NUREG-2195 

Consequential 

SGTR Analysis for 

Westinghouse and 

Combustion 

Engineering Plants 

with Thermally 

Treated Alloy 600 

and 690 Steam 

Generator Tubes 

Office of Nuclear Regulatory Research
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SR-CR 10/2017
NUREG-2195

Consequential 

SGTR Analysis for 

Westinghouse and 

Combustion 

Engineering Plants 

with Thermally 

Treated Alloy 600 

and 690 Steam 

Generator Tubes 

Manuscript Completed: July 2017

Date Published: May 2018

Prepared by:

S. Sancaktar, M. Salay, R. Iyengar 

A. Azarm 1

S. Majumdar 2

1 Innovative Engineering and Safety Solutions, LLC

20817 Spinning Wheel Pl.

Germantown, MD 20874

2 Argonne National Laboratory

9700 S. Cass Avenue

Argonne, IL 60439

Selim Sancaktar, NRC Project Manager

Office of Nuclear Regulatory Research

iii

ABSTRACT 

This report summarizes severe-accident-induced consequential steam generator (SG) tube 

rupture (C-SGTR) analyses recently performed by the U.S. Nuclear Regulatory Commission’s 

(NRC’s) Office of Nuclear Regulatory Research. C-SGTRs are potentially risk-significant events 

because thermally induced SG tube failures caused by hot gases from a damaged reactor core 

can result in a containment bypass event and a large release of fission products to the 

environment. The current analyses evaluate replacement SGs with thermally treated Alloy 600 

and Alloy 690 heat exchange tubes and use the latest tube flaw data available in the 2010 time 

frame. The methods developed were intended to address the contribution of thermally induced 

SGTR during severe accidents and pressure-induced SGTR during a number of design-basis 

accidents. The study developed the methods and the pilot applications so as to establish the 

framework for performing a more comprehensive probabilistic risk assessment that can address 

the C-SGTR at a level of detail suitable for other NRC needs. The main conclusion from this 

work is that the SG geometry and the fluid flow rates in different SG designs can significantly 

influence the potential likelihood of C-SGTRs. For the cases studied, SG designs with a shallow 

inlet plenum (resulting in the tubesheet located closer to the hotleg inlet) and a shorter hotleg 

can result in a greater likelihood of a C-SGTR following a core damage event associated with 

accident conditions that challenge SG tubes. A shallow inlet plenum design reduces the mixing 

of hot gases entering the SG, thereby creating a higher thermal load on the tubes. For the 

specific replacement SG geometries analyzed in this study, the Combustion Engineering plant 

design had an increased likelihood of a C-SGTR and a higher potential for a large early release, 

than the Westinghouse plant design.

v 

CONTENTS 

ABSTRACT............... .............................................................................................................iii 

LIST OF FIGURES .................................................................................................................... xi 

LIST OF TABLES .................................................................................................................... xxi 

EXECUTIVE SUMMARY ........................................................................................................ xxv 

ACKNOWLEDGMENTS ....................................................................................................... xxvii 

ABBREVIATIONS ................................................................................................................. xxix 

1 INTRODUCTION .................................................................................................................1-1

1.1 Background ..................................................................................................................1-1

1.2 Objectives ....................................................................................................................1-2

1.3 Scope...........................................................................................................................1-3

1.4 Summary of Differences from Previously Published Work ............................................1-3

1.5 Summary of Research Approach and Organization of Report ......................................1-4

1.6 References...................................................................................................................1-5

2 SEQUENCE DEFINITIONS .................................................................................................2-1

2.1 Pressure-Induced C-SGTR Sequences of Interest .......................................................2-1

2.1.1 Core Damage Bridge Event Tree......................................................................2-3

2.1.2 Level 2 Event Tree: LERF Determination..........................................................2-6

2.2 Thermally Induced C-SGTR Sequences.......................................................................2-8

2.3 Representative Sequences for a Westinghouse Plant ................................................ 2-11

2.4 Representative Sequences for a Combustion Engineering Plant................................ 2-13

2.5 Critical Leakage Area for C-SGTR.............................................................................. 2-15

2.5.1 Critical Leakage Areas for Design-Basis Accidents......................................... 2-15

2.5.2 Critical Leakage Areas for Severe Accidents .................................................. 2-16

2.6 A LERF Model............................................................................................................ 2-18

2.7 References................................................................................................................. 2-21

3 THERMAL-HYDRAULIC ANALYSES FOR WESTINGHOUSE AND COMBUSTION 

ENGINEERING PLANTS ....................................................................................................3-1

3.1 Introduction ..................................................................................................................3-1

3.1.1 Summary of Results Obtained in NUREG/CR-6995..........................................3-3

3.1.2 CE Plant Considerations...................................................................................3-7

3.2 Initial Deck and Analyses for the CE Plant....................................................................3-7

3.3 Computational Fluid Dynamics .....................................................................................3-8

3.3.1 Summary of NUREG-1922 Results for Westinghouse Plants ...........................3-9

3.3.2 CFD Results for a CE Plant ............................................................................ 3-11

3.3.3 Conclusions from the CFD Analyses .............................................................. 3-12

3.4 Deck Modifications and Modeling Assumptions for the CE Analysis ........................... 3-12

3.5 Loop Seal Clearing..................................................................................................... 3-15

3.6 Analysis Results ......................................................................................................... 3-19

3.6.1 Discussion of MELCOR Analyses................................................................... 3-19

3.6.2 Summary of Accident Sequences Studied and Nomenclature ........................ 3-21

3.6.3 Select CE Sequence Results.......................................................................... 3-23

3.6.4 Data Output Fields Provided for Use by External Failure Calculator and 

FE Analyses.................................................................................................... 3-42

3.6.5 MELCOR Cases to Support the C-SGTR Calculator....................................... 3-44
vi

3.6.6 MELCOR Cases to Support RCP Seal Leakage Sensitivity Evaluation...........3-45

3.7 Potential Future Analyses...........................................................................................3-47

3.8 Conclusions................................................................................................................3-49

3.8.1 Analysis-Based Conclusions...........................................................................3-49

3.8.2 Deck-Generation-Based Conclusions .............................................................3-51

3.9 References.................................................................................................................3-52

4 BEHAVIOR OF REACTOR COOLANT SYSTEM COMPONENTS OTHER THAN 

STEAM GENERATOR TUBES ...........................................................................................4-1

4.1 Introduction ..................................................................................................................4-1

4.2 Analyses of RCS Components for a Typical Westinghouse Plant.................................4-1

4.2.1 Hot Leg and Surge Line....................................................................................4-2

4.2.2 Steam Generator Primary Manway...................................................................4-3

4.2.3 Resistance Temperature Detector ....................................................................4-3

4.2.4 Socket Weld Connection of Instrument Line to the RTD Flange........................4-3

4.2.5 Power-Operated Relief Valve ...........................................................................4-4

4.3 Thermal-Mechanical Analyses of Selected RCS Components......................................4-5

4.3.1 SG Primary Manway.........................................................................................4-5

4.3.2 Resistance Temperature Detector Welds .......................................................4-12

4.3.3 Socket Weld that Connects Instrument Line to RTD Flange ...........................4-18

4.3.4 PORV Plug-to-Seat Impact Analysis...............................................................4-21

4.4 Thermal-Mechanical Analyses of the HL and Surge Line ...........................................4-28

4.4.1 FEM for Thermal Analysis and Boundary Conditions ......................................4-28

4.4.2 FEM for Structural Analysis and Boundary Conditions....................................4-30

4.4.3 Mechanical and Surface Heat Flux Loading....................................................4-32

4.4.4 Results of Thermal-Mechanical Analysis of HL and Surge Line ......................4-34

4.4.5 Evaluation of Structural Damage ....................................................................4-36

4.4.6 HL Model ........................................................................................................4-38

4.5 Conclusions................................................................................................................4-42

4.5.1 SG Primary Manway.......................................................................................4-42

4.5.2 RTD Welds .....................................................................................................4-43

4.5.3 Instrument Line...............................................................................................4-43

4.5.4 PORV Plug-to-Cage Impact............................................................................4-43

4.5.5 HL and Surge Line..........................................................................................4-44

4.6 References.................................................................................................................4-45

5 TECHNICAL BASIS FOR PREDICTING BEHAVIOR OF FLAWED STEAM 

GENERATOR TUBES IN SEVERE ACCIDENTS ...............................................................5-1

5.1 Introduction ..................................................................................................................5-1

5.2 Ligament-Rupture Pressure..........................................................................................5-2

5.2.1 Analytical Failure Models ..................................................................................5-2

5.2.2 Validation Tests for Ligament Rupture............................................................5-11

5.3 Crack-Opening Rate at High Temperature .................................................................5-20

5.3.1 Creep-Rate Equation for Alloy 600 .................................................................5-21

5.3.2 Crack-Opening Area for Axial Cracks .............................................................5-22

5.3.3 Tests on Specimens with Circumferential Notches at High Temperature........5-22

5.3.4 Predicted Axial Crack-Opening Rate at High Temperature .............................5-26

5.4 Stability of Flaws after Ligament Rupture ...................................................................5-27

5.4.1 Failure Modes of Specimens Tested at High Temperature .............................5-28

5.4.2 Lower Bound Flow Stress for Computing Unstable Burst at High 

Temperature ...................................................................................................5-31

5.5 References.................................................................................................................5-33
vii

6 ESTIMATION OF STEAM GENERATOR TUBE FLAW DISTRIBUTIONS .........................6-1

6.1 Introduction ..................................................................................................................6-1

6.2 Data Selection..............................................................................................................6-3

6.3 Estimation of SG Tube Flaw Distributions in Replacement SGs ...................................6-5

6.3.1 Summary ..........................................................................................................6-5

6.3.2 An Example Calculation....................................................................................6-6

6.3.3 Example Flaw Samples ....................................................................................6-8

6.4 OTSG Axial Loads on Tubes during Severe Accidents...............................................6-10

6.5 References.................................................................................................................6-10

7 CONSEQUENTIAL STEAM GENERATOR TUBE RUPTURE PROBABILISTIC RISK 

ASSESSMENT FOR THE EXAMPLE COMBUSTION ENGINEERING AND 

WESTINGHOUSE PLANTS ................................................................................................7-1

7.1 Example Westinghouse Plant.......................................................................................7-1

7.1.1 Description of the Selected TH Sequences for C-SGTR PRA for the 

Example Westinghouse Plant ...........................................................................7-1

7.1.2 Estimating the Entry Frequency from Level 1 PRA for C-SGTR........................7-8

7.1.3 Conditional Probability of C-SGTR at Each Flaw Bin ........................................7-9

7.1.4 Estimating C-SGTR Probability.......................................................................7-15

7.1.5 Estimating Containment Bypass Frequency....................................................7-24

7.1.6 Level 2 Analysis of C-SGTR for ZNPP............................................................7-30

7.1.7 Quantification of Level 2 Models .....................................................................7-34

7.1.8 Concluding Remarks ......................................................................................7-36

7.2 Example Combustion Engineering Plant.....................................................................7-37

7.2.1 Description of the Selected TH Sequences for C-SGTR PRA for the 

Example CE Plant...........................................................................................7-37

7.2.2 Estimating the Entry Frequency from Level 1 PRA for C-SGTR PRA 

Analysis ..........................................................................................................7-46

7.2.3 Flaw Bins to Calculate C-SGTR Probability ....................................................7-48

7.2.4 SGTR Probability Estimation Using Integrated Flaw Samples ........................7-50

7.2.5 Level 2 Models for Containment Bypass Evaluation .......................................7-56

7.2.6 Quantification of Probability of Containment Bypass due to C-SGTR .............7-59

7.2.7 Concluding Remarks ......................................................................................7-60

7.3 Sensitivity Analyses for C-SGTR in Different SG Types .............................................7-61

7.3.1 Summary of Sensitivity Analyses for the Westinghouse Plant.........................7-62

7.3.2 Summary of Sensitivity Analyses for Combustion Engineering Plant ..............7-63

7.4 Case Studies for Pressure-Induced C-SGTR Scenarios.............................................7-65

7.4.1 C-SGTR during Anticipated Transients without Scram....................................7-65

7.4.2 C-SGTR during Steamline Break Scenarios ...................................................7-67

7.4.3 C-SGTR during High-Pressure Feed-and-Bleed Operation.............................7-69

7.4.4 LERF and Core Damage Contribution of Pressure-Induced C-SGTR .............7-70

7.5 References.................................................................................................................7-72

8 PROBABILISTIC RISK ASSESSMENT CONCLUSIONS AND 

RECOMMENDATIONS .......................................................................................................8-1

8.1 Insights and Observations ............................................................................................8-1

8.2 Limitation of Supporting Analyses for PRA Models.......................................................8-4

8.2.1 Variations in Tube Temperatures by Average Hot Tube and the Hottest 

Tube .................................................................................................................8-5

8.2.2 TH Evaluation of Accident Sequences..............................................................8-5

8.2.3 Severe-Accident Analysis .................................................................................8-5

8.2.4 Creep-Rupture and Fracture-Mechanic Models ................................................8-5
viii

8.2.5 Leak-Area Models for Failed Tubes ..................................................................8-5

8.2.6 Creep-Rupture Models and Data for HL and Surge Line...................................8-6

8.2.7 Surveillance Data from SG Periodic Inspection.................................................8-6

8.2.8 Material Properties at High Temperature ..........................................................8-6

9 OVERALL SUMMARY ........................................................................................................9-1

9.1 PRA Conclusion Insights ..............................................................................................9-3

9.2 Conclusion on Other RCS Components (from Chapter 4).............................................9-3

9.3 MELCOR Conclusions for CE Plant..............................................................................9-3

9.4 References...................................................................................................................9-4

APPENDIX A HIGH-TEMPERATURE DEFORMATION AND DAMAGE OF REACTOR

COOLANT SYSTEM MATERIALS .................................................................. A-1

APPENDIX B CONSEQUENTIAL STEAM GENERATOR TUBE RUPTURE 

CALCULATOR ................................................................................................ B-1

APPENDIX C CONSIDERATIONS FOR PRESSURE-INDUCED CONSEQUENTIAL 

STEAM GENERATOR TUBE RUPTURE ........................................................ C-1

APPENDIX D UNCERTAINTY AND SENSITIVITY ANALYSIS ............................................. D-1

APPENDIX E WESTINGHOUSE STATION BLACKOUT SCENARIO AND 

SENSITIVITY CASES ...................................................................................... E-1

APPENDIX F PRESSURE-INDUCED CONSEQUENTIAL STEAM GENERATOR 

TUBE RUPTURE—SUPPORTING CALCULATIONS ..................................... F-1

APPENDIX G ESTIMATING THE ENTRY FREQUENCY FROM LEVEL 1 

PROBABILISTIC RISK ASSESSMENT FOR LEVEL 2 PROBABILISTIC 

RISK ASSESSMENT ANALYSIS .................................................................... G-1

APPENDIX H A SCREENING APPROACH BASED ON FLAW DEPTH AND LENGTH ....... H-1

APPENDIX I MELTING TEMPERATURES AND STEEL OXIDATION 

CONSIDERATIONS IN MELCOR MODELING ................................................. I-1

APPENDIX J LOOP SEAL CLEARING CONSIDERATIONS .................................................J-1

APPENDIX K FURTHER DISCUSSION OF STEAM GENERATOR TUBE FLAW 

DISTRIBUTIONS ............................................................................................. K-1

APPENDIX L A PROCESS TO COMPREHENSIVELY ESTIMATE CONSEQUENTIAL 

STEAM GENERATOR TUBE RUPTURE CORE DAMAGE FREQUENCY 

IN A PROBABILISTIC RISK ASSESSMENT MODEL..................................... L-1 
ix

LIST OF FIGURES 

Figure 1-1 Work and report layout......................................................................................1-5

Figure 2-1 Generic CD bridge event tree for DBA-induced C-SGTR ..................................2-5

Figure 2-2 Unmitigated ltsbo emergency response timeline .............................................2-20

Figure 2-3 Unmitigated stsbo emergency response timeline ............................................2-21

Figure 3-1 Severe accident natural circulation flows ..........................................................3-2

Figure 3-2 Conceptual model of loop seal clearing...........................................................3-16

Figure 3-3 Pertinent flows for loop seal clearing...............................................................3-17

Figure 3-4 Organization of C-SGTR decks.......................................................................3-22

Figure 3-5 Main pressures for the stsbo calculation .........................................................3-25

Figure 3-6 SG secondary collapsed liquid level for the stsbo calculation..........................3-25

Figure 3-7 Main structure temperatures for the stsbo calculation .....................................3-26

Figure 3-8 Creep-rupture indices for the stsbo calculation ...............................................3-26

Figure 3-9 HotAve tube creep-rupture indices for the stsbo calculation............................3-27

Figure 3-10 Hydrogen concentrations in SG A tubes for the stsbo calculation ...................3-27

Figure 3-11 Volatile FP release fractions for the stsbo calculation .....................................3-28

Figure 3-12 Main pressures for the ltsbo calculation ..........................................................3-28

Figure 3-13 SG secondary collapsed liquid level for the ltsbo calculation...........................3-29

Figure 3-14 Main structure temperatures for the ltsbo calculation ......................................3-29

Figure 3-15 Comparison of ltsbo pressures to those of stsbo.............................................3-30

Figure 3-16 Comparison of ltsbo SG boiler collapsed liquid levels to those of stsbo ..........3-30

Figure 3-17 Comparison of ltsbo loop A structure temperatures to those of stsbo..............3-31

Figure 3-18 Comparison of ltsbo loop B structure temperatures to those of stsbo..............3-31

Figure 3-19 Main pressures for the ltsbo-as calculation .....................................................3-32

Figure 3-20 SG secondary collapsed liquid level for the ltsbo-as calculation......................3-33

Figure 3-21 Main structure temperatures for the ltsbo-as calculation .................................3-33

Figure 3-22 Creep-rupture indices for the ltsbo-as calculation............................................3-34

Figure 3-23 HotAve tube creep-rupture indices for the ltsbo-as calculation........................3-34

Figure 3-24 Hydrogen concentrations in SG A tubes for the ltsbo-as calculation ...............3-35

Figure 3-25 Volatile FP release fractions for the ltsbo-as calculation..................................3-35

Figure 3-26 Main pressures for the stsbo-a calculation ......................................................3-36

Figure 3-27 Volatile FP release fractions for the stsbo-a calculation ..................................3-36

Figure 3-28 Main pressures for the ltsbo-a calculation .......................................................3-37

Figure 3-29 Volatile FP release fractions for the ltsbo-a calculation ...................................3-37

Figure 3-30 Main pressures for the stsbo-as calculation ....................................................3-38

Figure 3-31 Volatile FP release fractions for the stsbo-as calculation.................................3-38

Figure 3-32 Main pressures for the stsbo-ao calculation ....................................................3-39

Figure 3-33 Volatile FP release fractions for the stsbo-ao calculation ................................3-39

Figure 3-34 Primary pressure and secondary pressure for SG A and B for base case 

of short SBO with and without RCP seal leakage............................................3-46
x 

Figure 3-35 The HL structure and peak SG tube temperature for loop B for base case 

of short SBO with and without RCP seal leakage............................................ 3-46

Figure 3-36 Normalized temperature distribution at the SG tube sheet inlet for a 

CE plant.......................................................................................................... 3-47

Figure 4-1 Parts for the ZNPP HL primary manway ...........................................................4-5

Figure 4-2 Finite-element model of manway assembly.......................................................4-6

Figure 4-3 Time-temperature histories of inlet plenum .......................................................4-7

Figure 4-4 Elastic-creep analysis of manway bolts.............................................................4-8

Figure 4-5 Principal creep strain ........................................................................................4-9

Figure 4-6 Crack mouth pressure and opening area variations ........................................ 4-10

Figure 4-7 Variation of opening area with (a) time and (b) temperature for 

two temperature histories................................................................................ 4-10

Figure 4-8 Effect of steam leakage on opening area ........................................................ 4-11

Figure 4-9 Predicted vs. observed creep curves of SA 193-B7 for duplicate tests at 

20 and 30 ksi at (a) 550 degrees C and (b) 450 degrees C ............................. 4-12

Figure 4-10 RTD scoop and welds connecting it to HL....................................................... 4-13

Figure 4-11 Meshes used to analyze RTD scoop, welds, and HL ...................................... 4-13

Figure 4-12 Steam temperature histories for the hot side and the cool side of the RTD ..... 4-14

Figure 4-13 Closeup view of temperature (in °F) in HL RTD scoop at 14,400 s.................. 4-15

Figure 4-14 Variation of average temperature in ID and OD welds with time...................... 4-15

Figure 4-15 Von Mises effective stress (in psi) distribution at ID weld RTD interface 

at 14,148 s...................................................................................................... 4-16

Figure 4-16 Von Mises effective stress (in psi) distribution at OD weld RTD interface 

at 14,148 s...................................................................................................... 4-17

Figure 4-17 Time evolution of (a) average von Mises effective stress and (b) average 

effective creep strain at interfaces of ID and OD welds with RTD.................... 4-17

Figure 4-18 Simplified axisymmetric model for connection of instrument-line-to-RTDflange weld...................................................................................................... 4-19

Figure 4-19 Temperature loading applied as uniform temperature to model of 

connection of instrument-line-to-RTD flange weld........................................... 4-19

Figure 4-20 Time evolution of (a) average von Mises effective stress and (b) average 

effective creep strain at interfaces of weld with instrument line and RTD ........ 4-20

Figure 4-21 Effective creep strain distribution in instrument line at time t=14,230 s............ 4-20

Figure 4-22 Time evolution of average effective creep strain in instrument line away 

from welds ...................................................................................................... 4-21

Figure 4-23 Various parts included in the plug-to-cage impact analysis ............................. 4-24

Figure 4-24 Stress-plastic strain curves at 288 and 538 degrees C (550 and 

1,000 degrees F) used in analysis................................................................... 4-25

Figure 4-25 Variation of spring force with time during single impact................................... 4-26

Figure 4-26 Variation of equivalent plastic strain with (a) von Mises effective stress 

and (b) time for most highly strained element in plug at 288 and 

538 degrees C (550 and 1,000 degrees F)...................................................... 4-26
xi

Figure 4-27 Stress-plastic strain on 2-mm thick plug .........................................................4-27

(a) Simplified axisymmetric model of plug-to-cage impact, where satellite 

overlay on plug is 2-mmthick...........................................................................4-27

(b) stress-plastic strain curves used in impact analysis of plug with 2-mmthick Stellite overlay ........................................................................................4-27

Figure 4-28 Distribution of von Mises effective stress (in psi) near contact zone of 

cage and plug with 2-mm Stellite overlay ........................................................4-28

Figure 4-29 Components of first version of FEM for thermal conduction analysis...............4-29

Figure 4-30 FEM for thermal analysis ................................................................................4-29

Figure 4-31 Components of second version of FEM for structural analysis with 

supports, flailing restraints, and hangers.........................................................4-30

Figure 4-32 Control volumes for thermal-hydraulic analysis of the HL and surge line 

by RELAP5 .....................................................................................................4-33

Figure 4-33 Temperature-dependent stress strain curves for 316 stainless steel

(Appendix A)...................................................................................................4-34

Figure 4-34 Temperature contours at inner surface at 9,222 s indicate the steadystate condition of 623 K in the entire region of consideration ..........................4-35

Figure 4-35 Temperature contours at inner surface at 13,555 s indicate the higher 

temperature in the upper half of the HL region................................................4-35

Figure 4-36 Contours of accumulated creep strain at inner surface at 12,300 s 

indicate the significant creep strains in the upper half of the HL region ...........4-36

Figure 4-37 Contours of plastic strain at inner surface at 12,300 s indicate the 

concentration of plastic strains in the upper half of the HL region....................4-36

Figure 4-38 Contours of through-thickness damage at 12,300 s shown in the section 

of HL experiencing higher strains....................................................................4-38

Figure 4-39 Contours of creep damage at 12,300 s shown in the (a) outer surface and 

(b) inner surface of HL experiencing higher strains .........................................4-38

Figure 4-40 Contours of accumulated creep strain at inner surface at 12,430 s 

indicate the significant creep strains in the upper half of the HL region ...........4-39

Figure 4-41 Contours of accumulated plastic strain at inner surface at 12,430 s 

indicate the significant creep strains in the upper half of the HL region ...........4-39

Figure 4-42 Contours of through-thickness damage at 12,430 s shown in the section 

of HL experiencing higher strains....................................................................4-40

Figure 4-43 Contours of through-thickness damage assuming (a) creep-only 

behavior at 12,140 s and (b) plasticity-only behavior at 13,025 s ....................4-40

Figure 4-44 Contours of through-thickness damage assuming no spatial adjustment of 

heat transfer coefficient obtained from RELAP................................................4-41

Figure 4-45 Contours of through-thickness damage for the HL pipe with weld overlay 

at 12.500 s......................................................................................................4-42

Figure 5-1 Predicted vs. observed (a) ligament-rupture pressures and (b) unstable 

burst pressures of Alloy 600 tubes with axial notches at room temperature ......5-4

Figure 5-2 Flow-stress curves for various product forms of Alloy 600.................................5-5

Figure 5-3 Larson-Miller plot for Alloy 600 tubes ................................................................5-6
xii

Figure 5-4 Stress distributions through section at failure of tubes with (a) two 

symmetrically located part-through circumferential cracks and (b) single 

part-through circumferential crack.....................................................................5-8

Figure 5-5 Variations of experimental failure bending moments with crack angle and 

those predicted by (a) Kurihara model and (b) ANL model.............................. 5-10

Figure 5-6 Predicted vs. observed time to failure of flawed and unflawed tubes under 

constant temperature and pressure condition ................................................. 5-12

Figure 5-7 Predicted vs. observed failure pressures for isothermal (700–840 degrees 

C) pressure ramp tests on unflawed and flawed tubes 0.25–1 in. long and

65–80 percent deep by (a) creep-rupture model and (b) flow-stress model..... 5-13

Figure 5-8 Effective flow-stress curves (dashed lines) computed from the pressure 

ramp tests (symbols) vs. temperature of test................................................... 5-14

Figure 5-9 Comparison of observed failure temperatures with those predicted by 

(a) creep-rupture model and (b) flow-stress model for temperature

ramp tests....................................................................................................... 5-15

Figure 5-10 Comparison of predicted failure temperatures by the creep-rupture and 

flow-stress models for flawed specimens as a function of temperature 

ramp rate ........................................................................................................ 5-15

Figure 5-11 Calculated and ANL simulation of (a) INEL ramp and (b) EPRI ramp for 

high-temperature tests .................................................................................... 5-17

Figure 5-12 Observed vs. predicted failure temperatures by (a) creep-rupture model 

and (b) flow-stress model for tests simulating severe-accident transients ....... 5-17

Figure 5-13 Variation of failure temperatures with crack angle for specimens with 

two symmetrical cracks of various depths ....................................................... 5-18

Figure 5-14 Experimental failure temperatures and failure temperatures predicted by 

the Kurihara and ANL models for two symmetrical part-through 

circumferential cracks of various semiangular length θ ................................... 5-19

Figure 5-15 Failure temperatures for specimens with one (n = 1) and two (n = 2) 

circumferential cracks ..................................................................................... 5-20

Figure 5-16 INEL creep rate on Alloy 600 vs. stress data plotted using activation

energy of 65 kcal/mole and stress normalized by Young’s modulus 

at temperature ................................................................................................ 5-21

Figure 5-17 Variations of Crack Opening Parameters ........................................................ 5-22

Figure 5-18 Illustration of circumferential cracks ................................................................ 5-23

Figure 5-19 Variation of h2 with c/b for creep-rate exponents n = 3.7 and 6.1.................... 5-24

Figure 5-20 Experimentally measured and predicted variation of total notch opening 

with time for specimens with two 45-degree circumferential notches 

loaded at (a) 1,106.8 kgf (2,440 lb) and (b) 1,224.7 kgf (2,700 lb)................... 5-24

Figure 5-21 Experimentally measured and predicted variation of total notch opening 

with time for specimens with two symmetrical circumferential notches 

loaded at 1,108 kg (2,400 lb) for notch lengths (a) 6.35 mm (0.25 in.) and 

(b) 5.1 mm (0.20 in.) ....................................................................................... 5-25

Figure 5-22 Time vs. temperature plot for tests CR 106 and CR 108 ................................. 5-26

Figure 5-23 Comparison of predicted (solid line) and experimentally measured 

(symbols) notch-opening displacements for (a) Test CR 106 and (b) Test 

CR 108 ........................................................................................................... 5-26
xiii

Figure 5-24 Variations of (a) COD rate with through-wall axial crack length for a tube 

subjected to internal pressure of 2,350 psi at 700 degrees C and 

(b) crack-opening area with crack length at final temperatures 700 and 

750 degrees C for a tube subjected to severe-accident transient ....................5-27

Figure 5-25 Crack opening rate and time to reach COA of 45 degrees ..............................5-28

Figure 5-26 Measured (a) CODs and (b) COAs in failed high-temperature test 

specimens as a function of initial axial flaw depth and initial flaw length..........5-29

Figure 5-27 Test results for unstable burst pressure ..........................................................5-30

Figure 5-28 Variation of failure pressure with failure temperature for tests conducted 

on specimens with a 25-mm (1-in.)-long crack ................................................5-31

Figure 5-29 Temperature variation of flow stress (using k=0.5) of Alloy 600 

specimens derived from tensile test data as reported in the literature .............5-32

Figure 5-30 Pressure at failure as a function of temperature at failure for all 

specimens with a (a) 6-mm (0.25-in.)-long axial crack and (b) 51-mm 

(2-in.)-long axial crack.....................................................................................5-32

Figure 5-31 Critical crack length as a function of temperature for a 22.3-mm (7/8-in.)-

diameter Alloy 600 tube at an internal pressure of 16 MPa (2,350 psi)............5-33

Figure 6-1 Table 2 reproduced from NUREG/CR-6521......................................................6-2

Figure 6-2 Average number of flaws as a function of EFPY for four SGs ...........................6-8

Figure 6-3 600TT flaws for 10 SGs—distribution by length ................................................6-9

Figure 6-4 600TT flaws for 10 SGs—distribution by depth .................................................6-9

Figure 7-1 (a) TH results for Wnewbase ............................................................................7-4

Figure 7-1 (b) Difference between the HL temperature and the temperatures of the 

hottest tube (HTT) and the average hot tube (AHTT) and cold tube 

(ACTT) for Wnewbase ......................................................................................7-5

Figure 7-2 TH results for Case F2......................................................................................7-6

Figure 7-3 TH results for Case F3......................................................................................7-7

Figure 7-4 Shifted distribution for flaw depth ....................................................................7-12

Figure 7-5 Shifted distribution for flaw length ...................................................................7-12

Figure 7-6 RCS survival probability as a function of accident time for Wnewbase............7-18

Figure 7-7 Percentiles of the SG leak area distribution as a function of accident time......7-19

Figure 7-8 Survival functions for RCS and SG tube failures with critical leak rate ............7-20

Figure 7-9 Percentiles of the SG leak area distribution as a function of accident time......7-21

Figure 7-10 Survival probability functions for RCS and flawed tubes..................................7-21

Figure 7-11 Definition of bounding SBO sequences with high/dry/low (H/D/L) 

conditions .......................................................................................................7-26

Figure 7-12 An estimate of bounding SBO sequence frequencies leading to C-SGTR 

and containment bypass .................................................................................7-28

Figure 7-13 Another estimate of bounding SBO sequence frequencies leading to 

C-SGTR and containment bypass...................................................................7-29

Figure 7-14 Loop A temperature profiles of the HL and SG tubes for the SBO with an 

early failure of TDAFW pumps ........................................................................7-41
xiv

Figure 7-15 Loop B temperature profiles of the HL and SG tubes for the SBO with an 

early failure of TDAFW pumps [surge-line temperature of loop A is shown 

to facilitate comparison of loop A and B temperature trends] .......................... 7-41

Figure 7-16 Difference in loop A temperature of the HL and SG tubes for the SBO with 

an early failure of TDAFW pumps ................................................................... 7-42

Figure 7-17 (a) Difference in loop B temperature of the HL and SG tubes for the SBO

with an early failure of TDAFW pumps ............................................................ 7-42

Figure 7-17 (b) Primary and secondary pressure for the SBO with an early failure of

TDAFW pumps ............................................................................................... 7-43

Figure 7-18 Loop A temperature profiles of the HL and SG tubes for the SBO with a 

delayed failure of TDAFW pumps ................................................................... 7-43

Figure 7-19 Loop B temperature profiles of the HL and SG tubes for the SBO with a 

delayed failure of TDAFW pumps (surge-line temperature of loop A is 

shown to facilitate comparison of loop A and B temperature trends)............... 7-44

Figure 7-20 Difference in loop A temperature of the HL and SG tubes for the SBO with 

a delayed failure of TDAFW pumps................................................................. 7-44

Figure 7-21 (a) Difference in loop B temperature of the HL and SG tubes for the SBO

with a delayed failure of TDAFW pumps ......................................................... 7-45

Figure 7-21 (b) Primary and secondary pressure for the SBO with a delayed failure of

TDAFW pumps ............................................................................................... 7-45

Figure 7-22 The RCS survival probability and percentiles of SGTR leak areas for 

stsbo-a-average hot tubes .............................................................................. 7-51

Figure 7-23 The RCS survival probability and percentiles of SGTR leak areas for 

stsbo-a-hottest tubes ...................................................................................... 7-52

Figure 7-24 The RCS survival probability and the probability of SGTR with a leak area 

less than 3 cm2 for stsbo-a-b, aggregated over average hot and 

hottest tubes ................................................................................................... 7-53

Figure 7-25 The RCS survival probability and the probability of SGTR with a leak area 

less than 3 cm2 for stsbo-a-a, aggregated over average hot and hottest 

tubes............................................................................................................... 7-53

Figure 7-26 The RCS survival probability and the probability of SGTR with a leak area 

less than 3 and 6 cm2 for stsbo-a-b-scf ........................................................... 7-54

Figure 7-27 The RCS survival probability and the probability of SGTR with a leak area 

less than 6 cm2 for the whole plant for an SBO scenario with failure of 

TDAFW pump at time zero and no stuck-open secondary relief valves 

(stsbo-a-scf).................................................................................................... 7-55

Figure 7-28 The RCS survival probability and the probability of SGTR with leak areas 

less than 3 and 6 cm2 for ltsbo-a-b-scf ............................................................ 7-55

Figure 7-29 The sensitivity results for (stsbo-a) for C-SGTR leak areas of 12 cm2 and 

6 cm2 .............................................................................................................. 7-64

Figure A-1 Creep curves for SA 193 B7 material at (a) 450 oC, (b) 550 oC, (c) 650 o

C ....... A-4

Figure A-2 Comparison of fitted and test variation of creep strain vs. time for creep 

tests conducted on SA 193 B7 at 450 degrees C at (a) 20 ksi (138 MPa), 

(b) 30 ksi (207 MPa), and (c) 40 ksi (278 MPa)................................................ A-5
xv

Figure A-3 Comparison of fitted and test variation of creep strain vs. time for creep 

tests conducted on SA 193 B7 at 550 degrees C at (a) 10 ksi (69 MPa), 

(b) 20 ksi (138 MPa), and (c) 30 ksi (207 MPa)................................................A-6

Figure A-4 Comparison of fitted and test variation of creep strain vs. time for creep 

tests conducted on SA 193 B7 at 650 degrees C at (a) 7.5 (52 MPa), 

(b) 10 (69 MPa), and (c) 20 ksi (138 MPa) .......................................................A-6

Figure A-5 Creep strain vs. time curves of SA 240 Grade 316 stainless steel at 

700 degrees C (a) 26 ksi (179 MPa) and (b) 28 ksi (193 MPa) and 30 ksi 

(207 MPa)........................................................................................................A-8

Figure A-6 Creep strain vs. time curves of SA 240 Grade 316 stainless steel at 

800 o

C (a) 13 ksi (90 MPa) and (b) 15 ksi (103 MPa).......................................A-8

Figure A-7 Creep strain vs. time curves of SA 240 Grade 316 stainless steel at 

(a) 1,000 o

C, 4 ksi (28 MPa) and (b) 1,100 oC, 2 ksi (14 MPa) .........................A-9

Figure A-8 Predicted vs. test minimum creep rate of SA 240 Grade 316 

stainless steel ................................................................................................A-10

Figure A-9 Larson-Miller parameter plot for time to stress rupture of SA 240 

Grade 316 stainless steel at 538–1,100 o

C ....................................................A-11

Figure A-10 Predicted vs. test time to stress rupture of SA 240 Grade 316 stainless 

steel at 538–1,100 o

C.....................................................................................A-11

Figure A-11 Steady-state creep ductility vs. stress of SA 240 Grade 316 stainless 

steel at (a) 538 o

C and (b) 566 oC ..................................................................A-12

Figure A-12 Steady-state creep ductility vs. stress of SA 240 Grade 316 stainless 

steel at (a) 593 o

C and (b) 649 oC ..................................................................A-12

Figure A-13 Steady-state creep ductility vs. stress of SA 240 Grade 316 stainless 

steel at (a) 700 o

C and (b) 760 oC ..................................................................A-13

Figure A-14 Steady-state creep ductility vs. stress of SA 240 Grade 316 stainless 

steel at 800 o

C ...............................................................................................A-13

Figure A-15 Estimated mean, upper, and lower bounds to the steady-state creep 

ductility of SA 240 Grade 316 stainless steel .................................................A-14

Figure A-16 Creep strain vs. time curves of SA 351 Grade CF8M cast stainless steel 

at 700 o

C (a) 15–16 ksi (103–110 MPa) and (b) 17 ksi (117 MPa) ................. A-15

Figure A-17 Creep strain vs. time curves of SA 351 Grade CF8M cast stainless steel 

at 800 o

C (a) 12 and 14 ksi (83–97 MPa) and (b) 10 ksi (69 MPa) ................. A-16

Figure A-18 Creep strain vs. time curves of SA 351 Grade CF8M cast stainless steel 

at 1,000 o

C (a) 3 ksi (21 MPa) and (b) 2 ksi (14 MPa)....................................A-16

Figure A-19 Confidence bounds for the prediction of (a) creep rate and (b) LarsonMiller parameter for time to rupture of SA 351 Grade CF8M cast stainless 

steel based on ANL and Japanese data.........................................................A-18

Figure A-20 Predicted vs. observed time to stress rupture of SA 351 Grade CF8M cast 

stainless steel ................................................................................................A-18

Figure A-21 Variation of (a) steady-state ductility of U.S. and Japanese CF8M heats 

and (b) total elongation of U.S. CF8M heat with stress...................................A-19

Figure A-22 Creep curves for SA 516 Grade 70 carbon steel at (a) 500 o

C, (b) 650 oC, 

and (c) 800 o

C................................................................................................A-21

Figure A-23 (a) Predicted vs. observed creep rates...........................................................A-22
xvi

Figure A-23 (b) Larson-Miller plot for time to stress rupture of SA 516 Grade 70 and

SA 216 Grade WCC....................................................................................... A-22

Figure A-24 (a) Predicted vs. observed time to stress rupture ........................................... A-23

Figure A-24 (b) Variation of steady-state ductility with stress and temperature of

carbon steels ................................................................................................. A-23

Figure C-1 ATWS event tree top events to address Type-II C-SGTR ................................ C-4

Figure C-2 ATWS event tree top events to address Type-II C-SGTR—example 

quantification.................................................................................................... C-5

Figure C-3 L-SSB event tree top events to address Type-II C-SGTR ................................ C-6

Figure C-4 L-SSB event tree top events to address Type-II C-SGTR—

example quantification ..................................................................................... C-7

Figure D-1 Temperature and pressure profile of the base case (at the flaw location)......... D-2

Figure D-2 Leak area of the base case (4 cm wear flaw with 40 percent depth) ................ D-3

Figure D-3 Probabilities of HL and surge-line failure.......................................................... D-6

Figure D-4 Temperature and pressure profile of the case where secondary side is 

not depressurized .......................................................................................... D-13

Figure D-5 SBO with TDAFW pump operating for 0 hours with MSSVs stuck open; 

Calvert Cliffs .................................................................................................. D-25

Figure D-6 SBO with TDAFW pump operating for 0 hours; Calvert Cliffs loop A.............. D-26

Figure D-7 Temperature differences in SBO with TDAFW pump operating for 

0 hours; Calvert Cliffs loop A.......................................................................... D-26

Figure D-8 SBO with TDAFW pump operating for 0 hours; Calvert Cliffs loop B.............. D-27

Figure D-9 Temperature differences in SBO with TDAFW pump operating for 

0 hours; Calvert Cliffs loop B.......................................................................... D-27

Figure D-10 SBO with TDAFW pump operating for 4 hours; Calvert Cliffs loop A.............. D-28

Figure D-11 Temperature differences in SBO with TDAFW pump operating for 

4 hours; Calvert Cliffs loop A.......................................................................... D-28

Figure D-12 SBO with TDAFW pump operating for 4 hours; Calvert Cliffs loop B.............. D-29

Figure D-13 Temperature differences in SBO with TDAFW pump operating for 

4 hours; Calvert Cliffs loop B.......................................................................... D-29

Figure D-14 Probabilities of SGTR leak rates less than 3 and 6 cm2 vs. HL survival 

probability for stsbo-as-a-scf .......................................................................... D-30

Figure D-15 Probabilities of SGTR leak rates less than 3 and 6 cm2 vs. HL survival 

probability for stsbo-as-b-scf .......................................................................... D-31

Figure D-16 Probability of SGTR less than 6 cm2 and probability of RCS survival ............. D-31

Figure D-17 Probability of SGTR leak rate less than 3 cm2 for loop B with and without 

open secondary relief valves after SG dryout................................................. D-32

Figure D-18 Probability of SGTR leak rate less than 6 cm2 with and without open 

secondary relief valves after SG dryout.......................................................... D-33

Figure D-19 Probability of SGTR with leak rates smaller than a specific value and 

probability of RCS survival as a function of accident time .............................. D-34

Figure D-20 Probability of SGTR as a function of critical leak area.................................... D-35

Figure E-1 WNEWBASE scenario parameters .................................................................. E-2

Figure E-2 Delta T (in degrees Celsius) between HL and hot tube—WNEWBASE............ E-3
xvii

Figure E-3 Histogram for flaw distribution (by size) for 600TT ...........................................E-4

Figure E-4 Histogram for flaw distribution (by size) for 690TT ...........................................E-5

Figure F-1 Assumed TH behavior for ATWS for C-SGTR analysis.................................... F-2

Figure F-2 Assumed TH behavior for SLB for C-SGTR analysis ....................................... F-3

Figure I-1 The parabolic rate constant for steam-H2O reaction ......................................... I-2

Figure I-2 Steel mass loss at a fixed temperature ............................................................. I-3

Figure I-3 Loss of steel thickness...................................................................................... I-3

Figure K-1 Graphical presentation of aggregate flaw data.................................................K-2

Figure K-2 Graphical presentation of aggregate flaw data.................................................K-2

Figure K-3 Flaw depth distribution .....................................................................................K-4

Figure K-4 Flaw depth distribution (shifted gamma)...........................................................K-5

Figure L-1 Insertion of C-SGTR event tree node in SSB event trees..................................L-4

Figure L-2 Insertion of C-SGTR event tree node in ATWS event tree ................................L-5

xix

LIST OF TABLES 

Table 2-1 Selected DBA Sequences Causing Challenges to SG Tubes ...........................2-2

Table 2-2 Selected Sequences to Evaluate C-SGTR for Severe 

Accident Sequences .......................................................................................2-10

Table 3-1 The governing parameters for W and CE SGs ................................................3-12

Table 3-2 Timing of Selected Events ..............................................................................3-24

Table 3-3 Failure Times and Release Fractions to Environment .....................................3-42

Table 3-4 MELCOR Cases to Support C-SGTR Calculator.............................................3-45

Table 4-1 Spring Rates of Steam Generator Supports....................................................4-31

Table 4-2 Surge-Line Supports in FEM for Structural Analysis........................................4-32

Table 4-3 Weights and Pressure Loading and Mass Densities Used in 

Thermal-Mechanical Analysis of the HL and Surge Line .................................4-33

Table 4-4 Summary of Predicted HL Failure Times for the Various Analyses .................4-44

Table 6-1 SG Properties for Flaw Distribution Estimates for C-SGTR Studies ..................6-5

Table 6-2 SG Tube Flaw Distributions Taken from Reference 2 .......................................6-6

Table 7-1 Contributions of Various Events to Long-Term SBO Scenarios.........................7-8

Table 7-2 Related Information from Zion Nuclear Stations for This Study .........................7-9

Table 7-3 Probability that a Flaw that Belongs to a Bin Defined by Depth and Length 

Range Fails a before the HL Failure for Inconel 600 Tubes for 

“Wnewbase” TH File for the Selected W Plant ................................................7-10

Table 7-4 Probability that a Flaw that Belongs to a Bin Defined by Depth and Length 

Range Fails before the HL Failure for Inconel 690 Tubes for “Wnewbase” 

TH File for the Selected W Plant.....................................................................7-11

Table 7-5 Probability that a Detected Flaw Belongs to a Bin Size at 15 EFPYs ..............7-14

Table 7-6 Expected Number of Flaws that Belong to a Flaw Bin Defined by Depth 

and Length Range for Zion SGs with Tubes Made of Inconel 600...................7-14

Table 7-7 Expected Number of Flaws that Belong to a Flaw Bin Defined by Depth 

and Length Range for Zion SGs with Tubes Made of Inconel 690...................7-15

Table 7-8 C-SGTR probability summed over the flaw bins for Inconel 600/690 (W)........7-16

Table 7-9 Probability of Single and Multitube Failure in C-SGTR for Inconel

600/690 (W)....................................................................................................7-17

Table 7-10 Summary of 3 Types of C-SGTR Failure Probability Estimates Discussed 

in Sections 7.1.4.2, 7.1.4.3, and 7.1.4.4..........................................................7-23

Table 7-11 Timing of Major Events during an SBO with Early Failures of TDAFW 

Pumps (Wnewbase with Inconel 600TT SG)...................................................7-31

Table 7-12 Timing of Major Events during an SBO with Failures of TDAFW Pumps 

after Battery Depletion (SCDAP/RELAP Case 153 with Inconel 

600TT SG)......................................................................................................7-32

Table 7-13 Conditional LERF Probabilities for an SBO with Early and Late Failures of 

TDAFW Pump for the W Plant ........................................................................7-35

Table 7-14 Related Information from the Reference CE Plant...........................................7-47

Table 7-15 Contributions of Various Events to the Long-Term SBO Scenarios for 

Single and Dual Unit Core Damage ................................................................7-48
xx 

Table 7-16 Expected Number of Flaws per Each SG that Belong to a Flaw Bin 

Defined by Depth and Length Range .............................................................. 7-49

Table 7-17 Expected Number of Flaws per Loop A and Loop B (One Unit; Two SGs) 

that Belong to a Flaw Bin Defined by Depth and Length Range...................... 7-49

Table 7-18 Comparison of C-SGTR Probability for SBO................................................... 7-56

Table 7-19 Timing of Major Events during an SBO with Early Failures of 

TDAFW Pumps............................................................................................... 7-56

Table 7-20 Timing of Major Events during an SBO with Failures of TDAFW Pumps 

after Battery Depletion .................................................................................... 7-58

Table 7-21 Conditional LERF Probabilities for an SBO with Early and Late Failures of 

TDAFW Pumps for the Example CE Plant ...................................................... 7-59

Table 7-22 Sensitivity Results for Early Stick-Open Failures of the Secondary 

Relief Valves................................................................................................... 7-63

Table 7-23 Sensitivity Results for Opening the Secondary Relief Valves after SG 

Dryout............................................................................................................. 7-64

Table 7-24 Contributors to Electrical RPS Failures that Do Not Impact Manual Scram ..... 7-66

Table 7-25 Changes in Core Damage Frequency and LERF as a Result of 

Pressure-Induced C-SGTR for the Example W Plant ...................................... 7-71

Table 7-26 Changes in Core Damage Frequency and LERF as a Result of 

Pressure-Induced C-SGTR for the Example CE Plant ....................................7-71

Table 8-1 Summary of the Frequency Estimates for Containment Bypass and LERF.......8-3

Table 8-2 Summary Table for Conditional Probability of C-SGTR Studied as 

Base Cases ......................................................................................................8-3

Table A-1 Range of Temperatures (°C) for which High-Temperature Material 

Properties Data Are/Are Not Available ............................................................. A-2

Table A-2 Materials and Temperature Ranges (°C) over which Materials Properties 

Data Were Generated by ANL ......................................................................... A-2

Table A-3 Summary of Creep Data for SA 193 B7 Bolt Material....................................... A-3

Table A-4 Best-Fit Values of the Parameters B, m, Q, and n of SA 193 B7 As 

Determined from the Creep Tests .................................................................... A-5

Table A-5 Summary of Creep Data for SA 240 Grade 316 Stainless Steel....................... A-7

Table A-6 Creep Rate Parameters for Available Data on Type 316 Stainless Steel ......... A-9

Table A-7 Summary of Creep Data for SA 351 Grade CF8M Cast Stainless Steel......... A-15

Table A-8 Mean and ±95% Confidence Bounds of Creep-Rate Parameters for 

Combined ANL and Japanese Data on SA 351 Grade CF8M Cast 

Stainless Steel at Various Temperatures (Stress in ksi and Creep Rate 

in 1/h)............................................................................................................. A-17

Table A-9 Summary of Creep Data for SA 516 Grade 70 Carbon Steel ......................... A-20

Table A-10 Creep-Rate Parameters for Combined ANL and Literature Data on 

SA 216 Grade 70 and SA 216 Grade WCC Carbon Steels ............................ A-22

Table A-11 Summary of Creep Data for SA 240 Grade 316 /SA 516 Grade 

70 Weldment.................................................................................................. A-24

Table B-1 Example Input-Output (Condensed and Processed) ........................................ B-4

Table D-1 Output for the Total Leak Area in the Base Case ............................................. D-4
xxi

Table D-2 Probabilities of HL and Surge Line...................................................................D-7

Table D-3 Calculation of Margin for the Base Case ..........................................................D-9

Table D-4 Margin with Smaller Temperature Difference between HL and Hot Tube.......D-11

Table D-5 Margin with Thicker HL ..................................................................................D-12

Table D-6 Margin with Secondary Side NOT Depressurized (at 1,100 psi).....................D-14

Table D-7 T&H Input Parameters for Case 153 ..............................................................D-16

Table D-8 Margin for the Case with Failure of TDAFW Pump at 4 Hours........................D-21

Table D-9 Comparison of 690TT Cases of W vs. CE-Type SGs.....................................D-23

Table D-10 Sensitivity Results for Early Stick-Open Failures of the Secondary 

Relief Valves..................................................................................................D-32

Table D-11 Sensitivity Results for Opening the Secondary Relief Valves after 

SG Dryout......................................................................................................D-33

Table E-1 WNEWBASE Results for Case 1 .....................................................................E-6

Table E-2 Summary Output for the Final Scenario with 42 “Large” Flaws.........................E-8

Table E-3 WNEWBASE Results for Case 2 .....................................................................E-9

Table E-4 WNEWBASE Results for Case 3 with 690TT.................................................E-11

Table F-1 TH Input File for C-SGTR for Simulating ATWS Scenarios .............................. F-1

Table F-2 TH Input File for C-SGTR for Simulating SLB Scenarios.................................. F-2

Table F-3 Example of Expected Flaw Set Plus One Large Flaw of 70-Percent Depth 

and 3-cm Length for a CE Plant...........................................................................3

Table F-4 Results of Intermediate File from C-SGTR for Flaw #126, at 70-Percent 

Depth and 3-cm Length for a CE Plant and TH File Representing SLB............ F-4

Table F-5 Results of Cumulative Leak Area File from C-SGTR for Expected Flaws 

Plus One Flaw at 70-Percent Depth and 3-cm Length for a CE Plant and 

TH File Representing SLB ............................................................................... F-4

Table F-6 Case Results of Pressure-Induced C-SGTR during ATWS .............................. F-5

Table F-7 Case Results of Pressure-Induced C-SGTR during SLB.................................. F-5

Table F-8 Bounding C-SGTR Probability per a Flaw Bin to be Used for Both SLB 

and ATWS Scenarios for Westinghouse and CE Plants.......................................6

Table F-9 Bounding Probability for SGTR—Leak per a Flaw Bin to be Used for Both 

SLB and ATWS Scenarios for Westinghouse and CE Plants ...............................6

Table F-10 Probability that a Detected Flaw Belongs to a Bin Size at 15 Effective 

Full-Power Years .................................................................................................7

Table F-11 C-SGTR Probability for SLB or ATWS Scenarios per Flaw ..................................7

Table G-1 Information from Zion Nuclear Station..............................................................G-2

Table G-2 Information from Calvert Cliffs Nuclear Station.................................................G-5

Table G-3 Core Damage for SBO Scenarios with Early Failure of TDAFW Pumps...........G-6

Table G-4 CDF for the SBO and the Failures of TDAFW Pumps due to Overfill (for 

Internal Event Initiators Affecting One or Both Units) .......................................G-6

Table G-5 CDF for an SBO and the Failures of All TDAFW Pumps after the Battery 

Depletion (Internal Event Initiators Affecting One or Both Units) ......................G-6

Table G-6 CDF for the SBO and Failures of TDAFW Pumps due to a Potential 

Overfill (Seismic Events Affecting One or Both Units) ......................................G-7
xxii

Table G-7 CDF for SBO and Failures of TDAFW Pumps after the Battery Depletion 

(Seismic Events Affecting One or Both Units) .................................................. G-7

Table G-8 CDF for SBO and Failures of TDAFW Pumps due to Potential Overfill 

(Control Room Fire Events Affecting One or Both Units).................................. G-8

Table G-9 CDF for SBO and Failures of TDAFW Pumps after Battery Depletion 

(Control Room Fire Events Affecting One or Both Units).................................. G-8

Table H-1 Probability that a Large Wear Flaw in the Last Cycle Has the Specific

Length and Depth Ranges ............................................................................... H-2

Table H-2 Probability of C-SGTR Occurring before HL Failure for Different Sizes of 

Flaws in Inconel 600 in Zion Wnewbase Case ................................................. H-3

Table H-3 Probability of C-SGTR Occurring before HL Failure for Different Sizes of 

Flaws in Inconel 690 in Zion Wnewbase Case ................................................. H-3

Table H-4 Probability of Single and Multitube Failure in C-SGTR for Inconel 600/690...... H-4

Table L-1 Process Summary for Event Trees and CDF Sequences..................................L-4

Table L-2 Summary of C-SGTR Modeling Applied to a Specific PRA Model for a 

4-Loop Westinghouse Plant ..............................................................................L-7
xxiii

EXECUTIVE SUMMARY 

Over the last two decades, the U.S. Nuclear Regulatory Commission (NRC) and the nuclear 

industry have investigated the safety implications and risk associated with consequential steam 

generator tube rupture (C-SGTR) events (i.e., events in which steam generator (SG) tubes leak 

or fail as a consequence of high differential pressures or elevated temperatures during accident 

sequences). Various probabilistic risk assessments (PRAs) have shown accidents involving SG 

tube ruptures to be contributors to plant risk because of their potential for causing a release of 

fission products outside containment (containment bypass sequences).

The analysis methods, tools, and expertise previously developed as a part of the NRC Steam 

Generator Action Plan (SGAP) were sufficient to resolve the associated technical issues.

However, certain limitations restrict its usefulness in supporting future risk assessments.

Consequently, the agency identified several areas for additional research and updates. After 

closure of the SGAP in 2009, and building upon the research conducted to resolve the SGAP, 

the NRC chartered this study to address the development of a simplified method for assessing 

the risk associated with consequential tube rupture or leakage in design-basis-accident (DBA) 

and severe-accident events. This report integrates work done by three disciplines in the NRC 

Office of Nuclear Regulatory Research—thermal-hydraulic (TH) and computational fluid 

dynamics analysis, materials, and PRA. The study used updated SG flaw distributions 

representing the current population of SGs, along with the new TH results from the MELCOR 

TH code, for an example Combustion Engineering (CE) plant.

This report documents a method for a quantitative risk assessment of C-SGTR during a severe 

accident (i.e., after the onset of core damage) and during a DBA event (before the onset of core 

damage). The focus of this study is the estimation of the large early release frequency (LERF) 

because of C-SGTR and containment bypass. Specifically, the study estimated the probability of 

containment bypass because of C-SGTR and assessed the fraction of containment bypass that 

constitutes LERF. It developed simplified LERF calculation methods and applied them to two 

pressurized-water reactor plants: a Westinghouse (W) and a CE design. In addition, it used the 

generic stylized models to address C-SGTR related to DBA issues. The scope of this report 

does not include the development of Level 1 PRA modeling, although the study used full Level 1 

PRAs for internal and external events to obtain the frequency of the sequences related to the CSGTR. The method is illustrated with applications to plants containing replacement SGs with 

thermally treated Inconel Alloy 600 and Alloy 690 SG tubes.

A key consideration for C-SGTR sequences is the relative timing between the failure of SG 

tubes and the failure of other locations within the reactor coolant system (RCS). If a thermally 

induced failure sufficient to depressurize the primary coolant develops in another RCS location 

either before or shortly after SG tube failure, fission product release through failed SG tubes 

may be prevented or minimized. In that case, the RCS leakage will preferentially go into the 

containment, thus significantly reducing or altogether eliminating potential leakages from the 

RCS into the secondary side of the SG. To properly account for this relative timing, this analysis 

used the latest available TH analyses for both W and CE plant types, updated flaw statistics 

pertinent to current reactors, and the latest available models and software for estimating the 

failure probability and failure timing of SG tubes and other RCS components (i.e., hot leg (HL) 

and surge line). A software “calculator” was developed in conjunction with this study to simulate 

multiple flaws in SG tubes and to calculate C-SGTR tube leakage probabilities. Inputs for the 

calculator include TH parameters of an accident sequence, SG tube flaw distribution, and 

material properties. This software permits not only numerous “what-if” runs with a minimal effort, 
xxiv

to better understand the progression of an accident, but also pressure and temperature 

challenges to the tubes.

Several key assumptions were made to support this study:

• The SGs were assumed to have flaw distributions consistent with operating experience

obtained in the 2010 time frame. The flaw distributions were based on a statistical

analysis of a sample of SG tube inspection results obtained for replacement SGs with an

average operating history of 15 years in service.

• Existing models for the high-temperature behavior of RCS components and SG tubes

were used to estimate the potential for a C-SGTR event. Chapter 8 discusses the

limitations associated with these models.

• An SG “rupture” was defined as a total SG tube leak area equivalent to a guillotine break

of one or more tubes.

• A small secondary leak (equivalent to a flow area of 0.5 square inch) is assumed for all

accident sequences involving high pressure under primary coolant side and dry SG

conditions. This leakage area results in SG depressurization for all dry SG

conditions studied.

• A simplified model for HL failure was used for the probabilistic risk analysis portion of the

study. However, detailed structural analyses determined that the simplified model

consistently predicted later times to HL failure than more detailed modeling, without

introducing excessive conservatism. This detailed modeling also indicated that the upper

portion of the HL will fail earlier than other RCS regions.

• Mixing coefficients in the SG inlet plenum used in the MELCOR TH analysis were

determined based on a detailed computational fluid dynamics analysis, which has been

benchmarked using 1/7th scale test data.

The main conclusion from this work is that the SG geometry and the fluid flow rates in different 

SG designs can significantly influence the potential likelihood of C-SGTRs. For the cases 

studied, SG designs with a shallow inlet plenum (resulting in the tubesheet located closer to the 

HL inlet) and a shorter HL can result in a greater likelihood of a C-SGTR after a core damage 

event associated with high-dry-low conditions. A shallow inlet plenum design reduces the mixing 

of the hot gases entering the SG, thereby creating a higher thermal load on the tubes.

Therefore, for the specific replacement SG geometries analyzed in this study, the CE plant 

design had an increased likelihood of a C-SGTR, and thus a greater potential for a large early 

release, than the W plant design.

Moreover, the study has concluded that clearing the RCS cold leg loop seal, which changes the 

natural circulation flow path within the SG inlet plenum and subjects the SG tubes to hotter gas 

flow, could cause SG tube failure and be a contributor to C-SGTR for W plants. For CE plants, 

significant SG tube failures are expected even if the loop seal is not cleared.

The PRA method developed and illustrated in this report, although applied to specific plants and 

cases, may offer general insights and a process to obtain quantitative measures (e.g., the 

fraction of C-SGTR given a severe accident) that could be used to support risk-informed 

regulatory decisionmaking. For example, this work may benefit significance determination 

process reviews of findings related to SGs, inform NRC reviews for new reactors, or support 

license renewal reviews for issues related to SG material management. 
xxv

ACKNOWLEDGMENTS

In addition to the authors listed on the cover page of this document, many others from the 

U.S. Nuclear Regulatory Commission (NRC) and outside the NRC contributed to the analyses 

or documentation of the work. Former NRC employee Charles Harris contributed to Chapter 6 of 

this report, for the estimation of steam generator tube flaw distributions and related subjects 

discussed in that chapter. Kevin Coyne’s multiple rigorous reviews of this report, his persistence 

in moving the deliverables forward, and his technical understanding of the overall report also 

deserve to be mentioned.

In addition, the authors would like to acknowledge the following individuals (listed alphabetically 

by last name):

From the NRC:

Michelle Gonzalez

Ken Karwoski

Emmett Murphy

Antonios Zoulis

From Information Systems Laboratories and their contractors:

Robert Beaton (currently at the NRC)

Terry Gitnick

Maria Morell Gonzales

Qiming He

Andrew Mlynarczyk

Marcos Ortiz

Many other NRC staff members from different NRC offices contributed to this effort by reviews 

and meeting support.

 

xxvii

ABBREVIATIONS 

ac alternating current

ACRS Advisory Committee on Reactor Safeguards

ADAMS Agencywide Documents Access and Management System

AFW auxiliary feedwater

ANL Argonne National Laboratory

ARTIST Aerosol Trapping in Steam Generator

ATWS anticipated transient(s) without scram

CCDP conditional core damage probability

CCF common-cause failure

CCW component cooling water

CD core damage

CDF core damage frequency

CE Combustion Engineering

CFD computational fluid dynamics

COA crack-opening angle

COD crack-opening displacement

CSGTR (C-SGTR) consequential steam generator tube rupture

CST condensate storage tank

CVCS chemical volume control system

DBA design-basis accident

dc direct current

DEGB double-ended guillotine break

EAL emergency action level

EB emergency boration

ECCS emergency core cooling system

EDG emergency diesel generator

EDM electrostatic discharge machine

EDMG extensive damage mitigation guideline

EFPY effective full power year

EOP emergency operating procedure

EPRI Electric Power Research Institute

EQ equalization

FB feed and bleed

FE, FEM finite element model

FEA front-end analysis
xxviii 

FP fission product

HDL (H/D/L) high primary pressure, dry steam generator, and low secondary pressure

HL hot leg

HPI high-pressure injection

HPR high-pressure recirculation

HRA human reliability analysis

HTC heat transfer coefficient

ID inside diameter

IE initiating event

INEL Idaho National Engineering Laboratory

IPE individual plant evaluation

IPEEE individual plant evaluation for external events

ISI inservice inspection

L-SSB large secondary side break

LERF large early release frequency

LOCA loss-of-coolant accident

LOOP loss of offsite power

ltsbo long-term SBO (turbine-driven pump fails after battery depletion)

MA mill annealed

MDAFW motor-driven auxiliary feedwater (pump)

MFW main feedwater

MSIV main steam isolation valve

MSLB main steamline break

MSSV main steam safety valve

MTC moderator temperature coefficient (reactivity feedback)

NPP nuclear power plant

NRC U.S. Nuclear Regulatory Commission

OD outside diameter 

ODSCC outside-diameter stress-corrosion cracking

OTSG once-through steam generator

PDS plant damage state

POD probability of detection

PORV power-operated relief valve

PRA probabilistic risk assessment
xxix

PSA probabilistic safety assessment

PSF performance-shaping factor

PTW part-through-wall

PWR pressurized-water reactor

PWSCC primary water stress-corrosion cracking

PZR pressurizer

RCP reactor coolant pump

RCS reactor coolant system

RES Office of Nuclear Regulatory Research

RF release fraction

RHR residual heat removal

RPS reactor protection system

RPV reactor pressure vessel

RS recirculation spray

RTD resistance temperature detector

RV reactor vessel

RWST reactor water storage tank

RY reactor year

SAE site area emergency

SAMG severe-accident management guideline

SBO station blackout

SCF suppress creep failure

SG steam generator

SGAP Steam Generator Action Plan

SGT steam generator tube

SGTR steam generator tube rupture

SGTR-INIT steam generator tube rupture initiator

SHR secondary heat removal

SL surge line

SLB steamline break

SLBIC steamline break inside containment

SNL Sandia National Laboratories

SPAR standardized plant analysis risk

SRV safety relief valve

SSB secondary side break

stsbo short-term SBO (AFW pump fails early in SBO)

SW service water

TDAFW turbine-driven auxiliary feedwater (pump)

TH (T&H) thermal-hydraulic
xxx 

TT600 (600TT) thermally treated Inconel 600

TT690 (690TT) thermally treated Inconel 690

TYPE-I (C-SGTR) temperature-induced (by creep rupture) C-SGTR

TYPE-II (C-SGTR) pressure-induced C-SGTR

UET unfavorable exposure time

Vdc volts direct current

W Westinghouse

ZNPP Zion Nuclear Power Plant
1-1

1 INTRODUCTION 

1.1 Background 

The U.S. Nuclear Regulatory Commission (NRC) and the nuclear industry have expended 

considerable resources over the last two decades to better understand the safety implications 

and risk associated with consequential steam generator tube rupture (C-SGTR) events 

(i.e., events in which steam generator (SG) tubes leak or fail as a consequence of the high 

differential pressures or elevated temperatures during accident sequences. Various probabilistic 

risk assessments (PRAs) have shown accidents involving SG tube ruptures to be contributors to 

plant risk, mainly because of their potential for causing a release outside containment 

(containment bypass sequences).

The analysis methods, tools, and expertise previously developed as a part of the NRC Steam 

Generator Action Plan (SGAP) were sufficient to resolve the associated technical issues.

However, certain limitations restrict its usefulness in supporting future risk assessments.

Several areas were identified for additional research and updates. Building upon the research 

conducted to resolve the SGAP, the NRC chartered this study to address the development of “a 

simplified method for assessing the risk associated with consequential tube rupture/leakage in 

design-basis accident (DBA) and severe accident events.” The study used updated SG flaw 

distributions representing the current population of SGs, along with the new thermal-hydraulic 

(TH) results from the MELCOR TH code for Combustion Engineering (CE) plants.

The study applied to two sample pressurized-water reactor plants: a Westinghouse (W) and a 

CE design. The scope of this study is limited to estimating the probability of containment bypass 

because of C-SGTR and assessing the fraction of containment bypass that constitutes large 

early release frequency (LERF). It is assumed that a Level 1 PRA is available for both internal 

and external events such that the frequency of the sequences related to the C-SGTR evaluation 

can be easily obtained. The method defines the characteristics of the sequences of interest and 

demonstrates how they can be obtained from the existing PRAs or standardized plant analysis 

risk models for the two example plants. The scope also includes an assessment of the 

probability that tube failures (rupture and leaks) can occur before failure of other reactor coolant 

system (RCS) components. This is shown for two sets of sequences: severe accidents and 

DBAs. Severe accidents involve all sequences of core damage, where after the onset of core 

damage, the primary pressure is high (generally at the set point of the primary relief valves), and 

at least one SGs is dry (no secondary heat removal) with its secondary side depressurized 

(i.e., near atmospheric pressure). These severe accident sequences are referred to as HDL (or 

H/D/L), which stands for high primary pressure and dry steam generator(s) with low secondary 

side pressure. DBAs involve initiating conditions, where the pressure across the tubes is 

significantly higher than nominal pressure during operation. These sequences include:

steamline break, feedwater line break, stuck open SG safety valve or atmospheric dump valve, 

and anticipated transients without scram.

It is expected that the method described in this report can be applied to a range of PRA 

applications. The insights from this study can be used to better inform simplified risk approaches 

by relying on a set of probabilities to screen and categorize emergent issues, such as those 

identified through inspection findings or operational events. The more detailed methods used in 

this study could support a more comprehensive risk assessment suitable to support 

risk-informed decisions and the rulemaking process.
1-2

This work has significantly leveraged other ongoing or recently completed NRC activities 

associated with material characterization and behavior and severe accident analysis. 

For example, this project relied on updated flaw distributions for reassessment of the conditional 

probabilities of C-SGTR. The study analyzed flaw data from SG inservice inspections to 

characterize the flaw parameters and update flaw statistics. It also used TH runs for the 

example W plant generated by the RELAP code and documented in NUREG/CR-6995, 

“SCDAP/RELAP5 Thermal-Hydraulic Evaluations of the Potential for Containment Bypass 

during Extended Station Blackout Severe Accident Sequences in a Westinghouse Four-Loop 

PWR,” issued March 2010 (Ref. 1). New calculations using the MELCOR severe accident code 

were run for selected sequences for an example CE plant. This information was used as input to 

C-SGTR software to arrive at the probability of SG tube failure, before failure of the other RCS

components. Uncertainties were treated to the extent possible throughout this evaluation.

Although this study used the existing Electric Power Research Institute (EPRI) correlations for

failure of the hot leg (HL) and surge line (SL), these correlations can be readily updated within

the existing C-SGTR software calculator should the improved models become available.

This study represents an important update of the probability values used in prior analyses, 

which were based on the flaw data from earlier generations of SGs with older TH results, and 

for W plants only. It compared the updated conditional probability values with values from 

previous studies and found key areas of disagreement to be attributed to the updated 

methodology and data.

Past risk studies have commonly considered SGTRs as an initiating event and, in some cases, 

as the consequential SGTR, such as thermally induced C-SGTR. An example of the latter 

analyses can be found in NUREG-1570, “Risk Assessment of Severe Accident-Induced Steam 

Generator Tube Rupture,” issued March 1998 (Ref. 2); by EPRI in Technical Report 1006593, 

“Steam Generator Tube Integrity Risk Assessment,” issued 2002 (Ref. 3); and by the 

Westinghouse Owners Group at a PSA’05 conference, September 11–15, 2005 (Ref. 4). SGTR 

as an initiating event is a design-basis event for which plants are designed to cope without 

progressing to a severe accident. Plants have coped with all SGTRs to date. A C-SGTR differs 

from this sequence in that the severe accident causes the tube rupture.

NUREG/CR-6995 (Ref. 1) and NUREG-1570 (Ref. 2) extensively studied C-SGTR TH behavior 

for W plants. SCDAP/RELAP performed some work on CE plants but, having predated the final 

W analysis, it did not incorporate all the modeling improvements made for them. EPRI 

considered CE plants in its 2002 steam-generator-tube-related risk analysis (Ref. 3).

Because of the capability to predict fission product (FP) releases in addition to TH behavior, the 

decision was made to switch to the MELCOR code to perform the CE C-SGTR analysis.

Lessons learned during the previous W analyses were applied to the CE analysis during the 

work described in this report. Chapter 3 discusses this topic further.

1.2 Objectives 

The objective of this report is to document a simplified method for a quantitative assessment of 

the probability of C-SGTR and LERF associated with C-SGTR during a severe accident after 

the onset of core damage and during a DBA event before the onset of core damage. Estimating 

the probabilities of large early releases and containment bypass is the main focus for severe 

accidents. The report addresses screening probabilities for both core damage and containment 

bypass for DBA events.
1-3

The study used the latest available TH for both W and CE plant designs and the updated flaw 

statistics pertinent to current reactors. It also used software tools containing the latest available 

model for estimating the failure probability and timings of SG tubes and other RCS components 

(i.e., HL and SL). The results from these calculations were distilled into tables that showed the 

failure probabilities for SG tubes and RCS components. For PRA analysis, the bounding values 

for the probabilities of equipment failures and human errors were tabulated using of a spectrum 

of representative accident conditions. These tables could be used in lieu of conducting a 

detailed plant-specific analysis for performing a simplified C-SGTR LERF evaluation.

Although the methods developed here were intended to address the study objectives (i.e., the 

screening method), they are meant to establish the framework to perform a more 

comprehensive PRA that can address the C-SGTR at a level of detail suitable for other needs.

Extension of these methods can support the risk-informed decision process and also be used to 

update the PRA Standards and PRA Procedure Guide.

1.3 Scope 

The scope of this study is limited to estimating the probability of containment bypass because of 

C-SGTR and an assessment of the fraction of containment bypass that constitutes LERF. It is 

assumed that a Level 1 PRA is available for both internal and external events such that the 

frequency of the sequences related to the C-SGTR evaluation can be easily obtained. The 

method defines the characteristics of the sequences of interest and demonstrates how they can 

be obtained from the existing PRAs or standardized plant analysis risk models for the two 

selected plants. The scope also includes an assessment of the probability that tube failures 

(rupture and leaks) can occur before failure of other RCS components. This is shown for two 

sets of sequences: severe accidents and DBAs. Severe accidents involve all sequences of core 

damage, where the SGs are dry (no secondary heat removal), and the primary pressure is high 

(generally at the set point of the primary relief valves). DBAs involve initiating conditions, where 

the pressure across the tubes is significantly higher than nominal pressure during operation.

These sequences include: steamline break, feedwater line break, stuck open SG safety valve or 

atmospheric dump valve, and anticipated transients without scram.

1.4 Summary of Differences from Previously Published Work 

The study used the latest available THs for both plants, updated flaw statistics pertinent to 

current reactors, and the latest available models and software for estimating the failure 

probability and timings of other SG tubes and RCS components (i.e., HL and SL). A C-SGTR 

software “calculator” was developed in conjunction with this study to simulate multiple flaws in 

SG tubes and to calculate tube leakage probabilities. Inputs for the calculator include TH 

parameters of an accident sequence, tube flaws, and material properties. This software allows 

not only numerous “what-if” runs with minimal effort, to better understand the progression of an 

accident, but also pressure and temperature challenges to the tubes. Appendix B describes 

this software.

The other improvements for this study, as compared to previous studies, are the following:

• detailed computational fluid dynamics analysis and MELCOR severe accident modeling 

for the example CE plant design

• detailed finite element analysis for the RCS HL nozzle to confirm the timing of 

structural failure
1-4

• consideration of more typical replacement SG tube materials, such as thermally treated

Alloy 600 and Alloy 690

• comprehensive integration of analyses from different fields, which include TH analyses,

study of behavior of “other” RCS components, calculator software that allows study and

documentation of many sequences; limited extension into FP release analysis using

MELCOR; and, separately, estimation of LERF

• insights obtained about failure behavior of flaws by making a multitude of runs with

the calculator

1.5 Summary of Research Approach and Organization of Report 

The work described in this report uses a PRA approach. However, it includes other work from 

TH analyses using MELCOR (Chapter 3 of this report) and failure of assessment of “other RCS 

components” using ABAQUS (Chapter 4). Chapter 5 offers a detailed description and technical 

bases for predicting the severe accident behavior of SG tubes. In addition, it generates tube 

flaw distributions for tubes with Alloy 600 and Alloy 690 materials (Chapter 6); the PRA used 

these distributions.

The PRA sections of this report consist of Chapters 2, 7, and 8. Figure 1-1 outlines the report 

structure and the flow of information among the work generated by the three different fields; 

namely, PRA, TH analyses, and materials analyses.

The new TH analyses for the reference CE plant used the MELCOR software. The MELCOR 

output can be viewed as consisting of two sets of outputs:

• TH profiles (e.g., temperature and pressure as a function of time) in the SG tubes and

SG inlet regions (HL and SL) for severe accidents

• fission product release results

The TH results from these analyses (item 1 above) are used in the PRA as input. Further 

conclusions drawn by the MELCOR analyses for FP release, based on a set of modeling 

assumptions, are independently generated and are not used by the PRA, which defines and 

estimates C-SGTR and LERF frequencies, independent of the other types of analyses.

Similarly, PRA used the existing EPRI correlations to estimate failure times for HL and SL, 

compared to the failure times of the SG tubes. The extra analyses in Chapter 4 by ABAQUS are 

used for confirmatory purposes.

Chapter 8 summarizes the PRA conclusions. Chapter 9 presents the other overall conclusions 

for the materials TH and PRA work.
1-5

Figure 1-1 Work and report layout 

 

1.6 References 

1. U.S. Nuclear Regulatory Commission, “SCDAP/RELAP5 Thermal-Hydraulic Evaluations 

of the Potential for Containment Bypass during Extended Station Blackout Severe 

Accident Sequences in a Westinghouse Four-Loop PWR,” NUREG/CR-6995, 

March 2010, Agencywide Documents Access and Management System (ADAMS) 

Accession No. ML101130544.

2. U.S. Nuclear Regulatory Commission, “Risk Assessment of Severe Accident-Induced 

Steam Generator Tube Rupture,” NUREG-1570, March 1998, ADAMS Accession 

No. ML070570094. 

3. Electric Power Research Institute, “Steam Generator Tube Integrity Risk Assessment: 

Volume 1: General Methodology, Revision 1,” Technical Report 1006593, Palo Alto, 

CA, 2002.

4. Westinghouse Owners Group Simplified Level 2 Modeling Guidelines: Justin Robert 

Armstrong and Raymond E. Schneider—Westinghouse Electric Company, 

Westinghouse Owners Group, PSA’05, September 11–15, 2005, San Francisco, CA.

2-1

2 SEQUENCE DEFINITIONS 

This chapter discusses accident sequences that are of interest for consequential steam 

generator tube rupture (C-SGTR) analysis and that identify limiting (most challenging) 

sequences for steam generator (SG) types typically used in Westinghouse (W) and Combustion 

Engineering (CE) plants. The chapter initially describes accident sequence selection for 

pressure-induced failures of the SG tubes, which are caused by high differential pressure 

across the SG tubes but do not involve significant thermally induced creep growth of flaws. 

Next, the chapter describes accident sequences for thermally induced SG tube failures. The 

focus here is on severe accidents associated with high reactor coolant system (RCS) pressure 

and dry secondary-side conditions of one or more SGs. The sequences identified are expected 

to be typical of a pressurized-water reactor (PWR) probabilistic risk assessment (PRA). The 

remaining sections define the “critical” leak size for defining an SG fault as C-SGTR and provide 

a model for large early release frequency (LERF).

2.1 Pressure-Induced C-SGTR Sequences of Interest 

Table 2-1 lists the sequences of interest for pressure-induced SG tube failures, alternatively 

known as design-basis accident (DBA) events. These sequences could establish a delta 

pressure across the SG tube walls and, therefore, potentially challenge the integrity of the tubes 

because of pressure-induced failures. Several PRA sequences are combined and grouped, 

based on their thermal-hydraulic (TH) behavior, to yield a smaller set of candidate DBA 

sequences with similar challenges to the SG tubes. Plant-specific design features would 

determine if a sequence is applicable. For example, sequences involving a total loss of 

secondary cooling but successful feed and bleed (FB) operation are not applicable to plants that 

cannot FB (e.g., CE plants with no power-operated relief valves (PORVs)).

Generally, Level 1 PRA sequences can be grouped into one of these selected DBA sequences. 

The frequency of each of the DBA sequences can then be estimated by summing the individual 

frequencies of all the PRA sequences. PRAs compile the frequencies of the full accident 

sequences that result in core damage; however, they do not explicitly provide the frequencies of 

the partial accident sequences, which have not yet progressed to core damage (CD). The 

required information for estimating the frequencies of the partial sequences can be easily 

obtained from the Level 1 PRA for internal and external hazards.
2-2

Table 2-1 Selected DBA Sequences Causing Challenges to SG Tubes 

Delta P 

Across the 

Tubes

Conditions Causing Delta 

P Across the Tubes Accident Sequence

SG Secondary-Side 

Condition [Pressure, 

Water Inventory]

~ 6.9 mega

pascals (MPa) 

(1,000 pounds

per square 

inch (in.) (psi))

Normal power operation SGTR event Not known, will be 

determined by resulting 

CD sequences

~ 10.34 MPa 

(1,500 psi)

FB sequences with 

medium-head a emergency 

core cooling system 

(ECCS) pumps

All sequences involving 

loss of secondary heat 

removal but success 

of FB

Low pressure and dry SGs 

before rupture

Low pressure and dry SG 

condition is expected after 

CD 

~ 10.34 to 

11.75 MPa 

(1,500–

1,700 psi)

1. Unisolable main

steamline breaks

(MSLB)

2. Inadvertent opening of

SG relief valves or

turbine bypass valves

with failure to isolate

All sequences are 

expected to result in loss 

of secondary cooling 

followed by FB cooling.

Low pressure but not dry 

SGs before rupture

Low pressure and possibly 

dry SG condition after CD

~15.5 MPa

(2,250 psi)

FB with high-pressure 

ECCS pumps

All sequences involving 

loss of secondary heat 

removal but success of 

FB with stuck-open 

secondary relief valves

Low pressure and dry SGs 

before rupture

Low pressure and dry SG 

condition after CD

~15.2 MPa

(2,200 psi)

Anticipated transient 

without scram (ATWS) 

sequences when 

secondary cooling is not 

lost and pressure peak is 

limited to 22.06 MPa 

(3,200 psi) 

ATWS sequences with a 

favorable moderator 

temperature coefficient 

generally result in a 

pressure peak well below 

22.06 MPa (3,200 psi) in 

the primary. A bounding 

pressure of 22.06 MPa 

(3,200 psi) is considered 

for estimating the delta 

pressure across the 

SG tube.b

High pressure but not dry; 

however, failure of SG 

tube will induce CD.

All such CD sequences 

during ATWS are treated 

as LERF.

22.06 MPa 

(~3,200 psi)

ATWS sequences when 

secondary cooling is lost 

and pressure peak is 

limited to <22.06 MPa 

(<3,200 psi)

ATWS sequences with a 

favorable moderator 

temperature coefficient 

can result in a pressure 

peak as high as 

22.06 MPa (3,200 psi) in 

the primary.

High pressure and dry; 

however, failure of SG 

tube will induce CD. All 

such CD sequences 

during ATWS are treated 

as LERF.

a The ECCS pumps used in U.S. PWRs can have a shutoff head as low as 8.27 MPa (1,200 psi) and as high as 

18.27 MPa (2,650 psi). b UET (unfavorable exposure time) is defined as the time during the cycle when the reactivity feedback is not 

sufficient to prevent RCS pressure from exceeding 22.06 MPa (3,200 psi). Many factors, such as initial power 

level, time in cycle when transient occurs, reactivity feedback as a function of the cycle life, the number of 

available primary relief/safety valves, the failure or success of control rod insertion, and auxiliary feedwater 

(AFW) flow rates, affect UET. The noted pressure below 22.06 MPa (3,200 psi) is used as the bounding primary 

pressure value for cases when the moderator temperature coefficient is favorable.
2-3

2.1.1 Core Damage Bridge Event Tree 

As discussed in Section 2.1, Table 2-1 characterized DBA events of interest and the types of 

challenges to the SG tubes. The C-SGTR is characterized by its occurrence probability and the 

size of its leak area. The study estimated the occurrence probability of C-SGTR using the 

C-SGTR calculator (see Appendix B) and the latest flaw data, as discussed in Chapter 6. The 

leak area sizes could be divided into two or more bins (e.g., Small, Medium, and Large) to help 

in the estimation of time-sensitive human error probability values. A bridge tree was also 

developed to depict further progression of the accidents from the occurrence of C-SGTR 

through the onset of core damage. A general assumption used in developing this bridge tree is 

that the core damage has resulted from the C-SGTR, and it is not the result of the original 

initiator. It is assumed that the impact of the original initiator (e.g., MSLB or ATWS) would have 

been mitigated if C-SGTR had not occurred. For example, it is assumed that a proper response 

would be provided to an MSLB initiator, and the reactor would reach a safe, stable condition if 

C-SGTR had not occurred. The occurrence of C-SGTR, therefore, results in a transfer of the 

sequence of interest (entry level sequence) to a bridge tree that would be similar to that of an 

SGTR initiator (SGTR-INIT) tree in Level 1 PRAs. However, the boundary conditions imposed 

by the entry level sequence should be preserved by setting proper conditions on the branches 

of the SGTR-INIT event tree. Plant-specific standardized plant analysis risk trees for SGTR-INIT 

can be used for this purpose. Figure 2-1 shows the generic CD bridge event tree. The 

plant-specific event tree can be used if available.

The following headings define the top branches for the event tree in Figure 2-1:

• SGTR-INIT: Induced SGTR from DBA events

• HPI: High-pressure injection (HPI) systems: both safety injection pumps and charging 

pumps, if applicable

• SHR: Secondary heat removal (SHR) system: main feedwater (MFW) or AFW

• FB: FB operation and the supporting relief path

• EQ: Operator actions for equalization, which involves control of primary pressure, and 

depressurization below the pressure set point for the secondary relief valves

• RWST-MU: Long-term makeup water to the reactor water storage tank (RWST)

• HPR: High-pressure recirculation (HPR) and the associated operator action

• RHR: Operator action to cool down to cold shutdown and align the residual heat removal 

(RHR) system

• RS: Recirculation spray (RS) cooling in those plants that do not use RHR heat 

exchangers as a part of HPR

The end state CD refers to core damage.

With the exception of the ATWS sequence, the effect of other entry sequences will be 

superimposed on this bridge tree. For example, for sequences involving FB using the 

high-pressure ECCS, the following conditions will be imposed:

• Top event FB is set to success.

• SHR and EQ are both set to failure.
2-4

• Depending on plant-specific design features, HPR may not be possible, since the

leakages are through the SGTR ending up to secondary side of the SG rather than in the

containment sump.

For ATWS sequences, the C-SGTR is conservatively assumed to result in CD and LERF. This 

is caused by the difficulty in controlling the boron concentration because of the loss of borated 

coolant through the ruptured tubes. 
2-5

Figure 2-1 Generic CD bridge event tree for DBA induced C-SGTR 
2-6

2.1.2 Level 2 Event Tree: LERF Determination 

A detailed Level 2 PRA was considered to be out of scope for this project. A detailed Level 2 

PRA model should address the following:

• The availability of primary and secondary components after the occurrence of CD

combined with C-SGTR determines the timing and magnitude of releases to the

environment. The status of primary (e.g., pressure) and secondary (e.g., flooded or not)

are needed to determine different release categories. The status of primary and

secondary relief valves (open or close) (i.e., their possible failure modes under the harsh

environment of severe accidents) are also needed to determine the release categories

associated with C-SGTR.

• Modeling of severe accident management requires an understanding of when these

strategies could be effective and how the human reliability methods can address human

errors in decisionmaking under limited knowledge and guidance.

• Close coordination among PRA modeling needs, the supporting TH, and severe

accident analyses is needed to address adequately the effectiveness of severe accident

management guideline (SAMG) activities and their effects on release categories.

• Identifying the time when the emergency actions levels (EALs) are triggered, especially

the time when a general emergency is activated in comparison to the time of release, is

considered necessary to define the evacuation effectiveness and differentiate between

early and late releases.

Instead, a simplified Level 2 model was considered for this study and for the purpose of 

addressing LERF. The approach heavily relies on two commonly used definitions of LERF:

(1) American Society of Mechanical Engineers PRA Standard (Ref. 1) defines LERF as

“The rapid, unmitigated release of airborne fission products from the containment to the

environment occurring before the effective implementation of offsite emergency

response and protective actions.”

(2) Pursuant to Regulatory Guide 1.174, “An Approach for Using Probabilistic Risk

Assessment in Risk-Informed Decisions on Plant-Specific Changes to the Licensing

Basis” (Ref. 2), NRC Manual Chapter 0609, Appendix H, Section 3.2 (Ref. 3) defines

LERF as “The frequency of those accidents leading to significant, unmitigated releases

from containment in a time frame prior to effective evacuation of the close-in population

such that there is a potential for early health effect.”

Any large unisolable leakage outside containment through C-SGTR is considered as a site 

emergency, because it will affect both the reactor coolant and the containment barrier. A 

general emergency will ensue when potential fuel barrier degradation occurs (at the onset of 

core uncovery). Therefore, in both cases, there would be a high potential for 

effective evacuation.

The likelihood of the occurrence of LERF sequences for pressure-induced C-SGTR during DBA 

sequences is relatively low. The dominant contributor to the risk is the failure to equalize and 

isolate the faulted SG, followed by the failure to provide makeup water to the RWST. The CD 

resulting from such sequences typically occurs late enough that evacuation can be credited and 

LERF be eliminated. Early CD and potential LERF sequences require additional failures, such 

as failure of the HPI and dry SGs. SGs are generally not expected to be dry unless the 
2-7

sequence involves failure of both MFW and AFW systems. In such cases, there are two major 

SAMG actions typically credited for controlling the release and possibly mitigating the accident 

long before vessel breach. These SAMG actions are as follows:

• to arrest the core melt within the vessel by depressurizing and injecting water into the 

primary system before any significant fuel melting, core geometry change, or melt 

relocation has taken place

• to reduce the in-vessel release magnitude by flooding the vessel and scrubbing 

the releases

• to reduce releases to the environment via ruptured SG tubes by depressurizing the SG 

and filling it up with an alternate source of water

The vessel can be depressurized by opening all PORVs, thereby allowing coolant injection from 

the low-pressure ECCS. RCS depressurization could also take place because of a medium or a 

large LOCA but not generally from a small LOCA. Primary depressurization through secondary 

cool down using the intact SGs and the pressurizer spray could also be credited for the success 

of RCS depressurization. However, to provide this credit, the analyst should identify the 

probability that one or more SGs remain intact (not isolated because of SGTR). Although there 

could be several possible means for the primary depressurization, all are driven by dependent 

operator actions.

Primary depressurization could result in the injection of accumulator water into the vessel, which 

if it occurs at or shortly after the onset of CD, could provide additional time for the operator to 

align makeup water to the RWST for continued injection into the vessel. Injection to the vessel, 

if performed early, before significant core melt and debris relocation, could arrest further melting 

of the core. Therefore, it may significantly limit the amount of in-vessel releases. RCS 

depressurization or the occurrence of a medium or large LOCA would also create a major path 

of release to the containment rather than through SGTR. Therefore, if any of these SAMG 

actions are successful, the release through SGTR is expected to be negligible.

In addition, severe accident analyses are required to examine the effectiveness of such 

strategies. As an example, early injection into the vessel, when the CD is just initiated and fuel 

geometry has not significantly changed, could prevent the accident progression to fuel melting. 

However, a delay in vessel injection, after the fuel is partially melted and a significant change in 

core geometry has occurred, may not be effective. Failure to inject from the accumulators would 

significantly reduce the time available for operators to align makeup water to the RWST. It is, 

therefore, assumed that makeup water to the RWST cannot be successfully performed without 

the injections from accumulators.

A simplified model was proposed for the current study. This model relies on five factors as 

defined below:

(1) frequency of DBA sequences with potential for C-SGTR fAC

(2) C-SGTR probability PCSGTR

(3) conditional CD probability PCCD

(4) failure probability of all SAMG actions PSAMG

(5) probability that early effective evacuation is not successful PEVAC

The product of these five factors defines LERF. Conservative estimates were assigned to the 

above factors for the purpose of the screening study. Chapter 7 contains further discussion.
2-8

2.2 Thermally Induced C-SGTR Sequences 

This section details the sequences of interest for the potential occurrence of C-SGTR after the 

onset of CD during severe accidents. These sequences generally involve high primary pressure 

with at least one or more dry SGs and low secondary pressure, known as high-dry-low 

sequences. One way to identify such sequences is to use the binning information generated for 

defining plant damage states (PDSs) from Level 2 PRAs. Those PDSs that are binned into a 

class with a high primary pressure and with at least one or more dry SGs (i.e., loss of both MFW 

and AFW are required) are candidates for severe accidents with a potential for C-SGTR. Some 

Level 2 PRAs, however, identify the status of SG (i.e., dry or flooded SG) only for an SGTR-INIT 

and not for other sequences. Therefore, the determination of the frequencies for the pertinent 

sequences for thermally induced C-SGTR would require an additional examination of the 

sequences in Level 1 PRA models. It is strongly suggested that the status of SGs be defined for 

all sequences as part of the PDS identification in Level 2 PRAs to facilitate their use for 

C-SGTR evaluation.

Level 1 PRA sequences are to be examined for the sequences that include failure of feedwater 

(both main and auxiliary) to one or more SGs and where the primary pressure is expected to be 

high at the time of CD. Sequences involving large, medium, or interfacing system LOCAs could 

be considered as low primary pressure. Other sequences with low primary pressure could result 

from stuck-open PORVs or SRVs. Depending on the size of the primary PORVs and SRVs, lowpressure sequences may require the flow through more than one stuck-open valve. A 

depressurized primary system before CD caused by aggressive secondary cooling may not be 

considered as a low-pressure sequence, because the pressure is expected to become high at 

the onset of CD if secondary cooling is lost. For some sequences, SG cooling may not play a 

role in a CD scenario (such as a small LOCA with failure to inject). A small fraction of the 

sequence frequency accounting for AFW failure shall then be considered for 

C-SGTR evaluation.

A selected number of sequences are generically identified to allow a thermally induced C-SGTR 

screening analysis. This is done to avoid the complexity of identifying the C-SGTR sequences 

using the above process and for plants without proper Level 2 PRA models. These sequences

are identified for the purpose of defining representative TH analyses and determining the time of 

CD and other information important to C-SGTR. Table 2-2 below shows these sequences. They 

are selected based on the expected TH behavior and the type of challenges they will have on 

SG tubes. They are not the same as PRA CD sequences. Several PRA CD sequences from 

internal and external hazards with similar TH behavior are combined and grouped together 

under each of these selected sequences. There are five base case sequences, noted as Base 

Cases 1 through 5. Each base case sequence could be slightly changed to obtain some 

alternative sequences. The time of the onset of CD from the occurrence of an initiator is 

specified as early or late in the second column of the table. As will be discussed, “early” 

generally means less than 8 hours, and “late” generally means greater than 8 hours. The exact 

timing for “early” and “late” depends on the time when a general emergency is activated. The 

period of interest is generally between the activation of a general emergency and the onset of 

CD. It is not associated with the time that the plant initiator occurred.

The extended station blackout (SBO) sequences are the most representative sequences that 

can cover all the sequences identified in Table 2-2. Some insights for PRA modeling of 

thermally induced C-SGTR, based on TH results for SBO scenarios of a selected W and a CE 

plant, are in Sections 2.3 and 2.4, respectively. These analyses did not credit mitigation 

capabilities provided by FLEX and Extensive Damage Mitigating Guidelines (B.5.b) backup 
2-9

systems, and post-CD SAMG strategies. The current insights discussed in Sections 2.3 and 2.4 

are, therefore, somewhat conservative. Sections 2.5 and 2.6 discuss the critical size for

C-SGTR to be considered LERF and the proposed LERF model, respectively.
2-10

Table 2-2 Selected Sequences to Evaluate C-SGTR for Severe Accident Sequences (Cont.) 

Core Damage 

Sequences

Time for the Onset of 

Core Damage 

Relative to the 

Activation of a 

General Emergency 

Availability of DC 

Power for 

Primary/Secondary 

Depressurization and 

Performing 

SAMG Activities

Notes

Base Case-1: SBO with 

failure of TDAFW at 

time zero, small RCP 

leakagea,b (e.g., 

0.001325 m3/s 

(21 gpm) for some W 

pumps), and equivalent 

0.0127 meters 

(0.5 inches) of leakage 

(relief path) from the 

SG secondary to the 

environment

Early Yes Base case probability 

of C-SGTR before HL 

failure

Alternate 1: Base 

Case-1 and 1 PORV or 

an SRV sticks open

Early Yes Lower probability of 

C-SGTR before HL

failure due to lower

primary pressure

Alternate 2: Base 

Case-1 except RCP 

seal leakage greater 

than 0.01136 m3/s 

(180 gpm) per pump

Early Yes Possibly higher 

probability of C-SGTR 

due to possible 

clearing of the loop 

seals 

Alternate 3: Base 

Case-1 except no 

leakage or smaller 

leakages than 0.0127 

meters (0.5 in.) from 

secondary side of SG 

to the environment

Early Yes Lower probability of 

C-SGTR than nominal

since the secondary

pressure is maintained

and the delta pressure

across the tubes is

reduced

Alternative 4: Base 

Case-1 except larger 

leak area through the 

secondary of SGs 

(e.g., as a result of a 

stuck-open SG PORV)

Early Yes Higher probability of 

C-SGTR assumed

since, after tube failure,

the larger area through

SG secondary would

depressurize the

primary, and therefore,

reduce the likelihood of

HL failure

Base Case-2: SBO with 

failure to load shed to 

extend battery life, 

rendering the failure of 

TDAFW to continue 

to run 

Early or Late:

Depending on battery 

duration, could be 

considered either late 

or early

No Similar C-SGTR 

probability to Base 

Case-1 
2-11

Table 2-2 Selected Sequences to Evaluate C-SGTR for Severe Accident Sequences (Cont.) 

Core Damage 

Sequences

Time for the Onset of 

Core Damage 

Relative to the 

Activation of a 

General Emergency 

Availability of DC 

Power for 

Primary/Secondary 

Depressurization and 

Performing 

SAMG Activities

Notes

Base Case-3: SBO with 

successful load shed to 

extend battery life. 

Failure of TDAFW to 

continue to run after 

battery depletion 

Late No Similar C-SGTR 

probability to Base 

Case-1

Base Case-4: 

Non-SBO sequences 

with total failure of 

secondary cooling at 

time zero and failure to 

do FB operation

Early Yes Similar to Base Case-1 

probability

Base Case-5: 

Non-SBO sequences c

with delayed failure of 

secondary cooling and 

FB operation (e.g., loss 

of service water, loss of 

chilled water due to 

external hazards]

Late Yes Varying probability of 

C-SGTR, depending on 

plant-specific features 

and the details of the 

sequences. These 

sequences could also 

cause RCP seal 

failures, with varying 

degrees of leakages.

a RCP leakage for base SBO analyses set at 0.001325 m3/s (21 gallons per minute) per pump. This is typical of a W 

plant without SHIELD®2. CE plants with Flowserve or similar seals and W plants with SHIELD® mechanical seals

or Flowserve pumps or CE plants have very low leakages following SBOs. b Seal LOCAs for CE plants could occur as a result of loss of cooling and failure of the operator to trip the pumps. 

Seal leakages of 1,703 liters per minute (Lpm) (450 gpm) per pump could result. c Appendix L contains details of a somewhat modified sequence in Base Case-5. These sequences consider that 

AFW flow is isolated to at least one SG, intentionally by the operator, since the associated secondary relief 

valve has stuck open. 

2.3 Representative Sequences for a Westinghouse Plant 

The TH analysis and the success criteria used for developing the PRA models for C-SGTR for 

an example W plant were gleaned from the information reported in NUREG/CR-6995, 

“SCDAP/RELAP5 Thermal-Hydraulic Evaluations of the Potential for Containment Bypass 

during Extended Station Blackout Severe Accident Sequences in a Westinghouse Four-Loop 

PWR,” issued March 2010 (Ref. 4). NUREG/CR-6995 documents the TH evaluations performed 

using the SCDAP/RELAP5 systems analysis code and a model representing a W four-loop 

PWR (i.e., the Zion Nuclear Power Plant. The plant model benefitted from the following:

• extensive iterative comparisons with evaluations of natural circulation flows and turbulent 

mixing using a computational fluid dynamics code

• comparison with experimental data for pertinent fluid-mixing behavior
2-12

NUREG/CR-6995 also included some sensitivity evaluations and uncertainty analyses of the 

SBO accident sequences.

The base sequences were modeled assuming a preexisting leakage through the secondary side 

of each SG, equivalent to a hole of 3.2 square cm (cm2

) (0.5 square in. (in.2)). As discussed in 

Appendix A to Sandia National Laboratories (SNL) JCN Y6486, “Severe Accident Initiated 

Steam Generator Tube Ruptures Leading to Containment Bypass-Integrated Risk Assessment,” 

issued February 2008 (Ref. 5), this size of leakage is sufficient to ensure that the pressures in 

the secondary side of the SGs approach the atmospheric pressure after SG dryout. However, 

the assumed leakage area was shown to be insufficient to maintain a low SG secondary-side 

pressure after the occurrence of a guillotine break of a single SG tube.

The following points taken from Reference 5 emphasize the expectation that, during a severe 

accident sequence, the secondary-side depressurization is likely to be present:

• The findings from the TH analyses indicate that secondary leak areas of 3.22 and

6.45 cm2 (0.5 and 1.0 in.2

) result in essentially full depressurization of the SG by

the time the severe accident-induced temperature ramp occurs.

• Leaks directly to atmosphere. Given closure of the main steam isolation valves

(MSIVs), feedwater isolation valves, and SG blowdown valves, such leaks would

need to be in the stems or seals of these valves; the stems or seals of other

valves or ports upstream of these valves; or the stems, seals, or seats of the

secondary-side PORVs or SRVs. Such leaks would be present during normal

operation. Another potential leakage source could occur if a secondary-side

PORV or SRV recloses but does not reclose completely (e.g., allows a small

amount of leakage).

• Leaks into the secondary piping. Perhaps more significant is the potential for

leakage past the isolation valves into the downstream piping in the secondary

system. The long, large runs of piping have a significant volume and so could

accept small leakage rates without themselves pressurizing to provide any

backpressure. The amount of leakage past the valve seats would be very small

relative to the total size of the valve. A 508-cm (20-in.) diameter MSIV would

have a total flow area of over 1,935 cm2 (300 in.2

). Therefore, an MSIV that is

99.9-percent closed will still not be sufficient to maintain secondary pressure. Not

being part of the containment isolation boundary, SG isolation valves are not

required to meet containment isolation leak rate requirements. The performance

requirements for these valves are based on maintaining pressure in the SGs

when full, and so they are not required (nor are they designed, qualified, or

tested) for this kind of leak tightness.

The main two sequences modeled were as follows:

(1) SBO with early failure of the TDAFW pump, resulting in CD and a potential for C-SGTR

because of creep rupture

(2) SBO with failure of TDAFW after battery depletion
2-13

Several sensitivity case studies were also performed. These studies generally addressed 

different issues, as summarized below:

• A study examined the effect of RCP seal leakage by considering various sizes of RCP 

seal leakages from 79.5 Lpm (21 gpm) per pump and up. The case runs evaluated the 

pressure and temperature impact on primary and secondary systems and examined the 

impact on loop seal clearing potential.

• A study examined the effect of early depressurization on the sequence progression by 

considering the operator’s action to depressurize SGs at 30 minutes, by opening at least 

one SG atmospheric dump valve or SG PORV per SG. This action drops the primary 

pressure below 4.83 MPa (700 psi). This actuates the accumulator discharge. Two 

cases were analyzed, depending on the rate of depressurization (slower and 

faster rates).

• A study examined the effect of C-SGTR with an equivalent guillotine break of one tube 

on primary depressurization, thereby preventing or delaying HL failure. This resulted in a 

slow depressurization of the primary; however, it is not fast enough to prevent HL failure.

Section 7.1 contains a detailed discussion of several other sensitivity case runs, along with their 

TH behavior, and their effect on PRA results for the example W plant.

2.4 Representative Sequences for a Combustion Engineering Plant 

The TH analyses used to support the development of the PRA models and success criteria 

were based on the NRC-sponsored MELCOR evaluation of Calvert Cliffs Nuclear Power Plant 

for several SBO scenarios. Information contained in the Calvert Cliffs individual plant evaluation 

and the individual plant evaluation for external events was also used to support the sequence 

identification and development of the C-SGTR PRA. Chapter 3 details the TH evaluations 

performed using the MELCOR severe accident analysis code for Calvert Cliffs. MELCOR 

analyses were performed in two stages. The initial analyses identified additional enhancements 

to be incorporated into the MELCOR models. All discussion in this document relies on the 

second stage (enhanced modeling) of MELCOR analyses. Some insights gained from the 

first-stage sensitivity analyses were used to shape some of the PRA arguments.

The following two representative base sequences used the latest MELCOR analyses. These 

two sequences modeled a leakage through the secondary side of each SG, equivalent to an 

area of a 3.22-cm2 (0.5-in.2

) hole. The size of this leakage was sufficient to ensure that the 

pressure in the secondary side of the SGs approached the atmospheric pressure after SGs 

were dried out. The size of the leakage, however, is not sufficient to maintain low 

secondary-side pressure if SG tubes have ruptured.

The results from the MELCOR runs were slightly different in format from the SCDAP/RELAP5 

results reported in NUREG/CR-6995. The study provides the MELCOR results for each plant 

loop separately (i.e., RCS loop A with the pressurizer and RCS loop B without the pressurizer). 

Furthermore, the MELCOR results represent two types of hot tubes: one exposed to the hottest 

gas temperature and the other exposed to an average hot-gas temperature. This additional 

information was used in the PRA for CE plants.

(1) This sequence considered an SBO with failure of the TDAFW pumps early in the 

sequence (i.e., at time zero), followed by an early CD with a potential for 

C-SGTR because of creep rupture. The sequence also considered an RCP seal 
2-14

leakage of 79.5 Lpm (21 gpm) per pump. The 79.5-Lpm (21-gpm) pump seal 

leakage is typical of a W plant without SHIELD®2. CE plants with Flowserve or

similar seals and W plants with SHIELD® mechanical seals or Flowserve pumps 

or CE plants have very low leakages following SBOs (generally less than 

1.262X10-4 m3

/s (2 gpm). The 79.5-Lpm (21-gpm) leakage per RCP is assumed 

for a CE plant just for consistency with the W evaluation. A sensitivity analysis 

was performed by assuming no RCP seal leakages in the MELCOR model. 

Section 3.6.6 discusses this. The result of this sensitivity analysis showed that 

the RCP seal leakage had some impact on early primary depressurization but no 

impact on long-term primary pressure and temperature response (i.e., after the 

onset of CD). Therefore, the C-SGTR probability is not expected to be affected 

by the 79.5-Lpm (21-gpm) seal leakage per each RCP. The base MELCOR 

results for this SBO scenario (i.e., short SBO) are considered to be 

representative of several PRA accident sequences with similar behavior (see 

earlier discussion in this section). A short SBO includes an SBO sequence with 

simultaneous failures of TDAFW pumps because of common-cause failure to 

start, or an SBO with an initial availability of TDAFW pumps followed by their 

failures because of SG overfill in about an hour.

(2) An SBO with delayed failures of TDAFW pumps after battery depletion is

considered for this sequence (i.e., long SBO). TDAFW is initially available, but it

will fail shortly after the depletion of the battery because of the loss of direct

current power. The MELCOR analysis assumes that the TDAFW pumps were

operating for a period of 4 hours. A normal RCP seal leakage of 79.5 Lpm

(21 gpm) per pump is assumed. Similarly, a sensitivity analysis of RCP seal

leakage showed that the impact on the C-SGTR probability is insignificant

because of the RCP seal leakage assumption.

Additional sensitivity analyses used the MELCOR evaluation by assuming that there was zero 

leakage through the secondary system at the start of SBO (instead of the generally assumed 

leakage area of 3.2 cm2 (0.5 in.2

)), such that the secondary relief and safety valves will be 

demanded early during the accident and before the onset of CD. The MELCOR evaluation for 

this case further assumes that the secondary relief and safety valves fail to reclose after the 

first opening.

MELCOR evaluations performed other sensitivity analyses to further examine the effect of 

various sequences. The following were noted:

• C-SGTR with an equivalent leakage area of the guillotine break of less than one tube will

not result in depressurization of the primary.

• An equivalent leakage area of one or more tubes could result in a significant release if

one or more of the SG safeties or the relief valves are left open or stick open.

• The primary is initially depressurized and the accumulator discharges when one or more

secondary relief valves stick open early in the accident. This will further delay HL/surge

line creep rupture failures. The probability of C-SGTR because of creep rupture,

however, is not affected as much because the lower secondary-side pressure increases

the delta pressure across the tube.

Section 7.2 contains a detailed discussion of these sensitivity case runs, along with their TH 

behavior and their effect on PRA results for the example CE plant.
2-15

2.5 Critical Leakage Area for C-SGTR 

The leakage area through the failed SG tubes determines the consequence and severity of the 

C-SGTR accident. It is generally assumed that there is a threshold, or a critical leakage area, 

beyond which the impact of larger leak areas on the accident severity will be negligible. This 

section discusses the considerations for determining these critical leakage areas.

The occurrence of pressure-induced C-SGTR during some accident sequences considered for 

the PRA (e.g., large secondary-side break, ATWS) would require the operator to perform 

additional actions. These actions are beyond those generally required for the original accident 

sequence, and they are in response to and to cope with a C-SGTR event. These actions are 

similar to those operator actions that are generally performed in response to an SGTR initiator. 

For such events, the size of the leakage determines how fast the operator should attempt to 

cool down and depressurize the primary to isolate the affected SGs. The most striking PRA 

effect of larger leakage areas through SG tubes during DBA events is a higher failure probability 

of the related operator actions.

For thermally induced C-SGTR during a severe accident (i.e., after CD), the size of the leakage 

area would determine the size of release through the containment bypass. It determines if the 

end state of a particular containment bypass sequence should be categorized as LERF. For a 

small leakage, the primary is expected to stay pressurized (generally at the primary relief set 

point, which is about 15.5 MPa (2,250 psi)), resulting in a failure of other RCS components 

(e.g., HL) shortly after the failure of the tubes. The failure of the RCS component, therefore, 

significantly reduces and eliminates any release through the SG tubes. These sequences of 

containment bypass because of C-SGTR may not be categorized as LERF.

Larger leakages could pressurize the secondary side of the affected SG such that both primary 

and secondary sides equalize at the pressure set point of the SG relief valves (which are about 

8.27 MPa (1,200 psi)). In this case, there is a lower failure probability of the other RCS 

components (e.g., HL) because of lower primary pressure. This pressure assumes that the SG 

PORVs and SRVs cycle as many times as needed without any failures. If any of the SG relief 

valves fail to close (stick open), the primary will be depressurized, and this eliminates any

possibility of failure of other RCS components. There could also be a threshold for larger 

leakage areas through the failed SG tubes such that the countercurrent flow through the HL 

cannot be maintained. In such cases, the hot steam will flow through the SG tubes, causing a 

number of tube failures resulting in a large containment bypass. The TH analyses for the 

example CE and W plants have shown that a guillotine break of at least one SG tube is required 

to pressurize the SG secondary side such that SG PORVs and SRVs are demanded.

Sections 2.5.1 and 2.5.2 contain detailed discussion of the critical leak areas for DBA and 

severe accident sequences.

2.5.1 Critical Leakage Areas for Design-Basis Accidents 

The key mitigating actions, in response to a DBA-induced SGTR (except ATWS sequences), 

are as follows:

• Establish a secondary heat sink.

• Isolate the affected SGs.

• Depressurize the RCS to avoid cycling the safety valves on the affected SG.
2-16

• Refill the RCS.

• Establish long-term cooling.

If the secondary heat sink is lost, FB cooling can be used. When FB cooling is used, long-term 

actions are needed for cold leg recirculation or for continued makeup to the RWST.

All pressure-induced SGTRs (i.e., burst) during ATWS sequences are conservatively assumed 

to result in CD and LERF.

The main effect of larger leakage areas from SG tubes during DBAs is the reduction in the 

amount of time that the operators have to cool down and depressurize the primary system. 

Because of reduced time, the probability of an operator error causing an SG overfill could 

significantly increase. This, in turn, could result in flooding the steam lines and possibly causing 

an SG safety or relief valve to fail to reclose. SG overfill would also cause the failure of the 

TDAFW because of water carryover. If one were to assume a tube rupture sequence exceeding 

several tubes failing, it would ensure a stuck-open safety valve. This would lead to a failure to 

isolate the affected SG with an increased likelihood of CD. Although the timing for the plant 

response is shortened for some actions as described above, the remaining time available for 

other key actions in the accident sequence (such as initiation of FB) may not be affected by the 

size of the C-SGTR leakage areas.

This scoping study considered the following guidelines for the critical leakage areas associated 

with C-SGTR during DBA sequences. 

• For ATWS sequences, tube failures are assumed to directly result in core damage and

LERF, regardless of the size of leakage (without further analysis).

• For all other sequences, a leakage area equivalent to a guillotine break of one tube is

assumed to have occurred. This size of break requires the operator to follow the

emergency operating procedure associated with SGTR initiators. For PRA purposes,

such C-SGTR events are transferred to the PRA SGTR event tree for estimating the

delta CD frequency and delta LERF.

2.5.2 Critical Leakage Areas for Severe Accidents 

Earlier studies (such as the SNL study documented in Reference 5) showed that SG tube 

failures generally occur shortly after the onset of fuel damage for severe accidents. The SNL 

study performed a rough estimate of a critical SG tube leak area that could release the whole 

primary volume in 4 hours. This was done because of a lack of detailed severe accident 

analysis of post-SGTR. The SNL report therefore, determined the following:

• Flow through the cracks is choked (no secondary-to-primary pressure equalization).

• Early containment bypass occurs if the contents of the RCS are released through the

cracks in less than 4 hours (no HL failure or failure of other RCS components

was considered).
2-17

An uncertainty distribution for the required crack opening area was determined by considering 

the uncertainties in the following:

• the release time for containment bypass

• the temperature of the gas exiting the break

• the specific heat ratio for the gas mixture

• the average molecular weight of the gas mixture

Using this analytical approach, the mean crack opening area for containment bypass is 

calculated to be 0.52 cm2 (0.081 in.2

). The lower and upper 90-percent confidence limits for this 

value were calculated to be 0.34 cm2 (0.053 in.2

) and 0.8 cm2 (0.124 in.2), respectively.

This study considers SNL’s estimate to be conservative: for example, this size of leakage is not 

expected to depressurize the primary fast enough to prevent the failure of the HLs. The 

likelihood of the failure of an RCS component is expected to be close to 1, if the primary is not 

significantly depressurized. Furthermore, the analysis does not directly address the overall 

magnitude of release. 

The current study defines critical leak areas by considering the following three SGTR leak areas 

that could affect the progression of the accident and the amount of releases:

(1) For small C-SGTR leak areas less than a guillotine break of one tube between 

4.8–6.4 cm2 (0.75–1 in.2

), the primary is not expected to depressurize, and the likelihood 

of failure of the HL or other RCS components is expected to be quite high. For this leak 

area size, repeated cycling of primary SRVs, including the possibility that at least one 

SRV sticks open, is expected to be high. Therefore, most of the in-vessel releases will 

end up in the containment rather than leaking through the small C-SGTR leak area. The 

probability that such leakages (i.e., containment bypass) result in LERF is negligible.

(2) There is also a leak area that can pressurize the SG secondary side such that a 

significant amount of cycling of the SG PORV or SRV is expected (and therefore a 

release path to the environment). In such cases, the primary and secondary side will 

equalize at a pressure of around 8.3 MPa (1,200 psi), unless the SG PORV fails to 

reclose. The results of severe accident analysis (RELAP runs for the example W plant 

and MELCOR for the example CE plant) indicate that tube leak areas equivalent to a 

guillotine break of one or more tubes, between 4.8–6.4 cm2 (0.75–1 in.2

), generally 

satisfy this criterion. A typical guillotine break for plants, discussed in Chapter 7, has a 

maximum total leak area of about 6 cm2

(0.9 in.2).

(3) An SG tube leak area could be large enough to collapse the countercurrent flow 

described in Section 3.1 and transform it to a unidirectional flow regime. It is possible for 

the counter current flow to be reestablished after some time. However, a large number of 

tubes are assumed to fail because of exposure to hot gas temperatures. The release is 

also expected to be large and early, similar to the previous case, without sufficient time 

available for any recovery actions. 

From the discussion provided above, this scoping PRA considered a critical area of containment 

bypass. Leak areas equivalent to a 4.8–6.4-cm2 (0.75–1-in.2

) guillotine break of a tube are 

considered to have a potential for LERF, if an SG relief valve sticks open. On the contrary, this 

size of leakage has no LERF potential if the primary relief valve sticks open and none of the SG 
2-18

relief valves fail. The small secondary hole of 3.2 cm2 (0.5 in.2

) that is assumed in the analysis 

to depressurize a dry SG does not provide a significant contribution to LERF and it is not of 

sufficient size to depressurize the SG secondary side after C-SGTR occurs.

A leakage area equivalent to the areas of more than three tubes is always considered as LERF 

because repeated cycling is expected to cause the SG relief valves to fail eventually. The study 

made similar assumptions for cases where the loop seals are cleared during a severe accident.

For the purpose of this study, using simplified C-SGTR PRA models, a leakage area equivalent 

to a guillotine break of one or more SG tube if it occurs early, is considered as LERF. This 

corresponds to assuming a large leakage directly to the environment from the secondary 

system, equivalent to the area of one SG PORV or SRV. This is consistent with the latest 

information available from NUREG/CR-7110, “State-of-the-Art Reactor Consequence Analyses 

Project Volume 2: Surry Integrated Analysis,” Volume 2, Revision 1, issued August 2013 

(Ref. 6), which indicates that the SG SRVs will fail open within 10 cycles when the gas 

temperature exceeds 1,000 Kelvin. 

2.6 A LERF Model 

The end state associated with Level 1 event trees generally corresponds to the time when the 

fuel begins to uncover. For some sequences, there is a large inventory of water in the 

secondary sides of the SGs at the time when the fuel begins to be uncovered. It could, 

therefore, take some time (about an hour and a half) for the SG to become dry. The 

countercurrent flow regime occurs in the HLs after SGs become dry. If the PORV and the 

direct current power are available or recovered during this period, the operator could open the 

PORVs and depressurize the primary, thereby avoiding or significantly diminishing the 

probability of C-SGTR.

If the operators fail to depressurize the primary, and SGTR occurs before HL failure 

(i.e., C-SGTR), the primary pressure would remain high for small SGTR leak areas. The 

likelihood of HL failure should then be considered. For larger C-SGTR leaks, however, when the 

primary is depressurized partially through the ruptured tubes, the likelihood of HL failure is 

expected to be smaller. Furthermore, after SGs have dried up, it typically takes another 6 to 

8 hours for the vessel breach to occur. This provides sufficient time to perform SAMG activities 

(e.g., early vessel injection to help mitigate further fuel damage and flooding the SG secondary 

side to scrub any possible releases through the ruptured SG tubes).

The release through C-SGTR will nearly stop when the vessel is flooded and the SG secondary 

is filled with water. Therefore, the time it takes for SAMG actions to become effective 

determines the magnitude of the release. This is considered an important step for categorizing 

the size of releases in terms of the magnitude of the source term.

The release categories are generally binned into several groups, depending on the magnitude 

of release and the time of release after evacuation. Some past studies (Ref. 7) have suggested 

the following release bins:

• large-early release (LER)

• large-late release (LLR)

• medium-early release (MER)

• medium-late release (MLR)
2-19

• small-early release (SER)

• small-late release (SLR)

• negligible or controlled late releases (CLR)

The open literature has not yet reported the exact definitions of these categories in terms of the 

timing and the magnitude of the releases. The magnitude is sometimes defined by the fractional 

releases of iodine (I) and cesium (Cs). For example, large, medium, and small could correspond 

to a release fraction (RF) of either Cs or I to the environment of greater than 5 percent 

(RF>5%), between 1 and 5 percent (RF1%≤–≤5%), and less than 1 percent (RF<1%), 

respectively. The category of no release or negligible release is retained for cases where core 

damage is arrested within the vessel and all partial releases are scrubbed. The amount of 

release in the no-release category is generally comparable to that of the fuel gap release plus 

the radioactivity inventory in the primary coolant (it approximately translates into less than 

0.01 percent of I or Cs).

The study bases the definition of early and late on the duration of time between the activation of 

a general emergency, requiring the start of evacuation, and the time of major radioactivity

releases. Early generally reflects a duration of less than 12 hours, and late is defined as a 

duration greater than 12 hours. Using 12 hours as the threshold is intended to cover the 

external hazards; therefore, it is considered to be a conservative value for internal event 

initiators. For most internal event initiators in PRA, a value of 8 hours might be 

more appropriate.

Figure 2-2 shows an example of an emergency response timeline for the unmitigated long-term 

SBO (ltsbo) sequence (an SBO with failure of TDAFW after batteries are depleted) (Ref. 6). The 

timing of emergency classification declarations in this figure was based on the EALs contained 

in the site emergency plan implementing procedure at Surry. Surry was selected as a particular 

example. Similar timing of EAL classification declarations are also implemented in other PWRs 

(Ref. 7). Application of this method may be applied to other nuclear stations with proper 

consideration of possible site-specific issues. Note that this information is intended as an 

illustration of the general time frames and accident sequence progression. This sequence 

triggers EAL SS1.1, which specifies that a site area emergency (SAE) is declared if all offsite 

power and all onsite alternating current power are lost for more than 15 minutes. If the 

restoration of power seems unlikely within 4 hours, EAL SG1.1 requires that a general 

emergency be declared. SAE is, therefore, expected to be declared in about 15 minutes, and 

plant operators would recognize within the first 2 hours that restoration of power within 4 hours 

is unlikely. A period of 2 hours from the loss of power was selected as a reasonable time for 

declaration of a general emergency. From the MELCOR analysis, the first fission product gap 

release occurs 16 hours into the event. This timing diagram basically reveals a high likelihood of 

an effective evacuation during ltsbo sequences.
2-20

Figure 2-2 Unmitigated ltsbo emergency response timeline 

Similarly, Figure 2-3 shows the emergency response timeline for the unmitigated short-term 

SBO (stsbo) sequence (SBO with early failure of TDAFW). For this sequence, SAE is also 

declared after 15 minutes of SBO, because EAL SS1.1 is triggered. In stsbo, the core is 

expected to be uncovered in less than an hour and a half with the core exit thermocouple 

reading in excess of 648.89°C (1,200 °F), and with the reactor vessel water level lying below the 

top of active fuel, prompting the declaration of a general emergency. From the MELCOR 

analysis, the first fission product gap release occurs about 3 hours into the event, with a 

significant radioactive release through the containment, if no C-SGTR occurs, in 25.5 hours into 

the event. This timing diagram basically reveals that there is a high likelihood that an effective 

and complete public evacuation may not be possible before some radioactive releases.
2-21

Figure 2-3 Unmitigated stsbo emergency response timeline 

 

A simplified LERF model that relies on five factors, similar to what was defined earlier for 

C-SGTR because of DBAs, was also defined for C-SGTR because of severe accidents. LERF is 

estimated by the product of the five factors defined below:

(1) frequency of severe accident sequences with potential for C-SGTR fAC

(2) C-SGTR probability PCSGTR

(3) conditional probability that the subsequent failure of RCS, 

including the stuck-open relief valves, do not occur PNDEP

(4) failure probability of all SAMG actions PSAMG

(5) probability that early effective evacuation is not successful PEVAC

Chapter 7 uses the above model for the example W and CE plants to make LERF estimates.

2.7 References 

1. ASME/ANS RA-Sa-2009, “Standard for Level 1/Large Early Release Frequency 

Probabilistic Risk Assessment for Nuclear Power Plant Applications, Addendum A,” 

American Society of Mechanical Engineers, March 2009.

2. NRC, RG 1.174, An Approach for Using Probabilistic Risk Assessment in Risk Informed 

Decisions on Plant-Specific Changes to the Licensing Basis, Revision 2, May 

2011, ML100910006.
2-22

3. NRC Manual Chapter 0609, Appendix H, “Containment Integrity Significant

Determination Process, May 2011.

4. U.S. Nuclear Regulatory Commission, “SCDAP/RELAP5 Thermal-Hydraulic Evaluations

of the Potential for Containment Bypass during Extended Station Blackout Severe

Accident Sequences in a Westinghouse Four-Loop PWR,” NUREG/CR-6995,

March 2010. Agencywide Documents Access and Management System (ADAMS)

Accession No. ML101130544.

5. Sandia National Laboratories, “Severe Accident Initiated Steam Generator Tube

Ruptures Leading to Containment Bypass-Integrated Risk Assessment,” JCN Y6486,

February 2008.

6. U.S. Nuclear Regulatory Commission, “State-of-the-Art Reactor Consequence Analyses

Project Volume 2: Surry Integrated Analysis,” NUREG/CR-7110, Vol. 2, Rev. 1,

August 2013, ADAMS Accession No. ML13240A242.

7. Azarm, M.A., et al., “Feasibility Study of Risk Informing Emergency Action Levels of

Fission Product Barriers Using Level 2 PRA,” PSA 2013, Columbia, SC.
3-1

3 THERMAL-HYDRAULIC ANALYSES FOR WESTINGHOUSE AND 

COMBUSTION ENGINEERING PLANTS 

Thermal-hydraulic (TH) analyses were performed to study a Combustion Engineering (CE) 

plant’s response to reactor coolant system (RCS) conditions that could lead to consequential 

steam generator tube rupture (C-SGTR). The results and insights of Chapters 4, 5, and 7 were 

generated from the TH sequences associated with SCDAP/RELAP runs reported in 

NUREG/CR-6995, “SCDAP/RELAP5 Thermal-Hydraulic Evaluations of the Potential for 

Containment Bypass During Extended Station Blackout Severe Accident Sequences in a 

Westinghouse Four-Loop PWR,” issued March 2010 (Ref. 1), for the Westinghouse (W) plant, 

and the MELCOR runs discussed below for the CE plants.

This chapter summarizes the TH work conducted to study thermally induced C-SGTR for W 

plants and provides a detailed analysis for CE plants that use replacement steam generators 

(SGs). The work includes (1) the development of updated CE computation fluid dynamics (CFD) 

and MELCOR models, (2) the application of these models on select risk-significant sequences 

to evaluate expected TH behavior, (3) the comparison of results against previous analyses, 

(4) an uncertainty analysis for the effect of TH parameters, (5) the generation of TH data files in 

the SGTR probabilistic calculator and finite element (FE) analyses, (6) the generation of release 

data in updating the risk contribution from these events, and (7) an assessment of the effect of 

instrument tube failures.

Section 3.1 describes the TH analysis and lists the previous work on the subject. Section 3.2 

describes the Sandia National Laboratories (SNL) deck generation and summarizes some of its 

analyses. Section 3.3 describes the CFD analyses and input used for the SNL and U.S. Nuclear 

Regulatory Commission (NRC) analyses. Section 3.4 describes two stages of deck

modifications made by the NRC, one before the initial set of simulations and one used for the 

final set of simulations. Section 3.5 describes a conceptual model for loop seal clearing. 

Section 3.6 summarizes the major simulation results. Section 3.7 describes potential future 

analyses, and Section 3.9 provides conclusions and recommendations from the TH work.

3.1 Introduction 

C-SGTR accidents are of interest because of the potential for fission product (FP) releases 

direct to the environment, bypassing the containment. Reactor designs include containments 

that reduce releases in the event of an accident. A containment bypass release refers to a 

situation in which FPs released during core degradation bypass the containment and thus do 

not benefit from these reductions. Fission products that enter the SG secondary sides are 

prevented from reaching the environment solely by a series of valves the failure of any of which 

will result in an open path from the core to the environment.

There are two general types of C-SGTR sequences: one is a thermally induced C-SGTR, in 

which hot gases emanating from the core during a severe accident cause creep rupture of SG 

tubes. The second type of C-SGTR is pressure induced, in which a shock from some event, 

typically a main steamline break, causes tubes to rupture. This section of the report deals 

exclusively with thermally induced C-SGTR.

In the thermally induced C-SGTR, heat transfer to the tubes by natural circulation results in tube 

rupture. Figure 3-1 shows the two different forms of severe accident natural circulation flows. 

The left part of the diagram shows full-loop natural circulation conditions. Hot gases leaving the 
3-2

core flow through the hot leg (HL) and are cooled as they pass through the SG with the cooled 

gases returning to the core through the cold legs. The right part of the diagram shows 

closed-loop-seal natural circulation flow. For this situation, the water in the loop seal blocks the 

return flow to the core. The cooled gases can only return to the core through SG tubes and the 

HL. For this situation, a countercurrent flow situation exists where hot gases from the core are 

flowing to the SGs through the top of the HLs while cooled gases are returning through the 

bottom of the HL. The volumetric flow rate for countercurrent natural circulation is lower than 

that for full-loop natural circulation. Thus, closed-loop natural circulation transfers heat less 

efficiently to the SG tubes, and tube rupture is less likely to occur under these conditions.

Figure 3-1 Severe accident natural circulation flows 

The TH work described in this section deals primarily with closed-loop-seal natural circulation 

behavior, although open-loop natural circulation behavior is also discussed.

Although risk analyses have previously considered SG tube ruptures (SGTRs), they have 

typically not considered thermally induced C-SGTRs. In the previous analyses, the tube rupture 

was considered to be the initiating event. This rupture can lead to a severe accident if corrective 

actions are not taken in time. This type of SGTR is a design-basis event for which plants are 

designed to cope without progressing to a severe accident. Plants have coped with all 

SGTRs to date. A C-SGTR differs from this sequence in that the severe accident causes the 

tube rupture.

NUREG/CR-6995 (Ref. 1) extensively studied C-SGTR TH behavior for W plants. Some work 

was performed on CE plants (Ref. 2) with SCDAP/RELAP but, having predated the final W 

analysis, it did not incorporate all the modeling improvements made for the W designs. The 

Electric Power Research Institute (EPRI) considered CE plants in its 2002 SG-tube-related risk 
3-3

analysis (Ref. 3), which showed that CE plants were more vulnerable to C-SGTR than are W 

plants during station blackout (SBO) accidents.

Because of the capability to predict FP releases in addition to TH behavior, the decision was 

made to switch from SCDAP/RELAP to the MELCOR code to perform the CE C-SGTR analysis, 

taking advantage of the lessons learned during the previous W analyses.

3.1.1 Summary of Results Obtained in NUREG/CR-6995 

To put the analysis for CE plants in proper perspective, it is useful to include a summary of the 

TH results for W plants. The following are some pertinent excerpts from the Executive Summary 

of NUREG/CR-6995:

For PWRs [pressurized-water reactors] with U-tube SGs, the natural circulation 

of superheated steam in the loop piping during specific low probability severe 

accident conditions could result in sufficient heating of the SG tubes to induce 

creep-rupture failure under certain scenarios. To support an overall examination 

of the risk impacts of induced tube failure, thermal-hydraulic analyses have been 

performed. The analyses used the SCDAP/RELAP5 systems analysis computer 

code, aided by computational fluid dynamics (CFD) simulations, to examine the 

pressure and temperature conditions that challenge the integrity of the reactor 

coolant system pressure boundary and to estimate the timing of specific reactor 

coolant system component failures.

These evaluations have focused on station blackout (SBO) severe accident 

scenarios in Westinghouse four-loop PWRs. The scenarios that challenge the 

tubes primarily involve a counter-current natural circulation flow pattern during 

conditions referred to as high-dry-low. The high-dry-low scenario refers to a set 

of conditions that includes a high pressure in the reactor coolant system (RCS), a 

loss of SG water inventory and a failure to provide a source of feedwater (dry), 

and a significant leak from the SG secondary side boundary that results in a low 

pressure on the secondary side of the SG tubes. Another condition posing a 

challenge to steam generator tubes is associated with full-loop natural circulation 

flows that are possible if the water in the loop seal is cleared and the reactor 

vessel downcomer is cleared. Based on our recent SCDAP/RELAP5 analysis, 

this condition is considered to be much less likely than the condition of countercurrent natural circulation flow.

A severe accident-induced failure of an SG tube releases radioactivity from the 

RCS into the SG secondary coolant system from where it may escape to the 

environment through the pressure relief valves. An environmental release in this 

manner is called “containment bypass,” which contrasts with releases into the 

containment that result from failures of HL piping, pressurizer surge-line piping, 

or the lower head of the RV [reactor vessel]. The potential for steam generator 

tube failure by creep rupture and containment bypass under the high-dry-low 

conditions is effectively eliminated if (1) the RCS pressure is reduced because of 

operator actions to intentionally depressurize the RCS or primary system leakage 

(eliminating the high-pressure condition), (2) feedwater flow is maintained 

(eliminating the dry condition and reducing RCS pressure), or (3) the SG 

secondary system retains pressure (eliminating the low-pressure condition on the 

secondary side).
3-4

The clearing of a loop seal eliminates the counter-current flow pattern described 

above and creates a challenging environment for SG tubes. Loop seal clearing 

(along with a clearing of the fluid in the RV lower downcomer region) results in a 

direct natural circulation path around the coolant loop (RV, HL, SG, cold leg). 

Loop seals are more likely to clear when the water in the loop seals is heated 

and a rapid depressurization occurs. If loop seals are cleared and full loop 

natural circulation is established, the hot steam from the RV challenges the 

integrity of the SG tubes.

The timing of the failure of the system components is significant. If a[n] SG tube 

or tubes are predicted to fail prior to the HL or other RCS components, steam 

and radioactive FPs (released during core degradation) pass into the SG 

secondary system and provide a potential for containment bypass. Predictions 

indicate that a[n] HL or other RCS component will fail shortly after an SG tube 

fails because the SG tube failures do not immediately depressurize the system. 

The subsequent failure of the RCS boundary significantly reduces the rate of 

mass flow from the primary system into the SG secondary system. Alternatively, 

if a[n] HL or other RCS component of significant size fails prior to an SG tube, the 

release of contaminated steam would be completely into the containment 

because the resulting rapid RCS depressurization prevents subsequent failures 

of SG tubes and the associated containment bypass.

This report documents the current predictions for system behavior during 

extended SBO scenarios. The objective of this report is to combine the four-loop 

PWR extended SBO severe accident event sequences that fall into the following 

three categories:

(1) sequences resulting in containment bypass

(2) sequences providing a potential for containment bypass for which an

outcome may be determined by initially comparing the degradation of

tube strengths in a prototype SG against the SCDAP/RELAP5-predicted

tube-failure margins

(3) sequences not resulting in containment bypass

This categorization of event sequences provides information that—when 

combined with results from RCS component analyses, probabilistic risk 

assessments, and environmental release evaluations—will permit an evaluation 

of risks because of containment bypass for Westinghouse four-loop plants.

A model of a Westinghouse four-loop plant is developed for use with the 

SCDAP/RELAP5 thermal-hydraulic system code and employed to perform 

simulations of accident-event sequences pertinent for the containment bypass 

issue. The SCDAP/RELAP5 code calculates fluid and structure conditions, such 

as pressures and temperatures, throughout the regions of a plant model. In 

addition, the code includes models for calculating the progression of core 

damage behavior during severe accidents and simplified models for 

creep-rupture behavior of RCS components. In the Westinghouse four-loop plant 

model, creep-rupture behavior is evaluated with SCDAP/RELAP5 to predict 

failure times for the HLs, pressurizer surge line, and SG tubes. The creep-rupture 

model allows one to specify a “stress multiplier.” A multiplier of 1.0 provides a 
3-5

creep-rupture failure prediction based on no degradation of the structural 

strength of the material. Multipliers greater than 1.0 represent degraded 

structural strengths associated with preexisting tube flaws or degradation that 

may exist. A stress multiplier of 2.0, for example, represents a degraded-strength 

condition for which the creep-rupture failure of a structure is predicted when the 

stress applied is only 50 percent of that required to fail the undegraded structure. 

The term “SG tube failure margin” as used in this report refers to the tube-stress 

multiplier in the model that results in prediction of SG tube creep-rupture failure 

coincident with the earliest failure of another RCS pressure boundary 

component, typically a[n] HL. Therefore, tubes with higher stress multipliers are 

predicted to be the first RCS pressure-boundary components to fail, in which 

case containment bypass occurs. Two SG tube failure margins—one for the 

average tube and another for a tube in the hottest region of the SG—represent 

the key output from the SCDAP/RELAP5 event sequence simulations.

Event sequences are categorized relative to the potential for containment bypass 

using the following criteria based on the SCDAP/RELAP5-predicted hottest SG 

tube failure margin:

• Containment bypass is assumed if the 1.0-stress multiplier 

(i.e., undegraded) hottest SG tube is predicted to fail prior to the HL, 

pressurizer surge line, or RV.

• A potential for containment bypass is assumed if the hottest SG tube 

failure margin is between 1.0 and 3.0. In this case, data for the actual SG 

tube strengths and their distribution resident in a prototype SG are 

needed to determine the outcome.

• Containment bypass is not indicated if the hottest SG tube failure margin 

is 3.0 or higher.

The major findings of the extended SBO event sequence categorization for 

Westinghouse four-loop PWRs are summarized as follows.

For situations where the operators are assumed to take no action:

• Event sequences that do not involve secondary side depressurization 

(i.e., leakage from the secondary system of 0.64 cm2

/SG [0.1 in2 /SG] and 

smaller) generally do not result in containment bypass. The reduced SG 

tube stresses resulting from the SG secondary pressures remaining 

elevated prevent SG tubes from failing prior to the HL, surge line, or RV.

• Event sequences that assume reactor coolant pump (RCP) shaft seal 

leakage rates lower than 11.36 L/s [180 gpm] per pump generally provide 

a potential for containment bypass. Event sequences that assume RCP 

shaft seal leakage rates of 11.36 L/s [180 gpm] per pump and higher 

generally do not result in containment bypass. A high leak rate leads to 

lower RCS pressures, and the reduced SG tube stresses prevent SG 

tubes from failing prior to the HL, surge line, or RV. However, exceptions 

exist related to the time when RCP shaft seal failures are assumed to 

occur. For RCP shaft seal failures that occur late in the event sequences, 
3-6

loop seal clearing and, therefore, containment bypass can occur for 

leakage rates above 25.23 L/s [400 gpm] per pump.

• Event sequences in which the TDAFW [turbine-driven auxiliary feedwater]

system operates and continues operating (or alternate feedwater is

available) do not result in containment bypass. The outer surfaces of the

SG tubes remain wet, and the RCS heat removal provided prevents

system heatup.

For event sequences in which the TDAFW system is assumed to initially operate 

and later fail, the likelihood of tube rupture is predicted to be very similar to 

scenarios where the TDAFW does not operate at all because eventually, without 

other mitigation, the system may reach the high-dry-low condition. However, the 

timing of potential tube failures is significantly delayed by the initial operation of 

the TDAFW system. Challenges to continued TDAFW operation are a result of 

depletion of the station batteries or the depletion of the condensate storage tank 

inventory. Probabilistically, additional mitigation should be considered as well as 

the likelihood that auxiliary feedwater may not be maintained.

For situations where the operators take mitigative action:

• An evaluation was performed for a strategy in which operators implement

SG feed-and-bleed cooling at 30 minutes into the event sequence (using

the TDAFW system and opening the SG PORVs [power-operated relief

valves]). The evaluation shows that this strategy is effective in the short

term for preventing containment bypass. At a minimum, the onset of the

RCS heatup is significantly delayed, thereby providing additional time for

other plant recovery opportunities to be considered and implemented. In

the long term, the SG PORVs fail closed when the batteries are depleted,

and continued success of this strategy requires that a TDAFW water

source remains available along with some capability for delivering the

water into the SGs. For sequences in which the TDAFW system initially

operates but later fails, no large changes in SG tube failure margins

(relative to the no-intervention case) were predicted.

• An evaluation was also performed for a post-core damage strategy in

which the operators depressurize the RCS by opening one or two

pressurizer PORVs after plant instrumentation indicates that core cooling

is inadequate. PORVs are opened at the time when the core exit

temperature reaches 922 K (1,200 °F) or 12 minutes later. The evaluation

shows that opening only one PORV limits the cooling afforded to the

RCS, the core fails early (prior to battery depletion), and containment

bypass is avoided for both operator action times. The evaluations also

show that the greater RCS cooling afforded by opening two PORVs

prevents early core damage and also prevents early failure of the HL and

SG tube structures. When the PORVs fail closed after battery depletion,

the RCS begins repressurizing and reheating, and this subsequently

leads to HL and SG tube failures. The SG tube failure margins seen for

the operator intervention cases are significantly improved (relative to the

no intervention cases), and containment bypass is seen to be avoided for

both of the post-core damage operator action times.
3-7

3.1.2 CE Plant Considerations 

The increased vulnerability for CE plants is primarily because of a shorter HL length-to-diameter 

ratio and to shallower SG inlet plena compared to W SGs. This results in higher temperature 

gas reaching the SG tubes during closed-loop-seal natural circulation conditions. Consequently, 

the SG tubes are predicted to reach creep-rupture conditions sooner in CE plants, thus 

increasing the likelihood of containment bypass.

Several aspects are of interest for the purpose of determining FP releases to the environment: 

(1) whether an SG tube or some other part of the RCS pressure boundary fails first, (2) whether 

tube failure results in sufficient and rapid enough RCS depressurization to prevent rupture of some 

other part of the RCS boundary, and (3) whether the containment pressure is higher than the SG 

pressure in the long term, thus allowing release of revaporized FPs. This last aspect cannot be 

addressed in an SCDAP/RELAP analysis but can when using MELCOR. In the W analysis, the 

presence of a flaw was required for the prediction of tube failure before the failure of other RCS 

components. This condition leads to the prediction of failure of a single tube and a primary system 

depressurization rate that is not sufficient to prevent subsequent failure of other RCS components. 

For CE designs, however, unflawed tubes exposed to the relatively unmixed hot gases that reach 

the SG tubes can also fail. Moreover, more than one tube could fail, potentially depressurizing the 

RCS sufficiently to prevent the creep-rupture failure of other components, leaving the containment 

bypass pathway as the sole release path of FPs from the reactor.

The relatively shallow inlet plenum design of the SG under consideration for the CE plant has an 

effect on the results of the CFD predictions, as shown in Section 3.3.2 below. The shallow design 

limits the mixing of the hot gases that enter the SG and creates a higher thermal load on the tubes. 

The SG considered for the CE plant was a replacement SG. The earlier work on W plants focused 

on the Zion Nuclear Power Plant, with the associated W Model 51 SGs. To qualify, the applicability 

of these W predictions for W plants with replacement SGs, the NRC’s Office of Nuclear Regulatory 

Research (RES) has worked with the NRC’s Office of Nuclear Reactor Regulation to acquire 

plant-specific inlet plenum design information from a few plants. Although it was not practical to get 

design information for as many plants as desired, three sets of drawings were obtained. These 

included SG drawings from the Donald C. Cook Nuclear Plant, the Diablo Canyon Power Plant, and 

the Prairie Island Nuclear Generating Plant. The RES staff studied the dimensions for the inlet 

plenum region and found only small differences between the new designs and the previously 

studied Model 51 design. No shallow inlet plenum designs were found in the W samples. The 

expectation is that thermal mixing in the inlet plenums would not be significantly affected by the new 

SG designs for the sample plants considered.

3.2 Initial Deck and Analyses for the CE Plant 

SNL developed the MELCOR 1.8.6 initial deck used for the C-SGTR analyses. It exercised the 

deck on SBO calculations, compared results against those of previous SCDAP/RELAP 

analyses, and performed an uncertainty analysis to estimate the expected contribution to 

variability in component failure timing resulting from uncertainty or variability in TH parameters.1

 1 See Louie, D.L., et al., “A MELCOR Model of the Calvert Cliffs Two-Loop Pressurized Water Reactor and 

Containment for the Steam Generator Tube Rupture Scenarios,” Sandia National Laboratories, 

October 2012.
3-8

SNL generated the Calvert Cliffs Nuclear Power Plant deck based upon an earlier, less-complex 

MELCOR 1.8.5 demonstration deck and the 2006 SCDAP/RELAP Calvert Cliffs deck used for 

prior C-SGTR analyses (Ref. 2). During development, SNL exercised the deck on short-term 

SBO (stsbo) analyses using mixing parameters provided from initial CFD analyses. The SNL 

deck and analyses did not account for the temperature variability in the hot plume entering the 

SG tubes, so it cannot be used to test the failure of unflawed hottest tubes. SNL documented 

the updated deck and the results of the stsbo analysis.

SNL compared results from the new deck against those generated using SCDAP/RELAP 

(Ref. 1). This comparison required some modifications from the base version to more closely 

match the SCDAP/RELAP deck. They found that both codes predicted a similar sequence 

behavior and timing, although some later events occurred at somewhat different times. The 

analysts also found that component failure was not similarly predicted, which is not surprising 

considering that the MELCOR analysis did not include the hottest tube calculation.

SNL performed an uncertainty analysis to estimate the expected contribution to variability in 

component failure timing resulting from uncertainty or variability in TH parameters. The 

RCS-component-to-tube relative failure timing variation because of expected variations in TH 

parameters approximately followed a normal distribution with about a 600-s standard deviation. 

Although some aspects of the deck used to generate the failure timing distributions differ 

somewhat from the final version, the overall system response is not expected to change 

significantly. The variability in relative failure timing for the hottest tubes is likewise expected to 

be similar to that of the hot average tubes in the plume.

3.3 Computational Fluid Dynamics 

CFD is used to study the details of the three-dimensional (3D) mixing behavior in the primary 

side of a CE SG. The results are used to inform the system-level code of the expected flow 

rates and mixing parameters in this region of the reactor system during specific severe accident 

sequences. This work builds upon previous NRC studies. Test data are available from a 1/7th 

scale facility that provide valuable information on SG inlet plenum mixing and the natural 

circulation flows during severe accident conditions. These data, however, are limited to a single 

W-type inlet plenum design, and there are concerns related to the scaling of these data to fullscale conditions. A benchmark study by the NRC staff, documented in NUREG-1781, “CFD 

Analysis of 1/7th Scale Steam Generator Inlet Plenum Mixing during a PWR Severe Accident,” 

issued October 2003 (Ref. 4), demonstrate that CFD predictions can adequately predict the inlet 

plenum mixing observed in the 1/7th scale tests. A set of follow-on analyses, documented in 

NUREG-1788, “CFD Analysis of Full-Scale Steam Generator Inlet Plenum Mixing during a PWR 

Severe Accident,” issued May 2004 (Ref. 5), applied the same methods to study full-scale SGs 

under severe accident conditions. This study extends the experimental results at 1/7th scale to 

prototypical conditions and provides insights into the effect of the SG inlet plenum geometry and 

the potential effect of the secondary-side heat transfer conditions. After a review of these 

predictions, the Advisory Committee on Reactor Safeguards recommended extending the 

modeling to include a prediction of the full natural circulation flow path between the vessel upper 

plenum and the SG. A follow-on study, documented in NUREG-1922, “Computational Fluid 

Dynamics Analysis of Natural Circulation Flows in a Pressurized-Water Reactor Loop under 

Severe Accident Conditions,” issued October 2010 (Ref. 6), addressed this concern and 

incorporated other modeling improvements for W-type SGs. The improved modeling approach 

was then applied to a CE-type SG as a comparison study (Ref. 7).
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3.3.1 Summary of NUREG-1922 Results for Westinghouse Plants 

The analysis in NUREG-1922 used an improved CFD model to determine mixing parameters 

and coefficients for tuning a system-code model applied to severe accident simulations with 3D 

natural circulation flows. The CFD model used in this study encompasses a series of lessons 

learned from several years of analyses, including a benchmark study at 1/7th scale (Ref. 4) and 

a follow-on study of full-scale SGs (Ref. 5). The updated modeling also addresses the Advisory 

Committee’s comments (Ref. 8).

The natural circulation flows between the reactor vessel upper plenum and the SG were predicted 

under specific severe accident conditions that were obtained from prior system-code model 

predictions. A vessel model established the conditions in the upper plenum, which feeds the natural 

circulation flows in the HL, the pressurizer surge line, and the primary side of an SG. A 

countercurrent flow pattern is established that carries heat from the upper plenum to the SG tube 

bundle. An unsteady buoyant plume is predicted in the inlet plenum as the hot-steam-and-hydrogen 

mixture rises up and into the tube bundle. Time-averaged mass flows and temperatures are 

obtained throughout the system, and these predictions are used as a numerical experiment to 

define flow and mixing parameters for use in tuning a system-code model.

A modified mixing formulation is established to account for the HL and inlet plenum mixing, as 

well as the pressurizer surge-line flows. This updated formulation is considered to be an 

improvement over earlier models that focused solely on the inlet plenum mixing. In addition, a 

discharge coefficient is defined that can be used to predict the HL mass flow rates, based on the 

densities in the vessel upper plenum and the SG inlet plenum. The predictions provide a means 

of tuning a system code to obtain the mass flows and temperature distribution in the HL, surge 

line, and SG tube bundle. These predictions can be used to extend the existing experimental 

data into the specific SG geometry and severe accident conditions studied.

The recommended system-code modeling parameters for a W plant (assumed to have a 

Model 51 SG) or a plant with similar SG designs are summarized below.

f = 0.96 mixing fraction

r = 2.4 recirculation ratio

41% hot tube fraction

Cd = 0.12 discharge coefficient

Tm = 0.5 bounding normalized temperature of hottest tube

50 : 50 hot : cold flow split ratio into side-mounted pressurizer surge line

Sensitivity studies estimate the variation in these parameters under a variety of conditions and 

assumptions. In all cases, the discharge coefficient remained relatively constant with maximum 

variations of less than 8 percent. This demonstrates the benefits of using this approach to 

establish the HL flows in a system-code model. Similarly, the mixing fraction is found to vary by 

only a few percent over the range of conditions considered. The recirculation ratio is found to be 

sensitive to the secondary-side temperature, which affects the tube bundle heat transfer. The 

tube bundle heat-transfer rate was found to affect the recirculation ratio in previous work 

(Ref. 5), since the temperatures in the tube bundle affect the buoyancy driving forces. These 

parameters are found to have the largest effect on the recirculation ratio. The recirculation ratio 

suggested above, 2.4, is obtained using conditions pulled directly from a realistic system-code 

prediction of severe accident conditions in a W PWR.
3-10

The hot tube fraction is used for sizing the hot and cold SG tube sections in a system-code 

model. This parameter is difficult to predict with confidence because some of the tubes at the 

margin (i.e., tubes at the edge of the hot and cold regions) seem to occasionally change 

direction and the hot tube fraction can change by 10 percent or more in a given analysis. The 

predictions were not carried out long enough to obtain a consistent long-term average value. 

One important finding is that the hottest tube region does not appear to be significantly affected 

by changes in the overall size and shape of the hot tube region. In other words, the core of the 

hot tube region is somewhat consistent. Changes to the tube flow patterns occur at the edges of 

the hot tube region where the temperatures are more moderate. The base-case prediction had a 

long-time average hot tube fraction of 0.41. This value is in the middle of the range of all of the 

predictions. When the tube bundle flow is significantly increased, the hot tube fraction 

apparently tends to approach 0.5. At the lowest tube bundle flow rates predicted, the hot tube 

fraction is found to be as low as 0.26.

The normalized temperature of the hottest tube is a significant parameter because it refers to 

the portion of the tube bundle where the thermal loading is most severe. Recent NRC studies 

(Ref. 1) used this parameter to determine whether a tube will fail before the HL or some other 

RCS component. In the base-case prediction, the mass-averaged normalized temperature 

entering the hottest tube is found to be 0.43. The data sets were broken down into 40-second 

intervals, and the study found that the normalized temperature reached 0.5 over some of these 

intervals. For this reason, a value of 0.5 is recommended as a bounding value for system-code 

models. The sensitivity of this parameter to changes in the modeling parameters was significant. 

Average values ranging from 0.36 to 0.47 were obtained. The most significant variation came 

from changes in the secondary-side temperatures. A separate sensitivity study that moved the 

surge line to the top of the pipe also showed a significant impact on the hottest tube 

temperature. The top-mounted surge line removes some of the hottest flow, and the average 

normalized temperature of the hottest tube drops to 0.34.

The flow (hot:cold) split ratio into the surge-line pipe is predicted for simulations that included a 

pressurizer surge line. This variable remained generally within 5 percent of a 50:50 split ratio 

over the range of sensitivity studies, and a 50:50 split ratio is recommended for system-code 

models with a side-mounted surge line. The temporal variations in this parameter were very 

large and indicated significant turbulent fluctuations at the surge line-to-HL connection. The 

50:50 value represents a long-term average value. The one sensitivity that did significantly 

affect this result involved moving the surge line to the top of the HL. In this case, approximately 

75 percent of the flow into the surge line came from the hot flow in the upper pipe section. The 

top-mounted surge line, therefore, is subjected to a larger thermal challenge than a 

side-mounted surge line. This could be important in cases where the surge line is predicted to 

fail before the HL.

The series of predictions completed with a range of tube leakages from the primary-tosecondary side help to quantify the significance of tube leakage on the overall natural circulation 

flows. A leakage rate of 1.5 (kilograms (kg)/second (s) resulted in no significant variation. The 

countercurrent natural circulation between the vessel upper plenum and the SG is maintained 

for leakage rates up to 6 kg/s but, as the leakage rates increase, the average temperature of the 

flow entering the tube bundle increases. For a leakage rate of 12 kg/s, the countercurrent flow 

pattern is essentially broken and the steam temperatures entering the tube bundle begin to 

approach the HL (hot flow) temperatures.

Some prior qualitative CFD results highlighted the fact that some system-code models will 

underpredict the convective heat-transfer rates to critical regions of the HL and surge line. In the 
3-11

regions where the thermal boundary layer is still developing, the fully developed heat-transfer 

correlations used in system codes underpredict the heat-transfer rates. To account for this 

underprediction, a set of factors are provided that can be used to adjust the fully developed 

heat-transfer correlation to account for the local entrance region effect. These factors, or other 

data, if more appropriate, should be applied in the determination of the HL and surge-line 

convective heat-transfer rates. In addition to the thermal entrance effects, it is expected that 

much of the upper HL also will experience mixed convection that would further increase the 

convective heat transfer to the HL. This topic is suggested for future research if a more detailed 

analysis of the HL becomes necessary.

3.3.2 CFD Results for a CE Plant 

A simplified vessel upper plenum and an improved tube bundle are added to the CE SG 

geometry used in NUREG-1788, as summarized in Reference 7. The CFD model domain 

includes the upper plenum of the reactor vessel, an HL with the surge-line junction, the SG inlet 

plenum, and a simplified tube bundle. Symmetry is assumed at the vertical plane of the HL and 

SG. The tubes are modeled in a manner similar to that used for the W modeling documented in 

NUREG-1922. Groups of nine tubes are combined into a single tube that maintains the 

appropriate flow area. Loss coefficients and heat transfer enhancements are added to the tube 

models to ensure that the tube bundle has the same pressure drop and heat transfer 

characteristics as a prototypical SG. NUREG-1922 outlines this method for the W SG. The 

ANSYS/FLUENT v14.5 CFD code is used for the analysis. The predictions qualitatively show all 

of the flow features observed experimentally in the HL and SG regions. Steady boundary 

conditions are used that represent a snapshot in time of the severe accident conditions from 

system-code predictions of representative severe accident sequences. Average mass flows, 

temperatures, and mixing are predicted throughout the flow domain and used to define key 

parameters that are used in the 1-dimensional system-level codes to ensure consistency with 

the 3D CFD predictions.

A discharge coefficient related to a density-based Froude number is used to define the HL flow 

rates as a function of the densities in the vessel upper plenum and SG inlet plenum. 

NUREG-1922 outlines this approach. The discharge coefficient is predicted to be in the range 

from 0.13 to 0.14 for the CE reactor geometry considered.

This study uses the updated inlet plenum mixing model, which includes the HL mixing and 

entrainment. This approach is consistent with the most recent W CFD predictions. The mixing 

fraction is found to be within the range from 0.65 to 0.75 and the recirculation ratio is found in 

the range from 1.05 to 1.1.

Because system-code predictions have shown that the reactor loop with the pressurizer can 

have the earliest tube failures under some conditions, it is important to consider the effect of the 

flows into the pressurizer surge line. The mass flow into the surge line is accounted for in the 

updated mixing model. In addition, the CFD predictions are used to define the mixture of flows 

that enter the surge line during periods of countercurrent flow. For top-mounted surge lines, the 

flow entering the surge line enters mainly from the upper (hot) HL flows, and the temperature of 

the gas entering the surge line is consistent with these hotter temperatures. It is suggested that 

a top-mounted surge line on the large CE-type HLs would pull all of the incoming flow from the 

upper HL region.

A key aspect of these predictions is the determination of the tube bundle flows. System-code 

models typically use a single representative tube for the hot-tube flows, and the temperature is a 
3-12

mass-averaged value for the entire group of tubes carrying the hot flow. With over 1,000 tubes 

expected to carry hot flow in a prototypical SG during this sequence, a significant variation in 

temperature can exist between tubes with the highest and lowest temperatures. A normalized 

temperature is defined to make the results easy to apply under a variety of conditions. A value 

of 1.0 represents the temperature of the flow from the vessel upper plenum, and a value of 0.0 

represents the temperature of the flow returning to the inlet plenum through the cold-flow tubes. 

Tube entrance temperatures fall between 0 and 1 on this scale. The average normalized 

temperature of the hottest tube in the bundle is found to be in the range from 0.95 to 0.99. The 

total number of tubes that carry the upward hot average flow is found to be in the range from 20 

to 25 percent of the total number of tubes. Reference 7 contains the detailed CFD analyses of 

CE plants. This is discussed later (See Section 3.6.6 for Figure 3-36, which shows the 

normalized incoming tube temperatures from this work). 

3.3.3 Conclusions from the CFD Analyses 

The ranges of the parameters are not a measure of the true uncertainty because only a modest 

number of cases are considered. A range gives some idea of the variations observed in the 

limited number of predictions completed. The table below summarizes the parameters found for 

W and CE SGs.

Table 3-1 The governing parameters for W and CE SGs 

Parameter

Average from 

NUREG-1922 W SG

Predicted range

CE SG

Cd, discharge coefficient 0.12 0.13–0.14

f, mixing fraction 0.96 0.65–0.75

r, recirculation ratio 2.4 1.05–1.10

hot tube fraction 41% 20–25%

Tn, normalized (hottest tube) 0.43 0.95–0.99

These updated predictions build upon previous studies and provide an updated set of 

parameters for use in 1-dimensional system codes to predict 3D natural circulation flows in 

PWR loops under severe accident conditions. The results are specific to the geometry and 

conditions used in this study and in NUREG-1922 and are not considered to be universally 

applicable. They are used in, and apply to the geometries for, NUREG/CR-6995 (Ref. 1) and in 

the CE analysis documented in this report.

3.4 Deck Modifications and Modeling Assumptions for the CE Analysis 

The SNL deck was modified to account for the spatial variation in tube temperatures to more 

accurately determine tube failure and to apply other lessons learned from the W analyses during 

the Steam Generator Action Plan work, which included NUREG/CR-6995. The changes include 

modifications to tubesheet heat transfer, generation of alternate methods to calculate the hottest 

SG tube temperatures, modifications to the RCS-to-containment heat transfer, a modification to 

the HL creep-rupture calculation, and modification of the HL natural circulation modeling to 

match updated CFD-generated mixing parameters. Minor changes were required to merge 

different versions of the decks.

The primary modification was the determination of the temperature of the hottest tube and the 

inclusion of a method to calculate this temperature within the MELCOR simulations. To reliably 
3-13

estimate the time of tube failure, the nonuniformity of tube temperatures must be considered. 

System codes such as MELCOR only provide an average temperature in the hot plume, not the 

hottest temperature. Characterizing the effect of the temperature distribution is of particular 

concern for CE plants with shallow-inlet-plenum replacement SGs, as even unflawed tubes in 

the hottest section of the SG are susceptible to failure.

Some modifications were made to model heat transfer from flowing gases to RCS components. 

Because the relative failure timing of SG tubes and other RCS components affects the 

occurrence of containment bypass, accounting for significant heat transfer mechanisms to RCS 

components improves the prediction of containment bypass. Some of the aspects that should 

be considered are accounting for radiative heat exchange between the HL wall and the gases 

flowing through it and ensuring that significant aspects of heat exchange in the RCS are 

accounted for.

One of the RCS heat transfer modifications was the restructuring of SG tubesheet heat 

structures. These heat structures were originally generated to be in contact with the secondary 

side of SGs and with the SG inlet and outlet plena but not with the tubes themselves. Because 

the SG tubesheets are in contact with far more surface area, and thus have far more heat 

transfer with the outside of tubes than with the secondary side and inlet plena, these heat 

structures were modified to be in contact with the SG tube fluid rather than the secondary-side 

and inlet-plena fluid.

An attempt was made to determine the relative contributions of radiative and convective heat 

transfer, but it was only partially successful. An alternate radiative heat transfer model was applied 

to the MELCOR plotfile output to check if it would match that in the output file. The alternate 

model was used because details of the MELCOR model were not readily available. The heat 

transfer coefficient (HTC) contribution estimates did not match the output file results very well. The 

FE analyses used the combined HTC. If the increase relative to fully developed conditions in the 

HL heat transfer coefficient, because of a thinner boundary layer, affects both the convective and 

radiative HTCs equally, then the distinction between the two need not be made.

Previous NRC analyses only adjusted the convective HTC for boundary layer effects in the 

entrance region (Ref. 1), whereas other analyses adjusted both the convective and radiative 

HTCs. If it cannot be established with sufficient confidence that the boundary-layer entrance 

effects affect both the radiative and convective HTCs equally, these boundary layer effects (and 

the separation of radiative and convective HTCs) should be revisited to apply separate factors 

to the convective and radiative HTCs.

The modeling of thermal radiation exchange between HL surfaces and gas flowing through the 

HL was reviewed and considered to be acceptable for screening purposes. Because the 

convective heat transfer modeling in system codes such as MELCOR typically uses correlations 

applicable for fully developed flow, the enhanced heat transfer in entrance regions where 

boundary layers are developing, such as at the entrance to the HL—the very location where the 

HLs are susceptible to failure—are likely underpredicted. It is for this reason that, if RCS and 

SG tube failure timings are similar, an FE calculation should be used to account for this 

nonuniform heat transfer.

The original cases did not initially consider a secondary-side relief-valve fail-open model. 

However, for appreciable FP releases to occur, some secondary-side relief valves must stay 

open. Otherwise, no pathway (other than potential system leakage) exists for releases to the 

environment. Failure models were therefore added to the deck. Two modes of main steam 
3-14

safety valve (MSSV) failure were originally assumed: that valves may stick open when they 

open fully following heatup and thermal expansion, and that valves may fail open after a fixed 

amount of cycles. Only the first of the two models was implemented. These failure modes did 

not result in predictions of MSSVs sticking open.

Two additional MSSV failure modes were added after the initial calculations. One is that MSSVs 

can fail open after the first opening in the event of a common-cause maintenance failure. The 

second is not a failure mode but rather accounts for procedures in which the secondary relief 

valves are intentionally opened to reduce pressure so that water can be pumped in, if available.

The creep-rupture modeling for the HLs was also modified for a sensitivity calculation. The 

standard creep-rupture model for a single-material tube consists of calculating the stress history 

in the tube and calculating, from this stress history and the material creep properties, the 

accumulated damage from creep as a function of time. When this accumulated damage history, 

referred to as either the creep or damage index, reaches a value of 1, the component is 

considered to have failed. The HLs are made up of two layers of material, carbon steel and 

stainless steel. The original deck modeled the creep-rupture failure of the two-layered HLs as 

follows: determine the stress for both whole HL layers together, as though made of a single 

substance. The stresses are expected to be somewhat different in both materials. A creeprupture index was then calculated for each layer, as though the entire wall thickness was made 

of that material. The maximum of the two creep-rupture indices was then used to calculate HL 

failure. This model effectively assumes that the entire HL is made up of the weaker HL material. 

If the thicker layer is not made up of this material, the HL failure would be predicted earlier than 

it should be. Because HL failure before SG tube rupture prevents the tubes from rupturing, the 

effective assumption of the entire HL being made of the weaker material (maximum index) could 

make the difference between containment bypass and no containment bypass. It could be that 

the decision to use the minimum-creep-strength material was made with the knowledge that the 

thick layer in the HL was made of this weaker material. Unfortunately, a detailed justification for 

the use of the maximum was also not described in detail. The potentially nonconservative model 

was therefore changed instead to use the minimum of the two materials’ creep-rupture indices 

to assess the potential impact. This change results in an effective assumption that the entire HL 

is made of the stronger material. While this is not ideal, it avoids a potential major 

nonconservatism in containment bypass calculations. This change delayed the HL failure time 

by nearly 2 1/2 hours. It would be preferable to find or develop a model that accounts for the 

different stresses in the materials, perhaps even accounting for the different thermal expansions 

of the materials; find a justification for omitting the thin-layered material; or use FE analyses.

A choice had to be made for the number of unflawed tubes that fail, because the creep failure 

model does not predict this and a model has not been developed to estimate this parameter. 

The failure of a flawed tube is assumed to result in the failure of the single tube. Multiple tubes 

can fail almost simultaneously, however, if unflawed tubes reach failure conditions. The number 

of tubes that fail depends on the shape of the spatial temperature distribution in the hottest part 

of the SG tube, the variability in strength because of manufacturing flaws, and the 

depressurization of the system that occurs as the initial tubes start failing. Expert elicitation of 

NRC staff members previously involved in the issue resulted in a range from 10 to 100 tubes 

failing. For the MELCOR simulations, a value of 20 unflawed tubes were assumed to fail upon 

prediction of creep rupture. A single tube failure was assumed for the average hot (flawed) tube. 

The PRA analysis in Chapter 7 does not use the MELCOR analysis assumptions and 

conclusions regarding tube failure.
3-15

The number of tubes that fail does not directly affect RCS component failure beyond the point at 

which depressurization time becomes much shorter than the tube-to-other-RCS-component 

creep-rupture time for a situation where SG tubes fail first. Although this number was not 

identified, it can vary, depending on conditions; the failure of 20 tubes is generally sufficient 

under the conditions modeled.

It should be noted that this is a simplified model that does not account for the factors considered 

by the PRA analysis described in Chapter 7. The PRA analysis does not use the MELCOR 

conclusions regarding tube failure. Chapter 7 only uses the TH (pressure and temperature 

profiles as a function of time) in the progression of an accident sequence studied in MELCOR. 

Section 7.2.1 further discusses the use of TH for failure modeling in the PRA.

These modifications, which were originally made to an earlier version of the SNL Calvert Cliffs 

MELCOR deck, were later merged with the final version of the SNL deck.

An early set of runs was made using these selected TH results for use as initial and boundary 

conditions for the FE and SG-calculator calculations of RCS component failure. Chapter 4 

discusses these calculations.

Other changes to the plant model were made after further review of the results. These changes 

consist of modifications to HL natural circulation modeling during the reconciliation of 

differences in RCS flows between MELCOR and the previous SCDAP/RELAP simulations. The 

changes consist of modifications to HL natural circulation modeling, to be consistent with the 

CFD results, and further changes to the MSSV fail-open model.

Two separate modifications were made to HL natural circulation models—one that consisted of 

stabilizing an existing active control method and a second, new, method that consists of 

reformulating the Froude-based relationship to a standard friction form and determining an 

effective loss coefficient that represents countercurrent flow losses. Both methods produced 

stable velocities consistent with those determined from the CFD and Froude-based velocities 

and those of the previous SCDAP/RELAP runs. After testing, the new friction-based formulation 

was chosen for continued use.

3.5 Loop Seal Clearing 

One of the issues not fully addressed in the analyses is loop seal clearing. Although limitations 

in the deck did not allow this topic to be addressed within the simulation, a conceptual model 

was developed to aid in understanding the phenomena. It is based on a consideration of the 

loop seal bubble behavior to determine the loop seal clearing behavior.

Loop seal clearing was covered during the work for NUREG/CR-6995 (Ref. 1). The issue had 

also been covered previously.

Loop seal clearing can result in significant consequences compared to those of closed-loop-seal 

natural circulation. Loop seal clearing results in the development of full-loop natural circulation. 

This reduces the mixing of hot gases before it enters the tubesheet. For sequences where 

closed-loop-seal natural circulation would already result in tube failure, a cleared-loop-seal 

condition would advance the predicted tube failure time. For sequences in which tubes would 

not be predicted to rupture under closed-loop-seal natural circulation conditions, clearing of a 

loop seal may result in SG tube rupture. Previous analyses have concluded that unflawed, and 

therefore multiple, tubes are susceptible to rupture under open-loop-seal natural circulation.
3-16

Figure 3-2 depicts the conceptual model for loop seal clearing. The system is considered as two 

different-sized manometers at different elevations, coupled on both ends. The bubble regions 

are considered to consist of vapor and potentially noncondensables. A heat source at one end 

represents the reactor core. The bubble at the other end represents the gas in the SG outlet 

plenum. The core bubble and SG bubble are considered to be connected. The center bubble 

between the two manometers represents the cold-leg bubble. Some limited flow area between 

the core region and the center cold-leg bubble represents core bypass leakage. Heat transfer is 

considered to be possible from the core to the cold-leg bubble across the downcomer. Heat 

losses are also considered from the cold leg to the environment. The term HT in the figure 

refers to heat transfer with net heat flow either into or out of the cold-leg bubble.

The term “loop seal” in this section without a further description describes the SG-to-cold-leg 

loop seal.

The loop seal behavior is considered by focusing on the behavior of the lower (cold-leg) bubble 

between the two loop seals. The primary considered mechanism of clearing occurs when this 

bubble size decreases to the point that the loop seal water level rises to the bottom of the cold 

leg. At this point, the cold leg behaves like a siphon, even if only partially liquid filled, allowing 

water to flow from the loop seal to the downcomer until gases can pass the loop seal. At this 

point, the loop seal is considered to be cleared. If the net bubble growth rate is negative, the 

water level will eventually rise to the point that it crosses over the HL to the downcomer if the 

downcomer seal does not somehow clear first.

Side-to-side liquid motion or bubble compression and expansion that can occur during 

perturbations, such as PORV openings, are considered to affect the clearing timing somewhat, 

but overall loop seal clearing behavior, including whether the seal clears or not, should be 

largely determined by the net bubble growth behavior.

Figure 3-2 Conceptual model of loop seal clearing 
3-17

The following bubble mass sources and sinks are considered to contribute to the bubble growth 

rate and thus the loop seal clearing behavior:

• leakage from the system through pump seal leaks

• leakage into the system by core bypass leakage

• condensation of bubble vapors by heat transfer to the containment through RCS piping

• evaporation of downcomer-to-core loop seal water by heat transfer from the hot 

core barrel

An equation that describes the bubble growth rate is:

Dm_bubble/dt = leak in – leak out + evaporation rate – condensation rate

Figure 3-3 shows the relevant mass flow rates that affect loop seal clearing. This figure shows 

the cumulative downcomer-to-upper-vessel flows, each of the pump seal flows, and the net 

mass flow rate of the two combined. The remainder (i.e., the difference of the plotted net from 0) 

is expected to be made up of phase change in the bubble region, rate of change of bubble size, 

flow across cleared upper (standard) or lower (downcomer-to-core) loop seals, or some 

combination of the three.

In the absence of bypass leakage, a nonheated vapor bubble would collapse because of heat 

transfer through the RCS to the containment. Heat transfer from the core barrel to the 

downcomer may result in evaporation countering bubble collapse.

Figure 3-3 Pertinent flows for loop seal clearing 

A downcomer-to-core seal clearing event involves a sufficient level change that the seal is 

expected to allow gases to bubble through the downcomer-to-core loop seal before the water 

level rises to the cold leg. These gases transferring from the core region can replenish the loop 

seal bubble. This would be a transient and not a permanent clearing. Gas reaching the loop seal 
3-18

bubble through the downcomer could possibly result in a drop of the downcomer water level and 

could reseal the downcomer-to-core loop seal.

Such transient clearing, if the loop seal water inventory is insufficient to rise to the cold leg 

without gases passing through, can also occur for the loop seal, depending on geometry.

If sufficient leakage exists between both manometer bubbles (i.e., bypass leakage in the 

reactor) vapor can flow through the leak path to preserve the loop seal bubble or create a loop 

seal bubble if it does not already exist.

Loop seal water level changes alter the pressure drop between the two gas regions. If the 

pressure drop is less than the head of water required to reach the cold leg, the water level will 

not reach the cold leg, it will stabilize at a lower level, and the loop seal will not clear.

Previous SCDAP/RELAP results show significant cooling of the loop seal water after about 

8,000 seconds into the transient. Because of this, it is likely that, instead of forming a bubble, 

the steam will rapidly collapse and heat the water in the cold leg. Noncondensables could get 

trapped in the void region if this occurs before the seal is cleared. Despite the fact that the loop 

seal liquid appears to be cooling, the liquid level in the loop seal continues to decrease.

To summarize, in the absence of noncondensables and leaks, the bubble is expected to do 

the following:

• collapse (clear loop seal) if heat transfer out is greater than heat transfer in

• not collapse if heat transfer out is less than heat transfer in

Other expected behavior includes the following:

• Bubble will not collapse without net out leakage if sufficient noncondensables present.

• Leak out (pump seal leakage) accelerates bubble collapse.

• Leak in from upper vessel through core bypass counters bubble collapse.

• If the bubble shrinks (i.e., dm/dt < 0), then one of the following three things will happen

depending on system geometry and liquid inventory in both loop seals:

– The cold leg loop seal will clear.

– The core-to-downcomer loop seal will clear.

– The pressure difference will sufficiently change parameters (leaks and evaporation)

such that a steady state is reached (i.e., dm/dt = 0).

Both loop seals shown in Figure 3-2 for an individual RCS loop must clear for open-loop-seal 

natural circulation to occur.

If the lower downcomer-to-core loop seal is cleared, perturbations such as PORV openings are 

not expected to be sufficient to clear the loop seal, as similar pressure drops will occur on both 

sides of the loop seal.

If the loop seal clears first, the downcomer-to-core loop seal may subsequently clear by a 

reduction in water level through evaporation.
3-19

3.6 Analysis Results 

3.6.1 Discussion of MELCOR Analyses 

Two sets of simulations were conducted, one in October 2012 and another in 2013. The 2013 

set of simulations was run because HL flow rates in MELCOR under natural circulation for the 

October runs were found to be higher than those of the FLUENT and SCDAP/RELAP 

simulations. Higher HL velocities prefer tube over HL failure. To properly characterize 

component failure timing, it is essential that the HL flow rates be representative. Additional 

review indicated that the HL natural circulation modeling in the MELCOR deck needed to be 

modified to match updated FLUENT results.

The 2013 runs used the updated HL natural circulation modeling. The primary difference 

between the 2013 and 2012 runs is this modeling change. A second difference is that no 

secondary SG leakage to containment was assumed for most of the 2013 runs. Instead, 

updated MSSV stick-open modeling, the third difference, was relied upon to establish 

secondary-side pressure. The change to no-secondary-leakage and updated MSSV stick-open 

modeling was made because of the finding that assuming even 20 tubes to rupture at low 

pressure was not sufficient to fully open the MSSVs, which was the original simulated criterion 

for sticking to occur. Some of the MSSVs did partially open.

Section 3.6.3 provides plots and tabulations of select results.

Although a single case was desired, other cases had to be run to address behavior that had not 

previously been considered. A notable parameter that led to the requirement of more runs was 

the effect of sticking assumptions for secondary-side relief valves. Assumptions about 

secondary-side relief valves failing open, which was not a parameter originally focused on, was 

found to be a major parameter in system behavior. This was because previous analyses did not 

model secondary relief valve behavior but assumed that a bypass would occur if SG tubes failed 

or some fraction of the time that the tubes failed. It was found that, if valve failure was not 

explicitly modeled as an assumption, no appreciable releases would occur even if SG tubes had 

ruptured. The simulations had to be run repeatedly to come up with relief valve behavior that 

resulted in releases to the environment:

• assuming failure upon full valve opening following a tube rupture did not change 

releases, as the valves did not fully open and thus did not stick

• assuming a stick-open-failure upon full valve opening at any time also did not result in 

appreciable releases because, even for those cases, the valves did not stick open

• assuming that secondary-side relief valves stick as far as they have opened or assuming 

that they are opened by operators did result in releases

It appears that the secondary-side valves are not as pressure stressed when the tubes rupture 

several hours into the accident, so they do not leak. They may be thermally stressed, which is 

not considered for the valve-opening model.

The valve failure criteria were varied, not based on failure data, but rather to evaluate the failure 

criteria that would possibly result in FP releases to the environment. During the analyses for the 

Steam Generator Action Plan, tube failure was the criterion used to consider that containment 

had been bypassed. The initial CE simulations indicated that, if tubes failed while the SG 

secondary side was depressurized, the secondary-side relief valves opened for a short period 
3-20

before closing (if they opened at all), resulting in a small amount of FP releases to the 

environment. This behavior may be scenario dependent.

The base sequence consisted of a long-term SBO (ltsbo) with the TDAFW system and batteries 

assumed to be operating for 4 hours. The initial cases assumed a secondary-side-tocontainment leakage to ensure that the SG secondary sides were at low pressure. This 

approach for reducing SG secondary pressure has not been universally accepted. Cases with 

no SG-secondary-to-containment leakage were run using an MSSV stick-open model in which 

the valves were assumed to stick to the extent they had been predicted to open by the code. A 

situation was also simulated in which operators open the secondary-side relief valves soon after 

the accident to reduce SG secondary pressure to allow water to be pumped in.

Case run times were set based on the primary need to evaluate the TH system behavior. 

Because of this, some of the cases terminated before parts of the release occurred. Therefore, 

the release fractions listed in this table do not represent the total release fraction but the release 

fraction at the time of problem termination. On the other hand, the SG secondary-side 

decontamination determined from the Aerosol Trapping in Steam Generator (ARTIST) project 

was not included, which would reduce predicted releases. This decontamination would be 

expected to reduce release potentially by about a factor of 5. This decontamination factor 

cannot be directly applied to the result because the decontamination is particle-size dependent 

and because the decontamination would replace and not add to the SG decontamination 

already calculated by MELCOR during the run.

Two of the 2013 cases are considered representative, although the results are very different. 

Both cases use the updated natural circulation modeling. The difference between the -a case is 

otherwise identical to the base case. For the -as case, the secondary-side-to-containment 

leakage shut off and the MSSVs are assumed to stick open as far as they have been predicted 

to open by the code.

Whether the MSSV was assumed to stick open and whether SG secondary was assumed to 

leak to containment resulted in very different behavior. MELCOR predicted HL failure first and 

no environmental releases for the case with SG secondary-to-containment leakage and noMSSV-sticking model. For the case with the SG secondary-to-containment leakage and noMSSV-sticking model, the tubes were predicted to fail first with calculations predicting FP 

releases to the environment.

The ltsbo case with no secondary-side-to-containment leakage and sticking MSSVs had a Cs 

release of about 5 percent at the time the run terminated. This was, by far, the highest release 

of all run cases. For this sequence, FPs were being released at a significant rate at the end of 

the simulation so the actual predicted release fraction (RF) will be higher if the simulation is 

extended. To obtain the code-calculated RFs for the cases in question, the simulations would 

have to be run until the RFs reached their asymptotic values or at least beyond the time when 

risk analyses estimated that mitigative actions would occur.

Some of the sequences stopped upon reflood when a smaller time step would be required for 

stability. Because the primary purpose of the runs was to obtain the TH histories, the cases 

were not rerun if sufficient data were output to characterize TH behavior.

Other cases were run as needed to characterize unexpected behavior. These included cases to 

establish a suitable secondary-side relief-valve failure model, to assess the importance of 
3-21

parameters, and for somewhat different sequences, to address additional issues that 

were raised.

One of these was the high-dry-high sequence (high primary pressure, dry secondary side, high 

secondary pressure). This involved no SG-secondary-to containment leakage. Although an 

MSSV stick-open model was used that would predict sticking if valves fully opened, they did not 

do so. Even for HL flows that were higher than the CFD calculated, little damage occurred to 

tubes by the time the HLs failed.

This report added Appendix I to discuss melting temperatures and steel oxidation.

Appendix J discusses loop seal clearing considerations, both from a MELCOR modeling and 

from a PRA modeling point of view.

3.6.2 Summary of Accident Sequences Studied and Nomenclature 

This section summarizes the accident sequences modeled and analyzed by MELCOR. It also 

provides the nomenclature that is later used in the Section 7.2 PRA. The TH results from 

selected cases provide input for the PRA analysis.

Table 3-4 gives an inventory of CE MELCOR runs considered for the PRA, which considered 

12 cases. The base sequence being modeled (stsbo) is a high-pressure SBO with the 

following conditions:

• All emergency core cooling systems fail.

• TDAFW fails.

• Accumulators are operable.

• Dc power functions for 4 hours.

• There is a 3.23-cm2 (0.5-in.2

) leak in the SG secondary side.

• There is a 0.085-cm2 (0.013-in.2

) leak in loop seals through RCP seals (results in a 

~79.5 liters per minute (~21 gallons per minute) leak of water at high SRV-setpoint).

• Creep failure of AvgHot tube, which represents failure of a single flawed tube, is 

assumed to result in the opening of a flow area equal to a double-ended guillotine break 

(DEGB) of 1 tube (i.e., 2 tube flow areas).

• Creep failure of the hottest tube, which represents failure of unflawed tubes, results in 

the opening of a flow area equal to a DEGB of 20 tubes (40 tube flow areas).

For the equivalent ltsbo case, the TDAFW system functions for 4 hours.

Figure 3-4 shows the cases that were run. They are separated into two groups: the top group 

represents the original October 2012 cases, and the bottom group represents the July 2013 

cases that included modifications to the HL natural circulation modeling.2 The arrows from each 

 2 The stsbo-mssvstick model was run in 2013 and incorporated the alternate natural circulation modeling 

with a low effective counter-current-flow loss coefficient (which then results in a higher flow rate during 

closed-loop-seal natural circulation.)
3-22

deck point to its derivative decks. The smaller text indicates the deck files that were altered from 

the source deck.

Figure 3-4 Organization of C-SGTR decks 

The following are the October 2012 cases:

• stsbo base deck

• ltsbo the stsbo deck with TDAFW functioning for 4 hours and a longer run time

• modified versions of the stsbo and ltsbo cases:

– -SCF runs have creep failure suppressed.

– -MSSV1F runs modify the corresponding case with failure of MSSV assumed if they

open fully following an SGTR event.

– -noSGleak runs modify the corresponding case by removing secondary leakage.

This modification provides the high-dry-high scenario (high secondary pressure 

in addition to high primary pressure and dry secondary), if secondary-side relief 

valves are assumed to not stick open.

– -noSGleak-MSSV1F runs modify the corresponding case by applying both

no-secondary-side leakage and stick-open valve after full opening of secondary 

valve.

– -noSGleak-MSSV1F-minHLC same as -noSGleak-MSSV1F but uses the minimum

rather than the maximum of the two HL creep-rupture indices to predict failure. 

No ltsbo case was run.

– -sidecalcbc Original hottest tube calculation method. This method was replaced and

this document does not include results for it. 
3-23

The second set of cases in 2013 consisted of additional modifications to the original 

input decks:

• -fixnc Multiple stsbo decks used in modified natural circulation modeling method.

• -altnc Multiple stsbo decks used an alternate natural circulation model. The only 

difference between the different versions of this deck is that the effective counter-current 

loss coefficient is being numerically solved for. Versions 1–9 represent different stages 

in the iteration.

• -MSSVstick An MSSV sticking model was added, for which valves open, along with a 

low-resistance counter-current-flow loss coefficient using the alternative HL natural 

circulation modeling. No ltsbo case was run.

• -a This is the base deck with altered HL natural circulation modeling. It is the -altnc deck, 

which uses the “converged” counter-current-flow loss coefficient model so that the HL 

flow matches that predicted by the FLUENT CFD code (-altnc3).

• -as This is the -a alternate natural circulation deck with the secondary-to-containment 

leakage area closed and MSSVs sticking open as far as the code has predicted that they 

open. This MSSV sticking model can represent either a common-mode maintenance 

failure where the valves stick or operator action to open the valves.

• -ao This is the -a alternate natural circulation deck with the secondary-to-containment 

leakage area closed and full opening of secondary PORVs and MSSVs soon after the 

SBO. This simulates operator action to reduce secondary pressure. No ltsbo case 

was run.

• -as-SCF This is the -as case with component failure suppressed.

An additional –a-SCF (the –a case with component failure suppressed) was run upon request 

following the other analyses solely for the purpose of providing input for the C-SGTR calculator. 

The results for this case were not processed other than to provide data for the calculator.

3.6.3 Select CE Sequence Results 

Code results have been plotted for select cases. The output parameters presented include 

system pressures, structure temperatures, select RCS component creep-rupture indices, liquid 

levels, and gas concentrations. Select events are listed. Creep-rupture indices for the average 

tubes were also plotted for each case for stress multipliers ranging from 1 to 2.5.

Table 3-2 shows the timings of some of the major events for select sequences. The cases are ordered 

by time of initial gap release. Major features of the accident progression are discussed below.
3-24

Table 3-2 Timing of Selected Events 

Time (h)

Event 

stsboas stsbo-ao stsbo-a stsbo ltsbo-a ltsboltsboas

Station Blackout 0.0 0.0 0.0 0.0 0.0 0.0 0.0

Loss of TDAFW 0.0 0.0 0.0 0.0 4.0 4.0 4.0

ST Rupture Disk 1.8 1.6 2.1 2.1 9.1 9.0 14.1

Initial Gap Release 4.1 4.3 5.1 6.0 12.7 13.6 19.4

SG Tube Rupture 4.4 4.7 - 6.3 - 13.7 19.8

HL Rupture - - 5.9 7.2 13.2 14.7 -

Accumulator 

injection 4.7 0.1 5.9 7.3 13.2 14.7 1.7

The original stsbo base case will be used as the reference case, since all subsequent runs were 

compared to it. Some notable differences in other cases are also shown. The figures are listed 

first, as the chronological walkthrough below covers all cases simultaneously.

Several figures for the base case are provided: Figure 3-5 shows the main system pressures for 

the stsbo calculation. These pressures include primary system pressure, SG A and SG B 

secondary-side pressures, and containment pressure. Figure 3-6 shows the SG secondary 

collapsed liquid level for the stsbo calculation. Figure 3-7 shows the main structure 

temperatures for the stsbo calculation. Figure 3-8 shows the creep-rupture indices for the stsbo

calculation. Failures calculated with these components affected the accident sequence and 

subsequent TH behavior. Figure 3-9 shows the creep-rupture indices for various stress 

multipliers on the hot-average tubes for the stsbo calculation. These indices were only 

evaluated to obtain an indication of the flaw size that would be necessary to cause a failure and 

did not otherwise affect results (i.e., these failure predictions did not influence subsequent TH 

behavior). Figure 3-10 shows the hydrogen concentrations in different locations in the SG A 

tubes for the stsbo calculation. Figure 3-11 shows the volatile FP release fractions for the 

stsbo calculation.

A smaller set of figures are provided for the original ltsbo case. This set of figures includes 

pressures, SG water levels, and structure temperatures, along with direct comparisons of these 

pressures and structure temperatures to those of the stsbo calculation. These calculations 

demonstrate that the ltsbo calculation can be reasonably approximated by a time-shifted 

stsbo calculation.

Figure 3-12 shows the main pressures for the ltsbo calculation. Figure 3-13 shows the SG 

secondary collapsed liquid level for the ltsbo calculation. Figure 3-14 shows the main structure 

temperatures for the ltsbo calculation. Figure 3-15 compares the main pressures in the ltsbo

calculation to those of the stsbo calculation. Figure 3-16 compares the ltsbo calculation SG 

secondary-side collapsed liquid levels to those of the stsbo calculation. Figure 3-17 compares 

the ltsbo calculation loop A structure temperatures to those of the stsbo calculation. Figure 3-18 

compares the ltsbo calculation loop B structure temperatures to those of the stsbo calculation.
3-25

Figure 3-5 Main pressures for the stsbo calculation 

Figure 3-6 SG secondary collapsed liquid level for the stsbo calculation 
3-26

Figure 3-7 Main structure temperatures for the stsbo calculation 

Figure 3-8 Creep-rupture indices for the stsbo calculation 
3-27

Figure 3-9 HotAve tube creep-rupture indices for the stsbo calculation 

Figure 3-10 Hydrogen concentrations in SG A tubes for the stsbo calculation 
3-28

Figure 3-A Volatile FP release fractions for the stsbo calculation 

Figure 3-B Main pressures for the ltsbo calculation 
3-29

Figure 3-13 SG secondary collapsed liquid level for the ltsbo calculation 

Figure 3-14 Main structure temperatures for the ltsbo calculation 
3-30

Figure 3-15 Comparison of ltsbo pressures to those of stsbo 

Figure 3-16 Comparison of ltsbo SG boiler collapsed liquid levels to those of stsbo 
3-31

Figure 3-17 Comparison of ltsbo loop A structure temperatures to those of stsbo 

Figure 3-18 Comparison of ltsbo loop B structure temperatures to those of stsbo 

A full set of figures is provided for the ltsbo-a case because this is the case that experienced the 

highest releases before the calculation terminated. Figure 3-19 shows the main system 

pressures for the ltsbo-a calculation. Figure 3-20 shows the SG secondary collapsed liquid level 

for the ltsbo-a calculation. Figure 3-21 shows the main structure temperatures for the ltsbo-a
3-32

calculation. Figure 3-22 shows the creep-rupture indices for the ltsbo-a calculation. Figure 3-23 

shows the creep-rupture indices for various stress multipliers on the hot-average tubes for the 

ltsbo-a calculation. These were only evaluated to obtain an indication of the flaw size that would 

be necessary to cause a failure (i.e., these failure predictions were not made to influence 

subsequent TH behavior). Figure 3-24 shows the hydrogen concentrations in different location 

in the SG A tubes for the ltsbo-a calculation. Figure 3-25 shows the volatile FP release fractions 

for the ltsbo-a calculation.

Figure 3-19 Main pressures for the ltsbo-as calculation 

For other cases in the newer set of calculations, only the system pressures and volatile FP 

releases are provided. Figure 3-26 shows the main pressures for the stsbo-a calculation. 

Figure 3-27 shows the volatile FP release fractions for the stsbo-a calculation. Figure 3-28 

shows the main pressures for the ltsbo-a calculation. Figure 3-29 shows the volatile FP release 

fractions for the ltsbo-a calculation. Figure 3-30 shows the main pressures for the stsbo-as

calculation. Figure 3-31 shows the volatile FP release fractions for the stsbo-as calculation. 

Figure 3-32 shows the main pressures for the stsbo-ao calculation. Figure 3-33 shows the 

volatile FP release fractions for the stsbo-ao calculation.

This set of figures provides a fairly complete indication of results for the second set of 

simulations when considering the similarities in system behavior from case to case.
3-33

Figure 3-20 SG secondary collapsed liquid level for the ltsbo-as calculation 

Figure 3-21 Main structure temperatures for the ltsbo-as calculation 
3-34

Figure 3-22 Creep-rupture indices for the ltsbo-as calculation 

Figure 3-23 HotAve tube creep-rupture indices for the ltsbo-as calculation 
3-35

Figure 3-24 Hydrogen concentrations in SG A tubes for the ltsbo-as calculation 

Figure 3-25 Volatile FP release fractions for the ltsbo-as calculation 
3-36

Figure 3-26 Main pressures for the stsbo-a calculation 

Figure 3-27 Volatile FP release fractions for the stsbo-a calculation 
3-37

Figure 3-28 Main pressures for the ltsbo-a calculation 

Figure 3-29 Volatile FP release fractions for the ltsbo-a calculation 
3-38

Figure 3-30 Main pressures for the stsbo-as calculation 

Figure 3-31 Volatile FP release fractions for the stsbo-as calculation 
3-39

Figure 3-32 Main pressures for the stsbo-ao calculation 

Figure 3-33 Volatile FP release fractions for the stsbo-ao calculation 
3-40

All simulated accident sequences start with an SBO, which includes a loss of offsite power and 

a failure of emergency generators to start. The reactor and equipment are assumed to 

successfully trip. Valves, including main steam isolation valves (MSIVs), are assumed to close 

as planned. For some scenarios, the TDAFW pump was assumed to fail to start. Batteries are 

assumed to deplete at 4 hours. For others, the TDAFW pump was assumed to continue 

operating until assumed battery depletion at 4 hours. Scenarios for which the TDAFW pump 

was assumed to fail to start are referred to as short-term station blackout (stsbo). Scenarios for 

which the TDAFW pump was assumed to remain functional until batteries are depleted are 

referred to as long-term station blackout (ltsbo).

The loss of reactor power coupled with the continued removal of heat by the SG cools the 

system, which results in the condensation of steam and a reduction in system pressure. This 

can be seen in any of the main pressure figures (e.g., Figure 3-5).

As long as substantial water remains in the SG, secondary-side pressure is governed by the 

setpoint of the governing safety valves. This pressure is governed at first by the secondary 

PORVs (e.g., Figure 3-5), unless, for some reason, valves open at this time either by sticking or 

by operator action.

If secondary relief valves are open, this not only reduces the secondary pressures and 

temperatures down but it also reduces primary pressures. This occurs for both sticking (-as 

cases) (e.g., Figure 3-19) and by valve opening by operator action (-ao case), Figure 3-32. 

MELCOR predicted the pressure drop to be sufficient to drop pressures below the accumulator 

activation setpoint.

If the TDAFW pump remains operational (ltsbo cases), water remains in the secondary side 

when the batteries deplete and TDAFW pump fails. In this case, the secondary-side pressure is 

governed by the MSSVs. This can be seen as a jump in secondary pressure at 4 hours 

(14,400 s) for the ltsbo cases in which secondary valves are not open early on (i.e., ltsbo and 

ltsbo-a) (e.g., Figure 3-12 and Figure 3-28, respectively).

When the TDAFW pump stops replenishing water to the SGs, water in the SG secondary sides 

boils off. The boil-off begins soon after accident initiation for stsbo cases (e.g., Figure 3-6) and 

after the batteries deplete for ltsbo cases (e.g., Figure 3-13). Except for some 

RCS-to-containment heat losses, nearly all core decay power contributes to this boil-off as long 

as sufficient water is available in the SG secondary sides to reject the decay heat.

The SG water eventually boils off to a level at which the SGs can no longer remove all the 

decay heat. The primary pressure then begins to rise until the governing primary relief valve 

setpoint is reached. Before battery depletion, the PORVs govern the primary pressure. The 

SRVs govern the primary pressure following battery depletion.

During this time decay, heat boils off the primary inventory. When the core is liquid covered, 

temperatures stay at saturation. The saturation temperature can be seen to increase with 

increased primary pressure (e.g., Figure 3-7). Eventually the core uncovers and structure 

temperatures begin to rise. This rise is nearly linear in time.

This temperature rise occurs a little slower for the ltsbo cases because of the lower decay heat. 

This can be seen in Figure 3-17. Other than this minor effect, the ltsbo behavior is very similar 

to that for the equivalent stsbo case (Figures 3-15 through 3-17).
3-41

What differentiates one case from another is the timing of boil-off of both secondary and primary 

inventories and of the time those temperatures start to rise. Otherwise, scenario progression is 

rather similar. Cases where secondary valves are open lose heat sink faster than those that do 

not. If the valve opening cools the system and drops the primary system pressure below to the 

accumulator setpoint pressure, this additional water inventory delays the heatup time.

When the core is uncovered, the hot gases coming from the core establish a closed-loop-seal 

natural convection pattern, as described above. These hot gases heat up RCS structures, 

including the HLs and the SG tubes. The calculations predict the surge line to remain relatively 

cool from the presence of liquid water.

As mentioned earlier, a failure of an RCS component releases FPs to the containment, whereas 

the failure of tubes could result in FPs bypassing the containment and being released to the 

environment. The failure of another RCS component before SG tubes is preferred because the 

containment is not bypassed.

The SG tubes more closely track the adjacent gas temperature because they are thin and 

therefore have a short thermal response time. Thicker structures such as HLs respond more 

slowly to the adjacent gas temperature. The gas temperature adjacent to the tubes is somewhat 

cooler because of mixing with cooler gases between the HLs and the tubes.

When the structure temperatures increase sufficiently, the pressure differential across them can 

result in creep. The accumulated damage for vulnerable structures is tracked using 

creep-rupture indices. When a given creep-rupture index reaches a value of 1, that structure is 

considered to have failed. The creep-rupture indices, assuming no flaws in structures, are used 

to predict thermal and hydraulic system response (e.g., Figure 3-8).

For some scenarios the hottest SG tubes in loop B, the loop without the pressurizer, failed first, 

but the pressure remained high enough for other RCS components (i.e., HL) to subsequently fail 

(e.g., stsbo, ltsbo). For other cases, RCS components other than the SG tubes failed first, 

thereby depressurizing the primary system and preventing tube failure (e.g., stsbo-a, ltsbo-a). 

For still others cases, the hottest SG tubes failed first but depressurized the system sufficiently 

to prevent the failure of other RCS components (e.g., stsbo-as, ltsbo-as, stsbo-ao).

Although they did not otherwise influence the calculation, creep-rupture indices for hot average 

tubes for stress multipliers ranging from 1 to 2.5 were evaluated to give an indication of the tube 

failure timing for different sized flaws (e.g., Figure 3-9).

Components fail near the time of rapid zirconium (Zr) oxidation. A sharp rise in hydrogen 

concentrations provides an indication of when this occurs (e.g., Figure 3-10).

In cases where the HLs fail first, no bypass releases to the environment occur.

For scenarios that included SG secondary leakage to containment and no assumed valve failure 

or operator opening of these valves, either minimal release occurred because one of two things 

happened: (1) the secondary relief valves opened very briefly before FPs were leaked to the 

containment through the assumed leakage (stsbo, Figure 3-11, and ltsbo) or (2) the leakage 

kept the SG secondary pressure low enough that the secondary relief valves remained seated 

and no bypass FPs were released at all (e.g., stsbo-a, Figure 3-27, and ltsbo-a, Figure 3-29).
3-42

Cases that involved intentional opening or failed open secondary relief valves resulted in 

releases to the environment (stsbo-as (Figure 3-31), ltsbo-as (Figure 3-25), and stsbo-ao

(Figure 3-33)). Note that releases are not terminated for these cases. These cases were run to 

evaluate the TH behavior. They would have to be rerun to fully evaluate FP bypass releases.

Table 3-3 shows the RCS failure times and RFs to the environment. Because the primary 

purpose of the runs was to obtain the TH histories, cases were not rerun if sufficient data were 

output to characterize TH behavior. Because of this, some of the cases terminated before some 

of the release occurred. Therefore, the RFs listed in this table do not represent the total RF but 

the RF at the time of problem termination. It instead represents the releases when the more 

stringent time step restrictions upon material relocation or reflood caused the calculation to 

terminate. On the other hand, the SG secondary-side decontamination determined from the 

ARTIST project, which was not included, would reduce predicted releases. This 

decontamination would be expected to reduce the release potentially by about a factor of 5. This 

decontamination factor cannot be directly applied to the result because the decontamination is 

particle-size dependent and because the decontamination would replace and not add to the SG 

decontamination already calculated by MELCOR during the run.

Table 3-3 Failure Times and Release Fractions to Environment 

stsbo ltsbo

Fail t(h) RF** Fail t(h) RF**

SG HL SG HL

-a - 5.9 - - 13.2 -

-as 4.4 - *

0.006 19.8 - *0.048

-as-SCF 4.4 4.9 N/A 19.8 19.9 N/A

“base” 6.3 7.2 0.003 13.7 14.7 0.001

-SCF 6.3 6.5 N/A 13.7 13.9 N/A

-ao 4.7 - *

0.007 N/A N/A N/A

-MSSVstick 4.5 - *

0.009 N/A N/A N/A

-noSGleak - 8.1 - - 16.1 -

-MSSV1F 6.3 7.2 0.003 13.7 14.5 -

-noSGleak

-MSSV1F - 8.1 - - 16.1 - 

-noSGleak

-MSSV1F

-minHLC

N/A*** - 18.5 - 

* RF at the time of calculation termination. Releases are ongoing.

** Maximum of volatile (Cs, I, and Te) release fractions.

*** Case did not run to failure time.

3.6.4 Data Output Fields Provided for Use by External Failure Calculator and 

FE Analyses 

Data files are transmitted to perform independent assessments of component failure. The data 

channels in these files are generally labeled by parameter (e.g., P for pressure, T for 

temperature), location, and material. 
3-43

The main datafile for each loop provides the following data channels. Loop A labels are shown 

here. Data in items 1 through 7 are used as the TH input for the C-SGTR calculator in the 

Section 7.2 PRA analysis.

(1) Time

(2) Pp Primary system pressure

(3) TSL−s Inside surface temperature of the surge line

(4) TH LAt−s Inside surface temperature of the top of the HL 1

(5) TSGAhu−s Inside surface temperature of the hot-up 2 SG tubes

(6) TSGAcd−s Inside surface temperature of the cold-down SG tubes

(7) PsA Secondary-side pressure for SG

(8) TH LAt−g Gas temperature in the top of the HL

(9) TH LAb−s Inside surface temperature in the bottom of the HL

(10) TH LAb−g Gas temperature in the bottom of the HL

(11) TSGAhu−g Gas temperature in the hot-up SG tubes

(12) TSGAhd−g Gas temperature in the hot-down SG tubes

(13) TSGAhd−s Inside surface temperature of the hot-down SG tubes

(14) TSGAcd−g Gas temperature of the cold-down SG tubes

(15) TSL−g Gas temperature in the Surge Line

(16) hH LAt Heat transfer coefficient for the top of the HL

(17) hH Lab Heat transfer coefficient for the bottom of the HL

(18) hSGAhu−in Heat transfer coefficient on the inside of the hot-up SG tubes

(19) hSGAhu−out Heat transfer coefficient on the outside of the hot-up SG tubes

(20) ThA Thot used to scale the CFD hottest tube results. This is the gas

 temperature entering the SG inlet plenum from the HL

(21) TSGA−boil Gas temperature in the SG secondary side

(22) Pc1 Containment pressure

(23) TSGAhot−s The hottest tube temperature calculated with the side calculation

(24) TH LAt−smid HL temperature at middle

(25) TH LAt−sout HL outer surface temperature

Notes:

(1) HL temperatures are provided for the control volumes and heat structures that are 

adjacent to the reactor vessel. Tube temperatures are provided for the control volumes

and heat structures adjacent to the tubesheet. Surge-line temperatures are provided for 

the control volumes and heat structures adjacent to the HL.

(2) Up and down refer to the direction of flow during closed-loop-seal natural circulation. For 

example, hot up and cold down both represent tube sections adjacent to the SG inlet 

plenum. The surge-line temperatures were also provided in the data for loop B to 

preserve the data channel numbering.

(3) The SG-tube HTCs were used to estimate the hottest tube temperature using the CFD 

and the AvgHot tube results, which are provided in the datafiles.

The supplemental datafile provides the hottest SG tube gas and surface temperatures 

calculated from the output data, along with the parameters used to determine these values.
3-44

The supplemental datafile (-addl) for each loop provides the following data channels.

(1) Time

(2) TSGA−g−peak Hottest tube inlet gas temperature calculated using the CFD 

normalized temperature (see Figure 3-36), Thot, and Tcold. 

(3) ThA Thot used to scale the CFD hottest tube results. This is the same 

data as ThA in the main datafile.

(4) TcA Tcold used to scale the CFD hottest tube results. This is the same 

as the cold-down SG gas temperature in the main datafile.

(5) TSGA−g−mean Hot-up tube gas temperature to compare to the calculated 

gas temperature

(6) TSGA−s−peak Hottest tube temperature determined by a heat transfer calculation 

using secondary and calculated hottest-tube-primary gas 

temperatures along with the inside and outside heat 

transfer coefficients

(7) TSGA−s−mean Hot-up tube surface temperature to compare to the calculated 

tube temperature. This is the same curve as in the hot-up SG tube 

temperature in the main datafile.

(8) TSGA−boil SG secondary-side gas temperature. This is the same curve as in 

the main datafile.

3.6.5 MELCOR Cases to Support the C-SGTR Calculator 

Section 7.2 summarizes the use of the temperature and pressure profiles of the selected 

accident sequences for the C-SGTR calculator. These profiles are used as input files to the 

C-SGTR calculator to study the SG tube leak generation and HL and surge-line failure for given

flaws and materials.

Other examples of T&H files created from MELCOR output files as input files for the C-SGTR 

calculator can be found in the Appendices; Appendix D gives such an example.
3-45

Table 3-4 MELCOR Cases to Support C-SGTR Calculator 

AFW 

Fails 

at 

T=0

AFW 

Fails 

at T=4 

h

RCS 

Loop A 

(with 

PRZR)

RCS 

Loop 

B 

Secondary

-Side Leak 

at 0.5 in2

SecondarySide Relief 

Valve 

Sticks 

Open

Creep 

Rupture 

Suppressed

1 stsbo-a-SCF-a √ √ √ Yes

2 stsbo-a-SCF-b √ √ √ Yes

3 ltsbo-a-SCF-a √ √ √ Yes

4 ltsbo-a-SCF-b √ √ √ Yes

stsbo-as-SCF-a √ √ √ Yes

stsbo-as-SCF-b √ √ √ Yes

ltsbo-as-SCF-a √ √ √ Yes

ltsbo-as-SCF-b √ √ √ Yes

stsbo-a-a √ √ √ No

stsbo-a-b √ √ √ No

ltsbo-a-a √ √ √ No

ltsbo-a-b √ √ √ No

Cases 1 through 4 are used in the base case analyses in Section 7.2.

3.6.6 MELCOR Cases to Support RCP Seal Leakage Sensitivity Evaluation 

A TH sensitivity case was run to study the impact of RCP seal leakage on primary pressure, 

while failure timings of C-SGTR addressed the much smaller RCP seal leakages of a CE plant. 

The previous MELCOR runs considered an assumed 79.5 Lpm (21 gpm) RCP seal leakage for 

each RCP seal for the CE plant to be consistent with the W calculations. The question arose 

regarding the impact of this seal leakage on primary system pressure during auxiliary feedwater 

operation and how much it would change if CE seals leaked far less. To look at this issue, the 

base case was run with RCP seal leakage disabled (i.e., zero seal leakage flow).

Figure 3-34 compares the pressures predicted for the base case and for the no-seal-leakage 

case. Figure 3-35 shows structure temperatures, the ones that provide most stress for loop B, 

the loop that fails first. Preventing RCP seal leakage results in substantially less reduction in 

primary system pressure. Preventing RCP seal leakage also preserves inventory in the primary 

system, thereby delaying the temperature rise and thus component failure by nearly 10 minutes.
3-46

Figure 3-34 Primary pressure and secondary pressure for SG A and B for base case of short 

SBO with and without RCP seal leakage 

Figure 3-35 The HL structure and peak SG tube temperature for loop B for base case of short 

SBO with and without RCP seal leakage 
3-47

Figure 3-36 Normalized temperature distribution at the SG tube sheet inlet for a CE plant 

 

3.7 Potential Future Analyses 

Several aspects of the modeling and analyses were not pursued at this time in the interest of 

reducing the number of cases run and the level of effort involved with the idea of finding a 

representative “limiting” analysis. Additional analyses can be performed to explore pertinent 

aspects of system behavior and regions of the event tree and to look into different sensitivities in 

more detail.

Additional modeling may include the following:

• updating the deck to handle loop seal clearing, which involves switching SG tube natural 

circulation modeling from an active control to a friction-based method and a 

renodalization of the SG tubes and cold legs

• review of surge-line draining behavior and reconciliation of modeling

• performing a detailed review of HL creep-rupture modeling and materials

• updating some nodalization connectivity issues; double checking parameters found to 

significantly affect system behavior

• application of ARTIST SG decontamination factors in calculating environmental 

FP releases

• accounting for the likelihood of specific flaws coinciding with sections of SG tubes at 

specific locations in the SG tube spatial temperature distribution
3-48

It is also possible to eliminate the artificial natural-circulation-related pipe-switching logic, as the 

coupling between the upper and lower HL volumes should be applicable throughout the entire 

accident sequence.

Additional analyses may include the following:

• performing a detailed analysis of loop seal clearing

• reconciling surge-line discrepancies with previous analyses

• comparing and reconciling results with those of previous industry analyses

• studying HL creep-rupture behavior in more detail

• performing detailed sensitivities to better characterize the effect of parameters

• analyzing additional relevant sequences in the event tree or similar sequences for

somewhat different designs

Use of already-developed multiparameter variable-input scripts allow multiple input parameters 

to be varied so that the different sequences can easily be run with the same MELCOR input 

deck. For example, these scripts can be used to perform MELCOR analyses for all relevant 

permutations of the C-SGTR event tree with probabilistic sampling of nondiscretely defined 

events or other parameters if needed.

The text below provides additional information on a few of these items.

A change that could have the most significant effect on predicted consequences is updating the 

deck to address loop seal clearing. Should the loop seals clear for any of these cases, the 

enhanced heat transfer to the tubes would greatly accelerate tube failure thus increasing the 

potential for FP releases. The deck was not generated with the specific intent to resolve loop 

seal clearing. The active SG natural circulation control may significantly affect loop seal clearing 

behavior. Furthermore, some inconsistencies exist between the flow-path and control-volume 

nodalization for the cold legs in that they do not represent quite the same diameter.

As mentioned above, the SG decontamination factors determined from the ARTIST project, 

which were not included in the determination of FP releases to the environment, would be 

expected to reduce FP releases potentially by about a factor of 5.3 This was not updated.

The accuracy of the SG tube failure calculation can be improved by linking the SG temperature 

and flaw distributions to determine the likelihood of a flaw occurring at a hot location on a tube. 

Judging by the TH results, this improvement would result in a more accurate prediction of tube 

failure timing and would likely alter the expected tube failure time by several minutes. The flaw 

and temperature distributions within the SG can be combined to improve these estimates. This 

improvement is only worth implementing if the improved results would be used in the 

risk determination.

Significant conclusions were drawn about plant behavior that relate to the operation of the 

secondary-side relief valves. It would be prudent to check and document a comparison of relief 

3

 For example, NUREG/CR-7110, “State-of-the-Art Reactor Consequence Analyses Project, Volume 2: Surry 

Integrated Analysis,” issued August 2013, provides an estimate for SG aerosol decontamination between 4.7 and 9.
3-49

valve opening criteria with that described in plant documentation. Doing so is critical if safety 

decisions will be made from the analysis conclusions. If the modeled relief valve behavior is 

different than that for the plant, incorrect conclusions will be drawn.

Recommendations

Given the inherent uncertainties that cannot be reduced and the level of effort involved, it may 

not be worth the effort to further pursue some of the potential future work. However, several of 

the potential deck modifications should be made eventually, as they will likely affect other 

non-C-SGTR analyses. These include the following: 

• addressing differences between current pressurizer draining behavior and that of 

previous analyses

• switching from active control to a friction-based method to model SG natural circulation, 

along with preforming the associated renodalization

• analyzing loop seal clearing in more detail

The results release fraction calculation should be checked once against methods by running it 

on a problem for which releases have been extracted. A match in RFs for a simple case would 

confirm proper functionality.

3.8 Conclusions 

3.8.1 Analysis-Based Conclusions 

This study developed CE CFD and MELCOR models. These models were exercised on 

selected risk-significant sequences to evaluate expected TH behavior. Datafiles were generated 

from the system-code output and provided to RES analysts for use as initial and boundary 

conditions in their detailed component failure analysis. FP release data were generated from 

these analyses for use in updating the risk contribution from these events.

The initial planned single bounding case did not result in releases. Because of this, additional 

cases had to be run to address behavior that had not previously been considered.

Most of the additional run requirements resulted from analyzing the different aspects of the 

problem together, unlike in previous analyses. The coupling of phenomena was explicitly 

modeled rather than assumed or modeled separately, as in previous analyses. Unlike in 

previous analyses, RCS ruptures were modeled to alter TH behavior and affect 

subsequent failures.

The initial approach did not sufficiently capture the interactions between the different aspects of 

the sequence.

Unlike in previous TH analyses, FP releases were calculated in addition to the TH feedback. As 

part of this analysis, secondary-side relief valve behavior was explicitly modeled.

Accounting for these coupled phenomena led to feedback that had not been considered. To 

obtain reasonable results, further analyses had to be performed. A notable parameter that led to 

the requirement of additional runs was the effect of sticking assumptions for secondary-side 
3-50

relief valves. Addressing the valve behavior was not a consideration in the initial project 

planning but proved to have a major impact. This is apparent only upon an analysis of results.

The assumption of MSSVs failing open, which was not originally focused on, was found to 

significantly affect system behavior. This was the case because previous analyses did not 

model secondary relief valve behavior but assumed that a bypass would occur if SG tubes failed 

some time before other RCS components. It was found that, with the whole system being 

modeled, if valve failure was not explicitly modeled, no appreciable releases would result, even 

if a substantial number of SG tubes had ruptured. The simulations had to be run repeatedly to 

establish relief valve behavior that resulted in releases to the environment. Assuming failure 

upon full valve opening following a tube rupture did not change releases, as the valves did not 

fully open and thus did not stick. Assuming a stick-open-failure upon full valve opening at any 

time also did not result in appreciable releases because, even for those cases, the valves did 

not stick open. Assuming that secondary-side relief valves stick as far as they have opened or 

assuming that they are opened by operators did result in releases. It seems that the 

secondary-side valves are not as pressure stressed when the tubes rupture several hours into 

the accident so they do not leak. They may be thermally stressed, which is not considered for 

the valve-opening model.

Note that if an SG-secondary-to-containment leakage is assumed, as in the original model, and 

secondary-side valves are open, this constitutes a leak path from the containment to the 

environment. Perhaps it would be more appropriate, when assuming leakage, to assume that it 

occurs through secondary-side isolation valves.

The analyses results indicate the following:

• Even if an SGTR occurs first, without an assumption of secondary relief valves

stick-open-failure or opening by operator action, no or minimal releases will occur.

• For a high-pressure secondary side (high-dry-high) situation, an HL will fail before an

unflawed tube, thus preventing tube rupture in the absence of tube flaws.

The prediction of minimal releases without an assumption of secondary-side relief valve failure 

is rather insensitive to uncertainties in component failure timing. The amount of FPs released in 

a temporary partial valve opening immediately following tube rupture may be somewhat 

dependent on the assumption of the number of SG tubes that rupture. Twenty tubes are 

assumed to fail if unflawed tubes fail. Rupture of a flawed tube is considered to result in the full 

rupture of a single tube.

For the high-dry-high situation, by the time the HL was predicted to fail (damage index = 1), the 

tube damage index was very low, indicating a significant flaw would be required for tubes to fail 

first for this condition. Previous analyses, and earlier single-tube-failure analyses within this 

project, have shown that a single tube failure will not reduce pressure at a sufficient rate to 

prevent HL failure that limits the amount of FPs that can be released.

Considerable uncertainties exist in component failure timing.

An SNL uncertainty analysis using an earlier version of the Calvert Cliffs Nuclear Power Plant 

deck indicated that the RCS-component-to-tube relative failure timing variation because of 

expected variations in TH parameters approximately followed a normal distribution with about a 

600-s standard deviation.
3-51

A change of a few percent in the HL countercurrent flow rate alone was found in analyses to 

make the difference between HLs or SG tubes failing first. The SNL uncertainty analysis 

addressed this parameter w by varying the discharge coefficient and factored the parameter into 

the relative-failure-timing uncertainty distribution.

Results from a sensitivity analysis indicate that the impact of creep-rupture-related material 

properties not considered in the uncertainty analysis can also greatly affect HL failure timing.

The difference in the prediction of HL failure timing was found to vary greatly, simply by the 

assumption of material (stainless or carbon steel)—approximately 2.5 hours. Because the SG 

calculator and FE calculations are providing more precise estimates of component failure timing, 

the results from the calculator software was used for the PRA analysis. Therefore, updating the 

HL creep modeling within MELCOR was not prioritized over other modeling aspects that provide 

information not available from other sources.

Although this difference in failure timing is not directly applicable as an additional uncertainty in 

failure timing for this analysis, it does underscore the importance of using the correct 

creep-rupture-related material properties. It indicates that this material property can make the 

difference in whether an SG tube or an HL fails first.

The highest volatile-FP release was 5 percent at the time the run terminated for the ltsbo case 

with no secondary-side-to-containment leakage and sticking MSSVs. This was the highest 

release of all cases considered.

These RFs should be taken with caution. Some of the RFs reflect the releases at the time the 

problem terminated, not the overall release. For this sequence, FPs were being released at a 

significant rate at the end of the simulation, so the actual predicted RF will be higher if the 

simulation is extended. To obtain the code-calculated RFs for the cases in question, the 

simulations would have to be run until the RFs reached their asymptotic values or at least 

beyond the time when risk analyses estimated that mitigative actions would occur. If precise 

output RFs are needed, this can be done.

3.8.2 Deck-Generation-Based Conclusions 

Because the heat transfer and flow models are based on accepted practice and because natural 

circulation flow was set based on CFD analyses of a sequence for which the code has been 

validated, the MELCOR results are considered suitable for screening for component failure 

timing under closed-loop-seal natural circulation. The CFD modeling approach was validated 

against experiments representing somewhat different SG geometry.

MELCOR can therefore be used as a screening tool to establish which cases need further 

scrutiny by more detailed component failure calculation methods conducted using the SG tube 

failure calculator and FE analyses.

Primarily because of active SG natural circulation control, which can alter closed loop flows, 

loop seal clearing likely cannot be accurately predicted with the current deck. Even if this were 

updated, large uncertainties would remain in the prediction of loop seal clearing. Because 

natural circulation flows are consistent with those provided by CFD, active control is not 

expected to significantly affect tube failure timing.
3-52

A potential change that could have the most significant effect on predicted consequences is 

updating the deck to address loop seal clearing. Should the loop seals clear for any of these 

cases, the enhanced heat transfer to the tubes would greatly accelerate tube failure, thus 

increasing the potential for FP releases.

A conceptual model of loop seal clearing behavior was developed. It is based on considering 

the loop seal bubble behavior to determine what happens with the loop seal.

Another potential modification that may have a significant effect is resolving the difference in 

pressurizer draining time between current and previous analyses. The matter should be looked 

into further.

An attempt was made to determine the relative contributions of radiative and convective heat 

transfer, as only the combined heat transfer coefficient was available in the plot file to provide 

phenomena-specific HTCs for use in the FE calculation. It was not completely successful. The 

impact of this change should be assessed.

Previous NRC analyses only adjusted the convective HTC for developing-boundary-layer 

effects, whereas other analyses have adjusted both the convective and radiative HTCs. 

Because the two HTCs could not be distinguished in the MELCOR plotfile, both HTCs were 

adjusted for developing-boundary-layer effects for the FE analyses. This change would tend 

toward accelerating the prediction of HL failure.

The accuracy of the SG tube failure calculation can be improved by linking the SG temperature 

and flaw distributions to determine the likelihood of a flaw occurring at a hot location on a tube. 

This improvement would result in a more accurate screening-level prediction of tube failure 

timing and would likely alter the expected tube failure time by several minutes. This statement 

applies to predictions using MELCOR analyses; it does not apply to the PRA analyses in 

Chapter 7 of this report.

3.9 References 

1. U.S. Nuclear Regulatory Commission, “SCDAP/RELAP5 Thermal-Hydraulic Evaluations

of the Potential for Containment Bypass During Extended Station Blackout Severe

Accident Sequences in a Westinghouse Four-Loop PWR,” NUREG/CR-6995,

March 2010, Agencywide Documents Access and Management System (ADAMS)

Accession No. ML101130544.

2. Fletcher, C.D. and R.M. Beaton, “SCDAP/RELAP5 Station Blackout Analyses for the

Calvert Cliffs Plant,” Information System Laboratories, May 2006.

3. Fuller, E.L., et al., “Steam Generator Tube Integrity Risk Assessment: Volume 1:

General Methodology, Revision 1,” Electric Power Research Institute (EPRI) Technical

Report 1006593, Palo Alto, CA, 2002.

4. U.S. Nuclear Regulatory Commission, “CFD Analysis of 1/7th Scale Steam Generator

Inlet Plenum Mixing during a PWR Severe Accident,” NUREG-1781, October 2003,

ADAMS Accession No. ML033140399.

5. U.S. Nuclear Regulatory Commission, “CFD Analysis of Full Scale Steam Generator

Inlet Plenum Mixing during a PWR Severe Accident,” NUREG-1788, May 2004, ADAMS

Accession No. ML041380224.
3-53

6. U.S. Nuclear Regulatory Commission, “Computational Fluid Dynamics Analysis of 

Natural Circulation Flows in a Pressurized-Water Reactor Loop under Severe Accident 

Conditions,” NUREG-1922, October 2010, ADAMS Accession No. ML110110152.

7. Boyd, C., “CFD Prediction of Severe Accident Natural Circulation Flows in a Combustion 

Engineering Pressurized-Water Reactor Loop,” ADAMS Accession No. ML16068A170, 

International Topical Meeting on Advances in Thermal Hydraulics 2016, New 

Orleans, LA, June 2016.

8. U.S. Nuclear Regulatory Commission, Advisory Committee on Reactor Safeguards, 

letter to Travers, William D., May 21, 2004, ADAMS Accession No. ML041420237.

4-1

4 BEHAVIOR OF REACTOR COOLANT SYSTEM COMPONENTS 

OTHER THAN STEAM GENERATOR TUBES 

4.1 Introduction 

During postulated pressurized-water reactor severe accidents, there is a concern that degraded 

core effluents could be allowed to bypass the containment if the steam generator tubes (SGTs) 

experience structural failures. However, if other components of the reactor coolant system 

(RCS) (i.e., non-SGTs) fail before the SGTs, containment bypass could be averted if those 

failures prevent fission product (FP) releases outside of containment. Prediction of RCS 

component failure will help determine the related RCS thermal-hydraulic response and the 

relative sequence of the RCS failure, the risk importance, and the associated uncertainties.

The probabilistic risk assessment used the calculator software to predict the time-dependent 

failure probability for SGTs and for hot legs (HLs) and surge lines. The correlation used for 

estimating the failure probability for SGTs is based on previous NRC studies, mostly performed 

by Argonne National Laboratory (ANL). The calculator software also used empirical models to 

predict HL and SL failures, as documented in Information Systems Laboratories, 

ISL-NSAD-TR-10-13, “Technical Basis and Software User Guide for SGTR Probability,” issued 

December 2014, based on previous correlations by the Electric Power Research Institute.

Chapter 4 documents detailed structural analyses for the Zion Nuclear Power Plant (ZNPP), 

which were conducted to verify the adequacy of the RCS time-dependent failure times predicted 

by the simplified model in the calculator software. The results showed that the simplified models 

consistently predicted later times to HL failure than more detailed modeling. This detailed 

modeling also indicated that the upper portion of the HL will fail earlier than other RCS regions.

Chapter 5 documents the technical basis and the empirical model for predicting ligament rupture 

pressure, crack opening area, and unstable burst pressure of SGTs with flaws under 

severe-accident transients. The calculator software uses these same models. 

4.2 Analyses of RCS Components for a Typical Westinghouse Plant 

RCS drawings from ZNPP were studied (except drawings of the reactor vessel (RV), the SG, 

and the pressurizer (PZR) internals). It was determined that the following components qualify as 

potential failure sites:

• HL and surge line

• primary manway in the SG

• PZR power-operated relief valve (PORV), and safety valve (PSV)

• three resistance temperature detectors (RTDs) that penetrate the HL to monitor reactor 

coolant temperature

• socket weld connection of the instrument lines to the RTD flanges

• a small-diameter drain line that is attached to the bottom of the HL-pipe elbow at the HL 

connection to the SG
4-2

• a small-diameter sample line that is connected to the HL to monitor reactor coolant water 

chemistry before the coolant enters the SG

Failure or excessive creep deformation of the SG primary manway cover bolts, together with 

gasket creep, could lead to significant leakage of primary coolant and depressurization of the 

primary side. Of the two safety valves, the PORV is challenged more because it cycles more 

often than the PSV during a severe accident and is therefore hotter. Of the other remaining 

three items listed above, the welds, which join the RTD at the top of the HL to the HL, are the 

most vulnerable and have the highest potential to depressurize the primary side because they 

are located on the hot side of the HL during the severe-accident transient; also, their failure 

would create the largest diameter hole in the HL. Therefore, this particular RTD to the HL 

junction was analyzed in detail. Failure of the socket weld that attaches the instrument line to 

the RTD flange could open up a 25-millimeter (mm) (0.98-inch (in.)) diameter channel through 

which steam from the HL can vent and potentially reduce the primary-side pressure significantly. 

Because this instrument line is of the same diameter as the sample line and the drain line, but 

will be at a higher temperature, its weld connection to the RTD flange was analyzed in detail.

4.2.1 Hot Leg and Surge Line 

The Type 316 stainless steel HL has a straight 0.86-meter (m) (34-in.) outside diameter (OD) 

with a 6.4-centimeter (cm) (2.5-in.) wall thickness that extends 2.64 m (8 ft. 730/32 in.) from the 

end of the reactor vessel (RV) nozzle (A 508 Class 2) to the end of the loop isolation valve, 

which is a massive 11,364-kilogram (kg) (25,000-pound (lb)) dry weight motor-operated gate 

valve with a projected horizontal length of 1.68 m (5 ft., 6 in.). At the other end of the loop 

isolation valve is a 1.2-m (47.5-in.) mean radius, 50 degrees reducing elbow (CF8M A351) 

whose inner diameter increases from 0.74 m (29 in.) to 0.79 m (31 in.) at the SG nozzle 

(SA 216 WCC) end over a projected horizontal length of 1.05 m (3 ft., 53⁄8 in.). The RV and SG 

nozzles support the full weight of the HL and the loop isolation valve. The surge line intersects 

the HL at a distance of 2.19 m (7 ft., 21

/32 in.) from the end of the RV nozzle. The 36-cm (14-in.) 

OD, 3.6-cm (1.4-in.) wall thickness surge line is a long, sinuous Type 316 stainless steel pipe 

whose center line coordinates were obtained from Reference 1. The HL and surge line are 

insulated with Type 304 stainless steel.

The RV support system permits the reactor to expand radially but resists translational and 

rotational movements. It was assumed that the reactor end of the RV nozzle was fixed against 

translations and rotations but was free to expand radially during a severe-accident transient. 

The HL in the model extended from the reactor end of the RV nozzle to the lower head of the 

SG (including the inlet nozzle) and the supports for the SG. The surge-line model extended from 

the junction with HL to the junction of the PZR nozzle and the PZR, which was assumed to be 

fixed against translations and rotations but to be free to expand radially during the 

severe-accident transient. Nine surge line supports are present: three flailing restraints, one 

variable-support spring hanger, one threaded-rod support, one constant-support hanger, one 

sway-strut assembly, and two hydraulic-snubber restraints. The model included all of the 

surge-line supports except the hydraulic snubbers, which are not expected to be active during a 

slow severe-accident transient.

In addition to pressure-induced stresses, significant thermal membrane and bending stresses 

are expected to occur in the HL and surge line because of external constraints. Therefore, 

failure can occur either by creep rupture or, if the stresses are not relaxed rapidly enough by 

creep, by tensile rupture.
4-3

4.2.2 Steam Generator Primary Manway 

Each ZNPP SG contains two primary manways; the one that is in the inlet plenum was selected 

because it is hotter. This manway is on the lower head, in an area where, during a severe 

accident, the relatively cool recirculating steam flows down through the SGTs on its way to the 

HL and back to the RV. The manway consists of a 67.9-cm (26.73-in.) OD, 10.2-cm (4-in.) thick 

cover plate made of SA 533 Grade A Class I, a 52-cm (20.5-in.) OD, 13-mm (0.5-in.) thick insert 

made of SA 240 Type 304 stainless steel, and a 40.8-cm (16.06-in.) inside diameter (ID), 

45.9-cm (18.06-in.) OD, 4.4-mm (0.17-in.) thick spiral-wound gasket made of Inconel with 

asbestos filler. These components are secured to the lower head by 16 4.8-cm (1.88-in.) 

diameter, 19-cm (7.5-in.) long threaded bolts made of SA 193 Grade B7 on a 58.4-cm (23-in.) 

diameter bolt circle. The opening diameter of the manway is 40.6 cm (16 in.). The bolts are 

tightened in a crisscross pattern by using three torque passes with an initial torque of 

540±20 newton meters (N-m) (400±15 foot pounds (ft-lb)), an intermediate torque of 

1,490±54 N-m (1,100±40 ft-lb), and a final torque of 2,170±80 N-m (1,600±60 ft-lb). The final 

nominal bolt stress is 207 megapascals (MPa) (30,000 pounds per square inch (psi)). During 

high-temperature exposure, the bolts will lose most of their prestress, after which the cover plate 

will lift off from the mating flange of the lower head. Depending on the gasket springback (which 

may be minimal at high temperature because of creep), the liftoff could lead to significant 

leakage of steam and reduction of primary pressure.

4.2.3 Resistance Temperature Detector 

Three RTDs, 120 degrees apart, penetrate the HL and monitor the coolant temperature during 

normal operation. The 7-cm (2.75-in.) OD, 30-cm (1113/16-in.) long RTDs are made of forged 

A-182 F316 stainless steel and project 19.5-cm (711/16-in.) into the interior of the HL. The RTD 

scoops are welded to the HL elbow by full-penetration welds with A308 filler material. Failure of 

the welds at high temperature could potentially blow the RTD scoop out of the HL and open a

7-cm (2.75-in.) diameter hole in it, leading to rapid depressurization of the primary side. 

Because of the postulated recirculating flow of the hot steam during a severe accident 

(assuming maintenance of the loop seal), the RTD at the top of the HL is the most vulnerable of 

the three that are present, because it is exposed to the hottest steam temperature.

4.2.4 Socket Weld Connection of Instrument Line to the RTD Flange 

Failure of the socket weld that attaches the 25-mm (1-in.) diameter instrument line to the RTD 

flange could reduce the primary side pressure significantly. During a severe accident, hot steam 

flowing through the internal drilled channel of the RTD scoop, RTD flange, and then to the 

instrument line through the socket weld connection could heat the socket weld to high 

temperatures. The pressure forces acting on the instrument line could create shear stresses 

that are sufficiently high to cause creep failure of the socket weld and the possible expulsion of 

the instrument line, an event that could open up a 25-mm (1-in.) diameter channel through 

which steam could escape and depressurize the primary side, or at least reduce the system 

pressure significantly.

The dimensions of the socket weld of the ZNPP plant were not available. For the 25-mm (1-in.) 

ID and 34-mm (1.33-in.) OD instrument line, the minimum socket weld dimensions were 

obtained from Figure NB-4427-1 of the American Society of Mechanical Engineers (ASME) 

Boiler and Pressure Vessel Code (ASME Code), Section III (Ref. 2), which stipulates that the 

minimum dimension of the socket weld is 1.09 times the nominal pipe wall thickness, which, for 

the current case reduces to 4.5 mm (0.18 in.). In this analysis, the socket weld dimension of 
4-4

5 mm (0.2 in.) was used as a reference, to analyze the effect of a larger weld size on the failure 

as part of the sensitivity analysis.

4.2.5 Power-Operated Relief Valve 

Drawings of a typical PORV were obtained from a valve manufacturer. The PORV contains a 

50-mm (2-in.) diameter plug that is connected by a stem to the actuator that drives the plug up

and down inside the cage. During normal operation, a 45.7-cm (18-in.) long AISI 6150 low alloy

steel spring (spring constant = 814 N/mm (4,700 pound-force (lbf)/in.) holds the plug pressed

against the cage with a force of 43 kilonewton (kN) (9,760 lbf). The contact surfaces between

the plug and the cage are both tapered, with slightly different (2.5-degree) taper angles. Hence,

when the valve is closed, the plug makes a line contact with the cage. A solenoid valve controls

the air pressure (maximum 0.7 MPa (105 psi)) across a diaphragm that drives the actuator.

When activated, the air pressure is sufficient to overcome the closing force of the spring and

opens the passage for the subcooled water to flow through. When closed, the diaphragm

chamber is vented, and the spring forces the plug against the cage. The valve manufacturer has

estimated the impact velocity to be 32 mm/second (s) (1.25 in./s). The plug material is Type 316

stainless steel with a Stellite overlay, and the cage material is ASME SA 564 (17-4 PH steel).

The plug and cage are contained inside the valve body, which is sealed off at the top by a

bonnet. The bonnet is secured to the valve body by a bolted joint.

The PZR PORV, which is subjected to many opening and closing cycles during a 

severe-accident transient, can fail by several complex mechanisms. The frequent discharge of 

subcooled water through the PORV during the initial phase of a severe accident can lead to 

cavitation/erosion damage of the PORV internals by flashing of water to steam and subsequent 

two-phase flow. Chattering, which is also a potential problem during this phase of the accident, 

can lead to high-cycle fatigue failure caused by repeated plug-to-cage impact. PORVs are 

susceptible to surface galling of the valve stem, mainly because of differential thermal growth 

during a severe-accident transient. The cage material of PORVs (17-4 PH steel, condition 

H1100) is heat treated and tempered at 593 degrees Celsius (C) (1,100 degrees Fahrenheit 

(F)). Therefore, if the temperature of the cage exceeds 593 degrees C (1,100 degrees F), the 

cage will lose all of the mechanical properties that were obtained from heat treating. The high 

temperature, combined with the loss of some of the mechanical properties, can increase the 

galling potential between the plug and cage. Should galling occur, the valve would not be 

operational. Thermal binding of the plug and the cage is also possible. The body-to-bonnet 

gasket joint is held by SA 193 (B7) bolts, which are rated in the ASME Code to permit their use 

to less than or equal to 427 degrees C (800 degrees F) and which are susceptible to loss of 

prestress (with consequent leakage) and creep rupture at higher temperatures. The PORV 

actuator diaphragm is made of buna-N rubber, which could be damaged at temperatures that 

exceed 93 degrees C (200 degrees F). Although the diaphragm stays relatively cool during 

normal operation, repeated cycling of the PORV during severe accidents could increase its 

temperature by heat conduction to greater than 93 degrees C (200 degrees F). The proper 

functioning of the diaphragm is necessary to open the valve but is not necessary for the PORV 

to go to the fail-safe position, which is closed. However, the spring that keeps the PORV closed 

under normal operation may lose strength and stiffness at high temperatures, and the steam 

pressure may overcome the spring closing force and make the PORV behave like a PSV.

Each of the above failure mechanisms is a complex problem in its own right, and the

development of methods for predicting its failure would require analyses as well as extensive 

test programs. As a starting point, the problem of plug-to-cage impact was considered because 

it is amenable to front-end analysis (FEA), the results from which could be used to evaluate the 
4-5

potential for fatigue damage of the plug or the cage contact areas. Because the impacts occur 

over very short time intervals, tensile properties are sufficient to carry out the stress analyses, 

and creep properties are not needed.

4.3 Thermal-Mechanical Analyses of Selected RCS Components 

All of the thermal conduction and stress analyses were conducted with the commercially 

available finite-element program ABAQUS®. ABAQUS® is used widely in the nuclear and 

aerospace industry for conducting high-temperature nonlinear analyses and has been validated 

with a number of solutions for which analytical solutions are available. The thermal-hydraulic 

analysis results from the SCDAP/RELAP5 code were used as the starting point for all analyses

under the current program. The thermal mechanical analyses were performed in two steps. 

First, a thermal transient analysis was conducted to obtain the temperature distribution 

throughout the model, based on the heat transfer analysis by the SCDAP/RELAP5 code. 

Second, the nodal-temperature data, together with the pressure and structural-support and 

boundary condition data, were entered into the structural-analysis model. The following sections 

present the analyses for the selected RCS components, other than HL and surge line. Detailed 

analyses of HL and surge-line failure will be described later in this chapter.

4.3.1 SG Primary Manway 

Figure 4-1 shows the various parts (SG lower head, insert, cover plate, gasket, and bolts) of the 

structure that were analyzed.

Figure 4-1 Parts for the ZNPP HL primary manway 

The gasket was not included in the structural model, because high-temperature properties for it 

were not available. Because the stiffness of the gasket is small relative to the other parts, the 

stresses should not be affected significantly by its neglect. Once bolt preloads are relaxed by 

thermal creep, the area available for leakage will depend on the gasket springback, which is 
4-6

expected to be small because of gasket creep. However, gasket creep data at high 

temperatures are not available.

Figure 4-2 shows the finite-element model (FEM) of the full assembly, which uses a total of 

45,383 elements and 67,809 nodes. The manway assembly was structurally supported vertically 

at the top edge, which was allowed to deform radially in an unconstrained manner. A uniform 

and constant pressure of 16 MPa (2.35 kilopound per square inch [ksi]) was applied during the 

full transient.

Figure 4-2 Finite-element model of manway assembly 

The RELAP5 analysis did not report the temperature of the manway because the model did not 

include a cell at the location of the primary manway. The lower head region at the inlet plenum 

contained only three cells. The temperature of Cell 105 represented the hot inlet plenum wall 

and Cell 106 represented the mixed mean temperature of the inlet plenum wall (Figure 4-3a). 

Because the primary manway was at the bottom of the SGTs that contained the cooler steam of 

the return flow, the temperature history reported for Cell 106 should be closer to that of the 

manway than to the history reported for Cell 105. A more detailed computational fluid dynamics 

(CFD) calculation of the inlet plenum region has shown that the steam adjacent to the manway 

is even cooler than the mixed mean plenum steam temperature (Figure 4-3b). However, the 

heat transfer coefficients or the surface heat fluxes that correspond to the CFD calculations 

were not available. Using the surface heat flux history from RELAP5 on the ID surface of the

lower head plenum wall and on the interior surface of the insert, and assuming zero resistance 

to heat flow across all the interfaces, a transient heat conduction analysis of the manway was 

performed. The analysis gave an OD temperature for the lower head of 885 degrees C away 

from the manway and 760 degrees C near the manway, both much higher than that calculated 

by RELAP5. Because of the uncertainties in the heat transfer coefficients or surface heat fluxes 

and thermal resistances across various interfaces in the manway, results from transient thermal 

conduction analysis were not used in the stress analysis. Instead, a transient thermal 

conduction analysis was carried out, using the transient temperature history at the outside 

surface of the plenum wall as calculated by RELAP5 (Figure 4-3a) as boundary conditions, and 

considered it the reference case. It was decided to address the temperature effects on stress 

and deformation of the manway components by temperature uncertainty analyses.
4-7

(a) (b)

Figure 4-3 Time-temperature histories of inlet plenum 

(a) time-temperature histories of the inlet plenum wall for RELAP5 Cells 105

 and 106 

(b) RELAP5 and CFD-calculated steam temperatures near manway in inlet plenum

A critical input in the structural analysis of the manway is the initial bolt stress or prestress. 

Westinghouse (W) specifications for the ZNPP plant call for the torque on the SG primary 

manway bolts during the final pass to be 2,170±80 N-m (1,600±60 ft-lb) and their design manual 

assumes a nominal value for the initial bolt stress as 207 MPa (30,000 psi). The relationship 

between the applied torque and the resultant tensile stress in the bolts is highly complex. 

J. Shigley4 has reported the following simple relationship between the torque and the 

bolt preload:

T = KFd (4.1)

where T is torque, K is the torque coefficient, F is the bolt preload, and d is the fastener 

diameter. For typical values of friction coefficients (μ = 0.15), K = 0.2, which is found to be 

relatively insensitive to changes in the bolt diameter and the thread characteristics. For the 

ZNPP manway bolts, application of Equation 4.1 gives F = 225 kN (51,200 lbf), which 

corresponds to a bolt stress of 130 MPa (18,540 psi). A bolt prestress of 207 MPa (30,000 psi) 

was used as recommended in the W manual.

The structural analysis was carried out in three steps:

(1) Apply bolt preload at room temperature (elastic analysis).

(2) Increase temperature of manway assembly uniformly from room temperature to 

350 degrees C and apply coolant pressure (elastic analysis).

(3) Apply severe-accident-transient temperature history (elastic-creep analysis).

The bolt preloads were applied simultaneously to all 16 bolts with the bolt preload feature of 

ABAQUS. The bolts were stressed to a nominal tensile stress of 207 MPa (30 ksi).

 4 See J. Shigley, “Mechanical Engineering Design,” McGraw Hill, New York, NY, 1963.
4-8

Elastic-Creep Analysis

When creep deformation is taken into account, the bolt loads are relaxed rapidly, as shown in 

Figure 4-4a. Note that the bolt axial loads reach a lower plateau at 14,346 s, which corresponds 

to a temperature of 450 degrees C. A residual axial load is maintained in all of the bolts to 

balance the force because of the pressure loading on the insert. The exact relaxation history is 

dependent on the creep properties (both primary and secondary creep) of the material, which, 

as mentioned earlier, were not available for this material at the time the analysis was carried 

out. Figure 4-4b shows the variation of the maximum and minimum principal stresses, as well as 

the section average stresses across Bolt 1, indicating that the bolts are subjected to significant 

bending. The stresses are below yield at the relevant temperatures.

(a) (b)

Figure 4-4 Elastic-creep analysis of manway bolts 

(a) relaxation of preloads with time and temperature because of creep in Bolts

1, 5, 9, and 13

(b) changes in maximum and minimum principal stresses and average stress in

 Bolt 1 with time and temperature 

Figure 4-5a shows the distribution of the maximum principal creep strains in Bolt 1 at 

650 degrees C (1,202 degrees F) at 17,650 s; comparison with Figure 4-5b suggests a rapidly 

accumulating creep strain with time and temperature. A plot of the variation of maximum creep 

strain with time in Figure 4-5b confirms that, by the time the temperature reaches 

670 degrees C (1,238 degrees F) at 18,000 s, the maximum creep strain reaches 35 percent. If 

failure at 20-percent maximum creep strain is postulated, the failure time for the bolt is 17,770 s 

(Tests conducted subsequently by ANL have shown that this material has a tensile total 

elongation of 80 percent and creep ductility of 60–90 percent at 650 degrees C 

(1,202 degrees F)). However, the failure time does not appear to be strongly dependent on 

creep ductility.
4-9

(a) (b)

Figure 4-5 Principal creep strain 

(a) distribution of principal creep strain around circumference of bolt 1 at

 650 degrees C

(b) variation of principal creep strains in bolt 1 with time and temperature

An important objective of the present analysis is to quantify the lifting of the cover plate from the 

flange, thus creating a leakage flow path for the steam during the accident. Figure 4-6a shows 

the variation of the maximum contact pressure around the outer periphery of the insert with 

temperature. It is evident that the contact pressures are reduced to zero by 450 degrees C 

(14,346 s). Beyond 450 degrees C, the contact between the insert/cover plate and the lower 

head flange is lost all around, the cover plate begins to lift off from the lower head flange, and 

leakage of steam becomes possible. Figure 4-6b shows the variation of the total opening area 

with time and temperature because of the cover plate lifting. It is evident that, even when 8 of 

the 16 bolts are preloaded to 85 percent of the design preload, the opening characteristics are 

the same as in the reference case. An area of 19 square centimeters (cm2

) (3 square inches 

[in.2

]), which is approximately equivalent to a 50-mm (2-in.) diameter hole, is created by 

600 degrees C (1,112 degrees F) (16,726 s). The actual flow area will be less than 19 cm2

(3 in.2

) because of gasket spring-back, which should be minimal at these temperatures because 

of thermal creep. However, gasket creep data at high temperature are not currently available.
4-10

(a) (b)

Figure 4-6 Crack mouth pressure and opening area variations 

(a) Distribution of contact pressure between outer periphery of insert and

lower head flange as function of temperature and position

(b) Variation of opening area with time and temperature

To determine the effect of temperature on the opening area, an analysis was conducted with the 

temperature history of Cell 105 (average) (Figure 4-3a), which is considerably hotter than the 

reference case (Cell 106, OD). Figure 4-7a shows the variations of the opening area as a 

function of time and Figure 4-7b shows the same as a function of temperature for the two 

temperature loadings. Although the opening area histories differ widely when viewed as a 

function of time, they are much closer when viewed as a function of temperature, indicating that 

temperature is the predominant driving force for this problem.

(a) (b)

Figure 4-7 Variation of opening area with (a) time and (b) temperature for two 

temperature histories 

Another situation where temperature variation may have an important effect on the opening 

area arises after lift-off of the cover plate from the lower head flange when leakage of hot steam 

through the opening area will cause local heating of the bolts. The coupled 

structural/thermal-hydraulic analysis of this problem is complex and was not attempted. 
4-11

Instead, after lift-off of the cover plate, the temperature of the bolts was manually increased to 

that of the inlet plenum mixed mean steam temperature (Figure 4-3b), which is 

200–500 degrees C (392–932 degrees F) hotter than the RELAP5 OD temperature for Cell 106. 

This should be considered as an upper-bound effect and the result, plotted in Figure 4-8, 

indicates that a 19-cm2 (3-in.2

) opening area could be created in 15,200 s instead of the 

reference 16,726 s, a reduction in time of 1,500 s. In reality, the bolt temperatures will rise much 

less rapidly, particularly when the area of the opening is small. If a few hundred seconds in time 

can make a difference in the outcome of the accident, leakage must be considered in a more 

rigorous manner.

Figure 4-8 Effect of steam leakage on opening area 

Discussion of Results

The results presented here are based on creep curves for SA 193-B7 bolts that were estimated 

from available creep data for AISI 4140 steel. Appendix A presents more recent data on 

SA 193-B7 bolt material, based on tests conducted at ANL. The test data indicated that the 

creep equations used in this analysis overestimated the creep strains observed in the tests by a 

factor of 5-10, as shown in Figures 4-9a and 4-9b. Therefore, the calculated creep results for 

the bolts presented here overestimate the actual creep strains significantly, which would imply 

that the stresses in the bolts should relax significantly less rapidly during the severe accident 

than calculated here.
4-12

(a) (b)

Figure 4-9 Predicted vs. observed creep curves of SA 193-B7 for duplicate tests at 20 and 

30 ksi at (a) 550 degrees C and (b) 450 degrees C 

4.3.2 Resistance Temperature Detector Welds 

Three RTD scoops are located 120 degrees apart in the elbow of the HL; they are used to

monitor the primary-side temperature during normal operation. The analysis was done for the 

one at the top, which is the hottest of the three RTDs because of the counter flow coolant circuit 

postulated to occur during a severe-accident transient. Because creep failure of the welds that 

connect the RTD to the HL is of primary concern, it was assumed that the RTD was attached to 

a straight section of the HL, ignoring the curvature of the elbow.

The geometry information for the SG RTD scoop was assembled from the drawings obtained 

from ZNPP. The RTD is attached to the HL by full–penetration welds, as shown in Figure 4-10. 

Failure of the A 308 welds could potentially lead to the expulsion of the RTD scoop and the 

creation of a 7-cm (2.75-in.) diameter hole in the HL.

Figure 4-11 shows the finite element meshes used to analyze a 30-cm (12-in.) long section of 

the HL, the RTD, and the welds. A total of 5,144 elements were used to model the HL; 

1,110 elements to model the ID weld; 1,377 elements to model the OD weld; and 

1,488 elements to model the RTD. The total number of nodes was 6,329. The FEM included the 

drilled channel inside the RTD.
4-13

Figure 4-10 RTD scoop and welds connecting it to HL 

Figure 4-11 Meshes used to analyze RTD scoop, welds, and HL 

The heat transfer coefficients for the top half (hot side) and bottom half (cool side) of the HL and 

the respective steam temperatures were obtained from the RELAP5 analysis. Figure 4-12 

shows the steam temperatures as functions of time. The hot-side heat transfer coefficient and 

steam temperature were also applied to the outside surface of the portion of the RTD that 

projected into the HL. The heat transfer coefficients of the RTD should most likely be higher 

because the RTD is situated transverse to the flow direction. Heat should also flow into the RTD 

from the interior surface of the annular area through which the steam flows into the instrument 

line. However, because of the uncertainties in the heat transfer coefficients, in the reference 

case, heat transfer coefficients were applied only to the outside surface of the RTD. 
4-14

The potentially higher heat fluxes on the RTD outside surface, as well as heat fluxes on its 

internal surface, were treated as part of the sensitivity analyses.

Figure 4-12 Steam temperature histories for the hot side and the cool side of the RTD 

A constant pressure of 16 MPa (2.35 ksi) was applied on all the pressure boundaries. No axial 

constraint was applied on the HL. Although the HL has significant axial stress, the behavior of 

the welds (which are of primary focus here) should be relatively insensitive to this stress. The 

stress analysis was conducted in two steps. First, the pressure loading was applied at 

343 degrees C (650 degrees F); then, the severe-accident transient temperatures computed by 

the thermal conduction analysis were applied and the stress analysis was conducted by 

elastic-creep analysis.

Figure 4-13 shows the temperature distribution in the RTD, HL, and the welds at time 

t = 14,400 s. Note that the lower half of the HL is significantly cooler than the upper half, as 

expected. Also, because of its smaller mass, the RTD heats up much more rapidly than the HL. 

The maximum temperature in the RTD is 1,254 degrees C (2,289 degrees F). The RTD 

temperature approaches that of the HL at the junction with the HL. Figure 4-14 shows the 

average temperatures in the ID and OD welds at their junctions with the RTD. The average ID 

weld temperature is 50–80 degrees C (122–176 degrees F) hotter than the average OD 

weld temperature.

Figure 4-15 plots the distribution of von Mises effective stress at the ID weld/RTD interface at 

time t = 14,148 s; Figure 4-16 plots the same for the OD weld/RTD interface. Figure 4-17a plots 

the variations of the average von Mises effective stresses at these interfaces with time. The time 

at the maximum and minimum points in this figure coincide with the time at which there is a step 

increase in temperature ramp rate (see Figure 4-3a). Although, initially, the average stress is 

higher at the ID weld interface than at the OD weld interface, because of the higher temperature 

at the ID than at the OD, the average stress at the ID weld interface is reduced and that in the 

OD weld interface is increased with time. Creep effects begin to dominate and stresses are 

relaxed rapidly at 14,000 s, when the average temperature reaches 800 and 880 degrees C in 

the OD and ID weld interfaces, respectively. Some localized high-stress areas are present that 

would undergo plastic yielding and accumulate plastic strain (i.e., high strain rate creep), which 

the current analysis ignores. However, plastic yielding effects were considered as part of the 

sensitivity analysis.
4-15

Figure 4-13 Closeup view of temperature (in °F) in HL RTD scoop at 14,400 s 

To convert from degrees F to degrees C, subtract 32 and divide by 1.8. 

Figure 4-14 Variation of average temperature in ID and OD welds with time 
4-16

Figure 4-15 Von Mises effective stress (in psi) distribution at ID weld RTD interface 

at 14,148 s 

Note 1,000 psi = 6.895 MPa. 

Figure 4-17b plots the time evolution of the average effective creep strain in the ID and OD weld 

interfaces. Although the average stress in the ID weld interface is lower than in the OD weld 

interface, because of its higher temperature, the average creep strain in the ID weld is close to 

(actually slightly higher than) that in the OD weld interface. An average equivalent creep strain 

of 20 percent is reached in 13,890 and 14,000 s in the ID weld/RTD and OD weld/RTD 

interfaces, respectively.
4-17

Figure 4-16 Von Mises effective stress (in psi) distribution at OD weld RTD interface 

at 14,148 s 

Note 1,000 psi = 6.895 MPa. 

(a) (b)

Figure 4-17 Time evolution of (a) average von Mises effective stress and (b) average 

effective creep strain at interfaces of ID and OD welds with RTD 
4-18

Results from Sensitivity Analyses

Sensitivity analyses addressed the uncertainty in the current analysis arising from uncertainties 

in the temperatures, creep rates of the weld material, and possible creep-plasticityinteraction effects.

Sensitivity analyses showed that, when the outside heat transfer coefficients on the RTD are 

increased by a factor of 2 from the reference values, still ignoring the internal surface heating on 

the RTD, an average equivalent creep strain of 20 percent is reached in, respectively, 13,706 

and 13,725 s in the ID weld/RTD interface and OD weld/RTD interface, a reduction of 184 and 

275 s, respectively, from the reference times to reach 20-percent creep strain. If the reference 

heat transfer coefficients are applied equally to both the outside and inside surfaces of the RTD, 

an average equivalent creep strain of 20 percent is reached in 13,790 and 13,890 s in the ID 

weld/RTD interface and OD weld/RTD interface, a reduction of 100 and 110 s, respectively, 

from the reference times. Creep rate has a significant effect on the failure time. A factor of 10 

increase in creep rate reduces the time to accumulate 20-percent creep strain by 180 s in the ID 

weld interface and 90 s in the OD weld interface, when compared with the reference times.

Inclusion of both creep and plasticity effects in the analysis showed that the time to accumulate 

20-percent creep strain is increased by 176 s (tr =14,066 s) in the ID weld/RTD interface and

104 s (tr =14,104 s) in the OD weld/RTD interface, when compared with the reference case.

The times to accumulate 20-percent total inelastic strain (plastic plus creep) in the two weld

interfaces are virtually the same as the times to accumulate 20-percent creep strain. If a

2-percent average effective plastic strain failure criterion is adopted for the welds, the failure

times are 14,123 s and 13,930 s for the ID and OD weld interfaces, which are, respectively, 57 s

greater than and 74 s less than the corresponding times to accumulate 20-percent effective

creep strains. Thus, the inclusion of plasticity effects does not change the estimates of the

failure times significantly.

4.3.3 Socket Weld that Connects Instrument Line to RTD Flange 

The possible failure of the socket weld that attaches the 25-mm (1-in.) diameter instrument line 

to the RTD flange is considered. During a severe accident, pressure forces could create 

sufficiently high stresses to cause creep failure of the weld and the possible expulsion of the 

instrument line from the RTD flange. The resultant opening of a 25-mm (1-in.) diameter channel 

could potentially reduce the primary-side pressure significantly.

Figure 4-18 shows a simplified axisymmetric model for the instrument line connection to the 

RTD flange. There is no direct tie connection between the RTD flange and the instrument line, 

although contact elements were used to prevent penetration of the instrument line into the RTD 

flange. Restraint of the instrument line to vertical movement is provided by the weld, which is 

tied to both the RTD flange and the instrument line. The lower end of the RTD flange is 

supported in the vertical direction.

A constant internal pressure of 16 MPa (2.35 ksi) was applied to all of the pressure-retaining 

surfaces. The axial component of the internal pressure loading on the instrument line was 

applied as an axial pressure loading at the top end of the instrument line.

Internal heating of the RTD increases the temperature of the RTD at the top, near the 

connection with the instrument line. Therefore, a uniform temperature field was applied to the 

entire model (Figure 4-19).
4-19

Figure 4-18 Simplified axisymmetric model for connection of instrument-line-to-RTDflange weld 

Figure 4-19 Temperature loading applied as uniform temperature to model of connection 

of instrument-line-to-RTD flange weld 

A combined creep-plasticity analysis was conducted. Figures 4-20a and 4-20b plot the time 

evolution of the average von Mises effective stress and the effective creep strains in the weld 

interfaces with the instrument line and the RTD flange. Although, initially, (at low temperatures) 

the average stress at the weld/RTD flange interface is lower than that at the weld/instrument line 

interface, the two stresses tend to converge with time (at high temperatures). Therefore, creep 

strain was accumulated at both interfaces at the same rate. The average effective creep strain 

at the interfaces reaches 20 percent at time t = 14,230 s, which is about 440 s later than the 

failure of the RTD/HL ID weld, discussed in the previous section.
4-20

(a) (b)

Figure 4-20 Time evolution of (a) average von Mises effective stress and (b) average effective 

creep strain at interfaces of weld with instrument line and RTD 

Much larger creep strains than those in the weld are predicted to occur in the instrument line 

(assumed to be made of stainless steel) close to the weld, as shown in Figure 4-21. This is not 

surprising because the pressure-induced membrane stress in the instrument line is about 

65 MPa (9.5 ksi), which is larger than the maximum stress in the weld. Figure 4-22 shows that 

the average effective creep strain in the instrument line away from the weld reaches 20 percent 

at 14,150 s, which is about 80 s before the failure time of the instrument line/RTD flange weld.

Figure 4-21 Effective creep strain distribution in instrument line at time t=14,230 s 
4-21

Figure 4-22 Time evolution of average effective creep strain in instrument line away 

from welds 

Sensitivity analysis showed that the average stresses are reduced significantly by doubling the 

weld dimensions. However, in contrast to the reference case, the average stress in the 

weld/RTD interface remains less than that in the weld/instrument line at all times. Therefore, the 

creep strain accumulates faster in the weld/instrument line interface than in the weld/RTD flange 

interface. The time to accumulate an average creep strain of 20 percent in the weld/instrument 

line interface is 14,330 s, which represents a 100-s delay in failure time, compared to the 

reference case.

Increasing the creep rate by a factor of 10 compared to the reference case causes the stresses 

at the weld/RTD flange interface, which are initially lower than those at the weld/instrument line 

interface, to increase more rapidly than the stresses in the reference case. With time (at high 

temperatures), these stresses converge with those at the weld/instrument line interface. The 

average effective creep strain at the interfaces reaches 20 percent at time t = 14,110 s, which is 

about 120 s earlier than the reference case. The instrument line itself fails at 14,090 s, which is 

about 20 s before the failure time of the weld.

4.3.4 PORV Plug-to-Seat Impact Analysis 

The PZR PORV, which is subjected to many opening and closing cycles during a 

severe-accident transient, can fail by several complex mechanisms. The frequent discharge of 

subcooled water through the PORV during the initial phase of a severe accident can lead to 

cavitation and erosion damage of the PORV internals by flashing of water to steam and 

subsequent two-phase flow. Chattering, which is also a potential problem during this phase of 

the accident, can lead to high-cycle fatigue failure caused by repeated plug-to-cage impact. 

PORVs are susceptible to surface galling of the valve stem, mainly because of differential 

thermal growth during a severe-accident transient. The cage material of PORVs (17-4 PH steel, 

condition H1100) is heat treated and tempered at 593 degrees C (1,100 degrees F). Therefore, 

if the temperature of the cage exceeds 593 degrees C (1,100 degrees F), the cage will lose all 

of the mechanical properties that were obtained from heat treating. The high temperature, 

combined with the loss of some of the mechanical properties, can increase the galling potential 
4-22

between the plug and cage. Should galling occur, the valve would not be operational. Thermal 

binding of the plug and the cage is also possible. The body-to-bonnet gasket joint is held by 

SA 193 (B7) bolts, which are rated in the ASME Code to permit their use to less than or equal to 

427 degrees C (800 degrees F) and which are susceptible to loss of prestress (with consequent 

leakage) and creep rupture at higher temperatures. The PORV actuator diaphragm is made of 

buna-N rubber, which could be damaged at temperatures that exceed 93 degrees C 

(200 degrees F). Although the diaphragm stays relatively cool during normal operation, 

repeated cycling of the PORV during severe accidents could increase its temperature by heat 

conduction to greater than 93 degrees C (200 degrees F). The proper functioning of the 

diaphragm is necessary to open the valve but is not necessary for the PORV to go to the 

fail-safe position, which is closed. However, the spring that keeps the PORV closed under 

normal operation may lose strength and stiffness at high temperatures, and the steam pressure 

may overcome the spring closing force and make the PORV behave like a PSV.

Each of the above failure mechanisms is a complex problem in its own right, and the 

development of methods for predicting its failure would require analyses as well as extensive 

test programs. As a starting point, the problem of plug-to-cage impact was considered because 

it is amenable to FEA, the results from which could be used to evaluate the potential for fatigue 

damage of the plug or the cage contact areas. Because the impacts occur over very short time 

intervals, tensile properties are sufficient to carry out the stress analyses, and creep properties 

are not needed.

A literature search carried out on impact wear models and mechanisms collected the following 

recent publications:

• R.W. Fricke and C. Allen, “Repetitive impact wear of steels,” Wear, Vol. 162–164,

pp. 837–847, 1993

• Y. Yang, H. Fang, Y. Zheng, Z. Wang, and Z. Jiang, “The failure models induced by

white layers during impact wear,” Wear, Vol. 185, pp. 17–22, 1995

• A.A. Voevodin, R. Bantle, A. Matthews, “Dynamic impact wear of TiCxNy and Ti–DLC

composite coatings,” Wear, Vol. 185, pp. 151–157, 1995

• B. Zhang, Y. Liu, W. Shen, Y. Wang, X. Tang, and X. Wang, “A study on the behavior of

adiabatic shear bands in impact wear,” Wear, Vol. 198, pp. 287–292, 1996

• B. Zhang, W. Shen, Y. Liu, X. Tang, and Y. Wang, “Microstructures of surface white

layer and internal white adiabatic shear band,” Wear, Vol. 211, pp. 164–168, 1997

• B. Zhang, W. Shen, and Y. Liu, “Adiabatic shear bands in impact wear,” J. Mater. Sci.

Lett., Vol. 17, pp. 765–767, 1998

• G.Sheng, W. Hua, and J. Zhang, “Head-disk impact stresses in dynamic loading process

and the extrapolation of parameters for sliding rounding and interface durability,”

J. Information Storage and Processing Systems, Vol. 3, pp. 203–206, 2001

Most of the above publications deal with very high-speed, near-normal repetitive impact, where 

adiabatic shear bands form in steels at room temperature and, hence, are not directly relevant 

to the impact wear of PORVs during severe accidents. Only the first publication is somewhat 
4-23

relevant. It reports a study to determine the material, microstructural, design, and operating 

parameters of importance in minimizing the impact wear of valves operating in hydro-powered 

stopping mining equipment in South Africa. Tests were conducted to simulate the repetitive 

impact wear experienced by poppet valves. Wear damage occurred at the point of contact 

between the reciprocating valves and their seats. The tests were conducted with line-contact 

(which is also characteristic of PORV) specimens on various heat-treated alloys and stainless 

steels at frequencies between 5 and 50 hertz (Hz), impact velocities from 4 to 10 m/s, and 

impact energies from 2 to 5 joule (J). The line contact during the tests was achieved by using a 

flat-ended 8-mm diameter cylindrical striker repetitively striking a conical seat (made of the 

same material as the striker) with a 30-degree taper. All of the tests were conducted in a 

room-temperature water environment. The wear rates followed an empirical power law for tests 

carried out on AISI 431 steel:

W = KNEn (4.2)

where W = wear loss, N = number of impacts, E = impact energy, and K and n are empirical 

constants.

Under lubricated conditions, two wear mechanisms were observed—pitting and surface traction. 

Surface traction, which is a result of partial slip (i.e., slip occurs at the exit edge but not at the 

leading edge), was caused by metal-to-metal adhesion and produced most of the wear.

Initially, during impact testing with line contact, greater deformation occurred in the striker than 

in the seat. With each successive impact, the contact stresses were reduced. The greatest 

amount of deformation occurred during the first impact, and, in the absence of wear, the contact 

stresses were reduced with each successive impact until a steady state was reached when the 

material could support the impact load. An incubation period was observed preceding wear loss, 

a finding that indicated that wear proceeds only after surface material has been strained to 

capacity and stresses cycled a sufficient number of times for crack initiation and propagation to 

occur under the predominantly compressive stress conditions. Debris in the form of flakes or 

thin platelets was produced in this way. Following the incubation period, the wear rate was high 

and decreased toward zero as the contact area increased and the impact stress decreased. It 

was concluded that the rate of wear was a function of impact energy, material properties, 

contact areas, and wear mechanisms.

Although of much interest, the results from this study are not directly applicable to the impact 

wear of PORV during severe accidents for the following reasons:

The impact velocity of the plug in the PORV during closure is on the order of 0.5 cm/s 

(1.25 in./s), which is much smaller than the impact velocities used in the tests (4–10 m/s).

Tests were conducted at room temperature in a water environment, whereas the PORV will 

operate at high temperature, first in subcooled water and then in a superheated steam 

environment during severe accidents.

The plug in the PORV is Type 316 stainless steel with a hard Stellite overlay and the cage is 

heat-treated and tempered steel. The tests were conducted with the striker and the seat made 

of the same material without any overlay.

Although line contact was used in the tests, the angle between the two contacting surfaces was 

30 degrees, which is much greater than the 2.5 degrees for the PORV. Therefore, the PORV 
4-24

plug has a much greater parallel velocity component relative to the normal component than the 

tests. The frequency of impact in the tests was much greater than expected in the PORV during 

severe accidents.

Although the results from the tests are not directly applicable to the PORV during severe 

accidents, similar mechanisms should be operative, and crack initiation and propagation will 

play important roles in the wear rates and failure of the plug and cage.

The stress-strain field created by the repeated impact of the plug on the cage because of PORV 

cycling was analyzed. Figure 4-23 shows the various parts selected for impact analysis.

Figure 4-23 Various parts included in the plug to cage impact analysis 

The taper of the contacting surfaces of the plug and the cage differs slightly (2.5°). 

Consequently, the initial contact between the plug and the cage is almost tangential in the axial 

direction and along a line in the circumferential direction. For simplicity, the FEA was 

axisymmetric. The reference case analysis did not include the Stellite overlay but the sensitivity 

analysis did include it. During normal operation, a 46-cm (18-in.) long AISI 6150 low-alloy steel 

spring (spring constant = 814 N/mm [4,700 lb/in.]) holds the plug pressed against the cage with 

a force of 43 kN (9,760 lb). The FEM included the spring as a linear-spring element. The cage 

was supported in the vertical direction at the shoulder region. In view of the large relative 

contact displacement between the plug and the cage, and to handle the dynamics of the 

problem, a full nonlinear (finite deformation) analysis was implemented with ABAQUS-explicit.

The entire model was assumed to be at a uniform and constant temperature during the impact. 

Because of the high strain rate involved during the impact, the analysis was carried out with an 
4-25

elastic-plastic constitutive relationship for both the plug (Type 316 stainless steel) and the cage 

(17-4 PH steel H1100). A rate effect on the constitutive relationship was not included in the 

analysis. The strength properties were obtained from the ASME Code, Section II, and 

Figure 4-24 shows the bilinear stress-strain curves that the analysis used. Note the much higher 

strength of the cage when compared with that of the plug. At temperatures greater than 

593 degrees C (1,100 degrees F), the cage material will lose strength rapidly. However, 

because of lack of data, analyses were conducted for 288 and 538 degrees C (550 and 

1,000 degrees F) only.

Figure 4-24 Stress plastic strain curves at 288 and 538 degrees C (550 and 1,000  

degrees F) used in analysis 

In the reference case, the initial velocity of the plug was set at 32 mm/s (1.25 in./s), as 

recommended by the manufacturer, starting from a position just in contact with the cage. The 

analysis was continued until the elastic waves travelling back and forth were significantly 

reduced. The variation of the spring force with time for a single impact, plotted in Figure 4-25, 

shows that the time taken by the plug to come to a complete rest is 0.01 s. After the first impact, 

the plug was retracted rapidly to the same position it occupied before the first impact and was 

held in place for 0.005 s. It was then given the same initial velocity as in the first impact, and the 

analysis continued as before. Finally, the plug was retracted and a third impact was analyzed.
4-26

Figure 4-25 Variation of spring force with time during single impact 

Figures 4-26a and 4-26b show the variations of the maximum equivalent plastic strain with von 

Mises effective stress and time, respectively. The additional stress cycles in Figure 4-26a are 

because of elastic wave propagation in the plug. Note that the maximum effective plastic strain 

increases with each impact, although at a diminishing rate. After three impacts, residual 

effective plastic strains of 8.4 and 9.4 percent are created at 288 and 538 degrees C (550 and 

1,000 degrees F), respectively. Although plastic strain ratcheting occurred with each loading 

cycle, Figure 4-26a shows no open hysteresis loop in the stress-plastic strain plot, which 

indicates that low-cycle fatigue should not be a problem for this type of cycling. In contrast to the 

plug, the cage does not experience any plastic strain at these temperatures because the 

maximum stresses are too low.

(a) (b)

Figure 4-26 Variation of equivalent plastic strain with (a) von Mises effective stress and 

(b) time for most highly strained element in plug at 288 and 538 degrees C (550 

and 1,000 degrees F)
4-27

Stellite Overlay Effect

In practice, a hard Stellite overlay is present on the soft plug material; it will have a major 

influence on the stress-strain distribution in the plug. For the purpose of investigating the effect 

of the overlay, a simplified model of the plug-to-cage impact was adopted (Figure 4-27a). The 

impact analysis of the plug with a 2-mm (0.08-in.) thick Stellite overlay was conducted at 

538 degrees C (1,000 degrees F) with the stress-plastic strain curves shown in Figure 4-27b. At 

538 degrees C, the Stellite coating is stronger than the 17-4 PH steel and considerably harder 

than stainless steel. The FEA showed that no plastic strain was generated in the overlay, the 

plug, or the cage during the impact. A plot of the distribution of the von Mises effective stress, 

shown in Figure 4-28, shows that the maximum stresses in the overlay, the plug, and the cage 

are less than their respective yield stresses. The Stellite overlay effectively shields the 

underlying stainless steel plug from developing high contact stress and plastic strain.

(a) (b)

Figure 4-27 Stress-plastic strain on 2-mm thick plug 

(a) Simplified axisymmetric model of plug-to-cage impact, where satellite

 overlay on plug is 2-mmthick

(b) stress-plastic strain curves used in impact analysis of plug with 2-mm-thick

 satellite overlay 
4-28

Figure 4-28 Distribution of von Mises effective stress (in psi) near contact zone of cage 

and plug with 2-mm Stellite overlay 

Note 1,000 psi = 6.895 MPa.

4.4 Thermal-Mechanical Analyses of the HL and Surge Line 

The thermal mechanical analyses were performed in two steps. First, a thermal transient 

analysis obtained the temperature distribution throughout the model. Second, the 

nodal-temperature data, together with the pressure and structural-support and boundary 

condition data, were entered into the structural-analysis model. The basic nodal configuration 

and numbering of both models were the same.

4.4.1 FEM for Thermal Analysis and Boundary Conditions 

Two slightly different versions of the same basic FEM were used in two analyses in sequence. 

The first version was used to analyze the thermal model, which included all the components 

shown in Figure 4-29. The second version of the FEM was used to analyze the structural model, 

which, in addition to the components shown in Figure 4-29, included the supports and flailing 

restraints. The supports and flailing restraints were not included in the thermal FEM because 

they do not affect the thermal analysis of the HL or the surge line and were not of interest from a 

thermal standpoint. All of the components of the thermal model were modeled with secondorder (8 nodes) thick quadrilateral shell elements with five integration points across 

the thickness.

The finite element mesh, shown in Figure 4-30, for the thermal analysis was highly refined in 

areas suspected of damage, namely the elbow, HL, and nozzles. The number of finite elements 

is close to 4,000, with close to 63,000 degrees of freedom.
4-29

Figure 4-29 Components of first version of FEM for thermal conduction analysis 

Figure 4-30 FEM for thermal analysis 

The initial temperature was assumed to be the operating temperature of 300 degrees C 

(572 degrees F). The outer surfaces of the system, including the tube support plate, were 

assumed perfectly insulated. The ends of the RV and PZR nozzles were assumed insulated as 

well. The system was brought to steady-state conditions, with a heat flux value that was equal to 

that given at time zero. After the system reached steady state, a transient thermal solution 

ensued, driven by the heat flux profiles. Although the profiles extend to 32,000 s, the thermal 

simulations were terminated when the component temperatures exceeded 1,600 K 

(2,421 degrees F), because the structural models reveal significant damage at temperatures 
4-30

well below 1,600 K. In fact, the structural data do not support temperatures higher than 1,400 K. 

Although the tensile and creep-rupture properties of the materials used in these simulations are 

restricted to temperatures below 1,400 K, it is expected that these materials significantly soften 

and will experience rapid high-temperature damage at temperatures above 1,400 K. 

Section 4.5.5 discusses the implications of this.

4.4.2 FEM for Structural Analysis and Boundary Conditions 

The second version of the FEM, which is used to conduct the structural analysis, is identical to 

that of the thermal model (Figure 4-31), except that the supports and flailing restraints were 

included in the structural model, as shown in Figure 4-31. The temperature history obtained 

from the thermal analysis was entered directly into the structural model for stress and damage 

analysis. Because the severe-accident transient occurs at a relatively slow rate, the hydraulic 

snubbers were not included in the structural model. The surge line contains four supports and 

three flailing restraints. The flailing restraints were included in the structural model because 

preliminary results indicated that the surge line was experiencing significant rigid body 

displacements that exceeded the 12.5-cm (5-in.) radial gaps in the flailing supports. Only the 

bottom head of the SG was modeled with sufficient detail to capture the damage around the SG 

nozzle. Because the SG weight and center of mass were significant factors, their effect was 

included by modeling the remainder of the SG (above the tube support plate) by a rigid body 

(coupled with the bottom head) with an SG effective center of mass at an elevation of 

187.3 m (614.5 ft.).

Figure 4-31 Components of second version of FEM for structural analysis with supports, 

flailing restraints, and hangers 
4-31

Reactor Vessel Nozzle

The HL/surge line model extends to the junction of the RV and the RV nozzle. It is assumed that 

the RV provides full restraint against all rigid-body translations and rotations of the RV nozzle 

end but allows free growth in the radial direction.

Steam Generator

The support arrangement of the SG allows it to move as a rigid body, radially away from the RV, 

as the temperature of the system is increased from room to operating temperature. The gaps 

and shims are designed so the SG bears against the top and bottom bumpers at full power. 

During a severe-accident transient, when the HL temperature increases, the supporting 

structures restrain the SG from moving any further than allowed by the elastic deformation of 

the supports. These supports were modeled as nonlinear springs that can carry compressive 

but not tensile loads. Thus, the snubbers at the upper lateral support allow the SG to tip away 

from vertical toward the RV during a relatively slow severe-accident transient. The SG dead 

weight in such a scenario could potentially apply significant bending and twisting moments on 

the SG inlet nozzle.

The SG required six elastic supports in the direction of the six global rigid degrees of freedom; 

namely, three translations and three rotations. These supports were developed and are 

described according to the local coordinate system shown in Figure 4-31 and labeled as Radial, 

Tangential, Z, or 1, 2, 3. The SG rests on four gimbals that are modeled as simple beam 

members that provide axial elastic support in the vertical direction (Z) with an axial stiffness of 

KV2. Both ends of the beam members are pinned end boundaries.

The rotational stiffness of the SG in the Z direction is referred to as KR4. In the tangential 

direction, both axial and rotational elastic supports (KT3 and KR5) are at the bottom head, and 

the arrangement in the Radial direction along the HL (KT4 and KR5) is similar. Two elastic axial 

supports are at the top of the SG (close to the center of mass). The one in the tangential 

direction is KT5. The radial one (KT6) provides a nonlinear elastic support; if the top of the SG 

leans toward the HL, this support provides resistance only after a displacement of 210 mm 

(8.3 in.). If the top moves backward, away from the HL, the support resists at a different rate, as 

shown in Table 4-1.

Table 4-1 Spring Rates of Steam Generator Supports 

Support 

Name

Spring Rate

lb/ft N/mm Note

KT3 1.63E+08 2.38E+06 Linear

KT4 1.39E+08 2.03E+06 Linear

KT5 5.52E+08 8.06E+06 Linear

KT6 1.92E+08 2.80E+06 Moving toward HL after 210-mm (8.3-in.) 

displacement

KT6 1.24E+08 1.81E+06 Moving away from HL

KV2 2.24E+08 3.27E+06 Linear

KR4 1.51E+10* 2.05E+13** Linear

KR5 4.30E+09* 5.83E+12** Linear

* lb-ft/rad ** N-mm/rad
4-32

Surge Line Supports

The FEM for structural analysis contains nine surge-line supports: three flailing restraints, one 

variable support spring hanger, one threaded-rod support, one constant-support hanger, one 

sway strut assembly, and two hydraulic snubber restraints. The stiffness values for the various 

supports came from Reference 1.

The flailing restraints provide vertical and horizontal supports but a gap allows for thermal 

movement of up to 0.127 meters (5 in). Therefore, effectively, these supports do not provide any 

restraint until the surge line moves significantly. The vertical stiffness is 1.38X106 kN/m 

(9.475X107 lb/ft) and the horizontal stiffness is 3.60X107 kN/m (2.47X109 lb/ft) in compression 

and 4.13X106 kN/m (2.83X108 lb/ft) in tension.

The stiffness of the hanger of the variable-support spring 189.14 kN/m (12,960 lb/ft) is much 

smaller than the stiffness of the other restraints. The threaded support spring hanger exhibits a 

stiffness of 3.58X104 kN/m (2.45X106 lb/ft), and carries a vertical dead weight of 37,245 N 

(8,373 lb) during normal operation. The constant-support hanger supports a constant vertical 

dead weight of 30,248 N (6,800 lb). The stiffness of the sway strut assembly, which provides 

support in both the horizontal and vertical directions, is 1.36X106 kN/m (9.3X106 lb/ft).

The FEM included all of the supports except the snubbers. Figure 4-31 describes the four 

supports (excluding the flailing restraints) that are modeled for the surge line, and Table 4-2 lists 

their types. Three of the supports provide elastic support with a specified spring rate, while the 

fourth (RCH1003) provides a constant load. The other three supports are oriented as shown in 

Figure 4-32.

Table 4-2 Surge-Line Supports in FEM for Structural Analysis 

Pressurizer Nozzle

The HL/surge-line model extends to the junction of the PZR shell and the PZR nozzle. The PZR 

is rigidly supported by the upper and lower lateral supports, which prevent translational and 

torsional movements but allow free radial and vertical thermal growth. The vertical load is 

carried by four columns, attached rigidly to the ring beam of the lower lateral support. Therefore, 

it was assumed that the PZR provides full restraint against all rigid-body translations and 

rotations of the PZR nozzle end but allows free radial growth.

4.4.3 Mechanical and Surface Heat Flux Loading 

4.4.3.1 Gravity and Pressure Loading

The whole system was subjected to gravitational loading. The weight of the SG was applied at 

its center of mass. The weight of the HL valve was distributed throughout its volume. The surge 
4-33

line and the HL gravity loads were applied as body forces. Table 4-3 lists the weights and/or the 

mass densities used for gravity loading; it also shows that steam pressure used throughout the 

systems is 16.2 MPa (2,350 psi).

Table 4-3 Weights and Pressure Loading and Mass Densities Used in Thermal-Mechanical 

Analysis of the HL and Surge Line 

Metric English

Valve weight 111 KN 25,000 lb

SG weight 3,720 KN 836,476 lb

Surge-line mass density 7,500 kg/m3 0.28 lb/in3

HL mass density 7,500 kg/m3 0.28 lb/in3

Steam pressure 16.2 MPa 2,350 psi

4.4.3.2 Surface Heat Flux (Heat Transfer Coefficients)

The thermal model was driven by heat flux profiles as functions of time. Fourteen such profiles 

are assigned to 14 regions, as shown in Figure 4-32 and labeled according to heat flux 

information obtained from RELAP5 calculations.

Figure 4-32 Control volumes for thermal-hydraulic analysis of the HL and surge line 

by RELAP5 

RELAP5 divided the HL into two noninteracting independent halves. The top half carries the hot 

steam from the reactor to the SG and the bottom half returns the cool steam from the SG to the 

reactor. The top half of the HL was divided into five cells (1001001 through 1001005), each with 

constant heat flux. The bottom half of the HL was also divided into five cells (1011001 through 

1011005), each with constant heat flux. The outer surfaces of the HL and surge line were 
4-34

assumed to be perfectly insulated. The highest heat fluxes in the top and bottom halves are in 

cells 1001001 and 1011005, respectively. The lower head of the SG was assigned the SG inlet 

plenum heat flux. The surge line was divided into three cells, with the closest cell to the HL 

designated as 1531003. For the present analysis, the heat transfer coefficient from the RELAP5 

results was spatially adjusted in the HL and surge line, based on the developing curve provided 

in NUREG-1922, “Computational Fluid Dynamics Analysis of Natural Circulation Flows in a 

Pressurized-Water Reactor Loop under Severe Accident Conditions,” issued March 

2010 (Ref. 3).

4.4.4 Results of Thermal-Mechanical Analysis of HL and Surge Line 

The basic reference case used the thermal properties along with heat flux profiles discussed in 

the previous sections. The thermal transient analysis, after reaching the steady state, started at 

time = 9,222 s and terminated at ≈19,330 s. After completion of the thermal solution, the 

temperature time histories were input into the structural portion of the model. The components 

were assumed to respond to the structural, gravity, and thermal loads by an additive 

combination of elastic, rate-dependent plastic, and creep (visco-plastic) material behaviors. The 

material model consisted of using a simple thermal plasticity combined with a secondary creep 

law. Figure 4-33 shows the stress versus plastic strain curve used for the Type 316 stainless 

steel. Reference 1 was the source for the properties used for the A508 carbon steel and the 

Alloy 182 weld metal, and Appendix A contains the properties for the Type 316 stainless steel. 

Because material data were not available for temperatures higher than 1,373 K, these same 

properties were used at higher temperatures. However, as will be seen, failure is predicted 

before the temperatures get much higher than this.

Figure 4-33 Temperature-dependent stress strain curves for 316 stainless steel 

(Appendix A) 

An ABAQUS power-law model is chosen to model creep behavior, given by:

.

εε

cccc = AAqq�nnttmm (4.3)

0

100

200

300

400

500

600

700

800

0 0.5 1

Stress (MPa)

Plastic Strain (mm/mm)

T = 473 K

T = 573 K

T = 698 K

T = 823 K

T = 923 K

T = 973 K

T = 1023 K

T = 1173 K

T = 1373 K
4-35

where .

εε

cccc is the uniaxial equivalent creep strain rate, qq� is the uniaxial equivalent deviatoric 

stress, and t is the total analysis time, and A, n are temperature dependent constants and m=0. 

The analysis uses the creep properties given in Appendix A.

Figures 4-34 and 4-35 show representative temperature contours of the whole system, captured 

at 9,222 s and 13,555 s, respectively. The model was based on metric units, with temperature 

expressed in Kelvin. The steady-state temperature of 623 K is reached at 9,222 s in the entire 

region of consideration, as shown in Figure 4-34. The upper half of the HL experiences much 

higher temperatures during the transient, as shown in Figure 4-35.

Figures 4-36 and 4-37 show the contours of effective creep strain and plastic strains, 

respectively. Both the figures indicate that the upper half of the HL experiences higher creep 

and plastic strains. The plastic strains and creep strains are predicted to reach above 

30 percent and 7 percent in the upper half of the HL. These levels of strains are quite high and 

indicate potential failure in the regions of interest.

Figure 4-34 Temperature contours at inner surface at 9,222 s indicate the steady-state 

condition of 623 K in the entire region of consideration 

Figure 4-35 Temperature contours at inner surface at 13,555 s indicate the higher 

temperature in the upper half of the HL region 
4-36

Figure 4-36 Contours of accumulated creep strain at inner surface at 12,300 s indicate the 

significant creep strains in the upper half of the HL region 

Figure 4-37 Contours of plastic strain at inner surface at 12,300 s indicate the 

concentration of plastic strains in the upper half of the HL region 

4.4.5 Evaluation of Structural Damage 

Creep failure can be predicted either by exhaustion of material creep ductility or by 

accumulation of creep damage. Failure by exhaustion of creep ductility occurs when

Effective Creep Strain = ε = εc = Creep Ductility (4.4)

Because creep ductility data for the materials used in the analyses are available for the entire 

temperature range of interest, the linear time fraction damage rule was used to calculate the 

creep damage as follows:

Creep Damage = ∆t

tr

(T,σ) ∑

(4.5)

where Δt is the time interval at temperature T, σ is von Mises effective stress, and tr is the time 

to creep rupture at temperature T. Failure is predicted to occur when the creep damage is equal 

to 1.
4-37

Given the state of stress and temperature, the Larson Miller parameter was used to evaluate the 

time to rupture, tr:

tr = 10

PLM

T −C 











(4.6)

where T is the absolute temperature in Kelvin, PLM is the Larson Miller parameter, which can 

be obtained approximately as a function of effective stress σ as follows:

PLM = A*Log10(σ) + B (4.7)

and A, B, and C are material parameters given in Appendix A.

Creep damage was considered only if the in-plane principal stress was tensile, because 

compressive in-plane stress does not initiate cracking.

At elevated temperatures, creep deformation tends to relax the stresses and keep them below 

the yield strength of the material. However, in the presence of a time-dependent driving force, 

such as thermal expansion, creep deformation may not be fast enough to relax the stresses to 

below the yield stress. In such cases, failure by tensile rupture is a possibility.

Uniaxial tension tests conducted at high temperatures indicate that stainless steels and the 

ferritic steels experience a uniform elongation of the order of few percent (2–5 percent), beyond 

which necking and plastic strain localization occurs and any additional plastic displacement is 

negligible. Based on this, it is possible to determine failure time and location when a material 

point reaches a through-thickness plastic strain of 2 percent. Because this failure criterion is 

quite arbitrary, this study did not adopt it. Nonetheless, it should be pointed out that the plastic 

strains reach values of above 10 percent in the upper half of the HL before the failure is 

predicted using the Larsen-Miller parameter approach described above.

Figures 4-38 and 4-39 show the creep damage, calculated using Equation 4.5, in the section of 

HL experiencing higher creep and plastic strains. The through-thickness damage shown in 

Figure 4-38 indicates that the maximum damage of 1 (indicated by red color) occurs on the 

upper half of the HL away from the nozzle. The corresponding damage in the outer and inner 

surfaces shown in Figures 4-39a and 4-39b indicates that it is rather uniform through the 

thickness, although the maximum damage occurs in the inner surface earlier. This indicates that 

failure through the thickness is quite rapid, perhaps because of the steep increase in the 

temperature transient.
4-38

Figure 4-38 Contours of through-thickness damage at 12,300 s shown in the section of HL 

experiencing higher strains 

The red-colored regions reach the creep damage of unity.

The structural analysis of the system model considered here posed convergence issues beyond 

14,000 s. Although maximum damage is predicted much earlier, this model is not conducive to 

conducting additional analyses to examine the effect of weld-overlay and the effects of varying 

material response. In addition, the system model took considerable computer processing hours 

to perform the needed calculations. Because the failure occurs in the HL region, further 

analyses used a finite element model of the HL region.

(a) Outer surface (b) Inner surface

Figure 4-39 Contours of creep damage at 12,300 s shown in the (a) outer surface and 

(b) inner surface of HL experiencing higher strains

The red-colored regions reach the creep damage of unity. 

4.4.6 HL Model 

The thermal mechanical analysis using the smaller HL model employed the same procedure 

described for the system model. Figures 4-40 and 4-41 show the contours of effective creep 

strain and plastic strains, respectively, at time equals 12,430 s. The strain distributions in the 

upper half of the HL are similar to those shown in Figures 4-36 and 4-37 for the system model. 

Figures 4-40 and 4-41 indicate that the upper half of the HL experiences higher creep and 

plastic strains. The plastic strains and creep strains are predicted to reach above 40 percent 

and 6 percent in the upper half of the HL. These levels of strains are similar to those predicted 

using the system model. Thus, the smaller HL model yields similar results to the larger system 

model. Because of slightly lower levels of strains predicted using the smaller HL model, the 

failure time may be longer. However, because of the steep transient, the failure time using the 

HL model, shown in Figure 4-42, was only 126 s longer than the time predicted using the 

system model.
4-39

Figure 4-40 Contours of accumulated creep strain at inner surface at 12,430 s indicate the 

significant creep strains in the upper half of the HL region 

The strain distribution and maximum strain level are similar but not identical to 

the system model.

Figure 4-41 Contours of accumulated plastic strain at inner surface at 12,430 s indicate the 

significant creep strains in the upper half of the HL region 

The strain distribution and maximum strain level are similar but not identical to 

the system model. 
4-40

Figure 4-42 Contours of through-thickness damage at 12,430 s shown in the section of HL 

experiencing higher strains 

The red-colored regions reach the creep damage of unity.

Sensitivity Analyses

Several additional analyses examined the effects of material response and the effect of not 

spatially adjusting the heat transfer coefficients obtained from RELAP results. To examine the 

effect of material behavior, the analyses assumed only creep or plastic response. The earlier 

results were obtained using combined plasticity and creep response. Assuming only creep 

behavior accelerates the failure time to 12,140 s (Figure 4-43a), while assuming plasticity only 

delays the failure time to 13,205 s (Figure 4-43b). Assuming only plasticity behavior at the 

severe-accident temperatures is not realistic. Additionally, the damage is predicted using 

creep-rupture data. These two considerations, coupled with the observation that the effective 

plastic strain in the HL region reaches values beyond 400 percent, invalidate the use of the 

plasticity-only model.

(a) Creep Response (b) Plasticity Response

Figure 4-43 Contours of through-thickness damage assuming (a) creep-only behavior at 

12,140 s and (b) plasticity-only behavior at 13,025 s 

The red-colored regions reach the creep damage of unity. Note that damage is predicted in 

different sections of the upper half of the HL.

The earlier analyses accounted for the spatial adjustment of the heat transfer coefficient 

obtained from RELAP, based on the developing curve given in NUREG-1922 (Ref. 3). 
4-41

The spatial adjustment increases the surface temperature inside the HL, which may accelerate 

failure. Thus, one would expect the failure time to be longer without the spatial adjustment. 

Figure 4-44 shows contours of through-thickness damage assuming no spatial adjustment of e 

heat transfer coefficient obtained from RELAP. Failure is predicted at 12,610 s, which is 180 s 

longer than the result predicted with the spatial adjustment of heat transfer.

Figure 4-44 Contours of through-thickness damage assuming no spatial adjustment of heat 

transfer coefficient obtained from RELAP 

The red-colored regions reach the creep damage of unity.

Effect of Weld Overlay

The welded region between the HL nozzle and pipe could be prone to primary water 

stress-corrosion cracking. One of the preventive methods to mitigate potential failure of the pipe 

during normal operation involves applying a weld overlay, where additional material is welded 

over the pipe. This results in increasing thickness of pipe over the welded region. To examine 

the effect of the weld overlay in increasing the failure time during the severe-accident sequence 

considered in the previous analyses, an HL model with an overlay was analyzed. The boundary 

conditions and thermal transient were identical to the previous analyses. Contours of throughthickness damage for the HL pipe with weld overlay, shown in Figure 4-45, indicate failure at 

12,500 s. Note that the failure location is similar, and the failure time is increased by 72 s 

relative to the pipe with no weld overlay.
4-42

Figure 4-45 Contours of through-thickness damage for the HL pipe with weld overlay 

at 12.500 s 

Note that the failure location is similar to the pipe without a weld overlay. The failure time 

increases by 70 s relative to the pipe with no weld overlay.

4.5 Conclusions 

4.5.1 SG Primary Manway 

The bolt loads are fully relaxed by thermal creep, and the contact pressure in the joint was 

reduced to zero by the time the bolt temperature reached 450 degrees C (842 degrees F), 

which corresponds to 14,346 s. If 8 of the 16 bolts were initially loose (85-percent design 

preload), their loads would be relaxed out at 440 degrees C, or 824 degrees F (14,156 s). If the 

bolts were uniformly preloaded but if the creep rate were 10 times greater than the assumed 

reference creep rate, bolt loads would be relaxed out by 430 degrees C, or 806 degrees F 

(13,975 s). These calculations are based on estimated creep rate data of alloys similar to 

SA 193 (B7).

Rather than bolt rupture, a more likely sequence for the depressurization of the primary side is 

the lifting off of the cover plate after the bolt loads have relaxed out and created a leakage path 

for the steam. Considering a 5-cm (2-in.) diameter hole with an area 20 cm2 (3 in.2

) to be 

sufficient to rapidly depressurize the primary side, a leakage area equivalent to such a hole is 

created in the reference case by 600 degrees C, or 1,112 degrees F (16,726 s). The actual flow 

area will be less because of gasket springback, which should be minimal at these temperatures 

because of thermal creep. However, gasket creep data at high temperature are needed to 

verify this.

Sensitivity analyses showed that the time to open a sufficiently large leakage area is virtually 

unchanged, even if 8 of the 16 bolts were initially tightened to only 85 percent of the design 

preload. The opening time was also found to be strongly dependent on the bolt temperature. A 

simplified model of the effect of steam leakage on local heating of the bolts showed that the 

opening time could be reduced by more than 1,500 s relative to the reference case, which does 

not account for leakage effects. A more rigorous treatment of this problem must be obtained by 

a coupled thermal-hydraulics and stress analysis in the future. 
4-43

Finally, subsequent creep tests on SA 193-B7 have shown that the creep strains in the analysis 

were overestimated by a factor of 5 to 10. This would imply that the bolt load relaxation should 

be significantly less rapid than calculated here and the failure times calculated may be highly 

conservative (i.e., overestimated).

4.5.2 RTD Welds 

A heat conduction FEA of the RTD, the ID and OD attachment welds to the HL, and an axial 

segment of the HL showed that the average ID weld temperature is 50–80 degrees C 

(122–176 degrees F) hotter than the average OD weld temperature. The tip of the RTD scoop 

also is heated very rapidly to a high temperature.

Stress analysis showed that significant load is transferred between the ID and the OD welds 

because of creep effects. Inclusion of both creep and plasticity effects in the analysis showed 

that the initiation of tensile rupture failure is predicted to occur at the OD weld/RTD interface at 

13,930 s. On the other hand, if plastic yielding is suppressed, initiation of creep failure is 

predicted to occur at the ID weld/RTD interface at 13,890 s. Thus, regardless of which failure 

criterion is applied, the failure time is close to 13,900 s.

The sensitivity analysis showed that, when the outside heat transfer coefficients on the RTD are 

increased by a factor of 2 from the reference values, ignoring the internal surface heating on the 

RTD, failure time is reduced by 184 s from the reference failure time. If the reference heat 

transfer coefficients are applied equally to both the outside and inside surfaces of the RTD, 

failure time is reduced by 100 s from the reference failure time. A factor of 10 increase in creep 

rate reduces the creep failure time by 180 s when compared with the reference failure time.

4.5.3 Instrument Line 

The stress analysis showed that stresses at the weld interfaces with the instrument line and the 

RTD flange are at all times less than the yield strength. The reference creep failure time at both 

interfaces of the weld is 14,230 s. Because the maximum stress in the instrument line away from 

the weld is greater than the maximum stress in the weld, the instrument line itself fails at 14,150 s, 

which is 80 s earlier than failure at the interfaces.

The sensitivity analysis showed that, by doubling the weld dimensions, the average stresses are 

reduced significantly and the creep failure time is increased to 14,330 s. Increasing the creep 

rate by a factor of 10, when compared with the reference case, reduces the failure times of the 

instrument line and the instrument line weld to 14,090 and 14,110 s, respectively.

 

4.5.4 PORV Plug-to-Cage Impact 

An analysis of multiple impacts with 32-mm/s (1.25-in./s) impact velocity at 288 degrees C 

(550 degrees F) showed that, in the absence of the Stellite overlay on the plug, the maximum 

effective plastic strain in the plug increased from 3.8 percent, in the first impact, to 6.4 percent in 

the second impact, and to 8.4 percent in the third impact. At 538 degrees C (1,000 degrees F), 

the corresponding plastic strains were 4.1, 7.6, and 9.4 percent, respectively. The stress-plastic 

strain response showed no open hysteresis loop. The cage did not experience any plastic 

yielding. The plastic strains did not change if the plug impact velocity was doubled.
4-44

Inclusion of a 2-mm thick hard Stellite overlay on the plug suppressed plastic strain in the plug 

and in the overlay at 538 degrees C (1,000 degrees F). The cage also did not suffer any 

plastic strain.

Plastic strains will develop during impacts at higher temperatures because both the cage 

material (17-4 PH steel) and the Stellite overlay will lose strength at temperatures greater than 

593 degrees C (1,100 degrees F). Stress-strain properties of the cage material and the Stellite 

overlay are needed at higher temperature so similar impact analyses may be conducted.

4.5.5 HL and Surge Line 

The analyses presented in Section 4.4 indicate that the upper half of the HL will fail much earlier 

than the other RCS regions. Table 4-4 summarizes the failure times predicted by the various 

analyses considered in Section 4.4. The predicted failure times for all the cases considered are 

below the 5th percentile failure time of 12,800 s estimated by the C-SGTR calculator, assuming 

one HL. In addition, the 5th percentile failure time predicted by the C-SGTR calculator, 

assuming four HLs and a surge line, is 12,700 s. It is important to examine these results in the 

context of the assumptions. Firstly, the predicted values indicate the relative influence of various 

assumptions with respect to material behavior, such as creep and plasticity, spatial adjustment 

of heat-transfer coefficient, and weld overlay. Secondly, the predicted values fall within a narrow 

band of 500 s of predicted failure time. This is not surprising because, after an initial slow rise, 

the temperatures rise sharply beyond 12,000 s, imparting significant damage to the HL portion 

closer to the reactor pressure vessel nozzle. Hence, the various assumptions do not yield 

significantly different predicted failure times. It was pointed out earlier that the materials 

properties used in these simulations were restricted to temperatures below 1,400 K 

(1,126 degrees C or 2,060 degrees F), and that these materials will experience rapid 

high-temperature damage at temperatures above 1,400 K. This consideration implies that the 

actual failure times could be less than the predicted failure times. Nonetheless, this difference is 

not likely to be large because of the sharp rise in temperatures beyond 12,000 s. 

Table 4-4 Summary of Predicted HL Failure Times for the Various Analyses 

Finite Element Model Features Weld Overlay Failure Time (seconds)

Creep and Plasticity:

 HTC not adjusted spatially No 12560

Hot Leg Model

Creep and Plasticity:

Spatially Adjustment of HTC Yes 12500

Creep only:

Spatially Adjustment of HTC No 12140

System Creep and Plasticity:

Spatially Adjustment of HTC No 12300

Creep and Plasticity:

Spatially Adjustment of HTC No 12430
4-45

4.6 References 

1. Brust, F.W., et al., “Summary of Weld Residual Stress Analyses for Dissimilar Metal 

Weld Nozzles,” Proceedings of ASME PVP conference, July 2010, paper 

PVP2010-26106.

2. ASME BPVC-III, 2015 ASME Boiler and Pressure Vessel Code, Section III: Rules for 

Construction of Nuclear Facility Components, General Requirements for Division 1 and 

Division 2.

3. U.S. Nuclear Regulatory Commission, “Computational Fluid Dynamics Analysis of 

Natural Circulation Flows in a Pressurized-Water Reactor Loop under Severe Accident 

Conditions,” NUREG-1922, March 2010, Agencywide Documents Access and 

Management System (ADAMS) Accession No. ML110110152.

5-1

5 TECHNICAL BASIS FOR PREDICTING BEHAVIOR OF FLAWED 

STEAM GENERATOR TUBES IN SEVERE ACCIDENTS 

5.1 Introduction 

This report summarizes the technical basis for predicting ligament-rupture pressure, 

crack-opening area, and unstable burst pressure of steam generator (SG) tubes with flaws 

under severe-accident transients. The content of this report is based on research carried out by 

the Nuclear Engineering Division of Argonne National Laboratory (ANL), under U.S. Nuclear 

Regulatory Commission (NRC) sponsorship and the results reported in NUREG/CR-6575, 

“Failure Behavior of Internally Pressurized Flawed and Unflawed Steam Generator Tubing at 

High Temperatures—Experiments and Comparison with Model Predictions,” issued 1998

(Ref. 1), and NUREG/CR-6756, “Analysis of Potential for Jet-Impingement Erosion from Leaking 

Steam Generator Tubes during Severe Accidents,” issued May 2002 (Ref. 2).

To develop an understanding of the risks associated with SG tube rupture, the NRC contracted 

with ANL in 1995 to develop rupture pressure and leak rate correlations for tubes with flaws and 

validate them by subjecting them to pressures and temperatures associated with 

severe-accident transients. The NRC subsequently published the results from the ANL study in 

NUREG/CR-6575 and NUREG/CR-6756.

Operating experience with pressurized-water reactor SGs in both the United States and abroad 

has shown that cracks of various morphologies can and do occur in SG tubes, starting early in 

life. These may be single cracks that are axial or circumferential, inside diameter (ID) or outside 

diameter (OD) initiated, and part-through-wall or through-wall, or multiple cracks that are parallel 

or form a network. Tests have shown that, depending on the location and morphology of these 

cracks, the SG tubes can be weakened to various extents.

Under normal operating conditions, the temperature in an SG is about 300 degrees Celsius (C) 

(572 degrees Fahrenheit (F)), and the pressure across the tube wall, ∆pno, is about 

9 megapascals (MPa) (1,300 pounds per square inch (psi)). Under design-basis accidents, such 

as a main steamline break (MSLB) in which the secondary side has dropped to atmospheric 

pressure, the pressure across the tube wall, ∆pMSLB, is 18 MPa (2,560 psi) and the temperature 

of the SG tubing is less than 350 degrees C (662 degrees F). In this temperature range, creep 

effects are negligible in Alloy 600. Degraded tubes must actually be capable of withstanding 

3⋅∆pno ≈ 27 MPa (3,900 psi) and 1.4⋅∆pMSLB ≈25 MPa (3,660 psi) to meet requirements for 

continued operation. For typical unflawed SG tubes made of Alloy 600, the failure pressure, pb, 

at these temperatures is about 65 MPa (9,400 psi).

Severe accidents involving significant core damage are unlikely events in nuclear reactors. 

Even in the unlikely event that such an accident should occur, in most cases any potential risk 

to the public is mitigated by the presence of a robust containment. The behavior of SG tubing 

during such severe accidents is of particular interest, since failure of the SG tubes could lead to 

bypass of the containment. The accident sequences that appear to produce the greatest risk of 

SG tube failure are those in which the reactor pressure vessel fails to depressurize, but 

depressurization does occur on the secondary side. The NRC is pursuing studies to better 

understand the progression of such sequences, the temperature of the SG tubes during such 

accidents, and the behavior of SG tubes at the high temperatures associated with such

accidents. At these high temperatures, plastic deformation is likely to be much more extensive 

than at normal reactor operating temperatures, and creep effects may no longer be negligible. 
5-2

The development and validation of models to describe the failure of flawed SG tubes at high 

temperatures was a major objective of the ANL study. The tests conducted and the models 

developed do not attempt to accurately simulate any particular severe-accident scenario; rather 

they are intended to provide tools that can be used to determine failure under a broad range of 

pressure and temperature histories.

5.2 Ligament-Rupture Pressure 

5.2.1 Analytical Failure Models 

There is substantial literature on the development and validation of analytical models to 

describe the behavior of flawed tubes at normal reactor operating temperatures 

288–320 degrees C (550–608 degrees F). These models and data can be used to analyze the 

potential for failure during design-basis accidents, during which the temperature of the SG 

tubing is less than 350 degrees C (662 degrees F). In this temperature range, creep effects are 

negligible in Alloy 600. However, in postulated severe accidents, much higher temperatures are 

possible. At these higher temperatures, plastic deformation is likely to be much more extensive 

than at normal reactor operating temperatures, and creep effects can no longer be neglected. 

Until recently, there were no test data or validated models to predict the failure of flawed tubes 

at temperatures associated with postulated severe accidents.

5.2.1.1 Axial Cracks

5.2.1.1.1 Flow-Stress Model

ANL developed two analytical models for predicting ligament-rupture pressure of tubes with 

axial part-through-wall flaws at elevated temperatures. The first one, based on flow-stress 

theory, was obtained by slightly modifying an empirical stress magnification factor mp (Ref. 3), 

which depends only on the geometry of the flaw and the tube but is independent of the flow 

stress of the tube material. The modified form of the mp factor developed by ANL is as follows:

(5.1)

where

a = crack depth

h = tube wall thickness

m = bulging factor used for predicting unstable burst pressure of tubes with through-wall 

axial cracks and is given by
5-3

where

2c = axial crack length

Rm = mean radius of the tube

ν = Poisson’s ratio

The ligament rupture (psc) and unstable burst (pcr) pressures are obtained by reducing the 

unstable burst pressure (pb) of the unflawed tube by dividing it by mp and m, respectively; i.e.,

and (5.2a)

(5.2b)

where , the flow stress of the material, is defined as an average of the yield and ultimate 

tensile strengths (σy+σu)/2 and the unstable burst pressure of the unflawed tube is given by

(5.2c)

Tests conducted at ANL validated Equations 5.2a and 5.2b at low temperatures on Alloy 600 

tubes with axial EDM notches (Figures 5-1a and 5-1b). (An EDM notch is a mechanically 

simulated defect, which is made by removal of material with an electrostatic discharge 

machine (EDM).)

The generalized flow-stress model assumes that, for any arbitrary history of hoop stress σ(t) and 

temperature T(t), failure occurs at a temperature T and hoop stress σ whenever the following 

failure equation is satisfied, independent of stress-temperature history:
5-4

(a) (b)

Figure 5-1 Predicted vs. observed (a) ligament-rupture pressures and (b) unstable burst 

pressures of Alloy 600 tubes with axial notches at room temperature 

(5.3)

where is the flow stress at temperature T and mp is the stress-magnification factor.

Figure 5-2 plots flow stresses for Alloy 600 computed from the above data, together with others 

from various sources. Most of these tests were conducted under stroke-control at a nominal 

strain rate of 34 percent/minute (min). Figure 5-2 also shows data from room-temperature 

tensile tests on the tubing being tested at ANL. The flow stress decreases markedly with 

temperature above 600 degrees C (1,112 degrees F). Note that, although there may be a wide 

variation in the flow stress at low temperatures, the heat-to-heat and product form variations in 

the flow stress diminish rapidly with increasing temperature. The Idaho National Engineering 

Laboratory (INEL) flow-stress curve, which covers the widest range of temperature, is used for 

failure predictions.
5-5

Figure 5-2 Flow-stress curves for various product forms of Alloy 600 

5.2.1.1.2 Creep-Rupture Model

In the creep-rupture model, creep failure of an unflawed tube under a varying stress and 

temperature history can be predicted by a relatively straightforward analysis (Ref. 4), based on 

a linear time-fraction damage rule, such as used in the American Society of Mechanical 

Engineers (ASME) Boiler and Pressure Vessel Code, Section III, Subsection NH, as follows:

(4a)

where tR is the time to creep rupture for a uniaxial specimen under a stress σ and temperature 

T, both of which may be functions of time, and tf is the time to failure of the tube. In the 
5-6

creep-rupture model for flawed tubes, it was assumed that failure can be predicted by the 

following equation:

(4b)

The available literature data on the creep-rupture properties of Alloy 600 were reviewed. 

Figure 5-3 shows a least-squares best fit, along with the estimated ±95 percent 

confidence limits.

Figure 5-3 Larson-Miller plot for Alloy 600 tubes 

In equation form, the Larson-Miller parameter is given by

LMP = (23.2±0.7–2.4 lnσ) x 103 for σ > 5.7 ksi (5.4)

where the time to rupture tR is then given by

15

10 3

10 −

−

= T

LMP

Rt (5.5)

with tR in h and T in K.

5.2.1.2 Circumferential Cracks

5.2.1.2.1 Through-Wall Circumferential Cracks

Failure loads of tubes with a single circumferential crack critically depend on the bending 

constraint imposed externally on the tubes. The two extreme cases are the free-bending case 
5-7

and the fully constrained case. In reality, SG tubes are partially constrained against bending by 

tube support plates.

Free-Bending Case

For an unconstrained (free-to-bend) tube with a through-wall crack of angular length 2θ, 

where θ is the circumferential angle of the tube cross-section, and no applied primary bending 

stress, the critical failure pressure is (Ref. 5):

(7a)

where the angular location of the neutral axis is given by

(7b)

Fully Constrained Case

Equation 7a is applicable to one extreme case, where the tube is completely free to bend. In the 

opposite extreme case of total constraint against bending, a criterion based on maximum shear 

stress in the net section (Ref. 1) can be used to calculate the instability limit pressure:

(8a)

where

(8b)

The following thin-shell, uniaxial approximation to Equation 8a is often used to predict the failure 

of SG tubes that are fully constrained against bending:

(8c)

In reality, the tube support plates offer significant but not total restraint against bending, a 

circumstance that tends to increase the failure pressure to somewhere between the pressure of 

those predicted by Equations 7a and 8a (or 8c).

5.2.1.2.2 Part-Through-Wall Circumferential Cracks

Consider a tube with mean radius Rm and wall thickness h, that contains either two symmetrical 

part-through circumferential cracks (SC) (Figure 5-4a) or a single part-through circumferential 

crack (Figure 5-4b) of angular length 2θ and depth a. At low temperatures, where creep effects 
5-8

are negligible, the ligament-failure pressure (psc) is generally expressed in terms of a 

stress-magnification factor (mp) by equating the magnified axial stress in the ligament to the 

flow stress,

(5.6)

Failure pressure for circumferentially cracked tubes (i.e., the value of the stress-magnification 

factor mp), depends strongly on the degree of restraint the tubes are subjected to against 

bending. The two extreme cases (i.e., the free-bending case and the completely constrained 

case) are relatively easy to analyze. Generally, SG tubes are sufficiently constrained laterally 

that the failure loads are expected to be much closer to the completely constrained case than 

the free-bending case. The discussion here assumes that the tubes are either completely 

constrained or are completely free to bend.

(a) (b)

Figure 5-4 Stress distributions through section at failure of tubes with (a) two symmetrically 

located part-through circumferential cracks and (b) single part-through 

circumferential crack 

Fully Constrained Case

The fully constrained case would also include the case for an unrestrained tube that contains 

two symmetrical cracks (Figure 5-4a). In this case, the whole section that contains the crack (or 

cracks) is subjected to axial tensile stress, with the ligament (or ligaments) being subjected to 

stress intensification. If the average stress in the ligament (or ligaments) is expressed as 1/m 

times the average stress in the rest of the section that contains the crack (or cracks), the 

average ligament axial stress (σlig) can be calculated from a simple equilibrium of axial forces,
5-9

(10a)

where

n = 1 for a single crack

n = 2 for 2 symmetrical cracks.

Defining mp as the ratio of the average ligament axial stress and the average axial stress in the 

unflawed tube, mp is given by

(10b)

Originally, the following empirically obtained expression was used (Ref. 6).

(11)

with n = 1.

Although Kurihara recommended values of κ = 2 and μ = 0.2 for the exponents, the results are 

almost indistinguishable from those obtained by using κ = 3 and μ = 0.3. Because the behavior 

of Equation 11 is not correct (i.e., m does not tend to 0) when a/h tends to 1 for all θ, it was 

modified to have the same form as in the case of axial cracks; that is,

(12a)

where

(12b)

and λ and γ are fitting parameters.

Both the failure modes and moments of the original set of test data from four-point bending 

failure tests on pressurized part-through circumferentially cracked Type 304 stainless steel 

pipes at room temperature (used by Kurihara) can be predicted somewhat better by the current 

model with λ = 0.2 and γ = 0.2 and by defining the flow stress as 0.55[σy + σu], (see 

Figures 5-5a and 5-5b for two possible empirical models).
5-10

Unsymmetrical part-through circumferentially cracked 165.2-mm diameter (11-mm wall 

thickness) pipe specimens were subjected to a four-point bend test with a constant internal 

pressure of 6.9 MPa (1,000 psi) at room temperature). Dashed lines denote predicted failure 

bending moments for through-wall cracks, open symbols denote tests that failed by leakage, 

and filled symbols denote those that failed by breaking into two pieces.

(a) (b)

Figure 5-5 Variations of experimental failure bending moments with crack angle and those 

predicted by (a) Kurihara model and (b) ANL model 

Free-Bending Case

Figure 5-4b shows that, in the free-bending case, part of the section that contains the crack will, 

in general, be subjected to compressive stress. As a result, Equation 10a must be replaced by

(13a)

where the angle β that defines the location of the neutral axis is given by

(13b)

and Equation 10b has to be replaced by

(13c)

with m and N defined by Equations 12a and 12b, respectively.
5-11

5.2.2 Validation Tests for Ligament Rupture 

5.2.2.1 Validation Tests for Axial Notches

Seventy-three tests designed to validate the ANL creep-rupture model were carried out in the 

high-temperature test facility using three types of loading histories. The tests were conducted on 

19.1-mm (3

/4-in.) and 22.2-mm (7/8-in.) diameter Alloy 600 tubes that contained a variety of EDM 

flaws. Such flaws are typically 0.0203-centimeter (cm) (0.008-inch [in.]) wide and are not as 

sharp as real cracks, but previous tests at lower temperatures have shown that the failure 

pressures of specimens with corrosion cracks are at most about 10 percent less than those 

predicted by failure correlations developed from specimens with machined flaws (Ref. 7). At 

higher temperatures, because of crack tip blunting, the effect of the initial crack tip geometry 

would be expected to be of even less significance.

Measurement of Axial Flaw Depth

The flaw depth and length are critical parameters in calculating the expected failure pressures of

the tubes, and these dimensions must be determined as precisely as possible. The accurate 

determination of the flaw depths, in particular, poses some difficulties. Four methods were 

developed to measure the depths of the machined flaws. Two of these methods are applicable 

to the specimens before testing, one is performed after testing, and the fourth method is 

destructive and thereby prevents subsequent pressure testing of the specimen.

The first technique used to measure flaw depth was posttest fractography. In this method, the 

fracture surfaces of the failed specimen are photographed at a known magnification after the 

test, and the contrast between the machined portion of the fracture surface and the region of 

subsequent ductile fracture in the photograph permits a reasonably accurate determination of 

flaw depth.

The second technique used to measure flaw depth was replication of the premachined flaws. In 

this technique, a plastic replica was made of the flawed region of the specimen before testing, 

and the height of this replica, which corresponds to the depth of the flaw, was then determined 

by optical microscopy.

A third technique is to directly measure the flaw depth before testing with a traveling optical 

microscope that gives a digital readout of the x, y, and z positions of the objective lens. The flaw 

depth can be measured by focusing first on the outer surface of the specimen and then on the 

bottom of the machined flaw. The flaw depth corresponds to the movement of the microscope 

objective between these two steps; readings accurate to within about ±2,500 micrometer (μm) 

(±0.1 mil) are possible.

A fourth technique for determining flaw depth is destructive metallography of the flawed tube. 

The tube is simply sectioned through the flaw, and the depth at that position is determined from 

a microphotograph.

The ANL program used all four of these techniques, and NUREG/CR-6575 (Ref. 1) lists the 

results in a table. Aside from one invalid measurement, the agreement among the various 

techniques for these flaws was quite good. The largest variation in measured flaw depth was 

0.02 mm (0.9 mils), or about a 6-percent variation between the values measured by pretest 

optical microscopy and posttest metallography. In general, the flaw depth values obtained by 

replication are slightly greater than those obtained by posttest fractography; the pretest 
5-12

microscopy determinations agree reasonably well with the values obtained by replication. 

Because the posttest fractography values represent the only consistent set of values for all of 

the specimens, the analysis and modeling of the tests used these flaw-depth values.

5.2.2.1.1 Constant Temperature/Pressure Rupture Tests

Unflawed tubes, tubes with shallow notches (55–65-percent deep, 2.54 cm (1 in.) long) and 

tubes with deep notches (90-percent deep and 0.635–5.08 cm (0.25–2 in.) long) were tested 

under constant pressure and constant temperature conditions until failure. The unflawed tubes 

were tested at 700–800 degrees C (1,292–1,472 degrees F) and 12.4–31.0 MPa 

(1.8–4.5 kilopound per square inch [ksi]). The shallow notches were tested at 

667–800 degrees C (1,233–1,472 degrees F) and 9.6–31 MPa (1.4–4.5 ksi) pressure, and the 

deep notches were tested at 800 degrees C (1,292 degrees F) and 2.1–3.1 MPa 

(0.30–0.45 ksi). The unflawed tubes and the tubes with shallow notches burst in an unstable 

manner with large crack opening and notch tip tearing. The predicted ligament-rupture 

pressures of the tubes with shallow notches were greater than the burst pressure of the 

100-percent through-wall notches with the same length, thus precipitating burst immediately

after ligament rupture. There was enough strain energy stored in these specimens to drive them

to burst, even though the pump could not maintain the pressure after ligament rupture. The

deep flaws failed by ligament rupture with very little crack opening and stored energy. Figure 5-6

shows a plot of the predicted (creep-rupture model) vs. observed failure pressures of the

specimens. In all cases, the failure pressures are predicted to within ±95 percent prediction

limits. It should be noted that the flow-stress model is incapable of predicting time to failure for

tests of this type and, in fact, would predict that none of the tubes should have failed.

Figure 5-6 Predicted vs. observed time to failure of flawed and unflawed tubes under 

constant temperature and pressure condition 
5-13

5.2.2.1.2 Pressure and Temperature Ramp Tests

To evaluate the importance of loading rates on the failure conditions and compare the predictive 

capabilities of the creep-rupture model and the flow-stress model, two additional types of tests 

were conducted. In the first type, the specimens were heated to a temperature and then 

pressurized isothermally at a constant pressure ramp until failure. In the second type, the 

specimens were first pressurized at low temperature and then, with the pressure held constant, 

were subjected to a constant temperature ramp until failure.

5.2.2.1.3 Pressure Ramp Tests

Eleven pressure ramp tests were conducted on notched and unnotched specimens. Most of the 

tests were conducted at a pressure ramp of 16 MPa/min (2.3 ksi/min) while the specimens were 

held at a constant temperature. The test temperature varied between 700 and 840 degrees C 

(1,292 and 1544 degrees F). Two tests were conducted at 1.6 MPa/min (0.23 ksi/min) on 

unnotched specimens. Figures 5-7a and 5-7b show plots of the observed failure pressures vs. 

failure pressures predicted by the creep-rupture model and the flow-stress model, respectively. 

For both ramp rates, the creep-rupture model gives more consistent and accurate predicted 

failure pressures than the flow-stress model.

(a) (b)

Figure 5-7 Predicted vs. observed failure pressures for isothermal (700–840 degrees C) 

pressure ramp tests on unflawed and flawed tubes 0.25–1 in. long and 65–80 

percent deep by (a) creep rupture model and (b) flow-stress model 

Figure 5-8 shows a plot of the same set of data but plotted as effective flow stress (i.e., mp x σh

at failure) vs. test temperature. Figure 5-8 also includes a flow stress vs. temperature plot (solid 

line) obtained from conventional tensile tests. Note that the experimentally derived effective flow 

stress increases with the ramp rate and the flow-stress model using the flow-stress curve (from 

tensile tests) would underpredict the failure pressures significantly. Figure 5-8 clearly 

demonstrates that, for the flow-stress model to be able to predict the failure pressures correctly, 

the flow-stress curve has to be a function of the ramp rate. On the other hand, the creep-rupture 

model automatically takes the rate effect into account.
5-14

Figure 5-8 Effective flow-stress curves (dashed lines) computed from the pressure ramp 

tests (symbols) vs. temperature of test 

Also shown is the standard flow-stress curve of Alloy 600 (solid curve).

5.2.2.1.4 Temperature Ramp Tests

Thirteen flawed and unflawed specimens were tested at various temperature ramp rates. The 

flaw lengths in the tests varied from 0.64–5.1 cm (0.25–2 in.) and the flaw depths varied from 

65–93 percent. Three temperature ramp rates were chosen, 0.2, 2, and 20 degrees C/min. 

During the tests, the specimens were held at constant pressures ranging from 1.38–16.20 MPa 

(0.22–2.35 ksi). Figures 5-9a and 5-9b compares the observed failure temperatures with those 

predicted by the creep-rupture and flow-stress models, respectively. It is evident that the 

creep-rupture model predicts the failure temperatures much more accurately than the 

flow-stress model.

Two notched tests were specifically designed such that the product of mp and the nominal hoop 

stresses were approximately equal. Thus, the predicted failure temperatures for both 

geometries fall approximately on a single line for either the creep-rupture or flow-stress models, 

as shown in Figure 5-10. The experimental results are in much better agreement with the 

predictions of the creep-rupture model and confirm that the effect of flaws on failure can be 

characterized by the mp approach. Therefore, the creep-rupture model can be expected to 

predict failure under varying temperature and pressure histories during severe accidents more 

reliably than a simple rate-independent flow-stress model.
5-15

(a) (b)

Figure 5-9 Comparison of observed failure temperatures with those predicted by (a) creep 

rupture model and (b) flow-stress model for temperature ramp tests 

Figure 5-10 Comparison of predicted failure temperatures by the creep rupture and flow 

stress models for flawed specimens as a function of temperature 

ramp rate 

5.2.2.1.5 Tests under Simulated Severe Accident Time-Temperature Histories

Finally, ANL performed tests to determine the behavior of flawed tubes under time/temperature 

histories similar to those projected to occur under severe-accident conditions. The purpose of 

the tests was to further validate the creep-rupture model to support its use in determining the 

time to failure of flawed tubes under projected time/temperature histories that could reach 

temperatures as high as 850 degrees C (1,562 degrees F).
5-16

In all the tests, the internal pressure was held constant at 16.2 Mpa (2,350 psi). Tests were 

conducted on both 19.1-mm (3/4-in.) and 22.2-mm (7/8-in.) diameter tubes with wall thicknesses 

of 1 mm (0.043 in.) and 1.3 mm (0.050 in.), respectively. Four different nominal flaw geometries 

with axial lengths of 6 mm (0.25 in.), 25 mm (1 in.), and 50 mm (2 in.), and depths varying from 

20 percent to 65 percent of thickness were tested. Duplicate tests were run for all the 22.2-mm 

(7/8-in.) diameter tube tests. Rupture tests were also run on unnotched virgin samples.

The tests considered two time/temperature histories. Both were based on preliminary analyses 

of an accident sequence involving total station blackout (SBO) with a stuck-open SG 

secondary-side atmospheric dump valve, resulting in loss of feed water and secondary-side 

depressurization. One, which is referred to as the “INEL ramp,” was based on a preliminary 

analysis by INEL and the other, referred to as the “EPRI ramp,” was based on a preliminary 

analysis reported by the Electric Power Research Institute (EPRI). Figures 5-11a and 5-11b 

show the time-temperature scenarios calculated by INEL 5 and EPRI 6 for some postulated 

severe-accident sequences, respectively, which also show the time-temperature histories used 

in the ANL tests. In both series of tests, the specimens were first heated rapidly to 

300 degrees C (572 degrees F), equilibrated at 300 degrees C (572 degrees F), and then 

subjected to the test ramps. Both analyses also predict depressurization of the system because 

of the failure of the surge line. Because the primary purpose of the tests was to help develop a 

failure model, the tests have ignored the predicted depressurization. The EPRI analysis also 

predicts a reduction in temperature following a short 5-min hold at 667 degrees C 

(1,232 degrees F). To increase the contribution of creep damage in the tests, the EPRI 

temperature history was arbitrarily modified to include a 2-hour holdtime at 667 degrees C 

(1,232 degrees F) and ignored the predicted reduction of temperature after the hold. If the 

specimen did not fail in 2 hours of constant temperature hold, it was subjected to a temperature 

ramp of 2 degrees C/min until failure. Neither ramp chosen for the tests was intended to be an 

accurate representation of a particular sequence, but together they can represent a range of 

histories for which a failure model would be needed. Thus, although the INEL and EPRI 

analyses predict that failure of the surge-line nozzle and consequent depressurization of the 

system will occur before the failure of the SG tubes, with or without flaws, ANL continued the 

tests at full pressure until failure occurred.

Figures 5-12a and 5-12b compare the observed vs. predicted failure temperatures (calculated 

by the flow-stress and creep-rupture models). The creep-rupture model gives a uniformly more 

accurate prediction of the failure temperatures than the flow-stress-model. Again, the difference 

in prediction between the two models arises because the creep-rupture model includes rate 

effects, which are ignored by the flow-stress model.

5 See P. G. Ellison, et. al, “The Risk Significance of Induced Steam Generator Tube Rupture,” INEL-95/0641, 

Rev. 1 (Draft), Lockheed Martin Idaho Technologies, Inc., Idaho National Engineering Laboratory (now Idaho 

National Engineering and Environmental Laboratory (INEEL)), December 15, 1995.

6 See E. L. Fuller, et. al, “Risks from Severe Accidents Involving Steam Generator Tube Leaks or Ruptures,” 

EPRI TR--106194, Electric Power Research Institute, Palo Alto, CA (to be published).
5-17

(a) (b)

Figure 5-11 Calculated and ANL simulation of (a) INEL ramp and (b) EPRI ramp for high 

temperature tests 

(a) (b)

Figure 5-12 Observed vs. predicted failure temperatures by (a) creep-rupture model and (b) 

flow-stress model for tests simulating severe-accident transients 

Tests were conducted on 19-mm (0.75-in.) as well as 22-mm (0.875-in.) diameter 

Alloy 600 tubes. 

5.2.2.2 Validation Tests for Circumferential Notches

In contrast to axial cracks, only 15 failure tests with part-through circumferential cracks were 

conducted. These tests had a single loading history that consisted of a constant internal 

pressure of 16.2 MPa (2,350 psi) and a temperature ramp of 10 degrees C/min from 

300–600 degrees C, followed by a temperature ramp of 2 degrees C/min to ligament failure. As 

in the case of axial cracks, all specimens were depressurized immediately after ligament failure.

Constraint to bending was simulated by testing specimens with two symmetrically located 

cracks (Figure 5-4a). Tests were also conducted on unconstrained tubes with a single 

circumferential crack. In all but one case, the crack opening at failure was significantly smaller 

than the openings observed for axial cracks. The only exception was a single tube with a 

360-degree crack; this tube broke into two pieces. Most tests failed by developing pinhole leaks 
5-18

in the ligament. A single tube with a 240-degree crack failed by ligament failure across the 

whole front of the flaw.

As expected, all of the tubes with symmetrical flaws failed without significant bending. Tubes 

with deep flaws showed little or no bulging of the section that contained the flaws; those with 

shallower flaws showed some bulging. In contrast, all of the specimens with a single crack 

showed significant bending at failure (Ref. 8).

5.2.2.2.1 Tubes with Two Symmetrical Circumferential Flaws

Specimens with cracks of angular length 2θ = 90 degrees, 120 degrees, 150 degrees, and

180 degrees (which is a full 360-degree crack) were tested. To keep the effects of crack length 

separate from the effects of crack depth, the depth to thickness ratio a/h was kept approximately 

constant at 0.77 for most of the test specimens.

Figure 5-13 plots the failure temperatures against the flaw length of 2θ in. Because of the 

variability of the crack depth around the circumference, the specimens with 360-degree 

(2θ = 180 degrees) cracks showed the largest scatter. However, the specimens with the highest 

failure temperature contained the shallowest cracks. The failure temperatures increased 

significantly when the crack depth was reduced at any angular crack length.

Figure 5-13 Variation of failure temperatures with crack angle for specimens with two 

symmetrical cracks of various depths 

The failure temperatures for the tests were predicted by Equations 4b and 10b for mp. The mp

values were calculated with both the Kurihara model (Equation 11) and the ANL model 

(Equations 12a and 12b). Figure 5-14 presents the predicted failure temperatures with the 

experimentally observed failure temperatures. On average, the ANL model gives a closer 

prediction of the failure temperatures than the Kurihara model. The maximum error in predicted 

failure temperature for the ANL model is 43 degrees C (109 degrees F).
5-19

Figure 5-14 Experimental failure temperatures and failure temperatures predicted by the 

Kurihara and ANL models for two symmetrical part-through circumferential 

cracks of various semiangular length θ 

5.2.2.2.2 Tubes with a Single Circumferential Flaw

Three failure tests were conducted on free-to-bend specimens with a single circumferential flaw 

(Ref. 8). Specimens with cracks of angular length 2θ = 90 degrees, 180 degrees, and 

240 degrees were tested.

The failure temperatures for the tests were predicted by Equation 16b, with mp given by 

Equation 13c. The mp values were calculated with the ANL model (Equations 12a and 12b). The 

predicted failure temperatures were close to the experimentally observed failure temperatures in 

all cases (Ref. 8).

5.2.2.2.3 Comparison of Failure of Tubes with a Single Flaw and with Two Flaws

The failure of tubes with two symmetrical cracks was usually initiated on the crack with the 

greater depth. However, very little overall bending of the specimen occurred. Conversely, 

significant bending occurred in the specimens with a single crack. The longer the crack, the 

more bending the specimen sustained.

All but one specimen with a 360-degree crack failed by ligament failure. A single specimen out 

of three with 360-degree cracks broke into two pieces. In most cases, ligament failure occurred 

locally, leading to a pinhole leak. One specimen with a single 240-degree crack failed by full 

ligament failure (accompanied by a loud noise). However, because of rapid depressurization of 

the specimen, the resulting through-wall crack did not propagate unstably to give rise to a 

guillotine break.

To demonstrate the influence of bending on failure pressure, Figure 5-15 plots the test results 

from both types of specimens against the total angular crack length (n = 2θ). Note that the 

specimens with 360-degree cracks may be considered either as specimens with a single 

360-degree crack (n = 1) or two 180-degree cracks (n = 2). Thus, the failure temperatures for 

both types of cracked specimens coincide at n = 2θ = 360 degrees. However, at smaller angles, 
5-20

the free-to-bend specimens failed at lower temperatures than the specimens with two 

symmetrical cracks, as expected.

Figure 5-15 Failure temperatures for specimens with one (n = 1) and two (n = 2) 

circumferential cracks 

5.3 Crack-Opening Rate at High Temperature 

To determine the leak rate after through-wall penetration of axial cracks during severe 

accidents, it is necessary to estimate the crack opening area as a function of time. A simple 

model was developed to calculate the crack-opening area as a function of time and temperature 

during severe accidents. It is derived by analogy from a model that is applicable to cracks in a 

rectangular plate. The model was used to analyze crack-opening areas in flawed tubes 

subjected to severe-accident transients.

Consider a through-wall central crack of length 2c in a rectangular plate of width 2b (b>>c) 

subjected to a remotely applied axial load P. For a material with stress-plastic strain law

(14)

the crack-opening displacement (COD) at the middle of the crack, ignoring elastic displacement, 

is given by:

(15)

In Equation 15, P0 = plastic collapse load and the function h2 is tabulated in EPRI-NP-1931 

(Ref. 9). Equation 15 was applied to the case of an axial crack in a relatively long SG tube by 
5-21

replacing the remote stress with the nominal hoop stress σ = (R and h are the mean 

radius and thickness of the tube and ∆p is the pressure differential), the collapse stress with 

σ0/m (m is the bulging factor) and by putting c/b = 0; i.e.,

(16)

Equation 16 is expected to give reasonable estimates of CODs as long as the pressure is small 

compared to the unstable burst pressure.

Equation 16 can be generalized for the high-temperature creep case as follows. If the material 

obeys a power law creep-rate equation; i.e.,

(17)

then the crack-opening rate is given by analogy with Equations 14 and 16 as follows:

(18)

5.3.1 Creep-Rate Equation for Alloy 600 

Figure 5-16 plots the creep-rate data obtained by INEL. The data at three temperatures can be 

collapsed onto a bilinear plot (log-log basis) by using activation energy of 65 kilocalorie 

(kcal)/mole and plotting the stress normalized by the Young’s modulus at temperature, as 

shown in Figure 5-16.

Figure 5-16 INEL creep rate on Alloy 600 vs. stress data plotted using activation energy of 65 

kcal/mole and stress normalized by Young’s modulus at temperature 
5-22

5.3.2 Crack-Opening Area for Axial Cracks 

Figure 5-17a plots the function h2 (c/b, n) as a function of c/b for three values of n in. Since our 

interest is in the value of h2(0,n), the graphs were extrapolated to c/b = 0 by polynomial fits and 

the results plotted as a function of n in Figure 5-17b.

(a) (b)

Figure 5-17 Variations of Crack Opening Parameters 

(a) Variation of h2 (c/b,n) with c/b for various values of n 

(b) Variation of h2 (0,n) with n; Values of h2 (0,n) are 7.03 and 6.16 for n = 6.1

 and 3.7, respectively. 

5.3.3 Tests on Specimens with Circumferential Notches at High Temperature 

Because in a tube under internal pressure, the crack-opening area for a given crack length is 

much greater for an axial crack than it is for a circumferential crack, the primary interest is in 

axial cracks. It is, however, extremely difficult to carry out creep tests on tubular specimens with 

through-wall axial notches subjected to internal pressure. The validation tests were conducted 

instead on axially loaded tube specimens with two symmetrical through-wall circumferential 

EDM notches (Figure 5-18a). The symmetrical notches minimize bending and ensure a pure 

tensile loading on the notches similar to that experienced by axial cracks in an internally 

pressurized tube. By keeping the notch lengths small, the effects of tube curvature can be 

minimized. The small interaction between the two notches can be taken into account by using 

equations applicable to cracks in rectangular plates of finite width (Figure 5-18b).

As mentioned earlier, the periodicity of the circumferential crack geometry requires that the 

corresponding rectangular plate be of finite width (Figure 5-18b). Equation 16 gives the COD of 

cracks in plates of finite width. For the current geometry, the remotely applied axial load 

P = 2πRhσ and the plastic collapse load P0 = 2(π-2θ)Rhσ0, and Equation 16 reduces to 

the following:

(19)
5-23

where σ is the remotely applied axial stress, 2θ is the angular length of each circumferential 

crack, R and h are the mean radius and thickness of the tube, and

(c/b=0.25 for 45° cracks) (20)

(a) (b)

Figure 5-18 Illustration of circumferential cracks 

(a) Tube with two symmetrical through-wall circumferential notches 

(b) Axial loading on a tube with two symmetrical 45-degree notches plotted 

 after making an axial cut and unfolding the tube circumference into 

 a plane 

As before, under creep conditions, Equation 19 by analogy gives an expression for the 

displacement rate,

(21)

The variation of the function h2 (c/b, n) with c/b is shown in Figure 5-19 for two values of n 

applicable to Alloy 600. Note that, in contrast to axial cracks that were considered earlier, 

c/b ≠ 0 for the circumferential notches.
5-24

Figure 5-19 Variation of h2 with c/b for creep-rate exponents n = 3.7 and 6.1 

5.3.3.1 Validation Test Results

Six isothermal and nonisothermal tests were conducted to validate the approach. Two tests with 

45-degree circumferential EDM notches were first conducted. The predicted notch opening with 

time for two symmetrical 45-degree circumferential cracks at two applied axial loads is 

compared with the experimentally observed notch opening in Figures 5-20a and 5-20b. The test 

under an axial load of 1,106.8 kilogram force (kgf) (2,440 lbs) (Figure 5-20a) was started initially 

at 695  degrees C (1,283 degrees F), but changed to 685 degrees C (1,265 degrees F) after 

1 hour. The test under an applied axial load of 1,224.7 kgf (2,700 lb) (Figure 5-20b) was 

conducted at 665 degrees C (1,229 degrees F) with less variation in temperature. The 

agreement between experimentally measured notch openings and predicted values is 

reasonably good.

(a) (b)

Figure 5-20 Experimentally measured and predicted variation of total notch opening with 

time for specimens with two 45-degree circumferential notches loaded at (a) 

1,106.8 kgf (2,440 lb) and (b) 1,224.7 kgf (2,700 lb) 
5-25

The temperature control of the specimen was improved subsequently. The next series of tests 

involved 2 x 0.635 cm (0.25 in.) and 2 x 0.508 cm (0.20 in.) circumferential notches subjected to 

an axial load of 1,089 kg (2,400 lb) at a constant temperature of 700 degrees C 

(1,292 degrees F). Figures 5-21a and 5-21b show a comparison between measured and 

predicted notch openings with time for specimens with two symmetrical circumferential notches 

of length 0.635 cm (0.25 in.) and 0.508 cm (0.20 in.), respectively, each subjected to an applied 

axial load of 1,106.8 kgf (2,400 lbs.). As before, the predicted openings are close to the 

measured values.

(a) (b)

Figure 5-21 Experimentally measured and predicted variation of total notch opening with 

time for specimens with two symmetrical circumferential notches loaded at 1,108 

kg (2,400 lb) for notch lengths (a) 6.35 mm (0.25 in.) and (b) 5.1 mm (0.20 in.) 

All the tests reported so far were conducted isothermally. To validate the model for 

nonisothermal loading, two tests were conducted in which the temperature was ramped 

following the Case 6RU transient (Figure 5-22). In the nonisothermal tests, the displacements 

could only be measured at the end of the test. Both nonisothermal tests had a constant axial 

load of 1,362 kg (3,000 lb). Test CR 106 had 2 x 6.35 mm (0.25 in.) circumferential notches and 

Test CR 108 had 2 x 5.1 mm (0.20 in.) circumferential notches. Figures 5-23a and 5-23b give 

the predicted notch-opening displacement vs. temperature plots for the two tests, which also 

include the measured notch-opening displacements at the end of the tests. One of the predicted 

notch openings is close to the measured value, and the other one is off by 20 percent.
5-26

Figure 5-22 Time vs. temperature plot for tests CR 106 and CR 108 

The curve for CR 108 has been displaced in the horizontal direction for clarity.

(a) (b)

Figure 5-23 Comparison of predicted (solid line) and experimentally measured (symbols) 

notch-opening displacements for (a) Test CR 106 and (b) Test CR 108 

5.3.4 Predicted Axial Crack-Opening Rate at High Temperature 

Figure 5-24a shows the variation in the crack-opening rate with the crack length calculated 

using Equation 18 for SG tubes at 700 degrees C (1,292 degrees F) subjected to an internal 

pressure of 16.2 MPa (2,350 psi). Note that the crack-opening rate increases very rapidly for 

crack lengths greater than 10 mm (0.4 in.).

Figure 5-24b shows the crack-opening area at temperatures of 700 and 750 degrees C 

(1,292 and 1,382 degrees F) as a function of crack length for an SG tube subjected to a thermal 

transient characteristic of an SBO “high-dry” accident (Case 6RU in Reference 10). Note that, 

for temperatures greater than or equal to 750 degrees C (1,382 degrees F), cracks greater than 

15-mm (0.6-in.) long will have crack-opening areas that are greater than the tube 
5-27

cross-sectional flow area (303 square millimeters (0.47 square inch) for a 22.2-mm [0.875-in.] 

diameter tube).

(a) (b)

Figure 5-24 Variations of (a) COD rate with through-wall axial crack length for a tube subjected 

to internal pressure of 2,350 psi at 700 degrees C and (b) crack-opening area with 

crack length at final temperatures 700 and 750 degrees C for a tube subjected to 

severe-accident transient 

5.4 Stability of Flaws after Ligament Rupture 

To address the question of stability of part-through cracks after ligament failure, two specimens 

were fabricated with 12.7-mm (0.5-in.) through-wall cracks and with inside metallic liners to act 

as patches to prevent leakage of the pressurizing gas. It was hoped that the metallic liner would 

transmit the pressure to the tube wall by creep. In the first specimen, a 0.25-mm (0.01-in.)-thick 

pure nickel liner was used. It was first heated to 850 degrees C (1,562 degrees F) and then 

pressurized at a rate of 7 MPa/min (1,000 psi/min). The nickel liner developed a pinhole under 

the crack at a pressure of 10.3 MPa (1,500 psi), just as the cracked section of the tube started 

to bulge. The predicted instability pressure for the tube was 16 MPa (2,300 psi). A second 

specimen, also with a 12.7-mm (0.5-in.) through-wall crack but with a 0.2-mm (0.008-in.)-thick 

Type 304 stainless steel liner was heated to 750 degrees C, (1,382 degrees F), pressurized to 

16.2 MPa (2,350 psi) and then held. This specimen also developed a leak because of failure of 

the stainless steel liner after about 1 min of temperature and pressure hold. The measured 

crack opening after the test was 1.1 mm (0.043 in.). Subtracting the initial flaw width of 0.2 mm 

(0.008 in.), the crack-opening rate in this specimen because of creep was 0.89 mm/min 

(0.035 in./min). No other tests with through-wall cracks were performed.

Although none of the part-through flawed specimens failed in an unstable manner after ligament 

failure, some of the specimens with shallower initial flaws and higher failure pressure showed 

tearing at the crack tip. The tearing may indicate that these specimens were probably close to 

instability when the ligaments failed. At failure, the crack-opening angles (COAs) of these 

specimens were 40–50 degrees. To get an estimate of the time it would take for a through-wall 

crack to open to a COA of 45 degrees, the calculations based on C* analysis, Equation 19 and 

Figure 5-18, were performed, although admittedly a more rigorous analysis would require that 

the effects of finite deformation at the crack tip be taken into account. The calculations showed 

that the crack-opening rate for a pressure of 16.2 MPa (2,350 psi) is as plotted in Figure 5-25a. 
5-28

For a 6-mm (0.25-in.) crack, the times to open to 0.25 mm (0.010 in.) are about 2 minutes at 

732 degrees C (1,350 degrees F) and a few seconds at 871 degrees C (1,600 degrees F). 

Considering the measured COD result reported earlier for a 12.7-mm (0.5-in)-long through-wall 

crack with stainless steel liner, the calculated COD because of creep at 732 degrees C 

(1,350 degrees F), after correcting for hoop stress because of the stainless steel liner, is 

1.0 mm/min (0.04 in./min), which agrees reasonably well with the measured value of 

0.89 mm/min (0.035 in./min).

Figure 5-25b shows the times to open an initially closed through-wall crack of various lengths to 

a COA of 45 degrees at 732 degrees C (1,350 degrees F) and at 871 degrees C 

(1,600 degrees F) under an internal pressure of 16.2 MPa (2,350 psi). Note that the time varies 

from greater than 40 min for a 6.4-mm (0.250-in.)-long crack, to 3 min for a 12.7-mm (0.5-in.)-

long crack, and to 10 s for a 25.4-mm (1-in)-long crack at 732 degrees C (1,350 degrees F). The 

corresponding times at 871 degrees C (1,600 degrees F) are 4 min, 50 s, and 5 s, respectively. 

Because most of the failure temperatures for tests were in the range of 750 degrees C 

(1,382 degrees F) to 850 degrees C (1,562 degrees F), the times to open the cracks to a COA 

of 45 degrees are relatively short unless the cracks are less than 5 mm (0.2 in.).

(a) (b)

Figure 5-25 Crack opening rate and time to reach COA of 45 degrees 

(a) Crack-opening rate in mm/min versus crack length at 732 degrees C and

871 degrees C

(b) Time to open initially closed through-wall cracks to a COA of 45 degrees

for a 22.3-mm (7/8-in.) diameter SG tube at 732 degrees C (1,350 

degrees F) and 871 degrees C (1,600 degrees F) under a constant internal

pressure of 16 MPa (2,350 psi)

5.4.1 Failure Modes of Specimens Tested at High Temperature 

Depending on the absence or presence of flaws in the specimens and on the pressure and 

temperature at failure (independent of the details of the loading history), a variety of failure 

modes was observed.
5-29

5.4.1.1 Unflawed specimens

Typically, most of the unflawed specimens failed in an unstable manner. However, a single 

unflawed specimen subjected to 12.4 MPa (1,800 psi) at 800 degrees C (1,472 degrees F) 

showed a completely different failure mode that is more typical of creep failure of internally 

pressurized tubes. It failed in 4 hours by developing a pinhole leak and after accumulating a 

significant amount of creep deformation (ballooning). This was the only specimen that was 

tested at a pressure less than 14 MPa (2,000 psi). All the other unflawed specimens were tested 

at greater pressures and failed in an unstable manner, independent of the temperature history.

5.4.1.2 Flawed Specimens

None of the flawed specimens failed in an unstable manner with fishmouth opening. Test 

specimens with initial flaws that were 50-mm (2-in.) long/20 percent deep, 25-mm (1-in.) 

long/60 percent deep, and 6-mm (0.25-in.) long/90 percent deep, were depressurized 

immediately on ligament failure. At a given failure pressure and temperature, the longer and 

shallower the initial flaw, the greater was the crack opening at failure. The 50- and 25-mm 

(2- and 1-in.)-long cracks showed evidence of a slight tear at the crack tips.

The CODs in all the failed specimens with axial cracks were measured. Flaws that had a 

measurable crack opening are classified as “fishmouth,” and flaws that had no measurable COD 

are classified as leakers. Figures 5-26a and 5-26b plots the CODs and COAs against the initial 

flaw depths (a/h), respectively, where a trend of increased COD and COA with decreasing initial 

flaw depth is clearly evident. Intuitively, this is to be expected, because the shallower flaws 

require proportionately larger pressures or higher temperatures or longer times to cause failure 

of the ligament than the deeper flaws of the same length. The specimens with the 1-in. 

(2.54-cm) and 2-in. (5.1-cm) cracks, which showed the largest COA at failure, also had slight 

tears at the crack tips.

(a) (b)

Figure 5-26 Measured (a) CODs and (b) COAs in failed high-temperature test specimens as a 

function of initial axial flaw depth and initial flaw length 
5-30

At low temperatures, stability of a part-through crack after ligament failure can be determined 

from the following conditions:

If pcr > psc then the crack is stable (22a)

If pcr < psc then the crack is unstable (22b)

where pcr and psc are the unstable burst pressures of through-wall cracks and ligament-rupture 

pressures of part-through-wall cracks, respectively. In other words, the stability boundary on a 

plot with crack length (2c) and crack depth (a/h) as axes is given by

m = mp (23)

which is independent of the flow stress or loading and depends only on the crack length and the 

crack depth. Figure 5-27a plots the curve corresponding to Equation 23, together with all the 

high-temperature test data. Although the curve m = mp appears to separate the specimens that 

leaked from those that fishmouthed remarkably well, a closer examination of the data for 25 mm 

(1 in.) crack length shows that the correlation does not work for all constant pressure tests. 

Figure 5-27b plots constant pressure data (both isothermal and T-ramp tests) for specimens 

with a 25-mm (1-in.) crack. Contrary to what would be expected from the correlation, all the 

specimens below the m = mp line did not fishmouth. Figure 5-28 shows a better correlation that 

distinguishes specimens that fishmouthed from those that leaked for specimens with a 25-mm 

(1-in.) flaw in a plot of failure pressure versus temperature at failure.

(a) (b)

Figure 5-27 Test results for unstable burst pressure 

(a) Initial flaw depth (a/h) versus axial crack length plot for specimens tested

at high temperature

(b) Flaw depth (a/h) versus pressure plot for constant-pressure tests on

specimens with 25-mm (1-in.) part-through axial crack conducted

isothermally or under a temperature ramp
5-31

Figure 5-28 Variation of failure pressure with failure temperature for tests conducted on 

specimens with a 25 mm (1 in.)-long crack 

Open symbols denote specimens that leaked (no measurable COD) and filled 

symbols denote specimens whose cracks opened (fishmouthed). The numbers 

denote COD (in mm) at failure for the specimens that fishmouthed. 

 

5.4.2 Lower Bound Flow Stress for Computing Unstable Burst at High Temperature 

A lower bound to the flow stress for computing the unstable failure of tubes with through-wall 

cracks can be obtained by ignoring the time it takes for a crack to open to a critical COA after 

ligament failure and calculate effective flow stresses from the dashed line in Figure 5-28 by 

using Equation 2b. Such calculated flow stresses are plotted together with flow stresses 

obtained from tensile tests in Figure 5-29. Note that the calculated flow-stress curve lies 

considerably above those obtained from tensile tests at high temperatures but approaches the 

latter at lower temperatures. This is to be expected, because the tensile tests are normally 

conducted at about 10-3/s, whereas the maximum flow stresses at instability correspond to 

much higher strain rates. Although more data would be desirable, the instability pressures 

calculated from the flow-stress curve in Figure 5-29 and indicated by solid lines in Figures 5-30a 

and 5-30b are consistent with the failure modes of the test specimens with 0.6-cm (0.25-in.) and 

2-in. (5.1-cm) cracks. It is proposed that the higher flow-stress curve of Figure 5-29 can be used 

to determine the stability of a through-wall crack conservatively, using only the pressure and 

temperature at the moment of ligament failure and ignoring the pressure and temperature 

histories before ligament failure.
5-32

Figure 5-29 Temperature variation of flow stress (using k=0.5) of Alloy 600 specimens 

derived from tensile test data as reported in the literature 

Dashed line indicates a lower bound to flow stress (calculated from dashed line 

in Figure 5-28 using Equation 2b) for calculating instability pressures of tube 

specimens with through-wall cracks. 

(a) (b)

Figure 5-30 Pressure at failure as a function of temperature at failure for all specimens with a 

(a) 6 mm (0.25 in.)-long axial crack and (b) 51 mm (2 in.)-long axial crack

The solid lines are predicted from the higher flow-stress curve of Figure 5.2-32.

Figure 5-31 shows the critical crack length for a 22.2-mm (7/8-in.) diameter tube as a function of 

temperature at a pressure of 16.2 MPa (2,350 psi). For typical severe-accident temperatures 

(600–900 degrees C, or 1,112–1,652 degrees F) at a pressure of 16.2 MPa (2,350 psi), the 

critical crack length varies from 23 mm (0.9 in.) at 600 degrees C (1,112 degrees F) to 10 mm 

(0.4 in.) at 900 degrees C (1,652 degrees F). These represent minimum lengths of part-through 

cracks that will become unstable immediately after ligament rupture. However, at high 

temperatures, shorter cracks can grow in a stable manner by creep mechanisms before 

becoming unstable.
5-33

Figure 5-31 Critical crack length as a function of temperature for a 22.3 mm (7/8 in.)-diameter 

Alloy 600 tube at an internal pressure of 16 MPa (2,350 psi) 

5.5 References 

1. Cochet, B., J. Engstrom, and B. Flesch, “PWR Steam generator tube and tube support 

plate plugging criteria,” Paper 4.1, Steam Generator Tubes Mechanical, LBRB, and 

Probabilistic Studies, Electricité de France, France, 1990.

2. Flesch, B., and B. Cochet, “Crack stability criteria in steam generator tubes,”

International Conference on Pressure Vessel Technology, Beijing, China, 

September 1988.

3. Kiefner, J.F., et al., “Failure stress levels of flaws in pressurized cylinders,” Progress in 

Flaw Growth and Fracture Toughness Testing, Kaufman, J.G., National Symposium on 

Fracture Mechanics (6th: 1972: Philadelphia), American Society for Testing and 

Materials, Committee E–24 on Fracture Testing of Metals, American Society for Testing 

and Materials, ASTM Special Technical Publication 536, Philadelphia, PA, 1973.

4. Finnie, I. and W.R. Heller, “Creep of Engineering Materials,” New York, NY, 

McGraw-Hill, 1959.

5. Ranganath, S., and H.S. Mehta, “Engineering Methods for the Assessment of Ductile 

Fracture Margin in Nuclear Power Plant Piping,” Elastic Plastic Fracture Second 

Symposium, Vol. 2, Fracture Resistance Curves and Engineering Applications, 

American Society for Testing and Materials, ASTM Special Technical Publication 803, 

Philadelphia, PA, 1973.

6. Kurihara, R., S. Ueda, and D. Sturm, “Estimation of the ductile unstable fracture of pipe 

with a circumferential surface crack subjected to bending,” Nuclear Engineering and 

Design, Vol. 106, 1988.

7. Alzheimer, J.M., et al., “Steam Generator Tube Integrity Program Phase I Report,” 

NUREG/CR–0718, PNL-2937, Richland, WA, September 1979.
5-34

7. U.S. Nuclear Regulatory Commission, Rempe, J.L., et al., “Light Water Reactor Lower

Head Failure Analysis,” NUREG/CR-5642, EGG-2618, Idaho National Engineering

Laboratory, Idaho Falls, ID, October 1993.

8. Majumdar, S., et al., “Failure Behavior of Internally Pressurized Flawed and Unflawed

Steam Generator Tubing at High Temperatures – Experiments and Comparison with

Model Predictions,” NUREG/CR-6575, Argonne National Laboratory, 1998.

9. Kumar, V., M.D. German, and C.F. Shih, “An Engineering Approach for Elastic-Plastic

Fracture Analysis,” EPRI NP-1931, Electric Power Research Institute, 1981.

10. U.S. Nuclear Regulatory Commission, SGTR Severe Accident Working Group, “Risk

Assessment of Severe Accident-Induced Steam Generator Tube Rupture,”

NUREG-1750, 1998, Agencywide Documents Access and Management System

(ADAMS) Accession No. ML070570094.
6-1

6 ESTIMATION OF STEAM GENERATOR TUBE 

FLAW DISTRIBUTIONS 

6.1 Introduction 

This chapter presents the recent estimates for steam generator (SG) tube flaw distributions, 

based on selected inservice inspection (ISI) reports available to the U.S. Nuclear Regulatory 

Commission (NRC) for U-tube SGs (for Westinghouse (W) and Combustion Engineering (CE) 

nuclear power plants (NPPs).

Section 6.4 also includes the discussion for once-through SG axial loads on tubes during 

severe accidents.

The SG flaw distributions are used as input in estimating consequential SG tube rupture 

(C-SGTR) probabilities during severe accidents after core damage occurs, as well as for 

initiating events during power operation where sudden large pressure differences between the 

primary and the secondary sides can occur. Such probability estimates were done in support of 

the NRC’s Steam Generator Action Plan during the early 2000s but were not formally 

documented. In that work, the estimated flaw distributions available at that time were used in 

supporting probabilistic risk assessment (PRA) reports, such as Reference 1. Those flaw 

distributions were based on data for SGs that have been replaced since then. Reference 2 

provides the most recent SG flaw distributions, applicable to both the W and CE plants.

Table 2 in NUREG/CR-6521, “Estimating Probable Flaw Distributions in PWR Steam Generator 

Tubes,” issued 1996 (Ref. 3), summarizes the flaw distributions. This table, which is reproduced 

below as Figure 6-1, comes with the following clarification concerning primary water stresscorrosion cracking (PWSCC) and outer diameter stress-corrosion cracking (ODSCC):

The examples in Appendix C do not cover axial PWSCC at roll transitions, nor do 

they cover circumferential ODSCC at TTS.... (This quote is taken from page 17 

of the reference and applies to the table below.)

Table 6 of Section 3 of Reference 2 summarizes the new SG tube flaw distribution estimates. 

This table is reproduced as Table 6-2 for the convenience of the reader.
6-2

Figure 6-1 Table 2 reproduced from NUREG/CR 6521 
6-3

6.2 Data Selection 

To aid the PRA of SG tube rupture events, a series of plant SG tube inspection reports were 

chosen to represent the flaw distributions in SG tubes for current U.S. NPPs. The following 

paragraphs explain the rationale for the selection of specific reports. 

Pressurized water reactor (PWR) plants in the United States were divided into three main 

categories: CE-designed plants, W designs, and plants with once-through SG (OTSG) designs. 

For the W and the CE designs, specific power plants were selected. Raw data from the SG tube 

inspection reports for those plants were provided as input for estimating probable flaw 

distributions, as were primary coolant leakage estimates for various accident scenarios.

Regarding C-SGTR in OTSGs, Argonne National Laboratory (ANL) investigated an issue of 

axial loads on SG tubes during design-basis accidents. Other analyses have shown that the 

once-through design is not susceptible to the problems of steam backflow, and the associated 

much higher temperatures, which could occur during severe accidents in SGs with recirculating 

designs. Therefore, this study does not include ISI reports for OTSG plants.

Because most U.S. plants have replaced their original SGs, this study only includes ISI data for 

currently operating SGs. It considered only SG tubes made of either thermally treated (TT) 

nickel Alloy 600 or nickel Alloy 690, because those are the main tube materials in use in the 

United States. (There are some mill-annealed Alloy 600 tubes in service in the United States, 

but they are rare exceptions.)

NUREG-1771, “U.S. Operating Experience with Thermally Treated Alloy 600 Steam Generator 

Tubes,” issued April 2003 (Ref.4), and NUREG-1841, “U.S. Operating Experience with 

Thermally Treated Alloy 690 Steam Generator Tubes,” issued August 2007 (Ref.5), contained 

historical summaries of SG operating experience. Those documents were reviewed for a select 

group of plants that would be considered representative of the current NPPs with regard to the 

distributions of SG flaws.

The study collected and reviewed sets of consecutive inspection reports dating from the most 

recent inspection back through approximately 10 or 12 years, and even as far back as 20 years. 

The number of reports varied, of course, depending on the SG date of replacement.

It could be suggested that SGs in service for longer times would experience more tube 

degradation. However, that is not always the case, depending upon such factors as operating 

temperatures, water chemistry, contaminants, and others. So, to properly characterize the 

current fleet, it was decided to include plants that had a lot of degradation and those that had 

little degradation, regardless of the number of effective full-power years (EFPYs) of operation. In 

this way, the flaw distributions for C-SGTR would be bounded by best and worst cases. Indeed, 

it was found that some of the longest operating SGs have fewer flaws, while some of the newly 

replaced SGs have more flaws.

Two main categories are used here to characterize SG tube flaw types in the ISI reports: cracks 

and wear scars. Cracks are generally tight, sharp-tipped, irregularly shaped (jagged) defects, 

which can be described as a “tearing of the material.” Wear scars are usually of a more smooth 

and broader (not tight) shape. Wear scars are essentially a removal of surface material at areas 

where the tube comes in contact with another surface, such as a support plate, antivibration bar, 

loose part, or another tube. Wear defects have been found in all SGs, regardless of the 

materials used to manufacture the tubes. Cracks, however, have not yet been found in any Alloy 
6-4

690 SG tubes in the United States despite some being in operation for over 20 years. So, the 

ISI data used herein for flaw distribution estimates include cracks and wear defects for thermally 

treated Alloy 600TT SGs, but only wear flaws for SGs constructed with Alloy 690 material. It 

should be noted that the flaw data did not include any ISI data for mill-annealed tubes.

For CE plant designs, all of the replacement SGs have been constructed with tubes made of 

Alloy 690 material with the exception of Palisades. The following plants were selected:

• Millstone 2 was the first CE plant to employ Alloy 690. Reviewing the longer history of

Millstone 2 could provide insights into the progression of flaw growth and incidence of

new flaw initiation over time.

• Calvert Cliffs had several ISI reports that included extra dimensional data describing

tube defects, beyond the minimum information required. For example, one report lists

the length, depth, and width of defects, while only the depth (or through-wall percentage)

is required to be reported.

• St. Lucie 1, with relatively newer SG replacements, showed some more flaw defects,

compared to some of the older, similar SGs in service at CE plants.

W-design power plants in the United States use some SGs made with Alloy 600TT tubes, and

some SGs made with Alloy 690 tubes. Therefore, ISI reports from both of these categories of W

SGs were collected to characterize the current SGs used at W-design power plants.

Following a similar rationale as explained above for CE-design plants, ISI reports for certain 

power plants were selected to represent the current state of flaw distributions in the W NPPs. 

For the two major categories of tube materials (Alloy 690TT and Alloy 600TT), four plants were 

chosen to characterize the flaws in the SGs currently used at W plants.

To characterize Alloy 690TT SG tubes at W plants, the study compiled four sets of ISI reports 

from four different power plants (two lightly degraded plants and two of the more degraded 

plants): Donald C. Cook Unit 2, McGuire Unit 1, Prairie Island Unit 1, and Sequoyah Unit 1.

Likewise, for the W-design power plants with Alloy 600TT SG tubes, the following plants were 

chosen: Byron Unit 2, Seabrook Unit 1, Surry Unit 2, and Vogtle Unit 1.

Table 6-1 summarizes all the plants selected to have their ISI reports reviewed and compiled for 

the purpose of characterizing the state of flaw distributions in the current fleet, to be used in 

C-SGTR risk assessments.

In Table 6-1, the “current model” designations in the table refer to the SG manufacturers and the 

size or geometry of the SG. The basic design of all these SGs, at both CE and W plants, is a 

recirculating design with inverted U-bend-shaped tubes. However, different manufacturers have 

different designs as to the exact dimensions and the number of tubes. The symbols for the 

current manufacturers are explained as follows:

• BWC = Babcock and Wilcox Canada

• Fr = Framatome (now called AREVA)

• ABB/Doosan = ABB/Doosan

• all others are W (W/51 F, D5, F, and W/54F)
6-5

Table 6-1 SG Properties for Flaw Distribution Estimates for C-SGTR Studies 

CE Plant Designs

Plant Current Model Material Replace Date

Calvert Cliffs 1 BWC—7811 690TT Jun-02

Millstone 2 BWC 690TT Jan-93

St. Lucie 1 BWC 690TT Jan-98

W—Alloy 600TT SG Tubes

Plant Current Model Material Replace Date

Byron 2 D5 600TT Not Applicable (NA)

Seabrook 1 F 600TT NA

Surry 2 W/51 F 600TT Sep-80

Vogtle 1 F 600TT NA

W—Alloy 690TT SG Tubes

Plant Current Model Material Replace Date

Donald C. Cook 2 W/54F 690TT Mar-89

McGuire 1 BWC 690TT May-97

Prairie Island 1 Fr 56/19 690TT Nov-04

Sequoyah 1 ABB/Doosan 690TT Jun-03

This report reviewed and summarized all the raw data from the plants selected above, for the 

currently operating SGs. The data were used for statistical estimations of flaw distributions, with 

respect to size and number of flaws. Finally, the flaw numbers and sizes may be used as input 

for the overall estimation of the large early release consequences of an SG tube rupture caused 

by a severe accident.

6.3 Estimation of SG Tube Flaw Distributions in Replacement SGs 

6.3.1 Summary 

The data in previous work estimating SG tube flaw distributions for SGs existed before 1995. 

These (U-tube) SGs were replaced with those having new SG tube materials. Recent work has 

estimated a new set of flaw distributions for U-tube SGs (used by domestic W and CE NPPs) 

(Ref. 2). For this purpose, selected data from ISI reports available to the NRC were used, as 

discussed in Section 6.2. Reference 2 discusses this work and contains the analysis of the ISI 

reports, the creation of the database, and the estimation of flaw rate and other flaw 

characteristics. Because of the limitations of the detailed information available for the flaw 

characteristics, the data have been consolidated into Inconel 600 material applicable to all SGs 

(W and CE) as a function of EFPY (parameter K in the equations of Table 6-2), and similarly for 

Inconel 690. Thus, the equations are not distinguished by the SG-type but provide flaw 

distributions as a function of time (EFPYs).

The number of flaws generated in the last operating cycle K can be estimated by calculating the 

number of flaws at Kth and (K-1)th cycles and subtracting the two. This allows an estimation of 

the large (deep) cracks (e.g., greater than 30-percent deep) that may be present during an 

accident sequence in the Kth cycle. It can be assumed that flaws with 40 percent or more depth 

observed before the Kth cycle are removed by plugging the associated tubes.
6-6

Table 6-2 summarizes the new SG tube flaw distributions that can be used for NPPs with 

replacement SGs. These distributions are applicable to both W and CE replacement SGs with 

thermally treated Inconel 600 and 690 materials.

Appendix K contains a further discussion of input flaw data (empirical distribution) and shifted 

flaw distribution as used for PRA purposes. Section 7.1.3 of this report introduces the shifted 

flaw distribution.

Table 6-2 SG Tube Flaw Distributions Taken from Reference 2 

Flaw 

Characteristics Thermally Treated Inconel 600 Thermally Treated Inconel 690

Volumetric/Wear 

Flaw Rates

h(k) = 6.4166·10-5 K + 1.3236·10-3

μ = 6.4166·10-5, Ω = 1.3236·10-3

h(k) = 5.5826·10-5 K + 6.8627·10-4

μ = 5.5826·10-5, Ω = 6.8627·10-4

Axial Crack 

Flaw Rates

K<15, h(k) = Negligible

μ = 0.0, Ω = 0.0

K>15, h(k) = 2.0·10-4

μ = 0.0, Ω = 2.0·10-4

h(k) = Negligible

μ = 0.0, Ω = 0.0

Circumferential Crack 

Flaw Rates

K<15, h(k) = Negligible

μ = 0.0, Ω = 0.0

K>15, h(k) = 1.0·10-3

μ = 0.0, Ω = 1.0·10-3

h(k) = Negligible

μ = 0.0, Ω = 0.0

Axial Flaw Length: 

Axial Cracks, Wear 

Marks, or 

Volumetric Flaws

Gamma(α =2.33318781, β= 2.0847)

Circumferential Crack 

Angle 0.58 Gamma(α=28.6565, β=0.4187) + (1-0.58)·Gamma(α=9.5638, β=0.0670)

Flaw Depth: 

Cracks, Wear, 

Volumetric Flaws

Gamma(α =2.0658, β=16.3274)

Note: If the gamma function in EXCEL is to be used to evaluate values with the above parameters, the “beta” to be 

placed in the EXCEL gamma function is actually 1/ β of Table 6.3-1.

6.3.2 An Example Calculation 

Table 6-2 provides a linear hazard rate for the SG tube flaws as a function of EFPY. This hazard 

rate is defined by:

h(k) = μ * k + Ω

where k is EFPY, and both coefficients μ and Ω are positive.

Given the above hazard rate, the cumulative flaw probability can be expressed by:

P(f) = 1 - exp[-{(1/2) * μ * k2 + Ω * k}] (6.1)

A four-loop W plant (four SGs) with thermally treated Inconel 600 SG tubes is considered. Each 

SG is assumed to have 3,300 tubes, and the plant has accumulated 15.6 EFPYs of operation. 
6-7

The expected number of flaws (NFlaws-Avg) that will be identified at the end of the current cycle 

is estimated from the cumulative probability distribution using the following equation:

NFlaws-Avg = (3,300 * 4) * [1.0 - exp[-{(1/2) * μ * k2 + Ω * k}]] (6.2)

The values μ and Ω can be found in Table 6-2. For the case discussed above, it is expected that 

370 wear/volumetric flaws would be present in all the SGs (13,200 tubes). Thirty-one out of 

these 370 flaws will be generated in this cycle. This is estimated directly by setting k=15.6 in the 

equation for hazard rate

(h(k) = 6.4166·10-5 K + 1.3236·10-3

)

It also implies that the larger flaws could only be found in the last cycle (the estimated 31 flaws), 

since large flaws found earlier in a previous cycle were all subjected to plugging and other repair 

practices per inspection procedure.

The current statistical analysis and this illustrative example are based on flaws that are 

detected. They do not account for the hidden flaws that are not detected during ISIs. The 

number or fraction of the hidden flaws is generally estimated by using a probability of detection 

(POD). The POD delivers the realistic, statistical assessment of the reliability for a 

nondestructive testing method. The POD curves (typically S shaped) are developed as a 

function of flaw size and type. The larger and deeper the flaw, the higher the POD will be. The 

POD value also depends on the flaw type. For example, the POD value is larger for a crack with 

sharp edges than for a wear with smooth surface (see NUREG/CR-6791, “Eddy Current 

Reliability Results from the Steam Generator Mock-up Analysis Round-Robin,” Revision 1, 

issued October 2009 (Ref. 6). For more detailed analysis, the flaws in the last cycle should be 

adjusted for not considering the POD, using the information in NUREG/CR-6791. The impact of 

such adjustments for large flaws is expected to be around 10 percent.

Figure 6-2 shows the NFlaws-Avg, which includes both wear and cracks for 13,200 tubes, as a 

function of EFPY for both 600 and 690 thermally treated tubes.
6-8

Figure 6-2 Average number of flaws as a function of EFPY for four SGs 

6.3.3 Example Flaw Samples 

To illustrate the flaws that may be present during the 15th EFPY, 10 flaw samples were 

generated for one SG with 3,588 600TT tubes. It is assumed that the tubes with 40-percent 

deep and deeper flaws are plugged when revealed by tests. Analysts created 775 total flaws in 

10 samples, with an average of 78 flaws per sample per SG. The average length of the 

775 flaws is 1.1 centimeters (0.43 inch); the average depth is 18 percent. All flaws are of the 

“wear” type.

Histograms in Figures 6-3 and 6-4 show the distribution of the 775 flaws by length and depth. 

Note that all flaws of a depth of 40 percent or deeper are removed at or before the last outage; 

thus, such large flaws have been generated since the last refueling outage or were not detected 

(i.e., POD less than 1).

0

200

400

600

800

1000

1200

1400

0 5 10 15 20 25 30 35 40

Flaws per 13,200 tubes

EFPY (K)

Inconel 600

Inconel 690
6-9

Figure 6-3 600TT flaws for 10 SGs—distribution by length 

Figure 6-4 600TT flaws for 10 SGs—distribution by depth 

138

270

189

99

44

17

5 10 3

0

50

100

150

200

250

300

0.25 0.75 1.25 1.75 2.25 2.75 3.25 3.75 4.25

# of Flaws

Midpoint of bin in length (cm)

600TT Flaws for 10 SGs Distribution by 

Length in cm

# of Flaws

Example: There are 270 flaws longer 

than 0.25 cm but not longer than 

0.75 cm

131

393

176

61

14

0 0 0 0 0

0

50

100

150

200

250

300

350

400

450

0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95

# of Flaws

Midpoint of bin in depth

600TT Flaws for 10 SGs 

Distribution by Depth

# of...

Example: There are 176 flaws deeper 
6-10

6.4 OTSG Axial Loads on Tubes during Severe Accidents 

ANL has completed a study for NRC’s Office of Nuclear Regulatory Research (RES), “Stability 

of Circumferential Flaws in Once-Through Steam Generator Tubes under Loading during LOCA, 

MSLB, and FWLB,” now being reviewed, on the assessment for potential elevated axial tube 

loads because of thermal expansion between the SG shell and tubes during severe-accident 

conditions in OTSGs. Also, OTSG designs are not susceptible to a severe-accident effect of a 

backflow of steam, which may cause much higher local temperatures in recirculating SGs. 

Based on the preliminary results of the ANL work, and the backflow characteristics, RES’s 

current assessment is that the phenomenon investigated does not contribute significantly to 

C-SGTR for severe-accident conditions.

6.5 References 

1. Sandia National Laboratories, “Severe Accident Initiated Steam Generator Tube

Ruptures Leading to Containment Bypass—Integrated Risk Assessment,” JCN Y6486,

February 2008, Agencywide Documents Access and Management System Accession

No. ML15054A514.

2. Azarm, M.A., et al., “A Letter Report on Flaw Database and C-SGTR Calculator Flaw

Input,” Information Systems Laboratories, December 2014.

3. Gorman, J.A., et al., “Estimating Probable Flaw Distributions in PWR Steam Generator

Tubes,” U.S. Nuclear Regulatory Commission, NUREG/CR-6521 (ANL-96/20), 1996.

4. U.S. Nuclear Regulatory Commission, “U.S. Operating Experience With Thermally

Treated Alloy 600 Steam Generator Tubes,” NUREG-1771, April 2003.

5. U.S. Nuclear Regulatory Commission, “U.S. Operating Experience With Thermally

Treated Alloy 690 Steam Generator Tubes,” NUREG-1841, April 2003. Agencywide

Documents Access and Management System Accession No. ML072330588.

6. Kupperman, D.S., et al., “Eddy Current Reliability Results from the Steam Generator

Mock-up Analysis Round-Robin,” U.S. Nuclear Regulatory Commission,

NUREG/CR-6791, Revision 1, October 2009.
7-1

7 CONSEQUENTIAL STEAM GENERATOR TUBE RUPTURE 

PROBABILISTIC RISK ASSESSMENT FOR THE EXAMPLE 

COMBUSTION ENGINEERING AND WESTINGHOUSE PLANTS 

This chapter considers example Westinghouse (W) and Combustion Engineering (CE) plant 

designs to estimate both the consequential steam generator tube rupture (C-SGTR) 

probabilities and corresponding large early release frequency (LERF) fractions.

Section 7.1 discusses probabilistic risk assessment (PRA) for the example W plant; Section 7.2 

discusses PRA for the example CE plant.

7.1 Example Westinghouse Plant 

The information reported in NUREG/CR-6995, “SCDAP/RELAP5 Thermal-Hydraulic Evaluations 

of the Potential for Containment Bypass During Extended Station Blackout Severe Accident 

Sequences in a Westinghouse Four-Loop PWR,” issued March 2010 (Ref. 1), provided the 

thermal-hydraulic (TH) analysis and the success criteria used for developing the PRA models 

for C-SGTR for the example W plant. NUREG/CR-6995 documents the TH evaluations 

performed using the SCDAP/RELAP5 systems analysis code and a model representing a W 

four-loop pressurized-water reactor (PWR) (i.e., Zion Nuclear Power Plant (ZNPP), Unit 1). The 

plant model for TH evaluation benefitted from the following:

• extensive iterative comparisons with evaluations of natural circulation flows and turbulent 

mixing using a computational fluid dynamics code

• comparison with experimental data for pertinent fluid-mixing behavior

NUREG/CR-6995 also included some sensitivity evaluations and uncertainty analyses for the 

station blackout (SBO) accident sequences. ZNPP was the example W plant for the C-SGTR 

PRA evaluation, and the available documents on its PRA provided the other required input 

information for the C-SGTR PRA evaluation.

7.1.1 Description of the Selected TH Sequences for C-SGTR PRA for the Example 

Westinghouse Plant 

The following representative scenarios from NUREG/CR-6995 (Ref. 1) were examined for 

potential use in evaluating C-SGTR. These scenarios modeled leakage through the secondary 

side of each steam generator (SG), equivalent to a hole of 3.2 square centimeters (cm2

) 

(0.5 square inch (in.2

)). This size of leakage is sufficient to ensure that the pressure in the 

secondary side of the SGs approaches the atmospheric pressure after SG dryout. However, this 

assumed leakage area is not sufficient to maintain a low SG secondary-side pressure after the 

occurrence of a guillotine break of a single SG tube.

(1) Station Blackout with Early Failure of the Turbine-Driven Auxiliary 

Feedwater (TDAFW) Pump Resulting in Core Damage and a Potential for 

C-SGTR Caused by Creep Rupture: This scenario models the normal reactor 

coolant pump (RCP) seal leakage of 79.4 liters per minute (Lpm) (21 gallons per 

minute (gpm)) per pump. Core damage is expected in less than 2 hours. The 

potential for C-SGTR is considered after the onset of core damage. 
7-2

This scenario is referred to as the “Wnewbase” case. Figure 7-1a shows the 

primary and secondary-side pressure in pounds per square inch (psi) and the 

hot-leg (HL) temperature in degrees Celsius (C). Figure 7-1b shows the 

difference between the HL temperature and the hottest tube temperature, the 

average hot tube temperature, and the average cold tube temperature.

(2 & 3) Station Blackout with Failure of TDAFW Pump after Battery Depletion: The 

TDAFW pump is initially considered available, but it fails after loss of direct current (dc) 

as the batteries deplete. The model uses the normal RCP seal leakage of 79.4 Lpm 

(21 gpm) per pump. The operator’s action to depressurize SGs at 30 minutes, by 

opening at least one SG atmospheric dump valve or SG power-operated relief valve 

(PORV) per SG, drops the primary pressure below 4.82 megapascal (MPa) (700 psi). 

This actuates the accumulator discharge. The study analyzed two cases, referred to as 

Cases 153 and 153A, depending on the rate of depressurization (slower and faster 

rate). Case 153A results in sequence timing, including the CD that is delayed by at 

most 1.3 hours compared to Case 153, because of depressurization of the SGs to the 

lower pressure (120 psi absolute (psia), rather than 280 psia for Case 153). Greater 

depressurization of the RCS resulted in more accumulator injection.

(4) Station Blackout with Early Failure of the TDAFW Pump and Guillotine Break of 

One SG Tube after Core Damage: The model assumes the normal RCP seal leakage 

of 79.4 Lpm (21 gpm). Early core damage is expected in less than 2 hours because of a 

total loss of feedwater at the onset of the transient. At approximately 12,926 seconds, 

one of the flawed tubes with a stress magnification factor of 2 (mp = 2) ruptures. The 

resulting modeled leak area is equivalent to the area associated with a guillotine break 

of one tube. This will result in a slow depressurization of the primary; however, it is not 

fast enough to prevent HL failure. The HL fails shortly thereafter (13,630 seconds, 

approximately 11 minutes), terminating the containment bypass. Figure 7-2 shows the 

results of this scenario, referred to as Case F2.

Similar to Case F2 Except that the Failed Flawed Tube Has a Stress Magnification Factor 

of 3 (mp = 3): The flawed tube fails at 12,930 seconds. The model excluded the HL failure. 

Therefore, this case run captured the prolonged depressurization of the primary as a function of 

time because of the guillotine break of one SG tube. Figure 7-3 shows the results of this 

scenario, referred to as Case F3.

Similar to “Wnewbase” Case Except with Different Sizes of Reactor Coolant System Seal 

Leakages: Initial leakage is 79.4 Lpm (21 gpm) per RCP. At 13 minutes, leakage is increased 

to 226.8 Lpm (60 gpm) per RCP. Finally, when fluid in the RCPs becomes saturated, leakage is 

increased to 1,703 Lpm (450 gpm) per RCP. This case, called Case Run C21-60-450, resulted 

in a clearance of the loop seal.

The observations below result from the TH analyses used in developing the PRA models and 

the associated sensitivity runs.

As noted in Figures 7-1a and 7-1b, the HL temperature is significantly higher than the average 

hot tube and the hottest tube temperatures by as high as 400 degrees C 

(752 degrees Fahrenheit (F)). Figure 7-1b shows the differences between the HL temperature 

and the hottest tube temperature, average hot tube temperature, or average cold tube 

temperature. A higher HL temperature is the driving factor for HL failure before the failure of the 
7-3

SG tubes. This would also explain the lower estimate of the risk associated with the C-SGTR for 

the example W plant.

For those cases where the TDAFW pump is operating, the time to core uncovery depends on 

the scheme used for primary depressurization. In both cases analyzed by SCDAP/RELAP5 

models, Cases 153 and 153A, aggressive cooling and depressurization using the secondary 

system resulted in dropping the primary pressure below the accumulator discharge setpoint. 

The accumulator discharge resulted in a significant delay in core uncovery (about 11 hours for 

Case 153 and 13 hours for Case 153A). No case runs were performed for when the operator 

fails to depressurize the primary via rapid secondary cooldown. In such cases, it is assumed 

that the TH response will be similar to the Wnewbase case but shifted by at least 4 hours, 

corresponding to the battery duration.

As shown in Figure 7-3, the guillotine break of one tube will not depressurize the primary such 

that it prevents subsequent HL failure. Therefore, the PRA event trees and resulting estimated 

probabilities should differentiate between single tube failures and multiple tube failures.

As seen in Figure 7-3, the failure of SG tubes with a leak area equivalent to the guillotine break 

of one tube will result in the pressurization of the SG secondary side. For the purpose of 

severe-accident management guideline (SAMG) activities related to flooding the SG, the SG 

secondary side has to be fully depressurized. This requires opening the secondary-side PORVs 

or safety relief valves (SRVs). The opening of PORVs or SRVs occurs under the harsh 

environment caused by the core melt accident.

The TH runs showed that the loop seal is cleared when the RCP leakage is about 1,703 Lpm 

(450 gpm) per pump. The TH runs also indicate that the time of RCP seal failure, and its relation 

to the time when the cold leg becomes saturated, affects loop seal clearing.
7-4

Figure 7-1(a) TH results for Wnewbase 
7-5

Figure 7-1(b) Difference between the HL temperature and the temperatures of the 

hottest tube (HTT) and the average hot tube (AHTT) and cold tube (ACTT) 

for Wnewbase
7-6

Figure 7-2 TH results for Case F2 
7-7

Figure 7-3 TH results for Case F3 
7-8

7.1.2 Estimating the Entry Frequency from Level 1 PRA for C-SGTR 

ZNPP was selected for developing C-SGTR PRA models to ensure consistency with the TH 

analyses results. No current PRA or standardized plant analysis risk (SPAR) models are 

available for ZNPP, and ZNPP units are no longer in operation. The accident frequency for the 

entry point to the C-SGTR PRA was, therefore, estimated based on the plant design features 

and information from vintage ZNPP PRA documents. Appendix G provides a detailed discussion 

of various core damage frequency (CDF) contributors from SBO scenarios to overall CDF from 

both internal and external events. The technical discussion in Appendix G (Section G.1) 

supports the quantitative values used in this section.

Because of a long-term SBO (ltsbo) (beyond battery depletion) that can be used as the entry 

point for a Level 2 PRA, the CDF estimate is around 1.2X10-5 per reactor year (RY). This is 

consistent with the estimate of the ltsbo scenarios reported in NUREG-1935, “State-of-the-Art 

Reactor Consequence Analyses (SOARCA) Report,” issued November 2012 (Ref. 2) (between 

1.0X10-5 and 2.0X10-5 per RY). Table 7-1 shows the contributions from both internal and 

external hazards.

Table 7-1 Contributions of Various Events to Long-Term SBO Scenarios 

Initiating Event Long Term 

SBO CDF

Percent 

Contribution

Source

Internal events, including internal floods 5.2E-6 25.5% NUREG-4551

Seismic 5.6E-6 27.5% NUREG/CR-3300

Fire 9.5E-6 47.0% Appendix G

Total 2.03E-5 100.0%

The uncertainties associated with these frequencies are not presently estimated because of the 

lack of detailed models and data. Surrogate uncertainties from similar plants, such as Indian 

Point Unit 3, could be considered if needed.

Table 7-2 shows the main plant features of ZNPP that are pertinent to this study.
7-9

Table 7-2 Related Information from Zion Nuclear Stations for This Study 

Systems System Features

Number of SGs and number of 

tubes per SG

4 SGs each with 3,300 tubes

Emergency Power System

a. Each unit consists of 3 4160-VAC class 1E buses, each 

feeding 1 480-VAC class 1E bus and a motor control center.

b. For the 2 units, there are 5 diesel generators, with one being a 

swing diesel generator shared by both units.

c. 3 trains of dc power are supplied from the inverters and 3 unit 

batteries. It has a battery life of 6 hours.

Auxiliary Feedwater (AFW) 

System 

a. Two 50-percent motor-driven pumps and one 100-percent 

turbine-driven pump.

b. Pumps take suction from their own unit condensate storage 

tank (CST) but can be manually cross-tied to the other unit’s 

CST.

Service Water (SW)

a. Shared system between both units

b. Consists of 6 pumps and 2 supply headers

c. Cools component cooling heat exchangers, containment fan 

coolers, diesel generator coolers, AFW pumps

d. 2 out of 6 pumps can supply sufficient flow.

Component Cooling Water 

(CCW)

a. Shared system between both units

b. Consists of 5 pumps, 3 heat exchangers, and 2 surge tanks

c. Cools RHR heat exchangers, RCP motors and thermal 

barriers, RHR pumps, SI pumps, and charging pumps

d. One of 5 pumps can provide sufficient flow.

Secondary Relief

a. Steam dump valves

b. Atmospheric dump valves (one per SG)

c. SRVs

Primary Relief a. 2 PORVs

b. 3 SRVs

Containment

a. Large, dry, prestressed concrete

b. 2.6 million cubic foot volume

c. 49 psig design pressure

Reproduced from NUREG/CR-3300 (Ref. 3), NUREG/CR-4550 (Ref. 4), and NUREG/CR-4551 (Ref. 5).

7.1.3 Conditional Probability of C-SGTR at Each Flaw Bin 

In this section, the flaw distributions obtained in Chapter 6, and the Wnewbase sequence TH 

input discussed earlier in Section 7.1, serve to gain an understanding of various SG tube leaks 

and their relation to HL failure time for different individual flaw sizes; an analysis of the effect of 

multiple flaws appears later in this section.

A series of calculations used the C-SGTR calculator, which was developed to support the work in 

this report. The calculator is used to estimate the failure times and leak sizes of SG tubes with 

different types of flaws. The software also has built-in models for HL and surge-line failures 

caused by the creep-rupture failure mechanism, and it estimates the failure times and probabilities 

of the HL and surge line. The scope of the models currently includes new SG tube materials and 

the associated property data for thermally-treated Inconel 600 and 690 (600TT and 690TT). The 

C-SGTR calculator is designed to support the PRAs that address the risk associated with steam 

generator tube rupture (SGTR) scenarios—as an initiator, as a consequence of plant transients 

(design-basis accident (DBA) scenarios), and as a result of core damage sequences (C-SGTR). 

The calculator software uses plant-specific design information, material properties, plant-specific 

SG tube flaw data, and scenario-specific TH results as input to generate an estimate of the 
7-10

C-SGTR probability. Appendix B discusses examples of calculator runs, as well as input files 

and runs.

Flaw bins were developed to represent different sizes of flaws. Using Wnewbase as the TH 

input file, and the flaw length and depth representing the midpoint of each flaw bin, a series of 

case runs were performed, using the C-SGTR calculator. Each case run estimated the 

probability of an SGTR with an area of at least 1 cm2 (0.16 in.2

) before HL or surge-line failure. 

The 1 cm2 (0.16 in.2

) threshold leak area was conservatively selected as the criterion for 

potential gross tube failure.

All case runs for the W plant in Section 7.1.4 assumed that a flawed tube can be exposed to 

either an average hot tube temperature or an average cold tube temperature. The fraction of 

tubes exposed to the average hot temperature and average cold temperature used in the 

analysis were 0.45 and 0.55, respectively. The contribution from the hottest tubes was not 

included in these analyses and was judged to be insignificant. The hottest tube temperature 

deviates significantly from the average hot tube temperature for temperatures exceeding 

850 degrees C (1,562 degrees F) (e.g., see Figure 7-1a, around 225 minutes). HL will be 

exposed to a very high elevated temperature, and HL failure is generally expected to occur 

before this deviation takes place. Therefore, the effect of the hottest tube temperature could be 

enveloped with the average hot tube temperature for flawed tubes.

Table 7-3 presents the results from these case runs for each flaw bin for Inconel 600 and 

Table 7-4 presents them for Inconel 690. The results reaffirm that, for the wear flaws, the 

bounding probability of tube failure is only a function of the flaw depth. These results show that 

a significant contribution to C-SGTR probability for the selected W plant comes only from flaws 

with a depth greater than 60 percent. For all smaller flaw sizes, the probability that the SG tubes 

fail before the HL fails is estimated to be negligible (i.e., zero). 

Table 7-3 Probability that a Flaw that Belongs to a Bin Defined by Depth and Length Range 

Fails a before the HL Failure for Inconel 600 Tubes for “ Wnewbase” TH File for the 

Selected W Plant 

Depth/ 

Length 1 cm 2 cm 3 cm 4 cm 5 cm 6 cm

Average 

Across 

Length

0.0 to 0.1 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0

0.1 to 0.2 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0

0.2 to 0.3 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0

0.3 to 0.4 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0

0.4 to 0.5 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0

0.5 to 0.6 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0

0.6 to 0.7 ~ 0.05 ~ 0.05 ~ 0.05 ~ 0.05 ~ 0.05 ~ 0.05 ~ 0.05

0.7 to 0.8 ~ 0.8 ~ 0.8 ~ 0.8 ~ 0.8 ~ 0.8 ~ 0.8 ~ 0.8

0.8 to 0.9 ~ 1 ~ 1 ~ 1 ~ 1 ~ 1 ~ 1 ~ 1

0.9 to 1.0 ~ 1 ~ 1 ~ 1 ~ 1 ~ 1 ~ 1 ~ 1

a For Tables 7-6 and 7-7, a conservative screening criterion of a flaw leak area greater than 1 square cm is used to 

determine failure.
7-11

Table 7-4 Probability that a Flaw that Belongs to a Bin Defined by Depth and Length Range 

Fails before the HL Failure for Inconel 690 Tubes for “ Wnewbase” TH File for the 

Selected W Plant 

Depth/ 

Length 1 cm 2 cm 3 cm 4 cm 5 cm 6 cm

Average 

Across 

Length

0.1 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0

0.2 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0

0.3 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0

0.4 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0

0.5 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0 ~ 0

0.6 ~ 0.05 ~ 0.05 ~ 0.05 ~ 0.05 ~ 0.05 ~ 0.05 ~ 0.05

0.78 ~ 0.75 ~ 0.75 ~ 0.75 ~ 0.75 ~ 0.75 ~ 0.75 ~ 0.75

0.8 ~ 1 ~ 1 ~ 1 ~ 1 ~ 1 ~ 1 ~ 1

0.9 ~ 1 ~ 1 ~ 1 ~ 1 ~ 1 ~ 1 ~ 1

Tables 7-3 and 7-4 show the probability of a C-SGTR with leakage areas greater than 1 cm2

(0.16 in.2

), from a single flawed tube as a function of the flaw depth. These probabilities could be 

viewed as relative indications of the effect of flaw depth on the C-SGTR probability for the W 

plant. Two observations are based on these results:

(1) The contribution to C-SGTR probability from flaws with a depth less than 60 percent is 

expected to be small.

(2) Inconel 600TT and 690TT tube materials have comparable performance when 

considering the overall C-SGTR probability.

The first observation signifies that flawed tubes should be plugged at a threshold depth 

significantly less than 60 percent, so that the possibility of a flaw growing to a depth greater than 

60 percent in the next cycle is minimized. It also signifies that a more accurate estimate of the 

rate of flaw generation with large depths is necessary for risk assessment of C-SGTR scenarios. 

The second observation emphasizes that a lower flaw rate generation in Inconel 690 is offset 

with a slightly higher creep-rupture resistance of the Inconel 600.

Current W plants use SGs with Inconel 600TT and 690TT. The number of flaws per cycle for 

600TT and 690TT SG tubes is significantly lower than the older SG tubes made of mill-annealed 

Inconel 600. As Chapter 6 discusses, the available surveillance data were the basis for the size 

distributions of flaws in terms of flaw length and depth. Because of the limited number of plants 

and inspection cycles in the surveillance data, the estimated flaw rates and flaw characteristics 

are significantly dependent on the degree to which the surveillance data represent the 

U.S. plants. Any potential anomalies in the data of even one plant would significantly affect the 

estimates because of the small number of plant samples. 

Lack of surveillance data from a larger population of plants limits the range of the applicability of 

the estimates, and it causes uncertainties in the estimated parameters for characterizing the 

flaws. As an example, a large number of unreliable small-depth measurements; less than 

10 percent, from one of the plants in the surveillance data, significantly skewed the depth 

distribution toward the shallow flaws. This issue was compounded because surveillance records 

had a large number of missing depth measurements. The depth distribution generated from the 
7-12

data, therefore, is expected to be skewed toward the lower depth values. Some adjustments 

were made to the original estimated distributions of flaw depth and length to compensate for the 

potential shift of flaw size distributions toward the shallower and smaller flaws. This was done by 

shifting the depth distribution by 7 percent deeper and the length distribution by 0.8 cm (0.31 in.) 

longer to ensure that the numbers of large flaws (i.e., flaws that are plugged) have been 

maintained. The raw data for plugging are readily available in the flaw database. The flaw data 

show that, out of 2,440 flaws, 233 were plugged (about 9.5 percent). Furthermore, a plugged 

tube is expected to have a flaw with an average length of 1.3 cm (0.5 in.), and a depth greater 

than 30 percent. The size distributions are shifted such that the probability of an occurrence of a 

flaw below these sizes accounts for 90 percent (it is approximately equal to 100 percent minus 

the 9.5 percent of tubes that were plugged) of the total number of flaws. Figures 7-4 and 7-5 

show the shifted distribution for flaw depth and flaw length. These distributions apply to both CE 

and W SGs and to both Inconel 600TT and 690TT. 

Figure 7-4 Shifted distribution for flaw depth 

Figure 7-5 Shifted distribution for flaw length 

0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

0 0.5 1

Probability 

Depth 

Shifted Flaw Depth Distribution

Cumulativ

e

0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

0 2 4 6 8

Probability

Length (Cm)

Shifted Flaw Length Distribution

Cumulativ

e
7-13

ZNPP had four SGs, each with about 3,300 tubes that this study assumes could be made of 

either Inconel 600 or Inconel 690. There are, therefore, 13,200 unplugged tubes for a unit of 

ZNPP. The average number of flaws generated for the first 14 effective full-power years 

(EFPYs) of operation using the Inconel 600TT flaw generation rate equation, is about 323 flaws 

per one unit of ZNPP. (Section 6.3.2 includes a sample calculation.) At the end of the 

14 EFPYs, the study assumed that there was a periodic SG inspection; therefore, all the large 

flaws out of 322 flaws per unit are expected to be plugged (approximately 30 plugged tubes for 

four SGs). An additional 31 flaws will be generated during the 15 EFPYs of operation. 

Therefore, 323 flawed tubes were expected for all four SGs during the operating period at 

15 EFPYs, with an average of about 2 to 3 large flaws that may need plugging at the end of the 

15 EFPYs.

Flaw lengths and depths are sorted into a set of bins. Table 7-5 shows the probability that a flaw 

resides in one of the bins at a time of 15 EFPYs for ZNPP SG tubes made of either Inconel 600 

or 690. The length and depth distributions shown in Figures 7-4 and 7-5 form the basis for these 

estimated probabilities, apply to both Inconel 600TT and 690TT, and do not differentiate 

between the W and CE plants. These probabilities are multiplied by the number of flaws 

estimated earlier to determine the average numbers of flaws for each flaw bin. The estimates for 

bins consisting of large flaws consider the expected number of flaws only in the last cycle. All 

flaws deeper than approximately 0.3 (bin with a depth between 0.3 and 0.4) discovered in the 

previous cycles are assumed to have been plugged. The total number of flaws used for 

calculating the expected number of flaws for each bin, therefore, follows the following rules:

• For flaw bins with a depth of less than 0.3 (30 percent of the wall thickness), the total 

number of flaws used to estimate the expected number of flaws was the summation of 

all flaws in previous cycles plus the number of flaws in the last cycle. For Inconel 600, 

this value is 354 flaws (322 flaws in previous cycle plus 31 flaws in the last cycle). For 

Inconel 690, this value is 218 flaws (198 flaws in previous cycle plus 20 flaws in the 

last cycle).

• For flaw bins with a depth greater than 0.3 (30 percent of the wall thickness), the total 

number of flaws is based on the flaws generated in the last cycle (cycle 15). The values 

for Inconel 600 and 690 are 31 and 20, respectively.

Tables 7-6 and 7-7 show the average number of flaws for Inconel 600 and 690, respectively. 

The values shown in these tables represent the expected number of flaws in each bin, rounded 

to the nearest integer. Therefore, a value of zero for the expected numbers of flaws in a bin 

should not be construed as having a zero probability of occurrence. To find the probability that a 

flaw is realized in each flaw bin, consult Table 7-5.
7-14

Table 7-5 Probability that a Detected Flaw Belongs to a Bin Size at 15 EFPYs 

Flaw Length

Total

0 cm to 

1 cm

1 cm to 

2 cm

2 cm to 

3 cm

3 cm to 

4 cm

4 cm to 

5 cm

5 cm to 

6 cm

Flaw Depth%/100

0 to 0.1 2.74E-3 4.62E-2 2.23E-2 5.38E-3 1.04E-3 1.80E-4 7.78E-2

0.1 to 0.2 1.86E-2 3.14E-1 1.52E-1 3.66E-2 7.08E-3 1.23E-3 5.29E-1

0.2 to 0.3 9.59E-3 1.62E-1 7.81E-2 1.89E-2 3.64E-3 6.31E-4 2.73E-1

0.3 to 0.4 3.09E-3 5.21E-2 2.52E-2 6.07E-3 1.17E-3 2.03E-4 8.78E-2

0.4 to 0.5 8.47E-4 1.43E-2 6.90E-3 1.66E-3 3.22E-4 5.57E-5 2.41E-2

0.5 to 0.6 2.14E-4 3.61E-3 1.74E-3 4.21E-4 8.13E-5 1.41E-5 6.08E-3

0.6 to 0.7 5.14E-5 8.67E-4 4.19E-4 1.01E-4 1.95E-5 3.38E-6 1.46E-3

0.7 to 0.8 1.19E-5 2.01E-4 9.73E-5 2.35E-5 4.54E-6 7.86E-7 3.39E-4

0.8 to 0.9 2.71E-6 4.57E-5 2.21E-5 5.32E-6 1.03E-6 1.78E-7 7.70E-5

0.9 to 1.0 small

Total 3.51E-2 5.93E-1 2.87E-1 6.92E-2 1.34E-2 2.32E-3 1.00E+00

Table 7-6 Expected Number of Flaws that Belong to a Flaw Bin Defined by Depth and Length 

Range for Zion SGs with Tubes Made of Inconel 600 

Depth/ 

Length

0 cm to 

1 cm

1 cm to 

2 cm

2 cm to 

3 cm

3 cm to 

4 cm

4 cm to 

5 cm

5 cm to 

6 cm

Total

0 to 0.1 1 16 8 2 0 0 27

0.1 to 0.2 7 111 54 13 3 0 188

0.2 to 0.3 3 57 28 7 1 0 96

0.3 to 0.4 1 2 1 0 0 0 4

0.4 to 0.5 0 0 0 0 0 0 0

0.5 to 0.6 0 0 0 0 0 0 0

0.6 to 0.7 0 0 0 0 0 0 0

0.7 to 0.8 0 0 0 0 0 0 0

0.8 to 0.9 0 0 0 0 0 0 0

Total 12 186 91 22 4 0 315

The expected values of flaws in each bin illustrate the expected size distribution of flaws. The 

values shown in the tables also account for the flaws detected in previous cycles that were so 

large that the affected tubes were plugged. The approximation used in these calculations, plus 

the effect of rounding off the expected number of flaws per bin, has generally resulted in slightly 

fewer flaws than expected. As an example, for Inconel 600, Table 7-6 indicated an expected 

number of 315 flaws, rather than the 323 flawed tubes estimated earlier.
7-15

Table 7-7 Expected Number of Flaws that Belong to a Flaw Bin Defined by Depth and Length 

Range for Zion SGs with Tubes Made of Inconel 690 

Depth/ 

Length

0 cm to 

1 cm

1 cm to 

2 cm

2 cm to 

3 cm

3 cm to

4 cm

4 cm to 

5 cm

5 cm to 

6 cm

Total

0 to 0.1 1 10 5 1 0 0 17

0.1 to 0.2 4 68 33 8 2 0 115

0.2 to 0.3 2 35 17 4 1 0 59

0.3 to 0.4 1 1 1 0 0 0 3

0.4 to 0.5 0 0 0 0 0 0 0

0.5 to 0.6 0 0 0 0 0 0 0

0.6 to 0.7 0 0 0 0 0 0 0

0.7 to 0.8 0 0 0 0 0 0 0

0.8 to 0.9 0 0 0 0 0 0 0

Total 8 114 56 13 3 0 194

The information generated in Tables 7-5 through 7-7 can be used to obtain an initial estimate of 

the C-SGTR probability.

7.1.4 Estimating C-SGTR Probability 

This section estimates the C-SGTR probability. The analyses are performed in a progressive 

manner, starting with the least rigorous method for estimating the C-SGTR probability using the 

individual flaw depth, assuming that the flaw length is sufficiently large that it can create 

substantial C-SGTR leakage. Next, the section considers information on flaw lengths and the 

impact of multiple tube failures, rather than the failure of a single tube. Finally, the section 

discusses a rigorous method for aggregating over all flawed tubes with various depths 

and lengths.

7.1.4.1 C-SGTR Probability Based on a Single Flaw with Large Lengths and 

Varying Depths

The following discussion is a simple and quick estimate of C-SGTR probability using information 

obtained in the previous section. This approach assumes that only large flaws generated during 

the last operating cycle significantly contribute to C-SGTR. The analysis can be used for 

risk-informed screening purposes or for evaluating inspection findings in which the surveillance 

data are only available for flaw depth. This assumes that all flaws with greater than 30-percent 

depth were plugged during the last inspection outage. The analysis does not use information on 

flaw length to estimate the C-SGTR leakage area, and it includes all leakage areas of 1 cm2

(0.16 in.2

) or larger.

The approach consists of the following steps:

(1) Estimate the number of flaws generated during the last operating cycle using 

distributions in Chapter 6.

(2) Using Table 7-5, estimate the expected number of flaws in each depth bin, based 

on the total number of flaws generated during the cycle.
7-16

(3) Determine the probability of one or more flaws failing during a high/dry/low

accident sequence by multiplying the expected number of flaws in each depth bin

by the conditional probability of the flaw leak area exceeding 1 cm2 (0.16 in.2

)

during a representative C-SGTR accident sequence (obtained from Table 7-3 for

Alloy 600TT and Table 7-4 for Alloy 690TT tubes) and summing across all

depth bins.

As discussed in Section 7.1.3, assume that 31 flaws were generated during the last cycle for SG 

tubes made of Inconel 600TT. The probability that at least one flaw out of these flaws belongs to 

the three large bins that contribute to C-SGTR (depths of 0.6, 0.7, and 0.8) is estimated by 

multiplying the cell probabilities in Table 7-3 by 31 flaws. The C-SGTR probability for each flaw 

bin is then estimated by multiplying the resulting number by the conditional C-SGTR probability 

for that bin from Table 7-6. The overall C-SGTR probability is then estimated by summing over 

the bins. This is shown below:

Table 7-8 C SGTR probability summed over the flaw bins for Inconel 600/690 (W) 

Depth Bin Probability of 

Flaw Belonging 

to Depth Bin 

(Table 7-3)

Expected 

Number of Flaws 

in Depth Bin

Probability of 

C-SGTR from a

Single Flaw in

Depth Bin 

(Table 7-6)

Conditional 

Probability of 

C-SGTR for

Accident 

Sequence

0.6 – 0.7 1.46E-3 0.0453 0.05 0.00226

0.7 – 0.8 3.39E-4 0.0105 0.80 0.00841

0.8 – 0.9 7.70E-5 0.0024 1.00 0.00239

0.9 – 1.0 small small 1.00 small

Total 0.01310

A similar example using Alloy 690TT tubes with 20 flaws generated during the last operating 

cycle yields an estimate of 8.1X10-3 for the conditional probability of C-SGTR for the 

representative accident sequence.

Although this approach provides a relatively straightforward method for estimating the potential 

for an SG flaw to lead to C-SGTR, it does not consider the potential for the failure of multiple 

flaws, and it assumes that deep flaws have large lengths. The next section includes multiple 

flaws. The length assumption is also relaxed by only including the flaw lengths greater than 

2 cm (0.78 in.) in the analysis. The criteria for gross tube failure was increased from a 1-cm2

(0.16-in.2

) leak area to 2 cm2 (0.32 in.2), to reduce the conservatism in the C-SGTR estimates. 

The fractions of the C-SGTR probability caused by failure of multiple tubes (i.e., two or three 

tubes) are estimated. This analysis is more rigorous and involves additional calculations to 

estimate the C-SGTR probability.
7-17

7.1.4.2 Approach Based on Flaw Depth and Length; Addressing Failures of Multiple 

Flawed Tubes

Appendix H describes in detail a refined method that accounts for the distributions of both flaw 

lengths and depths. This approach focuses on large flaws generated in the last cycle and 

neglects all smaller flaws that have no potential for C-SGTR. Large flaws are characterized as 

flaws that, if detected, would require the associated tube to be plugged. It is believed that the

data associated with flaw sizes of large flaws, which are subject to tube plugging, are more 

precise and less susceptible to measurement errors. This approach evaluated both single and 

multiple tube failures with flaw sizes capable of creating leakage areas to be considered 

C-SGTR. The results showed that the contribution from single tube failure is comparable to the 

estimates obtained from the previous method. The results also showed that, for Inconel 600, the 

single tube failure contribution to C-SGTR is about 1.31X10-2 from both this and previous 

methods. Similarly, for Inconel 690, the single tube failure contribution to C-SGTR is 8.1X10-

3 and 8.9X10-3 from the previous and this method, respectively. The estimated contribution of 

multiple tube failures causing C-SGTR was 8.2X10-5 and 3.8X10-5 for Inconel 600 and 690. The 

results in Table 7-9 generally show that the contribution of multiple tube failures to C-SGTR is 

negligible compared to single large tube failure in the example W plant.

Table 7-9 Probability of Single and Multitube Failure in C SGTR for Inconel 600/690 (W) 

(Sequences with early failure of TDAFW pump)

Tube Materials C-SGTR: One Tube 

Failure

C-SGTR: Two Tube 

Failures

C-SGTR: More Than 

Two Tube Failures

Inconel 600 1.31E-2 8.24E-5 Negligible

Inconel 690 8.90E-3 3.85E-5 Negligible

7.1.4.3 C-SGTR Probability Estimation Using Integrated Flaw Samples

This approach estimates and aggregates the leak rate over all flawed tubes and assumes that 

the flaw lengths and depths are available for all tubes in each SG, based on the SG periodic 

inspection data. This approach could also be used with simulated flaw data for SG tubes, 

generated by statistical sampling of flaw generation rate, depth, and size distribution. In this 

manner, the approach accounts for the distributions of flaw depth, flaw length, and number of 

flawed tubes. The approach demonstrated in this study for W SGs simulated a set of flaws that 

included at least one large flaw (a set of expected flaws plus one large flaw). This method 

accounted for single and multiple tube failures and the likelihood that the leak area exceeds the 

critical leak area discussed in Section 2.5 (i.e., 6 cm2 (0.93 in.2

)). This is the most flexible 

approach for a state-of-the-art PRA. It has wide applicability to various regulatory evaluations, 

including cases where the actual data from SG periodic surveillance are available.

As an example, assume that an expected flaw sample consists of 315 flaws shown earlier in 

Table 7-6. A case run was performed with the C-SGTR calculator to estimate the conditional 

probability of C-SGTR for these 315 expected flaws in the four SGs. Each flaw was modeled 

using the mid-point of its associated flaw bin. For example, a flaw cell with a length ranging from 

2 to 3 cm (0.79 to 1.18 in.), and a depth ranging from 0.2 to 0.3 cm (0.08 to 0.12 in.) was 

represented by a flaw with a length of 2.5 cm (0.98 in.) and a depth of 0.25 (25 percent of wall 

thickness). There would be 28 flaws for this flaw bin; therefore, the same flaw size is repeated 

28 times in the flaw file. A C-SGTR software case run then used this flaw file and the TH case 

run of Wnewbase. The results from this case run were used to estimate the failure probability 
7-18

(or survival probability) of the reactor coolant system (RCS) and C-SGTR as a function of 

accident time.

The survival probability of the RCS at a given time is defined by the probability that the surge 

line has not failed and that none of the four HLs has experienced any failures. An easy way to 

combine these probabilities is to estimate the individual hazard rates (h(t)) of each of the RCS 

components (four HLs and one surge line) as a function of time. This is done for the individual 

RCS components using the following equation.

h(tt) = �

dd�FF(tt)�

dd

1−FF(tt)

� = ([FFii+1 − FFii]/[TTii − TTii+1])/(1 − FFii) (7.1)

where F(t) is the cumulative failure probability.

The failure rate for the RCS (λRCS) can then be estimated by the sum of the hazard rates for the 

four HLs and the one surge line. λRCS is used to estimate the survival function of RCS, shown in 

Figure 7-6. The probability that the RCS has not failed at a given time can be read from the 

curve. The graph shows a very rapid drop of the survival probability as a function of time. This 

indicates that the survival distribution has a small variance. RCS failure probability can be 

estimated by the complement of the survival probability (1-Survival probability).

Figure 7-6 RCS survival probability as a function of accident time for Wnewbase 

The failure probability for SG tubes was estimated by examining the percentiles of the leak area 

at the critical leak area (6 cm2 (0.93 in2

) for this case study) as generated by the C-SGTR 

software. The survival probability then was estimated by one minus the failure probability. 

Figure 7-7 shows the percentiles of leak rate area for this case run.

0

0.2

0.4

0.6

0.8

1

12000 12500 13000 13500 14000

Probability

Time (S)

Survival Probability RCS
7-19

Figure 7-7 Percentiles of the SG leak area distribution as a function of accident time 

The study used the percentile of the leak area probability at the critical area of 6 cm2 (0.93 in.2

) 

to generate the probability distribution for critical failure time and used this distribution to 

calculate the SG survival probability. Figure 7-8 shows the resulting survival probabilities for 

RCS components and the survival and failure probabilities for SG tubes (with a leak area less 

than the critical area).

The probability of C-SGTR between t to (t + dt), was estimated by the product of the 

probabilities that RCS has survived up to time (t) and the SG failure with critical area has 

occurred between t and (t + dt).

PPPPPPPP(CCCCCC CC) =

∫ PPPPPPPP ( ssss ssssssss aa tt) ∗ PPPPPP (CCCCCC CC oooo bb bb tt aa aa (tt + ) ∗ (7.2)

0

1

2

3

4

5

6

7

8

9

10

14000 14050 14100 14150 14200 14250 14300

Tube leak area (Cm^2)

Accident Time (Sec)

Critical Area

Am

A0.05

A0.25

A0.50

A0.75

A0.95
7-20

Figure 7-8 Survival functions for RCS and SG tube failures with critical leak rate 

Figure 7-8 shows no overlap between the SG failure probability and RCS survival function, 

thereby indicating a negligible probability of the occurrence of C-SGTR for this set of flaws 

(i.e., SGTR failure with an area greater than the critical area can occur before RCS fails). 

Simple numerical integration, using spreadsheet calculations, shows that this probability is 

practically zero because of the very small variances of the two random variables depicted by the 

survival graphs (less than 1.0X10-10).

Although the above conclusion is valid for the expected flaw sample set, it may not hold when a 

flaw sample deviates from the expected set. Past experiences have shown that, even with a low 

probability, there is some possibility of detecting one or two large flaws at the end of an 

operating cycle. This is the main reason why the previous sections calculated much higher 

SGTR probabilities. To examine this hypothesis and its effect on C-SGTR probability, further 

case runs used the earlier expected flaw sample and added a large flaw. The earlier results 

showed that the additional large flaw needs to be larger than 60 percent of the nominal depth to 

effectively change the C-SGTR probability.

A new case run, therefore, used the expected flaw set and an added flaw with a length of 

3.5 cm (1.4 in.) and a depth of 65 percent. Figure 7-9 shows the percentiles of leak rate area for 

this case run.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

12000 12500 13000 13500 14000 14500 15000

Probability 

Time (S)

Survival Probability 

 RCS Survival

SG Survival

SG Failure Probability
7-21

Figure 7-9 Percentiles of the SG leak area distribution as a function of accident time 

Using the percentile of the leak area probability at the critical area of 6 cm2 (0.93 in.2

), the 

probability distribution for critical failure time was generated. This distribution was used to 

calculate the SG survival probability. Figure 7-10 shows the resulting survival probabilities for 

RCS components and SGs for this case.

Figure 7-10 Survival probability functions for RCS and flawed tubes 

This graph shows a significant overlap between the two survival probabilities. When the RCS 

survival probability is very close to one (around 12,900 seconds), the probability of C-SGTR is 

as high as 40 percent (i.e., 1 ‒ 0.6). Therefore, the probability that C-SGTR could occur before 

HL failure is expected to be greater than 40 percent. In fact, simple numerical integrations, using 

spreadsheet calculations, show that the conditional C-SGTR probability, given the specified 

0

2

4

6

8

10

12

14

16

18

20

10000 11000 12000 13000 14000 15000

Leak area for SGTR (Cm^2)

Time (s)

Am

A0.05

A0.25

A0.50

A0.75

A0.95

0

0.2

0.4

0.6

0.8

1

1.2

10000 11000 12000 13000 14000 15000 16000

Probability

Time (S)

Survival Probability Functions

RCS Survival

CSGTR
7-22

65-percent depth flaw and accident sequence, is about 0.47. A better estimate of the C-SGTR

probability can be obtained by estimating the C-SGTR probabilities for a large number of flaw

samples and averaging them over the flaw samples. The C-SGTR probability is expected to be

negligible for the majority of flaw samples except for a few of them that include at least one

large flaw. The C-SGTR probability from such an analysis is expected to be about 1.0X10-2.

7.1.4.4 Summary of the Results of C-CSGTR Calculations

Sections 7.1.4.1 to 7.1.4.3 calculated the C-SGTR probability for the W-type SGs by 

three methods, each with different assumptions and complexity. This is so that the calculator 

does not directly assess the C-SGTR probability but only calculates the progression of the total 

leak area resulting from a set of input flaws. Other calculations must be made to get a 

probability of C-SGTR for a specified critical leak area. Therefore, it would be difficult to use the 

calculator to determine the distribution of C-SGTR probability, which accounts for variations 

among the plants and the performance of their SGs, as reflected by a large number of flaw sets. 

A set of flaws, which are determined, or sampled, external to the calculator, are placed as an 

input for the calculator. Thus, the three methods discussed in this section are designed to 

provide quantitative insights to the expected probability of C-SGTR without performing large 

numbers of simulations.

Table 7-10 summarizes the results of each of the methods, along with the assumptions used. 

The following briefly discusses the benefits and limitations of each approach:

• Integrated Analysis: The method in Section 7.1.4.3 uses a single flaw set to determine

the expected probability of C-SGTR among all similar W plants. This flaw set reflects the

flaws and the flaw sizes expected (i.e., averaged over all similar plants) in cycle 15 of

their operations. Using the average flaw set as input, the calculator is expected to

estimate the probability of C-SGTR in an average plant. There could be plants with

higher or lower C-SGTR probability, as reflected by their plant-specific flaw sets. The

method in Section 7.1.4.3 is the most rigorous, and it can be used for plant-specific

analysis when plant-specific flaw data are available. It involves calculations that are in

the spirit of this project. The results from this method indicated that the C-SGTR

probability is generally negligible unless the flaw set includes one or more large flaws.

The estimated probability that a plant experienced such a flaw set is about 0.01 per year.

The result, described as “negligible” in Table 7-10, showed that the analysis used an

average flaw set that did not include any large flaws. C-SGTR probability for W plants

with no large flaw is expected to be negligible.

• Refined Screening Approach: The calculation in Section 7.1.4.2 uses an expected

plugging rate (average over all plants) at cycle 15 of operation. The number of tubes that

will be plugged at the end of cycle 15, therefore, follows a binomial distribution with the

specified rate. The flaw sizes associated with these plugged tubes (i.e., the flaw bins)

are estimated based on the tails of the flaw size distributions. This can be done for W

plants because only large flaw sizes will contribute to the probability of C-SGTR. This

method estimates the contribution to C-SGTR from failures of single and double large

flaws. It shows that the contribution of failures of multiple flaws to C-SGTR probability is

much smaller than the contribution of the failure of a single flaw. However, the probability

of C-SGTR or its contribution from each flaw bin estimated by this method is not as

rigorous as the method in Section 7.1.4.3. The contribution to the probability of C-SGTR,

as a result of the failure of a flaw in a bin, is estimated approximately by the probability

that a relatively large C-SGTR leakage occurs before the time of HL failure. The time of
7-23

HL failure is defined when the HL failure probability reaches 0.5. Relative large leakage 

should be defined here as a leakage area below the critical C-SGTR leakage area 

(guillotine break of one tube), since each flaw is examined individually as its potential 

contribution to C-SGTR. This method used a value of 2 cm2 (0.32 in.2

) as the minimum 

leakage area.

• Screening Approach: The calculation in Section 7.1.4.1 is very similar to the calculation 

in Section 7.1.4.2, with the following differences:

– No specific rate for plugged tubes was used and the expected number of flaws in a 

large flaw bin was estimated based on the distributions of flaw depth and length. 

Possible variations of the number of flaws within a flaw bin of large flaws is not 

considered (i.e., no binomial distribution was applied).

– A value of 1 cm2 (0.16 in.2

) rather than 2 cm2 (0.32 in.2) was used for the minimum 

leakage area.

Although this method is the least rigorous of the three methods, it generated similar 

quantitative results for the probability of C-SGTR and offered a quick method to estimate 

the C-SGTR probability using the “lookup tables” calculated from the results of the 

calculator for a set of runs. This method is, therefore, quite easy to use and provides 

reasonable estimates for many PRA applications for similar W PWR plants.

Table 7-10 Summary of 3 Types of C-SGTR Failure Probability Estimates Discussed in 

Sections 7.1.4.2, 7.1.4.3, and 7.1.4.4 

I. Considering Deep Flaws 

Only (7.1.4.2) > = 60% Deep

Screening Approach

II. Considering Deep Flaws 

with Size Distribution Only 

(7.1.4.3) >= 50% Deep

Refined Screening Approach

III. Considering a Sample of 

Flaws (7.1.4.4) of All Sizes and 

Depths

Integrated Analysis

EFPY = 15 EFPY = 15 EFPY = 15

31 flaws generated in the last 

cycle—with earlier deep 

flaws plugged

1 to 3 deep flaws generated in 

the last cycle (binomial 

probability with a fixed rate)—

with earlier deep flaws plugged

315 flaws in 4 SGs

(statistical sample)

Critical area for declaring SGTR 

is >= 1 cm2

Critical area for declaring SGTR 

is >= 2 cm2

Critical area for declaring SGTR 

is >= 6 cm2 (equivalent to a 

guillotine break of one tube)

C-SGTR Probability

Alloy 600 1.3E-2 Alloy 600 1.3E-2 1 tube (*) Negligible (**) 

Estimated for a flaw set that did 

not include any large flaws

Alloy 690 8.1E-3 Alloy 690 8.1E-3 1 tube

Alloy 600 8.2E-5 2 tubes (**)

Alloy 690 3.9E-5 2 tubes

Greater than 2 tubes—negligible

Notes:

* This uses the probability that one large flaw is created in the 15th cycle.

** This is based on C-SGTR runs with a limited sample of flaws that did not include any large flaw with a depth of 

50% or more. For these cases, the margin between HL failure time and SG tube failure time (for the critical leak 

area to be reached) is large and the overlap in uncertainty is insignificant.
7-24

The two screening approaches are applicable only if the major contribution to C-SGTR is from a 

few large flaws. The screening approaches cannot be used if the TH run for an accident 

scenario, used as an input to the calculator, indicates that small flaws will also contribute to the 

probability of C-SGTR. For these cases, only the integrated analysis method should be used for 

either generic industrywide analysis or plant-specific analysis. This is the case for the TH results 

of the SBO scenarios for the selected CE plant. Therefore, the CE plant analysis, which follows 

in Section 7.2, will not discuss these two screening approaches.

7.1.5 Estimating Containment Bypass Frequency 

Table 7-10 of Section 7.1.4.4 estimates the probabilities of C-SGTR for Inconel 600/690 for a 

core damage sequence with behavior similar to those initiated by SBO and with an early failure 

of the TDAFW pump. The occurrence of such C-SGTR would lead to a containment bypass 

scenario. All the containment bypass scenarios have a potential to become a LERF, if the 

release is large; it starts early, before an effective evacuation; and it is not terminated by 

successful SAMG actions.

In section 7.1.4, the preliminary estimate of the annual frequency of containment bypass 

because of consequential failures of one or more tubes was discussed. The earlier estimates 

did not include two additional contributors to containment bypass caused by C-SGTR:

(1) Operators are expected to start the RCPs (bump the pumps) and transfer the

accumulated water in the loop seal into the vessel, thereby clearing the loop seal. This is

only applicable if offsite power is recovered after the onset of core damage. A cleared

loop seal can cause the failure of additional SG tubes only if the operator fails to restore

the secondary cooling first. Unlike CE and Babcock & Wilcox (B&W) plants, the W

SAMG does not explicitly require the operator to bump the pumps. It is, therefore,

unlikely that the operators at a W plant would inadvertently perform such errors

of commission.

(2) Operators are expected to introduce secondary cooling to an SG that has dried out, after

alternating current (ac) power is recovered. This action is expected to be performed

slowly, and the operator should maintain certain cooling/flow limits. The SG tubes are

considered ductile and, for recirculating (U-tube) SGs, the tubes can expand axially.

Both the SAMG and the emergency operating procedure (EOP) provide some guidance

on limiting the cooling rate/secondary flow, which appears to be intended to limit the

added strain caused by thermal shock and the resulting steep temperature gradient

across the tube wall. For the purpose of PRA analysis, it is assumed that a significant

deviation from the recommended limits for introducing the cold feedwater into a hot SG

could result in tube failures. Introduction of cold water into a dry SG could also take

place before the onset of core damage. Therefore, it has a specific procedure under

EOPs. Operators are fully aware of the limits associated with this action. Should tubes

rupture as a result of the introduction of cold water into a dry SG, the radioactive

releases are expected to be significantly less than a C-SGTR accident with a dry SG

secondary side. The presence of subcooled water in the secondary side of the SG is

expected to provide a scrubbing action of the radioactive releases and to significantly

reduce the offsite consequences. The contribution from this mechanism to the LERF,

therefore, is expected to be significantly lower than other mechanisms for multiple

tube failures.
7-25

A simplified SBO event tree in Figure 7-11 depicts the three types of SBO core damage 

sequence most likely to dominate the C-SGTR risk:

(1) Sequences with early failure of AFW: For these sequences, the containment bypass 

fraction is defined as Q1. The value of Q1 is approximately set to 0.01 for both Inconel 

600 and 690 (see Table 7-9 in Section 7.1.4.2).

(2) Sequences with loop seal clearance are assigned to the containment bypass fraction 

Q2: the value of Q2 is equal to 1.0. Note that TH runs indicated that the probability that 

the loop seal is cleared is almost certain if the RCP leakage is about 1,703 Lpm 

(450 gpm) per pump. For RCP seal leakage of 1,135 Lpm (300 gpm), the TH analysis 

predicted no possibility that the loop seal would be cleared. For the purpose of a 

bounding analysis, the probability of loop seal clearing is considered to be 0.1 when the 

proceduralized operator action of rapid depressurization fails (seal leakage range of 

1,135–1,817 Lpm (300–480 gpm) per pump exists); 0.0025 when this operator action is 

successful (only 1,817 Lpm (480 gpm) per pump seal leakage scenario is postulated).

(3) Sequences with the failure of the TDAFW pump in the intermediate timeframe 

(approximately 4 hours):7 although the C-SGTR probability and the fraction of 

containment bypass could vary, depending on the depressurization scheme, it is 

bounded by twice the values estimated for the SBO sequences with an early failure of 

the TDAFW pump. The containment bypass fraction Q3 is assigned to these sequences. 

The estimate for this fraction is currently considered to be twice the value for the 

sequences with early failure of the TDAFW pump, namely 2Q1.8

These containment bypass (Cont.-BP) fractions are to be used with individual core damage 

sequences. Figure 7-12 gives an example of using these containment bypass fractions in a 

sequence from an internal event SBO sequence. The probabilities used are deemed to be 

representative of the event tree nodes typically used in PRA models.

For other SBO events, such as those induced during seismic, external flooding, and high-windrelated events, the ac power recovery could be drastically different from the internal events. 

Figure 7-13 presents an example of an external-event-driven SBO event tree for quantification 

of containment bypass probability due to C-SGTR.

One can also define an additional containment bypass fraction that could be used with an SBO 

CDF (instead of being used with an individual SBO sequence). Figures 7-12 and 7-13 calculate 

this frequency as the ratio of the total C-SGTR frequency to the total CDF frequency. The 

values estimated in these two figures are 0.02 and 0.018, respectively.

 7 PRAs sometimes consider a longer timeframe for ac recovery. They are related to the recovery of ac for 

crediting SAMG actions and other recovery actions for controlling the radioactive releases

8 Both in W and CE plants, TH input files exhibit the following property when the SG tube temperatures 

reach the creep-rupture range, namely 600–700 degrees C (1,112–1,292 degrees F): the temperature difference 

between the HL and the average tube temperature is larger for the scenarios where the TDAFW pump fails at T = 

0, compared to when the AFW fails at T = battery depletion. This results in a slightly higher likelihood for HL failure 

in the case with earlier AFW failure. Thus, the C-SGTR probability is slightly higher for the sequences with “late” 

failure of AFW. The event trees in Figures 7.12 and 7.13 use an approximate value of 0.01 for C-SGTR probability 

for stsbos and 0.02 for ltsbos. It should be noted that the C-SGTR, if it occurs, occurs much later in the sequences 

with late AFW failure, compared to sequences where AFW fails at T = 0, so it is not generally considered as a large 

early release.
7-26

SBO AFW 

Operating

ST 

Power 

Recovery

Rapid 

Secondary 

Depressurization

Loop 

Seal 

Intact

IT Power 

Recovery

CD 

with

H/D/L

Loop 

Seal 

Intact

AFW Failure C-SGTR

Fraction

YES 1 No

YES

NO 2 Yes Yes Intermediate None

YES

YES 3 No

NO

NO 4 Yes No Intermediate None

YES 5 No

YES N/Q YES

NO 6 Yes Yes Intermediate Q3

NO

YES 7 No

NO

NO 8 Yes No Intermediate Q2

YES 9 No

NO

NO 10 Yes N/Q Early Q1

Figure 7-11 Definition of bounding SBO sequences with high/dry/low (H/D/L) conditions 
7-27

General Notes:

a. N/Q = Not Questioned

b. ST (short term ac power recovery) refers to 1–2 hours following failure of TDAFW 

Pump (fails to start)

c. IT (intermediate term ac power recovery) refers to 4–6 hours following later 

failure of TDAFW Pump (fails to run, battery depletion)

d. The ac power can also be recovered later than the IT window. This can be 

credited for release frequency calculations: it is not used in the current estimates.

e. SBO refers to occurrence of a loss of offsite power event coupled with a loss of 

emergency ac power.

f. Power recovery refers to reestablishment of either offsite or onsite emergency 

power to at least one of the safety-related ac buses.

g. Loop seal is intact if 1,817 Lpm (480 gpm) per pump and 1,135 Lpm (300 gpm) 

per pump RCP seal loss-of-coolant accident (LOCA) does not occur.

h. If rapid secondary depressurization is successful, the primary is depressurized 

similar to SCDAP/RELAP case runs 153 and 153A. The core damage and CSGTR is occurring late due to accumulator discharge.

i. If rapid secondary depressurization is not successful, then the sequence is 

assumed to be the same as an SBO with early failure of the TDAFW pump with 

the time line shifted by 4 hours.
7-28

SBO Occurs 

(Frequency)

AFW 

Operates

ST 

Power 

Recovery

Rapid Secondary 

Depressurization

Loop 

Seal 

Intact

IT Power 

Recovery

Sequence 

Frequency

C-SGTR

Fraction

Cont. BP

Frequency

% 

Contribution 

to Cont. BP

1

1.0E+00

2.0E-01 2 9.E-07 0.02 1.8.E-08 70%

1.0E+00

3 

2.5E-03

4.0E-01 4 4.E-09 1. 4.0.E-09 15%

5 

9.0E-01 9.0E-01

2.0E-01 6 4.E-09 0.01 4.E-11 0.1%

5.0E-03

5.0E-06 7 

1.0E-01

4.0E-01 8 9.E-10 1 9.E-10 3%

5.0E-01 9 

1.0E-01

5.0E-01 10 3.E-07 0.01 3.E-09 12%

Sum = 1.2E-06 2.6E-08 100%

Figure 7-12 An estimate of bounding SBO sequence frequencies leading to C-SGTR and 

containment bypass 
7-29

SBO 

Occurs 

(Seismic, 

Ext. 

Flooding, 

Wind)

AFW 

Operates

ST 

Power 

Recovery

Rapid Secondary 

Depressurization

Loop 

Seal 

Intact

IT Power 

Recovery

Sequence 

Frequency

C-SGTR 

Fraction

Cont. BP

Frequency

% 

Contribution 

to Cont. BP

1

1.0E+00

5.0E-01 2 2.E-06 0.02 4.E-08 72.7%

1.0E+00

3

2.5E-03

7.0E-01 4 8.E-09 1 8.E-09 14.5%

5

9.0E-01 9.0E-01

5.0E-01 6 1.E-08 0.01 1.E-10 0.2%

5.0E-03

5.0E-06 7

1.0E-01

7.0E-01 8 2.E-09 1 2.E-09 3.6%

0.0E+00 9

1.0E-01

1.0E+00 10 5.E-07 0.01 5.E-09 9.0%

Sum = 3.E-06 5.5E-08 100%

Figure 7-13 Another estimate of bounding SBO sequence frequencies leading to C SGTR 

and containment bypass 
7-30

This section showed earlier that the total frequency of SBO core damage sequences for internal 

events only, and for all hazard categories, were 5.2X10-6/year and 2.0X10-5/year, respectively. 

The estimate for the containment bypass frequency caused by C-SGTR for these two cases will 

use a containment bypass fraction of 0.02. Note that this fraction is consistent with the two 

corresponding values estimated in Figures 7-12 and 7-13.

For internal event SBOs:

Cont.BPC-SGTR = CDF * 0.02 = 5.2X10-6 * 0.02 = 10-7/year

For SBOs from all hazard categories:

Cont.BPC-SGTR = CDF * 0.02 = 2.0X10-5 * 0.02 = 4X10-7/year

Table 7-13 further summarizes the estimates from this section.

7.1.6 Level 2 Analysis of C-SGTR for ZNPP 

This section expands on the discussion provided in Section 2.6 on a simplified Level 2 analysis. 

An SBO event is considered as an entry level for the Level 2 analysis. The TDAFW pump is 

demanded right after SBO. The time required for SG dryout is about an hour and a half based 

on the TH analysis shown in Figure 7-1 for the Wnewbase case. The vessel breach is not 

expected until at least 8 hours after core uncovery. The recovery of offsite power in less than 

8 hours is needed to credit the SAMG activities. Table 7-11 shows the timing for the major 

events corresponding to the accident progression of a scenario of an SBO and early failure of 

TDAFW pumps. A combination of RELAP results and sensitivity case runs with C-SGTR 

software generates these timings.

Based on an examination of the information shown on this table, three observations can 

be made:

(1) For cases where the primary pressure is maintained at the primary relief set point

(approximately 15.2 MPa, or 2,200 psi), the HL is expected to fail before the occurrence

of SGTR unless there are one or more large flaws with a depth of at least 60 percent in

one of the SGs. This is generally consistent with the deterministic results obtained from

RELAP runs.

(2) For cases where there is at least one large flaw in one of the SGs, such that C-SGTR

occurs early and shortly after core uncovery, the HL is expected to fail in less than

15 minutes after C-SGTR, as long as the primary is not significantly depressurized.

Therefore, the releases through containment bypass are expected to be small and be of

short duration. This statement is valid even if the primary is somewhat depressurized, as

long as it stays above the accumulator setpoint (4.82 MPa, or 700 psi).

(3) For cases where primary pressure is reduced below 4.82 MPa (700 psi), such that the

accumulators are discharged, HL failure is not expected to occur until the core is

uncovered and repressurization of the primary system takes place. In such cases, the

releases are expected to be late and possibly diverted into the containment rather than

through the ruptured SG tubes.
7-31

Based on the above discussion, a large early release (LER) can mainly occur if secondary relief 

valves are open (either intentionally or by stick-open failures) post-C-SGTR, such that the 

primary system remains depressurized and the probability of HL failure is significantly reduced.

Table 7-11 Timing of Major Events during an SBO with Early Failures of TDAFW Pumps 

 (Wnewbase with Inconel 600TT SG) 

Time Events for Extended SBO with Early Failure of TDAFWs

0 SBO started

~ 14 minutes ECCS signal actuated

~ 2 hours, 30 minutes Onset of core uncovery, corresponding to 648.69°C (1,200 °F)

~3 hours, 30 minutes 50% probability of HL failure if the primary pressure remains 

around 15.17 MPa (2,200 psi) after onset of core uncovery (as 

estimated by C-SGTR software)

~3 hours, 30 minutes Cladding damage and start of gap release

Around 3 hours, 30 minutes to 

3 hours, 45 minutes

Some likelihood of SGTR with varying leak rates if there is at least 

one flaw larger than 60% of nominal depth 

Around 3 hours, 45 minutes HL failure if the primary pressure reduced to around 4.826 MPa 

(700 psi) but above accumulator discharge pressure) at the time 

of core uncovery due to the opening of a PORV or a single PORV 

and SRV b stuck open

~ 4 hours DC assumed depleted a

Between 7 and 8 hours Core structure failures, fuel melting and quenching; start of 

in-vessel releases 

~ 8 hours HL failure if the primary system is fully depressurized at the onset 

of core uncovery b

a Although RELAP models assume dc is depleted in 4 hours for both early and late failure of TDAFW pumps, 

PRA considers dc to be available for a longer duration for the case when TDAFW pumps were not available at 

time zero. The availability of dc will facilitate SAMG activities such as primary and secondary depressurization. b These values were supported by sensitivity runs performed using C-SGTR software.

For those cases where TDAFW pumps are operating, the time to core uncovery depends on the 

scheme used for primary depressurization. RELAP models analyzed two cases: Cases 153 

and 153A. In both cases, aggressive cooling and depressurization using the secondary system 

resulted in the dropping of primary pressure below the accumulator discharge setpoint. The 

discharge of accumulator resulted in core uncovery being delayed significantly (about 11 hours 

for Case 153 and 13 hours for Case 153A). The C-SGTR and HL failure occurs shortly after the 

onset of core uncovery. If the operators do not take any action to depressurize and perform 

aggressive cooling, although they are instructed by the EOPs to do so, the scenario is expected 

to be similar to that of SBO with early failures of TDAFW pumps but after the secondary cooling 

is lost. The time associated with the sequence of events in this case is similar to the Wnewbase 

case, but they are shifted by about 4 hours. As an example, in this case, the onset of core 

uncovery is expected to occur in 6 hours and 33 minutes, with the core damage starting at 

around 8 hours. There is currently no SCDAP/RELAP case run available for this case.

Table 7-12 shows the timing for the major events corresponding to the accident progression of a 

scenario of an SBO and the failure of TDAFW pumps after battery depletion for a normal 

depressurization scheme (RELAP Case 153). A combination of SCDAP/RELAP results and 

sensitivity case runs with C-SGTR generates these timings.
7-32

Table 7-12 Timing of Major Events during an SBO with Failures of TDAFW Pumps after 

 Battery Depletion (SCDAP/RELAP Case 153 with Inconel 600TT SG) 

Time Events for Extended SBO with Early Failure of TDAFWs

0 SBO started

~ 4 hours Dc assumed depleted

~ 11 hours, 30 minutes Onset of core uncovery, corresponding to 1,200 °F

~12 hours, 30 minutes to 

12 hours, 45 minutes 

Some likelihood of SGTR with varying leak rates if there is at least 

one flaw bigger than 50% depth

~12 hours, 45 minutes HL failure

~13 hours, 30 minutes Cladding damage and start of gap release

Section 7.1.4 contained a detailed estimate of the frequency of containment bypass because of 

C-SGTR. The fractions of containment bypass scenarios that can lead to an LER depend on the

following three factors:

(1) For an LER to occur after C-SGTR, a large release path must lead directly to the

environment through the open secondary side, such as an open path caused by one or

more SG PORVS/RVs failing in the open position (stuck open).

(2) For an LER to occur, the radioactive releases from C-SGTR should occur early

(i.e., before commencement of an effective evacuation).

(3) For an LER to occur, both of the following SAMG actions should fail:

‒ Flood the vessel by depressurization and injection of water. This action should

preferably take place early enough after core damage but before significant fuel melt and

changes in core configuration.

‒ Flood the SG secondary side by depressurizing the SG and filling it up with an alternate

water source, to significantly reduce the magnitude of radioactive releases by scrubbing.

This study assumes that a large leakage path always exists on the SG secondary side. The 

cycling of SG PORVs/SRVs during the harsh environment after core damage is not reliable and 

could result in one or more valves sticking open. Furthermore, these valves could be opened 

intentionally as a part of SAMG actions.

This study also assumes that the releases from all C-SGTR scenarios associated with 

short-term SBO (stsbo) will be early and before commencement of an effective evacuation. The 

study, however, acknowledges that the diverse and flexible mitigation capabilities (FLEX) 

equipment, including the extended dc, could delay the core damage and the occurrence of 

C-SGTR. The authors decided, however, that a quantitative analysis of FLEX strategies within

the PRA is not currently a state of practice, and it cannot be performed unless better knowledge

is gained about the timing and the effectiveness of these strategies.

The authors reviewed the SAMG actions, as discussed in the W SAMGs but decided that a 

quantitative analysis is not currently within the scope of this project. The paragraphs below 

discuss some aspects of the SAMGs.
7-33

The vessel can be depressurized by opening all PORVs (both PORVs are required to open, 

based on the success criteria identified in TH case runs for post-core damage in ZNPP). Dc 

power is required for PORV operations after core damage occurs. This is possible if ac power is 

restored or the availability of dc power is ensured by load shedding or through other means. 

Relieving the primary pressure would allow injection from either the high-pressure or 

low-pressure emergency core cooling system (ECCS). RCS depressurization could also take 

place because of a medium or large LOCA but not because of post-core damage from a 

small LOCA.

Primary depressurization for SBO scenarios with early failure of TDAFW pumps could result in 

discharge of the accumulator water into the vessel, which could provide more time for the 

operator to align the makeup water sources to the reactor water storage tank (RWST) for later 

injection into the vessel. Injection into the vessel, if occurring early, could arrest core melt and 

reduce in-vessel releases. In both cases analyzed in NUREG/CR-6995 (Ref. 1) (Cases 153 

and 153A), aggressive cooling and depressurization using the secondary system dropped 

primary pressure below the accumulator discharge setpoint. The discharge of accumulators 

resulted in core uncovery being delayed significantly (about 11 hours for Case 153 and 13 hours 

for Case 153A). These cases were not considered to be contributors to LERF, since the 

radioactive releases would be late and be expected to occur after the initiation of 

effective evacuation.

RCS depressurization through the PORVs or the occurrence of a medium or large LOCA would 

also create a major path of release into the containment rather than through the ruptured SG 

tubes. A lower release magnitude would, therefore, be expected. These cases were also not 

considered to be contributors to LERF.

SAMG also recommends both depressurizing the SG using the available relief paths when an 

SG tube ruptures and filling the SG secondary side using motor-driven AFW trains after power 

is recovered. If power is not recovered, injection from low-pressure alternate water sources, 

such as fire water, could be used. As guided by TH analysis, operation of the atmospheric dump 

valve (one per SG) or opening of main steam isolation valves (MSIVs) and bypass valves, will 

be required if an alternate source of water is used. SG depressurization would require dc power 

as well as instrument air. In addition, local manual operation would be possible and might not 

require dc power. However, the possibility of a high-radiation environment should also 

be considered.

Section 2.6 discussed the emergency response timeline and the process for effective 

evacuation of the SBO scenario with early and late failure of TDAFW pumps (e.g., after 

batteries are depleted). The conclusion was that the evacuation is most likely effective for 

C-SGTR containment bypass events during SBO scenarios with late failures of TDAFW pumps 

and not effective for SBO scenarios with early failure of TDAFW pumps. The only exception to 

this general rule is the C-SGTR containment bypass scenarios of SBO with late failure of 

TDAFW pumps and the failure of operators to rapidly depressurize the primary through 

secondary systems. As discussed earlier, in such scenarios, the time available for effective 

evacuation could be reduced to less than 10 hours for some plants, such that assuming 

probability of 1 for successful and effective evacuation during some external events may not be 

conservative. Site- and plant-specific analysis may be needed to address the probability of 

effective evacuation for such cases.
7-34

7.1.7 Quantification of Level 2 Models 

Section 2.6 discussed a simplified LERF model that relies on five factors:

(1) frequency of severe accident sequences with potential for C-SGTR (fAC), as discussed in

Section 7.1.2

(2) C-SGTR probability (PCSGTR) (see discussion for estimating containment bypass

probability in Section 7.1.5)

(3) conditional probability that the subsequent failure of RCS, including the stuck-open relief

valves, does not occur (PNDEP)

(4) failure probability of all SAMG actions (PSAMG)

(5) probability that early and effective evacuation is not successful (PEVAC)

The issues considered for estimating PNDEP, PSAMG, and PEVAC are qualitatively discussed below. 

Some values are suggested for each of these three parameters for estimating the bounding 

values of LERF.

PNDEP: Failure of the HL shortly after C-SGTR or stick-open failures of at least two primary relief 

valves (SRVs/PORVs) will divert most of the releases into the containment, thereby significantly 

reducing the conditional LER probability, given a containment bypass caused by C-SGTR. For 

cases where only one relief valve fails to reclose (sticks open), the HL failure would be delayed 

because of primary depressurization. The conditional LER probability, given containment 

bypass, will therefore increase. Note that the above discussion is not applicable when the 

TDAFW pump is initially available and the primary is further depressurized by rapid secondary 

cooling. In such cases, the primary pressure is expected to be initially reduced below 4.82 MPa 

(700 psi) because of rapid primary depressurization through the secondary and through the 

stick-open primary relief valve. Accumulators are then discharged, core melt is delayed, and 

C-SGTR and HL failure are not expected to occur before the restart of core melt. The release

through containment bypass is expected to be relatively small (a portion of the release will be

diverted into the containment through stick-open relief valves) and the release would be late. It

is, therefore, not considered as an LER. Generally, the conditional probability that C-SGTR is

not followed shortly (e.g., less than 30 minutes) by a large primary opening (i.e., PNDEP) is

expected to be small (much less than 1). As discussed, the only possible way for a containment

bypass because of C-SGTR to result in an LER is when only one of the primary relief valves

(SRVs or PORVs) sticks open after core uncovery. However, the performance of these relief

valves after onset of core damage is not well understood. The probability that the relief valves

stick because of limited clearance in some parts, under the harsh environment after core

damage in severe accident scenarios, is not known. These components are demanded under a

severe accident condition, although they are generally qualified for DBAs. For these reasons

and for the purpose of a bounding evaluation, a value of 1.0 is assigned to PNDEP.

PSAMG: A bounding value of 1.0 is proposed for PSAMG to obtain a bounding estimate for LERF. 

This crude approach is implemented because the state of knowledge is limited for both 

equipment operation and operator performance for performing SAMG activities after core 

damage. SAMG’s actions are not procedure based; they are directed by emergency directors, 

coordinated by emergency coordinators, and executed by emergency responders and 

operators. For the SAMG, there is no scripted compliance. The appropriate actions must be 
7-35

defined “on the fly,” based on understanding the plant conditions and the pros and cons of 

carrying out a particular set of actions versus an alternative set of actions or no action at all (see 

Reference 8). This is considered as a human decisionmaking process that would be influenced 

by the complexity of the situation, training, and other personal attributes of the operator. The 

human reliability model for these actions, under severe accident conditions, is expected to be 

different than those governed by EOPs. Finally, the effectiveness of SAMG activities under 

different accident conditions is not known.

PEVAC: The timing diagrams discussed in Section 2.5 indicate that there is a high likelihood that 

effective evacuation can be completed for all SBO scenarios with an initial availability of TDAFW 

pumps and a successful aggressive depressurization through secondary cooling. Therefore, for 

all these scenarios, the value estimated for PEVAC is considered to be zero. For SBO scenarios 

with initial availability of TDAFW pumps but failure of aggressive depressurization through 

secondary cooling, releases can occur at an earlier time but only after at least 8 hours. The 

timing of the release will depend on the battery capacity and the duration of dc power 

availability, including potential load shedding. Furthermore, the failure probability for aggressive 

depressurization is expected to be small, about 1.0 × 10-3 per demand. Therefore, for all SBO 

scenarios with an initial availability of TDAFW pumps, PEVAC was assigned a value of zero.

The same timing diagrams revealed that there is a high likelihood that effective evacuation 

cannot be completed in time for all SBO scenarios with early failure of TDAFW pumps. 

Therefore, PEVAC is assigned a failure value of 1.0 to all SBO scenarios with an early failure of 

TDAFW pumps.

Table 7-13 summarizes the conditional LERF probabilities because of C-SGTR for SBOs with 

early or late failures of TDAFW pumps.

Table 7-13 Conditional LERF Probabilities for an SBO with Early and Late Failures of TDAFW 

 Pump for the W Plant 

Factors Applicability LERF Factors a

PCSGTR Because of one or more tube breaks in an SBO CD sequence 1.3E-2

— Due to single tube breaks only 1.3E-2

— Due to multiple tube breaks 8.2E-5

In an SBO, CD sequence with loop seal clearing 1.0

PNDEP In an SBO, CD sequence with loop seal clearing or multiple tube breaks 1.0

In an SBO, CD sequence with one tube breaks 1.0 b

PSAMG In an SBO, CD sequence with loop clearing or multiple tube breaks 1.0

In an SBO, CD sequence with one tube breaks 1.0 b

PEVAC In an SBO, CD sequence with early failure of TDAFW 1.0

In an SBO, CD sequence with late failure of TDAFW (at least with 

4 hours battery capacity) 0

a LERF factors are applicable to SBO scenarios with both early and late failure of TDAFW pumps unless this is 

specifically identified. b This value is believed to be conservative, and it is used for screening purposes only.
7-36

A crude estimate of the conditional probability of containment bypass for all the prolonged SBO 

scenarios is about 0.02 when considering scenarios involving loop seal clearing. The CDF from 

SBO sequences, considering all hazard categories, is about 2.0X10-5/year from Table 7-1. This 

CDF multiplied by the conditional probability of containment bypass (0.02) gives a bounding 

containment bypass frequency estimate of 4X10-7/yr for all hazard categories. Please note that 

the LERF estimate is negligible (approximately 0), since only the containment bypass resulting 

from the SBO scenarios with early failure of TDAFW pumps have a potential for an LER.

A bounding estimate of the conditional LERF probability, given an SBO with early failure of 

TDAFW pumps, is about 0.02. The all-hazard CDF, multiplied by the early failure probability of 

TDAFW pumps (approximately 0.1) and the LERF fraction of 0.02, gives a bounding LERF 

estimate of 4X10-8/yr for all hazard categories. Considering SBO CDF for internal events only is 

5.2X10-6/yr, the LERF estimate due to C-SGTR for the W plant is about 1.0X10-8/yr for 

internal events.

7.1.8 Concluding Remarks 

The TH results obtained from various case studies significantly influenced the occurrence of 

C-SGTR, containment bypass probability, and LERF. These TH results reflect the specific

design, configuration, and geometry of the plant systems, specifically the SG design and

primary connections, such as HL and surge line. They should not be interpreted as generic

results for W plants. The following are the eight more important plant features that can affect

the results:

(1) mixing in the SG inlet plenum (deep or shallow SG inlet plenum)

(2) mixing in HL (physical characteristics such as length and diameter of HL)

(3) pressure drop in HL and SG tubes (i.e., an integral effect)

(4) heat transfer and heat losses from the HL walls (e.g., heat up inertia, including condition

of the insulation on the HL)

(5) performance of primary and secondary relief valves before or after onset of core damage

(6) duration of dc availability, including load shedding capabilities

(7) effectiveness and success of SAMG activities

(8) success of other severe accident mitigation measures that are provided by extensive

damage mitigation guidelines (EDMGs) and FLEX, including extended diversified power

sources, black start, and extended operation of TDAFW pumps without dc.

This study makes the following conclusions of this study, based on the case studies performed 

for the example W plant, as described in this chapter:

• The contribution of C-SGTR to LERF is expected to be about 4.0X10-8 when all hazard

categories applicable to the site are included.

• The contribution of C-SGTR to LERF is expected to be about 1.0X10-8 when only

internal event SBO core damage sequences are considered.
7-37

• Based on the existing PRAs, C-SGTR appears not to be a major contributor to LERF for 

these types of plant design.

• It is generally concluded that, in plants with designs similar to the example W plant, the 

C-SGTR and the associated LERF do not make a significant contribution, unless large 

and deep flaws exist in one or more SGs.

7.2 Example Combustion Engineering Plant 

MELCOR analyses were performed in two stages over a given time period to study Calvert 

Cliffs Nuclear Power Plant (CCNPP) as an example of a CE plant’s response to RCS conditions 

that could lead to C-SGTR. The first stage analyses were completed in October 2012. These 

analyses were initially used in the PRA evaluation of C-SGTR probability. The second stage of 

MELCOR analyses were completed in August 2013. The updated PRA evaluation discussed in 

this section used these updated MELCOR analyses and results.

The second stage TH analyses are mainly used in support of the development of the 

PRA models. 

Therefore, the C-SGTR PRA used CCNPP as an example CE plant. The documents for the 

CCNPP individual plant evaluation (IPE) and individual plant evaluation for external events 

(IPEEE) provided the other required information for C-SGTR PRA evaluation. Chapter 3 

contains a detailed discussion of the MELCOR model and the results of the MELCOR 

evaluation for CCNPP.

7.2.1 Description of the Selected TH Sequences for C-SGTR PRA for the Example 

CE Plant 

A specific naming scheme is used in defining main features of various scenarios evaluated in 

this section. The general format for the naming scheme is “SBO type,” “Secondary side relief 

mode,” “Creep-rupture failure progression,” and “plant loop.” These are further defined below:

(1) SBO type (stsbo or ltsbo)

‒ stsbo: SBO scenario with failure of TDAFW pump at time zero

‒ ltsbo: SBO scenario with failure of TDAFW pump after batteries are depleted 

(i.e., after 4 hours of operation)

(2) Secondary side relief mode (a/as)

‒ a: no stick-open failure of either primary PORVs or SRVs, or secondary PORVs 

or main steam safety valves (MSSVs); an assumed preexisting leakage area of 

3.22 cm2 (0.5 in.2

) on the secondary side

‒ as: no stick-open primary PORVs or SRVs but failure of MSSVs to reclose when 

first demanded (before onset of core damage); no other preexisting 

leakage assumed
7-38

(3) Creep-rupture failure progression (SCF)

‒ Suppress creep failure (SCF) nomenclature is used when creep-rupture failure is 

suppressed. In such cases, the scenario will proceed without any failure of RCS 

components or SG tubes caused by creep rupture.

(4) Plant loop (a/b)

‒ a: refers to the plant loop equipped with the pressurizer

‒ b: refers to the plant loop without pressurizer

The MELCOR predicts the temperature profile for the average hot tube where the gas flows 

from the hot side of the SG to the cold side and the average temperature of cold tubes where 

the gas flow is reversed. The average hot tube is divided into two sections: the section where 

the gas flows upward and the section where the gas flows downward. The average temperature 

of the upward flow section is higher than the downward flow section. The average hot tube 

temperature in the following graphs refers to the section of the hot tubes where the hot gas 

flows upwards. The average section where the gas flows downward has a temperature profile 

similar to that of the cold tubes, and they are averaged with the temperature of cold tubes to 

obtain an average cold tube temperature for the purpose of estimating the C-SGTR probability 

using the C-SGTR software. The fraction of tubes considered to be exposed to the average hot 

temperature, where the gas flow is upward, is estimated to be around 0.25 for the base case 

analysis. This same fraction was also used as the probability that a flaw in an SG will be 

exposed to the average hot tube temperature for all base-case evaluation. The sensitivity 

analysis used a fraction of 0.125 instead of 0.25 and estimated its impact on the final C-SGTR 

probability, as discussed in Section 7.3.2.

The number of tubes exposed to the hottest temperature is approximated by the number of 

tubes exposed to a normalized temperature of 0.9 to 0.99 for a CE plant. Multiple unflawed 

tubes generally could fail because of creep rupture before HL failures with a varying leakage 

area. Expert elicitation of staff members of the Nuclear Regulatory Commission previously 

involved in the issue resulted in a range from 10 to 100 tubes failing (see Section 3.4). The PRA 

study, therefore, considered a small number of tubes; it assumed about 100 tubes in each SG 

would be exposed to hotter gas temperatures.

These tubes are referred to as the hottest tube and presented by a single average hottest 

temperature. Considering 8,247 tubes per SG, the fraction of the hottest tubes is estimated to 

be around 0.01.

The evaluation of the following two representative base scenarios used the second stage of the 

MELCOR evaluation in estimating the base probability of C-SGTR. These two scenarios 

modeled a leakage through the secondary side of each SG, equivalent to a hole with an area of 

3.2-cm2 (0.5-in2

). This size of leakage was sufficient to ensure that the pressure in the 

secondary side of the SGs approached the atmospheric pressure after SGs have been dried 

out. This size of leakage, however, is not sufficient to maintain low secondary-side pressure if 

SG tubes have ruptured.

• The first scenario considers an SBO with failure of the TDAFW pumps early in the

sequence (i.e., at time zero), followed by early core damage with a potential for C-SGTR

because of creep rupture. This scenario also considered an RCP seal leakage of

79 Lpm (21 gpm) per pump. The MELCOR results for these case runs are applicable to
7-39

several PRA accident sequences with similar behavior (see the discussion in Chapter 2). 

For SBO sequences, this includes an SBO scenario with simultaneous failures of 

TDAFW pumps (i.e., two pumps for CCNPP) because of common-cause failure (CCF) to 

start, and an SBO with an initial availability of TDAFW pumps followed by their failures 

because of SG overfill in an hour. For this case run, the onset of core damage is 

expected to occur in less than 2 hours. The scenario considers the potential for the 

occurrence of C-SGTR after the onset of core damage. Figure 7-14 shows the 

temperature at the inner surface of the top section of the HL in degrees Celsius, the 

average temperature of the hot SG tubes, the average temperature of the cold SG 

tubes, and the temperature of the hottest SG tube for loop A, which is equipped with a 

pressurizer. Figure 7-15 shows similar results for the loop without the pressurizer 

(loop B). Figures 7-16 and 7-17a show the differences between the HL temperature and 

the average tube and the hottest tube temperature for loops A and B, respectively. 

These graphs show that the temperature response for HL heatup after core damage is 

slower than the SG tube temperature response. Therefore, the HL is expected to be 

initially at a lower temperature than the average hot and the hottest tube after the onset 

of core damage. This would increase the probability of C-SGTR. Figure 7-17b shows the 

pressure in the primary and the secondary sides of SGs. This graph shows that 3.2 cm2

(0.5 in.2

) of assumed leakage will cause the secondary side to depressurize. The 

primary side pressure is maintained at the set point of primary SRVs.

• The second scenario considers an SBO with delayed failures of TDAFW pumps after 

battery depletion. The TDAFW pump is initially available, but it will fail shortly after the 

depletion of the batteries. The scenario considers a normal RCP seal leakage of 79 Lpm 

(21 gpm) per pump. The MELCOR analysis assumes that the TDAFW pumps were 

operating for a period of 4 hours. Figure 7-18 shows the temperature at the inner surface 

of the top section of the HL in degrees Celsius, the surge-line temperature, the average 

temperature of the hot SG tubes, the average temperature of the cold SG tubes, and the 

temperature of the hottest SG tube for loop A. Figure 7-19 shows similar results for 

loop B. Figures 7-20 and 7-21a show the differences between the HL temperature and 

the temperature of the different SG tubes for Loops A and B, respectively. These graphs 

show that the temperature response for HL heat up after core damage is much slower 

than the SG tube temperature response. Therefore, the HL is initially expected to be at a 

lower temperature than the average hot and the hottest tube after the onset of core 

damage. This results in a higher probability of failure of SG tubes caused by creep 

rupture, before creep-rupture failure of the HL. Figure 7-21b shows the pressure in the 

primary and the secondary sides of SGs. This graph shows that the secondary side will 

be depressurized due to 3.2 cm2 (0.5 in.2

) of assumed leakage. The primary side 

pressure is maintained at the set point of primary SRVs.

As discussed in Section 2.5, for C-SGTR during a severe accident, the size of the leak area 

would determine the size of the release through containment bypass (i.e., it determines if the 

containment bypass should be categorized as an LER). For a small leak, the primary is 

expected to stay pressurized (generally at primary relief set point approximately 15.5 MPa 

(2,250 psi)), resulting in the failure of other RCS components (e.g., HL) shortly after the failure 

of the tubes. This significantly reduces and eliminates any release through the SGs. Larger 

leaks could pressurize the secondary side of the affected SG such that both the primary and 

secondary sides equalize at the pressure set point of the SG relief valves. In this case, there is 

a lower probability of the failure of other RCS components (e.g., HL) because of a lower primary 

pressure (approximately 8.3 MPa (1,200 psi)). This pressure assumes that the SG PORVs and 

MSSVs cycle as many times as needed without any failures. If any of the SG relief valves fails 
7-40

open (sticks open) early during an accident, the primary will be depressurized, and it will 

practically eliminate any possibility of the HL failure (or other RCS components). The SG relief 

valves could also be opened and potentially stick open, in stsbo scenarios by the operators 

following the onset of core damage per SAMG. In SBO scenarios where the TDAFW pump is 

initially operating, the probability that the operator opens any of the secondary relief valves after 

the onset of core damage is small, since the batteries are assumed to have been depleted, and 

the recovery of dc power in the short period of time after the onset of core damage and before 

C-SGTR, is less likely. There could also be a threshold for larger leak areas through the failed

SG tubes, such that the countercurrent flow through the HL can no longer be maintained. In

such cases, the hot steam will flow through the SG tubes, causing failures of a number of tubes,

resulting in a large containment bypass.

A sensitivity analysis using the MELCOR evaluation assumed that there is zero leakage through 

the secondary system at the start of SBO (instead of the generally assumed leakage area of 

3.2 cm2 (0.5 in.2

)), such that the secondary relief and safety valves will be demanded early 

during the accident and before the onset of core damage. The MELCOR evaluation for this case 

further assumes that the secondary relief and safety valves fail to reclose after the first opening. 

The result of this sensitivity case run shows an increase in C-SGTR probability and discusses it 

in Section 7.3 as part of the sensitivity case studies.

Additional sensitivity analyses were performed by Stage 1 and 2 MELCOR evaluations to further 

examine the impact of various scenarios. The following were noted:

• C-SGTR with an equivalent leakage area of the guillotine break of less than one tube will

not result in depressurization of the primary.

• An equivalent leakage area of one or more tubes could result in a significant release if

one or more of the SG safeties, or the relief valves, are open intentionally or stick open.

• The primary is initially depressurized and accumulator discharges when one or more

secondary relief valves stick open early in the accident. This will further delay

HL/surge-line creep-rupture failures. The probability of C-SGTR caused by creep

rupture, however, is not affected as much, since the lower secondary-side pressure

increases the delta pressure across the tube.

For PRA quantifications and in PRA models (event trees and probability estimations), the 

analyst should, therefore, differentiate between C-SGTR equivalent leakage areas less than or 

greater than the guillotine break of a single tube. PRA models also should consider the 

probability that manual secondary-side depressurization is performed to facilitate the 

performance of SAMG activities for flooding the SG secondary side. MELCOR runs were not 

performed for such scenarios. In addition, MELCOR runs did not provide any information about 

the conditions for loop seal clearing or the large C-SGTR leakages that could possibly reverse 

the direction of the cold gas flow, eliminating the countercurrent flow regime in the HL.
7-41

Figure 7-14 Loop A temperature profiles of the HL and SG tubes for the SBO with an early 

failure of TDAFW pumps 

Figure 7-15 Loop B temperature profiles of the HL and SG tubes for the SBO with an early 

failure of TDAFW pumps [surge-line temperature of loop A is shown to facilitate 

comparison of loop A and B temperature trends] 

0

200

400

600

800

1000

1200

1400

0 100 200 300 400 500 600

Temperature (in 

oCelsius)

Time (in minutes)

SBO with TDAFW Operating for 0 Hours; 

Calvert Cliffs Loop A

Surge

Line

Temp

0

200

400

600

800

1000

1200

1400

0 100 200 300 400 500 600

Temperature (in 

oCelsius)

Time (in minutes)

SBO with TDAFW Operating for 0 Hours; 

Calvert Cliffs Loop B

Surge

Line

Temp
7-42

Figure 7-16 Difference in loop A temperature of the HL and SG tubes for the SBO with an 

early failure of TDAFW pumps 

Figure 7-17(a) Difference in loop B temperature of the HL and SG tubes for the SBO with 

an early failure of TDAFW pumps 

-100

-50

0

50

100

150

200

250

0 200 400 600

Temperature (in 

oCelsius)

Time (in minutes)

SBO with TDAFW Operating for 0 Hours; 

Calvert Cliffs Loop A

 Hot Leg Temp-Hottest

Tube Temp

 Hot Leg Temp-Av. Hot

Tube Temp

-150

-100

-50

0

50

100

150

200

250

0 200 400 600

Temperature (in oCelsius)

Time (in minutes)

SBO with TDAFW Operating for 0 Hours; 

Calvert Cliffs Loop B

Hot Leg Temp-Hottest

Tube Temp

 Hot Leg Temp-AV. Hot

Tube temp
7-43

Figure 7-17(b) Primary and secondary pressure for the SBO with an early failure of 

TDAFW pumps 

 

Figure 7-18 Loop A temperature profiles of the HL and SG tubes for the SBO with a delayed 

failure of TDAFW pumps 

0.00E+00

5.00E+02

1.00E+03

1.50E+03

2.00E+03

2.50E+03

3.00E+03

0 100 200 300 400 500 600

Pressure (psi)

Time (min)

Primary and Secondary Pressure for SBO 

with TDAFW Operating for 0 Hours; 

Calvert Cliffs 

Primary Pressure

Secondary Pressure

0

200

400

600

800

1000

1200

1400

1600

0 500 1000 1500

Temperature (in 

oCelsius)

Time (in minutes)

Extended SBO with TDAFW Operating for 

4 Hours; Calvert Cliffs Loop A

Surge

Line

Temp
7-44

Figure 7-19 Loop B temperature profiles of the HL and SG tubes for the SBO with a delayed 

failure of TDAFW pumps (surge-line temperature of loop A is shown to facilitate 

comparison of loop A and B temperature trends) 

Figure 7-20 Difference in loop A temperature of the HL and SG tubes for the SBO with a 

delayed failure of TDAFW pumps 

0

200

400

600

800

1000

1200

1400

1600

0 500 1000 1500

Temperature (in 

oCelsius)

Time (in minutes)

Extended SBO with TDAFW Operating for 

4 Hours; Calvert Cliffs Loop B

Surge

Line

Temp

-100

0

100

200

300

400

500

600

0 500 1000 1500

Temperature (in 

oCelsius)

Time (in minutes)

Extended SBO with TDAFW Operating for 4 

Hours; Calvert Cliffs Loop A

 Hot Leg Temp. - Hottest

Tube Temp.

 Hot Leg Temp. - Av. Hot

Tube Temp.
7-45

Figure 7-21(a) Difference in loop B temperature of the HL and SG tubes for the SBO with a 

delayed failure of TDAFW pumps

Figure 7-21(b) Primary and secondary pressure for the SBO with a delayed failure of 

TDAFW pumps 

-600

-500

-400

-300

-200

-100

0

100

200

-300 200 700 1200 Temperature (in 

oCelsius)

Time (in minutes)

Extended SBO with TDAFW Operating for 4 

Hours; Calvert Cliffs Loop B

Hot Leg Temp. - Hottest

Tube Temp.

Hot leg Temp. - Ave. Hot

Tube Temp.

0.00E+00

5.00E+02

1.00E+03

1.50E+03

2.00E+03

2.50E+03

3.00E+03

0 200 400 600 800 1000

Pressure (psi)

Time (min)

Primary and Secondary Pressure for 

Extended SBO with TDAFW Operating for 

4 Hours; Calvert Cliffs 

Primary Pressure

Secondary Pressure
7-46

7.2.2 Estimating the Entry Frequency from Level 1 PRA for C-SGTR PRA Analysis 

This study also selected CCNPP as the reference plant for developing the PRA models, to 

ensure consistency with the TH analyses results. The estimates for a prolonged SBO condition, 

as the entry point for C-SGTR PRA, were based on the plant design features and the 

information obtained from SPAR models for the internal events, and from the vintage CCNPP 

IPE/IPEEE9 documents for external and other internal hazards. This section discusses the 

process to develop the Level 2 PRA entry condition for containment bypass resulting from 

C-SGTR for CCNPP Unit 1. Appendix G (Section G.2) provides a detailed discussion of various

CDF contributors from SBO scenarios to overall CDF from both internal and external events.

The technical discussion in Appendix G supports the quantitative values used in this section. All

potential conditions from the internal and external hazards resulting in a prolonged SBO

are considered.

Table 7-14 provides relevant plant information for CCNPP Units 1 and 2. Each CCNPP unit is 

equipped with two TDAFW pumps, and the duration to battery depletion is nominally 2 hours, 

although they are expected to last for 4 hours. TH runs in MELCOR also used a value of 

4 hours for battery depletion.

The frequency of SBO with either early failures of AFW or failure of AFW after battery depletion, 

which is used as the entry point for a Level 2 PRA, is estimated based on the discussion 

provided for each internal and external hazard for the single and dual unit core damage. 

Table 7-15 shows the contributions from both the internal and external hazards, broken down 

for the two scenarios of the SBO with early and delayed failures of AFW, for single and dual 

unit CDF.

The CDF contributions of SBO scenarios from internal and external initiating events, for both 

units of CCNPP, are partitioned into two bins as follows:

(1) The frequency of those SBO core damage scenarios affects only one unit (i.e., only one

unit experiences SBO). For example, a single unit loses offsite power with failure of its

emergency power system (e.g., diesel generators).

(2) The frequency of those SBO core damage scenarios affects both units (e.g., a dual unit

loss of offsite power (LOOP) followed by failure of emergency power systems in both

units (e.g., CCF of all emergency diesel generators (EDGs))).

9 See IPE Summary Report, “Calvert Cliffs Nuclear Power Plant December 1993,” IPEEE Summary Report, 

Vol. 1, Calvert Cliffs Nuclear Power Plant, August 1997.
7-47

Table 7-14 Related Information from the Reference CE Plant 

Systems System Features

Emergency Power System • Currently there are 5 EDGs for the 2 units. One of these 

5 EDGs is the SBO EDG, which can power any safety-related 

4-kV bus at either unit. The operation of 1 EDG with success 

of 1 TDAFW pump per unit is adequate for long-term SG heat 

removal. The SBO EDG requires operator action to align it to 

a safety bus and is credited as a recovery action in the PRA 

models.

• At the time when plant IPE/IPEEE was performed, each unit 

had a dedicated EDG with a shared EDG for both units. 

Therefore, the information contained in IPE/IPEEE should be 

used as a guide, and they are not directly applicable.

• Each unit has 3 4,160-VAC Class 1E buses, each feeding 

1 480-VAC Class 1E bus and motor control center.

• 3 trains of dc power are supplied from the inverters and 3 unit 

batteries. The battery duration is 2 hours, but it is expected to 

last 4 hours during most scenarios.

Auxiliary Feedwater System Each unit is equipped with 2 TDAFW pumps and 1 motor-driven 

(MDAFW) pump. There is a cross-connection to the other unit’s 

MDAFW discharge line.

Salt Water System (SW) There are 2 cross-tied trains, each with 1 pump and 1 heat 

exchanger. A third pump could also supply either train, if needed.

Service Water (SRW) There are 2 trains, each with a salt-water pump, a CCW HX, an

SRW HX, and ECCS pump room air cooler. A third pump could 

be aligned to each train if needed.

Component Cooling Water (CCW) The CCW pumps do not restart automatically after a LOOP. The 

operators manually reestablish RCP seal cooling after a LOOP.

Secondary Relief • 4 Turbine Bypass Valves—TBVs (2 SG)

• Atmospheric dump valve (1 per SG)

• MSSRV (8 per SG)

Primary Relief • 2 reverse-seated PORVs 16.547 Mpa (2,400 psi): 

1. The PORVs do not require dc power for once-through 

cooling (feed and bleed).

2. 2 block valves are powered from the opposite 480 VAC 

with respect to their PORVs.

• 2 spring-loaded SRVs (P>17.237 MPa) or (P>2,500 psig)

Containment Large, dry

The SBO frequency for single and double units is then further evaluated to arrive at the CDF for 

stsbo and ltsbo contributions of single and double units. The overall frequency of the 

SBO scenarios can be categorized in the following six bins:

(1) the CDF for stsbo scenarios affecting Unit 1 only

(2) the CDF for ltsbo scenarios affecting Unit 1 only

(3) the CDF for stsbo scenarios affecting Unit 2 only

(4) the CDF for ltsbo scenarios affecting Unit 2 only

(5) the CDF for stsbo scenarios affecting both units

(6) the CDF for ltsbo scenarios affecting both units
7-48

The results shown in Table 7-15 indicate that the risk of the SBO scenarios is dominated by the 

SBO scenarios with the failure of TDAFW trains, after the depletion of the battery. A similar 

conclusion is reached for the dual unit SBO scenarios. The uncertainties associated with these 

frequencies are not presently estimated, because of the lack of detailed models and data. 

Surrogate uncertainties from similar plants could be considered, if needed.

Table 7-15 Contributions of Various Events to the Long-Term SBO Scenarios for Single and 

 Dual Unit Core Damage 

Initiating 

Event

SBO with Early 

Failure of AFW

SBO with Failure of 

AFW after 

Battery Depletion

Unit CDF from SBO Scenarios 

with

Single 

Unit *

Dual Unit Single 

Unit *

Dual 

Unit

Early Failure 

of AFW

Failure of 

AFW after 

Battery 

Depletion

Internal 

events 1.9E-8 5.5E-9 4.5E-8 1.2E-7 2.5E-8(~13%)

1.7E-7 

(~87%)

Seismic 5.0E-8 1.4E-8 ε + 2.0E-7 6.4E-8

(24%)

2.0E-7

(~76%)

Fire ε 2.4E-6 2.2E-5 2.2E-6 2.4E-6

(~9%)

2.4E-5 

(~91%)

Flood ε ε 1.6E-6 ε ε

1.6E-6 

(~100%)

High wind ε 4.7E-8 ε 4.3E-6 4.7E-8

(~1%)

4.3E-6 

(~99%)

Total 6.9E-8 2.5E-6 2.4E-5 6.8E-6 2.6E-6

(~8%)

3.1E-5 

(~92%)

* The unit with the largest CDF contribution is used. + For the details of the quantitative values, consult Appendix G (G-2). “ε” generally indicates a value less than

1.0E-8 per year that could not be easily quantified by the results of plant-specific PRA.

7.2.3 Flaw Bins to Calculate C-SGTR Probability 

CE plants use SGs with Inconel 690TT. Similar to the discussion in the previous chapter, the 

number of flaws per cycle for these SG tubes is significantly lower than the older SG tubes 

made of mill-annealed Inconel 600. For Inconel 690TT, the estimated probability that a flaw 

length and depth belong to a certain range (or bin) uses the adjusted flaw distributions (see 

Section 7.1.3). Note that the flaw distribution equations derived earlier apply to any SGs (W and 

CE), as long as the same tube material is used.

Each CCNPP unit has two SGs with 8,471 Inconel 690TT tubes. There are, therefore, 

16,942 tubes for each unit and 33,884 tubes for both units. The average number of flaws 

generated for the first 14 EFPYs of operation using the Inconel 690 flaw-generation rate 

equation (first row, second column of Table 6-2) is about 127 flaws per SG, or 253 flaws per 

unit. It is further assumed that the last periodic SG inspection occurred at the end of the 

14 EFPYs. All the large flaws, therefore, are assumed to have been plugged (approximately 

12 plugged tubes per SG) before EFPY 15 begins. An additional 13 flaws are expected to be 

generated for each SG during EFPY 15. Therefore, about 128 flawed tubes per SG (or 

256 flaws per unit—two SGs) were expected during EFPY 15, with an average of two large 
7-49

flaws that could need to be plugged at the end of EFPY 15. The expected number of flaws (the 

expected flaw sample) is estimated to be about 125 flawed tubes per each SG (about 253 per 

each unit and 505 tubes for both units—all four SGs). The number of flaws is rounded off to 

avoid fractional tubes. Tables 7-16 and 7-17 show the expected sample flaw for one SG and 

one unit, respectively.

Table 7-16 Expected Number of Flaws per Each SG that Belong to a Flaw Bin Defined by 

 Depth and Length Range 

Depth / 

Length 1 cm 2 cm 3 cm 4 cm 5 cm 6 cm Total

0.1 0 6 3 1 0 0 10

0.2 3 44 21 5 1 0 74

0.3 1 23 11 3 1 0 39

0.4 0 2 0 0 0 0 2

0.5 0 0 0 0 0 0 0

0.6 0 0 0 0 0 0 0

0.7 0 0 0 0 0 0 0

0.8 0 0 0 0 0 0 0

0.9 0 0 0 0 0 0 0

Total 4 75 35 9 2 0 125

Table 7-17 Expected Number of Flaws per Loop A and Loop B (One Unit; Two SGs) that 

Belong to a Flaw Bin Defined by Depth and Length Range 

Depth / 

Length 1 cm 2 cm 3 cm 4 cm 5 cm 6 cm Total

0.1 1 13 7 2 0 0 22

0.2 6 88 43 11 2 1 151

0.3 3 45 22 5 1 0 76

0.4 1 1 1 0 0 0 3

0.5 0 1 0 0 0 0 1

0.6 0 0 0 0 0 0 0

0.7 0 0 0 0 0 0 0

0.8 0 0 0 0 0 0 0

0.9 0 0 0 0 0 0 0

Total 10 148 73 18 3 1 253

The expected values of flaws in each bin illustrate the expected size distribution of flaws. The 

values shown in the tables also account for the flaws detected in previous cycles that were large 

enough to require the affected tubes to be plugged. The approximation used in these 

calculations, plus the effect of rounding off the expected number of flaws per bin, generally 

resulted in slightly fewer flaws than expected. As an example, Table 7-16 shows an expected 

set of 125 flaws per each SG, rather than the 128 flawed tubes (127 flaws in previous cycles, 

plus 13 flaws in the last cycle, and minus approximately 12 plugged tubes) estimated earlier.
7-50

For CE plants, TH results are different for the loop with a pressurizer (loop A) and the loop 

without a pressurizer (loop B). Therefore, the probability of C-SGTR is calculated for each loop 

separately. Table 7-17 shows the expected number of flaws for the whole plants (i.e., two loops 

and two SGs). However, the analysis does not use this flaw set, and it is only presented for 

consistency with W plant and as an illustrative example of a unit flaw set.

7.2.4 SGTR Probability Estimation Using Integrated Flaw Samples 

An integrated plant wide analysis would involve generating a large number of flaw samples for 

the hottest tube, hot tubes, and cold tubes for both loops A and B, and performing integrated 

C-SGTR calculator case runs to establish sufficient statistics to estimate C-SGTR probability

and its uncertainty distribution. Because the C-SGTR software is not designed to accept

different TH files for different loops and treat temperature distributions for the tubes

(e.g., average hot, hottest, and cold), such an integrated analysis is impractical.

Short of performing an integrated analysis, the study took the following steps to obtain an 

estimate for C-SGTR using a sample of flaws:

(1) The 125 expected flaws per each SG, as shown in Table 7-16, was considered for

performing C-SGTR case runs.

(2) A C-SGTR case run was performed with the 125 expected flaws. A 0.25 probability was

used for a flaw to be exposed to the average hot tube temperature. A probability of 0.75

was used to indicate that a flawed tube is exposed to the average cold tube temperature.

(3) Step 2 was repeated for the hottest tubes with the 125 expected flaws. A probability of

0.01 was assigned for a flawed tube (any of the 125 flaws) to be exposed to the hottest

tube temperature.

(4) The distribution percentiles (5 percent to 95 percent) of SGTR cumulative leak areas

estimated by the C-SGTR code for each time step was transformed to the probability of

a leak size at each time step for the average hot and the hottest tube for loop A. These

leak area distributions were then added probabilistically (i.e., by convolution of leak

distributions) at each time step to obtain the cumulative C-SGTR leak area distribution

for loop A, from both the average and the hottest tubes.

(5) The probability of RCS failure (i.e., HL or surge-line failure) was also estimated for each

time step for loop A.

(6) Steps 2 through 5 were repeated for loop B. The probability of HL failure was used as

the probability of RCS failure for loop B.

(7) The integrated C-SGTR leak areas from loop A and loop B were then probabilistically

added (i.e., the two distributions were convolved at each time step). Similarly, the

probability of RCS failure was estimated by aggregating the probabilities of RCS failure

of loop A with loop B.

(8) For a critical SG leak area (i.e., 6 cm2 (0.93 in.2

)), the probability of RCS survival was

multiplied with the probability that the SG leak area distribution exceeds the critical

C-SGTR leak area for each time step. The resulting probability value is then integrated
7-51

over all time steps to obtain the C-SGTR probability. This is shown in the 

equation below:

PPPPPPPP(CCCCCC CC) =

∫ PPPPPPPP ( ssss ssssssss aa tt) ∗ PPPPPPPP�CCCCCC CC oooo bb bb tt aa aa (tt + )� ∗ (7.3)

Figures 7-22 and 7-23 show examples of the graphical results generated from Steps 2 and 3 for 

the stsbo scenario for the average hot and the hottest tubes. These graphs show the probability 

of RCS survival and the distributional percentiles of the SGTR leak areas as a function of time. 

The graphs also show that there is significantly more spread for leak area distribution 

associated with the hottest tube. For a leak area of 3 cm2 (0.46 in.2

), the graphs show that the 

survival probability of RCS could vary from 0.03–0.17 for the average hot tube and from 0–0.43 

for the hottest tubes.

Figure 7-22 The RCS survival probability and percentiles of SGTR leak areas for 

stsbo-a-average hot tubes 

Figures 7-24 and 7-25 present the graphical results from Steps 4 and 5 for loop B and loop A, 

respectively. Figure 7-24 shows that, at about 2,000 seconds, the probability of RCS survival is 

0.5 and the probability that the SGTR leak exceeds 3 cm2 (0.46 in.2

) is approximately 0.4 

(1 ‒ 0.6). Similarly, at 2,080 seconds, the probability that RCS has survived is 0.6 and the 

probability that SGTR leak exceeds 3 cm2 (0.46 in.2

) is approximately 0.02 (1 ‒ 0.98). The 

current method can generate similar graphs for any size of SGTR leak areas. Figure 7-26 

contains an example showing the leak probability curves for both a 3 and 6 cm2 (0.46 and 

0.93 in.2

) SGTR leak area for the stsbo-a-b-scf sequence.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

1

2

3

4

5

6

20000 21000 22000 23000 24000 25000

Leak area cm2

Time (s)

Am

A0.05

A0.25

A0.50

A0.75

A0.95

RCS Survival

Probability
7-52

Figure 7-23 The RCS survival probability and percentiles of SGTR leak areas for 

stsbo-a-hottest tubes 

Figure 7-27 shows the graphical results from Step 7 of the approach. It shows the probability of 

RCS integrity and the time-dependent probability that the SGTR leak area from both SGs is less 

than a predefined critical leak area criterion (i.e., 6 cm2 (0.93 in.2

)).

A C-SGTR probability of about 0.2 was estimated for the stsbo-a sequence based on the 

procedure given in Step 8 of the approach.

Table 7-18 shows the results for the probability of SGTR exceeding 6 cm2 (0.93 in.2

) for loop B 

before the failure of its HL. This result could also represent a bounding estimate for the plant 

C-SGTR, which is the equivalent of assuming that both loops (A and B) experience the TH

behavior of loop B (i.e., worse condition for C-SGTR), and both loops fail dependently. The next

paragraphs discuss more detailed calculations that differentiate between the TH behaviors of

the two loops. These calculations showed that the probability of C-SGTR for the selected CE

plant is about 0.2 for SBO scenarios where the TDAFW pump(s) failed initially and about 0.3

when the TDAFW pump(s) operated for at least 4 hours. These results show that, if the TH

behavior of loop B is only used for a simplified PRA analysis, the resulting C-SGTR probability

will not be significantly overestimated (less than 10 percent overestimation). For these analyses,

primary or secondary relief valves are assumed to reclose after opening and no failure to stick

open is considered. Section 7.3.2 discusses the sensitivity results for cases where one or more

of the secondary relief valves may fail open (i.e., stick open). Figure 7-28 shows an example of

calculations for loop B resulting from Step 6 of the approach to compare with Figure 7-26.

Table 7-18 shows the comparative results for the probability of SGTR exceeding 3 or 6 cm2

(0.46 or 0.93 in.2

) for loop B before the failure of HL.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

1

2

3

4

5

6

7

8

18000 19000 20000 21000 22000 23000 24000 25000

Leak Area (cm2)

Time (s)

Am

A0.05

A0.25

A0.50

A0.75

A0.95

RCS Survival

Probability
7-53

Figure 7-24 The RCS survival probability and the probability of SGTR with a leak area less 

than 3 cm2 for stsbo-a-b, aggregated over average hot and hottest tubes 

Figure 7-25 The RCS survival probability and the probability of SGTR with a leak area less 

than 3 cm2 for stsbo-a-a, aggregated over average hot and hottest tubes 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

18000 19000 20000 21000 22000 23000 24000

Probability

Time (s)

P(SGTR < 3

cm^2)

P(RCSSurvive)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

18000 19000 20000 21000 22000 23000 24000 25000

Probability

Time (s)

P(SGTR

Leak<3

cm^2)

P(RCSSurvive)
7-54

Figure 7-26 The RCS survival probability and the probability of SGTR with a leak area less 

than 3 and 6 cm2 for stsbo-a-b-scf 

The probability of C-SGTR for the selected CE plant is, therefore, 0.2 for SBO scenarios where 

the TDAFW pump(s) failed initially and 0.3 when TDAFW pump(s) operated for at least 4 hours. 

Similar observations were noted for the W case studies. The following discusses the main 

reasons behind the higher probability of C-SGTR for ltsbo compared to stsbo. 

For both the CE and W cases, the conditional C-SGTR probability is higher for the severe 

accident sequences with late failure of AFW than those sequences with early failure of AFW. 

Both W and CE TH input files exhibit a slower temperature ramp in ltsbo than stsbo after the SG 

tube temperatures reach the creep-rupture range; namely, 600–700 degrees C 

(1,112–1,292 degrees F). However, the difference between the HL and SG tube temperatures 

remains approximately the same for long and short SBOs. The notion that the probability of 

containment bypass is governed by the difference in HL and SG tube temperatures should be 

tempered by the effect of the absolute temperature and the rate of temperature ramp. The 

equations for creep-rupture failures of HL and SG tubes depend on the absolute temperature 

and the time temperature integral. The probability of containment bypass, therefore, is governed 

not only by the difference in HL and SG tube temperatures but also by the absolute temperature 

and the rate of the temperature ramp in severe accidents. Figures 7-15 and 7-16 illustrate this 

phenomenon for early AFW failure and Figures 7-18 and 7-19 for late AFW failure. It should be 

noted that the C-SGTR, if it occurs, occurs much later in the sequences with late AFW failure 

(ltsbos) and carries significantly less public consequence (i.e., not considered an LER), 

compared to the sequences where AFW fails at T=0 (stsbos).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

18000 19000 20000 21000 22000 23000 24000

Probability

Time (s)

P(SGTR < 3

cm^2)

P(RCSSurvive)

P(SGTR<6

cm^2)
7-55

Figure 7-27 The RCS survival probability and the probability of SGTR with a leak area less 

than 6 cm2 for the whole plant for an SBO scenario with failure of TDAFW pump 

at time zero and no stuck-open secondary relief valves (stsbo-a-scf) 

Figure 7-28 The RCS survival probability and the probability of SGTR with leak areas less 

than 3 and 6 cm2 for ltsbo-a-b-scf 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

18000 19000 20000 21000 22000 23000 24000

Probability

Time (s)

p(sgtr<6

cm^2)

P(RCSSURVIVE)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

44000 44500 45000 45500 46000 46500 47000 47500 48000

Probability

Time (s)

P(SGTR<3 cm2)

P(SGTR<6 cm2)

P(RCS Survive)
7-56

Table 7-18 Comparison of C SGTR Probability for SBO 

Case Run (Sequence) P(C-SGTR>6 cm2

) using TH of 

loop B for both loops

Short-Term SBO 0.22

Long-Term SBO 0.31

7.2.5 Level 2 Models for Containment Bypass Evaluation 

Table 7-19 shows the timing for the major events corresponding to the accident progression of a 

scenario of an SBO and early failure of TDAFW pumps. A combination of MELCOR results and 

sensitivity case runs with C-SGTR software generates these timings.

Table 7-19 Timing of Major Events during an SBO with Early Failures of TDAFW Pumps 

Time Events for SBO with Early Failure of TDAFWs

0 SBO started

~ 14 minutes ECCS signal actuated

~ 4 hours Dc assumed depleted a

~ 5 hours Onset of core uncovery, corresponding to 648.89 °C (1,200 °F)

Between 5 hours and 30 minutes 

and 5 hours and 45 minutes b

SGTR expected with varying leak rates c

Between 5 hours and 21 minutes 

and before 5 hours and 50 

minutes

HL failure if the primary pressure remains around 15.17 MPa 

(2,200 psi) as estimated by C-SGTR software 

Between 5 hours and 8 minutes 

and 5 hours and 30 minutes 

Gap release from rod groups 1 through 5

Around 5 hours and 54 minutes HL failure if the primary pressure remains around 8.27 MPa 

(1,200 psi) b (SG relief set point) after 65 hours, 30 minutes 

Around 6 hours HL failure if the primary pressure is reduced around 4.83 MPa 

(700 psi)

Between 7 and 8 hours Core structure failures, multiple melting and quenching; start of 

in-vessel releases 

~ 11 hours Vessel breach, HL failure not expected if primary is fully 

depressurized 

a Although MELCOR assumes dc is depleted in 4 hours for both early and late failure of TDAFW pumps, PRA 

considers dc would be available for a longer time for the case when TDAFW pumps were not available at time 

zero. The availability of dc will facilitate SAMG activities such as depressurization of primary and secondary. b The ranges are defined based on 10 and 90 percentiles of the associated failure distribution. c These values were supported by sensitivity runs performed using C-SGTR software.

An examination of the information shown in this table leads to the following six observations:

(1) For cases when C-SGTR occurs before HL failure but the primary pressure is

maintained at the primary relief set point (approximately 15.2 MPa (2,200 psi)), the HL is

expected to fail shortly after the occurrence of SGTR. The size of the SGTR leak for

such cases is approximately equivalent to the area of a guillotine break of one tube.
7-57

MELCOR runs show that this amount of SGTR leakage may not demand any cycling of 

the secondary relief valves. In general, no depressurization of the primary system is 

expected. The releases are therefore limited to a fraction of the fuel gap release plus the 

radioactivity source term contained in the primary reactor system. These are categorized 

under negligible releases. Larger releases are possible only if the secondary-side relief 

valves sticks open during or before C-SGTR.

(2) For cases where the primary pressure equalizes with the secondary pressure and the

pressure remains at the secondary relief set point (approximately 8.3 MPa (1,200 psi))

after the occurrence of C SGTR, the HL failure would be delayed but it occurs before the

vessel breach. The status of SG relief valves (stuck open or not) would determine the

magnitude of release. It is expected that the larger the C-SGTR leak area, the larger the

release magnitude would be. The releases are generally not categorized as LERs if no

secondary relief valve sticks open.

(3) If the primary system is somewhat depressurized to an intermediate pressure of about

4.83 MPa (700 psi); for example, caused by the failure of one primary relief valve in a

partially open position, the failure of HL will be delayed and, if one or more secondary

relief paths have stuck open, there is a potential for some early releases. The releases,

however, will be limited, since the stuck-open primary relief valve will cause some

fraction of releases to end up in the containment.

(4) For cases where the secondary relief valves stick open early in the accidents, the

primary is expected to depressurize below the accumulator discharge set point. This will

delay the failure of HL and the occurrence of SGTR. Higher delta P on the tubes is

expected, however, because of lower secondary-side pressure, which can increase the

probability of SGTR. For these cases, the probability of C-SGTR is expected to increase,

and the releases are considered to be LERs because of a large containment bypass

area provided by the stuck-open secondary relief valves. Section 7.3.2 discusses the

specific set of MELCOR runs for this case in more detail.

(5) For cases where the primary and secondary are equalized and both are depressurized

completely, the HL may not fail until vessel breach (approximately 11 hours) occurs. All

in-vessel releases should then be considered as a part of the source term. This situation

could occur if the operator has depressurized the primary system for SAMG actions but

failed to flood the secondary side of the SG or the primary system. The primary

depressurization could also take place by failures of multiple primary relief valves (stuck

open) under the harsh environment associated with post-core melt.

(6) The occurrence of a very large C-SGTR leak area (because of loop seal clearing, or the

failure of three or more tubes) is conservatively categorized as an LER. Such cases can

demand secondary-side relief, and multiple secondary-side relief paths could fail open.

However, the release could be significantly reduced if the secondary side of SG is filled

with fire water as a part of SAMG actions.

Table 7-20 shows the timing for the progression of accidents for a scenario of an SBO and 

failures of TDAFW pumps after 4 hours. A combination of MELCOR results and sensitivity case 

runs with C-SGTR software similarly generates these timings. They follow very similar trends as 

those for the first scenario when TDAFW failed early. There are two differences between the 

accident progressions of an SBO with failures of TDAFW pumps after battery depletion and an 
7-58

SBO with the early failure of TDAFW pumps. These differences are important for developing 

and quantifying the Level 2 models for C-SGTR:

(1) Dc is expected to be depleted by 4 hours, so no operation of active components from the

control room can be credited unless the power is recovered. If the offsite power is

recovered, credits for successful SAMG actions can be provided.

(2) Extended dc could be provided through portable generators and other means. This could

also facilitate the long-term availability of dc for SAMG actions or to maintain the

operation of the TDAFW pumps. The success probability for such actions could be

increased if they are initiated early after the occurrence of an SBO. This is a

plant-specific PRA issue that cannot be addressed generically at this time.

Table 7-20 Timing of Major Events during an SBO with Failures of TDAFW Pumps after 

Battery Depletion 

Time Events for SBO with Early Failure of TDAFWs

0 SBO started

~ 14 minutes ECCS signal actuated

~ 4 hours Dc assumed depleted

~ 12 hours and 05 minutes Onset of core uncovery, corresponding to 648.89 °C (1,200 °F)

Between 12 hours and 45 

minutes and 13 hours and 

05 minutes 

SGTR expected with varying leak rates 

Between 12 hours and 30 

minutes and 13 hours and 

15 minutes (average 12 hours 

and 55 minutes)

HL failure if the primary pressure remains around 15.17 MPa 

(2,200 psi) as estimated by C-SGTR software 

Between 12 hours and 40 

minutes and 13 hours and 

15 minutes 

Gap release from rod groups 1 through 5 

Between 13 hour and 

20 minutes 

HL failure if the primary pressure remains around 8.27 MPa 

(1200 psi) (SG relief set point) after the onset of core damage 

Around 17 hours Core structure failures, multiple melting and quenching; start of 

in-vessel releases 

~ 18 hours Vessel breach, if primary fully depressurized

Similar to the discussion of the W plant in the previous section, a five-factor formula was used to 

estimate the frequency of containment bypass and LERF because of C-SGTR. The fractions of 

containment bypass scenarios that can lead to LERs depend on the success probabilities of 

SAMG actions and effective evacuation. The SAMG actions for the CE plant are similar and 

comparable to those of the W plant, as discussed previously.

Section 2.5 discussed the emergency response timeline and the process for effective 

evacuation of the SBO scenario with the early and late failure of TDAFW pumps (e.g., after 

batteries are depleted). That discussion applies to both the W and CE plants. It is assumed that, 

for the CE plants similar to the W plant, the evacuation is most likely effective for C-SGTR 

containment bypass events during SBO scenarios with late failures of TDAFW pumps and not 

effective for SBO scenarios with early failure of TDAFW pumps. This assumption is valid despite 
7-59

the fact that the estimated time to core damage for the CE plant was somewhat longer than for 

the W plant.

7.2.6 Quantification of Probability of Containment Bypass due to C-SGTR 

A simplified five-factor formula for LERF, as discussed in Section 2.5, was used. The five factors 

are as follows:

(1) frequency of severe accident sequences with potential for C-SGTR (fAC), as discussed in 

Section 7.2.2

(2) C-SGTR probability (PCSGTR); see the discussion for estimating C-SGTR and 

containment bypass probability in Section 7.2.4

(3) conditional probability that the subsequent failures of RCS components, including the 

stuck-open primary relief valves, do not occur (PNDEP)

(4) failure probability of all SAMG actions (PSAMG)

(5) probability that early effective evacuation is not successful (PEVAC)

The qualitative discussion provided in the previous section for estimating the 

parameters—PNDEP, PSAMG, and PEVAC—are considered to be applicable here. Bounding values 

for each of these three parameters, similar to what was suggested in Section 7.1, were also 

used. Table 7-21 shows the values for SBOs, with early or late failures of TDAFW pumps.

Table 7-21 Conditional LERF Probabilities for an SBO with Early and Late Failures of TDAFW 

Pumps for the Example CE Plant 

Factors Applicability LERF Factors 

(early, late)a b

PCSGTR Sequences with no stick-open primary or secondary relief 

valves 

(0.2, 0.3)

Sequence with loop seal clearing (1.0,1.0)

PNDEP Sequence without loop seal clearing (1.0, 1.0)

Sequence with loop seal clearing (1.0, 1.0)

PSAMG Sequence without loop seal clearing (1.0, 1.0)

Sequence with loop seal clearing (1.0, 1.0)

PEVAC For all sequences (1.0, 0.0)

a The two numbers in parenthesis are for SBO scenarios with early and late failure of TDAFW pumps. b This value is considered to be conservative, and it is used for screening purposes only.

Table 7-15 showed earlier that more than 92 percent of the total SBO scenarios; from both 

internal and external events, resulted from the SBO scenarios with the failure of TDAFW pumps 

after battery depletion for the selected plant (last row last column of Table 7-15). Moreover, the 

results for internal event models also showed that 87 percent of the total SBO scenarios 

resulted from the SBO scenarios with the failure of both TDAFW pumps after battery depletion 

for the selected plant (last column, first row after headings). The CDF from SBO sequences, 

considering all hazard categories, is about 3.3X10-5

/year, and for the internal event, is about 1.9
7-60

X10-7/year (obtained from Table 7-15). This CDF, multiplied by the conditional probability of 

containment bypass (0.2), gives a bounding containment bypass frequency estimate of 

~6.8X10-6/year for all hazard categories, and ~4.0X10-8/year for internal events only. The overall 

LERF estimate from each unit is about 5.1X10-7, since only the containment bypass resulting 

from the SBO scenarios with early failure of both TDAFW pumps (i.e., about 8 percent of the 

total CDF) has a potential for an LER.

The relatively small values for LERF for the selected CE plant (i.e., CCNPP) are the result of the 

unique design feature of its AFW system. CCNPP is equipped with two TDAFW pumps that 

significantly reduce the CDF resulting from the SBO scenarios with the early failure of TDAFW 

pumps. This design feature is not generally shared by other CE plants. However, all current 

U.S. plants are equipped with additional SBO diesel generators and will have a set of new FLEX 

equipment to significantly reduce the probability of core damage during all SBO scenarios.

This study does not currently use detailed quantification of Level 2 PRA models, considering the 

complexity of human reliability analysis for SAMG actions and the survivability of equipment 

after core melt. It is expected that plant-specific features will play important roles in the detailed 

quantification of containment bypass probability.

7.2.7 Concluding Remarks 

The TH results obtained from various case studies significantly influence C-SGTR, containment 

bypass probability, and LERF. These TH results reflect the specific design, configuration, and 

geometry of the plant systems (specifically the SG design), and primary connections such as HL 

and surge line. They should not be interpreted as generic results for CE plants. The more 

important plant features that can affect the results are as follows:

• SG flaws (i.e., number, type, depth, and size of the flaws)

• mixing in SG inlet plenum (e.g., deep or shallow SG inlet plenum and the angle of

HL entry)

• mixing and heat transfer in HL (e.g., HL diameter and length)

• reliability of primary and secondary relief valves pre/post onset of core damage

• operational procedures regarding the depressurization of the secondary side of SGs

• duration of dc availability, including load shedding capabilities

• effectiveness and success of SAMG activities

• success of FLEX and EDMG

The paragraphs below discuss the conclusions of this study, based on the case studies 

performed for the selected CE plant described in this chapter.

• The contribution of C-SGTR to LERF is expected to be about 5.1X10-7/yr when all

hazard categories applicable to the site are included.
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The contribution of C-SGTR to LERF is expected to be about 5.0X10-9

/yr when only internal 

event SBO core damage sequences are considered. This value is lower than the expected 

value for other CE plants, since the selected CE plant is equipped with two TDAFW trains; 

however, current plants are equipped with additional SBO diesel generators and a set of new 

FLEX equipment.

• All the hazard models for the SBO scenarios considered for this study showed that the 

large fraction of core damage scenarios will involve both units (approximately 

86 percent). This issue may be considered further as a part of the integrated site PRA.

• There is a significantly higher probability for C-SGTR for the CE plant compared to the 

W plant—this conclusion focuses too heavily on the unique PRA aspects of the 

reference plant—particularly that relatively shallow flaws can provide a significant 

contribution to C-SGTR probability in the CE plant.

• The CE plant has unique safety features that may not be representative of the PWRs 

using similar SGs. (For example, the two TDAFW pumps, as mentioned above, are 

deemed to be an asset, since it would make the failure of the TDAFW pumps less likely 

than at a typical plant with only one TDAFW pump.)

The following observations consider the frequency of containment bypass, which may or may 

not result in an LER:

• For the selected CE plant, the contribution of C-SGTR to containment bypass could be 

as high as 6.8X10-6

, considering contributions from all hazard categories. If only internal 

events are considered, this contribution is expected to be about 4.0X10-8

.

• Based on the existing PRAs, C-SGTR appears to be the highest contributor to 

containment bypass scenarios.

• The containment bypass contribution occurs mainly from the scenarios where the 

TDAFW pump initially worked but was later rendered inoperable after the depletion of 

batteries. This is mainly because the CDF contribution from the scenarios with failure of 

TDAFW pump(s) after battery depletion is much larger than the CDF from the SBO 

scenarios with the early failure of TDAFW pump(s). However, these scenarios are not 

considered to contribute to LERF, since evacuation is expected to be effective.

• Extending the battery life and operation of TDAFW pumps can reduce the frequency of 

containment bypass, by reducing the frequency of the core damage sequences that 

challenge the SG tubes. This also facilitates the use of additional equipment, such as the 

existing EDMG or the future equipment in response to the FLEX program.

7.3 Sensitivity Analyses for C-SGTR in Different SG Types 

This section examines the robustness of the results and conclusions discussed earlier in 

Sections 7.1 and 7.2 under varying sets of assumptions. These sensitivity analyses are also 

designed to support the development of Level 2 PRA models. Appendix D provides a detailed 

discussion on the approach, assumptions, case runs, and results of the analysis for both the 

selected W and the CE plants.
7-62

Section 7.3.1 is devoted to the example W plant and summarizes the results and insights from a 

series of sensitivity analyses that Appendix D discusses in detail. Section 7.3.2 similarly 

summarizes the results and insights from different sets of sensitivity analyses for the example 

CE plants. In some cases, the results of sensitivity analysis performed for one example plant 

could be applicable and provide insights for the other plant.

7.3.1 Summary of Sensitivity Analyses for the Westinghouse Plant 

The following sensitivity analyses were performed for the W plant. The measure of comparison 

used for these sensitivity analyses was based on the difference between the time when HL 

failure is imminent and the time when C-SGTR is expected. The ratio of this time margin over 

the base time margin is used as a means of qualitatively ranking the impact of sensitivity results.

7.3.1.1 Uncertainty in Predicting the HL and SG Tube Temperatures

This sensitivity analysis studied the effect of uncertainties of TH prediction in terms of the delta 

temperature between the HL and the average hot tube. It is generally expected that, if the 

difference between the HL temperature and the SG tube temperature decreases, the probability 

of C-SGTR would increase. This assumes that the delta-T between the HL and hot tube is only 

50 percent as large as the base case. The results of the sensitivity analysis for the example W 

plant showed that the time margin measure is reduced by 4 minutes. This is considered to be a 

low impact.

7.3.1.2 Sensitivity of HL Thickness

The HL materials and thickness are clearly defined plant-specific parameters. There could, 

however, be some variations across similar plants because of the differences in the thickness of 

the weld overlay. In this sensitivity case, the effect of an increase in HL thickness caused by a 

weld overlay is examined to gain insights on the potential variability across plants. For this 

purpose, the HL thickness of 6.35 cm (2.5 in.) in the base case is increased by 50 percent, to 

9.5 cm (3.74 in.). This sensitivity analysis showed a reduction of 2 minutes in the time margin, 

and it is, therefore, categorized as low impact.

7.3.1.3 Secondary Side Not Depressurized

In this sensitivity study, it is assumed that the secondary side will not be depressurized, either 

as a result of preexisting leakage or because of intentional opening or stick-open failure of one 

or more secondary relief valve before and after the onset of core damage. The results of 

sensitivity analysis show that the time margin actually increases, since HL failure time is not 

affected, but the tube flaw failure time is considerably delayed. This sensitivity analysis shows 

no adverse impact on C-SGTR probability.

7.3.1.4 Early Secondary-Side Depressurization

In this sensitivity analysis, the operator depressurizes SGs at 30 minutes by opening at least 

one atmospheric dump valve or PORV for each SG, thereby dropping the primary pressure 

below 4.82 MPa (700 psi). This actuates the accumulator discharge. The TDAFW pump will fail 

after the batteries are depleted. The results of this sensitivity analysis show that the time margin 

is increased by about 4 minutes, and, furthermore, the onset of core damage is delayed 

significantly. This sensitivity analysis, therefore, shows no adverse impact on 

C-SGTR probability.
7-63

7.3.1.5 Tube Material; Comparison of Alloy 600TT and 690TT Tubes

This sensitivity analysis compared the W SG types with 600TT and 690TT tube material. The 

results showed that the margin for 690TT is reduced by about 10 minutes, indicating that 690TT 

material with a “large” flaw will leak earlier than SG tubes with 600TT material with the same 

“large” flaw. However, the number of flaws and the flaw sizes for 690TT are expected to be 

smaller than those of 600TT. Therefore, the performance of 690TT is expected to be similar to 

600TT as far as C-SGTR is concerned. However, large flaws, if detected in 690TT, could be 

more prone to C-SGTR than similar flaws in 600TT.

7.3.2 Summary of Sensitivity Analyses for Combustion Engineering Plant 

The following sensitivity analyses were performed for the example CE plant. The measure of 

comparison used for these sensitivity analyses was based on the reevaluation of C-SGTR 

probability for short SBO sequences where LERF is of concern. In some cases; the C-SGTR 

probability was only reevaluated for one loop, rather than for the reactor unit (i.e., two loops: 

loop A and loop B). When the reevaluation for sensitivity analysis was limited to one loop, 

loop B was selected because of its higher contribution to C-SGTR. The difference between the 

revised C-SGTR probability and the base C-SGTR probability was used to prioritize the effect of 

the sensitivity results. A change of less than 25 percent is assigned as low, 25 to 50 percent as 

moderate, 50 to 100 percent as high, and any increases above 200 percent as significant.

7.3.2.1 Stick-Open Failure of Secondary Relief Valves before SG Dryout

In SBO scenarios, before SG dryout, the secondary-side relief valves (SG PORVs or MSSVs) 

could be demanded and fail to reclose. This could happen in either or both SGs. Stuck-open 

relief valves initially depressurize and cool the primary below the accumulator discharge 

setpoint. However, the primary will repressurize and the onset of core damage will be reached, 

although slightly delayed. A bounding analysis of this scenario was evaluated using the 

MELCOR package. This scenario is referred to as stsbo-as or ltsbo-as in Chapter 3. The overall 

C-SGTR was reevaluated for this scenario. The results show that the failure of secondary-side 

relief valves early during the sequence can have a significant impact on the LERF contribution 

due to C-SGTR. Table 7-22 below shows the results of this reevaluation.

Table 7-22 Sensitivity Results for Early Stick-Open Failures of the Secondary Relief Valves 

Case Runs Loop b C-SGTR>3 cm2 Loop a C-SGTR>3 cm2 C-SGTR> 6 cm2

Short-Term SBO—Base 0.45 0.227 0.20

Short-Term SBO [Stuck-open secondary 

relief valve]

0.999 0.997 0.990

7.3.2.2 Opening of Secondary Relief Valves after SG Dryout

The operators are guided to depressurize the SGs by opening the secondary relief valves in 

anticipation of using an alternate source of water to refill the SGs as a part of SAMGs. This 

sensitivity analysis examines the effect of an intentional opening of the secondary relief valve 

after the onset of core damage when the operators fail to refill the SGs. This sensitivity analysis 

sets the secondary-side pressure to 1.0X105 Pa (1 bar or 14.5 psi) after the hot gas temperature 

reaches about 640 degrees C (1,184 degrees F). The effects on primary pressure or 

temperature are not expected to be significant. The results show that the opening of 
7-64

secondary-side relief valves after SG dry out and the onset of core damage can increase the 

LERF contribution from C-SGTR by about 65 percent (from 0.2 to 0.33) for stsbo-a scenarios. 

Failures of one or more secondary relief valves to reclose are therefore considered to have a 

moderate impact on C-SGTR probability. However, the additional benefit of SAMG could 

outweigh this higher probability of C-SGTR. Table 7-23 below shows the results of 

this reevaluation.

Table 7-23 Sensitivity Results for Opening the Secondary Relief Valves after SG Dryout 

Case Runs Loop b C-SGTR > 3 cm2 Loop a C-SGTR > 3 cm2 C-SGTR > 6 cm2

Short-Term SBO—Base (stsbo-a) 0.450 0.217 0.20

Short-Term SBO [Stuck-open secondary 

relief valve—after SG dryout] (stsbo-a)

0.591 0.262 0.33

7.3.2.3 Critical C-SGTR Leak Area

The critical area equivalent to a guillotine break of one tube (approximately 6 cm2 (0.93 in.2

])) 

was chosen as a sufficient leakage area that can be considered to be an LER if the 

secondary-side relief valves are open. Some MELCOR analyses showed that this size of 

leakage may not be sufficient to depressurize the primary or pressurize the secondary, such 

that SG relief valves are demanded. These analyses, however, assumed that there is a 

preexisting secondary leakage area of 3.2 cm2 (0.5 in.2

) for each SG from the starting point of 

the sequence. To ensure that the secondary relief valves are demanded and the primary can be 

depressurized, a larger critical C-SGTR leak area needs to be considered. A critical C-SGTR 

leak area of 12 cm2 (1.86 in.2

) instead of 6 cm2 (0.93 in.2) reduces the probability of C-SGTR 

from 0.2 to 0.06. The effect is, therefore, considered to be high for reducing C-SGTR probability. 

Figure 7-29 shows the results for the stsbo-a sequence. Similar graphs can be generated for 

any size of critical leak area, and they generally follow the trend shown in Figure 7-29.

Figure 7-29 The sensitivity results for (stsbo-a) for C-SGTR leak areas of 12 cm2 and 6 cm2 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

18000 20000 22000 24000

Probability

Time (s)

P(SGTR<6cm^2)

P(RCS-SURVIVE)

P(SGTR<12 cm^2)
7-65

7.4 Case Studies for Pressure-Induced C-SGTR Scenarios 

Section 2.1 summarized the sequences of interest for DBA events that could establish a delta 

pressure across the SG tube walls, and therefore, potentially challenge the integrity of the tubes 

because of pressure-induced failures. A limited effort was devoted to evaluating the bounding 

contribution of C-SGTR to CDF and LERF as a result of these sequences.

These evaluations considered two bounding scenarios represented by stylized TH inputs for the 

C-SGTR software. This eliminated the need for performing specific MELCOR or RELAP runs for 

these case studies. Furthermore, these bounding analyses apply to both W and CE plants.

The section below summarizes the two TH scenarios and the corresponding accident 

conditions, including the bounding estimates in terms of the increase in CDF and LERF. 

Appendices C and F contain additional supporting analyses.

7.4.1 C-SGTR during Anticipated Transients without Scram 

This bounding scenario selected for evaluation the loss of a main feedwater anticipated 

transients without scram (ATWS) event. The termination of feedwater flow to the SGs results in 

a large imbalance in the heat source/sink relationship. This heat buildup in the primary system 

also raises the RCS temperature and pressure. In general, the availability of main feedwater for 

ATWS events results in a less severe power mismatch between the heat source and the heat 

sink; therefore, the peak pressure attained in the primary system will not be as severe as the 

case with loss of feedwater.

The ATWS event considered here is for the case when the moderator temperature coefficient 

(MTC) is considered favorable. UET (unfavorable exposure time) is defined as the time during 

the cycle when the reactivity feedback is not sufficient to prevent RCS pressure from exceeding 

22.1 MPa (3,200 psig). Many factors, such as initial power level, time in cycle when transient 

occurs, reactivity feedback as a function of the cycle life, number of available primary relief or 

safety valves, failure or success of control rod insertion, and AFW flow rates affect UET. The 

primary pressure during favorable MTC is below about 22.1 Mpa (3,200 psi). For bounding 

evaluation, a primary pressure of about 22.1 Mpa (3,200 psi) is used for cases when the MTC 

is favorable. For unfavorable MTC when the pressure exceeds about 22.1 Mpa (3,200 psi), 

rupture of one or more components in the primary system and the occurrence of core damage 

are assumed. C-SGTR is not considered for LERF analysis, since most releases will be into the 

containment through failed primary components. 

If the failure of the reactor protection system (RPS) is not caused by the failure to insert 

sufficient rods (i.e., mechanical rod failures), manual actions to trip the reactor and the backup 

to the reactor trip system provided by the ATWS Mitigation System Actuation Circuitry can be 

credited to eventually scram the reactors. However, such actions are not fast enough to prevent 

the formation of an early primary pressure peak, which can induce a C-SGTR. If C-SGTR 

occurs and the reactor scram is subsequently successful, the event would behave like that of 

SGTR with the failure of the main feedwater (MFW) system. However, if C-SGTR occurs in 

ATWS scenarios because of the mechanical failure of the rods, or in the unlikely event that the 

backup manual scram actions are not successful, the accident progression may differ from the 

traditional SGTR scenario. In most PRAs, such scenarios are considered as eventual core 

damage because of the following issues:
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• A C-SGTR following an ATWS could result in an uncontrolled cooldown of the primary

system unless the faulted SGs are isolated. Such cooldown and its reactivity feedback

could render emergency boration (EB) ineffective.

• A C-SGTR following an ATWS could reduce the boron concentration in the primary

system through primary-to-secondary leakage.

The effect of C-SGTR on the reactivity feedback and the effectiveness of EB would depend on 

the size of the primary-to-secondary leakage. This study considers the leakages greater than an 

equivalent guillotine break of one tube to be of a sufficient size to influence the effectiveness 

of EB.

ATWS scenarios will expose all SGs to a higher pressure; therefore, C-SGTR can occur at any 

of the SGs. Appendix F used the probability that a flaw belongs to a flaw bin and multiplied that 

by the probability that the flawed tube fails under induced pressure to arrive at the probability of 

C-SGTR during ATWS. The analysis in Appendix F conservatively concludes that a single failed

tube should have a flaw length of about 3 cm (1.2 in.) or more to be a consequential source of

SGTR leakage for ATWS conditions. When considering the number of flawed tubes, this

translated to a C-SGTR probability of 0.01 for the example W plant with four SGs, and 8.0X10-3

for the example CE plant with two SGs, for the 15th cycle of operation.

Simplified PRA calculations used a PWR SPAR model (Shearon Harris plant) for the two ATWS 

scenarios of concern, discussed below.

7.4.1.1 ATWS with Successful Manual Scram but Occurrence of C-SGTR

For all ATWS scenarios, where the failure of RPS is not caused by the inability to insert a 

sufficient number of rods and subsequent manual/backup scram through the ATWS Mitigation 

System Actuation Circuitry are successful, the C-SGTR accident progression will proceed as if 

the SGTR were the initiator. The probability of ATWS because of electrical RPS failure is 

generally set at about 1.5X10-5 per demand, assuming that there is about 1 transient per year 

demanding the RPS. Table 7-24 lists the main contributors.

Table 7-24 Contributors to Electrical RPS Failures that Do Not Impact Manual Scram 

Basic Event Name Failure Probability Description

RPS-UVL-CF-UVDAB 1.040E-5 CCF UV DRIVERS TRAINS A AND B (2 OF 2)

RPS-TXX-CF-6OF8 2.700E-6 CCF 6 BISTABLES IN 3 OF 4 CHANNELS

RPS-CCX-CF-6OF8 1.830E-6 CCF 6 ANALOG PROCESS LOGIC MODULES IN 3 OF 4 

CHANNELS

RPS-BME-CF-RTBAB 1.610E-6 CCF OF RTB-A AND RTB-B (MECHANICAL)

The probability of electrical ATWS and C-SGTR is about 1.5X10-7 per year. This scenario has a 

frequency that is about 4 orders of magnitude smaller than the frequency of the SGTR initiator, 

which is about 2.0X10-3 per year. The C-SGTR initiator and these scenarios will progress 

similarly if the manual scram is successful.
7-67

7.4.1.2 Nonrecoverable ATWS Followed by C-SGTR

The probability of ATWS because of mechanical failures to insert a sufficient number of rods is 

estimated to be about 1.2X10-6

, if one transient per year is assumed. The main contributor for 

this event as reported by SPAR model is specified below.

Basic Event Name Failure Probability Description

RPS-ROD-CF-RCCAS 1.2E-6 CCF 10 OR MORE RCCAS FAIL TO DROP

The probability of mechanical ATWS and C-SGTR is about 1.2X10-8 per year.

7.4.2 C-SGTR during Steamline Break Scenarios 

Several sequences identified earlier in Table 2-1 can be bounded by an unisolable main 

steamline break (MSLB). These sequences could also include spurious opening of one or more 

SG relief valves in addition to MSLVs. The TH behavior of these scenarios can be bounded by 

high primary pressure at about 15.5 MPa (2,250 psi) and a low atmospheric secondary 

pressure. The resulting delta pressure across the SG tubes is expected to be between 10.34 

and 11.72 MPa (1,500 and 1,700 psi), since the secondary leakages tend to cool and 

depressurize the RCS. The use of 15.51 MPa (2,250 psi), therefore, is considered to be 

conservative and bounding. The primary temperature is generally expected to be subcooled. A 

temperature of 300 degrees C (572 degrees F) is used, since the saturated primary temperature 

at 15.5 MPa (2,250 psi) is about 345 degrees C (653 degrees F). Atmospheric pressure is also 

considered for the secondary-side pressure at the faulted SG. The scenario considered that the 

MSIV on all unaffected SGs will close, thereby blowing the steam out of only one SG and 

eliminating the potential for pressurized thermal shock sequences because of excessive 

overcooling. This was considered as the bounding TH behavior for these sequences when 

evaluating the potential pressure-induced C-SGTR. In such a scenario, tubes in all SGs will be 

initially exposed to high delta pressure with a potential for C-SGTR. However, after the MSIV 

closure, only one faulted SG would remain unisolated. The C-SGTR probability of the faulted 

SG is used for the PRA evaluation, since the CDF and LERF contributions result mainly from 

the unisolated SG.

Appendix F used the probability that a flaw belongs to a flaw bin and multiplied that by the 

probability that the flawed tube fails because of induced delta pressure caused by a steamline 

break (SLB) to arrive at the probability of C-SGTR. The analysis in Appendix F conservatively 

concludes that a single failed tube should have a flaw length of about 3 cm (1.2 in.) or more to 

cause enough leakage for it to be consequential under SLB conditions. When considering the 

number of flawed tubes, this translated to a C-SGTR probability of about 2.5X10-3 for the 

example W plant and a probability of about 4.0X10-3 for the example CE plant for the 15th cycle 

of the operation.

The initiating event (IE) frequency for the different types of SLB accidents could vary amongst 

the plants. The information provided in NUREG-1570, “Risk Assessment of Severe 

Accident-Induced Steam Generator Tube Rupture,” issued March 1998 (Ref. 6), is mainly used 

for establishing the IE frequency for bounding analysis. NUREG/CR-6928, “Industry-Average 

Performance for Components and Initiating Events at U.S. Commercial Nuclear Power Plants,” 

issued February 2007 (Ref. 7), was used when more recent updates were reported. The 

following summarizes the impact on accident progression for each of these initiating events, 

when a C-SGTR occurs.
7-68

7.4.2.1 SLB Inside Containment 

SLB inside containment (SLBIC) has an approximate IE frequency of 1.0X10-3 per reactor year 

as reported in NUREG-1570. If this initiating event induces a C-SGTR, all releases will remain 

inside the containment; therefore, they will not contribute to LERF caused by containment 

bypass. However, they will contribute to CDF. It is also assumed that the MSIV on all unaffected 

SGs will close, thereby eliminating the potential for pressurized thermal shock sequences 

because of excessive overcooling.

When SLBIC is followed by C-SGTR, the PRA models should be integrated by transferring the 

SLBIC event tree branch that includes C-SGTR, to the SGTR event tree discussed in Chapter 2 

and shown in Figure 2-1. However, some of the C-SGTR branches will be affected through this 

transfer, as summarized below:

• It would be more difficult to diagnose the SGTR at the faulted SG because the operator

should mainly rely on high secondary-side activity (high-radiation alarm), rather than on

a high uncontrollable level in the affected SG. The operator may terminate the high

pressure injection in response to SLBIC, if he/she is not able to diagnose C-SGTR in the

early stages. However, the operator could reestablish the high head injection after a

short period due to a low pressurizer level. The failure rate for high head injection should

be increased to account for the potential of operator failure to diagnose the occurrence

of C-SGTR in time.

• It will not be possible to isolate the faulted SG because of SLBIC, although the feedwater

to the faulted SG will be isolated. The conditional core damage probability for C-SGTR

should be reevaluated without any credit for isolation.

The release of radioactivity because of a potential core damage scenario involving SLBIC and 

induced C-SGTR is mainly to the containment; therefore, it is not considered to be a LERF 

contributor. The SLBIC IE is also an order of magnitude lower than an SLB outside containment 

(SLBOC) IE. The SLBIC scenarios are not considered any further, since they are not expected 

to contribute to LERF.

7.4.2.2 Spurious Opening of SG-PORVs or Stuck-Open MSSVs (SGR)

This IE includes the spurious opening of an SG-PORV during a fire event or other events, and 

the potential for one or more MSSVs to stick open after a demand. The spurious opening of an 

SG PORV could be mitigated by isolating the path, whereas the spurious opening of MSSVs 

cannot be recovered. The frequency of the IE for spurious openings (and subsequently to 

stick/remain open) of one or more SG relief valves is taken to be 3.0X10-3 per reactor year from 

NUREG/CR-6928, which was an update to NUREG-1570. This value in NUREG/CR-6928 is 

generically applicable to safety/relief valves both for primary and secondary systems. It should 

be noted that the failure of one MSSV can cause a severe overcooling transient with primary 

depressurization if feeding to the SG is maintained (not a C-SGTR concern). The scenario of 

interest for C-SGTR, however, assumes that the operator will terminate feedwater to the 

affected SG and thereby let the SG go dry and depressurized. This scenario is only applicable 

to one specific SG and does not affect others. Therefore, the appropriate estimated C-SGTR 

probability of one SG is to be used for the PRA estimations (i.e., a C-SGTR probability of 

2.5X10-3 for the example W and 4.0X10-3 for the example CE plant).
7-69

When a spurious opening of one or more SG relief valves is followed by a C-SGTR, the 

accident progression will be similar to SLBIC with C-SGTR. However, the latter could result in 

containment bypass and an LER, since the releases will be made outside the containment.

7.4.2.3 SLB Outside Containment

SLBOC has an approximate IE frequency of 1.0X10-2 per reactor year. This initiating event can 

expose the tubes in all SGs to a higher delta pressure, therefore, with some possibility that 

C-SGTR occurs. Sequences where only one MSIV fails to fully close were considered, thereby 

eliminating the potential for pressurized thermal shock sequences caused by excessive 

overcooling in this scenario. The estimated probability that one out of the four MSIVs will fail to 

close is about 4.0X10-3 per demand. This estimate uses the MSIV failure probability of 9.51 X10-

4 per demand from the Shearon Harris SPAR event MSS-AOV-00-SGMSIV (i.e., 4X9.51X10-4

about 4.0 X10-3

). The IE frequency of an unisolable SLBOC is, therefore, estimated at about 4.0

X10-5 per year.

When an unisolable SLBOC is followed by C-SGTR, the impact on SGTR branches will be the 

same as when the SLBIC is followed by C-SGTR. The core damage that results when an 

unisolable SLBOC is followed by C-SGTR will also bypass containment and should be 

considered as an LER.

7.4.3 C-SGTR during High-Pressure Feed-and-Bleed Operation 

Some of the U.S. PWRs have high-pressure ECCS pumps supporting feed-and-bleed 

operations with shutoff pressure above the primary pressure relief set points. For all initiating 

events that involve the loss of the MFW system followed by the failure of the AFW system, there 

could be a possibility of C-SGTR. For these scenarios, the secondary sides of SGs are 

assumed to be dry and depressurized. Small leaks of less than 3.2 cm2 (0.5 in.2

) are sufficient to 

depressurize the SGs during the feed-and-bleed operation. The occurrence of C-SGTR during 

such events is not expected to increase the CDF because high-pressure injection (HPI) is 

assumed to be injecting makeup flow because of the success of the initial phase of feed and 

bleed operation. All core damage sequences where a feed and bleed operation is initially 

successful but is followed by C-SGTR are considered a containment bypass with the potential of 

contributing to LERF.

The Shearon Harris SPAR model was the basis for estimating the IE frequency that can put the 

plant in a condition where a feed-and-bleed operation is initiated. This estimate added the 

frequency of transients where MFW is lost i.e., IE-LOCHS, IE-LOIA, IE-LOMFW, and 

IE-LONSW). A bounding value of 0.2 per year was assigned to the IE frequency. This initiating 

event frequency must then be multiplied by the probability that the AFW system is not available. 

The base nominal failure probability of AFW is 2.0X10-5 per SPAR model. However, the specific 

value of AFW failure probability would be different for different initiators. A bounding value of 

1.0X10-4 for generic AFW failure probability was used. The bounding IE frequency for this 

category of pressure-induced C-SGTR sequences is, therefore, estimated to be about 2.0X10-5

per reactor year. There could be an additional contribution in some plants from possible fire 

scenarios causing spurious ECCS actuations. The LERF contribution from these scenarios is 

not expected to be significant. 

All SGs will be exposed to an environment conducive to C-SGTR during a high-pressure feed 

and bleed operation. The C-SGTR probability is, therefore, bounded by 0.01 for the example W 

plant and 8.0X10-3 for the example CE plant at the 15th cycle of operation.
7-70

7.4.4 LERF and Core Damage Contribution of Pressure-Induced C-SGTR 

The contribution of pressure-induced C-SGTR to CDF and LERF is estimated by the 

following equations:

PP(CCCC ) = ff(IIII) ∗ PP(CCCCCC CC|IIII) ∗ PP(CCCC|IIII, CCCCCC CC) (7.4)

PP(LL ) = ff(IIII) ∗ PP(CCCCCC CC|IIII) ∗ PP(CCCC|IIII, CCCCCC CC) ∗ PP(LL |IIII, CCCCCC CC, CCCC) (7.5)

The estimates for f (IE), P (C-SGTR|IE), and P (LERF|IE, C-SGTR, CD) were discussed for 

each sequence separately (see Appendix C). P (CD|IE, C-SGTR) is estimated using the SPAR 

model for the Shearon Harris PRA. This conditional probability is estimated by modifying the 

probability of the appropriate event tree branches to reflect the impact of the sequence. As an 

example, for ATWS scenarios, the branch heading associated with EB is set to true.

For SLB sequences, two other branches should be modified. The HPI branch should reflect that 

there is a possibility for the operator to terminate the HPI in response to SLB, not knowing that 

C-SGTR has occurred. Operators should also fail to recognize the need to reestablish HPI flow

even after pressurizer low level is indicated. The event tree branch for isolating the faulted SG

should also be set to true.

The probability that the operator fails to diagnose the occurrence of C-SGTR after an SLB 

scenario was estimated, using the SPAR-H worksheet, to be around 2.5X10-2. Four adjustments 

were made to the nominal values of the SPAR-H worksheet for diagnosis:

(1) Available time: The radiation alarms in the secondary side and the low pressurizer level

indication will alert the operator of the possibility of C-SGTR at least an hour before the

onset of core damage. Extra time is, therefore, assigned with a performance-shaping

factor of 0.1.

(2) An extreme stress condition is expected to be present in SLB combined with C-SGTR

scenarios, since such events are uncommon and the changes in plant parameters will

be rapid. A performance-shaping factor of 5 is assigned.

(3) Procedures are available for SLB and SLB with C-SGTR. However, the transition

between the two procedures and the required monitoring would be difficult. A

performance-shaping factor of 5 is assigned.

(4) All other PSF values were considered to be nominal.

The conditional core damage probability for high-pressure feed-and-bleed scenarios were 

estimated by using the MFW event tree and setting the failure of both the initiator and the failure 

of AFW to true.

The conditional core damage probabilities were then estimated using the SPAR model for 

Shearon Harris PRA and the proposed changes. Tables 7-25 and 7-26 summarize the results of 

these analyses for the example W and CE plants, respectively.
7-71

Table 7-17 Changes in Core Damage Frequency and LERF as a Result of Pressure Induced 

C-SGTR for the Example W Plant 

IE f(IE)

per year

P(CSGTR|IE) P(CD|IE,C

SGTR)

P(LERF|

IE,CSGTR,

CD)

Δ-CDF

per year

Δ-LERF

per year

ATWS-Electrical 1.5E-5 0.01 1.6E-4 1 <1.0E-9 <1.0E-9

ATWS-Failure of Rods 1.2E-6 0.01 1 1 1.2E-8 1.2E-8

SLBIC 1.0E-3 2.50E-3 3.2E-2 0 8.0E-8 0

Spurious Opening of SG 

Relief Valves

3.0E-3 2.50E-3 3.2E-2 1 2.4E-7 2.4E-7

SLBOC 4.0E-5 2.50E-3 3.2E-2 1 3.2E-9 3.2E-9

High-Pressure Feed-andBleed Scenarios2.0E-5 0.01 2.5E-2 1 5.0E-9 5.0E-9

All IEs—Total Contribution 3.4E-7 2.6E-7

These bounding values are deemed to be acceptable. Maintaining a low probability for a large 

flaw to develop during operation via an adequate periodic surveillance program will help to 

control this risk contributor. For example, for a PWR with a total CDF of 2X10-5 per year and 

LERF of 1.0X10-6

, the additional CDF and LERF of 5.3X10-7 and 4.0X10-7 would add less than 

3 percent to CDF and 40 percent to LERF. The LERF contribution is expected to be an order of 

magnitude lower if SAMGs are considered as a part of the PRA analysis. The results indicate 

that the CDF and LERF contribution of pressure-induced C-SGTR cannot be considered 

negligible, although they are within the acceptable ranges, based on these bounding 

estimations for a generic U.S. PWR.

Table 7-18 Changes in Core Damage Frequency and LERF as a Result of Pressure Induced 

C-SGTR for the Example CE Plant 

IE f(IE)

per year

P(CSGTR|IE) P(CD|IE,C

SGTR)

P(LERF|

IE,CSGTR,

CD)

Δ-CDF

per year

Δ-LERF

per year

ATWS-Electrical 1.5E-5 8.0E-3 1.6E-4 1 <1.0E-9 <1.0E-9

ATWS-Failure of Rods 1.2E-6 8.0E-3 1 1 9.6E-9 9.6E-9

SLBIC 1.0E-3 4.0E-3 3.2E-2 0 1.3E-7 0

Spurious Opening of SG 

Relief Valves

3.0E-3 4.0E-3 3.2E-2 1 3.8E-7 3.8E-7

SLBOC 4.0E-5 4.0E-3 3.2E-2 1 5.1E-9 5.1E-9

High-Pressure Feed-andBleed Scenarios2.0E-5 8.0E-3 2.5E-2 1 4.0E-9 4.0E-9

All IEs—Total Contribution 5.3E-7 4.0E-7
7-72

7.5 References 

1. U.S. Nuclear Regulatory Commission, “SCDAP/RELAP5 Thermal-Hydraulic Evaluations

of the Potential for Containment Bypass During Extended Station Blackout Severe

Accident Sequences in a Westinghouse Four-Loop PWR,” NUREG/CR-6995,

March 2010, Agencywide Documents Access and Management System (ADAMS)

Accession No. ML101130544.

2. U.S. Nuclear Regulatory Commission, “State-of-the-Art Reactor Consequence Analyses

(SOARCA), Final Report,” NUREG-1935, November 2012, ADAMS Accession

No. ML12332A057.

3. U.S. Nuclear Regulatory Commission, “Review and Evaluation of the Zion Probabilistic

Safety Study: Plant Analysis,” NUREG/CR-3300, May 1984, ADAMS Accession

No. ML091540533.

4. U.S. Nuclear Regulatory Commission, “Analysis of Core Damage Frequency: Internal

Events Methodology,” Vol. 1, Rev. 1, NUREG/CR-4550, SAND86-2084, January 1990.

5. U.S. Nuclear Regulatory Commission, “Evaluation of Severe Accident Risks:

Methodology for the Containment, Source Term, Consequence, and Risk Integrations

Analyses,” NUREG/CR-4551, December 1993, ADAMS Accession No. ML072710062.

6. U.S. Nuclear Regulatory Commission, “Risk Assessment of Severe Accident-Induced

Steam Generator Tube Rupture,” NUREG-1570, March 1998, ADAMS Accession

Number ML070570094.

7. U.S. Nuclear Regulatory Commission, “Industry-Average Performance for Components

and Initiating Events at U.S. Commercial Nuclear Power Plants,” NUREG/CR-6928,

February 2007, ADAMS Accession No. ML070650650.

8. Lutz, Robert and Melissa Lucci, “Modeling Post-Core Damage Operator Actions in the

PRA,” ANS PSA 2008 Topical Meeting, Knoxville, TN, September 7–11, 2008.
8-1

8 PROBABILISTIC RISK ASSESSMENT CONCLUSIONS 

AND RECOMMENDATIONS 

The conclusions in this chapter are based on the probabilistic risk assessment (PRA) analysis in 

Chapter 7. Chapter 9 summarizes the insights from additional analyses for fission product 

release, discussed in Chapter 3, for the failure of other reactor coolant system (RCS) 

components, discussed in Chapter 4. 

This report documents a method for a quantitative risk assessment of consequential steam 

generator (SG) tube rupture (C-SGTR) during a severe accident, after the onset of core 

damage, and during a design-basis-accident event, before the onset of core damage. The 

method is illustrated with applications to two plants containing replacement SGs with thermally 

treated Inconel Alloy 600 and 690 tubes. Appendix L summarized additional examples of 

C-SGTR risk assessment, using an existing internal-event PRA model.

The focus of this study is on estimating the probability of large early release (LER) because of 

C-SGTR and containment bypass. It applies the simplified methods to two selected 

pressurized-water reactor (PWR) plants: a Westinghouse (W) and a Combustion Engineering 

(CE) design. In addition, the generic stylized models addressed C-SGTR related to pressureinduced C-SGTRs, as discussed in Section 7.4.3 and Appendix C. Section 8.1 provided the 

insights and observations obtained for these applications.

The study used the latest available thermal hydraulics (TH) for both plants, updated flaw 

statistics pertinent to current reactors, and the latest available models and software for 

estimating the failure probability and timings of other SG tubes, as well as RCS components 

(i.e., hot leg (HL) and surge line).

The scope of this study is limited to estimating the probability of containment bypass because of 

C-SGTR and to a bounding assessment of the fraction of containment bypass that constitutes 

LER frequency (LERF). The scope does not include the development of a Level 1 PRA, 

although the study used full Level 1 PRAs for internal and external events to obtain the 

frequency of the sequences related to the C-SGTR.

This study used the existing results from other related research as input. It made no attempt to 

conduct additional research or develop new models. The study is, therefore, limited by the

available supporting analyses and models. These are referred to as limitations of supporting 

analyses for PRA models, as discussed in Section 8.2.

8.1 Insights and Observations 

This study concluded that the overall contribution of C-SGTR scenarios to containment bypass 

is about a factor of 10 larger for the selected CE plant than for the W plant. This conclusion is 

valid because, although the station blackout (SBO) contributions to core damage frequency 

(CDF) are comparable between the two plants, conditional C-SGTR is an order of magnitude 

higher. It further demonstrated that the contribution of C-SGTR to containment bypass is 

negligible for the selected W plant. The study also considered that the size of C-SGTR leaks 

that contribute to LERF is equivalent to the area of at least the guillotine breaks of one tube. 

Moreover, the study concluded that the cleared loop seal, which causes the failure of multiple 

tubes, could be a contributor to C-SGTR for the selected W plant. For the CE plant, multiple 
8-2

tube failures could occur even if the loop seal is not cleared; therefore, loop seal clearing will not 

have significant impact on C-SGTR probability.

This study generally found that the flaw sizes that do not meet the integrity performance criteria 

(e.g., safety factor of 3)10 have a low probability of survival during the severe accident scenarios 

discussed in this report. Table 7-7 showed that the C-SGTR probability for the W plant for large 

flaws with a through-wall depth greater than 0.7 is about 80 percent. Similar tables for the CE 

plant (not included in the report) show a probability close to 1.0.

The estimated frequency of containment bypass was further adjusted to estimate the fraction of 

all containment bypass scenarios that can contribute to LERF. This was done by examining the 

timing of the accident progression for each type of accident scenario to determine if the effective 

evacuation can be credited. The LERF did not include those containment bypass scenarios 

where the releases were expected to occur after an effective evacuation (i.e., late releases). 

The report also identified and discussed the severe accident management guideline (SAMG) 

activities that could mitigate core damage or reduce the release magnitude, although they were 

not credited in further reducing the LERF.

Table 8-1 summarized the high-level quantitative conclusions of the study for both containment 

bypass and LERF. The paragraphs below, based on Sections 7.1.8 and 7.2.6, further discuss 

these results.

Note that the estimates for the frequency of the containment bypass because of C-SGTR and 

LERF, as shown in Tables 8-1a and 8-1b, are for all-hazards CDF sequences, which include 

both the internal events and all external event CDF sequences leading to C-SGTR. Although the 

all-hazards sequence CDF estimates might not be as robust as those for internal events, 

consideration of all-hazards CDF as a measure for comparisons could provide further insights 

for the following reasons:

• Accident sequences for hazard categories other than internal events may have a higher

contribution to multiunit SBOs on sites with multiple units.

• The evacuation times for accident sequences for other hazard categories could be

considerably longer than those for internal events.

• Some important recovery actions credited in internal-event sequences may not be

feasible or may be seriously delayed for other hazard categories.

Section 7.1 discussed and quantified the LERF scenarios for the example W plant. The study 

estimated the conditional C-SGTR (i.e., containment bypass) probability for SBOs with early or 

late failures of turbine-driven auxiliary feedwater (TDAFW) pumps at approximately 0.02, 

excluding the scenarios involving the clearing of the loop seals. This conditional containment 

bypass probability, when multiplied by the CDF of SBO with an early or late failure of TDAFW 

pumps, results in a frequency of 1.5×10-07 per reactor year for both SBO scenarios. Table 8-1 

shows the more precise estimates of the containment bypass frequency. These estimates 

include the contributions of the scenarios in which the loop seals have been cleared. Table 8-1 

shows that the containment bypass frequency estimates are 2.3X10-7 for Inconel 600 and 1.6

X10-7for Inconel 690, considering the internal-event initiators.

10 See the letter transmitting TSTF-449, Revision 4, “Steam Generator Tube Integrity,” dated April 14, 2005 

(Agencywide Documents Access and Management System Accession No. ML051090200).
8-3

Table 8-1 Summary of the Frequency Estimates for Containment Bypass and LERF 

SG 

Type

Tube 

Material

#of 

SGs

EFPY Hazard 

Category

SBO CDF 

Frequency 

(per RY)

Cont.-

Bypass 

Frequency 

per Year

LERF

Fraction 

(%)

LERF

(per RY)

CE 690 2 15 All a 3.3E-5 b 1.0E-5 b 5.6% b 5.7E-7

CE 690 2 15 Internal 1.9E-7 5.7E-8 9.5% 5.4E-9

W 600 4 15 All 2.0E-5 c 8.8E-7 3.7% 3.2E-8

W 600 4 15 Internal 5.2E-6 2.3E-7 3.6% 8.4E-9

W 690 4 15 All 2.0E-5 6.3E-7 3.5% 2.2E-8

W 690 4 15 Internal 5.2E-6 1.6E-7 3.5% 5.8E-9

a “All” refers to the contribution of CDF from internal events, internal flood, fire, and seismic PRA. b From Table 7.2-2, the CDF for short-term SBO (stsbo) and long-term SBO (ltsbo) from all-hazards models are 

~2.6E-6/RY and 3.1E-5/RY, respectively. The total containment bypass (Cont.-Bypass) probability is estimated 

by [(2.6E-6*.22+3.1E-5*.31) = [5.72E-7+9.61E-5] =1.02E-5. The LERF contribution is from the stsbo. It is 

estimated at 5.7E-7 or about 5.6%. c Per the discussion in Section 7.1.5, the probability of C-SGTR is about 1.3E-2 for stsbo with Inconel 600 

materials and 8.9E-3 for Inconel 690. The probability of C-SGTR caused by a cleared loop seal due to reactor 

coolant pump seal failures was also estimated at 2.5E-03. The overall probability of C-SGTR is estimated to be 

about 1.6E-2 and 1.1E-2 for stsbo and for Inconel 600 and 690, and 2.85E-2 and 2.0E-2 for ltsbo and for 

Inconel 600 and 690.

Table 8-2 summarizes the conditional probability of C-SGTR calculated for the base 

cases studied.

Table 8-2 Summary Table for Conditional Probability of C-SGTR Studied as Base Cases 

Conditional Probability of C-SGTR

SG Type SBO with TDAFW 

Pump Failure at Time 

= 0

SBO with AFW 

Failure at Battery 

Depletion

Inconel Material

CE 2.2E-1 3.1E-01 690

W 1.3E-2 (*) 600

W 8.9E-3 (*) 690

* This sequence is not studied as a base case.

Section 7.1 discussed and quantified the LERF scenarios for the example W plant and made 

the following observations:

• For the W plant, the contribution of C-SGTR to containment bypass could be as high as 

9×10-07 per year, considering all hazard categories. If only internal events are 

considered, this value would be 2×10-07 per year or lower.

• Based on the existing PRAs, C-SGTR does not appear to be a major contributor to 

LERF for the example W plant.

• The containment bypass contribution is mainly from the scenarios where the TDAFW 

pump initially worked but was later rendered inoperable after the depletion of batteries. 

Such scenarios are not generally considered as contributors to LERF.
8-4

• It is generally concluded that, for the selected W plant, the C-SGTR and the associated 

LERF do not make any significant contribution, unless large and deep flaws exist in one 

or more SGs.

This study focused on a four-loop W plant and used the design parameters and measurement of 

original W Model 51 SGs. Many of the current operating W plants are equipped with 

replacement SGs with different design features and measurements. The conclusions and 

results noted above, therefore, should be tempered with the specific design of SGs.

Section 7.2 discussed and quantified the LERF scenarios for the example CE plant. The 

conditional containment bypass probabilities from C-SGTR for SBOs with early or late failures of 

TDAFW pumps were about 0.22 and 0.31, respectively. These conditional probabilities of 

containment bypass, when multiplied by the frequency of the entry conditions (i.e., SBO with 

early or late failure of TDAFW pumps (Table 7-14)), resulted in a frequency of approximately 

1.1×10-05 per reactor year for both SBO scenarios (i.e., 9.5×10-06 for SBO scenarios with failures 

of TDAFW pumps after battery depletion and 5.7×10-07 for SBO scenarios with early failure of 

TDAFW pumps). The LERF contribution is from those scenarios where early failures of TDAFW 

pumps occurred. 

The study made the following observations for the CE plant:

• For the selected CE plant, the contribution of C-SGTR to containment bypass could be 

as high as 1.0×10-05, considering contributions from all hazard categories. If only internal 

events are considered, this contribution is expected to be about 5.65×10-08.

• Based on the existing PRAs, C-SGTR appears to be the highest contributor to LERF for 

all hazard models.

• The containment bypass contribution mainly results from the scenarios where the 

TDAFW pumps initially worked but were later rendered inoperable after the depletion of 

batteries. Such scenarios are not generally considered as contributors to LERF.

• Extending the battery life and operation of TDAFW pumps can reduce the frequency of 

containment bypass. This also facilitates the SAMG operation and use of additional 

equipment, such as the existing extensive damage mitigation guidelines or the future 

equipment supplied in response to the FLEX program.

8.2 Limitation of Supporting Analyses for PRA Models 

This PRA study relied on the following existing models and analyses:

• representing variations in tube temperatures by average hot tube and the hottest tube

• TH evaluation of accident sequences

• severe accident analysis

• creep-rupture and fracture-mechanic models for failure of flawed and pristine tubes

• leak-area models for failed tubes

• creep-rupture models and data for HL and surge line

• surveillance data from SG periodic inspections

• material properties at high temperature
8-5

The sections below summarize the status of each of the above elements and their limitations.

8.2.1 Variations in Tube Temperatures by Average Hot Tube and the Hottest Tube 

The tube temperature varies across the tubes and within a tube (along the tube length). This 

temperature profile is varying in a continuous manner. It may be represented with a set of 

temperature bins to capture temperature variations among the tubes and within a tube. The 

larger the number of bins or the higher the bin resolutions, the more calculations and increased 

code capabilities are required. This study currently uses two temperature bins, reflecting the 

average hot tube temperature and the hottest tube temperature. Small uncertainties 

(approximately 0.3 percent) are built into the code to capture slight temperature variations within 

a bin.

8.2.2 TH Evaluation of Accident Sequences 

TH analyses used RELAP code for W plants and MELCOR for CE plants. Consistent use of 

either MELCOR or RELAP for both CE and W plants will provide a better basis for comparing 

the results and will help to better characterize the uncertainties.

8.2.3 Severe-Accident Analysis 

A limited number of MELCOR analyses of severe accidents were available for CE plants to 

address such Level 2 PRA issues as the magnitude of releases. These are in addition to and 

independent of the simple LERF model used in the PRA analysis. Additional MELCOR runs 

informed by PRA assumptions will be needed to develop the Level 2 PRA for C-SGTR for both 

CE and W plants.

8.2.4 Creep-Rupture and Fracture-Mechanic Models 

The creep-rupture and pressure-induced fracture-mechanic models for tube failures are only 

available for tubes with a crack flaw. Wear flaws are the dominant flaw mechanisms for replaced 

SGs. The models for crack flaws do not necessarily apply to wear flaws. This study used a tube 

thinning model to approximate the failure probability of a tube with a wear flaw. Fracture 

mechanics and creep-rupture models for wear flaws, when available, can improve the results of 

this study. For the pristine tubes, fracture-mechanic models are available to predict the tube 

failures but not the resulting leak rates. The study estimated the tube leak rates for wear flaws 

using the equations for the crack flaws with the equivalent flaw sizes. 

8.2.5 Leak-Area Models for Failed Tubes 

The models to predict the resulting leak area from a failed tube are available for a tube with a 

crack flaw. Leak models, however, are not available for failed pristine tubes. The leak areas 

estimated for crack flaws from these models have relatively large uncertainties. The models 

used to predict failures from wear flaws have not yet been studied at the same level as the 

failure models for the cracked flaws. This could result in additional uncertainties. Enhanced 

models to estimate leak areas for a wear flaw can reduce the uncertainties associated with the 

quantitative results.
8-6

8.2.6 Creep-Rupture Models and Data for HL and Surge Line 

The study used Electric Power Research Institute (EPRI) models to predict the failures of HLs 

and surge lines caused by creep rupture in the PRA analysis. Failures were assumed to be 

catastrophic, resulting in a very large leak area. This study neither performed, nor found any 

reference to confirm the EPRI correlations. However, the more detailed analyses performed for 

HL failures, as discussed in Chapter 4, showed consistent results.

8.2.7 Surveillance Data from SG Periodic Inspection 

This study used the most recent data from periodic surveillance inspections to better represent 

the flaw generation rate and characteristics. However, the number of plants with available data 

was quite limited, and the data on flaw size may not be representative. Updating flaw 

characteristics on a periodic basis will not only help the PRA quantification process but will also 

help the U.S. Nuclear Regulatory Commission’s oversight program on SGs.

8.2.8 Material Properties at High Temperature 

The primary circuits, including the SG tubes, are expected to be exposed to high temperatures 

because of severe accidents (after core damage). The study obtained the material properties of 

interest from various sources. Additional work for the same materials for nuclear application 

could improve the prediction of fracture-mechanic models.
9-1

9 OVERALL SUMMARY 

The work documented in this report, performed over multiple years by different disciplines, has 

evolved into its current scope and form during those years because of technical and 

project-related constraints. The main thrust of the report is on estimating the potential 

consequential steam generator tube rupture (C-SGTR) risk in different types of steam 

generators (SGs), using quantitative probabilistic risk assessment (PRA) methods. In parallel 

with this PRA work, the report includes two other types of analyses: thermal-hydraulic (TH) 

analyses and structural analyses. Thus, these three types of independent analyses make up the 

report’s contents.

The objective of this chapter is to summarize the nature and conclusions of the three types of 

analyses mentioned above. The following chapters contain these: 

• Chapter 7 and 8 for PRA

• Chapter 3 for TH using MELCOR for a Combustion Engineering (CE) plant

• Chapter 4 for structural analyses of other reactor coolant system (RCS) components

The conclusions of these three analyses appear at the end of this section, following a 

discussion of some of the modeling aspects.

Chapter 2 defines three basic modeling pieces to define and focus the scope of PRA work:

• accident sequences to be modeled

• “critical tube-leak size” for PRA purposes

• a large early release frequency (LERF) model for PRA purposes

In Chapter 3, MELCOR software is used to model key accident sequences for a CE plant. This 

work, carried out specifically for this project, can be viewed in terms of two parts:

(4) generation of accident sequence TH parameters (e.g., pressure and temperature 

as a function of time)

(5) estimation of fission product (FP) release characteristics for these sequences

The results of the first part serve as input into the PRA model, which Chapter 7 documents. 

Additionally, MELCOR is used for calculating FP release characteristics. This information is not 

used in PRA models for the following reasons:

• the PRA model uses a more advanced flawed tube model, whereas MELCOR modeled 

tube flaws using stress multiplication factors

• definition of what constitutes a C-SGTR (critical size, failure of other RCS components)

• definition of a LERF model in PRA as a surrogate to model FP release

The PRA analysis takes the accident sequence TH parameters for the example Westinghouse 

(W) plant from NUREG/CR-6995 (Ref. 1), “SCDAP/RELAP5 Thermal-Hydraulic Evaluations of 

the Potential for Containment Bypass During Extended Station Blackout Severe Accident 

Sequences in a Westinghouse Four-Loop PWR,” issued March 2010, which used 
9-2

SCDAP/RELAP5 for analysis. Chapter 3 contains the accident sequence TH parameters for the 

example CE plant, generated by MELCOR.

Conclusions about FP release characteristics for a CE plant, as discussed in Chapter 3, versus 

those in Chapters 7 and 8, should be viewed in light of the independent modeling assumptions 

for MELCOR analyses and PRA models.

The PRA model includes credit for the failure of another RCS component before the failure of 

SG tubes, thus resulting in a lesser release consequence. The PRA model uses an existing hotleg (HL)/surge-line failure model developed by the Electric Power Research Institute. Chapter 4 

contains later confirmatory work in structural analysis using more state-of-the art modeling on W 

sequences. It should be noted that the PRA calculations did not include the confirmatory work 

models and their results discussed in Chapter 4.

Although the PRA models focused on the “temperature-induced” C-SGTR sequences (after 

occurrence of core damage) caused by creep rupture, the report models two types of tube 

failure correlations:

(1) a high-pressure, low-temperature (e.g., below creep-rupture range) correlation

(2) a high-temperature correlation for temperatures in the creep-rupture range

The second correlation was not deemed suitable at lower temperatures with high pressure. 

Section 7.4 discusses the risk estimates for potential pressure-induced C-SGTR sequences 

(such as anticipated transients without scram and large steamline breaks). Such sequences 

might contribute to additional core damage frequency, as opposed to temperature-induced 

C-SGTR sequences, which are initiated by already identified core damage sequences. It

requires very large pressure differences across the SG tubes at lower temperatures to cause

the failure of flawed tubes, and the contribution of pressure-induced sequences to plant core

damage frequency is not expected to be significant, since the probability that a tube with a deep

flaw (e.g., more than 70-percent deep) exists in at least one SG is quite low.

Another new analysis, in Chapter 6, is the generation of tube-flaw distributions for thermally 

treated Alloy 600 and 690 material used in replacement SGs of the current fleet of plants. These 

distributions are generated from a limited set of SG inspection reports submitted to the 

U.S. Nuclear Regulatory Commission. The analysis resulted in the following observations on 

these tube materials:

• There were mostly “wear-type” flaws (volumetric, as opposed to the circumferential and

axial cracks found in the previous generation of SG tubes).

• Some cracks (i.e., crack flaws) started to appear around the 15th effective full-power

year of operation in thermally treated 600 Inconel tubes.

The PRA model uses the 15-year flaw distribution as the base criterion to make estimates and 

comparisons. SG tubes with fewer years of operation will have more favorable estimates and 

vice versa.

Software referred to as the C-SGTR calculator was developed to support the work in this report. 

The calculator is used to estimate failure times and leak sizes of SG tubes with different types of 

flaws. The software also has built-in models for HL and surge-line failure because of the 

creep-rupture failure mechanism, and it estimates HL and surge-line failure times and 
9-3

probabilities. The scope of the models currently includes new SG tube materials and the 

associated property data for both thermally treated Inconel 600 and 690. Appendix B briefly 

discusses this calculator.

9.1 PRA Conclusion Insights 

The main PRA conclusion is that the conditional probability of creep rupture of C-SGTR in core 

damage scenarios with high primary pressure, dry SGs, and low secondary pressure (HDL) is 

about a factor of 10 larger for plants with shallow inlet SG plenum (e.g., the selected CE plant) 

than the plants with deep inlet SG plenum (e.g., the example W plant). The contribution of HDL 

scenarios to core damage and subsequently to LERF, from creep-rupture failure of SG tubes, is 

driven by the plant-specific design and operational features (e.g., availability of two trains of 

TDAFW pumps). 

Previous conclusions on the effect of “loop seal clearing” are not changed; for any of the SG 

geometries, if loop seal clearing occurs in an accident sequence (such as the one caused by a 

large reactor coolant pump (RCP) seal leak), the tube failures are expected to happen early. 

The TH analysis reported in NUREG/CR-6995 indicated that the probability that the loop seal is 

cleared is almost certain if the RCP leakage is about 1,700 liters per minute (Lpm) (450 gpm). 

For RCP seal leakage of 1,135 Lpm (300 gpm), the TH analysis predicted no possibility that the 

loop seal is cleared.

9.2 Conclusion on Other RCS Components (from Chapter 4) 

The analyses in Section 4.4 indicated that the upper half of the HL will fail much earlier than the 

other RCS regions. Table 4.4 summarized the failure times predicted by the various analyses 

considered in Section 4.4. The predicted failure times for all the cases considered are below the 

median failure time of 12,600 seconds estimated by the C-SGTR calculator, but not excessively 

so. Therefore, the C-SGTR calculator provides a reasonable estimation of HL failure.

9.3 MELCOR Conclusions for CE Plant 

CE plants with replacement SGs receive additional scrutiny because their geometry is more 

susceptible to C-SGTR than the W designs. The short HL length-to-diameter ratio and relatively 

shallow SG inlet plena in some replacement SGs results in high-temperature gas reaching the 

SG tubes during closed-loop-seal natural circulation conditions. Hotter gases reaching the SG 

tube reduce the time before tube failure, which increases the likelihood of containment bypass. 

A station blackout (SBO) is the situation in which thermally induced C-SGTR is expected to 

occur. A few aspects of the scenario are of interest in determining FP releases to the 

environment: (1) whether an SG tube or some other part of the RCS pressure boundary fails 

first, and (2) whether tube failure results in sufficient and rapid enough RCS depressurization to 

prevent rupture of some other part of the RCS boundary. In the W analysis, the presence of a 

flaw is required for the prediction of tube failure before other RCS component failures. For a W 

plant, failure of a single tube does not depressurize the primary at a rate sufficient to prevent the 

subsequent failure of other RCS components. However, the possibility of multiple tube failures 

exists in CE plants, which could result in primary depressurization. Unlike the W example, the 

unflawed tubes exposed to the relatively unmixed hot gases that reach the SG tubes in CE 

designs with shallow-inlet-plenum replacement SGs can also fail multiple tubes, which can 

depressurize the RCS sufficiently to prevent the creep-rupture failure of other components, thus 

leaving the containment bypass pathway as the sole release path of FPs from the reactor.
9-4

The MELCOR analyses were performed somewhat independently from the PRA, with their own 

set of assumptions and conclusions. These are summarized below.

The relatively shallow inlet plenum design of the replacement SG under consideration for the 

CE plant has an impact on the results of the computational fluid dynamic predictions. The 

shallow design limits the mixing of the hot gases that enter the SG, which creates a higher 

thermal load on the tubes.

The study reached the following conclusions:

• Even if an SGTR occurs before HL failure, as long as no failure or intentional opening of

relief valves follows, the magnitude of release through the repeated cycling of relief

valves is expected to be small, as indicated by the MELCOR runs. This conclusion

differs from the PRA, which conservatively assumes all releases will be significant

enough to be considered as LERF (i.e., the relief valves are assumed to stick open

rather than continue cycling).

• For a high-pressure secondary-side (high-dry-high situation) scenario, an HL will fail

before an unflawed tube fails, thus preventing multiple unflawed tube failures. This

conclusion is consistent with PRA calculations.

9.4 References 

1. U.S. Nuclear Regulatory Commission, “SCDAP/RELAP5 Thermal-Hydraulic Evaluations

of the Potential for Containment Bypass During Extended Station Blackout Severe

Accident Sequences in a Westinghouse Four-Loop PWR,” NUREG/CR-6995,

March 2010, Agencywide Documents Access and Management System (ADAMS)

Accession No. ML101130544.
A-1

APPENDIX A 

 

HIGH-TEMPERATURE DEFORMATION AND DAMAGE OF REACTOR 

COOLANT SYSTEM MATERIALS 

A.1 Material Properties Used in Chapter 4 

Section A-2 gives the results of a literature search conducted for high-temperature material 

properties data that are needed to carry out the analyses. Table A-1 lists the various 

components in the Zion Nuclear Power Plant (ZNPP) that were analyzed, the materials used, 

and the range of temperatures for which high-temperature tensile and creep properties were 

initially collected. The table identifies gaps in the required database, which Argonne National 

Laboratory (ANL) partially filled by conducting a materials testing program during the follow-on 

program funded by the U.S. Nuclear Regulatory Commission (NRC) to obtain high-temperature 

tensile and creep properties of materials identified in Table A-1. Section A.2 contains the details 

of the test results. The base materials tested were as follows:

• SA 516 Grade 70 carbon steel

• SA 240 Grade 316 stainless steel

• SA 351 Grade CF8M cast stainless steel

• SA 193 B7 bolt material

In addition, the program tested the following weldments:

• stainless (SA 240 Grade 316) steel plate to carbon steel (SA 516 Grade 70) 

plate weldment

• wrought stainless (SA 240 Grade 316) plate to cast stainless steel (SA 351 

Grade CF8M) plate weldment

• stainless (SA 240 Grade 316) steel plate to stainless (SA 240 Grade 316) steel 

plate weldment

Table A-2 gives the temperature range for the various tests.
A-2

Table A-1 Range of Temperatures (°C) for which High-Temperature Material Properties 

Data Are/Are Not Available

RCS 

Component Material

Tensile Properties Creep Properties

Stress–

Strain 

Curves

Tensile 

Strengths

Creep Rate Rupture 

Time

Piping, 

RTD Body

PORV plug

SA 240 Grade 

Type 316 SS 400–982 400–1093 538–816 427–1093

HL Elbow SA 351 Grade

CF8M 400–871 538–649 454–1000

Surge Line to 

HL Nozzle

SA 182

F316 Not found 400–538 Not found 549–699

Weld 308 SS 565 482–593 593 454–704

RV Nozzle A–508 Class 2 Not found 400–727 627–752 627–95

SG and PZR 

Nozzles

SA 216

WCC Not found 400–538 Not found Not found

Manway Cover SA 533 A1

(SA 533 B1)

Not found

(649–1200)

400–538

(400–1200)

Not found

(400–1100)

Not found

(400–1100)

Manway Insert Type 304 SS 700–1100 400–1100 427–1077 538–1077

Manway Bolts A 193 (B7) Not found Not found Not found Not found

PORV Cage

SA 564 

(17–4PH) 

H1100

Not found 400–538 Not found Not found

Table A-2 Materials and Temperature Ranges (°C) over which Materials Properties Data 

Were Generated by ANL

Material

Tensile Properties Creep Properties

Stress–

Strain 

Curves

Tensile 

Strengths

Creep 

Rate

Rupture 

Time

SA 240 Grade Type 316 SS 700–1100 700–1100 700–1100 700–1100

SA 351 Grade

CF8M 700–1000 700–1000 700–1000 700–1000

SA 516 Grade 70

Carbon steel 500–800 500–800 500–800 500–800

SA 193 B7 Bolts 450–650 450–650 450–650 450–650

SA 240 Grade 316 to SA 516 

Grade 70 weldment 700–1000 700–1000 700–1000 700–1000

SA 240 Grade 316 to SA 240 

Grade 316 weldment 700–1000 700–1000

SA 240 Grade 316 to SA 351 

Grade CF8M weldment 700–1000 700–1000
A-3

A.2 High-Temperature Creep-Rupture Test Data 

Bolt Material (SA 193 B7)

Table A-3 lists all of the bolt creep tests, which were run in duplicate. Because our interest is in 

station blackout (SBO) severe accidents, which last several hours, tests that did not fail by 

100 hours (h) were interrupted. Creep curves at 450, 550, and 650 degrees Celsius (C) (842, 

1,022, and 1,202 degrees Fahrenheit (F)) are given in Figures A-1a to A-1c, respectively. Note 

that, although the tests at 450 and 550 degrees C (842 and 1,022 degrees F) experienced 

primary creep, those at 650 degrees C (1,202 degrees F) did not.

Table A-3 Summary of Creep Data for SA 193 B7 Bolt Material

Specimen 

No.

Temperature 

°C (°F)

Stress

ksi (MPa)

Rupture 

Time (h)

% Elongation %

RA

Minimum Creep 

Rate (%/h)

B-4 450 (842) 40 (276) * 100 - - 0.0031

B-5 450 (842) 40 (276) * 100 - - 0.0026

B-22 450 (842) 30 (207) * 100 - - 0.0013

B-7 450 (842) 30 (207) * 100 - - 0.0013

B-8 450 (842) 20 (138) * 100 - - 0.0007

B-9 450 (842) 20 (138) * 100 - - 0.0004

B-10 550 (1022) 30 (207) 57.9 49.4 78.2 0.2923

B-11 550 (1022) 30 (207) 53.1 48.2 78.8 0.3071

B-12 550 (1022) 20 (138) * 100 - - 0.0354

B-13 550 (1022) 20 (138) * 100 - - 0.0377

B-14 550 (1022) 10 (69) * 100 - - 0.0033

B-15 550 (1022) 10 (69) * 100 - - 0.0043

B-16 650 (1202) 20 (138) 0.8 73.1 89.3 -

B-17 650 (1202) 20 (138) 0.8 56.9 87.6 27.0500

B-18 650 (1202) 10 (69) 17.5 96.8 89.8 1.6283

B-19 650 (1202) 10 (69) 17.7 85.8 89.1 1.6456

B-20 650 (1202) 7.5 (52) 40.2 87.7 91.9 0.8178

B-21 650 (1202) 7.5 (52) 45.4 91.3 88.1 0.7560

* Test interrupted
A-4

 (a) (b)

 (c)

Figure A-1 Creep curves for SA 193 B7 material at (a) 450 oC, (b) 550 oC, (c) 650 oC 

The built-in equation for the creep strain rate in the finite-element program ABAQUS can be 

either in the time-hardening form; that is,

(0a)

or in the strain-hardening form; that is,

(1b)

where A, n, and m are functions of temperature, σ is stress, is creep strain, is creep 

strain rate, and t is time. An integrated version of the creep rate equation is

(0a)

where . Writing Eq. 2 in an Arrhenius form,

(2b)
A-5

where T is absolute temperature, Q is a fitting parameter, and B = B0exp(Q/T). Equation 2b was 

used to determine the parameters B, m, Q, and n from the creep tests. Table A-4 tabulates the 

best-fit parameters, with creep strain εc in m/m, stress σ in kilopounds per square inch (ksi), 

time t in h, and absolute temperature T in K. The fitted creep curves are compared with the test 

curves in Figures A-2 to A-4. Except for a few tests, the fit in the first 2 hours, which is of interest 

for SBO severe accidents, is reasonable.

Table A-4 Best-Fit Values of the Parameters B, m, Q, and n of SA 193 B7 As Determined 

from the Creep Tests

T (°C) B m Q A N

450 16800 -0.501 17300 3.45E-7 1.80

550 16600 -0.363 19700 6.5E-7 2.60

650 26000 -0.187 18700 3.19E-5 2.78

 (a) (b)

 (c)

Figure A-2 Comparison of fitted and test variation of creep strain vs. time for creep tests 

conducted on SA 193 B7 at 450 degrees C at (a) 20 ksi (138 MPa), (b) 30 ksi 

(207 MPa), and (c) 40 ksi (278 MPa)
A-6

(a) (b)

(c)

Figure A-3 Comparison of fitted and test variation of creep strain vs. time for creep tests 

conducted on SA 193 B7 at 550 degrees C at (a) 10 ksi (69 MPa), (b) 20 ksi 

(138 MPa), and (c) 30 ksi (207 MPa)

(a) (b)

(c)

Figure A-4 Comparison of fitted and test variation of creep strain vs. time for creep tests 

conducted on SA 193 B7 at 650 degrees C at (a) 7.5 (52 MPa), (b) 10 (69 MPa), 

and (c) 20 ksi (138 MPa)

SA 240 Grade 316 Stainless Steel
A-7

Table A-5 is a summary of all the creep tests, all of which were run in duplicate. Figures A-4 to 

A-6 plot the representative creep strain vs. time curves at 700, 800, 1,000, and 1,100 degrees C 

(1,292, 1,472, 1,832, and 2,012 degrees F). In most cases, primary creep is absent and the 

tests show either a steady-state creep behavior or a steady state followed by tertiary creep 

behavior. All available U.S. creep rate data were fitted to Eq. 1a, to obtain the parameters A, n, 

and m at various temperatures, as listed in Table A-6. The fitted creep rates are plotted against 

the test creep rates in Figure A-7, which shows that the bulk of the creep rate data can be 

predicted to within a factor of 4.8, and the ANL data fall within the scatter band of the much 

larger database.

Table A-5 Summary of Creep Data for SA 240 Grade 316 Stainless Steel

Specimen 

No.

Temperature 

°C (°F)

Stress

ksi (MPa)

Rupture 

Time (h)

% Elongation %

RA

Minimum Creep 

Rate (%/h)

O-4 700 (1292) 30 (207) 7.2 49.5 80.9 -

O-5 700 (1292) 30 (207) 7.0 51.5 81.7 2.99

O-10 700 (1292) 28 (193) 12.3 61.2 81.2 2.40

O-11 700 (1292) 28 (193) 14.5 48.4 84.0 1.25

O-16 700 (1292) 26 (179) 31.3 51.6 76.8 0.70

O-17 700 (1292) 26 (179) 28.6 54.1 80.9 0.73

O-6 800 (1472) 19.0 (131) 2.4 64.7 89.0 -

O-7 800 (1472) 19.0 (131) 2.4 61.0 88.4 -

O-12 800 (1472) 15.0 (103) 14.2 67.0 86.8 1.44

O-13 800 (1472) 15.0 (103) 12.9 70.3 89.1 1.68

O-18 800 (1472) 13.0 (90) 35.4 82.9 89.4 0.73

O-19 800 (1472) 13.0 (90) 30.6 84.0 89.7 0.85

O-14 1000 (1832) 4.0 (28) 11.5 75.7 88.2 0.70

O-15 1000 (1832) 4.0 (28) 10.3 76.6 89.8 1.11

O-20 1100 (2012) 2.0 (14) *100 - - 0.079

O-21 1100 (2012) 2.0 (14) *100 - - 0.079

O-8 1100 (2012) 4.0 (28) 0.5 75.6 91.3 -

O-9 1100 (2012) 4.0 (28) 0.6 82.7 90.8 -

* Test interrupted
A-8

 (a) (b)

Figure A-5 Creep strain vs. time curves of SA 240 Grade 316 stainless steel at 

700 degrees C (a) 26 ksi (179 MPa) and (b) 28 ksi (193 MPa) and 30 ksi 

(207 MPa)

 (a) (b)

Figure A-6 Creep strain vs. time curves of SA 240 Grade 316 stainless steel at 800 oC 

(a) 13 ksi (90 MPa) and (b) 15 ksi (103 MPa)
A-9

Table A-6 Creep Rate Parameters for Available Data on Type 316 Stainless Steel

Mean and ±95% confidence bounds at various temperatures

(stress in ksi and creep rate in 1/h)

T (°C) m N A (mean) A(-95%) A (+95%)

350 0 9.35 4.4925E-30 9.3594E-31 2.1564E-29

450 0 9.35 1.1269E-24 2.3478E-25 5.4093E-24

500 0 9.35 1.6894E-22 3.5195E-23 8.1090E-22

550 0 9.35 1.3778E-20 2.8703E-21 6.6133E-20

600 0 9.35 6.7869E-19 1.4139E-19 3.2577E-18

650 0 9.35 2.1918E-17 4.5663E-18 1.0521E-16

675 0 8.80 9.8651E-16 2.0552E-16 4.7352E-15

700 0 7.20 2.7813E-13 5.7945E-14 1.3350E-12

750 0 6.52 3.9794E-11 8.2904E-12 1.9101E-10

800 0 6.52 3.8282E-10 7.9755E-11 1.8376E-09

850 0 6.52 3.3115E-09 6.8990E-10 1.5895E-08

900 0 6.52 2.3829E-08 4.9643E-09 1.1438E-07

1000 0 6.52 7.4218E-07 1.5462E-07 3.5625E-06

1100 0 6.52 1.2748E-05 2.6558E-06 6.1190E-05

 (a) (b)

Figure A-7 Creep strain vs. time curves of SA 240 Grade 316 stainless steel at 

(a) 1,000 oC, 4 ksi (28 MPa) and (b) 1,100 oC, 2 ksi (14 MPa)
A-10

Figure A-8 Predicted vs. test minimum creep rate of SA 240 Grade 316 stainless steel

The available time-to-stress-rupture U.S. data for Grade 316 stainless steel were fitted with a 

Larson-Miller parameter, as shown in Figure A-9. In equation form, the Larson-Miller plot is 

given by

(A0)

and the time to rupture tR in h is given by

(A0) 

where T = temperature in K. Figure A-9 also shows the parameter values for ±95-percent 

confidence limits. The predicted times to rupture are plotted against test rupture times in 

Figure A-10, which shows that the bulk of the data can be predicted to within a factor of 6.
A-11

Figure A-9 Larson-Miller parameter plot for time to stress rupture of SA 240 Grade 316 

stainless steel at 538–1,100 oC

The steady-state creep ductility, defined as the product of the steady-state (or minimum) creep 

rate and the time to rupture, is plotted as a function of stress and temperature in Figures A-11 to 

A-14. There is significant scatter in the data but no definite trend as a function of stress. 

However, the steady-state ductility shows an increase with increasing temperature and leveling 

off at high temperatures, as shown in Figure A-15.

Figure A-10 Predicted vs. test time to stress rupture of SA 240 Grade 316 stainless steel 

at 538–1,100 oC
A-12

(a) (b)

Figure A-11 Steady-state creep ductility vs. stress of SA 240 Grade 316 stainless steel at 

(a) 538 oC and (b) 566 oC

(a) (b)

Figure A-12 Steady-state creep ductility vs. stress of SA 240 Grade 316 stainless steel at 

(a) 593 oC and (b) 649 oC
A-13

(a) (b)

Figure A-13 Steady-state creep ductility vs. stress of SA 240 Grade 316 stainless steel at 

(a) 700 oC and (b) 760 oC

Figure A-14 Steady-state creep ductility vs. stress of SA 240 Grade 316 stainless steel 

at 800 oC
A-14

Figure A-15 Estimated mean, upper, and lower bounds to the steady-state creep ductility 

of SA 240 Grade 316 stainless steel

SA 351 Grade CF8M Cast Stainless Steel

Table A-7 summarizes the creep tests conducted at ANL. Representative creep strain vs. time 

curves at 700, 800, and 1,000 degrees C are plotted in Figures A-16 to A-18. In many cases, 

primary creep is absent, and the tests show either a steady-state creep behavior or a steady 

state followed by tertiary creep behavior. The available creep database for CF8M cast stainless 

steel is rather limited. Harada in Japan has reported creep data on CF8M cast stainless steel. 

The combined creep-rate data were fitted to Eq. 1a to obtain the parameters A, n, and m at 

various temperatures, as listed in Table A-8. The fitted creep rates are plotted against the test 

creep rates in Figure A-19a, which shows that the bulk of the creep rate data can be predicted 

to within a factor of 10.7. The uncertainty is larger than SA 240 Grade 316 stainless steel 

because of the much more limited database available for SA 351 Grade CF8M cast stainless 

steel. Note that the ANL data fall within the scatter band of the combined data base.
A-15

Table A-7 Summary of Creep Data for SA 351 Grade CF8M Cast Stainless Steel

Specimen No. Temperature

°C (°F)

Stress

ksi (MPa)

Rupture Time 

(h)

% Elongation %

RA

Minimum 

Creep Rate 

(%/h)

ATLAS-4 700 (1292) 15 (103) 60.9 8.4 24.3 7.46E-02

ATLAS-5 700 (1292) 15 (103) * 100.0 - - 9.04E-02

ATLAS-10 700 (1292) 17 (117) 8.0 5.7 18.9 1.67E-01

ATLAS-13 700 (1292) 17 (117) 7.5 3.4 7.9 2.49E-01

ATLAS-14 700 (1292) 16 (110) 0.5 3.5 14.3 -

ATLAS-15 700 (1292) 16 (110) 29.2 8.4 18.3 1.40E-01

ATLAS-6 800 (1472) 14 (97) 2.1 13.5 19.7 3.88E+00

ATLAS-7 800 (1472) 14 (97) 1.3 10.4 30.8 4.32E+00

ATLAS-11 800 (1472) 12 (83) 1.3 5.2 10.0 2.20E+00

ATLAS-16 800 (1472) 12 (83) 0.7 10.0 18.3 -

ATLAS-17 800 (1472) 10 (69) 0.9 5.3 8.6 -

ATLAS-18 800 (1472) 10 (69) 7.4 12.5 23.0 8.81E-01

ATLAS-8 1000 (1832) 6 (41) 0.1 13.1 29.9 -

ATLAS-9 1000 (1832) 6 (41) 0.1 8.9 16.4 -

ATLAS-12 1000 (1832) 3 (21) 13.3 19.1 26.9 1.19E+00

ATLAS-19 1000 (1832) 3 (21) 0.9 9.1 17.0 1.96E+00

ATLAS-20 1000 (1832) 2 (14) * 100.0 - - 9.96E-02

ATLAS-21 1000 (1832) 2 (14) 14.1 5.8 12.8 2.58E-01

* Test interrupted

 (a) (b)

Figure A-16 Creep strain vs. time curves of SA 351 Grade CF8M cast stainless steel at 

700 oC (a) 15–16 ksi (103–110 MPa) and (b) 17 ksi (117 MPa)
A-16

 (a) (b)

Figure A-17 Creep strain vs. time curves of SA 351 Grade CF8M cast stainless steel at

800 oC (a) 12 and 14 ksi (83–97 MPa) and (b) 10 ksi (69 MPa)

 (a) (b)

Figure A-18 Creep strain vs. time curves of SA 351 Grade CF8M cast stainless steel at 

1,000 oC (a) 3 ksi (21 MPa) and (b) 2 ksi (14 MPa)
A-17

Table A-8 Mean and ±95% Confidence Bounds of Creep-Rate Parameters for Combined 

ANL and Japanese Data on SA 351 Grade CF8M Cast Stainless Steel at 

Various Temperatures (Stress in ksi and Creep Rate in 1/h)

T (°C) m n A (mean) A (-95%) A (+95%)

350 0 9.5 5.233E-25 5.599E-24 4.891E-26

450 0 9.5 5.866E-21 6.276E-20 5.482E-22

500 0 9.5 2.513E-19 2.689E-18 2.349E-20

550 0 9.5 6.820E-18 7.297E-17 6.374E-19

600 0 9.5 1.268E-16 1.357E-15 1.185E-17

650 0 9.5 6.919E-16 7.403E-15 6.466E-17

700 0 9.5 3.585E-15 3.836E-14 3.351E-16

750 0 8.7 2.661E-13 2.847E-12 2.487E-14

800 0 5.0 2.003E-08 2.143E-07 1.872E-09

850 0 5.0 4.609E-07 4.932E-06 4.308E-08

900 0 5.0 3.357E-06 3.592E-05 3.137E-07

950 0 5.0 2.281E-05 2.441E-04 2.132E-06

1000 0 5.0 1.143E-04 1.223E-03 1.068E-05

1050 0 5.0 6.393E-04 6.841E-03 5.975E-05

1100 0 5.0 3.156E-03 3.376E-02 2.949E-04

The available time to stress rupture for the combined Japanese and U.S. data for SA 351 

Grade CF8M cast stainless steel were fitted with a Larson-Miller parameter, as shown in 

Figure A-19b. In equation form, the Larson-Miller plot is given by

(A0)

where stress σ is in ksi and the time to rupture tR in h is given by

(A0)

where T = temperature in K. Figure A-19b also shows the parameter values for ±95-percent 

confidence limits. Figure A-20 plots the predicted times to rupture against test rupture times, 

which shows that the bulk of the combined data can be predicted to within a factor of 4.8.

The steady-state ductility of the ANL CF8M specimens is considerably less than that of the 

Japanese CF8M heat (Figure A-21a) and also much less than that of the SA 240 Grade 316 

stainless steel (Figure A-15). The total elongation of the U.S. CF8M heat is comparable to the 

steady-state ductility of the Japanese CF8M heat (Figure A-21b).
A-18

 (a) (b)

Figure A-19 Confidence bounds for the prediction of (a) creep rate and (b) Larson-Miller 

parameter for time to rupture of SA 351 Grade CF8M cast stainless steel 

based on ANL and Japanese data

Figure A-20 Predicted vs. observed time to stress rupture of SA 351 Grade CF8M cast 

stainless steel
A-19

 (a) (b)

Figure A-21 Variation of (a) steady-state ductility of U.S. and Japanese CF8M heats and 

(b) total elongation of U.S. CF8M heat with stress

SA 516 Grade 70 Carbon Steel

Table A-9 summarizes the creep-rupture tests conducted at ANL. The creep curves at 500, 650, 

and 800 degrees C (932, 1,202, and 1,472 degrees F) are plotted in Figures A-22a to A-22c, 

respectively. The ANL data for SA 516 Grade 70 were combined with available data for SA 216 

Grade WCC from the literature and the combined data fitted to Eq. 1a to obtain the parameters 

A, n, and m at various temperatures, as listed in Table A-10. Figure A-23a shows that the 

combined creep-rate data can be predicted to within a factor of 3 by using Eq. 1a and the 

parameters listed in Table A-10. Although the data sets are limited, both fall within the same 

scatter band.

The available time to stress rupture for the combined ANL data for SA 516 Grade 70 and 

literature data on SA 216 Grade WCC carbon steels were fitted with a Larson-Miller parameter, 

as shown in Figure A-23b. In equation form, the Larson-Miller plot is given by

(A0)

where stress σ is in ksi and the time to rupture tR in h is given by

, (A0)

where T = temperature in K. Figure A-23b also shows the parameter values for ±95-percent 

confidence limits. Figure A-24a plots the predicted times to rupture against test rupture times, 

which shows that the bulk of the combined data can be predicted to within a factor of 4.9. The 

steady-state creep ductility of SA 216 is 2–5 percent at 500 degrees C (932 degrees F) but 

increases with temperature to greater than 10 percent at 650 and 800 degrees C (1,202 and 

1,472 degrees F) (Figure A-24b).
A-20

Table A-9 Summary of Creep Data for SA 516 Grade 70 Carbon Steel

Specimen No. Temperature 

°C (°F)

Stress

ksi (MPa)

Rupture 

Time (h)

% Elongation%

RA

Minimum 

Creep Rate 

(%/h)

6-4 500 (932) 40 (276) 4.70 17.20 37.40 1.01

6-5 500 (932) 40 (276) 5.90 21.00 42.00 0.81

6-10 500 (932) 38 (262) 8.70 24.90 44.00 0.49

6-13 500 (932) 38 (262) 7.40 16.20 41.50 0.50

6-14 500 (932) 35 (241) 15.90 22.20 44.00 0.17

6-15 500 (932) 35 (241) 11.10 23.50 47.00 0.18

6-6 650 (1202) 18.5 (128) 0.20 60.90 77.50 -

6-7 650 (1202) 18.5 (128) 0.10 69.90 79.30 -

6-11 650 (1202) 15.5 (107) 0.50 69.40 77.00 28.23

6-16 650 (1202) 14 (97) 1.60 59.50 78.00 5.36

6-17 650 (1202) 12 (83) 3.60 65.00 77.60 3.21

6-19 650 (1202) 10 (69) 9.10 76.70 17.00 1.02

6-8 800 (1472) 9 (62) 0.20 42.80 41.50 -

6-9 800 (1472) 9 (62) 0.10 43.70 29.90 -

6-12 800 (1472) 7 (48) 0.60 45.90 16.40 36.40

6-18 800 (1472) 5 (34) 3.30 48.50 26.90 4.81

6-20 800 (1472) 5 (34) 3.10 46.20 - 5.72

6-21 800 (1472) 4 (28) 6.40 50.10 12.80 1.94
A-21

 (a) (b)

 (c)

.

Figure A-22 Creep curves for SA 516 Grade 70 carbon steel at (a) 500 oC, (b) 650 oC, and 

(c) 800 oC
A-22

Table A-10 Creep-Rate Parameters for Combined ANL and Literature Data on 

SA 216 Grade 70 and SA 216 Grade WCC Carbon Steels

Mean and ±95% confidence bounds at various temperatures

(stress in ksi and creep rate in 1/h).

T (°C) m n A (mean) A(-95%) A (+95%)

300 0 5.439 4.844E-19 1.615E-19 1.453E-18

400 0 5.439 8.654E-15 2.885E-15 2.596E-14

500 0 5.439 1.228E-11 4.092E-12 3.683E-11

550 0 5.439 2.387E-10 7.955E-11 7.159E-10

600 0 5.439 3.303E-09 1.101E-09 9.907E-09

650 0 5.439 3.438E-08 1.146E-08 1.031E-07

700 0 5.439 2.813E-07 9.377E-08 8.439E-07

750 0 5.439 1.874E-06 6.248E-07 5.623E-06

800 0 5.439 1.046E-05 3.488E-06 3.139E-05

850 0 5.439 5.013E-05 1.671E-05 1.504E-04

900 0 5.439 2.101E-04 7.004E-05 6.304E-04

950 0 5.439 7.834E-04 2.611E-04 2.350E-03

1,000 0 5.439 2.634E-03 8.779E-04 7.901E-03

(a) (b)

Figure A-23(a) Predicted vs. observed creep rates

Figure A-23(b) Larson-Miller plot for time to stress rupture of SA 516 Grade 70 and

SA 216 Grade WCC
A-23

(a) (b)

Figure A-24(a) Predicted vs. observed time to stress rupture

Figure A-24(b) Variation of steady-state ductility with stress and temperature of 

carbon steels

SA 240 Grade 316/SA 516 Grade 70 Weldment

Table A-11 summarizes the creep tests conducted on SA 240 stainless steel/SA 516 carbon 

steel. Since the strain distribution in the gauge length is nonuniform, the strain and minimum 

creep-rate data reported in the table represent average values over the entire gauge length, 

with significantly more strain occurring in the carbon steel than in the stainless steel half. The 

primary purpose of these tests was to determine the loss of ductility and time to rupture of the 

weldment relative to the base metals. At 700 degrees C (1,292 degrees F), most of the failure 

occurred in the weaker SA 516 carbon steel by ductile necking away from the weld. Even in the 

single specimen (6W-14) in which failure occurred at the weld interface, necking is visible in the 

carbon steel away from the weld. At 800 degrees C (1,472 degrees F), all of the failure occurred 

by shear at the SA 516/weld interface at a significantly reduced ductility. At 900 and 

1,000 degrees C (1,652 and 1,832 degrees F), failure occurred in the middle of the weld either 

by shear or flat fracture, and the overall ductility of the specimens was significantly reduced 

compared to that at 700 degrees C (1,292 degrees F). Necking was not observed in any of the 

tests conducted at 800–1,000 degrees C (1,472–1,832 degrees F).
A-24

Table A-11 Summary of Creep Data for SA 240 Grade 316 /SA 516 Grade 70 Weldment

Spec. 

No.

Temp 

°C (°F)

Stress ksi 

(MPa)

Rupture 

Time (h)

% Elongation% RA Min. Creep 

Rate (%/h)

Failure Location

6W-6 700 (1292) 13 (90) 0.2 29.2 77.8 3.07 necking of SA 516

6W-7 700 (1292) 13 (90) 0.1 29.1 81.0 5.16 necking of SA 516

6W-8 700 (1292) 17 (117) F.O.L. 24.5 65.9 1.61 necking of SA 516

6W-9 700 (1292) 17 (117) F.O.L. 21.8 76.3 1.28 necking of SA 516

6W-14 700 (1292) 10 (69) 0.6 22.4 52.6 0.36

shear at weld 

(SA 516 side)

6W-17 700 (1292) 6 (41) 9.0 29.0 69.5 necking of SA 516

6W-10 800 (1472) 8 (55) 0.2 8.3 14.3

shear at weld 

(SA 516 side)

6W-11 800 (1472) 8 (55) 0.2 7.2 14.4

shear at weld 

(SA 516 side)

6W-12 800 (1472) 10 (69) F.O.L. 5.4 8.4

shear at weld 

(SA 516 side)

6W-13 800 (1472) 10 (69) F.O.L. 7.5 12.9 1.29

shear at weld 

(SA 516 side)

6W-15 800 (1472) 4 (28) 2.5 4.5 13.2

shear at weld 

(SA 516 side)

6W-18 800 (1472) 2 (14) 30.3 6.0 ***

shear at weld 

(SA 516 side)

6W-19 900 (1472) 2 (14) 33.1 8.4 *** Flat fracture at weld

6W-20 900 (1472) 1 (7) 100** -

Flat fracture at weld 

(middle)

6W-16 1000 (1832) 2 (14) 7.0 8.1 14.2

Shear at weld

(middle)

6W-21 1000 (1832) 1 37.2 6.0 6.6

Flat fracture at weld 

(middle)
B-1

APPENDIX B 

 

CONSEQUENTIAL STEAM GENERATOR TUBE 

RUPTURE CALCULATOR 

This study developed software referred to as the consequential steam generator (SG) tube 

rupture (C-SGTR) calculator to support the work in this report. The calculator is used to estimate 

failure times and leak sizes of SG tubes with different types of flaws. The software also has 

built-in models for hot leg (HL) and surge-line (SL) failure caused by the creep-rupture failure 

mechanism, and it estimates failure times and HL and SL probabilities. The scope of the models 

currently includes new SG tube materials and the associated property data for both thermally 

treated Inconel 600 and 690 (600TT and 690TT) tubes.

The Information Systems Laboratories document, ISL-NSAD-TR-10-13, “Technical Basis and 

Software User Guide for SGTR Probability,” issued December 2014 (Ref. B-1), stores the 

calculator user manual and basis report. The same document also contains the results of a 

review of the basis report by Argonne National Laboratory.

It is emphasized that the software does not directly calculate a “C-SGTR probability.” This 

probability can be calculated after a case run by using the information from two output files and 

the probabilities assigned to the set of input flaws. However, the user can observe from the 

output files whether the HL (or SL) fails before a specified integrated tube leak size (defined as 

critical leak size in the report) is reached or not.

Section B-1 provides a short discussion of software input-output with an example case. 

Section B-2 has comments on the uncertainty modeling. Reference B-1 contains 

more information.

B.1 Example Case 

This software is designed to support the probabilistic risk assessments (PRAs) that address the 

risk associated with SG tube rupture (SGTR) scenarios; as an initiator, as a consequence of 

plant transients (design-basis-accident scenarios), and because of core damage sequences 

(C-SGTR). Plant-specific material properties, plant-specific SG tube flaw data, and 

scenario-specific thermal-hydraulic (TH) input are required to use this software to support 

PRA analysis.

An event sequence (scenario) can be defined as the input to the calculator. To define a 

scenario, the calculator expects five input files:

(7) plant information file

(8) time, temperature, pressure profile of the SG tubes, SL, and HL (TH) file

(9) SG tube flaws file

(10) material properties file (e.g., 600TT or 690TT)

(11) calculation parameters file

The underlying calculations are deterministic. The calculation parameters file is used to apply a 

probability and to sample the information that comes from the flaw and TH files. This provides 

probabilistic results. For those characteristics of the scenario that go into the calculations 
B-2

without uncertainty parameters, no sampling occurs; thus, they do not contribute to the 

probability calculations.

The software produces the following three output files:

(5) CumulativeLeakAreaFile-XXXX.txt

(12) CSGTRProbabilityFile-XXXX.txt

(13) IntermediateFile-TH-XXXX.txt

This appendix contains an example Table B-1 of some key inputs and outputs, with annotations, 

and additional example cases are in the later appendices of this report.

The output in Table B-1 allows for the calculation of a “margin,” which is defined as the number 

of minutes between the failure of HL (or SL, whichever occurs first) and the failure of more than 

one-tube guillotine break equivalent of SG tubes (6 square centimeters (cm2

) (0.93 square inch 

(in.2

)) for this example). For example, from Table B-1, a margin M of

M = 221 – 235 = -14 minutes

can be determined. A negative margin is favorable, since tube failures and a fission product 

release to the atmosphere would be limited or avoided.

Some noteworthy aspects of the software are listed below:

• Axial, circumferential and wear-type SG tube flaws are modeled.

• The software estimates HL and SL failure probabilities. Caution: in this estimation, the

effect of SG tube failures on the HL and SL failures is not considered. The software

calculates each of the three types of failures, HL, SL, and SG tube, independently.

• Two types of correlations are used to estimate SG tube leakage; one for

low-temperature (e.g., much lower than creep-rupture region) but potentially

high-pressure cases; the other for temperatures in the creep-rupture range. The

threshold temperature for switchover to creep-rupture correlation is a software input: the

default is set to 600 degrees Celsius (C) (1,112 degrees Fahrenheit (F))

(ThresholdCreepRupture 600.0, in the calculation parameters file).

The following comments apply to Table B-1:

• Columns A, F–J are input. Columns B–E are output.

• If one tube has a guillotine break, the total leak area would be 6 cm2 (0.93 in.2

).

• At 238 minutes into this core damage event, the total expected leak area from multiple

partial breaks is 28 cm2 (4.34 in.2

), which is equivalent to about 5 guillotine tube breaks.

• At 95-percent confidence level, the total expected leak area from multiple partial breaks

is 37 cm2 (5.7 in.2

), which is equivalent to about 6 guillotine tube breaks.

• HL fails around 220 minutes.
B-3

• SL failure probability is 68 percent at 238 minutes.

• HL and SL failure probabilities are calculated without considering SG tube failures. A 

substantial failure of SG tubes (greater than 6 cm2 (0.93 in.2

) total leakage area) would 

reduce the reactor coolant system pressure and could delay HL and SL failures.

• This example estimates multiple wear flaws with different sizes and depth.

• The tube material is Alloy 600TT.

• The event is core damage from station blackout with no recovery and early loss of 

turbine-driven auxiliary feedwater pumps in a PWR.

B.2 Uncertainty Parameters 

The software uses a set of input uncertainty parameters to sample from distributions that apply 

to various key inputs. Table A-2 of Reference B-1 defines these inputs and their uncertainty 

parameters. This table is titled “Statistical Parameters in the Calculation: Properties Input File.” 

If an input parameter is not in this table, then the software does not sample for that parameter 

but uses the expected value provided.

B.3 References 

B-1. Information Systems Laboratories, “Technical Basis and Software User Guide for SGTR 

Probability,” ISL-NSAD-TR-10-13, December 2014, Agencywide Documents Access and 

Management System Accession No. ML15054A495.
B-4

Table B-1 Example Input-Output (Condensed and Processed)

A B C D E F G H I J

Time 

(min)

Amean

(cm2) 

A0.95 

(cm sq

) 

HL % Surge 

Line %

Surge 

Line 

Temp 

°C

HL 

Temp 

°C

Averag

e Hot 

Tube 

Temp 

°C

Averag

e Cold 

Tube 

Temp 

°C

Delta P 

in psi

210 0.027 0.18 0.000 0.000 621 713 574 499 15

210 0.027 0.18 0.000 0.000 617 715 581 500 15

211 0.030 0.18 0.000 0.000 619 722 588 504 15

212 0.034 0.18 0.002 0.000 622 730 593 507 15

213 0.037 0.19 0.013 0.000 626 738 597 510 15

214 0.039 0.20 0.041 0.000 629 746 601 513 15

215 0.039 0.20 0.104 0.000 633 755 606 516 15

216 0.039 0.20 0.267 0.000 637 764 611 519 15

217 0.039 0.20 0.511 0.000 641 772 615 522 15

218 0.039 0.20 0.795 0.000 672 786 613 524 15

219 0.039 0.20 0.884 0.000 661 791 619 524 15

219 0.039 0.20 0.945 0.000 661 797 626 526 15

220 0.039 0.20 0.987 0.000 666 809 634 530 15

221 0.039 0.20 1.000 0.000 671 822 640 534 15

222 0.039 0.20 1.000 0.000 678 836 646 537 15

223 0.039 0.20 1.000 0.000 685 854 654 540 15

224 0.039 0.20 1.000 0.000 716 868 648 540 15

224 0.039 0.20 1.000 0.000 711 879 658 542 15

225 0.039 0.20 1.000 0.000 727 925 673 545 15

225 0.039 0.20 1.000 0.000 855 1057 679 545 15

226 0.039 0.20 1.000 0.000 826 1097 710 548 15

226 0.043 0.20 1.000 0.000 839 1137 725 552 15

227 0.051 0.68 1.000 0.000 855 1162 728 556 15

227 0.061 0.83 1.000 0.000 916 1193 719 556 15

228 0.082 0.89 1.000 0.000 905 1,209 733 558 15

228 0.119 0.90 1.000 0.000 908 1,233 745 560 15

229 0.186 0.91 1.000 0.002 917 1,261 756 562 15

229 0.267 0.91 1.000 0.006 925 1,281 764 564 15

230 0.353 0.91 1.000 0.025 954 1,304 772 565 15

230 0.423 0.91 1.000 0.067 973 1,314 766 565 15

231 0.480 0.91 1.000 0.100 965 1,319 776 566 15

232 0.589 0.91 1.000 0.183 969 1,332 787 570 15

233 1.080 3.55 1.000 0.312 977 1,343 797 575 15

235 3.462 7.36 1.000 0.430 985 1,354 808 580 15

236 11.535 17.04 1.000 0.571 994 1,368 819 585 15

238 28.206 36.86 1.000 0.681 1002 1,374 827 591 15
C-1

APPENDIX C 

 

CONSIDERATIONS FOR PRESSURE-INDUCED CONSEQUENTIAL 

STEAM GENERATOR TUBE RUPTURE 

C.1 Introduction 

Past studies (like NUREG-1570, “Risk Assessment of Severe Accident-Induced Steam 

Generator Tube Rupture,” issued March 1998) discussed two types of potential consequential 

steam generator (SG) tube rupture (C-SGTR) challenges:

Type-I. temperature-induced C-SGTR (mainly driven by creep rupture at higher 

temperatures) and

Type-II. pressure-induced C-SGTR (mainly driven by the pressure difference across the 

SG tube boundary, rather than the temperature).

Later studies, benefiting from the probabilistic risk assessments (PRAs), identified 

risk-significant core damage sequences, such as unrecovered station blackout, to be Type-I 

challenges. Thus, the analyses were focused on Type-I C-SGTR challenges with good reason. 

Note that the Type-I challenges thus analyzed occur after core damage, which is the cause of 

the high SG tube temperatures. Type-I C-SGTRs do not increase the plant core damage 

frequency (CDF) but may affect the magnitude and timing of fission product release.

This appendix discusses Type-II C-SGTR challenges. The discussion does not claim to be 

exhaustive. However, the insights discussed and overall results are applicable in a larger 

context, since the assumptions used are prudently conservative.

Initiating events challenge and induce a Type-II (pressure-induced) C-SGTR. No core damage 

exists until additional component failures occur as the event proceeds. In earlier studies, it 

appeared that the main concern for a Type-II C-SGTR was that it could complicate the original 

event in progress and might affect the operator response and operator success probability. 

Type-II C-SGTRs could increase the already calculated plant CDF, if they are added to a PRA 

model that does not originally consider them.

Potential pressure-induced C-SGTRs, following an initiating event and before core damage, are 

of interest for some initiating events, including large secondary-side breaks (SSB), spurious 

opening of one or more secondary relief valves, and anticipated transients without scram 

(ATWS) scenarios. The initiating events other than ATWS are collectively named L-SSBs. In 

these initiating events, a pressure spike on the primary side, or a sudden pressure drop on the 

secondary, or a combination of both could provide high delta pressure (pressure difference) 

across the SG tube boundary.

In PRA studies, once the reactor coolant system (RCS) pressure reaches 22–22.7 megapascals 

(MPa) (3,200–3,300 pounds per square in (psi)) (design pressure of the primary side), core 

damage is postulated (see ATWS event tree modeling in Section C..2.1). Assuming that the 

operating primary and secondary-side pressure difference is about 6.9 MPa (1,000 psi), the 

range of interest for an analysis of Type-II C-SGTR PRA scenarios is 

6.9–33.7 MPa (1,000–3,300 psi) across the tube boundary.
C-2

For a pristine tube (no flaw) made of Alloy 600, the burst pressure varies as a function of tube 

temperature. It is typically about 65 MPa (9.4 kilopounds per square inch (ksi)) at room 

temperature and about 58.7 MPa (8.5 ksi) at 500 degrees Celsius (C) (932 degrees Fahrenheit 

(F)). Therefore, there is generally no concern about the burst probability of a flawless tube due 

to the various pressure-induced scenarios identified by PRAs. However, the tube failure and 

burst pressure drops when there are one or more flaws on the tube wall. There are many 

different degradation mechanisms that could generate flaws. As the degradation mechanism for 

a type of flaw is better understood, indebted to information generated from the surveillance 

program in operating reactors, enhancements are identified and implemented to limit the 

number of flaws generated by that degradation mechanism. In the past, this has resulted in 

changes in plant operational practices, introduction of new tube materials, and other design 

modifications implemented to alleviate the identified issues. In fact, many plants have already 

replaced their SGs with either thermally treated Inconel 690 or Inconel 600, have improved their 

surveillance program, and have enhanced control of their water chemistry. According to a 

licensee event report (LER) search, there have been no SG tube leaks in the past 6 years since 

the 2004 event at Palo Verde (notwithstanding the 2012 SONGS 1 event).

Temperature-induced correlations, which are perfectly adequate for Type-I challenges, are 

deemed to underestimate the magnitude of the potential failure of a flaw when the SG tubes are 

subjected to relatively low (e.g., at the order of normal operating) temperatures with high 

pressure differences across the tube boundary (from the RCS side to the secondary side). At 

temperatures well below the creep-rupture range, the C-SGTR calculator uses the 

pressure-induced correlations to accommodate the effect of Type-II challenges. The software 

switches to thermally induced correlations when a user-specified transition temperature is 

reached in the scenario of interest. The region of temperature where creep rupture starts to 

become effective is 600–800 degrees C (1,112–1,472 degrees F). The value of 600 degrees C 

(1,112 degrees F) is used as the transition between the pressure-induced and the creep-rupture 

tube failure models. The default user input for the transition temperature is given as 

600 degrees C (1,112 degrees F).

C.2 Events of Interest 

Some initiating event categories that are included in both design-basis accident analyses and 

PRAs are candidates for potentially causing consequential Type-II SG tube failures. These 

failures may be designated as “leaks” (leak area of less than the equivalent area of a single 

guillotine tube break). For most of the leak sizes, the RCS inventory can be maintained by the 

normal capacity of the chemical and volume control system (CVCS). Other larger failures can 

be designated as leakage from one or more tubes, with a total leak area equal to or greater than 

the equivalent size of a one-tube guillotine break. Such larger failures will be designated as 

C-SGTR for the purposes of the discussion in this appendix. For such magnitude of failures (in 

the small loss-of-coolant-accident range), the flow capacity of the CVCS will not be sufficient 

and injection from high-pressure safety systems will be needed to maintain the RCS inventory. 

Also, the leakage will cause a reactor trip, even if the original initiating event had not already 

tripped the reactor and the turbine.

 1 As identified in the San Onofre Nuclear Generating Station root cause analysis, the cause of the SG 

degradation was tube-to-tube wear caused by in-plane fluid-elastic instability of the tube u-bends. A design error 

resulted in the actual SGs having more severe thermal-hydraulic conditions than expected, which contributed, 

along with other factors, to the rapid SG tube wall degradation.
C-3

This appendix discusses the following initiating events that can potentially create pressure 

differences considerably exceeding normal operating pressure across the SG tube boundaries:

• ATWS

• large SSBs

Several other scenarios could cause pressure differences across SG tubes exceeding normal 

operating pressure. Station blackout (SBO) scenarios would demand frequent lifting of main 

steam safety valves (MSSVs), followed by one of them sticking open. Such scenarios are 

bounded by L-SSB and they have significantly smaller occurrence probabilities.

C.2.1 ATWS Event 

Given the failure of the reactor protection system (RPS) to trip the reactor, the RCS system 

pressure is questioned to ensure that the reactor vessel is not pressurized to a greater extent 

than the design pressure. If the RCS pressure exceeds design pressure, core damage 

is assumed.

The ATWS event tree has the following events arranged in the approximate order in which they 

would be expected to occur after a failure to scram the reactor, given a transient event. 

Figure C-1 shows a partial ATWS event tree developed to discuss the Type-II C-SGTR issues. 

A transient event is used in this example as the initiator; other initiating events of lesser 

frequency could also be followed by ATWS scenarios.

(1) IE-TRANS

The first top event refers to the initiating event that creates the demand for a reactor trip (in this 

case, a transient).

(2) RPS

This top event signifies that a transient occurred and the RPS failed to trip the reactor. Credit 

can be taken for a manual trip in a short time—say, within a minute—but not before the 

pressure peak has been realized. There are several options for manual trip that can be effective 

for all ATWS scenarios except those caused by mechanical failures of a sufficient number of 

rods to inset. There is a high likelihood of success for the operators to perform a manual scram 

after observing compelling alarms and signals in the main control room.

(3) PR-REL

This top event represents success or failure of the reactor pressure vessel. Success implies that 

the ATWS event did not increase the RCS pressure above the reactor vessel design pressure 

boundary. Success also implies that the RCS relief valves opened to relieve RCS pressure.

Success requires that the RCS pressure be limited to less than 22 MPa (3,200 psi). This implies 

a favorable moderator temperature coefficient. Above this pressure, unpredictable pressure 

boundary and component failures are assumed to occur. Success also requires three-of-three 

safety relief valves (SRVs) and two-of-two power-operated relief valves (PORVs) to open and 

relieve RCS pressure.
C-4

Event Tree Nodes 4 and 5 are intended to help calculate the probability of getting a leak or a 

C-SGTR, given that ATWS pressure relief was successful, but the pressure difference across

SG tubes exceeded the normal operational values; namely, it was in the range of

ΔP = (6.89–20.6 MPa (1,000–3,300 psi). The upper values of this pressure range could only be

reached if the secondary side were also depressurized. That scenario would be highly unlikely,

since the heat removal is done through SGs with auxiliary feedwater (AFW) pumps operating.

The highest ΔP of interest is, therefore, 15.2 MPa (2,200 psi) unless failure of the AFW pump is

also assumed.

The nature of these two event tree nodes is dictated by how the conditional C-SGTR 

probabilities are calculated for Type-II challenges and how the results are binned. Appendix F 

provides a detailed discussion of these calculations, and Section C-3 summarizes them.

Section C-3 gives the estimation of some values for these event tree nodes.

IE-TRANS RPS PR-REL FL-DPT P-L/R CCDP End State

1 2 3 4 5 6 7 8

Success 1 No ATWS

Small 2 No leak

Yes. 2,200 < P< 3,300 Medium 3 CD-Leak

Occurs

Large 4 CD-C-SGTR

Fails

No. P >3,300 5 CD

Figure C-1 ATWS event tree top events to address Type-II C-SGTR

(4) FL-DPT

This node represents the probability of having a “small,” “medium,” or “large” flaw depth, given 

that a flaw has originated since the last refueling outage. Any flaws of a depth of 40 percent or 

less are assumed identified and their tubes plugged, if they occurred before the last outage.

(5) P-L/R

This node represents the probability of leak or C-SGTR, given that a flaw with a depth specified 

in the FL-DPT node exists. No credit is taken for this event tree node in the current calculations 

(e.g., set equal to 1.0 when the critical size Ac is reached).

(6) CCDP

This is the conditional core damage probability (CCDP) assigned to the sequence defined so far 

with Nodes 1 through 5 in the event tree. This CCDP represents the additional failures needed 

to reach the core damage end state, given that the sequence in question has progressed to the 

point defined by Nodes 1 through 5.
C-5

The event tree Sequences 3 and 4 in column 7 of the figure are the new potential core damage 

sequences associated with the Type-II C-SGTR challenges. Sequence 4 represents a sequence 

with a C-SGTR end state, in which an integrated tube break size equivalent to a full guillotine 

break of one or more tubes is created by the Type-II challenge. The CCDP for this sequence is 

estimated by crediting manual scram but failing the emergency boration (EB). It is 

conservatively assumed that the operation of EB cannot be ensured after C-SGTR, so a 

bounding failure rate of one is assigned for EB. Sequence 3 represents integrated tube break 

sizes less than the one above, in which CVCS would be able to make up the RCS inventory.

Using the values in Section C-3, Sequences 3 and 4 are quantified (their CDF values are 

estimated), as shown in Figure C-2.

IE-TRANS RPS PR-REL FL-DPT P-L/R CCDP End State CDF

1 2 3 4 5 6 7 8 9

Success 1 No ATWS

1.0

Small 2 No leak

0.95

Yes. 2,200 < P < 3,300 Medium 3 CD-Leak 2E-10

Occurs 0.95 0.04 1 1E-03

1 Large 4 CD-C-SGTR 5E-11

Fails 0.01 1 0.1

5E-06

No. P >3,300 5 CD

0.05

Figure C-2 ATWS event tree top events to address Type-II C-SGTR—example 

quantification

C.2.2 Large Secondary-Side Break Event 

Given an initiating event like a large steamline break (SLB) or stuck-open secondary-side 

valves, L-SSBs, it is possible for a large delta P across the SG tubes to be generated. This 

pressure difference can be as high as 15.9 MPa (2,300 psi), assuming that the secondary-side 

pressure drops to zero at once and the primary pressure is at 15.9 MPa (2,300 psi) initially. The 

primary pressure is expected to start dropping because of the rapid cooldown.

Note that the size of the SSB, large, that would cause a significant increase in delta P across 

the SG tubes is not specified. In fact, a cursory examination of main steamline events reported 

in LERs points out that almost all such events have small steam leaks that do not even cause a 

reactor trip but eventually may end up with a manual trip.
C-6

The L-SSB event tree has the following events arranged in the approximate order in which they 

would be expected to occur. Figure C-3 shows for a partial L-SSB event tree developed to 

discuss the Type-II C-SGTR issues.

IE-LSSB RPS Large dP FL-DPT P-L/R CCDP End State

1 2 3 4 5 6 7 8

No. dP = 1,000 psi 1 L-SLB

Success Small 2 No leak

Yes. dP = 2,300 

psi Medium 3 CD-Leak

Occurs

Large 4 CD-C-SGTR

Fails 5 ATWS

Figure C-3 L-SSB event tree top events to address Type-II C-SGTR

(1) IE-L-SSB

The first top event refers to the initiating event of an L-SSB, such as a large SLB or stuck-open 

secondary-side valves.

(2) RPS

This top event addresses the need for a reactor trip. Failure of RPS would lead to an ATWS 

event, which was already discussed in the previous section and is not pursued any further here.

(3) LARGE-DP

This top event discusses whether the event across the SG tubes creates a large differential 

pressure (DP). For the purposes of this appendix, it is postulated that the nature of the event 

creates a large DP in the range of 6.9–15.9 MPa (1,000–2,300 psi).

Event Tree Nodes 4 and 5 are intended to help calculate the probability of getting a leak or a 

C-SGTR, given that a Type-II challenge is created.

Section C.3 gives the estimates of some values for these event tree nodes.

(4) FL-DPT

This node represents the probability of getting a “small,” “medium,” or “large” flaw depth, given 

that a flaw has originated since the last refueling outage. Any flaws with a depth of 40 percent or 

less are assumed identified and their tubes plugged, if they occurred before the last outage.
C-7

(5) P-L/R

This node represents the probability of leak or C-SGTR, given that a flaw with a depth specified 

in the FL-DPT node exists. No credit is taken for this event tree node in the current calculations 

(e.g., set equal to 1.0 when the critical size Ac is reached).

(6) CCDP

This is the CCDP assigned to the sequence defined so far with Node 1 through 5 in the event 

tree. This CCDP represents the additional failures needed to reach a core damage end state, 

given that the sequence in question has progressed to the point defined by Nodes 1 through 5.

The event tree Sequences 3 and 4 in column 7 of the figure are the new potential core damage 

sequences associated with the Type-II C-SGTR challenges. Sequence 4 represents a sequence 

with a C-SGTR end state, in which an integrated tube break size equivalent to a full guillotine 

break of one or more tubes is created by the Type-II challenge. In such sequences, the CCDP 

accounts for the following two additional possible failures: 

(1) a higher probability for the failure of high-pressure injection, accounting for the possible 

termination of injection if the operators do not recognize the occurrence of C-SGTR

(2) a higher probability of isolating the affected SG because main steam isolation valves 

(MSIVs) might have failed to close as indicated by the initiator.

Sequence 3 represents integrated tube break sizes less than the above, in which the CVCS 

would be able to make up the RCS inventory.

Using the values in Section C.3, Sequences 3 and 4 are quantified (their CDF values are 

estimated), as shown in Figure C-4.

IE-L-SSB RPS Large dP FL-DPT P-L/R CCDP End State CDF

1 2 3 4 5 6 7 8 9

No. dP = 1,000 psi 1 L-SSB

Success Small 2 No leak

1.0 0.95

Yes. dP = 2,300 

psi Medium 3 CD-Leak 1E-07

Occurs 1 0.04 1 1E-03

0.003 Large 4 CD-C-SGTR 4E-08

0.01 1 1.3E-03

Fails 5 ATWS

1E-05

Figure C-4 L-SSB event tree top events to address Type-II C-SGTR—

example quantification
C-8

C.3 Example for Estimating CDF from Type-II C-SGTR Challenges

The event tree models described in Figures C-1 and C-3 can be quantified to illustrate the 

model usage and the resulting C-SGTR frequencies. Although these C-SGTR frequencies are 

for illustration purposes and apply to the cases studied, their values are deemed to be 

representative of similar plant-specific sequences, as long as the specific plant in question is not 

an outlier for the event tree nodes considered in the models.

The following data quantify the two event trees mentioned above:

(1) Initiating-event frequency

For the ATWS event, a transient initiating-event frequency of 1 per year is used. The current 

standardized plant analysis risk (SPAR) model frequency is 0.69 events per year. Other 

transients have considerably lower frequencies.

For the L-SSB event, a frequency of 0.001 per year is generally used. SPAR models do not 

have a frequency for such an event. Considering the more than 3,000 plant years of 

pressurized-water reactor (PWR) experience for U.S. domestic and similar French plants, 

postulating one such event per 1,000 years of operation is deemed reasonable for this 

illustration. The location of an SLB could be inside or outside the containment. Breaks inside the 

containment do not contribute to containment bypass probability, and MSIVs could isolate 

breakers outside containment. Bounding calculations in Section 7.4 also show that the SLB 

scenarios followed by pressure-induced C-SGTR have small contributions to both large early 

release frequency (LERF) and to CDF. Other events, however, such as a spurious opening 

followed by sticking of MSSVs or SG PORVs could also contribute to a transient with rapid 

secondary depressurization. It should be noted that the SG PORVs could be isolated by 

manually closing the block valves, if available. Although the closure of block valves may not 

occur in time to prevent C-SGTR, it could be credited for isolating the faulted SG after C-SGTR 

occurred. Considering these other events, a bounding frequency of 3X10-3/yr from information 

available in NUREG/CR-6928, “Industry-Average Performance for Components and Initiating 

Events at U.S. Commercial Nuclear Power Plants,” issued February 2007, is assigned to this 

class of initiators.

(2) RPS success/failure

The failure of the reactor protection system from all failure mechanisms is assigned a probability 

of 5X10-5 per demand. This includes potential credit for the operator action to trip the reactor 

early on, based on the early symptoms of transient and before the scram signal is initiated. The 

early symptoms generally include applicable alarms and cues that are observed in the main 

control room. SPAR model probability for this failure is generally lower than this value.

(3) Failure of RCS pressure relief (thus avoiding high delta P across the SG

tube boundary)

For L-SSB, a failure probability of 1 is used, since the nature of the initiating event causes the 

high delta P.

(4) and (5) Probability of having at least one (large) SG tube subject to C-SGTR or leak.

Probability of C-SGTR or leak, if such a tube is present and high delta occurs
C-9

Appendix F discusses the calculation of these probabilities for the example case in Section F-2 

for C-SGTR and Section F-3 for SGTR-leak. The highest probability for C-SGTR and 

SGTR-leak for ATWS or L-SSB scenarios is estimated to be 0.01 and 0.043, respectively. This 

is the probability estimate based on the example Westinghouse plant at cycle 15 of operation.

(6) Sequence CCDP for C-SGTR (or for SG leak sequence), given high delta P and 

large flaws

For an ATWS event, a screening CCDP of 0.1 is used, given C-SGTR.

The CCDP value for L-SSB events given C-SGTR is taken as 1.3X10-3

. This value is an order of 

magnitude higher than those in SPAR models (with SGTR event CCDPs in the range of 10-4

and 10-5

). This order of magnitude increase in CCDP is postulated to allow for presumed 

complications in the sequence, potentially increasing operator failure probabilities.

Because an SG-leak sequence is considerably more benign and the CVCS can cope with it, a 

slightly lower CCDP of 1 X10-3 is used.

These values are placed in the event tree model to obtain C-SGTR (and SG leak) sequence 

frequencies for the events studied. Figures C-2 and C-4 give the quantification results.

These results are deemed to be prudently conservative. Section C.4 gives conclusions about 

Type-II challenges to the SG tubes based on these illustrative examples.

C.4 Conclusions 

This appendix examines the pressure-induced C-SGTR challenges (Type-II C-SGTR 

challenges) by referring to specific examples. The examples cover two main Type-II 

challenge sources:

(6) A sudden pressure spike in the primary side, exemplified by an ATWS event

(7) A sudden pressure drop on the secondary side, exemplified by L-SSBs

By referring to Figure C-2, one concludes that C-SGTR frequencies for ATWS events are not 

risk significant for the cases studied in this example. This assertion is deemed to be generic for 

all PWRs, unless a specific plant characteristic is not covered (or bounded) by the assumptions

used in the ATWS case of this appendix.

As for the L-SSB event, referring to Figure C-4, one observes that with the prudently 

conservative assumptions used, the C-SGTR CDF frequency is on the order of 4X10-8

/year. For 

example, for a PWR with a total CDF of 2X10-5 per year and a LERF of 1X10-6

, the additional 

CDF and LERF would add about 2 percent to CDF and 4 percent to LERF. The actual LERF 

contribution may be even lower if credit is given for severe-accident management guidelines. 

However, there is also possible core damage contribution from those sequences defined with 

the end state “core damage-leak.” A simple estimation of CDF of such lesser magnitude SG 

tube leaks is more dependent on plant-specific modeling and, thus, more elusive.

Further fine tuning to reduce some of the conservativeness may lower this value, but then it 

could reduce the generic applicability of the conclusions, considering large uncertainties and 

variations. For example, one obvious possibility of reduction is to recognize that the “length” of a 

typical flaw is about 1.1 cm, or 0.43 in. (for the 600TT and 690TT flaw distributions discussed in 
C-10

Appendices B and C). According to the models in the C-SGTR calculator, such a flaw cannot 

produce more than a leak and cannot reach the critical size of 6 square centimeters 

(0.93 square inch) assigned to declare a tube failure as a C-SGTR. This could reduce the above 

CDF for an L-SSB CDF sequence by a factor of 10. But, on the other hand, it would require 

consideration of multiple smaller tube flaws whose integrated failure area could reach or exceed 

the critical size. To avoid an explosion of analysis cases and details, further attempts to reduce 

the above bounding value at this time are not being carried out or recommended.
D-1

APPENDIX D 

 

UNCERTAINTY AND SENSITIVITY ANALYSIS 

The basic tool used to generate steam generator (SG) tube leak area estimates, hot-leg (HL) 

and surge-line failure probabilities is the consequential steam generator tube rupture (C-SGTR) 

calculator. The correlations used for these calculations are basically deterministic and would 

provide nonprobabilistic results unless uncertainty distributions are assigned to certain input 

parameters. The calculator samples the input parameters for which uncertainty distributions are 

specified and generates N cases (trials) for each of which it calculates outputs like integrated 

tube leak area (A), HL and surge-line failure times. These results are then ordered to provide 

estimates for Am, A95, etc. In such estimates, no underlying distribution is assumed. No 

sampling is done for any parameter for which distributions are not specified.

In addition, a set of sensitivity analyses designed to evaluate the impact of changing the main 

assumptions or input data in the base case evaluations were performed. The results of these 

sensitivity analyses could also support development of the Level 2 probabilistic risk assessment 

(PRA) models. This appendix provides a detailed discussion on the approach, assumptions, 

case runs, and results of the analyses for both the selected Westinghouse (W) and the 

Combustion Engineering (CE) plants.

D.1 Sensitivity Analyses for the Selected W Plant 

The following sensitivity analyses were performed for the example W plant. The measure of 

comparison used for these sensitivity analyses is based on the difference between the time 

when HL failure is imminent and the time when C-SGTR is expected. The ratio of this time 

margin over the base time margin is used as a means of qualitatively ranking the impact of 

sensitivity results.

D.1.1 Base Case Evaluation and the Uncertainties Calculated 

For the purposes of the uncertainty discussion in this appendix, the following base case is used:

• ZION with thermally treated Inconel 600 SG tubes

• Wnewbase; station blackout (SBO) with early failure of turbine-driven auxiliary feed 

water (TDAFW) pump without recovery of alternating current power, resulting in core 

damage, is considered. The input file provides the relevant temperatures and pressure 

for a time window of 300 minutes, starting from the reactor trip and SBO. Figure D-1 

summarizes the main parameters of the base case. Note that the secondary side 

is depressurized.

• A wear-type flaw of 4 centimeters (cm) (1.6 inch (in.)) in length and 40 percent in depth 

was considered. Such a flaw would require tube plugging when identified at the end of 

the cycle.

• 2,000 trials were used with the calculator.
D-2

• “Critical Area” (Ac) is taken as 6 square centimeters (cm2) (0.93 square inch (in.2)),

which is equivalent to a guillotine break of a single tube in this SG. The above flaw is

capable of generating an equivalent leak area to the Ac.

• In this sequence, the main driver of the SG tube failure is the creep-rupture failure,

induced by the high temperature at the flaw location.

Figure D-1 Temperature and pressure profile of the base case (at the flaw location)

This report has already discussed the analyses associated with such a sequence in detail. Here, 

the focus is mainly on the uncertainty aspects of the results.

When the above case is studied, two types of output of interest are generated:

(8) Estimates of Integrated SG Tube Leak Area (A)

For this output, Am, A05, A25, A50, A75, and A95, and Asd (standard deviation) are reported. 

Figure D-2 shows the output for the percentiles of the leak area distribution. Note that, although 

the time window of the sequence is 300 minutes, the tube failure develops in a relatively narrow 

time window of 230–240 minutes into the event. This is the time window shown in the figure. 

Table D-1 shows the relevant input-output data.

0

500

1000

1500

2000

2500

3000

0

200

400

600

800

1000

1200

0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00

Pressure (psi)

Temperature (oC)

Time in Minutes

Avr. Hot Tube Temp

C HT
D-3

Figure D-2 Leak area of the base case (4 cm wear flaw with 40 percent depth)

0

1

2

3

4

5

6

7

225 230 235 240 245

Leak Area (cm2)

Time in minutes

Base Case Leak Area
D-4

Table D-1 Output for the Total Leak Area in the Base Case

Time in 

Minutes

Am 

in °C A0.05 A0.25 A0.50 A0.75 A0.95 Asd

HL 

Failure 

Prob.

Surge 

Line 

Failure 

Prob.

Avr. Hot 

Tube 

Temp °C 

HL 

Temp 

°C

Dt 

Between 

HL and 

Hot Tube

230 0.00 0.00 0.00 0.00 0.00 0.00 0.14 1 0.02 772 1304 532

230 0.00 0.00 0.00 0.00 0.00 0.00 0.14 1 0.07 766 1314 548

231 0.01 0.00 0.00 0.00 0.00 0.00 0.16 1 0.10 776 1319 543

232 0.08 0.00 0.00 0.00 0.00 0.00 0.65 1 0.19 787 1332 545

233 0.90 0.00 0.00 0.00 0.00 6.08 2.10 1 0.33 797 1343 546

235 2.88 0.00 0.00 3.51 5.94 6.11 2.71 1 0.47 808 1354 546

236 4.82 0.00 4.08 6.01 6.08 6.13 1.92 1 0.59 819 1368 549

238 5.71 3.17 5.92 6.06 6.1 6.14 0.97 1 0.70 827 1374 547

239 5.94 5.31 5.98 6.06 6.1 6.14 0.37 1 0.78 836 1381 545

241 5.96 5.34 6.00 6.06 6.1 6.14 0.29 1 0.86 845 1385 540

243 5.96 5.34 6.00 6.07 6.1 6.14 0.28 1 0.91 855 1393 538

245 5.96 5.34 6.00 6.07 6.1 6.14 0.29 1 0.94 862 1394 532

247 5.96 5.39 6.00 6.07 6.1 6.14 0.29 1 0.95 869 1391 522

250 5.96 5.39 6.00 6.07 6.1 6.14 0.30 1 0.97 879 1393 514

252 5.96 5.39 6.00 6.07 6.1 6.14 0.30 1 0.97 886 1389 503

255 5.96 5.39 6.00 6.07 6.1 6.14 0.29 1 0.98 894 1388 494

257 5.96 5.39 6.00 6.07 6.1 6.14 0.29 1 0.98 898 1379 481

260 5.96 5.39 6.00 6.07 6.1 6.14 0.29 1 0.99 907 1376 469

263 5.96 5.39 6.00 6.07 6.1 6.14 0.30 1 0.99 915 1375 460

266 5.96 5.39 6.00 6.07 6.1 6.14 0.29 1 0.99 922 1377 455

270 5.96 5.39 6.00 6.07 6.1 6.14 0.29 1 0.99 932 1383 451

273 5.97 5.39 6.00 6.07 6.1 6.14 0.28 1 0.99 941 1388 447

277 5.97 5.39 6.00 6.07 6.1 6.14 0.28 1 0.99 950 1395 445

280 5.97 5.39 6.00 6.07 6.1 6.14 0.29 1 0.99 958 1401 443

284 5.97 5.39 6.00 6.07 6.1 6.14 0.29 1 0.99 967 1405 438

288 5.97 5.39 6.00 6.07 6.1 6.14 0.29 1 1.00 975 1408 433

292 5.97 5.39 6.00 6.07 6.1 6.14 0.29 1 1.00 982 1410 428

296 5.97 5.39 6.00 6.07 6.1 6.14 0.29 1 1.00 990 1412 422

300 5.97 5.39 6.00 6.07 6.1 6.14 0.29 1 1.00 997 1414 417
D-5

(2) Estimates of HL and Surge-Line Failure Probabilities

The calculator also provides estimates of HL and surge-line failure probabilities as a function of 

time, without reporting uncertainties. Figure D-3 and Table D-2 show the probabilities for this 

base case. Also reported are the ratios of the average tube leak area to the critical leak 

area (Am / Ac).

Because HL failure occurs earlier than surge-line failure in this case, it will be used for 

further discussions.

The above two sets of estimates of tubes and HL failure are done independently. As long as the 

leak area is small (less than the critical area), the reactor coolant system (RCS) is deemed to 

not depressurize sufficiently to affect the temperature and pressures experienced by other parts 

of the RCS; thus, this independence assumption is valid for this “small” range of integrated SG 

leaks (from one or more flaws).

One can define a simple measure of comparison between the HL failure time and the tube 

failure time. This measure is called the Margin in minutes and is defined as:

Margin = {time in minutes of failure of HL when its failure probability reaches 1} ‒ 

{time in minutes of integrated SG tube leak area reaches Ac: Am/Ac=1}

For this base case, the margin is -18 minutes (221–239 = 18 minutes), as reported in Table D-3. 

Large, negative margin is considered to be favorable, because it would arrest or reduce SG 

tube leak area generation or its fission product release. It should be noted that Table D-2 shows 

that there is a period of about 20 minutes when a nonzero probability of HL is estimated. 

Therefore, any negative margin value greater than 20 minutes will be indicative of zero 

probability of C-SGTR.

Figure D-2 also shows that the spread in the time of tube failure is very narrow, although the 

leak size has a range of 0–6 cm2 (0–0.93 in.2

), which reaches Ac. The following should be 

noted:

• No uncertainty distributions are provided for the thermal-hydraulic (TH) input file.

• No uncertainty results are reported for HL and surge-line failures.

Thus, deriving robust uncertainty insights solely based on the calculator should not be expected. 

Sensitivity analyses on what is deemed as other parameters of significance could be and should 

be done.

Because the margin as defined above is a simple yet important indicator of avoidance of early 

and large fission product releases, this appendix offers some sensitivity analyses to determine 

the uncertainty spread in the margin.
D-6

Figure D-3 Probabilities of HL and surge-line failure

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

210 220 230 240 250 260 270 280 290

Ratio or Probability 

Time in Minutes

Hot Leg failure prob.

Surge Line Failure prob.

Am / Ac
D-7

Table D-2 Probabilities of HL and Surge Line (Cont.)

Time (m) HL Failure Prob. Surge-Line Failure Prob. Am / Ac

211 0.00 0.000 0.000

212 0.00 0.000 0.000

213 0.01 0.000 0.000

214 0.04 0.000 0.000

215 0.13 0.000 0.000

216 0.31 0.000 0.000

217 0.52 0.000 0.000

218 0.79 0.000 0.000

219 0.87 0.000 0.000

219 0.93 0.000 0.000

220 0.99 0.000 0.000

221 1.00 0.000 0.000

222 1.00 0.000 0.000

223 1.00 0.000 0.000

224 1.00 0.000 0.000

224 1.00 0.000 0.000

225 1.00 0.000 0.000

225 1.00 0.000 0.000

226 1.00 0.000 0.000

226 1.00 0.000 0.000

227 1.00 0.000 0.000

227 1.00 0.000 0.000

228 1.00 0.000 0.000

228 1.00 0.002 0.000

229 1.00 0.003 0.000

229 1.00 0.008 0.000

230 1.00 0.024 0.001

230 1.00 0.070 0.001

231 1.00 0.100 0.001

232 1.00 0.190 0.013

233 1.00 0.330 0.150

235 1.00 0.470 0.480

236 1.00 0.590 0.800

238 1.00 0.700 0.950

239 1.00 0.780 0.990

241 1.00 0.860 0.990

243 1.00 0.910 0.990

245 1.00 0.940 0.990

247 1.00 0.950 0.990

250 1.00 0.970 0.990
D-8

Table D-2 Probabilities of HL and Surge Line (Cont.)

Time (m) HL Failure Prob. Surge-Line Failure Prob. Am / Ac

252 1.00 0.970 0.990

255 1.00 0.980 0.990

257 1.00 0.980 0.990

260 1.00 0.990 0.990

263 1.00 0.990 0.990

266 1.00 0.990 0.990

270 1.00 0.990 0.990

273 1.00 0.990 0.990

277 1.00 0.990 0.990

280 1.00 0.990 0.990

284 1.00 0.990 0.990

288 1.00 1.000 0.990

292 1.00 1.000 0.990

296 1.00 1.000 0.990

300 1.00 1.000 0.990
D-9

Table D-3 Calculation of Margin for the Base Case

Time in Minutes

NUREG/

CR-6995 Calculator Comment

1 Event starts 000 000

2 SG dryout 100

3 Evacuation starts 120

4 HL fails 13% 215

5 First fuel rod clad rupture 217

6 HL fails 52% 217

7 HL fails 100% 221

8 HL 1 fails by creep rupture 227

9 SL fails 18% 232

10 Hottest tube creep-rupture failure 233

11 SL fails 59% 236

12 Hot tube fails 6 cm2 (1 tube equivalent) 239

13 Hot tube fails xx cm2 (n tube equivalent)

14 Hot tube fails max 6 cm2 (1 tube equivalent) 239

15 SL fails 100% 280

16 Evacuation ends for internal events 360

17 Evacuation ends for external events 600

Margin = HL fails 100%—Hot tube fails 6 cm2

(0.93 in.2) -18

The definition of margin is based on the crucial TH assumption that a full break of a single SG 

tube (6 cm2 (0.93 in.2

)) would not depressurize the RCS to prevent RCS failure elsewhere.

Hot tube fraction = 1.0 (all flaws are assumed to be on the hot tubes)

NUREG/CR-6995, “SCDAP/RELAP5 Thermal-Hydraulic Evaluations of the Potential for 

Containment Bypass During Extended Station Blackout Severe Accident Sequences in a 

Westinghouse Four-Loop PWR” (RELAP 2010)

The following sensitivity calculations are made to seek some insights into these questions:

Case 1: Sensitivity on delta-T (between HL and hot tube)

Assume that the delta-T between the HL and hot tube temperatures is only 50 percent as large 

as the base case. Make a run where, at each time step, the base case delta-T is cut in half by 

reducing the HL temperature.
D-10

Case 2: Sensitivity to HL thickness (assessing the potential effect of an overlay)

Although placement of weld overlays at the HL safe-ends may provide a safety enhancement 

against potential cracks and resulting RCS leaks at those locations, an undesirable side effect 

may be to delay the expected earlier failure of the HL, thus reducing the margin. To estimate the 

effect of an overlay on the margin, the HL thickness is increased in this case.

The paragraphs below discuss the results of these cases.

Throughout this report, it is deemed that, in temperature challenges, where core damage has 

already occurred, the secondary side is depressurized. A small preexisting leak area of 

3.22 cm2 (0.5 in.2

) is shown in previous TH analyses to be sufficient to depressurize the 

secondary side. Another sensitivity case run, reported below, questioned: “what would be the 

effect on the margin if the secondary side is not depressurized?”

Case 3: Secondary side not depressurized (see Section D.1.4)

This case is not made to address uncertainty but to illustrate the effect of the secondary side 

being pressurized on the margin.

Appendix E provides additional sensitivity cases with multiple tube flaws.

D.1.2 Sensitivity on Temperature Difference between HL and Hot Tube

The TH input file for this case is a modified version of the Wnewbase-short, where the HL 

temperature at each time step is reduced so that the difference between it and the hot tube 

temperature is only 50 percent of the difference in the base case.

Table D-4 gives the resulting margin calculation. The margin for this case is -14 minutes, 

reduced by 4 minutes due to a significant reduction in the delta T. Thus, even if the initial TH 

analysis is off by a factor of 2 in estimating the temperature difference between the HL and the 

hot tube, where the flaw is located, the margin is not significantly affected.
D-11

Table D-4 Margin with Smaller Temperature Difference between HL and Hot Tube

Time in Minutes

NUREG/

CR-6995 Calculator Comment

1 Event starts 000 000

2 SG dryout 100

3 Evacuation starts 120

4 HL fails 12% 224

5 First fuel rod clad rupture 217

6 HL fails 56% 225

7 HL fails 100% 225

8 HL 1 fails by creep rupture 227

9 SL fails 17% 232

10 Hottest tube creep-rupture failure 233

11 SL fails 57% 236

12 Hot tube fails 6 cm2 (1 tube equivalent) 239

13 Hot tube fails xx cm2 (n tube equivalent)

14 Hot tube fails max 6 cm2 (1 tube equivalent) 239

15 SL fails 100 % 280

16 Evacuation ends for internal events 360

17 Evacuation ends for external events 600

Margin = HL fails 100%—Hot tube fails 6 cm2

(0.93 in.2) -14

The definition of margin is based on the crucial TH assumption that a full break of a single SG 

tube (6 cm2 (0.93 in.2

) would not depressurize the RCS to prevent RCS failure elsewhere.

Hot tube fraction = 1.0 (all flaws are assumed to be on the hot tubes)

NUREG/CR-6995 (RELAP 2010)

D.1.3 Sensitivity to HL Thickness (Potential Effect of an Overlay) 

This sensitivity case examines the effect of an increase in HL thickness due to a weld overlay, 

on the margin. For this purpose, the HL thickness of 6.35 cm in the base case is increased by 

50 percent, to 9.5 cm (3.74 in.). This increase is deemed to be a fair representation of what a 

weld overlay would provide.

Table D-5 gives the resulting margin calculation. The margin for this case is -16 minutes, 

reduced by 2 minutes because of a significant increase in HL thickness, which is presumed to 

delay HL failure. Thus, even if the HL contains weld overlay, which increases its thickness by 

50 percent, the margin is not significantly affected.
D-12

Table D-5 Margin with Thicker HL

Time in Minutes

NUREG/

CR-6995 Calculator Comment

1 Event starts 000 000

2 SG dryout 100

3 Evacuation starts 120

4 HL fails 18% 219

5 First fuel rod clad rupture 217

6 HL fails 61% 220

7 HL fails 100% 223

8 HL 1 fails by creep rupture 227

9 SL fails 19% 232

10 Hottest tube creep-rupture failure 233

11 SL fails 58% 236

12 Hot tube fails 6 cm2 (1 tube equivalent) 239

13 Hot tube fails xx cm2 (n tube equivalent)

14 Hot tube fails max 6 cm2 (1 tube equivalent) 239

15 SL fails 100 % 288

16 Evacuation ends for internal events 360

17 Evacuation ends for external events 600

Margin = HL fails 100%—Hot tube fails 6 cm2

(0.93 in.2) -16

The definition of margin is based on the crucial TH assumption that a full break of a single SG 

tube (6 cm2 (0.93 in.2

)) would not depressurize the RCS to prevent RCS failure elsewhere.

Hot tube fraction = 1.0 (all flaws are assumed to be on the hot tubes)

NUREG/CR-6995 (RELAP 2010)

D.1.4 Secondary Side Not Depressurized

To assess the effect of the secondary side not being depressurized, the TH input file is modified 

to have the secondary pressure set at 7.6 megapascals (MPa) (1,100 pounds per square inch 

(psi)), the remaining input values being the same as the base case. Figure D-4 summarizes the 

main parameters of this case. The TH input file for this case is labeled as 

TH-wnewbase-short-1100psi.txt.

Table D-6 summarizes the output of the case. The margin is calculated to be 45 minutes. This 

large margin seems to indicate that the tube is more sensitive than the HL to pressure reduction 

at the creep-rupture failure temperature range. In fact, as seen in the table below, the HL failure 

time is not affected, but the tube flaw failure time is considerably delayed.
D-13

Figure D-4 Temperature and pressure profile of the case where secondary side is 

not depressurized

0

200

400

600

800

1000

1200

1400

1600

1800

0

200

400

600

800

1000

1200

0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00

Pressure (psi)

Temperature (°C)

Time in Minutes

Avr. Hot Tube Temp C HT

delta P in psi
D-14

Table D-6 Margin with Secondary Side NOT Depressurized (at 1,100 psi)

Time in Minutes

NUREG/

CR-6995 Calculator Comment

1 Event starts 000 000

2 SG dryout 100

3 Evacuation starts 120

4 HL fails 13% 215

5 First fuel rod clad rupture 217

6 HL fails 55% 217

7 HL fails 100% 221

8 HL 1 fails by creep rupture 227

9 SL fails 16% 232

10 Hottest tube creep-rupture failure 233

11 SL fails 55% 236

12 Hot tube fails 6 cm2 (1 tube equivalent) 266

13 Hot tube fails xx cm2 (n tube equivalent)

14 Hot tube fails max 6 cm2 (1 tube equivalent) 266

15 SL fails 100% 280

16 Evacuation ends for internal events 360

17 Evacuation ends for external events 600

Margin = HL fails 100%—Hot tube fails 6 cm2

(0.93 in.2) -45

The definition of margin is based on the crucial TH assumption that a full break of a single SG 

tube (6 cm2 (0.93 in2

)) would not depressurize the RCS to prevent RCS failure elsewhere.

Hot tube fraction = 1.0 (all flaws are assumed to be on the hot tubes)

NUREG/CR-6995 (RELAP 2010)

The margins are as follows:

Case Name Margin T HL—T Hot Tube

Base Case -18 minutes 221–239

Secondary NOT depressurized -45 minutes 221–266
D-15

D.1.5 Late Failure of Turbine-Driven AFW Pump 

This case study is performed for the W SBO scenario number 153:

Station Blackout with Failure of TDAFW Pump after Battery Depletion: The TDAFW pump 

is initially considered available, but it fails a short time after battery depletion due to loss of 

direct current (dc). 

The study modeled the normal reactor coolant pump seal leakage of 79.5 liters per minute 

(Lpm) (21 gallons per minute (gpm)) per pump. Operator action to depressurize SGs at 

30 minutes by opening at least one SG atmospheric dump valve or SG PORV per SG drops the 

primary pressure below 4.82 MPa (700 psi). This actuates the accumulator discharge.

Table D-7 shows the input TH parameters taken from the file named 153short-end. Other input 

files used are as follows:

• ZION- TT600

• Flaw-W4-40.txt

Table D-8 summarizes the results. As shown in this table, the margin is -22 minutes, which is 

close to the base case margin of -18 minutes. However, both the HL failure and C-SGTR occur 

much later than in the base case—in about 13 hours into the SBO event. For the base case, this 

time was 4 hours into the SBO event. The additional 7 hours gained could allow for evacuation, 

even for the SBOs that may follow seismic or external flooding events.
D-16

Table D-7 T&H Input Parameters for Case 153 (Cont.)

Time 

in 

Minutes

Primary 

Pressure 

(Pa)

Surge-Line 

Temperature 

(°C)

HL 

Temperature 

(°C)

Hot Tube 

Temperature 

(°C)

Cold Tube 

Temperature 

(°C)

Secondary 

Pressure 

(Pa)

Primary 

Pressure 

in psi

Secondary 

Pressure 

in psi

Delta 

P in 

psi

Avr. 

Hot 

Tube 

Temp 

°C HT

HL to 

Tube 

Hot Side 

Delta T

600 11187857 317 309 316 316 1816161 1622 263 1359 316.5 -7.2

604 11953517 321 318 323 323 1562022 1733 226 1507 323.5 -5.1

608 12497496 320 314 321 321 1321353 1812 192 1621 320.7 -6.3

612 13511729 320 317 320 320 1114784 1959 162 1798 320.4 -3.5

616 14437555 320 320 321 321 937642 2093 136 1957 320.6 -0.5

620 15378100 320 324 321 321 787000 2230 114 2116 320.8 3.0

624 15935722 322 336 331 331 659257 2311 96 2215 330.8 5.5

628 16616382 333 333 344 344 558371 2409 81 2328 344.4 -11.0

632 16439831 332 334 343 343 465514 2384 67 2316 342.6 -8.9

636 17106500 332 335 342 342 388108 2480 56 2424 341.7 -6.5

640 17552148 332 337 341 341 323280 2545 47 2498 340.9 -3.8

644 16971320 345 342 343 343 268863 2461 39 2422 343.1 -1.4

648 17878938 349 350 353 353 224552 2592 33 2560 353.0 -3.3

652 16650259 351 350 351 351 186259 2414 27 2387 350.7 -0.3

656 16952404 352 352 352 352 157992 2458 23 2435 352.1 -0.5

660 16895284 352 351 352 352 139242 2450 20 2430 351.8 -0.3

664 17016836 352 352 352 352 125068 2467 18 2449 352.5 -0.4

666 17627418 355 353 355 355 119016 2556 17 2539 355.2 -2.7

667 16689429 353 351 352 351 116987 2420 17 2403 351.6 -0.6

668 16922776 352 351 352 352 115081 2454 17 2437 351.9 -1.1

668 17383652 353 352 354 354 113502 2521 16 2504 354.1 -1.9

669 17783698 355 354 356 356 112031 2579 16 2562 356.0 -2.3

670 16704144 357 353 353 351 110248 2422 16 2406 353.2 -0.3

671 17124176 354 356 359 354 109030 2483 16 2467 359.3 -3.5

672 17433450 355 358 360 356 107944 2528 16 2512 360.1 -1.7

672 17725334 356 361 363 358 106925 2570 16 2555 363.1 -2.3

673 16603548 364 359 356 353 105650 2408 15 2392 355.7 3.0

674 16998104 358 362 64 356 104833 2465 15 2450 363.7 -1.6

675 17214120 354 365 364 359 104169 2496 15 2481 364.3 0.4

676 17420130 355 367 367 361 103625 2526 15 2511 366.9 0.0

676 17613248 355 369 370 363 103102 2554 15 2539 369.5 -0.3

678 16692531 368 370 364 360 101998 2420 15 2406 363.6 6.8

679 16964364 361 374 375 364 101783 2460 15 2445 375.0 -1.4

680 17130560 354 376 375 366 101655 2484 15 2469 375.4 1.0

680 17302764 354 379 378 368 101566 2509 15 2494 378.3 0.8

682 17598950 358 384 384 373 101468 2552 15 2537 383.5 0.7

683 16488133 403 384 381 372 101305 2391 15 2376 380.9 3.0

684 16850458 372 389 388 373 101385 2443 15 2429 387.6 1.6

685 17014836 363 392 392 377 101427 2467 15 2452 391.9 0.5
D-17

Table D-7 T&H Input Parameters for Case 153 (Cont.)

Time 

in 

Minutes

Primary 

Pressure 

(Pa)

Surge-Line 

Temperature 

(°C)

HL 

Temperature 

(°C)

Hot Tube 

Temperature 

(°C)

Cold Tube 

Temperature 

(°C)

Secondary 

Pressure 

(Pa)

Primary 

Pressure 

in psi

Secondary 

Pressure 

in psi

Delta 

P in 

psi

Avr. 

Hot 

Tube 

Temp 

°C HT

HL to 

Tube 

Hot Side 

Delta T

687 17269158 363 398 396 381 101449 2504 15 2489 396.0 2.2

688 17473758 359 404 401 386 101438 2534 15 2519 401.3 2.6

690 17651938 358 410 407 390 101434 2560 15 2545 406.6 3.0

691 16515044 427 410 405 390 101328 2395 15 2380 405.1 5.3

692 16806486 382 416 408 389 101380 2437 15 2422 408.4 7.4

693 16980630 370 419 417 394 101419 2462 15 2447 416.9 2.6

695 17173498 366 426 420 398 101443 2490 15 2475 419.7 6.3

696 17335400 364 432 425 403 101437 2514 15 2499 424.9 7.3

697 17415656 356 435 427 405 101434 2525 15 2511 427.5 7.8

699 17610018 356 441 432 409 101431 2553 15 2539 432.0 8.6

700 17541364 400 445 437 413 101424 2543 15 2529 436.6 8.9

701 16712065 392 447 427 408 101365 2423 15 2409 427.4 19.6

702 16932056 375 451 442 412 101406 2455 15 2440 441.9 9.2

703 17060404 355 454 444 415 101422 2474 15 2459 444.4 10.0

704 17304860 355 460 447 419 101434 2509 15 2494 446.6 13.0

706 17532364 355 466 451 423 101427 2542 15 2527 451.3 15.0

707 17742650 355 472 456 427 101421 2573 15 2558 455.7 16.0

708 16541230 419 471 445 423 101337 2398 15 2384 445.0 26.0

709 16814356 380 476 455 425 101387 2438 15 2423 455.0 21.0

710 16960858 364 479 463 429 101407 2459 15 2445 462.9 17.0

710 17093302 354 482 465 431 101417 2479 15 2464 464.5 18.0

712 17346446 355 488 467 435 101425 2515 15 2501 467.3 21.0

714 17562786 364 495 471 439 101418 2547 15 2532 471.1 24.0

714 17644584 373 499 475 441 101417 2558 15 2544 474.8 24.0

715 17722210 383 503 477 442 101417 2570 15 2555 477.4 25.0

716 16605336 486 519 473 441 101350 2408 15 2393 473.2 45.0

717 16726971 427 513 470 439 101374 2425 15 2411 469.6 43.0

718 16866784 425 515 482 443 101398 2446 15 2431 482.4 33.0

719 17023420 433 521 488 448 101412 2468 15 2454 487.5 33.0

721 17168432 441 527 491 451 101418 2489 15 2475 491.0 36.0

722 17309840 449 534 496 455 101416 2510 15 2495 495.6 38.0

724 17445408 456 540 500 459 101413 2530 15 2515 500.3 40.0

726 17576558 463 547 505 462 101412 2549 15 2534 504.6 42.0

727 17677886 470 553 509 466 101410 2563 15 2549 508.8 44.0

729 17756554 477 560 513 469 101408 2575 15 2560 513.2 47.0

730 17257022 495 566 509 467 101377 2502 15 2488 509.1 57.0

730 16494932 530 573 509 467 101352 2392 15 2377 509.3 64.0

731 16655850 508 572 514 467 101380 2415 15 2400 513.9 59.0

732 16710891 508 575 521 471 101392 2423 15 2408 520.6 54.0
D-18

Table D-7 T&H Input Parameters for Case 153 (Cont.)

Time 

in 

Minutes

Primary 

Pressure 

(Pa)

Surge-Line 

Temperature 

(°C)

HL 

Temperature 

(°C)

Hot Tube 

Temperature 

(°C)

Cold Tube 

Temperature 

(°C)

Secondary 

Pressure 

(Pa)

Primary 

Pressure 

in psi

Secondary 

Pressure 

in psi

Delta 

P in 

psi

Avr. 

Hot 

Tube 

Temp 

°C HT

HL to 

Tube 

Hot Side 

Delta T

734 16775306 513 584 526 476 101401 2432 15 2418 525.8 58.0

736 16790980 517 590 529 479 101402 2435 15 2420 529.4 61.0

737 16802604 521 597 534 482 101400 2436 15 2422 533.8 63.0

739 16809486 525 604 538 485 101399 2437 15 2423 538.3 66.0

741 16821192 528 611 543 488 101398 2439 15 2424 542.8 68.0

742 16828688 532 618 547 491 101398 2440 15 2425 547.1 71.0

744 16835622 535 625 552 494 101398 2441 15 2426 551.6 73.0

745 16837316 539 632 556 497 101398 2441 15 2427 556.1 76.0

747 16847754 542 640 561 500 101398 2443 15 2428 560.9 79.0

749 16864748 546 648 566 503 101399 2445 15 2431 565.7 82.0

750 16878606 549 655 570 506 101399 2447 15 2433 570.2 85.0

752 16892486 552 663 575 510 101399 2449 15 2435 574.9 89.0

753 16903808 556 672 580 513 101399 2451 15 2436 579.6 92.0

755 16916818 559 680 584 516 101399 2453 15 2438 584.4 95.0

757 16930512 563 688 589 519 101399 2455 15 2440 589.3 99.0

758 16945692 566 696 594 522 101399 2457 15 2442 594.2 102.0

760 16961192 570 705 599 526 101399 2459 15 2445 598.9 106.0

761 16978144 573 713 604 529 101399 2462 15 2447 603.8 109.0

763 16995640 577 722 609 532 101399 2464 15 2450 608.8 113.0

764 17013394 581 731 614 536 101399 2467 15 2452 613.8 117.0

766 17031428 584 740 619 539 101399 2470 15 2455 618.8 121.0

768 17049492 588 749 624 542 101399 2472 15 2457 623.7 125.0

769 17068202 592 758 629 545 101399 2475 15 2460 628.9 129.0

771 17087730 596 767 634 549 101399 2478 15 2463 634.1 133.0

772 17107852 600 777 639 552 101399 2481 15 2466 639.4 137.0

774 17129464 605 787 645 556 101399 2484 15 2469 644.8 142.0

776 17150636 609 796 650 559 101399 2487 15 2472 650.1 146.0

777 17173824 614 807 656 562 101399 2490 15 2476 655.7 151.0

779 17198290 618 818 661 566 101399 2494 15 2479 661.4 156.0

780 17225090 623 829 667 569 101399 2498 15 2483 667.3 161.0

782 17255404 629 840 673 573 101400 2502 15 2487 673.3 167.0

783 17289820 635 853 680 576 101401 2507 15 2492 679.5 173.0

785 17328194 641 866 686 580 101402 2513 15 2498 686.4 180.0

787 17371994 648 881 694 584 101404 2519 15 2504 693.6 188.0

788 17424672 656 898 702 588 101406 2527 15 2512 701.6 197.0

789 17454806 660 908 706 590 101408 2531 15 2516 705.9 202.0

790 17486682 665 918 710 592 101410 2536 15 2521 710.4 208.0

791 17523474 670 929 715 594 101412 2541 15 2526 715.2 214.0

791 17565386 676 942 720 596 101415 2547 15 2532 720.4 221.0
D-19

Table D-7 T&H Input Parameters for Case 153 (Cont.)

Time 

in 

Minutes

Primary 

Pressure 

(Pa)

Surge-Line 

Temperature 

(°C)

HL 

Temperature 

(°C)

Hot Tube 

Temperature 

(°C)

Cold Tube 

Temperature 

(°C)

Secondary 

Pressure 

(Pa)

Primary 

Pressure 

in psi

Secondary 

Pressure 

in psi

Delta 

P in 

psi

Avr. 

Hot 

Tube 

Temp 

°C HT

HL to 

Tube 

Hot Side 

Delta T

792 17610286 681 954 726 598 101418 2553 15 2539 725.6 229.0

793 17671602 689 972 732 601 101423 2562 15 2548 732.1 239.0

794 17295002 826 1,013 739 603 101419 2508 15 2493 738.8 274.0

795 16933844 804 1,077 743 599 101410 2455 15 2441 743.2 334.0

795 17161326 832 1,188 784 608 101485 2488 15 2474 783.6 404.0

796 17240314 851 1,223 788 613 101523 2500 15 2485 788.3 435.0

797 17288726 864 1,245 797 616 101533 2507 15 2492 796.8 448.0

798 17324848 877 1,275 806 618 101527 2512 15 2497 806.1 468.0

799 17355544 887 1,306 816 620 101509 2517 15 2502 816.4 489.0

799 17374412 898 1,341 828 622 101488 2519 15 2505 828.4 512.0

800 17369112 906 1,365 838 623 101473 2519 15 2504 837.5 528.0

801 17362924 914 1,386 846 626 101461 2518 15 2503 845.6 541.0

802 17346996 921 1,401 853 628 101453 2515 15 2501 852.5 548.0

803 17295070 930 1,413 864 632 101441 2508 15 2493 863.8 549.0

806 17222752 937 1,411 875 638 101419 2497 15 2483 875.2 536.0

808 17168220 941 1,409 885 644 101411 2489 15 2475 885.4 524.0

811 17100416 943 1,405 896 651 101400 2480 15 2465 895.5 509.0

814 17033290 941 1,398 904 658 101394 2470 15 2455 903.9 494.0

818 17023456 943 1,387 912 665 101390 2468 15 2454 911.8 475.0

822 17100190 945 1,370 918 673 101383 2480 15 2465 918.4 452.0

826 17211974 950 1,360 926 681 101380 2496 15 2481 925.9 434.0

830 17194184 945 1,350 931 688 101376 2493 15 2478 930.6 420.0

833 17074150 934 1,345 934 694 101374 2476 15 2461 934.3 411.0

836 16953292 922 1,339 937 700 101373 2458 15 2444 937.2 402.0

838 16845614 911 1,334 939 704 101372 2443 15 2428 938.8 395.0

841 16757801 901 1,331 942 710 101374 2430 15 2415 942.0 389.0

843 16804596 905 1,313 941 715 101371 2437 15 2422 941.2 372.0

844 16781984 901 1,300 939 715 101368 2433 15 2419 938.8 361.0

845 16777074 899 1,283 934 716 101364 2433 15 2418 934.3 348.0

849 16719079 890 1,294 940 718 101364 2424 15 2410 940.2 354.0

851 16631669 880 1,299 944 721 101365 2412 15 2397 944.3 355.0

853 16539559 870 1,302 948 725 101365 2398 15 2384 947.6 355.0

856 16444167 860 1,304 950 729 101365 2384 15 2370 949.8 354.0

858 16351976 850 1,303 951 732 101365 2371 15 2356 951.3 352.0

860 16267959 840 1,303 953 735 101364 2359 15 2344 952.6 350.0

863 16149878 828 1,301 953 738 101364 2342 15 2327 953.2 348.0

865 16039874 817 1,300 954 741 101363 2326 15 2311 954.2 346.0

868 15936266 807 1,300 955 743 101363 2311 15 2296 955.4 344.0

870 15829010 796 1,299 957 746 101363 2295 15 2281 956.6 342.0
D-20

Table D-7 T&H Input Parameters for Case 153 (Cont.)

Time 

in 

Minutes

Primary 

Pressure 

(Pa)

Surge-Line 

Temperature 

(°C)

HL 

Temperature 

(°C)

Hot Tube 

Temperature 

(°C)

Cold Tube 

Temperature 

(°C)

Secondary 

Pressure 

(Pa)

Primary 

Pressure 

in psi

Secondary 

Pressure 

in psi

Delta 

P in 

psi

Avr. 

Hot 

Tube 

Temp 

°C HT

HL to 

Tube 

Hot Side 

Delta T

872 15719427 785 1,298 958 749 101362 2279 15 2265 957.8 341.0

876 15764007 794 1,298 963 753 101363 2286 15 2271 963.1 335.0

883 15720647 783 1,307 969 760 101362 2279 15 2265 968.7 338.0

885 15609858 772 1,310 970 762 101362 2263 15 2249 970.3 340.0

887 15493158 761 1,312 972 765 101362 2247 15 2232 971.7 340.0

890 15376555 750 1,313 973 767 101361 2230 15 2215 973.0 340.0

891 15452803 759 1,314 975 769 101364 2241 15 2226 974.8 339.0

892 16746626 832 1,316 994 772 101383 2428 15 2414 994.1 321.0

893 16766600 1,172 1,356 997 771 101351 2431 15 2416 997.4 359.0

894 17313854 1,109 1,351 981 766 101360 2511 15 2496 981.0 370.0

895 17545106 1,117 1,338 968 763 101358 2544 15 2529 968.0 370.0

895 17177846 1,182 1,336 963 762 101351 2491 15 2476 963.5 372.0

153short-end Case 153 (late TDAFW pump failure) is shortened by removing some of the earlier time steps

not contributing to results

0.01 Significance factor to reduce time steps (0.0 uses all time steps input)

1.00 Fraction of “hot” SG tubes (1.00 means all flaws (100 percent) are on the hot tubes)
D-21

Table D-8 Margin for the Case with Failure of TDAFW Pump at 4 Hours

Time in Minutes

NUREG/

CR-6995

Calculator Comment

1 Event starts 000 000

2 TDAFW pump fails 240

3 Evacuation starts 240

4 Evacuation ends for internal events 480

5 SGs dryout 583

6 Evacuation ends for external events 720

7 HL fails 26% 768

8 HL fails 49% 769

9 HL fails 100% 777

10 HL 1 fails by creep rupture 793

11 Hot tube fails 6 cm2 (1 tube 

equivalent)

799

12 Hot tube fails max 6 cm2 (1 tube 

equivalent)

799

13 SL fails 33% 808

14 SL fails 58% 818

15 SL fails 100% 893

Margin = HL fails 100%—Hot tube fails 6 cm2

(0.93 in.2)

-22

The definition of margin is based on the crucial T&H assumption that a full break of a single SG 

tube (6 cm2 (0.93 in.2

)) would not depressurize the RCS to prevent RCS failure elsewhere.

Hot tube fraction = 1.0 (all flaws are assumed to be on the hot tubes)

NUREG/CR-6995 RELAP 2010 Case 153

D.1.6 Effect of 690TT Material 

This sensitivity analysis studies a comparison of both W and CE SG types with 690TT tube 

material. For this purpose, two cases are defined and are simulated by the calculator:

Case 1:

Calvert Cliffs with 690TT tubes; a “large” wear-type flaw 4 cm (1.6 in.) and 40 percent deep. 

SBO with failure of the turbine-driven pump at the start of the event; loop A with average SG 

tubes used from the TH analysis.
D-22

Case 2:

Zion with 690TT tubes; a “large” wear-type flaw 4 cm (1.57 in.) and 40 percent deep. SBO with 

failure of the turbine-driven pump at the start of the event; Wnewbase case used from the 

TH analysis.

In terms of the calculator input files used, the case information can be summarized as 

shown below:

Case 1: Case 2:

TH-CE-A-0-Avr-short TH-Wnewbase-short

W4-40 W4-40

Calvert Cliffs (TT690) ZION690

Table D-9 summarizes the results. When 690TT material is postulated to be used in a W-type 

SG, the margin is still favorable for the failure of the HL before the large-flawed SG tube, but it is 

shortened compared to the same case with 600TT material (Case 3). Case 3 is defined as

Case 3:

TH-Wnewbase-short

W4-40

ZION600

Table D-9 also shows the Case 3 margin. The result that the Case 3 margin is larger than the 

Case 2 margin seems to indicate that SG tubes with 690TT material with a “large” flaw will leak 

earlier than SG tubes with 600TT material with the same “large” flaw (in 233 minutes versus 

243 minutes in this case).
D-23

Table D-9 Comparison of 690TT Cases of W vs. CE-Type SGs

Time in Minutes

NUREG/

CR-6995

Case 1 

Calculator

Case 2 

Calculator

Case 3 

Calculator

Comment

1 Event starts 000 000

2 TDAFW pump fails 240

3 Evacuation starts 240

4 Evacuation ends for internal 

events

480

5 SG dryout 583

6 Evacuation ends for external 

events

720

7 HL fails 26%

8 HL fails 49%

9 HL fails 100% 357 221 219

10 HL 1 fails by creep rupture 793

11 Hot tube fails 6 cm2 (0.93 in.2) 

(1 tube equivalent)

325 233 243 Case 1 max. 

failure area 

is 4.5 cm-sq.

12 Hot tube fails max. 6 cm2

(0.93 in.2) (1 tube equivalent)

13 SL fails 33%

14 SL fails 58%

15 SL fails 100%

Margin = HL fails 100%—Hot 

tube fails 6 cm2 (0.93 in.2)

32 -12 -24

The definition of margin is based on the crucial TH assumption that a full break of a single SG 

tube (6 cm2 (0.93 in.2

)) would not depressurize the RCS to prevent RCS failure elsewhere.

Hot tube fraction = 1.0 (all flaws are assumed to be on the hot tubes)

NUREG/CR-6995 RELAP 2010 Case 153

D.1.7 Conclusions 

The analyses elsewhere in this report rely on the C-SGTR calculation results. The C-SGTR 

calculator provides some estimates of uncertainties, especially for the integrated leak areas. 

However, it does not provide a robust uncertainty estimate for uncertainties in the scenario TH 

input. For better understanding of the effect of TH uncertainties, sensitivity analyses were 

performed on a base case (W SBO core-damage sequence with a large flaw subject to 

temperature challenges). The sensitivity analyses indicate that, for this base case, the margin 

between the HL failure occurring first and tube failure growing into a large leak is not sensitive to 

changes to the base values of two major modeling parameters. These two modeling parameters 

are the HL thickness (to account for the existence of weld overlays) and the temperature 

difference between the HL and the hot tube.
D-24

The margins are as follows:

Case Name Margin

Base Case -18 minutes

Reduced dT between HL and hot tube -14 minutes

Increased HL thickness -16 minutes

The -18-minute base margin is a reliable good margin, which appears to have a tight spread 

when other major modeling parameters are changed in an unfavorable direction.

Although these conclusions apply to this scenario with these cases, they also provide 

the following:

• insights about the model stability against some key changes

• some confidence that the margin point estimate is stable

An additional sensitivity analysis was made with the secondary-side pressure set at 6.9 MPa 

(1,100 psi). The result shows that the margin increases to 45 minutes.

Finally, if the TDAFW pump fails at 4 hours, the HL and C-SGTR failures are pushed further in 

time to about 13 hours following the SBO.

D.2 Sensitivity Analyses for the Selected CE Plant

The following sensitivity analyses were performed for the example CE plant. The measure of 

comparison used for these sensitivity analyses was based on the reevaluation of C-SGTR 

probability for short-term SBO (stsbo) sequences where large early release frequency (LERF) is 

of concern. In some cases; the C-SGTR probability was only reevaluated for one loop rather 

than for both loop A and loop B (i.e., the reactor unit). When the sensitivity analysis was limited 

to one loop, loop B was selected because of its higher contribution to C-SGTR. The difference 

between the revised C-SGTR probability and the base C-SGTR probability was used to 

prioritize the effect of the sensitivity results. The changes of less than 25 percent are assigned 

as low, 25 to 50 percent as moderate, 50 to 100 percent as high, and any increases above 

200 percent as significant.

D.2.1 Stuck-Open Failure of Secondary Relief Valves before SG Dryout

In SBO scenarios, before SG dryout, the secondary-side relief valves (SG power-operated relief 

valves or main steam safety valves (MSSVs) could be demanded and fail to reclose. This could 

happen in either or both SGs. Stick-open relief valves initially depressurize and cool the primary 

below the accumulator discharge setpoint. After accumulator discharge, the SGs will go dry, the 

primary will repressurize, and the onset of core damage will be reached, although slightly 

delayed. The probability of C-SGTR is expected to be higher because of a lower secondary-side 

pressure and delayed HL failure. A bounding analysis of this scenario was evaluated using the 

MELCOR package. Chapter 3 of this report refers to this scenario to as stsbo-as and long-term 

SBO (ltsbo)-as. 
D-25

Figures D-6 through D-9 shows the following graphs for the stsbo-as scenario. Figures D-10 

through D-13 show the same graphs for ltsbo-as scenarios. The specific information presented

in each figure for stsbo-as and ltsbo-as is shown below:

• Figure D-5 shows the primary and secondary pressure

• Figures D-6 and D-10: Overall results for loop A

• Figures D-7 and D-11: Difference of HL temperature and average hot/hottest tube 

temperature for loop A

• Figures D-8 and D-12: Overall results for loop B

• Figures D-9 and D-13: Difference of HL temperature and average hot/hottest tube 

temperature for loop B

Figure D-5 SBO with TDAFW pump operating for 0 hours with MSSVs stuck open; 

Calvert Cliffs

0.00E+00

5.00E+02

1.00E+03

1.50E+03

2.00E+03

2.50E+03

3.00E+03

0 100 200 300 400 500 600

Pressure (in psi)

Time (in Minutes)

Primary Pressure

Secondary Pressure
D-26

Figure D-6 SBO with TDAFW pump operating for 0 hours; Calvert Cliffs loop A

Figure D-7 Temperature differences in SBO with TDAFW pump operating for 0 hours; 

Calvert Cliffs loop A

0

200

400

600

800

1000

1200

1400

1600

1800

0 100 200 300 400 500 600

Temperature (in 

oCelsius)

Time (in Minutes)

Surge Line Temp

Top Hot Leg Temp

Ave Hot SG Tube

Temp

-300

-250

-200

-150

-100

-50

0

50

100

150

200

0 100 200 300 400 500 600

Temperature (in 

oCelsius)

Time (in Minutes)

Hottest Tube - Top Hot Leg C

Average Hot - Top Hot Leg C
D-27

Figure D-8 SBO with TDAFW pump operating for 0 hours; Calvert Cliffs loop B

Figure D-9 Temperature differences in SBO with TDAFW pump operating for 0 hours; 

Calvert Cliffs loop B

0

200

400

600

800

1000

1200

1400

1600

1800

0 100 200 300 400 500 600

Temperature (in 

oCelsius)

Time (in Minutes)

Surge Line Temp

Top Hot Leg Temp

Ave Hot SG Tube Temp

Ave Cold SG Tube Temp

Hottest Tube Temp

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 100 200 300 400 500 600

Temperature (in 

oCelsius)

Time (in Minutes)

Hottest Tube - Top Hot Leg C

Average Hot - Top Hot Leg C
D-28

Figure D-10 SBO with TDAFW pump operating for 4 hours; Calvert Cliffs loop A

Figure D-11 Temperature differences in SBO with TDAFW pump operating for 4 hours; 

Calvert Cliffs loop A

0

200

400

600

800

1000

1200

1400

1600

0 500 1000 1500 2000

Temperature (in oCelsius)

Time (in Minutes)

Surge Line Temp

Top Hot Leg Temp

Ave Hot SG Tube Temp

Ave Cold SG Tube Temp

Hottest Tube Temp

-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

0 500 1000 1500 2000

Temperature (in 

oCelsius)

Time (in Minutes)

Hottest Tube - Top Hot Leg C

Average Hot - Top Hot Leg C
D-29

Figure D-12 SBO with TDAFW pump operating for 4 hours; Calvert Cliffs loop B

Figure D-13 Temperature differences in SBO with TDAFW pump operating for 4 hours; 

Calvert Cliffs loop B

0

200

400

600

800

1000

1200

1400

1600

0 500 1000 1500 2000

Temperature (in 

oCelsius)

Time (in Minutes)

Surge Line Temp

Top Hot Leg Temp

Ave Hot SG Tube

Temp

-60

-40

-20

0

20

40

60

80

100

120

140

0 500 1000 1500

Temperature (in 

oCelsius)

Time (in Minutes)

Hottest Tube - Top Hot Leg C

Average Hot - Top Hot Leg C
D-30

Separate C-SGTR runs were performed for the average hot and hottest tube for loop A and 

loop B. The results for average hot and hottest tube for each loop were then combined to 

estimate the single loop probabilities of C-SGTR. Figures D-14 and D-15 show the results for 

loops A and B.

As shown in both figures, the curves associated with RCS survival probability are significantly 

shifted to the right compared to the probability of SG tube rupture (SGTR) with leak areas less 

than 3 and 6 cm2

(0.46 and 0.93 in.2). This indicates that an SGTR that exceeds the critical leak 

area will occur before the HL failure; therefore, the C-SGTR probability will be very high (close 

to 1).

Figure D-16 shows a similar graph when the results from loop A and loop B are combined. This 

figure also shows that the RCS survival probability is on the right side of the graph for SGTR 

leak probability curves. The results show that the failure of the secondary-side relief valve early 

during the sequence can have a significant effect on the LERF contribution because of 

C-SGTR. Table D-10 below shows the results of this reevaluation for stsbo-as sequences. As

shown in Table D-10, the C-SGTR probability is almost one (0.99) for this scenario.

Figure D-14 Probabilities of SGTR leak rates less than 3 and 6 cm2 vs. HL survival 

probability for stsbo-as-a-scf

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

15500 16000 16500 17000 17500 18000

Probability

Time (s)

P(SGTR<3cm^2)

P(SGTR<6cm^2)

P(RCS Survive)
D-31

Figure D-15 Probabilities of SGTR leak rates less than 3 and 6 cm2 vs. HL survival 

probability for stsbo-as-b-scf

Figure D-16 Probability of SGTR less than 6 cm2 and probability of RCS survival

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

15000 15500 16000 16500 17000 17500 18000

Probability

Time (s)

P(SGTR<3cm^2)

P(SGTR<6cm^2)

P(RCS Survive)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

18000 19000 20000 21000 22000 23000 24000

Probability

Time (s)

P(SGTR<6cm^2)

P(RCS-SURVIVE)
D-32

Table D-10 Sensitivity Results for Early Stick-Open Failures of the Secondary 

Relief Valves

Case runs Loop B CSGTR

> 3 cm2

Loop A CSGTR

> 3 cm2

CSGTR

> 6 cm2

Stsbo-a [base] 0.45 0.217 0.2

Stsbo-as [stick-open secondary relief valve] 0.999 0.997 0.99

Opening of Secondary Relief Valves after SG Dryout

The operators are guided to depressurize the SGs by opening the secondary relief valves in 

anticipation of using an alternate source of water to refill the SGs as a part of the severeaccident management guidelines. This sensitivity analysis examines the effect of intentionally 

opening the secondary relief valve after the onset of core damage when the operators fail to 

refill the SGs. The analysis was performed by setting the secondary-side pressure to 1X105

Pascal after the hot-gas temperature reaches about 640 degrees Celsius 

(1,184 degrees Fahrenheit) (i.e., at 16,800 seconds for stsbo-a). The effects on primary 

pressure or temperature are not expected to be significant; therefore, no changes were made to 

these inputs. Figure D-17 shows the results for loop B with and without open secondary relief 

valves after SG dryout. As can be seen, the graph for the case where the secondary relief valve 

is open is shifted further to the left, indicating that the likelihood of C-SGTR greater than 3 cm2

(0.46 in.2

) is higher than the base case.

Figure D-18 shows the aggregate effect of opening secondary relief valves after SG dryout for 

both loops. Similar to the previous graph, the SGTR curve associated with open secondary 

relief valves is shifted to the right, indicating a higher probability of C-SGTR.

Figure D-17 Probability of SGTR leak rate less than 3 cm2 for loop B with and without 

open secondary relief valves after SG dryout

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

15000 17000 19000 21000 23000 25000

Probability

Time (s)

STSBO-a with stick open

secondary relief

STSBO-a with no failure

of Secondary relief

P(RCS-SURVIVE)
D-33

In summary, the results show that the opening of secondary-side relief valves after SG dryout 

and the onset of core damage can increase the LERF contribution caused by C-SGTR by about 

65 percent (from 0.2 to 0.33) for stsbo-a scenarios. Table D-11 shows the results of 

this reevaluation.

Figure D-18 Probability of SGTR leak rate less than 6 cm2 with and without open 

secondary relief valves after SG dryout

Table D-11 Sensitivity Results for Opening the Secondary Relief Valves after SG Dryout

Case runs Loop B CSGTR

> 3 cm2

Loop A CSGTR

> 3 cm2

CSGTR

> 6 cm2

Stsbo-a [base] 0.450 0.217 0.200

Stsbo-a [secondary relief valve left opened 

after SG dryout] 0.591 0.262 0.330

D.2.2 Critical C-SGTR Leak Area 

The critical area equivalent to a guillotine break of one tube (approximately 6 cm2 (0.93 in.2

)) 

was considered to be sufficient to meet the LERF threshold if the secondary-side relief valves 

are open. Some MELCOR analyses showed that this size of leakage may not pressurize the 

secondary, such that SG relief valves are demanded. These MELCOR analyses assumed that 

there is a preexisting secondary leakage area of 3.22 cm2 (0.5 in.2

) from the starting point of the 

sequence. To ensure that the secondary relief valves are demanded and the primary can be 

depressurized, a larger critical C-SGTR leak area may have to be considered. Figure D-19 

shows the probability graph of various leak rates for the stsbo-a sequence when considering the 

expected flaw sample used for this study. The probability of RCS survival is also displayed on 

the same figure, clearly showing the relative positions of the probability curves for various leak 

rates to the probability curve of RCS survival.

Figure D-20 shows another way of presenting this information in terms of the probability of 

C-SGTR. This figure shows how the C-SGTR probability decreases for larger critical leak rates 

for the stsbo-a sequence. It should be emphasized that these curves are only for the expected 

flaw sample used for this study and shall not be considered generic. Similar graphs, however, 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

18000 20000 22000 24000

Probability

Time (s)

P(SGTR<6cm^2)

P(RCS-SURVIVE)

P(SGTR<6cm^2) w/o open

secondary
D-34

could be generated for different accident sequences and for another set of flaws for each SG 

using the existing tools and approach.

Using Figure D-20, it can be shown that the probability of C-SGTR is reduced from 0.2 to 0.06 if 

one assumes a critical C-SGTR leak area of 12 cm2 (1.86 in.2

) instead of 6 cm2 (0.93 in.2). 

Figure D-19 Probability of SGTR with leak rates smaller than a specific value and 

probability of RCS survival as a function of accident time

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

18000 19000 20000 21000 22000

Probability

Time (S)

P(SGTR<1cm^2)

P(SGTR<2cm^2)

P(SGTR<3cm^2)

P(SGTR<4cm^2)

P(SGTR<5cm^2)

P(SGTR<6cm^2)

P(SGTR<7cm^2)

P(SGTR<8cm^2)

P(SGTR<9cm^2)

P(SGTR<10cm^2)

P(SGTR<11cm^2)

P(SGTR<12cm^2)

P(RCS-SURVIVE)
D-35

Figure D-20 Probability of SGTR as a function of critical leak area

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 2 4 6 8 10 12 14

P(CSGTR)

Leak Area (cm^2)

P(CSGTR)

E-1

APPENDIX E 

 

WESTINGHOUSE STATION BLACKOUT SCENARIO AND 

SENSITIVITY CASES 

This appendix contains additional sensitivity cases for consequential steam generator (SG) tube 

rupture (C-SGTR) cases in a Westinghouse 4-loop plant with a station blackout (SBO) core 

damage sequence.

E.1 Westinghouse SBO Scenario and Sensitivity Cases 

The following SBO scenario is considered for the sensitivity cases for temperature-induced 

C-SGTR events:

Scenario Name Scenario Description (Westinghouse 4-loop NPP–ZION-like)

WNEWBASE

SBO at time zero, no turbine-driven auxiliary feedwater (TDAFW) pump, 

3.22-cm2 (0.5-in2) leak area in each SG allowing depressurization after 

dryout. Reactor coolant pump seal leakage of 79.5 liters per 

minute/pump (21 gallons per minute (gpm)/pump). Ac power is not 

recovered during this scenario.

This core damage scenario included the following three cases:

Case 1 studies the above scenario with thermally treated 600TT material and 1 large SG tube 

flaw.

Case 2 studies the above scenario with 600TT material and 10 large SG tube flaws in each of 

the four SGs.

Case 3 studies the above scenario with 690TT material and 5 large SG tube flaws in each of the 

four SGs.

The C-SGTR calculator is used for the calculations. The margin between HL failure time and 

large SG leak time is estimated. The input files used for the three cases are as follows:

Plant 

Information 

File Case

TH Scenario File 

Name Flaw File Name

Total # of 

Flaws in all 

SGs

Case 1 ZION600TT TH-wnewbase-short Flaw-W3-50 1

Case 2 ZION600TT TH-wnewbase-short Flaw-Multi-42 42

Case 3 ZION690TT TH-wnewbase-short Flaw-Multi-21-TT690 21

For comparison with other scenarios, the margin Mt between HL and tube failure is defined as

Mt = Mean time of likely HL failure – mean time of maximum tube flaw failure in terms of minutes
E-2

Choosing the mean time of likely HL failure and hot-tube failure is left to the judgment of 

the analyst.

Figures E-1 and E-2 summarize the relevant scenario parameters.

Figure E-1 WNEWBASE scenario parameters

Figures E-3 and E-4 summarize the flaw distributions for 600TT and 690TT SG tube materials.

0

500

1000

1500

2000

2500

3000

0

200

400

600

800

1000

1200

0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00

Pressure (psi)

Temperature (oC)

Time in Minutes

Avr. Hot Tube Temp C HT delta P in psi
E-3

Figure E-2 Delta T (in degrees Celsius) between HL and hot tube—WNEWBASE

0

100

200

300

400

500

600

0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00

Axis Title

Time in Minutes

HL to Tube Hot Side Delta T

HL to Tube hot side delta T
E-4

Bin size is ±0.25 centimeter (cm) from the bin center shown above. (For example, bin 0.75 goes 

from 0.5 to 1.0 cm.)

Flaw Bin (cm) # of Flaws

0.25 138

0.75 270

1.25 189

1.75 99

2.25 44

2.75 17

3.25 5

3.75 10

4.25 3

Total = 775

Average Size = 1.1 cm Average Depth = 13%

Largest flaw is 4.46 cm (1.76 in.) in size with a depth of 32%.

Figure E-3 Histogram for flaw distribution (by size) for 600TT

Total of 10 flaw samples for a Zion-like SG with 3,880 600TT tubes after the 

15th “cycle”; all flaws are wear type

138

270

189

99

44

17

5 10 3

0

50

100

150

200

250

300

0.25 0.75 1.25 1.75 2.25 2.75 3.25 3.75 4.25

#

o

f

F

l

a

w

s

i

n

B

i

n

Length in cm up to the value shown

600TT Flaws for 10 SGs 

Distribution by Length in cm

Example: There are 270 flaws longer 

than 0.25 cm but not longer than 

0.75 cm 
E-5

Total # of Flaws = 421

Average Size = 1.1 cm

Average Depth = 13%

Max Length = 4.4 cm

Max Depth = 47%

Largest flaw is 4.4 cm in size with a depth of 20%.

Deepest flaw is 47% with a size of 1.8 cm.

Figure E-4 Histogram for flaw distribution (by size) for 690TT

Total of 10 flaw samples for a Zion-like SG with 3,880 690TT tubes after the 

15th “cycle”; all flaws are wear type

Note: All flaws 40 percent or deeper and generated before K=15 are assumed to be identified 

and removed by plugging the tubes. Thus, only flaws 40 percent or deeper that are generated in 

the last cycle would show up in the flaw samples.

0

20

40

60

80

100

120

140

160

0.25 0.75 1.25 1.75 2.25 2.75 3.25 3.75 4.25

Midpoint of Bin in cm

# of Flaws for 10 SGs with 690TT after the 15th 

Cycle

# of Flaws
E-6

E.2 Case 1: WNEWBASE with 1 Large Flaw and 600TT

The case with 600TT and a single large flaw of W3-50 (wear-type flaw with length 3 cm 

(1.18 inches (in.)) and depth 50 percent) produced the results shown in Table E-1.

Table E-1 WNEWBASE Results for Case 1

Time in 

Hours

Time in 

Seconds

HL Failure 

Prob.

Surge Line 

Failure Prob.

Amean

cm2

A75

cm2

A95

cm2

3.52 12656 0.00 0.00 0.00 0.00 0.00

3.53 12716 0.00 0.00 0.00 0.00 0.00

3.55 12776 0.00 0.00 0.00 0.00 0.00

3.56 12830 0.02 0.00 0.00 0.00 0.00

3.58 12884 0.07 0.00 0.00 0.00 0.00

3.59 12938 0.17 0.00 0.00 0.00 0.00

3.61 12992 0.33 0.00 0.00 0.00 0.00

3.62 13048 0.55 0.00 0.00 0.00 0.00

3.63 13084 0.70 0.00 0.00 0.00 0.00

3.64 13090 0.72 0.00 0.00 0.00 0.00

3.64 13096 0.75 0.00 0.00 0.00 0.00

3.64 13108 0.79 0.00 0.00 0.00 0.00

3.65 13132 0.86 0.00 0.00 0.00 0.00

3.66 13162 0.91 0.00 0.00 0.00 0.00

3.67 13204 0.97 0.00 0.00 0.00 0.00

3.68 13246 0.99 0.00 0.00 0.00 0.00

3.69 13288 1.00 0.00 0.00 0.00 0.00

3.70 13330 1.00 0.00 0.00 0.00 0.00

3.84 13812 1.00 0.19 0.01 0.00 0.00

3.84 13836 1.00 0.22 0.05 0.00 0.00

3.85 13872 1.00 0.26 0.56 1.30 2.02

3.87 13938 1.00 0.32 3.23 4.47 4.93

3.89 14012 1.00 0.43 4.40 4.66 4.94

3.91 14078 1.00 0.50 4.46 4.66 4.94

3.93 14150 1.00 0.59 4.46 4.67 4.94

.....

4.88 17556 1.00 0.99 4.47 4.67 4.96

4.94 17778 1.00 0.99 4.47 4.67 4.96

5.00 18000 1.00 0.99 4.47 4.67 4.96

The conclusions are as follows:

• Hot leg fails at 217 minutes.

• Hot tube fails at 232 minutes.

• Surge line fails at 233 minutes.

• Expected value of the maximum SG tube leak area reached is 4.5 cm2 (0.69 in.2

).
E-7

• Maximum flow area from a single tube is 6.1 cm2 (0.94 in.2).

• Margin is -15 minutes.

Because the maximum leak area of 6 cm2 (0.93 in.2

) (critical leak area) is not reached in this 

case, the margin is defined as follows:

Margin = {time at which HL failure probability exceeds 50%} –

{time at which integrated tube leak probability exceeds 50% of critical leak area}

E.3 Case 2: WNEWBASE with 42 Flaws and 600TT 

A second case is run as follows.

From the 10 flaw samples generated for 600TT, 42 flaws of the largest size and the largest 

depth are chosen. This corresponds to about 10 large flaws per SG. Other parameters of this 

case are the same as the one discussed above. All flaws are placed in hot tubes.

Out of the 42 flaws modeled for this case:

Largest flaw is 4.46 cm (1.76 in.) in size with a depth of 32 percent.

Deepest flaw is 40 percent with a size of 0.83 cm (0.32 in.).

The results are summarized in Tables E-2 and E-3.

Max # of tube-equivalent failures = 21 tubes at 250 minutes

Margin = -15 minutes

(Margin = HL fails 100%—Hot tube fails 6 cm2 (0.93 in.2

))
E-8

Table E-2 Summary Output for the Final Scenario with 42 “Large” Flaws

Time in Minutes

NUREG/CR-6995 Calculator Comment

Event starts 000 000

SG dryout 100

Evacuation starts 120

HL fails 14% 215

First fuel rod clad rupture 217

HL fails 54% 217

HL fails 100% 221

HL 1 fails by creep rupture 227

Surge line fails 16% 232

Hottest tube creep-rupture failure 233

Surge line fails 55% 236

Hot tube fails 6 cm2 (0.93 in.2) (1-tube 

equivalent) 236

Hot tube fails 22 cm2 (3.41 in.2) (4-tube 

equivalent) 238

Hot tube fails max 125 cm2 (19.375 in.2)(21-tube 

equivalent) 252

Surge line fails 100% 280

Evacuation ends for internal events 360

Evacuation ends for external events 600

Margin = HL fails 100%—Hot tube fails 6 cm2

(0.93 in.2) -15

Note: Surge line results are given for completeness only. The surge line correlation and materials assumed may 

need further examination but are not needed for the purposes of this analysis.
E-9

Table E-3 WNEWBASE Results for Case 2

Time in 

Hours

Time in 

Minutes

HL Failure 

Prob.

Surge Line 

Failure Prob. Amean cm2 A75cm2

A95

cm2

3.52 211 0.00 0.00 0.00 0.00 0.00

3.54 212 0.00 0.00 0.00 0.00 0.00

3.56 213 0.01 0.00 0.00 0.00 0.00

3.57 214 0.04 0.00 0.00 0.00 0.00

3.59 215 0.14 0.00 0.00 0.00 0.00

3.61 216 0.31 0.00 0.00 0.00 0.00

3.62 217 0.54 0.00 0.00 0.00 0.00

3.64 218 0.78 0.00 0.00 0.00 0.00

3.65 219 0.87 0.00 0.00 0.00 0.00

3.65 219 0.94 0.00 0.00 0.00 0.00

3.67 220 0.99 0.00 0.00 0.00 0.00

3.69 221 1.00 0.00 0.00 0.00 0.00

3.70 222 1.00 0.00 0.00 0.00 0.00

3.72 223 1.00 0.00 0.00 0.00 0.00

3.80 228 1.00 0.00 0.00 0.00 0.00

3.80 228 1.00 0.00 0.00 0.00 0.00

3.81 229 1.00 0.00 0.00 0.00 0.00

3.82 229 1.00 0.01 0.00 0.00 0.00

3.83 230 1.00 0.03 0.00 0.00 0.00

3.84 230 1.00 0.08 0.00 0.00 0.00

3.85 231 1.00 0.10 0.00 0.00 0.00

3.86 232 1.00 0.16 0.00 0.00 0.00

3.89 233 1.00 0.28 0.01 0.00 0.00

3.91 235 1.00 0.41 0.46 0.61 0.89

3.94 236 1.00 0.55 5.40 6.40 9.90

3.96 238 1.00 0.67 22.00 24.00 27.00

3.99 239 1.00 0.76 36.00 38.00 40.00

4.02 241 1.00 0.85 44.00 45.00 45.00

4.05 243 1.00 0.89 49.00 50.00 54.00

4.08 245 1.00 0.91 71.00 75.00 81.00

4.12 247 1.00 0.93 103.00 105.00 110.00

4.16 250 1.00 0.95 123.00 125.00 127.00

4.20 252 1.00 0.96 125.00 126.00 127.00

4.24 255 1.00 0.97 125.00 126.00 127.00

4.61 277 1.00 0.98 125.00 126.00 127.00

4.67 280 1.00 0.99 125.00 126.00 127.00

5.00 300 1.00 0.99 125.00 126.00 127.00
E-10

E.4 Case 3: WNEWBASE with 21 Flaws and 690TT

A third case is run as follows.

From the 10 flaw samples generated for 690TT, 21 flaws of largest size and largest depth are 

chosen. This corresponds to about 2 large flaws per SG. Other parameters of this case are the 

same as for the one discussed above.

Out of the 21 flaws modeled for this case:

Largest flaw is 4.4 cm (1.73 in.) in size with a depth of 20 percent.

Deepest flaw is 47 percent with a size of 1.8 cm (0.71 in.).

Table E-4 summarizes the results. The margin is -7 minutes. Max number of tube-equivalent 

failures is nine and occurs at 4 hours.

Max # of tube-equivalent failures = 9 tubes at 4 hours

Margin = -7 minutes

(Margin = HL fails 100%—Hot tube fails 6 cm2 (0.93 in.2

))
E-11

Table E-4 WNEWBASE Results for Case 3 with 690TT

Time in 

Hours

Time in 

Seconds

HL Failure 

Prob.

Surge Line 

Failure Prob.

Amean 

cm2 A75 cm2 A95 cm2

3.61 216 0.35 0.00 0.01 0.02 0.02

3.62 217 0.54 0.00 0.02 0.02 0.03

3.64 218 0.79 0.00 0.04 0.05 0.06

3.65 219 0.88 0.00 0.05 0.06 0.07

3.65 219 0.93 0.00 0.07 0.08 0.09

3.67 220 0.98 0.00 0.11 0.12 0.13

3.69 221 1.00 0.00 0.17 0.18 0.20

3.70 222 1.00 0.00 0.24 0.25 0.28

3.72 223 1.00 0.00 0.33 0.35 0.39

3.73 224 1.00 0.00 0.40 0.42 0.47

3.74 224 1.00 0.00 0.46 0.49 0.54

3.75 225 1.00 0.00 0.56 0.60 0.66

3.75 225 1.00 0.00 0.69 0.73 0.80

3.76 226 1.00 0.00 0.97 1.03 1.13

3.77 226 1.00 0.00 1.60 1.70 1.80

3.78 227 1.00 0.00 2.40 2.50 2.80

3.79 227 1.00 0.00 3.20 3.40 3.70

3.80 228 1.00 0.00 4.10 4.30 4.70

3.80 228 1.00 0.00 5.50 5.80 6.30

3.81 229 1.00 0.00 7.50 7.90 8.50

3.82 229 1.00 0.01 10.10 10.60 11.30

3.83 230 1.00 0.02 13.20 13.80 14.90

3.84 230 1.00 0.07 16.30 17.10 18.00

3.85 231 1.00 0.11 19.30 20.00 20.80

3.86 232 1.00 0.18 24.70 25.40 26.60

3.89 233 1.00 0.32 31.10 31.80 33.00

3.91 235 1.00 0.44 36.80 37.50 38.70

3.94 236 1.00 0.60 42.80 43.60 44.70

3.96 238 1.00 0.70 48.10 49.00 49.90

3.99 239 1.00 0.80 50.50 51.10 52.00

4.02 241 1.00 0.90 51.70 52.20 53.00

4.05 243 1.00 0.90 51.80 52.30 53.00

4.08 245 1.00 0.90 51.80 52.30 53.00

F-1

APPENDIX F 

 

PRESSURE-INDUCED CONSEQUENTIAL STEAM GENERATOR TUBE 

RUPTURE—SUPPORTING CALCULATIONS 

F.1 Estimation of C-SGTR for a Flaw Bin 

The study selected the loss of a main feedwater anticipated transient without scram (ATWS) 

event for evaluating the bounding scenario. The analysis used a primary pressure of 

22 megapascals (MPa) (3,200 pounds per square inch (psi)), a primary temperature of 

370 degrees Celsius (C) (698 degrees Fahrenheit (F)), and a secondary pressure of 6.89 MPa 

(1,000 psi). The temperature of 370 degrees C (698 degrees F) was selected because it is the 

saturated temperature of water/steam at 22 MPa (3,200 psi). Table F-1 and Figure F-1 show the 

thermal-hydraulic (TH) input file for the analysis.

Table F-1 TH Input File for C-SGTR for Simulating ATWS Scenarios

Time (s) Primary 

Pressure (pa)

Surge Line 

Temp (°C)

HL 

Temp (°C)

Hot SG 

Tube 

Temp (°C)

Cold SG Tube

Temp (°C)

Secondary 

Pressure (pa)

0.0 1.56E+7 311.21 311.21 311.21 311.21 6.10E+6

2.0 2.20E+7 370.00 370.00 370.00 370.00 6.10E+6

4.0 2.20E+7 370.00 370.00 370.00 370.00 6.10E+6

6.0 2.20E+7 370.00 370.00 370.00 370.00 6.10E+6

8.0 2.20E+7 370.00 370.00 370.00 370.00 6.10E+6

10.0 2.20E+7 370.00 370.00 370.00 370.00 6.10E+6

20.0 2.20E+7 370.00 370.00 370.00 370.00 6.10E+6

30.0 2.20E+7 370.00 370.00 370.00 370.00 6.10E+6

40.0 1.55E+7 370.00 370.00 370.00 370.00 6.10E+6

50.0 1.55E+7 370.00 370.00 370.00 370.00 6.10E+6

60.0 1.55E+7 370.00 370.00 370.00 370.00 6.10E+6

120.0 1.55E+7 370.00 370.00 370.00 370.00 6.10E+6

Similarly, Table F-2 and Figure F-2 show the TH behavior assumed for steamline break 

(SLB) scenarios.

A set of case runs was performed using the consequential steam generator (SG) tube rupture 

(C-SGTR) software, the TH files discussed earlier, and a set of flaws representing the expected 

flaws plus one large flaw. Table F-3 shows an example of a flaw set consisting of the expected 

flaw set plus one large flaw of 70-percent depth and 3-centimeter (cm) (1.2-inches (in.)) length.

Tables F-4 and F-5 show portions of the two C-SGTR output files (i.e., “intermediate Probability” 

and “cumulative leak Area” files). Table F-4 shows the flaw failure results for the flaw #126, 

which corresponds to a large flaw when the SLB TH file is used. The probability of tube failure 

for a flaw with 70-percent depth and 3-cm (1.2-in.) length is about 0.57 during a severe SLB 

scenario. It also appears that the upper bound of the leak rate (95 percentile values) is about 

4.529, which is approximately equivalent to the guillotine break of one tube in the example 
F-2

Combustion Engineering (CE) plant. This is further confirmed by examining the Cumulative 

Leak Area output in Table F-5. Table F-5 also shows that the expected set of flaws do not 

contribute to C-SGTR during an SLB accident.

Figure F-1 Assumed TH behavior for ATWS for C-SGTR analysis

Table F-2 TH Input File for C-SGTR for Simulating SLB Scenarios

Time (s) Primary 

Pressure (pa)

Surge Line 

Temp (°C)

HL 

Temp (°C)

Hot SG 

Tube 

Temp (°C)

Cold SG Tube

Temp (°C)

Secondary 

Pressure (pa)

0.0 1.56E+7 311.21 311.21 311.21 311.21 6.10E+6

2.0 1.56E+7 300.00 300.00 300.00 300.00 9.60E+4

4.0 1.56E+7 300.00 300.00 300.00 300.00 9.60E+4

6.0 1.56E+7 300.00 300.00 300.00 300.00 9.60E+4

8.0 1.56E+7 300.00 300.00 300.00 300.00 9.60E+4

10.0 1.56E+7 300.00 300.00 300.00 300.00 9.60E+4

20.0 1.56E+7 300.00 300.00 300.00 300.00 9.60E+4

30.0 1.56E+7 300.00 300.00 300.00 300.00 9.60E+4

40.0 1.56E+7 300.00 300.00 300.00 300.00 9.60E+4

50.0 1.56E+7 300.00 300.00 300.00 300.00 9.60E+4

60.0 1.56E+7 300.00 300.00 300.00 300.00 9.60E+4

120.0 1.56E+7 300.00 300.00 300.00 300.00 9.60E+4

0

500

1000

1500

2000

2500

300

310

320

330

340

350

360

370

380

0 20 40 60 80 100 120 140

Temp (°C)

Time (s)

Tube temp (Deg. C)

Delta P (psi)-2ndary Y-axis
F-3

Figure F-2 Assumed TH behavior for SLB for C-SGTR analysis

Table F-3 Example of Expected Flaw Set Plus One Large Flaw of 70-Percent Depth and 

3-cm Length for a CE Plant

Flaw 

orientation

Flaw 

length

(cm)

Circ. 

Angle

Depth Axial 

Location 

(not 

used)

Flaw 

type

SD of Error Mean of 

Error

Flow 

reduction 

factor

A 1.5 0 0.05 0 2 0.03 0 1

A 1.5 0 0.05 0 2 0.03 0 1

A 1.5 0 0.05 0 2 0.03 0 1

A 1.5 0 0.05 0 2 0.03 0 1

A 1.5 0 0.05 0 2 0.03 0 1

A 1.5 0 0.05 0 2 0.03 0 1

A 2.5 0 0.05 0 2 0.03 0 1

A 2.5 0 0.05 0 2 0.03 0 1

A 2.5 0 0.05 0 2 0.03 0 1

A 3.5 0 0.05 0 2 0.03 0 1

--- --- --- --- --- --- --- --- ---

--- --- --- --- --- --- --- --- ---

A 1.5 0 0.35 0 2 0.03 0 1

A 1.5 0 0.35 0 2 0.03 0 1

A 3.0 0 0.70 0 2 0.03 0 1

0

500

1000

1500

2000

2500

298

300

302

304

306

308

310

312

0 20 40 60 80 100 120 140

Temp (°C)

Time (s)

Hot SG Tube Temp (oC)

Delta P (psi)

Delta P (Psi)
F-4

Table F-4 Results of Intermediate File from C-SGTR for Flaw #126, at 70-Percent Depth 

and 3-cm Length for a CE Plant and TH File Representing SLB

Flaw #

Time

(s)

Pleak

Pburst

PCR

(NA)

Abm

(mean burst 

area)

Ab0.05

(5% burst 

area)

Ab0.95

(95% burst 

area)

Alm

(mean leak 

area)

Al0.05

(5% leak

area)

Al0.95

(95% leak 

area)

Acrm

(mean CR 

area)

Acr0.05

(5% CR

area)

Acr0.95

(95% CR 

area)

126 0 0.000 0.000 0 0.000 0 0.000 0.000 0 0.000 0.000 0 0

126 2 0.569 0.569 0 2.546 0 4.528 2.546 0 4.528 0.000 0 0

126 4 0.569 0.569 0 2.798 0 4.528 2.798 0 4.528 2.546 0 0

126 6 0.569 0.569 0 2.939 0 4.528 2.939 0 4.528 2.798 0 0

126 8 0.569 0.569 0 3.018 0 4.528 3.018 0 4.528 2.939 0 0

126 10 0.569 0.569 0 3.119 0 4.529 3.119 0 4.529 3.018 0 0

126 20 0.569 0.569 0 3.119 0 4.529 3.167 0 4.529 3.119 0 0

126 30 0.569 0.569 0 3.119 0 4.529 3.184 0 4.529 3.119 0 0

126 40 0.569 0.569 0 3.119 0 4.529 3.210 0 4.529 3.119 0 0

126 50 0.569 0.569 0 3.119 0 4.529 3.244 0 4.529 3.119 0 0

126 60 0.569 0.569 0 3.119 0 4.529 3.266 0 4.529 3.119 0 0

126 120 0.569 0.569 0 3.119 0 4.529 3.291 0 4.529 3.119 0 0

Table F-5 Results of Cumulative Leak Area File from C-SGTR for Expected Flaws Plus 

One Flaw at 70-Percent Depth and 3-cm Length for a CE Plant and TH File 

Representing SLB

Time Am A0.05 A0.25 A0.50 A0.75 A0.95 Asd

0 0.000 0 0 0.00 0.00 0.00 0.00

2 2.546 0 0 4.41 4.49 4.53 2.213

4 2.798 0 0 4.45 4.49 4.53 2.160

6 2.939 0 0 4.45 4.49 4.53 2.116

8 3.018 0 0 4.45 4.49 4.53 2.087

10 3.119 0 0 4.45 4.49 4.53 2.044

20 3.167 0 0 4.46 4.49 4.53 2.021

30 3.184 0 0 4.46 4.49 4.53 2.013

40 3.210 0 0 4.46 4.49 4.53 1.999

50 3.245 0 0 4.46 4.49 4.53 1.981

60 3.266 0 0 4.46 4.49 4.53 1.969

120 3.291 0 0 4.46 4.49 4.53 1.954

Tables F-6 and F-7 summarize the results of these evaluations for the example CE plant for 

ATWS and SLB scenarios, for Inconel 690, and considering all large flaw bins. The results show 

that a large flaw with 70-percent depth has about 70-percent chance of failure during ATWS and 

57-percent probability of failure during SLB. Furthermore, the results showed that the minimum 

size of the flaw has to be at least 3 cm (1.2 in.) to create a large enough leak area to be 

considered as C-SGTR. Limited runs were also performed for the example Westinghouse plant 

and Inconel 600 tubes for comparison with the CE results. These runs indicated that the 

probability of the tube failure is slightly lower for the Westinghouse plant because of the 

differences between the material properties of Inconel 600 and Inconel 690. For example, for a 
F-5

flaw with 70-percent depth, the tube failure probability for Westinghouse is about 0.46 rather 

than the 0.57 estimated for the CE plant. The comparison also revealed that the leak area for 

the Westinghouse plant is slightly larger because of its larger tube diameter. 

For example, for a 3-cm (1.2-in.) flaw, the leak area for the example Westinghouse plant was 

estimated to be about 4.93 square centimeter (cm2

) (0.76 square inch (in.2)), compared to the 

leak area of 4.46 cm2 (0.69 in.2

) for the example CE plant.

Table F-6 Case Results of Pressure-Induced C-SGTR during ATWS

Case Run Am Pl Pb

Expected Flaw Sample 0.000 0.000 0.000

Expected Flaw Sample + 1 Flaw with 60% depth 

and 3-cm length

0.004 0.001 0.001

Expected Flaw Sample + 1 Flaw with 70% depth 

and 3-cm length

4.400 0.676 0.676

Expected Flaw Sample + 1 Flaw with 80% depth 

and 3-cm length

4.397 1.000 1.000

Expected Flaw Sample + 1 Flaw with 60% depth 

and 4-cm length

0.009 0.002 0.002

Expected Flaw Sample + 1 Flaw with 70% depth 

and 4-cm length

3.659 0.687 0.687

Expected Flaw Sample + 1 Flaw with 80% depth 

and 4-cm length

4.497 1.000 1.000

Table F-7 Case Results of Pressure-Induced C-SGTR during SLB

Case Run Am Pl Pb

Expected Flaw Sample 0.00 0.00 0.00

Expected Flaw Sample + 1 Flaw with 60% depth 

and 3-cm length

0.00 0.00 0.00

Expected F-aw Sample + 1 Flaw with 70% depth 

and 3-cm length

3.29 0.57 0.57

Expected Flaw Sample + 1 Flaw with 80% depth 

and 3-cm length

4.40 1.00 1.00

Expected Flaw Sample + 1 Flaw with 60% depth 

and 4-cm length

0.00 0.00 0.00

Expected Flaw Sample + 1 Flaw with 70% depth 

and 4-cm length

4.40 0.55 0.55

Expected Flaw Sample + 1 Flaw with 80% depth 

and 4-cm length

4.40 1.00 1.00

The probability of C-SGTR for the example CE plant bounds the C-SGTR probability for the 

example Westinghouse plant. Furthermore, the C-SGTR failure probability for ATWS bounds 

the C-SGTR failure probability for SLB scenarios. Therefore, Tables F-8 and F-9 provide the 

bounding probability of C-SGTR for both ATWS and SLB scenarios, covering both 

Westinghouse and CE plants, for each of the flaw bins tabulated in Section 7.1.
F-6

Table F-9 shows the probability that the SG tubes fail but without creating sufficient leak rate to 

be considered as C-SGTR (i.e., called SGTR-Leak). These are caused by flaws with a depth of 

70 percent or more but a length of 3 cm (1.18 in.) or less.

Table F-8 Bounding C-SGTR Probability per a Flaw Bin to be Used for Both SLB and 

ATWS Scenarios for Westinghouse and CE Plants

Depth/ 

Length

0 cm to 

1 cm

1 cm to 

2 cm

2 cm to 

3 cm

3 cm to 

4 cm

4 cm to 

5 cm

5 cm to 

6 cm

0.1 to 0.6 0 0 0 0 0 0

0.6 to 0.7 0 0 0 1.0E-03 1.0E-03 1.0E-03

0.7 to 0.8 0 0 0 5.7E-01 5.7E-01 5.7E-01

0.8 to 0.9 0 0 0 1.0E+00 1.0E+00 1.0E+00

Table F-9 Bounding Probability for SGTR—Leak per a Flaw Bin to be Used for Both SLB 

and ATWS Scenarios for Westinghouse and CE Plants

Depth/ 

Length

0 cm to 

1 cm

1 cm to 

2 cm

2 cm to 

3 cm

3 cm to 

4 cm

4 cm to 

5 cm

5 cm to 

6 cm

0.1 to 0.6 0 0 0 0 0 0

0.6 to 0.7 0 0 0 0 0 0

0.7 to 0.8 0.57 0.57 0.57 0 0 0

0.8 to 0.9 1.00 1.00 1.00 0 0 0

Table F-10 reproduces Table 7-3, which shows, for both Inconel 600 and 690 SG tubes, the 

probability that a flaw belongs to a flaw bin. Table F-11 shows that the probability of a flaw 

residing in a flaw bin multiplied by the probability of C-SGTR will yield the probability of C-SGTR 

per flaw tubes. The bounding probability that a flawed tube results in C-SGTR during ATWS or 

SLB is estimated to be approximately 2.3X10-5. Similarly, the bounding probability that a flawed 

tube fails, not with a sufficient leak area to be considered C-SGTR but considered as an 

SGTR-Leak, is 1.4X10-4. 
F-7

Table F-10 Probability that a Detected Flaw Belongs to a Bin Size at 15 Effective 

Full-Power Years

Depth/ 

Length

0 cm to 

1 cm

1 cm to 

2 cm

2 cm to 

3 cm

3 cm to 

4 cm

4 cm to 

5 cm

5 cm to 

6 cm

Total

0 to 0.1 2.74E-3 4.62E-2 2.23E-2 5.38E-3 1.04E-3 1.80E-4 7.78E-2

0.1 to 0.2 1.86E-2 3.14E-1 1.52E-1 3.66E-2 7.08E-3 1.23E-3 5.29E-1

0.2 to 0.3 9.59E-3 1.62E-1 7.81E-2 1.89E-2 3.64E-3 6.31E-4 2.73E-1

0.3 to 0.4 3.09E-3 5.21E-2 2.52E-2 6.07E-3 1.17E-3 2.03E-4 8.78E-2

0.4 to 0.5 8.47E-4 1.43E-2 6.90E-3 1.66E-3 3.22E-4 5.57E-5 2.41E-2

0.5 to 0.6 2.14E-4 3.61E-3 1.74E-3 4.21E-4 8.13E-5 1.41E-5 6.08E-3

0.6 to 0.7 5.14E-5 8.67E-4 4.19E-4 1.01E-4 1.95E-5 3.38E-6 1.46E-3

0.7 to 0.8 1.19E-5 2.01E-4 9.73E-5 2.35E-5 4.54E-6 7.86E-7 3.39E-4

0.8 to 0.9 2.71E-6 4.57E-5 2.21E-5 5.32E-6 1.03E-6 1.78E-7 7.70E-5

Total 3.52E-2 5.93E-1 2.86E-1 6.91E-2 1.34E-2 2.31E-3 ~1

Table F-11 C-SGTR Probability for SLB or ATWS Scenarios per Flaw

Depth 0 cm to 1 cm

0.0 to 0.5 0 

0.6 to 0.7 1.24E-7

0.7 to 0.8 1.64E-5

0.8 to 0.9 6.52E-6

Total 2.30E-5

F.2 Estimation of Pressure-Induced C-SGTR Probability 

For ATWS scenarios, all SGs will be exposed to potentially high reactor coolant system 

pressure, which could cause C-SGTR. The probability of C-SGTR is estimated by considering 

the total number of flaws at Cycle 15 for the example Westinghouse and CE plants.

For most SLB scenarios, one or more SGs could be exposed to the pressure environment 

conducive to the pressure-induced C-SGTR. This would depend on what has led to secondary 

depressurization and how many main steam isolation valves have closed. A specific SG may be 

of interest for some scenarios of SLB, rather than all SGs.
F-8

The bounding C-SGTR probability for ATWS and SLB, is, therefore, estimated twice; once for 

one specific SG, and then for all SGs. This is shown below:

Example Westinghouse Plant at Cycle 15

Expected number of flaws in each SG = 79

Expected number of flaws in all four SGs = 315

Probability of C-SGTR for the specific SG = (1-(1-2.3X10-5

)

79) = 2.5 X10-3

Probability of C-SGTR for ATWS for any of four SGs = (1-(1-2.3X10-5

)

315) = 0.01

Example CE Plant at Cycle 15

Expected number of flaws in each SG = 125

Expected number of flaws in both SGs = 253

Probability of C-SGTR for the specific SG = (1-(1-2.3X10-5

)

125) = 4.0X10-3

Probability of C-SGTR for ATWS for any of four SGs = (1-(1-2.3X10-5

)

253) = 

8.0X10-3

Section 7.4 and Appendix C use the above values.

F.3 Estimation of Pressure-Induced SGTR-Leak Probability 

The bounding SGTR-Leak probability for ATWS and SLB is estimated twice; once for one 

specific SG, and then for all SGs. This is shown below:

SGTR-Leak Probability for Example Westinghouse Plant at Cycle 15

Expected number of flaws in each SG = 79

Expected number of flaws in all four SGs = 315

Probability of C-SGTR for the specific SG = (1-(1-1.4X10-4

)

79) = 1.1X10-2

Probability of C-SGTR for ATWS for any of four SGs = (1-(1-1.4X10-4

)

315) 

= 4.3X10-2

SGTR-Leak Probability for Example CE Plant at Cycle 15

Expected number of flaws in each SG = 125

Expected number of flaws in both SGs = 253

Probability of C-SGTR for the specific SG = (1-(1-1.4X10-4

)

125) = 1.7X10-2

Probability of C-SGTR for ATWS for any of four SGs = (1-(1-1.4X10-4

)

253) = 

3.5X10-2

Appendix C uses the above values.
G-1

APPENDIX G 

 

ESTIMATING THE ENTRY FREQUENCY FROM LEVEL 1 

PROBABILISTIC RISK ASSESSMENT FOR LEVEL 2 PROBABILISTIC 

RISK ASSESSMENT ANALYSIS 

G.1 Zion Nuclear Power Plant 

This study selected the Zion Nuclear Power Plant (ZNPP) for developing the Level 2 

probabilistic risk assessment (PRA) models to ensure consistency with the thermal-hydraulic 

(TH) analyses results. No current PRA or standardized plant analysis risk (SPAR) models are 

available for ZNPP, and ZNPP units are no longer in operation. The estimates for a prolonged 

station blackout (SBO) condition, as the entry point for the Level 2 PRA, was, therefore, 

estimated based on the plant design features and information from vintage ZNPP PRA 

documents. This appendix discusses the process for developing the Level 2 PRA entry 

condition for containment bypass resulting from a consequential steam generator (SG) tube 

rupture (C-SGTR) for ZNPP Unit 1. It considers all potential conditions from internal and 

external hazards resulting in a prolonged SBO.

G.1.1 Internal Event 

Table G-1 provides the relevant information for ZNPP. The frequency of all scenarios resulting 

in prolonged SBOs (greater than battery duration of 6 hours) was estimated for internal initiating 

events excluding internal fires and floods (i.e., from Table 2.2-2 of NUREG/CR-4551, 

“Evaluation of Severe Accident Risks: Methodology for the Containment, Source Term, 

Consequence, and Risk Integrations Analyses,” issued December 1993). The overall frequency 

estimated from this process for ZNPP is about 5.23X10-6 per year.

The reasonableness of the overall frequency of prolonged SBO was examined using the current 

information on the loss of offsite power (LOOP) from NUREG/CR-6890, “Reevaluation of Station 

Blackout Risk at Nuclear Power Plants,” issued December 2005. This independent examination 

used both single and dual unit LOOP frequencies, along with the latest common-cause alpha 

factor model in SPAR.

The frequencies of single- and dual-unit LOOP exceeding 6 hours were estimated as 7.72X10-4

and 1.64X10-3

. A success criterion for a dual LOOP event was defined as having at least three 

emergency diesel generators (EDGs) operating. This success criterion could include either of 

the following:

• at least the three dedicated EDGs operating

• two dedicated EDGs operating in one unit and a swing EDG aligned to the other unit, 

which will meet all the operational requirements for the service water and the component 

cooling water (CCW) systems

For single LOOP events, the success criteria were two dedicated EDGs operating or one 

dedicated EDG in the affected unit plus the operation of the shared EDG.
G-2

For a dual unit LOOP, common-cause failures of three out of five EDGs, and for a single LOOP, 

common-cause failures of three out of three EDGs, will result in an SBO.

Table G-1 Information from Zion Nuclear Station

Systems System Features

Emergency Power System

a. Each unit consists of 3 4160-VAC class 1E buses, each

feeding 1 480-VAC class 1E bus and motor control center.

b. For the 2 units, there are 5 diesel generators, with 1 being a

swing diesel generator shared by both units.

c. 3 trains of dc power are supplied from the inverters and 3 unit

batteries. The battery duration is 6 hours.

Auxiliary Feedwater System

a. Two 50 percent motor-driven pumps and one 100 percent

turbine-driven pump.

b. Pumps take suction from own unit condensate storage tank

(CST) but can be manually cross-tied to the other unit’s CST.

Service Water (SW)

a. Shared system between both units.

b. Consists of 6 pumps and 2 supply headers.

c. Cools component cooling heat exchangers, containment fan

coolers, diesel generator coolers, auxiliary feedwater pumps.

d. 2 out of 6 pumps can supply sufficient flow.

Component Cooling Water 

(CCW)

a. Shared system between both units.

b. Consists of 5 pumps, 3 heat exchangers, and 2 surge tanks.

c. Cools RHR heat exchangers, reactor coolant pump motors

and thermal barriers, RHR pumps, SI pumps, and charging

pumps.

d. One of 5 pumps can provide sufficient flow.

Secondary Relief

a. steam dump valves

b. atmospheric dump valves (1 per SG)

c. safety relief valves

Primary Relief a. 2 PORVs

b. 3 safety relief valves

Containment

a. large, dry, prestressed concrete

b. 2.6 million cubic foot volume

c. 49 psig design pressure

Reproduced from NUREG/CR-3300, NUREG/CR-4550, and NUREG/CR-4551

The study obtained a point estimate of the frequency for short SBOs’ core damage scenarios 

(entry point for a Level 2 PRA), for a plant with the same features as ZNPP, including the 

contribution of extreme weather. This value was about 2.1X10-6 per year.

The value estimated independently for the frequency of prolonged SBO did not include all the 

contributors to the SBO events. For example, the mode did not include potential test and 

maintenance unavailability, human errors in aligning the electrical bus, and common-cause 

failures (CCFs) of other electrical components such as breakers. The comparison of this limited 

independent estimation with the PRA results clearly shows that the internal event contribution to 

the frequency of prolonged SBO as documented in NUREG/CR-4551 is reasonable.
G-3

G.1.2 Seismic Initiating Event 

An examination of the Zion probabilistic safety assessment (PSA) (NUREG/CR-3300, “Review 

and Evaluation of the Zion Probabilistic Safety Study: Plant Analysis,” Vol. 1, issued May 1984) 

indicated that the frequency of loss of total nonrecoverable alternating current (ac) power is 

about 5.6X10-6 per year because of seismic events. The two major contributors to a 

seismic-induced SBO in ZNPP are the following:

(9) LOOP because of a seismic event with a median ground acceleration of 0.3 g

(10) failure of SW pumps caused by a seismic event with median ground acceleration of 

0.63 g

The failure of SW pumps will result in an eventual failure of EDGs, because SW supports the 

operation of EDGs and most of the emergency core cooling system (ECCS) components.

The failure of SW pumps during a seismic event could result for one or more of the 

following reasons:

• failure of the pumps (the largest contributor)

• failure of all the underground SW piping

• failure of the crib house roofing

Considering the seismicity of the area surrounding ZNPP, NUREG/CR-3300 estimated a total 

core damage probability of 5.6X10-6 per reactor year because of an extended SBO beyond the 

battery duration.

G.1.3 Fire Initiating Event 

The Zion PSA performed a very limited fire analysis, as indicated in NUREG/CR-3300. It 

basically identified two areas that contributed the most to fire risk: the auxiliary equipment room 

and the cable-spreading room. The fire in the auxiliary equipment room damaged cabinets to 

the extent that the operators received incorrect diagnostic information. The loss of diagnostic 

information also impeded the recovery actions involving auxiliary feedwater (AUX) pumps or 

high-pressure injection.

The fire in the cable-spreading room damaged the motor-driven AUX pump power cables, the 

turbine-driven auxiliary feedwater (TDAFW) pump failed randomly, and the operators failed to 

initiate feed-and-bleed operation for decay heat removal. NUREG/CR-3300 did not agree with 

the ZNPP assessment of the cable-spreading room. As noted in NUREG/CR-3300, it appears 

that the ZNPP Unit 1 cable-spreading room contains the following cables:

• power feeds for three CCW pumps and three SW pumps

• power feeds for two charging pumps

• power feeds for two AFW pumps

• control cabling for five fan coolers

• control cabling for at least two containment spray pumps

Docketed information from Commonwealth Edison also indicated that the cable-spreading room 

contains power cables for the steam supply valves of the TDAFW pump, which is separated by 
G-4

a minimum distance of 20 feet from the motor-driven AFW pump power cables. Information on 

the location of safety injection pump cables and the third containment spray pump was not 

available at the time of evaluation.

Based on this information, it appears that a relatively large fire in the cable-spreading room 

would have a similar effect as the total loss of ac. However, the TDAFW pump is not expected 

to be affected, and its operation would not be limited by the battery depletion time similar to 

other extended SBO scenarios. Because of a lack of detailed cable routing and other fire-related 

information, NUREG/CR-3300 estimated a core damage probability of 4.0X10-5 per year. A 

reanalysis of this scenario was performed with less conservative assumptions and was based 

on recent data on ignition, detection, and suppression of fires. Furthermore, for this scenario, 

the operation of the TDAFW pump was assumed to be unaffected by the fire, and it could only 

fail for reasons independent from the fire scenario. This updated analysis resulted in an 

estimated core damage probability that was much smaller than the bounding estimate reported 

in NUREG/CR-3300 (9.5X10-7/reactor year (RY)). The assumptions used in this calculation, 

which is equivalent to the earlier calculation, are as follows:

• cable-spreading room ignition frequency = 1.9X10-3 per year

• location and severity factor = 0.1

• failure of Halon fire suppression system = 0.05

• failure of TDAFW pump early or late = 0.1

The initiating event frequency for prolonged SBOs, which is required for the entry point to a 

Level-2 analysis, should exclude the failure of the TDAFW pump. Therefore, the resulting 

initiating event frequency would be about 9.5X10-6 per year. It is important to note that the 

current plants are equipped with additional SBO diesel generators and a set of new FLEX 

equipment, which can further reduce this frequency. 

G.2 Calvert Cliffs Nuclear Power Plant

Table G-2 provides the relevant plant information for Calvert Cliffs Units 1 and 2 (CCNP). Each 

CCNP unit is equipped with two TDAFW pumps, and the duration to battery depletion is 

nominally 2 hours, although they are expected to last 4 hours in the case that was modeled in 

TH runs.

The SPAR model estimated the scenarios associated with the SBOs with early failures of both 

TDAFW pumps, reproduced in Table G-3. The early failures of both TDAFW pumps was 

dominated by the operator’s failure to control the flow, causing SG overfill, and failing the 

TDAFW pumps by carrying water to turbine. The overall frequency estimated from this process 

is about 1.88X10-8 and 2.47X10-8 per year, for Units 1 and 2, respectively. The higher 

contribution for Unit 2 resulted from the asymmetric dependence on SW. For example, EDG 12 

can be supplied with cooling water from the SW system of either Unit 1 or Unit 2.

For losses of offsite power (LOOPs), especially those related to the grid and weather-related 

causes, there is a high potential that both units experience a LOOP (i.e., a dual LOOP 

scenario). The following equation provides a rough estimate of the major contributors to the 

frequency of early core damage in both units from the occurrence of a dual LOOP initiator:

CD due to Dual LOOP = [Frequency of Dual Unit LOOP]* [CCF probability of all Five EDGs]*

[Probability the TDAFW fails due to SG overfill in both units]
G-5

Substituting the estimates from the SPAR model,

[Frequency of Dual Unit LOOP] = [Frequency of LOOP-GR]+LOOP-WR] = 1.86 X10-2 + 

4.83X10-3

= 2.4X10-2

,

[CCF probability of all Five EDGs directly from SPAR models] = 2.13X10-5

, and 

[Probability the TDAFW fails due to SG overfill] = 

[SPAR model for failure of both TDAFW failure in one Unit due to overfilling = 0.3*0.12 = 0.036]* 

[Conditional Probability of failing both TDAFW due to SG overfill in the second Unit = 0.3; 

estimated] = 1.08X10-2

Table G-4 shows the single and dual LOOP core damage frequency (CDF) results for the SBO 

with the early failures of both TDAFW pumps for internal events.

Table G-2 Information from Calvert Cliffs Nuclear Station

Systems System Features

Emergency Power System a. Currently there are 5 diesel generators for the 2 units. One of 

these 5 EDGs is the SBO EDG, which can power any safety 

related 4-kV bus at either unit. The operation of 1 EDG with 

success of 1 TDAFW pump per unit is adequate for long-term 

SG heat removal. The SBO EDG requires operator action to 

align it to a safety bus and is credited as a recovery action in 

the PRA models.

b. At the time when individual plant evaluation/individual plant 

evaluation for external events (IPE/IPEEE) was performed, 

each unit had a dedicated EDG with 1 shared EDG for both 

units. Therefore, the information contained in IPE/IPEEE 

should be used as a guide, and they are not 

directly applicable.

c. Each unit has 3 4160-VAC Class 1E buses, each feeding 

1 480-VAC Class 1E bus and motor control center.

d. 3 trains of dc power are supplied from the inverters and 3 unit 

batteries. The battery duration is 2 hours, but it is expected to 

last 4 hours during most scenarios.

Auxiliary Feedwater System Each unit is equipped with 2 turbine-driven pumps (TDAFW) and 

1 motor-driven pump (MDAFW). There is a cross-connection to 

the other unit’s MDAFW discharge line.

Salt Water System (SW) There are 2 cross-tied trains, each with 1 pump and 1 heat 

exchanger. A third pump could also supply either train, if needed.

Service Water (SRW) There are 2 trains, each with a salt water pump, a CCW HX, an

SRW HX, and ECCS pump room air cooler. A third pump could 

be aligned to each train, if needed.

Component Cooling Water (CCW) The CCW pumps do not restart automatically after a LOOP. The 

operators manually reestablish RCP seal cooling after a LOOP.

Secondary Relief a. 4 turbine bypass valves—TBVs (2 SG)

b. atmospheric dump valve (1 per SG)

d. main steam safety relief valve (8 per SG)
G-6

Systems System Features

Primary Relief a. 2 reverse-seated PORVs (2400 psi);

b. the PORVs do not require dc power for once-through cooling

(feed and bleed)

c. 2 block valves that are powered from the opposite 480 VAC

with respect to their PORVs

d. 2 spring-loaded safety relief valves (P>2500 psig)

Containment Large, dry

Note: The information in this table is reproduced from the CCNP individual plant evaluation (IPE)/IPE for external 

events (IPEEE).

Table G-5 provides similar results for SBO with the failure of TDAFW pumps after battery 

depletion. The core damage frequencies are estimated by removing the probability of SG overfill 

and including a probability of about 0.24 for the recovery of power from the EDG or offsite (0.7 

for recovery of the EDG in 4 hours and 0.34 for recovery of the offsite power from weather or 

grid-related causes).

Table G-3 Core Damage for SBO Scenarios with Early Failure of TDAFW Pumps

Calvert Cliffs Unit 1 Calvert Cliffs Unit 2

Initiator IE Frequency CDF 

Contribution Initiator IE Frequency

CDF 

Contribution

LoopGR 1.86E-2 1.02E-8 LoopGR 1.86E-2 1.43E-8

LoopPC 2.07E-3 2.15E-10 LoopPC 2.07E-3 3.24E-10

LoopSC 1.04E-2 2.87E-9 LoopSC 1.04E-2 3.99E-9

LoopWR 4.83E-3 5.48E-9 LoopWR 4.83E-3 6.14E-9

Total 3.59E-2 1.88E-8 Total 3.59E-2 2.47E-8

Table G-4 CDF for the SBO and the Failures of TDAFW Pumps due to Overfill (for Internal 

Event Initiators Affecting One or Both Units)

Affected Unit CDF Estimates (Per Reactor Year)

Unit 1 [only] 1.3E-8 = [1.88E-8 – 5.5E-9]

Unit 2 [only] 1.9E-8 = [2.47E-8 – 5.5E-9]

Both Units 5.5E-9

Table G-5 CDF for an SBO and the Failures of All TDAFW Pumps after the Battery 

Depletion (Internal Event Initiators Affecting One or Both Units)

Affected Unit CDF Estimates (Per Reactor Year)

Unit 1 [only] 5.0E-9 = [1.25E-7 – 1.20E-7]

Unit 2 [only] 4.5E-8 = [1.65E-7 – 1.20E-7]

Both Units 1.2E-7

G.2.2 Seismic Initiating Event

An examination of the CCNP IPEEE indicated that the frequency of loss of the total 

nonrecoverable ac power is about 1.3X10-5 and 1.5X10-5 per year due to seismic events for 

Units 1 and 2. These estimates were found when both units were equipped with only 

three EDGs, rather than the current configuration of five EDGs. However, the original IPEEE 
G-7

stated that all EDGs are dependent on SW, and the SW has significantly lower fragility than 

EDGs. A further examination of the two new EDGs, the SBO EDG, and EDG 1A, revealed that 

these two EDGs are not dependent on SW for cooling. This is expected to reduce the seismic 

contribution by a factor of 10. Following the approach used for internal events for the single and 

dual unit core damage and no recovery credit for ac power after a seismic event, the following 

results were estimated.

Table G-6 CDF for the SBO and Failures of TDAFW Pumps due to a Potential Overfill 

(Seismic Events Affecting One or Both Units)

Affected Unit CDF Estimates (Per Reactor Year)

Unit 1 [only] 3.3E-8 = [4.7E-08 – 1.4E-8]

Unit 2 [only] 5.0E-8 = [5.4E-8 – 1.4E-8]

Both Units 1.4E-8

Table G-7 CDF for SBO and Failures of TDAFW Pumps after the Battery Depletion 

(Seismic Events Affecting One or Both Units)

Affected Unit CDF Estimates (Per Reactor Year)

Unit 1 [only] Negligible = [1.3E-6 – 1.30E-6]

Unit 2 [only] 2.0E-7 = [1.5E-6 – 1.30E-6]

Both Units 1.30E-6

G.2.3 Fire Initiating Event 

The CCNP IPEEE estimates the contributions from internal fire are 7.3X10-5 and 1.1X10-4 for 

Units 1 and 2, respectively. Fires in the control room resulting in its abandonment were the 

major contributors to the overall fire CDF. This is important because the main control room is 

shared between the two units, although there are two cable-spreading rooms. Therefore, the 

majority of the CDF resulting from fires in the control room is considered to affect both units.

Severe fires in control room cabinets are assumed to result in control room evacuation. Once 

the control room is evacuated, the operators are required to load shed most of the electrical 

loads, and manually restart these loads. If not restarted, the site would lead to a self-induced 

SBO. This condition will eventually result in a loss of the 125-volt direct current batteries. Even if 

the operators successfully reload the buses, a failure of either of the EDGs supporting the fire 

safe-shutdown trains will eventually result in a loss of two of the four batteries. It will indicate a 

loss of <something> in the auxiliary shutdown panels, which is the only source of indication for 

the operators. Therefore, most of the scenarios involving an EDG failure would involve an 

extended LOOP with initial successful actuation and control of equipment, initially establishing 

AFW flow but followed by failure of AFW sometime later caused by battery depletion.

The CCNP fire PRA in IPEEE, consistent with the methodology of that time, had several 

conservative assumptions and used somewhat conservative data. For example, it did not 

adequately account for fire severity and the plant layout effect on fire ignition frequency. In 

addition, the analysts considered relatively high heat-release rates, and they did not develop 

and use scenario-specific propagation and suppression. Conservative assumptions were also 

made regarding the human error probabilities, specifically for the mitigation of control room fires. 

Control room fires are significantly affected by the failure of the operator to perform local manual 

actions and, in some cases, may rely on a self-imposed SBO to avoid spurious actuations. 
G-8

Subsequent to the submittal of the CCNP IPEEE, several studies were performed to eliminate 

some of these conservatisms.1 The results of these studies lowered the CDF contribution of the 

main control room fire by one unit to 2.45X10-5 per reactor year. Note that this estimate does not 

reflect the additional credits for the two added EDGs. The probability of early core damage, 

before battery depletion, is driven by the human error probabilities. This core damage probability 

is not generally affected by the added EDGs. The single unit CDF is approximately apportioned 

(split) to 0.1 and 0.9 for the early and late core damage, which corresponds to the failures of 

TDAFW pumps before or after battery depletion. As a result, the early CDF of the control room 

fire would be about 2.4X10-6 per reactor year. The late core damage (i.e., TDAFW pump failures 

after the depletion of the batteries, requires the failure of EDGs. This split fraction will then be 

affected by the addition of two EDGs at Calvert Cliffs. An additional credit of 0.1 is, therefore, 

assigned to reflect the credit for the added EDGs. For the late core damage affecting both units, 

this will reduce the fraction of the CDF from 0.9 down to 0.09 (0.1*0.9).

Table G-8 CDF for SBO and Failures of TDAFW Pumps due to Potential Overfill (Control 

Room Fire Events Affecting One or Both Units)

Affected Unit CDF Estimates (Per Reactor Year)

Unit 1 [only] Negligible

Unit 2 [only] Negligible

Both Units 2.45E-6 (0.1*2.45E-5)

Table G-9 CDF for SBO and Failures of TDAFW Pumps after Battery Depletion (Control 

Room Fire Events Affecting One or Both Units)

Affected Unit CDF Estimates (Per Reactor Year)

Unit 1 [only] 2.2E-5 = [2.45E-5*0.9]

Unit 2 [only] 2.2E-5 = [2.45E-5*0.9]

Both Units 2.2E-6 = [2.45E-5*0.9*0.1]

G.2.4 Contributions from Other Initiating Events

Two initiating events, high wind and internal flood, were considered in estimating the 

frequencies of the entry points for determining the CSGTR probabilities. The internal flood core 

damage was estimated at 1.55X10-5 per reactor year. Most of the flood scenarios resulted in 

eventual core damage as a result of losing the SW, main feedwater, AFW, and ECCS systems. 

The failure of the AFW crosstie between the units is needed for core damage if not affected by 

the flood initiator itself (e.g., if the flood were due to a break in the AFW suction line, which could 

impede the AFW crosstie). The flood scenarios developed in IPEs are expected to result in core 

damage that is generally considered late (approximately 12 hours or more after the initiator); 

therefore, it may not be considered for evaluating containment bypass. The original flood 

analysis in the IPE also suffered from conservative assumptions and the high flood initiating 

event frequency. A PRA update of the flood model in 2 January 2000 2 resulted in an updated 

1 A letter from Charles H. Cruse, Baltimore Gas and Electric Vice President of Nuclear Energy, to 

U.S. Nuclear Regulatory Commission, May 18, 1999, “Additional Response to Request for Additional Information 

on Calvert Cliffs Nuclear Power Plant, Unit Nos. 1 and 2, Individual Plant Examination of External Events Submittal 

(TAC Nos. M83603 and M83604).” 2 See a presentation by Bruce Mrowca on Calvert Cliffs PRA update, January 2001, titled “Calvert Cliffs PRA, 

January 22, 2000,” Agencywide Documents Access and Management System Accession No. ML010400376.
G-9

estimate of 1.6X10-6 for flood CDF. This value is conservatively used as a single unit CDF 

contributor due to internal flood for estimating the C-SGTR frequency for scenarios where the 

AFW system has operated for 4 hours.

The high-wind contribution to the core damage is estimated to be 4.4X10-6

. The main 

contributors to this estimate were the SBO scenarios. This contribution of CDF is considered to 

affect both units. The frequency of dual LOOP and early failures of TDAFW pumps was thought 

to be similar to the internal event CDF [i.e., 4.7X10-8 per reactor year = 0.0108×4.4X10-6

]. The 

remaining CDF of 4.3X10-6 per reactor year was estimated for those scenarios where TDAFW 

pumps operated early and failed after battery depletion.

H-1

APPENDIX H 

A SCREENING APPROACH BASED ON FLAW DEPTH AND LENGTH 

This approach both accounts for the distribution of flaw lengths and depths and considers the 

possibility of multiple flaws. It evaluates the consequential steam generator (SG) tube rupture 

(C-SGTR) probability based on the failure of one or more tubes and estimates the contributions 

of single-tube and multiple-tube failures separately. This approach has less conservatism than 

Approach 1, and it can be used for progressive screening of probabilistic risk assessment (PRA) 

scenarios or for evaluating inspection findings where the surveillance data for both depths and 

lengths are available, especially for large flaws.

This approach considers the contribution of shallower (less than 45-percent deep) and shorter 

(less than 2-centimeter (cm) (0.79-inch (in.)) flaws to C-SGTR to be negligible and considers the 

following large flaw bin sizes for this approach:

(11) size bins for length: flaw length from 1.5 to 2.5 cm (0.59 to 0.98 in.), 2.5 to 3.5 cm (0.98

to 1.38 in.), and 3.5 to 4.5 cm (1.38 to 1.77 in.)

(12) size bins for depth: flaw depth from 45 percent to 55 percent, from 55 percent to

65 percent, from 65 percent to 75 percent, from 75 percent to 85 percent, and from

85 percent to 95 percent

The probability that a flaw belongs to each size bin was calculated using following equation.

PPPPPPPP [( 1 < ffff ff h < 2), ( 1 < ffff ff ff h < 2)]

= PPPPPPPP [FF ) ∗ PPPPPPPP PP PP[( 1 < ffff ff h < 2)|ffff ff ff ]

∗ PPPP[( 1 < ffff ff h < 2)|ffff ]

A large flaw here is defined as a flaw large enough to require the tube to be plugged. As 

discussed earlier, a plugged tube is expected to have a flaw with an average length of 1.3 cm 

and a depth of 30 percent or more. They account for 0.95 percent of all flawed tubes. The 

conditional probabilities for a flaw to be in such a flaw bin are estimated from the associated 

gamma distributions, divided by the probability that a large flaw is observed [1-cumulative 

gamma (1.3 cm (0.51 in.) and 30 percent; the large flaw thresholds)].

Table H-1 shows the probability that a flaw resides in one of the large-size bins. The size 

distribution length and depth do not differentiate between Inconel 600 and 690.
H-2

Table H-1 Probability that a Large Wear Flaw in the Last Cycle Has the Specific 

Length and Depth Ranges 

Depth Range 1.5 cm to 2.5 cm

2.5 cm to 

3.5 cm

3.5 cm to 

4.5 cm

Total Probability 

for Length > 1.5 cm

45%<d<55% 5.70E-2 1.26E-2 2.34E-3 7.19E-2

55%<d<65% 1.36E-2 3.01E-3 5.59E-4 1.71E-2

65%<d<75% 3.14E-3 6.95E-4 1.29E-4 3.96E-3

75%<d<85% 7.09E-4 1.57E-4 2.91E-5 8.95E-4

85%<d<95% 1.57E-4 3.48E-5 6.47E-6 1.99E-4

Total Probability of a flaw is considered large and has a length greater than 

2 cm and less than 4.5 cm, and depth between 45% and 95% 9.41E-2 

For a wear flaw, the probability of a tube failure is a function of flaw depth only. This is because 

the current C-SGTR software conservatively models the wear flaw as tube thinning (flaws were 

assumed to be relatively large). So, the probability of tube failure before the failure of the hot leg 

(HL) is only a function of the flaw depth. The maximum leak area, however, is a function of the 

wear length as estimated by C-SGTR software. For a 2-cm (0.78-in.) wear flaw, the maximum 

area is about 2 square centimeters (cm2

) (0.31 square inch (in.2)), for 3-cm (1.18-in.) flaws, it is 

close to 5 cm2 (0.77 in.2

), and for larger flaws, the leak area is limited by twice the crosssectional area of the tube (approximately 6.08 cm2 (0.94 in.2

). There are large uncertainties 

associated with the estimated leak area as a result of tube failure because of wear flaw. As a 

bounding approach, it was considered that the failure of at least one large flaw with a length 

greater than 2 cm (0.78 in.) is required for C-SGTR to occur. The C-SGTR probability 

estimations in this appendix have considered the following two contributions:

(13) the existence of one tube with a large flaw in any of the plant SGs

(14) the existence of two or more tubes with large flaws

The approach taken here is considered somewhat conservative. For example, the best estimate 

of the number of tubes resulting in a leak rate equivalent to a guillotine break of one whole tube 

for a 2-cm (0.78-in.) flaw is about three tubes. However, in this approach, the failure of any one 

tube is considered sufficient. This conservative approach was adopted to avoid considering 

several smaller (less than 2-cm (0.78-in.) long) deep flaws as a part of this analysis.

The probabilities of C-SGTR occurring before HL failure for different bin sizes are shown in 

Table H-2 for Inconel 600 and Table H-3 for Inconel 690. These probabilities are estimated 

using the C-SGTR calculator for predicting the C-SGTR probability and a thermal-hydraulic (TH) 

input file for the example plant, which simulates station blackout (SBO) with failure of the 

turbine-driven auxiliary feedwater (TDAFW) pump at the start of the accident 

(Case Wnewbase).

The study assumes a tube has failed if it exhibits a leak area of at least 1 cm2 (0.16 in.2

). The 

threshold leak area is conservatively selected to account for the existing large uncertainties 

associated with the predicted leak area for wear. The results shown in these tables reaffirm that 

for the wear flaws, the bounding probability of tube failure is only a function of the flaw depth.
H-3

Table H-2 Probability of C-SGTR Occurring before HL Failure for Different Sizes of Flaws 

in Inconel 600 in Zion Wnewbase Case

Flaw Depth Maximum Leak 

50% 60% 70% 80% 90% Area

Flaw Length

2 cm ~ 0 ~ 0.05 ~0.8 ~1.0 NA: May leak 

during operation ~2.0 cm2

3 cm ~ 0 ~ 0.05 ~0.8 ~1.0 NA: May leak 

during operation ~5.0 cm2

4 cm ~ 0 ~ 0.05 ~0.8 ~1.0 NA: May leak 

during operation

Limited by 

guillotine break of 

the tube 6.08 cm2

Table H-3 Probability of C-SGTR Occurring before HL Failure for Different Sizes of Flaws 

in Inconel 690 in Zion Wnewbase Case

Flaw 

Depth ->

Flaw Length

50% 60% 70% 80% 90% Maximum Leak 

Area

2 cm ~ 0 ~ 0.00 ~0.75 ~1.0 NA: May leak during 

operation ~2.0 cm2

3 cm ~ 0 ~ 0.00 ~0.75 ~1.0 NA: May leak during 

operation ~5.0 cm2

4 cm ~ 0 ~ 0.00 ~0.75 ~1.0 NA: May leak during 

operation

Limited by guillotine 

break of the tube 

6.08 cm2

The above estimates need to be aggregated through a probability model to produce an estimate 

of the probability of C-SGTR. To do so, the following terms are defined:

N: Number of Flaws

Subscript “i”: for defining the length bins

Subscript “j”: for defining the depth bins

Qi,j: The probability that a large flaw belongs to bin i, j (obtained from Table H-1)

Θi,j: The C-SGTR probability associated with a flaw that belongs to bin i, j (obtained from 

Table H-2 for 600TT and H-3 for 690TT tubes)

The aggregate probability of C-SGTR (P) is given by the following equation using the variables 

defined earlier:

PP = NN ∗ ��QQii,jj ∗ θθii,jj

jj ii

If Θi,j, the C-SGTR probability of a flaw with depth index j and length index i does not depend on 

index i as it is true for wear flaw (not true for cracks). Then, the above equation is simplified to:
H-4

PP = NN ∗� θθjj

jj

� QQii,jj

ii

For one flaw; with N set to one, the value of P was estimated based on the results in 

Tables 7.1-9 and 7.1-10 for Inconel 600, and Tables 7.1-9 and 7.1-11 for Inconel 690. These 

are the values obtained for this single flaw: P600=4.92X10-3, and P690=4.72X10-3. 

As discussed earlier, it is expected that 31 flawed tubes will be generated in Cycle 15 

(15 effective full-power years (EFPYs) of operation) for Inconel 600 tubes and 20 flaws for 

Inconel 690. The probability that one tube fails before HL failure can be estimated using the 

following equation:

PPPPPPPP (1 tt CCCCCC CC) = �

NNNN>0

PPPPPPPP (NN tt h ffff ) ∗ NN ∗ PPPPPPPP(tt ff ff )

The probability of a two-tube failure can be estimated using the following equation:

PPPPPPPP(2 tt CCCCCC CC)

= � PP

NNNN>1

(NN tt h ffff ) ∗ �NN

2 � ∗ PPPPPPPP(tt ff ff ) ∗ [1

− PPPPPPPP(tt ff ff )]NNNN−2

Similarly, higher numbers of tube failures causing C-SGTR (e.g., 3, 4) can be estimated. 

Table H-4 shows the results of these calculations for Inconel 600 and 690.

Table H-4 Probability of Single and Multitube Failure in C-SGTR for Inconel 600/690

Tube Materials C-SGTR: One Tube

Failure

C-SGTR: Two-Tube

Failure

C-SGTR: More Than

Two-Tube Failure

Inconel 600 1.31E-2 8.24E-5 Negligible

Inconel 690 8.90E-3 3.85E-5 Negligible

The two probabilities of a single tube failure and multiple tube failures are useful in PRA 

evaluations. For Inconel 600, these values are 0.013 and 8.23X10-5; for Inconel 690, the values 

are 0.0089 and 3.85X10-5 for EFPY 15. The probabilities of Inconel 690 are a factor of 1.5 less 

than Inconel 600. Similar analyses for a limited number of flaw sizes were performed for the 

SBO scenarios with late failure of TDAFW pumps after battery depletion (Case 153). The 

preliminary results showed that the probability of single and multiple tube failures is about a 

factor of 2 higher for Case 153 compared to the Wnewbase case. All analysis results shown in 

the remainder of this appendix are performed for the Wnewbase case with Inconel 600. The 

scaling factors—an increase of twofold is used for SBO cases with late failure of TDAFW 

pumps, and a decrease of one-and-a-half-fold is used for Inconel 690.

The contribution to C-SGTR from a single tube failure can be compared to the estimates 

obtained from the first approach. The results show that, for Inconel 600, the single tube failure 

contribution to C-SGTR is about 1.31X10-2 from both methods. Similarly, for Inconel 600, the 

single tube failure contribution to C-SGTR is 8.1X10-3 and 8.90X10-3 from the first and the 

second approach, respectively. This provides some confidence that the estimated results are 

consistent from two different approaches.
I-1

APPENDIX I 

 

MELTING TEMPERATURES AND STEEL OXIDATION 

CONSIDERATIONS IN MELCOR MODELING 

The melting temperatures for stainless steel and Inconel (1,725 kelvin (K) 

(1,452 degrees Celsius (C))) originate from the Steam Generator Action Plan (SGAP) analysis. 

These temperatures are consistent with those listed in the SCDAP/RELAP (1,671–1,727 K 

(1,398–1,454 degrees C)) and MELCOR (1,700 K (1,426 degrees C)) manuals. The 

temperatures are also consistent with typical listings of light-water reactor melting temperatures 

such as those shown in NUREG/CR-6042, “Perspectives on Reactor Safety,” issued 

March 2002 (R-800 course material).

The list shows that the lowest melting temperature for iron is for eutectics with zirconium (Zr) 

(approximately 940 degrees C (1,724 degrees Fahrenheit (F))) and boron carbide (B4C) 

eutectics (approximately 1,150 degrees C (2,102 degrees F)). MELCOR models steel reactions 

with Zr and with B4C.

Severe accident analyses do not typically consider steel oxidation of reactor coolant system 

(RCS) components. Although the SGAP analysis did not consider the oxidation of RCS 

components, it did analyze the influence of oxidation on core components. The conclusion was 

that variations in oxidation of additional metal affect absolute failure timing but do not 

significantly affect the relative failure timing of different components that are of interest in 

evaluating whether the containment is bypassed.

MELCOR contains steel oxidation models but they are applied in components in the COR 

module rather than the HS (heat structure) module used to model the RCS piping.

The analysis below discusses assessing the possible effects of oxidation in the RCS, using the 

MELCOR steel-H2O oxidation model. External sources for steel oxidation or steel oxide melting 

were not sought, since it is expected that the major oxidation mechanisms should have been 

captured during the study of degradation of steel present in the reactor core.

The steel-H2O rate constant in MELCOR is calculated using the following equation:

K(T) = 2.42 * 109 * exp(-42,400/T)

The analysis is continued, assuming that the steel-H2O rate constant listed in MELCOR applies 

to units of kilogram and square meters.

This was verified in the literature. A paper by the same author as the primary reference in 

MELCOR (J.F. White)1 but published 3 years after the MELCOR reference lists the following 

parabolic rate constant:

w2

/t = 2.4 * 1012 * exp(-84,300/(RT))

 1 See J.T. Bittel, L. H. Sjodahl, and J. F. White, “Oxidation of 304L Stainless Steel by Steam and by Air,” 

Corrosion-NACE, Vol. 25, No. 1, January 1969.
I-2

where w is the weight gain (in fact the mass of oxygen added to steel) per unit area in mg/cm2

, 

R is the gas constant in cal/(mole-K), T in K, and t in s.

Applying the universal gas constant of R = 1.987 cal/(mole-K), the equation becomes:

w2

/t = 2.4 * 1012 * exp(-42,426/T)

Because the units of w2 are mg2

/cm4, to convert to rate to kg2/m4, the constant should be 

multiplied by 10-4

. This was also the factor used in the conversion of the Urbanic-Heidrich 

constant for Zr in the MELCOR manual. 

The MELCOR manual refers to w as the mass of metal oxidized per unit area, whereas the 

paper refers to w as the weight gain per unit area. Assuming that the oxidation product is 

ferrous oxide (FeO), the ratio of weight gain to metal mass oxidized should be the ratio of 

atomic weights—about 16/56 or 0.29. In parabolic reaction rate, this translates to a factor of 

about 10, which corresponds to the MELCOR correlation for the stainless steel reaction rate. 

Figure I-1 shows the parabolic rate constant for steam-H2O reaction.

Figure I-1 The parabolic rate constant for steam-H2O reaction

In the C-SGTR analyses, RCS failures typically occur when temperatures are substantially 

below 1,750 K (1,476 degrees C). The temperatures are rapidly rising, limiting the time at high 

temperatures. The following plot shows the steel mass loss at a fixed temperature over the 

course of 1 day for select temperatures below 1,750 K (1,476 degrees C).

1.E-14

1.E-13

1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

5 7.5 10 12.5 15

K (kg^2 m^-4 s^-1)

1/T [K^-1] *10^-4

Steel-H2O Consumption Rate Constant
I-3

Figure I-2 Steel mass loss at a fixed temperature

Figure I-3 shows the corresponding loss of steel thickness, assuming a density of 8,000 

kilogram per cubic meter (kg m-3

).

Figure I-3 Loss of steel thickness

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

100 1000 10000 100000

w (kg m^-2)

Time (s)

Reaction of Steel with Steam

Steel Mass Loss

750 K 1000 K 1250 K 1500 K 1750 K

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

100 1000 10000 100000

Thickness Loss (cm)

Time (s)

Reaction of Steel with Steam

Steel Thickness Consumed

750 K 1000 K 1250 K 1500 K 1750 K
I-4

The steel-H2O model in the MELCOR reference manual 2 predicts no appreciable oxidation 

(approximately greater than 1 millimeter (0.04 inch)) except for extended durations 

(approximately 1 day) at near the melting point. It is assumed that, at these temperatures, 

failure by creep will occur long before oxidation is significant.

The stainless steel oxidation paper presented steam oxidation for different stainless steels and 

mild steel with the data points falling in the same general range. It is assumed that the relation is 

generally applicable to other steels.

The approach to RCS steel oxidation in this report is consistent with how phenomena are 

handled in severe accident analysis and previous consequential steam generator tube 

rupture analyses.

Because the existing oxidation model does not predict appreciable oxidation in the absence of 

the hydrogen affect except at high temperatures, no attempt was made to consider the influence 

of hydrogen on oxidation, to identify low-melting-point iron oxides, to consider additional heat 

and hydrogen generation, or to consider the effects of stainless steel foaming, including 

insulation for the oxidation of RCS components. If additional effects of foaming and other effects 

are significant, they should probably be considered first for the core, where temperatures 

are hottest.

2 “In the MELCOR reference manual” refers to both the use of 9 rather than 8 as the exponent for the 

reaction rate and the interpretation of the parabolic rate referring to metal mass consumed rather than mass gain 

(oxide mass gained–metal mass consumed).
J-1

APPENDIX J 

 

LOOP SEAL CLEARING CONSIDERATIONS 

This appendix discusses assumptions related to loop seal clearing. Opinions differ between 

NUREG/CR-6695, “SCDAP/RELAP5 Thermal-Hydraulic Evaluations of the Potential for 

Containment Bypass During Extended Station Blackout Severe Accident Sequences in a 

Westinghouse Four-Loop PWR,” issued March 2010, and various sections of this report 

(e.g., Section 3.7, Section 8.1). 

J.1 TH Analysis-Related Considerations 

The assumptions in Section 3.7 build upon NUREG/CR-6995. The issue was not explored fully. 

Any difference is not expected to be a significant issue for the Combustion Engineering (CE) 

configuration analyzed in this work. The current scope of the project did not include a 

thermal-hydraulics (TH) assessment of loop seal clearing for CE. Section 3.7 simply noted that 

the loop seals did not clear in the simulations that were run.

One of the reasons that this TH analysis was not prioritized is that a high degree of containment 

bypass was concluded for CE, even in the absence of loop clearing, as a result of the high 

temperatures to which the steam generator (SG) tubes are exposed. Because the effect of loop 

seal clearing primarily results from hotter (near core temperature) gases reaching SG tubes, 

which already occurs in the CE design analyzed even for closed-loop-seal natural circulation, 

the additional impact of loop seal clearing on the risk for CE is not expected to be significant.

The initial intent to address loop seal clearing for this project was to test the different failure 

mode hypotheses and to determine whether apparent differences in loop seal behavior were 

inherent to designs or because of differences in codes or differences in user choices. The plan 

was to perform a quick related “hand calculation” to ascertain what parameters would be 

important to both hypothesized failure modes and expected behavior, verify these relevant 

parameters in the input decks, and then run a series of simulations to test the extent to which 

the failure modes affected behavior. When the work was initially planned, it included only a 

general outline for approaching the problem. The text for loop seal clearing in the TH section 

(Section 3.5) of this report reflects this initial outline. However, the assumptions for loop seal 

clearing described in the same section do not factor into results, since neither geometry nor 

system-code models changed. Rather these assumptions factor into how the results are 

interpreted and to help decide what to look for.

The assumptions for loop seal clearing do not differ appreciably from those in 

NUREG/CR-6995. One additional factor is considered explicitly: the upper-vessel-to-downcomer 

leakage. The knowledge of the influence of this leakage is not new. In fact, individuals involved 

with the Steam Generator Action Plan and NUREG/CR-6695 indicated that core-to-downcomer 

bypass leakage had also been considered during the development of the system-code inputs. 

The choice of a small upper-core-to-downcomer leakage area for these Westinghouse analyses 

resulted in loop seal clearing.

What was planned to be explored further during this study is the expectation that the amount of 

seal leakage that results in loop seal clearing depends on both the assumed upper-vessel-todowncomer leakage area and (perhaps to a lesser extent) reactor coolant system (RCS)-tocontainment heat transfer.
J-2

Additional details of the expected behavior follows:

Upper-loop-seal water can be lost in three different ways:

(14) Flow over to the downcomer or out of the reactor coolant pump (RCP) seal before

bubble formation or if the bubble shrinks or water level oscillates (bubble shrinking/not

initially forming). In fact, in the absence of upper-vessel-to-downcomer leakage, a bubble

should not even form until either the loop-seal water reaches saturation or until the SG

side water level drops to the horizontal pipe section of the seal, thereby allowing steam

to bubble through. (This seems to be a new consideration for this report.)

(15) Entrainment to the RCP seal once (or if) steam flows through the upper loop seal (lower

loop seal must still be intact to maintain differential pressure. This is the primary

mechanism for loop seal clearing described in NUREG/CR-6995.

(16) Evaporation/flashing. This is an additional mechanism described in NUREG/CR-6995.

To create sufficient differential pressure across the upper loop seal to cause steam to bubble 

through it (and thereby remove inventory by the second mechanism listed above) other inleakage to the upper horizontal part of the cold leg must not be significant. This means that— 

• The lower loop seal (downcomer-core) must be intact.

• The upper-vessel-to-downcomer leakage area should not be large relative to the RCP

seal leakage area.

If one of the other in-leakage pathways is open, gas driven by the evaporation of any saturated 

water in the system would take that pathway rather than bubbling through the upper cold-leg 

loop seal.

The following seven questions for a more detailed treatment of loop seal clearing come to mind 

for potential future analyses on this subject:

(17) How do the flow resistances across core and SGs in the code input compare with

measurements?

(18) How do the Westinghouse and CE flow resistances compare, including the relative flow

resistances between SGs and core?

(19) What is the maximum range of pressure drop and pressure drop difference achievable?

That is, neglecting any liquid flashing to steam, what would the steam pressure drops

across core and SG tubes be for an infinite volume of steam at cold legs if flow is limited

by a choked condition at the safety relief valves (parallel channel problem)?

(20) How much does flashing affect behavior—from lower head and from loop seals? How do

the elevations of the downcomer skirts in the inputs match expectations?

(21) How do these elevations and those of the loops differ between Westinghouse and CE

designs and how would this be expected to affect clearing behavior?
J-3

(22) How much condensation is occurring? How does the magnitude compare to that of the 

Westinghouse calculations?

(23) Are differences primarily because of differing geometry surface areas or because of 

differing heat transfer coefficients? Do the Westinghouse and CE reactor vessels have 

differing discharge rates?

J.2 PRA-Analysis-Related Considerations 

The probabilistic risk assessment (PRA) model used in this report postulates that the loop seal 

issue will occur for both Westinghouse and CE cases in severe accident sequences where a 

1,135–1,817 liters per minute/pump (300–480 gallons per minute/pump) leakage exists. These 

leakage sequences are generally well delineated in PRA studies. Such sequences are assumed 

to lead to consequential SG tube rupture end state.

K-1

APPENDIX K 

 

FURTHER DISCUSSION OF STEAM GENERATOR TUBE 

FLAW DISTRIBUTIONS 

This appendix contains a further discussion of steam generator (SG) tube flaw distributions, as 

already given in Chapter 6 of this report, and their application, as covered in Section 7.1.3. The 

material in this appendix is based on an Advisory Committee on Reactor Safeguards (ACRS) 

subcommittee briefing 1 on consequential SG tube rupture (C-SGTR).

K.1 On Development of Distributions in Chapter 6 

The previous work on estimating SG tube flaw distributions was for 600 mill annealed (MA) tube 

materials (NUREG/CR-6521, “Estimating Probable Flaw Distributions in PWR Steam Generator 

Tubes,” issued 1996 (Gorman Report)) and for cracks only using data that existed before 1995. 

These (U-tube) SGs have been replaced with those having new SG tube materials (thermally 

treated Alloy (600TT and 690TT). Use of the information from previous studies could not be 

justified. The objective is to update the previous study on flaw statistics and provide current 

statistics sufficient to generate flaw samples for C-SGTR analysis (input to the 

C-SGTR calculator).

Flaw data for Inconel 600 and 690 (600TT and 690TT) were collected from selected in-service 

inspection reports available to the U.S. Nuclear Regulatory Commission. Flaw data were 

manually extracted and compiled into a data base for further analyses. Figures K-1 and K-2 

show the empirical data used for the flaw depth and length parameters, before a fitted gamma 

distribution was imposed. The data were binned against operating time (measured in effective 

full-power years (EFPYs)) and flaw types. The flaw generation rate per tube as a function of SG 

service life (measured in EFPYs) is generated for the following:

• Volumetric/Wear Flaw 600TT

• Volumetric/Wear Flaw 690TT

• Axial Cracks 600TT

• Circumferential Cracks 600TT

No crack data were found for 690TT.

 1 See the transcript of the ACRS Meeting of the Subcommittees on Metallurgy & Reactor Fuels and PRA 

Consequential Steam Generator Tube Rupture (C-SGTR) Subcommittee Briefing, April 7, 2015 (Agencywide 

Documents Access and Management System Accession No. ML15182A262).
K-2

Figure K-1 Graphical presentation of aggregate flaw data

Empirical depth distribution using all flaws in the database

Figure K-2 Graphical presentation of aggregate flaw data

Empirical distribution of axial length of all flaws in the database

Model Parameters

A flaw model was developed by doing the following:

• linearly increasing rate of volumetric flaws generation as a function of time (i.e., EFPY)

• linearly increasing rate of crack flaws generation as a function of EFPY

• gamma distribution of flaw length

• gamma distribution of flaw depth
K-3

The statistical estimation approach included the following:

• regression using Excel routine for estimating the linearly increasing rates

• matching the first two moments for estimating the parameters of gamma distributions

General Findings

The following general findings were made: 

• Sufficient statistical results were developed to generate flaw samples for the C-SGTR 

calculator software.

• New material 600TT/690TT flaw rate generation is about an order of magnitude less 

than what was reported for MA 600.

• The majority of flaws observed are volumetric rather than cracks.

• The flaw length and depth distribution is somewhat smaller than for MA 600.

The most important flaw parameter that specifies failure resistance of a tube is the flaw depth, 

as confirmed by the probabilistic risk assessment (PRA) models and the C-SGTR calculator in 

Chapter 7 of this report. Figure K-3 shows the fitted and empirical cumulative distribution for 

flaw depth.

The high-end tail of the distribution is affected by the tubes removed because of plugging, 

because these flaws will not be available for further growth to larger flaws in the next cycle. 

Section K-2 (also Section 7.1.3) gives the correction for that (shifted distribution) for PRA 

modeling purposes.

The lower tail of empirical distribution is affected by the error associated with measuring small 

flaws. With small and shallow flaws, in the relatively small database being used, one plant 

reported many flaws that were very shallow, at the range of 2-, 3-, and 5-percent depth, where 

the other plant did not report such small flaws. Knowing that there could be relatively large 

errors in the identification and size determination of small flaws, the lower tail may not be very 

accurate, even for the empirical distribution.
K-4

Figure K-3 Flaw depth distribution

Distribution of percentage of flaw depth

K.2 he Adjusted (Shifted) Flaw Distributions Used in PRA

As discussed in Section 7.1.3, during PRA analysis, adjustments were made to the original 

estimated distributions of Chapter 6 for flaw depth and length.

To improve the distribution fit for large flaws, which are more important to C-SGTR, and to 

compensate for the perceived distortion of flaw size distributions toward the shallower and 

smaller flaws, the previous distributions were shifted by a small amount of depth and length 

(adding a scale variable to gamma distribution).

This adjustment also provided much closer estimates of the number of tubes that are plugged in 

each cycle (better estimate of the number of large and deep flaws at the tails).

For example, for the Westinghouse plant, the large and deep flaws were the major contributor to 

C-SGTR fraction estimates. Therefore, the PRA needed to model better fits at the tail of

distributions of length and depth.

There were also a large number of unreliable small depth and length measurements (i.e., depth 

less than 10 percent), which skewed the size distributions of depths and lengths toward the 

lower values, whereas tube plugging criteria removed those larger flaws that could have grown 

into even larger ones if they had been allowed to remain.

0.9

0.91

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

1 21 41 61 81

Cumulative Probability

% Penetration Depth

Fitted and Shifted Depth Distribution

Empirical CDF

Fitted Gamma

Shifted Gamma
K-5

Figure K-4 compares the cumulative probabilities of the empirical, fitted, and shifted flaw 

distributions for flaw depth. Section 7.1.3 of this report contains additional discussion, figures, 

and tables.

Figure K-4 Flaw depth distribution (shifted gamma)

Fitted and shifted depth distribution

0.9

0.91

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

1 21 41 61 81

Cumulative Probability

% Penetration Depth

Fitted and Shifted Depth Distribution

Empirical CDF

Fitted Gamma

Shifted Gamma

L-1

APPENDIX L 

 

A PROCESS TO COMPREHENSIVELY ESTIMATE CONSEQUENTIAL 

STEAM GENERATOR TUBE RUPTURE CORE DAMAGE FREQUENCY 

IN A PROBABILISTIC RISK ASSESSMENT MODEL 

L.1 Introduction 

This appendix outlines a process to include consequential steam generator (SG) tube rupture 

(C-SGTR) in a probabilistic risk assessment (PRA) Level 1 model to collect those end states for 

further modeling in a Level 2 analysis. Section L.2 discusses the PRA Level 1 modeling detail 

deemed to be sufficient and cost effective to capture the bulk of the potential C-SGTR core 

damage frequency (CDF) for further modeling in a PRA Level 2 analysis. The validity of this 

approach was tested by applying it to a PRA model for a 4-loop Westinghouse plant. 

Section L.3 summarizes the results of this application.

All domestic nuclear power plants already have mature PRA studies that do not necessarily 

attempt to model C-SGTR in a detailed manner in their event trees. This process is also 

intended to assess the contribution of those deliberately “unmodeled” potential C-SGTR 

sequences in an existing PRA study. The example provided in Section L.3 attempts to illustrate 

such an assessment.

A guidance document containing an expanded version of this process may be produced in the 

future for use by U.S. Nuclear Regulatory Commission risk analysts.

L.2 The Process 

The objective of this appendix is to outline a process to model C-SGTR in a PRA Level 1 to 

collect those end states for further consideration in a Level 2 analysis. The process aims to 

provide PRA Level 1 modeling details sufficient and cost effective enough to capture the bulk of 

the potential C-SGTR CDF for further treatment in a PRA Level 2 analysis (i.e., to focus effort in 

collecting C-SGTR CDF from the most likely sources).

The process discussed is for the internal event hazard category during a power operation 

Level 1 PRA for a pressurized-water reactor; extension to other hazard categories is considered 

to be straightforward.

An internal events PRA model may have 20-30 event trees leading to numerous accident 

sequences. It is assumed that, initially, C-SGTR is not modeled, and the objective is to capture 

C-SGTR candidate sequences for further treatment in the Level 2 model with minimal intrusion 

into the existing model, yet ensuring the identification of a large fraction of such sequences. For 

this purpose, two modeling actions may be considered:

(1) Explicitly insert event tree nodes that query sequences to lead to identification of 

C-SGTR end states (i.e., sequences with C-SGTR occurring before core damage).

(2) Use sequence rules on core damage sequences to mark high primary pressure, dry SG, 

and low secondary pressure (HDL or H/D/L) sequences and others, if necessary, as 
L-2

C-SGTR candidates (i.e., sequences with the potential for C-SGTR to occur after

core damage).

Both of these approaches are used in this process. Those sequences that may have some 

C-SGTR potential but are deliberately not modeled are termed unmodeled sequences. As long

as the unmodeled sequences are expected to contribute a very small percentage to the total of

all C-SGTR sequences, they can be left unmodeled.

The process examines different event trees and accident sequence sets to provide C-SGTR 

modeling suggestions in five steps. The first two steps are for screening out sequences.

(1) Those event trees and sequences that are already SG tube ruptures (SGTRs)

SGTR event tree already has end states for SGTR; thus, there is no need to model C-SGTR.

(2) Those event trees that cannot cause C-SGTR or have very little potential for C-SGTR

Such event trees and their sequences can be identified and removed from further consideration 

for C-SGTR. Examples of such event trees are:

• large loss-of-coolant-accident (LOCA) (LLOCA)

• excessive LOCA (vessel failure XLOCA, LOCA beyond emergency core cooling system

(ECCS) capacity)

• interfacing systems LOCA (ISLOCA)

Since the primary system is depressurized and stays so in such events, C-SGTR challenges are 

not expected.

(3) Those event trees where pressure-induced C-SGTR may occur early in the event

Such event trees include anticipated transient without scram (ATWS), secondary-side break 

(SSB), and consequential secondary side break (CSSB). Whenever possible, an event tree 

node could be inserted in an early part of such event trees to query for C-SGTR and then the 

ensuing sequence could be transferred to an SGTR event tree with the appropriate boundary 

conditions. Figures L-1 and L-2 give suggestions for ATWS and SSB event tree modifications 

for C-SGTR. Note that these figures introduce a conditional probability of an existing large flaw 

of 0.01. This value is derived from Appendix C (and, in turn, Appendix F) of this NUREG.

(4) HDL core damage sequences

When the core damage sequences are examined, it is possible to identify those sequences that 

can clearly be marked as HDL. This can be done either manually or by defining sequence rules. 

Thus, such sequences can be assigned to the C-SGTR end state (or otherwise tagged) to be 

modeled in Level 2. The conditional C-SGTR probability for HDL sequences can be calculated 
L-3

for the plant-specific case; if not, a generic value of 0.02 to 0.031 is in order, depending on the 

type of SGs in question. Use probability of 1 if the primary side loop is cleared.

(5) Indeterminate or faulted SG (FSG) core damage sequences

After Step 4 above, there will be sequences that are indeterminate as to their C-SGTR potential.

Such sequences may arise from the following:

• Auxiliary feedwater (AFW) status is not asked in the sequence definition, which does let 

the sequence be qualified as HDL or otherwise (indeterminate core damage sequences).

• AFW appears as successful but flow to one or more AFW trains may fail, still meeting 

the success criteria. If AFW to an SG fails, the operator will isolate that SG by 

procedures, leading to a dry SG. Similarly, secondary-side leakage (isolation failure, 

SSB condition) may occur in a fed SG, with other SG loops operating as intended, 

leading to an FSG that would be isolated. In such scenarios, some level of C-SGTR 

challenge may exist. The conditional probability of C-SGTR in such SGs can be 

calculated if the TH properties of such scenarios are known. However, in a typical PRA, 

such analyses are not readily available. Based on TH expert opinion, the potential for a 

C-SGTR challenge in such SGs is estimated to be lower or much lower than HDL 

conditions with no AFW.

This process suggests that the potential C-SGTR that may stem from indeterminate core 

damage sequences should not be modeled (e.g., they are in the unmodeled C-SGTR category) 

to avoid extensive modeling. It is deemed that such unmodeled sequences will be a small 

fraction of the total SG tube rupture frequency captured in Steps 1, 3, and 4.

Two parameters of importance are used in the claim that such sequences are deemed to be a 

small fraction of the total C-SGTR:2

(1) Failure probability of SSB (unisolated leaking loop) in one or more loops, Qfsg = 0.13, 

given that operators isolate an SG because of AFW failure 

(2) The conditional probability of C-SGTR = Qcsgtr = 0.01, given that an indeterminate core 

damage sequence occurs.

As an approximation, the C-SGTR CDF of unmodeled sequences above can be estimated by 

multiplying the CDF with the fraction Qfsg*Qcsgtr = 0.0013. Section L.3 includes an 

example application.

 1 This range is for SGs with favorable geometry, such as those seen in Westinghouse pressurized-water 

reactors. For other SGs, values could be used from the main body of this report, or plant-specific calculations, if 

thermal-hydraulic (TH) analyses are available.

2 These values are given as expert judgment since they are not supported by publicly available calculations. 

If plant-specific values are available, they should be used.
L-4

Table L-1 summarizes the five steps discussed above.

Table L-1 Process Summary for Event Trees and CDF Sequences

Category Treatment

1 Event Tree: SGTR as the initiator Use IE-SGTR ET; no additional C-SGTR.

2 Event Trees: LLOCA/XLOCA No potential for C-SGTR due to depressurization

Event Tree: ISLOCA No treatment of C-SGTR due to existing bypass

3 

Event Tree: ATWS

If primary pressure relief fails, assume C-SGTR; 

otherwise, no C-SGTR on basis of very 

low frequency.

Event Trees: SSB/CSSB

Add new node (SSB-CSGTR) that equates to 

probability of existence of large flaw depth and 

route up-branch to the existing (non-C-SGTR) 

portion of the tree and down-branch to a 

consequential (subtree) version of the SGTR tree.

4 CDF Sequences: HDL Identify and label for Level 2 treatment; to be 

multiplied by P(C-SGTR), etc.

5 CDF Sequences: Non-HDL 

or Indeterminate 

Do not model further based on discussion in 

Step 5 above.

As a final sanity check, examine the ratio of the following:

(24) (HDL CDF)/(Frequency of indeterminate core damage sequences)

The larger this ratio is, the less significant the unmodeled sequences in Step 5 will be.

IE-SSBI 

(or IE-SSBO) RPS SSB-CSGTR End State

1 2 3

No C-SGTR continue with the 

existing SSB ET logic

Success (~1)

Occurs C-SGTR Transfer to SGTR ET

(0.01)

Fails CD-CSGTR (*)

Figure L-1 Insertion of C-SGTR event tree node in SSB event trees

Note: (*) Although this sequence can be transferred to the ATWS event tree 

for further treatment, it may be more practical to assign it to the core 

damage end state for further treatment in L2 analysis, since the expected 

frequency of such a sequence is small.
L-5

IEV RPS PR-REL AFW ATWSCSGTR End State

1 2 3 4

Success

Yes continue with the 

existing ET logic

Occurs Yes. 2200 < P < 3300 No C-SGTR

continue with the 

existing ET logic

No ~1

C-SGTR CD-CSGTR

Fails (0.01)

(ATWS) Yes CD-CSGTR

No. P > 3300

No CD-CSGTR

Figure L-2 Insertion of C-SGTR event tree node in ATWS event tree

RPS = Reactor Protection System (trip)

PR-REL = Primary system pressure relief

P > 3300 = RCS pressure greater than 3,300 psi

L.3 Summary of the Results of the Application 

The above approach was applied to a 4-loop Westinghouse PRA model that did not originally 

have C-SGTR explicitly modeled in its Level 1 PRA.

Some changes were made to the base model to capture pressure-induced SGTR (PI-SGTR) 

CDF sequences. The CDF sequences that are identifiable as HDL are marked by event tree 

rules to be transferred to the Level 2 model as C-SGTR. Those CDF sequences not captured in 

the above process, labeled as “unmodeled” sequences that may have some C-SGTR 

consequence, are then examined for their potential impact. Table L-2 summarizes the results. 

Based on these results, the following are observed:

• C-SGTR (and IE-SGTR) is a small fraction of CDF (<2 percent).

• C-SGTR potential is dominated by post core damage temperature-induced SGTR 

(TI-SGTR) (89 percent).

• PI-SGTR is a small contributor to C-SGTR (7 percent) and a very small contributor to 

CDF (<1 percent).

• Unmodeled C-SGTR sequences in this PRA model would be a small fraction of modeled 

C-SGTR sequences (3 percent).
L-6

The following are important qualifiers on these findings:

• Consistent with the approach outlined in Section L.2, and with the state of practice in

C-SGTR modeling, leaks below the critical break area (one double-ended tube break)

are not considered.

• These results are for a given version of a PRA model. Any changes made to the model

can affect these numbers, although there is no reason to believe that such changes

would be significant enough to affect the above findings.

• These estimates (necessarily) project what the Level 2 TI-SGTR frequency will be,

based on the H/D/L frequency and the conditional TI-SGTR probability. This capturing

does not include any “benefit” that the Level 2 will ultimately estimate with respect to

operator actions before HL creep rupture. But again, this is not likely to affect the

above findings.

Developing the estimates provided above was a tedious process, because (1) the H/D/L 

assignment was a manual exercise, and (2) most of the underlying frequencies come from 

consequential trees and were extracted manually. The former issue can be avoided if event tree 

rules that identify HDL sequences and label them as such for Level 2 analysis are built into the 

PRA model as a one-time effort. The latter issue may not apply to some model architecture and 

software package combinations.

This application to a PRA model illustrates, but does not prove, that the assumptions stated in 

the modeling approach of Section L.2 for the “unmodeled” sequences are valid. This exercise 

also demonstrated that this comprehensive, yet limited, intrusion into the PRA Level 1 model to 

estimate C-SGTR CDF is feasible.
L-7

Table L-2 Summary of C-SGTR Modeling Applied to a Specific PRA Model for a 

4-Loop Westinghouse Plant

Initiator Sequence CDF C-GTR 

Multiplier

C-SGTR 

Frequency

% of 

C-SGTR

IE-SGTR All 7.6E-8 0

IE-LLOCA/XLOCA/ISLOCA All 2.1E-7 0

Transients/SLOCA/MLOCA 

--> ATWS IE*RPS*/PR-REL*AFW 6.9E-8 0.01 6.9E-10 0.06%

Transients/SLOCA/MLOCA 

--> ATWS IE*RPS*PR-REL 6.2E-8 1 6.2E-8 5.00%

IE-SSB --> ATWS IE-SSBI*RPS 5.9E-9 1 5.9E-9 0.50%

IE-SSB --> ATWS IE-SSBO*RPS 3.0E-8 1 3.0E-8 2.40%

SSBI/SSBO IE-SSBI*/RPS*PI-SGTR 4.5E-10 1 4.5E-10 0.04%

SSBI/SSBO IE-SSBO*/RPS*PI-SGTR 2.3E-9 1 2.3E-9 0.20%

All transients --> 

consequential SSB

Transient IE*/RPS*...--

>CSSB-->PI-SGTR 2.0E-9 1 2.0E-9 0.16%

HDL No loop clearing 4.5E-5 0.024 1.1E-6 88.70%

HDL With loop clearing (*) 1

Non-HDL (b) Non-HDL with FSG 2.7E-5 0.0013 3.5E-8 2.90%

Non-HDL (a)

Non-HDL with possible 

AFW failure (**)

Sum = 7.3E-5 1.2E-6 100%

The items marked in yellow are not modeled.

(*) No sequences showed up among the dominant CDF sequences; not further examined in this calculation.

(**) Estimated to be a small contributor

(a) and (b) refer to Step 5 in Section L.2 (1).

RPS = Reactor Protection System

PR-REL = Primary System Pressure Relief

SSBI (SSBO) = Secondary Side Break Inside (Outside) Containment

LLOCA (MLOCA, SLOCA) = Large (Medium, Small) LOCA

IE = Initiating Event

NUREG-2195

S. Sancaktar, M. Salay, R. Iyengar, A. Azarm, S. Majumdar 

Innovative Engineering and Safety Solutions, LLC, 20817 Spinning Wheel Pl., Germantown, MD 20874

Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439

 

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, D.C. 20555-0001

This report summarizes consequential steam generator (SG) tube rupture (C-SGTR) analyses recently 

performed. C-SGTRs are potentially risk significant events because thermally induced SG tube failures 

caused by hot gases from a damaged reactor core can result in a containment bypass event and a large 

release of fission products to the environment. The analyses evaluate SGs with thermally treated Alloy 

600 and Alloy 690 heat exchange tubes. The methods developed addressed the contribution of thermally 

induced SGTR during severe accidents and pressure-induced SGTR during a number of design basis 

accidents. The study developed the methods and the pilot applications so as to establish the framework 

for performing a more comprehensive probabilistic risk assessment that can address the C-SGTR risk. 

The main conclusion from this work is that the SG geometry and the fluid flow rates in different SG designs 

can significantly influence the potential likelihood of C-SGTRs. For SG geometries analyzed in this study, 

the Combustion Engineering plant design had an increased likelihood of a C-SGTR and a higher potential 

for a large early release, than the Westinghouse plant design.

Steam Generator Tube Rupture, SGTR, Consequential SGTR, C-SGTR, CSGTR, 

Probabilistic Risk Assessment, PRA, MELCOR

May 2018

Technical

Consequential SGTR Analysis for Westinghouse and Combustion 

Engineering Plants with Thermally Treated Alloy 600 and 690 Steam 

Generator Tubes

 



NUREG-2195 Consequential SGTR Analysis for Westinghouse and Combustion Engineering Plants with 

Thermally Treated Alloy 600 and 690 Steam Generator Tubes 

May 2018