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Hermann1994-DecayHeatGuide-cr5625.pdf
NUREG/CR-5625
ORNL-6698
Computing Applications Division
TECHNICAL SUPPORT FOR A PROPOSED DECAY HEAT
GUIDE USING SAS2H/ORIGEN-S DATA
O. W. Hermann, C. V. Parks, and J. P. Renier
Manuscript Completed: June 1994
Date Published: July 1994
Prepared for the
Division of Regulatory Applications
Office of Nuclear Regulatory Research
U.S. Nuclear Regulatory Commission
Washington, DC 20555
NRC FIN B0846
Prepared by the
OAK RIDGE NATIONAL LABORATORY
managed by
MARTIN MARIETTA ENERGY SYSTEMS, INC.
for the
U.S. DEPARTMENT OF ENERGY
under contract DE-AC05-84OR21400
ABSTRACT
This report was prepared to provide support for major revisions to the current U.S. Nuclear Regulatory Commission decay
heat rate guide entitled "Regulatory Guide 3.54, Spent Fuel Heat Generation in an Independent Spent Fuel Storage
Installation," using a new data base produced by the SAS2H analysis sequence of the SCALE-4 system. The new data base
of heat generation rates provides a significant improvement by increasing the number and range of parameters that
generally characterize pressurized-water-reactor (PWR) and boiling-water-reactor (BWR) spent fuel assemblies. Using
generic PWR and BWR assembly models, calculations were performed with each model for six different burnups at each of
three separate specific powers to produce heat rates at 20 cooling times in the range of 1 to 110 y. A procedure that
includes proper interpolation formulae for the tabulated heat generation rates is specified. Adjustment formulae for the
interpolated values are provided to account for differences in initial 235U enrichment and changes in the specific power of a
cycle from the average value. Finally, safety factor formulae were derived as a function of burnup, cooling time, and type of
reactor. The procedure included in this report was developed with the intention of providing one that was easier to use than
that in the current Regulatory Guide. Also, the complete data base and procedure is incorporated into an interactive code
called LWRARC which can be executed on a personal computer.
The report shows adequate comparisons of heat rates computed by SAS2H/ORIGEN-S and measurements for 10 BWR and
10 PWR fuel assemblies. The average differences of the computed minus the measured heat rates of fuel assemblies were
–0.7 ± 2.6% for the BWR and 1.5 ± 1.3% for the PWR. In addition, a detailed analysis of the proposed procedure indicated
the method and equations to be valid.
iii
NUREG/CR-5625
NUREG/CR-5625
iv
CONTENTS
Page
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
vii
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
FOREWORD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 Background of Current Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Improvements in the Proposed Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Overview of Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1
1
2
2. SOURCES OF DATA FOR COMPUTING HEAT RATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
3. COMPARISONS OF COMPUTED AND MEASURED HEAT RATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.1 Assembly Design and Operating Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.2 Discussion of Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
4. HEAT RATE DATA COMPUTED FOR PROPOSED GUIDE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
5. PROPOSED REGULATORY GUIDE PROCEDURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1 Definitions and Derivations of Required Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 Heat Generation Rate of the Assembly (p) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.2 Cycle and Cycle Times of the Assembly (Ti) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.3 Fuel Burnup of the Assembly (Bi and Btot) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.4 Specific Power of the Fuel (Pi , Pe , and Pave) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.5 Assembly Cooling Time (Tc) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.6 Assembly Initial Fuel Enrichment (Es) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Determination of Heat Generation Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1 Computing Heat Rate Provided by Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.2 The Short Cooling Time Factors f7 and fN7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.3 The Excess Power Adjustment Factor fp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.4 The Enrichment Factor fe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.5 Safety Factor S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.6 Final Heat Generation Rate Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Acceptability and Limits of the Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Glossary of Terms and Unit Used in Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
16
16
16
16
16
17
17
17
17
25
26
26
26
26
26
28
6. DISCUSSION OF THE PROPOSED PROCEDURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1 Variations in Operating History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Interpolation Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 Discussion of the Short Cooling Time Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4 Discussion of the Excess Power Adjustment Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5 Discussion of the Initial Enrichment Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6 Formulation of the Safety Factor Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6.1 Error From Random Data Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6.2 Error From Cross Sections and Computational Model Bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
29
32
35
40
40
42
43
48
v
NUREG/CR-5625
CONTENTS (continued)
Page
6.6.3 Error in Procedure of Guide and Extra Parameter Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6.4 Total Safety Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7. THE LWRARC CODE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1 Using the Menu System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 Menu System Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3 The LWRARC Code Distribution Diskette . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
55
59
59
59
64
8. SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
9. REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
APPENDIX A.
APPENDIX B.
APPENDIX C.
APPENDIX D.
APPENDIX E.
DATA AND SAMPLE INPUT TO TABULATED CASES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
SAMPLE CASE USING HEAT GENERATION RATE TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
LWRARC CODE SAMPLE RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ACTINIDE, FISSION PRODUCT, AND LIGHT-ELEMENT TABLES . . . . . . . . . . . . . . . . . . . . . . . .
PLOTS OF MAJOR DECAY HEAT RATE NUCLIDES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
NUREG/CR-5625
vi
71
79
81
87
97
LIST OF FIGURES
Page
6.1 Diagrammatic illustration of operating history variations having same total burnup and cycle times . . . . . . . . . . . . . 30
6.2 Cooper Nuclear Station operating history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
6.3 Cooper Nuclear Station assembly CZ515 operating history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
6.4 Cooper Nuclear Station assembly CZ102 operating history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
vii
NUREG/CR-5625
LIST OF TABLES
Page
2.1
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
3.15
3.16
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
5.10
5.11
6.1
6.2
6.3
6.4
List of nuclides updated as a function of burnup in the SAS2H analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Point Beach Unit 2 PWR assembly description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Point Beach Unit 2 PWR operating history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Point Beach Unit 2 assembly burnups and powers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Turkey Point Unit 3 PWR assembly description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Turkey Point Unit 3 PWR operating history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Turkey Point Unit 3 assembly burnups and powers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Cooper Nuclear Station BWR assembly description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Cooper Nuclear Station BWR operating history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Cooper Nuclear Station adjusted cycle burnups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Cooper Nuclear Station assembly powers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Element contents from clad, structure, and water (for BWR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Uranium isotope dependence23 on X wt % 235U enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Point Beach PWR measured and computed decay heat rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Turkey Point PWR measured and computed decay heat rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Cooper Nuclear Station BWR measured and computed decay heat rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Summary of decay heat rate comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
BWR spent fuel heat generation rates, watts per kilogram U, for specific power = 12 kW/kgU . . . . . . . . . . . . . . . . 19
BWR spent fuel heat generation rates, watts per kilogram U, for specific power = 20 kW/kgU . . . . . . . . . . . . . . . . 20
BWR spent fuel heat generation rates, watts per kilogram U, for specific power = 30 kW/kgU . . . . . . . . . . . . . . . . 21
BWR enrichments for burnups in tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
PWR spent fuel heat generation rates, watts per kilogram U, for specific power = 18 kW/kgU . . . . . . . . . . . . . . . . 22
PWR spent fuel heat generation rates, watts per kilogram U, for specific power = 28 kW/kgU . . . . . . . . . . . . . . . . 23
PWR spent fuel heat generation rates, watts per kilogram U, for specific power = 40 kW/kgU . . . . . . . . . . . . . . . . 24
PWR enrichments for burnups in tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Enrichment factor parameter values for BWR assemblies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Enrichment factor parameter values for PWR assemblies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Parameter ranges for applicability of the proposed regulatory guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Comparison of heat rates from operating history variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Evaluation of accuracy in table interpolations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Evaluation of heat rates after adjustments for extreme power history changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Excess power adjustment of decay heat, in W/kgU, using Eq. (14) compared with actual SAS2H
calculations as percentage differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
6.5 Evaluation of adjustments for decreased initial enrichments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
6.6 Evaluation of adjustments for increased initial enrichments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
6.7 Percentage fission-product yields for fissile isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
6.8 Percentage standard deviations in data for dominant fission products and light elements . . . . . . . . . . . . . . . . . . . . 47
6.9 Computed standard deviation in nuclides and their total heat rate at 1 year for typical BWR . . . . . . . . . . . . . . . . . . 48
6.10 Computed standard deviation in nuclides and their total heat rate at 110 years for typical BWR . . . . . . . . . . . . . . . 49
6.11 Percentage standard deviation in fission-product and light-element heat rate applying Q, 8,
and fission yield uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
NUREG/CR-5625
viii
LIST OF TABLES
(continued)
Page
6.12 Code comparisons of heat rate at 10-year cooling from actinides, light element activation products
plus two fission products (134Cs and 154Eu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.13 Summary of cross-section bias estimates and safety factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.14 Contribution of cross-section (F) bias to safety factor of total heat rate at 1 year . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.15 Contribution of cross-section (F) bias to safety factor of total heat rate at 110 years . . . . . . . . . . . . . . . . . . . . . . . . .
6.16 Summary of percentage safety factors for BWR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.17 Summary of percentage safety factors for PWR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1 BWR fuel assembly loadings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 PWR fuel assembly loadings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3 Files required by LWRARC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.1 BWR assembly design description for tabulated cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.2 PWR assembly design description for tabulated cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.3 Operating history data and fuel isotopic content of BWR cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.4 Operating history data and fuel isotopic content of PWR cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.1 Sample case operating history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.1 BWR decay heat rates (W/kgU) of light elements, actinides and fission products, for
specific power = 12 kW/kgU, set 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.2 BWR decay heat rates (W/kgU) of light elements, actinides and fission products, for
specific power = 12 kW/kgU, set 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.3 BWR decay heat rates (W/kgU) of light elements, actinides and fission products, for
specific power = 12 kW/kgU, set 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.4 BWR decay heat rates (W/kgU) of light elements, actinides and fission products, for
specific power = 20 kW/kgU, set 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.5 BWR decay heat rates (W/kgU) of light elements, actinides and fission products, for
specific power = 20 kW/kgU, set 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.6 BWR decay heat rates (W/kgU) of light elements, actinides and fission products, for
specific power = 20 kW/kgU, set 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.7 BWR decay heat rates (W/kgU) of light elements, actinides and fission products, for
specific power = 30 kW/kgU, set 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.8 BWR decay heat rates (W/kgU) of light elements, actinides and fission products, for
specific power = 30 kW/kgU, set 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.9 BWR decay heat rates (W/kgU) of light elements, actinides and fission products, for
specific power = 30 kW/kgU, set 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.10 PWR decay heat rates (W/kgU) of light elements, actinides and fission products, for
specific power = 18 kW/kgU, set 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.11 PWR decay heat rates (W/kgU) of light elements, actinides and fission products, for
specific power = 18 kW/kgU, set 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.12 PWR decay heat rates (W/kgU) of light elements, actinides and fission products, for
specific power = 18 kW/kgU, set 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.13 PWR decay heat rates (W/kgU) of light elements, actinides and fission products, for
specific power = 28 kW/kgU, set 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ix
51
53
54
54
57
57
62
63
64
71
72
73
73
79
88
88
89
89
90
90
91
91
92
92
93
93
94
NUREG/CR-5625
LIST OF TABLES
(continued)
Page
D.14 PWR decay heat rates (W/kgU) of light elements, actinides and fission products, for
specific power = 28 kW/kgU, set 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.15 PWR decay heat rates (W/kgU) of light elements, actinides and fission products, for
specific power = 28 kW/kgU, set 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.16 PWR decay heat rates (W/kgU) of light elements, actinides and fission products, for
specific power = 40 kW/kgU, set 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.17 PWR decay heat rates (W/kgU) of light elements, actinides and fission products, for
specific power = 40 kW/kgU, set 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.18 PWR decay heat rates (W/kgU) of light elements, actinides and fission products, for
specific power = 40 kW/kgU, set 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
NUREG/CR-5625
x
94
95
95
96
96
FOREWORD
This report will provide technical support for major revisions proposed to the current U.S. Nuclear Regulatory Commission
(NRC) decay heat rate guide entitled "Regulatory Guide 3.54, Spent Fuel Heat Generation in an Independent Spent Fuel
Storage Installation." A proposed revised guide is now under development by the NRC staff. The proposed procedure
applies computed results of the SAS2H/ORIGEN-S analyses sequence of the SCALE-4 system, a more recent version of the
software than that used for the current guide. The calculated decay heat rate data base proposed here has a broader
application and is designed to be easier to use than that in the current guide.
This report is not a substitute for NRC regulation, and compliance is not required. The approaches and/or methods
described in this document are provided for information only. Publication of this report does not necessarily constitute NRC
approval or agreement with the information contained herein.
Donald A. Cool, Chief
Radiation Protection and Health Effects Branch
Division of Regulatory Applications
Office of Nuclear Regulatory Research
xi
NUREG/CR-5625
NUREG/CR-5625
xii
ACKNOWLEDGMENTS
This project was sponsored by the Office of Nuclear Regulatory Research, U.S. Nuclear Regulatory Commission. The
authors are grateful to C. W. Nilsen and F. P. Cardile for their advice and guidance as the NRC Technical Monitors.
Special appreciation is expressed to E. R. Knuckles and associated staff members of Florida Power and Light Company for
providing improved Turkey Point Reactor data. Also, the authors are indebted to S. M. Bowman for his development of the
interactive full-screen menus provided with the LWRARC code. The technical review of the draft document by J. C.
Ryman and M. C. Brady provided valuable suggestions that were incorporated in the final document.
Finally, a special thanks for her skillful preparation of the manuscript is extended to Lindy Norris.
xiii
NUREG/CR-5625
1 INTRODUCTION
Heat is generated during the radioactive decay of
discharged fuel from nuclear power reactors. The
assurance of proper methods of storing the spent fuel
assemblies requires knowledge of their decay heat
generation rates (also, known as decay heats or afterheat
powers). Regulatory Guide 3.54, "Spent Fuel Heat
Generation in an Independent Spent Fuel Storage
Installation," that was issued in September 1984,
addresses acceptable methods for calculating long-term
heat generation rates. Recently, improved nuclear data
libraries and computational models incorporated into
ORIGEN-S1 and the SAS2H control module2 of the
SCALE-4 system3 have been used to develop a basis for a
substantial revision to the current decay heat rate guide.
The purpose of this report is to present the data and
analysis performed to support a proposed revision to the
regulatory guide.
current guide to reduce the conservatism by (1) developing
separate decay heat data bases for PWR and BWR fuel and
(2) increasing the decay heat data base to encompass a
broader range of parameters selected to characterize the
PWR and BWR spent fuel.
1.2 Improvements in the Proposed
Guide
In developing a proposed revision to the current
regulatory guide, the goal is to provide significant
technical improvements while also providing an easier-touse format and/or formulae. The technical improvements
discussed in this report were made by adding a data base
for BWR assemblies and increasing the number and range
of parameters selected to characterize the spent fuel (i.e.,
burnup, specific power, initial enrichment). This
subsection briefly discusses these improvements.
1.1 Background of Current Guide
Analyses performed to provide a basis for the current
guide used the SAS2 analysis sequence provided in the
SCALE-2 and SCALE-3 releases of the SCALE code
system. This earlier SAS2 procedure used a unit-fuelpin-cell model at each depletion time step to obtain the
flux spectrum required to obtain burnup- dependent cross
sections for the fuel depletion analysis. This simple
neutronics model was shown4 to produce slightly
conservative actinide inventories for PWR spent fuel and
did not provide the flexibility required to model BWR fuel.
After the release of the current guide, the neutronic
analysis capabilities of SAS2 were significantly enhanced
to form an updated sequence called SAS2H that was
released as a module of the SCALE-4 system. The new
SAS2H sequence was used to calculate the PWR and BWR
decay heat rates used in preparing this revision to the
current guide procedure. For each depletion time step,
SAS2H performs one-dimensional (1-D) neutron transport
analyses of the reactor fuel assembly using a two-part
procedure with two separate unit-cell-lattice models. The
first model considered in the sequence is a unit fuel-pin
cell from which cell-weighted cross sections are obtained
for use in the second model that represents a larger unit
cell (e.g., an assembly) within an infinite lattice. The
larger unit cell zones can be structured for different types
of BWR or PWR assemblies. The neutron flux spectrum
obtained from the large unit cell model is used to
determine the appropriate nuclide cross sections for the
specified burnup-dependent fuel composition.
The current version of Regulatory Guide 3.54 (issued in
1984) was developed upon the concept of providing a
procedure that specifies proper interpolation and
adjustment formulae for a data base of computed heat
generation rates. The technical basis for the data and
safety factors used in the current guide is reported in Ref.
4. The current guide relies on a decay heat data base
calculated only for pressurized-water-reactor (PWR) fuel.
With no measured heat generation data or validated
calculations for boiling-water-reactor (BWR) fuel, the
guide incorporated large safety factors to prevent the
possibility of specifying nonconservative heat generation
rates. In addition, only a single maximum specific power
(rather than a range of specific power values) was used in
the analyses. The current guide provides decay heat rates
that are fairly accurate (within several percent) for PWR
assemblies that were operated at or near the maximum
power and decayed for relatively short cooling times.
However, for BWR assemblies and PWR assemblies with
more typical power densities (commonly with average
specific power levels near half the maximum used for the
guide basis), conservative heat rates are produced by the
current guide. The main cause for this overestimation of
heat rates is the result of using an upper envelope of the
possible operating powers and is not the result of the
computational model.
Since completion of the technical basis for the current
guide, a number of decay heat measurements have
been performed for PWR and BWR spent fuel. Thus, the
NRC decided to study the possibility of revising the
1
NUREG/CR-5625
Introduction
A more detailed description of the improved analysis
method is given in Sects. S2.2.2 through S2.2.5 of the
SCALE-4.0 documentation.3 Essentially, this expanded
depletion model removes most of the conservatism from
the computed actinide decay heat rates and, also, provides
a procedure for calculating decay heat rates of spent fuel
from BWRs as well as PWRs. Prior to generating the data
base of decay heat rates, the SAS2H analysis procedure
was validated using measured decay heat data obtained for
PWR and BWR spent fuel assemblies.
a cooling time of 2 years, the computed heat rate is 3.632
W/kgU. Had the heat rate result been determined from
calculations using the maximum power of 40 kW/kgU, for
which the computed heat rate is 5.129 W/kgU, the result
would have been excessively conservative by 41%. Of
course the differences between the heat rates at these two
powers is decreased considerably at increased decay times.
The data base for a proposed guide revision has been
developed to encompass the defining characteristics of the
vast majority of spent fuel that is discharged from the
mainstream of normal reactor operations. It was decided
not to include assemblies with atypical characteristics
because it would force the guide to be overly conservative
for typical assemblies and/or significantly increase the
computational effort and/or guide procedure.
The current regulatory guide is formatted to provide a set
of tables containing decay heat rates as a function of
parameter values that characterize a particular assembly.
Using the appropriate table and interpolation guidelines,
an appropriate decay heat value can be obtained from the
tabular data base. This basic concept of interpolating a
reference data base to obtain the decay heat value has been
continued in preparing the proposed revisions to the
current guide. However, the revised data base has been
improved significantly by incorporating computed decay
heat rates at six different burnups for each of three specific
powers (compared with one maximum specific power in
the current guide). Within each case, final decay heat
generation rates were computed at 20 different cooling
times in the range of 1 to 110 years. The ranges of the
BWR burnup and power were 20 to 45 MWd/kgU and 12
to 30 kW/kgU, respectively. The PWR burnup and power
ranges were 25 to 50 MWd/kgU and 18 to 40 kW/kgU,
respectively. Also, additional cases were computed in
which the 235U enrichment was either decreased or
increased by one-third from that of the standard case.
Thus, the calculated decay heat rate data were produced as
a function of burnup, specific power, cooling time, initial
fuel 235U enrichment, and assembly type (i.e., BWR or
PWR).
1.3 Overview of Report
This introduction has provided a brief background of the
current guide and a discussion giving justification for a
proposed revision. The sources of the data used for the
analyses are presented in Sect. 2. Section 3 presents the
validation of the decay heat rate computational model
performed by comparison with measured calorimetric
data. A description of the cases producing heat rate data
for a guide revision is given in Sect. 4. The tabulated
data and complete procedure proposed for a revised guide
are presented in Sect. 5. This section is followed by a
detailed analysis of the method and equations. Finally,
Sect. 7 provides a brief description of the LWRARC code
(for use on a personal computer), which is an easy-to-use
code applying the data base and procedures presented in
Sect. 5. Also included are the addresses of two code
centers from which the LWRARC code may be requested.
The Appendix contains assembly design and operation
data, examples of the input for two of the tabulated cases,
a sample problem using the proposed procedure, plots
showing heat rates of major isotopes, and examples of the
LWRARC code printouts.
An example demonstrating the significance of the
improvement in using the actual specific power as opposed
to a single maximum power can be seen in the following
comparison. Consider a PWR assembly that has a burnup
of 30 MWd/kgU and a specific power of 18 kW/kgU. At
NUREG/CR-5625
2
2 SOURCES OF DATA FOR COMPUTING HEAT RATES
The ORIGEN-S nuclear data library5 provided with the
SCALE-4 system was the source of data for the half-lives,
decay branching fractions, and recoverable energy per
decay for all fission products and significant actinide and
light element nuclides. These data were taken from either
ENDF/B-V6 or ENSDF.7 A more detailed description of
the source of all nuclear data is presented in Sect. M6.2.6
of Ref. 5. The fission product yield data were taken
entirely from ENDF/B-V.6 A convenient formatted listing
of these yield data is presented in Ref. 8.
181 fission products, and provided a base PWR or BWR
library to replace the outdated default ORIGEN-S library
(made with circa 1960 data). The subsequent SAS2H
cases used the BWR or PWR preSAS library as the base
library and generated updated cross sections for 38 to 39
significant nuclides (plus 6 gadolinium isotopes for the
BWR) as a function of burnup. A list of the nuclides that
were updated as a function of burnup is provided in Table
2.1. The cross-section update was obtained from the
neutronics analysis of the larger unit cell model which
simulates the fuel assembly. The fuel spectrum from this
analysis also provides new values for the spectral
parameters THERM, RES, and FAST used by ORIGEN-S
to model energy dependence within the depletion
calculation.
The SCALE 27-energy-group depletion cross-section
library (27BURNUPLIB)9 was used in all the SAS2H
cases. This library contains ENDF/B-IV data for the
major actinides and pre-release ENDF/B-V data for the
fission products. For each reactor type (i.e., BWR or
PWR), a preliminary SAS2H case was performed to
produce an ORIGEN-S library (sometimes called a
"preSAS library") to be used as the initial library in all
subsequent SAS2H cases. Each preliminary SAS2H case
performed one pass through the neutronics portion of the
sequence in order to produce updated cross sections for
The above data sources were applied to all the standard
cases used to produce data for the proposed decay heat
guide revision. Other sources of data used to evaluate the
validity of the SAS2H data will be referred to later in this
report.
Table 2.1 List of nuclides updated as a function
of burnup in the SAS2H analyses
1
H
B
11 a
B
16
O
59
Co
94
Zr
99
Tc
106
Ru
103
Rh
105
Rh
131
Xe
135
Xe
133
Cs
134
Cs
144
Ce
10
a
143
Pr
Nd
145
Nd
147
Nd
147
Pm
149
Sm
151
Sm
152
Sm
153
Eu
154
Eu
155
Eu
154
Gdb
155
Gdb
156
Gdb
157
Gdb
143
158
Gdb
Gdb
234
U
235
U
236
U
238
U
237
Np
238
Pu
239
Pu
240
Pu
241
Pu
242
Pu
241
Am
243
Am
244
Cm
160
Only in PWR cases.
Only in BWR cases.
b
3
NUREG/CR-5625
3 COMPARISONS OF COMPUTED AND MEASURED HEAT RATES
The reliability of a computer code to calculate decay heat
generation rates can be demonstrated by comparing
calorimetric measurements of heat rates of spent fuel
assemblies with values computed by using code input
similar to the design and operating characteristics of the
fuel assemblies. In this study, results were compared for
ten PWR and ten BWR spent fuel assemblies. In the
comparison benchmarks, the fuel came from three
reactors—Point Beach Unit 2 PWR, Turkey Point Unit 3
PWR, and Cooper Nuclear Station BWR. The heat rates
of the Turkey Point assemblies were measured10 at the
Engine Maintenance Assembly and Disassembly Facility
at the Nevada Test Site. The measurements of the Point
Beach and Cooper Station assemblies were performed11,12
at General Electric's Morris Facility. Decay heat results
from these sets of measurements were taken from Refs. 13
through 15.
from the uncertainty in the cobalt contents listed in Table
3.11. Measurements25,26 of cobalt in clad and structural
materials known to the authors indicate amounts
significantly less than that used here. In order to be
consistent, the same cobalt content per kgU for each
reactor type was applied in both the cases for measurement
comparisons and the cases for the new decay heat data
base of Sect. 5.
From the tabulated data on the measured assemblies, note
that some of the assemblies were in the reactor during the
same cycles (i.e., had similar overall operating histories)
and had approximately equal burnups (within 5%). These
similarities in assembly characteristics permitted a more
efficient use of computational time because a separate
SAS2H calculation was not needed for each assembly.
Instead, for each set of assemblies with similar
characteristics, the SAS2H sequence was used to perform
a reactor depletion analysis with an approximate operating
history. The burnup-dependent cross-section libraries
created by the SAS2H case were then accessed in separate
stand- alone ORIGEN-S cases that modeled the specific
operating history and decay time for each applicable
assembly. In these cases, the heat rate difference from not
using SAS2H for individual assemblies was estimated to
be <1%.
This section presents a description of the design and
reactor operating characteristics of the spent fuel used in
the measurements. Then, the comparison of measured and
calculated heat rates is listed and summarized.
3.1 Assembly Design and Operating
Characteristics
The design and operating history data of each measured
assembly from the three types of reactors is listed in
Tables 3.1 through 3.12, inclusive. The data in these
tables are sufficient for the required input to the SAS2H
and ORIGEN-S modules used for computing heat rates of
all the fuel assemblies in this comparison study. However,
more detailed operating histories15 than the data in Table
3.9 were used for some of the Cooper Nuclear Station
assemblies when considered necessary to account for large
power fluctuations over a fuel cycle. Initial uranium
isotopic contents were determined from Table 3.12, as in a
previous similar procedure.23 The isotopic ratio factors in
Table 3.12 were simply taken from those derived from
mass spectrometer analyses24 of initial fuel for the Yankee
Reactor Core V. Part of the assembly data (e.g., some of
the temperatures) were not available in the references on
the experiments and assembly designs. In those cases, the
values were taken from Ref. 17 for the generic case of the
reactor. Table 3.11 lists the element contents (excluding
that of uranium) of the measured assemblies along with
the amounts applied in the PWR and BWR cases used to
create the decay heat data base presented in Sect. 5.
3.2 Discussion of Comparisons
Comparisons of measured and SAS2H/ORIGEN-S
calculated decay heat rates of spent fuel assemblies from
the three reactors in this study are listed in Tables 3.13,
3.14, and 3.15. The major parameters of total burnup, 235U
enrichment, and cooling time of each assembly are shown.
The measured and computed heat rates for each
experiment are listed. Percentage differences between the
measured and calculated values are presented to provide a
measure of the comparison. In addition to the percentage
difference for each measurement, the average percentage
difference of all the measurements on each assembly is
indicated. Averages of both types of percentage
differences and the standard deviations of the average
differences are also provided.
There is at least one excessively high percentage
difference in each of the three tables. These data were not
excluded because it was decided to use comparisons for all
reported measurements for which pertinent parameters
were available. Each of the calculated heat rates reported
for the Point Beach PWR assemblies in Table 3.13 was
higher than the measured value. However, except for the
The greatest uncertainty in the calculated decay heat rates
caused by inaccurate input data is probably that resulting
NUREG/CR-5625
4
Comparisons
Table 3.1 Point Beach Unit 2 PWR assembly description
Parameter
Data
Assembly general data
Designer
Lattice
Fuel weight, kg U
Water temperature, K
Water pressure, psia (12/73)
Water density, avg, g-cm-3
Soluble boron, cycle avg, ppm (wt)
Number of fuel rods
Number of guide tubesb
Number of instrument tubes
Fuel rod data
Type fuel pellet
Pellet stack density, g-cm-3
Rod pitch, cm (in.)
Rod OD, cm (in.)
Rod ID, cm (in.)
Active fuel length, cm (in.)
Clad material
234
U wt %
U wt %
236
U wt %
238
U wt %
Effective fuel temperature, K
Clad temperature, K
Reference
Westinghouse
14 × 14
386
579
2000
0.7115a
550
179
16
1
16
16
14
16
16
–
17
18
18
18
UO2
9.467a
1.412 (0.556)
1.0719 (0.422)
0.9484 (0.3734)
365.8 (144)
Zircaloy-4
0.030a
3.397
0.016a
96.557a
811
620
16
–
18
18
18
18
18
–
14
–
–
17
17
0.6845 (0.539)
0.6414 (0.505)
Zircaloy-4
18
18
18
235
Guide tube datab
Inner radius, cm (ID, as in.)
Outer radius, cm (OD, as in.)
Tube material
These data were calculated from other data in the table.
Control rods were considered to be fully withdrawn during reactor uptime.
a
b
5
NUREG/CR-5625
Comparisons
Table 3.2 Point Beach Unit 2 PWR operating historya
Cycle
Startup
Shutdown
Uptime, d
Downtime, d
1A
1B
2
3
8/01/72b
5/01/73b
12/20/74
3/29/76
10/16/74b
2/26/76
3/03/77
273
533
433
339
0
65
32
–
Core-avg burnup,
MWd/kgU
1.070
15.993
11.806
10.040
a
See Ref. 14.
Cycle 1 was split in order to apply significantly different powers more correctly.
b
Table 3.3 Point Beach Unit 2 assembly burnupsa and powers
Fuel assembly ID
C-64
C-66
Burnup, MWd/kgU
C-52
C-56
Cycle 1
Cycle 2
Cycle 3
10.801
12.316
8.797
16.475
12.881
9.561
16.920
12.844
9.620
0.958
7.332
10.979
10.017
1.461
11.183
11.483
10.887
1.500
11.485
11.450
10.954
C-67
C-68
11.668
13.256
10.509
16.600
12.801
9.545
13.034
13.908
10.115
1.035
7.920
11.817
11.966
1.472
11.268
11.412
10.868
1.156
8.847
12.398
11.517
Power,b MW/assembly
Cycle 1A
Cycle 1B
Cycle 2
Cycle 3
a
See Ref. 14.
Computed from the uptimes and core-averaged burnups in Table 3.2, 386 kgU/assembly, and the above burnups.
b
NUREG/CR-5625
6
Comparisons
Table 3.4 Turkey Point Unit 3 PWR assembly description
Parameter
Data
Reference
Assembly general data
Designer
Lattice
Fuel weight of B-43, kgU
Fuel weight of D-15, kgU
Fuel weight of D-22, kgU
Fuel weight of D-34, kgU
Water temperature, K
Water density, g-cm3
Soluble boron, cycle avg, ppm (wt)
Number of fuel rods
Number of guide tubesb
Number of instrument tubes
Westinghouse
15 × 15
447.8a
456.1a
458.0a
455.2a
570
0.7311
450
204
20
1
19
19
–
–
–
–
4
4
4
4,18
18
18
Fuel rod data
Type fuel pellet
Stack density (B-43), % TD
Stack density (D-15), % TD
Rod pitch, cm (in.)
Rod OD, cm (in.)
Rod ID, cm (in.)
Pellet OD, cm (in.)
Active fuel length
Clad material
234
U wt %
235
U wt % (B-assemblies)
235
U wt % (D-assemblies)
236
U wt %
238
U wt % (B-assemblies)
238
U wt % (D-assemblies)
Effective fuel temperature, K
Clad temperature, K
UO2
91.53c
93.23c
1.4300 (0.563)
1.0719 (0.422)
0.9484 (0.3734)
0.9296 (0.366)
365.8 (144)
Zircaloy-4
0.023c
2.559a
2.557a
0.012c
97.406c
97.408c
922
595
4,18
–
–
4,18
4,18
4,18
4
4,18
4,18
–
–
–
–
–
–
4
4
Guide tube datab
Inner radius, cm (ID, as in.)
Outer radius, cm (OD, as in.)
Tube material
0.6502 (0.512)
0.6934 (0.546)
Zircaloy-4
18
18
18
Florida Power and Light Co. data provided by E. R. Knuckles.
Control rods were considered to be fully withdrawn.
c
These data were calculated from other data in the table.
a
b
7
NUREG/CR-5625
Comparisons
Table 3.5 Turkey Point Unit 3 PWR operating historya
Cycle
Startup
Shutdown
Uptime, d
Downtime, d
1
2
3
4
10/20/72
12/16/74
12/23/75
1/16/77
10/04/74
10/26/75
11/15/76
11/24/75
714
314
327
312
73
58
62
–
Florida Power and Light Co. data provided by E. R. Knuckles.
a
Table 3.6 Turkey Point Unit 3 assembly burnupsa and powers
Burnup, MWd/kgU
Cycle 1
Cycle 2
Cycle 3
Cycle 4
B-43
Fuel assembly ID
D-15
D-22
D-34
15.998
8.829
–
–
–
9.480
9.752
8.920
–
9.826
8.867
7.253
–
9.488
9.338
8.794
10.033
12.591
–
–
–
13.771
13.603
13.040
–
14.332
12.419
10.647
–
13.756
13.000
12.831
Power,b MW/assembly
Cycle 1
Cycle 2
Cycle 3
Cycle 4
Florida Power and Light Co. data obtained from PDQ-7 analyses and provided by E. R. Knuckles.
Computed from the uptimes in Table 3.5, the uranium weights per assembly in Table 3.4 and
the above burnups.
a
b
NUREG/CR-5625
8
Comparisons
Table 3.7 Cooper Nuclear Station BWR assembly description
Parameter
Data
Reference
Assembly general data
Designer
Lattice
Fuel weight, kgU
Water temperature, K
Water vol-avg density, g-cm-3
Number of fuel rods
Burnable poison element
Number containing poison
Assembly pitch, cm (in.)
Shroud (tube) thickness, cm (in.)
Shroud inside flat-to-flat, cm (in.)
Shroud material
Shroud temperature, K
Channel water density, g-cm-3
Channel water temperature, K
Channel avg 10B content, atom/b-cm
General Electric
7×7
190.2a
558
0.4323
49
Gd
4
15.24 (6.0)
0.2032 (0.08)
13.406 (5.278)
Zircaloy-4
558
0.669b
552
7.15 × 10-6 (see footnote c)
20
20
15
17
17
20
20
17
15
15
15
17
17
17
17
–
Fuel rod data
Type fuel pellet
Pellet stack density, g-cm-3
Rod pitch, cm (in.)
Rod OD, cm (in.)
Rod ID, cm (in.)
Active fuel length, cm (in.)
Clad material
Gadolinia bearing rods, Gd wt %
UO2
9.96d
1.8745 (0.738)
1.4300 (0.563)
1.2421 (0.489)
365.76 (144)
Zircaloy-2
3.5e
18
–
15
15
15
20
20
–
Assembly CZ102 average U content:
234
U wt %
235
U wt %
236
U wt %
238
U wt %
0.010d
1.100
0.005d
98.885d
–
15
–
–
Average U content, all except CZ102:
234
U
235
U
236
U
238
U
0.022d
2.500
0.012d
97.466d
–
15
–
–
Effective fuel temperature, K
Clad temperature, K
840
620
17
17
Some assemblies had 190.5 kgU. However, the 190.2 value was used in the analyses.
Reduced the 0.743 g-cm-3 bottom node density by 10% to account for control cruciform displacement.
c
Applied in channel region for boron cruciform; used content producing average keff of approximately unity.
d
These data were calculated from other data in the table.
e
Used the average of 3 and 4 wt % Gd, each the content of two rods.
a
b
9
NUREG/CR-5625
Comparisons
Table 3.8 Cooper Nuclear Station BWR operating historya
Cycle
Cycle
start
1
2
3
4
5
6
7
7/03/74
11/15/76
10/18/77
5/05/78
5/10/79
6/07/80
6/07/81
Since
startup, d
Shutdown
0
866
1203
1402
1772
2166
2531
Since
startup, d
Uptime, d
807
1172
1367
1749
2068
2483
2879
807
306
164
347
296
317
348
9/17/76
9/17/77
3/31/78
4/17/79
3/01/80
4/20/81
5/21/82
Downtime, d
59
31
35
23
98
48
–
See Ref. 15.
a
Table 3.9 Cooper Nuclear Station adjusted cycle burnupsa
Assembly
CZ102
CZ205
CZ209
CZ259
CZ331
CZ369
CZ429
CZ515
CZ526
CZ528
Cycle 1
9.394
10.298
10.651
6.026
12.875
11.162
10.878
11.003
10.939
10.996
Cycle 2
Cycle 3
Cycle 4
Cycle 5
Cycle 6
2.273
7.414
7.669
4.339
5.495
8.035
7.833
7.922
7.875
7.917
2.987
3.110
2.555
2.962
2.481
2.899
0
2.734
0
0
0
8.511
0
0
2.165
1.864
2.296
2.870
2.781
1.657
0
0
0
0
0
0
0
2.691
0
2.692
1.982
3.232
4.121
3.239
4.110
2.916
2.799
2.809
See Ref. 15.
a
Table 3.10 Cooper Nuclear Station assembly powers
Assembly
CZ102
CZ205
CZ209
CZ259
CZ331
CZ369
CZ429
CZ515
CZ526
CZ528
Cycle 1
2.214
2.427
2.510
1.420
3.034
2.631
2.564
2.593
2.578
2.592
Powersa by cycles, MW/assembly
Cycle 2
Cycle 3
Cycle 4
Cycle 5
1.413
4.608
4.767
2.697
3.416
4.994
4.869
4.924
4.895
4.921
3.464
3.607
2.963
3.435
2.877
3.362
0
3.171
0
0
0
4.665
0
0
0
0
0
Computed from uptimes in Table 3.8, burnups in Table 3.9 and 190.2 kgU/assembly.
a
NUREG/CR-5625
10
Cycle 7
Cycle 6
Cycle 7
0
0
1.391
1.118
1.378
1.722
1.520
0.906
0
0
1.729
0
1.730
1.189
1.939
2.473
1.943
2.466
1.594
1.530
1.535
Comparisons
Table 3.11 Element contentsa from clad, structure, and water (for BWR)
BWR
g/kgU
Elementb
H
B
O
Cr
Mn
Fe
Co
Ni
Zr
Nb
Sn
Gd
Cooper
Station
kg/assembly
PWR
g/kgU
16.4
0.068
265.0
2.4
0.15
6.6
0.024
2.4
516.0
0
8.7
c
3.1
0.013
50.5
0.45
0.029
1.2
0.0046
0.45
98.2
0
1.6
0.544
135.0
5.9
0.33
12.9
0.075
9.9
221.0
0.71
3.6
Point
Beach
kg/assembly
52.0
2.3
0.13
5.0
0.029
3.8
85.0
0.27
1.4
Turkey
Point
kg/assembly
62.0
2.7
0.15
5.9
0.034
4.5
101.0
0.32
1.6
Calculated from data and factors in Ref. 21, except for spectral correction factors in Ref. 22 for PWRs.
Included only elements with contents exceeding 0.5 g/kgU plus Mn, Co, and B (for BWR only).
c
The Gd in BWR standard cases varied with wt % Gd in pins.
a
b
Table 3.12 Uranium isotope dependence23
on X wt % 235U enrichment
Isotope
Assay, wt %
234
U
U
236
U
238
U
0.0089 X
1.0000 X
0.0046 X
100 – 1.0135 X
235
Table 3.13 Point Beach PWR measureda and computed decay heat rates
Assembly
ID
Burnup,
MWd/kgU
Initial
U wt %
C-52
31.914
3.397
C-56
C-64
38.917
39.384
3.397
3.397
C-66
C-67
C-68
35.433
38.946
37.057
3.397
3.397
3.397
235
Cooling
time, d
1635
1635
1634
1633
1633
1630
1629
1630
Heat rate, W
Meas.
Calc.
724b
723c
921
931b
825c
846
934
874
Average
Standard deviation
732.2
732.2
943.3
959.0
959.0
852.2
946.5
898.0
% Difference % Difference
(C/M-1)100% assembly-avg
1.1
1.3
2.4
3.0
16.2
0.7
1.3
2.7
3.6
±2.3
1.2
2.4
9.6
0.7
1.3
2.7
3.0
±1.9
See Ref. 14.
Static test.
c
Recirculation test.
a
b
11
NUREG/CR-5625
Comparisons
16.2% value, the differences did not exceed 3%. This
reactor was the only reactor for which the average
difference exceeded the standard deviation (i.e., 3.0 ±
1.9%) and, therefore, it indicates there is a systematic
bias to calculate decay heat rates higher than the
measured data. The burnups and 235U enrichments also
were higher than the other assemblies compared. The
3% difference for the C-64 assembly was the result of a
comparison with a measurement by a static test, whereas
the 16.2% resulted from a comparison with a
measurement that was determined by a recirculation test.
Had the assembly been excluded from consideration, the
average percentage difference of the other assemblies
would have been 1.7 ± 0.9%.
The percentage differences in the comparisons in Table
3.15 for the Cooper Nuclear Station BWR assemblies
extended through a much wider range than those for the
PWRs. However, the decay heat measurements were
much lower values (62.3 to 395.4 W) than those
measured for the PWRs (625 to 1550 W). Because
measurement precision tends to be represented as a
constant heat rate instead of a percentage of the total heat
rate, the percentage uncertainty in the measured data
would increase as the measured value decreases. Thus,
the broader range of percentage differences in measured
and calculated decay heat rates is expected. The increase
in the number of measurements and assemblies, however,
has somewhat reduced the final standard deviation. The
average assembly difference of –0.7 ±2.6% shows good
agreement between calculated and measured values for
the BWR assemblies.
The computed heat rates of the Turkey Point PWR
assemblies in Table 3.14 were both higher and lower
than measured values. A previous comparison4 of SAS2
results with measurements applied equal burnups and
specific powers13 for the three cycles of the D-assemblies.
This rather rough estimate of operating history was
improved in the present calculations by using more
complete data given by the operating utility (see Tables
3.5–3.6). The results in Table 3.14 show that three of the
assembly average differences were within 2.3%. The
remaining assembly, B-43 (which had a –4.5%
difference), was the only one of the four that was in the
reactor during the first cycle. The lower calculated value
for assembly B-43 could be caused by extremely low
operating powers during initial reactor startup. This
extremely low power during the early period of the first
cycle lowered the average cycle power below that used for
most of the cycle-1 burnup. Thus, the measured decay
heat rate of assembly B-43 is greater than it would have
been for the use of a constant power in cycle 1, because
the decay time of part of the fission products is less. The
average assembly percentage difference, however, of –0.7
± 1.7% indicates good agreement.
NUREG/CR-5625
A summary of percentage differences in comparisons of
measured and calculated spent fuel decay heat rates for
all cases and assemblies is presented in Table 3.16. The
average heat rate computed was less than the measured
value for the BWR assemblies and the opposite was true
for the PWR assemblies. The final average difference for
all 20 LWR spent fuel assemblies was 0.4 ± 1.4%. Then
at the confidence level associated with 2 standard
deviations the percentage differences should lie in the
range –2.4 to 3.2%. Thus, at the 2F confidence level and
for the design and operating parameters of the given
assemblies, the nonconservative error in computed decay
heat rates should not exceed 2.4% plus any
nonconservative bias in the measurements. The
comparisons of measured and calculated decay heat rates
shown in this section provide the basis for the
calculational bias that will be used in development of a
proposed regulatory guide.
12
Comparisons
Table 3.14 Turkey Point PWR measureda and computed decay heat rates
Assembly Burnup,
ID
MWd/kgU
Initial
U wt %
235
B-43
D-15
24.827
28.152
2.559
2.557
D-22
D-34
25.946
27.620
2.557
2.557
Cooling
time, d
Heat rate, W
Meas.
Calc.
1782
962
1144
2077
963
864
637
1423
1126
625
1284
1550
608.1
1436.0
1172.0
628.4
1255.0
1582.0
Average
Standard deviation
a
% Difference
(C/M-1)100%
% Difference
assembly-avg
–4.5
0.9
4.1
0.5
–2.3
2.1
–4.5
0.1
±1.3
–0.7
±1.7
1.8
–2.3
2.1
See Ref. 14.
Table 3.15 Cooper Nuclear Station BWR measureda and computed decay heat rates
Assembly Burnup,
ID
MWd/kgU
Initial
U wt %
Cooling
time, d
Heat rate, W
Meas.
Calc.
2565
2645
857
867
871
872
886
887
892
896
899
930
936
946
891
1288
1340
2369
2457
888
889
1254
1285
864
1286
62.3
70.4
324.0
361.0
343.5
353.2
331.8
338.7
327.5
313.1
311.4
314.0
331.2
317.1
279.5
247.6
288.5
162.8
180.1
347.6
385.6
294.0
296.0
395.4
297.6
235
CZ102
11.667
1.1
CZ205
25.344
2.5
CZ209
CZ259
25.383
26.466
2.5
2.5
CZ331
21.332
2.5
CZ369
CZ429
CZ515
26.576
27.641
25.737
2.5
2.5
2.5
CZ526
CZ528
27.596
25.715
2.5
2.5
Average
Standard deviation
a
78.9
77.8
328.3
325.3
324.1
323.8
319.8
319.5
318.1
316.9
316.1
307.8
306.2
303.7
290.1
285.7
278.5
161.6
158.2
340.4
366.5
282.3
276.7
374.7
275.4
% Difference
(C/M-1)100%
26.6
10.5
1.3
–9.9
–5.6
–8.3
–3.6
–5.7
–2.9
1.2
1.5
–2.0
–7.5
–4.2
3.8
15.4
–3.5
–0.7
–12.2
–2.1
–5.0
–4.0
–6.5
–5.2
–7.5
–1.4
±1.7
% Difference
assembly-avg
18.6
–3.8
3.8
6.0
–6.5
–2.1
–5.0
–5.3
–5.2
–7.5
–0.7
±2.6
See Ref. 15.
13
NUREG/CR-5625
Comparisons
Table 3.16 Summary of decay heat rate comparisons
Type of summary
Summary by cases:
Average Point Beach case
Average Turkey Point case
Average Cooper case
Average PWR case
Average BWR case
Number
8
6
25
14
25
Average, PWR and BWR avg-case
Summary by assemblies:
Average Point Beach assembly 6
Average Turkey Point assembly
Average Cooper assembly
Average PWR assembly
Average BWR assembly
Final average, all assemblies
a
3.6 ± 2.3
0.1 ± 1.3
–1.4 ± 1.7
2.1 ± 1.4
–1.4 ± 1.7
–0.3 ± 1.1
3.0 ± 1.9
4
10
10
10
20
(Calculated/measured B 1)100%.
NUREG/CR-5625
% Differencea ± std dev
14
–0.7 ± 1.7
–0.7 ± 2.6
1.5 ± 1.3
–0.7 ± 2.6
0.4 ± 1.4
Comparisons
4 HEAT RATE DATA COMPUTED FOR PROPOSED GUIDE
This section provides a few summary remarks about the
SAS2H/ORIGEN-S cases used to calculate the decay heat
rates. For each reactor type, combinations of six different
burnup values and three different specific powers were
considered. The ranges of the BWR burnup and power
were 20 to 45 MWd/kgU and 12 to 30 kW/kgU,
respectively. The PWR burnup and power ranges were 25
to 50 MWd/kgU and 18 to 40 kW/kgU, respectively. Final
decay heat generation rates were calculated in each case at
20 different cooling times ranging from 1 to 110 years. A
total of 720 decay heat generation rates were calculated
from the 18 PWR and 18 BWR cases.
downtimes) were used for all cycles except the last one
was considered to be 100% uptime. Three cycles were
used for the two lowest burnup cases, four cycles for the
next two higher in burnup and five cycles for the two
highest in burnup.
In the procedure provided in Sect. 5, the heat rate
corresponding to the conditions given for a particular
assembly is first determined by interpolating tabulated
values linearly between powers and burnups and
logarithmically between cooling times. However, this
interpolated value corresponds to the computed heat rate at
only the power, burnup, and cooling time specified. The
interpolated heat rate value must be corrected for
significant changes between other conditions used in the
calculations and those of the given assembly (e.g., 235U
enrichment or operating history). Most of these different
parameter variations cause small enough changes in the
results that their effects could be conveniently included in
the safety factor. However, explicit factors are derived for
deviations from the calculations in parameters of the
assembly such as the initial 235U enrichment and the last
two operating cycle powers. These factors are then
applied as adjustments to the interpolated value. An
additional safety factor is applied as a function of reactor
type, burnup, and cooling time. A more detailed analysis
and discussion of the factors and the method in general are
given in Sect. 6.
The PWR and BWR assembly design and operating
characteristics applied in the SAS2H/ORIGEN-S cases are
taken from the generic data provided in Ref. 17. The
specific data used for the cases are provided in detail in
Appendix A. For the BWR cases, the contents of
gadolinium in the fuel, the boron in the cruciform control
assemblies and the coolant density between the assembly
shrouds were changed from the generic-case values to
represent more realistic data. The specific powers,
burnup, and initial235U fuel enrichments were changed
from that provided in Ref. 17 to those needed to span the
desired range for each parameter. The cycle times were
changed to produce the proper burnup and power.
Uptimes of 80% (which includes the effect of reload
15
NUREG/CR-5625
Comparisons
NUREG/CR-5625
16
Procedure
5 PROPOSED REGULATORY GUIDE PROCEDURE
This section of the report presents the proposed procedure
for use in a revision to the NRC regulatory guide on spent
fuel heat generation in an independent spent fuel storage
installation. Section 5.1 contains the definitions, as used
here, of parameters needed in the determination of the
heat generation rate of a fuel assembly. Section 5.2.1
contains the procedure for interpolating tables to derive
the uncorrected heat rate of an assembly. Sections 5.2.25.2.6 include the final evaluation method that uses simple
adjustment factors for cases that are somewhat nontypical,
in addition to the specified safety factor.
for the initially loaded or reloaded reactor to the time at
which the next reloaded core becomes critical. The
exception is for the last cycle where the cycle ends with the
last reactor shutdown before discharge of the assembly. Ti
denotes the elapsed time during cycle i for the assembly.
Specifically, the first and last cycles are denoted by i = s (for
start) and i = e (for end), respectively. Tres, the total
residence time of the assembly, is the sum of all Ti for i = s
through e, inclusive. Except for the last cycle for an
assembly, the cycle times include the downtimes during
reload. Cycle times, in this guide, are in days.
There may be fuel assemblies with characteristics that lie
sufficiently outside the mainstream of typical plant
operations as to require a separate method for predicting
the heat generation rate. Assemblies whose parameters lie
outside the range of values used in the guide may be
considered atypical for the purposes of using the proposed
guide revision. A discussion of the characteristics of
assumed typical reactor operations is in Sect. 5.3. A
glossary of terms is given in Sect. 5.4.
5.1.3 Fuel Burnup of the Assembly (Bi and Btot )
The fuel burnup of cycle i, Bi , is the recoverable thermal
energy per unit fuel mass during the cycle in units of
megawatt days per metric ton (tonne) initial uranium
(MWd/tU) or in the SI units* of mass used in the guide,
megawatt day per kilogram U (MWd/kgU). Bi is the
maximum estimate of the fuel assembly burnup during cycle
i. Btot is the total operating history burnup:
e
Btot ' j Bi .
5.1 Definitions and Derivations of
Required Parameters
The following definitions are used in the proposed guide
procedure.
5.1.4 Specific Power of the Fuel (Pi , Pe , and
Pave)
5.1.1 Heat Generation Rate of the Assembly
(p)
Specific power has a unique meaning in the guide. The
reason for developing this definition is to take into account
the differences between the actual operating history of the
assembly and that used in the computation of the tabulated
heat generation rates. The calculational model applied an
uptime (time at power) of 80% of the cycle time in all
except the last cycle (of the discharged fuel assembly),
which had no downtime. The definition of specific power,
used here, has two basic characteristics. First, when the
actual uptime experienced by the assembly exceeds the 80%
applied in the SAS2H/ORIGEN-S calculations, the heat rate
changes by less than 1%. Second, when the actual uptime
experienced is lower than the 80% applied in the
calculations, the heat rate is reduced.
The heat generation rate of the spent fuel assembly is the
recoverable thermal energy (from radioactive decay) of the
assembly per unit time per unit fuel mass. The units for
heat generation rate used in this guide are W per kg U,
where U is the initial uranium loaded. Heat generation
rate has also been referred to as decay heat rate, afterheat,
or afterheat power.
5.1.2 Cycle and Cycle Times of the Assembly
(Ti)
A cycle of the operating history for a fuel assembly is the
duration between the time criticality is obtained
*
(1)
i's
The adopted International System of units.
17
NUREG/CR-5625
Procedure
5.1.6 Assembly Initial Fuel Enrichment (Es)
The technical basis for these characteristics is presented in
Sect. 6.1.
The initial enrichment, Es , of the fuel assembly is
considered to be the average wt % 235U in the uranium when
it is first loaded into the reactor. Heat generation rates vary
with initial enrichment for fuel having the same burnup and
specific power; the heat rate increases with lower
enrichment. If the enrichment is different than that used in
the calculations at a given burnup and specific power, a
correction factor is applied.
The specific power of cycle i, or e (last cycle), in kW/kgU,
using burnup in MWd/kgU, is defined as
Pi '
Pe '
1000 Bi
0.8 Ti
1000 Be
Te
for i < e ;
(2)
for i ' e .
5.2 Determination of Heat Generation
Rates
The average specific power over the entire operating
history of a fuel assembly, using the same units as in Eq.
(2), is defined as
Pave '
1000 Btot
Te % 0.8 jei '& s1 Ti
.
Directions for determining the heat generation rates of
light-water-reactor (LWR) fuel assemblies from Tables 5.15.8 are given in this section. First, a heat rate, ptab , is found
by interpolation from Tables 5.1–5.3 or Tables 5.5–5.7.
Then, a safety factor and all the necessary adjustment
factors are applied to determine the final heat generation
rate, pfinal . There are three adjustment factors (see Sects.
5.2.2–5.2.4) plus a safety factor (see Sect. 5.2.5) that are
applied in computing the final heat generation rate, pfinal ,
from ptab . In many cases, the adjustment factors are unity
and thus are not required. An alternative to these directions
is the use of the LWRARC code on a personal computer (see
Sect. 7). This code evaluates ptab and pfinal using the data and
procedures established in this section.
(3)
The average specific power through the next to last cycle
is used in applying the adjustment factor for short cooling
time (see Sect. 5.2.2). This parameter is defined as
Pave, e & 1 '
1000 (Btot & B e )
0.8 (Tres & T e )
.
(4)
Note that Btot and Pave , as derived in these definitions, are
used in determining the heat generation rate from the
guide. Also, for cooling times #7 years, Pe is used in an
adjustment formula. The method applied here
accommodates storage of a fuel assembly outside the
reactor during one or two cycles and returning it to the
reactor. Then, Bi = 0 may be set for all intermediate
storage cycles. If the cooling time is short (i.e., <10
years), the results derived here may be excessively high for
cases in which the fuel was temporarily discharged. Other
evaluation methods that include the incorporation of
storage cycles in the power history may be preferable.
5.2.1 Computing Heat Rate Provided by Tables
Use Tables 5.1–5.3 for BWR fuel or Tables 5.5–5.7 for
PWR fuel. The heat rates in each table pertain to a single
specific power and are listed as a function of total burnup
and cooling time. After determining Pave , Btot , and Tc , as
defined above, select the next lower (L-index) and next
higher (H-index) heat rate values from the tables so that:
PL # Pave # PH ;
BL # Btot # BH ;
and
5.1.5 Assembly Cooling Time (Tc)
TL # Tc # TH .
The cooling time, Tc , of an assembly is the time elapsed
from the last downtime of the reactor prior to its discharge
(at end of Te) to the time at which the heat generation rate
is desired. Cooling times, in the guide, are in years.
NUREG/CR-5625
18
Procedure
Table 5.1 BWR spent fuel heat generation rates, watts per
kilogram U, for specific power = 12 kW/kgU
Cooling
time,
years
1.0
1.4
2.0
2.8
4.0
5.0
7.0
10.0
15.0
20.0
25.0
30.0
40.0
50.0
60.0
70.0
80.0
90.0
100.0
110.0
Fuel burnup, MWd/kgU
20
25
30
35
40
45
4.147
3.132
2.249
1.592
1.111
0.919
0.745
0.645
0.569
0.518
0.477
0.441
0.380
0.331
0.292
0.259
0.233
0.212
0.194
0.179
4.676
3.574
2.610
1.893
1.363
1.146
0.943
0.819
0.721
0.656
0.603
0.556
0.478
0.416
0.365
0.324
0.291
0.263
0.241
0.222
5.121
3.955
2.933
2.174
1.608
1.371
1.142
0.996
0.876
0.795
0.729
0.672
0.576
0.499
0.438
0.387
0.347
0.313
0.286
0.263
5.609
4.370
3.281
2.472
1.865
1.606
1.349
1.180
1.037
0.940
0.861
0.792
0.678
0.587
0.513
0.454
0.405
0.365
0.333
0.306
6.064
4.760
3.616
2.764
2.121
1.844
1.562
1.369
1.202
1.088
0.995
0.914
0.781
0.674
0.589
0.520
0.464
0.418
0.380
0.348
6.531
5.163
3.960
3.065
2.384
2.087
1.778
1.561
1.370
1.240
1.132
1.039
0.886
0.764
0.666
0.587
0.523
0.470
0.427
0.391
19
NUREG/CR-5625
Procedure
Table 5.2. BWR spent fuel heat generation rates, watts per
kilogram U, for specific power = 20 kW/kgU
Cooling
time,
years
1.0
1.4
2.0
2.8
4.0
5.0
7.0
10.0
15.0
20.0
25.0
30.0
40.0
50.0
60.0
70.0
80.0
90.0
100.0
110.0
NUREG/CR-5625
Fuel burnup, MWd/kgU
20
25
30
35
40
45
5.548
4.097
2.853
1.929
1.262
1.001
0.776
0.658
0.576
0.523
0.480
0.444
0.382
0.332
0.292
0.259
0.233
0.211
0.193
0.178
6.266
4.687
3.316
2.296
1.549
1.251
0.985
0.838
0.731
0.663
0.608
0.560
0.481
0.417
0.365
0.324
0.290
0.262
0.239
0.220
6.841
5.173
3.718
2.631
1.827
1.501
1.199
1.023
0.890
0.805
0.737
0.678
0.579
0.501
0.438
0.386
0.345
0.311
0.283
0.260
7.455
5.690
4.142
2.982
2.117
1.760
1.420
1.215
1.056
0.954
0.871
0.800
0.682
0.588
0.513
0.452
0.403
0.362
0.329
0.302
8.000
6.159
4.540
3.324
2.410
2.024
1.650
1.413
1.227
1.107
1.009
0.925
0.786
0.677
0.589
0.518
0.460
0.413
0.375
0.343
8.571
6.647
4.950
3.673
2.705
2.292
1.882
1.616
1.403
1.263
1.150
1.053
0.893
0.767
0.666
0.585
0.519
0.465
0.421
0.385
20
Procedure
Table 5.3. BWR spent fuel heat generation rates, watts per
kilogram U, for specific power = 30 kW/kgU
Cooling
time,
years
1.0
1.4
2.0
2.8
4.0
5.0
7.0
10.0
15.0
20.0
25.0
30.0
40.0
50.0
60.0
70.0
80.0
90.0
100.0
110.0
Fuel burnup, MWd/kgU
20
25
30
35
6.809
4.939
3.368
2.211
1.381
1.063
0.797
0.666
0.579
0.525
0.482
0.445
0.382
0.332
0.292
0.259
0.232
0.210
0.192
0.177
7.786
5.721
3.958
2.651
1.705
1.335
1.015
0.850
0.737
0.667
0.611
0.563
0.482
0.418
0.366
0.323
0.289
0.261
0.238
0.219
8.551
6.357
4.463
3.050
2.016
1.605
1.239
1.039
0.898
0.811
0.741
0.681
0.581
0.502
0.438
0.386
0.344
0.310
0.282
0.259
9.337
7.006
4.979
3.460
2.339
1.885
1.471
1.237
1.067
0.962
0.877
0.805
0.685
0.589
0.513
0.451
0.401
0.361
0.327
0.300
40
10.010
7.579
5.453
3.855
2.663
2.172
1.713
1.443
1.242
1.117
1.017
0.931
0.790
0.678
0.589
0.517
0.459
0.411
0.372
0.340
45
10.706
8.169
5.938
4.256
2.991
2.462
1.958
1.653
1.422
1.276
1.160
1.061
0.898
0.769
0.666
0.584
0.517
0.463
0.418
0.382
Table 5.4 BWR enrichments for burnups in tables
Average initial
enrichment,
wt % U-235
Fuel burnup,
MWd/kgU
20
25
30
35
40
45
1.9
2.3
2.7
3.1
3.4
3.8
21
NUREG/CR-5625
Procedure
Table 5.5. PWR spent fuel heat generation rates, watts per
kilogram U, for specific power = 18 kW/kgU
Cooling
time,
years
1.0
1.4
2.0
2.8
4.0
5.0
7.0
10.0
15.0
20.0
25.0
30.0
40.0
50.0
60.0
70.0
80.0
90.0
100.0
110.0
NUREG/CR-5625
Fuel burnup, MWd/kgU
25
30
35
40
45
50
5.946
4.485
3.208
2.253
1.551
1.268
1.008
0.858
0.744
0.672
0.615
0.566
0.487
0.423
0.372
0.330
0.296
0.268
0.245
0.226
6.574
5.009
3.632
2.601
1.835
1.520
1.223
1.044
0.905
0.816
0.746
0.686
0.588
0.510
0.447
0.396
0.355
0.321
0.293
0.270
7.086
5.448
4.004
2.921
2.108
1.769
1.439
1.232
1.068
0.963
0.879
0.808
0.690
0.597
0.522
0.462
0.413
0.372
0.339
0.312
7.662
5.938
4.411
3.263
2.398
2.030
1.666
1.430
1.239
1.116
1.018
0.934
0.797
0.688
0.601
0.530
0.473
0.426
0.387
0.356
8.176
6.382
4.793
3.595
2.685
2.294
1.897
1.633
1.414
1.272
1.159
1.063
0.904
0.780
0.680
0.599
0.534
0.480
0.436
0.399
8.773
6.894
5.223
3.962
2.997
2.576
2.143
1.847
1.599
1.437
1.308
1.197
1.017
0.875
0.762
0.670
0.596
0.536
0.486
0.445
22
Procedure
Table 5.6. PWR spent fuel heat generation rates, watts per
kilogram U, for specific power = 28 kW/kgU
Cooling
time,
years
1.0
1.4
2.0
2.8
4.0
5.0
7.0
10.0
15.0
20.0
25.0
30.0
40.0
50.0
60.0
70.0
80.0
90.0
100.0
110.0
Fuel burnup, MWd/kgU
25
30
35
40
7.559
5.593
3.900
2.641
1.724
1.363
1.045
0.873
0.752
0.677
0.619
0.569
0.488
0.424
0.372
0.330
0.295
0.267
0.244
0.225
8.390
6.273
4.432
3.054
2.043
1.637
1.271
1.064
0.915
0.823
0.751
0.690
0.590
0.511
0.447
0.396
0.354
0.319
0.291
0.268
9.055
6.836
4.894
3.435
2.352
1.911
1.500
1.261
1.083
0.973
0.886
0.813
0.693
0.599
0.523
0.461
0.411
0.371
0.337
0.310
9.776
7.441
5.385
3.835
2.675
2.195
1.740
1.465
1.257
1.128
1.027
0.941
0.800
0.689
0.601
0.529
0.471
0.424
0.385
0.352
23
45
10.400
7.978
5.838
4.220
2.999
2.486
1.987
1.677
1.438
1.289
1.171
1.072
0.909
0.782
0.680
0.598
0.531
0.477
0.432
0.396
50
11.120
8.593
6.346
4.642
3.346
2.793
2.248
1.900
1.627
1.457
1.322
1.208
1.023
0.877
0.762
0.668
0.593
0.531
0.481
0.440
NUREG/CR-5625
Procedure
Table 5.7. PWR spent fuel heat generation rates, watts per
kilogram U, for specific power = 40 kW/kgU
Cooling
time,
years
Fuel burnup, MWd/kgU
25
1.0
1.4
2.0
2.8
4.0
5.0
7.0
10.0
15.0
20.0
25.0
30.0
40.0
50.0
60.0
70.0
80.0
90.0
100.0
110.0
8.946
6.514
4.462
2.947
1.853
1.429
1.067
0.881
0.754
0.678
0.619
0.570
0.488
0.423
0.371
0.329
0.294
0.266
0.243
0.224
30
10.050
7.400
5.129
3.441
2.212
1.728
1.304
1.078
0.921
0.827
0.754
0.693
0.592
0.512
0.448
0.396
0.353
0.319
0.290
0.267
35
10.900
8.111
5.692
3.884
2.554
2.021
1.543
1.278
1.091
0.978
0.890
0.816
0.695
0.599
0.522
0.461
0.410
0.369
0.336
0.308
40
11.820
8.863
6.284
4.346
2.910
2.327
1.793
1.488
1.268
1.136
1.032
0.945
0.803
0.691
0.601
0.529
0.470
0.422
0.383
0.351
Table 5.8 PWR enrichments for burnups in tables
Average initial
enrichment,
wt % U-235
Fuel burnup,
MWd/kgU
25
30
35
40
45
50
NUREG/CR-5625
2.4
2.8
3.2
3.6
3.9
4.2
24
45
12.580
9.514
6.821
4.787
3.265
2.639
2.052
1.705
1.452
1.298
1.178
1.077
0.912
0.783
0.680
0.597
0.530
0.475
0.430
0.393
50
13.466
10.254
7.418
5.267
3.647
2.970
2.325
1.936
1.645
1.469
1.331
1.215
1.026
0.879
0.762
0.668
0.592
0.530
0.479
0.437
Procedure
5.2.2 The Short Cooling Time Factors f7
and fN7
Compute ptab , the heat generation rate, at Pave , Btot , and Tc
, by proper interpolation between the tabulated values of
heat rates at the parameter limits of Eqs. (5) through (7).
A linear interpolation should be used between heat rates
for either burnup or specific power interpolations. In
computing the heat rate at Tc , the interpolation should be
logarithmic in heat rate and linear in cooling time.
Specifically, the interpolation formulae for interpolating in
specific power, burnup, and cooling time, respectively, are
p ' pL %
p ' pL %
pH & pL
PH & PL
pH & p L
BH & B L
p ' pL exp
(Pave & PL ) ,
(5)
(Btot & BL ) ,
(6)
ln ( pH /pL )
T H & TL
The heat rates presented in Tables 5.1–5.3 and Tables
5.5–5.7 were computed from operating histories in which
a constant specific power and an uptime of 80% of the
cycle time were applied. Expected variations from these
assumptions cause only minor changes (<1%) in decay
heat rates beyond approximately 7 years of cooling.
However, if the specific power near the end of the
operating history is significantly different than the average
specific power, Pave , then ptab needs to be adjusted if Tc #
7. The ratios Pe /Pave and Pe-1 /Pave,e-1 are used, respectively,
to determine the adjustment factors f7 and fN7 . The factors
reduce the heat rate ptab if the corresponding ratio is less
than 1 and increase the heat rate ptab if the corresponding
ratio is greater than 1. The formulae for the factors are
defined below.
f7 ' 1
(Tc & TL ) ,
when Tc > 7 years or e '
(i.e., 1 cycle only)
f7 ' 1 % 0.35R/ Tc when 0 # R # 0.3 ,
f7 ' 1 % 0.25R/Tc when &0.3 # R < 0 ,
f7 ' 1 & 0.075/Tc when R < &0.3 ,
(7)
where pL and pH represent the tabulated or interpolated
heat rates at the appropriate parameter limits
corresponding to the L and H index. If applied in the
sequence given above, Eq. (5) would need to be used four
times to obtain p values that correspond to BL and BH at
values of TL and TH . A mini-table of four p values at Pave
is now available to interpolate on burnup and cooling
time. Equation (6) would then be applied to obtain two
values of p at TL and TH . One final interpolation of these
two p values (at Pave and Btot ) using Eq. (7) is needed to
calculate the final ptab value corresponding to Pave , Btot ,
and Tc . The optional Lagrangian interpolation scheme
offered by the LWRARC code is also considered an
acceptable method for interpolating the decay heat data,
but is not discussed in this section.
(8)
where
R '
Pe
& 1.
(9)
when Tc > 7 years or
e < 3,
N
f7 ' 1 % 0.10 RN/ Tc when 0 # RN # 0.6,
(10)
Pave
N
f7 ' 1
N
f7
N
f7
If Pave or Btot falls below the minimum table value range,
the minimum table specific power or burnup, respectively,
may be used conservatively. If Pave exceeds the maximum
table value, the table with the maximum specific power
(Table 5.3 for BWR fuel and Table 5.7 for PWR fuel) may
be used in addition to the adjustment factor, fp , described
in Sect. 5.3.2. The tables should not be applied if Btot
exceeds the maximum burnup in the tables, or if Tc is less
than the minimum (1 year) or exceeds the maximum (110
years) cooling time of the tables.
' 1 % 0.08 RN/Tc when &0.5 # RN < 0
' 1 & 0.04/Tc
when RN < &0.5 ,
where
RN '
25
Pe&1
Pave,e & 1
& 1.
(11)
NUREG/CR-5625
Procedure
It is recommended not to use the decay heat values of this
report if any of the following conditions occur:
if Tc # 10 years and Pe /Pave > 1.3,
if 10 years < Tc # 15 years and Pe /Pave > 1.7,
if Tc # 10 years and Pe-1 /Pave,e-1 > 1.6.
where the parameters a, b, and d vary with reactor type,
Es, Etab , and Tc . These variables are defined in Tables 5.9
and 5.10.
5.2.5 Safety Factor S
(12)
Before obtaining the final heat rate pfinal , an appropriate
estimate of a percentage safety factor S must be
determined. Evaluations of uncertainties performed as
part of this project indicate the safety factor should vary
with burnup and cooling time.
Although it is safe to use the procedures herein, the heat
rate values for pfinal may be excessively high when
Tc # 7 years and Pe /Pave < 0.6,
Tc # 7 years and Pe-1 /Pave,e-1 < 0.4.
(13)
For BWR assemblies:
5.2.3 The Excess Power Adjustment Factor fp
S = 6.4 + 0.15 (Btot – 20) + 0.044 (Tc – 1) .
The maximum specific power, Pmax , used to generate the
data in Tables 5.1–5.3 and Tables 5.5–5.7 is 40 kW/kgU
for a PWR and 30 kW/kgU for a BWR. If Pave , the
average cumulative specific power, is more than 35%
higher than Pmax (i.e., 54 kW/kgU for PWR fuel and 40.5
kW/kgU for BWR fuel), then the guide should not be used.
When 1 < Pave /Pmax < 1.35, the guide can still be used, but
an excess power adjustment factor, fp , must be applied.
The excess power adjustment factor is
fp =
Pave /Pmax .
For PWR assemblies:
S = 6.2 + 0.06 (Btot – 25) + 0.050 (Tc – 1) .
(14)
5.2.6 Final Heat Generation Rate Evaluation
5.2.4 The Enrichment Factor fe
The equation for converting ptab , determined in Sect.
5.2.1, to the final heat generation rate of the assembly, is
The decay heat rates of Tables 5.1–5.3 and Tables 5.5–5.7
were calculated using initial enrichments of Tables 5.4
and 5.8. The enrichment factor fe is used to adjust the
value ptab for the actual initial enrichment of the assembly
Es . To calculate fe , the data in Tables 5.4 (BWR) or 5.8
(PWR) should be interpolated linearly to obtain the
enrichment value Etab that corresponds to the assembly
burnup, Btot . If Es /Etab < 0.6, it is recommended not to use
the guide. Otherwise, set the enrichment factor as follows:
pfinal = (1 + 0.01S) f7 fN7 fp fe ptab ,
(18)
where f7 , fN7 , fp , fe , and S are determined by the
procedures given in Sects. 5.2.2 through 5.2.5.
5.3 Acceptability and Limits of the
Guide
fe = 1 + 0.01[a + b(Tc - d)][1 - Es /Etab ]
Inherent difficulties arise in attempting to prepare a heat
rate guide that has appropriate safety factors, is not
excessively conservative, is easy to use, and applies to all
commercial reactor spent fuel assemblies. In the endeavor
to increase the value of the guide an effort was made to
ensure that safe but not overly conservative heat rates were
computed. The procedures and data recommended in the
guide should be appropriate for the mainstream of power
reactor operations with only minor limitations in the range
of applicability.
when Es /Etab # 1.5
fe = 1 – 0.005 [a + b(Tc - d)]
NUREG/CR-5625
(17)
The purpose of deriving spent fuel heat generation rates is
usually to apply the heat rates in the computation of the
temperatures for storage systems. A preferred engineering
practice may be to calculate the temperatures prior to
application of a final safety factor. This practice is
acceptable if S is accounted for in the more comprehensive
safety factors applied to the calculated temperatures.
For Pave # Pmax , fp = 1.
when Es /Etab > 1.5
(16)
(15)
26
Procedure
Table 5.9 Enrichment factor parameter values for BWR assemblies
Parameter value
Es /Etab < 1
Es /Etab > 1
Parameter in
Eq. (15)
1 # Tc # 40
Tc > 40
1 # Tc # 15
Tc > 15
a
b
d
5.7
–0.525
40
5.7
0.184
40
0.6
–0.72
15
0.6
0.06
15
Table 5.10 Enrichment factor parameter values for PWR assemblies
Parameter value
Parameter in
Eq. (15)
a
b
d
Es /Etab < 1
1 # Tc # 40
Es /Etab > 1
Tc > 40
1 # Tc # 20
Tc > 20
4.8
0.133
40
1.8
–0.51
20
1.8
0.033
20
4.8
–0.6
40
In general, the guide should not be applied outside the
ranges of the parameters of Tables 5.1 through 5.8. These
restrictions, in addition to certain limits on adjustment
factors, are given in the text. The major table limits are
summarized in Table 5.11.
correct for variations in power history from that used in
the generation of the tables. For example, the heat rate at
1 year is increased substantially if the power in the last
cycle is twice the average power of the assembly. The
limits in Eqs. (12) and (13) on ratios of cycle to average
specific power are required, first, to derive cooling time
adjustment factors that are valid and, second, to exclude
cases that are extremely atypical. Although these limits
were determined so that the factors are safe, a reasonable
degree of discretion should be used in the considerations
of atypical assemblies— particularly with regard to their
power histories.
In using the guide, the range in cooling time, Tc , and the
upper limit on burnup, Btot should never be extended. An
adjustment factor, fp , can be applied if the specific power,
Pave , does not exceed the maximum value of the tables by
more than 35%. Thus, if Pave is greater than 54 kW/kgU
for PWR fuel or 40.5 kW/kgU for a BWR fuel, then the
guide should not be applied. The minimum table value of
specific power or burnup can be used for values below the
table range; however, if the real value is considerably less
than the table minimum, the heat rate derived can be
excessively conservative.
Another variable that requires attention is the 59Co content
of the clad and structural materials. Cobalt-59 is partly
transformed to 60Co in the reactor and subsequently
contributes to the decay heat rate. The 59Co content used
in deriving the tables here should apply only to assemblies
containing Zircaloy-clad fuel pins. The 60Co contribution
can become excessive for 59Co contents found in stainlesssteel clad. Thus, the use of the guide for stainless-steelclad assemblies should be limited only to cooling times
that exceed 20 years. Because 60Co has a 5.27-y half-life,
the heat rate contribution from 60Co is reduced by the
factor of 13.9 in 20 years.
In preparing generic depletion/decay analyses for use in
specific applications, the most difficult condition to model
is the power operating history of the assembly. Although
a power history variation (other than the most extreme)
does not significantly change the decay heat rate after a
cooling time of approximately 7 years, it can have
significant influence on the results in the first few years.
Cooling time adjustment factors, f7 and fN7 , are applied to
27
NUREG/CR-5625
Procedure
Table 5.11 Parameter ranges for applicability
of the proposed regulatory guide
Parameter
Tc(y)
Btot (MWd/kgU)
Pave (kW/kgU)
BWR
1–110
20–45
12–30
In addition to parameters used here, decay heat rates are a
function of other variables to a lesser degree. Variations
in moderator density (coolant pressure, temperature) can
change decay heat rates, although calculations indicated
that the expected differences (approximately 0.2% heat
rate change per 1% change in water density, during first
30-year decay) are not sufficient to require additional
corrections. The PWR decay heat rates in the tables were
calculated for fuel assemblies containing water holes.
Computed decay heat rates for assemblies containing
burnable poison rods (BPRs) did not change significantly
(<1% during first 30-year decay) from fuel assemblies
containing water holes.
1–110
25–50
18–40
Whenever there is a unique difference in either the design
or operating conditions of a spent-fuel assembly that is
more extreme than that accepted here, another wellqualified method of analysis that accounts for the
difference should be used.
5.4 Glossary of Terms and Units Used
in Guide
Be
Be-1
Bi
Btot
Es
P
Several conditions were considered in deriving the safety
factors [Eqs. (16) and (17)] that were developed for use in
the guide. Partial uncertainties in the heat generation
rates were computed for selected cases (see Sect. 6.6.1)
applying the known standard deviations of half-lives,
Q-values, and fission yields of all the fission product
nuclides that have a significant contribution to decay heat
rates. This calculation did not account for uncertainties in
contributions produced by the neutron absorption in
nuclides in the reactor flux (see Sect. 6.6.2), or from
variations in other parameters (see Sect. 6.6.3). In
addition to the standard deviations in neutron cross
sections, much of the uncertainty from neutron absorption
was found to derive upon approximations in the model
used in the depletion analysis. In developing the safety
factors, these more indirect uncertainties were determined
from comparisons of the calculated total or individual
nuclide decay heat rates with those determined by
independent computational methods, as well as heat rate
measurements obtained for a variety of reactor spent fuel
assemblies. Note from the equations that the safety factors
increase with both burnup and cooling time. This increase
in the safety factor is a result of the increased importance
of the actinides to the decay heat with increased burnup
and cooling time, together with the larger uncertainty in
actinide predicitons caused by model approximations and
limited experimental data.
NUREG/CR-5625
PWR
Pave
Pave,e-1
Pe
Pe-1
S
Tc
Te
Te-1
Ti
Tres
f7
fN7
fe
fp
p
28
- burnup in last cycle, MWd/kgU
- burnup in next-to-last cycle, MWd/kgU
- fuel burnup increase for cycle i, MWd/kgU
- total burnup of discharged fuel, MWd/kgU
- initial fuel enrichment, wt % 235U
- specific power of fuel as in Eqs. (2) and (3),
kW/kgU
- average cumulative specific power during 80%
uptime, kW/kgU
- average cumulative specific power (at 80%)
through cycle e-1, the next-to-last cycle
- fuel specific power during the last cycle e
- fuel specific power during cycle e-1, the nextto-last cycle
- percentage safety factor applied to decay heat
rates, ptab
- cooling time of an assembly, years
- cycle time of last cycle before discharge, days
- cycle time of next-to-last cycle, days
- cycle time of ith reactor operating cycle
including downtime for all but last cycle of
assembly history, days
- reactor residence time of assembly, from first
loading to discharge, days
- last-cycle short cooling time modification
factor
- next-to-last cycle short cooling time factor
- 235U initial enrichment modification factor
- excess power adjustment factor
- heat generation rate of spent fuel assembly,
W/kgU
6 DISCUSSION OF THE PROPOSED PROCEDURE
The purpose of this section is to describe and discuss the
work performed to develop the procedures and formulae
presented in Sect. 5. Section 6.1 discusses the
investigation to determine the sensitivity of the decay heat
rate to variations in the reactor operating history. Section
6.2 discusses and demonstrates the accuracy of the
techniques recommended for interpolation of the data in
Tables 5.1–5.3 and Tables 5.5–5.7. The remaining
sections provide the basis for the adjustment factor and
safety factor formulae.
determining the heat rate from the tabulated data, can be
properly defined from only the total burnup and cycle
times. The three-cycle PWR operating histories shown in
Figure 6.1 were developed to investigate operating history
changes under the conditions that the total burnup, the
cycle times, and the average power are unchanged.
All the cases illustrated in Figure 6.1 have the same total
burnup of 30 MWd/kgU and cycle times of 400, 400, and
320 days. Thus, the average specific power of 31.25
kW/kgU [computed from Eq. (3) of Sect. 5.1.4] is the
same for all of the cases. The "standard case" of Figure
6.1(A) has the general operating history described above
and was used for all the three-cycle cases used in
producing Tables 5.1–5.3 and 5.5–5.7.
6.1 Variations in Operating History
The decay heat rates presented in Tables 5.1–5.3 and
Tables 5.5–5.7 were calculated by applying different total
burnups and average specific powers to a "standard"
operating history profile. The distribution of uptime and
downtime in the operating history of an actual assembly
could be considerably different from that used in the
calculations. The purpose of this section is to present the
work performed to determine which types of variations
have significant effects upon the decay heat rates of
reactor spent fuel.
If the total burnup, cycle times, and average power are
unchanged, the only possible changes in the operating
history of Figure 6.1(A) pertain to the uptime and
downtime during a cycle, the distribution of power within
a cycle (accounting for within-cycle changes) and the
burnup distribution to the various cycles (between cycle
changes).
The change in downtime during a cycle is illustrated in
Figure 6.1(B) and (C). In order to keep the cycle burnups
the same as the standard case [Figure 6.1(A)] and in order
to reduce the uptime by the factor 7/8, a power equal to
8 P /7 is required in the case shown in Figure 6.1(B).
Similarly, in Figure 6.1(C), the illustrated uptime change
by the factor 9/8 requires a power of 8 P /9. Table 6.1
gives a list of the decay heat rates for several cooling times
as calculated by ORIGEN-S using the basic LWR
ORIGEN-S library. The table also lists the percentage
differences in decay heat rates as compared with results for
the standard case. As a general criterion, consider here
that a 1% difference can adequately be covered in a safety
factor. The conclusion from studying the results from
operating histories A through C is that differences in the
cycle downtime (which is a very common difference)
produce only small conservative changes in decay heat
rate results.
As noted in Sect. 4, the standard power history profile
used to generate the tabulated heat rate data had either
three, four, or five power cycles. Commonly, cycle time
refers only to the time between cycle startup of a loaded or
a partially reloaded core and shutdown for another partial
core reloading. In order to simplify operating histories,
the definition in the procedure of Sect. 5 would extend the
cycle time, except for the last cycle of an assembly, to
include the downtime for reloading.
The first cycle of the standard profile had a downtime (i.e.,
nonpower operation time) of 20% at the middle of the
cycle. The second cycle (and optionally third and fourth
cycles) had a 10% downtime both near the midpoint and at
the end of the cycle, thus producing an 80% uptime (i.e.,
power operation time). The last cycle had an uptime of
100%. The power was held constant during all the time
the reactor was in operation and the burnups in each cycle
were equal.
Note again the objective of this analysis was to determine
if normal differences in the actual operating experiences of
fuel assemblies from that assumed in the standard case
have significant effects upon their decay heat rates. In
essence, comparisons in the results of these differences are
needed to support the premise, mathematically stated in
Eq. (3) of Sect. 5.1.4, that the specific power to be used in
29
NUREG/CR-5625
Discussion
NUREG/CR-5625
30
Table 6.1 Comparison of heat rates from operating history variations
% differencea of (A) and (X)
Cooling time, years
Decay heat rates (W/kgU)
Cooling time, years
Case
(A) Std case 8.888
(B) 30% downtime
(C) 10% downtime
(D) ) P > Pe
(E) ) P > Pe-1
(F) Pe = 1.2 P
(G) Pe-1 = 1.2 P
31
a
1
4.644
8.824
8.879
8.995
8.912
9.567
9.040
2
2.095
4.601
4.635
4.674
4.656
4.917
4.716
4
1.069
2.079
2.087
2.102
2.098
2.159
2.111
10
0.6909
1.064
1.063
1.069
1.069
1.071
1.069
30
0.2675
0.6882
0.6872
0.6911
0.6908
0.6915
0.6909
110
0.2666
0.2661
0.2676
0.2675
0.2686
0.2680
1
2
4
10
30
–0.7
–0.1
1.2
0.3
7.6
1.8
–0.9
–0.2
0.6
0.3
5.9
1.6
–0.8
–0.4
0.3
0.2
3.1
0.8
–0.5
–0.6
0.0
0.0
0.2
0.0
–0.4
–0.5
0.1
<0.1
0.1
0.0
110
–0.3
–0.5
0.1
0.0
0.4
0.2
The percentage differences of case (A) heat rate, HA, from case (X) heat rate, HX: 100% (HX B HA)/HX.
Discussion
NUREG/CR-5625
Discussion
The changes in power distribution within a cycle were
investigated using the operating histories shown in Fig.
6.1(D) and (E) where the last and middle cycles,
respectively, differ from the standard case in Figure
6.1(A). The power during the last 20% of the cycle
uptime is 1.25 times that of the first 80%. The average
cycle power is unchanged from that of Figure 6.1(A).
Table 6.1 shows the percentage differences in heat rate
(from the standard case) for these two cases to be less than
1% in magnitude for all comparisons except the 1-year
cooling time for case D. The heat rate difference for case
D at 1-year cooling is 1.2% greater than the corresponding
heat rates from case A. Using a 1% difference as a safe
criterion, it would appear that the procedure of Sect. 5
should not be used for cooling times less than 2 years if
there is a 25% increase in the power in the last one-fifth of
the last cycle operation. Typically, however, the specific
power decreases (or at most remains constant) during the
end interval of a cycle. An example showing the
operating history of the first seven cycles of the Cooper
Nuclear Station BWR27 is presented in Figure 6.2. This
case with the large power increase is used for amplifying
the effects of small increases only and should actually be
considered to be an atypical case, outside the mainstream
of commercial power operations.
with half-lives that are long with respect to cycle times.
Thus, from the results of these comparisons, it was
concluded that a proper adjustment factor needs to be
applied to the tabulated data for short cooling times (e.g.,
the first 7 years) to adjust for increased specific power in
the last two cycles. This short cooling time adjustment
factor was presented in Sect. 5.2.2 and will be discussed
further in Sect. 6.3.
In summarizing the comparisons of Table 6.1, it is clear
that differences in the distribution among cycles of the
burnup between operating histories has a significantly
greater effect on heat rate than the other two types of
changes which were studied. The basic difference in the
operating history changes illustrated in Figure 6.1 is that
burnup is redistributed (from the burnup of the standard
case) within a cycle in Figures 6.1(B)–(E), whereas a
larger magnitude of burnup is moved to an entirely
different cycle in Figures 6.1(F)– (G). The quantity or the
percentage difference in the decay heat rate is increased as
the amount of burnup moved to a later time is increased
and as the shift in time becomes greater. Thus, it is
concluded that the effects from within-cycle changes
[Figures 6.1(B)–(E)] produce differences from the
standard case that are satisfactory (i.e., <1% different),
while a proper short cooling-time factor is required for
conditions where the cycle burnups [Figures 6.1(F)–(G)]
vary from the standard case. It is further concluded that
Eqs. (1) through (4) are appropriate definitions to allow
accurate use of the decay heat rates in Tables 5.1–5.3 and
5.5–5.7.
It is a fairly common occurrence for operating histories
that produce the same total burnup to have differences in
the average power or burnup of a cycle. Examples of a
last-cycle power increase and decrease from the average
power are given in Figures 6.3 and 6.4, respectively, for
two Cooper Nuclear Station spent fuel assemblies.15
Changes in the average power or burnup of a cycle were
studied using the operating histories shown in Figure
6.1(F) and (G). In Figure 6.1(F) the first-cycle power and
burnup are decreased by 20% and the last-cycle power and
burnup are increased by 20% from the similar cycle data
of the standard case. In the final case, Figure 6.1(G), the
increased values are in the next-to-last cycle instead of the
last cycle. The first five cases (A–E) of Figure 6.1 have
equal burnups within each cycle, whereas the final two
cases have cycle burnups that are not equal. For cases
A–E, burnup was redistributed from the standard case
within the same cycle only. As might be expected, the
more significant redistribution of burnup from one cycle to
another causes greater differences in the decay heat rates
than observed for cases A–D. The magnitudes of the
largest differences from the standard case for cases F and
G, listed in Table 6.1, are 7.6% and 1.8%, respectively.
These magnitudes are significantly nonconservative.
However, the differences are considerably reduced after
10-year cooling time. This smaller reduction at longer
decay times is caused by the predominance of isotopes
NUREG/CR-5625
6.2
Interpolation Accuracy
The effective tabulated heat generation rate, ptab , is
derived by interpolation of tabulated heat rates for the
given parameters Pave, Btot , and Tc . A linear interpolation
is used between heat rates for either burnup or power. The
decay time interpolation is logarithmic in heat rate and
linear in cooling time. Estimated magnitudes of the
interpolation error are presented in this section.
The initial effort of this study was to determine if the
tabulated decay heat rates were computed for intervals
of burnup, power, and cooling time that are sufficiently
fine to produce an acceptable accuracy with areasonable
interpolation scheme. Two different methods could be
used to estimate the interpolation errors. One method
requires execution of a number of SAS2H/ORIGEN-S
cases at numerous intermediate parameter values to
produce results for comparisons. However, the number of
SAS2H/ORIGEN-S cases needed would be too numerous
32
Discussion
Figure 6.2 Cooper Nuclear Station operating history (from Ref. 27)
33
NUREG/CR-5625
Discussion
NUREG/CR-5625
34
Discussion
to sufficiently cover the parameter ranges. The other
method uses a polynomial fit to the tabulated heat rates
as a function of one of the variables with the other two
parameters held constant. The polynomial fit is applied
to derive intermediate results for comparison. This latter
method was chosen because it was both easy to
implement and appeared adequate to assess the accuracy
of the simpler interpolation schemes proposed in Sect. 5.
It was necessary to limit the equation to a quadratic fit for
the specific powers since only three different powers were
used. A quadratic fit was also considered adequate for
the burnups because the tabulated heat rates as a function
of the burnup exhibited significantly less variation than
heat rates as a function of power. The errors vary from a
zero error when exactly at a parameter value to the
maximum error near the midpoint between two values.
Interpolated values using Eqs. (5) through (7) were
compared with those computed from the quadratic
equation at ten equal intervals between adjacent values in
Tables 5.1–5.3 and Tables 5.5–5.7. The plot of the
logarithm of decay heat rates as a function of cooling
time is a curve that is concave upward. Thus, the
interpolated value between two cooling times would be
greater than the corresponding value on the log curve.
The equations and limits of the short cooling-time
factors, f7 and fN7 , are specified in Eqs. (8) through (13)
of Sect. 5.2.2. The factors are dependent on the variables
Tc , R, and RN. The parameters R and RN, respectively, are
the fractional changes in the last and next-to-last cycle
specific power from the average specific power of the
fuel.
The nonconservative percentage differences between the
interpolated and the more correctly estimated values of
decay heat rates are shown in Table 6.2. It can be seen
that after approximately 10 years, the error (#0.3%) is
small. The maximum percentage difference of 1.1% at
1 year is considered to be acceptable.
Table 6.3 contains an evaluation of the ability of the short
cooling-time factors to adjust the tabulated data properly
for cases having large fractions of redistributed burnup.
There are 22 cases, A through V, listed in the table.
There is one reference case for each set of cases having
similar residence time (number of cycles times cycle
length), total burnup, and average specific power. Each
reference case has a constant specific power, similar
(except for downtime) to the cases that were used to
produce the tabulated data. The other cases listed are
compared with its defined reference case. The power
history diagram shows for each cycle the ratio of power
to the average assembly power. From the diagram
information and Eqs. (9) and (11) of Sect. 5.2.2, the
values listed under R and RN were calculated. Then, R
and RN were used in Eqs. (8) and (10) to compute f7 and
fN7 , respectively. The heat rates of the reference case,
corrected by factors f7 and fN7 , were compared with heat
rates from the case computed by ORIGEN-S for the
operating history shown. Comparisons of the percentage
difference between the adjusted (reference case) heat rate
and the computed heat rate value (of case X) are shown
at four cooling times in Table 6.3. Additional
comparisons of uncorrected heat rates are listed as
percentage differences at 8 and 10 years.
6.3
The short cooling-time factors were derived and tested in
22 cases using widely different conditions. The cases
were computed for no downtime because only the effect
of moving burnup between cycles was analyzed. Also, it
was expected that there would be insignificant differences
between PWRs and BWRs in regard to operating history
effects. The reason for this expectation is that at shorter
cooling times there is significantly less decay heat rate
from the neutron absorption-dependent actinides (which
vary considerably with reactor type) than from the fission
products (which are essentially dependent only upon
fission yields).4,18 Also, the results from similar sets of
cases using both a BWR and a PWR library indicated
that the type of reactor library was not significant to these
short cooling-time analyses. Thus, the PWR library was
used in all of the other cases of this sensitivity study.
Discussion of the Short CoolingTime Factors
The standard cases producing the tabulated heat rates
(i.e., Tables 5.1–5.3 and Tables 5.5–5.7) for the proposed
guide use operating histories with constant specific power
during the entire operational uptime as shown in Figure
6.1 (A). Differences in heat rates caused by operating
history variations of the types discussed in Sect. 6.1 and
listed in Table 6.1 appear to be satisfactory at 10 years
and longer cooling times. However, unacceptably large
(>1%) differences in the results were produced over a
shorter cooling-time range for cases in which large
quantities of burnup and power were moved from one
cycle to another, as in Figure 6.1 (F) and (G). It was
noted in Sect. 6.1 that short cooling-time adjustment
factors would be required to account for these larger
redistributions in burnup.
35
NUREG/CR-5625
Discussion
Table 6.2 Evaluation of accuracy in table interpolations
Nonconservative % differencesa
Independent variables of the decay heat rate
Specific power
Burnup
Cooling time
Cooling
time, d
BWR
PWR
BWR
PWR
BWR or PWR
1
2
4
7
10
20
40
70
110
1.1
1.1
0.7
0.4
0.3
0.2
0.1
<0.1
<0.1
0.9
0.9
0.6
0.3
0.2
0.1
0.1
<0.1
<0.1
0.4
0.4
0.1
<0.1
<0.1
<0.1
<0.1
0.1
0.1
0.3
0.2
0.1
<0.1
<0.1
<0.1
<0.1
0.1
0.1
<0
<0
<0
<0
<0
<0
<0
<0
<0
a
(Correct/interpolated B 1)100%.
Cases for two, three, four, and five cycles are shown in
Table 6.3. Case A is a reference two-cycle case. Note that
for a two-cycle case, the factor fN7 = 1 [see Eq. (10) of Sect.
5.2.2], and so RN does not need to be used. The results
computed for case B, in which the last cycle power was 1.2
times the average, indicated the corrected reference case
heat rates to be conservative by 0.3 to 2.0%. The value of
R in case C is increased to 0.3, the limit specified in Eq.
(12) of Sect. 5.2.2 for cooling times less than 10 years.
The percentage differences of 0.4 to 3.1% for this case are
an increase from those in case B by a scale factor very
similar to the increase in R, as would be expected. Note
that throughout the cases listed in Table 6.3, numerous
changes are made in the number of cycles, cycle length,
total burnup, and average specific power. In some cases,
either R, RN, or both are made positive to demonstrate
increasing power. Also, cases having negative values of R
or RN test decreasing powers that cause the corresponding
f7 or fN7 to be less than unity. Cases E and F were
computed using a BWR library, whereas similar cases G
and H used a PWR library. The percentage differences
listed for cases F and H are sufficiently close to indicate
that the type of reactor library does not appear to be
significant. Note that R, in most of the cases, is set to
either positive or negative 0.2. The differences for these
cases can be scaled up to the magnitude for R of 0.3, the
limit. Extremes in increases or decreases of specific power
in both the last and next-to-last cycles, in addition to other
operating history parameter variations, appear to be
adequately covered in the 22 cases. Even an out-of-reactor
cycle case is shown in case Q, although it is more
NUREG/CR-5625
36
conservative than that obtained by dividing the first cycle
burnup between the first two cycles.
In summary, the results shown in Table 6.3 demonstrate
that the short cooling-time factors f7 and fN7 ensure
conservative decay heat values are obtained by the new
procedure. The cases used to develop Table 6.3 span a
burnup range of 25 to 49.5 MWd/kgU, cycle times from
300 to 450 days, and average powers from 24 to 50
kW/kgU. Only three of the corrected values were
nonconservative (5% of the corrections) and the largest in
magnitude was –0.2%. The largest nonconservative
discrepancy beyond the 7-year cooling time when f7 and fN7
are applicable was –0.7% (at 8-year cooling). Although a
small nonconservative error (<0.5%) may be produced in
computing f7 and fN7 , it can be easily incorporated into the
safety factor. Table 6.3 shows that typically the factors f7
and fN7 yield conservative errors of 3 to 4% maximum and
1 to 2% on the average.
6.4
Discussion of the Excess Power
Adjustment Factor
The maximum specific powers of the decay heat rates
provided in Tables 5.1–5.3 and Tables 5.5–5.7 are
probably greater than the average power derived by Eq. (3)
for all current U.S. commercial reactors. Although it is
not expected that the average specific power will exceed
the maximum tabulated values of 30 kW/kgU for the BWR
and 40 kW/kgU for the PWR, it was determined that a
Discussion
37
NUREG/CR-5625
Discussion
NUREG/CR-5625
38
Discussion
39
NUREG/CR-5625
Discussion
simple adjustment factor fP could be applied to extend
the specific power range. This factor, computed by Eq.
(14) of Sect. 5.2.3, is simply the square root of the ratio
of the average power of the assembly to the maximum
used in computing the tabulated data. A user should
be aware that other characteristics of the assembly and
operating conditions may force the assembly to be
considered as atypical if the excess specific power
significantly exceeded the maximum values used to
generate the tables.
In addition to the 18 standard cases computed for each
reactor type, ten cases were calculated using different
enrichments. At the minimum and maximum burnups
and specific powers (i.e., for the parameters in Tables
5.1–5.8) of each type of reactor, SAS2H/ ORIGEN-S
cases were computed with all the data unchanged
except for an increase and a decrease by one-third in
the initial 235U enrichment from that of the standard
cases. Also, at a one-third decrease of the initial
enrichment, two cases were computed at a middlevalue burnup and the two highest specific powers for
each reactor. Then, for each of these altered
enrichment cases, the maximum percentage heat rate
change was used in deriving fe . The extreme variation
of the burnup and specific power in each set of cases
appeared to be sufficient to provide a conservative
envelope of the percentage heat rate changes needed to
produce a conservative formula for fe . The maximum
difference was not always in the same case, but it was
always in one of the cases having a maximum or
minimum burnup and power. Thus, the two middle
burnup cases at the lower enrichments were not
computed at the higher enrichments.
The formula for the excess power factor was validated
by performing select calculations using SAS2H/
ORIGEN-S. The maximum excess power allowed by
the procedure of Sect. 5 is 35% greater than the
maximum tabulated powers, or 40.5 kW/kgU for the
BWR and 54 kW/kgU for the PWR. SAS2H cases
were then calculated using these specific powers and
the lowest, the highest, and the second from the
highest burnups used in determining the tabulated
data. The decay heat rates derived using the
adjustment factor of Eq. (14), and those computed by
SAS2H are listed in Table 6.4. The comparisons show
that the adjusted heat rates are conservative in all of
the PWR cases and in all cases at cooling times greater
than 1 year for the BWR. The nonconservative
differences (<1.4%) in the range less than 2-year
cooling time for the BWR are judged to be small
enough to be appropriately accounted for in the final
safety factor.
6.5
Data showing the percentage heat rate changes for
cases using a one-third decrease in initial enrichment
are presented in Table 6.5. For both the BWR and
PWR, the average and maximum percentage changes
are given at cooling times from 1 to 110 years. The
percentage changes for (fe – 1) as derived from Eq.
(15) and Tables 5.9–5.10 are shown under the column
labeled "Equation." Table 6.5 shows that the decrease
in initial enrichment causes an increase in the decay
heat that is conservatively bounded by the initial
enrichment factor of Eq. (15) (one exception is the
0.1% difference at 4 years for the PWR). Similarly,
Table 6.6 shows that an increase in initial enrichment
decreases the decay heat and that Eq. (15) again
provides an adequately conservative estimate of the
decay heat change. In summary, Tables 6.5 and 6.6
provide sufficient evidence that the formula for fe
provides an adequately conservative method for
adjusting the tabulated decay heat rate for different
initial enrichment values.
Discussion of the Initial
Enrichment Factor
The average initial 235U enrichments considered as
typical for present and extended burnup reactor fuel are
listed in Tables 5.4 and 5.8. These 235U enrichments
are selected so that the reactor has sufficient reactivity
to maintain criticality throughout the operation that
produces the corresponding burnup specified in the
tables. Lower enrichments may be insufficient,
whereas higher enrichments may be less economical.
However, because commercial reactor data exhibit
significant variations from the burnup and enrichment
sets tabulated and used in computing the standard
cases, an enrichment adjustment factor is applied to
correct the decay heat rates. This enrichment factor fe
is given by Eq. (15) in Sect. 5.2.4. This section
describes the method used in determining the formula
for fe .
NUREG/CR-5625
6.6
Formulation of the Safety
Factor Equations
The safety factor, S, applied in the final equation for
heat generation rate is computed from either Eq. (16)
or Eq. (17). The development of the safety factor
formulae is presented in this section.
40
Table 6.4. Excess power adjustment of decay heat, in W/kgU, using Eq. (14)
compared with actual SAS2H calculations as percentage differencesa
Reactor
type
Burnup
MWd/kgU
Guide
procedures
1 year
SAS2H
% diff.
Guide
procedures
2 years
SAS2H
% diff.
Guide
procedures
20 years
SAS2H
% diff.
Guide
procedures
110 years
SAS2H
% diff.
BWR
BWR
BWR
PWR
PWR
PWR
20
35
45
25
40
50
7.911E+00
1.085E+01
1.244E+01
1.039E+01
1.373E+01
1.565E+01
7.716E+00
1.093E+01
1.260E+01
1.009E+01
1.361E+01
1.557E+01
2.5
-0.8
-1.3
3.1
0.9
0.5
3.913E+00
5.785E+00
6.899E+00
5.184E+00
7.301E+00
8.619E+00
3.706E+00
5.663E+00
6.786E+00
4.888E+00
7.030E+00
8.329E+00
5.6
2.2
1.7
6.1
3.9
3.5
6.100E-01
1.118E+00
1.483E+00
7.878E-01
1.320E+00
1.707E+00
5.218E-01
9.657E-01
1.284E+00
6.747E-01
1.133E+00
1.463E+00
16.9
15.7
15.5
16.8
16.5
16.7
2.057E-01
3.486E-01
4.438E-01
2.603E-01
4.078E-01
5.077E-01
1.755E-01
2.985E-01
3.798E-01
2.220E-01
3.476E-01
4.321E-01
17.2
16.8
16.9
17.2
17.3
17.5
a
(Guide procedure value/SAS2H calculated value B 1)100%.
41
Table 6.5 Evaluation of adjustments for decreased initial enrichments
% heat rate changea for a 1/3 decrease in enrichment
Cooling
time, days
a
BWR
Maximum
Equation
6.6
7.1
6.1
3.9
2.2
1.6
1.3
1.4
1.9
2.9
7.6
8.4
8.0
6.5
4.6
3.2
1.9
2.8
4.3
6.2
8.7
8.6
8.2
7.7
6.3
4.5
1.9
3.1
4.4
6.2
(Decreased case/standard B 1)100%.
Average
6.8
7.7
7.1
5.2
2.9
1.9
1.2
0.9
1.1
1.7
PWR
Maximum
Equation
7.7
8.7
8.9
7.4
5.1
3.4
1.6
2.2
3.1
4.7
9.4
9.2
8.8
8.2
6.6
4.6
1.6
2.5
3.4
4.7
Discussion
NUREG/CR-5625
1
2
4
7
15
25
40
60
80
110
Average
Discussion
Table 6.6 Evaluation of adjustments for increased initial enrichments
% heat rate changea for a 1/3 increase in enrichment
Cooling
time, days
1
2
4
7
15
25
40
60
80
110
a
Average
–5.3
-5.5
-4.4
-2.6
-1.5
-1.4
-1.7
-2.4
-3.2
-4.3
BWR
Maximum
–3.8
-4.5
-3.1
-1.2
-0.2
-0.5
-1.3
-1.4
-1.7
-2.1
Equation
Average
PWR
Maximum
Equation
–3.6
-3.3
-2.8
-2.1
-0.2
-0.4
-0.7
-1.1
-1.5
-2.0
–5.3
-5.8
-5.0
-3.3
-1.9
-1.5
-1.6
-2.0
-2.7
-3.6
–4.0
-4.8
-4.0
-2.1
-0.7
-0.7
-1.3
-1.2
-1.3
-1.6
–3.8
-3.7
-3.3
-2.8
-1.5
-0.7
-0.8
-1.0
-1.3
-1.6
(Increased case/standard B 1)100%.
NUREG/CR-5625
42
Discussion
the standard deviation in z from standard deviations in xi
may be derived by the partial differential equation:
A large quantity of data is input to a rather complex
computational model to compute the tabulated heat rates
in the set of 36 standard cases. Also, procedures involving
both interpolations and adjustment factors are applied to
the tabulated data. An appropriate safety factor to be
applied to the final results should account for both random
and systematic errors, computational model bias,
procedural guide inaccuracies, and any significant
parameter variations that have not already been taken into
account. Examples of random data errors in the heat rate
calculation are the standard deviations in fission yields,
half-lives, recoverable energies (Q-values), and neutron
cross sections. The overriding systematic data error and
computational bias is in the calculation of neutron cross
sections. All the actinides and light-element activation
products, plus a few fission products, are mainly
dependent on cross sections. The procedural inaccuracies
are caused by interpolations and adjustment factor errors.
Also, there are several minor parameter variations that are
not taken into account.
Fz ' j
i
2
1
2
,
(20)
where,
Fz is the standard deviation in z,
Fx is the standard deviation in xi .
i
Equation (20) will be applied to several equations later in
this section. First, the effective yield, y, of a fission
product nuclide from the individual yields due to 235U,
239
Pu, and 238U fissions is determined by
y ' j f i yi ,
3
(21)
i'1
where
It appears that there is a natural division of the errors into
the following four types:
y = the fraction of all fissions yielding the fission
product nuclide,
fi = the fraction of fissions produced from fissile
isotope i,
yi = the fraction of fissions from isotope i yielding
the fission product,
i = 1, 2, and 3 for 235U, 239Pu, and 238U, respectively.
1. error from random data uncertainty;
2. error in cross sections resulting from data
uncertainty and computational model bias;
3. procedural inaccuracy and extra parameter
variation error; and
4. other contingency errors.
Note that in the ORIGEN-S code,1 the calculation of y
from Eq. (21) is never executed explicitly. Instead, a
transition constant equal to yi times the fission cross
section of isotope i is used as an element of the transition
data matrix. The fission yield rates of a fission product
nuclide are added for each isotope i, and the nuclide is
accumulated and depleted over the entire irradiation
period. However, with the correct effective values of fi Eq.
(21) will represent a good approximation for the
propagation of uncertainties of yi . The error in fi is not
considered as a random uncertainty because it results from
the cross-section and computational bias. Thus, fi is given
no standard deviation here, and its error will be considered
as part of the cross-section bias in the next section.
A discussion of these four error categories is given in
Sects. 6.6.1–6.6.4.
6.6.1 Error From Random Data Uncertainty
The random errors considered here are the standard
deviations in fission product yields, half-lives, and
Q-values. Both fission products and light element
activation products are included in this analysis. The
conventional type of quadratic propagation of standard
deviations, described below, is applied to determine the
final standard deviation. First, the equations for final
uncertainty will be derived. Then tables listing the input
standard deviations and the final heat rate standard
deviations at different cooling times for several of the
standard cases are presented.
Fission-product yields in this project were taken from
ENDF/B-V6 files. The individual and accumulated (by
mass number) fission product yields and their standard
deviations have been conveniently listed in Ref. 8. The
accumulated yields and percentage standard deviations for
the dominant (in decay heat rate) 20 fission product
nuclides are given in Table 6.7. There are three
Given a general equation for z as a function of variables xi
z = F(x1 ,x2 ,...,xi ,...) ,
MF
F
Mxi xi
(19)
43
NUREG/CR-5625
Discussion
Table 6.7 Percentage fission-product yields for fissile isotopes
235
239
U
100 Fy
238
Pu
100 Fy
1
Totala,b
U
100 Fy
2
100 Fy
3
Nuclide
y1 , %
y1
y2 , %
y2
y3 , %
y3
y, %
Kr-85
Sr-89
Sr-90
Y-90
Y-91
Zr-95
Nb-95
Ru-106
Rh-106
Ag-109
Sb-125
Te-125m
Cs-133
Cs-137
Ba-137m
Ce-144
Pr-144
Pm-147
Eu-153
Eu-155
1.310
4.900
5.900
5.900
5.900
6.500
6.500
0.400
0.400
0.034
0.029
0.029
6.700
6.200
6.200
5.500
5.500
2.250
0.161
0.032
0.35
1.40
0.70
0.70
0.50
0.70
0.70
1.00
1.00
11.00
4.00
4.00
0.35
0.35
0.35
0.50
0.50
1.00
2.80
4.00
0.570
1.700
2.100
2.100
2.500
4.900
4.900
4.300
4.300
1.880
0.111
0.111
7.000
6.700
6.700
3.700
3.700
2.040
0.360
0.166
0.50
2.80
2.00
2.00
1.40
2.00
2.00
2.80
2.80
8.00
8.00
8.00
0.70
0.50
0.50
0.50
0.50
1.40
6.00
11.00
0.730
2.800
3.200
3.200
4.100
5.100
5.100
2.500
2.500
0.270
0.053
0.053
6.600
6.000
6.000
4.500
4.500
2.530
0.411
0.133
1.40
2.00
2.00
2.00
2.80
1.00
1.00
4.00
4.00
11.00
8.00
8.00
1.40
1.00
1.00
1.00
1.00
1.40
2.80
16.00
0.938
3.324
4.012
4.012
4.260
5.684
5.684
2.284
2.284
0.865
0.067
0.067
6.824
6.404
6.404
4.628
4.628
2.180
0.269
0.099
a
y is computed from Eq. (21).
Percentage standard deviations in y are computed from Eq. (22).
b
NUREG/CR-5625
44
y
0.284
1.182
0.687
0.687
0.536
0.853
0.853
2.347
2.347
7.657
5.912
5.912
0.373
0.292
0.292
0.344
0.344
0.771
3.646
8.316
Discussion
that are not depleted and y is the applicable cumulative
yield from Eq. (21), Eq. (25) becomes
exceptions in the dominant nuclides. The yields are
given for 109Ag, 133Cs, and 153Eu because these isotopes
appear after neutron absorption in the path to essentially
all of the dominant nuclides 110mAg, 134Cs, and 154Eu,
respectively. Then, one can apply Eq. (20) to compute
the standard deviation in y as given by Eq. (21),
Fy
y
1
2
j (f y F /y )
y i'1 i i yi i
3
'
1
2
.
x t ' C y e &8t .
The constant C cancels out in the final error equation.
Note that y is not applicable to the daughter nuclide of
two nuclides in secular equilibrium. In this case, it is
required that the rate in which both parent and daughter
atoms disintegrate are identical:
(22)
Values of fi , the fraction of fissions from isotope i, were
computed from the concentrations and fission cross
sections of fissile isotope i for a typical SAS2H case.
Then, the fraction for 239Pu was increased by 10% and
that for 235U was reduced similarly. This was done to
account for the increase of 239Pu fissions later in the
irradiation period. Applying f1 = 0.48, f2 = 0.44, and f3 =
0.08, the total yields and the percentage standard
deviations in the yields were determined from Eq. (22)
and listed in Table 6.7. Data for the Q-values and decay
constants (8) were taken from ENSDF.7 Standard
deviations of the half-lives and the $ and ( energies and
intensities for ENSDF data have been tabulated in Ref.
28. The equation for Q is
Q ' j Ei Ii /100 ,
x1 81 ' x2 82 ,
xt ' x2 '
FQ ' 0.01 j
i
%
1
2
.
&81 t
,
(28)
(29)
Then, the most general equation for heat rate of the
nuclide is
h ' x t8Q ' CN82Qy1e
&81 t
.
(30)
If the nuclide is not the daughter in a secular equilibrium
pair, then 8 = 81 = 82 , and
h ' C 8 Q y e &8t .
(31)
Applying Eq. (20) to Eq. (31) yields
(24)
Mh
' C8ye &8t '
MQ
Mh
h
' ;
My
y
Mh
' CQye &8t &
M8
h(1 & 8t)
'
8
Fh /h ' [(FQ /Q)2 %
Now, the percentage standard deviation in the decay heat
rate of a nuclide is to be determined. First, the equation
for heat rate is required. Consider d to be the number of
atoms of a nuclide at discharge. The depleted number of
atoms at cooling time t is
x t ' de &8t .
82
x1 ' CN y1 e
CN ' C81 /82 .
The standard deviation in Q can be obtained using Eq.
(20) to be
2 2
I i FE )
i
81
where
where,
Ei = ( line or average $ energy,
Ii = intensity of Ei as percentage of the total
disintegrations.
2 2
(Ei FI
i
(27)
where x1 and x2 are the parent and daughter nuclide
concentrations, respectively. Thus, the number of atoms
of the daughter nuclide is
(23)
i
(26)
(25)
h
;
Q
tC8Qye &8t
(32)
(Fy /y)2 % (F8 /8)2
1
2 2
(1 & 8t) ] .
Then, by substituting d = Cy, where C is the total
number of fissions times the fraction of the nuclide atoms
45
NUREG/CR-5625
Discussion
more recent ENSDF data base28 that was used in the
uncertainty analysis. The adequacy of the selection of
dominant nuclides can be seen in comparisons of their
totals with totals listed by ORIGEN-S. It would require a
project that is both too extensive and unnecessary to
calculate FH for all 20 cooling times of all of the 36
standard cases computed here. The reason this
computation is considered unnecessary is because FH was
determined to be small in comparison with other errors
that contribute to the safety factors. Data from four of
the standard cases (see Tables 5.1–5.8) were used in this
study. A case having a power and burnup that are typical
and a case having an extended burnup for both the BWR
and PWR were used. The calculation of FH was
performed for a total of 24 separate cases comprising
cooling times of 1, 1.4, 4, 10, 50, and 110 years.
Table 6.9 (for the typical BWR case) shows the
individual percentage standard deviations, 100 Fh /hi
Similarly, the uncertainty propagated through Eq. (30)
for the secular equilibrium daughter is
Fh /h ' [(FQ /Q)2 % (Fy /y)2 % (F8 /82)2 %
2
(33)
At discharge (t = 0), the fractional standard deviation in
the heat rate ho is computed from only the first three
terms of Eq. (33), and, then, Eqs. (32) and (33) are
identical.
The percentage standard deviations in Q, 81 , 82 , y, and
ho , as computed from Eqs. (32) and (33) for t = 0, are
listed in Table 6.8 for the dominant (i.e., in heat rate) 20
fission products and dominant 5 light-element nuclides.
Note that the yield data for 109Ag, 133Cs, and 153Eu were
substituted for that of 110mAg, 134Cs, and 154Eu,
respectively.
i
Associated with data for half-lives were standard
deviations. Some of the half-lives were taken from a
more recent version of ENSDF (see Ref. 28) than that
used in the ORIGEN-S libraries.5 If the decay constant
(derived from the half-life) were larger in ORIGEN-S
than in Ref. 28, it produced a more conservative decay
heat rate for the nuclide. However, if the decay constant
were smaller in ORIGEN-S than in Ref. 28, one-half the
difference between the two values was added to the
standard deviation. Thus, when 2F is used in applying
the contribution of this error to the safety factor, the full
bias is taken into account.
from Eqs. (32) or (33), hi from the SAS2H/ ORIGEN-S
case, and the resulting standard deviations in hi. Also,
the standard deviation in the total heat rate of the 25
nuclides and its conversion to percentage of the total heat
rate, including that from actinide nuclides, is
summarized in the bottom line of Table 6.9. It is seen
that the percentage standard deviation of the total heat
rate from the above uncertainties is 0.70% at 1-year
decay for the typical BWR case. Also, it is seen in Table
6.10 that the percentage standard deviation (from the
random errors) in the total heat rate is 0.10% at the
cooling time of 110 years. The reason for the significant
reduction to 0.10% is due to the essential vanishing of
heat rate from nuclides having the larger standard
deviations. Note that 0.0 W denotes the 10-78 limit of the
floating-point numbers on the IBM 3090 mainframe.
If hi and Fhi are the heat rate and the standard deviation
in the heat rate for nuclide i, then the total heat rate, H, is
H ' j hi ,
(34)
i
Finally, in order to reduce the number of tables listing
detailed data, as in Tables 6.9 and 6.10, a summary of
the percentage standard deviations in the total heat rates
is listed in Table 6.11. Note that the maximum
percentage of the total is 0.72% for the typical PWR case
at 1.4-year cooling time. These data will be used in Sect.
6.6.4 in the determination of safety factors.
and its standard deviation is
FH ' j
i
2
Fh
i
1
2
.
(35)
Thus, Eqs. (32) through (35) may be used with Table 6.8
data to compute the approximate standard deviation due
to random data uncertainty (excluding cross sections) for
the sum of heat rates from the dominant fission products
and light elements. The increase in computed
uncertainty from applying t > 0 instead of t = 0 in Eqs.
(32) and (33) is sufficiently cancelled by the increase in
the long cooling time heat rates calculated from using a
larger half-life for 90Sr in ORIGEN-S than that in the
NUREG/CR-5625
6.6.2 Error From Cross Sections and
Computational Model Bias
This section includes a discussion of error in the cross
sections resulting from both data uncertainty and
computational model bias. The reason for combining
these two types of errors is that it would be extremely
complex to propagate standard deviations of each energy
46
Discussion
Table 6.8 Percentage standard deviations in data for dominant
fission products and light elements
100FQ
Type
100F8
1
100F8
100Fy
100Fh
ho
2
o
Q
81
82
y
Kr-85
Sr-89
Sr-90
Y-90
Y-91
Zr-95
Nb-95
Ru-106
Rh-106
Ag-110m
Sb-125
Te-125m
Cs-134
Cs-137
Ba-137m
Ce-144
Pr-144
Pm-147
Eu-154
Eu-155
0.320
0.260
0.410
0.130
0.160
1.190
0.020
0.800
0.420
0.410
0.550
1.020
0.220
0.290
0.320
1.120
0.150
1.400
1.340
2.030
0.090
0.180
1.920
1.920
0.100
0.060
0.060
0.330
0.330
0.040
1.440
1.440
0.242
0.099
0.099
0.106
0.106
0.006
1.160
0.202
0.090
0.180
1.920
0.160
0.100
0.060
0.380
0.330
0.800
0.040
1.440
1.720
0.242
0.099
0.080
0.106
0.170
0.006
1.160
0.202
0.284
1.182
0.687
0.687
0.536
0.853
0.853
2.347
2.347
7.657
5.912
5.912
0.373
0.292
0.292
0.344
0.344
0.771
3.646
8.316
0.437
1.223
2.080
0.718
0.569
1.466
0.934
2.502
2.515
7.668
6.110
6.241
0.496
0.423
0.440
1.176
0.412
1.598
4.054
8.562
Co-60
Zr-95
Nb-95
Sb-125
Eu-154
0.010
1.190
0.020
0.550
1.340
0.020
0.060
0.060
1.440
1.160
0.020
0.060
0.380
1.440
1.160
0.000
0.000
0.000
0.000
0.000
0.022
1.192
0.381
1.541
1.772
Nuclide
Fission
products
Light
elements
47
NUREG/CR-5625
Discussion
Table 6.9 Computed standard deviation in nuclides and their
total heat rate at 1 year for typical BWR
Nuclide
or total
Co-60
Kr-85
Sr-89
Sr-90
Y-90
Y-91
Zr-95(FP)
Nb-95(FP)
Ru-106
Rh-106
Ag-110m
Sb-125(FP)
Te-125m
Cs-134
Cs-137
Ba-137m
Ce-144
Pr-144
Pm-147
Eu-154(FP)
Eu-155
Zr-95(LE)
Nb-95(LE)
Sb-125(LE)
Eu-154(LE)
100 Fi
hi
hi, W
F h i, W
0.022
0.437
1.223
2.080
0.718
0.569
1.466
0.934
2.502
2.515
7.668
6.110
6.241
0.496
0.423
0.440
1.176
0.412
1.598
4.054
8.562
1.192
0.381
1.541
1.772
3.668E-02
1.099E-02
1.007E-02
7.235E-02
3.456E-01
2.779E-02
8.234E-02
1.754E-01
1.137E-02
1.840E+00
1.516E-02
1.504E-02
9.848E-04
8.349E-01
1.016E-01
3.410E-01
1.797E-01
1.991E+00
3.610E-02
7.733E-02
3.809E-03
6.576E-03
1.401E-02
3.922E-03
1.277E-03
8.202E-06
4.803E-05
1.231E-04
1.505E-03
2.480E-03
1.580E-04
1.207E-03
1.639E-03
2.844E-04
4.627E-02
1.163E-03
9.189E-04
6.146E-05
4.139E-03
4.296E-04
1.501E-03
2.113E-03
8.202E-03
5.770E-04
3.135E-03
3.262E-04
7.835E-05
5.330E-05
6.046E-05
2.263E-05
6.234
6.251
6.841
4.751E-02
Sum of above
All FP and LEa
Total, incl. actinidesb
Percentage std. dev. in total
0.70%
a
This is sum of heat rates from all fission products (FP) and light elements
(LE) computed by ORIGEN-S.
b
Total heat rate as tabulated in Table 5.2.
NUREG/CR-5625
48
Discussion
Table 6.10 Computed standard deviation in nuclides and their
total heat rate at 110 years for typical BWR
100 Fh
i
Nuclide
hi
Co-60
Kr-85
Sr-89
Sr-90
Y-90
Y-91
Zr-95(FP)
Nb-95(FP)
Ru-106
Rh-106
Ag-110m
Sb-125(FP)
Te-125m
Cs-134
Cs-137
Ba-137m
Ce-144
Pr-144
Pm-147
Eu-154(FP)
Eu-155
Zr-95(LE)
Nb-95(LE)
Sb-125(LE)
Eu-154(LE)
0.022
0.437
1.223
2.080
0.718
0.569
1.466
0.934
2.502
2.515
7.668
6.110
6.241
0.496
0.423
0.440
1.176
0.412
1.598
4.054
8.562
1.192
0.381
1.541
1.772
Sum of above
All FP and LEa
Total, incl. actinidesb
Percentage std. dev. in total
hi, W
F h i, W
2.182E-08
9.547E-06
0.000E+00
5.402E-03
2.580E-02
0.000E+00
0.000E+00
0.000E+00
3.185E-35
5.154E-33
1.653E-50
2.142E-14
1.405E-15
1.018E-16
8.298E-03
2.787E-02
1.250E-43
1.385E-42
1.119E-14
1.182E-05
9.229E-10
0.000E+00
0.000E+00
5.585E-15
1.953E-07
4.880E-12
4.173E-08
0.000E+00
1.124E-04
1.852E-04
0.000E+00
0.000E+00
0.000E+00
7.968E-37
1.296E-34
1.267E-51
1.309E-15
8.769E-17
5.045E-19
3.510E-05
1.227E-04
1.470E-45
5.706E-45
1.789E-16
4.792E-07
7.902E-11
0.000E+00
0.000E+00
8.609E-17
3.461E-09
0.06739
0.06750
0.260
2.514E-04
0.10%
a
Sum of heat rates from all fission products (FP) and light elements (LE)
computed by ORIGEN-S.
b
Total heat rate as tabulated in Table 5.2.
49
NUREG/CR-5625
Discussion
group (or point) cross section through the computations of
the resonance cross sections and the final neutron
transport calculation. Furthermore, it would be difficult to
estimate the bias in the resonance, transport, and pointdepletion types of computations.
10 years. Similar cases were computed by SAS2H/
ORIGEN-S, where only burnups, powers, and enrichments
were changed from the standard cases used to create the
decay heat data base provided in Sect. 5. The heat rates
from the same set of nuclides as used for ORIGEN2 were
also determined for SAS2H/ORIGEN-S. The comparisons
for these cross-section-dependent heat rates as computed
by SAS2H/ORIGEN-S and ORIGEN2 and their
percentage differences are listed in Table 6.12 for the two
typical and extended burnup BWR and PWR cases. The
agreement for the typical burnup cases was relatively
good, while differences of 7.2 and 15.9% for the extended
burnup PWR and BWR cases, respectively, were
considerably more. A larger fraction of the heat rate for
the extended burnup cases is produced from nuclides
farther down the various transition chains of the actinides
as the burnup is increased. The effect of propagating
uncertainty or bias from cross sections of these additional
nuclides correspondingly increases the final uncertainty in
the heat rate.
Instead of analyzing the uncertainty of data, as used in
standard deviation calculations of Sect. 6.6.1, a more
global type of technique is applied to determine the error
from cross sections and computational bias. Although
certain approximations were necessary in parts of the
evaluation, a somewhat larger than expected quantity of
data were available. The major global technique used here
is the comparisons of SAS2H/ORIGEN-S results with
other code computations and measurements. In referring
to cross-section error here, it is meant to include that error
due to the cross-section data uncertainty and code
computational bias of the actinides, the light-element
activation products, and three fission products (133Cs,
153
Eu, and 109Ag). Two additional error types—decay data
uncertainties in the actinide production and any other code
biases—are also included as a very small part of the total
error discussed as cross-section error.
The code system that produced data for the ORIGEN2
libraries is denoted as GPRCYCLE.30 This code system
uses a more complex method of computing cross sections
than that used by SAS2H in part because it performs
multidimensional depletion calculations. Axial variations,
changes in fuel pin enrichments, and different fuel zones
within the core may be explicitly included in the reactor
model.
The use of previously documented14,17 comparisons of
decay heat rates calculated by different codes is inadequate
to evaluate the uncertainty in the present work. The
comparison of results from ORIGEN229 and ORIGEN-S in
Ref. 14 involved the 1978 ORIGEN2 library21 and the
earlier SCALE-3 version of SAS2H. The multicode
comparisons of Ref. 17, although more recent, are not
sufficiently current because the ORIGEN2 library21 has
been substantially improved,30 the ORIGEN-S fission
product yields have been updated, the BWR cases have
been changed with more realistic data, and the
EPRI-CELL code31 (used with CINDER-232) has been
enhanced significantly.33
Reactor calculations performed by the GPRCYCLE system
can compute the soluble boron in the moderator of a PWR
through a criticality search. Repeated soluble boron
computations34 during a fuel exposure cycle produced data
fitting closely the "boron letdown curve." Changes in
boron content is a form of determining variations in the
keff of the core because moderator boron content may be
converted into reactivity worth. In turn, although
cross-section error can be partially cancelled in deriving a
keff (due to similar data in numerator and denominator),
the cancellation can never be complete at all points on the
boron let-down curve.
For this uncertainty study, a comparison of heat rates
computed by ORIGEN2 using improved BWR and PWR
libraries30 with heat rates computed by SAS2H/
ORIGEN-S was made. Note that the improved PWR and
BWR libraries available for ORIGEN2 were prepared for
only two specific burnups (typical and extended burnups of
27.5 and 40 MWd/kgU for BWR and 33 and 50
MWd/kgU for PWR) and corresponding initial
enrichment. The sum of the heat rates at 10 years from
the actinides, the light-element activation products and
fission products 134Cs and 154Eu computed by ORIGEN2,
was determined from Ref. 30. The two fission product
heat rates were converted from curies, as listed, to W and
added to total heat rates of the other two types of nuclides.
The quantity of 110mAg is insignificant at the decay time of
NUREG/CR-5625
In the application of the cross-section data provided by
GPRCYCLE, the ORIGEN2 library was designed to
include burnup-dependent cross sections for 239Pu through
242
Pu and 241Am and initial or midpoint burnup cross
sections for the other nuclides. In deriving the
SAS2H/ORIGEN-S BWR extended burnup heat rate listed
in Table 6.12 (the case having the greatest difference) only
midpoint burnup cross sections were applied for all
nuclides besides plutonium and 241Am. Executing
SAS2H/ORIGEN-S in this fashion for the extended BWR
50
Discussion
Table 6.11 Percentage standard deviation in fission-product and lightelement heat rate applying Q, 8, and fission yield uncertainties
Percentage standard deviation
in total heat rate
Reactor
type, final
uncertainty
Power,
kW
kgU
BWR
BWR
PWR
PWR
20
30
28
40
Burnup,
Cooling time, y
MWd
kgU
1
1.4
4
10
50
110
30
40
30
50
0.70
0.69
0.71
0.68
0.70
0.69
0.72
0.67
0.40
0.40
0.42
0.38
0.30
0.30
0.30
0.29
0.21
0.21
0.21
0.20
0.10
0.10
0.10
0.10
1.4
1.4
0.8
0.6
0.4
0.2
Uncertainty:
2Fmax
Table 6.12 Code comparisons of heat rate at 10-year cooling from actinides,
light-element activation products plus two fission products (134Cs and 154Eu)
Burnup,
Reactor
type
BWR
BWR
PWR
PWR
Cross-section-dependent heat rate, W
MWd
kgU
SAS2H/
ORIGEN-S
GPRCYCLE/
ORIGEN2
27.5
40.0
33.0
50.0
257.9
508.9
368.4
729.3
265.7
605.2
360.4
785.5
51
% difference
ORS
& 1 100%
OR2
–2.9
–15.9
2.2
–7.2
NUREG/CR-5625
Discussion
case increased the heat rate provided by normal
execution of SAS2H/ ORIGEN-S. The 15.9%
difference provided in Table 6.12 is most likely caused
by multidimensional effects such as axial variation in
the moderator density, partial insertion of boron
cruciform control rods, and different fuel enrichments
within an assembly. Another reason for the difference
may be the use of different ENDF versions of cross
sections, in addition to the application of data having
different energy group structures. The significant
differences in the methodology and approach used to
generate the ORIGEN2 and ORIGEN-S cross sections
provide a basis for using the heat rate results of Table
6.12 to estimate a cross-section bias for use in
formulating the safety factor. The differences provided
in Table 6.12 are used in Table 6.13, which
summarizes the contribution to the total safety factor.
ORIGEN-S and measured heat rates, as listed on the
third line in Table 6.13.
In addition to the two major methods discussed above
for determining cross-section biases, it appeared
reasonable to consider other information pertaining to
the reliability of the calculated decay heat values.
During the development of SAS2H for the SCALE-4
system, cases were executed producing isotopic
contents that could be compared with experimental
determinations of the isotopic inventories of various
PWR assemblies. The comparison of measured and
computed contents of uranium and plutonium isotopes
for a Turkey Point Unit 3 assembly is given in Ref. 35.
The largest difference was the nonconservative 8.9%
for 240Pu; however, it is not a significant contributor to
heat rate. The next largest difference was the
conservative 6.1% for 241Pu. No large nonconservative
bias in heat rate is indicated. However, the
measurement of a significant decay heat rate
contributor, 244Cm, was not given. Comparisons were
also made for PWR assemblies from the H. B.
Robinson Unit 2 Reactor4 in South Carolina and the
Obrigheim (KWO) Reactor36 in the Federal Republic of
Germany. These comparisons included measurements
of 244Cm. The H. B. Robinson measurements included
134
Cs. Although the " spectrometer standard deviations
of 244Cm results are quoted as ± 20 to 30%, there were
also measurements of the Obrigheim samples in which
the much more precise method of isotope dilution
analysis was used for 244Cm. Although it does not
appear to be within the scope of this project or report to
give detailed comparisons, note that agreement in the
total cross-section-dependent heat rate would be well
below 10% and would possibly be conservative. Note
that this applies only to PWR assemblies in the typical
burnup region.
Now consider comparisons of SAS2H/ORIGEN-S
calculations of heat rates with measurements. Note
that a comparison of computed total heat rates with
measurements for ten BWR and ten PWR assemblies
was presented in Sect. 3. The results were summarized
in Table 3.16. Also, it is seen that the random type of
error or standard deviation computed, as listed in Table
6.11, is approximately 0.5% in the 3– to 4-year range
in which the measurements were performed. The error
due to cross-section-dependent nuclides should be at
least several times the random type error. For the
purpose of estimating a measurement of the
cross-section-dependent error, the assumption is made
that the entire difference between computed and
measured decay heat rates is completely due to crosssection bias. Assuming other biases are small, the
difference is actually a good estimate of the
cross-section error. If there were no systematic bias,
the standard deviations of the percentage differences in
computed and measured values are large enough to
indicate that these data are simply not a very precise
estimate of the cross-section bias. Nevertheless, it may
be considered to be one of the best available global
measurements of cross-section-dependent heat rate
error. The fraction of the total heat rate that is
produced from the cross-section-dependent nuclides
was computed as 0.311 and 0.315 of the averages of
two typical BWR and PWR cases, respectively.
Dividing the differences of –0.7 ± 2.6% and 1.5 ±
1.3% (from Table 3.16) by the above fractions
produces cross-section bias estimates of –2.3 ± 8.4%
and 4.8 ± 4.1% for the BWR and PWR, respectively.
Thus, the second type of consideration used in
estimating the cross-section error and the safety factor
is that derived from comparisons of SAS2H/
NUREG/CR-5625
Isotopic analyses of BWR spent fuel were performed
using SAS2H/ORIGEN-S as part of a study on using
actual spent fuel isotopics in the criticality safety
analyses of transport casks.37 Average assembly
isotopic concentrations for some of the most significant
nuclides (e.g., 244Cm and 133Cs) were calculated using
multi-axial-node models and SAS2H. The isotopic
differences between the multi-node and single-node
models using SAS2 were less than half the differences
observed in the GPRCYCLE/ORIGEN2 and SAS2H
comparison.
Some select cases were also run to investigate the effect
of the energy grouping in the SCALE 27-group cross
sections used by SAS2H to calculate the tabulated
52
Discussion
Table 6.13 Summary of cross-section bias estimates and safety factors
BWR
Burnup, MWd/kgU
Difference in codes, %a
Difference in measurements, %b
Average difference, %
Safety factor for F-error, %c
27.5
–2.9
–2.3 ± 8.4
–2.6
11.0
PWR
40.0
–15.9
—
–15.9
16.0
33.0
2.2
4.8 ± 4.1
3.5
10.0
50.0
–7.2
—
–7.2
11.0
a
Comparisons shown in Table 6.12.
Assuming differences between computed and measured heat rates (Table 3.16) caused by
cross-section error.
c
Safety factors, applied as adequate, for cross-section uncertainty and computation model
bias in heat rate of nuclides produced primarily by neutron absorption.
b
decay heat values. The PWR case for 28 kW/kgU and 45
MWd/kgU was executed using the 218-energy- group
ENDF/B-IV library in the SCALE system. The total heat
rates computed by the 218-group case were greater by
0.3% at 1 year, about equal at 5 years, and 1.5% smaller
than those of the 27-group case at 110 years. In another
study, the typical and extended burnup BWR cases (27.5
and 40 MWd/kgU, respectively) were executed on the
CRAY X-MP using ENDF/B-V cross sections, which
resulted in an increase in the computed actinide and total
heat rates.
shows good validation of the mathematical model of
ORIGEN-S.
The major discussion in this section has been concerned
with the error in cross sections resulting from both data
uncertainty and computational model bias. The effect of
these has been demonstrated via code comparison and the
differences between computed and measured
cross-section-dependent heat rates. Using the percentage
differences derived for Table 6.12 and the comparisons
with measurements, a summary of estimates of the
cross-section bias are presented in Table 6.13. For the
same cases, the differences between the code computations
(GPRCYCLE/ ORIGEN2 and SAS2H/ORIGEN-S) and
the differences between the calculations and measurements
(after assuming they may be converted to cross-section
bias) are in moderate agreement. The average differences
for the typical BWR and PWR are –2.6 and 3.5%,
respectively. After consideration of these data and other
information discussed above, it was decided to apply an
11% safety factor to the lower burnup BWR
cross-section-dependent heat rates. A 10% safety factor
was given to the lower burnup PWR values. Although the
PWR results appear to have significantly less
nonconservative bias, the 10% minimum is reasonably
liberal and not greatly overconservative. Indications were
seen that the extended burnup PWR results are
approximately the same as the lower burnup BWR and
should have a similar safety factor. Also, from all
comparisons of calculations for the extended burnup
BWR, it appeared that a 16% safety factor for
cross-section bias was both sufficient and reasonable.
These factors will be used in determining the contribution
from cross-section bias to the safety factors of the total
heat rate. Examples of these contributions are given in
Tables 6.14 and 6.15, which show the itemized calculation
of the safety factor in the total heat rate due to
cross-section bias for four cases at 1 and 110 years,
The actinide heat rates increased by 3 and 6% and the
total heat rates increased by 0.2 and 1.6% in the typical
and extended burnup cases, respectively. All of
these values are within the uncertainty envelope provided
by the code comparison of Table 6.12.
Another comparison study38 was performed on an
international scale to determine differences between the
mathematical models of codes computing decay heat rates.
Contributions to the study were received from China,
France, Germany (FRG), Japan, Sweden, UK, USA, and
USSR, applying the following codes: AFPA, CINDER-10,
CINDER, DCHAIN, FISP6, INVENT, PEPIN, FISPIN,
KORIGEN, MECCYCO, and ORIGEN-S. By starting
with identical model and library data, each code computed
decay heat rates for each decade from 1 to 1013 s, applying
a 235U fission pulse and a long irradiation (3 × 107 s) in the
two benchmark cases. The total heat rates for the 13
decay times computed by all codes are within 0.7% from
the average for the pulse case and within 1.6% for the long
irradiation case. The total heat rates from ORIGEN-S are
within 0.5% from the average for the pulse case and
within 0.4% for the long irradiation case. A significant
part of the ORIGEN-S difference can arise from the
roundoff in the three-place printout. The agreement
53
NUREG/CR-5625
Discussion
Table 6.14 Contribution of cross-section (F
F) bias to safety
factor of total heat rate at 1 year
Type of data
Cases
Reactor type
Specific power, MW/kgU
Burnup, MWd/kgU
Actinide heat rate, W/kgU
Light-element heat rate, W/gU
134
Cs heat rate, W/gU
154
Eu heat rate, W/gU
110m
Ag heat rate, W/gU
BWR
20
20
296
62
487
43
10
BWR
20
45
1129
77
1356
133
23
PWR
28
25
387
136
707
59
16
PWR
28
50
1282
177
1773
158
43
Sum F-dependent heat rate, W/gU
Total heat rate for case, W/gU
Percentage of total from Fsa
898
5548
16.2
2718
8571
31.7
1305
7559
17.3
3433
11120
30.9
Safety factor for F-error, %
Safety factor in total from Fs, %a
11.0
1.8b
16.0
5.1
10.0
1.7
11.0
3.4
a
The term "from Fs," as used here, means the heat rate of nuclides produced primarily by
neutron absorption.
b
This part of the total heat rate safety factor due to cross-section bias is the product of fraction of
heat rate from F-dependent nuclides and their safety factor (see also Table 6.13) or 16.2 × 11.0/100 =
1.8%.
Table 6.15 Contribution of cross-section (F) bias to safety
factor of total heat rate at 110 years
Type of data
Cases
Reactor type
Specific power, MW/kgU
Burnup, MWd/kgU
Actinide heat rate, W/kgU
Other F-dependent heat rates
BWR
20
20
132
0
BWR
20
45
287
0
PWR
28
25
167
0
PWR
28
50
328
0
Sum F-dependent heat rate, W/gU
Total heat rate for case, W/gU
Percentage of total from Fsa
132
178
74.2
287
385
74.5
167
225
74.2
328
440
74.5
Safety factor for F-error, %
Safety factor in total from Fs, %a
11.0
8.2b
16.0
11.9
10.0
7.4
11.0
8.2
The term "from Fs," as used here, means the heat rate of nuclides produced primarily by
neutron absorption.
b
This part of the total heat rate safety factor due to cross-section bias is computed as the product
of values on last two prior lines as 74.2 × 11.0/100 = 8.2%.
a
NUREG/CR-5625
54
Discussion
respectively. The lowest and highest burnup cases for the
middle specific power of the tabulated data of each reactor
type are used in the example shown. The portion of the
total heat rate safety factors due to cross-section bias listed
on the last line of these tables is applied in the final safety
rate determination in Sect. 6.6.4.
procedure to a PWR fuel assembly containing BPRs
instead of guide tubes for control rods.
Inaccuracies in the proposed procedure of Sect. 5 are
discussed in Sects. 6.1–6.5. Summaries listing the results
of several types of comparisons indicating these
inaccuracies are shown in Tables 6.1–6.6. In general, the
nonconservative differences do not exceed 1%. The only
exceptions to this limit were the errors in the
interpolations of heat rate with respect to specific power
for short cooling times that are in error by 1.1%. The
error diminishes for longer cooling times. Other
parameter variations not taken into account in the previous
discussions are (1) different reactor designs, (2) fuel
assemblies (PWR) containing BPRs, and (3) PWR
moderator density variations.
Consideration was given to comparing cross-sectiondependent decay heat rates computed by SAS2H/
ORIGEN-S with other accepted procedures for computing
decay heat rates. The American National Standard for
Decay Heat Power in Light Water Reactors39 (ANSI 5.1)
computes heat rates from 239U and 239Np (significant in
loss-of-coolant accidents), but it does not compute other
actinide heat rates that have significant contributions at 1
year and later cooling times. Thus, no comparison was
made in this study. A draft document (from the
International Organization for Standardization) of a
standard on decay heat power40 (which is not referred to
officially as the international standard until publication)
applies a contribution of the actinide heat rate in addition
to that from 239U and 239Np. The proposed method
multiplies an actinide factor, A(t), times the summed heat
rate of fission product decays, PS , to determine the
actinide contribution, PA . Values of A(t) are tabulated as a
function of time only. Thus, A(t) does not vary with
burnup. A value with the same definitions as A(t) may be
computed from the SAS2H data in Table 6.14. The
summed heat rates of fission products, PS, for the SAS2H
data are simply the difference given by the "total heat rate
for the case" minus the "sum F-dependent heat rate."
Then, for the BWR cases at 1-year decay, the SAS2 values
of A(1) are 296/(5548-898) = 0.064 in the 20-MWd/kgU
case and 0.193 in the 45-MWd/kgU case. Similarly, for
the low- and high-burnup cases of the PWR, the A(1)
values are 0.062 and 0.167, respectively. The value at 1
year, A(1), in the proposed standard is 0.214. The simple
formalism used by the proposed standard necessitates the
conservatism shown by the comparison with the SAS2H
values.
An earlier version of SAS2H was used to compare heat
rates4 for PWR fuel assemblies of four different array
designs from three different vendors. The cooling time
range was 0–10 years. The largest difference was 0.6%
for the cooling time of 10 years. The average differences
were 0.3 and 0.4% at 1 and 10 years, respectively. These
differences, although small, were considered in developing
the safety factor.
Cases with fuel assemblies containing BPRs for one of the
cycles were computed by SAS2H/ORIGEN-S for both a
typical (33 MWd/kgU) and an extended (50 MWd/kgU)
burnup of a PWR. Although there were no significant
differences for short cooling times, the maximum was a
nonconservative 2.2% for 110 years in the typical case.
Likewise, reasonable moderator density changes in a PWR
provided a slight heat rate change for short cooling and
increased to about 2% for long decay times. Changes in
the actinide production caused by BPRs and/or water
density variations causes the differences in decay heat to
appear only at long cooling times where actinides become
important to the total decay heat.
It was concluded that an adequate magnitude of safety
factor for the procedural inaccuracy and extra parameter
variation is 1.5% at 1 year and linearly increased to 2.0%
at 110 years. This factor would tend to cover the
interpolation error plus other small bias at 1 year, in
addition to somewhat larger differences from the above
considerations at long cooling times.
6.6.3 Error in Procedure of Guide and Extra
Parameter Variation
This section deals with inaccuracies in the proposed
procedure of Sect. 5 in addition to bias that can arise from
variations in parameters not previously taken into account.
An example of a procedural guide error is that resulting
from the interpolation of heat rate data in Tables 5.1–5.3
and Tables 5.5–5.7. An example of a parameter variation
not taken into account is the application of the revised
6.6.4 Total Safety Factors
This section uses data from Sects. 6.6.1–6.6.3 to determine
the total safety factors in the decay heat rates. The total
55
NUREG/CR-5625
Discussion
safety factors for 16 cases are compared with those
computed by formulae given in Sect. 5. Then additional
comments are given on other comparisons not explicitly
shown.
completeness of the safety factor formulation. The totals
of the first four lines of Tables 6.15 and 6.16, shown on
the fifth line, are of total required safety factors. The final
line of each table contains the safety factors for BWR and
PWR as produced by Eqs. (16) and (17), respectively. In
all of the 16 cases, except the 2 cases at 110 years for the
BWR, the equations sufficiently cover the safety factor. In
these two cases, the differences are 0.1 and 0.2%. In
addition to the cases in Tables 6.16 and 6.17, the safety
factors and equation values were calculated for a variety of
other cases. The required safety factor and equation value
for the lower specific power cases tended to compare more
closely than other cases. For only a few PWR cases, the
equation value was lower by a magnitude as large as 0.1%.
Only two BWR cases had equation values below the
required safety factor. These two BWR 110-year cooling
time cases had differences of 0.3 and 0.4% below the
equation values. Note that the total safety factors for these
two cases exceeded 11%. Thus, because there are only
rare exceptions in which the equations are even slightly
nonconservative, Eqs. (16) and (17) are considered to
appropriately envelop all required safety factors.
The determination and summary of the safety factors for
the BWR and PWR are presented in Tables 6.16 and 6.17,
respectively. The data on the first line under the case
parameter heading are the 2F random data uncertainties
discussed in Sect. 6.6.1 and given in Table 6.11. The
values on the next line are the contributions of the
cross-section bias to the total safety factor as derived in
Sect. 6.6.2 and given in the last lines of Tables 6.14 and
6.15 for cooling times of 1 and 110 years. Similar data
were calculated for the cooling times of 4 and 10 years.
The safety factor contributions on the next line are for
errors in the procedure and extra parameter variation. A
discussion of these data is given in Sect. 6.6.3. On the
next line a contingency safety factor of 1% was arbitrarily
chosen for all the cases. It is simply a small, although
significant, increase in the safety factor to cover any other
or unexpected error not adequately taken into account.
The 1% magnitude, although a matter of judgment,
appears to be commensurate with the relative
NUREG/CR-5625
The final equation to be analyzed here is Eq. (18). This
equation simply applies all adjustment factors and the
safety factor to the heat rate determined through
interpolation of tabulated data.
56
Discussion
Table 6.16 Summary of percentage safety factors for BWR
20
Type of error
or safety factor;
Section
discussed
2F
F(Q,8,y), FP + LEa
Cross-section bias
Procedure and extra bias
Contingency
Total
S, Eq. (16)
a
kW
MWd
, 20
kgU
kgU
20
Cooling time, years
kW
MWd
, 45
kgU
kgU
Cooling time, years
1
4
10
110
1
4
10
110
6.6.1
6.6.2
6.6.3
6.6.4
1.4
1.8
1.5
1.0
0.8
3.0
1.5
1.0
0.6
2.9
1.6
1.0
0.2
8.2
2.0
1.0
1.4
5.1
1.5
1.0
0.8
6.4
1.5
1.0
0.6
5.7
1.6
1.0
0.2
11.9
2.0
1.0
5.2.5
5.7
6.4
6.3
6.5
6.1
6.8
11.4
11.2
9.0
10.2
9.7
10.3
8.9
10.6
15.1
15.0
FP: fission products; LE: light elements.
Table 6.17 Summary of percentage safety factors for PWR
28
kW
MWd
, 25
kgU
kgU
28
Cooling time, years
Type of error
or safety factor;
Section
discussed
2F(Q,8,y), FP + LEa
Cross-section bias
Procedure and extra bias
Contingency
Total
S, Eq. (17)
a
kW
MWd
, 50
kgU
kgU
Cooling time, years
1
4
10
110
1
4
10
110
6.6.1
6.6.2
6.6.3
6.6.4
1.4
1.7
1.5
1.0
0.8
3.0
1.5
1.0
0.6
2.9
1.6
1.0
0.2
7.4
2.0
1.0
1.4
3.4
1.5
1.0
0.8
4.6
1.5
1.0
0.6
4.2
1.6
1.0
0.2
8.2
2.0
1.0
5.2.5
5.6
6.2
6.3
6.4
6.1
6.7
10.6
11.1
7.3
7.7
7.9
7.9
7.4
8.2
11.4
12.7
FP: fission products; LE: light elements.
57
NUREG/CR-5625
Discussion
NUREG/CR-5625
58
7 THE LWRARC CODE
The LWRARC (Light Water Reactor Afterheat Rate
Calculation) code is a Microsoft BASIC program that
follows the complete procedure as described in Sect. 5. It
runs on an IBM-compatible personal computer.
LWRARC features a pulldown menu system with
sophisticated data entry screens containing contextsensitive help messages. The menu system organizes the
major command categories as menu titles and pulldown
commands. The program performs checking for each
input screen and presents warning and error message
boxes and yes/no dialog boxes to verify that the user wants
to perform certain functions (e.g., write over files that
have been saved previously). The menus may be used with
either a keyboard or a mouse.
Some pulldown menu commands are black with a hot key,
while others are gray. The black commands are active; the
gray commands are inactive and produce no effect if
selected. Commands are activated as necessary data are
entered. For example, once cases have been entered or
files have been retrieved, the Review Cases and the
Execute Cases options are active.
7.2 Menu System Options
This section presents an overview of the menu system
commands. Menu bar options are presented next to round
bullets; corresponding pulldown commands are listed next
to diamond bullets. The underlined letter in commands
discussed below represents the hot key for the command;
these hot keys appear on screen as bright letters, and they
allow immediate access to an item by pressing the
highlighted key.
7.1 Using the Menu System
The pulldown menu system contains a menu bar across the
top of the screen. Under each menu bar option there is a
unique pulldown menu. The menu bar options are
summarized below.
Files
Data
Run
• Files – The Files menu allows the user to retrieve and
save files and to exit the program.
• Retrieve Files – This option allows the user to
retrieve files which the user has previously saved
with LWRARC. The user selects the desired
input file from a list of all LWRARC input files in
the current directory. LWRARC then loads the
input file and the output file (if it exists) with that
file name. The input and output files for a set of
cases have the same file name specified by the
user, but a different file extension designated by
LWRARC (".INP" for input and ".OUT" for
output). The program copies the files to a set of
temporary files, ARCXXYYZ.* (i.e., file
extensions remain the same). A set of sample
files has been provided on the distribution
diskette. The input and output files are
SAMPLE.INP and SAMPLE.OUT, respectively.
Options to retrieve files, save files, and exit
the program
Options to input data and review a list of
case titles
Options to execute cases and browse and
print output
When LWRARC begins, it presents the Files pulldown
menu. The user may scan across the menu bar by using
the left and right arrow keys. The user may select an
option from a pulldown menu by using the up and down
arrow keys. A description of the highlighted option
appears on the bottom line of the screen. To execute the
option, simply press the <Enter> key or the highlighted
letter (known as the "hot key") of the desired option.
The mouse may also be used to select an option by moving
it left or right along the menu bar or up and down on a
pulldown menu. To choose a pulldown menu command,
simply move the mouse cursor over the desired option and
click the left mouse button. Some users may prefer to
"drag" the mouse (holding the left mouse button) over the
menus and then release the left button when the cursor is
over the desired command. One difference between the
two methods of using the mouse is that dragging the
mouse causes the description of the highlighted option
to be displayed on the bottom of the screen as when using
the keyboard.
• Save Input File – LWRARC automatically saves the
input file when cases are executed, so this option
is only needed when a user wants to save the input
file without executing cases. This option is
designed to allow the user to occasionally save
input data while entering a large number of cases,
so that it will not be lost if the program terminates
abnormally.
Note that if LWRARC does fail, the data entered still exist
in the ARCXXYYZ.* files. When LWRARC is
subsequently run, it will notify the user that it has detected
59
NUREG/CR-5625
LWRARC Code
these files and will give him an opportunity to rename and
save them.
letter on the keyboard moves the cursor to the
next choice which begins with that letter. If there
is not a choice that begins with that letter, the
cursor moves to the beginning of the list. The up
and down arrow keys, <PgUp>, <PgDn>, or the
mouse may be used to make a selection. <Home>
moves the cursor to the first choice, and <End>
moves the cursor to the last choice. Once the
desired choice is highlighted, press <Enter> or
double click the left mouse button to select it and
remove the menu.
• Quit – This option terminates the program. If the
input file has not been saved and cases have not
been executed since the user last selected the
Enter Data option, the program verifies that this
is what the user wants to do. Since this option
does not save files, the user may also use this
option to cancel any changes he has made since
the last time the input file was saved or cases were
executed.
The date fields accept dates in the form MM-DDYYYY from 01-01-1900 to 01-01-2065. The
default for the first two digits of the year are "19."
The cursor automatically skips the first two
characters of the year. To modify them, use the
backspace key to delete them and then type the
new values.
• Data – The Data menu provides the user with selections
to enter and review the fuel assembly data.
• Enter Data – This is the only active option other than
Retrieve Files when the user enters the program.
When this option is selected, the fuel assembly
data input screen is displayed. The cursor appears
at the first data field. To move from one field to
the next, press <Enter> or <Tab>. To move
backward to the previous field, press <Shift+Tab>
or <Backspace>. If a field is protected, the cursor
skips that field and moves to the next unprotected
field. The cursor must be at the beginning of the
field for <Backspace> to move to the previous
field, because within a data field it moves back
one space and deletes the previous character. The
user may also change fields with the up and down
arrow keys, but the movement is somewhat erratic
as the cursor skips fields if there is more than one
field per screen line. <Home> moves the cursor
to the beginning of the field, and <End> moves to
the end of the field. The <Ins> and <Del> keys
perform their normal functions for editing a field.
<Ctrl+Home> moves the cursor to the first field
on the screen, and <CTRL+End> moves the
cursor to the last field. <PgUp> and <PgDn>
performs the same respective functions. Most
fields have a help message associated with them.
Pressing <F1> displays the message.
Press <Enter> or <Esc> to remove the message
from the screen.
Pressing <Ctrl+B> while the cursor is in a date
field will blank that field. The data for a case are
saved by pressing <F10> to advance to the next
case, or <F9> to go back to the previous case.
The <Ctrl+D> key combination allows the user to
duplicate a case by changing the case number to
the next available case number. Any unsaved
changes on the screen when <Ctrl+D> is pressed
are not saved for the original case number, but are
carried to the new case number. Thus, the user
may press <Ctrl+D> either before or after making
changes to the old case he wants to copy. Once he
is finished with the changes to the new copy, he
should press <F9> or <F10> to save them. To
avoid saving changes on the screen at any time,
press <F4> to return to the main menu system.
LWRARC asks the user if he wants to save the
changes on the screen before returning.
The <Ctrl+E> key combination erases an
unwanted case. LWRARC verifies that the user
wants to delete the case. To review existing cases,
press <Ctrl+R> to view a list of case numbers and
titles.
The input parameters are described below. The
variable names in parentheses refer to those used
in Sect. 5.
Some fields have a multiple choice menu
associated with them. Pressing <Enter> or the
Space Bar at one of these fields activates the
multiple choice menu. When this menu is
displayed, all other processing and functions keys
are disabled until a choice is selected and the
menu disappears from the screen. Pressing a
NUREG/CR-5625
1. Title – 56-character maximum.
2. Reactor type –BWR or PWR.
60
LWRARC Code
3. Fuel type – Select from the multiple-choice
menu. Based on the fuel assembly type
selected, the code automatically supplies the
generic kilograms of uranium per assembly
for that type (Tables 7.1 and 7.2) in the next
field and protects the field. These generic
values are only typical loadings taken from
Ref. 41. If the user wishes to input a more
exact value for the next parameter, he should
select "Other." LWRARC then unprotects
the next field and allows the user to input his
own value.
14. End of cooling date – used to calculate the
cooling time parameter.
4. Fuel loading – the kgU/assembly is used to
convert the decay heat from watts per kgU
(as given in the tables in Sect. 5.2) to watts
per assembly. Enter 0 if this calculation is
not desired.
18. Cycle N-1 time (Te-1) – next-to-last cycle
time, startup to startup, days.
15. Cooling time (Tc) – time since final
discharge of assembly in years.
16. Total residence time (Tres) – assembly
residence time from first loaded to final
discharge in days.
17. Cycle N time (Te) – last cycle time, startup to
discharge, days.
The date parameters are optional. If they are
input, the code calculates the time
parameters automatically and protects the
time fields. Otherwise, the user inputs the
time parameters. The time and burnup for
the last and next-to-last cycles may be set to
zero if the cooling time is greater than 15
years.
5. Interpolation – Log-linear (duplicates hand
calculation) or Lagrangian42 (typically a
more precise interpolation scheme).
6. Enrichment (Es) – initial fuel enrichment, wt
% 235U.
• Review Cases (Ctrl+R) – This option displays a list
of case numbers and titles for all cases that
have been created. This function may also
be performed by pressing <Ctrl+R> at the
main menu or while entering data. To
remove the list from the screen, press
<Enter> or <Esc>.
7. Total burnup (Btot) – for the assembly,
MWd/kgU or GWd/MTU.
8. Cycle N burnup (Be) – last cycle burnup,
MWd/kgU or GWd/MTU.
9. Cycle N-1 burnup (Be-1) – next-to-last cycle
burnup, MWd/kgU or GWd/MTU.
• Run – The Run menu provides the user with selections
to execute cases and view the output.
10. Initial startup date – cycle startup date for
the initial cycle for this assembly, used to
calculate the total residence time parameter.
• Execute Cases – This option performs the decay heat
calculations based on the entire procedure
given in Sect. 5 for the cases entered. A
message box is displayed when execution is
completed. When cases are executed, the
input file and the output file are saved to the
file name specified by the user.
11. Cycle N-1 startup date – next-to-last cycle
startup date used to calculate the next-to-last
cycle time parameter.
12. Cycle N startup date – Last cycle startup
date, used to calculate the next-to-last and
last cycle time parameters.
• Browse Output File – This option allows the user to
browse the output file generated when the
cases are executed. The top line of the
screen shows the file name and line number.
The bottom line of the screen shows the keys
that may be used to move within the file
while browsing.
13. Final shutdown date – last cycle shutdown
date, used to calculate the last cycle time, the
total residence time, and the cooling time
parameters.
61
NUREG/CR-5625
LWRARC Code
Table 7.1 BWR fuel assembly loadings
Assembly
manufacturer
ANF
ANF
ANF
ANF
ANF
General Electric
General Electric
General Electric
General Electric
General Electric
General Electric
General Electric
General Electric
General Electric
General Electric
General Electric
General Electric
Array
size
7×7
8×8
9×9
8×8
9×9
7×7
7×7
8×8
8×8
8×8
7×7
7×7
7×7
8×8
8×8
8×8
8×8
Class
GE BWR/2,3
GE BWR/2,3
GE BWR/2,3
GE BWR/4-6
GE BWR/4-6
BWR/2,3
BWR/2,3
BWR/2,3
BWR/2,3
BWR/2,3
BWR/4-6
BWR/4-6
BWR/4-6
BWR/4-6
BWR/4-6
BWR/4-6
BWR/4-6
Version
2a
2b
4
5
2
3a
3b
4a
4b
5
Kilograms U
per assembly
184
174
168
177
173
196
193
183
177
176
193
188
190
184
186
183
183
Plant-specific designs
General Electric
ANF
ANF
General Electric
ANF
NUREG/CR-5625
9×9
11 × 11
6×6
6×6
10 × 10
Big Rock Pt.
Big Rock Pt.
Dresden 1
Humboldt Bay
LaCrosse
62
138
132
95
76
108
LWRARC Code
Table 7.2 PWR fuel assembly loadings
General designs
Assembly
manufacturer
ANF
ANF
ANF
ANF
ANF
Babcock & Wilcox
Babcock & Wilcox
Combustion Engineering
Combustion Engineering
Westinghouse
Westinghouse
Westinghouse
Westinghouse
Westinghouse
Westinghouse
Westinghouse
Westinghouse
Array
size
14 × 14
14 × 14
14 × 14
15 × 15
17 × 17
15 × 15
17 × 17
14 × 14
16 × 16
14 × 14
14 × 14
14 × 14
15 × 15
15 × 15
17 × 17
17 × 17
17 × 17
Version
WE
CE
Top Rod
WE
WE
Mark C
Std
Std/LOPAR
OFA
Model C (CE)
Std/LOPAR
OFA
Std/LOPAR
OFA
Vantage 5
Kilograms U
per assembly
379
381
365
432
401
464
456
386
426
389
336
397
456
463
464
426
423
Plant-specific designs
Combustion Engineering
Westinghouse
Babcock & Wilcox
ANF
Combustion Engineering
Combustion Engineering
Westinghouse
ANF
Combustion Engineering
14 × 14
15 × 15
15 × 15
15 × 15
15 × 15
16 × 16
14 × 14
15 × 16
15 × 16
63
Fort Calhoun
Haddam Neck
Haddam Neck
Palisades
Palisades
St. Lucie 2
San Onofre 1
Yankee Rowe
Yankee Rowe
376
413
409
401
413
390
373
236
231
NUREG/CR-5625
LWRARC Code
• Print Output File – This option allows the user to
print the output file. There is one page of
output per case.
The latest LWRARC code version may be requested from
either the Radiation Shielding Information Center (RSIC)
or the Energy Science and Technology Software Center
(ESTSC):
7.3 The LWRARC Code Distribution
Diskette
Radiation Shielding Information Center
Oak Ridge National Laboratory
P.O. Box 2008
Oak Ridge, TN 37831-6362
Telephone: (615) 574-6176
FAX: (615) 574-6182
Files included on the LWRARC distribution diskette are
listed in Table 7.3. LWRARC.EXE is the executable
program. LWRARC.QSL is the screen library. This
library contains all the input screens displayed by
LWRARC. The files with the ".FRM" extension contain
the form definition for each of the screens in the library.
The files with the ".BSV" extension were written with
Microsoft BASIC's BSAVE command and contain the
regulatory guide decay heat data from the tables in Sect.
5.2 and the fuel assembly kgU loadings. In addition to
these files, LWRARC input and output files for the sample
cases in Appendix C are included on the diskette. These
files are SAMPLE.INP and SAMPLE.OUT. The user may
retrieve them in LWRARC.
Energy Science and Technology
Software Center
P.O. Box 1020
Oak Ridge, TN 37831-1020
Telephone: (615) 576-2606
FAX: (615) 576-2865
For inquiries about the latest version date, the user may
contact RSIC or one of the following:
C. V. Parks (615) 574-5280
O. W. Hermann (615) 574-5256
S. M. Bowman (615) 574-5263
No matter how carefully a computer code is written, it is
inevitable that some option combination or set of data
requires modifications or corrections to the code. In order
to be certain that a calculated case was performed with an
approved version of the code, the creation date of the
version used is printed in the case output heading. The
current approved creation date, at the publication time of
this report, is 5/30/94.
Table 7.3 Files required by LWRARC
File name
ARCDATA1
ARCDATA2
ARCDATE1
FUELASSY
LWRARC
LWRARC
RENAMFIL
SAMPLE
SAMPLE
SAVEFIL
SAVEINP
NUREG/CR-5625
Extension
BSV
BSV
FRM
BSV
EXE
QSL
FRM
INP
OUT
FRM
FRM
64
8 SUMMARY
Proper methods of storing spent fuel from nuclear power
plants require knowledge of their decay heat generation
rates. Presently, the NRC has issued the decay heat guide
entitled "Regulatory Guide 3.54, Spent Fuel Heat
Generation in an Independent Spent Fuel Storage
Installation." A significant revision to the heat generation
rate guide will be developed by expanding the data base,
simplifying the procedure, and using improved
computational methods. This report was written to
provide the necessary technical support for a proposed
decay heat guide.
The validation of using SAS2H/ORIGEN-S for computing
heat rates was provided by comparing predicted results
with measurements performed on discharged fuel
assemblies. The fuel was taken from Cooper Nuclear
Station BWR, Point Beach Unit 2 PWR, and Turkey Point
Unit 3 PWR. All design and operating history data for the
20 measured assemblies are tabulated in the report. The
measured and computed results are also listed, along with
the average of all case differences and the average of
differences by assemblies. The average differences of the
calculated minus the measured heat rates of fuel
assemblies were –0.7 ± 2.6% for the BWR and 1.5 ± 1.3%
for the PWR. These comparisons are considered to be
acceptable.
The primary purposes in revising the guide are to use
accurate heat rates that are adjusted with adequate safety
factors and, at the same time, avoid excess conservatism.
There are three reasons that the current guide is overly
conservative. First, the SAS2 calculations used in
producing the guide were conservative because not all of
the moderator (i.e., the water in and surrounding the guide
tubes) was taken into account. Second, the current guide
is conservative because the decay heat data base was
calculated at several burnups but only for one specific
power. Although the power was large enough to envelop
most operating LWR reactors, the use of an excessive
power will decrease the fuel exposure time which, in turn,
increases predicted decay heat rates computed for the
range of the cooling times considered. The final reason
for excess conservatism in the present guide is that no data
base was provided for BWR fuel and a simple conservative
safety factor was applied instead.
The complete procedure to be included in a proposed
regulatory guide is included in Sect. 5. Attention is given
to special definitions of cycle time and specific power. A
total of 720 decay heat rates computed by SAS2H/
ORIGEN-S as a function of the fuel assembly's total
burnup, specific power, cooling time, and reactor type
(BWR or PWR) are tabulated in a data base in Sect. 5.
The interpolation of the heat rate using the specified
values of the above four parameters for the assembly is
then used with any of the required adjustment factors and
the safety factor to determine the final decay heat rate.
A detailed analysis of the proposed procedure for
determining decay heat rates is presented in Sect. 6. The
derivation and/or discussion of each equation of Sect. 5 is
given in sequential order. The definitions of parameters
applied and the reasons behind the use of certain variables
are extensively discussed in order to more clearly explain
why the procedure of the proposed guide revision is
appropriate. Also, the accuracies of both the
interpolations and the adjustment factor equations are
properly analyzed. The formulation of the safety factors is
presented in detail. The discussion and analysis of the
safety factor is separated into several natural divisions:
random data uncertainty, cross-section-dependent error
from both data uncertainty and computational model bias,
procedural guide inaccuracy, extra parameter (i.e., those
not previously applied) variation error, and contingency
error. The report discusses and demonstrates why the
safety factor ranges of 6.4 to 14.9% for the BWR and
6.2–13.2% for the PWR are considered adequate. The
decay time-dependent standard deviations for fission
products and light-element activation products (excluding
cross-section-dependent error) are listed in Table 6.11.
These uncertainties are derived from the standard
deviations in data for the fission-product yields, the
half-lives, and the recoverable energies of the nuclides.
These reasons for excess conservatism will be eliminated
in the proposed guide revision discussed in this report.
The SCALE-4 version of SAS2 (also known as SAS2H)
applies a second pass in the depletion analysis that
simulates water holes or BPRs more correctly and provides
substantially better calculations of isotopic contents. Also,
the channel water in a BWR can be better simulated in the
current SAS2H version. A data base of decay heat is
provided for PWR and BWR fuel by computing cases for
six different burnups at each of three separate specific
powers. Decay heat values at twenty different cooling
times from 1 to 110 years were tabulated for each case. A
prescribed interpolation procedure gives accurate heat
rates over all ranges of burnup, specific power, and
cooling time within the limits of the tabulated data. Also,
adjustments in the interpolated heat rate take into account
variations in the initial 235U enrichment and the short
cooling time effects from having an average power within
a cycle that is different than the average constant power
over all cycles.
65
NUREG/CR-5625
Summary
Also, an extensive discussion of cross-section bias is
summarized in Table 6.13. Finally, the four types of
errors considered in the analysis are summarized, totaled,
and compared with the safety factor equation values in
Tables 6.16 and 6.17.
Plots of the heat rates from dominant nuclides and the
total for all of the tabulated cases in Sect. 5 are shown in
Appendix E. These plots show more completely the major
components to the computed decay heat rates.
Although it was not intended in this study to evaluate
other methods of determining decay heat rates, the
question may be asked concerning other suitable methods.
The authors recognize that there are various other methods
for deriving decay heat rates, at least in part or under
certain conditions. Some of the appropriate codes or
standards for calculating decay heat rates are the
following: ORIGEN2,29 CELL-233 or EPRI-CELL31/
CINDER2,32 KORIGEN,36 the American National
Standard for Decay Heat Power in LWRs39 (ANSI/ANS
5.1-1979), the international decay heat power standard40
(draft ISO/DIS 10645), and SAS2H/ORIGEN-S. Of
course, the use of any proper method requires adequate
safety factors that envelop uncertainties such as those
discussed in Sect. 6.6.
The report also includes a description of LWRARC, a
BASIC PC code for easily applying the revised procedure
presented in Sect. 5. The executable and data files of the
LWRARC code are on the diskette, available at either
RSIC or ESTSC (Sect. 7.3).
Heat generation rate tables listed separately for actinides,
fission products, and light element activation products are
included in Appendix D. These tables are for information
purposes only and would not be used directly in the guide's
method for determining heat rates.
NUREG/CR-5625
66
9 REFERENCES
1.
2.
3.
4.
5.
O. W. Hermann and R. M. Westfall, "ORIGEN-S:
SCALE System Module to Calculate Fuel
Depletion, Actinide Transmutation, Fission
Product Buildup and Decay, and Associated
Radiation Source Terms," as described in Sect. F7
of SCALE: A Modular Code System for
Performing Standardized Computer Analyses for
Licensing Evaluation, NUREG/CR-0200, Rev. 4
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National Laboratory as CCC-545.
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Shielding Information Center at Oak Ridge
National Laboratory as CCC-545.
C. V. Parks, O. W. Hermann, and B. L.
Broadhead, "The SCALE Analysis Sequence for
LWR Fuel Depletion," Proc. of ANS/ENS
International Topical Meeting, Pittsburgh, PA,
April 28-May 1, 1991, pp. 10.2 3.1–10.2 3-14.
See also O. W. Hermann, "SAS2: A Coupled
One-Dimensional Depletion and Shielding
Analysis Module," as described in Sect. S2 of
SCALE: A Modular Code System for Performing
Standardized Computer Analyses for Licensing
Evaluation, NUREG/CR-0200, Rev. 4
(ORNL/NUREG/CSD-2/R4), Vols. I-III (draft
November 1993). Available from Radiation
Shielding Information Center at Oak Ridge
National Laboratory as CCC-545.
SCALE: A Modular Code System for Performing
Standardized Computer Analyses for Licensing
Evaluation, NUREG/CR-0200, Rev. 4
(ORNL/NUREG/CSD-2/R4), Vols. I-III (draft
November 1993). Available from Radiation
Shielding Information Center at Oak Ridge
National Laboratory as CCC-545.
J. C. Ryman et al., Fuel Inventory and Afterheat
Power Studies of Uranium-Fueled Pressurized
Water Reactor Fuel Assemblies Using the SAS2
and ORIGEN-S Modules of SCALE with an
ENDF/B-V Updated Cross Section Library,
NUREG/CR-2397 (ORNL-CSD-90), Union
Carbide Corp., Nucl. Div., Oak Ridge Natl. Lab.,
September 1982.
J. C. Ryman, "ORIGEN-S Data Libraries," as
described in Sect. M6 of SCALE: A Modular
Code System for Performing Standardized
Computer Analyses for Licensing Evaluation,
NUREG/CR-0200, Rev. 4 (ORNL/NUREG/
CSD-2/R4), Vols. I-III (Version 4.0 released
67
6.
The Evaluated Nuclear Data File, Versions IV
and V (ENDF/B-IV and -V), available from and
maintained by the National Nuclear Data Center
at Brookhaven National Laboratory.
7.
W. B. Ewbank et al., Nuclear Structure Data
File: A Manual for Preparation of Data Sets,
ORNL-5054, Union Carbide Corp., Nucl. Div.,
Oak Ridge Natl. Lab., June 1975.
8.
T. R. England et al., Summary of ENDF/B-V Data
for Fission Products and Actinides, EPRI
NP-3787 (LA-UR 83-1285, ENDF-322), Electric
Power Research Institute, December 1984.
9.
W. C. Jordan "SCALE Cross-Section Libraries,"
as described in Sect. M4 of SCALE: A Modular
Code System for Performing Standardized
Computer Analyses for Licensing Evaluation,
NUREG/CR-0200, Rev. 4
(ORNL/NUREG/CSD-2/R4), Vols. I-III (Version
4.0 released February 1990). Available from
Radiation Shielding Information Center at Oak
Ridge National Laboratory as CCC-545.
10.
J. M. Creer and J. W. Shupe, Jr., Development of
a Water-Boiloff Spent Fuel Calorimeter System,
PNL-3434, Pacific Northwest Laboratory, May
1981.
11.
B. F. Judson et al., In-Plant Test Measurements
for Spent Fuel Storage at Morris Operation,
NEDG-24922-3, General Electric Company,
February 1982.
12.
M. A. McKinnon et al., Decay Heat
Measurements and Predictions of BWR Spent
Fuel, EPRI NP-4269, Electric Power Research
Institute, 1985.
13.
F. Schmittroth, G. J. Neely, and J. C. Krogness, A
Comparison of Measured and Calculated Decay
Heat for Spent Fuel Near 2.5 Years Cooling Time,
TC-1759, Hanford Engineering Development
Laboratory, August 1980.
NUREG/CR-5625
References
14.
15.
16.
17.
18.
19.
F. Schmittroth, ORIGEN2 Calculations of PWR
Spent Fuel Decay Heat Compared With
Calorimeter Data, HEDL-TME 83-32, Hanford
Engineering Development Laboratory, January
1984.
24.
J. B. Melehan, Yankee Core Evaluation Program
Final Report, WCAP-3017-6094, Westinghouse
Nuclear Energy Systems, January 1971.
25.
M. A. McKinnon et al., Decay Heat
Measurements and Predictions of BWR Spent
Fuel, EPRI NP-4619, Electric Power Research
Institute, June 1986.
R. W. Rasmussen, D. F. French, and H. T. Sneed,
"Duke Power Spent Fuel Storage and
Transportation Experience," Trans. Am. Nucl.
Soc. 44, 479 (1983).
26.
Point Beach 1 and 2, Section in Nuclear Power
Experience, Plant Descriptions and Histories,
Vol. PWR-1, March 1974.
TN-REG Spent Fuel Package–Safety Analysis
Report for Transport, Document No. E-7451,
Transnuclear, Inc., October 1985.
27.
L. E. Wiles et al., BWR Spent Fuel Storage Cask
Performance Test, PNL-5777, Vol. II, Pacific
Northwest Laboratory, June 1986.
28.
D. C. Kocher, Radioactive Decay Data Tables,
DOE/TIC-11026, U.S. Department of Energy,
1981.
29.
A. G. Croff, ORIGEN2–A Revised and Updated
Version of the Oak Ridge Isotope Generation and
Depletion Code, ORNL-5621, Union Carbide
Corp., Nucl. Div., Oak Ridge Natl. Lab., July
1980.
30.
S. B. Ludwig and J. P. Renier, Standard- and
Extended-Burnup PWR and BWR Reactor Models
for the ORIGEN2 Computer Code,
ORNL/TM-11018, Martin Marietta Energy
Systems, Inc., Oak Ridge Natl. Lab., December
1989.
31.
T. R. England, W. B. Wilson, and M. G.
Stamatelatos, Fission Product Data for Thermal
Reactors, Part 2: User's Manual for
EPRI-CINDER Code and Data, EPRI NP-356,
Part 2 (LA-6746-MS), Electric Power Research
Institute, 1976.
32.
T. R. England, CINDER–A One-Point Depletion
and Fission Product Program, WAPD-TM-334,
Westinghouse Electric Corp., 1962 (Rev. 1964).
33.
M. L. Williams, Validation of CELL-2
Calculations for Predicting the Isotopic Content
of Exposed LWR Fuel, EPRI NP-6440, Electric
Power Research Institute, September 1986.
O. W. Hermann et al., Multicode Comparison of
Selected Source Term Computer Codes,
ORNL/CSD/TM-251, Martin Marietta Energy
Systems, Inc., Oak Ridge Natl. Lab., April 1989.
J. W. Roddy et al., Physical and Decay
Characteristics of Commercial LWR Spent Fuel,
ORNL/TM-9591/V1, Martin Marietta Energy
Systems, Inc., Oak Ridge Natl. Lab., October
1985.
Turkey Point Units 3 and 4, Section in Nuclear
Power Experience, Plant Descriptions and
Histories, Vol. PWR-1, December 1972.
20.
Cooper Nuclear Station, Section in Nuclear
Power Experience, Plant Descriptions and
Histories, Vol. BWR-1, March 1974.
21.
A. G. Croff et al., Revised Uranium-Plutonium
Cycle PWR and BWR Models for the ORIGEN
Computer Code, ORNL/TM-6051, Union Carbide
Corp., Nucl. Div., Oak Ridge Natl. Lab., 1978.
22.
A. T. Luksic, Spent Fuel Assembly Hardware:
Characterization and 10 CFR 61 Classification
for Waste Disposal, Pacific Northwest Laboratory,
PNL-6906, Vol. I, June 1989.
23.
S. P. Cerne, O. W. Hermann, and R. M. Westfall,
Reactivity and Isotopic Composition of Spent
PWR Fuel as a Function of Initial Enrichment,
Burnup, and Cooling Time, ORNL/CSD/TM-244,
Martin Marietta Energy Systems, Inc., Oak Ridge
Natl. Lab., October 1987.
NUREG/CR-5625
68
References
34.
35.
36.
37.
F. J. Sweeney and J. P. Renier, Sensitivity of
Detecting In-Core Vibrations and Boiling in
Pressurized Water Reactors Using Ex-Core
Neutron Detectors, NUREG/CR-2996
(ORNL/TM-8549), Martin Marietta Energy
Systems, Inc., Oak Ridge Natl. Lab., July 1984.
C. V. Parks, Summary Description of the SCALE
Modular Code System, NUREG/CR-5033
(ORNL/CSD/TM-252), Martin Marietta Energy
Systems, Inc., Oak Ridge Natl. Lab., December
1987.
U. Fischer and H. W. Wiese, Improved and
Consistent Determination of the Nuclear
Inventory of Spent PWR Fuel on the Basis of
Cell-Burnup Methods Using KORIGEN, KFK
3014 (ORNL-tr-5043), Karlsruhe Nuclear
Research Center, Federal Republic of Germany
(January 1983). Available from Radiation
Shielding Information Center at Oak Ridge
National Laboratory as CCC-457.
B. L. Broadhead, Feasibility Assessment of
Burnup Credit in the Criticality Analysis of
Shipping Casks with Boiling Water Reactor Spent
Fuel, ORNL/CSD/TM-268, Martin Marietta
Energy Systems, Inc., Oak Ridge Natl. Lab.,
August 1991.
69
38.
B. Duchemin and C. Nordborg, DECAY HEAT
CALCULATION An International Nuclear Code
Comparison, Nuclear Energy Agency Report
NEACRP-319"L," NEANDC-275"U," 1989.
39.
American National Standard for Decay Heat
Power in Light Water Reactors,
ANSI/ANS-5.1-1979, American Nuclear Society,
1979.
40.
Nuclear Energy–Light Water
Reactors–Calculation of the Decay Heat Power in
Nuclear Fuels, ISO/DIS 10645, Draft of an
International Standard, International
Organization for Standardization, May 1990.
41.
Characteristics of Potential Repository Wastes –
Appendix 2A. Physical Descriptions of LWR Fuel
Assemblies, DOE/RW-0184-R1, U.S. Department
of Energy, July 1990.
42.
F. D. Hammerling, DLAG–Lagrangian
Interpolation for Function of Two Variables,
Chapter I The Computing Technology Center
Numerical Analysis Library, G. W. Westley and
J. A. Watts, Eds., CTC-39, Union Carbide Corp.,
Nucl. Div., October 1970.
NUREG/CR-5625
References
NUREG/CR-5625
70
APPENDIX A
DATA AND SAMPLE INPUT TO TABULATED CASES
Table A.1 BWR assembly design description for tabulated cases
Parameter
Data
Assembly general data
Designer
Lattice
Type
Water temperature, K
Water vol-avg density, g-cm3
Number of fuel rods
Number of holes
Burnable poison element
Number containing poison
Poison content as wt % Gd2O3
Assembly pitch, cm (in.)
Shroud (tube) thickness, cm (in.)
Shroud outside flat-to-flat, cm (in.)
Shroud material
Shroud temperature, K
Channel water density, g-cm-3
Channel water temperature, K
Channel avg 10B content,c atoms/b-cm
General Electric
8×8
Burnable poison
558
0.4323
63
1
Gd as Gd2O3
4
0.8–4.8a
15.24 (6.0)
0.3048 (0.12)
13.40 (5.275)
Zircaloy
558
0.669b
552
7.15 × 10-6
Fuel rod data
Type fuel pellet
Pellet stack density, g-cm-3
Rod pitch, cm (in.)
Rod OD, cm (in.)
Rod ID, cm (in.)
Active fuel length, cm (in.)
Effective fuel temperature, K
Clad temperature, K
Clad materiale
UO2d
9.871
1.6256 (0.640)
1.25222 (0.493)
1.0795 (0.425)
375.9 (148)
840
620
Zircaloy
a
Changed Gd2O3 content linearly with burnup over this range.
Reduced the 0.743 g-cm-3 bottom node density17 by 10% to account for control rod displacement.
c
Applied in channel region for boron cruciform; used content producing average keff of approximately unity.
d
The uranium isotopes were determined from Tables 5.4 and 3.12.
e
Clad and other light-element data except for Gd were determined from Table 3.11.
b
71
NUREG/CR-5625
Appendix A
Table A.2 PWR assembly design description for tabulated cases
Parameter
Data
Assembly general data
Designer
Lattice
Water temperature, K
Water density, g-cm-3
Soluble boron, cycle avg, ppm (wt)
Number of fuel rods
Number of guide tubes
Number of instrument tubes
Westinghouse
17 × 17
570
0.7295
550
264
24
1
Fuel rod data
Type fuel pellet
Pellet stack density, % TD
Rod pitch, cm (in.)
Rod OD, cm (in.)
Rod ID, cm (in.)
Pellet diameter, cm (in.)
Active fuel length, cm (in.)
Effective fuel temperature, K
Clad temperature, K
Clad materialb
UO2a
94.5
1.25984 (0.496)
0.94966 (0.374)
0.83566 (0.329)
0.81915 (0.3225)
365.8 (144)
811
620
Zircaloy
Guide tube datac
Inner radius, cm (ID, as in.)
Outer radius, cm (OD, as in.)
Tube material
0.5715 (0.45)
0.61214 (0.482)
Zircaloy
a
The uranium isotopes were determined from Tables 5.8 and 3.12.
Clad and other light-element data were determined from Table 3.11.
c
Control rods were considered to be withdrawn during reactor uptime.
b
NUREG/CR-5625
72
Appendix A
Table A.3 Operating history data and fuel isotopic content of BWR cases
Specific
Burnup,
power,
MWd/kgU kW/kgU
20
25
30
35
40
45
20
25
30
35
40
45
20
25
30
35
40
45
12
12
12
12
12
12
20
20
20
20
20
20
30
30
30
30
30
30
Cycles
per case
3
3
4
4
5
5
3
3
4
4
5
5
3
3
4
4
5
5
Cycle time, d
Uptime Downtime
555.55
694.44
625.00
729.17
666.67
750.00
333.33
416.67
375.00
437.50
400.00
450.00
222.22
277.78
250.00
291.67
266.67
300.00
138.89
173.61
156.25
182.29
166.67
187.50
83.33
104.17
93.75
109.37
100.00
112.50
55.56
69.44
62.50
72.92
66.67
75.00
234
U
0.017
0.020
0.024
0.028
0.030
0.034
0.017
0.020
0.024
0.028
0.030
0.034
0.017
0.020
0.024
0.028
0.030
0.034
U-isotopic content, wt %
235
236
U
U
1.900
2.300
2.700
3.100
3.400
3.800
1.900
2.300
2.700
3.100
3.400
3.800
1.900
2.300
2.700
3.100
3.400
3.800
0.009
0.011
0.012
0.014
0.016
0.017
0.009
0.011
0.012
0.014
0.016
0.017
0.009
0.011
0.012
0.014
0.016
0.017
238
U
98.074
97.669
97.264
96.858
96.554
96.149
98.074
97.669
97.264
96.858
96.554
96.149
98.074
97.669
97.264
96.858
96.554
96.149
Table A.4 Operating history data and fuel isotopic content of PWR cases
Specific
Burnup,
power,
MWd/kgU kW/kgU
25
30
35
40
45
50
25
30
35
40
45
50
25
30
35
40
45
50
18
18
18
18
18
18
28
28
28
28
28
28
40
40
40
40
40
40
Cycles
per case
3
3
4
4
5
5
3
3
4
4
5
5
3
3
4
4
5
5
Cycle time, d
Uptime Downtime
462.96
555.56
486.11
555.56
500.00
555.56
297.62
357.14
312.50
357.14
321.43
357.14
208.33
250.00
218.75
250.00
225.00
250.00
115.74
138.89
121.53
138.89
125.00
138.89
74.40
89.29
78.12
89.29
80.36
89.29
52.08
62.50
54.69
62.50
56.25
62.50
73
234
U
0.021
0.024
0.028
0.032
0.034
0.037
0.021
0.024
0.028
0.032
0.034
0.037
0.021
0.024
0.028
0.032
0.034
0.037
U-isotopic content, wt %
235
236
U
U
2.400
2.800
3.200
3.600
3.900
4.200
2.400
2.800
3.200
3.600
3.900
4.200
2.400
2.800
3.200
3.600
3.900
4.200
0.011
0.012
0.014
0.016
0.017
0.019
0.011
0.012
0.014
0.016
0.017
0.019
0.011
0.012
0.014
0.016
0.017
0.019
238
U
97.568
97.164
96.758
96.352
96.049
95.744
97.568
97.164
96.758
96.352
96.049
95.744
97.568
97.164
96.758
96.352
96.049
95.744
NUREG/CR-5625
Appendix A
The following is the entire input for the 12-kW/kgU,
20-MWd/kgU BWR case using SAS2H to generate
the burnup-dependent cross-section libraries,
ORIGEN-S to provide detailed decay heat rate
tables, and PLORIGEN to plot selected results.
=SAS2
PARM='HALT03,SKIPSHIPDATA'
BWR 12 KW/KGU 20 MWD/KGU, NRC SPENT-FUEL HEAT RATE REG-GUIDE 3.54, 1990
'
' - - - - - - - - - - - - - - - - - - - - - - - - - - - - - '
'
MIXTURES OF FUEL-PIN-UNIT-CELL:
'
27BURNUPLIB
LATTICECELL
UO2 1 DEN=9.871 1 840
92234 0.017 92235 1.900 92236 0.009 92238 98.074 END
'HOT-DEN=10.96(THE THEOR.-DEN)*0.94(%-TD)*(.416/.425)**2 COLD/HOT DIAM
CO-59 3 0 1-20 558 END
ZR-94 1 0 1-20 840 END
TC-99 1 0 1-20 840 END
RU-106 1 0 1-20 840 END
RH-103 1 0 1-20 840 END
RH-105 1 0 1-20 840 END
XE-131 1 0 1-20 840 END
CS-134 1 0 1-20 840 END
CE-144 1 0 1-20 840 END
PR-143 1 0 1-20 840 END
ND-143 1 0 1-20 840 END
ND-145 1 0 1-20 840 END
ND-147 1 0 1-20 840 END
PM-147 1 0 1-20 840 END
SM-149 1 0 1-20 840 END
SM-151 1 0 1-20 840 END
SM-152 1 0 1-20 840 END
EU-153 1 0 1-20 840 END
EU-154 1 0 1-20 840 END
EU-155 1 0 1-20 840 END
ZIRCALLOY 2 1 620
END
H2O 3 DEN=0.4323 1 558 END
'
'
' - - - - - - - - - - - - - - - - - - - - - - - - - - - - - '
'
MIXTURES OF LARGER-UNIT-CELL:
'
UO2 9 DEN=9.871 1 840
92234 0.017 92235 1.900 92236 0.009 92238 98.074 END
ARBM-GDBURN 9.871 7 0 1 1
64154 2.18 64155 14.80 64156 20.47
64157 15.65 64158 24.84 64160 21.86
8016 150.0 9 0.008 840 END
'
....ABOVE IS 0.8 WT % GADOLINIUM (AS GD2-OX3) IN THE
'
BURNABLE POISON PINS OF BWR ASSEMBLY....
ZIRCALLOY 10 1 588 END
'
....ABOVE IS ZIRCALLOY CASING AROUND ASSEMBLY
B-10
11 0 7.15-6 552 END
H2O
11 0.669 552 END
'
....ABOVE IS CHANNEL MODERATOR AT HIGHER DENSITY
END COMP
'
' - - - - - - - - - - - - - - - - - - - - - - - - - - - - - '
'
FUEL-PIN-CELL GEOMETRY:
'
SQUAREPITCH
1.6256 1.0795 1 3 1.25222 2 END
'
' - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
NUREG/CR-5625
74
Appendix A
'
'
ASSEMBLY AND CYCLE PARAMETERS:
'
NPIN/ASSM=63 FUELNGHT=1993.26 NCYCLES=3 NLIB/CYC=1
PRINTLEVEL=4 LIGHTEL=10 INPLEVEL=2 NUMZONES=6
END
9 0.53975 2 0.62611 3 0.91715 500 3.6398 10 3.8103 11 4.3261
'
..THESE MIXTURES & RADII PLACE GADOLINIUM PIN AT CENTER
'
OF 1/4 OF ASSEMBLY FUEL, CASING & CHANNEL MOD.
'(COMMENT) POWER=12
BURN=555.55 DOWN=DDDDDD
END
'(COMMENT) POWER=12
BURN=555.55 DOWN=DDDDDD
END
POWER=12
BURN=555.55 DOWN=138.89
END
POWER=12
BURN=555.55 DOWN=138.89
END
POWER=12
BURN=555.55 DOWN=3652.5
END
H 16.4 B 0.068
O 265 CR 2.4 MN 0.15
FE 6.6 CO 0.024 NI 2.4
ZR 516 SN 8.7
'
' - - - - - - - - - - - - - - - - - - - - - - - - - - - - - '
END
=ORIGENS
0$$ 58 A3 57 A11 19 E 1T
NRC REGULATORY GUIDE 3.54 HEAT RATE PROJECT, O. W. HERMANN 1989-90
54$$ 2 E 3$$ 33 0 1
A16 2 E 2T
4T
56$$ 10 A5 10 3 A9 1 A13 15 4 3 0 4 1 E 57** A3 10 0.33333 E 5T
NRC REGULATORY GUIDE 3.54 HEAT RATE PROJECT, O. W. HERMANN 1989-90
1000 KG U LOADED
58** 4R12 1-22 0 4R12
60** 8I69.444 694.44
66$$ A1 2 A5 2 E 76$$ 50100 77** 0.5963E-07 78$$ 1
73$$ 922340 922350 922360 922380 640000
10000 50000 80000 240000 250000
260000 270000 280000 400000 500000
74** 0.017+4 1.900+4 0.009+4 98.074+4 0.50000+3
16.4+3 0.068+3 265+3 2.4+3 0.15+3
6.6+3 0.024+3 2.4+3 516+3 8.7+3
75$$ 4R2 11R4 6T
NRC REGULATORY GUIDE 3.54 HEAT RATE PROJECT, O. W. HERMANN 1989-90
'
'
' COMMENT SPACES OVER -2ND SUBCASE OF CYC-5 CASES
'
'
'
'
'
3$$ 34 0 1
E 2T
4T
56$$ 10 A5 10 3 A9 1 10 A17 4 1 E 57** A3 10 0.33333 E 5T
44** A15 1.248 E
58** 4R12 0 4R12 1-22
60** 8I69.444 694.44
66$$ A1 2 A5 2 E 76$$ 50100 77** 0.6095E-07 78$$ 1 6T
NRC REGULATORY GUIDE 3.54 HEAT RATE PROJECT, O. W. HERMANN 1989-90
'
'
' COMMENT SPACES OVER 4RTH SUBCASE OF CYC-5 CASES
'
'
'
'
'
3$$ 35 0 1
E 2T
4T
56$$ 10 A5 10 A9 1 10 A17 4 1 E 57** A3 10 0.33333 E 5T
75
NUREG/CR-5625
Appendix A
44** A15 1.248 E
58** F12
60** 8I61.728 555.55
66$$ A1 2 A5 2 E 76$$ 50100 77** 0.6583E-07 78$$ 1 6T
56$$ A5 5 A10 -10 A14 5 3 57 4 E 54$$ A6 12 0 1 E 5T
HEAT RATE OF 12KW-20MWD/KGU BWR SPENT FUEL
1 KILOGRAM U (AS LOADED)
61** F0.01 65$$ A12 1 A33 1 A54 1 E 79** F1-3
60** 1 1.4 2 2.8 4
5 7 10 15 20 6T
56$$ 0 -10 A10 1 E 5T
56$$ A5 3 A10 10 A14 5 2 57 4 E 57** 20 E 5T
1 KILOGRAM U (AS LOADED)
61** F0.001 65$$ A12 1 A33 1 A54 1 E
60** 25 7I 30 110 6T
56$$ 0 -10 A10 1 E 5T
56$$ F0 5T
END
=PLORIGEN
PLOTDEF=NO
NUMUNIT=19
NPRINT=58
NCOMP=15 MINPOS=1 MAXP=20
TYXAXIS=TLOG XHEAD=TIME SINCE DISCHARGED, YEARS
YHEADING=CURIES / KG URANIUM LOADED
TITLE=SPENT-FUEL RADIOACTIVITY / KGU
TMIN=1 TMAX=110 END
PLOTDEF=NO
NUMUNIT=19
NCOMP=15 TYPLOT=TOTWATTS
TYXAXIS=TLOG XHEAD=TIME SINCE DISCHARGED, YEARS
YHEADING=WATTS / KG URANIUM LOADED
MINPOS=1 MAXP=20 TITLE=12KW-20MWD/KGU BWR FUEL AFTERHEAT
TMIN=1 TMAX=30 NPRINT=58
END
END
NUREG/CR-5625
76
Appendix A
The following is the entire input for the 18-kW/kgU,
25-MWd/kgU PWR case using SAS2H to generate
the burnup-dependent cross-section libraries,
ORIGEN-S to provide detailed decay heat rate
tables, and PLORIGEN to plot selected results.
=SAS2
PARM='HALT03,SKIPSHIPDATA'
PWR 18 KW/KGU 25 MWD/KGU, NRC SPENT-FUEL HEAT RATE REG-GUIDE 3.54, 1990
'
' - - - - - - - - - - - - - - - - - - - - - - - - - - - - - '
'
MIXTURES OF FUEL-PIN-UNIT-CELL:
'
27BURNUPLIB
LATTICECELL
UO2 1 0.945 811 92234 0.021 92235 2.4 92236 0.011 92238 97.568 END
CO-59 3 0 1-20 570 END
ZR-94 1 0 1-20 811 END
TC-99 1 0 1-20 811 END
RU-106 1 0 1-20 811 END
RH-103 1 0 1-20 811 END
RH-105 1 0 1-20 811 END
XE-131 1 0 1-20 811 END
CS-134 1 0 1-20 811 END
CE-144 1 0 1-20 811 END
PR-143 1 0 1-20 811 END
ND-143 1 0 1-20 811 END
ND-145 1 0 1-20 811 END
ND-147 1 0 1-20 811 END
PM-147 1 0 1-20 811 END
SM-149 1 0 1-20 811 END
SM-151 1 0 1-20 811 END
SM-152 1 0 1-20 811 END
EU-153 1 0 1-20 811 END
EU-154 1 0 1-20 811 END
EU-155 1 0 1-20 811 END
ZIRCALLOY 2 1 620
END
H2O 3 DEN=0.7295 1 570 END
ARBM-BORMOD 0.7295 1 1 0 0 5000 100 3 550.0E-6 570 END
'
' 550 PPM BORON (WT) IN MODERATOR
' - - - - - - - - - - - - - - - - - - - - - - - - - - - - - END COMP
'
' - - - - - - - - - - - - - - - - - - - - - - - - - - - - - '
'
FUEL-PIN-CELL GEOMETRY:
'
SQUAREPITCH
1.25984 0.81915 1 3 0.94966 2 0.83566 0 END
'
' - - - - - - - - - - - - - - - - - - - - - - - - - - - - - '
'
ASSEMBLY AND CYCLE PARAMETERS:
'
NPIN/ASSM=264 FUELNGHT=787.28 NCYCLES=3 NLIB/CYC=1
PRINTLEVEL=4 LIGHTEL=9 INPLEVEL=1 ORTUBE=0.61214 SRTUBE=0.5715
NUMINSTR=1 END
POWER=18 BURN=462.96 DOWN=115.74
END
POWER=18 BURN=462.96 DOWN=115.74
END
POWER=18 BURN=462.96 DOWN=3652.5
END
O 135 CR 5.9 MN 0.33
FE 13. CO 0.075 NI 9.9
ZR 221 NB 0.71 SN 3.6
'
' - - - - - - - - - - - - - - - - - - - - - - - - - - - - - '
END
77
NUREG/CR-5625
Appendix A
=ORIGENS
0$$ 58 A3 57 A11 19 E 1T
NRC REGULATORY GUIDE 3.54 HEAT RATE PROJECT, O. W. HERMANN 1989-90
3$$ 33 0 1 A5 58 A16 2 E 2T
4T
56$$ 10 A5 10 3 A13 13 4 3 0 4 1 E 57** A3 10 0.333333 E 5T
NRC REGULATORY GUIDE 3.54 HEAT RATE PROJECT, O. W. HERMANN 1989-90
1000 KG U LOADED
58** 4R18 1-22 0 4R18
60** 8I57.870 578.70
66$$ A1 2 A5 2 E
73$$ 922340 922350 922360 922380
80000 240000 250000 260000 270000 280000
400000 410000 500000
74** 0.021+4 2.400+4 0.011+4 97.568+4
135+3 5.9+3 0.33+3 13+3 75 9.9+3 221+3 0.71+3 3.6+3
75$$ 4R2 9R4 6T
NRC REGULATORY GUIDE 3.54 HEAT RATE PROJECT, O. W. HERMANN 1989-90
3$$ 34 0 1 A5 58 E 2T
4T
56$$ 10 A5 10 3 A10 10 A17 4 1 E 57** A3 10 0.333333 E 5T
58** 4R18 0 4R18 1-22
60** 8I57.870 578.70
66$$ A1 2 A5 2 E 6T
NRC REGULATORY GUIDE 3.54 HEAT RATE PROJECT, O. W. HERMANN 1989-90
3$$ 35 0 1 A5 58 E 2T
4T
56$$ 10 A5 10 A10 10 A17 4 1 E 57** A3 10 0.333333 E 5T
58** F18
60** 8I51.440 462.96
66$$ A1 2 A5 2 E 6T
56$$ A5 5 A10 -10 A14 5 3 57 4 E 54$$ A6 12 0 1 E 5T
HEAT RATE OF 18KW-25MWD/KGU PWR SPENT FUEL
1 KILOGRAM U (AS LOADED)
61** F0.01 65$$ A12 1 A33 1 A54 1 E 79** F1-3
60** 1 1.4 2 2.8 4
5 7 10 15 20 6T
56$$ 0 -10 A10 1 E 5T
56$$ A5 3 A10 10 A14 5 2 57 4 E 57** 20 E 5T
1 KILOGRAM U (AS LOADED)
61** F0.001 65$$ A12 1 A33 1 A54 1 E
60** 25 7I 30 110 6T
56$$ 0 -10 A10 1 E 5T
56$$ F0 5T
END
=PLORIGEN
PLOTDEF=NO
NUMUNIT=19
NPRINT=58
NCOMP=15 MINPOS=1 MAXP=20
TYXAXIS=TLOG XHEAD=TIME SINCE DISCHARGED, YEARS
YHEADING=CURIES / KG URANIUM LOADED
TITLE=SPENT-FUEL RADIOACTIVITY / KGU
TMIN=1 TMAX=110 END
PLOTDEF=NO
NUMUNIT=19
NCOMP=15 TYPLOT=TOTWATTS
TYXAXIS=TLOG XHEAD=TIME SINCE DISCHARGED, YEARS
YHEADING=WATTS / KG URANIUM LOADED
MINPOS=1 MAXP=20 TITLE=18KW-25MWD/KGU PWR FUEL AFTERHEAT
TMIN=1 TMAX=30 NPRINT=58
END
END
NUREG/CR-5625
78
APPENDIX B
SAMPLE CASE USING HEAT GENERATION RATE TABLES
A BWR fuel assembly with an average fuel enrichment of
2.6 wt % 235U was in the reactor for four cycles.
Determine its final heat generation rate with safety factors,
using the method in the guide, at 4.2 years after discharge.
Adequate details of the operating history associated with
the fuel assembly are shown in Table B.1.
Relative Time from startup of fuel, days Accumulated burnup
fuel
(best maximum estimate),
cycle Cycle startup Cycle shutdown
MWd/kgU
0
340
630
940
300
590
910
1240
Pave = 26,300/[300 + 0.8 (940)] = 25.00 kW/kgU.
Using Sect. 5.2
Now, ptab should be determined from Pave , Btot , and Tc , as
described in Sect. 5.2.1. First, select the nearest heat rate
values in Tables 5.1 and 5.2 for the following limits:
Table B.1 Sample case operating history
1
2
3
4
Pave,e-1 = 20,900/[0.8(940)] = 27.793 kW/kgU,
PL = 20 # Pave # PH = 30,
BL = 25 # Btot # BH = 30,
8.1
14.7
20.9
26.3
TL = 4 # Tc # TH = 5.
Next, use the prescribed interpolation procedure for
computing ptab from the tabular data. Although the order
is optional, the example here interpolates between specific
powers, burnups, and, then, cooling times. Denote the
heat rate, p, as a function of specific power, burnup, and
cooling time by p(P,B,T). Then, the table values at PL and
PH for BL and TL are
Note that the output of the LWRARC code for this case is
shown in the first case of Appendix C.
Using Sect. 5.1:
The following were given in the sample case (see Sect. 5.1
for definitions):
p(PL , BL , TL ) = p(20,25,4) = 1.549,
p(PH , BL , TL ) = p(30,25,4) = 1.705.
Tres = 1240 d,
First, interpolate the above heat rates to Pave using
Btot = 26.30 MWd/kgU,
Tc = 4.2 y,
p(Pave ,25,4) = p(20,25,4) + Fp [p(30,25,4) - p(20,25,4)],
Es = 2.6 wt % 235U.
where
Fp = (Pave – PL )/(PH –PL ) = 0.5.
Compute Te , Be , Pe , Te-1 , Pe-1 , and Pave from Sect. 5.1 and
Eqs. (2) through (4):
The result at p(Pave ,25,4) is
Te = 1240 – 940 = 300 d,
p(Pave ,25,4) = 1.549 + 0.5 (1.705 – 1.549) = 1.627.
Be = 26,300 – 20,900 = 5,400 kWd/kgU,
The other three values at Pave are computed with a similar
method:
Pe = (26,300 – 20,900)/300 = 18.00 kW/kgU,
Te-1 = 940 – 630 = 310 d,
p(Pave ,30,4) = 1.827 + 0.5 (2.016 – 1.827) = 1.9215,
Be-1 = 20,900 – 14,700 = 6,200 kWd/kgU,
p(Pave ,25,5) = 1.293,
Pe-1 = 6,200/[0.8(310)] = 25.0 kW/kgU,
p(Pave ,30,5) = 1.553.
79
NUREG/CR-5625
Appendix B
These are heat rates at the burnup and time limits.
RN = Pe-1 /Pave,e-1 – 1 = –0.1005,
Second, interpolate each of the above pairs of heat rates to
Btot from the values at BL and BH :
fN7 = 1 + [0.08(–0.1005)]/4.2 = 0.998.
FB
Since Pave < PH = Pmax , the excess power factor, fp , is
unity. Interpolating Table 5.4 enrichments to obtain the
enrichment associated with the burnup yields
= (Btot – BL )/(BH – BL ) = 0.26,
p(Pave ,Btot ,4) = 1.627 + 0.26 (1.9215 – 1.627)
= 1.7036,
Etab = 2.3 + (2.7 – 2.3)(26.3 – 25)/(30 - 25) = 2.404.
p(Pave ,Btot ,5) = 1.3606.
The enrichment factor fe is then calculated using Eq. (15):
Third, compute the heat rate at Tc from the above values at
TL and TH by an interpolation that is logarithmic in heat
rate and linear in time:
FT
fe = 1 + 0.01 (8.376)(1 – 2.6/2.404) = 0.993,
because Es > Etab .
= (Tc –TL )/(TH –TL ) = 0.2
The safety factor, S, for a BWR is given in Eq. (16):
log[p(Pave ,Btot ,Tc )] = log 1.7036 + 0.2 (log 1.3606 –
log 1.7036)
= 0.2118.
S = 6.4 + 0.15 (26.3 – 20) + 0.044 (4.2 – 1) = 7.49%.
ptab = p(Pave ,Btot ,Tc )
Then, using Eq. (18),
pfinal = (1 + 0.01 S) f7 fN7 fp fe ptab ,
= 100.2118 = 1.629 W/kgU.
With the value for ptab , the formulae of Sects. 5.2.2– 5.2.6
can be used to determine pfinal . Since Tc < 7 y, use Eqs. (8)
through (11) to calculate the short cooling time factors:
R = Pe /Pave – 1 = (18/25) – 1 = – 0.28,
pfinal = 1.0749 × 0.983 × 0.998 × 1 × 0.993 × 1.629
= 1.0749 × 1.587 = 1.706 W/kgU.
f7 = 1 + [0.25(-0.28)]/4.2 = 0.983,
NUREG/CR-5625
with the above adjustment factors and ptab yields
Thus, the final heat generation rate, including the safety
factor, of the given fuel assembly is 1.706 W/kgU.
80
APPENDIX C
LWRARC CODE SAMPLE RESULTS
***************************************************
*
*
* HEAT GENERATION RATE OF BWR SPENT-FUEL ASSEMBLY *
*
(PERTAINING TO USNRC GUIDE 3.54)
*
*
LWRARC CODE CREATION DATE : 05/30/94
*
*
*
***************************************************
TITLE: REG GUIDE SAMPLE CASE FOR BWR - AS HAND CALC.
.ASSEMBLY INPUT DESCRIPTION.
______________________________________________________________________
PARAMETER
DATA, UNITS
DEFINITION, IN GUIDE
E(S)
2.600 WT-% U-235
INITIAL FUEL ENRICHMENT
KGU(S)
0.000 KGU/ASSY
ASSEMBLY FUEL LOADING
T(C)
4.200 YEARS
ASSEMBLY COOLING TIME
B(TOT)
26.300 MWD/KGU
BURNUP, BEST MAXIMUM ESTIMATE
T(RES) 1240.000 DAYS
ASSEMBLY RESIDENCE TIME IN REACTOR
T(E)
300.000 DAYS
LAST CYCLE TIME, STARTUP-DISCHARGE
B(E)
5.400 MWD/KGU
LAST CYCLE BURNUP
T(E-1)
310.000 DAYS
NEXT-TO-LAST-CYC TIME, STARTUP-STARTUP
B(E-1)
6.200 MWD/KGU
NEXT-TO-LAST-CYCLE BURNUP
______________________________________________________________________
.CORRECTION FACTORS COMPUTED.
______________________________________________________________________
F(P)
1.000
EXCESS POWER ADJUSTMENT
F(E)
0.993
INITIAL U-235 ENRICHMENT CORRECTION
F(7)
0.983
LAST CYCLE HISTORY CORRECTION
F-PRIME(7)
0.998
NEXT-TO-LAST-CYC HISTORY CORRECTION
F-SAFE
1.075
SAFETY FACTOR APPLIED TO RESULT
______________________________________________________________________
*CASE DUPLICATES HAND COMPUTATION OF GUIDE.
.HEAT GENERATION RESULTS, W/KGU.
__________________________________________________
AFTER TABLE INTERPOLATION
1.629
AFTER ALL CORRECTIONS EXCEPT SAFETY FACTOR
1.588
AFTER SAFETY FACTOR INCLUDED
1.706
__________________________________________________
--- FINAL HEAT GENERATION RATE IS
1.706 WATTS PER KILOGRAM U LOADED
81
NUREG/CR-5625
Appendix C
***************************************************
*
*
* HEAT GENERATION RATE OF PWR SPENT-FUEL ASSEMBLY *
*
(PERTAINING TO USNRC GUIDE 3.54)
*
*
LWRARC CODE CREATION DATE : 05/30/94
*
*
*
***************************************************
TITLE: TRES=1944, T(E)=556, BU=30.001, T(C)=10.01, 2.8 WT%
.ASSEMBLY INPUT DESCRIPTION.
______________________________________________________________________
PARAMETER
DATA, UNITS
DEFINITION, IN GUIDE
E(S)
2.800 WT-% U-235
INITIAL FUEL ENRICHMENT
KGU(S)
0.000 KGU/ASSY
ASSEMBLY FUEL LOADING
T(C)
10.010 YEARS
ASSEMBLY COOLING TIME
B(TOT)
30.001 MWD/KGU
BURNUP, BEST MAXIMUM ESTIMATE
T(RES) 1944.000 DAYS
ASSEMBLY RESIDENCE TIME IN REACTOR
T(E)
556.000 DAYS
LAST CYCLE TIME, STARTUP-DISCHARGE
B(E)
10.000 MWD/KGU
LAST CYCLE BURNUP
T(E-1)
694.000 DAYS
NEXT-TO-LAST-CYC TIME, STARTUP-STARTUP
B(E-1)
10.000 MWD/KGU
NEXT-TO-LAST-CYCLE BURNUP
______________________________________________________________________
.CORRECTION FACTORS COMPUTED.
______________________________________________________________________
F(P)
1.000
EXCESS POWER ADJUSTMENT
F(E)
1.000
INITIAL U-235 ENRICHMENT CORRECTION
F(7)
1.000
LAST CYCLE HISTORY CORRECTION
F-PRIME(7)
1.000
NEXT-TO-LAST-CYC HISTORY CORRECTION
F-SAFE
1.070
SAFETY FACTOR APPLIED TO RESULT
______________________________________________________________________
*CASE DUPLICATES HAND COMPUTATION OF GUIDE.
.HEAT GENERATION RESULTS, W/KGU.
__________________________________________________
AFTER TABLE INTERPOLATION
1.044
AFTER ALL CORRECTIONS EXCEPT SAFETY FACTOR
1.044
AFTER SAFETY FACTOR INCLUDED
1.116
__________________________________________________
--- FINAL HEAT GENERATION RATE IS
NUREG/CR-5625
1.116 WATTS PER KILOGRAM U LOADED
82
Appendix C
***************************************************
*
*
* HEAT GENERATION RATE OF PWR SPENT-FUEL ASSEMBLY *
*
(PERTAINING TO USNRC GUIDE 3.54)
*
*
LWRARC CODE CREATION DATE : 05/30/94
*
*
*
***************************************************
TITLE: POINT BEACH 2, ASSY C-52, DECAY HEAT=723.5 W/ASSY MEAS
.ASSEMBLY INPUT DESCRIPTION.
______________________________________________________________________
PARAMETER
DATA, UNITS
DEFINITION, IN GUIDE
E(S)
3.397 WT-% U-235
INITIAL FUEL ENRICHMENT
KGU(S)
386.000 KGU/ASSY
ASSEMBLY FUEL LOADING
T(C)
4.476 YEARS
ASSEMBLY COOLING TIME
B(TOT)
31.914 MWD/KGU
BURNUP, BEST MAXIMUM ESTIMATE
T(RES) 1675.000 DAYS
ASSEMBLY RESIDENCE TIME IN REACTOR
T(E)
339.000 DAYS
LAST CYCLE TIME, STARTUP-DISCHARGE
B(E)
8.797 MWD/KGU
LAST CYCLE BURNUP
T(E-1)
465.000 DAYS
NEXT-TO-LAST-CYC TIME, STARTUP-STARTUP
B(E-1)
12.316 MWD/KGU
NEXT-TO-LAST-CYCLE BURNUP
______________________________________________________________________
.CORRECTION FACTORS COMPUTED.
______________________________________________________________________
F(P)
1.000
EXCESS POWER ADJUSTMENT
F(E)
0.985
INITIAL U-235 ENRICHMENT CORRECTION
F(7)
1.024
LAST CYCLE HISTORY CORRECTION
F-PRIME(7)
1.025
NEXT-TO-LAST-CYC HISTORY CORRECTION
F-SAFE
1.068
SAFETY FACTOR APPLIED TO RESULT
______________________________________________________________________
*CASE USES MORE PRECISE INTERPOLATIONS THAN THAT OF METHOD IN GUIDE.
.HEAT GENERATION RESULTS, W/KGU.
__________________________________________________
AFTER TABLE INTERPOLATION
1.837
AFTER ALL CORRECTIONS EXCEPT SAFETY FACTOR
1.900
AFTER SAFETY FACTOR INCLUDED
2.029
__________________________________________________
--- FINAL HEAT GENERATION RATE IS
OR
2.029 WATTS PER KILOGRAM U LOADED
783.1 WATTS PER ASSEMBLY
83
NUREG/CR-5625
Appendix C
***************************************************
*
*
* HEAT GENERATION RATE OF BWR SPENT-FUEL ASSEMBLY *
*
(PERTAINING TO USNRC GUIDE 3.54)
*
*
LWRARC CODE CREATION DATE : 05/30/94
*
*
*
***************************************************
TITLE: COOPER BWR 4-CYC, ASSY CZ528, 297.6 W/ASSEMBLY MEAS
.ASSEMBLY INPUT DESCRIPTION.
______________________________________________________________________
PARAMETER
DATA, UNITS
DEFINITION, IN GUIDE
E(S)
2.500 WT-% U-235
INITIAL FUEL ENRICHMENT
KGU(S)
190.500 KGU/ASSY
ASSEMBLY FUEL LOADING
T(C)
3.521 YEARS
ASSEMBLY COOLING TIME
B(TOT)
25.715 MWD/KGU
BURNUP, BEST MAXIMUM ESTIMATE
T(RES) 2483.000 DAYS
ASSEMBLY RESIDENCE TIME IN REACTOR
T(E)
317.000 DAYS
LAST CYCLE TIME, STARTUP-DISCHARGE
B(E)
4.110 MWD/KGU
LAST CYCLE BURNUP
T(E-1)
394.000 DAYS
NEXT-TO-LAST-CYC TIME, STARTUP-STARTUP
B(E-1)
2.692 MWD/KGU
NEXT-TO-LAST-CYCLE BURNUP
______________________________________________________________________
.CORRECTION FACTORS COMPUTED.
______________________________________________________________________
F(P)
1.000
EXCESS POWER ADJUSTMENT
F(E)
0.995
INITIAL U-235 ENRICHMENT CORRECTION
F(7)
1.006
LAST CYCLE HISTORY CORRECTION
F-PRIME(7)
0.993
NEXT-TO-LAST-CYC HISTORY CORRECTION
F-SAFE
1.074
SAFETY FACTOR APPLIED TO RESULT
______________________________________________________________________
*CASE USES MORE PRECISE INTERPOLATIONS THAN THAT OF METHOD IN GUIDE.
.HEAT GENERATION RESULTS, W/KGU.
__________________________________________________
AFTER TABLE INTERPOLATION
1.578
AFTER ALL CORRECTIONS EXCEPT SAFETY FACTOR
1.568
AFTER SAFETY FACTOR INCLUDED
1.684
__________________________________________________
--- FINAL HEAT GENERATION RATE IS
OR
NUREG/CR-5625
1.684 WATTS PER KILOGRAM U LOADED
320.8 WATTS PER ASSEMBLY
84
Appendix C
***************************************************
*
*
* HEAT GENERATION RATE OF BWR SPENT-FUEL ASSEMBLY *
*
(PERTAINING TO USNRC GUIDE 3.54)
*
*
LWRARC CODE CREATION DATE : 05/30/94
*
*
*
***************************************************
TITLE: COOPER BWR 3-CYC, ASSY CZ331, 162.8 W/ASSEMBLY MEASURED
.ASSEMBLY INPUT DESCRIPTION.
______________________________________________________________________
PARAMETER
DATA, UNITS
DEFINITION, IN GUIDE
E(S)
2.500 WT-% U-235
INITIAL FUEL ENRICHMENT
KGU(S)
190.500 KGU/ASSY
ASSEMBLY FUEL LOADING
T(C)
6.486 YEARS
ASSEMBLY COOLING TIME
B(TOT)
21.332 MWD/KGU
BURNUP, BEST MAXIMUM ESTIMATE
T(RES) 1367.000 DAYS
ASSEMBLY RESIDENCE TIME IN REACTOR
T(E)
164.000 DAYS
LAST CYCLE TIME, STARTUP-DISCHARGE
B(E)
2.962 MWD/KGU
LAST CYCLE BURNUP
T(E-1)
337.000 DAYS
NEXT-TO-LAST-CYC TIME, STARTUP-STARTUP
B(E-1)
5.495 MWD/KGU
NEXT-TO-LAST-CYCLE BURNUP
______________________________________________________________________
.CORRECTION FACTORS COMPUTED.
______________________________________________________________________
F(P)
1.000
EXCESS POWER ADJUSTMENT
F(E)
0.983
INITIAL U-235 ENRICHMENT CORRECTION
F(7)
0.998
LAST CYCLE HISTORY CORRECTION
F-PRIME(7)
1.003
NEXT-TO-LAST-CYC HISTORY CORRECTION
F-SAFE
1.068
SAFETY FACTOR APPLIED TO RESULT
______________________________________________________________________
*CASE USES MORE PRECISE INTERPOLATIONS THAN THAT OF METHOD IN GUIDE.
.HEAT GENERATION RESULTS, W/KGU.
__________________________________________________
AFTER TABLE INTERPOLATION
0.865
AFTER ALL CORRECTIONS EXCEPT SAFETY FACTOR
0.852
AFTER SAFETY FACTOR INCLUDED
0.910
__________________________________________________
--- FINAL HEAT GENERATION RATE IS
OR
0.910 WATTS PER KILOGRAM U LOADED
173.3 WATTS PER ASSEMBLY
85
NUREG/CR-5625
Appendix C
***************************************************
*
*
* HEAT GENERATION RATE OF PWR SPENT-FUEL ASSEMBLY *
*
(PERTAINING TO USNRC GUIDE 3.54)
*
*
LWRARC CODE CREATION DATE : 05/30/94
*
*
*
***************************************************
TITLE: TURKEY PT. 3, ASSY D-15, TC=2077 D, 625 W/ASSEMBLY MEAS
.ASSEMBLY INPUT DESCRIPTION.
______________________________________________________________________
PARAMETER
DATA, UNITS
DEFINITION, IN GUIDE
E(S)
2.557 WT-% U-235
INITIAL FUEL ENRICHMENT
KGU(S)
456.100 KGU/ASSY
ASSEMBLY FUEL LOADING
T(C)
5.687 YEARS
ASSEMBLY COOLING TIME
B(TOT)
28.152 MWD/KGU
BURNUP, BEST MAXIMUM ESTIMATE
T(RES) 1073.000 DAYS
ASSEMBLY RESIDENCE TIME IN REACTOR
T(E)
312.000 DAYS
LAST CYCLE TIME, STARTUP-DISCHARGE
B(E)
8.920 MWD/KGU
LAST CYCLE BURNUP
T(E-1)
389.000 DAYS
NEXT-TO-LAST-CYC TIME, STARTUP-STARTUP
B(E-1)
9.752 MWD/KGU
NEXT-TO-LAST-CYCLE BURNUP
______________________________________________________________________
.CORRECTION FACTORS COMPUTED.
______________________________________________________________________
F(P)
1.000
EXCESS POWER ADJUSTMENT
F(E)
1.009
INITIAL U-235 ENRICHMENT CORRECTION
F(7)
0.997
LAST CYCLE HISTORY CORRECTION
F-PRIME(7)
1.000
NEXT-TO-LAST-CYC HISTORY CORRECTION
F-SAFE
1.066
SAFETY FACTOR APPLIED TO RESULT
______________________________________________________________________
*CASE USES MORE PRECISE INTERPOLATIONS THAN THAT OF METHOD IN GUIDE.
.HEAT GENERATION RESULTS, W/KGU.
__________________________________________________
AFTER TABLE INTERPOLATION
1.386
AFTER ALL CORRECTIONS EXCEPT SAFETY FACTOR
1.394
AFTER SAFETY FACTOR INCLUDED
1.487
__________________________________________________
--- FINAL HEAT GENERATION RATE IS
OR
1.487 WATTS PER KILOGRAM U LOADED
678.2 WATTS PER ASSEMBLY
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
*
CONGRATULATIONS ... YOU HAVE COMPLETED LWRARC
*
*
*
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
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APPENDIX D
ACTINIDE, FISSION PRODUCT, AND LIGHT-ELEMENT TABLES
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Appendix D
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Appendix D
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Appendix D
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Appendix D
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Appendix D
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Appendix D
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Appendix D
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Appendix D
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APPENDIX E
PLOTS OF MAJOR DECAY HEAT RATE NUCLIDES
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Appendix E
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Appendix E
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Appendix E
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Appendix E
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Appendix E
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Appendix E
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Appendix E
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Appendix E
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Appendix E
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Appendix E
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Appendix E
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