 2.2.3, LBB.ENG2 method, Section 2.2.4, andothers), the flow resistance, and the actual flow rate (Henry-Fauske model, Section 2.4.4,
NEA LEAK RATE BENCHMARK FINAL REPORT36  NEA/CSNI/R(2022)9
Metastable jet model, Section 2.4.5, modified Bernoulli model, Section 2.4.6, Pana model,
Section 2.4.7, and others). The programme structure allows for a combination of thedifferent approaches and a comparison of the models’ accuracy by simultaneous
application on selected cases. This advantage allows to study specific model influences andalso to identify uncertainties in reference test cases. A GUI (see Figure 2.4), a
documentation, a validation report and tools for performing parameter studies are included.

Figure 2.4. Interface of the WinLeck code

The WinLeck code is validated in numerous experiments and has a formal quality
assurance procedure [28]. It is applied in research projects, case studies and LBB
evaluations. The code can be made available to organisations on request without additionalcosts based on a licensing agreement.

2.6. Regulatory perspective
As leak rate computation is an essential part of LBB assessment, it is also subject to codesand standards. Within an LBB assessment, the leak rate computation is used to predict theflow through a postulated defect and to estimate the size of a defect that is reliably detectedby leak monitoring devices. In this approach, the underestimation of the actual leak rate isconservative because a higher leak rate is more likely to be detected than a smaller leakrate. The situation is different in loss-of-coolant scenarios, where typically anoverestimation of the coolant loss is conservative because the focus of the safetyassessment is on the impact on pressure and temperature in the entire coolant loop.
The Standard Review Plan [29] does not specify details about recommended computational
tools. The KTA standard [20] proposes several procedures in an Annex.

NEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  37

3. First benchmark phase
The first benchmark phase took place from 2019 to 2020. This phase concentrated on postcomputation: the measured leak rates were communicated to the participants together withthe circumstances of the operation and the leak. The first benchmark phase consists of four
exercises: a laboratory test of an artificial slit, a laboratory test of a fatigue crack, ananalysis of a real event in a nuclear power plant, and a sensitivity study on leak ratecomputation within an LBB assessment.

3.1. Exercise set
The exercise sets were provided to the participants in tabular form. These tables followed
a structure of category, attribute, variable, value, and unit, in order to unify the presentationof leak settings and avoid misunderstandings. The exercise set categories were structure,
structure material, loads, leak geometry, morphology and fluid. In the individual exercises,
only those categories relevant for the individual case were provided. For example, in caseof a fixed laboratory specimen with leaks, the material and load categories were omitted
because their values do not enter the computation.

3.1.1. Artificial slit
The test case on the artificial slit specimen is based on the specimen “010T30”
manufactured and measured in the “FSI” test rig at the University of Stuttgart. The
information provided to the participants is summarised in Table 3.1; additional informationon the tests is given in the appendix.

Table 3.1. Phase 1 artificial slit specification
Category
Structure

Leak geometry

Attribute
Geometry type

Variable
-

Value
Plate

Unit
-

Wall thickness
Additional loads
Approximate shape
Interior
Full length

t

mm

2c

30
none
Rectangle
27

COD
COA
2c
COD

192-190-201
5.22
28.15
185-229-239

µm
mm²
mm
µm

Cross section
Damage mechanism
Inlet form loss
Roughness Local

COA
zeta_inRz

6.22
Artificial
Unknown
22mm²µm

GlobalLocal
Global
Measured total resistance

Rz
N
N
Zeta

22
0
0
4.32

µm
-

Pressure
TemperaturepTvariablevariable

MPa°C

Exterior

Morphology

Maximal width
Cross section
Full length
Maximal width

Bends

Fluid (stagnation)

NEA LEAK RATE BENCHMARK FINAL REPORTmm

38  NEA/CSNI/R(2022)9
In the laboratory test, the temperature and pressure were variated, and the leak mass flow
was measured. Two measurement principles were applied in the test (additional
information on the instrumentation is given in the appendix). The fluid conditions and themeasured values chosen for the computation benchmark are reproduced in Table 3.2.

Table 3.2. Phase 1 artificial slit fluid conditions and measured leak rates

233.9
216.9

Measured mass
flow rate [kg/s]
0.122
0.201

Second estimate[kg/s]
0.117
0.189

250.5
161.4
122.4
79.3

0.183
0.166
0.214
0.104

0.174
0.157
0.203
0.1

Test no.

Data set

Pressure [bar]Temperature [°C]

1
2

10
13

45.2
70.3

3
4
5
6

14
20
33
38

75.2
35.4
48.6
10.4

This information was the basis for each participant’s evaluation.

3.1.2. Fatigue crack
The fatigue crack test case is based on the specimen “R5” tested at the University of
Stuttgart. The specimen is made of a fatigue crack in a plate. The information provided forthis exercise is summarised in Table 3.3; additional information on the tests is given in the
appendix.

Table 3.3. Phase 1 fatigue crack specification
Category
Structure

Attribute
Geometry type
Wall thickness
Additional loads

Variable
t

Value
Plate
7.8
None

Unit
mm

Leak geometry

Approximate shape
Interior
Full length
Maximal width
Cross section

2c
COD
COA

Rectangular
53.89
79
4.26

mm
µm
mm²

Exterior

Full length
Maximal width
Cross section
Damage mechanism

2c
COD
COA
-

39.04
48
1.87
Fatigue

mm
mm
mm²
-

Inlet form loss
Roughness Local
GlobalBends
Local

zeta_inRz
Rz
N

Unknown
Unknown
40
Unknownµmµm-

Global
Measured total resistancePressure
Temperature

N
Zeta
p
T

Unknown
ca. 40variablevariable

MPa°C

Morphology

Fluid

From the variation of pressure and temperature in the test, six points were selected for theevaluation within the benchmark study. The selected points are shown in Table 3.4,
NEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  39

together with the measured flow rates as observed in the tests. As for the artificial slit case,a second estimate of the leak flow rate is also shown (additional information on the mass
flow measurement can be found in the appendix).

Table 3.4. Phase 1 fatigue crack fluid conditions and measured leak rates
Test no.

Data set

Pressure [bar]Temperature [°C]
204.3
204.4
254.4

Measured mass
flow rate [kg/s]
0.016
0.00610.0164

Second estimate[kg/s]
0.02260.01450.0182

1
2
3

2
9
27

65.7
20.8
70.7

4
5
6

45
61
80

76.7
77.2
62.1

20.8
229.9
161.8

0.04080.01650.03310.04780.0217
0.0369These two tables contain the information with which the participants started the evaluation.

3.1.3. Real event
The third exercise is the assessment of a real leak event from the operation of a nuclear
power plant. A case discussed in [31] was chosen. The tabular specification of this test caseis shown in Table 3.5. Due to a transcription error, a leak rate of 0.013 kg/s instead of
0.13 kg/s was used in the benchmark.

Table 3.5. Phase 1 real event case specification
Category
Structure

Attribute
Geometry type
Outer diameter
Wall thickness

Variable
D
t

Value
Pipe
37.7
4.33

Unit
mm
mm

Material

NumberYoung's Modulus
Yield stress
Ultimate stress

E
Rp0,1
Rm

“1.4550”
186 000
167
409

MPa
MPa
MPa

Poisson number
RambergPrefactor
OsgoodExponent
Pressure

nu
alpha
n
p

0.3
15.5
2.5
15.9

-

Bending
Orientation
Approximate shape
Interior
Full length
Estimatedmaximal width
Cross sectionM
2c

Unknown
Circumferential
Unknown
40

Nm
mm

COD

<0.05?

mm

COA

Unknownmm²

Mean

Full length
Estimatedmaximal width
Cross section

2c
COD

36
0.05?

mm
mm

COA

Unknown

mm²

Exterior

Full length
Estimatedmaximal width
Cross section

2c
COD

34
0.01?

mm
mm

COA

Unknownmm²

Loads
Leak geometry

NEA LEAK RATE BENCHMARK FINAL REPORTMPa40  NEA/CSNI/R(2022)9

Table 3.5. Phase 1 real event case specification (Continued)
Category
Morphology

Fluid
Leak rate

Attribute
Damage mechanism
Inlet form loss
AverageLocalroughness
GlobalMeanroughness
Maximalroughness
Bends
Local
Global
Measured total resistancePressure
Temperature
Measured flow rate

Variable
zeta_in
Rz
Rz
Ra

Value
Fatigue
Unknown
Unknown
7.6
2.3

Rt

10.6

N
N
Zeta
p
T
m

Unknown
Unknown
Unknown
15.9
40-70
0.013(0.13)

Unit
µm
µm

MPa
°C
kg/s

A key uncertainty in the analysis is the bending moment which influences the crack
opening. Therefore, the variation of the bending moment and the assessment of the trend
was part of the evaluation.

3.1.4. LBB sensitivity analysis
A leak assessment from the parallel LBB benchmark activity was included to study thesensitivity of the leak rate assessment in detail. The specification of the pipe in the LBB
assessment is summarised in Table 3.6. This exercise represents a circumferential weld ina medium-sized pipe.

Table 3.6. Phase 1 LBB sensitivity study pipe specification
Category
Structure

Base material

Attribute
Geometry type
Outer diameter
Wall thickness
Weld width
Yield strength
Ultimate tensile strength
Elastic modulus
Poisson number
Ramberg-Osgood

Weld material

Yield strength
Ultimate tensile strength
Elastic modulus
Poisson number
Ramberg-Osgood

Loads

Axial force (prim.)
Axial force (sec.)
Crack face pressure
Bending (prim.)
Bending (sec.)

Variable
D
t
h
Rp02
Rm
E
nu
σo
εo
α
n
Rp02
Rm
E
nu
σo
εo
α
n
F
F
p
M
M

Value
Pipe weld
406.4
40.462
50.8
153.6
443
176.7
0.3
200.9
0.00114
15.64
3.75
316.5
542.4
196.8
0.3
332.350.00169
0.386
11.39
17.34
-4
7.75
21.59
68

Unit
mm
mm
mm
MPa
MPa
GPa
MPa
MPa
MPa
GPa
MPa
kN
kN
MPa
kNm
kNm

NEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  41

The leak in this pipe is specified in the additional information shown in Table 3.7. A
variation of the leak size in a circumferential through-wall flaw is assumed to conduct asensitivity study.

Table 3.7. Phase 1 LBB sensitivity study leak specification
Category
Leak geometry

Morphology

Attribute
Orientation

Variable-

Value
Circumferential

Unit-

Approximate shape
CentreFull length
Maximal width
Cross section

2c
COD
COA

Unknown
50-300Unknown
Unknownmm
mm
mm²

Damage mechanism
Entry discharge coefficient
Roughness Local
Global

c_d
µL
µG

PWSCC
0.95
17 or 114
114

µm
µm

Bends

N
N
K
K

5 940
5 020
1.2
1.2

1/m
1/m
-

Zeta
p
T
m

Unknown
15.5
340
Around 0.0608

MPa
°C
kg/s

Path
deviation
Fluid
Leak rate

COD-dep.
COD-indep.
Local
Global

Measured total resistancePressure
Temperature
Measured flow rate

Two evaluations were requested: one for a local roughness value of 114 µm, and one forthe local roughness of 17 µm.

3.2. Computation
3.2.1. BARC
BARC’s analyses of the benchmark problems are performed with the SCALE (Slit andCrack Analysis for Leak Estimation) code (see Section 2.5.7).

3.2.2. GRS
GRS’s analyses of the benchmark problems are performed with the WinLeck code (seeSection 2.5.9) developed by GRS. WinLeck make it possible to flexibly specify the input
variables of the individual benchmark exercises.
The artificial slit case provides the measured flow resistance value. Consequently, it is usedas the best available information, while the surface morphology is not considered. As
critical flow conditions are expected, the cross section on the exterior side is chosen for themodelling. Two different flow models are applied: the Pana model (Section 2.4.7) and the
ATHLET-CDR model (Section 2.4.2). Both are considered as best-estimate descriptions,with the notable difference that the Pana model is based on equilibrium flow assumptions,while the ATHLET-CDR model considers non-equilibrium effects. The computed valuesof both models are shown in Table 3.8. Note that the CDR model only predicts critical flow
and is not applicable to subcritical flow.

NEA LEAK RATE BENCHMARK FINAL REPORT42  NEA/CSNI/R(2022)9

Table 3.8. GRS results of the artificial slit case
Data number
Pressure [bar]Temperature [°C]

10
45.2
233.9

13
70.3
216.9

14
75.2
250.5

20
35.4
161.4

33
48.6
122.4

38
10.4
79.3

ATHLET-CDR [kg/s]
Pana [kg/s]
Reference [kg/s]

0.131
0.115
0.122

0.217
0.204
0.201

0.192
0.168
0.183

0.169
0.163
0.166

0.211
0.214

0.09690.104

The two models predict very similar results, with the ATHLET-CDR model showing a
trend to higher mass flow rates, and the Pana model to lower rates. The experimental
measurements mostly lie between the two models’ results (with one exception, where it isslightly below the Pana value).
The fatigue crack analysis is done in analogy to the artificial slit case, but only the Panamodel is applied. The results are shown in Table 3.9.

Table 3.9. GRS results of the fatigue crack
Data number
Pressure [bar]Temperature [°C]

2
65.7
204.3

9
20.8
204.4

27
70.7
254.4

45
76.7
20.8

61
77.2
229.9

80
62.1
161.8

Computed leak rate [g/s]Measured leak rate [kg/s]

25.4
16.0

8.75
6.1

20.4
16.4

34.8
40.8

24.6
16.5

28.0
33.1

The deviation between the model computation and the measurement is significantly larger
than for the artificial slit case. In four cases, the computed leak rate is higher, and in twocases it is lower than the measured flow rate.
In the real event analysis, two different approaches are chosen for the leak opening area:
one underestimating approach based on GRS-PB (see Section 2.2.3), and one based on a
best-estimate approach, considering the LBB.ENG2 method (see Section 2.2.4). In bothcases, the friction effects are modelled using the approach by Paul et al. (see Section 2.3.3),
and the fluid motion is modelled using the Bernoulli model (the temperature is notconsidered to be of importance in this case). The high bending moment value is set to
0.1 kNm by engineering judgement, and the moderate bending moment to half of this value.
The computed values are shown in Table 3.10.

Table 3.10. GRS result of the real event analysis
Bending moment
[kNm]
0
0.05
0.1

Leak rate [g/s]Unterestimation
7.1
16
28

Best-estimate
24
54
110

Compared with the reference result, the underestimation analysis includes a value below
the reported value in the analysis example (13 g/s), while all best-estimate computations
are above this value. Besides the uncertainty in resistance- and crack opening computation,

NEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  43

a negative bending moment could be an explanation for this discrepancy. The main
conclusion from this task is that real events have possibly large uncertainties that lead to alarge scatter band in a computational assessment. With respect to LBB-conservativity, atleast in this example all best-estimate values overpredict the actual leak rate.
The LBB sensitivity problem consists of the computation of the COD (with the LBB.ENG2
method, see Section 2.2.4), the friction factor and flow resistance, and finally the fluid
motion (with the ATHLET-CDR method, see Section 2.4.2), which represent analytical
approaches of best-estimate quality. The two options of local roughness have the meaningof either using or ignoring an improved morphology model, making it possible to consider
the roughness-bends transition for small crack openings. The result is shown in Table 3.11.

Table 3.11. Result of the LBB sensitivity analysis
Local roughness
Full crack length
Crack open.
displ.
[mm]
[mm]
50
25
75
39

114 µmFriction factor
Mass flow rate

17 µm
Friction factor
Mass flow rate

[-]
∞
∞

[g/s]
0
0

[-]
10.8
1.26

[g/s]
0.05
4.63

100
125
150
175

55
71
90
113

∞
∞
∞
∞

0
0
0
0

0.59
0.39
0.29
0.23

12.42
25.05
41.45
63.01

200
225
250
275

139
167
198
231

113.3
7.48
2.67
1.42

11
55
107
167

0.19
0.164
0.15
0.134

90.73
124.32166.58213.57

300

284

0.76

258

0.12

289.53

It is worth comparing the COD to the effective roughness in this table, because the friction
factor by Paul et al. becomes very large as they are of the same order. Obviously, thecomputed friction factor is much higher if no adjustment of the roughness is considered,
which leads to a divergence of the friction factor below a full crack length of 200 mm. This
divergence is avoided by assuming a local roughness value – although the friction factor
for the smallest crack is also very high.
In conclusion, the exercise set was fully treatable with the WinLeck software. The
individual exercises showed that leak rate predictions can be very accurate (artificial slitcase) in idealised situations, but that in practice uncertainties are important to consider,where assessment can give an estimate of the range of possible values. The last exercise,the sensitivity analysis, showed clearly that careful choices of input parameters are required
because this might have a large effect.

3.2.3. KEPCO E&C
KEPCO E&C’ analyses of the benchmark problems were performed using a PICEP codedeveloped by EPRI (see Section 2.5.6). PICEP is based on Henry's homogeneous nonequilibrium critical flow model as modified by Abdollahian and Chexal (see Section 2.4.4).
The wall thickness, full lengths of the crack at both interior and exterior, COD values
measured at three different positions, and COA were provided for the artificial slit case.
The wall thickness and full lengths were employed for the analysis, and the COD values at
NEA LEAK RATE BENCHMARK FINAL REPORT44  NEA/CSNI/R(2022)9
both interior and exterior were assumed to be 0.193 and 0.221 mm, respectively, so that thecalculated cross section is the same as the provided COA. For crack morphology
parameters, a surface roughness of 22 μm was applied and the number of turns was
assumed to be 0 m-1. The calculated values are summarised in Table 3.12. These results are
generally underestimated compared to the measured values.

Table 3.12. Results of the artificial slit case calculated by KEPCO E&C
Data number
Pressure [bar]

10
45.2

13
70.3

14
75.2

20
35.4

33
48.6

38
10.4

Temperature [°C]
Computed leak rate [kg/s]
Reference [kg/s]

233.9
0.095
0.122

216.9
0.163
0.201

250.5
0.141
0.183

161.4
0.127
0.166

122.4
0.149
0.214

79.3
0.081
0.104

In case of the fatigue crack analysis, global roughness was provided, and the statisticalnumber of turns value of 6 730 m-1 was adopted according to Rahman’s research [14]. The
predicted leak rates, as listed in Table 3.13, are lower than the measured leak rates. There's
a more significant discrepancy between the model computation and the measured values(as referenced in Table 3.13) in case of low pressure and temperature.

Table 3.13. Results of the fatigue crack calculated by KEPCO E&C
Data number
Pressure [bar]

2
65.7

9
20.8

27
70.7

45
76.7

61
77.2

80
62.1

Temperature [°C]
Computed leak rate [kg/s]
Measured leak rate [kg/s]

204.3
0.012
0.016

204.4
0.00240.0061254.4
0.00890.016420.8
0.015
0.0408229.9
0.01230.0165161.8
0.0116
0.0331

The real event analysis includes the calculation of the COD. Participants in this benchmark
project were required to select three levels of applied moment. The elastic-plastic
estimation scheme, based on the GE/EPRI ductile fracture handbook (see Section 2.2.1),
was adopted to predict the COD. In case of the applied moment, the high bending moment
value (MH.L) was calculated based on the design bending moment described in the ASME
Boiler and Pressure Vessel (B&PV) Code Section NB [32]. Below is the equation used forthis calculation:
𝑀𝐻.𝐿. =2𝐼
𝑃𝑖 𝐷𝑜
(1.5𝑆𝑚 −)𝐷𝑜
2𝑡where I, Do, Pi and Sm are the moment of inertia, outer diameter, internal pressure, anddesign stress intensity, respectively. The Sm value of 138 MPa was used according to ASME
B&PV Code Sec. II. The medium and zero level of bending moments are set to be half of
MH.L and zero, respectively. The evaluated values are shown in Table 3.14. The assumptionof applied bending moment caused the overestimation of the COD values as compared to
the reference values and resulted in the over-prediction of the leak rate as well.

NEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  45

Table 3.14. Result of the real event analysis evaluated by KEPCO E&C
Bending moment[kNm]

Leak rate [g/s]best-estimate

0
0.235
0.470

64.9
1 038.9
4 409.8

The LBB sensitivity analysis aims to find out the effect of local roughness, especially forthe tight crack case. For the COD prediction, the elastic-plastic estimation scheme was
employed based on the GE/EPRI ductile fracture handbook (see Section 2.2.1). Henry's
homogeneous non-equilibrium critical flow model was adopted. Since PICEP receives one
variable for surface roughness, only the results for a surface roughness of 114 µm arepresented in Table 3.15.

Table 3.15. Result of the LBB sensitivity analysis by KEPCO E&C
Local roughness
Full crack length
Crack open. displ.
[mm]
[µm]

114 µmMass flow rate
[g/s]

50
75
100
125

26
41
58
77

1.3
3
5.6
9.4

150
175
200
225

99
124
155
191

14.4
21.2
31.1
47.3

250
275
300

233
283
342

69.7
100.3
141.5

In conclusion, the exercise set for Phase I was treatable with the PICEP software. It is worth
noting that there is a more significant discrepancy between the model computation and themeasured values (Table 3.13) in case of low pressure and temperature.

3.2.4. KINS
KINS’ analyses of the benchmark problems were performed using a LEAPOR codedeveloped by Oak Ridge National Laboratory (see Section 2.5.4). LEAPOR is based on themodified Henry-Fauske model for the thermo-hydraulic calculation (see Section 2.4.4).
The wall thickness, full lengths of the crack at both interior and exterior, COD values
measured at three different positions, and COA were provided for the artificial slit case.
The wall thickness and full lengths were employed for the analysis, and the COD values atboth interior and exterior were assumed to be 0.193 and 0.221 mm, respectively, so that thecalculated cross section is the same as the provided COA. For crack morphology
parameters, both local and global roughness were assumed to be 22 μm, and local andglobal path deviations of 1.1 were applied. The calculated values are summarised inTable 3.16. This result is generally underestimated compared to the measured values.

NEA LEAK RATE BENCHMARK FINAL REPORT46  NEA/CSNI/R(2022)9

Table 3.16. Results of the artificial slit case calculated by KINS
Data number
Pressure [bar]Temperature [°C]

10
45.2
233.9

13
70.3
216.9

14
75.2
250.5

20
35.4
161.4

33
48.6
122.4

38
10.4
79.3

Computed leak rate [kg/s]
Reference [kg/s]

0.095
0.122

0.167
0.201

0.143
0.183

0.131
0.166

0.153
0.214

0.104

For the fatigue crack analysis, global roughness was provided, and the statistical local
roughness value of 8.814 μm was adopted according to Rahman’s research [14]. Local andglobal path deviations were assumed to be 1.017 and 1.06, respectively [14]. The predictedleak rates, as listed in Table 3.17, are higher than the measured leak rates. There's asignificant discrepancy between the model computation and the measured values (asreferenced in Table 3.17) as compared to the artificial slit case.

Table 3.17. Results of the fatigue crack calculated by KINS
Data number
Pressure [bar]Temperature [°C]
Computed leak rate [kg/s]

2
65.7
204.3
0.0285

9
20.8
204.4
0.0077

27
70.7
254.4
0.026

45
76.7
20.8
-

61
77.2
229.9
0.0293

80
62.1
161.8
0.03

Measured leak rate [kg/s]

0.016

0.00610.01640.04080.01650.0331

The real event analysis includes the calculation of the COD. Participants in this benchmark
project were required to select three levels of applied moment. The elastic-plastic
estimation scheme, based on the GE/EPRI ductile fracture handbook (see Section 2.2.1),
was adopted to predict the COD. In case of the applied moment, the high bending moment
value (MH.L.) was calculated based on the design bending moment described in the ASME
Boiler and Pressure Vessel (B&PV) Code Section NB [32]. Below is the equation used forthe calculation:
𝑀𝐻.𝐿. =2𝐼
𝑃𝑖 𝐷𝑜
(1.5𝑆𝑚 −)𝐷𝑜
2𝑡where I, Do, Pi and Sm are the moment of inertia, outer diameter, internal pressure, anddesign stress intensity, respectively. The Sm value of 138 MPa was used according to ASME
B&PV Code Sec. II. The medium and zero level of bending moments are set to be half ofMH.L. and zero, respectively. The evaluated values are shown in Table 3.18. The assumptionof the applied bending moment caused the overestimation of the COD values as comparedto the reference values and resulted in the over-prediction of the leak rate as well.

Table 3.18. Result of the real event analysis evaluated by KINS
Bending moment[kNm]

Leak rate [g/s]best-estimate

0
0.235
0.470

3 727
1 538

NEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  47

The LBB sensitivity analysis aims to find out the effect of local roughness, especially forthe tight crack case. For the COD prediction, the elastic-plastic estimation scheme was
employed based on the GE/EPRI ductile fracture handbook (see Section 2.2.1). The
modified Henry-Fauske model was adopted to evaluate the friction factor, flow resistance,
and fluid motion (see Section 2.4.4). The results are summarised in Table 3.19.

Table 3.19. Result of the LBB sensitivity analysis by KINS
Local roughness
Full crack length
Crack open.
displ.
[mm]
[µm]
50
26
75
40

114 µmFriction factor
Mass flow rate

17 µm
Friction factor
Mass flow rate

[-]
0.924
0.924

[g/s]
2
5.4

[-]
0.924
0.924

[g/s]
2
5.4

100
125
150
175

56
73
93
116

0.924
0.924
0.924
0.924

11.2
20
32.8
50.7

0.639
0.416
0.310
0.248

12.4
24.1
40.4
62.3

200
225
250
275

143
175
212
255

0.924
0.924
0.924
0.924

75.2
108.4
152.8
211.8

0.209
0.182
0.162
0.147

91.3
129.5
179.5
245

300

306

0.636

302.9

0.136

330.6

When the full crack length is less than 275 mm, the computed friction factors with the local
roughness of 114 µm are much higher than those with adjusted local roughness of 17 µm,
which leads to the underprediction of the leak rate.
In conclusion, the exercise set for Phase I was treatable with the LEAPOR software except
for the low pressure and temperature case (see Table 3.16 and Table 3.17). In addition, theartificial slit case, which is an idealised experimental case, shows a good agreement withmeasured results, while the results of fatigue crack and real event analysis were quite
different. This is attributed to the fact that the greater the number of variables to be
assumed, the greater is the difference from the referenced value.

3.2.5. KIWA
KIWA’s analyses of the benchmark problems are done with the ExcelSQUIRT code (seeSection 2.5.2). ExcelSQUIRT has a simplified user interface as compared to previous
versions (SQUIRT or WinSQUIRT). ExcelSQUIRT also lacks an opportunity to obtain
intermediate results that are part of an analysis (leak rate is the only result from an analysis).
The artificial slit case provides the measured flow resistance values. KIWA used the mean
COD values as input data for the analysis, although a better agreement was observed whenusing the maximum COD values (see Figure 3.1).

NEA LEAK RATE BENCHMARK FINAL REPORT48  NEA/CSNI/R(2022)9

Table 3.20. KIWA results of the artificial slit case
Data number
Pressure [bar]Temperature [°C]

10
45.2
233.9

13
70.3
216.9

14
75.2
250.5

20
35.4
161.4

33
48.6
122.4

38
10.4
79.3

KIWA [kg/s]
Reference [kg/s]

0.0918
0.122

0.154
0.201

0.1345
0.183

0.12
0.166

0.137
0.214

0.08050.104

Figure 3.1. KIWA results of the artificial slit case, sensitivity analysis using different COD
Leakage rate [kg/s]

Case 1: Artificial Slit Case
0.25
Measurement
ExcelSQUIRT (CODmean)
ExcelSQUIRT (CODmax)
0.2

0.15

0.1

0.05

0
38

10

20

14

13

33
Data id

The fatigue crack analysis is done in analogy to the artificial slit case. The results areshown in Table 3.21.

Table 3.21. KIWA results of the fatigue crack
Data number
Pressure [bar]Temperature [°C]

2
65.7
204.3

9
20.8
204.4

27
70.7
254.4

45
76.7
20.8

61
77.2
229.9

80
62.1
161.8

Computed leak rate [kg/s]
Measured leak rate [kg/s]

0.023
0.016

0.00550.0061

0.021833
0.01640.04080.024
0.01650.024
0.0331As shown in Table 3.21, no result was obtained for case 45 using ExcelSQUIRT. In orderto get a valid result, it was necessary to assume a higher temperature for this case.

NEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  49

In the real event analysis, the bending moment in the plant is unknown, but relevant for
the answer. Also, other inputs are given with great uncertainty. A sensitivity analysis istherefore needed, and KIWA investigated different bending moments that cause bending
stress between 0 and 50 MPa. The internal pressure of 15.9 MPa causes an axial stress of
23.2 MPa. The COD evaluation using KIWA’s in-house code gave inconsistent results.
Therefore, checks were also performed with the WinLeck code from GRS. The results areshown in Figure 3.2.

Figure 3.2. KIWA results of the real event analysis, sensitivity analysis using different
global bending stresses

Leakage rate [kg/s]

Case3: Real event analysis
0.03

Measurement
0.025

ExcelSQUIRT

0.02

0.015

0.01

0.005
0

10

20

30

40

50

Bending stress [MPa]As can be seen from this sensitivity analysis, the best agreement was obtained using a
global bending stress of 15 MPa.
The LBB sensitivity problem involves analysing how the results are affected by using
different crack lengths (50 to 300 mm). An investigation of the influence of the local
roughness was also part of this analysis. The results are shown in Figure 3.3 (using a local
roughness of 17 m).

NEA LEAK RATE BENCHMARK FINAL REPORT50  NEA/CSNI/R(2022)9

Figure 3.3. KIWA results of the LBB sensitive study, sensitivity analysis using different
crack lengths
Leakage rate [kg/s]

Case 4: LBB Sensitivity Study
0.5
Measurement
ExcelSQUIRT
0.4

0.3

0.2

0.1

0
0

50

100

150

200

250

300

Crack length at Rm [mm]3.2.6. NRC
The leak rate for the artificial slit case was determined using LEAPOR, (see Section 2.5.4).
The geometry and thermodynamic parameters for the artificial slit problem that were givenin the problem description were used for the inputs to the calculation using LEAPOR and
its GUI input programme, LEAPOR-SA. The specified inside diameter and outside
diameter crack lengths (2c) were used and the COD values were the average of the three
specified in the problem description. A rectangular crack cross section was assumed. A
second set of calculations was performed using COD values derived from the tabulated 2c
and COA values. The specified total resistance value, zeta, was not used in the calculation
as LEAPOR internally performs its own calculation of the Darcy friction factor. Since theslit was artificial and no further information was given, a value of zero was assumed forthe number of turns per unit length parameter, and an entry loss coefficient of 0.95 is hardcoded in LEAPOR. The leak path deviation parameters were assumed to be unity. The
calculation for single-phase leak, data number 38, could not be performed because
LEAPOR is specifically designed for two-phase calculations, and the LEAPOR solver
could not converge for the data number 33 calculation; no leak rate data are reported forthese two cases.

NEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  51

Table 3.22. NRC results of the artificial slit case
Data number
Pressure [bar]Temperature [°C]

10
45.2
233.9

13
70.3
216.9

14
75.2
250.5

20
35.4
161.4

33
48.6
122.4

38
10.4
79.3

Leak rate (2c, COD) [kg/s]
Leak rate (2c, COA) [kg/s]

0.09690.13100.17380.24950.148020.20790.13671
0.1957

N/A
N/A

N/A
N/A

The results of the artificial slit calculations mirror the measured mass flow rates given in
Table 3.2, with the predicted leak rate calculated using the average of the three values of
the COD, 194 and 218 µm for interior and exterior, respectively, consistently
underestimating the measured values. Using the COD calculated from the COA and 2c forthe interior and exterior, 230 and 185 µm, respectively, the calculated leak rates
consistently overestimated the measured values.
As for the artificial slit case, LEAPOR was used to perform the leak rate estimates for thefatigue cracks. COD-dependent crack morphology parameters for CF with local roughnessof 8.8 µm, global roughness of 40.5 µm, turns per metre of 6 730, global path length of
1.017 and global plus local path length of 1.06 were chosen. As before, the COD was
evaluated from the COA and 2c values, but since the calculated COD values did not differ
significantly from the tabulated COD values, only calculations using the tabulated COD
values were performed. Data number 45 could not be evaluated because it involved asingle-phase leak.

Table 3.23. NRC results of the fatigue crack
Data number
Pressure [bar]Temperature [°C]

2
65.7
204.3

9
20.8
204.4

27
70.7
254.4

45
76.7
20.8

61
77.2
229.9

80
62.1
161.8

Leak rate [g/s]0.028

0.00770.0261

N/A

0.02930.030

As opposed to the artificial slit case, LEAPOR tended to overestimate the measured leakrate for the fatigue crack cases. This result was somewhat surprising since the morphology
parameters that were used had a relatively large value for the number of turns, a parameterthat has a strong influence on the calculated leak rate. The difference between the measured
leak rate value and the LEAPOR estimate did not show a correlation with the degree ofundercooling, which could have indicated errors in the model implementation. Since thetemperatures and pressures for the different measurements were generally similar, there isa possibility that the differences lie in the leak rate measurements. This hypothesis may besupported by the spread in measured values between the first and second measurements.
The NRC could not provide leak rate data for the real event analysis because the watertemperature for this problem, 40–70°C, would have resulted in single-phase flow. The bestestimate COD values for each bending moment were evaluated for 50% crack face pressure(CFP), the under-estimate for 0% CFP and the over-estimate for 100% CFP. All of thereported COD values are those at the mid-wall. The moment for the medium bending
moment was selected so that the sum of the axial stress and the bending stress wasapproximately 25% of the yield stress, and the high moment resulted in approximately
60 MPa bending stress. No additional axial force beyond that from internal pressure wasadded to any of the evaluations.

NEA LEAK RATE BENCHMARK FINAL REPORT52  NEA/CSNI/R(2022)9

Table 3.24. NRC result of the real event analysis
Bending moment [kNm]0

Under est.
0.075Best est.
0.120

COD [mm]Over est.
0.177

Comment
Zero moment

0.06
0.2

0.178
0.658

0.249
0.806

0.334
0.972

Medium moment
High moment

The last Phase I exercise was the LBB sensitivity analysis, where the leak rate wasestimated for varying crack lengths and two different local roughnesses, 114 and 17 µm.
Table 3.25 shows the friction factors and mass flow rates for each of the crack lengths, aswell as the COD-dependent effective roughness (mueff) and effective number of turns perunit length (ntLeff). For most crack lengths, the friction factor remained constant for the
114 µm local roughness until very long crack lengths, and corresponding CODs werereached. The COD-dependent effective number of turns changed only slightly. For the
17 µm local roughness, the friction factor decreased rapidly for longer crack lengths, andthe effective roughness increased. Since the effective number of turns only depends on theratio of the COD to global roughness, the effective number of turns was the same for the
114 and 17 µm local roughness calculations.

Table 3.25. NRC result of the LBB sensitivity analysis
Local roughness
Full crack
Cracklengthopen.
displ.
[mm]
[mm]
50
0.019
75
0.030
100
0.042

114 µm

17 µm

Frictionfactormueff

ntLeffMass flowrate

Frictionfactormueff

ntLeffMassflow rate

[-]
0.924
0.924
0.924

[µm]
114
114
114

[1/m]
5 904
5 852
5 795

[kg/s]
0.00130.00360.0076

[-]
0.924
0.924
0.924

[µm]
17.7
18.6
19.6

[1/m]
5 904
5 852
5 795

[kg/s]
0.00130.00360.0076

125
150
175
200

0.056
0.072
0.091
0.111

0.924
0.924
0.924
0.924

114
114
114
114

5 729
5 653
5 563
5 468

0.01410.02350.03720.0549

0.634
0.426
0.318
0.260

20.8
22.2
23.8
25.6

5 729
5 653
5 563
5 468

0.01570.02830.04580.0676

225
250
275
300

0.133
0.157
0.183
0.223

0.924
0.834
0.573
0.385

114
114
114
114

5 364
5 250
5 127
4 938

0.07770.10640.14190.1985

0.222
0.196
0.177
0.158

27.5
29.5
31.7
35.2

5 364
5 250
5 127
4 938

0.09480.12830.16890.2321

3.2.7. OCI
OCI’s analyses of the benchmark problems were carried out with the LOCI™ code (seeSection 2.5.5), developed by OCI.
In the context of an LBB assessment where emphasis is placed on the detection of small
leakage rates, the distinction between conservative and best-estimate models becomes very
important. This classification can provide guidance on where these models can beappropriately applied, taking account of margins and uncertainties. A conservative leakagerate model is required to consistently underestimate the actual leakage rate and is typicallyapplied in deterministic procedures, e.g. the deterministic approach in the German standard

NEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  53

KTA 3206. A best-estimate leakage-rate model places greater emphasis on predictive
accuracy. In a probabilistic framework, this model’s estimated solutions can serve as ameasure of central tendency (mean, median, or mode) for a prescribed statistical
distribution characterising the uncertainties in the leakage-rate predictions. LOCI™
provides both best-estimate and conservative leakage-area and leakage-rate models.

Note on morphology parameters
LOCI™ contains a database of morphology parameters preselected as a function of damage
mechanism. In Table 3.26, the values from this database are compared to the parametersprovided in the problem statements for three cases: (1) Fatigue crack, (2) Real event, and(3) LBB sensitivity.

Table 3.26. Morphology parameters as a function of damage mechanism
Data

DamageSourceRz(local) Rz(global)

Rt(max)

h tL

KG

K G+L

Mechanism (microns) (microns)(microns)

1/m

(-)

(-)

LOCI Databasefatigue

8.814

40.51

NA

6730

1.017

1.060

Fatigue Crack Casefatigue

NA*

40.00

NA

NA

NA

NA

Real Event Casefatigue

NA

7.60

10.6

NA

NA

NA

LOCI Database

PWSCC

16.86

114

NA

5940

1.009

1.243

LBB Sensitivity

PWSCC

17 or 114

114

NA

5940

1.2

1.2

*NA = not available

OCI results for the artificial slit case
Two leakage-rate models included in LOCI™ are applied in the analysis of the artificial
slit case: 1) the extended Henry-Fauske best-estimate model (see Section 2.4.4) and 2) the
conservative modified Bernoulli model (see Section 2.4.6). The computed values from bothmodels are shown in Table 3.27 and comparisons to the measured leakage rates for thiscase are presented in Figure 3.4.
As shown in Figure 3.4, the leakage-rate results for the modified Bernoulli model
consistently underestimate the actual leakage rate for this case, thus satisfying the design
intent of a conservative model as required by the KTA 3206 standard [20]. Compared tothe modified Bernoulli model, the results from the Henry-Fauske model provide predictedleakage rates that are closer to the experimentally-measured data for the artificial slit case,as expected for a best-estimate model.

Table 3.27. OCI results for the artificial slit case using LOCI™
Data number
Pressure [bar]

10
45.2

13
70.3

14
75.2

20
35.4

33
48.6

38
10.4

Temperature [°C]
Henry-Fauske [kg/s]
modified Bernoulli [kg/s]
Measured leak rate [kg/s]

233.9
0.0966
0.0563
0.122

216.9
0.171
0.102
0.201

250.5
0.146
0.0844
0.183

161.4
0.134
0.0818
0.166

122.4
0.156
0.105
0.214

79.3
0.09320.0496
0.104

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Figure 3.4. Artificial slit case LOCI™ solutions from Henry-Fauske and modified
Bernoulli models

Predicted Mass Flowrate (kg/sec)

Henry-Fauske
modified Bernoulli
Henry-Fauske trend curvemod. Bernoulli trend curve--

Artificial Slit Case
Solutions by LOCITMHenry-Fauske

mod.
Bernoulli

overpredicts experimental data

0.1

underpredicts experimental data
0.0

0.0

0.1

Measured Mass Flowrate [kg/sec]

OCI results for the fatigue crack case
LOCI ™ analysis results for the fatigue crack case are listed in Table 3.28 and shown in
Figure 3.5. Flow-rate solutions were calculated for each case using the conservative
modified Bernoulli and the best-estimate Henry-Fauske models. For the Henry-Fauske
solutions, a comparison is made in Table 3.28 between the morphology parametersprovided in the fatigue crack problem statement and the parameters taken from the LOCI™
database (see Table 3.26).

Table 3.28. OCI results for the fatigue crack case using LOCI™
Data number
Pressure [bar]Temperature [°C]
Henry-Fauske* [g/s]

2
65.7
204.3
28.1

9
20.8
204.4
7.7

27
70.7
254.4
25.7

45
76.7
20.8
34.7

61
77.2
229.9
28.9

80
62.1
161.8
29.6

Henry-Fauske** [g/s]
modified Bernoulli [g/s]Measured leak rate [g/s]

28.4
15.3
16.0

7.7
4.3
6.1

26.0
11.1
16.4

35.0
20.6
40.8

29.2
15.1
16.5

30.0
16.8
33.1

*Morphology parameters provided in fatigue crack case problem statement.
**Morphology parameters taken from Table 3.26 LOCI™ database.

NEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  55

Figure 3.5. Fatigue crack case solutions from the Henry-Fauske and modified Bernoulli
models0.100

Predicted Mass Flowrate (kg/sec)

Henry-Fauske
modified Bernoulli
Henry-Fauske trend curvemod. Bernoulli trend curve--

Fatigue Crack Case
Solutions by LOCITMHenry-Fauske

overpredicts experimental data

modified
Bernoulli

0.010

underpredicts experimental data
0.001
0.001

0.010

0.100

Measured Mass Flowrate [kg/sec]

As observed for the artificial slit case, the conservative modified Bernoulli leakage-rate
solutions are consistently lower than the best-estimate Henry-Fauske predictions. The
modified Bernoulli leakage-rate predictions trend towards underestimating theexperimental data.

OCI results for the real event case
LOCI ™ analysis results for the real event case are listed in Table 3.29 for three bending
levels: 1) no bending, 2) medium bending at 0.05 [kN-m], and 3) high bending at 0.1 [kN
m]. In addition to the applied bending moment, pressure loading is also included in therequired leakage-area analysis using the modified GE/EPRI model available in LOCI™.

Table 3.29. OCI results for the real event case using LOCI™
Bending moment [kN-m]
00.05

Under-estimate
29.2
31.5

Leak rate [g/s]Best-estimate
54.8
59.2

0.1

33.9

63.8

Over-estimate
291
292
292

The Henry-Fauske solutions in Table 3.29 make use of the LOCI™ flow regimes that are
defined in a transition model developed for the MERIT project and described in [44]. Thistransition model is divided into four flow regimes as shown in Figure 3.6.
•

Regime 1: Leff / Dh  30 (Henry-Fauske model for two-phase critical [choked]
flow)

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Regime 2: Bridge between Regime 1 and Regime 3 (Henry-Fauske model at
Leff / Dh = 30 )•

Regime3:–linearOrificeflow

Transitioninterpolationof

Gc2 solutionofsubcooledbetween

4.6  Leff / Dh  12•

Regime4:liquid–pc p0 = 0.522 (fixed) at Leff Dh = 4.6

where
Leff = effective crack flow length including morphology effects
Dh = hydraulic diameter of crack flow channel
Gc = critical leakage rate of mass flux at crack exit
pc = critical pressure at crack exit
p0 = fluid pressure inside of pipe

In Table 3.29, three estimation types are included:
1. an under-estimate solution based on the linear-elastic GE/EPRI leakage-areamodel (Section 2.2.2) and the modified Bernoulli leakage-rate model (Section
2.4.6),
2. a best-estimate solution based on the linear-elastic GE/EPRI leakage-area model(Section 2.2.2) and the Henry-Fauske leakage-rate model (Section 2.4.4) (Regime
1 – two-phase critical flow), and3. an over-estimate solution based on the elastic-plastic GE/EPRI leakage-area model(Section 2.2.1) and the LOCI™ leakage-rate model for high flows (Regime 2 –bridge between Regime 1 and Regime 3).

Figure 3.6. Transition model in LOCI™ – flow regime definitions.

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OCI results for the LBB sensitivity case
The OCI results for the LBB sensitivity case are presented in Table 3.30, where all cases
were executed using the Henry-Fauske model implemented in LOCI™. The CODs were
calculated using the EPFM GE/EPRI method (Section 2.2.1).

Table 3.30. OCI results of the LBB sensitivity analysis
Local roughness
Crack length,
Average
2c
COD
[mm]

[µm]

Rz (local) = 114 µm
Darcy
Mass flow
frictionrate
factor, f
[-]
[g/s]

Rz (local) = 17 µm
Darcy
Mass flow
frictionrate
factor, f
[-]
[g/s]

50
75
100
125

26
40
55
72

0.924
0.924
0.924
0.924

2.83
7.59
15.3
26.9

0.924
0.516
0.322
0.236

2.83
8.87
18.9
33.3

150
175
200
225

94
117
143
171

0.924
0.924
0.924
0.924

44.7
68.9
101
141

0.188
0.159
0.141
0.127

54.3
82.1
118
163

250
275
300

202
234
290

0.661
0.475
0.326

200
271
389

0.118
0.111
0.103

218
286
401

For the local roughness of 114 m, the primary contributors to the total pressure drop areshown as percentages of the total pressure loss in Figure 3.7. For short cracks, the frictionalpressure drop plays a dominant role. As the crack becomes longer, this wall friction effectfalls off and the morphology of the crack face becomes more dominant. Figure 3.8
demonstrates that the same trends can be observed when the local roughness is 17 m;however, the contribution of the wall friction to the total pressure loss decreases more
rapidly than in the 114 m case. In both cases the pressure drop due to crack path tortuosity
dominates for longer crack lengths.

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Figure 3.7. Primary contributors to total pressure drop with local Rz = 114 m.
100

80

Percentage of Total Pressure Drop (%)

LBB Sensitivity Study
Solutions by LOCITMLBB Sensitivity Study
Henry-Fauske Flow Rate ModelPWSCC Morphology Modelcollapse moment M0 = 1,674,682,188 N-mm
GE/EPRI leak area model
T0 = 340 C, P0 = 15.5 MPa

90vaporization
friction70

tortuosity
path tortuosity

60

GE/EPRI plastic
w/pressure50

Rz (local) = 114 m
Rz (global) = 114 mwall friction

40

30

20

acceleration by vaporization

10

0

50

100

150

200

250

300

Average Crack Length, 2c [mm]Figure 3.8. Primary contributors to total pressure drop with local Rz = 17 m
100
LBB Sensitivity Study
Henry-Fauske Flow Rate ModelPWSCC Morphology Modelcollapse moment M0 = 1,674,682,188 N-mm
GE/EPRI leak area model
T0 = 340 C, P0 = 15.5 MPa

90Percentage of Total Pressure Drop (%)

80

LBB Sensitivity Study
Solutions by LOCITM

vaporization
friction70

path tortuosity

tortuosity

60

GE/EPRI plastic
w/pressure50

Rz (local) = 17 m
Rz (global) = 114 m

40

30
acceleration by vaporization

20

10

wall friction

0
50

100

150

200

250

300

Average Crack Length, 2c [mm]

NEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  59

3.2.8. PSI
PSI used the LEAPOR (see Section 2.5.4) code with the Henry-Fauske model (seeSection 2.4.4) to calculate the friction and resistance, and the homogeneous equilibrium
model (HEM) was used as the flow model. The HEM approach considers the two-phasemixture to be a pseudo-fluid, which can be described by the same conservation law
principles that are valid for a single-phase flow condition. In this model, the two phases are
assumed to be everywhere in a state of both thermal and mechanical equilibrium. For
adiabatic flow, the process is assumed to be reversible and, therefore, isentropic, and thevelocities of the two phases are assumed to be equal. The equilibrium properties of the twophases can be obtained from a water-property formulation (“Steam Tables”) implemented
in the code or from some general equation of state.
Note that LEAPOR can only deal with pipe cases. Therefore, the plate was approximatedas a very large pipe with an outer diameter of 1010 mm.

Table 3.31. PSI results of the artificial slit case
Data number
Pressure [bar]Temperature [°C]

10
45.2
233.9

13
70.3
216.9

14
75.2
250.5

20
35.4
161.4

33
48.6
122.4

38
10.4
79.3

Measured mass flow rate [kg/s]
Second estimate [kg/s]
Leak rate [kg/s]
Difference [%]

0.122
0.1
0.102
2

0.201
0.203
0.172
2.9

0.183
0.157
0.15
3.3

0.166
0.174
0.135
3.1

0.214
0.189
0.161
5.3

0.104
0.117
0.16
5.1

Compared with the measured mass flow rate, the numerical leak rate is a bit lower when
the temperature and pressure exceed 122.4°C and 35.4 MPa, respectively, but is more inagreement with the second estimate. However, the calculated flow rates are in good
agreement with the measured ones because the difference between the measured andcalculated rate is less than 5%. Note that the calculated leak rate is higher than the measured
one when the temperature and pressure are lower, i.e. 79.3°C and 10.4 MPa, respectively.
It can be inferred that there exists a pressure and temperature limit in the implemented
model of LEAPOR, below which the leak rate would be overestimated.
In addition, it is found for the artificial slit case that the internal pressure has more influenceon the leak rate than the temperature. When the pressure is increased from 45.2 bar to
48.6 bar, the leak rate is increased by 50% although the temperature is reduced from
233.9°C to 122.4°C. Likewise, the leak rate increased also by 50% with the temperaturearound 240°C when the pressure is increased from 45.2 bar to 75.2 bar.

Table 3.32. PSI results of the fatigue crack
Data number
Pressure [bar]Temperature [°C]

2
65.7
204.3

9
20.8
204.4

27
70.7
254.4

45
76.7
20.8

61
77.2
229.9

80
62.1
161.8

Measured mass flow rate [kg/s]
Second estimate [kg/s]
Leak rate from LEAPOR [kg/s]
Difference [%]0.016
0.02260.019718.7

0.00610.01450.004632.6

0.01640.01820.01819.4

0.04080.04780.04529.7

0.01650.02170.020318.7

0.03310.03690.020859.1

NEA LEAK RATE BENCHMARK FINAL REPORT60  NEA/CSNI/R(2022)9
In the fatigue crack case, it is found that some leak rates calculated with LEAPOR are far
from the measured mass flow rates, especially if the pressure and temperature are 62.1 barand 161.8°C, respectively. When both pressure and temperature are at high levels, thesimulated leak rate results are a bit higher than the measured ones. The leak rates areoverestimated by the numerical method.

Table 3.33. PSI result of the real event analysis
Reference leak rate: 0.013 kg/s
Zero Bending
Bending Moment [kNm]
Medium Bending
Large Bending

Underestimation0Best-Estimate
0Overestimation
0

Leak rate [kg/s]
Bending Moment [kNm]
Leak rate [kg/s]
Bending Moment [kNm]

00.6
0.00913
1.61

0
1.11
0.04613
1.81

0
1.31
0.05953
2.01

Leak rate [kg/s]

0.08157

0.108930.12509

As LEAPOR code cannot deal with the variable bending moment, we can refer to the COD
and leak rate calculation methods implemented into this code (Zahoor, see Section 2.2.1).
Finally, we can conclude that the leak rate is regarded as zero when no bending moment isintroduced. Hence, the best estimate lies on the applied medium bending moment range
between 0.6 and 1.11 kNm, which causes the leak rate to approach the reference leak rate.
It also reveals that the crack is closed without a bending moment.

Table 3.34. Result of the LBB sensitivity analysis
Local roughness
Full crack
Crack open.
lengthdispl.
[mm]
[mm]
50
0.024
75
0.0368114 µmFriction
Mass flow
factorrate[-][kg/s]
0.013361172
0.00195
0.013361172
0.00529

17 µm
Friction
Mass flow
factorrate[-][kg/s]
0.009418383
0.00195
0.009418383
0.00533

100
125
150
175

0.05030.06490.08080.098

0.013361172
0.013361172
0.013361172
0.013361172

0.01075
0.018840.03009
0.044990.009418383
0.009418383
0.009418383
0.009418383

0.01134
0.02211
0.03667
0.05532

200
225
250
275

0.117
0.137
0.15950.183

0.013361172
0.013361172
0.013361172
0.013361172

0.064430.088450.118930.15534

0.009418383
0.009418383
0.009418383
0.009418383

0.07893
0.10740.143310.18439

300

0.209

0.013361172

0.200020.009418383

0.23477

As shown in Table 3.34, a higher local roughness increases the friction factor and as a result
the mass flow rate is reduced. With an increase of the full crack length, the COD also
increases, which results in the rise of the mass flow rate. The leak rate difference causedby different local roughness is bigger when the crack is longer. The conclusion is that the
COD has more influence on the mass flow rate than the local roughness.
LEAPOR is a simple tool to simulate the leak rate. Therefore, external loadings are notconsidered as variables; only the definition of pressure and temperature is possible once
the geometries and sizes of pipe and flaws are given.
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3.2.9. SNC
For the artificial slit and fatigue crack exercise problems, the leak rate is estimated using
LEAPOR (Section 2.5.4), SQUIRT (Section 2.5.8) and CFX’s software (Section 2.5.1). In
both SQUIRT and LEAPOR, the structure is considered a large diameter pipe
(D>1000mm) instead of a plate and the COD is estimated from the crack length and crosssectional area, considering it was a rectangular shaped flaw. In SQUIRT, both ID and OD
crack length are considered as average values of crack lengths provided in Table 3.1, while
in LEAPOR, the actual crack lengths are used. For both these problems, CF is assumed in
SQUIRT with crack morphology parameters from Table 3.9 of Reference [14]. Crackmorphology parameter in Table 3.1 is used in LEAPOR.
In the CFX calculation, the flow inlet is modelled using the subsonic flow regime with
“Total Pressure (stable)” option for mass and momentum setting. Medium turbulence(intensity = 5%) and the “Total Temperature” option are used for heat transfer setting. The
flow outlet is modelled using the subsonic flow regime with “Average Static Pressure”
option (pressure profile blend = 0.05) for mass and momentum setting. Pressure isconsidered averaging over the whole outlet. The pipe wall boundary is modelled using the“No Slip Wall” option for mass and momentum setting and the “Adiabatic” option for heattransfer setting. The “Rough Wall” option with different sand grain roughness is adopted.
The results of the artificial slit and fatigue crack exercise problems are presented inTable 3.35 and Table 3.36.

Table 3.35. SNC results of the artificial slit case
Data number
Pressure [bar]Temperature [°C]
LEAPOR [kg/s]

10
45.2
233.9
0.0950

13
70.3
216.9
0.1580

14
75.2
250.5
0.1379

20
35.4
161.4
0.1245

33
48.6
122.4
0.1475

38
10.4
79.3
-

SQUIRT [kg/s]
CFX [kg/s]
Reference [kg/s]

0.09320.10800.122

0.15350.13600.201

0.13450.13700.183

0.12020.20000.166

0.15380.24000.214

0.07110.1116
0.104

When compared to the measured leak rate, both LEAPOR and SQUIRT underpredict theleak rate with a maximum absolute percentage difference of 46.3%. Since the temperaturefor data number 38 is low and it can be considered a single-phase flow, LEAPOR did notachieve a converged solution, and thus data number 38 is not considered in percentage
difference calculations.
Ansys CFX overestimated the leak rate for three of the test data and underestimated it forthe other three, with a maximum percentage difference of 47.8%.

NEA LEAK RATE BENCHMARK FINAL REPORT62  NEA/CSNI/R(2022)9

Table 3.36. SNC results of the fatigue crack
Data number
Pressure [bar]Temperature [°C]

2
65.7
204.3

9
20.8
204.4

27
70.7
254.4

45
76.7
20.8

61
77.2
229.9

80
62.1
161.8

LEAPOR [kg/s]
SQUIRT [kg/s]
CFX [kg/s]
Measured leak rate [kg/s]

0.02820.02960.02400.016

0.00780.00830.01200.00610.02580.02710.03000.01640.04630.03800.04080.02900.03050.03800.01650.02970.03120.03720.0331For the fatigue crack, in summary, all three methods overestimate the leak rate whencompared to the measured one, except for data numbers 80 and 45 (CFX only). Due to the
low temperature in data number 45 resulting in a single-phase flow, LEAPOR did notachieve a converged solution. The maximum absolute percentage differences for LEAPOR,SQUIRT and CFX are 58.3%, 45.9% and 56.6%, respectively.
The leak rate for the real event exercise problem is estimated with SQUIRT (Section 2.5.8)
with crack morphology parameter of CF. An elliptical crack shape and an operating
temperature of 40°C are assumed for the leak rate estimation in SQUIRT. For each level ofbending moment, COD at mid-wall is estimated using an in-house solution. Mid-wall COD
is assumed at both ID and OD surfaces.
The high bending moment was calculated using equation (9) in Article 3652 of ASMEBPVC Section III using the Code value of design stress intensity of SA-312 Type 304. The
medium bending moment was taken as half of the high bending moment, and the low
bending moment was defined as zero. Results of the real event analysis are presented inTable 3.37.

Table 3.37. SNC result of the real event analysis
Reference leak rate: 0.013 kg/s
Zero Bending
Bending Moment [kNm]
Leak rate [kg/s]
Medium Bending
Bending Moment [kNm]
Large Bending

Leak rate [kg/s]
Bending Moment [kNm]
Leak rate [kg/s]

Best-estimate
00.0294293.790.2384587.581.87

For the real event analysis, even with zero bending moment, the predicted leak rate is above
the measured leak rate of 0.013 kg/s. Uncertainty in temperature can be ignored as the given
range of temperature from 40°C-70°C typically results in single-phase flow. Uncertainties
in the crack morphology, COD solution and shape of the crack can be attributed todifferences in the estimated leak rate.
Both SQUIRT and LEAPOR are used to estimate leak rates for LBB sensitivity analysis
where COD was calculated using an in-house solution with weld material properties. As
expected, the predicted leak rate is higher for lower local roughness parameters, but at alower COD level, the leak rate is not sensitive to local roughness.

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Table 3.38. SNC result of the LBB sensitivity analysis
Local roughness
Full crack
Cracklengthopen.
displ.

114 µmSQUIRT
LEAPOR
Friction
Mass
FrictionMassfactorflow rate
factorflow rate[-][kg/s][-][kg/s]
0.00290.92425
0.0025

17 µm
SQUIRT
LEAPOR
Friction
Mass flow
Friction
Mass flow
factorrate
factorrate[-][kg/s][-][kg/s]
0.00270.92425
0.0025

[mm]
50

[mm]
0.0312

75
100
125
150

0.04850.06740.08880.11310.00790.01630.02910.04740.924250.924250.924250.92425

0.00710.01440.02570.04190.00730.01740.03230.05270.841170.46856
0.327400.25528

0.00730.01700.0316
0.0516

175
200
225
250

0.14130.17420.21280.25830.07270.107
0.15460.21520.924250.924250.924250.92425

0.0647
0.09610.1386
0.19590.08040.11730.16630.23130.21149
0.18235
0.16171
0.146450.07870.11480.16280.2263275
300

0.31200.37540.30680.41920.60823
0.41379

0.28620.40420.31760.43280.13484
0.125810.3106
0.4230In general, both LEAPOR and SQUIRT where able to predict the leak rates reasonably
well; no consistent trend of overestimation or underestimation could be established and theresults are very sensitive to the input parameters.

3.2.10. UJVÚJV analyses of the benchmark problems are done with the LeakH code (see Section 2.5.3)
developed by ÚJV. Results are presented in the form of intervals corresponding to the COD
scatter as defined in the input. Compliance between the measured and calculated flow rates
is excellent, with a reasonable level of conservativity (lower values are conservative for
LBB).

Table 3.39. ÚJV results of the artificial slit case
Pressure [bar]Temperature [°C]

Measured mass
flow rate [kg/s]

45.2
70.3

233.9
216.9

0.122
0.201

Numerical
participant result[kg/s]
0.087 – 0.112
0.157 – 0.203

75.2
35.4
48.6
10.4

250.5
161.4
122.4
79.3

0.183
0.166
0.214
0.104

0.130 – 0.169
0.126 – 0.163
0.162 – 0.209
0.074 – 0.096

In the case of fatigue crack, the COD was defined by one value in the input, contrary to
artificial crack, and therefore the calculated leak rate can be expressed by one value. The
code LeakH was used in this calculation, as in the previous case. The results are shown in
Table 3.40.

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Table 3.40. ÚJV results of the fatigue crack
Pressure [bar]Temperature [°C]

Measured mass
flow rate [kg/s]

65.7
20.8
70.7

204.3
204.4
254.4

0.016
0.00610.0164

Numerical
participant result[kg/s]
0.03170.01050.0248

76.7
77.2
62.1

20.8
229.9
161.8

0.04080.01650.0331

0.04250.03140.0347The deviation between the model computation and the measurement is significantly larger
than for the artificial slit case. In four cases, the computed leak rates are higher, while intwo cases the measured values are practically identical with the calculated values.
In the real event analysis, low, medium and high bending moments were defined as 0 Nm,
40% of maximum allowable stress and 80% of maximum allowable stress of uncracked
pipe. The maximum allowable stress was calculated according to the Czech code A.S.I.
Only the best estimated value was calculated for both 40°C and 70°C. The COD was
calculated according to Akram Zahoor Ductile Fracture Handbook (Section 2.2.1). One
roughness of 7.6 μm was used. The computed values are shown in Table 3.41.

Table 3.41. ÚJV results of the real event analysis
Bending moment[kNm]

COD [mm]

0
0.187
0.374

Leak rate [kg/s]

0.075

40°C
0.159

70°C
0.158

0.597
2.021

1.79
6.19

1.77
6.14

The detected leakage of 0.013 kg/s is lower than the minimum calculated leakage
corresponding to zero bending moment. This may be due to the effect of plugging. The
effect of plugging is higher for lower COD. The influence of temperature is negligible.
Results of LBB sensitivity tasks are presented in Table 3.42 below. LEAKH is not able tocalculate local surface roughness, only a global one can be entered as input. Instead ofinfluence of roughness, the influence of type of turnings (either 90° or 45°) is considered.
The COD was calculated according to the Akram Zahoor Ductile Fracture Handbook (seeSection 2.2.1). The number and type of turning are crucial for LBB analysis, as seen in
Table 3.42.

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Table 3.42. ÚJV results of the LBB sensitivity analysis
Number of turns
Full crack
Crack open.
lengthdispl.
[mm][mm]
50
0.12008100
0.306417
150
200
250
300

0.602961.110101
2.002956
3.622305

90° turns 240
Mass flow
rate[kg/s]
0.00313
0.036545° turns 240
Mass flow
rate[kg/s]
0.0232
0.377

0.162
0.473
1.22
3.48

1.79
5.39
13.8
37.9

3.3. Comparison
3.3.1. Artificial slit
In total, 12 contributions were received for the computation of the mass flow rates throughartificial slits. The received computations and the reference values are shown in Figure 3.9.
The tests were of data set numbers 10, 13, 14, 20, 33 and 38, and were numberedconsecutively.

Figure 3.9. Left: Comparison of the calculated leak rates (coloured) with the reference(black). Right: The test conditions in the pT-diagram of water

From this figure, it can be confirmed that most methods have a good qualitative agreementwith the relation between thermodynamic conditions and mass flow rate. All except one
are carried out as a best-estimate analysis, while one analysis is done as an underestimation(which consistently reports the lowest rates well below the measured values). For anunderstanding of the different approaches among the participants, a classification of thecontributions is proposed.

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Figure 3.10 shows which geometrical information is used by each participant, since theexercise table provides information about the inlet and the exit. In this graph, it is visiblethat the participants that use both sides are the largest group. Only one participant uses the
COD specification as geometry information, which leads to significant differences to theother teams. Thus, the different choice in geometric information can be identified as apossible reason for a different leak rate prediction.

Figure 3.10. Analysis results for the artificial slit with emphasis on the leak geometry

The second evaluation is done with respect to the friction and resistance model. There aredifferent approaches: One fraction is computing a friction factor based on the morphology(roughness) information using a relation as the one by Paul et al., John et al., or KTA 3206.
Two contributions use the single-phase flow resistance measured for the leak. One
contribution assumes only a form loss coefficient and no frictional loss. In twocontributions, the treatment of flow resistance cannot be well separated from the approach.
The comparison of all approaches is shown in Figure 3.11.

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Figure 3.11. Influence of friction modelling to the leak rate computation

From this figure, it seems to be clear that the use of the actual resistance value yields ahigher accuracy than the use of the morphology. The result for the inlet loss is also very
good in this case. The use of the KTA 3206 relation is the key to obtaining theunderestimating trend in this result, which is well achieved.
The third classification is the actual flow model, which describes the evolution ofthermodynamical properties of water along the flow channel. The models according toHenry and Pana, a homogenous equilibrium approach, the modified Bernoulli equation, acomputational fluid dynamic (CFD) approach, the CDR model, and the model from
Zaloudek are used. A classification according to the actual flow model in the simulation isapplied in Figure 3.12.

Figure 3.12. Evaluation of flow models in the artificial slit exercise

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It is evident from this figure that the grouping influenced by the aforementioned geometry
and resistance assumptions remains. The grouping of the Henry-like models with accurate
cross-section and roughness-determined resistance is clearly visible. Compared with theother contributions, they do not have the highest accuracy, but rather show a trend tosmaller leakage rates. To separate the flow model influence from geometrical andresistance assumptions, the dependency of the leak rate on the test number (i.e. fromthermodynamic conditions) is a good measure. Most model computations (despite outliers)
follow the measured trend, with the notable exception of the CFD contribution (test No. 3
and 4).

3.3.2. Fatigue crack
The 12 contributions for the fatigue crack are shown in Figure 3.13. One is anunderestimating analysis, while all others are best-estimate analyses. As before, the tests
are numbered consecutively.

Figure 3.13. Phase 1 fatigue crack result

The differences between measured and computed values are satisfying; the worst examples
differ by about a factor of 2. The underestimating analysis is below the measured values,
but not the lowest of all.
The friction and resistance assumption are important building blocks of the analysis. In theassessment of the fatigue crack, different levels of information can be used:•

the fact that it is a fatigue crack and assuming standard values for the morphology;•

the measured surface roughness as morphology, and computing the friction factor
by standard relations;•the measured resistance as obtained in cold flow tests.

The classification according to this scheme is visualised in Figure 3.14.

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Figure 3.14. Resistance classification for fatigue crack exercise

The use of the measured resistance leads to a good agreement between computation andmeasurement, but some of the results based on the measured morphology are of similar
precision. The results based on the damage mechanism show a lower accuracy. The
underestimating contribution is based on the conservative computation of the resistanceand is therefore shown as a particular class (KTA 3206).
The influence of the flow model is discussed with help of Figure 3.15. Most of theparticipants use implementations of the Henry model – the users of the LEAPOR
implementation are shown as a class of their own. The other participants use the Panamodel, a homogeneous equilibrium approach, or the modified Bernoulli approach.

Figure 3.15. Flow model analysis for fatigue crack case

Test No. 4 is a cold water test, and several Henry model implementations fail to treat (orcatch) this case correctly, mostly skipping the value (note the missing points in the
diagram). The modified Bernoulli approach is not appropriate for the cold flow test either;

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consequently, the behaviour at that point is of minor quality. However, the modified
Bernoulli equation, the homogeneous equilibrium approach and the Pana model are theonly models in the contributions that show the correct qualitative trend for all points – many
Henry models fail to predict the increase in leak rate between point 5 and 6.

3.3.3. Real event
For the analysis of the real event, the task was to estimate the unknown bending acting ona circumferential crack, and to perform a sensitivity study with different bending
assumptions. Fourteen different computations were received: nine best-estimate analyses,
three under-estimations and two over-estimates. The predicted leak rates for the individual
bending moment assumptions as chosen by each participant are shown in Figure 3.16.

Figure 3.16. Phase 1 real event

The under-estimates are significantly lower than the over-estimates, but the best-estimates
range from very low to very high values. While the participants’ assumptions of the realistic
bending moment are in good agreement (between 0.1 and 1.0 kNm), the leak rates vary by
three orders of magnitude.
One important assessment step is the computation of the leak opening, as manifested in the
COD. Most participants use the GE/EPRI method from the ductile fracture handbook, andanother significant group uses the elastic version of this method. One participant uses the
LBB-ENG2-method and one (under-estimate) uses the GRS-PB method; other participants
are not reporting the (intermediate) COD values and are thus not included in the comparisonin Figure 3.17.

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Figure 3.17. Phase 1 real event: COD analysis by method

The figure shows that the COD values differ greatly. The elastic methods show an affinelinear dependence of the COD with the applied bending, as expected. As the material
properties are not proposed, the contributions based on the same methods are notnecessarily identical.

3.3.4. LBB sensitivity
In the analysis of the LBB sensitivity, eight contributions were received. As this analysis
involves the whole computation from crack opening to mass flow (see Section 2), it ispreferable to compare the results of intermediate steps. The first step, the computation of
the COD as a function of crack length, is shown in Figure 3.18. The different contributions
rely mostly on the ductile fracture handbook solution (GE/EPRI), its derivate LBB.ENG2
and the elastic approximation. The method of the xLPR code is also used in thecontributions.

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Figure 3.18. Phase 1 LBB sensitivity study crack opening displacement as a function of fullcrack length

Most methods are in good agreement with each other, with two notable exceptions: The
SQUIRT-implementation of the elastic EPRI method predicts a shrinking COD withincreasing crack length, and one participant reports a very steep increase of the COD
compared with the others.
The next step is assessing the friction factor as a function of the COD. All participants referto the friction factor relation according to Paul et al., so it is not necessary to distinguishbetween the models. Unfortunately, only five participants reported this value in theircontributions, so only those values are included in the comparison of models shown in
Figure 3.19. Solid lines indicate the assumption of 114 µm local roughness, while dashedlines correspond to 17 µm.

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Figure 3.19. Friction factor as a function of the crack opening displacement

The results for 17 µm are in reasonable agreement, while the results for 114 µm differ
significantly. In addition, all but one of the participants assume a saturation of the friction
factor, i.e. the value is limited to unity, while the value is not truncated for the single
participant.
The last step in the assessment is the computation of the leak flow rate for a given crack
opening. This is clearly influenced by the friction factor modelling, as discussed above.
The participants’ results are compared in Figure 3.20. The line styles are identical to theones in the previous figure.

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Figure 3.20. Mass flow rate as a function of crack opening displacement

Many mass flow rate computations for a given COD coincide, resulting in similar COD
computations and similar friction factors. The exceptions discussed previously can be
identified in this figure as well. The small values of one solid curve, leading to very smallvalues of leak rates for finite crack openings of about 0.1 mm, are a result of the diverging
friction factor.

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4. Second benchmark phase

The second benchmark phase was started after the results of the first benchmark phase werediscussed. The computational phase was prolonged in order to allow blind computations
even in case of delayed contributions.

4.1. Exercise set
4.1.1. Blind calculation of artificial slit
The exercise sheet for the blind calculation is given in Table 4.1. This test was done inanalogy to the artificial slit test described in the first benchmark phase (Section 3.1.1), butwith different specimen dimensions.

Table 4.1. Exercise sheet for the blind calculation of artificial slit
Category
Structure

Attribute
Geometry type
Wall thickness
Additional loads

Variable
t

Value
Plate
16.85

Unit
mm

Leak geometry

Approximate shape
Interior
Full length
Maximal width
Cross section

2c
COD
COA

20.5
138-158-147
3.08

mm
µm
mm²

Exterior

Full length
Maximal width
Cross section
Damage mechanism

2c
COD
COA
-

20.9
211-213-204
4.39
Eroded slit

mm
µm
mm²
-

Inlet form loss
Roughness Local
GlobalBends
Local

zeta_inRz
Rz
N

Unknown
Unknown
22
Unknownµmµm-

Global
Measured total resistancePressure
Temperature

N
Zeta
p
T

Unknown
4.56
variablevariablebar°CMorphology

Fluid (stagnation)

The pressure and temperature variations are given in Table 4.2.

Table 4.2. Pressure and temperature variation of the blind artificial slit case
Test No.
Data set
Pressure [bar]

1
8
60.4

2
15
10.5

3
18
45

4
38
45.4

5
40
63.6

6
55
25.5

Temperature [°C]

19.9

122.1

122.3

234.6

213

206.1

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4.1.2. Blind calculation of fatigue crack
The blind computation of a fatigue crack is the continuation of the first benchmark phasefatigue crack computation. The data sheet is reproduced in Table 4.3.

Table 4.3. Exercise sheet for the blind calculation of fatigue crack
Category
Structure

Leak geometry

Attribute
Geometry type
Wall thickness

Variable
t

Value
Plate
7.05

Unit
mm

Additional loads
Approximate shape
Interior
Full length
Maximal width

2c
COD

None
Rectangular
52
94

mm
µm

Cross section
Full length
Maximal width
Cross section

COA
2c
COD
COA

4.89
41.05
84
3.45

mm²
mm
mm
mm²

Damage mechanism
Inlet form loss
Roughness Local
Globalzeta_inRz
Rz

Fatigue
Unknown
Unknown
40

µm
µm

Bends

Local
Global
Measured total resistancePressure

N
N
Zeta
p

Unknown
Unknown
ca. 32variablebar

TemperatureTvariable°C

Exterior

Morphology

Fluid

The pressure- and temperature variation is in the same range as for the artificial slit caseand the first phase exercises. The six selected points are shown in Table 4.4.

Table 4.4. Pressure and temperature variation for the blind calculation of fatigue crack
Test No.
Data set
Pressure [bar]Temperature [°C]

1

2

3

4

5

6

31
75.3
199.4

18
65.5
234.8

32
15.7
200

13
45.4
238

44
50.6
16.7

49
30.1
151.9

4.1.3. Blind calculation of real event analysis
The blind calculation of a real event proposes the computation of an axial crack in a reducer.
The data sheet is shown in Table 4.5.

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Table 4.5. Exercise sheet for the blind calculation of real event
Category
Structure

Attribute
Geometry type

Variable-

Value
Reducer (3 inch to 2
inch)
75 to 50
12
AISI type 304

Unit
-

D
t

Material

Outer diameter
Wall thickness
NumberYoung's Modulus
Yield stress
Ultimate stress
Poisson number
RambergPrefactor
OsgoodExponent

E
Rp0,1
Rm
nu

Unknown
Unknown
Unknown
Unknown

MPa
MPa
MPa
-

alpha
n
p
M

Unknown
Unknown
7
Unknown

MPa
Nm

mm
mm
-

Loads

Pressure
Bending

Leak geometry

Orientation
Approximate shape
Interior
Full length
Estimatedmaximal width
Cross section
Mean
Full length
Estimatedmaximal width
Cross section
Exterior
Full length
Estimatedmaximal width
Cross section
Damage mechanism

2c
COD

Axial
Wall
Unknown
Unknown

mm
mm

COA
2c
COD

Unknown
Unknown
Unknown

mm²
mm
mm

COA
2c
COD

Unknown<25
Unknown

mm²
mm
mm

COA
-

Unknown
Thermal fatigue

mm²-

Inlet form loss
AverageLocalroughness
Globalzeta_inRz
Rz
Ra

Unknown
Unknown
Unknown
Unknownµmµm

Rt

UnknownMorphology

Meanroughness
Maximalroughness
Bends

Fluid
Leak rate

Local

N

Unknown-

Global
Measured total resistancePressure
Temperature

N
Zeta
p
T

Unknown
Unknown
7
280

MPa
°C

Measured flow ratem

(blind)kg/s

Since this evaluation is only done with one single measured value, it is proposed to makea best estimate, an underestimation and an overestimation analysis.

4.1.4. LBB sensitivity analysis
The finding of the parallel LBB benchmark activity, that the computed leak opening has astrong effect on the leak rate, motivated the analysis of a past experiment on COD.

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Table 4.6 summarises the test conditions of a pipe with a circumferential flaw under interiorpressure and a variable bending load.

Table 4.6. Exercise sheet for the LBB sensitivity analysis
Category
Structure

Material

Loads

Leak geometry

Attribute
Geometry type
Outer diameter

VariableD

Value
Cylinder
796

Unit
mm

Wall thickness
Type
Yield strength
Ultimate tensile strength

t
Rp02
Rm

47.3
NiMoCr-Cast
479.6
663

mm
MPa
MPa

Elastic modulus
Poisson number
Ramberg-Osgood

E
nu
σo
εo

196
0.3
479
0.02

GPa
MPa
-

Interior pressure
Temperature

α
n
p
T

3.9
6
15.8
140

MPa
°C

Bending moment
Orientation
Approximate shape
CentreFull length

M
tial
2c

Variable

417

MNm
mm

2 gamma

63.8°

Full angle

The change in COD as the bending moment increases was measured in the test andcomputed by the participants. The measured dCOD values are shown in Table 4.7.

Table 4.7. Bending moment and resulting crack opening for the LBB sensitivity analysis
Bending moment
M
[MNm]
0.00

Crack opening
displacement change
dCOD
[mm]
0.00

0.55
0.98
1.47
2.00

0.23
0.38
0.48
0.64

2.51
2.92
3.43
4.00

0.86
1.08
1.44
1.79

4.49
5.08
5.45

2.53
3.52
5.08

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The dCOD value is defined to be zero at vanishing bending; due to the test conditions, acrack opening solely due to pressure is not relevant for this exercise.

4.1.5. Steam generator tube leak analysis
This exercise is different from the others, since a very thin test specimen with a leak isinvestigated. The test was also conducted at MPA University of Stuttgart, and the test
conditions are summarised in Table 4.8.

Table 4.8. Exercise sheet for the SGT analysis
Category
Structure
Leak geometry

Morphology

Attribute
Geometry type

Variable
-

Value
Plate

Unit
-

Wall thickness
Approximate shape
Interior
Diameter
Cross section

t
D
COA

1.23
Circle0.3
0.0707mmmmmm²Exterior

Diameter
Cross section
Damage mechanism
Inlet form loss

D
COA
zeta_in

0.3
0.0707
Eroded holeUnknownmm
mm²-

Roughness

Rz
Rz
N
N

Unknown
7.4
Unknown
Unknown

µm
µm
-

Zeta
p
T

Unknown
variablevariable

MPa
°C

Bends

Local
GlobalLocal
Global

Measured total resistancePressure

Fluid
Stagnation

As in the cases of the artificial slit tests and the fatigue crack tests, six fluid conditions are
selected. The test conditions are summarised in Table 4.9.

Table 4.9. Pressure and temperature variation for the SGT analysis
Data number

10

13

19

20

22

24

Pressure [MPa]

7.59

2.09

8.08

5.55

6.54

7.45

Temperature [°C]

16.7

128.6

128.9

263.1

262.9

262.8

It was left to the discretion of the participants whether these tests were to be assessed withthe same methods used for thick-walled components or with specific methods for steam
generator tube leaks.

4.2. Computation
In this section, the individual participants’ contributions are documented and shortly
discussed. The subsections are arranged according to the participants’ organisations.

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4.2.1. BARC
BARC used the SCALE code (see Section 2.5.7) for the assessment; the Burnell model(Section 2.4.3), the Zaloudek model (Section 2.4.6) and the Henry model (Section 2.4.4)
are compared. The results for the artificial slit cases are summarised in Table 4.10.

Table 4.10. BARC results of the artificial slit case
Data number

8

15

18

38

40

55

Pressure

[bar]

60.4

10.5

45.0

45.4

63.6

25.5

Temperature

[°C]

19.9

122.1

122.3

234.6

213

206.1

Burnell[kg/s]

0.195

0.073

0.161

0.107

0.161

0.082

Zaloudek[kg/s]

0.186

0.067

0.151

0.084

0.145

0.062

Henry

[kg/s]

0.220

0.024

0.123

0.091

The fatigue crack case is analysed with the same methods. The BARC result for this caseis given in Table 4.11.

Table 4.11. BARC results of the fatigue crack case
Data number

31

18

32

13

44

49

[bar]

75.3

65.5

15.7

45.4

50.6

30.1

Temperature

[°C]

199.4

234.8

200

238

16.7

151.9

Burnell[kg/s]

0.209

0.165

0.053

0.115

0.119

0.138

Zaludek[kg/s]

0.192

0.142

0.010

0.087

0.189

0.127

Henry

[kg/s]

0.086

0.082

0.038

0.128

0.224

0.033

Pressure

4.2.2. GRS
As the organiser of the benchmark exercises, GRS was involved in the selection of theindividual problem sets and the preparation of the descriptions. Therefore, GRS’s analysesof the fatigue crack, the artificial slit and the real event are not performed as blind
computations.
In the LBB sensitivity analysis, two analytical methods are chosen for the computation of
the incremental COD change: the underestimating GRS-PB approach (see Section 2.2.3)
and the best-estimate LBB.ENG2 approach (see Section 2.2.4). While the latter considersa Ramberg-Osgood material stress-strain relation, the plastic strain parts of GRS-PB are
more qualitative and, in addition, conservative. The result is shown in Table 4.12; thedCOD values were obtained by considering the COD at zero bending moment.

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Table 4.12. GRS’ result of the LBB sensitivity analysis
Underestimating(GRS-PB)

Best-Estimate(LBB.ENG2)

Bending
moment

Total
COD

dCOD

Total
COD

dCOD

Measured
dCOD

[MNm]

[mm]

[mm]

[mm]

[mm]

[mm]

0

0.37

0.00

0.37

0.00

0.00

0.55

0.52

0.15

0.55

0.17

0.23

0.98

0.64

0.27

0.68

0.31

0.38

1.47

0.77

0.40

0.84

0.46

0.48

2.00

0.92

0.55

1.00

0.63

0.64

2.51

1.06

0.69

1.16

0.79

0.86

2.92

1.17

0.80

1.29

0.92

1.08

3.43

1.31

0.94

1.45

1.08

1.44

4.00

1.46

1.09

1.63

1.26

1.79

4.49

1.60

1.23

1.79

1.42

2.53

5.08

1.76

1.39

1.97

1.60

3.52

5.45

1.86

1.49

2.09

1.72

5.08

The conservative dCOD computation is well below the measurement. In the more elastic
regime up to about 3 MNm bending moment, the best-estimate values and the measurement
are in sufficient agreement, but at larger bending moments, the non-linearity of the dCOD
cannot be predicted quantitatively by the analytical method.
The steam generator tube leak case computation is based on the Pana model, but it isquestionable if such an equilibrium two-phase flow model is appropriate here, since itcannot be expected that the phase transition in this very short channel is in equilibrium.
The computed values are shown in Table 4.13.

Table 4.13. GRS’ result of the SGT analysis
Pressure
Temperature
Measured leak rate
Computed leak rate

[MPa]
[°C]
[g/s]
[g/s]

7.59
16.7
6.43
6.6

2.09
128.6
3.00
3.2

8.08
128.9
6.31
6.6

5.55
263.1
3.70
2.1

6.54
262.9
4.12
2.7

7.45
262.8
4.57
3.4

It can be seen that the accuracy is good for low temperature discharge, but the real leak rate
is significantly underestimated for high temperatures, when evaporation is expected. This
underlines the importance of the effect of a correct phase transition model for short orificeleaks.
As a conclusion from this second phase, the LBB sensitivity exercise showed that analyticalmethods for the computation of the CODs have inevitable accuracy limitations, especiallywhen leaving the elastic regime. For higher accuracy levels, an analysis with Finite
Elements Analysis (FEA) would be a better choice. However, conservative
underestimation can be achieved with this approach. The steam generator tube case is a
NEA LEAK RATE BENCHMARK FINAL REPORT82  NEA/CSNI/R(2022)9
good demonstration that LBB-related methods assuming friction and evaporation havetheir limitations for thin-walled specimens, and tailored suitable methods are required here.

4.2.3. KINS
KINS’ analyses of the benchmark problems were performed using a LEAPOR codedeveloped by Oak Ridge National Laboratory (see Section 2.5.4). LEAPOR is based on themodified Henry-Fauske model for the thermo-hydraulic calculation (Section 2.4.4).
The wall thickness, full lengths of the crack at both interior and exterior, COD values
measured at three different positions, and COA were provided for the artificial slit case.
The wall thickness and full lengths were employed for the analysis, and the COD values atboth interior and exterior were assumed to be 0.148 and 0.209 mm, respectively, so that thecalculated cross section is the same with the provided COA. For crack morphology
parameters, both local and global roughness were assumed to be 22 μm, and local andglobal path deviations of 1.1 were applied. The calculated values are summarised inTable 4.14.

Table 4.14. Results of the artificial slit case calculated by KINS
Data number

8

15

18

38

40

55

Pressure

[bar]

60.4

10.5

45

45.4

63.6

25.5

Temperature

[°C]

19.9

122.1

122.3

234.6

213

206.1

Computed leak rate[kg/s]

00.05070.10690.06370.11750.0406

In case of the fatigue crack analysis, global roughness was provided, and the statistical local
roughness value of 8.814 μm was adopted according to Rahman’s research [14]. Local andglobal path deviations were assumed to be 1.017 and 1.06, respectively [14]. As shown in
Table 4.15, LEAPOR treats all cases except the case of low pressure and temperature (datanumber 44).

Table 4.15. Results of the fatigue crack estimated by KINS
Data number

31

18

32

13

44

49

Pressure

[bar]

75.3

65.5

15.7

45.4

50.6

30.1

Temperature

[°C]

199.4

234.8

200

238

16.7

151.9

Computed leak rate[kg/s]

0.0543

0.045

0.008

0.0284-

0.036

The real event analysis includes the calculation of COD with limited material properties.
The elastic-plastic COD estimation of the GE/EPRI ductile fracture handbook (seeSection 2.2.1) requires the Ramberg-Osgood parameter. R-O fit, proposed by Kim et al.
[33], was employed using the material properties given. R-O parameters (α, n) can be
determined as follows when considering only yield (σ0.2) and tensile strength (σu):α=

0.002𝐸
𝜎0.2

1
𝜎0.2
𝜎0.2 2
𝜎0.2 3= 0.629 − 1.536 () + 1.723 () − 0.814 (
)
𝑛
𝜎𝑢
𝜎𝑢
𝜎𝑢

NEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  83

Based on this approach, α and n were determined to be 1.76 and 5.48, respectively. The
opening displacement of the crack with a length of 25 mm was obtained using R-O
parameters. The statistical local roughness value of 8.814 μm and global roughness valueof 40.51 μm were adopted according to Rahman’s research [14]. Local and global pathdeviations were assumed to be 1.017 and 1.06, respectively [14]. The computed COD andleak rate are shown in Table 4.16.

Table 4.16. Result of the real event analysis calculated by KINS
Best-estimate
Crack opening displacement[mm]
0.01429

Leak rate
[g/s]
0.5

In the LBB sensitivity analysis, participants were required to calculate the crack opening
by using incrementally increased bending moment. As stated in the previous exercise, the
GE/EPRI elastic-plastic analytical method was used to calculate the COD. Table 4.17
shows the dCOD values obtained by considering the COD at zero bending moment.

Table 4.17. Result of the LBB sensitivity analysis estimated by KINS
Bending
momentMeasureddCOD

Computed
COD
Total
COD

dCOD

[MNm]

[mm]

[mm]

[mm]

0

0.37

0.00

0.00

0.55

0.55

0.18

0.23

0.98

0.70

0.32

0.38

1.47

0.86

0.49

0.48

2.00

1.06

0.69

0.64

2.51

1.26

0.89

0.86

2.92

1.44

1.07

1.08

3.43

1.70

1.33

1.44

4.00

2.07

1.69

1.79

4.49

2.47

2.09

2.53

5.08

3.13

2.76

3.52

5.45

3.68

3.31

5.08

Overall, the calculation of dCOD shows a good agreement compared to the measured
dCOD up to about 4 MNm of bending moment. The GE/EPRI method, however,underestimates the dCOD at the larger bending moments.
In the case of the steam generator tube leak, participants were required to predict the leakrate through the hole with a diameter of 0.3 mm in the thin plate specimen. Regarding crackmorphology parameters, the local roughness was assumed to be 7.4 μm, which is the same

NEA LEAK RATE BENCHMARK FINAL REPORT84  NEA/CSNI/R(2022)9
as the given global value. Local and global path deviations were both assumed to be 1. The
calculated values are shown in Table 4.18.

Table 4.18. Result of the SGT analysis by KINS
Pressure
Temperature
Measured leak rate
Computed leak rate

[MPa]
[°C]
[g/s]
[g/s]

7.59
16.7
6.43
1.9

2.09
128.6
3.00
5.3

8.08
128.9
6.31
5.3

5.55
263.1
3.70
7.6

6.54
262.9
4.12
7.6

7.45
262.8
4.57
7.6

In conclusion, the exercise set for Phase II was treatable with the LEAPOR software except
in the case of low pressure and temperature (see Table 4.15). Overall, the calculation of thedCOD shows a good agreement with the measured dCOD in the LBB sensitivity case. It is
worth noting that the applicability of leak rate calculation software for short flow length islimited.

4.2.4. KIWA
KIWA’s analyses of the benchmark problems are done with the ExcelSQUIRT code (seeSection 2.5.2). ExcelSQUIRT has a simplified user interface as compared to previous
versions (SQUIRT or WinSQUIRT). ExcelSQUIRT also lacks an opportunity to obtain
intermediate results that are part of an analysis (leak rate is the only result from an analysis).
The artificial slit blind case has detailed information about the size of the crack and
COD/COA values. However, some information regarding the crack morphology is missing.
The global roughness is 22 mm. The unknown value for the local roughness does not havea large impact on the results. KIWA’s results are given in Table 4.19, and the results froma sensitivity analysis are given in Figure 4.1.

Table 4.19. KIWA results of the artificial slit blind case
Data number

8

15

18

38

40

55

[bar]

60.4

10.5

45

45.4

63.6

25.5

Temperature

[°C]

19.9

122.1

122.3

234.6

213

206.1

Computed leak rate[kg/s]---

0.05880.11730.07850.13580.0522Pressure

As shown in Table 4.19, no result was obtained for case 8 using ExcelSQUIRT. In order to
get a valid result, it would have been necessary to assume a higher temperature for this case(> 52°C).

NEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  85

Figure 4.1. KIWA results of the artificial slit blind case, with a sensitivity analysis using
different local roughness (1-22 m)

The fatigue crack blind case has detailed information about the size of the crack and that it
is a fatigue crack (with “Global Roughness” = 40 m given in the input data). KIWA
performed a sensitivity analysis using different “Local Roughness” values and also
compared its results with default data for CF (as given in ExcelSQUIRT). KIWA’s results
are given in Table 4.20, and the results from a sensitivity analysis is given in Figure 4.2.

Table 4.20. KIWA results of the fatigue crack blind case
Data number

31

18

32

13

44

49

[bar]

75.3

65.5

15.7

45.4

50.6

30.1

Temperature

[°C]

199.4

234.8

200

238

16.7

151.9

Computed leak rate[kg/s]

0.057

0.04720.008

0.0262---0.0373Pressure

Figure 4.2. KIWA results of the fatigue crack blind case, with a sensitivity analysis using
different local roughness (1-40 m) and predefined data within ExcelSQUIRTNEA LEAK RATE BENCHMARK FINAL REPORT86  NEA/CSNI/R(2022)9
For the real event leak case, the actual position of the axial crack has a significant influenceon the numerical result. However, this information is not given or known for this case.
Furthermore, almost no information about the geometry and COD/COA of the crack isprovided; the only value given is that the exterior crack length is less than 25 mm. Finally,
the bending load is also unknown.
KIWA performed a number of sensitivity analyses of this case, based on what is stated in
the input data (crack length less than 25 mm, wall thickness 12 mm and outer diameter 5075 mm). Reasonable input data gave a very small leak rate (~0 kg/s); an attempt to get theupper bound value gave a leak rate in the interval 0.002-0.01 kg/s.
In the LBB sensitivity study, a sealed through-wall crack in a cylindrical pipe is subjectedby a four-point bending at a constant pressure of 15.8 MPa. At the crack centre, the change
in COD is measured as a function of the bending moment. The purpose of this study is tocalculate the additional COD given by the bending moment and compare it with themeasured values.
KIWA uses an in-house tool to calculate COD (inner, centre, outer position). The tool
calculates an elastic and an elastic-plastic estimate of the COD. KIWA’s results arepresented in Figure 4.3 and Figure 4.4.

Figure 4.3. KIWA results of the LBB sensitivity study, using elastic COD estimates

NEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  87

Figure 4.4. KIWA results of the LBB sensitivity study, using elastic-plastic COD estimates

The steam generator tube leak specimen is a case with a very thin wall thickness (1.23 mm).
This case differs from the others as it is a round hole to be analysed. KIWA’s results using
ExcelSQUIRT are presented in Table 4.21 and Figure 4.5.

Table 4.21. KIWA’s results for the steam generator tube leak specimen
Data number
Pressure
Temperature
Measured leak rate
Computed leak rate

[MPa]
[°C]
[g/s]
[g/s]

10
7.59
16.7
6.43
3.67

13
2.09
128.6
3.00
1.83

19
8.08
128.9
6.31
3.67

20
5.55
263.1
3.70
2.83

22
6.54
262.9
4.12
3.00

24
7.45
262.8
4.57
3.33

Figure 4.5. KIWA’s results for the steam generator tube leak specimen

NEA LEAK RATE BENCHMARK FINAL REPORT88  NEA/CSNI/R(2022)9

4.2.5. NRC
The leak rates for the blind artificial slit case (Table 4.22) were determined using LEAPOR(see Section 2.5.4) and its GUI input programme, LEAPOR-SA. The geometry andthermodynamic parameters for the Artificial Slit problem that were given in the problem
description were used for the specified inside diameter and outside diameter. Crack lengths(2c) were used, and the COD values were the average of the three values specified in the
problem description: 147.7 and 209.3 µm for the inside and outside, respectively. Further,a rectangular crack cross section was assumed. A second set of calculations was performed
using COD values derived from the tabulated 2c and COA values: 150.2 and 210.0 µm forthe inside and outside, respectively. The specified total resistance value, zeta, was not usedin the calculations as LEAPOR internally performs its own calculation of the Darcy friction
factor. Since the slit was artificial and no further information was given, a value of zero
was assumed for the number of turns per unit length parameter. The leak path deviation
parameters were assumed to be unity and an entry loss coefficient of 0.95 is hard-coded in
LEAPOR. The calculation for single-phase leak, data number 8, could not be performed
because LEAPOR is specifically designed for two-phase calculations. The calculation (2c,
COA) for data number 18 did not converge so no result is given.

Table 4.22. NRC results for the blind artificial slit case
Data number

8

15

18

38

40

55

Pressure

[bar]

60.4

10.5

45

45.4

63.6

25.5

Temperature

[°C]

19.9

122.1

122.3

234.6

213

206.1

Leak
rate
(2c, COD)
Leak
rate(2c, COA)[kg/s]

N/A

0.05070.10700.06370.11750.0406[kg/s]

N/A

0.0517

N/A

0.06490.11950.0414

For the fatigue crack case, COD-dependent crack morphology parameters for CF with local
roughness of 8.8 µm, global roughness of 40.5 µm, 6 730 turns per metre, global path
length of 1.017 and global plus local path length of 1.06 were chosen. As before, the COD
was evaluated from the COA and 2c values, but since the calculated COD values did not
differ significantly from the tabulated COD values, only calculations using the tabulated
COD values were performed (Table 4.23). Data number 45 could not be evaluated because
it involved a single-phase leak.

Table 4.23. NRC results for the blind calculation of fatigue crack
Test No

1

2

3

4

5

6

Data set

8

15

18

38

40

55

Pressure

[bar]

75.3

65.5

15.7

45.4

50.6

30.1

Temperature

[°C]

199.4

234.8

200

238

16.7

151.9

Leak rate[kg/s]

0.0786

0.06960.01350.0499N/A

0.0582

Input parameters for the blind calculation of the real event, i.e. wall thickness, internalpressure and temperature, and crack shape and axial orientation, were specified in the
problem description. Other parameters, i.e. material properties, leak geometry, and crackmorphology, were supplied by the participants for best- as well as under- and overestimates (Table 4.24). The NRC chose the values to minimise the COD and leak rate as
the under-estimate.

NEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  89

Material parameters were those of 304 stainless steel taken from the xLPR Inputs Group
Report [36], and the COD was calculated using the xLPR axial crack COD module [37].
Crack morphology parameters were those of air fatigue of stainless steel [14]. Local andglobal roughness values were varied for the under- and over-estimation, but the number ofturns per length of 2520/m and the global and local + global deviation factors of 1.07 and
1.33, respectively, were held constant for all three cases.

Table 4.24. NRC exercise sheet for the blind calculation of real event
Underestimation

Assumptions

Parameter
estimates

Crack opening
area results

Overestimation

Best-stimate

Comment

Straight pipe
assumedPipe diameter

D = 50D = 62.5

D = 75

Justification

Min D → min
COD, min leak

Mean D →nominalMax D → max
COD, max leak

Young's Modulus [MPa]203 200

176 700

150 200

Yield stress [MPa]

190

153

123

Ultimate stress [MPa]

507

442

438.6

Poisson number [-]

0.3

0.3

0.3

Ramberg-Osgood alpha [-]

2.137

2.314

2.439

Ramberg-Osgood n [-]

3.838

3.558

3.253

Bending [kNm]

0

0

0

Axial flaw: nobending effect

Full crack length [mm]

15

18

22

Engineering
judgement

Local roughness [µm]

15

8

3

Global roughness [µm]

50

33.65

20

Air fatigue (SS)
NUREG/CR-6004
Under- and overestimation:
Engineering
judgement

Crack opening
displacement [mm]Crack opening area [mm²]0.00272

0.00358

0.00521

Midwall

0.03200.05060.0900

Midwall

Hydraulic diameter [mm]0.00420.00550.0080

NEA LEAK RATE BENCHMARK FINAL REPORT

304SS from xLPR
Inputs Report[35]

90  NEA/CSNI/R(2022)9

Table 4.24. NRC exercise sheet for the blind calculation of real event (Continued)
Underestimation

Effective
morphology
results
Flow resistanceresults

Best-stimate

Overestimation

Effective roughness [µm]

15.0

8.02

3.28

Effective flow length [mm]

16.0

16.0

16.0

Effective number of turns

2 520

2 519

2 483

Inlet resistanceDarcy Friction Factor

Comment

CD = 0.95
0.924

0.924

0.854

2.76E-05

4.95E-05

1.04E-04

Frictional resistance
Total resistance
Leak rate

Mass flow rate [kg/s]

For the LBB sensitivity analysis (Table 4.25), the COD for zero bending moment wascomputed for an axial force that resulted from the internal pressure. Two sets of inputs werechosen for the computation of the COD. The first set included the influence of 50% crack
face pressure (CFP, 7.9 MPa) while the second set did not include CFP in the COD
calculation. The dCOD values were calculated by subtracting the COD value at zero
bending moment from the COD value at the applied bending moment (Table 4.25). All of
the reported COD values are those at the mid-wall.

Table 4.25. NRC result of the LBB sensitivity analysis
COD with 50% crack facepressure

COD without crack facepressure

Measured dCOD

Bending
moment

Total
COD

dCOD

Total
COD

dCOD

[MNm]

[mm]

[mm]

[mm]

[mm]

[mm]

0

0.495

0

0.382

0.000

0.00

0.55

0.718

0.224

0.606

0.224

0.23

0.98

0.895

0.400

0.782

0.400

0.38

1.47

1.099

0.604

0.985

0.603

0.48

2.00

1.327

0.832

1.211

0.829

0.64

2.51

1.561

1.066

1.442

1.060

0.86

2.92

1.765

1.271

1.643

1.261

1.08

3.43

2.052

1.557

1.921

1.539

1.44

4.00

2.436

1.941

2.292

1.910

1.79

4.49

2.846

2.351

2.686

2.304

2.53

5.08

3.482

2.987

3.294

2.912

3.52

5.45

3.989

3.494

3.777

3.395

5.08

For both sets of input, the calculated dCOD was smaller than the measured values. For
lower bending moments, M ≤ 1 MNm, where the strains were probably elastic, the dCOD
for the calculations with and without CFP were identical and closely mirrored the measured
COD values. However, for larger applied moments where plasticity was presumably

NEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  91

involved, the calculated dCOD lagged the measured dCOD values. The dCOD values when
CFP was included became increasingly larger than those when CFP was not included, as
might be expected when plastic deformation is occurring.
For the steam generator tube leak case, the wall thickness of 1.23 mm and the tube holediameter of 0.3 mm resulted in a thickness to diameter ratio of 4.1, which placed it within
the LEAPOR orifice flow regime (Regime 4). The computed values for all cases except forthe single-phase leak case are shown in Table 4.26.

Table 4.26. NRC result of the SGT analysis
Pressure
Temperature
Measured leak rate
Computed leak rate

[MPa]
[°C]
[g/s]
[g/s]

7.59
16.7
6.43
N/A

2.09
128.6
3.00
2.05

8.08
128.9
6.31
4.04

5.55
263.1
3.70
3.05

6.54
262.9
4.12
3.31

7.45
262.8
4.57
3.54

As was the case for the artificial slit, LEAPOR significantly underestimated the real leakrate. The reason for this underestimate is not clear as the LEAPOR Regime 4 for orificeflow was specifically developed for such a problem.

4.2.6. OCI
Blind artificial slit case – LOCI™ solutions using the extended Henry-Fauske model forthe blind artificial slit case are presented in Table 4.27.

Table 4.27. OCI results for blind artificial slit case
Data number

8

15

18

38

40

55

Pressure

[bar]

60.4

10.5

45.0

45.4

63.6

25.5

Temperature

[°C]

19.9

122.1

122.3

234.6

213.0

206.1

Henry-Fauske[kg/s]

0.179

0.051

0.107

0.064

0.118

0.041

Blind fatigue crack case – LOCI™ solutions using the extended Henry-Fauske model forthe blind Fatigue Crack Case are presented in Table 4.28. The morphology parameters wereobtained from the LOCI™ morphology database for the fatigue damage mechanism as
given in Table 3.26.

Table 4.28. OCI Results for blind fatigue crack case
Data number

31

18

32

13

44

49

Pressure

[bar]

75.3

65.5

15.7

45.4

50.6

30.1

Temperature

[°C]

199.4

234.8

199.4

238.0

16.7

151.9

Henry-Fauske*

[g/s]

54.3

45.0

8.0

28.4

51.6

36.0

*Morphology parameters taken from Table 3.26 LOCI™ database for fatigue.

Blind real event case – LOCI™ solutions for the blind real event case are presented inTable 4.29. The morphology parameters were obtained from the LOCI™ morphology
database for the fatigue damage mechanism as given in Table 3.26. The COA for arectangle is calculated by the GE/EPRI EPFM model with crack face pressure included.
The under-estimate solution was obtained with the modified Bernoulli model; the best-

NEA LEAK RATE BENCHMARK FINAL REPORT92  NEA/CSNI/R(2022)9
estimate solution applied the Henry-Fauske model, and the over-estimate solution applied
the Bernoulli model.

Table 4.29. OCI Results for blind real event case
Leak rate [g/s]Best-estimate
0.243

Under-estimate
0.158

Over-estimate
0.545

Blind LBB sensitivity case – LOCI™ solutions for the blind LBB Sensitivity Case arepresented in Table 4.30. The COD for a rectangle is calculated by the GE/EPRI EPFM
model with crack face pressure included.

Table 4.30. OCI Results for blind LBB sensitivity caseBest-estimate(EPRI/GE EPFM)
Bending
moment

Total
COD

dCOD

Measured
dCOD

[MNm]

[mm]

[mm]

[mm]

0

0.34

0.00

0.00

0.55

0.49

0.15

0.23

0.98

0.61

0.27

0.38

1.47

0.74

0.40

0.48

2.00

0.89

0.55

0.64

2.51

1.03

0.69

0.86

2.92

1.14

0.80

1.08

3.43

1.28

0.94

1.44

4.00

1.44

1.10

1.79

4.49

1.58

1.24

2.53

5.08

1.74

1.41

3.52

5.45

1.85

1.51

5.08

Blind SGT case – Applying the modified Bernoulli model, the LOCI™ solutions for theblind SGT case are presented in Table 4.31.

Table 4.31. OCI results for blind SGT case
Pressure
Temperature
Measured leak rate
Computed leak rate

[MPa]
[°C]
[g/s]
[g/s]

7.59
16.7
6.43
5.58

2.09
128.6
3.00
2.65

8.08
128.9
6.31
5.48

5.55
263.1
3.70
1.41

6.54
262.9
4.12
2.28

7.45
262.8
4.57
2.85

4.2.7. PSI
PSI applied the LEAPOR and the WinLeck code. The analysis results for the blind artificial
slit case are shown in Table 4.32.

NEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  93

Table 4.32. PSI results of the blind artificial slit case
Pressure

[MPa]

6.04

1.05

4.5

4.54

6.36

2.55

Temperature

[°C]

19.9

122.1

122.3

234.6

213

206.1

Leak rate[kg/s]

0.044630.019410.03933

0.029170.043880.02064

Table 4.32 shows that the leak rate calculated with LEAPOR increases with higher pressure
and temperature. At pressures above 6 MPa, its influence on the leak rate increases. The
leak rate is 0.45 kg/s and 0.44 kg/s when the temperature is 19.9°C and 213°C, respectively.
For the eroded slit, it is likely that the leak rate is influenced more by the primary loadings,
e.g. internal pressure and bending moment, than by the thermal stress caused bytemperature difference.

Table 4.33. PSI results of the blind fatigue crack
Pressure
Temperature

[MPa]
[°C]

7.53
199.4

6.55
234.8

1.57
200

4.54
238

5.06
16.7

3.01
151.9

Leak rate[kg/s]

0.135290.104280.01946

0.07126

0.04470.08925

For the blind fatigue case, the highest leak rate is obtained at the highest pressure andtemperature. It is found that at higher temperature, the leak rate is increased. Around acertain temperature (i.e. 200°C), the leak rate drops by six times when the pressure is
reduced from 7.53 MPa to 1.57 MPa. However, when the pressure is around a certain value(i.e. 4.54 MPa and 5.06 MPa), the leak rate drops by 1.6 times when the temperature is
reduced from 238°C to 16.7°C. The leak rate drops from 0.13 to 0.1 (by 23%) when theinternal pressure is reduced by 1 MPa, despite a temperature increase of 34°C. It is likelythat the leak rate is more influenced by internal pressure rather than by the temperature.
The results for the blind real event case are shown in Table 4.34; a crack length of 50 mm
was assumed to produce these results.

Table 4.34. PSI result of the real event analysis
Leak rate[kg/s]

Underestimation

Best-estimate

Overestimation

0.01440.0173

0.019

The moment of inertia I and the polar moment of inertia W are given in the following
formulas,𝐼=

𝜋(𝐷𝑜4 − 𝐷𝑖4 )
64

(65)

𝜋(𝐷𝑜4 − 𝐷𝑖4 )
32𝐷𝑜

(66)

𝑊=

where Do and Di are the outer diameter and the inner diameter of the pipe, respectively.
Given a certain thickness, both I and W increases with larger Do. The maximum bending
moment is given as below:

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𝑀𝑏𝑚𝑎𝑥 =

𝜎∙𝐼
=𝜎∙𝑊
𝐷𝑜 ⁄2

(67)

Therefore, 𝑀𝑏𝑚𝑎𝑥 is proportional to the polar moment of inertia W. It can be concluded fromthis case that with a certain wall thickness, a larger outer diameter increases the bending
moment linear, causing a higher mass flow rate.

Table 4.35. PSI results of the LBB sensitivity analysis
Bending
moment
[MNm]
0
0.55
0.98
1.47
2.00
2.51
2.92
3.43
4.00
4.49
5.08
5.45

Total
COD
[mm]
0.002
0.180107279
0.318699101
0.478282791
0.651598229
0.817816256
0.949308716
1.11521434
1.301953353
1.459980559
1.652111781
1.773389307

COA

dCOD

Measured dCOD

[mm2]0.65469
58.95721712
104.3245571
156.5634802
213.2974221
267.7080624
310.7514615
365.0598381
426.1879203
477.9173361
540.810531
580.5101226[mm]
00.178107279
0.316699101
0.476282791
0.649598229
0.815816256
0.947308716
1.11321434
1.299953353
1.457980559
1.650111781
1.771389307

[mm]
0.00
0.23
0.38
0.48
0.64
0.86
1.08
1.44
1.79
2.53
3.52
5.08

Figure 4.6. PSI result for bending moment and COD

As LEAPOR code cannot deal with the variable bending moment, the COD calculation
method implemented into this code (Zahoor, see Section 2.2.1) can be referred to.
Meanwhile, WinLeck software was also applied in this case. The calculated results fromthese two different tools are in good agreement, but the computation results do not agreewith experimental findings if the bending moment is over 2.5 MNm. One possible reason

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for the difference in COD is that the implemented models in LEAPOR and WINLECK can
only assume the conservative CODs at lower bending moment.

Table 4.36. PSI results of the SGT analysis
Pressure

[MPa]

7.59

2.09

8.08

5.55

6.54

7.45

Temperature
Measured leak rate
Computed leak rate[°C]
[kg/s][kg/s]

16.7
0.006430.00517128.6
0.00300
0.00263128.9
0.006310.00517263.1
0.003700.0039262.90.004120.00424262.8
0.00457
0.00453

Because LEAPOR-SA can only be used for cylindrical pipes, here it is assumed that theouter diameter of this pipe is very large (106 mm) and can be regarded as a plate. It is
assumed that the crack length is 0.6 mm and the COD is 0.3 mm. The final results are ingood agreement with the measured results. There is only one exception: The calculated
leak rate with lower temperature is lower than the measured leak rate. It is likely that there
is a temperature limit in the LEAPOR code, as mentioned in Section 3.2.8.

4.2.8. SNC
Leak rates for the exercise set in Phase II of the benchmark are estimated using LEAPOR,
and for single-phase flow problems with low temperature, a single-phase flow equation isused.
For the blind artificial slit problem, a pipe with a large diameter (D=2000 mm) is
considered instead of a rectangular shaped plate. Based on the crack length and COA, theCOD is calculated at ID and OD. As the information of local roughness was not provided,
it is assumed to be the same as the global roughness (22 µm). The results of the blind
artificial slit problem are provided in Table 4.37.

Table 4.37. SNC results of the blind artificial slit case
Pressure
Temperature

[MPa]
[°C]

60.4
19.9

10.5
122.1

45
122.3

45.4
234.6

63.6
213

25.5
206.1

Leak rate[kg/s]

0.127

0.052

0.109

0.065

0.12

0.041

For the test cases with temperatures of 19.9°C and 122.3°C, LEAPOR was unable toconverge to a solution, hence a single-phase flow equation was used.
Similarly, for the blind fatigue crack problem, a pipe with large diameter (D=2000 mm) is
considered instead of a plate, and a local roughness of 40 µm is used, which is the same as
the global roughness. The results of the blind fatigue crack problem are provided inTable 4.38.

Table 4.38. SNC results of the blind fatigue crack
Pressure
Temperature

[MPa]
[°C]

75.3
199.4

65.5
234.8

15.7
200

45.4
238

50.6
16.7

151.9
151.9

Leak rate[kg/s]

0.073

0.059

0.012

0.043

0.106

0.049

The leak rates for all test cases were estimated using LEAPOR, except for the case with atemperature of 16.7°C, for which a single-phase flow equation was used.
For the real event analysis, a full crack length of 25 mm is considered for all the cases. For
underestimation and best-estimation case, the crack is assumed to be smaller than the OD
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The COD is computed using the formulation used in xLPR. The effect of the bending
moment on the axial crack COD is not considered. The material property in theunderestimation case is based on reference material property provided in the test problem.
Experimental data is used for estimating the material properties for best-estimate andoverestimation cases. For all the three cases, crack morphology due to CF (Table 3.9 ofReference [14]) is considered.

Table 4.39. SNC result of the real event analysis
Leak rate[kg/s]

Underestimation

Best-estimate

Overestimation

1.07E-04

1.16E-04

2.39E-04

The COD in the LBB sensitivity analysis is computed using the solution available in API
579-1/ASME FFS-1, June 2016, which is based on the WRC method (see Section 2.2.6),
with plastic correction factor applied. The correction factor is purely based on reference
stress solution with yield strength.

Table 4.40. SNC result of the LBB sensitivity analysis
Bending
moment

Total
COD

COA

dCOD

Measured
dCOD

[MNm]

[mm]

[mm]

[mm]

[mm]

0

0.444

145.247

0.000

0.00

0.55

0.605

197.916

0.161

0.23

0.98

0.726

237.743

0.283

0.38

1.47

0.868

284.175

0.424

0.48

2.00

1.033

338.216

0.589

0.64

2.51

1.218

398.863

0.775

0.86

2.92

1.399

457.879

0.955

1.08

3.43

1.692

554.041

1.249

1.44

4.00

2.151

704.355

1.708

1.79

4.49

2.687

879.592

2.243

2.53

5.08

3.582

1 172.710

3.138

3.52

5.45

4.324

1 415.600

3.880

5.08

The computed COD reasonably agrees well with the measured one, expect for a few cases.
In general, the calculated COD is lower than the measured one for the load levels.
For steam generator tube leak assessment, LEAPOR is used without any modification to
the programme. A pipe with a large diameter and an elliptical crack is considered. The
CODs at ID and OD are calculated from the crack diameter and COA provided.
Additionally, local roughness is assumed to be the same as global roughness.

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Table 4.41. SNC result of the SGT analysis
Pressure
Temperature
Measured leak rate
Computed leak rate

[MPa]
[°C]
[kg/s][kg/s]

7.59
16.7
0.006430.00402.09
128.6
0.00300
0.00218.08
128.9
0.006310.00405.55
263.1
0.003700.0031

6.54
262.9
0.004120.00337.45
262.8
0.00457
0.0035LEAPOR under-predicts the leak rate for all the cases considered and the percentage
difference varies from 21.25% to 58.9%.

4.3. Comparison
In this section, the individual submissions are compared, and the agreement among theparticipants as well as the accuracy relative to the reference values is discussed.

4.3.1. Blind artificial slit caseSeven organisations submitted a total of eight contributions with analyses of the artificial
slit case. Due to a unit mistake in the evaluation sheet, two evaluations were asked to berepeated as they deviated by several orders of magnitude, but they were also received
without information about the actual measured leak rate values. All evaluations are basedon the COD values of the slit and the roughness value; one participant used the flow
resistance value. The graph with the individual mass flow rates and the reference (themeasured mass flow in the experiment) is shown in Figure 4.7.

Figure 4.7. Result comparison for the blind artificial slit case

The contributed values are mostly very close to each other. All computed values
underestimate the real leak rate for most cases. The accuracy is in most cases between about
20% and 30%, which is in agreement with the non-blind artificial slit cases and evaluation
based on roughness instead of measured resistance. Two contributions (two variants
produced by a single participant) are significantly lower than the rest. For the analysis of
the influence of different approaches, the flow contributions are ordered according to theused flow model in Figure 4.8.

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Figure 4.8. Comparison of flow model influence in the artificial slit case (blind
contributions)This evaluation shows that participants with the same model have very similar results, evenin a blind analysis. There were also four non-blind contributions of two participants, which
are evaluated separately in Figure 4.9.

Figure 4.9. Comparison of non-blind contributions for the artificial slit caseIn this comparison, it is visible that the contributions are in good agreement with thereference result. The agreement of three of the contributions is apparently better than thatof the blind contributions, which justifies the separate analysis.

4.3.2. Blind fatigue crack case
For the blind fatigue crack case, eight contributions from six participants were received.
Due to a unit conversion mistake in the case definition, three contributions originallydeviated by several orders of magnitude from the rest; these analyses were done again
without knowledge of the actual leak rates in the tests. Most evaluations are based on the
COD values, and all but one participant based their evaluations on the reported roughness
values instead of the total resistance measured in the test. The comparison of the results isshown in Figure 4.10.

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Figure 4.10. Result comparison of the blind fatigue crack case

The agreement of most participants with the measured leak rate in the actual test issatisfying. Most participants have a good agreement between each other and with respect
to the measurement in test 3, which is close to the saturation line. Another qualitative
difference is observed for test 5, which is in the cold water regime. This overall result iscomparable with the observations in the non-blind fatigue crack test. Contributions 2, 3 and5 show a systematic overestimation – while 2 and 3 originate from the same contributor, 2
and 5 are both produced with LEAPOR.
To analyse the differences between the contributions, the friction characterisation isconsidered first, as some participants report the friction factor λ. The indication of thefriction influence in each contribution is shown in Figure 4.11. It can be verified that thethree contributions with a friction factor of 0.14 are very accurate and very close to eachother (there is an exception for the cold test No 5). However, the other contributions are
not directly scaling with the friction factor, which could be explained by different effective
flow paths and additional pressure loss effects considered by the participants.

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Figure 4.11. Characterisation of friction and pressure loss in the blind fatigue crack case

Concerning the flow model, all contributions but one use a Henry-based approach, while
contribution 3 applies a modified Bernoulli model. The latter has the tendency tounderpredict leak rates close to saturation conditions, so one could argue that the good
match for test 3 compensates a general overestimation by chance. This can be verified in
Figure 4.12.

Figure 4.12. The blind fatigue crack case by applied flow modelAs with the artificial slit case, non-blind contributions were received to this case as well.
They are compared in Figure 4.13. Analyses 1 and 5 show a better agreement than analyses
2, 3 and 4; in general, the non-blind contributions have a similar accuracy as the blind
contributions.

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Figure 4.13. Comparison of non-blind analyses of the fatigue crack

In summary, it can be concluded that some participants from the blind comparison wereable to accurately and consistently predict the leakage rate of the specimen. Most have amoderate accuracy, and two outliers show a good result close to saturation conditions andminor quality for the rest of the tests.

4.3.3. Blind real event caseSeven analysis contributions were received from six organisations for the blind real event
case, but two contributions were based on significantly different geometry assumptions andproduced very different results; these two contributions were therefore removed from thecomparison. All but one of the remaining contributions gave underestimating, best-estimate
and overestimating predictions for the leak rate. The trend was obtained by choosing
different ODs (from 50 mm to 75 mm), motivated by the fact that the crack is located at a
reducer. Another uncertainty was the actual crack length, which is only known to be smaller
than 25 mm (full crack length), and which was also used for estimating the possible rangeof leak rates. Both choices have a significant impact on the crack opening, as shown clearlyin Figure 4.14 (one contribution did not indicate the COD values and is not included in thisevaluation).

Figure 4.14. COD as a function of the full crack length in the blind real event case; thedifferent choices of the effective pipe radius (not indicated) are a reason for verticalscattering

In this figure, the deviations in COD for the same 2c are mostly due to different choices ofeffective pipe diameter: Larger CODs correspond to larger radii since the pressure-induced
hoop stress acting on the axial crack is larger. By virtue of their geometry alone, these
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different leak areas already have a strong effect on the mass flow rate; other influences
originate from friction and flow model. The comparison is shown in Figure 4.15 (the overestimate contribution 4 did not indicate its COA value, and its reported value is hence
shown as a horizontal line in the comparison).

Figure 4.15. Leak rate as a function of the leak opening area

The figure shows clearly that the COA is the main influence on the computed leak rate, andfriction/morphology effects and model differences between participants seem to be ofminor importance. With regard to the reported leak rate, all teams compute much smaller
mass flow values. The overall comparison of all contributions, ordered by underestimation,
best-estimate and overestimation, is shown in Figure 4.16.

Figure 4.16. Result comparison of the blind real event case

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From this figure, it is visible that most contributors underestimate the reported leak rate
significantly.
Three non-blind contributions were also received for this analysis. They assume a crack
length of 25-27.4 mm and also underestimate the reported leak rate (Figure 4.17).

Figure 4.17. Results comparison of non-blind analyses of the real event caseThis finding raises the question about the reason for the systematic underestimation for allcomputation with consistent crack geometry. In principle, two mechanisms are observedthat cause an excess of the leak rate from the fracture mechanical idealisation: Material loss
due to (possibly flow accelerated) corrosion causes a larger leak opening than the puremechanical displacement of the crack faces, and plastic deformations due to overloading
which cause a permanent plastic opening in addition to the load-induced contribution.
(Since clogging of narrow cracks is a well-known mechanism for the contrary effect.) This
seems to be more likely than an error in the event report (for instance, the leak rate of 20 g/s
is an estimated and not a measured value).

4.3.4. LBB sensitivity case
For the computation of the differential leak opening (dCOD) as a function of the applied
bending moment in a full-scale test for the LBB sensitivity case, seven organisations
provided nine contributions in total. One contribution is overestimating (1), two areunderestimating (3 and 8) and the rest is best-estimate. The results are compared in
Figure 4.18.

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Figure 4.18. Result comparison for the LBB sensitivity caseIn the result, all contributions (except the intentionally overestimating contribution 1) findthe correct elastic behaviour at small bending moment; deviations appear as plastic effects
are manifest in the measured differential COD. The overestimating trend of contribution 1
and the underestimating trend of contribution 8 are clearly verified. In the best-estimate
approaches, contributions 4, 5, 6 and 7 have the best accuracy event for large bending
moments. The analysis of the contributions by method is shown in Figure 4.19.

Figure 4.19. LBB sensitivity case by COD model

In this comparison, it is visible that the two Wüthrich-based approaches (which use the
GRS-PB and the KTA 3206 approach) are very close. The GE/EPRI based contributions
differ much (note that the intentionally overestimating contribution is an elastic approach).
The two contributions classified as “Other” are most accurate.

4.3.5. Steam generator tube leak case
The steam generator tube leak case was analysed by seven participants with a total of nine
contributions. The comparison of the leak rate computation with the actual measured leakrates is shown in Figure 4.20.

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Figure 4.20. Result comparison for the steam generator tube leak case

The measured leak rate is in most cases higher than the computed values of the participants.
Contributions 2 and 8 show a good agreement with the measured leak rate in specificregimes. Contribution 3 does not include a value for the cold water case (test No. 1). Most
others qualitatively follow the trend between the selected test points, except forcontribution 7. A remarkable difference compared to e.g. the artificial slit case is the factthat the accuracy varies with the thermodynamic fluid conditions (test number), rather thanthem being a rough scaling factor. For an improved understanding of the different
predictions, the applied flow models are indicated in Figure 4.21. Note that one LEAPORHenry contribution does not include a cold water test (test No. 1) and is almost identical toa Henry-based contribution for the other test numbers.

Figure 4.21. Steam generator tube leak case analysed by model

Most of the participants use Henry-based approaches (although the strict Henry model is
not applicable since the ratio of wall thickness to hole diameter is too small), three of themby applying the LEAPOR code. The Pana model, the modified Bernoulli model and themetastable jet model are all used by one contribution each. Apparently, the Pana andmodified Bernoulli contributions resemble each other, and they both underestimate the leakrate at high temperatures (test nos. 4-6). The metastable jet approach instead overestimates
the high-temperature points. Two participants using the Henry approach and one using the
LEAPOR analysis have very similar results, underestimating the measured leak rates
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systematically with a slightly better performance for the tests closer to the saturation line
(2, 4, 5, 6). One other LEAPOR analysis has a quite good agreement with the measurement(also with larger deviations for tests 1 and 3), while the others are different.
These findings indicate that the thermodynamic phenomena for steam generator leaks canbe different from thick-walled piping leaks in specific regimes of fluid conditions. It canbe expected that the vapour content in a short leak channel is smaller compared to longleaks, which increases the density and hence the mass flow rate. This could be an
explanation for the systematic underestimating trend of most model predictions in this caseand the rather good performance of uncommon models.

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5. Conclusions and recommendations for further work

The two-phase activity on leak rate computation makes it possible to draw several
conclusions on different levels. The following section summarises the conclusions from thebenchmarking approach, the result analysis and the lessons learnt. It also provides
recommendations for future activities.
The instructions for the benchmark exercises in tabular sheet form can be seen as a good
approach to define the different test cases. However, additional details about the laboratory
tests would be beneficial, as well as schematic drawings to make geometric settings clearer.
In general, the participants saw the benchmarking as an effective way to understand leakrate computation. The combination of open and blind sections was informative and can beseen as a distinct feature of this activity.
An important conclusion is that the participants applied different software (see Section 2.5),
but these software tools often implement the same models and should consequently lead tosimilar results. In this way, this benchmarking was technically a code comparison, but theanalysis of the contributions made it possible to identify the imprints of the model
implementations. This reveals details about the individual tools used in the analysis andemphasises the (software) design background of each tool and what distinguishes themfrom one another. This survey gives an overview of the state of the art of approaches,
methods and tools. The experience gained in this round robin activity can also help toimprove the programmes in the future, while the experiment analysis and code comparison
contribute to their validation.
The leakage model perspective (in contrast to the computation code perspective) played a
key role in the analysis of the different contributions. Starting from fixed settings orassumptions of structure geometry, leak geometry and loads, the leak rate computation
involves a model for leak opening (such as COD), for flow resistance and friction, and forthe actual fluid motion. Each analysis approach, in principle, combines a model for leak
opening, one for friction and one for fluid motion. In the analysis of contributions, thismade it possible to track differences and agreements between different participants tomodel choices – even despite blind test case settings, as notably seen in Section 4.3.1.
Given this insight in the analysis of the contributions, it is possible to estimate theagreement between prediction and measurement with each model. As an alternative to theabsolute accuracy, the suitability of approaches for underestimation or overestimation is
also discussed. Thus, the round robin activity gives indications on the uncertainties in leakrate predictions and the approaches used by the participants. The limited selection of cases
is not sufficient to quantify the uncertainties (e.g. for statements concerning probabilistic
treatments). A preliminary conclusion is that the relevant influence factors on accuracy andthe reliability of the leak rate prediction can be traced back to the performance of individualmodels and to detailed knowledge about the leak situation. Moreover, the present
comparison gives an impression about the general range of variability to be expected inleak rate predictions.
From the perspective of individual computer codes, the margin between predicted andmeasured leak rates within the benchmark cases is interesting, as several codes were able
to find that the difference is bounded by a factor of 2 (for the laboratory tests). Also, it isinteresting that several analyses show conservative underestimating behaviour, which isalso relevant from a regulatory perspective. The benchmarking showed also that there is

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indeed a difference between blind and non-blind computations, though blind analyses also
have a good accuracy.
Within the different test cases in the round robin, the analyses of real leak events stand out
from the rest. These open analyses in the first benchmark phase and the blind analysis in
the second benchmark phase have a surprising outcome. The first phase test case is basedon a publication that demonstrates the capability of a leak rate software. The analysis result
for this case shows that most participants are able to explain the reported leakage rate, but
the uncertainties in the case definition due to unknown parameters allow for a larger rangeof possible leak rates. The second phase test case is based on event data and was selectedaccording to the availability of data allowing an accurate model. The uncertainties in thiscase seem to be under control, but, remarkably, no model can explain the observed leakage
rate. The actual leak rate is beyond the range that seems to be possible under the allowed
conditions.
This behaviour of leakage rate is, of course, a singular observation, and it is too early todraw conclusions about this finding. However, the behaviour of real leaks from theoperational experience is relevant for all leak rate assessments, and also for LBB
procedures. While most analyses and model validations in leak rate analysis concentrated
on laboratory specimens, it seems justified to think about validation of leak rate models
also under consideration of real leaks from the operational experience. This would also bein accordance with the IAEA guide for deterministic safety analyses [35]. This finding
could motivate follow-up activities in analysing leak events.
One of the test cases discussed within the benchmark was a steam generator tube-likespecimen, which is different from ordinary LBB-related leak rate setups by a much smaller
wall thickness and a smaller mass flow rate. This turned out to be an unusual case for leakassessment based on the traditional models, which provided new data for modelcomparison and showed a different behaviour than the other cases (namely a variation of
the accuracy with the thermodynamic stagnation conditions).
Finally, the leak rate benchmark within the WGIAGE can also be seen as an update offormer CSNI leak rate benchmark activities. A benchmark performed about 15 years ago[46] came to the conclusion that “the compilation of the results shows very large
scatterbands in general, with deviations equally large between the calculations of thedifferent participants and the calculation and the measurements.” Progress has beenachieved in gaining a deeper understanding of the phenomena, and improved analysis tools
have been developed. Therefore, the current activity shows a rather good accuracy, at least
for the (well-controlled) laboratory leak tests. Also, the comparative assessment approachis able to understand in detail the differences between approaches and to explain deviations.

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References[1] Heckmann, K., J. Sievers and F. Weyermann (2018), Leak Rate Computation: Flow Resistance vs.
Thermal-Hydraulic Aspect, ASME Pressure Vessel and Piping Conference, 15-20 July 2018,
Prague.
[2] Kumar, V., M.D. German and C.F. Shih (1981), An Engineering Approach for Elastic-Plastic
Fracture Analysis, Electric Power Research Institute, Palo Alto.
[3] Kumar, V. et al. (1984), Advances in Elastic-Plastic Fracture Analysis, Electric Power ResearchInstitute, Palo Alto.
[4] Heckmann, K., C. Bläsius and J. Sievers (2019), WinLeck 5.0: User's Manual and Validation
Report. GRS-P-6, Vol. 1-2, Rev. 9, Handbuch, Cologne.
[5] Rahman, S. et al. (1998), “Crack-opening-area analyses for circumferential through-wall cracks inpipes - Part I: analytical models”, International Journal of Pressure Vessels and Piping, 75 (5),pp. 357 ‐ 373.
[6] Wüthrich, C. (1983), “Crack opening areas in pressure vessels and pipes”, Engineering Fracture
Mechanics, 18 (5), pp. 1049-1057.
[7] Gilles, P. and F.W. Brust (1991), “Approximate fracture methods for pipes - Part I: theory”,
Nuclear Engineering and Design, 127 (1), pp. 1-17.
[8] Tada, H., P.C. Paris and G.R. Irwin (2000), The Stress Analysis of Cracks Handbook, ASME Press.
[9] Anderson, T.L. (2003), “Stress intensity and crack growth opening area solutions for through-wallcracks in cylinders and spheres”, WRC Bulletin 478, Welding Research Council, New York.
[10] John, H. et al. (1988), “Critical two-phase flow through rough slits”, International Journal ofMultiphase Flow, 14 (2), pp. 155-174.
[11] Paul, D.D. et al. (1991), Evaluation and refinement of leak-rate estimation models, US Nuclear
Regulatory Committee, Washington, United States.
[12] Burnell, J.G. (1947), “Flow of boiling water through nozzles, orifices and pipes”, Engineering,
164, pp. 572-576.
[13] Henry, Robert E. (1970), “The Two-Phase Critical Discharge of Initially Saturated or Subcooled
Liquid”, Nuclear Science and Engineering, 41 (3), pp. 336-342.
[14] Rahman, S. et al. (1995), Probabilistic Pipe Fracture Evaluations for Leak-Rate-Detection
Applications” NUREG/CR-6004, BMI-2174.
[15] Abdollahian, D. and B. Chexal (1983), “Calculation of Leak Rates Through Cracks in Pipes andTubes”, EPRI NP-3395, Project 1757-19, Campbell.
[16] Nikuradse, J. (1933), Strömungsgesetze in rauhen Rohren“, Forschung auf dem Gebiet desIngenieurwesens, 361 (B4), pp. 1-22.
[17] Heckmann, K. et al. (2022), “A Metastable Jet Model for Leaks in Steam Generator Tubes”,
Nuclear Engineering and Design, Vol. 389.
[18] Zaloudek, F.R. (1963), The critical flow of hot water through short tubes, US Atomic Energy
Commission (USAEC), Richland.
[19] Pana, P. (1975), A modified Bernoulli-equation for the computation of fluid flow in the subcooled
regime (in German), Cologne.

NEA LEAK RATE BENCHMARK FINAL REPORT

110  NEA/CSNI/R(2022)9[20] Nuclear Safety Standards Commission (KTA) (2016), Break Preclusion Verifications for
Pressure-Retaining Components in Nuclear Power Plants, KTA 3206, Bundesamt fuer
kerntechnische Entsorgungssicherheit (BfE), Salzgitter.
[21] Pana, P. and M. Müller (1978), “Subcooled and two phase critical flow states and comparison withdata”, Nuclear Engineering and Design, 45 (1), pp. 117-125.
[22] ANSYS (2020), ANSYS CFX-Solver Theory Guide, Release 2020 R1 ANSYS, Inc.
[23] Cox, A., B.A. Young and P.M. Scott (2013), “Advances in COD Modeling: Validation of an
Analytical Model to Experimental Results”, Structural Mechanics in Reactor Technology (SMiRT)
22, Division II – Fracture Mechanics and Structural Integrity, San Francisco.
[24] Young, B.A., R.J. Olson. and P.M. Scott (2013), “Advances in COD Modeling – Multiple Loading
Modes: Concurrent Axial and Crack Face Pressure with a Subsequent Applied Bending Moment”,
Structural Mechanics in Reactor Technology (SMiRT) 22, Division II – Fracture Mechanics andStructural Integrity, San Francisco.
[25] Young, B.A., R.J. Olson and M. Kerr (2012), “Advances in COD Modeling: Circumferential
Through-Wall Cracks”, ASME International, PVP 2012, Toronto.
[26] The International Association for the Properties of Water and Steam (IAPWS) (2005), Obsolete
IAPWS recommendations.
[27] Norris, D.M. and B. Chexal (1987), PICEP: Pipe Crack Evaluation Program (Revision 1), Report
EPRI-NP-3596-SR-Rev.1, Electric Power Research Institute, Palo Alto.
[28] Bläsius, C., K. Heckmann and J. Sievers (2019), “Quality Management, Verification, andValidation of Structure Mechanical Computer Codes at GRS. Division III”, Structural Mechanics
in Reactor Technology (SMiRT-25), 4-9 August 2019, Charlotte.
[29] US NRC (2007), “Standard Review Plan: 3.6.3 Leak-Before-Break Evaluation Procedures”,
NUREG-0800, Rev. 1, US Nuclear Regulatory Commission, Washington DC.
[30] Silber, F. et al. (2017), “Investigation of Leakage Rates in Pressure Retaining Piping”, ASME
2017 Pressure Vessels and Piping Conference, 16-20 July 2017, Waikoloa.
[31] Herbst, O., N. Huber and W. Kastner (2001), “Application of the Leak Flow Rate Calculation
Program FLORA to Real Cracks in Piping”, SMiRT 16, August 2001, Washington DC.
[32] The American Society of Mechanical Engineers (ASME) (2021), Boiler and Pressure Vessel Code(BPVC) Section III – Rules for Construction of Nuclear Facility Components-Division 1Subsection NB-Class 1 Components, BPVC-III NB – 2021.
[33] Kim, Y.-J. et al. (2004), “On Relevant Ramberg-Osgood Fit to Engineering Nonlinear Fracture
Mechanics Analysis”, Journal of Pressure Vessel Technology, Vol. 126, pp. 277-283.
[34] xLPR
Technical
Seminar
Series(2020):
ModelsOverview,
http://www.youtube.com/watch?v=vsOOtdXYxoY (deterministic models start at 25:30; COD at
57:30; LEAPOR at 59:30, accessed 8 December 2023).
[35] Scott, P. et al. (2010), Development of the PRO-LOCA Probabilistic Fracture Mechanics Code,
MERIT
Final
Report,https://inis.iaea.org/collection/NCLCollectionStore/_Public/42/
011/42011406.pdf?r=1&r=1, Swedish Radiation Safety Authority.
[36] Homiack, M. and M. Burkardt (2017), xLPR Version 2.0 Inputs Group Report, Appendix B,
ADAMS Accession Number ML19337B876.
[37] Benson, M., B. Young, D-J. Shim and F. Brust (2013), Crack Opening Displacement Model for
Through-Wall Axial Cracks in Cylinders, Proceedings of the 2013 ASME Pressure Vessels andPiping conference, 14-28 July 2013, Paris.
NEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  111[38] Henry, R.E. and H.K. Fauske (1970), “Two-Phase Critical Flow at Low Qualities, Part II:
Analysis”, Nuclear Science and Engineering, 41 (1970), pp. 92-98.
[39] Williams, P.T. et al. (2017), LEAPOR – A Computer Code for Leakage-Rate Calculations Cracks
in Cooling Water Piping Systems,Proceedings of the ASME 2017 Pressure Vessels and Piping
Conference, 16-20 July 2017, Waikoloa.
[40] Williams, P.T. et al. (2021), Comparative Assessments of Different Leakage-Rate Models for
ATLAS+, Proceedings of the ASME 2021 Pressure Vessels and Piping Conference, 12-16 July2021.
[41] Young, B.A. (2013), xLPR Software Design Description for a Circumferential Through-Wall
Combined Tension and Bending COD Module.
[42] Kumar, V. and M.D. German (1988), Elastic-Plastic Fracture Analysis of Through-Wall andSurface Flaws in Cylinders, EPRI Report NP-5596, Research Project 1237-5, Electric Power
Research Institute, Palo Alto.
[43] Keim, E. and R. Rippel (1991), Bestimmung von Leckflächen, Rißöffnungen und Leckraten, KWU
E121/91/058, 1991.
[44] Reimann J. (1984), “Vergleich von Kritischen Massenstrom-Modellen im Hinblick auf die
Strömung Durch Lecks,” Leck-vor-Bruch-Verhalten Druckbeaufschlagter Komponenten,
Fortschr.-Ber. VDI-Z. 18(14), pp. 63-95.
[45] IAEA (2019), “Deterministic safety analysis of nuclear power plants”, Specific Safety Guide SSG2 Rev. 1, International Atomic Energy Agency, Vienna.
[46] NEA (1995), Report on round robin activities on the calculation of crack opening behaviour andleak rates for small bore piping components, OECD/NEA, OCDE/GD(95)90, NEA/CSNI/R(95)4,
OECD publishing, Paris, www.oecd-nea.org/jcms/pl_16054.
[47] Schmid, S. (2021), “Leak rate testing in the range of leak detection systems”, Nuclear Engineeringand Design, 372 111000.

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112  NEA/CSNI/R(2022)9

Appendix

This appendix presents the leak rate tests and the test facility where the main source ofcases was performed. It should be stated that the information presented in this appendix
was not distributed to the participants in the analysis phase of the benchmark; it serves atthis place for further information for interested readers of this report. The test facility is thefluid-structure-interaction (FSI) test rig, depicted in Figure A.1, which is located at theMaterials Testing Institute (MPA) at the University of Stuttgart, Germany.

Figure A.1 FSI test rig

In this test rig, water as a fluid circulates within a closed loop and allows a variety ofexperimental opportunities. It can be operated up to pressure of 8 MPa and temperatures of
up to 270°C. The leakage module within the test rig makes it possible to insert a specific
type of leak specimens; due to the operating requirements of the test rig, specimens with aleak rate of up to 0.2 kg/s can be tested. The water and steam lost through the leak arecondensed and collected in a vessel equipped with a load cell. The leak rate can bequantified from the increase of mass in the vessel over time; an additional estimate comesfrom differential flow measures in the test rig upstream and downstream of the leakmeasurements with Coriolis flow meters. The specimens used in the first benchmark phaseare shown in Figure A.2, while the specimens used in the second benchmark phase areshown in Figure A.3.

NEA LEAK RATE BENCHMARK FINAL REPORTNEA/CSNI/R(2022)9  113

Figure A.2. First benchmark phase artificial slit specimen (left) and fatigue crack
specimen (right)

Figure A.3. Second benchmark phase specimens: Artificial slit (left), fatigue crack(centre), and a detail of the thin specimen for steam generator tube leak testing (right)

From a large number of different fluid test conditions available, six points were selected
for each specimen for this benchmark study. More details about the test procedures andadditional results can be found in [30] and [47].

NEA LEAK RATE BENCHMARK FINAL REPORT