Abstract. STAHALA, MIKE PETER. High Level Nuclear Waste Repository Thermal Loading Analysis. (Under the direction of Man-Sung Yim and David McNelis)

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1 Abstract STAHALA, MIKE PETER. High Level Nuclear Waste Repository Thermal Loading Analysis. (Under the direction of Man-Sung Yim and David McNelis) A spent nuclear fuel (SNF) decay heat model was developed by revising an existing analytical decay heat model to include factors for enrichment, irradiation time, and burnup beyond 37,000 MWd/MTU. Because many radioactive decay processes occur during the decay of SNF, the 10,000 year time range of interest was broken down into time regions when a specific isotopic decay process (or group of processes) dominates in the contribution of decay heat in SNF. The data for each time region was also divided for SNF with burnup greater and less than 10,000 MWd/MTU. Multivariate regression analysis was performed to fit a multivariate equation, as a function of burnup, enrichment, and irradiation time, for each time and burnup region to develop the SNF decay heat model. A MATLAB program implementing the decay heat model was developed to rapidly calculate the decay heat of each SNF dataset. Comparing the results of this model to SNF data generated in ORIGEN-ARP yielded maximum errors less than 7% for 120 time points with varying burnup, enrichment, and irradiation time. The MATLAB SNF decay heat model was used to determine the decay heat of the nation s inventory of SNF up to the year 2002 and SNF projected to be discharged through2010. The archived SNF information was provided by the Department of Energy (DOE) Energy Information Administration (EIA). It was determined that applying areal

2 power density (APD), or linear thermal loading, values to the calculated decay heat would not be suitable because a derived APD assumes a decay characteristic specific to the fuel used for the APD calculation. Because areal power density and linear thermal loading could not be applied to the calculated decay heat values, an alternative method for repository thermal analysis was required. A computer model that calculates the temperature distribution of a repository, called RETA, was used to calculate the temperature distribution at (1) the SNF cladding, (2) the drift wall, and (3) the mid-drift for the Yucca Mountain repository assuming a SNF inventory of 70,000 MTIHM. For the default decay heat values used by the RETA code, none of the temperature limits were exceeded. Applying the decay heat calculated using the actual SNF data provided by the EIA to the RETA code resulted in temperatures exceeding the mid-drift temperature limit. The minimum drift distance for the EIA applied data to meet repository temperature limits was 89 meters. When 81 meter drift spacing was utilized, a cooling time of 64 years was required to meeting repository temperature limits. An analysis on the impact of implementing high burnup SNF was performed based on the total energy produced by low and high burnup values. The results showed that for high burnup SNF the drift wall temperature limit was the most limiting. If interim storage, on the order of approximately 30 to 40 years, was implemented for high burnup SNF, the drift wall temperature limit would no longer be exceeded and drifts could be moved closer together to minimize the repository footprint. When a 36 year cooling period was

3 applied to the 58,000 MWd/MTU burnup case, the required repository foot print for the 63,000 MTU (legislative limit) of spent commercial fuel was 865 acres, i.e., smaller than the area designated for the repository, assuming that geological conditions are appropriate. The ability to significantly increase the capacity of the repository through the application of interim storage was demonstrated.

4 HIGH LEVEL NUCLEAR WASTE REPOSITORY THERMAL LOADING ANALYSIS by MIKE PETER STAHALA A thesis submitted to the Graduate Faculty of North Carolina State University In partial fulfillment of the Requirements for the Degree of Master of Science NUCLEAR ENGINEERING Raleigh, NC 2006 APPROVED BY: Man-Sung Yim (Chair of Advisory Committee) David McNelis (Co-chair of Advisory Committee) Morton Barlaz

5 Dedication To my family, thanks for putting up with me over the last two years. Mom and Dad, thank you for your unconditional love and support, and for always believing in me. Caroline thank you for pushing me to always expect and pursue more. Philipp, thank you for being not only a great brother, but also a great friend. ii

6 Biography Mike Peter Stahala received a Bachelors of Science in Electrical Engineering from North Carolina State University in December iii

7 Acknowledgement I would like to thank my advisors Drs. Yim and McNelis. Without their patience and guidance this work would not have been possible. Thank you for giving me the freedom to pursue my own ideas while offering persistent guidance to develop these ideas into a tangible research project. Both of you have helped me to progress academically and professionally. This research has been supported by a grant from the U.S. Environmental Protection Agency's Science to Achieve Results (STAR) program. Although the research described in this publication has been funded in part by the U.S. Environmental Protection Agency's STAR program through grant FP , it has not been subjected to any EPA review and therefore does not necessarily reflect the views of the Agency, and no official endorsement should be inferred. I would also like to acknowledge the assistance with SAS programming provided by Dr. Cavell Borwnie and Shuming Li of the NCSU Statistics Department. iv

8 Table of Contents List of Figures... vii List of Tables... ix List of Abbreviations... xi 1 Introduction Chapter 1 References Development of SNF Decay Heat Models Computer Model for Decay Heat Calculation Analytical Decay Heat Models Spent Nuclear Fuel Composition Burnup Enrichment & Average Power Revision to Malbrain Analytical Decay Heat Models PWR Fuel vs. BWR Fuel Summary of Changes Required to Malbrain SNF Decay Heat Models Effect of Burnup On SNF Decay Heat Malbrain Model Coefficients Decay Heat Time Regions Time Region I Time Region II Time Region III Time Region IV Time Region Selection Summary Generation of ORIGEN-ARP SNF Decay Heat Values with Varying SNF Characteristics Multivariable Regression Analysis to Determine Analytical SNF Decay Heat Model Coefficients Model Burnup Range Revised Decay Heat Model Coefficients Validation of Revised SNF Analytical Decay Heat Models Revised SNF Decay Heat Model MATLAB Application PWR & BWR SNF Decay Heat Calculations Total Decay Heat MATLAB Code Validation Chapter 2 References Repository Capacity Analysis Based on Areal Power Density Limits Application of Spent Nuclear Fuel Data Projected RW-859 Data Decay Heat Inventory Analysis Application of Spent Nuclear Fuel Decay Heat Inventory Yucca Mountain Thermal Limits Areal Power Density, Line Averaged Loading, and Age of Spent Nuclear Fuel at Time of Emplacement Converting Line Loading to Areal Power Density Repository Capacity based on APD Caution in the Use of Linear Loading and Areal Power Density Chapter 3 References v

9 4 Repository Capacity Assessment Based on Explicit Thermal Design Limit Calculations The RETA Program Areal Power Densities for Varying SNF Cooling Time Decay Heat Assumptions for Thermal Analysis Sensitivity of Thermal Analysis Results to Burnup Comparisons of SNF Decay Heat Values RETA Analysis with Varying Decay Heat Input Minimum Cooling Time for Cases 2 & 3 for 81 m Drift Spacing Minimum Drift Distances for Cases 2 & 3 for 26 Year Cooling Maximum Capacity for Case 1 Decay Heat Input Thermal Repository Impact of Increasing Reactor Burnup Relationship Between Burnup and Megawatt Days Burnup Effects on Repository Temperatures Conclusion on Burnup Effects on Repository Temperature Chapter 4 Summary Chapter 4 References Conclusions Chapter Summaries Chapter 2 Summary Chapter 3 Summary Chapter 4 Summary Conclusions on Repository Needs Recommendations for Future Work Repository Area Interim Storage & Removal of High Heat Radioisotopes Chapter 5 References Appendices Appendix A: SAS 9.1 Regression Analysis Code Appendix B: SAS Output: Revised Model Statistics Appendix C: SNF Decay Heat MATLAB Code for 10,000 Year Time Range, BWR Appendix D: SNF Decay Heat MATLAB Code for 10,000 Year Time Range, PWR Appendix E: MATLAB file Total_heat_analysis.m Appendix F:MATLAB Code future_addition.m Appendix G: Decay Heat Values for 58,000 MWd at Varying Burnup Appendix H: RETA Code Repository Variables vi

10 List of Figures Figure 2-1: Malbrain Model Results Compared to ORIGEN-ARP Figure 2-2: Historical Burnup Trends for Commercial U.S. Light Water Reactors Figure 2-3: Spent Nuclear Fuel Decay Heat versus Time for Varying Burnup Values (Enrichment = 3 wt % 235 U) Figure 2-4: Dominant Spent Nuclear Fuel Decay Heat Contributors for Time Zero to 10 Years after Discharge Figure 2-5: Dominant SNF Decay Heat Contributing Radioisotopes for Time Less Than 50 Years after Reactor Discharge Figure 2-6: Dominant SNF Decay Heat Radioisotopes for Time Greater than 49 years but Less then Figure 2-7: 241 Am Concentration (grams/mtu) over Time (years) Figure 2-8: Peak 241Am Concentration (grams/mtu) After Reactor Discharge Figure 2-9: Relative 137 Cs and 90 Sr Concentrations Over Time Figure 2-10: Relative 137 Cs and 90 Sr Decay Heat Over Time Figure 2-11: Dominant SNF Decay Heat Radioisotopes for Time Greater than 1500 years but Less then 10, Figure 2-12: Residual Plot for Model fit to 1,000 58,500 MWd/MTU Burnup Range. 35 Figure 2-13: BWR Spent Nuclear Fuel Decay Heat Values vs. Model Estimates, Time Region 1 to 8 years Figure 2-14: BWR Spent Nuclear Fuel Decay Heat Values vs. Model Estimates, Time Region 8 to 49 years Figure 2-15: BWR Spent Nuclear Fuel Decay Heat Values vs. Model Estimates, Time Region 49 to 74 years Figure 2-16: BWR Spent Nuclear Fuel Decay Heat Values vs. Model Estimates, Time Region 74 to 150 Years Figure 2-17: BWR Spent Nuclear Fuel Decay Heat Values vs. Model Estimates, Time Region 150 to 300 Years Figure 2-18: BWR Spent Nuclear Fuel Decay Heat Values vs. Model Estimates, Time Region 300 to 1500 Years Figure 2-19: BWR Spent Nuclear Fuel Decay Heat Values vs. Model Estimates, Time Region 1500 to 10,000Years Figure 3-1: Spent Nuclear Fuel Decay Heat Inventory (total watts) over Time (Year), for Commercial SNF discharged through 2010 (63,000 MTIHM) Figure 3-2: Spent Nuclear Fuel Decay Heat Inventory per Metric Ton of SNF (watts/mtu) over Time (Year), for Commercial SNF Discharged through 2010 (63,000 MTIHM) Figure 3-3: Repository Cross-Section Design Figure 3-4: Yucca Mountain Drift Layout Figure 3-5: Plan View Schematic for Areal Power Density Calculation Figure 3-6: Decay Heat over Time for Constant an Areal Power Density Met with Varying SNF Age vii

11 Figure 4-1: RETA Code Yucca Mountain Repository Layout Figure 4-2: Comparison of ORIGEN-ARP 5.01 and burnup.dat Decay Heat Values Figure 4-3: Plot of ORIGEN-ARP 5.01, burnup.dat, and Analytical Decay Heat Values (watts/mtu) Figure 4-4: Maximum Mid-Drift Temperature Profile Over Time for Cases 1 to Figure 4-5: Maximum Spent Nuclear Fuel and Outer Drift Wall Surface Temperature Profile over Time for Cases 1 to Figure 4-6: Decay Heat (watts/mtu) vs. Time for Varying Burnup SNF Figure 4-7: Decay Heat over Time to Produce the Same Amount of Energy (58,000 MWd) at Varying Burnup Figure 4-8: Transition Region of Decay Heat Contribution for Varying Burnup Producing 58,000 MWd Figure 4-9: Actinide Decay Heat Contribution for Varying Burnup Levels, per MWd Production Basis Figure 4-10: Fission Fragment Decay Heat Contribution for Varying Burnup Levels, per MWd Production Basis Figure 4-11: Dominant Actinide Decay Heat Contributors Figure 5-1: Full Recycle Fuel Cycle Process viii

12 List of Tables Table 2-1: ORIGEN Data Versus Malbrain Models Table 2-2: Select Radioisotope Concentrations (grams/mtu) with Varying Reactor Operation Characteristics, 1 Year After Reactor Discharge * Table 2-3: SNF Decay Heat* (watts/mtu) with Varying Reactor Operation Characteristics Table 2-4: PWR and BWR Fuel Assembly Characteristics Table 2-5: PWR and BWR Decay Heat Comparison* Table 2-6: Significant Fission Fragment SNF Decay Heat Contributors Table 2-7: Parent Daughter Relationship for 90 Sr and 137 Cs and 90 Y and 137m Ba Table 2-8: Selected Time Regions for Revised Decay Heat Models Table 2-9: Fuel Characteristics Used to for ORIGENARP 5.01 Data Generation Table 2-10: Years After Discharge Time Points Used for ORIGEN-ARP Data Generation, Regions Defined in Table Table 2-11: Sample ORIGEN-ARP SNF Decay Heat Output with Varying SNF Parameters Table 2-12: Revised SNF Decay Heat Model Coefficients, Burnup Greater than 10,000 MWd/MTU, for PWR Spent Nuclear Fuel Table 2-13: Revised SNF Decay Heat Model Coefficients, Burnup Less than 10,000 MWd/MTU, for PWR Spent Nuclear Fuel Table 2-14: Revised SNF Decay Heat Model Coefficients, Burnup Greater than 10,000 MWd/MTU, for BWR Spent Nuclear Fuel Table 2-15: Revised SNF Decay Heat Model Coefficients, Burnup Less than 10,000 MWd/MTU, for BWR Spent Nuclear Fuel Table 2-16: Revised Decay Heat Model Correlation Coefficients Table 2-17: Revised SNF Decay Heat Model Relative Error, PWR Spent Nuclear Fuel 45 Table 2-18: Revised SNF Decay Heat Model Relative Error, BWR Spent Nuclear Fuel 45 Table 2-19: Input File Structure for MATLAB Code Table 2-20: Explanation of MATLAB SNF Decay Heat Input File Variables Table 2-21: Spent Nuclear Fuel Characteristics for Future Reactor Designs Table 2-22: TEMPFILE.XLS Output Format Table 2-23: Comparison of SNF Decay Heat Data for 1 MTU PWR Irradiated at 50,000 MWd/MTU, 600 days, 4.4% 235 U and1 MTU BWR Irradiated at 48,000MWd/MTU, 550 Days, 4.1% 235 U Table 2-24: Comparison of SNF Decay Heat Data for 1 MTU PWR Irradiated at 3,000 MWd/MTU, 400 days, 2.1% 235 U and1 MTU BWR Irradiated at 25,000MWd/MTU, 450 Days, 3.1% 235 U Table 2-25:Comparison of SNF Decay Heat Data for 1 MTU PWR and 1 MTU BWR Irradiated at 34,000 MWd/MTU, 800 days, 3.5% 235 U Table 2-26: Comparison of SNF Decay Heat Data for 1 MTU PWR Irradiated at 38,000 MWd/MTU, 550 days, 3.9% 235 U and 1 MTU BWR Irradiated at 10,000 MWd/MTU, 220 days, 1.9% 235 U Table 3-1: Cumulative SNF Discharged by Year Table 3-2: Projected SNF Data, Table 3-3: 2010 Commercial SNF Decay Heat Values Over Time ix

13 Table 3-4: Additional Repository Engineering Design Factors Table 3-5: DOE Temperature Scenarios Table 3-6: Repository Capacity Limits if Constant Areal Power Density Values Could be Applied to Different SNF Cooling Times Table 4-1: Maximum SNF Cooling Times for Varying Areal Power Densities Using Constant Burnup Data Table 4-2: Comparison of Decay Heat (watts/mtu) for Designated and Averaged Burnup Values Table 4-3: Comparison of ORIGEN-ARP 5.01 and burnup.dat Decay Heat Values (watts/mtu) Table 4-4: Maximum Mid-drift Temperature Values ( C) for burnup.dat and ORIGEN- ARP Decay Heat Values (watts/mtu) Table 4-5: Other Maximum Temperature Values ( C) for burnup.dat and ORIGEN-ARP Decay Heat Values (watts/mtu) Table 4-6: Comparison of ORIGEN-ARP 5.01, burnup.dat, and Analytical Decay Heat Values (watts/mtu) Table 4-7: Comparison of Decay Heat Values with Low Burnup Projection (watts/mtu) Table 4-8: Cases for SNF Decay Heat Input to RETA Table 4-9: Maximum Temperatures at Repository Mid-drift Points for Varying Decay Heat Cases, Cases Defined in Table Table 4-10: Maximum Temperatures ( C) for Minimum Drift Distances for Cases 2 & 3 for 26 Cooled SNF Table 4-11: Metric Tons Uranium Required to Produce 58,000 MWd at Varying Burnup Table 4-12: EIA Selected Enrichments for Desired Burnup Level Table 4-13: 239 Pu and 240 Pu Production per MWd for Varying Reactor Burn-up Table 4-14: Decay Heat (watts/mtu) for Varying SNF Burnup Table 4-15: Maximum Temperatures for Varying Burnup Scenarios on a Megawatt Day Production Basis Table A-1: SAS Model Statistics, 1-8 Years PWR Table A-2: SAS Model Statistics, 8-49 Years PWR Table A-3: SAS Model Statistics, Years PWR Table A-4: SAS Model Statistics, Years PWR Table A-5: SAS Model Statistics, Years PWR Table A-6: SAS Model Statistics, 300-1,500 Years PWR Table A-7: SAS Model Statistics, 1,500-10,000 Years PWR Table A-8: SAS Model Statistics, 1-8 Years BWR Table A-9: SAS Model Statistics, 8-49 Years BWR Table A-10: SAS Model Statistics, Years BWR Table A-11: SAS Model Statistics, Years BWR Table A-12: SAS Model Statistics, Years BWR Table A-13: SAS Model Statistics, 300-1,500 Years BWR Table A-14: SAS Model Statistics, 1,500-10,000 Years BWR Table A-15: Decay Heat Values (watts/mwd) for 58,000 MWd at Varying Burnup Table A-16: Data from variable.dat x

14 List of Abbreviations Abbreviation AP1000 BWR DOE EIA ESBRW LWR MTU MTIHM MW/MTU MWd/MTU PWR RETA RW-859 SNF TSPA-LA Wt. % 235 U Definition Advanced Passive A pressurized water reactor designed by the Westinghouse Corporation. Boiling Water Reactor. The United States of America Department of Energy Energy Information Agency. Under the direction of the Department of Energy Economically Simplified Boiling Water Reactor. A boiling water reactor designed by General Electric. Light Water Reactor; A nuclear reactor that uses ordinary water as the neutron moderator and coolant. Metric Tons Uranium Metric Tons Initially Heavy Metal; the weight of SNF after irradiation Megawatts per Metric Ton Uranium. The power produced by a metric ton of nuclear reactor fuel (burnup). Megawatt Days per Metric Ton Uranium. A measure of the total power produced by a metric ton of nuclear reactor fuel. Pressurized Water Reactor REpository Thermal Analysis; A repository temperature analysis code developed at North Carolina State University. Nuclear Fuel Data Survey. A database on every fuel assembly irradiated in commercial nuclear reactors operating in the United States. Spent Nuclear Fuel Total System Performance Analysis License Application Percentage, by weight, of the isotope 235 U in nuclear reactor fuel before irradiation. The remainder of the fuel is 238 U. xi

15 1 Introduction The Nuclear Waste Policy Act of , as amended, sets the statutory limit of the proposed Yucca Mountain Nuclear Waste Repository at 63,000 metric tons initially heavy metal (MTIHM) of commercial spent nuclear fuel (SNF). It also requires that between 2007 and 2010 the Secretary of Energy report to the President on the need for a second U.S. High Level Nuclear Waste (HLW) repository. Given the high economic, social, and political costs associated with the siting of a HLW repository, investigating the expansion of the proposed Yucca Mountain statutory limit to beyond 63,000 MTIHM, rather than siting a second repository, is of significant interest. The factor that limits the amount of SNF that can safely be emplaced per unit area in a geologic repository is not the volume of the SNF, but rather the decay heat of the SNF in conjunction with the thermal loading scenario chosen for the geologic repository. The decay heat emanating from SNF is a function of the fuel burn-up, average power, initial enrichment, and cooling period. The purpose of this work is to perform a thermal analysis based repository capacity analysis on the proposed Yucca Mountain nuclear waste repository site by using actual spent nuclear fuel (SNF) decay heat data. Data of the U.S. inventory of SNF was acquired from the Department of Energy (DOE) Energy Information Administration (EIA) in the database RW-859 Nuclear Fuel Data Survey. The database includes the metric tons of uranium (MTU) at initial loading, burnup, enrichment, irradiation start date, and discharge date for all U.S. commercial SNF assemblies discharged through 1

16 December 31, A decay heat model was required to determine the decay heat of this SNF data. Chapter 2 discusses the development of an analytical decay heat model to quickly process large amounts of SNF data. Fast processing capability was necessary because the RW-859 data set consists of data for over 169,000 SNF assemblies. Changes to an existing analytical model were necessary to improve the model s accuracy for enrichment, irradiation time, and high burnup. Chapter 3 explains the application of the EIA data to the revised decay heat model and discusses caveats of applying areal power density or linear thermal loading to the decay heat inventory for repository thermal analysis for varying SNF cooling times. Chapter 4 presents the analysis of Yucca Mountain repository capacity for different repository scenarios based on the use of the computer program RETA (REpository Temperature Analysis). The chapter goes on to discuss the application of the SNF inventory derived in chapter 3 as input to the RETA code and how these values differ from the default values used by the code. Different repository scenarios were evaluated to demonstrate the effect SNF cooling time and drift distance have on maintaining a repository below defined temperature limits. Chapter 4 closes with an analysis on the effect of high and low burnup SNF on repository temperature limits. Chapter 5 provides a synopsis of the conclusions and work performed in this research, along with recommendations for future work. 2

17 1.1 Chapter 1 References 1 Nuclear Waste Policy Act of U.S.C et esq. Readily available. 3

18 2 Development of SNF Decay Heat Models This chapter discusses the background on existing models for the calculation of SNF decay heat and the basis for the selection of one for the purposes of this research. An analytical SNF decay heat model was selected so that large datasets could be processed in a rapid manner. Changes to an existing analytical model were required to incorporate the trend of high burnup irradiation currently utilized by commercial nuclear power reactors. Upon development of a more applicable SNF decay heat model, a MATLAB code was developed incorporating this model so that large datasets could easily be processed. 2.1 Computer Model for Decay Heat Calculation ORIGEN-ARP (Automatic Rapid Processing) is an isotopic depletion and decay analysis computer module developed by Oak Ridge National Laboratory. ORIGEN-ARP is part of one of the most widely used and internationally recognized class of depletion and decay codes applied in the nuclear industry for the comprehensive analysis of nuclide compositions, decay heat, and radiation sources from SNF. The first version of the ORIGEN code was developed in 1973 and has been regularly updated, with the latest release made available in June of 2005 (release 5.01). The numerical methods used by the code have remained relatively unchanged, but significant improvements have been made in the nuclear decay data, cross-section libraries, and photon yield data utilized by the code. The nuclear decay and cross-section data for the 5.01 release utilize a compilation of the Evaluated Nuclear (reaction) Data File B-VI (ENDF/B-VI), the Fusion Evaluated Nuclear Data Library (FENDL-2.0), and European Activation Library (EAF- 4

19 99) cross-section data bases. In order to represent a continuous neutron flux spectrum representative of a typical light water reactor (LWR), the pointwise cross-sections from these files were combined into the basic three-energy-group structure used by ORIGEN. For Uranium based fuels, cross-sections are interpolated for burnup, enrichment, and moderator density for all nuclides in the ORIGEN-S library (composed of approximately 1400 nuclides), rather than only a subset of the most important actinides. 2 Although ORIGEN-ARP could be used to determine the decay heat of large SNF data sets, doing so would require vast amount of computer time. Running one ORIGEN-ARP calculation takes approximately 11 seconds on a 1.79 GHz Intel Pentium M processor with 1.5 GB of RAM. The current inventory of over 160,000 SNF assemblies would require over 20 days of continuous computing time, not including the computing time required for additional SNF assemblies or additional calculations desired for various purposes. It was thus desired to utilize an analytical decay heat model that can process large data sets relatively quickly to calculate decay heat for SNF with various characteristics (burnup, enrichment, irradiation time, and cooling time). As discussed in section 0, ORIGEN-ARP 5.01 was utilized to generate data for the decay heat of SNF with varying burnup, enrichment, and average power level values to develop an analytical model. 2.2 Analytical Decay Heat Models A literature search was performed to determine the performance characteristics of existing analytical decay heat models. Pond and Matos 3 present a compilation of four decay heat models based on irradiation days (t i ), constant fuel assembly power (P) and 5

20 days after irradiation (t d ) to determine the decay heat (H) load power (watts) per assembly for research test reactors (Equations (2.1), (2.2), (2.3), (2.4)). 0.2 d i d ) H = P ( t ( t t ) Watts (2.1) 0.2 d i d ) H = P ( t ( t t ) Watts (2.2) H = P td ( td ( ti + td ) ) Watts (2.3) where: H = watts per assembly t i = Days irradiated t d = Days after discharge P = Average Power (watts/assembly) H = 0.1 P [( t P [( t d d + 10) ) ( t + t i 0.2 d ( t + t i + 10) d ] ) 0.2 ] Watts (2.4) where: H = watts per assembly t i = Seconds irradiated t d = Seconds after discharge P = Average Power (watts/assembly) Although these models provide relatively accurate results for research test reactors for a time period of up to approximately nine years after irradiation, they are not applicable to LWR SNF data for two reasons: (1) the Pond and Matos models assume research test reactor SNF that is highly enriched (19.75 to 93 weight percent 235 U) and (2) the applicable decay periods are only on the order of a few thousand days. The application 6

21 of SNF data to this research requires a decay heat model that will accommodate post irradiation decay periods on the order of thousands of years for light water reactor spent nuclear fuel with enrichment values typical of light water reactors( between 1 to 5 weight percent 235 U enrichment). A decay heat model for LWR SNF for thousands of years after discharge was presented by Malbrain, et. al. 4 This model was based on a Pressurized Water Reactor (PWR) operating at an average fuel burnup of 33,000 megawatt days/metric ton uranium (MWd/MTU), an average power of 37.5 megawatts/metric tons uranium (MW/MTU), for an irradiation time of 880 days at 3.2 weight percent enrichment 235 U. Burnup is defined as a measure of reactor fuel consumption expressed as the percentage of fuel atoms that have undergone fission, or the amount of energy produced per unit weight of fuel. There is a direct correlation between burnup history and thermal output. 5 The Malbrain decay heat models were broken up into two post irradiation time regions: (1) 1 < t < 30 years and (2) 30 < t < 10 6 years. The time period 1 < t < 30 years was selected because, during this time period, there are many fission product isotopes that are significant contributors 6 to decay heat and could thus be expressed in an asymptotic form when derived on a log scale. The time period 30 < t < 10 6 years was chosen for two reasons: (1) the decay heat for the time period 30 to 300 years is dominated by 137 Cs and 90 Sr fission fragments and (2) for time periods beyond 10 5 years, the decay heat falls substantially by several orders of magnitude, so very accurate approximations are less important because of the relatively small magnitudes of the dependent variables. 6 7

22 The derivation of this model was performed by selecting a simple linear correlation. Time was selected as the only independent variable because it was the only independent variable thought to be influential. 6 The basic form of the model for 30 < t < 10 6 years can be seen in equation (2.5). To linearize equation (2.5), a log transform was performed, leading to equations (2.6) and (2.7). The coefficients a and b were then determined by using a linear least squares method from SNF decay heat data obtained by ORIGEN2. y( t) = a + b t (2.5) log( y( t)) = a + b log( t) (2.6) y b ( t) = a t (2.7) The final form of this derivation for a PWR reactor is seen in equation (2.8) β Q( t) = D1 t (watts/mtu) where: (2.8) D 1 = 9,410 β = < t < 10 6 years A similar approach was used to develop an equation for the time period 1 < t < 30 years. Because many radioactive processes occur in the 1 < t < 30 year time range, an equation that would fit the decay heat better but still be able to be linearized by simple transformations was selected (equation (2.9)), leading to the non-linear expression (2.10) and (2.11) and finally resulting in equation (2.12). 4 p Y ( t) = ( c + t) (2.9) 8

23 p y( t) = a + b( c + t) (2.10) = a + b log( c + t) for p = 0 ( c t) = a + b e for p = ± 1 log( y ( t)) = a + b ( c + t) (2.11) C3 t ) ( C Q ( t) = C1 e (watts/mtu) (2.12) where: C 1 = 550 C 2 = C 3 = < t < 30 years Because commercial nuclear power reactors operate at different burnup values, an additional factor for changing burnup was added to the models. At the time of the Malbrain publication, the sensitivity of variations in burnup were not available in ORIGEN, so CINDER code was used to determine that the decay heat of SNF varies almost linearly with fuel burnup for values between 0 to 37,000 MWd/MTU. This approximation leads to the final forms of the Malbrain models, seen in equations (2.13) and (2.14). Q( t) where 1 ( C2 + C3 t ) = C1 e ( B / 33,000) C 1 = 550 C 2 = (watts/mtu) (2.13) 9

24 C 3 = < B < 37,000 MWd/MTU β Q( t) = D1 t ( B / 33,000) (watts/mtu) (2.14) where: D 1 = 9,410 Β = < t < 10 6 years 0 < B < 37,000 MWd/MTU The Malbrain models were an attractive choice as analytical decay heat models with quoted error generally less than 10% and no case exceeding 35%. 4 A comparison between the Malbrain models and ORIGEN-ARP 5.01 data was made to justify the use of these models. Using the parameters utilized by Malbrain (Burnup = 33,000 MWd/MTU, Enrichment = 3 wt. % 235 U, Average Power = 37.5 MW/MTU), the results are comparable, as observed in Table 2-1 and Figure 2-1. Table 2-1: ORIGEN Data Versus Malbrain Models Burnup = 33,000 MWd/MTU, Enrichment =3 wt % 235 U, Average Power = 37.5 MW/MTU Time Watts (ORIGEN) Watts (Malbrain) Relative error (%):

25 Decay Heat (watts/mtu) ORIGEN-ARP Malbrain Time (years) Figure 2-1: Malbrain Model Results Compared to ORIGEN-ARP (Burnup = 33,000 MWd/MTU, Enrichment =3 wt % 235U, Average Power = 37.5 MW/MTU) 2.3 Spent Nuclear Fuel Composition Burnup Early U.S. commercial nuclear reactor designs were developed to achieve maximum burnup in the range of 30,000 to 40,000 MWd/MTU. For many reasons (to reduce energy cost and SNF inventory, for example), commercial nuclear power plants have been increasing fuel burnup over the past few decades, as observed in Figure Because the Malbrain decay heat models produce reliable data only for burnup values from 0 to 37,000 MWd/MTU, the current form of the model may not be accurate for high burnup SNF. 11

26 Figure 2-2: Historical Burnup Trends for Commercial U.S. Light Water Reactors Enrichment & Average Power It was previously stated that the only independent variable thought to be significant in the Malbrain decay heat models was time. The fundamental law of radioactive decay states that the total activity emanating from a radioactive source is a function of the number of atoms in the source, the decay constant, and time. This fundamental law is seen in equation (2.15). Because the half-life for each radioisotope is a constant, it can be observed that time indeed is a significant variable to the activity of a radioisotope / 1 / 2 ( t t T ) e α = α o (2.15) where: α(t) = activity at time (t) 12

27 α 0 = activity at time t = 0 t = time T 1/2 = Half-life SNF is composed of many radioisotopes, each of which has a unique half-life and decay constant. When a reactor is operated at varying burnup, enrichment, or average power, the SNF will be composed of a different number of atoms of each radioisotope, as seen in Table 2-2, which gives to total grams/mtu of select radioisotope concentrations one year after reactor discharge. The number of atoms impacts the total activity in equation (2.15) due to the correlation between activity (α), the decay constant (λ), and the total number of atoms, as seen in equation (2.16). 8 α ( t) = λ n( t) (2.16) where: α(t) = activity at time (t) λ = decay constant n = number of atoms at time (t) Because the isotopic inventory of SNF changes as a function of the fuel characteristics, the decay heat emanating from SNF, which is a function of these radioisotope concentrations, is affected by changes in reactor fuel characteristics. Thus the burnup, enrichment, and average power utilized during reactor operation each directly impact the decay heat of SNF, as observed in Table

28 Table 2-2: Select Radioisotope Concentrations (grams/mtu) with Varying Reactor Operation Characteristics, 1 Year After Reactor Discharge * Case 1 Case 2 Case Pu Pu Pu Np Pu Burnup = 33,000 MWd/MTU, Enrichment = 2% 235 U, Avg. Power = 37.5 MW/MTU 2 Burnup = 33,000 MWd/MTU, Enrichment = 5% 235 U, Avg. Power = 37.5 MW/MTU 3 Burnup = 33,000 MWd/MTU, Enrichment = 5% 235 U, Avg. Power = 17.5 MW/MTU *Obtained by ORIGEN-ARP 5.01 Simulation Table 2-3: SNF Decay Heat* (watts/mtu) with Varying Reactor Operation Characteristics Time (years) Case 1 25,940 10,260 3,248 1, Case 2 25,570 9,690 3,053 1, Case 3 34,710 12,480 3,649 1, Burnup = 33,000 MWd/MTU, Enrichment = 3.5% 235 U, Avg. Power = 37.5 MW/MTU 2 Burnup = 33,000 MWd/MTU, Enrichment = 5% 235 U, Avg. Power = 37.5 MW/MTU 3 Burnup = 33,000 MWd/MTU, Enrichment = 5% 235 U, Avg. Power = 47.5 MW/MTU *Obtained by ORIGEN-ARP 5.01 Simulation 2.4 Revision to Malbrain Analytical Decay Heat Models Because it can be seen that burnup, enrichment, and average power impact the decay heat emanating from SNF, it was determined that the Malbrain models would not only need to be revised to be valid for higher burnup values, but also to incorporate variables for enrichment and average power. The half-lives of the radioisotopes contained in SNF were not factored in as variables in the Malbrain models. But isotope half-lives are accounted for because the Malbrain models were fit to decay heat data that functions as a 14

29 combination of the half-life of all of the radioisotopes contained in SNF. This approach was followed in this research. The U.S. inventory of SNF is composed of PWR and BWR SNF. The Malbrain decay heat models were developed based on PWR SNF, so before proceeding with revising the Malbrain models for burnup, enrichment, and average power, it was necessary to determine if the decay heat of BWR SNF varies significantly from PWR SNF. If significant differences exist, then this factor would also have to be included in the final version of the model adapted for this research PWR Fuel vs. BWR Fuel Although pressurized and boiling water reactors both use low enriched uranium (below 5 weight % 235 U) and water as the coolant and moderator, the configuration of the reactor core and the fuel assemblies are unique for each reactor type. Table 2-4 shows the differences between typical PWR and BWR fuel assemblies. 15

30 Table 2-4: PWR and BWR Fuel Assembly Characteristics 9 Characteristics BWR PWR Overall assembly length, m Cross section, cm 13.9 x x 21.4 Fuel rod length, m Active fuel height, m Fuel rod outer diameter, cm Fuel rod array 8 x 8 17 x 17 Fuel rods per assembly Assembly total weight, kg Uranium/assembly, kg UO 2 /assembly, kg Zircaloy/assembly, kg a b Hardware/assembly, kg 8.6 c 26.1 d Total metal/assembly, kg Nominal volume/assembly, m e e Metric Tons Uranium at Loading < 140 a Includes Zircaloy fuel-rod spacers and fuel channel. b Includes Zircaloy control-rod guide thimbles. c Includes stainless steel tie-plates, Inconel springs, and plenum springs. d Includes stainless steel nozzles and Inconel-718 grids. e Based on overall outside dimension. Includes spacing between the stacked fuel rods of an assembly. Because PWR and BWR fuel assemblies and core configurations have different characteristics, the isotopic composition, and thus decay heat, of SNF from each reactor type may be different. To determine if these differences do exist for PWR and BWR SNF, a comparison of decay heat values utilizing constant irradiation parameters (burnup, enrichment, average power) was performed. The results, as observed in Table 2-5, demonstrated that PWR and BWR assemblies do yield different decay heat values. It was thus determined that individual decay heat models would have to be developed for each reactor type. 16

31 Table 2-5: PWR and BWR Decay Heat Comparison* Time (years after discharge) BWR Decay Heat (watts/mtu) PWR Decay Heat (watts/mtu) % difference *Data Acquired from ORIGEN-ARP Summary of Changes Required to Malbrain SNF Decay Heat Models It was shown that in order to apply the Malbrain analytical decay heat models to PWR and BWR SNF data, it would be necessary to revise the decay heat models to account for reactor type (PWR/BWR), burnup values greater than 37,000 MWd/MTU, and include variables for enrichment and average power. The following section discusses how these revisions were performed Effect of Burnup On SNF Decay Heat For the Malbrain decay heat model, CINDER code was used to generate a correlation for changing burnup values up to 37,000 MWd/MTU. The latest release of ORIGEN-ARP 5.01 has the capability to yield SNF decay heat data for fuel irradiated up to 58,500 MWd/MTU (if desired, the user can generate libraries for higher bun-up values as well) 2. As seen in Figure 2-3, the change in decay heat over the burnup spectrum (0 to 58,500 MWd/MTU) is not linear, as assumed by the Malbrain models based on CINDER results. It was thus decided that the factor for burnup in the Malbrain decay heat model, which 17

32 was a linear coefficient (burnup/37,000), would need to be incorporated into the model as a nonlinear relation. Figure 2-3: Spent Nuclear Fuel Decay Heat versus Time for Varying Burnup Values (Enrichment = 3 wt % 235 U) Malbrain Model Coefficients When investigating how to append factors for fuel parameters (enrichment, average power, and higher burnup) in the Malbrain decay heat models (equation (2.8) and (2.12)), it was noted that the models contain constant coefficients (C 1, C 2, C 3, D 1, and β). These coefficients were derived by using a linear least squares method for PWR SNF decay heat data from one constant set of fuel parameters. It was determined that it would be possible to utilize a set of decay heat data, with variable SNF characteristics, to construct each 18

33 coefficient into a polynomial function of burnup, enrichment, and average power by utilizing multivariable regression analysis. Because this approach is computationally intensive (in this case regression analysis for three variables), the computer software SAS was utilized. 11 Before the multivariable regression analysis was performed, additional SNF decay heat analysis was required. Section established the need to distinguish between PWR and BWR SNF in a decay heat model. Rather than inserting an additional variable for PWR or BWR SNF in the decay heat model, it was determined that one set of equations would be developed for each reactor type. Summarizing the requirements for a revised analytical decay heat model, the form of the revised SNF decay heat model is seen below: For PWR SNF: Q( t) = D1 PWR * t β PWR * ( burnup/33,000) D1 = f ( burnup, enrichment, daysirradiated) PWR β = f ( burnup, enrichment, daysirradiated) PWR (2.17) For BWR SNF: Q( t) = D1 BWR * t β BWR * ( burnup/33,000) D1 = f ( burnup, enrichment, daysirradiated) BWR β = f ( burnup, enrichment, daysirradiated) BWR (2.18) Decay Heat Time Regions Before proceeding with the analysis of the effects of fuel characteristics on SNF, a further investigation into the time regions for each model was performed. As stated in section 19

34 2.2, the Malbrain SNF decay heat models were broken up into two time regions, time less than 30 years and time greater than 30 but less than 100,000 years. The radioactive decay process of SNF covers a time frame in the order of hundreds of thousands of years. SNF is composed of many radioisotopes with varying half-lives, thus different isotopes dominate in the contribution of decay heat at different time periods. In general, fission fragments, the radioisotopes formed as a result of fission that have relatively short half-lives (2.19), dominate in the contribution of decay heat in the short term (tens to hundreds of years). Actinides (2.20), with long half-lives, dominate in the long term (hundreds to thousands of years). 235 U + n 236 U * 144 Ba + 90 Kr +2n 90 Kr 32.3s 90 Rb 2.61m 90 Sr 29.1y 90 Y 2.67d 90 Zr (2.19) U + n 239 U 239 Np + β - (2.20) 12 Rather than utilizing the two time periods used in the Malbrain decay heat models, an investigation was performed to determine time periods when individual radioisotopes, or groups of radioisotopes, dominate in the emission of thermal radiation. For the application of this research, the time frame up to 10,000 years was of interest Time Region I The first time region when a significant group of decay process occurred was determined to be from one to eight years after reactor discharge. During this time period, many fission fragments, such as those seen in Table 2-6, significantly contribute to decay heat but decay away quickly due to their relatively short half-lives. Eight years was chosen as 20

35 the end of this time region because that is when 134 Cs has decayed to a level similar to many of the other significant decay heat contributors, as observed in Figure 2-4. Table 2-6: Significant Fission Fragment SNF Decay Heat Contributors Fission Fragment* Half-life** 85 Kr years 134 Cs 2.06 years 155 Eu 4.76 years 125 Sb 2.76 years 113m Cd metastable 126 Sb days 121 Sn hours *Data Acquired from ORIGEN-ARP 5.01 ** RADIATION DECAY, Version 4 Decay Heat (watts) 1.60E E E E E E E E E Time (Years) y90 ba137m am241 pu238 cs137 sr90 cm244 pu240 pu239 eu154 kr85 pu241 am243 cm242 cs134 cm243 pm147 pu242 np239 eu155 b125 Figure 2-4: Dominant Spent Nuclear Fuel Decay Heat Contributors for Time Zero to 10 Years after Discharge Time Region II The second time region was selected from 8 to 49 years after reactor discharge. During this time period 134 Cs ceased to dominate over other decay heat contributing 21

36 radioisotopes, and 90 Y and 137m Ba clearly dominate the contribution of decay heat emanating from SNF. At 49 years, 241 Am becomes the dominating contributor to decay heat (Figure 2-5) Decay heat (Watts) y90 ba137m am241 pu238 cs137 sr90 pu240 pu Time (Years) Figure 2-5: Dominant SNF Decay Heat Contributing Radioisotopes for Time Less Than 50 Years after Reactor Discharge Although the dominate decay heat contributors during this time frame are 90 Y and 137m Ba, the source of the decay heat emanating from these radioisotopes is attributed to 90 Sr and 137 Cs. 90 Y and 137m Ba have very short half-lives; 64 hours for 90 Y and approximately 2.52 minutes for 137m Ba. With such short half-lives it would be expected that the decay heat contribution from these radioisotopes would be negligible very quickly (general rule of thumb is that a radioisotope loses a majority of its activity after 10 half-lives). But 90 Y and 137m Ba are daughter products of the parent radionuclides 90 Sr and 137 Cs, which have half-lives of approximately 30 years, as seen in Table 2-7. Because the half-life of the 22

37 parents ( 90 Sr and 137 Cs) are much longer than the Daughters ( 90 Y and 137m Ba), the radioisotopes 90 Sr and 90 Y and 137 Cs and 137m Ba, respectively, are said to be in secular equilibrium. When two radioisotopes are in secular equilibrium, the parent and daughter decay at the same rate until the parent isotope has been depleted, which is why 90 Y and 137m Ba are grouped with 90 Sr and 137 Cs. 13 Table 2-7: Parent Daughter Relationship for 90 Sr and 137 Cs and 90 Y and 137m Ba Decay Process Parent Half-life 90 Sr 90 Y+ β years 137 Cs 137m Ba+ β years Time Region III The next selected time period where a unique radioactive decay process occurs during the decay of SNF was from 49 to 1500 years. During this time period 241 Am is the dominant contributor to the decay heat of SNF, as observed in Figure ,500 years after reactor discharge, Plutonium isotopes ( 239 Pu and 240 Pu) become the dominant sources of decay heat for SNF. 23

38 Decay heat (Watts) am241 pu240 pu239 am time (Years) Figure 2-6: Dominant SNF Decay Heat Radioisotopes for Time Greater than 49 years but Less then 1500 It is interesting to note that the decay heat from 241 Am is initially increasing over time, (Figure 2-7). The increase of the concentration of 241 Am is initially increasing due to the neutron absorption of 239 Pu and 240 Pu followed by the beta decay of 241 Pu to 241 Am, as seen in the following series reactions 14 : 239 Pu + 1 n 240 Pu + γ 240 Pu + 1 n 241 Pu + γ (2.21) (2.22) 241 Pu 241 Am + β - (2.23) 24

39 Figure 2-7: 241 Am Concentration (grams/mtu) over Time (years) Because the decay heat of 241 Am, the dominant decay heat contributor in this time period, is initially increasing and then decreasing, the time region was further broken down into two periods: (1) increasing 241 Am concentration and (2) decreasing 241 Am concentration. The concentration of 241 Am peaks 74 years after reactor discharge, as observed in Figure 2-8. The 241 Am dominated decay heat period was thus broken down into the time regions years and 74 to 1500 years. The 74 to 1500 year region was further broken down to 74 to 300 and 300 to 1500 years because the concentrations of 137 Cs and 90 Sr are negligible after 300 years (300 years is approximately 10 half-lives for 137 Cs and 90 Sr, see Figure 2-9 and Figure 2-10). When a model was derived for the time period 74 to 300 years, the maximum error (27%) was higher than other regions (a table of model errors is provided in section 2.4.8). It was decided that the 74 to 300 year period should also be further broken down. 25

40 Examining the decay heat contributors in the time region 74 to 300 years, it was noted that after approximately 5 half-lives of 137 CS and 90 Sr, approximately 150 years, the decay heat from these isotopes has subsided substantially (Figure 2-9 and Figure 2-10). For this reason the time period 74 to 300 years was broken down into two regions: (1) 75 to 150 years and (2) 150 to 300 years. Figure 2-8: Peak 241Am Concentration (grams/mtu) After Reactor Discharge 26

41 Figure 2-9: Relative 137 Cs and 90 Sr Concentrations Over Time Figure 2-10: Relative 137 Cs and 90 Sr Decay Heat Over Time The final time regions selected for the development of a SNF decay heat model for the time period from 49 to 1500 years were 49 to 74 years, 74 to 150 years, 150 to 300 years, and 300 to 1500 years Time Region IV The final time period was selected from 1500 to 10,000 years after discharge. During this time region the Plutonium isotopes 239 Pu and 240 Pu dominate as the source of decay heat emanating from SNF, as observed in Figure

42 Decay Heat (Watts) Time (Years) pu240 pu239 am241 Figure 2-11: Dominant SNF Decay Heat Radioisotopes for Time Greater than 1500 years but Less then 10, Time Region Selection Summary Rather than using the two time regions utilized in the Malbrain SNF decay heat models, 0 to 30 and 30 to 100,000 years, seven time intervals were selected for the development of the revised decay heat models (Table 2-8). For each of these time regions a SNF decay heat model that incorporates high burnup values, enrichment, and average power was developed for PWR and BWR SNF. The incorporation of the fuel characteristics to the SNF decay heat model is given in the following section. 28

43 Table 2-8: Selected Time Regions for Revised Decay Heat Models Region Time Range (years) Dominant Decay Heat Contributor Region I 1 < t 8 Fission fragments Region II 8 < t Cs and 90 Sr Region III 49 < t Am concentration increasing 74 < t Am concentration decreasing 150 < t Am concentration decreasing, 90 Sr and Cs below 10 half-lives 300 < t Am concentration decreasing, 90 Sr and Cs beyond 10 half-lives Region IV 1500 < t 10, Pu and 240 Pu Generation of ORIGEN-ARP SNF Decay Heat Values with Varying SNF Characteristics In order to revise the Malbrain SNF decay heat models to factor for changes in SNF composition, a data set of decay heat values at varying SNF parameters was required. ORIGEN-ARP 5.01 was used to generate SNF decay heat data for varying burnup, enrichment, and irradiation time values specified in Table 2-9 at time after discharge points shown in Table Although average power was used as an input for ORIGEN- ARP, the number of days an assembly is irradiated was used instead of average power as a variable in the decay heat model. Irradiation time was selected as a variable because the SNF data file that the decay heat models were applied to are in terms of enrichment, burnup and days irradiated. The average power (MW/MTU) of a reactor is directly related to the burnup (MWd/MTU) and duration of time (days) at which a fuel assembly is irradiated, as seen in equation (2.24). Days Irradiated = (burn up) (average power) = MWd MTU MW MTU = days irradiated (2.24) 29

44 Table 2-9: Fuel Characteristics Used to for ORIGENARP 5.01 Data Generation Burnup (MWd/MTU) Enrichment (wt % 235 U) Irradiation Time (days)

45 Table 2-10: Years After Discharge Time Points Used for ORIGEN- ARP Data Generation, Regions Defined in Table 2-8 Region I Region II Region III Region IV

46 A sample of the SNF decay heat values generated by ORIGEN-ARP 5.01 at varying time, average power, and enrichment is given in Table Only a sample of these values is provided due to the extensive nature of the results. Table 2-11: Sample ORIGEN-ARP SNF Decay Heat Output with Varying SNF Parameters Watts/MTU, Years After Reactor Discharge Burnup (MWd/MTHM) Days Irradiated Average Power (MW/MTU) Enrichment (wt %U- 235) Multivariable Regression Analysis to Determine Analytical SNF Decay Heat Model Coefficients For each of the time regions given in Table 2-8, a revised version of the Malbrain SNF analytical decay heat model was developed. This was accomplished by developing a multivariable curve fitting code in SAS 9.1 (see Appendix A for the raw code). The original Malbrain decay heat models were broken up into two forms, as discussed in section 2.2. Equation (2.12) was used to model time periods less than 30 years, where it is difficult to establish an asymptotic expression due to the many decay process occurring in the time period. Equation (2.8) was used to model the decay heat for time greater than 30 years, where an asymptotic relationship is easier to establish because there are dominant decay heat contributors. For the revised SNF decay heat models, the 10,000 32

47 decay heat time region of interest was broken down into seven regions (as seen in Table 2-8), which allowed for an asymptotic relationship to be established in each time region. Thus a model based on equation (2.8) could be used to model each time region, rather than using both equations (2.8) and (2.12) to model different time regions. To account for the effects that enrichment, irradiation days, and burnup have on the decay heat of SNF, the constants in equation (2.8), D 1 and β, were transformed into polynomial functions of burnup, irradiation days, and enrichment see (equations (2.26) and (2.27),). The SAS 9.1 code was used to determine the coefficients α i and γ i. β Q( t) = D1 * t *( burnup/33,000) (2.25) D = α + α ln( burnup) + α IrradiationDays + α enrichment α IrradiationDays Enrichment + α ln( burnup) 2 3 α ln( burnup) IrradiationDays + α ln( burnup) enrichment + + α enrichment α IrradiationDays 9 2 (2.26) β = γ + γ ln( burnup) + γ IrradiationDays + γ enrichment γ ln( burnup) IrradiationDays + γ ln( burnup) enrichment + γ IrradiationDays Enrichment + γ ln( burnup) + γ enrichment γ IrradiationDays 9 2 (2.27) To determine the coefficients α i and γ i for each time period, the iterative function PROC NLIN 15 was used in the SAS 9.1 program. The PROC NLIN function uses a system of equations represented by the nonlinear model: Y * ( β, β,..., β, Z, Z,... Z,) + ε = ( β ) ε = f f n + r (2.28) where: 33

48 Y = the non-linear model values Z = a matrix of independent variables β * = vector of the parameters ε = error vector f = function of the independent variables and the parameters. For the application of the revised SNF decay heat model, equations (2.26) and (2.27) were defined in f; burnup, irradiation days, and enrichment were defined in matrix Z; and α i and γ i were defined in the vector of parameters β *. This system of equations was evaluated using an iterative technique similar to a series of linear regressions. 15 This process was performed for SNF decay heat data for each of the time regions discussed in Table Model Burnup Range When data from the burnup range 1000 to 58,500 MWd/MTU was fit to the revised decay heat model using the procedure described in section 2.4.6, there was an obvious trend that relatively high error occurred at low burnup values (less than 10,000MWd/MTU). This trend can be observed in the residual plot Figure 2-12, where the residual is the difference between the estimated value and the actual value. 16 Plotting the residual verses the system variables can graphically show which variables cause the most significant error. In Figure 2-12 a model was fit to SNF decay heat characteristics of a PWR reactor for the time range 49 to 74 years. The highest error occurred in the burnup range below 10,000 MWd/MTU. The maximum error for this model was 41.1% and average error was 5.1%. When the burnup range was broken up into two regions, greater and less than 10,000 MWd/MTU, the maximum error decreased to 9.12 % and 34

49 4.68% and the average error decreased to 0.91% and 0.54% for low and high burnup values, respectively. Because splitting the burnup range into two regions would yield a SNF decay heat model with lower error, the burnup for each time region for each reactor type was split into (1) 1000 to 10,000 MWd/MTU and (2) greater than 10,000 to 58,500 MWd/MTU. Figure 2-12: Residual Plot for Model fit to 1,000 58,500 MWd/MTU Burnup Range Revised Decay Heat Model Coefficients Applying the two burnup regions (greater and less than 10,000 MWd/MTU) in each time region (Table 2-10) to PWR and BWR SNF, a set of constants α 1, α 2,,α 10 and γ 1, γ 2,, γ 10 was derived for the polynomial function with burnup, enrichment, and irradiation days as variables using the SAS 9.1 code. These functions replaced the constants D 1 and β in 35

50 the Malbrain model of the revised SNF decay heat model (Equations (2.25), (2.26), and (2.27)). The coefficients for each model are given in Table 2-12, Table 2-13, Table 2-14, and Table Plots comparing SNF decay heat values (black) and derived model values (red) for various irradiation days and enrichments, for each time period, are given in Figure 2-13 though Figure Figure 2-13: BWR Spent Nuclear Fuel Decay Heat Values vs. Model Estimates, Time Region 1 to 8 years 36

51 Figure 2-14: BWR Spent Nuclear Fuel Decay Heat Values vs. Model Estimates, Time Region 8 to 49 years Figure 2-15: BWR Spent Nuclear Fuel Decay Heat Values vs. Model Estimates, Time Region 49 to 74 years 37

52 Figure 2-16: BWR Spent Nuclear Fuel Decay Heat Values vs. Model Estimates, Time Region 74 to 150 Years Figure 2-17: BWR Spent Nuclear Fuel Decay Heat Values vs. Model Estimates, Time Region 150 to 300 Years 38

53 Figure 2-18: BWR Spent Nuclear Fuel Decay Heat Values vs. Model Estimates, Time Region 300 to 1500 Years Figure 2-19: BWR Spent Nuclear Fuel Decay Heat Values vs. Model Estimates, Time Region 1500 to 10,000Years 39

54 Table 2-12: Revised SNF Decay Heat Model Coefficients, Burnup Greater than 10,000 MWd/MTU, for PWR Spent Nuclear Fuel Time Region α α α α α α α α α α E-05 α 3-5.7E-05 α E-05 α α α α α E-05 α E-06 α E-06 α E-05 α α α α α 7-1.4E-05 α E-06 α E-07 α E-06 α α α α α E-07 α E-09 α E-09 α E-08 α α α α γ γ γ γ γ γ γ γ γ γ E-05 γ E-05 γ E-06 γ γ γ γ γ E-05 γ 5-5.4E-06 γ E-06 γ E-06 γ γ γ γ γ E-06 γ E-06 γ E-07 γ E-06 γ γ γ γ γ E-07 γ E-10 γ 9-8E-10 γ E-09 γ E-05 γ γ γ Time Region α α α α α α α α α E-05 α α α α α E-05 α E-05 α α α α E-05 α 7-5.7E-06 α E-06 α α α α E-08 α E-08 α E-08 α α α γ γ γ γ γ γ γ E-05 γ E-05 γ E-05 γ γ γ γ E-05 γ E-06 γ E-06 γ γ γ γ E-06 γ E-06 γ E-07 γ γ γ γ E-08 γ E-08 γ E-09 γ γ γ

55 Table 2-13: Revised SNF Decay Heat Model Coefficients, Burnup Less than 10,000 MWd/MTU, for PWR Spent Nuclear Fuel Time Region α α α α α α α α α α E-05 α E-05 α E-05 α α α α α E-05 α E-05 α E-05 α E-05 α α α α α E-06 α E-06 α E-06 α E-06 α α α α α E-07 α E-09 α E-09 α E-09 α α α α γ γ γ γ γ γ γ γ γ γ E-05 γ E-05 γ E-05 γ γ γ γ γ E-05 γ E-06 γ E-06 γ E-06 γ γ γ γ γ E-06 γ E-07 γ E-07 γ E-07 γ γ γ γ γ E-07 γ E-09 γ E-09 γ E-09 γ γ γ γ Time Region α α α α α α α α α α α α α E-05 α E-05 α E-05 α α α α E-05 α E-06 α E-06 α α α α E-08 α E-08 α E-08 α α α γ γ γ γ γ γ γ E-05 γ E-05 γ E-05 γ γ γ γ E-06 γ E-06 γ E-06 γ γ γ γ E-06 γ E-07 γ E-07 γ γ γ γ E-10 γ E-09 γ E-09 γ γ γ

56 Table 2-14: Revised SNF Decay Heat Model Coefficients, Burnup Greater than 10,000 MWd/MTU, for BWR Spent Nuclear Fuel Time Region 1<8 8<49 49<74 74 to 150 α α α α α α α α α α E-05 α E-05 α E-05 α α α α α E-05 α E-06 α E-06 α E-05 α α α α α E-05 α E-06 α 7 4.9E-07 α E-06 α α α α α E-07 α E-09 α E-09 α E-08 α α α α γ γ γ γ γ γ γ γ γ γ E-05 γ E-05 γ E-06 γ γ γ γ γ E-05 γ E-06 γ E-06 γ E-06 γ γ γ γ γ E-06 γ E-06 γ E-07 γ E-06 γ γ γ γ γ E-07 γ E-10 γ E-10 γ E-09 γ γ γ γ Time Region 150< < <10000 α α α α α α α α α E-05 α α α α α E-05 α E-05 α α α α E-05 α E-06 α E-06 α α α α E-07 α E-08 α E-08 α α α γ γ γ γ γ γ γ E-05 γ E-05 γ E-05 γ γ γ γ E-05 γ E-06 γ E-06 γ γ γ γ E-06 γ E-06 γ E-07 γ γ γ γ E-08 γ E-08 γ E-09 γ γ γ

57 Table 2-15: Revised SNF Decay Heat Model Coefficients, Burnup Less than 10,000 MWd/MTU, for BWR Spent Nuclear Fuel Time Region 1<8 8<49 49<74 74 to 150 α α α α α α α α α α E-05 α E-05 α E-05 α α α α α E-05 α E-05 α E-05 α E-05 α α α α α E-06 α E-06 α E-06 α E-06 α α α α α E-07 α E-09 α E-09 α E-09 α α α α γ γ γ γ γ γ γ γ γ γ E-05 γ 3-2.3E-05 γ E-05 γ γ γ γ γ E-05 γ E-06 γ E-06 γ E-06 γ γ γ γ γ E-06 γ E-06 γ E-07 γ E-07 γ γ γ γ γ E-07 γ E-09 γ E-09 γ E-09 γ γ γ γ Time Region 150< < <10000 α α α α α α α α α α α α α E-05 α E-05 α E-05 α α α α E-05 α E-06 α E-07 α α α α E-08 α E-08 α E-08 α α α γ γ γ γ γ γ γ E-05 γ E-05 γ E-05 γ γ γ γ E-06 γ E-06 γ E-06 γ γ γ γ E-06 γ E-07 γ E-07 γ γ γ γ E-09 γ E-09 γ E-09 γ γ γ

58 2.4.8 Validation of Revised SNF Analytical Decay Heat Models The final form of the revised SNF analytical decay heat models is given in equation (2.29), with equations for the parameters D 1 and β given in equations (2.30) and (2.31). The Parameters for equation (2.30) and (2.31) are given in Table 2-12 through Table The R-Square values of D 1 and β for each time interval and burnup region is given in Table 2-16, where the R-Square value is defined as a value between 0 and 1 that indicates the portion of the (corrected) total variation that is attributed to the fit rather than left to residual error. 15 Additional model fit statistics, such as the t-statistic and P- value, are available in Appendix B: SAS Output: Revised Model Statistics. β Q( t) = D1 * t *( burnup/33,000) (2.29) D = α + α ln( burnup) + α IrradiationDays + α enrichment α IrradiationDays Enrichment + α ln( burnup) 2 3 α ln( burnup) IrradiationDays + α ln( burnup) enrichment + + α enrichment α IrradiationDays 9 2 (2.30) β = γ + γ ln( burnup) + γ IrradiationDays + γ γ IrradiationDays Enrichment + γ ln( burnup) 2 3 γ ln( burnup) IrradiationDays + γ ln( burnup) enrichment + + γ enrichment enrichment + + γ IrradiationDays 9 2 (2.31) 44

59 Table 2-16: Revised Decay Heat Model Correlation Coefficients Decay Region Time Range (years) Variable PWR <=10,000 MWd/MTU PWR >10,000 MWd/MTU BWR <=10,000 MWd/MTU BWR >10,000 MWd/MTU Region I 1 < t 8 D β Region D < t 49 II β < t 74 D β D < t 150 Region β III 150 < t D β < t D ,500 β Region 1500 < t D IV 10,000 β The average and maximum percent error for each model, relative to the ORIGEN-ARP 5.01 SNF decay heat data used to develop the models, are given in Table 2-17 and Table Table 2-17: Revised SNF Decay Heat Model Relative Error, PWR Spent Nuclear Fuel Time Region (years) Burnup above Average Error: ,000 MWd/MTU Max Error: Burnup below Average Error: ,000 MWd/MTU Max Error: Table 2-18: Revised SNF Decay Heat Model Relative Error, BWR Spent Nuclear Fuel Time Region (years) Burnup above Average Error: ,000 MWd/MTU Max Error: Burnup below Average Error: ,000 MWd/MTU Max Error:

60 2.5 Revised SNF Decay Heat Model MATLAB Application A MATLAB code was developed using the revised SNF decay heat models to calculate the decay heat of SNF for time points between 1 to 10,000 years for SNF with values for burnup between 1,000 58,500 MWd/MTU, irradiation time days, and enrichment from 1.5 to 5 weight percent 235 U. This code was designed to call SNF information from a text file in the format shown in Table 2-19, where each column is separated by a tab character, and defined in Table Table 2-19: Input File Structure for MATLAB Code Reactor Month Type Discharged MTU Burnup Enrichment Irradiation Days Day Discharged Year Discharged Table 2-20: Explanation of MATLAB SNF Decay Heat Input File Variables MTU The metric tons of uranium at initial loading Burnup Burnup of the SNF in units of MWd/MTU Enrichment The weight percent of 235 U. The remainder of the fuel is assumed to be 238 U. Irradiation Days The total number of days the SNF was irradiation in the reactor Reactor Type PWR = 1 BWR = 2 Month Discharged 1-12 Day Discharged 1-31 Year discharged Four digit year PWR & BWR SNF Decay Heat Calculations To calculate decay heat of SNF for user defined times in the future, the MATLAB code was divided into four files. The first file PWRanalysis.m, provided in Appendix D, loads SNF data given in a file named allpwrdata.txt, which contains PWR SNF information in the format described in Table The file PWRanalysis.m then opens a file named timepoints.dat that contains a column vector of the points in time that the user would like to calculate the total decay heat for SNF. The points in time specified in timepoints.dat 46

61 are treated as years since 2010 (2010 was chosen because that is when the commercial SNF statutory limit of 63,000 metric tons initially heavy metal (MTIHM) will be reached, but can easily be changed in the code, as discussed below). For example, if the user would like to determine the total decay heat of PWR SNF in 2015, only the time point 5 (5 years) would need to be specified in the timepoints.dat file. Likewise, if the user would like to determine the decay heat in 2015, 2020, 2030, 2050, and 2100, the timepoint.dat file would contain a column vector comprised of the points 5, 10, 25, 50, and 90. Using the specified time points, the file PWRanalysis.m determines the decay heat, due to the total PWR inventory, at each time point using the revised SNF decay heat model defined in section The total decay heat is then divided by the total metric tons of PWR SNF to determine the decay heat per unit mass for the specified time points. The same process occurs in BWRanalysis.m (see Appendix C), with the exception that BWR SNF information is called from the file allbwrdata.txt and that the program makes calculations based on the BWR revised decay heat model and SNF Total Decay Heat To calculate the total decay heat from the inventory of PWR and BWR SNF, the user does not need to manually run the files PWRanalysis.m and BWRanalysis.m. These files are called when the file Total_heat_analysis.m is run in the MATLAB command prompt. Total_heat_analysis.m has three major functions: Calls PWRanalysis.m and BWRanalysis.m Calls future_addition.m, a file that can add additional SNF for future discharge Compiles SNF decay heat information from PWRanalysis.m and BWRanalysis.m to output the total decay heat, per MTU, in the file TEMPFILE.XLS. 47

62 The file future_addition.m allows the user to add additional SNF for future discharges. In Total_heat_analysis.m SNF data is only defined for data up to the year 2010 (see Chapter Error! Reference source not found. for EIA SNF information). Because it may be of interest to determine the impact of SNF discharged in the future, future_addition.m allows the user to specify what year to continue current discharge rates until (assumed to be 2,100 MTU/year, 2/3 PWR, 1/3 BWR, see section 3.2 for additional information) and then performs the decay heat calculation. There is also a variable, num_additional_yrs, which can be toggled to add discharges for new reactors (in addition to the projected 2,100 MTU/year). If num_additional_yrs is set to zero (default) the program assumes that no new reactors are brought online. If num_additional_yrs is set to 1, it assumes that five new reactors will come on line in 2018 (3 PWR, 2 BWR), discharging an additional 123 MTU/year. The additionally discharged MTU for num_additional_yrs was based on projections by the EIA that the total projected increase in nuclear capacity between 2004 and 2030 includes 6 gigawatts of capacity at newly constructed (nuclear) power plants. 17 The fuel and irradiation characteristics of the projected PWR reactors are based on the Westinghouse Advanced Passive 1000 (AP1000) design and BWR reactor projections are based on the General Electric (GE) Economically Simplified Boiling Water Reactor (ESBWR). These projections are provided in Table Because the maximum allowable burnup for the revised SNF decay heat models is 58,500 MWd/MTU, 58,500 MWd/MTU was designated as the future SNF burnup for PWR fuel instead of 60,000 MWd/MTU, as listed for the AP

63 Table 2-21: Spent Nuclear Fuel Characteristics for Future Reactor Designs Characteristic AP ESBWR 19 Average fuel burnup at discharge 60,000 ~50,000 MWd/MTU Enrichment < 4.95 wt. % 235 U 4.2 wt. % 235 U Operating Cycle Length 18 months months Annual SNF Generated 24.4 metric tons 50 metric tons After the user runs the file Total_heat_analysis.m, which runs the files PWRanalysis.m, BWRanalysis.m, and future_addition.m, the average decay heat per MTU of SNF for each time point specified in timepoints.dat is saved as an Excel file named TEMPFILE.XLS. The output structure of TEMPFILE.XLS is given as year and decay heat per MTU, as seen in Table The year outputted in TEMPFILE.XLS is the discharge time points defined by the user in timepoints.dat. If the user wishes to change the year at which to begin SNF decay heat calculations (pre-set at years since 2010), the variable start_year in the file Total_heat_analysis.m can be changed to the desired start year. Table 2-22: TEMPFILE.XLS Output Format Decay Heat Year (watts/mtu)

64 2.5.3 MATLAB Code Validation Before the MATLAB spent nuclear fuel decay heat code was applied to actual SNF data, it was desired to benchmark the MATLAB results to ORIGEN-ARP 5.01 SNF values, and also to compare the results to Malbrain model results. Four scenarios were evaluated with varying burnup, enrichment, and days irradiated values for time spans from 3 to 10,000 years. A comparison of the results demonstrated the validity of the revised SNF decay heat models used in the MATLAB code to estimate the SNF decay heat values produced by ORIGEN-ARP The maximum error in these cases was 8.5%, with a mean error (over a range of 120 point) of 2.9%. See Table 2-23, Table 2-24, Table 2-25, and Table 2-26 for individual data point comparisons of ORIGEN-ARP 5.01 and the MATLAB model values. Table 2-23 and Table 2-24 also compare the revised model results to Malbrain decay heat model results. This comparison demonstrates the increased accuracy of the revised decay heat model for SNF with varying burnup, enrichment, and irradiation-time values. 50

65 Table 2-23: Comparison of SNF Decay Heat Data for 1 MTU PWR Irradiated at 50,000 MWd/MTU, 600 days, 4.4% 235 U and1 MTU BWR Irradiated at 48,000MWd/MTU, 550 Days, 4.1% 235 U Year ORIGEN (watts/mtu) Revised Model (watts/mtu) Revised Model% Error Malbrain Model (watts/mtu) Malbrain Error mean error: max error:

66 Table 2-24: Comparison of SNF Decay Heat Data for 1 MTU PWR Irradiated at 3,000 MWd/MTU, 400 days, 2.1% 235 U and1 MTU BWR Irradiated at 25,000MWd/MTU, 450 Days, 3.1% 235 U Year ORIGEN (watts/mtu) Revised Model (watts/mtu) Revised Model% Error Malbrain Model (watts/mtu) Malbrain Error mean error: max error:

67 Table 2-25:Comparison of SNF Decay Heat Data for 1 MTU PWR and 1 MTU BWR Irradiated at 34,000 MWd/MTU, 800 days, 3.5% 235 U MATLAB Model (watts/mtu) % Error Year ORIGEN Table 2-26: Comparison of SNF Decay Heat Data for 1 MTU PWR Irradiated at 38,000 MWd/MTU, 550 days, 3.9% 235 U and 1 MTU BWR Irradiated at 10,000 MWd/MTU, 220 days, 1.9% 235 U MATLAB Model (watts/mtu) % Error Year ORIGEN

68 2.6 Chapter 2 References 2 I.C. Gauld, B.D. Murphy, and M.L. Williams. ORIGEN-S Data Libraries. ORNL/TM- 2005/39, UT-Battelle, LLC, Oak Ridge National Laboratory, April R.B Pond and J.E. Matos, Nuclear Mass Inventory, Photon Dose Rate and Thermal Decay Heat of Spent Research Reactor Fuel Assemblies (Rev 1), ANL/RERTR/TM-26, Argonne National Laboratory, Argonne, IL (December 1996). 4 Marlbrain, Carl M.. Analytical Approximations for the Long-term Decay Behavior of Spent Nuclear Fuel and High-Level Waste. Nuclear Technology. May 1982, vol Nuclear Waste Technical Review Board. Sixth Report to the U.S. Congress and the U.S. Secretary of Energy, June Available online at < Accessed February 14, Malbrain, Carl M. Analytical Characterization of Spent Fuels and High Level Wastes and Application to the Thermal Design of a Geological Repository in Salt. Master s Thesis, Massachusetts Institute of Technology. June Bale, Michael G., and Thomas A. Thorton. Spent Fuel Characteristics Potentially Relevant to Repository Design Assessment. High Level Radioactive Wate Management Conference J.R. Lamarsh. Introduction to Nuclear Engineering. Prentice Hall, Inc. New Jersey U.S. Department of Energy Office of Environmental Management. IDB Reference Characteristics of LWR Nuclear Fuel Assemblies. < January 22, Uranium Information Center. Nuclear Power Reactors, Briefing Paper # 64. October < 11 SAS Institute Inc., SAS Cary, NC: SAS Institute Inc., Murray, Raymond L. Nuclear Energy, An Introduction to the Concepts, Systems, and Applications of Nuclear Processes. Butterworth-Heinemann. Woburn, MA Appendix A Glossary of Nuclear Terms. Lawrence Berkeley Laboratory. < January 23, The Search for Heavy Elements. < October 4, SAS Institute Inc., SAS. SAS Help and Documentation: Computational Methods, The NLIN Procedure Devore, Jay L. Probability and Statistics, for Engineering and the Sciences. Thomson Learning, Pacific Grove, CA U.S. Department of Energy, Energy Information Administration. Annual Energy Outlook 2006 with Projections to 2030 (Early Release) Overview. < February 7, Westinghouse Corp. Technology Fact Sheet: Westinghouse AP1000. < February 7,

69 19 General Electric. Technology Fact Sheet; General Electric ESBWR. < February 7,

70 3 Repository Capacity Analysis Based on Areal Power Density Limits 3.1 Application of Spent Nuclear Fuel Data By mandate of Public Law (Federal Energy Administration Act of 1974), Sec. 13(b), 5(a), 5(b) 52, all commercial nuclear utilities operating in the United States must report data on every nuclear fuel assembly irradiated, as well as current SNF inventories, discharges, and storage capabilities of commercial nuclear reactors. U.S. commercial nuclear power plants report this data the Department of Energy (DOE) Energy Information Administration (EIA) via form RW-859, Nuclear Fuel Data Survey. The latest public release (as of December 2005) of the RW-859 database contains SNF information on nuclear fuel discharged through December 31, For each assembly in the RW-859 database, the metric tons of uranium (MTU), burnup, enrichment, irradiation start date, and discharge date, among additional information, is provided. This data, if applied to a SNF decay heat model, can be used to determine the decay heat of the nation s inventory of SNF. Because the factor that limits the amount of SNF that can be emplaced per unit area in a geologic repository is the decay heat emanating from SNF, not the volume of the fuel, calculating the decay heat of the nation s SNF inventory can be beneficial to repository analysis. This chapter discusses the application of the RW- 859 data to the MATLAB SNF decay heat model derived in Chapter 2 and how the results can be applied to repository temperature analysis based on the current DOE areal power density limits

71 3.2 Projected RW-859 Data The statutory capacity limit for the proposed Yucca Mountain nuclear waste repository is 70,000 metric tons initially heavy metal (MTIHM). Of the 70,000 MTIHM, 10% (7,000 MTIHM) is reserved for Defense waste while the remainder (63,000 MTIHM) is designated for commercial SNF. 21 As of December 31, 2002, the total mass of discharged commercial SNF in the United States was 46,998 MTIHM. 22 If it is desired to perform a thermal analysis on the proposed Yucca Mountain repository, it is necessary to acquire information on all of the SNF that will be emplaced into the repository. The RW- 859 database provides some information on projected SNF and fuel cycles beyond 2002, but not a comprehensive inventory of the 63,000 MTIHM repository limit (this data is incomplete because reporting future data in the RW-859 survey is optional). A DOE Office of Environmental Land Management report on future fuel cycles provides projected SNF discharges for dates beyond This information was tabulated for years , which is when the 63,000 MTIHM commercial limit for Yucca Mountain will be met, as provided in Table 3-1. Table 3-1: Cumulative SNF Discharged by Year 23 Cumulative SNF Year Discharged (MTIHM) , , , , , , , ,400 57

72 All of the SNF characteristics (burnup, enrichment, irradiation time) for fuel discharged between 2003 and 2010 are not available, so estimates were made for these parameters by taking the mean values of the available projected data in the RW-859 database. No future discharge information was available for irradiation time, so the mean irradiation time for SNF discharged in 2002, 527 days, was used. The total amount of SNF discharged per year was based on the discharge projections provided in Table 3-1 assuming 2/3 discharged as PWR SNF and 1/3 as BWR SNF (current discharge fractions). It was also assumed that each discharge occurred on the last day of each respective year, a conservative assumption. A compilation of this projected data, formatted for input for the MATLAB decay heat analysis code, is provided in Table 3-2. Table 3-2: Projected SNF Data, Reactor MTU Burnup Enrichment Days Irradiated Type Month Day Year

73 3.3 Decay Heat Inventory Analysis The projected SNF discussed in section 3.2 was added to the EIA RW-859 data to yield a total SNF inventory dataset of 63,000 MTIHM (the current Yucca Mountain statutory commercial SNF limit). This data was applied to the MATLAB decay heat models discussed in section 2.5 to determine the total decay heat radiating from the 63,000 MTU inventory of commercial SNF over time (Figure 3-1 and Table 3-3). This model was also used to determine the average decay heat per unit mass (watts/mtihm) of the nations SNF inventory (Figure 3-2, Table 3-3). Figure 3-1: Spent Nuclear Fuel Decay Heat Inventory (total watts) over Time (Year), for Commercial SNF discharged through 2010 (63,000 MTIHM) 59

74 Figure 3-2: Spent Nuclear Fuel Decay Heat Inventory per Metric Ton of SNF (watts/mtu) over Time (Year), for Commercial SNF Discharged through 2010 (63,000 MTIHM) 60

75 Table 3-3: 2010 Commercial SNF Decay Heat Values Over Time Year Total Watts Watts/MTU Year Total Watts Watts/MTU E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

76 3.4 Application of Spent Nuclear Fuel Decay Heat Inventory Yucca Mountain Thermal Limits Three thermal limits must be met for the proposed Yucca Mountain nuclear waste repository; (1) SNF cladding temperatures below 350 C, (2) drift wall temperature below 200 C, and (3) mid-drift temperatures below 96 C. The 350 C cladding limit is utilized to minimize creep in the cladding of the fuel rods. The integrity of SNF cladding is important to repository safety because the cladding provides a secondary containment of the radioactive material (the primary being the SNF cask). The 200 C drift wall temperature limit was introduced to limit stresses in the tuff from the mineral crystobalite dispersed in the tuff which changes phase and expands by 5% between 200 C and 250 C. 24 The 96 C temperature limit between drifts was selected as to keep the mid-point between drifts below boiling. Below boiling conditions between drifts allows water that is boiled away from the drifts to flow between the drifts, thus water can flow through the repository without contacting the waste packages, as seen in Figure 3-3. Additional repository engineering design factors are provided in Table 3-4. The application of factors such as areal-heat-generation, line averaged thermal load, and the age of SNF at time of emplacement are analyzed and discussed in the remainder of this chapter. 62

77 Figure 3-3: Repository Cross-Section Design 25 Table 3-4: Additional Repository Engineering Design Factors 26 Overall areal-heat-generation density of waste inventory Line-averaged thermal load along drifts Age of spent nuclear fuel at time of emplacement Location of repository horizon with respect to stratigraphy Repository Footprint Waste Package spacing (line load vs. point load) Waste package sequencing Duration and heat removal efficiency of drift ventilation In-drift design and materials Areal Power Density, Line Averaged Loading, and Age of Spent Nuclear Fuel at Time of Emplacement When discussing heat loading on a repository scale, some references apply the use of linear averaged loading (line loading) or areal power density (APD). 26 Line loading assumes that the SNF waste canisters are spaced nearly end to end so that adjacent waste packages couple and share their heat output more effectively, acting as a uniform (line) source of heat. The converse to line loading is point loading, where waste packages are spaced far enough apart from each other that heating conditions along the drift are less uniform. The Total System Performance Analysis License Application (TSPA-LA) for Yucca Mountain utilizes line loading because it is more efficient at shedding condensate between drifts and because point loading results in less uniform rock dryout around the 63

78 drifts and less uniform thermohydrologic conditions along the drifts. 26 Areal power density can be defined as the concentration of thermal energy produced by emplaced waste, which is averaged over the area of the repository and expressed in watts per square meter or kilowatts per acre Converting Line Loading to Areal Power Density Linear loading and APD are both ways of expressing the same overall quantity, the amount of heat emanating from SNF in a repository at a given point in time. A basic repository layout is given in Figure 3-4, where drifts are represented as evenly spaced lines. If the line load and drift distance is specified, the areal power density can be calculated as follows. Figure 3-4: Yucca Mountain Drift Layout 28 If it is assumed that each drift has a length L, the line load is 1.45 kw/m, and drifts are separated by 81m, as seen in the generic plan view of Figure 3-5, the APD is determined by the flowing steps: 64

79 Linear Load = 1.45 kw/m Rectangle Width = 83 m Length =L Drift Distance = 81 m Drift Distance = 81 m Figure 3-5: Plan View Schematic for Areal Power Density Calculation Draw a rectangle of width 81 m and length L centered over a drift. The thermal load inside the drift is L( m) 1.45( kw / m) = 1.45 L ( kw ) (3.1) The area inside the rectangle is 83( m) L( m) = 83 L( m 2 ) (3.2) The areal power density of the rectangle is: L( kw ) = ( kw / m 2 83 L( m ) ) (3.3) There are 4047 m 2 per acre, so 65

80 2 2 (3.4) ( kw / m ) 4047( m / acre) = 70.7kW / acre Thus the APD for a repository where the drift distance is 81 m with a uniform linear load of 1.45 kw/m is 70.7 kw/acre. As long as the drift lengths are uniform, this method can be used no matter what the drift length is, since (L) cancels out of the derivation Repository Capacity based on APD Linear loading and APD can be useful tools for discussing repository thermal loading scenarios. In a paper titled White Paper, Thermal Operating Modes, the DOE presents linear loading values and drift distances for various repository temperature scenarios, as provided in Table The calculated APD for each drift distance is also given in the table. Parameters Table 3-5: DOE Temperature Scenarios Spacing Between Drifts (meters) Linear Thermal Loading Objective (kw/m) Areal Power Density (kw/acre) A: S&ER 1 Design B: SSPA C: SSPA Increased WP spacing D: SSPA Increased drift spacing E: SSPA Derated WPs F: WP spacing and extended ventilation G: Derated or smaller waste packages H: > Waste Package spacing and duration of forced ventilation I: Surface aging with forced ventilation J: Extended natural ventilation S&ER: Yucca Mountain Science and Engineering Report 2. SSPA: Supplemental Science and Performance Analysis 66

81 The data in Table 3-5 can be very useful in comparing the repository footprint of different temperature scenarios when a complete thermal analysis is completed, taking into consideration factors such as SNF cooling time before repository closure. Table 3-6 provides the maximum capacity and the year at which the capacity inventory will be reached for a repository operating at a maximum APD of 57 kw/acre (1.16 kw/m 2 ), using actual and projected SNF data. Table 3-6: Repository Capacity Limits if Constant Areal Power Density Values Could be Applied to Different SNF Cooling Times Years Cooled: APD Year Reached Total MTU Year Reached Total MTU Year Reached Total MTU Years Cooled: APD Year Reached Total MTU Year Reached Total MTU Year Reached Total MTU Caution in the Use of Linear Loading and Areal Power Density It is important to note that because a thermal loading scheme is valid for one scenario does not mean that the derived APD or linear thermal load for that scenario can be 67

82 applied to other scenarios. For example, if the APD of 57 kw/acre is determined to meet the repository thermal constrains discussed in section for 26 year cooled SNF, it would not be accurate to apply the same APD (57 kw/acre) to 50 years cooled SNF. The reason APD (or linear loading) cannot be applied to varying SNF cooling times is because the temperature within the repository is not a direct function of the maximum heat loading at the time of emplacement. The temperature within the repository is a function of the integral of the heat deposited in the repository over a period of hundreds of years. It may seem that the integral of the heat for any constant APD would be the same since the starting thermal load was the same. But the integral of the decay heat for a constant APD can be different because the integral heat deposited in the repository is a function of the decay rate of the emplaced SNF. If SNF that has cooled for 5 years is used to determine an APD, using this APD for 10 year cooled SNF would mean that more 10 year SNF could be placed into the repository. Because SNF heat decays exponentially, the magnitude of decay heat decreases more quickly over time for 5 year cooled SNF than for 10 year cooled SNF. Thus the integral of the decay heat for the 10 year cooled SNF would actually be greater, meaning the repository temperature would be greater. This is explained mathematically and graphically as follows. Using the general form of the Malbrain decay heat model, DecayHeat = 9410* t watts/mtu (3.5) 68

83 The decay heat at 5 years after reactor discharge is: DecayHeat = 9410* = watts/mtu (3.6) The decay heat at 10 years after reactor discharge is: DecayHeat = 9410*10 = watts/mtu (3.7) If we assume an APD of 57 kw/acre (1.16 kw/m 2 ), the total metric tons of SNF that can be placed per acre for 5 year cooled SNF is 20 MTU/acre (equation (3.8)) watts acre watts MTU = 20 MTU / acre (3.8) If we assume an APD of 57 kw/acre (1.16 kw/m 2 ), the total metric tons of SNF that can be placed per acre for 10 year cooled SNF is 34 MTU/acre (equation (3.9)) watts acre watts MTU = 34 MTU / acre (3.9) To determine the MTU of 10 years cooled SNF than can be emplaced per MTU of 5 year cooled SNF to reach the same APD, the total MTU of 10 year cooled SNF (found in equation (3.9)) is divided by the total MTU of 5 year cooled SNF (found in equation (3.8)), as seen in equation (3.10). 10yearcooled MTU 5 yearcooled MTU acre acre = = 1.68 (3.10) 69

84 But if one integrates the total decay heat of the 5 and 10 years cooled SNF, it is shown that using a constant APD for SNF cooled for varying times would yield different total heat deposited into the repository, potentially exceeding temperature limits. For 5 years cooled SNF: totalwatts = MTU 1MTU 10, t 9410 t dt = 322,220 = watts (3.11) For 10 years cooled SNF at the same APD: totalwatts = MTU 1.68MTU 10, t 9410 t dt = = 523,600 watts (3.12) Thus it can be seen that for the same initial APD (and thus linear thermal loading), using a constant APD for SNF aged for 5 years totals 322,220 watts and for SNF aged 10 years totals 523,600 watts. Thus different cooling periods for SNF emplaced at a constant APD yield different total (integrated) decay heat (see Figure 3-6 for a graphical representation), demonstrating that APD and linear loading are not accurate to apply to SNF cooled for different times. A study by Mansure and Petney 30 agrees with the conclusion that a constant APD cannot be applied to SNF with a cooling period different than the one used to derive the APD. In their study, when using a burnup value of 40,000 MWd/MTU, the maximum APD was 76.3 kw/acre for 5 year cooled SNF and

85 kw/acre for 25 year cooled SNF. Thus the capacity projections in Table 3-6 are considered to be too optimistic to meet repository thermal limits. Figure 3-6: Decay Heat over Time for Constant an Areal Power Density Met with Varying SNF Age Because areal power density and linear thermal loading cannot be used for thermal repository analysis, an alternative approach was required to determine repository capacity for varying SNF cooling periods. The selected approach utilized a semi-infinite medium repository model to determine repository temperatures for various scenarios and is discussed in the following chapter (chapter 4). 71

86 3.5 Chapter 3 References 20 United States Department of Energy, Energy Information Administration. < February 11, Nuclear Waste Policy Act of U.S.C et esq. Readily available. 22 U.S. Department of Energy, Energy Information Administration, Nuclear Fuel Data Form RW-859, Washington, D.C. (data as of December 31, 2002). 23 U.S. Department of Energy, Office of Land Management. < February 11, Johnson, Gary L. Thermal Performance of a Buried Nuclear Waste Container Storing a Hybrid Mix of PWR and BWR Spent Nuclear Fuel Rods. Lawrence Livermore National Lab. September R. A. Wigeland & T. H. Bauer. Eighth Information Exchange Meeting on Actinide and Fission Product Partitioning and Transmutation Nov. 2004, Las Vegas, NV. 26 U.S. Department of Energy, Office of Civilian Radioactive Waste Management. Mutliscale Thermogeological Model. ANL-EBS-MD October, Las Vegas, NV. 27 Nuclear Waste Technical Review Board. Sixth Report to the U.S. Congress and the U.S. Secretary of Energy, June Available online at < Accessed February 14, U.S. Department of Energy, of Civilian Radioactive Waste Management. Viability Assessment of a Repository at Yucca Mountain, Overview. North Las Vegas, NV. December U.S. Department of Energy February 2002, White Paper Thermal Operating Modes. Yucca Mountain Site Characterization Office, North Las Vegas, NV. 30 Mansure, A.J., and S.V. Petney Determination of Equivalent Thermal Loading as a Function of Waste Age and Burnup. Sandia Report SAND , Sandia National Laboratories, Albuquerque, New Mexico. 72

87 4 Repository Capacity Assessment Based on Explicit Thermal Design Limit Calculations Because the calculated decay heat (watts) emanating from the nations inventory of SNF cannot directly be used in repository thermal analysis by APD or linear thermal loading, an alternative approach was required. An in-house computer program called RETA (REpository Thermal Analysis) was used to perform repository thermal analysis. 4.1 The RETA Program RETA is a computer program developed as a summer undergraduate research project in the Nuclear Engineering department at North Carolina State University. RETA is useful for the application of this research because it calculates the thermal environment of a specified repository structure. The RETA code is based on the capabilities of the U.S. Nuclear Regulatory Commission (NRC) Total Performance Assessment (TPA) code by using the NFENV Module of TPA. The code has been separated from the TPA program and modified to fit more flexible models. 31 The NFENV module utilized in RETA computes the repository-horizon rock temperature using an analytic conduction-only model for mountain-scale heat transfer. 32 The model is based on thermal line sources laid out in parallel to represent drifts residing in a semiinfinite medium. Because many line sources exist (one for each drift), the temperature increase in the semi-infinite medium is the sum of the contributions of each source. The NFENV model determines the general solution for the temperature at any point in space and time by equation (4.1). 32 The default geology variables and values, such as rock mass 73

88 density or thermal conductivity, used in the RETA program are provided in Appendix H: RETA Code Repository Variables. T ( x, y, z, t) = ( t') 4k π B y erf ( ) + erf ( 4α ( t t') t 0 αq '' rep 1 L x L + x erf ( ) + erf ( ) 4α ( t t') 4α ( t t') 4α ( t t') 2 B + y z ( z 2H ) ) exp( ) exp( 4α ( t t') 4α ( t t') 4α ( t t') 2 ) dt' (4.1) where: T ( x, y, z, t) Increase in temperature at time t at point (x,y,z) in the semiinfinite medium due to one line source [C] '' q rep ( t') Time dependent repository heat flux [W/m 2 ] α k Thermal diffusivity of the semi-infinite medium [m 2 /s] Thermal conductivity of the semi-infinite medium [W/(m- C)] L Half-length of a line source [m] B Half-width of a line source [m] H Depth of a line source below the ground surface [m] t Actual time after activation of heat flux [s] t Time of integration [s] x,y,z Location of interest [m] The RETA program divides the total repository area of 1,165 acres into 10 sub-areas, as depicted in Figure 4-1. RETA performs temperature calculations in each sub-area, in addition to any additional points specified by the user. For the sub-area temperature calculations, the maximum calculated temperature for each sub-area is displayed to the user and all calculated temperature values are saved in an output file (TempDriftIS.dat and TempDriftSF.dat). 74

89 UTM Northing [m] UTM Easting [m] Region 1 Region 2 Region 3 Region 4 Region 5 Region 6 Region 7 Region 8 Region 9 Region 10 Figure 4-1: RETA Code Yucca Mountain Repository Layout (Note that the actual repository sub-areas do not overlap) 4.2 Areal Power Densities for Varying SNF Cooling Time The maximum APD values for SNF cooled for different time periods were determined using RETA. Although it was shown in section that the use of APD and linear loading should be exercised with caution, determining maximum APD values for varying cooling periods can tell us the maximum SNF cooling time that can be used for a given APD (Table 4-1). When applying APD for repository analysis, is it important to select an APD that meets the characteristics of the SNF applied for the analysis. For example, performing repository analysis with a constant APD to scenarios of varying interim storage time could lead to less than optimal results since higher APD values can be applied to SNF cooled for shorter periods. For example, if an APD of 35.8 kw/acre is used, no SNF 75

90 older than 75 years should be utilized. If older SNF is applied, a new maximum APD for the SNF, which will be a value below 35.8 kw/acre, must be determined. Like wise, if younger fuel is used for repository analysis, for example 10 year cooled fuel, a higher APD could be applied, in this case up to 84.8 kw/acre. It is important to note that one should not conclude that APD and linear loading cannot be applied to repository analysis. Rather, it should be concluded that APD and linear loading values should be derived for the specific SNF characteristics assumed for each repository analysis scenario. For this reason, APD values derived as a function of cooling time, using the default RETA decay heat input values, are provided below. Table 4-1: Maximum SNF Cooling Times for Varying Areal Power Densities Using Constant Burnup Data Years Cooling Repository Area (acres) MTU decay heat (watts/mtu) Max Temp b/w Drift (C): Max SNF Temp (C) Max Drift Wall Temp (C) Drift Dist (m) APD (kw/acre) Linear Load (kw/m): Decay Heat Assumptions for Thermal Analysis In order to determine the temperature at a point in time and space, the NFENV model in the RETA program calls a file named burnup.dat to determine the decay heat of SNF in terms of watts/mtu (it is important to note that though the file is named burnup.dat, it actually contains decay heat values (watts/mtu) and is not refereeing to reactor burnup as defined in this work). The decay heat value called from burnup.dat is stored as the 76

91 variable Q mtu (t). The input file burnup.dat has values for Q mtu ranging from 1 to 100,000 years, so when a particular value is called from the input file Q mtu is a function of time (hence Q mtu (t)). Q mtu (t) is multiplied by the areal mass loading (AML) to determine the '' value q rep ( t' ) used in equation (4.1), as seen in equation (4.2). q '' rep ( t') = AML Q ( t) (4.2) mtu where: AML = Areal Mass loading for the area occupied by the drifts (MTU/m 2 ) Q mtu (t) = Time-dependent heat output per MTU of waste [W/MTU] The decay heat values in burnup.dat are based on averaging a blend of 65% PWR SNF with a burnup of 42 GWd/MTU and 35% BWR SNF with a burnup of 32 GWd/MTU to a mean burnup value of 38.5 GWd/MTU (38,500 MWd/MTU). Examining values provided by the EIA, the enrichment for SNF irradiated at a burnup of 38,500 MWd/MTU was between 3.5 and 4.2 wt. % 235 U enrichment. The mean values of these enrichments, 3.85 wt. % 235 U, was used with the burnup 38,500 MWd/MTU to generate decay heat data from ORIGEN-ARP 5.01 to compare to the burnup.dat values. In Table 4-2 it can be seen that using decay heat values from the average burnup of 38.5 GWd/MTU rather than summing the decay heat from the two burnup levels, 42 and 32 GWd/MTU, does not cause a significant error. 77

92 Table 4-2: Comparison of Decay Heat (watts/mtu) for Designated and Averaged Burnup Values TIME PWR 38.5 GWd/MTU 3.85 % U BWR 38.5 GWd/MTU 3.85 % U 65% PWR, 35% BWR mix PWR 42 GWd/MTU, 4.07 % U PWR BWR 32 Gwd/MTU, 3.47% U BWR 65% PWR, 35% BWR mix % difference But comparing the ORIGEN-ARP 5.01 derived decay heat values to those existing in the burnup.dat file, it is seen that there is a significant difference between the two decay heat data sets (Table 4-3, Figure 4-2). The significance of these differences on repository temperature performance is discussed in the following section. 78

93 Table 4-3: Comparison of ORIGEN-ARP 5.01 and burnup.dat Decay Heat Values (watts/mtu) TIME ORIGEN- ARP 38.5 GWd/MTU Values in burnup.dat % difference in burnup.dat and ORIGEN Values

94 Figure 4-2: Comparison of ORIGEN-ARP 5.01 and burnup.dat Decay Heat Values 4.4 Sensitivity of Thermal Analysis Results to Burnup The sensitivity of the RETA code to the difference between the ORIGEN-ARP 5.01 and burnup.dat values was evaluated by performing simulations with the ORIGEN-ARP 5.01 and burnup.dat decay heat values, with all other RETA parameters constant. Both cases assume a 1165 acre repository with drift distance of 81 meters at an areal mass loading of MTU/acre for SNF aged 26 years. For the burnup.dat decay heat data, the maximum mid-drift temperature was C. For the ORIGEN-ARP 5.01 decay heat data, the maximum mid-drift temperature was C (a difference of approximately 13.7 %). All temperature calculations are given in Table 4-4 and Appendix G: Decay Heat Values for 58,000 MWd at Varying Burnup. It can thus be seen that the RETA 80

95 code is sensitive to the decay heat values (watts/mtu) stored in burnup.dat used to determine temperature calculations. Table 4-4: Maximum Mid-drift Temperature Values ( C) for burnup.dat and ORIGEN-ARP Decay Heat Values (watts/mtu) Subarea burnup.dat Max Temp At Time [C] [yr] ORIGEN-ARP Max Temp At Time [C] [yr] Table 4-5: Other Maximum Temperature Values ( C) for burnup.dat and ORIGEN- ARP Decay Heat Values (watts/mtu) burnup.dat ORIGEN-ARP 5.01 Max Temp [C] At Time [Yr] Max Temp [C] At Time [Yr] Sub- Area OS IS SF OS IS SF OS IS SF OS IS SF OS = Outer Drift Sufrace IS = Inner Drift Surface SF = Spent Fuel 81

96 4.5 Comparisons of SNF Decay Heat Values The decay heat values used in the burnup.dat file are based on SNF with assumed uniform burnup (38 GWd/MTU), enrichment, and discharge date. The actual U.S. inventory of SNF is composed of SNF with varying burnup and enrichment, discharged from 1968 to 2010 (projected). To estimate the decay heat of actual SNF discharge data, the MATLAB code discussed in chapter 2 was applied to the EIA RW-859 data to determine the decay heat of SNF for the 70,000 MTIHM Yucca Mountain statutory limit. Because information on the decay characteristics of Defense waste was not available, the 7,000 MTIHM Defense waste was assumed to have the decay heat of the average decay heat value for commercial SNF. This assumption should be conservative since most defense wastes have longer cooling times than commercial SNF. The decay heat values calculated by applying the EIA SNF inventory to the MATLAB code (henceforth referred to as the analytical decay heat values), including the future projections for discussed in section 3.2, compared to the burnup.dat file and ORIGEN-ARP 5.01 data, based on 38GWd/MTU burnup, are provided in Table 4-6 and Figure 4-3. Table 4-6: Comparison of ORIGEN-ARP 5.01, burnup.dat, and Analytical Decay Heat Values (watts/mtu) ORIGEN- ARP 5.01 (watts/mtu) Analytic (watts/mtu) Burnup.dat Years (watts/mtu)

97 Figure 4-3: Plot of ORIGEN-ARP 5.01, burnup.dat, and Analytical Decay Heat Values (watts/mtu) Comparing the three sets of decay heat data, analytical decay heat values are initially below the values given in burnup.dat and the ORIGEN-ARP decay heat values. As time increases, the decay heat of the ORIGEN-ARP and EIA applied data become greater than the burnup.dat decay heat data. The initially lower decay heat for the analytical values can best be attributed to the fact that the burnup.dat and ORIGEN-ARP decay heat data sets assume a lump sum discharge, whereas the analytical model applies discharge over a period of 42 years (1968 to 2010). 17 Heat generated by SNF decays exponentially, thus one would expect the EIA dataset to be initially lower because it has had more time to decay. The higher decay heat produced later in time by the EIA dataset is likely the product of high burnup SNF. As seen in Figure 2-2: Historical Burnup Trends for 83

98 Commercial U.S. Light Water Reactors, the burnup used by commercial nuclear power plants has been steadily increasing over the past decade. High burnup SNF produces more decay heat per unit mass of SNF, so the higher decay heat later in time is expected. To test the sensitivity of the EIA decay heat data results to the projected irradiation parameters assumed for fuel irradiated between 2002 and 2010, a case was run where the burnup values were lower than the projected values applied in section 3.2; the PWR parameters were reduced from 47,550 MWd/MTU at 4.25 % enrichment to 42,000 MWd/MTU at 3.9 % enrichment; the BWR parameters were reduced from 42,132 MWd/MTU at 3.9 % enrichment to 34,000 MWd/MTU at 3.2 % enrichment. Reducing the projected values for years yielded a slightly lower total decay heat value (watts/mtu), as observed in Table 4-7. Table 4-7: Comparison of Decay Heat Values with Low Burnup Projection (watts/mtu) Years ORIGEN- ARP 5.01 Burnup.dat EIA Data + Projected Burnup EIA Data + Projected Low Burnup

99 4.6 RETA Analysis with Varying Decay Heat Input It has been shown that the RETA code is sensitive to changes in the decay heats values (watts/mtu) used for repository temperature analysis. Since it has also been shown that there are differences between the decay heat values of the burnup.dat file, the analytical model applying EIA data and projected high burnup SNF, and the analytical model applying EIA data and projected low burnup SNF, a comparative analysis of these cases was performed in the RETA code. For ease of discussion, these cases were named case 1, case 2, and case 3, respectively, and are defined in Table 4-8. Table 4-8: Cases for SNF Decay Heat Input to RETA Case Number Source of Decay Heat Data (watts/mtu) Case 1 burnup.dat input file Case 2 EIA data up to projected burnup values for based on 47,550 MWd/MTU for PWR at 4.25% enrichment and 42,123 MWd/MTU at 3.91 %enrichment for BWR Case 3 EIA data up to projected burnup values for based on 42,000 MWd/MTU at 3.9% enrichment for PWR and 35,000 MWd/MTU at 3.2% enrichment for BWR Simulations were performed with the RETA code to determine the maximum mid-drift temperature for the three cases. The mid-drift temperature was selected because it is the first temperature limit reached for the high temperature mode of operation the repository is currently designed for (other temperature calculations are provided to demonstrate this). Each simulation assumed a repository area of 1165 acres containing 70,000 MTIHM at a drift spacing of 81 m (areal mass loading of 60 MTU/acre). The 70,000 MTIHM decay heat inventory (watts/mtu) for each case assumed a cooling period of 26 years (the default value in the RETA code). The maximum temperatures and the years after emplacement the maximum occurs for each case is provided in Table 4-9, Figure 4-4, and Figure 4-5. For the burnup.dat decay heat input (case 1), the maximum mid- 85

100 drift temperature (93 C) remains below the mid-drift temperature limit (96 C). For case 2 (103 C) and case 3 (101 C), the mid-drift temperature limit is exceeded for both cases. The SNF and outer drift surface temperatures are well below their respective temperature limits for all cases. It is worth noting that for cases 2 and 3, the cooling time of 26 years assumes that the repository would be fully loaded by 2036 (last discharge years cooling). The estimated emplacement period for the Yucca Mountain repository is 24 years, so that means that fuel shipments would have to begin in 2012 for the results for cases 2 and 3 to be valid. Longer cooling time (i.e., delaying the complete loading of the repository to after 2036) would lead to cooler mid-drift temperatures. For this reason the minimum cooling time required for case 2 and case 3 to meet temperature limits was examined in the following section. Table 4-9: Maximum Temperatures at Repository Mid-drift Points for Varying Decay Heat Cases, Cases Defined in Table 4-8 Max Temp [ C] Case 1 Case 2 Case 3 At Time Max Temp At Time Max Temp [Yr] [ C] [Yr] [ C] At Time [Yr] Sub-Area See Table 4-8 for the Definition of Cases 1, 2, and 3 86

101 Figure 4-4: Maximum Mid-Drift Temperature Profile Over Time for Cases 1 to 3 Figure 4-5: Maximum Spent Nuclear Fuel and Outer Drift Wall Surface Temperature Profile over Time for Cases 1 to 3 87

102 4.6.1 Minimum Cooling Time for Cases 2 & 3 for 81 m Drift Spacing Further simulations were performed on case 2 and case 3 to determine the necessary cooling time required to meet temperature limits. It was determined that a minimum cooling time of 64 years would be required for case 2. The maximum temperatures for this case were C at the mid-drift, C at the outer drift surface, and C for the SNF. For case 3, it was determined that a minimum cooling time of 51 years would be required. The maximum temperatures for this case were 95.9 C at the middrift, C at the outer drift surface, and C for the SNF. Thus according to these RETA simulations, the earliest repository closure for case 2 is the year 2074 and for case 3 the year Increasing the drift distances for case 2 and case 3 could serve to minimize the time need for the SNF to cool before emplacement, as discussed in section Minimum Drift Distances for Cases 2 & 3 for 26 Year Cooling For the both case 2 and case 3, as defined in Table 4-8, the temperature limit of 96 C was violated for 26 year cooled SNF for drift distances of 81 meters for 70,000 MTU of SNF. An investigation was performed to determine the minimum distance between drifts required to not violate any repository temperature limits for 70,000 MTU of SNF. For case 2, the minimum drift distance for 26 years cooling (emplacement in 2036) was 89 meters. For case 3 the minimum drift distance was determined to be 87 meters. All temperature points for these scenarios are presented in Table

103 Table 4-10: Maximum Temperatures ( C) for Minimum Drift Distances for Cases 2 & 3 for 26 Cooled SNF Case 2, 89 m Drift Spacing Case 3, 87 m Drift Spacing Outer Drift Outer Drift Mid-Drift SNF Surface Mid-Drift SNF Surface Subarea Max Temp [C] At Time [Yr] Max Temp [C] At Time [Yr] Max Temp [C] At Time [Yr] Max Temp [C] At Time [Yr] Max Temp [C] At Time [Yr] Max Temp [C] At Time [Yr] Maximum Capacity for Case 1 Decay Heat Input Because the maximum mid-drift temperature for case 1 (93.04 C) was below the 96 C mid-drift temperature limit, an examination was made to determine the maximum capacity (MTU) and optimal drift distance, assuming 26 year cooled SNF. It was determined that the maximum capacity for case 1 was 89,091 MTU at a drift spacing of 80 meters. For this scenario the maximum temperatures were: C mid-drift, C at the outer drift surface, and C for SNF. If a cooling period of 50 years were employed for the SNF before it was placed in the repository for case 1, the maximum capacity would be 95,000 MTIHM at a drift distance of 74.7 meters. The maximum temperatures for this scenario are C at the mid-drift, 89

104 119.9 C for the outer drift surface, and C for the SNF. If the commercial SNF discharge rate continues at the current rate of 2100 MTIHM/year, the 95,000 MTIHM capacity means that the repository is capable of storing waste generated through year Because the waste would require a 50 year cooling period, this would mean the repository could not be completely filled until 2072, at the earliest. Because the burnup utilized by commercial power plants is increasing and is projected to continue to increase with current plant up-rates and future plant additions, this estimation of repository capacity likely overestimates the potential capacity of the 1165 acre repository, based on case 1 inputs. The results demonstrate that the 1165 acre repository area currently cited by the RETA code has the capability to store more than the statutory limit of 70,000 MTIHM, if case 1 is indeed representative of the actual waste that will be emplaced in Yucca Mountain. Results from cases 2 and 3 require greater cooling times to reach the repository capacities derived in case 1. This demonstrates that using actual SNF data, rather than a general estimation of SNF decay heat yields different results when estimating repository thermal performance. 4.7 Thermal Repository Impact of Increasing Reactor Burnup Relationship Between Burnup and Megawatt Days Previous sections (2.4.2, 4.4, and 4.6) have discussed the impact of high burnup SNF on repository thermal performance. On a per metric ton basis, higher burnup fuels have higher decay heat, as seen in Figure 4-6. Because the factor that limits the amount of 90

105 SNF that can be placed per unit area in a repository is the decay heat of the SNF, it would appear that the trend of increasing burnup in commercial reactors has a negative impact on repository performance. Though higher burnup fuel cycles produce more decay heat per MTU, they also produce more electricity per MTU. This section investigates the thermal repository impact of high burnup SNF in a basis of total electricity produced, megawatt days (MWd) to determine if the greater quantity of electricity produced by high burnup SNF offsets the higher decay heat of high burnup SNF. Figure 4-6: Decay Heat (watts/mtu) vs. Time for Varying Burnup SNF To determine the impact of high burnup SNF on repository thermal loading, three burnup levels, 20,000, 35,000, and 58,000 MWd/MTU, were utilized to generate a total of 58,000 MWd. The total MTU required to produce 58,000 MWd for each burnup is given in Table

106 Table 4-11: Metric Tons Uranium Required to Produce 58,000 MWd at Varying Burnup Burnup (MWd/MTU) MTU Required to Produce 50,000 MWd 20, , ,000 1 ORIGEN-ARP 5.01 was utilized to determine the decay heat over time for each burnup level and MTU to produce 58,000 MWd. The enrichment for each burnup was based on data form the EIA RW-859 database. 17 The enrichments selected for each case are: Table 4-12: EIA Selected Enrichments for Desired Burnup Level Burnup Enrichment (MWd/MTU) (wt. % 235 U) 20, % 35, % 58, % The decay heat values (watts/mwd) over 10,000 years are given in Figure 4-7 and in Appendix G. High burnup SNF initially has higher decay heat, per MWd, than low burnup SNF. After approximately 100 years, the decay heat of low burnup SNF is greater, as seen in Figure

107 Figure 4-7: Decay Heat over Time to Produce the Same Amount of Energy (58,000 MWd) at Varying Burnup Figure 4-8: Transition Region of Decay Heat Contribution for Varying Burnup Producing 58,000 MWd 93

108 The high decay heat of the high burnup SNF for the initial time period is due to the decay heat contribution from actinides, as seen in Figure 4-9. After approximately years after reactor discharge, the decay heat contribution per MWd from actinides is higher from the lower burnup SNF. The total fission product decay heat (Figure 4-10) is generally the same for the three burnup cases. Thus the observation that high burnup SNF is initially hotter and then becomes cooler than low burnup SNF (on a per MWd basis) can be attributed to actinide decay heat. The dominant actinide decay heat contributors are 238 Pu, 239 Pu, 240 Pu, 241 Am, and 244 Cm, as seen in Figure On a per MWd production basis, more 239 Pu and 240 Pu is produced by low burn-up SNF than high burn-up SNF, as seen in Table Thus more 239 Pu and 240 Pu is available to breed 241 Am for low burn-up SNF, as discussed in section 0, explaining the increasing actinide decay heat over time for the low burn-up SNF. Figure 4-9: Actinide Decay Heat Contribution for Varying Burnup Levels, per MWd Production Basis 94

109 Figure 4-10: Fission Fragment Decay Heat Contribution for Varying Burnup Levels, per MWd Production Basis Figure 4-11: Dominant Actinide Decay Heat Contributors 95

110 Table 4-13: 239 Pu and 240 Pu Production per MWd for Varying Reactor Burn-up Burn-up (MWd/MTU) 239 Pu (grams/mwd) 240 Pu (grams/mwd) 20, , , Burnup Effects on Repository Temperatures As discussed in section , the temperature in a repository is a function of the integral of the decay heat over time, not of the instantaneous decay heat at emplacement. For this reason the RETA program was utilized to determine the temperature effects of high and low burnup SNF on a megawatt day basis. The base RETA case assumed 70,000 MTU of SNF irradiated at 38,000 MWd/MTU. These fuel characteristics would produce a total of 2.66*10 9 MWd. This value, 2.66*10 9 MWd, was used as the total energy production applied to the study of burnup effects on repository performance on a per MWd basis (any general number would produce similar results). The input necessary for RETA for this analysis was the total MTU at each burnup to produce 2.66*10 9 MWd and the decay heat per MTU for each burnup. The total MTU to produce 2.66*10 9 MWd was 133,000 MTU for 20,000 MWd/MTU, 76,000 MTU for 35,000 MWd/MTU, and 45,862 MTU for 58,000 MWd/MTU. The decay heat value (watts/mtu) for each burnup is given in Table The total MTU and decay heat (watts/mtu) was input for each burnup in the RETA code based on a repository area of 1165 acres. If none of the maximum temperatures were exceeded, the minimal drift distance without exceeding temperature limits was determined. The results of the RETA analysis (Table 4-15) yielded the drift distance necessary to store the SNF and maximum temperatures at the 96

111 drift wall, SNF cladding, and the mid-drift point. These results demonstrate that on a per megawatt day production basis, utilizing high burnup in commercial nuclear reactors is beneficial to reducing the mid-drift temperature, though for the 58,000 MWd/MTU burnup the outer drift temperature limit (200 C) was exceeded. Low burnup SNF resulted in lower SNF and drift temperatures, but yield higher mid-drift temperatures. Because the 58,000 MWd/MTU burnup went over the 200 C outer drift temperature limit, an analysis was performed to determine the maximum burnup without exceeding the temperature limits. Table 4-14: Decay Heat (watts/mtu) for Varying SNF Burnup Time (years) 20,000 MWd/MTU 35,000 MWd/MTU 51,500 MWd/MTU 58,000 MWd/MTU The highest burnup scenario without exceeding the outer drift wall temperature limit was determined to be 51,500 MWd/MTU. If the entire 1165 acre repository area were utilized for the 51,500 MWd/MTU burnup case, the distance between drifts would be m. 97

112 Because the between drift maximum temperature is below 96 C, this drift distance can be minimized. The minimum drift distance for the 51,500 MWd/MTU burnup case, assuming 26 year cooling, was 113 meters, producing maximum temperatures of 95.2 C between drifts, C at the outer drift wall, and C at the SNF. Using this drift spacing would reduce the total repository footprint by approximately 200 acres to a total footprint of approximately 967 acres. All of these cases were based on a 26 year cooling period, the default for the RETA code. If longer cooling periods were employed, higher burnup scenarios could meet temperature limits. For example, the 58,000 MWd/MTU burnup scenario would meet temperature limits after 36 year of cooling with the maximum temperatures of C at the drift wall, C between drifts, and C at the SNF. The results for these cases are provided in Table

113 Table 4-15: Maximum Temperatures for Varying Burnup Scenarios on a Megawatt Day Production Basis 58,000 20,000 MWd/MTU 35,000 MWd/MTU 51,500 MWd/MTU 51,500 MWd/MTU, Minimizing Drift Distance 58,000 MWd/MTU MWd/MTU, Extended Cooling, Minimizing Drift Distance 133,000 76,000 51,650 51,650 45,862 45,862 Burnup: Total MTU to produce 2.66*10 9 MWd Repository Drift Distance (m) Maximum SNF temperature ( C) * Maximum Drift Outer Surface Temperature ( C) ** Maximum Middrift Temperature ( C) *** Repository Footprint (acres) Year Cooling *Limit is 96 C ** Limit is 200 C ***Limit is 350 C Conclusion on Burnup Effects on Repository Temperature The results in Table 4-15 show that if the goal is to minimize maximum temperatures at the SNF cladding and drift wall, low burnup fuel cycles are the most advantageous. If the goal is to reduce the mid-drift temperature and minimize the total MTIHM emplaced in the repository, high burnup fuel cycles can be beneficial to repository performance. If high burnup SNF is cooled long enough to meet the SNF and outer drift wall surface temperature requirements, the repository footprint can be minimized and the capacity can be maximized. 99

114 4.8 Chapter 4 Summary This discussed the application of the RETA code to perform repository thermal analysis. Before repository analysis was performed, APD values were derived for varying SNF cooling time for the 63,000 MTU Yucca Mountain commercial SNF limit. A discussion on how APD values can be applied to repository analysis was provided to supplement the APD discussion in chapter 3. ORIGEN-ARP was used to calculate decay heat values (watts/mtu) to compare to the default RETA code decay heat values and the decay heat values calculated from the EIA SNF dataset (see chapter 3). It was shown that differences do exist between the three sets of values. When applied to the RETA code, the differences between the three decay heat sets resulted in varying repository temperature calculations, as discussed in section 4.4 and 4.5. Three cases were defined as decay heat value (watts/mtu) inputs to the RETA code in Table 4-8. Section 4.6 discusses the application of these cases to determine minimum cooling time and drift distances to meet repository thermal conditions. The minimum cooling time for cases 2 and 3 when using 81m drift spacing was 64 and 51 years, respectively. The minimum drift distance for 26 year cooling time for cases 2 and 3 was determined to be 89 and 87 meters, respectively. For the case 1decay heat input, the maximum capacity of the repository was determined to be 89,091 MTU when applying a 26 year cooling period with 80 meter drift spacing. When a cooling period of 50 years 100

115 was applied to case 1, the maximum capacity was determined to be 95,000 MTU at a drift distance of 74.1 meters. Section 4.7 discussed the impact of the trend in increasing reactor burnup on repository capacity. Though high burnup SNF has higher decay heat per MTU, on a per energy production basis (MWd), it was determined that high burnup fuel can minimize the repository footprint, though some interim storage may be required to meet drift wall temperature limits. For a burnup value of 58,000 MWd/MTU, a cooling period of 36 years was calculated to meet the drift wall temperature limit. It was determined that high burnup SNF can reduce the footprint of a repository on a per energy production basis. This demonstrates that the trend in high reactor burnup can be beneficial to minimize the repository footprint for the storage of SNF. 101

116 4.9 Chapter 4 References 31 Proctor, Cyrus. Program TEMPERATURE Description. August 29, U.S. Nuclear Regulatory Commission. Total-System Performance Assessment (TPA) Version 4.0 Code: Module Descriptions and User s Guide. Contract NRC January

117 5 Conclusions 5.1 Chapter Summaries This work served to accomplish four tasks: (1) develop a model that could quickly calculate the decay heat of spent nuclear fuel (SNF) at varying burnup, enrichment, and irradiation time, (2) apply the decay heat model to actual SNF data to determine the decay heat of the 63,000 MTU commercial SNF statutory limit for Yucca Mountain, (3) apply the decay heat model results to the repository temperature analysis code RETA to investigate the required SNF cooling time and drift separation distances for different decay heat inputs, and (4) to demonstrate this methodology for determining repository capacity and needs as a function of storage or cooling time, enrichment, irradiation time, and burnup Chapter 2 Summary A SNF decay heat model was developed by revising the existing Malbrain 33 decay heat model to include factors for enrichment, irradiation time, and burnup levels beyond 37,000 MWd/MTU. Because many radioactive decay processes occur during the decay of SNF, the 10,000 year time range of interest was broken down into seven time regions when a specific isotopic decay process (or group of processes) dominates in the contribution of decay heat in SNF. The regions were selected when the dominant contribution to decay heat over a range of time could be attributed to a single isotope or group of isotopes. The error term for these regions was computed and for those for which the error term remained large, further subdivision was implemented. 103

118 The first region was from 0 to 8 years, where the major contribution of decay heat is from the short-lived fission products. In the second region, 8 to 49 years, the largest contribution of decay heat originates from the daughter products, 90 Y and 137m Ba, that are in secular equilibrium with their respective parents 90 Sr and 137 Cs. The third region selected was from 49 to 1,500 years because, during this period, 241 Am dominates in the contribution of decay heat. The 49 to 1,500 years region was divided to 49 to 74 and 74 to 1,500 years because during this period the concentration of 241 Am is increasing. After approximately 74 years, the concentration of 241 Am is decreasing as a function of its halflife. The time period 74 to 1,500 years was further divided to 74 to 300 and 300 to 1,500 years because 300 years is approximately 10 half-lives of 137 CS and 90 Sr. The region 75 to 300 years was further broken down because there was relatively high error when a model was fit to this entire region. The region was divided to 74 to 150 years and 150 to 300 years because using 150 years yielded relatively accurate model results. The final time region for the decay of SNF was selected from 1,500 to 10,000 years because during this time the isotopes 239 Pu and 240 Pu dominate in the contribution of decay heat. When these time regions were fit to SNF data with burnup ranging from 1,000 to 58,000 MWd/MTU, a large error was computed for the fuel with burnup less than 10,000 MWd/MTU. Each time region was thus divided into burnup greater than and less than 10,000 MWd/MTU. A multivariable regression analysis tool was used to fit a polynomial equation, as a function of burnup, enrichment, and irradiation time, for each time and burnup region to develop the SNF decay heat model. 104

119 A MATLAB program implementing the decay heat model was developed that could quickly calculate the decay heat of a dataset of SNF. Comparing the results of this model to actual SNF data generated in ORIGEN-ARP yielded maximum errors less than 7% for 120 time points with varying burnup, enrichment, and irradiation time. Comparing the revised decay heat model results to Malbrain model results, at varying burnup, enrichment, and irradiation time, demonstrated the improvement of the revised models, where maximum error for the Malbrain model was 48.1% for the same time 120 points (some of this error can be attributed to the fact that the Malbrain model is not accurate for high burnup and does not factor for enrichment and irradiation perios) Chapter 3 Summary The MATLAB SNF decay heat model was used to determine the decay heat of nation s inventory of SNF discharged through December 31, 2002 and SNF projected to be discharged through December 31, The year 2010 was selected for this analysis because that is when the 63,000 MTU Congressional limit of commercial SNF for the Yucca Mountain repository will be reached. It was initially desired to apply the total calculated decay heat to areal power density limits referenced in Department of Energy (DOE) documents. Upon investigation it was determined that applying APD (or linear thermal loading) values to scenarios with SNF cooling times different than those used to determine the DOE derived APD values would not be accurate. The reason for this is that derived APD s assume decay characteristics specific to the fuel used to calculate the APD. If the APD is applied to SNF cooled for a longer time period, the emplaced SNF will deposit a different amount of total watts because the older SNF decays at a different rate. Different decay rates vary the temperature in the repository because the temperature 105

120 at any point in time and space of the repository is a function of the integral of the total heat generated in the repository. Because areal power density and linear thermal loading could not be applied to the calculated decay heat inventory, an alternative method for repository thermal analysis was required Chapter 4 Summary The computer code RETA was used to calculate the temperature at the three points where temperature limits exist for the proposed Yucca Mountain nuclear waste repository; (1) the SNF cladding, (2) the drift wall, and (3) the mid-drift. 34 For the default decay heat values used by the RETA code, no temperature limits were exceeded. Applying the decay heat calculated using the actual SNF data provided by the EIA to the RETA code resulted in temperatures exceeding the mid-drift temperature limit for cases with high and low burnup projections for the years 2002 to 2010 at drift spacing of 81 meters. Further analysis was performed to determine the minimum cooling time and drift distances for the two cases to meet the thermal requirements of the repository. The minimum drift distance for the averaged EIA projected burnup fuel, stored outside the repository for 26 years, for 2002 to 2010 was 89 meters. For low projected burnup values for years 2002 to 2010, 87 meter drift spacing was calculated. When 81 meter drift spacing was utilized for the low burnup and average projected burnup decay heat values for 2002 to 2010, cooling times of 51 and 64 years were required, respectively. Finally, an analysis on the impact of high burnup SNF was performed on the basis of total energy produced. The results showed that for high burnup SNF, assuming the 1,165 acre repository area used in the RETA code, the first temperature limit that would be 106

121 exceeded would be the drift wall temperature. If interim storage, on the order of approximately 36 years, was implemented for high burnup SNF, the drift wall temperature limit would no longer be exceeded and drifts could be moved closer together to minimize the repository footprint. When a 36 year cooling period was applied to the 58,000 MWd/MTU burnup case, the repository foot print was shrunk to 865 acres (which means that additional fuel could be emplaced in the 1,165 repository area). 5.2 Conclusions on Repository Needs The conclusions of this work demonstrate the need for additional repository area for the disposal of SNF if the U.S. continues the policy of the once through fuel cycle at current discharge rates of 2100 MTIHM/year. This conclusion was reached based on the following results. Section 4.6 showed that additional cooling time would be required to meet thermal repository limits for the cases when ORIGEN-ARP and EIA applied SNF decay heat data (watts/mtu) was applied to the RETA code. For case 1 input (where the default RETA decay heat values, watts/mtu, are utilized), all temperature calculation results were below repository thermal limits and a repository capacity limit of 89,091 MTU was calculated (assuming 26 year cooling time). At current discharge rates, 89,091 MTU, assuming 7,000 MTU defense waste, can be expected to be discharged by the end of year With nuclear plant license extensions expected for a large majority of the commercial reactor fleet 35, additional land will be required to store SNF for the oncethrough fuel cycle. This could potentially be accomplished by the expansion of the Yucca Mountain repository or by the siting of a second high level nuclear waste repository. 107

122 Siting a second high level nuclear waste repository presents a considerable challenge due to the high economic, social, and political costs associated with the siting of a repository. The application of an alternative fuel cycle, such as the Advanced Fuel Cycle Initiative (AFCI), could serve to minimize the volume of SNF waste required for disposal in a geologic repository, as well as to remove the high heat radioisotopes from SNF to maximize the amount of waste that can be emplaced per unit area in the repository, therefore minimizing the repository footprint. For example, utilizing a full recycle nuclear waste management policy, as depicted in Figure 5-1, could serve to mitigate the need for a second repository, though the Yucca Mountain statutory limit would be required to be increased. 36 Thus it is recommended that additional research into alternative waste management strategies in conjunction with research into the area expansion of the Yucca Mountain repository footprint be performed. Figure 5-1: Full Recycle Fuel Cycle Process 36 Future work, as discussed in the following section, could be performed to determine the thermal repository impacts of some of the other nuclear waste management strategies potentially available in conjunction with the expansion of the 1,165 acre footprint used in this analysis. 108