Criticality Model REV 00A CAL-DS0-NU-000003 2 September 2004 EXECUTIVE SUMMARY Disposal Criticality Analysis Methodology Topical Report1 describes the methodology for performing postclosure criticality analyses for Light Water Reactor and Department of Energy- Environmental Management-owned Spent Nuclear Fuel2 within the repository at Yucca Mountain, Nevada. An important component of the methodology is the criticality model. This analysis documents the criticality model and its benchmarking process. The criticality model is to be used for evaluating the criticality potential of configurations of fissionable materials. The criticality model uses the MCNP Monte Carlo computer code to analyze the geometry and materials that define a configuration, and to calculate the effective neutron multiplication factor (keff). The criticality model is benchmarked so that the range of applicability covers the various configurations of intact and degraded fuel that could occur in the repository over the preclosure and postclosure time periods. This analysis addresses three open items (13, 15, and 17) from the “Safety Evaluation Report for Disposal Criticality Analysis Methodology Topical Report, Revision 0.”3 These open items are as follows: Open Item 13: “The DOE should address the types of criticality uncertainties and biases, which is based on ANSI/ANS-8.17-1984, presented by the staff.” Open Item 15: “The DOE is required to include the isotopic bias and uncertainties as part of .kc if not included as isotopic correction factors.” Open Item 17: “The DOE should subject the method used for extending the trend to the procedures defined in ANSI/ANS-8.1-1998, C4(a) and C4(b).” Open Items 13, 15 and 17 are addressed in Section 6.3. Uncertainties based on extension of range of applicability and isotopic composition are accounted for in the critical limit calculation. Material and fabrication tolerances and uncertainties due to geometric or material representations used in the computational method are obviated by using bounding representations. The procedures defined in ANSI/ANS-8.1-1998, C4(a) and C4(b) are applied for extending the range of applicability. This analysis provides a description of the criticality model and benchmarking process, the intended use of the criticality model, the limitations of the criticality model, and a discussion of how the criticality model fits within the overall methodology from Disposal Criticality Analysis Methodology Topical Report. 1 Yucca Mountain Site Characterization Project 2003. Disposal Criticality Analysis Methodology Topical Report. YMP/TR-004Q, Rev. 02D. Las Vegas, Nevada: Yucca Mountain Site Characterization Office. ACC: MOL.20030617.0322. TBV-5172. 2 The methodology for performing postclosure criticality analyses within the repository at Yucca Mountain, Nevada for Naval Nuclear Propulsion Program spent nuclear fuel is described in the License Application. 3 Reamer, C.W. 2000. “Safety Evaluation Report for Disposal Criticality Analysis Methodology Topical Report, Revision 0.” Letter from C.W. Reamer (NRC) to S.J. Brocoum (DOE/YMSCO), June 26, 2000, with enclosure. In this analysis, the criticality model is benchmarked using applicable light water reactor, Department of Energy-owned spent nuclear fuel, and external configurations benchmark experiments. 1. PURPOSE The Disposal Criticality Analysis Methodology Topical Report (YMP 2003) presents the methodology for evaluating potential criticality situations in the monitored geologic repository. As stated in the referenced Topical Report, the detailed methodology for performing the disposal criticality analyses will be documented in model reports. Many of the models developed in support of the Topical Report differ from the definition of models as given in the Office of Civilian Radioactive Waste Management procedure AP-SIII.10Q, Models, in that they are procedural, rather than mathematical. These model reports document the detailed methodology necessary to implement the approach presented in the Disposal Criticality Analysis Methodology Topical Report and provide calculations utilizing the methodology. Thus, the governing procedure for this type of report is AP-3.12Q, Design Calculations and Analyses. The Criticality Model is of this latter type, providing a process evaluating the criticality potential of in-package and external configurations. The purpose of this analysis is to layout the process for calculating the criticality potential for various in-package and external configurations and to calculate lower-bound tolerance limit (LBTL) values and determine range of applicability (ROA) parameters. The LBTL calculations and the ROA determinations are performed using selected benchmark experiments that are applicable to various waste forms and various in-package and external configurations. The waste forms considered in this calculation are pressurized water reactor (PWR), boiling water reactor (BWR), Fast Flux Test Facility (FFTF), Training Research Isotope General Atomic (TRIGA), Enrico Fermi, Shippingport pressurized water reactor, Shippingport light water breeder reactor (LWBR), N-Reactor, Melt and Dilute, and Fort Saint Vrain Reactor spent nuclear fuel (SNF). The scope of this analysis is to document the criticality computational method. The criticality computational method will be used for evaluating the criticality potential of configurations of fissionable materials (in-package and external to the waste package) within the repository at Yucca Mountain, Nevada for all waste packages/waste forms. The criticality computational method is also applicable to preclosure configurations. The criticality computational method is a component of the methodology presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003). How the criticality computational method fits in the overall disposal criticality analysis methodology is illustrated in Figure 1 (YMP 2003, Figure 3). This calculation will not provide direct input to the total system performance assessment for license application. It is to be used as necessary to determine the criticality potential of configuration classes as determined by the configuration probability analysis of the configuration generator model (BSC 2003a). Benchmarking of the criticality computational method for potential waste form configuration classes is provided in the attachments to this calculation. CAL-DS0-NU-000003 REV 00A 13 September 2004 Criticality Model iil iign istics liiiIdentiiiion class liiii class ii(kclass) (3) iAll confiiclitionally (4) All ll iil l isfy desility (11)liiNo of critiil iiiiiNo No Waste form characterstics Geochemcal materiaperformance characteristics Waste package / EBS design characteristcs Waste package / EBS redesRepository site characterMaster Scenariost and associated confguraton classes fy applcable confguratfrom Master Scenariost (configuration class provides range of parameters) Estimate probability of achieving each confguraton class (1) Does confgurationsatisfy probability screening criterion? Perform criticality analyses for each confguraton class eff range for configuration (2) Does configuration class keff satisfy criticality acceptance criterion? Estimate probability of criticality for each configuraton class waste form configuration classes evaluated? Waste form guraton asses condacceptable waste package types evaluated? (5) Awaste forms evaluated? (8) Perform consequence analyses onndividual configuration classes that contrbute to total probability (7) Does totaprobability satisfy regulatory probability criterion? (6) Does totaprobability satgn probabicriterion? Acceptable repository design (9) Based on consequence analyses, perform TSPA dose analysis (10) Does TSPA dose satisfy reguatory performance objectives? Does not satisfy Satsfy Satsfy Does not satisfy Yes Yes Establish total probability calty (sum of alconfguraton class probabilities) Yes Satsfy Satsfy Satsfy Does not satisfy TSPA Evaluations Waste Package Type Evaluations Waste Form Configuration Class Evaluations Does not satisfy Does not satisfy NOTE: EBS = Engineered Barrier System, TSPA = Total System Performance Assessment. Figure 1. Disposal Criticality Analysis Methodology CAL-DS0-NU-000003 REV 00A 14 September 2004 Criticality Model This analysis addresses specific Open Items 13, 15, and 17 from the “Safety Evaluation Report for Disposal Criticality Analysis Methodology Topical Report, Revision 0” (Reamer 2000, Section 4), which are as follows: • Open Item 13: “The DOE should address the types of criticality uncertainties and biases, which is based on ANSI/ANS-8.17-1984, presented by the staff.” (Addressed in Section 6.3) • Open Item 15: “The DOE is required to include the isotopic bias and uncertainties as part of .kc if not included as isotopic correction factors.” (Addressed in Section 6.3.1) • Open Item 17: “The DOE should subject the method used for extending the trend to the procedures defined in ANSI/ANS-8.1-1998, C4(a) and C4(b).” (Addressed in Section 6.3.1.2). 2. QUALITY ASSURANCE Development of this analysis and the supporting activities have been determined to be subject to the Yucca Mountain Project’s quality assurance program in Section 8 of Technical Work Plan for: Criticality Department Work Packages ACRM01 and NSN002 (BSC 2004a). Approved quality assurance procedures identified in the Technical Work Plan (BSC 2004a, Section 4) have been used to conduct and document the activities described in this analysis. The Technical Work Plan also identifies the methods used to control the electronic management of data (BSC 2004a, Section 8) during the analysis and documentation activities. 3. USE OF SOFTWARE The software used or referenced in this report includes MCNP and CLREG as discussed in Sections 3.1 and 3.2. 3.1 MCNP The baselined MCNP code (MCNP V4B2LV, CSCI: 30033 V4B2LV) was used in the supporting documentation for keff calculations. MCNP is used in this report to generate output file tally edits for spectral characteristics, which are documented in Attachment III. The software specifications are as follows: • Software Title: MCNP • Version/Revision Number: Version 4B2LV • Status/Operating System: Qualified/HP-UX B.10.20 • Computer Software Configuration Item Number: 30033 V4B2LV • Computer Type: Hewlett Packard 9000 Series Workstations. The input and output files for the MCNP calculations are documented in Attachment I (Attachment I provides a listing of the files contained in Attachment II on compact disc) such that an independent duplication of the software use and the results could be performed. CAL-DS0-NU-000003 REV 00A 15 September 2004 Criticality Model The MCNP software used was (1) appropriate for the application of keff and spectral characteristic calculations, (2) used only within the range of validation as documented throughout MCNP-A General Monte Carlo N-Particle Transport Code (Briesmeister 1997) and Software Qualification Report for MCNP Version 4B2, A General Monte Carlo N-Particle Transport Code (CRWMS M&O 1998a), and (3) obtained from Software Configuration Management in accordance with appropriate procedures. 3.2 CLREG The CLREG software code (CLREG V1.0, STN: 10528-1.0-01) was used to calculate the LBTL for the benchmark experiments included in this report and extend the range of applicability for the critical limit (CL). The software specifications are as follows: • Software Title: CLREG • Version/Revision Number: V1.0 • Status/Operating System: Qualified/Windows 2000 • Software Tracking Number: 10528-1.0-01 • Computer Type: DELL OPTIPLEX GX240 Personal Computer. CLREG is a computer program that calculates sets of LBTL (LBTL functions) for waste packages under certain conditions. These limits account for the criticality analysis method bias and uncertainty of the calculated keff values for a set of critical experiments that represent the waste package, as determined by linear regression trending. The input and output files for the CLREG calculations are included in Attachment II on compact disc, such that an independent duplication of the software use and results could be performed. The CLREG software used was: (1) appropriate for the calculation of LBTL, (2) used only within the range of validation as documented in the CLREG documentation (BSC 2001c), and (3) obtained from Software Configuration Management in accordance with appropriate procedures. 4. INPUTS 4.1 CODES AND STANDARDS The following standard(s) are used for the bases of this report: • ANSI/ANS-8.1-1998. Nuclear Criticality Safety in Operations with Fissionable Material Outside Reactors. • ANSI/ANS-8.17-1984. Criticality Safety Criteria for the Handling, Storage, and Transportation of LWR Fuel Outside Reactors. 4.2 MATERIAL CROSS SECTIONS Nuclear cross section data are available from several source evaluations (data libraries). Utilizing the appropriate material cross sections in a criticality calculation is essential to CAL-DS0-NU-000003 REV 00A 16 September 2004 Criticality Model obtaining credible results. The cross sections are used to describe the physical interactions of neutrons with the materials of the SNF and waste package as the nuclear chain reaction process is simulated. The MCNP neutron interaction tables are processed from either the Evaluated Nuclear Data File (ENDF)/B-V, ENDF/B-VI, LLNL, LANL: T-2, or LANL: XTM evaluations. The sources for the neutron interaction tables are listed by material in MCNP-A General Monte Carlo N-Particle Transport Code (Briesmeister 1997, Appendix G). The cross sections in an evaluation are usually generated for elements or isotopes at a specific temperature, with a few exceptions, including cross sections for nuclides at multiple temperatures so systems with varying operating temperatures can be evaluated. For a particular table, the cross sections for each reaction are given on one energy grid that is sufficiently dense so linear-linear interpolation between points reproduces the evaluated cross sections within a specified tolerance, generally within one percent or less of the evaluated data (Briesmeister 1997, p. 2-18). Neutron interaction table designations are included as part of the material composition input to MCNP. Each material composition is composed of one or more elements or isotopes designated by an identifier that takes the form “ZZZAAA.nnX,” where ZZZ is the atomic number, AAA is the atomic mass, nn is the library identifier, and X is the class of data. A more complete description of the ZAID nomenclature is available in MCNP-A General Monte Carlo N-Particle Transport Code (Briesmeister 1997, Appendix G). 4.2.1 Light Water Reactor Spent Nuclear Fuel Cross Sections Table 1 lists elements and isotopes selected for use in the criticality calculations for PWR and boiling water reactor (BWR) SNF in accordance with Selection of MCNP Cross Section Libraries (CRWMS M&O 1998b). The criteria for the cross sections selected included use of standard versions of ENDF/B (ENDF/B-VI and ENDF/B-V, which contain evaluations at the elevated temperatures found in an operating reactor) whenever possible. It should be noted that the calculations of isotopic concentrations by the isotopic model (BSC 2004b) are performed at elevated reactor temperatures, as are the commercial reactor criticals (CRCs). Calculations using the criticality computational method for repository applications are performed using room- temperature cross sections since the temperatures for preclosure and postclosure conditions are lower than reactor temperatures, and it is conservative to use the lowest temperature cross section evaluations for the repository environment. The selected cross section sets are used in Attachment III. CAL-DS0-NU-000003 REV 00A 17 September 2004 Criticality Model Table 1. Selected MCNP ZAIDs for Various Elements and Isotopes for PWR SNF Element Isotope Cross Section Library ZAIDa Element Isotope Cross Section Library ZAID Hydrogen 1H 1001.50c Barium 138Ba 56138.50c 2H 1002.55c Praseodymium 141Pr 59141.50c 3H 1003.50c Neodymium 143Nd 60143.50c Helium 3He 2003.50c 145Nd 60145.50c 4He 2004.50c 147Nd 60147.50c Lithium 6Li 3006.50c 148Nd 60148.50c 7Li 3007.55c Promethium 147Pm 61147.50c Beryllium 7Be 4007.35c 148Pm 61148.50c 9Be 4009.50c 149Pm 61149.50c Boron 10B 5010.50c Samarium 147Sm 62147.50c 10B 5010.53c 149Sm 62149.50c 11B 5011.56c 150Sm 62150.50c Carbon C (natural) 6000.50c 151Sm 62151.50c 12C 6012.50c 152Sm 62152.50c 13C 6013.35c Europium 151Eu 63151.55c Nitrogen 14N 7014.50c 152Eu 63152.50c 15N 7015.55c 153Eu 63153.55c Oxygen 16O 8016.50c 154Eu 63154.50c 16O 8016.53c 155Eu 63155.50c 16O 8016.54c Gadolinium 152Gd 64152.50c 17O 8017.60c (B-VI.0) 154Gd 64154.50c Fluorine 19F 9019.50c 155Gd 64155.50c Sodium 23Na 11023.50c 156Gd 64156.50c Magnesium Mg (natural) 12000.50c 157Gd 64157.50c Aluminum 27Al 13027.50c 158Gd 64158.50c Silicon Si (natural) 14000.50c 160Gd 64160.50c Phosphorus 31P 15031.50c Holmium 165Ho 67165.55c Sulfur S (natural) 16000.60c (B-VI.0) Thulium 169Tm 69169.55c 32S 16032.50c Hafnium Hf (natural) 72000.50c Chlorine Cl (natural) 17000.50c Tantalum 181Ta 73181.50c Argon Ar (natural) 18000.59c 182Ta 73182.60c (B-VI.0) Potassium K (natural) 19000.50c Tungsten W (natural) 74000.55c Calcium Ca (natural) 20000.50c 182W 74182.55c 40Ca 20040.21c 183W 74183.55c Scandium 45Sc 21045.60c (B-VI.2) 184W 74184.55c Titanium Ti (natural) 22000.50c 186W 74186.55c Vanadium V (natural) 23000.50c Rhenium 185Re 75185.50c Chromium 50Cr 24050.60c (B-VI.1) 187Re 75187.50c 52Cr 24052.60c (B-VI.1) Iridium Ir (natural) 77000.55c 53Cr 24053.60c (B-VI.1) Platinum Pt (natural) 78000.35c 54Cr 24054.60c (B-VI.1) Gold 197Au 79197.50c CAL-DS0-NU-000003 REV 00A 18 September 2004 Criticality Model Table 1. Selected MCNP ZAIDs for Various Elements and Isotopes for PWR SNF (Continued) Element Isotope Cross Section Library ZAIDa Element Isotope Cross Section Library ZAID Manganese 55Mn 25055.50c Lead Pb (natural) 82000.50c Iron 54Fe 26054.60c (B-VI.1) 206Pb 82206.60c (B-VI.0) 56Fe 26056.60c (B-VI.1) 207Pb 82207.60c (B-VI.1) 57Fe 26057.60c (B-VI.1) 208Pb 82208.60c (B-VI.0) 58Fe 26058.60c (B-VI.1) Bismuth 209Bi 83209.50c Cobalt 59Co 27059.50c Thorium 230Th 90230.60c (B.VI.0) Nickel 58Ni 28058.60c (B-VI.1) 231Th 90231.35c 60Ni 28060.60c (B-VI.1) 232Th 90232.50c 61Ni 28061.60c (B-VI.1) 233Th 90233.35c 62Ni 28062.60c (B-VI.1) Protactinium 231Pa 91231.60c (B-VI.0) 64Ni 28064.60c (B-VI.1) 233Pa 91233.50c Copper 63Cu 29063.60c (B-VI.2) Uranium 232U 92232.60c (B-VI.0) 65Cu 29065.60c (B-VI.2) 233U 92233.50c Gallium Ga (natural) 31000.50c 234U 92234.50c Arsenic 74As 33074.35c 235U 92235.50c 75As 33075.35c 235U 92235.53c Bromine 79Br 35079.55c 235U 92235.54c 81Br 35081.55c 236U 92236.50c Krypton 78Kr 36078.50c 237U 92237.50c 80Kr 36080.50c 238U 92238.50c 82Kr 36082.50c 238U 92238.53c 83Kr 36083.50c 238U 92238.54c 84Kr 36084.50c 239U 92239.35c 86Kr 36086.50c 240U 92240.35c Rubidium 85Rb 37085.55c Neptunium 235Np 93235.35c 87Rb 37087.55c 236Np 93236.35c Yttrium 88Y 39088.35c 237Np 93237.50c 89Y 39089.50c 238Np 93238.35c Zirconium Zr (natural) 40000.60c (B-VI.1) 239Np 93239.60c (B-VI.0) 93Zr 40093.50c Plutonium 236Pu 94236.60c (B-VI.0) Niobium 93Nb 41093.50c 237Pu 94237.35c Molybdenum Mo (natural) 42000.50c 238Pu 94238.50c 95Mo 42095.50c 239Pu 94239.55c Technetium 99Tc 43099.50c 240Pu 94240.50c Ruthenium 101Ru 44101.50c 241Pu 94241.50c 103Ru 44103.50c 242Pu 94242.50c Rhodium 103Rh 45103.50c 243Pu 94243.60c (B-VI.2) 105Rh 45105.50c 244Pu 94244.60c (B-VI.0) CAL-DS0-NU-000003 REV 00A 19 September 2004 Criticality Model Table 1. Selected MCNP ZAIDs for Various Elements and Isotopes for PWR SNF (Continued) Element Isotope Cross Section Library ZAIDa Element Isotope Cross Section Library ZAID Palladium 105Pd 46105.50c Americium 241Am 95241.50c 108Pd 46108.50c 242mAm 95242.50c Silver 107Ag 47107.60c (B-VI.0) 243Am 95243.50c 109Ag 47109.60c (B-VI.0) Curium 241Cm 96241.60c (B-VI.0) Cadmium Cd (natural) 48000.50c 242Cm 96242.50c Indium In (natural) 49000.60c (B-VI.0) 243Cm 96243.35c Tin Sn (natural) 50000.35c 244Cm 96244.50c Iodine 127I 53127.60c (T-2) 245Cm 96245.35c 129I 53129.60c (B-VI.0) 246Cm 96246.35c 135I 53135.50c 247Cm 96247.35c Xenon Xe (natural) 54000.35c 248Cm 96248.60c (B-VI.0) 131Xe 54131.50c Berkelium 249Bk 97249.60c (B-VI:XTM) 134Xe 54134.35c Californium 249Cf 98249.60c (B-VI:XTM) 135Xe 54135.50c 250Cf 98250.60c (B-VI.2)) 135Xe 54135.53c 251Cf 98251.60c (B-VI.2) 135Xe 54135.54c 252Cf 98252.60c (B-VI.2) Cesium 133Cs 55133.50c 134Cs 55134.60c (B-VI.0) 135Cs 55135.50c (B-VI.0) 136Cs 55136.60c (B-VI.0) 137Cs 55137.60c (B-VI.0) Source: CRWMS M&O 1998b, Table 4.1 a NOTE: Information in parentheses “()” for the ENDF/B-VI cross sections indicate release number. 4.2.2 U.S. Department of Energy Environmental Management-Owned Spent Nuclear Fuel Cross Sections Table 2 lists elements and isotopes selected for use in the criticality computational method for the waste package configurations containing various U.S. Department of Energy Environmental Management (DOE EM-Owned) SNF. The selected cross section libraries have been used consistently in the analyses of the applicable critical benchmark experiments (BSC 2002, BSC 2003b). Table 2. Selected MCNP ZAIDs for Various Elements and Isotopes for DOE EM-Owned SNF Element Isotope Cross Section Library ZAID Element Isotope Cross Section Library ZAID Hydrogen 1H 1001.50c Molybdenum Mo (natural) 42000.50c 2H 1002.55c 95Mo 42095.50c 3H 1003.50c Silver 107Ag 47107.50c Helium 3He 2003.50c 109Ag 47109.50c 4He 2004.50c Cadmium Cd (natural) 48000.50c CAL-DS0-NU-000003 REV 00A 20 September 2004 Criticality Model Table 2. Selected MCNP ZAIDs for Various Elements and Isotopes for DOE EM-Owned SNF (Continued) Element Isotope Cross Section Library ZAID Element Isotope Cross Section Library ZAID Lithium 6Li 3006.50c Tin Sn (natural) 50000.35c 7Li 3007.55c Cesium 133Cs 55133.50c Beryllium 7Be 4007.35c 135Cs 55135.50c 9Be 4009.50c Barium 138Ba 56138.50c Boron 10B 5010.50c Gadolinium Gd (natural) 64000.35c 11B 5011.56c 152Gd 64152.50c Carbon C (natural) 6000.50c 154Gd 64154.50c 12C 6012.50c 155Gd 64155.50c 13C 6013.35c 156Gd 64156.50c Nitrogen 14N 7014.50c 157Gd 64157.50c 15N 7015.55c 158Gd 64158.50c Oxygen 16O 8016.50c 160Gd 64160.50c Fluorine 19F 9019.50c Hafnium Hf (natural) 72000.50c Sodium 23Na 11023.50c Tantalum 181Ta 73181.50c Magnesium Mg (natural) 12000.50c Tungsten W (natural) 74000.55c Aluminum 27Al 13027.50c 182W 74182.55c Silicon Si (natural) 14000.50c 183W 74183.55c Phosphorus 31P 15031.50c 184W 74184.55c Sulfur 32S 16032.50c 186W 74186.55c Chlorine Cl (natural) 17000.50c Gold 197Au 79197.50c Argon Ar (natural) 18000.59c Lead Pb (natural) 82000.50c Potassium K (natural) 19000.50c Thorium 232Th 90232.50c Calcium Ca (natural) 20000.50c Uranium 233U 92233.50c Titanium Ti (natural) 22000.50c 234U 92234.50c Vanadium V (natural) 23000.50c 235U 92235.50c Chromium Cr (natural) 24000.50c 236U 92236.50c Manganese 55Mn 25055.50c 237U 92237.50c Iron Fe (natural) 26000.55c 238U 92238.50c Cobalt 59Co 27059.50c Plutonium 238Pu 94238.50c Nickel Ni (natural) 28000.50c 239Pu 94239.55c Copper Cu (natural) 29000.50c 240Pu 94240.50c Gallium Ga (natural) 31000.50c 241Pu 94241.50c Zirconium Zr (natural) 40000.56c 242Pu 94242.50c Niobium 93Nb 41093.50c Americium 241Am 95241.50c Source: BSC 2003b, Table 5-3 5. ASSUMPTIONS None CAL-DS0-NU-000003 REV 00A 21 September 2004 Criticality Model 6. METHODOLOGY 6.1 PROCESS The criticality computational method uses a process for establishing criticality potential of configurations of fissionable materials within the repository at Yucca Mountain, Nevada. A configuration is defined by a set of parameters that characterize the amount and physical arrangement of materials that affect criticality (e.g., fissionable, neutron absorbing, moderating, and reflecting materials). A set of similar configurations whose composition and geometry are defined by specific parameters that distinguish them from other configurations is referred to as a configuration class. The criticality potential evaluation process follows the methodology described in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Section 3.5.3.2), and the guidance given in ANSI/ANS-8.1-1998, Nuclear Criticality Safety in Operations with Fissionable Material Outside Reactors. An overview of the criticality computational method is presented in Figure 2. As shown in Figure 2, keff evaluations are performed over the range of parameters (ROP) and parameter values for configurations in each class, as determined by the configuration generator model (BSC 2003a). Input for waste form compositions and characteristics come from waste form characteristics reports and applications of the isotopic model (BSC 2004b). Based on benchmark experiment evaluations, a range of applicability is established and an allowable limit (or CL) is calculated for a given configuration class. This CL, which is the value of keff at which a configuration is considered potentially critical, accounts for the criticality analysis method bias and uncertainty. The range of parameters and parameter values applied to the keff evaluations are checked against the range of parameters and parameter values that were used in establishing the CL. The process for establishing CL values is discussed in Section 6.3.1. A description of the process for defining the range of applicability of the CL values based on the experimental database used in establishing the CL values is presented in Section 6.3.1.1. A CL is established applicable to the range of parameter values that are used in the keff evaluation(s) so a comparison can be made to assess the criticality potential of the configuration(s). If the calculated keff is less than the CL for all configurations within a class, the configuration class is acceptable for disposal. A configuration class with one or more configurations with calculated keff values greater than or equal to the CL has the potential for criticality. Criticality experiments are selected from a group of experiments that include laboratory critical experiment (LCEs) and commercial reactor critical (CRCs) and are used to determine a bias and uncertainty associated with computer code analysis of the experiments. The bias is the deviation of the calculated keff values from unity. The range of certain physical characteristics of these experiments establish its ROA. This analysis focuses on in-package and external configurations and parameters. Benchmark experiments applicable to the configuration classes are selected, LBTL are established, and other margins or penalties, as necessary, are established for determining the CL. The term “penalty” is used in conjunction with extension of the ROA. The term “margin” is used to denote further reductions in the CL. CAL-DS0-NU-000003 REV 00A 22 September 2004 Criticality Model Evaluated Configuration Benchmark Generator Experiments Model ROP that defines Select experiments configuration class(es) Waste form characteristics Perform criticality analysis over additional Evaluate Establish ROA the range of parameter values for experiments of experiments configurations in each class (keff and spectral parameters) Yes Are there other Does ROA Spectral experiments? No include ROP? parameters Isotopic Model No Yes k eff Establish additional Establish CL .k ISO margin ) (.kEROA .k m Satisfy Yes Is k< CL? eff No Does Not Satisfy NOTES: .kEROA = penalty for extending the range of applicability. .kISO = penalty for isotopic composition bias and uncertainty. .km = an arbitrary margin ensuring subcriticality for preclosure and turning the CL function into an upper subcritical limit function (it is not applicable for use in postclosure analyses because there is no risk associated with a subcritical event). CL = critical limit, ROA = range of applicability, ROP = range of parameters. Figure 2. Criticality Potential Evaluation Process Overview 6.2 COMPUTATIONAL METHOD The criticality potential evaluation process applies the Monte Carlo simulation method (implemented by MCNP) along with the material cross section data identified in Tables 1 and 2 in calculating the keff for potential waste package configurations. The Monte Carlo simulation CAL-DS0-NU-000003 REV 00A 23 September 2004 Criticality Model method for representing neutron transport can best be described by the Neutron Transport Equation shown in Equation 1 (Duderstadt and Hamilton 1976, p. 113). . n 8 . + ·+ .. .t E r n ,. ,t) = d. '.dE'. '. (E'. E,. . . )E r n , ' . , ' t) + E r s ,. ,t) (Eq. 1) .n (, '(, (, s .4p . t 0 where (a complete description of all variables is provided by Duderstadt and Hamilton [1976, pp. 103 to 114]) r = coordinates in space (x, y, z) . = neutron direction defined in terms of the spherical coordinate angles T and F t = time E = energy n() = neutron density specification s() = neutron source specification v = velocity. MCNP is a general purpose computer code that can be used for neutron, photon, electron, or coupled neutron/photon/electron transport including the capability to calculate eigenvalues for various systems. The code treats an arbitrary three-dimensional configuration of materials in geometric cells bounded by first- and second-degree surfaces and fourth-degree elliptical tori (Briesmeister 1997, p. ix). The Monte Carlo method is used to theoretically duplicate a statistical process. The individual probabilistic events that comprise a process are simulated sequentially. The probability distributions governing these events are statistically sampled to describe the total phenomenon (Briesmeister 1997, p. 1-3). The Monte Carlo method allows explicit geometrical representation of material configurations. The appropriate material cross section data, as described in Section 4.2, is used. The accuracy of the Monte Carlo method for criticality calculations is limited only by the accuracy of the material cross section data, a correct explicit representation of the geometry, and the duration of the computation. The accuracy of the method and cross section data is established by evaluating critical experiments as shown in Attachments III through XII. MCNP calculates the following three keff estimates for each cycle in a given problem: 1. Collision 2. Absorption 3. Track length. A detailed description of the three keff estimates may be found in MCNP-A General Monte Carlo N-Particle Transport Code (Briesmeister 1997, Chapter 2, Section VIII, Part B). The keff estimate used in the criticality analyses and in the bias value determination is the statistical combination of all three keff estimates. CAL-DS0-NU-000003 REV 00A 24 September 2004 Criticality Model 6.3 ESTABLISHING CRITICALITY POTENTIAL The criticality potential is determined by the final comparison of a configuration’s keff with the applicable CL. This will determine which configuration classes have a potential for criticality. In equation notation the criticality potential criterion for a waste package system is as follows: kS + .kS < CL (Eq. 2) where ks = Calculated system keff .ks = An allowance for: (a) statistical and convergence uncertainties, or both in the computation of ks, (b) material and fabrication tolerances, and (c) uncertainties due to the geometric or material representations used in the computational method (Note: (b) and (c) can be obviated by using bounding representations) CL = The value of keff at which a configuration is considered potentially critical, accounting for the criticality analysis method bias and uncertainty, and any additional uncertainties (i.e., .kEROA or .kISO, or both). The criticality computational method provides a means for calculating ks and .ks using the Monte Carlo method and material cross section data identified in Tables 1 and 2 as implemented by MCNP. The criticality computational method also provides a means for determining the penalty for extending the range of applicability (EROA) (.kEROA) in the CL calculation, and allows the determination of whether a configuration has the potential for criticality. Additional uncertainty arising from isotopic composition calculations will be propagated to the CL calculation through the isotopic model (BSC 2004b). 6.3.1 Determining the Critical Limit An essential element of the criticality computational method used for calculating keff for a waste form configuration is the determination of the CL. The CL includes the bias and uncertainties associated with the criticality code and representation process. The CL for a configuration class is a limiting value of keff at which a configuration is considered potentially critical. The CL is characterized by statistical tolerance limits that account for biases and uncertainties associated with the criticality code trending process, and any uncertainties due to extrapolation outside the range of experimental data, or limitations in the geometrical or material representations used in the computational method. CAL-DS0-NU-000003 REV 00A 25 September 2004 Criticality Model The CL is represented as: CL(x) = f(x) -.kEROA -.kISO -.km (Eq. 3) where x = a neutronic parameter used for trending f(x) = the lower-bound tolerance limit function accounting for biases and uncertainties that cause the calculation results to deviate from the true value of keff for a critical experiment, as reflected over an appropriate set of critical experiments .kEROA = penalty for extending the range of applicability .kISO = penalty for isotopic composition bias and uncertainty .km = an arbitrary margin ensuring subcriticality for preclosure and turning the CL function into an upper subcritical limit function (it is not applicable for use in postclosure analyses because there is no risk associated with a subcritical event). A CL is associated with a specific type of waste package and its state (intact or various stages of degradation described by the master scenarios [YMP 2003, Figures 3-2a and 3-2b]). The CL is characterized by a representative set of benchmark criticality experiments. This set of criticality experiments also prescribes the basic range of applicability of the results. The steps that must be completed to establish a CL are: (1) selection of benchmark experiments, (2) establishment of the range of applicability of the benchmark experiments (identification of physical and spectral parameters that characterize the benchmark experiments), (3) establishment of a LBTL, and (4) establishment of additional uncertainties due to extrapolations or limitations in geometrical or material representations. 6.3.1.1 Range of Applicability In ANSI/ANS-8.1-1998 (p. 1), the term “area of applicability” means “the limiting ranges of material compositions, geometric arrangements, neutron energy spectra and other relevant parameters (such as heterogeneity, leakage, interaction, absorption, etc.) within which the bias of a calculational method is established.” The term “area of applicability” and ROA are used interchangeably here. When evaluating biases and uncertainties and choosing parameters (or areas) for which a bias would exhibit a trend, there are three fundamental areas (Lichtenwalter et al. 1997, p. 179) that should be considered: 1. Materials of the waste package and the waste form, especially the fissionable materials 2. Geometry of the waste package and waste forms 3. Inherent neutron energy spectrum affecting the fissionable materials. There are substantial variations within each of these categories that require further considerations. These are discussed by Lichtenwalter et al. (1997, p. 180). Quantifying the CAL-DS0-NU-000003 REV 00A 26 September 2004 Criticality Model various categories of parameters is complicated and generally requires approaches that use benchmark experiments characterized by a limited set of physical and computed neutron parameters and then compared with the neutronic parameters of a waste package. In this case, the application is a particular waste package in various forms of degradation as defined by the master scenarios (YMP 2003, Figures 3-2a and 3-2b). In the general practice of characterizing biases and trends in biases, one would first look at those fundamental parameters that might create a bias. That is, those parameters that could be in error with the most significant effect on the accuracy of the calculation. Important areas for evaluating criticality are configuration geometry, important materials concentration (reflecting materials, moderating materials, fissionable materials, and significant neutron absorbing materials), and nuclear cross sections characterizing the nuclear reaction rates that will occur in a system containing fissionable and absorbing materials. It is desirable for the range of the fundamental parameters of the benchmark critical experiments to encompass the range of the fundamental parameters of the system. This is not usually practical, and for those parameters that do not show a bias, it is acceptable to use critical benchmark experiments that cover most, but not all, of the ROP of the system under evaluation. In these situations, expert judgement may be used to determine if there is a reasonable assurance that the two are sufficiently close. 6.3.1.2 Extension of the Range of Applicability This section describes a process for extending the ROA. The means used to extend the ROA will depend on a number of factors, including (1) the nature of the critical experiments used to determine the ROA and trends with biases, (2) the particular waste form involved, and (3) the availability of other proven computer codes or methods used to evaluate the situation. The process described in ANSI/ANS-8.1-1998 (p. 18, C4) is used for the extension of the range of applicability: The area (or areas) of applicability of a calculational method may be extended beyond the range of experimental conditions over which the bias is established by making use of correlated trends in the bias. Where the extension is large, the method should be: • Subjected to a study of the bias and potentially compensating biases associated with individual changes in materials, geometries or neutron spectra. This will allow changes that can affect the extension to be independently validated. In practice this can be accomplished in a step-wise approach; that is, benchmarks for the validation should be chosen (where possible) such that the selected experiments differ from previous experiments by the addition of one new parameter so the effect of only the new parameter on the bias can be observed. • Supplemented by alternative calculational methods to provide an independent estimate of the bias (or biases) in the extended area (or areas) of applicability. CAL-DS0-NU-000003 REV 00A 27 September 2004 Criticality Model If a ROA is extended where there is a trend in the data without the use of additional experiments, additional penalty will be added to determine whether a system is critical. The penalty for EROA (.kEROA) will be subtracted from the LBTL as part of establishing a CL for a prescribed parameter range. The following techniques for extending the ROA when there are trends may be used to determine the additional penalty: (1) expert judgment (an evaluation by someone skilled by training and experience in criticality analysis); (2) sensitivity analysis; (3) statistical evaluation of the importance of these parameters, including regression analyses of more than one additional selected experiment with more than one predictor variable; or (4) comparison with other credible methods (code-to-code comparisons). For situations where a bias (trend) is not established, there are two options for extending the ROA. If the extension of the ROA is small and the understanding of the performance of the criticality code for these parameter ranges is also understood, it would be appropriate to use the established lower-bound tolerance limit and an appropriate penalty. If the extension is not small then more data covering the ROA will be necessary. When more data are obtained, the process shown in Figure 2 must be applied to the new data set. This applies when the ROA for fundamental parameters (material concentrations, geometry, or nuclear cross sections) does not cover the ROP of the waste package configuration and no trend is exhibited. 6.3.1.3 Lower-Bound Tolerance Limit A LBTL function may be expressed as a regression-based function of neutronic or physical variable(s), or both. In application, a LBTL function could also be a single value, reflecting a conservative result over the range of applicability for the waste form characterized. Geometric representation and inputs for computing the keff for a critical experiment with a criticality code often induce bias in the resulting keff value. Bias is a measure of the systematic differences between the results of a calculational method and experimental data. Uncertainty is a measure of the random error associated with the difference between the calculated and measured result. These keff values deviate from the expected result (keff = 1) of benchmark sets of critical experiments. The experimental value of keff for some benchmarks may not be unity (some are extrapolations to critical); however, this value is used for purposes of calculating errors. The application of statistical methods to biases and uncertainties of keff values is determined by trending criticality code results for a set of benchmark critical experiments that will be the basis of establishing lower-bound tolerance limits for a waste form. This process involves obtaining data on various neutronic parameters that are associated with the set of critical experiments used to benchmark the code-calculated values for keff. These data, with the calculated values of keff, are the basis of the calculation of the LBTL. The purpose of the LBTL function is to translate the benchmarked keff values from the criticality code to a design parameter for a waste form–waste package combination. This design parameter is used in criticality potential criteria. The LBTL definition addresses biases and uncertainties that cause the calculation results to deviate from the true value of keff for a critical experiment, as reflected over an appropriate set of critical experiments. CAL-DS0-NU-000003 REV 00A 28 September 2004 Criticality Model Figure 3 displays the following general processes for establishing LBTL functions: (1) regression-based methods reflecting criticality code results over a set of critical experiments that can be trended, and (2) random sample based methods that apply when trending is not an appropriate explanation of criticality code calculations. The regression approach addresses the calculated values of keff as a trend of neutronic and physical parameters. That is, regression methods are applied to the set of keff values to identify trending with such parameters. The trends show the results of systematic errors or bias inherent in the calculational method used to estimate criticality. In some cases, a data set may be valid, but might not cover the full range of parameters used to characterize the waste form. The area (or areas) of applicability of a calculational method may be extended beyond the range of the experimental conditions of the data set over which the bias is established by making use of correlated trends in the bias. Define set of validation experiments to be processed by Monte Carlo code encompassing desired range of applicability effl i) Output k values, spectraparameters, physcal parameters (enrichment, burnup, etc. Perform regression fits of keff on predictor variables to identify the trending parameter i(s)iwiive liiefftolit it itolit Normal? No No Applit Is regressonsignificant? Select predctor th conservatcorreaton Examne k data set for normality Use LUTB method to establish lower bound erance limUse NDTL method to establish lower bound tolerance limUse DFTL method to establsh lower bound erance limYes Yes y lower bound tolerance lim NOTE: DFTL = distribution free tolerance limit, NDTL = normal distribution tolerance limit, LUTB = lower uniform tolerance band. Figure 3. Process for Calculating Lower-Bound Tolerance Limits CAL-DS0-NU-000003 REV 00A 29 September 2004 Criticality Model If no trend is identified, a single value may be established for a lower-bound tolerance limit that provides the desired statistical properties associated with the definition of this quantity. The data are treated as a random sample of data (criticality code values of keff) from the waste form population of interest and straightforward statistical techniques are applied to develop the LBTL. For purposes of differentiation, this technique will be described as “nontrending.” The normal distribution tolerance limit (NDTL) method and the distribution-free tolerance limit method, discussed in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Sections 3.5.3.2.8 and 3.5.3.2.9), are “nontrending” methods. The regression or “trending” methods use statistical tolerance values based on linear regression techniques to establish a LBTL function. Trending in this context is linear regression of keff on the predictor variable(s). Statistical significance of trending is determined by the test of the hypothesis that the regression method mean square error is zero (YMP 2003, Section 3.5.3.2.6). Here the predictor variable(s) may be a parameter such as burnup or a parameter that indicates the distribution of neutrons within the system such as the average energy of a neutron that causes either fission or absorption. Where multiple candidates are found for trending purposes, each regression method will be applied and the conservative parameter will be used to determine the value of the LBTL. The lower uniform tolerance band (LUTB) method, discussed in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Section 3.5.3.2.7), trends a single parameter against keff. Multiple regression methods that trend multiple parameters against keff may also be used to establish the LBTL function. In either single or multiple situations, the statistically significant regression trend that produces the lowest LBTL is defined to be the more conservative regression. In all calculations of LBTL functions, the concept described as the “no positive bias” (Lichtenwalter et al. 1997, p. 160) rule must be accommodated. This rule excludes benefits for raising the LBTL for cases in which the best estimate of the bias trend would result in a LBTL greater than 1.0. The treatment of this element is discussed below in the context of each method used to establish the basic LBTL function. The LBTL function is defined as: f(x) = kC(x) -.kC(x) (Eq. 4) where x = parameter vector used for trending kC (x) = the value obtained from a regression of the calculated keff of benchmark critical experiments or the mean value of keff for the data set if there is no trend .kC (x) = the uncertainty of kC based on the statistical scatter of the keff values of the benchmark critical experiments, accounting for the standard deviation, the proportion of the population covered, and the size of the data set. The statistical description of the scatter quantifies the variation of the data set about the expected value and the contribution of the variability of the calculation of the keff values for the benchmark critical experiments. CAL-DS0-NU-000003 REV 00A 30 September 2004 Criticality Model Based on a given set of critical experiments, the LBTL is estimated as a function (f [x]) of a parameter(s). Because both .kC (x) and kC (x) can vary with this parameter, the LBTL function is typically expressed as a function of this parameter vector, within an appropriate range of applicability derived from the parameter bounds, and other characteristics that define the set of critical experiments. The calculational bias, ß, is defined as ß = kC - 1 (Eq. 5) and thus the uncertainty in the bias is identical to the uncertainty in kC (i.e., .kC = .ß). This makes the bias negative if kC is less than 1.0 and positive if kC is greater than 1.0. To prevent taking credit for a positive bias, the lower-bound tolerance limit is further reduced by a positive bias adjustment. The positive bias adjustment sets kC equal to 1.0 when kC exceeds 1.0. 6.4 DISCUSSION OF UNCERTAINTIES 6.4.1 Light Water Reactor Spent Nuclear Fuel Due to a lack of prototypic SNF criticality benchmark experiments (LCEs using SNF), and the wide range of potential configurations of waste package internal components over the regulatory period of the repository, a combination of LCEs and CRCs are necessary. The establishment of the MCNP code bias can be made using the LCEs and CRCs to provide .kc (discussed in Attachments III through XI) needed for the determination of the CL. Sources and impacts of uncertainty for commercial SNF involve the following: • CRC calculations of keff are performed at elevated reactor temperatures. However, not all isotopes in the selected MCNP cross section library have tabulated cross section data available at elevated reactor temperatures, although 235U is available at higher temperatures, as is 238U, which dominates the SNF inventory and resonance absorption. This uncertainty is inherent in the computed code bias. • An integral benchmark approach is used with regard to CRCs. The calculation of SNF isotopic material compositions produces uncertainty in the calculated SNF inventory that is used as input to MCNP. This uncertainty is accounted for by the isotopic model (BSC 2004b) and is assessed as an additional penalty on the CL. • Additional bias and uncertainty is caused by the water scattering kernel. A scattering kernel is used to adjust cross section data for the effects of molecular bonding, which is particularly important for the hydrogen as the principal means of slowing down neutrons to thermal energies that can cause fission in SNF. Water at higher temperatures (e.g., 587 K) will require benchmark cases (CRCs) to use a higher-temperature scattering kernel, while lower-temperature systems (e.g., waste package and LCEs) will use a lower-temperature kernel (e.g., 300 K). In a water-moderated thermal neutron CAL-DS0-NU-000003 REV 00A 31 September 2004 Criticality Model system, higher-temperature scattering results in more energetic scattering reactions, thereby causing the system to have a slightly harder neutron spectrum. This will result in a slightly lower keff than if using the lower-temperature scattering kernel. Therefore, this bias and uncertainty is accounted for by using the higher-temperature scattering kernel for computations of code bias from the CRCs, but using the lower-temperature kernel for applications in the waste package configurations. 6.4.2 U.S. Department of Energy Environmental Management-Owned Spent Nuclear Fuel There are no additional uncertainties associated with the criticality computational method for the selected DOE EM-Owned SNF types analyzed in this report and the cross section data identified in Table 2 other than those inherent to cross section data evaluations, which are already taken into account by using the process described in this analysis. 6.5 DISCUSSION OF ALTERNATIVES Alternative methods and alternative code implementations of Monte Carlo, as well as alternate nuclear data sets, were considered. 6.5.1 Method Alternatives The Monte Carlo option is not the only means of solving the Neutron Transport Equation (Equation 1). Other solution methodologies include the Discrete Ordinates Method (Duderstadt and Hamilton 1976, pp. 117 to 120) and the Diffusion Theory Method (Duderstadt and Hamilton 1976, pp. 149 to 226). Both of these methodologies have been used successfully in reactor applications. The principal advantage of the Monte Carlo methodology over the Discrete Ordinates Method is that the Monte Carlo approach facilitates solutions in complex geometries like the waste package. Diffusion theory codes do not work well in the presence of strong neutron absorbers, such as the boron contained in the steel of the waste package basket structure. Thus, the Monte Carlo methodology provides the strongest alternative for repository criticality calculations. 6.5.2 Code Alternatives The Monte Carlo simulation of the Neutron Transport Equation is implemented in a number of different computer codes. MCNP is one of the best known codes and is supported by Los Alamos National Laboratory. An alternative code supported by Oak Ridge National Laboratory is the KENO code, which is part of the SCALE system (CRWMS M&O 2000d). KENO is often used by the U.S. Nuclear Regulatory Commission to check calculations for spent nuclear fuel casks, as is the British MONK code. The KENO code requires that its nuclear data libraries (typically derivatives of ENDF/B) be prepared explicitly for the type of fuel to be analyzed, because the neutron spectrum of the fuel is used in the preparation of a compressed form of the nuclear data library. The variable neutron spectra of different fuel configurations under repository conditions would make it difficult to prepare an appropriate KENO library. MCNP and MONK do not require such nuclear data compression. MONK must be purchased via a commercial license, while MCNP is a DOE-supported code. Thus, MCNP is the preferred implementation of the Monte Carlo methodology. CAL-DS0-NU-000003 REV 00A 32 September 2004 Criticality Model 6.5.3 Data Set Alternatives 6.5.3.1 Light Water Reactor Spent Nuclear Fuel The criticality analysis that will be applied in evaluating waste package designs for commercial SNF uses a subset of the isotopes present in commercial SNF. The process for establishing the isotopes to be included is based on the nuclear, physical, and chemical properties and the presence of the commercial SNF isotopes in the nuclear data library. The nuclear properties considered are cross sections and half-lives of the isotopes; the physical properties are concentration (amount present in the SNF) and state (solid, liquid, or gas); and the chemical properties are the volatility and solubility of the isotopes. Time effects (during disposal) and relative importance of isotopes for criticality (combination of cross sections and concentrations) are considered in this selection process. None of the isotopes with significant positive reactivity effects (fissionable isotopes or isotopes that are significant moderators or reflectors) are removed from consideration, only nonfissile absorbers that are not significant moderators or reflectors. Thus, the selection process is conservative from a nuclear criticality perspective. The selection process results in 14 actinides and 15 fission products (referred to as principal isotopes) as the SNF isotopes to be used for burnup credit applications. Table 3 lists these isotopes. The actinide 233U from this table is not present in current generation commercial SNF. However, for long disposal time periods (beyond the regulatory period of concern), 233U buildup is sufficient to be a potential criticality concern. Analyses supporting the selection of these isotopes are presented in Principal Isotope Selection Report (CRWMS M&O 1998c). Table 3. Principal Isotopes for Commercial SNF Burnup Credit 95Mo 145Nd 151Eu 236U 241Pu 99Tc 147Sm 153Eu 238U 242Pu 101Ru 149Sm 155Gd 237Np 241Am 103Rh 150Sm 233U 238Pu 242mAm 109Ag 151Sm 234U 239Pu 243Am 143Nd 152Sm 235U 240Pu CRCs are used to support the selection of the principal isotopes. This was accomplished by using SNF depleted isotopic inventories calculated using the SAS2H control module of the SCALE code package as discussed in Summary Report of Commercial Reactor Critical Analyses Performed for the Disposal Criticality Analysis Methodology (CRWMS M&O 1998d), using reactor operating history data from four different PWRs: Three Mile Island Unit 1, Crystal River Unit 3, Sequoyah Unit 2, and McGuire Unit 1. In addition, SNF from one BWR-Grand Gulf Unit 1-was also used. The reactor operating history information, pertinent details regarding assembly design schematics, and loading patterns were obtained from several technical reports (Punatar 2001a; CRWMS M&O 1998e; CRWMS M&O 1998f; Wimmer 2001; and Punatar 2001b). Four different sets of burned fuel isotopes, in addition to 16O, were represented for each of the PWR CRC statepoints: best-estimate (consisting of up to 84 isotopes); principal isotopes (consisting of 29 “most important with respect to reactivity” fission products and actinides); principal actinides (consisting of 14 isotopes from uranium, plutonium, and americium); and CAL-DS0-NU-000003 REV 00A 33 September 2004 Criticality Model actinide only (consisting of 10 major actinide elements found in spent nuclear fuel). The isotope sets used are presented in Table 4. The CRC benchmark cases evaluated cover an initial enrichment range of 1.93 to 4.167 weight percent 235U and an assembly average burnup range of 0.0 to 49.0 GWd/MTU. Core average burnups range from 0 GWd/MTU for the beginning of life CRC statepoints to 33 GWd/MTU. Figure 4 illustrates the keff values from the PWR CRC benchmark results that were taken from Summary Report of Commercial Reactor Critical Analyses Performed for the Disposal Criticality Analysis Methodology (CRWMS M&O 1998d, pp. 40 to 43). The results indicate, as expected, that as the number of SNF isotopes represented increases, the scatter in the keff values decrease. The significance of this observation is that as the fuel composition is more accurately represented, the uncertainty in the bias decreases. Table 4. CRC Fuel Isotopes Set Description Isotope Seta Isotope Seta Isotope Seta Isotope Seta 3H BE 108Pd BE 153Eu BE, PI 238Pu BE, PI, PA, AO 4He BE 107Ag BE 154Eu BE 239Pu BE, PI, PA, AO 6Li BE 109Ag BE, PI 154Eu BE 240Pu BE, PI, PA, AO 7Li BE 131Xe BE 152Gd BE 241Pu BE, PI, PA, AO 9Be BE 134Xe BE 154Gd BE 242Pu BE, PI, PA, AO 16O BE, PI, PA, AO 135Cs BE 155Gd BE, PI 241Am BE, PI, PA, AO 75As BE 138Ba BE 156Gd BE 242Am BE, PI, PA 80Kr BE 141Pr BE 157Gd BE 243Am BE, PI, PA 82Kr BE 143Nd BE, PI 158Gd BE 242Cm BE 83Kr BE 145Nd BE, PI 160Gd BE 243Cm BE 84Kr BE 147Nd BE 233Pa BE 244Cm BE 86Kr BE 148Nd BE 233U BE, PI, PA 245Cm BE 89Y BE 147Pm BE 234U BE, PI, PA, AO 246Cm BE 93Zr BE 148Pm BE 235U BE, PI, PA, AO 247Cm BE 93Nb BE 149Pm BE 236U BE, PI, PA, AO 248Cm BE 95Mo BE, PI 147Sm BE, PI 237U BE 135Xe BE 99Tc BE, PI 149Sm BE, PI 238U BE, PI, PA, AO 133Cs BE 101Ru BE, PI 150Sm BE, PI 235Np BE 165Ho BE 103Ru BE 151Sm BE, PI 236Np BE 232Th BE 103Rh BE, PI 152Sm BE, PI 237Np BE, PI, PA 105Rh BE 151Eu BE, PI 238Np BE 105Pd BE 152Eu BE 237Pu BE NOTE: aBE = best-estimate; PI = principal isotope; PA = principal actinide; AO = actinide only. CAL-DS0-NU-000003 REV 00A 34 September 2004 Criticality Model 1.12 1.1 1.08 1.06 1.04 1.02 1 0.98 0.96 0 5 101520253035404550 k eff l Isotope Priiinily SQ2CR2 Best-Estimate Principancpal Actde Actinide-OnMG1 TMI1 Statepoint ID Source: CRWMS M&O 1998d, pp. 40 to 43 NOTE: CR3 (Crystal River Unit 3), SQ2 (Sequoyah Unit 2), MG1 (McGuire Unit 1), TMI1 (Three Mile Island Unit 1). Figure 4. PWR CRC Eigenvalues 6.5.3.2 U.S. Department of Energy Environmental Management-Owned Spent Nuclear Fuel There are no alternative data sets for the DOE EM-Owned SNF types mentioned in this report. 6.6 CONFIGURATION CLASSES A standard set of degradation scenarios based on features, events, and processes that may affect criticality have been identified in the Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Section 3.3) that must be considered as part of the criticality analysis of any waste form. Following degradation scenario chains to their end-states results in a series of configurations. A configuration is defined by a set of parameters characterizing the quantity and physical arrangement of materials at a specific location that have a significant effect on criticality (e.g., fissile materials, neutron absorbing materials, reflecting materials, and moderators). A configuration class is a set of similar configurations whose composition and geometry are defined by specific parameters that distinguish one class from another. Within a class, the configuration parameters may vary over a given range. CAL-DS0-NU-000003 REV 00A 35 September 2004 Criticality Model The scenarios are grouped according to three general locations for potentially critical degraded configurations: (1) inside the waste package, (2) outside the waste package in the near-field environment, and (3) outside the waste package in the far-field environment. 6.6.1 In-Package Configuration Classes Configuration Class IP-1a: For this configuration class, the fissile material separates from the neutron absorber, which remains in place within the waste package. This configuration class can be reached from scenario IP-1 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Figure 3-2a) where the waste form degrades faster than the waste package internal structures. In this configuration class, the neutron absorber is not released from its carrier before the waste form degrades and the fissionable material degrades in place. Configuration Class IP-1b: For this configuration class, the fissile material separates from the neutron absorber, which remains in place within the waste package. This configuration class can be reached from scenario IP-1 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Figure 3-2a) where the waste form degrades faster than the waste package internal structures. The neutron absorber is not released from its carrier before the waste form degrades and the degraded waste form is mobilized. The mobilized fissionable material accumulates at the bottom of the waste package. A mechanism to mobilize the degraded waste form is needed. Configuration Class IP-2a: For this configuration class, both the waste package internal structures and the waste form degrade simultaneously. The corrosion product composition is a mixture of fissile material and degradation products from other internal structures. This configuration class can be reached from scenario IP-2 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Figure 3-2a) and will result in the fissionable material accumulating at the bottom of the waste package. Since both fissionable waste form and waste package internal structures are fully degraded, with all the soluble degradation products removed, the only residual effect of a difference in degradation rates is the nature of any separation between the degradation products of the fissionable waste form and waste package internal structures. Intermediate configurations in which only the basket or the waste form is degraded first are covered by scenario IP-1 (configuration classes IP-1a and IP-1b), or scenario IP-3 (configuration classes IP-3a, IP-3b, IP-3c, and IP-3d). Configuration Class IP-3a: For this configuration class, the waste package internal structures degrade, but the waste form remains relatively intact. This configuration class can be reached from scenario IP-3 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Figure 3-2a), and results in an intact waste form at the bottom of the waste package surrounded by, and/or beneath, the degraded corrosion products. Configuration Class IP-3b: For this configuration class, the waste package internal structures degrade but the waste form remains relatively intact. This configuration class can be reached from scenario IP-3 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Figure 3-2a). This configuration class has the waste package internal basket structure collapsing with the waste form and degraded corrosion products stratified. Neutron absorbers are flushed from the waste package. CAL-DS0-NU-000003 REV 00A 36 September 2004 Criticality Model Configuration Class IP-3c: For this configuration class, the waste package internal structures degrade but the waste form remains relatively intact. This configuration class can be reached from scenario IP-3 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Figure 3-2a). This configuration class is characterized by the complete degradation of the basket structure support and neutron absorber plates. The soluble neutron absorber is flushed from the waste package. Two paths that lead to this configuration class apply to the waste package design in which either the basket structural support degrades prior to the neutron absorber plates or the neutron absorber plates degrade prior to the waste package internal structures. Configuration Class IP-3d: For this configuration class, the waste package internal structures degrade but the waste form remains relatively intact. This configuration class can be reached from scenario IP-3 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Figure 3-2a). The neutron absorbing structure degrades significantly before structural collapse occurs. The absorber separates from the waste form and remains inside the waste package. The waste form and waste package internal structures maintain their integrity. Configuration Class IP-4a: For this configuration class, the fissile material degrades faster than the waste package internal structures in a flow through geometry and moves away from the neutron absorber, which remains in the waste package. This configuration class can be reached from scenario IP-4 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Figure 3-2b). In this configuration class, the waste form degrades prior to the neutron absorber being released from its carrier. The fissionable material remains in place to be locked in by its own hydration or by the hydration of waste package internal structures. Configuration Class IP-4b: For this configuration class, the fissile material degrades faster than the waste package internal structures in a flow through geometry and moves away from the neutron absorber, which remains in the waste package. This configuration class can be reached from scenario IP-4 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Figure 3-2b). This configuration class considers the mobilization of the degraded waste form and its separation from the neutron absorber. The mobilized fissionable material hydrates and collects with other hydrated corrosion products and accumulates at the waste package bottom. A mechanism to mobilize the degraded waste form is needed. Configuration Class IP-5a: For this configuration class, both the waste package internal structures and waste form have degraded at similar rates. This configuration class can be reached from scenario IP-5 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Figure 3-2b) (i.e., flow-through geometry occurring either before or after the waste form and basket degrade and hydrated products collect at the bottom of waste package). Flow-through flushing removes soluble neutron absorbers. This configuration class can also be obtained from degradation scenarios IP-1 or IP-3. In IP-1, the waste form degrades faster than the basket, and in IP-3, the basket degrades faster than the waste form, but ultimately the waste form and other internal components degrade and accumulate at the bottom of the waste package. Configuration Class IP-6a: For this configuration class, the waste package internal structures degrade faster than the waste form. This configuration class can be reached from scenario IP-6 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, CAL-DS0-NU-000003 REV 00A 37 September 2004 Criticality Model Figure 3-2b). The waste form is relatively intact and sitting at the bottom of the waste package either surrounded by or beneath the degraded corrosion products. This configuration class is also obtained from degradation scenario IP-3 where the neutron absorber and waste package basket structure have significantly degraded before the waste package bottom failure. 6.6.2 External Configuration Classes External accumulation of fissile material can occur in the near-field or the far-field. The near-field is defined as the invert, which is the part of the drift that is directly underneath the waste package. The invert is made up of crushed tuff with a high porosity. The far-field is defined as several meters of tuff underneath the drift, which has a distribution of fractures and lithophysae (cavities in the rock). 6.6.2.1 Near-Field (NF) Configuration Classes Configuration Class NF-1a: For this configuration class, fissionable material accumulates in fractures and other void spaces of the near-field. This configuration class can be reached from scenario NF-1 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Figure 3-3a). This configuration is obtained from processes such as adsorption (sorption) of fissile materials in tuff as a result of a reducing reaction. Configuration Class NF-1b: For this configuration class, fissionable material accumulates in fractures and other void spaces of the near-field. This configuration class can be reached from scenario NF-1 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Figure 3-3a). This configuration is obtained from chemistry changes due to carrier plume interaction with surrounding rock and pore waters that result in precipitation of fissile material by tuff. Configuration Class NF-1c: For this configuration class, fissionable material accumulates at the low point of the emplacement drift (or any connecting drift). This configuration class can be reached from scenario NF-1 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Figure 3-3a). The scenario leading to this configuration class must have a mechanism for sealing the fractures in the drift floor so that the effluent from individual waste packages can flow to, and accumulate at, a low point in the drift or repository, possibly in combination with effluent from other waste packages. Such a pool would be expected to occur only within a short time (weeks or less) following a high infiltration episode. Configuration Class NF-2a: For this configuration class, fissionable material accumulates at the surface of the invert due to filtration by the degradation products, or remnants, of the waste package and its contents, for the cases in which the fissionable material may be carried as a slurry. This configuration class can be reached from scenario NF-2 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Figure 3-3a). Configuration Class NF-3a: For this configuration class, fissionable material accumulates at the surface of the invert due to filtration by the degradation products, or remnants, of the waste package and its contents, for the cases in which the fissionable material may be carried as a colloid. This configuration class can be reached from scenario NF-3 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Figure 3-3a). CAL-DS0-NU-000003 REV 00A 38 September 2004 Criticality Model Configuration Class NF-3b: For this configuration class, fissionable material accumulates by processes involving the formation, transport, and eventual breakup (or precipitation) of fissionable material containing colloidal particles. This configuration class can be reached from scenario NF-3 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Figure 3-3a). This configuration class is characterized by the final accumulation in the invert in open fractures of solid material. Configuration Class NF-3c: For this configuration class, fissionable material accumulates by processes involving the formation, transport, and eventual breakup (or precipitation) of fissionable material containing colloidal particles. This configuration class can be reached from scenario NF-3 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Figure 3-3a). This configuration class is characterized by the final accumulation in the invert in pore space of granular material. Configuration Class NF-4a: For this configuration class, fissionable material accumulates in water that has pooled in the drift. This configuration class can be reached from scenario NF-4 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Figure 3-3a). This configuration class is reached from the scenario involving waste packages that may not have been directly subjected to dripping water but are located in a local depression so that water from other dripping sites may collect around the bottom of the package during periods of high flow. Configuration Class NF-5a: This configuration class has the intact or degraded waste form in water that has pooled in the drift. This configuration class can be reached from scenario NF-5 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Figure 3-3a). This configuration class is a variant of NF-4a. Such a configuration class would be evaluated for waste forms that could be demonstrated to be more robust with respect to aqueous corrosion than their waste package materials. 6.6.2.2 Far-Field Configuration Classes Configuration Class FF-1a: For this configuration class, fissionable material accumulates by precipitation in fractures and other void spaces of the far-field. This configuration class can be reached from scenario FF-1 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Figure 3-3b). This configuration is obtained from processes such as adsorption, from a reducing reaction, or from chemistry changes made possible by carrier plume interaction with surrounding rock and pore waters. Configuration Class FF-1b: For this configuration class, fissionable material accumulates by sorption, onto clay or zeolite. Such material may be encountered beneath the repository. This configuration class can be reached from scenario FF-1 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Figure 3-3b). Configuration Class FF-1c: For this configuration class, fissionable material accumulates by precipitation from encountering perched water (groundwater deposit isolated from the nominal flow and not draining because of impermeable layer beneath) having significantly different chemistry from the fissionable material carrier plume. This configuration class can be reached CAL-DS0-NU-000003 REV 00A 39 September 2004 Criticality Model from scenario FF-1 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Figure 3-3b). Configuration Class FF-2a: For this configuration class, fissionable material accumulates by processes involving the formation, transport, and eventual breakup (or precipitation) of fissionable material containing colloidal particles. This configuration class can be reached from scenario FF-2 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Figure 3-3b). It has been suggested that the colloid-forming tendency of plutonium will enhance its transport capability, providing the potential for accumulation at some significant distance from the waste package. This configuration class is characterized by the final accumulation in dead-end fractures. Configuration Class FF-2b: For this configuration class, fissionable material accumulates by processes involving the formation, transport, and eventual breakup (or precipitation) of fissionable material containing colloidal particles. This configuration class can be reached from scenario FF-2 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Figure 3-3b). It has been suggested that the colloid-forming tendency of plutonium will enhance its transport capability, providing the potential for accumulation at some significant distance from the waste package. This configuration class is characterized by the final accumulation in clay or zeolites. Configuration Class FF-2c: For this configuration class, fissionable material accumulates by processes involving the formation, transport, and eventual breakup (or precipitation) of fissionable material containing colloidal particles. This configuration class can be reached from scenario FF-2 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Figure 3-3b). It has been suggested that the colloid-forming tendency of plutonium will enhance its transport capability, providing the potential for accumulation at some significant distance from the waste package. This configuration class is characterized by the final accumulation in topographically low regions. Configuration Class FF-3a: For this configuration class, fissionable material accumulates by precipitation in the saturated zone at the contact between the waste-package plume and a hypothetical up welling fluid. This configuration class can be reached from scenario FF-3 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Figure 3-3b). Configuration Class FF-3b: For this configuration class, fissionable material accumulates by precipitation in the saturated zone at the contact between the waste-package plume and a redox front (where the plume meets a different groundwater chemistry so that an oxidation-reduction reaction can take place). This configuration class can be reached from scenario FF-3 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Figure 3-3b). Configuration Class FF-3c: For this configuration class, fissionable material accumulates by chemical reduction of fissionable material by a mass of organic material (reducing zone). Such a deposit might be located beneath the repository. This configuration class can be reached from scenario FF-3 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Figure 3-3b). CAL-DS0-NU-000003 REV 00A 40 September 2004 Criticality Model Configuration Class FF-3d: For this configuration class, fissionable material accumulates by chemical reduction of fissionable material by a mass of organic material (reducing zone). Such a deposit might be located at a narrowing of the tuff aquifer. This configuration class can be reached from scenario FF-3 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Figure 3-3b). Configuration Class FF-3e: For this configuration class, fissionable material accumulates by chemical reduction of fissionable material by a mass of organic material (reducing zone). Such a deposit might be located at the surface outfall of the saturated zone flow. This configuration class can be reached from scenario FF-3 presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003, Figure 3-3b). 7. RESULTS The criticality potential evaluation process results in establishing biases and uncertainties over the range of parameters of benchmark experiments. Criticality acceptance criteria for various waste forms are summarized in Table 5. The lower-bound tolerance limits are equivalent to the CL for the ROA of the experiment subsets provided in Attachments III through XII. If an ROP provided by the configuration generator model is beyond the ROA, either additional benchmark experiments to encompass the ROP or applicable penalties (either .kEROA or .kISO,, or both) will need to be applied to the lower-bound tolerance limit in establishing the CL. The criticality potential is determined by the final comparison of a configuration’s keff with the applicable CL. CAL-DS0-NU-000003 REV 00A 41 September 2004 Criticality Model Table 5. Criticality Acceptance Criteria for Experiment Subsets Waste Form Subset Trend Parameter Criticality Acceptance Criterion PWR and BWR SNF Intact Moderated (CRCs) Core Average Burnup (BU) ks + .ks < -0.0003 × BU + 0.9866 (0 < BU < 33 GWd/MTU) Intact Moderated (LCEs) Pin Pitch (P) ks + .ks < 7.0175E-03 × P + 0.9677 (1.32 cm = P = 1.89 cm); ks + .ks < 0.982 (1.89 cm < P = 2.64 cm) Degraded Moderated None ks + .ks < 0.952 (UO2 Solutions) Degraded Moderated (Plutonium Solutions) (AENCF) ks + .ks < 0.980 (2.46E-03 MeV = AENCF = 5.96E-02 MeV) LWBR SNF Intact Moderated None ks + .ks < 0.9751 Degraded Moderated ks + .ks < 0.9748 Enrico Fermi SNF Intact Moderated None ks + .ks < 0.9751 Intact Nonmoderated None ks + .ks < 0.9872 Degraded Moderated None ks + .ks < 0.9659 N-Reactor SNF Intact Moderated AENCF ks + .ks < 0.0765 × AENCF + 0.9434 (0 < AENCF < 0.175 MeV) ks + .ks < 0.9568 (AENCF > 0.175 MeV) Degraded Moderated None ks + .ks < 0.9748 FFTF SNF Intact Moderated None ks + .ks < 0.9786 Melt and Dilute Ingots Degraded Moderated None ks + .ks < 0.9659 TRIGA SNF Moderated Degraded None ks + .ks < 0.9796 Fort St. Vrain SNF Intact Moderated AENCF ks + .ks < 0.9575 (0 < AENCF < 0.386) ks + .ks < -0.0226 × AENCF + 0.9674 (0.386 < AENCF < 0.8015 MeV) Degraded Moderated AENCF ks + .ks < 0.9608 (0 < AENCF < 0.4625) ks + .ks < -0.0183 × AENCF + 0.9687 (0.4625 < AENCF < 0.8015 MeV) Shippingport PWR SNF Intact Moderated AENCF ks + .ks < 0.969 (0 < AENCF < 0.0278) ks + .ks < -0.2336 × AENCF + 0.9755 (0.0278 < AENCF < 0.0922 MeV) LEU External Homogeneous (Solution) None ks + .ks < 0.9842 IEU External Homogeneous (Solution) AENCF ks + .ks < 0.97841 (0 < AENCF < 0.1518 MeV) ks + .ks < -1.9322e-02*AENCF + 0.981339 (0.1518 = AENCF < 0.482 MeV) HEU External Homogeneous (Solution) None ks + .ks < 0.970611 (0 0.175 MeV 1.05 1.04 1.03 1.02 1.01 1.00 0.99 0.98 0.97 0.96 0.95 0.94 litLower Bound Toerance Lim 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 AENCF (MeV) Figure VI-2. Lower-Bound Tolerance Limit Applicable for N-Reactor SNF for Intact (Heterogeneous) Moderated Configurations The results of the trending parameter analysis for the critical benchmark subset representative for moderated degraded configurations of the waste package containing N-Reactor SNF are presented in Table VI-7. CAL-DS0-NU-000003 REV 00A VI-8 September2004 Criticality Model Table VI-7. Trending Parameter Results for the Critical Benchmark Subset Representative for Moderated Degraded Configurations of the Waste Package Containing N-Reactor SNF Trend Parameter n Intercept Slope r2 T t0.025,n-2 P-Value Goodness-of-Fit Tests Valid Trend AENCF 37 1.0012 -0.0215 0.1478 -2.4635 1.960 0.0188 Failed No Enrichment (235U/U) 37 1.0017 -1.25E-03 0.2261 -3.1975 1.960 2.938E-03 Failed No H/X 31 0.9956 4.66E-06 0.1148 1.9394 1.960 0.0622 Failed No Source: BSC 2003b, p. 58 Figure VI-3 presents the keff values and the calculated LBTL. The LBTL value calculated with DFTL method for this subset (normality test failed) is 0.9748 (BSC 2003b, Attachment I). keff lit 0.970 0.975 0.980 0.985 0.990 0.995 1.000 1.005 1.010 1.015 Lower Bound Toerance Lim 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 AENCF (MeV) Figure VI-3. Lower-Bound Tolerance Limit Applicable for N-Reactor SNF for Degraded (Homogeneous) Moderated Configurations Table VI-8 presents a summary of the results of the analyses performed on the subsets of critical benchmark experiments applicable to the waste package containing N-Reactor SNF and the calculated LBTL values. CAL-DS0-NU-000003 REV 00A VI-9 September2004 Criticality Model Table VI-8. Lower-Bound Tolerance Limits for Benchmark Subsets Representative for the Configurations of the Waste Package Containing N-Reactor SNF Trend Parameter Test for Applied Calculational Lower-Bound Tolerance Limit Values Subset (x) Normality Method or Functions Intact (heterogeneous) AENCF N/A LUTB f(AENCF) = 0.0765 × AENCF + 0.9434 Moderated for 0 < AENCF < 0.175 f(AENCF) = 0.9568 for AENCF > 0.175 Degraded (homogeneous) None Failed DFTL 0.9748 Moderated Source: BSC 2003b, p. 59 CAL-DS0-NU-000003 REV 00A VI-10 September2004 Criticality Model ATTACHMENT VII LBTL CALCULATION AND ROA DETERMINATION FOR FFTF CAL-DS0-NU-000003 REV 00A September 2004 Criticality Model CAL-DS0-NU-000003 REV 00A September 2004 Criticality Model ATTACHMENT VII LBTL CALCULATION AND ROA DETERMINATION FOR FFTF VII.1 INTRODUCTION This attachment presents the calculations of the LBTL and the determination of ROA for benchmarks that could potentially be applicable to waste package configurations containing Fast Flux Test Facility (FFTF) SNF. A listing of corroborating and supporting data, models, or information used for the calculation is provided in Table VII-1. Table VII-1. Supporting Information and Sources Description Source Guidance for benchmarking a calculational method Dean and Tayloe 2001 Criticality benchmark experiments, trending parameters, and CL calculations BSC 2002; BSC 2003b; NEA 2001 FFTF summary report CRWMS M&O 1999f FFTF fuel is the representative fuel for the mixed-oxide (MOX) fuel group, which is a mixture of uranium and plutonium oxides. This group is one of nine representative fuel groups designated by the National Spent Nuclear Fuel Program for disposal criticality analyses based on the fuel matrix composition, primary fissile isotope and enrichment (DOE 2002, Sections 5.2 and 5.3). The following information regarding FFTF SNF characteristics is collected from Evaluation of Codisposal Viability for MOX (FFTF) DOE-Owned Fuel (CRWMS M&O 1999f, Section 2.1.4), unless otherwise noted. The FFTF standard driver fuel assembly (DFA) contains 217 cylindrical fuel pins and is hexagonally shaped. The assembly is 3,657.6 mm long. The overall height of a fuel pin is 2,372.36 mm for Types 3.1 and 4.1 fuel pins, and 2377.44 mm for Types 3.2 and 4.2 fuel pins (Figure VII-1). The Stainless Steel Type 316 cladding is 0.381 mm (0.015 in.) thick. The inner and outer diameters of the cladding are 5.08 mm (0.200 in.) and 5.842 mm (0.230 in), respectively. Each fuel pin has a 914.4-mm (36-in.) long fuel region containing fuel pellets with an outer diameter of 4.9403 mm (0.1945 in.). Each fuel pin is helically wrapped with a 1.4224 mm (0.056 in.) diameter Stainless Steel Type 316 wire to provide lateral spacing along its length. The fuel pins are arranged with a triangular pitch within the hexagonal duct. The fuel density is reported as 90.4 percent of the theoretical density, which corresponds to a fuel density of 10.02 g/cm3. The mixed oxide (MOX – UO1.96 and PuO1.96) fuel region is followed by 20.32 mm (0.8 in.) of natural UO2 insulator pellets and 144.78 mm (5.7 in.) of Inconel 600 reflector on each end. The density of natural uranium insulator pellets is 10.42 ± 0.22 g/cm3. CAL-DS0-NU-000003 REV 00A VII-1 September 2004 Criticality Model Figure VII-1. Simplified Axial View of a Standard FFTF Driver Fuel Assembly Fuel Pin Above the top reflector is a Stainless Steel Type 302 spring (125.5 mm long by 0.8052 mm in diameter) and a Stainless Steel Type 316 plenum (862.1 mm long with a 4.9022 mm outer diameter). The maximum stainless steel spring volume is 2.7264 cm3. The fuel pin is closed with top and bottom caps having a 5.842 mm diameter. The length of the top cap is 104.6 mm. The bottom cap length for Type 3.1 and 4.1 fuels is 35.6 mm. The bottom cap length for Type 3.2 and 4.2 fuels is 40.6 mm. Each fuel pin weighs 455 g (approximately 1 lb). The fuel enrichments and isotopic fractions for all four types of fresh FFTF fuel are provided in Table VII-2. Note that Types 3.1 and 4.1 fuel pins have similar dimensions and Types 3.2 and 4.2 fuel pins have the same dimensions. The driver fuel assembly (DFA) comprises a hexagonal duct that surrounds the fuel pins, discriminator, inlet nozzle, neutron shield and flow orifice region, load pads, and handling socket. The duct is stainless steel Type 316 with a wall thickness of 3.048 mm (0.12 in.). The duct-tube outer dimension is 116.205 mm (4.575 in.) across the hexagonal flats and 131.064 mm (5.16 in.) across the opposite hexagonal points. The fuel pin pitch is 7.2644 mm (0.286 in.). The maximum assembly width is determined by the load pads, which are 138.1125 mm (5.4375 in.) across the opposite hexagonal points. The assembly is 3657.6 mm (144 in.) high. The total weight of a DFA is 172.819 kg (approximately 381 lb). Some of the assemblies have been disassembled and the fuel pins placed in fuel pin (Ident-69) containers. Although there are several types of pin containers, the most reactive one is the compartmented representation (Figure VII-2), which can hold up to 217 fuel pins (CRWMS M&O 1999f, Section 2.1.4). The total container length is 3,657.6 mm (144 in.). The Ident-69 CAL-DS0-NU-000003 REV 00A VII-2 September 2004 Criticality Model containers are made with 5-in. Stainless Steel Type 304L pipe (actual diameter is 5.563 in. or 141.30 mm) with a transition to 2.5-in. pipe (actual diameter is 2.875 in or 73.02 mm) at 431.8 mm (17 in.) from the bottom. The inside diameter of the container is 135.763 mm (5.345 in.). The fuel pins are supported on a grid plate with 1.5875-mm (0.0625-in.) diameter holes. The central compartment has inside and outside radii of 20.701 mm (0.815 in.) and 22.225 mm (0.875 in.), respectively. The divider plates have the same thickness as the center tube. The empty weight of an Ident-69 pin container is 59.09 kg (130 lb). A cross section of a partially loaded fuel pin container is shown in Figure VII-2. Fuel Pins l) Ident-69 Container Center Tube (typicaDivider Not to Scale Figure VII-2. Cross-Section of a Partially Loaded Ident-69 Fuel Pin Container (Compartmented Representation) Table VII-2. Uranium and Plutonium Content of Fresh Driver Fuel Assembly Driver Fuel Type 3.1 3.2 4.1 4.2 Plutonium Content (wt. % Pu/[Pu+U]) 27.37 22.43 29.28 25.14 Pu mass in assembly (kg) 9.071 7.421 9.722 8.333 Pu mass in pin (g) 41.8 34.2 44.8 38.4 Isotopic fraction 239Pu 0.8696 0.8696 0.8711 0.8711 240Pu 0.1173 0.1173 0.1163 0.1163 241Pu 0.0104 0.0104 0.0102 0.0102 Uranium Content (wt. % U/[Pu+U]) 72.63 77.57 70.72 74.86 U mass in assembly (kg) 24.070 25.666 23.481 24.813 U mass in pin (g) 110.9 118.3 108.2 114.3 Isotopic fraction 235U 0.007 0.007 0.002 0.002 238U 0.993 0.993 0.998 0.998 Source: CRWMS M&O 1999f, Table 2-4 NOTE: Each assembly nominally holds 1.5 kg of U in insulator pellets. CAL-DS0-NU-000003 REV 00A VII-3 September 2004 Criticality Model Some of the Ident-69 containers contain experimental MOX fuel pins that have a larger diameter (0.69 cm). The waste package configuration that holds the DOE SNF canister with FFTF (MOX) SNF also contains five high-level radioactive waste (HLW) glass pour canisters and a carbon steel basket. The FFTF SNF canister is placed in a carbon-steel support tube located in the center of the waste package (Figure VII-3). The five HLW canisters are evenly spaced around the FFTF SNF canister, which is designed for five intact FFTF fuel assemblies spaced around a center position. The center position will contain either another assembly or a pin container, referred to as Ident-69, which holds up to 217 individual FFTF fuel pins. The Ident-69 can only fit in the center position. The current design solution (CRWMS M&O 1999f, Section 7.6) requires only four DFAs to be loaded when the center position is occupied by the Ident-69 container. The DOE SNF canister basket structure is composed of a cylindrical stainless-steel tube, which occupies the center position and is supported by five equally spaced external divider plates that separate the intact FFTF assemblies from one another in the outer ring. FFTF Driver HLW Fuel Canister Assembly Supporting Structure Inside DOE SNF Canister Waste DOE SNF Package Canister Inner Supporting Structure NOTE: DOE SNF = U.S. Department of Energy spent nuclear fuel, FFTF = Fast Flux Test Facility, HLW = high-level radioactive waste. Figure VII-3. Cross Section of the DOE SNF Canister Containing FFTF SNF Placed Inside Waste Package VII.2 SELECTION OF THE CRITICALITY BENCHMARK EXPERIMENTS The critical experiments selected for inclusion in benchmarking must be representative of the types of materials, conditions, and parameters to be represented using the calculational method. A sufficient number of experiments with varying experimental parameters should be selected for inclusion in the benchmarking to ensure as wide an area of applicability as feasible and statistically significant results. While there is no absolute guideline for the minimum number of critical experiments necessary to benchmark a computational method, the use of only a few (i.e., less than 10) experiments should be accompanied by a suitable technical basis supporting the rationale for acceptability of the results (Dean and Tayloe 2001, p. 5). CAL-DS0-NU-000003 REV 00A VII-4 September 2004 Criticality Model For the present application (codisposal of FFTF SNF), the selected benchmark experiments are included in one subset in Benchmark and Critical Limit Calculation for DOE SNF (BSC 2002, Section 6.1.5) as moderated heterogeneous experiments. The benchmark experiments are from International Handbook of Evaluated Criticality Safety Benchmark Experiments (NEA 2001), unless otherwise noted. The selection process was initially based on prior knowledge regarding the possible degraded configurations of the waste package (CRWMS M&O 1999f, Section 7), and the subset has been constructed to accommodate large variations in the range of parameters of the configurations and to provide adequate statistics for the LBTL calculations. The selected benchmark experiments for the subset are presented in Benchmark and Critical Limit Calculation for DOE SNF (BSC 2002) with MCNP cases constructed and calculation results. The cases, keff results, and their uncertainties are also summarized in Analysis of Critical Benchmark Experiments and Critical Limit Calculation for DOE SNF (BSC 2003b, Attachment II). Table VII-3 presents the list of the benchmark experiments and the number of cases for the subset selected for FFTF SNF. Table VII-3. Critical Benchmarks Selected for FFTF SNF Subset Benchmark Experiment Identificationa No. of Cases Included Heterogeneous Moderatedb MIX-COMP-THERM-001 4 MIX-COMP-THERM-003 6 MIX-COMP-THERM-004 11 MIX-COMP-THERM-010 11 Source: Subset defined and evaluated in BSC 2002, Section 5 NOTES: aThe convention for naming the benchmark experiments is from NEA 2001. bIdentification of subset from BSC 2002 has been modified to better reflect the subset’s main characteristics. The benchmark experiments in the subset have not been affected. The FFTF SNF configuration class that the experiments are considered to cover is IP-1a as described in Section 7 for the degraded waste package containing FFTF SNF. VII.3 Range of Applicability of Selected Critical Benchmark Experiments This section summarizes in Table VII-4 the range of applicability of the experiments listed in Table VII-3. The information is partly excerpted from Benchmark and Critical Limit Calculation for DOE SNF (BSC 2002, Table 6-17), which presents a less comprehensive set of parameters. The tables have been enhanced by adding information regarding the spectral characteristics of the experiments (available for the majority of the benchmarks in International Handbook of Evaluated Criticality Safety Benchmark Experiments [NEA 2001]) to construct a collective area of applicability to directly compare with the range of parameters of codisposal configurations. CAL-DS0-NU-000003 REV 00A VII-5 September 2004 Criticality Model Table VII-4. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with Heterogeneous Moderated Configurations of FFTF SNF Experiment Experiment Experiment Experiment MIX-COMP- MIX-COMP- MIX-COMP- MIX-COMP- Category/ THERM-001 THERM-003 THERM-004 THERM-010 Description Parameter (4 cases) (6 cases) (11 cases) (11 cases) Materials/ Fissionable Plutonium + Uranium Plutonium + Uranium Plutonium + Uranium Plutonium +Uranium Fissionable Element Material Physical Form PuO2+UO2 PuO2+UO2 PuO2+UO2 PuO2+UO2 and U-Pu nitrate solution Isotopic Composition 19.70 wt. % Pu in pellets 85.5 wt. % 239Pu in Pu 2.5 wt. % 241Pu in Pu 5.8 wt. % Pu in pellets (6.6 wt. % PuO2) 90.5 wt. % 239Pu in Pu 3.01 wt. % PuO2 in pellets 68.2 wt. % 239Pu in Pu 7.26 wt. % 241Pu in Pu In Pellets 19.8 wt. % Pu in pellets 86.6 wt. % 239Pu in Pu 1.45 wt. % 241Pu in Pu Natural U in UO2 0.89 wt. % 241Pu in Pu Natural U in UO2 Natural U in UO2 Solution Natural U in UO2 Pu/(U+Pu)=0.22 (weight ratio) 91.1 wt. % 239Pu in Pu 0.4 wt. % 241Pu in Pu Natural U in solution Atomic Density (atoms/b-cm) 239Pu: 4.20e-03 241Pu: 8.75e-05 235U: 1.22e-04 239Pu:1.35e -03 241Pu: 1.14e-05 235U: 1.53e-04 239Pu: 2.75e -04 241Pu: 2.42e-05 235U: 9.39e-05 In pellets239Pu: 4.24e-03 241Pu: 4.11e-05 235U: 1.22e-04 In solution 239Pu: 2.02e-06 to 2.38e-04 241Pu: 9.21e-09 to 1.09e-06 235U: 4.89e-08 to 6.59e-06 Temperature Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Element H H H H Moderator Physical Form Water Water Water Pu-U nitrate solution Atomic Density 6.67e-02 6.66e-02 to 6.67e-02 5.54e-02 to 6.61e-02 (atoms/b-cm) 6.68e-02 Ratio to Fissile Material (In Region Containing Fissile Material) Range: H/X= 50.4 to 265b (X include 235U, 239Pu and 241Pu) Range: H/X= 74 to 473b (X include 235U, 239Pu and 241Pu) Range: H/X= 411 to 945b (X include 235U, 239Pu and 241Pu) Not available Temperature Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Material/ Reflected by water Reflected by water Reflected by water Reflected by water and Reflector Physical Form carbon steel Materials/ Element None None None Gd for 5 cases Neutron Absorber Physical Form N/A N/A N/A Gd in Pu-U nitrate solution Atomic Density (atoms/b-cm) N/A N/A N/A 1.88e-06 to 8.27e-06 Geometry Heterogeneity Heterogeneous square pitched lattice Heterogeneous square pitched lattice Heterogeneous square pitched lattice Heterogeneous cylindrical square pitched lattice of of pins (pitch: 0.9525 of pins (pitch: 1.3208 of pins (pitch: 1.825 to pins (pitch = 1.4 cm) to 1.905 cm) to 2.6416 cm) 2.474 cm) Shape Parallel-piped Parallel-piped Parallel-piped Cylinder Neutron AENCF 0.0635 to 0.1717 MeV 0.08 to 0.2294 MeV 0.0747 to 0.1218 MeV 0.033 to 0.153 MeV Energy EALF 0.12 to 1.07 eV 0.103 to 0.922 eV 0.082 to 0.149 eV Not available Neutron Energy Spectraa T: 5.6 to 23% I: 28.8 to 37.1% T: 6.9 to 27.1% I: 27.4 to 38% T: 20.1 to 33.2% I: 26.9 to 33.3% Not available F: 48.2 to 57.3% F: 45.5 to 55.1% F: 39.9 to 46.6% Fission Rate T: 71.7 to 91.5% T: 75.1 to 93.2% T: 90.6 to 94.7% Not available vs. Neutron I: 5.9 to 20.8% I: 4.0 to 16.4% I: 2.8 to 5.3% Energya F: 2.6 to 7.5% F: 2.8 to 8.5% F: 2.5 to 4.1% Source: BSC 2002; NEA 2001, Spectra NOTES: aSpectral range defined as follows: thermal (T) [0 to 1 eV], intermediate (I) [1eV to 100 keV], fast (F) [100 keV to 20 MeV]. bCalculated in this report based on unit cell. c AENCF = average energy of a neutron causing fission, EALF = energy of average lethargy causing fission. CAL-DS0-NU-000003 REV 00A VII-6 September 2004 Criticality Model VII.4 CALCULATION OF THE LOWER-BOUND TOLERANCE LIMIT The following results are excerpted from Analysis of Critical Benchmark Experiments and Critical Limit Calculation for DOE SNF (BSC 2003b), which presents in detail the methodology and calculations performed for evaluating the LBTL for each set of configurations of the waste package containing FFTF SNF. The calculated keff values for the critical benchmarks are taken from Analysis of Critical Benchmark Experiments and Critical Limit Calculation for DOE SNF (BSC 2003b, Attachment II). The results of the trending parameter analysis for the critical benchmark subset representative for moderated intact (heterogeneous) configurations of the waste package containing FFTF SNF are presented in Table VII-5. The parameters in the following tables describe the regression statistics for the linear trend evaluations (see Attachment III for definitions). The P-value parameter gives a direct estimation of the probability of having a linear trending due to chance only. Table VII-5. Trending Parameter Results for the Critical Benchmark Subset Representative for Moderated Intact Fuel (Heterogeneous) Configurations of the Waste Package Containing FFTF SNF Trend Parameter n Intercept Slope r2 T t0.025,n-2 P-Value Goodness-of-Fit Tests Valid Trend AENCF 32 1.0045 -0.0382 0.1454 -2.2591 1.960 0.0313 Failed No keff Source: BSC 2003b, p. 44 NOTE: AENCF = average energy of a neutron causing fission. Figure VII-4 presents the keff values and the calculated LBTL. The LBTL value calculated with DFTL method for this subset (normality test failed) is 0.9786 (BSC 2003b, Attachment I). 1.015 1.010 1.005 1.000 0.995 0.990 0.985 0.980 0.975 0.00 0.05 0.10 0.15 0.20 0.25 litLower Bound Toerance Lim AENCF (MeV) Figure VII-4. Lower-Bound Tolerance Limit Applicable for FFTF DOE SNF for Intact (Heterogeneous) Moderated Configurations CAL-DS0-NU-000003 REV 00A VII-7 September 2004 Criticality Model INTENTIONALLY LEFT BLANK CAL-DS0-NU-000003 REV 00A VII-8 September 2004 Criticality Model ATTACHMENT VIII LBTL CALCULATION AND ROA DETERMINATION FOR MELT AND DILUTE INGOTS CAL-DS0-NU-000003 REV 00A September 2004 Criticality Model CAL-DS0-NU-000003 REV 00A September 2004 Criticality Model ATTACHMENT VIII LBTL CALCULATION AND ROA DETERMINATION FOR MELT AND DILUTE INGOTS VIII.1 INTRODUCTION This attachment presents the calculations of the LBTL and the determination of ROA for benchmarks that could potentially be applicable to waste package configurations containing Melt and Dilute ingots. A listing of corroborating and supporting data, models, or information used for the calculation is provided in Table VIII-1. Table VIII-1. Supporting Information and Sources Description Source Guidance for benchmarking a calculational method Dean and Tayloe 2001 Criticality benchmark experiments, trending parameters, and CL calculations BSC 2002; BSC 2003b; NEA 2001 Melt and Dilute summary report BSC 2001a NOTE: CL=critical limit. Melt and Dilute is the representative type of the high-enriched U-Al fuel group. This group is one of nine representative fuel groups designated by the National Spent Nuclear Fuel Program for disposal criticality analyses based on the fuel matrix composition, primary fissile isotope and enrichment (DOE 2002, Sections 5.2 and 5.3). The following information regarding Melt and Dilute ingots characteristics is collected from Evaluation of Codisposal Viability for Melt and Dilute DOE-Owned Fuel (BSC 2001a, Section 2.1.4) unless otherwise indicated. The current Melt and Dilute technology program is focused on the development and implementation of a treatment technology for diluting high-enriched U-Al SNF to low enriched U levels (less than 20 wt. %) and qualifying this low-enriched U-Al SNF form (Melt and Dilute ingots) for geologic repository disposal (BSC 2001a, p. 1-1). The Melt and Dilute ingots are homogeneous and monolithic cylinders that will range in height from 15 to 30 in (381 mm to 762 mm) and will likely be contained in a plain carbon steel crucible liner. The liner will have the maximum outer diameter of 16.5 in. (419.1 mm). The mass of the Melt and Dilute ingot is dictated by the geometry assumed for a given configuration using an ingot density of approximately 3 g/cm3 and an ingot porosity of 5 to 10 percent. The composition of the ingot is 13.2 plus or minus 5 wt. % uranium, enriched at less than 20 wt. % 235U and 0.5 wt. % gadolinium metal, with the balance of the ingot being aluminum. A second composition is considered, which is identical to the first for uranium and gadolinium, except that in this case 2.5 wt. % of the ingot is hafnium, with the balance of the ingot being aluminum. The DOE-standardized canister will contain three to six Melt and Dilute ingots that are homogenous and monolithic, depending on the dimensions of the individual ingots as described above. Figure VIII-1 presents a cross section of the DOE SNF canister containing Melt and Dilute ingots placed in a waste package (BSC 2001a, pp. vii and viii). CAL-DS0-NU-000003 REV 00A VIII-1 September 2004 Criticality Model ll Waste Package Outer SheWaste Package Inner Shell Waste Package Basket Support tube DOE SNF Canister Melt and Dilute Ingot DHLW Glass NOTE: DOE SNF = U.S. Department of Energy Spent Nuclear Fuel. Figure VIII-1. Cross-Section of the DOE SNF Canister Containing Melt and Dilute Ingots Placed Inside Waste Package VIII.2 SELECTION OF THE CRITICALITY BENCHMARKS The critical experiments selected for inclusion in benchmarking must be representative of the types of materials, conditions, and parameters to be represented using the calculational method. A sufficient number of experiments with varying experimental parameters should be selected for inclusion in the benchmarking to ensure as wide an area of applicability as feasible and statistically significant results. While there is no absolute guideline for the minimum number of critical experiments necessary to benchmark a computational method, the use of only a few (i.e., less than 10) experiments should be accompanied by a suitable technical basis supporting the rationale for acceptability of the results (Dean and Tayloe 2001, p. 5). For the present application (codisposal of Melt and Dilute ingots) the selected benchmark experiments are included in one subset in Benchmark and Critical Limit Calculation for DOE SNF (BSC 2002, Section 6.1.3) as moderated homogenous experiments. The benchmark experiments are from International Handbook of Evaluated Criticality Safety Benchmark Experiments (NEA 2001), unless otherwise noted. The selection process was initially based on prior knowledge regarding the possible degraded configurations of the waste package (BSC 2001a, Section 7), and the subset has been constructed to accommodate large variations in the range of parameters of the configurations and to provide adequate statistics for the lower-bound tolerance limit calculations. The selected benchmark experiments for the subset are presented in CAL-DS0-NU-000003 REV 00A VIII-2 September 2004 Criticality Model Benchmark and Critical Limit Calculation for DOE SNF (BSC 2002) with MCNP cases constructed and calculation results. The cases, keff results, and their uncertainties are also summarized in Analysis of Critical Benchmark Experiments and Critical Limit Calculation for DOE SNF (BSC 2003b, Attachment II). Table VIII-2 presents the list of the benchmark experiments and the number of cases for the subset selected for FFTF SNF. Table VIII-2. Critical Benchmarks Selected for Melt and Dilute Ingots Subset Benchmark Experiment Identificationa No. of Cases Included Homogeneous Moderatedb IEU-SOL-THERM-001 4 IEU-COMP-THERM-001 29 LEU-SOL-THERM-003 9 LEU-SOL-THERM-004 7 LEU-SOL-THERM-006 5 LEU-SOL-THERM-007 5 LEU-SOL-THERM-008 4 LEU-SOL-THERM-009 3 LEU-SOL-THERM-010 4 LEU-SOL-THERM-016 7 LEU-SOL-THERM-017 6 LEU-SOL-THERM-018 6 LEU-SOL-THERM-019 6 LEU-SOL-THERM-020 4 LEU-SOL-THERM-021 4 Source: Subset defined in BSC 2002 a NOTES: The convention for naming the benchmark experiments is from NEA 2001. b Identification of subset from BSC 2002 has been modified to better reflect the subset’s main characteristics. The benchmark experiments in the subset have not been affected. The experiments cover configuration class IP-2a for the degraded waste package containing Melt and Dilute ingots as described in Section 7. VIII.2.1 Range of Applicability of Selected Critical Benchmark Experiments This section summarizes in a set of tables (Tables VIII-3 to VIII-5) the range of applicability of the experiments listed in Table VIII-2. The information is partly excerpted from Benchmark and Critical Limit Calculation for DOE SNF (BSC 2002, Section 6.2), which presents a less comprehensive set of parameters. The tables have been enhanced by adding information regarding the spectral characteristics of the experiments (where available in International Handbook of Evaluated Criticality Safety Benchmark Experiments [NEA 2001]) to construct a collective area of applicability that will be used to directly compare with the range of parameters of the codisposal configurations. CAL-DS0-NU-000003 REV 00A VIII-3 September 2004 Criticality Model Table VIII-3. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with Homogeneous Moderated Configurations of Melt and Dilute Ingots (Set 1) Experiment Experiment Experiment Experiment Experiment IEU-SOL-IEU-COMP- LEU-SOL-LEU-SOL-LEU-SOL- Category/ THERM-001 THERM-001 THERM-003 THERM-004 THERM-006 Description Parameter (4 cases) (29 cases) (9 cases) (7 cases) (5 cases) Materials/ Fissionable Uranium Uranium Uranium Uranium Uranium Fissionable Element Material Physical Form Aqueous solution of uranyl sulfate UF4 compound with polytetra- fluoroethylene Aqueous solution of uranyl nitrate Aqueous solution of uranyl nitrate Aqueous solution of uranyl nitrate Isotopic Composition 20.9 wt. % 235U 29.83 wt. % 235U 10 wt. % 235U 9.97 wt. % 235U 10 wt. % 235U Atomic Density (atoms/b-cm) 235U: 1.40e-04 to 2.68e-04 238U: 5.26e-04 to 1.01e-03 235U: 2.37e-03 238U: 5.50e-03 235U: 4.34e-05 to 7.64e-05 238U: 3.82e-04 to 6.73e-04 235U: 5.76e-05 to 7.92e-05 238U: 5.13e-04 to 7.06e-04 235U: 1.09e-04 238U: 9.56e-04 Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Element H H; C H H H Moderator Physical Form Solution Polyethylene Solution Solution Solution Atomic 5.83e-02 to H: 7.5224e-02 5.89e-02 to 5.70e-02 to 5.77e-02 Density 6.20e-02 C: 3.9232e-02 6.23e-02 5.86e-02 (atoms/b-cm) Ratio to Fissile 217 to 444 Range: H/235U = 4 to 222 770 to 1437 719 to 1018 532 Material Temperature Room Temp. Room Temp. Room Temp. 298 293 Materials/ Material/ Reflected by Unreflected or Unreflected Reflected by Reflected by Reflector Physical Form graphite reflected by water water paraffin Materials/ Element None B or Cd for some None None B Neutron experiments Absorber Physical Form N/A Metallic sheets N/A N/A B4C rods Atomic N/A Not needed for N/A N/A Not needed for Density ROA and ROP ROA and ROP (atoms/b-cm) comparison comparison Geometry Heterogeneity Homogeneous solution contained Heterogeneous small cubes of Homogeneous solution in a Homogeneous solution in a Homogeneous solution in a in a cylindrical tank fissile compound interspersed with moderator cubes spherical tank cylindrical tank cylindrical tank Shape Cylinder Cuboid Sphere Cylinder Cylinder Neutron AENCFb 0.0149 to 0.0455 to 0.0114 to 0.0142 to 0.0245 to Energy 0.0275 MeV 0.2168 MeV 0.0186 MeV 0.0188 MeV 0.0257 MeV EALFb 4.96e-02 to 0.11 to 9.09 eV 3.46e-02 to 3.75e-02 to 4.86e-02 to 7.93e-02 eV 4.14e-02 eV 4.21e-02 eV 4.99e-02 eV Neutron T: 19.3 to 29.3% T: 1.8 to 22.8% T: 37.6 to 49.1% T: 36.8 to 43.1% T: 26 to 31.2% Energy Spectraa I: 31.5 to 35.2% F: 39.2 to 45.5% I: 24.9 to 40.2% F: 49.6 to 63% I: 22.7-27.3% F: 28.2-35.1% I: 25.3-27.8% F: 31.6-35.4% I: 30-30.5% F: 38.8-43.5% Fission Rate T: 90.7 to 94.6% T: 49.9 to 90.9% T: 96.2 to 97.6% T: 96.1 to 97.0% T: 94.7 to 95.0% vs. Neutron I: 4.7 to 8.1% I: 7.1 to 42.8% I: 2 to 3.1% I: 2.5 to 3.2% I: 4.1 to 4.3% Energya F: 0.7 to 1.2% F: 2.5 to 11.1% F: 0.4 to 0.7% F: 0.5 to 0.7% F: 0.9 to 1.0% Source: BSC 2002 and NEA 2001, Spectra NOTES: a Spectral range defined as follows: thermal (T) [0 to 1 eV], intermediate (I) [1eV to 100 keV], fast (F) [100 keV to 20 MeV]. bAENCF = average energy of a neutron causing fission, EALF = energy of average lethargy causing fission. CAL-DS0-NU-000003 REV 00A VIII-4 September 2004 Criticality Model Table VIII-4. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with Homogeneous Moderated Configurations of Melt and Dilute Ingots (Set 2) Experiment Experiment Experiment Experiment Experiment LEU-SOL-LEU-SOL-LEU-SOL-LEU-SOL-LEU-SOL- Category/ THERM-007 THERM-008 THERM-009 THERM-010 THERM-016 Description Parameter (5 cases) (4 cases) (3 cases) (4 cases) (7 cases) Materials/ Fissionable Uranium Uranium Uranium Uranium Uranium Fissionable Element Material Physical Form Aqueous solution Aqueous Aqueous Aqueous Aqueous of uranyl nitrate solution of uranyl solution of uranyl solution of uranyl solution of uranyl nitrate nitrate nitrate nitrate Isotopic Composition 9.97 wt. % 235U 9.97 wt. % 235U 9.97 wt. % 235U 9.97 wt. % 235U 9.97 wt. % 235U Atomic 235U: 6.18e-05 to 235U: 6.13e-05 to 235U: 6.25e-05 to 235U: 6.18e-05 to 235U: 7.65e-5 to Density 8.00e-05 6.16e-05 6.26e-05 6.21e-05 1.19e-04 (atoms/b-cm) 238U: 5.5e-04 to 238U: 5.46e-04b 238U: 5.57e-04 to 238U: 5.51e-04 to 238U: 6.82e-04 to 7.12e-04 to 5.49e-04 5.58e-04 5.54e-04 1.06e-03 Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Element H H H H H Moderator Physical Form Solution Solution Solution Solution Solution Atomic 5.67e-02 to 5.86e-02 5.85e-02 5.85e-02 5.56e-02 to Density 5.82e-02 5.91e-02 (atoms/b-cm) Ratio to 709 to 942 951 to 956 934 to 936 942 to 946 469 to 772 Fissile Material Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Material/ Unreflected Reflected by Reflected by Reflected by Reflected by Reflector Physical Form concrete borated concrete polyethylene water Materials/ Element None None None None None Neutron Absorber Physical Form N/A N/A N/A N/A N/A Atomic N/A N/A N/A N/A N/A Density (atoms/b-cm) Geometry Heterogeneity Homogeneous solution contained Homogeneous solution Homogeneous solution Homogeneous solution in a Homogeneous solution in a in a cylindrical tank contained in a cylindrical tank contained in a cylindrical tank cylindrical tank rectangular slab tank Shape Cylinder Cylinder Cylinder Cylinder Rectangular slab Neutron AENCFb 0.0159 to 0.0152 to 0.0155 to 0.0153 to 0.0180 to Energy 0.0200 MeV 0.0154 MeV 0.0158 MeV 0.0154 MeV 0.0267 MeV EALFb 3.87e-02 to 3.84e-02 to 3.89e-02 eV 3.84e-02 eV 4.15e-02 to 4.28e-02 eV 3.85e-02 eV 5.22e-02 eV Neutron T:35.9 to 41.1% T: 41.5 to 41.7% T: 40.8 to 41% T: 41.6% T:29.1 to 37.7% Energy Spectraa I: 26 to 28.1% F:32.9 to 36% I: 25.9 to 26% F: 32.4 to 35% I: 26.2 to 26.3% F: 32.8 to 32.9% I: 25.8 to 25.9% F: 32.5 to 32.6% I: 27.7 to 31.2% F: 34.7 to 39.7% Fission Rate T: 95.9 to 96.7% T: 96.8% T: 96.7% T: 96.8% T: 94.3 to 96.2% vs. Neutron I: 2.7 to 3.4% I: 2.6% to 2.8% I: 2.7% I: 2.6% I: 3.2 to 4.6% Energya F: 0.6 to 0.7% F: 0.6% F: 0.6% F: 0.6% F: 0.7 to 1.0% Source: BSC 2002 and NEA 2001, Spectra a NOTES: Spectral range defined as follows: thermal (T) [0 to 1 eV], intermediate (I) [1eV to 100 keV], fast (F) [100 keV to 20 MeV]. b AENCF = average energy of a neutron causing fission, EALF = energy of average lethargy causing fission. CAL-DS0-NU-000003 REV 00A VIII-5 September 2004 Criticality Model Table VIII-5. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with Homogeneous Moderated Configurations of Melt and Dilute Ingots (Set 3) Experiment Experiment Experiment Experiment Experiment LEU-SOL-LEU-SOL-LEU-SOL-LEU-SOL-LEU-SOL- Category/ THERM-017 THERM-018 THERM-019 THERM-020 THERM-021 Description Parameter (6 cases) (6 cases) (6 cases) (4 cases) (4 cases) Materials/ Fissionable Uranium Uranium Uranium Uranium Uranium Fissionable Element Material Physical Form Aqueous solution of uranyl nitrate Aqueous solution of uranyl nitrate Aqueous solution of uranyl nitrate Aqueous solution of uranyl nitrate Aqueous solution of uranyl nitrate Isotopic Composition 9.97 wt. % 235U 9.97 wt. % 235U 9.97 wt. % 235U 9.97 wt. % 235U 9.97 wt. % 235U Atomic 235U: 8.05e-05 to 235U: 7.87e-5 to 235U: 8.07e-05 to 235U: 4.95e-05 to 235U: 4.95e-5 to Density 1.19e-04 8.04e-05 8.13e-05 6.21e-05 6.21e-05 (atoms/b-cm) 238U: 7.17e-04 to 238U: 7.01e-04 238U: 7.19e-04 to 238U: 4.41e-04 to 238U: 4.41e-04 to 1.06e-03 to 7.16e-04 7.24e-04 5.53e-04 5.53e-04 Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Element H H H H H Moderator Physical Form Solution Solution Solution Solution Solution Atomic 5.56e-02 to 5.87e-02 to 5.87e-02 6.03e-02 to 6.03e-02 to Density 5.87e-02 5.91e-02 6.13e-02 6.13e-02 (atoms/b-cm) Ratio to 469-729 731 to 751 721 to 728 971 to 1,239 971 to 1,239 Fissile Material Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Material/ Unreflected Reflected by Reflected by Reflected by Unreflected Reflector Physical Form concrete polyethylene water Materials/ Element None None None None None Neutron Absorber Physical Form N/A N/A N/A N/A N/A Atomic N/A N/A N/A N/A N/A Density (atoms/b-cm) Geometry Heterogeneity Homogeneous solution in a Homogeneous solution in a Homogeneous solution in a Homogeneous solution in a Homogeneous solution in a rectangular slab tank rectangular slab tank rectangular slab tank cylindrical tank cylindrical tank Shape Rectangular slab Rectangular slab Rectangular slab Cylinder Cylinder Neutron AENCFb 0.0192 to 0.0183 to 0.0189 to 0.0125 to 0.0127 to Energy 0.0275 MeV 0.0188 MeV 0.0191 MeV 0.0150 MeV 0.0154 MeV EALFb 4.24e-02 to Not available Not available Not available Not available 5.23e-02 eV Neutron Energy Spectraa T: 28.9 to 36.5% I: 28 to 31.1% F: 35.5 to 40.0% Not available Not available Not available Not available Fission Rate T: 94.3 to 96.0% Not available Not available Not available Not available vs. Neutron I: 3.3 to 4.6% Energya F: 0.7 to 1.0% Source: BSC 2002 and NEA 2001, Spectra a NOTES: Spectral range defined as follows: thermal (T) [0 to 1 eV], intermediate (I) [1eV to 100 keV], fast (F) [100 keV to 20 MeV]. bAENCF = average energy of a neutron causing fission, EALF = energy of average lethargy causing fission. CAL-DS0-NU-000003 REV 00A VIII-6 September 2004 Criticality Model VIII.5 CALCULATION OF THE LOWER-BOUND TOLERANCE LIMIT The following results are excerpted from Analysis of Critical Benchmark Experiments and Critical Limit Calculation for DOE SNF (BSC 2003b) which present in detail the methodology and calculations performed for evaluating the LBTL for each set of configurations of the waste package containing Melt and Dilute ingots. The calculated keff values for the critical benchmarks are taken from Analysis of Critical Benchmark Experiments and Critical Limit Calculation for DOE SNF (BSC 2003b, Attachment II). The results of the trending parameter analysis for the critical benchmark subset representative for moderated degraded configurations of the waste package containing Melt and Dilute ingots are presented in Table VIII-6. The parameters in the following tables describe the regression statistics for the linear trend evaluations (see Attachment III for definitions). The P-value parameter gives a direct estimation of the probability of having a linear trending due to chance only. Table VIII-6. Trending Parameter Results for the Critical Benchmark Subset Representative for Moderated Degraded (Homogeneous) Configurations of the Waste Packages Containing Melt and Dilute Ingots Trend Parameter n Intercept Slope r2 T t0.025,n-2 P-Value Goodness-of-Fit Tests Valid Trend AENCF 103 1.0018 -0.0218 0.0369 -1.9659 1.960 0.0521 Failed No Enrichment (U235/U) 103 1.0048 -2.5E-04 0.1300 -3.8842 1.960 1.84E-04 Failed No H/U235 103 0.9984 3.93E-06 0.0664 2.6792 1.960 0.0086 Failed No Source: BSC 2003b, p. 37 Figure VIII-2 presents the keff values and the calculated LBTL. The LBTL value calculated with the DFTL method for this subset (the normality test failed) is 0.9659 (BSC 2003b, Attachment I). klit 0.960 0.965 0.970 0.975 0.980 0.985 0.990 0.995 1.000 1.005 1.010 1.015 eff Lower Bound Toerance Lim 0.00 0.05 0.10 0.15 0.20 0.25 AENCF (MeV) Figure VIII-2. Lower-Bound Tolerance Limit Applicable for Melt And Dilute Ingots Degraded (Homogeneous) Moderated Configurations CAL-DS0-NU-000003 REV 00A VIII-7 September 2004 Criticality Model INTENTIONALLY LEFT BLANK CAL-DS0-NU-000003 REV 00A VIII-8 September 2004 Criticality Model ATTACHMENT IX LBTL CALCULATION AND ROA DETERMINATION FOR TRIGA SNF CAL-DS0-NU-000003 REV 00A September 2004 Criticality Model CAL-DS0-NU-000003 REV 00A September 2004 Criticality Model ATTACHMENT IX LBTL CALCULATION AND ROA DETERMINATION FOR TRIGA SNF IX.1 INTRODUCTION This attachment presents the calculations of the LBTL and the determination of ROA for benchmarks that could potentially be applicable to waste package configurations containing TRIGA SNF. A listing of corroborating and supporting data, models, or information used for the calculation is provided in Table IX-1. Table IX-1. Supporting Information and Sources Description Source Guidance for benchmarking a calculational method Dean and Tayloe 2001 Criticality benchmark experiments, trending parameters, and CL calculations BSC 2002; BSC 2003b; NEA 2001 TRIGA summary report CRWMS M&O 2000b NOTE: CL = critical limit, TRIGA = training, research, isotopes, general atomics. The TRIGA SNF is representative of the uranium-zirconium hydride (UZrH) SNF group. This group is one of nine representative fuel groups designated by the National Spent Nuclear Fuel Program for disposal criticality analyses based on the fuel matrix composition, primary fissile isotope and enrichment (DOE 2002, Sections 5.2 and 5.3). The following information regarding TRIGA SNF is collected from Evaluation of Codisposal Viability for UZrH (TRIGA) DOE-Owned Fuel (CRWMS M&O 2000b, Section 2.1.4). TRIGA reactors are a light-water-cooled, graphite- or water-reflected reactor designed for training, research, and isotope production. TRIGA reactors utilize solid fuel rods, in which the zirconium-hydride matrix is homogeneously combined with the enriched uranium and loaded into cylindrical rods 38.10 mm (1.5 in.) in diameter and 762.0 mm (30.0 in.) long. The inventory of TRIGA SNF falls into the following three basic categories: aluminum-clad fuel, stainless steel clad fuel, and fuel-follower control rods (fuel rod with neutron absorber axial section). Each of these basic fuel types has differences in uranium loading, enrichment, dimensions, and rod components. The TRIGA SNF considered in this report contains a uranium loading of 137g per rod, with 70 percent enrichment of 235U, dispersed in the uranium-zirconium hydride matrix, which corresponds to the Fuel Life Improvement Program stainless steel clad rods. The H/Zr ratio is nominally 1.6. The waste package configuration contains five HLW canisters surrounding a DOE-standardized (18-in. outer diameter) SNF canister. The outer diameters for the waste package and the 5-HLW glass canisters are 2120 mm and 610 mm, respectively. The isometric view of the TRIGA SNF canister is shown in Figure IX-1. The stainless steel canister will accommodate one, two, or three carbon steel baskets each loaded with 37 TRIGA fuel rods. For fuel rods with a maximum length of 774.7 mm, three baskets will be stacked in the SNF canister, so there will be a maximum of 111 rods per canister. For fuel rods with a maximum length of 1,143 mm, two baskets will be stacked in the SNF canister, so there will be 74 rods per canister. For fuel rods with a maximum length of 1,689.1 mm, one basket will be placed in the SNF canister so CAL-DS0-NU-000003 REV 00A IX-1 September2004 Criticality Model there will be only 37 rods per canister. A 1-mm advanced neutron absorber tube matrix (Alloy 22 with 8 wt. % Gd) is placed inside of 12 structural tubes per basket Evaluation of Codisposal Viability for UZrH (TRIGA) DOE-Owned Fuel (CRWMS M&O 2000b, Section 2.1.3). The arrangement of the absorber tubes is shown in Figure IX-2. A cross section of an arrangement of TRIGA SNF rods in an 18-in. DOE SNF canister is shown in Figure IX-3. The rest of the waste package is not shown in order to enhance clarity of the constituents inside the DOE SNF canister. Figure IX-1. Isometric View of the TRIGA SNF Canister Figure IX-2. Emplacement of the Advanced Neutron Absorber Matrix CAL-DS0-NU-000003 REV 00A IX-2 September2004 Criticality Model NOTE: DOE SNF = U.S. Department of Energy Spent Nuclear Fuel, TRIGA = training, research, isotopes, general atomics. Figure IX-3. Cross Section of an Arrangement of TRIGA-SS Rods in an 18-inch DOE SNF Canister IX.2 SELECTION OF THE CRITICALITY BENCHMARKS The critical experiments selected for inclusion in benchmarking must be representative of the types of materials, conditions, and parameters to be represented using the calculational method. A sufficient number of experiments with varying experimental parameters should be selected for inclusion in the benchmarking to ensure as wide an area of applicability as feasible and statistically significant results. While there is no absolute guideline for the minimum number of critical experiments necessary to benchmark a computational method, the use of only a few (i.e., less than 10) experiments should be accompanied by a suitable technical basis supporting the rationale for acceptability of the results (Dean and Tayloe 2001, p. 5). For the present application (codisposal of TRIGA SNF), the selected benchmark experiments have been grouped in 2 subsets (BSC 2002, Section 6.1.2) that include moderated heterogeneous and homogeneous experiments. The benchmark experiments are from International Handbook of Evaluated Criticality Safety Benchmark Experiments (NEA 2001), unless otherwise noted. The selection process was initially based on prior knowledge regarding the possible degraded configurations of the waste package (CRWMS M&O 2000b, Section 7), and the subsets have been constructed to accommodate large variations in the range of parameters of the configurations and to provide adequate statistics for LBTL calculations. The selected benchmark experiments for each subset are presented in Benchmark and Critical Limit Calculation for DOE SNF (BSC 2002, Tables 6-5 and 6-7) with MCNP cases constructed and calculation results. The cases, keff results, and their uncertainties are also summarized in Analysis of Critical Benchmark Experiments and Critical Limit Calculation for DOE SNF (BSC 2003b, Attachment II). Table IX-2 presents the list of the benchmark experiments and the number of cases for each subset selected for TRIGA SNF. CAL-DS0-NU-000003 REV 00A IX-3 September2004 Criticality Model Table IX-2. Critical Benchmarks Selected for TRIGA SNF Subset Benchmark Experiment Identificationa No. of Cases Included Heterogeneous Moderatedb HEU-COMP-THERM-002 25 HEU-COMP-THERM-003 15 HEU-COMP-THERM-004 4 HEU-COMP-THERM-005 1 HEU-COMP-THERM-006 3 HEU-COMP-THERM-007 3 HEU-COMP-THERM-008 2 HEU-COMP-THERM-010 21 HEU-COMP-THERM-011 3 HEU-COMP-THERM-012 2 HEU-COMP-THERM-013 2 HEU-COMP-THERM-014 2 HEU-MET-THERM-006 23 IEU-COMP-THERM-003 2 Homogeneous Moderatedb HEU-SOL-THERM-001 10 HEU-SOL-THERM-005 17 HEU-SOL-THERM-006 29 HEU-SOL-THERM-008 5 HEU-SOL-THERM-009 4 HEU-SOL-THERM-010 4 HEU-SOL-THERM-011 2 HEU-SOL-THERM-012 1 HEU-SOL-THERM-013 4 HEU-SOL-THERM-014 3 HEU-SOL-THERM-015 5 HEU-SOL-THERM-016 3 HEU-SOL-THERM-017 8 HEU-SOL-THERM-018 12 HEU-SOL-THERM-019 3 HEU-SOL-THERM-021 32 HEU-SOL-THERM-025 18 HEU-SOL-THERM-027 9 HEU-SOL-THERM-028 18 HEU-SOL-THERM-029 7 HEU-SOL-THERM-030 7 HEU-SOL-THERM-031 4 HEU-SOL-THERM-032 1 HEU-SOL-THERM-033 26 HEU-SOL-THERM-035 9 HEU-SOL-THERM-036 4 HEU-SOL-THERM-037 9 HEU-SOL-THERM-043 3 HEU-SOL-THERM-044 16 Source: Subsets defined in BSC 2002 a NOTES: The convention for naming the benchmark experiments is from NEA 2001. b Identification of each subset from BSC 2002 has been changed to better reflect the subset’s main characteristics. The benchmark experiments in each subset have not been affected. The experiments cover configuration classes IP-2a, IP-3a, IP-3b, IP-3c, and IP-3d for the degraded waste package containing TRIGA SNF as described in Section 7. CAL-DS0-NU-000003 REV 00A IX-4 September2004 Criticality Model IX.2.1 Range of Applicability of Selected Critical Benchmark Experiments This section summarizes in a set of tables (Tables IX-3 to IX-12) the range of applicability of the experiments listed in Table IX-2. The information is partly excerpted from Benchmark and Critical Limit Calculation for DOE SNF (BSC 2002, Section 6.2), which presents a less comprehensive set of parameters. The tables have been enhanced by adding information regarding the spectral characteristics of the experiments (available for the majority of the benchmarks in International Handbook of Evaluated Criticality Safety Benchmark Experiments [NEA 2001]). The purpose is to construct a collective area of applicability that will be used to directly compare with the range of parameters of the codisposal configurations. Table IX-3. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with Heterogeneous Moderated Configurations of TRIGA SNF (Set 1) Experiment Experiment Experiment Experiment HEU-COMP- HEU-COMP- HEU-COMP- HEU-COMP- Category/ THERM-002 THERM-003 THERM-004 THERM-005 Description Parameter (25 cases) (15 cases) (4 cases) (1 case) Materials/ Fissionable Uranium Uranium Uranium Uranium Fissionable Element Material Physical Form U-Dicarbide UO2 + Cu UO2 + Cu UO2 + Cu Isotopic Composition 93.15 wt.% wt. % 235U 79.66 wt. % 235U 88.87 wt. % 235U 79.66 wt. % 235U Atomic Density 235U: 235U: 3.63e-03 235U: 5.13e-03 235U: 4.42e-03 (atoms/b-cm) 9.98E-04 to 1.13e-03 238U: 8.72e-04 238U: 5.77e-04 238U: 1.06 e-03 238U: 7.24e-05 to 8.18e-05 Temperature Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Element Hydrogen H Hydrogen Hydrogen Moderator Physical Form Water, Graphite Water Water Water Atomic Density (atoms/b-cm) H: 6.67e-2 C: 8.98e-2 to 9.80e-2 6.67e-02 6.67e-02 6.67e-02 (in fuel) Ratio to Fissile C/X = 87 to 88.9 51 to 349 35 23 Material (In Region Containing Fissile Material) Temperature Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Material/ Reflected by water Reflected by water Reflected by water Reflected by water Reflector Physical Form and stainless steel and stainless steel and stainless steel Materials/ Neutron Element None None Gd; Sm None Absorber Physical Form N/A N/A Gd2O3 or Sm2O3 Rods N/A Atomic Density (atoms/b-cm) N/A N/A Gd: 3.11e-04 N/A Geometry Heterogeneity Various arrays of Al tuned or bare fuel elements (hexagonal graphite blocks containing uranium-dicarbide Cylindrical two zones hexagonally pitched lattice of cross-shaped fuel rods Cylindrical hexagonally pitched double lattice of cross-shaped fuel rods and absorber rods Hexagonally pitched array of fuel rod clusters (each containing a hexagonally pitched lattice of beads) cross-shaped fuel rods) Shape Cylinder Cylinder Cylinder Cylinder CAL-DS0-NU-000003 REV 00A IX-5 September2004 Criticality Model Table IX-3. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with Heterogeneous Moderated Configurations of TRIGA SNF (Set 1) Category/ Description Parameter Experiment HEU-COMP- THERM-002 (25 cases) Experiment HEU-COMP- THERM-003 (15 cases) Experiment HEU-COMP- THERM-004 (4 cases) Experiment HEU-COMP- THERM-005 (1 case) Neutron Energy AENCFb 0.0094 to 0.0244 MeV 0.0139 to 0.0467 MeV 0.0736 to 0.0756 MeV 0.0764 MeV EALFb 0.05 to 0.15 eV 0.06 to 0.40 eV 1.27 to 1.52 eV 1.46 eV Neutron Energy Spectraa T: 15.2 to 49.4% I: 22.5 to 35.2% F: 28.1 to 50.6% T: 9.9-37.7% I: 27.4 to 37% F: 36.9 to 53.1% T: 3.6 to 4.1% I: 38.2 to 38.5% F: 57.4 to 58.1% T: 6.5% I: 38.4% F: 55.1% Fission Rate vs. Neutron Energya T: 85.6 to 95.8% I: 3.6 to 12.8% F: 0.5 to 1.6% T: 75.3 to 94.1% I: 5.2 to 21.9% F: 0.7 to 2.8% T: 60.6 to 62.6% I: 32.9 to 34.7% F: 4.5 to 4.7% T: 61.3% I: 33.8% F: 4.9% Source: BSC 2002 and NEA 2001, Spectra NOTES: a Spectral range defined as follows: thermal (T) [0 to 1 eV], intermediate (I) [1eV to 100 keV], fast (F) [100 keV to 20 MeV]. b AENCF = average energy of a neutron causing fission, EALF = energy of average lethargy causing fission. Table IX-4. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with Heterogeneous Moderated Configurations of TRIGA SNF (Set 2) Experiment Experiment Experiment Experiment HEU-COMP- HEU-COMP- HEU-COMP- HEU-COMP- Category/ Description Parameter THERM-006 (3 cases) THERM-007 (3 cases) THERM-008 (2 cases) THERM-010 (21 cases) Materials/ Fissionable Uranium Uranium Uranium Uranium Fissionable Element Material Physical Form UO2 + Cu UO2 + Cu UO2 + Cu UO2 + BeO Isotopic Composition 79.66 wt. % 235U 79.66 wt. % 235U 80 wt. % 235U 62.4 wt.% wt. % 235U Atomic Density (atoms/b-cm) 235U: 4.42e-03 238U: 1.06 e-03 235U: 3.63e-03 238U: 8.72e-04 235U: 4.42e-03 238U: 1.06 e-03 235U: 3.83E-03 238U: 2.24E-03 For solution: (cases 20-21) 235U: 9.43E-06 238U: 7.44E-07 Temperature Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Moderator Element Hydrogen Hydrogen Hydrogen Hydrogen Physical Form Water Water; ZrH rods Water Water Atomic Density 6.67e-02 6.67e-02 (H2O) 6.67e-02 6.67e-02 (atoms/b-cm) 5.34e-02 (ZrH) For solution: 6.65e-02 to 6.68e-02 Ratio to Fissile 30 to 716 60 to 91 25 36 to 302 Material (In Region Containing Fissile Material) Temperature Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Material/ Reflected by water and Reflected by water Reflected by water Reflected by water Reflector Physical Form stainless steel and stainless steel and stainless steel CAL-DS0-NU-000003 REV 00A IX-6 September2004 Criticality Model Table IX-4. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with Heterogeneous Moderated Configurations of TRIGA SNF (Set 2) (Continued) Experiment Experiment Experiment Experiment HEU-COMP- HEU-COMP- HEU-COMP- HEU-COMP- Category/ THERM-006 THERM-007 THERM-008 THERM-010 Description Parameter (3 cases) (3 cases) (2 cases) (21 cases) Materials/ Element None None Boron B as Boric Acid Neutron (few cases) Absorber Physical Form N/A N/A B4C rods In solution Atomic Density N/A N/A B10: 1.12e-03 to B-10: 4.32E-07 to (atoms/b-cm) 3.92e-03 3.49E-06 (cases 17 to 21) Geometry Heterogeneity Cylindrical hexagonally pitched lattice of cross-shaped fuel rods Cylindrical hexagonally pitched double lattice of cross-shaped fuel rods and ZrH rods Cylindrical hexagonally double lattice of fuel rods and B4C rod Square or cylindrical assemblies with square or hexagonal pitched lattices Shape Cylinder Cylinder Cylinder Cylinder Neutron AENCFb 0.0104 to 0.0720 MeV 0.0339 to 0.0882 to 0.0230 to Energy 0.0475 MeV 0.0922 MeV 0.0800 MeV EALFb 0.05 to 1.12 eV 0.257to 0.445 eV 2.5 to 2.9 eV 0.08 to 0.88 eV Neutron Energy Spectraa T: 4.9 to 47% I: 23.2 to 37.7% T: 8.0 to 11.9% I: 36.9 to 38.0% T: 2.5 to 3.0% I: 38.9 to 39.1% T: 6.1 to 28.2% I: 25.4 to 36.7% F: 29.8 to 57.4% F: 51.2 to 54.0% F: 57.9 to 58.6% F: 46.4 to 57.2% Fission Rate vs. T: 64.1 to 96.1% T: 73.8 to 80.9% T: 53.6 to 55.2% T: 67.7 to 92.5% Neutron I: 3.4 to 31.5% I: 17.1 to 23.3% I: 39.2 to 40.6% I: 6.3 to 27.8% Energya F: 0.5 to 4.4% F: 2 to 2.9% F: 5.6 to 5.8% F: 1.2 to 4.5% Source: BSC 2002 and NEA 2001, Spectra NOTES: a Spectral range defined as follows: thermal (T) [0 to 1 eV], intermediate (I) [1eV to 100 keV], fast (F) [100 keV to 20 MeV]. b AENCF = average energy of a neutron causing fission, EALF = energy of average lethargy causing fission. CAL-DS0-NU-000003 REV 00A IX-7 September2004 Criticality Model Table IX-5. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with Heterogeneous Moderated Configurations of TRIGA SNF (Set 3) Experiment HEU-COMP- Experiment HEU-COMP- Experiment HEU-COMP- Experiment HEU-COMP- Category/ THERM-011 THERM-012 THERM-013 THERM-014 Description Parameter (3 cases) (2 cases) (2 cases) (2 cases) Materials/ Fissionable Uranium Uranium Uranium Uranium Fissionable Element Material Physical Form UO2 + Al alloy UO2 + Al alloy UO2 + Al alloy UO2 + Al alloy Isotopic Composition 79.4 wt. % 235U 79.4 wt. % 235U 79.4 wt. % 235U 79.4 wt. % 235U Atomic Density (atoms/b-cm) 235U: 2.66e-03 238U: 6.47e-03 235U: 2.66e-03 238U: 6.47e-03 235U: 2.66e-03 238U: 6.47e-03 235U: 2.66e-03 238U: 6.47e-03 Temperature Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Element Hydrogen Hydrogen Hydrogen Hydrogen Moderator Physical Form Water Water Water Water Atomic Density 6.68e-02 6.68e-02 6.68e-02 6.68e-02 (atoms/b-cm) Ratio to Fissile 170 35 40 170 Material (In Region Containing Fissile Material) Temperature Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Material/ Reflected by water Reflected by water Reflected by water Reflected by water Reflector Physical Form Materials/ Element None None None None Neutron Absorber Physical form N/A N/A N/A N/A Atomic Density (atoms/b-cm) N/A N/A N/A N/A Geometry Heterogeneity Square clusters of cylindrical fuel rods arranged in square Square clusters of cylindrical fuel rods arranged in square Square clusters of cylindrical fuel rods arranged in square Square clusters of cylindrical fuel rods arranged in square geometry geometry geometry geometry Shape Cylinder Cylinder Cylinder Cylinder Neutron Energy AENCFb 0.047 to 0.053 MeV 0.051 to 0.055 MeV 0.043 to 0.048 MeV 0.023 to 0.026 MeV EALFb 0.43 to 0.72 eV 0.43 to 0.56 eV 0.32 to 0.45 eV 0.10 to 0.12 eV Neutron Energy Spectraa T: 6.6 to 10.0% I: 37.6 to 40.1% T: 7.3 to 9.4% I: 37.1 to 38.4% T: 8.6 to 12.1% I: 36 to 37.9% T: 17.0 to 20.6% I: 31.4 to 33.1% F: 52.4 to 53.5 F: 53.5 to 54.3% F: 51.9 to 53.5% F: 48.0 to 49.9% Fission Rate vs. T: 68.4 to 74.2% T: 71.8 to 74.7% T: 73.7 to 77.6% T: 87.9 to 89.8% Neutron Energya I: 22.8 to 28.2% I: 22.2 to 24.8% I: 19.7 to 23.2% I: 8.9 to 10.6% F: 3.0 to 3.4% F: 3.1 to 3.4% F: 2.7 to 3.1% F: 1.3 to 1.5% Source: BSC 2002 and NEA 2001, Spectra NOTES: aSpectral range defined as follows: thermal (T) [0 to 1 eV], intermediate (I) [1eV to 100 keV], fast (F) [100 keV to 20 MeV]. bAENCF = average energy of a neutron causing fission, EALF = energy of average lethargy causing fission. CAL-DS0-NU-000003 REV 00A IX-8 September2004 Criticality Model Table IX-6. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with Heterogeneous Moderated Configurations of TRIGA SNF (Set 4) Experiment HEU-MET- Experiment IEU-COMP- Category/ THERM-006 THERM-003 Description Parameter (23 cases) (2 cases) Materials/ Fissionable Element Uranium Uranium Fissionable Material Physical Form U-Al alloy (fuel plates) U-ZrH Isotopic Composition 93.17 wt. % 235U 19.9 wt. % 235U Atomic Density (atoms/b-cm) 235U: 1.85E-03 238U: 1.13E-04 For U in solution (4 cases): 235U: 1.02E-05 238U: 6.98E-07 235U: 3.68e-04 238U: 1.46e-03 Temperature Room Temp. Room Temp. Materials/ Element Hydrogen H Moderator Physical Form Water ZrH; Water Atomic Density (atoms/b-cm) 6.67e-02 For solution: 5.53e-02 (in ZrH) 6.69e-02 (H2O) 6.62e-02 to 6.64e-02 Ratio to Fissile Material 134 to 500 150.1 (In Region Containing Fissile Material) Temperature Room Temp. Room Temp. Materials/ Material/Physical Form Reflected by water or Reflected radially by Reflector dilute aqueous uranyl graphite and axially by nitrate solutions water Materials/ Element B or Cd (few cases) B Neutron Absorber Physical Form In solution B4C absorber rods Atomic Density (atoms/b-cm) B-10: 4.27E-06 B10: 2.14e-02 9.57E-06 (cases 19 to 23) Cd: 4.63e-02 (cases 17 and 18) Geometry Heterogeneity Rectangular arrays of fuel elements with various Complex cylindrical arrays of pins spacing Shape Slab (fuel plates) Cylinder Neutron Energy AENCFb 0.010 to 0.015 MeV 0.0240 MeV EALFb 0.05 to 0.09 eV N/A Neutron Energy Spectraa T: 18.5 to 33.3% N/A I: 25.3 to 36.5% F: 41.1 to 45% Fission Rate vs. Neutron Energya T: 89.9 to 95% N/A I: 4.4 to 9.2% F: 0.5 to 0.9% Source: BSC 2002 and NEA 2001, Spectra NOTES: aSpectral range defined as follows: thermal (T) [0 to 1 eV], intermediate (I) [1eV to 100 keV], fast (F) [100 keV to 20 MeV]. b AENCF = average energy of a neutron causing fission, EALF = energy of average lethargy causing fission. CAL-DS0-NU-000003 REV 00A IX-9 September2004 Criticality Model Table IX-7. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with Homogeneous Moderated Configurations of TRIGA SNF (Set 1) Experiment Experiment Experiment Experiment Experiment HEU-SOL- HEU-SOL- HEU-SOL- HEU-SOL- HEU-SOL- Category/ THERM-001 THERM-005 THERM-006 THERM-008 THERM-009 Description Parameter (10 cases) (17 cases) (29 cases) (5 cases) (4 cases) Materials/ Fissionable Uranium Uranium Uranium Uranium Uranium Fissionable Element Material Physical Form Aqueous solution of uranyl nitrate Aqueous solution of uranyl Aqueous solution of Aqueous solution of uranyl Aqueous solution of uranium nitrate uranium nitrate oxyfluoride oxyfluoride Isotopic Composition 93.17 wt. % 235U 87.4 to 93.2 wt. % 235U 93.06 wt. % 235U 93.17 wt. % 235 93.18 wt. % 235U Atomic Density (atoms/b-cm) 235U: 1.31E-04 to 8.54E-04 238U: 7.46E-06 to 4.86E-05 235U: 2.33-04 to 7.42E-04 238U: 3.32e-5 to 1.06E-03 235U: 7.00e-04 to 7.1E-04 238U: 4.31e-5 to 4.37e-5 235U: 1.44E-04 to 8.50E-04 238U: 8.20e-6 to 4.84E-05 235U: 5.09E-04 to 1.66E-03 238U: 2.88e-5 to 9.41E-05 Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Element H H H H H Moderator Physical Form Solution Solution Solution Solution Solution Atomic Density 5.82e-02 to 5.95e-02 to 5.91e-02 to 5.84e-02 to 5.964e-02 to (atoms/b-cm) 6.54e-02 6.41e-02 6.00e-02 6.53e-02 6.44e-02 Ratio to Fissile 86 to 499 80 to 276 84 to 85 69 to 454 35.8 to 126.5 Material Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Reflector Material/ Physical Form Unreflected (concrete walls) Unreflected or reflected (side and bottom) by water Unreflected or reflected (side and bottom) by water, borated Plexiglas Water water. Nickel, water+nickel, borated water + nickel Materials/ Element None Boron Boron None None Neutron Absorber Physical Form N/A Boron in Pyrex glass Enriched Boron in Boric Acid N/A N/A Atomic Density N/A B10: 9.82e-4 B10: 2.49e-5 – N/A N/A (atoms/b-cm) 8.03e-5 Geometry Heterogeneity Homogeneous solution Homogeneous solution Homogeneous solution Arrays of cylindrical tanks Homogeneous solution contained in a contained in a contained in a placed in a contained in a cylindrical tank cylindrical spherical rectangular spherical Al stainless steel stainless steel geometry vessel tank vessel Shape Cylinder Cylinder Cylinder Cylinder Sphere Neutron AENCFb 0.0065 to 0.0110 to 0.0320 to 0.0064 to 0.0180 to Energy 0.0410 MeV 0.0410 MeV 0.0430 MeV 0.0367 MeV 0.0450 MeV EALFb 0.04 to 0.29 eV 0.06 to 0.33 eV 0.20 to 0.44 eV 0.04 to 0.25 eV 0.09 to 0.52 eV Neutron Energy Spectraa T: 8.1 to 31.1% I: 29.1 to 36.5% T: 5.6 to 21.7% I: 32.5 to 39.2% T: 7.4 to 9.7% I: 35.9 to 39.5% T: 8.5 to 30.8% I: 29.1 to 36.3% T: 5.8 to 15.4% I: 34 to 35.7% F: 39.8 to 55.6% F: 45.8 to 55.5% F: 53 to 54.5% F: 40.0 to 55.5% F: 50.6 to 58.5% Fission Rate vs. T: 77.5 to 95.5% T: 75.4 to 92.8% T: 72.5 to 81.4% T: 78.9 to 95.5% T: 71.8 to 89.1% Neutron Energya I: 4.1 to 20.3% I: 6.6 to 22.3% I: 16.8 to 25.2% I: 4.1 to 19.0% I: 9.9 to 25.0% F: 0.4 to 2.2% F: 0.6 to 2.3% F: 1.8 to 2.4% F: 0.4 to 2.1% F: 1.0 to 3.2% Source: BSC 2002, and NEA 2001, Spectra NOTES: a Spectral range defined as follows: thermal (T) [0 to 1 eV], intermediate (I) [1eV to 100 keV], fast (F) [100 keV to 20 MeV]. b AENCF = average energy of a neutron causing fission, EALF = energy of average lethargy causing fission. CAL-DS0-NU-000003 REV 00A IX-10 September2004 Criticality Model Table IX-8. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with Homogeneous Moderated Configurations of TRIGA SNF (Set 2) Experiment HEU-SOL- Experiment HEU-SOL- Experiment HEU-SOL- Experiment HEU-SOL- Experiment HEU-SOL- Category/ THERM-010 THERM-011 THERM-012 THERM-013 THERM-014 Description Parameter (4 cases) (2 cases) (1case) (4 cases) (3 cases) Materials/ Fissionable Uranium Uranium Uranium Uranium Uranium Fissionable Element Material Physical Form Aqueous solution of Aqueous solution of Aqueous solution of Aqueous solution of Aqueous solution of uranyl uranium uranium uranium uranyl nitrate nitrate oxyfluoride oxyfluoride oxyfluoride Isotopic Composition 93.12 wt. % 235U 93.12 wt. % 235U 93.2 wt. % 235U 93. 2 wt. % 235U 89 wt. % 235U Atomic 235U: 2.44E-04 to 235U: 1.24E-04 to 235U: 5.24e-4 235U: 4.80E-05 235U: 1.54E-04 to Density 2.66E-04 1.27E-04 238U: 2.97e-6 to 6.79E-05 1.60E-04 (atoms/b-cm) 238U: 1.36e-5 to 238U: 7.04e-6 to 238U: 2.80e-6 to 238U: 1.68e-5 to 1.49E-05 7.16E-06 3.97E-06 1.74E-0 Temperature 300.5 to 358.5 K Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Element H H H H H Moderator Physical Form Solution Solution Solution Solution Solution Atomic 6.36e-02 to 6.62e-02 to 6.67e-02 6.58e-02 to 6.47e-02 to Density 6.57e-02 6.63e-02 6.60e-02 6.50e-02 (atoms/b-cm) Ratio to 239 to 270 523 to 533 1272 971 to 1375 405 to 421 Fissile Material Temperature 300.5 to 358.5 K Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Material/ Water Water Water Unreflected Water Reflector Physical Form Materials/ Element None None None Boron (3 cases) Gd (2 cases) Neutron Absorber Physical Form N/A N/A N/A In solution (boric acid) In solution Atomic N/A N/A N/A B10: 1.04e-6 3.83e-07 to Density to 2.55e-06 7.39e-07 (atoms/b-cm) Geometry Heterogeneity Homogeneous solution Homogeneous solution Homogeneous solution Homogeneous solution Homogeneous solution contained in a contained in a contained in a contained in a contained in a spherical Al vessel spherical Al vessel spherical Al vessel spherical Al vessel cylindrical stainless steel vessel Shape Sphere Sphere Sphere Sphere Cylinder Neutron Energy AENCF 0.0090 to 0.0050 MeV 0.0027 MeV 0.0026 to 0.0071 to 0.010 MeV 0.0038 MeV 0.0076 MeV EALF 0.05 to 0.06 eV 0.04 eV 0.03 eV 0.033 to 0.036 eV 0.046 to 0.050 eV Neutron T: 23 to 24.7% T: 34.9 to 35.2% T: 49.5% T: 41.4 to 49.5% T: 27.7 to 28.9% Energy Spectraa I: 31.1 to 31.6% F: 44.2 to 45.4% I: 27.5 to 27.6% F: 37.3 to 37.5% I: 22.2% F: 28.3% I: 22.3 to 25.8% F: 28.2 to 32.8% I: 30.1 to 31.4% F: 40.9 to 41% Fission Rate T: 93.3 to 94.0% T: 96.3% T: 97.9% T: 97.1 to 97.9% T: 94.4 to 95.0% vs. Neutron I: 5.5 to 6.1% I: 3.4% I: 1.9% I: 1.9 to 2.7% I: 4.6 to 5.2% Energya F: 0.5 to 0.6% F: 0.3% F: 0.2% F: 0.2% F: 0.4% Source: BSC 2002 and NEA 2001, Spectra a NOTE: Spectral range defined as follows: thermal (T) [0 to 1 eV], intermediate (I) [1eV to 100 keV], fast (F) [100 keV to 20 MeV]. CAL-DS0-NU-000003 REV 00A IX-11 September2004 Criticality Model Table IX-9. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with Homogeneous Moderated Configurations of TRIGA SNF (Set 3) Experiment HEU-SOL- Experiment HEU-SOL- Experiment HEU-SOL- Experiment HEU-SOL- Experiment HEU-SOL- Category/ Description Parameter THERM-015 (5 cases) THERM-016 (3 cases) THERM-017 (8 cases) THERM-018 (12 cases) THERM-019 (3 cases) Materials/ Fissionable Uranium Uranium Uranium Uranium Uranium Fissionable Element Material Physical Form Aqueous Aqueous Aqueous solution Aqueous solution Aqueous solution solution of uranyl solution of uranyl of uranyl nitrate of uranyl nitrate of uranyl nitrate nitrate nitrate Isotopic Composition 89 wt. % 235U 89 wt. % 235U 89 wt. % 235U 89 wt. % 235U 89 wt. % 235U Atomic 235U: 2.17E-04 to 235U: 3.29E-04 to 235U: 4.25E-04 to 235U: 6.38E-04 to 235U: 8.98E-04 to Density 2.29E-04 3.57E-04 4.62E-04 6.84E-04 1.02E-03 (atoms/b-cm) 238U: 2.37e-5 to 238U: 3.59e-5 to 238U: 4.63e-5 to 238U: 6.95e-5 to 238U: 9.79e-5 to 2.50E-05 3.89E-05 5.03E-05 7.46E-05 1.11E-04 Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Element H H H H H Moderator Physical Form Solution Solution Solution Solution Solution Atomic 6.38e-02 to 6.26e-02 to 6.13e-02 to 5.89e-02 to 5.58e-02 to Density 6.40e-02 6.30e-02 6.23e-02 5.97e-02 5.66e-02 (atoms/b-cm) Ratio to 278 to 295 175 to 192 133 to 147 86 to 94 55 to 63 Fissile Material Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Material/ Water Water Water Water Water Reflector Physical Form Materials/ Element Gd (3 cases) Gd (2 cases) Gd (5 cases) Gd (9 cases) Gd (2 cases) Neutron Absorber Physical Form In solution In solution In solution In solution In solution Atomic 7.54e-07 to 1.15e-06 to 1.14e-06 to 1.90e-06 to 2.48e-06 to Density 1.53e-06 2.01e-06 3.03e-06 7.44e-06 4.44e-06 (atoms/b-cm) Geometry Heterogeneity Homogeneous solution Homogeneous solution Homogeneous solution Homogeneous solution contained Homogeneous solution contained contained in a cylindrical vessel made of contained in a cylindrical vessel made of contained in a cylindrical vessel made of in a cylindrical vessel made of stainless steel in a cylindrical vessel made of stainless steel stainless steel stainless steel stainless steel Shape Cylinder Cylinder Cylinder Cylinder Cylinder Neutron AENCFb 0.0100 to 0.0151 to 0.0189 to 0.0285 to 0.0393 to Energy 0.0113 MeV 0.0161 MeV 0.0221 MeV 0.0329 MeV 0.0425 MeV EALFb 0.056 to 0.078 to 0.097 to 0.16 to 0.29 to 0.066 eV 0.092 eV 0.135 eV 0.27 eV 0.35 eV Neutron T: 21.7 to 23.3% T: 16.9 to 17.6% T: 13.3 to 14.9% T: 9.5 to 11.0% T: 7.7 to 8.4% Energy Spectraa I: 31.9 to 34.0% F: 44.3 to 45.1% I: 33.9 to 35.6% F: 47.5 to 48.7% I: 34.6 to 36.9% F: 49.5 to 51.1% I: 35.6 to 38.3% F: 51.9 to 53.9% I: 36.4 to 37.3% F: 54.7 to 55.9% Fission Rate T: 92.1 to 93.4% T: 89.0 to 90.4% T: 85.3 to 88.4% T: 78.3 to 83.6% T: 75.9 to 77.6% vs. Neutron I: 6.1 to 7.3% I: 8.8 to 10.1% I: 10.6 to 13.5% I: 14.8 to 19.8% I: 20.2 to 21.8% Energya F: 0.6% F: 0.8 to 0.9% F: 1.0 to 1.2% F: 1.6 to 1.9% F: 2.2 to 2.4% Source: BSC 2002 and NEA 2001, Spectra NOTES: aSpectral range defined as follows: thermal (T) [0 to 1 eV], intermediate (I) [1eV to 100 keV], fast (F) [100 keV to 20 MeV]. b AENCF = average energy of a neutron causing fission, EALF = energy of average lethargy causing fission. CAL-DS0-NU-000003 REV 00A IX-12 September2004 Criticality Model Table IX-10. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with Homogeneous Moderated Configurations of TRIGA SNF (Set 4) Experiment HEU-SOL- Experiment HEU-SOL- Experiment HEU-SOL- Experiment HEU-SOL- Experiment HEU-SOL- Category/ THERM-021 THERM-025 THERM-027 THERM-028 THERM-029 Description Parameter (32 cases) (18 cases) (9 cases) (18 cases) (7 cases) Materials/ Fissionable Uranium Uranium Uranium Uranium Uranium Fissionable Element Material Physical Form Aqueous solution Aqueous Aqueous solution Aqueous solution Aqueous solution of uranyl nitrate solution of uranyl of uranyl nitrate of uranyl nitrate of uranyl nitrate nitrate Isotopic Composition 92.6 wt. % 235U 89 wt. % 235U 89 wt. % 235U 89 wt. % 235U 89 wt. % 235U Atomic 235U: 1.50E-04 to 235U: 1.15E-04 to 235U: 3.10e-04 235U: 1.73e-4 to 235U: 6.53e-04 Density (atoms/b-cm) 9.85E-04 238U: 9.45e-6 to 1.76E-04 238U: 1.27e-5 to 238U: 3.38e-05 6.52e-4 238U: 1.89e-5- 238U: 7.10e-05 6.19E-05 1.92E-05 7.1e-05 Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Element H H H H H Moderator Physical Form Solution Solution Solution Solution Solution Atomic 5.79e-02 to 6.48e-02 to 6.32e-02 5.97e-02 to 5.97e-02 Density 6.53e-02 6.50e-02 6.50e-2 (atoms/b-cm) Ratio to 59 to 435 61.8 to 556 203.6 91.5 to 374.5 91.5 Fissile Material Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Material/ Water, Plexiglas, Water Unreflected Water Water Reflector Physical Form paraffin Materials/ Element None Gd (1 case) B or Cd B (9 cases) B (6 cases) Neutron Absorber Physical Form N/A In solution Absorber rods B4C rods B4C rods Atomic N/A 4.09e-7 B10: 1.08e-2 B-10: 1.08e-2 B-10: 1.08e-2 Density Cd: 4.63e-2 (atoms/b-cm) Geometry Heterogeneity Arrays of cylindrical containers placed in a rectangular geometry Homogeneous solution contained in a cylindrical stainless steel vessel Homogeneous solution contained in a cylindrical stainless steel vessel Homogeneous solution contained in a cylindrical stainless steel vessel Homogeneous solution contained in a cylindrical stainless steel vessel Shape Cylinder Cylinder Cylinder Cylinder Cylinder Neutron AENCFb 0.0067 to 0.0050 to 0.014 to 0.007 to 0.027 0.027 to 0.029 Energy 0.0437 MeV 0.0280 MeV 0.015 MeV EALFb 0.04 to 0.33 eV 0.041 to 0.18 eV 0.074 to 0.076 eV 0.047 to 0.153 eV 0.156 to 0.167 eV Neutron T: 7.6 to 30.% T: 16.5 to 34.2% T: 8.4 to 25.0% T: 5.8 to 28.1% T: 8.2 to 11.1% Energy Spectraa I: 29.5 to 36.5% F: 40.3 to 56% I: 28.2 to 35.6% F: 37.6 to 47.9% I: 29.9 to 39.3% F: 40.8 to 61.0% I: 30.4 to 35.7% F: 41.5 to 61.7% I: 34.4 to 35.8% F:53.1 to 57.4% Fission Rate T: 76.4 to 95.4% T: 81.5 to 96.1% T: 90.5 to 90.8% T: 84.0 to 94.9% T: 82.9 to 83.8% vs. Neutron I: 4.2 to 21.2% I: 3.6 to 16.9% I: 8.4 to 8.6% I: 4.7 to 14.5% I: 14.7 to 15.5% Energya F: 0.4 to 2.4% F: 0.3 to 1.6% F: 0.8 to 0.9% F: 0.4 to 1.5% F: 1.5 to 1.6% Source: BSC 2002 and NEA 2001, Spectra NOTES: a Spectral range defined as follows: thermal (T) [0 to 1 eV], intermediate (I) [1eV to 100 keV], fast (F) [100 keV to 20 MeV]. b AENCF = average energy of a neutron causing fission, EALF = energy of average lethargy causing fission. CAL-DS0-NU-000003 REV 00A IX-13 September2004 Criticality Model Table IX-11. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with Homogeneous Moderated Configurations of TRIGA SNF (Set 5) Experiment HEU-SOL- Experiment HEU-SOL- Experiment HEU-SOL- Experiment HEU-SOL- Experiment HEU-SOL- Category/ THERM-030 THERM-031 THERM-032 THERM-033 THERM-035 Description Parameter (7 cases) (4 cases) (1 case) (26 cases) (9 cases) Materials/ Fissionable Uranium Uranium Uranium Uranium Uranium Fissionable Element Material Physical Form Aqueous solution of uranyl nitrate Aqueous solution of uranyl nitrate Aqueous solution of uranyl nitrate Aqueous solution of uranyl nitrate Aqueous solution of uranyl nitrate Isotopic Composition 89 wt. % 235U 89 wt. % 235U 93.2 wt. % 235U 93.2 wt. % 235U 89 wt. % 235U Atomic 235U: 235U: 6.60e-4 235U: 3.62e-5 235U: 8.54e-4 235U: 8.56e-5 to Density (atoms/b-cm) 1.73e-04 to 6.60e-4 238U: 7.17e-5 238U: 1.99e-6 238U: 4.85e-5 3.74e-4 238U: 9.31e-06 to 238U: 1.89e-05 3.78e-5 to 7.17e-5 Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Element H H H H H Moderator Physical Form Solution Solution Solution Solution Solution Atomic 6.01e-02 to 6.01e-2 6.64e-2 5.81e-02 6.28e-2 to Density 6.50e-02 6.56e-02 (atoms/b-cm) Ratio to 91.1 to 374.6 91.1 1835 68.1 181 to 767 Fissile Material Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Material/ Water Water unreflected concrete water Reflector Physical Form Materials/ Neutron Element B (5 cases) B (9 cases) None B and Cd B Absorber Physical Form B4C rods B4C rods N/A B and Cd in solution B4C rods Atomic Density (atoms/b-cm) B-10: 1.08e-2 B-10: 9.54e-3 N/A B-10:1.74e-8 Cd: 1.49e-8 B-10:1.08e-2 Geometry Heterogeneity Homogeneous solution contained Homogeneous solution Homogeneous solution Homogeneous solution Homogeneous solution in a cylindrical stainless steel vessel made contained in a cylindrical stainless steel vessel contained in a spherical Al vessel contained in a nested structure of cylindrical stainless steel contained in a cylindrical stainless steel tank tanks Shape Cylinder Cylinder Sphere Cylinder Cylinder Neutron AENCF 0.008 to 0.028 0.028 to 0.031 0.0021 0.032 to 0.036 0.004 to 0.016 Energy EALF 0.048 to 0.164 eV 0.163 to 0.187 eV 0.031 eV 0.269 to 0.316 eV 0.038 to 0.084 eV Neutron T: 8.5 to 27.7% T: 7.6 to 8.9% T: 54.6% T: 8.1 to 8.8% T: 14.7 to 38.7% Energy Spectraa I: 30.5 to 35.8% F: 41.7 to 56.% I: 35.5 to 35.9% F: 55.7 to 56.6% I: 20.3% F: 25.1% I: 38.2 to 39% F: 52.6 to 53.4% I: 26.7 to 34.3% F: 34.6 to 51.2% Fission Rate T: 83.2 to 94.7% T: 81.7 to 83.3% T: 98.3% T: 76.2 to 78.0% T: 89.6 to 96.8% vs. Neutron I: 4.8 to 15.2% I: 15.1 to 16.6% I: 1.6% I: 20.1 to 21.7% I: 3.0 to 9.5% Energya F: 0.4 to 1.6% F: 1.6 to 1.7% F: 0.1% F: 1.9 to 2.1% F: 0.2 to 0.9% Source: BSC 2002 and NEA 2001, Spectra a NOTE: Spectral range defined as follows: thermal (T) [0 to 1 eV], intermediate (I) [1eV to 100 keV], fast (F) [100 keV to 20 MeV]. CAL-DS0-NU-000003 REV 00A IX-14 September2004 Criticality Model Table IX-12. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with Homogeneous Moderated Configurations of TRIGA SNF (Set 6) Experiment Experiment Experiment Experiment HEU-SOL- HEU-SOL- HEU-SOL- HEU-SOL- Category/ THERM-036 THERM-037 THERM-043 THERM-044 Description Parameter (4 cases) (9 cases) (3 case) (16 cases) Materials/ Fissionable Uranium Uranium Uranium Uranium Fissionable Element Material Physical Form Aqueous solution of uranyl nitrate Aqueous solution of uranyl nitrate Aqueous solution of uranium oxyfluoride Aqueous solution of uranyl nitrate Isotopic Composition 89 wt. % 235U 89 wt. % 235U 93.2 wt. % 235U 93.17 wt. % 235U Atomic Density (atoms/b-cm) 235U: 2.12e-4 238U: 2.29e-5 235U: 9.56e-5 to 1.89e-4 238U: 1.04e-5 to 2.06e-5 235U: 4.77e-05 to 3.20e-04 238U: 2.86e-06 to 1.79e-05 235U: 8.65e-4 238U: 4.95e-5 Temperature Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Element H H H H Moderator Physical Form Solution Solution Solution Solution Atomic Density 6.40e-2 6.43e-02 to 6.53e-2 to 6.67e-2 5.81e-02 (atoms/b-cm) 6.55e-02 Ratio to Fissile 302.5 340 to 685 204 to 1392 67.2 Material Temperature Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Material/ Unreflected Water Unreflected Concrete Reflector Physical Form Materials/ Element B (3 cases) B (6 cases) None B, Cl, Cd, and Gd Neutron Absorber Physical Form B4C rods B4C rods N/A Absorbers are in various forms (pyrex glass, boraflex rubber, Cd sleeves, etc.) Atomic Density (atoms/b-cm) B-10: 1.08e-2 B-10: 1.08e-2 N/A B-10: 6.99e-03 to 9.57e-4 Cd: 5.19e-03 to 4.63e-02 Geometry Heterogeneity Homogeneous solution contained Homogeneous solution contained Homogeneous solution contained Homogeneous solution contained in a nested in a square stainless steel and in a cylindrical stainless steel in a spherical Al vessel structure of cylindrical stainless steel tanks Cd (inner wall) tank vessel Shape Parallel-piped Cylinder Sphere Cylinder Neutron AENCF 0.010 to 0.012 0.005 to 0.009 0.003 to 0.014 0.0340 to 0.0470 Energy EALF 0.056 to 0.063 eV 0.038 to 0.054 eV 0.033 to 0.075 eV N/A Neutron Energy Spectraa T: 12.5 to 23.1% I: 31.9 to 32.9% T: 21.1 to 37.1% I: 27.1 to 32.4% T: 18.0 to 49.8% I: 22.2 to 33.7% N/A F: 44.9 to 54.6% F: 35.8 to 46.5% F: 28.0 to 48.3% Fission Rate vs. Neutron Energya T: 92.0 to 93.3% I: 6.1 to 7.3% T: 93.5 to 96.6% I: 3.2 to 6.0% T: 90.8 to 97.9% I: 1.9 to 8.4% N/A F: 0.6 to 0.7% F: 0.2 to 0.5% F: 0.1 to 0.8% Source: BSC 2002 and NEA 2001, Spectra NOTES: aSpectral range defined as follows: thermal (T) [0 to 1 eV], intermediate (I) [1eV to 100 keV], fast (F) 100 keV to 20 MeV]. b AENCF = average energy of a neutron causing fission, EALF = energy of average lethargy causing fission. CAL-DS0-NU-000003 REV 00A IX-15 September2004 Criticality Model IX.3 CALCULATION OF THE LOWER-BOUND TOLERANCE LIMIT The following results are excerpted from Analysis of Critical Benchmark Experiments and Critical Limit Calculation for DOE SNF (BSC 2003b), which present in detail the methodology and calculations performed for evaluating the LBTL for each set of configurations of the waste package containing TRIGA SNF. The calculated keff values for the critical benchmarks are taken from Analysis of Critical Benchmark Experiments and Critical Limit Calculation for DOE SNF (BSC 2003b, Attachment II). The results of the trending parameter analysis for the critical benchmark subset representative for moderated intact (heterogeneous) configurations (configuration classes IP-3a, IP-3b, IP-3c, and IP-3d) of the waste package containing TRIGA SNF are presented in Table IX-13. The parameters in the following tables describe the regression statistics for the linear trend evaluations (see Attachment III for definitions). The P-value parameter gives a direct estimation of the probability of having a linear trending due to chance only. Table IX-13. Trending Parameter Results for the Critical Benchmark Subset Representative for Moderated Intact Fuel Configurations of the Waste Package Containing TRIGA SNF Trend Parameter n Intercept Slope r2 T t0.025,n-2 P-Value Goodness-of-Fit Tests Valid Trend AENCF 108 1.0120 -0.3315 0.4566 -9.4373 1.960 1.04E-15 Passed Yes H/235U 81 0.9945 2.56E-05 0.1321 3.4679 1.960 8.52E-04 Passed Yes Source: BSC 2003b, p. 30 NOTE: aAENCF = average energy of a neutron causing fission. Figure IX-4 presents the keff values and the calculated lower-bound tolerance limit. Details for the calculation of the LBTL function are provided in Analysis of Critical Benchmark Experiments and Critical Limit Calculation for DOE SNF (BSC 2003b, Attachment I) with the results as follows: Lower-bound tolerance limit = 0.9668 for 0 MeV < AENCF < 0.0404 MeV Lower-bound tolerance limit = -0.3315 × AENCF + 0.9788 for 0.0404 MeV < AENCF < 0.0922 MeV CAL-DS0-NU-000003 REV 00A IX-16 September2004 Criticality Model keff 1.04 1.03 1.02 1.01 1.00 0.99 0.98 0.97 0.96 0.95 0.94 Lower Bound Tolerance Limit 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 AENCF (MeV) Figure IX-4. Lower-Bound Tolerance Limit Applicable for TRIGA SNF Intact Moderated (Heterogeneous) Configurations The results of the trending parameter analysis for the critical benchmark subset representative for moderated degraded configurations (homogeneous) (configuration class IP-2a) of the waste package containing TRIGA SNF are presented in Table IX-14. Table IX-14. Trending Parameter Results for the Critical Benchmark Subset Representative for Moderated Degraded Configurations of the Waste Package Containing TRIGA SNF Trend Parameter n Intercept Slope r2 T t0.025,n-2 P-Value Goodness-of-Fit Tests Valid Trend AENCF 273 1.0046 -0.0055 9.10E-05 -0.1571 1.960 0.8753 Failed No H/X 273 1.0045 -1.82E-07 3.31E-05 -0.0947 1.960 0.9246 Failed No Source: BSC 2003b, p. 32 a NOTE: AENCF=average energy of a neutron causing fission. Figure IX-5 presents the keff values and the calculated LBTL. The LBTL value calculated with DFTL method for this subset (normality test failed) is 0.9796 (BSC 2003b, Attachment I). CAL-DS0-NU-000003 REV 00A IX-17 September2004 Criticality Model 1 ) keff limit 0.97 0.98 0.99 1.01 1.02 1.03 1.04 1.05 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 AENCF (MeVLower Bound Toerance L NOTE: AENCF = average energy of a neutron causing fission. Figure IX-5. Lower-Bound Tolerance Limit Applicable for TRIGA SNF Degraded (Homogeneous) Moderated Configurations CAL-DS0-NU-000003 REV 00A IX-18 September2004 Criticality Model ATTACHMENT X LBTL CALCULATION AND ROA DETERMINATION FORT ST. VRAIN SNF CAL-DS0-NU-000003 REV 00A September 2004 Criticality Model CAL-DS0-NU-000003 REV 00A September 2004 Criticality Model ATTACHMENT X LBTL CALCULATION AND ROA DETERMINATION FOR FORT ST. VRAIN SNF X.1 INTRODUCTION This attachment presents the calculations of the LBTL and the determination of ROA for benchmarks that could potentially be applicable to waste package configurations containing Fort St. Vrain (FSVR) SNF. A listing of corroborating and supporting data, models, or information used for the calculation is provided in Table X-1. Table X-1. Supporting Information and Sources Description Source Guidance for benchmarking a calculational method Dean and Tayloe 2001 Criticality benchmark experiments, trending parameters, and BSC 2002; BSC 2003b, NEA 2001, Putman 2003 CL calculations Fort St. Vrain summary report BSC 2001b Fort St. Vrain SNF is the representative fuel for the Th/U carbide fuel group, which is one of nine representative fuel groups designated by the National Spent Nuclear Fuel Program for disposal criticality analyses based on the fuel matrix composition, primary fissile isotope and enrichment (DOE 2002, Sections 5.2 and 5.3). The following information regarding Fort St. Vrain SNF is collected from Evaluation of Codisposal Viability for Th/U Carbide (Fort Saint Vrain HTGR) DOE-Owned Fuel (BSC 2001b, Section 2.1.4). Fort St. Vrain SNF consists of small particles (spheres of the order of 0.5-mm diameter) of thorium carbide or thorium and high-enriched uranium carbide mixture, coated with multiple, thin layers of pyrolytic carbon and silicon carbide, which serve as miniature pressure vessels to contain fission products and the U/Th carbide matrix. The coated particles are bound in a carbonized matrix, which forms fuel rods or “compacts” that are loaded into large hexagonal graphite prisms. The graphite prisms (or blocks) are the physical forms that are handled in reactor loading and unloading operations, and which will be loaded into the DOE-standardized SNF canisters. The Fort St. Vrain fuel element is hexagonal in cross section with dimensions of 360.0 mm (14.172 in.) across flats by 793.0-mm (31.22-in.) high. The active fuel is contained in an array of small-diameter holes, which are parallel with the coolant channels, and occupy alternating positions in a triangular array within the graphite structure. The fuel holes are drilled from the top face of the element to within approximately 7.6 mm (0.3 in.) of the bottom face. A cemented graphite plug that is 12.7-mm (0.5-in.) long closes the top of each fuel channel after the fuel compacts are installed. The fuel holes in all elements are 12.7 mm (0.5 in.) in diameter. The bonded rods (also referred to as “fuel compacts”) of coated fuel particles are stacked within the hole. These rods had a nominal dimension of 12.5 mm (0.49 in.) in diameter. The fuel holes and coolant channels are distributed on a triangular array with a pitch of approximately 18.8 mm (0.74 in.). CAL-DS0-NU-000003 REV 00A X-1 September2004 Criticality Model A fuel rod is a column of coated fuel particles bonded together by a binder matrix. Fuel rods are cylinders 12.45 mm (0.49 in.) in diameter and 49.276-mm (1.94-in.) long. The chemical characteristics can be varied considerably depending upon blending ratios of the fuel kernels. For initial core loading, and the first reload segment, the Fort St. Vrain fuel rod design utilized a homogeneous mixture of a graphite filler material and carbonized coal tar pitch as the binder. Beginning with the second reload (segment 8), petroleum-derived pitch was used as the binder, and isotropic shim particles, nominally 800 µm in diameter, were used to accommodate differences in heavy metal loading within the compacts. Hot injection molding process is the reference process for Fort St. Vrain fuel rod fabrication. The individual fuel compact fissile loading in a fuel block may have incorporated either a single or binary fuel mix number as shown in Table X-2. Table X-2. Fuel Compact Composition Used Element Compact Composition (g) Comments Thorium (as ThC2) 3.447 Based on 10789.97 g Th (EOL), and 3130 compacts per fuel element Uranium (as UC2) 0.474 Based on 1485 g maximum total U (BOL) and 100% 235U enrichment (BSC 2001b, p. 2-10, Combination 4) Silicon (as SiC) 0.800 Based on assumption of uniform coating on particles Carbon Pyrolytic 4.100 Based on assumption of uniform coating on particles Coating Compact Matrix 3.858 Calculated based on mass differences between loaded fuel elements and components Fuel Matrix 0.399 Calculated from ThC2 and UC2 masses (per compact) SiC Layer 0.341 Calculated as a percentage of SiC from reported pure Si mass Source: BSC 2001b, p. 2-11 The following four isotopic combinations were evaluated and compared for maximum keff in the same MCNP representation (the load values are reported per fuel element) in the criticality calculations for Fort St. Vrain SNF (BSC 2001b, Section 2.1.4.2). In the following, BOL denotes beginning of life and EOL denotes end of life. A. BOL 235U load of 1,256.61 g, EOL 233U load of 135.79 g B. BOL 235U load of 1,172.0 g, EOL 233U load of 239.63 g C. BOL 235U load of 1,168 g, EOL 233U load of 248.95 g D. 1,485.0 g BOL 235U load as maximum case and EOL 233U + 238U load of 0.0 g. The current conceptual design for disposing FSVR SNF (BSC 2001b, Section 2.1.1) in the repository contains five HLW glass canisters and one DOE SNF canister loaded with five Fort St. Vrain SNF elements. The DOE SNF canister containing five Fort St. Vrain fuel elements is placed in a carbon steel support tube that becomes the center of the waste package (see Figure X-1). The DOE SNF canister is surrounded by five 4.5-m-long Hanford HLW glass canisters. The five HLW glass canisters are evenly spaced around the DOE SNF canister. CAL-DS0-NU-000003 REV 00A X-2 September2004 Criticality Model DOE SNF HLW Glass SuppWP Basket ll Fort St. Vrain Canister ort Tube WP Inner Shell WP Outer SheSNF Element NOTE: WP = waste package, HLW = high-level waste, DOE SNF = U.S. Department of Energy Spent Nuclear Fuel. Figure X-1. Cross Section of the Waste Package Containing Fort St. Vrain SNF X.2 SELECTION OF THE CRITICALITY BENCHMARKS The critical experiments selected for inclusion in benchmarking must be representative of the types of materials, conditions, and parameters to be represented using the calculational method. A sufficient number of experiments with varying experimental parameters should be selected for inclusion in the benchmarking to ensure as wide an area of applicability as feasible and statistically significant results. While there is no absolute guideline for the minimum number of critical experiments necessary to benchmark a computational method, the use of only a few (i.e., less than 10) experiments should be accompanied by a suitable technical basis supporting the rationale for acceptability of the results (Dean and Tayloe 2001, p. 5). For the present application (codisposal of Fort St. Vrain SNF), the selected benchmark experiments have been grouped in two subsets (BSC 2002, Section 6.1.6) that include moderated heterogeneous and homogeneous experiments. The benchmark experiments are from International Handbook of Evaluated Criticality Safety Benchmark Experiments (NEA 2001), unless otherwise noted. The selection process was initially based on prior knowledge regarding the possible degraded configurations of the waste package (BSC 2001b, Section 7), and the subsets have been constructed to accommodate large variations in the range of parameters of the configurations and to provide adequate statistics for LBTL calculations. The selected benchmark experiments for each subset are presented in Benchmark and Critical Limit Calculation for DOE SNF (BSC 2002, Section 6.1.6) with MCNP cases constructed and calculation results. CAL-DS0-NU-000003 REV 00A X-3 September2004 Criticality Model Additional benchmarks cases were added the keff results and their uncertainties are summarized in Analysis of Critical Benchmark Experiments and Critical Limit Calculation for DOE SNF (BSC 2003b, Attachment II). Table X-3 presents the list of the benchmark experiments and the number of cases for each subset selected for Fort St. Vrain SNF. Table X-3. Critical Benchmarks Selected for Fort St. Vrain SNF Subset Benchmark Experiment Identificationa No. of Cases Included Heterogeneous Moderatedb Experiment with SB Coresc 8 HEU-COMP-THERM-002 25 HEU-COMP-MIXED-001 4 HEU-MET-INTER-006 2 U-233-SOL-THERM-006 6 Homogeneous Moderatedb U-233-SOL-THERM-001 5 U-233-SOL-THERM-002 17 U-233-SOL-THERM-003 10 U-233-SOL-THERM-004 8 U-233-SOL-THERM-005 2 U-233-SOL-THERM-008 1 U-233-SOL-THERM-006 6 HEU-COMP-THERM-002 25 HEU-COMP-MIXED-001 4 HEU-MET-INTER-006 2 Source: Subsets defined and evaluated in BSC 2002 NOTES: a The convention for naming the benchmark experiments is from NEA (2001). b Identification of each subset from BSC 2002 has been modified to better reflect the subset’s main characteristics. The benchmark experiments in each subset have not been affected. c These experiments are described in Section 5.1.1 in BSC 2003b. The experiments cover configuration classes IP-1a, IP-1b, IP-2a, IP-3a, IP-3b, IP-3c, and IP-3d for the degraded waste package containing FSVR SNF as described in Section 7. X.2.1 Range of Applicability of Selected Critical Benchmark Experiments This section summarizes in a set of tables (Tables X-4, X-5, and X-6) the range of applicability of the experiments listed in Table X-3. The information is partly excerpted from Benchmark and Critical Limit Calculation for DOE SNF (BSC 2002), which presents a less comprehensive set of parameters. The tables have been enhanced by adding information regarding the spectral characteristics of the experiments (available for the majority of the benchmarks in NEA [2001]). The purpose is to construct a collective area of applicability that will be used to directly compare with the range of parameters of the codisposal configurations. CAL-DS0-NU-000003 REV 00A X-4 September2004 Criticality Model Table X-4. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with Heterogeneous Moderated Configurations of Fort St. Vrain SNF Experiment Experiment Experiment Experiment Category/ Experiment SB-Cores HEU-COMP- THERM-002 HEU-COMP- MIXED-001 HEU-MET- INTER-006 U-233-SOL- THERM-006 Description Parameter (8 cases) (25 cases) (26 cases) (2 cases) (6 cases) Materials/ Fissionable Uranium Uranium Uranium Uranium Uranium Fissionable Element Material Physical Form 235UO2- ZrO2 Uranium UO2 U metal discs Uranyl nitrate (3 cases) or 233UO2-ZrO2 dicarbide (5 cases) Isotopic Composition 92.73 wt. % 235U (3 cases) 97.19 wt. % 233U 93.15 wt. % 235U 93.15 wt. % 235U 93.2 wt. % 235U (Average) 97.56 or 97.54 wt. % 233U (3 cases) 97.29 wt. % 233U (5 cases) Atomic Density (atoms/b-cm) 235U: 3.8791e-03 (3 cases) 235U: 9.98e-04 to 1.13e-03 235U: 4.48e-03 to 1.39e-02 235U: 4.48e-02 to 1.15e-02 233U:5.14e-04 to 8.64e-04 233U: 2.23e-4 to 3.84e-3 Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Element H H, C H C H Moderator Physical Form Water C: Carbide H: Water Water,Alcohol-w ater Graphite Water in aqueous solution,plexigla solution of s uranyl nitrate Atomic Density (atoms/b-cm) 6.67e-2 C:8.98e-2 to 9.8e-2 H: 6.67e-2 Fuel Region: 2.16e-2 (few cases) 5.68e-2 8.54e-2 to 8.58e-2 5.89e-02 to 6.15e-02 (Plexiglas) 6.24e-2 (alcohol-water) Ratio to Fissile Material 37 to 110 C/X: 87 to 88.9 H/X=0 to 49 C discs C/235U =52 H/X=69 to 121 (In Region Containing Fissile Material) Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Material/ Reflected by Reflected by Reflected by Reflected by Cu Unreflected Reflector Physical Form water water polyethylene Materials/ Element None None None None None Neutron Absorber Physical Form N/A N/A N/A N/A N/A Atomic Density (atoms/b-cm) N/A N/A N/A N/A N/A CAL-DS0-NU-000003 REV 00A X-5 September2004 Criticality Model Table X-4. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with Heterogeneous Moderated Configurations of Fort St. Vrain SNF (Continued) Experiment Experiment Experiment Experiment Category/ Experiment SB-Cores HEU-COMP- THERM-002 HEU-COMP- MIXED-001 HEU-MET- INTER-006 U-233-SOL- THERM-006 Description Parameter (8 cases) (25 cases) (26 cases) (2 cases) (6 cases) Geometry Heterogeneity Various arrays (triangular or square pitched lattices) of fuel rods surrounded by a blanket region and water Various arrays (triangular or square pitched lattices) of Al tubed or bare fuel elements (hexagonal graphite blocks containing uranium Complex arrays of cans in rectangular geometry Cylindrical assembly of alternating U and C discs (53.34-cm diameter) Arrays of cans containing uranyl nitrate solution in rectangular geometry dicarbide beads) surrounded by water Shape Rectangular, hexagonal Cylinder Cylinder Cylinder Cylinder Neutron AENCFb 0.057 to 0.0094 to 0.1045 to 0.3423 to 0.0344 to Energy 0.095 MeV 0.0244 MeV 0.8015 MeV 0.3864 MeV 0.0599 MeV EALFb Not available 0.054 to Not available Not available Not available 0.145 eV Neutron Energy Spectraa Not available T: 15.2 to 49.4% I: 22.5 to 35.2% F: 28.1 to 50.6% Not available Not available Not available Fission Rate vs. Not available T: 85.6 to 95.8% Not available Not available Not available Neutron Energya I: 3.6 to 12.8% F: 0.5 to 1.6% Source: BSC 2002 and NEA 2001, Spectra; BSC 2003b, Section 5.1.1; and Putman 2003 for SB cases NOTES: aSpectral range defined as follows: thermal (T) [0 to 1 eV], intermediate (I) [1eV to 100 keV], fast (F) [100 keV to 20 MeV]. b AENCF = average energy of a neutron causing fission, EALF = energy of average lethargy causing fission. CAL-DS0-NU-000003 REV 00A X-6 September2004 Criticality Model Table X-5. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with Homogeneous Moderated Configurations of Fort St. Vrain SNF (Set 1) Experiment Experiment Experiment Experiment Experiment U-233-SOL- U-233-SOL- U-233-SOL- U-233-SOL- U-233-SOL- Category/ THERM-001 THERM-002 THERM-003 THERM-004 THERM-005 Description Parameter (5 cases) (17 cases) (10 cases) (8 cases) (2 cases) Materials/ Fissionable Uranium Uranium Uranium Uranium Uranium Fissionable Element Material Physical Form Uranyl nitrate Uranyl nitrate Uranyl fluoride Uranyl nitrate Uranyl nitrate Isotopic Composition 97.7 wt. % 233U 98.7 wt. % 233U 98.7 wt. % 233U 98.7 wt. % 233U 98.7 wt. % 233U Atomic 233U: 4.33e-05 233U: 8.71e-05 233U: 8.56e-05 233U: 4.15e-04 233U: 1.27e-04 and Density (atoms/b-cm) to 5.00e-05 to 9.84e-04 to 1.55e-03 to 9.84e-04 1.60e-04 Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Element H H H H H Moderator Physical Form Solution Solution Solution Solution Solution Atomic 6.63e-02 to 5.62e-02 to 6.05e-02 to 5.62e-02 to 6.50e-02 and Density 6.64e-02 6.56e-02 6.57e-02 6.22e-02 6.54e-02 (atoms/b-cm) Ratio to 1324 to 1533 57.1 to 752.6 39.4 to 775 57.1 to 149.2 405 and 514 Fissile Material Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Material/ Unreflected Reflected by Reflected by Reflected by Reflected by water Reflector Physical Form paraffin paraffin paraffin Materials/ Element B None None None None Neutron Absorber Physical Form Solution N/A N/A N/A N/A Atomic Density (atoms/b-cm) B10: 2.65e-0 to 1.01e-6 N/A N/A N/A N/A Geometry Heterogeneity Solution contained in an Solution contained in an Solution contained in Solution contained in 2 configurations: first has solution Al sphere Al sphere single Al cylindrical vessel single Al cylindrical vessel contained in a spherical Al vessel; second has solution contained in single Al cylindrical vessel Shape Sphere Sphere Cylindrical Cylindrical Cylindrical, spherical Neutron AENCFb 0.0038 to 0.0056 to 0.0056 to 0.0208 to 0.0078 to Energy 0.0043 MeV 0.0490 MeV 0.0693 MeV 0.0493 MeV 0.0094 MeV EALFb 0.0392 to 0.0464 to 0.046 to 0.133 to Not available 0.0417 eV 0.471 eV 1.03 eV 0.486 eV Neutron T: 48.9 to 52.5% T: 7.7 to 42.2% T: 5.2 to 42.6% T: 7.8 to 17.2% Not available Energy Spectraa I: 21.0 to 22.6% F: 26.5 to 28.5% I: 24.8 to 33.9% F: 33.0 to 58.3% l: 24.6 to 34.2% F: 32.7 to 60.6% I: 32.4 to 34.0% F: 50.4 to 58.3% Fission Rate vs. Neutron Energya T: 94.0 to 94.8% I: 5.0 to 5.8% F: 0.2% T: 63.7 to 92.5% I: 7.1 to 33.5% F: 0.3 to 2.8% T: 54.5 to 92.7% I: 7.0 to 41.5% F: 0.3 to 4.0% T: 63.8 to 79.5% I: 19.3 to 33.4% F: 1.2 to 2.8% Not available Source: BSC 2002 and NEA 2001, Spectra a NOTES: Spectral range defined as follows: thermal (T) [0 to 1 eV, intermediate (I) [1eV to 100 keV], fast (F) [100 keV to 20 MeV]. b AENCF = average energy of a neutron causing fission, EALF = energy of average lethargy causing fission. CAL-DS0-NU-000003 REV 00A X-7 September2004 Criticality Model Table X-6. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with Homogeneous Moderated Configurations of Fort St. Vrain SNF (Set 2) Experiment Experiment Experiment Experiment Experiment U-233-SOL- U-233-SOL- HEU-COMP- HEU-COMP- HEU-MET- Category/ THERM-008 THERM-006 THERM-002 MIXED-001 INTER-006 Description Parameter (1 case) (6 cases) (25 cases) (26 cases) (2 cases) Materials/ Fissionable Uranium Uranium Uranium Uranium Uranium Fissionable Element Material Physical Form Uranyl nitrate Uranyl nitrate Uranium dicarbide UO2 U metal discs Isotopic Composition 97.67 wt. % 233U 97.56 or 97.54 wt. % 233U 93.15 wt. % 235U 93.15 wt. % 235U 93.2 wt. % 235U (Average) Atomic Density (atoms/b-cm) 233U: 3.34e-05 233U:5.14e-04 to 8.64e-04 235U: 9.98e-04 to 1.13e-03 235U: 4.48e-03 to 1.39e-02 235U: 4.48e-02 to 1.15e-02 Temperature Room Temp. Room Temp. Room Temp Room Temp. Room Temp. Materials/ Element H H H,C H C Moderator Physical Form Solution Water in C: Carbide Water, Graphite aqueous solution of uranyl nitrate H: Water Alcohol-water solution, Plexiglas Atomic Density (atoms/b-cm) 6.64e-02 5.89e-02 to 6.15e-02 C:8.98e-2 to 9.8e-2 H: 6.67e-2 Fuel Region: 2.16e-2 ; 5.68e-2 8.54e-2 to 8.58e-2 (Plexiglas) 6.24e-2 (alcohol-water) Ratio to Fissile 1985 H/X=69 to 121 C/X: 87 to 88.9 H/X=0 to 49 C discs Material C/X=52 Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Reflector Material/ Physical Form Unreflected Unreflected Reflected by water Reflected by polyethylene Reflected by Cu Materials/ Element None None None None None Neutron Absorber Physical Form N/A N/A N/A N/A N/A Atomic Density (atoms/b-cm) N/A N/A N/A N/A N/A Geometry Heterogeneity Solution contained in an Al sphere Complex arrays of cans containing uranyl nitrate solution in rectangular geometry Various arrays (triangular or square pitched lattices) of Al tubed or bare fuel elements surrounded by Complex arrays of cans in rectangular geometry Cylindrical assembly of alternating U and C discs (53.34 cm diameter) water Shape Sphere Cylinder Cylinder Cylinder Cylinder Neutron AENCFb 0.0030 MeV 0.0344 to 0.0094 to 0.0244 0.1045 to 0.3423 to Energy 0.0599 MeV 0.8015 MeV 0.3864 MeV EALFb 0.037 eV Not available 0.054 to Not available Not available 0.145 eV Neutron Energy Spectraa T: 57.0% I: 19.3% Not available T: 15.2 to 49.4% I: 22.5 to 35.2% Not available Not available F: 23.7% F: 28.1 to 50.6% Fission Rate T: 95.5% Not available T: 85.6 to 95.8% Not available Not available vs. Neutron I: 4.3% I: 3.6 to 12.8% Energya F: 0.2% F: 0.5 to 1.6% Source: BSC 2002 and NEA 2001, Spectra NOTES: aSpectral range defined as follows: thermal (T) [0 to 1 eV], intermediate (I) [1eV to 100 keV], fast (F) [100 keV to 20 MeV]. b AENCF = average energy of a neutron causing fission, EALF = energy of average lethargy causing fission. CAL-DS0-NU-000003 REV 00A X-8 September2004 Criticality Model X.3 CALCULATION OF THE LOWER-BOUND TOLERANCE LIMIT The following results are excerpted from Analysis of Critical Benchmark Experiments and Critical Limit Calculation for DOE SNF (BSC 2003b), which present in detail the methodology and calculations performed for evaluating the LBTL for each set of configurations of the waste package containing Fort St. Vrain SNF. The calculated keff values for the critical benchmarks are taken from Analysis of Critical Benchmark Experiments and Critical Limit Calculation for DOE SNF (BSC 2003b, Attachment II). The results of the trending parameter analysis for the critical benchmark subsets representative for moderated intact (heterogeneous) configurations of the waste package containing Fort St. Vrain SNF are presented in Table X-7. The parameters in the following tables describe the regression statistics for the linear trend evaluations (see Attachment III for definitions). The P-value parameter gives a direct estimation of the probability of having a linear trending due to chance only. Table X-7. Trending Parameter Results for the Critical Benchmark Subset Representative for Moderated Intact (Heterogeneous) Configurations of the Waste Package Containing FSVR SNF Trend Parameter n Intercept Slope r2 T t0.025,n-2 P-Value Goodness-of-Fit Tests Valid Trend AENCFa 73 1.0099 -0.0226 0.35 -6.1832 1.960 3.55E-08 Passed Yes H/X 71 0.9982 1.19E-04 0.2537 4.8430 1.960 7.6E-06 Passed Yes Source: BSC 2003b, p. 48 NOTE: a AENCF = average energy of a neutron causing fission. Figure X-2 presents the keff values and the calculated lower-bound tolerance limit. Details for the calculation of the lower-bound tolerance limit function are provided in Analysis of Critical Benchmark Experiments and Critical Limit Calculation for DOE SNF (BSC 2003b, Attachment I) with the results as follows: Lower-bound tolerance limit = 0.9575 for 0 MeV < AENCF < 0.386 MeV Lower-bound tolerance limit = -0.0226 × AENCF + 0.9674 for 0.386 MeV < AENCF < 0.8015 MeV CAL-DS0-NU-000003 REV 00A X-9 September2004 Criticality Model klit 0.94 0.95 0.96 0.97 0.98 0.99 1.00 1.01 1.02 1.03 eff Lower Bound Toerance Lim 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 AENCF (MeV) Figure X-2. Lower-Bound Tolerance Limit Applicable for Fort St. Vrain SNF for Intact (Heterogeneous) Moderated Configurations The results of the trending parameter analysis for the critical benchmark subset representative for moderated degraded (homogeneous) configurations of the waste package containing Fort St. Vrain SNF are presented in Table X-8. Table X-8. Trending Parameter Results for the Critical Benchmark Subset Representative for Moderated Degraded Configurations of the Waste Packages Containing Fort St. Vrain SNF Trend Parameter n Intercept Slope r2 T t0.025,n-2 P-Value Goodness-of-Fit Tests Valid Trend AENCF a 108 1.0079 -0.0183 0.2098 -5.3049 1.960 6.22E-07 Passed Yes H/X 103 1.0064 -4.14E-06 0.0245 -1.5911 1.960 0.1147 Failed No Source: BSC 2003b, p. 50 NOTE: a AENCF = average energy of a neutron causing fission. Figure X-3 presents the keff values and the calculated LBTL. Details for the calculation of the LBTL function are provided in Analysis of Critical Benchmark Experiments and Critical Limit Calculation for DOE SNF (BSC 2003b, Attachment I) with the results as follows: Lower-bound tolerance limit = 0.9608 for 0 MeV < AENCF < 0.4625 MeV Lower-bound tolerance limit = -0.0183 × AENCF + 0.9687 for 0.4625 MeV < AENCF < 0.8015 MeV CAL-DS0-NU-000003 REV 00A X-10 September2004 Criticality Model () klit 0.95 0.96 0.97 0.98 0.99 1.00 1.01 1.02 1.03 1.04 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 AENCFMeVeff Lower Bound Toerance Lim NOTE: AENCF = average energy of a neutron causing fission. Figure X-3. Lower-Bound Tolerance Limit Applicable for Fort St. Vrain SNF for Degraded (Homogeneous) Moderated Configurations Table X-9 presents a summary of the results of the analyses performed on the subsets of critical benchmark experiments applicable to the waste package containing Fort St. Vrain SNF and the calculated LBTL values or functions. Table X-9. Lower-Bound Tolerance Limits For Benchmark Subsets Representative For Configurations of Waste Packages Containing Fort St. Vrain SNF Trend Test for Applied Calculational Subset Parameter Normality Method Lower-Bound Tolerance Limit Intact (Heterogeneous) AENCF a N/A LUTB a 0.9575 for 0 < AENCF < 0.386 Moderated -0.0226 × AENCF + 0.9674 for 0.386 MeV < AENCF < 0.8015 MeV Degraded (Homogeneous) Moderated AENCF a N/A LUTB a 0.9608 for 0 < AENCF < 0.4625 -0.0183 × AENCF + 0.9687 for 0.4625 MeV < AENCF < 0.8015 MeV Source: BSC 2003b, p. 52 NOTE: a AENCF = average energy of a neutron causing fission, LUTB = lower uniform tolerance band, N/A = not applicable. CAL-DS0-NU-000003 REV 00A X-11 September2004 Criticality Model INTENTIONALLY LEFT BLANK CAL-DS0-NU-000003 REV 00A X-12 September2004 Criticality Model ATTACHMENT XI LBTL CALCULATION AND ROA DETERMINATION FOR SHIPPINGPORT PWR CAL-DS0-NU-000003 REV 00A September 2004 Criticality Model CAL-DS0-NU-000003 REV 00A September 2004 Criticality Model ATTACHMENT XI LBTL CALCULATION AND ROA DETERMINATION FOR SHIPPINGPORT PWR XI.1 INTRODUCTION This attachment presents the calculations of the LBTL and the determination of ROA for benchmarks that could potentially be applicable to waste package configurations containing Shippingport PWR SNF. A listing of corroborating and supporting data, models, or information used for the calculation is provided in Table XI-1. Table XI-1. Supporting Information and Sources Description Source Guidance for benchmarking a calculational method Dean and Tayloe 2001 Criticality benchmark experiments, trending parameters, and BSC 2002; BSC 2003b, NEA 2001 CL calculations Shippingport PWR summary report CRWMS M&O 2000a NOTE: CL = critical limit, PWR = pressurized water reactor. The Shippingport PWR SNF is the representative fuel for the highly enriched uranium oxide (HEU) SNF group. This group is one of nine representative fuel groups designated by the National Spent Nuclear Fuel Program for disposal criticality analyses based on the fuel matrix composition, primary fissile isotope and enrichment (DOE 2002, Sections 5.2 and 5.3). The following information regarding Shippingport PWR SNF is collected from Evaluation of Codisposal Viability for HEU Oxide (Shippingport PWR) DOE-Owned Fuel (CRWMS M&O 2000a, Section 2.1.4). The Shippingport PWR was a “seed and blanket” reactor that underwent multiple modifications to provide higher thermal outputs. The blankets will be shipped and handled as individual fuel assemblies. The low enrichments of the blankets (less than one percent) allow the use of the same packaging associated with either PWR or BWR commercial fuels. Therefore, this analysis does not address the disposal of blanket assemblies in the repository. The waste package that holds the DOE SNF canister with Shippingport PWR fuel also contains five HLW glass pour canisters and a carbon steel basket. The DOE SNF canister is placed in a support tube that becomes the center of the waste package, as shown in Figure XI-1. The five HLW canisters are evenly spaced around the DOE SNF canister. The DOE SNF canister is designed to hold one Shippingport PWR fuel assembly. The basket structure of the DOE SNF canister comprises a stainless-steel rectangular grid that is a 208-mm square. An isometric of the DOE SNF canister containing one Shippingport PWR fuel assembly is shown in Figure XI-2. CAL-DS0-NU-000003 REV 00A XI-1 September2004 Criticality Model Figure XI-1. 5-HLW/DOE SNF Waste Package with Shippingport PWR Fuel Assembly ily iing Rods Base Plate DOE Standardized SNF Canister Shppingport PWR Basket AssembSpacer Plate Spacer Spacer Lft Figure XI-2. Isometric View of the Shippingport PWR SNF Canister Two seeds, Seed 1 and Seed 2, which had identical geometrical dimensions but different 235U enrichment and chemical composition, were designed for Shippingport PWR Core 2 operation. The assembly is composed of Zircaloy-4 and consists of four subassemblies and a cruciform-shaped channel in the center to accommodate a control rod. Figure XI-3 shows the CAL-DS0-NU-000003 REV 00A XI-2 September2004 Criticality Model cross section of a single subassembly. Each subassembly is composed of 19 fuel plates and 20 channels. Each plate is formed by sandwiching an enriched U-Zr alloy strip between two Zircaloy-4 cover plates and four side strips. There are five types of fuel plates located in the assembly. As shown in Table XI-2, the three assembly regions (i.e., Zones 1, 2, and 3) have different fissile loadings. Outer Zone 3 Middle Zone 2 Inner Zone 1 Water Channels Zircaloy Figure XI-3. Shippingport PWR Core 2 Seed 2 SNF Subassembly Cross Section Table XI-2. Geometry and Material Specifications for the Shippingport PWR Core 2 Seed 2 Assembly Component Material Characteristic Value Assembly Total mass (kg) 357 Length (cm) 265.43 Transverse dimensions 18.7325 (cm) Fuel plate Active fuel length (cm) 246.38 Fuel wafer UO2-ZrO2-CaO Length (cm) 2.07264 93.2% 235U beginning Width (cm) 0.64008 of life (BOL) enrichment Thickness (cm) 0.09144 Fuel Zone 1 UO2-ZrO2-CaO Weight (wt) % UO2 54.9 wt. % CaO 5.2 wt. % ZrO2 39.9 Fissile loading (kg) 7.076 Fuel Zone 2 UO2-ZrO2-CaO wt. % UO2 40.2 wt. % CaO 5.8 wt. % ZrO2 54 Fissile loading (kg) 8.987 CAL-DS0-NU-000003 REV 00A XI-3 September2004 Criticality Model Table XI-2. Geometry and Material Specifications for the Shippingport PWR Core 2 Seed 2 Assembly (Continued) Component Material Characteristic Value Fuel Zone 3 UO2-ZrO2-CaO wt. % UO2 26.5 wt. % CaO 6.4 wt. % ZrO2 67.1 Fissile loading (kg) 3.437 Borated stainless steel Stainless Steel Type 304 Mass (g) 6,001 B-10 Mass (g) 26 B-11 Mass (g) 114 Spacer rings Inconel X Mass (g) 546 Chrome plating Cr Mass (g) 325 Cladding Zircaloy-4 Thickness (cm) 0.05207 Source: CRWMS M&O 2000a, Section 2.1.4 XI.2 SELECTION OF THE CRITICALITY BENCHMARK EXPERIMENTS The critical experiments selected for inclusion in benchmarking must be representative of the types of materials, conditions, and parameters to be represented using the calculational method. A sufficient number of experiments with varying experimental parameters should be selected for inclusion in the benchmarking to ensure as wide an area of applicability as feasible and statistically significant results. While there is no absolute guideline for the minimum number of critical experiments necessary to benchmark a computational method, the use of only a few (i.e., less than 10) experiments should be accompanied by a suitable technical basis supporting the rationale for acceptability of the results (Dean and Tayloe 2001, p. 5). For the present application (codisposal of Shippingport PWR SNF), only benchmark experiments including moderated heterogeneous experiments (BSC 2002, Section 6.1.1) have been selected. The benchmark experiments are from International Handbook of Evaluated Criticality Safety Benchmark Experiments (NEA 2001), unless otherwise noted. The selection process was initially based on prior knowledge regarding the possible degraded configurations of the waste package (CRWMS M&O 2000a), and the subset has been constructed to accommodate large variations in the range of parameters of the configurations and to provide adequate statistics for LBTL calculations. The selected benchmark are presented in Benchmark and Critical Limit Calculation for DOE SNF (BSC 2002) with MCNP cases constructed and calculation results. The cases, keff results, and their uncertainties are also summarized in Analysis of Critical Benchmark Experiments and Critical Limit Calculation for DOE SNF (BSC 2003b, Attachment II). Table XI-3 presents the list of the benchmark experiments and the number of cases selected for Shippingport PWR SNF. CAL-DS0-NU-000003 REV 00A XI-4 September2004 Criticality Model Table XI-3. Critical Benchmarks Selected for Shippingport PWR SNF Subset Benchmark Experiment Identificationa No. of Cases Included Heterogeneous Moderatedb HEU-MET-THERM-006 23 HEU-COMP-THERM-003 15 HEU-COMP-THERM-005 1 HEU-COMP-THERM-006 3 HEU-COMP-THERM-007 3 HEU-COMP-THERM-008 2 HEU-COMP-THERM-010 21 HEU-COMP-THERM-011 3 HEU-COMP-THERM-012 2 HEU-COMP-THERM-013 2 HEU-COMP-THERM-014 2 Source: Subsets defined in BSC 2002 NOTES: a The convention for naming the benchmark experiments is from NEA (2001). bdentification of each subset from BSC 2002 has been changed to better reflect the subset’s main characteristics. The benchmark experiments in each subset have not been affected. The experiments cover configuration classes IP-1a, IP-1b, IP-3a, IP-3b, and IP-3c for the degraded waste package containing Shippingport PWR SNF as described in Section 7. XI.2.1 Range of Applicability of Selected Critical Benchmark Experiments This section summarizes in a set of tables (Tables XI-4 through XI-6) the range of applicability of the experiments listed in Table XI-3. The information is partly excerpted from Benchmark and Critical Limit Calculation for DOE SNF (BSC 2002, Section 6.2), which presents a less comprehensive set of parameters. The tables have been enhanced by adding information regarding the spectral characteristics of the experiments (available for the majority of the benchmarks in NEA [2001]). The purpose is to construct a collective area of applicability that will be used to directly compare with the range of parameters of the codisposal configurations. Table XI-4. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with Heterogeneous Moderated Configurations of Shippingport PWR SNF (Set 1) Category/ Description Parameter Experiment HEU-MET- THERM-006 (23 cases) Experiment HEU-COMP- THERM-003 (15 cases) Experiment HEU-COMP- THERM-005 (1 case) Experiment HEU-COMP- THERM-006 (3 cases) Materials/ Fissionable Fissionable Element Uranium Uranium Uranium Uranium Material Physical Form U-Al alloy (fuel plates) UO2 + Cu UO2 + Cu UO2 + Cu Isotopic Composition 93.17 wt. % 235U 79.66 wt. % 235U 79.66 wt. % 235U 79.66 wt. % 235U Atomic Density (atoms/b-cm) 235U: 1.85E-03 238U: 1.13E-04 For solution (cases 19 to 23): 235U: 1.02E-05 238U: 6.98E-07 235U: 3.63e-03 238U: 8.72e-04 235U: 4.42e-03 238U: 1.06 e-03 235U: 4.42e-03 238U: 1.06 e-03 Temperature Room Temp. Room Temp. Room Temp. Room Temp. CAL-DS0-NU-000003 REV 00A XI-5 September2004 Criticality Model Table XI-4. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with Heterogeneous Moderated Configurations of Shippingport PWR SNF (Set 1) (Continued) Experiment Experiment Experiment Experiment HEU-MET-HEU-COMP- HEU-COMP- HEU-COMP- Category/ THERM-006 THERM-003 THERM-005 THERM-006 Description Parameter (23 cases) (15 cases) (1 case) (3 cases) Materials/ Element Hydrogen H Hydrogen Hydrogen Moderator Physical Form Water Water Water Water Atomic 6.67e-02 6.67e-02 6.67e-02 6.67e-02 Density For solution: (atoms/b-cm) 6.62e-02 to 6.64e-02 Ratio to fissile 134 to 500 51 to 349 23 30 to 716 Material (In Region Containing Fissile Material) Temperature Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Material/ Reflected by water or Reflected by water Reflected by water Reflected by water Reflector Physical Form dilute aqueous uranyl and stainless steel and stainless steel and stainless steel nitrate solutions Materials/ Element B (few cases) None None None Neutron Absorber Physical Form In solution N/A N/A N/A Atomic B-10: 4.27E-06 to N/A N/A N/A Density 9.57E-06 (only in (atoms/b-cm) 4 cases) Geometry Heterogeneity Rectangular arrays of fuel elements with various spacing Cylindrical two zones hexagonally pitched lattice of cross-shaped fuel rods Hexagonally pitched array of fuel rod clusters (each containing a hexagonally pitched lattice of Cylindrical hexagonally pitched lattice of cross-shaped fuel rods cross-shaped fuel rods) Shape Slab (fuel plates) Cylinder Cylinder Cylinder Neutron AENCF 0.0100 to 0.0150 MeV 0.0139 to 0.076 MeV 0.0104 to Energy 0.0467 MeV 0.0720 MeV EALF 0.05 to 0.09 eV 0.06 to 0.40 eV 1.46 eV 0.05 to 1.12 eV Neutron T: 18.5 to 33.3% T: 9.9 to 37.7% T: 6.5% T: 4.9 to 47% Energy Spectraa I: 25.3 to 36.5% F: 41.1 to 45% I: 27.4 to 37% F: 35.9 to 53.1% I: 38.4% F: 55.1% I: 23.2 to 37.7% F: 29.8-57.4% Fission Rate T: 89.9 to 95% Handbook T: 61.3% T: 64.1 to 96.1% vs. Neutron I: 4.4 to 9.2% T: 75.3 to 94.1% I: 33.8% I: 3.4 to 31.5% Energya F: 0.5 to 0.9% I: 5.2 to 21.9% F: 4.9% F: 0.5 to 4.4% F: 0.7 to 2.8% Source: BSC 2002 and NEA 2001, Spectra a NOTES: Spectral range defined as follows: thermal (T) [0 to 1 eV], intermediate (I) [1eV to 100 keV], fast (F) [100 keV to 20 MeV]. CAL-DS0-NU-000003 REV 00A XI-6 September2004 Criticality Model Table XI-5. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with Heterogeneous Moderated Configurations of Shippingport PWR SNF (Set 2) Experiment Experiment Experiment Experiment HEU-COMP- HEU-COMP- HEU-COMP- HEU-COMP- Category/ THERM-007 THERM-008 THERM-010 THERM-011 Description Parameter (3 cases) (2 cases) (21 cases) (3 cases) Materials/ Fissionable Uranium Uranium Uranium Uranium Fissionable Element Material Physical Form UO2 + Cu UO2 + Cu UO2 + BeO UO2 + Al alloy Isotopic Composition 79.66 wt. % 235U 79.66 wt. % 235U 62.4 wt.% wt. % 235U 80 wt. % 235U Atomic Density (atoms/b-cm) 235U: 3.63e-03 238U: 8.72e-04 235U: 4.42e-03 238U: 1.06 e-03 235U: 3.83E-03 238U: 2.24E-03 For solution 235U: 2.66e-03 238U: 6.47e-03 (cases 20-21): 235U: 9.43E-06 238U: 7.44E-07 Temperature Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Element Hydrogen Hydrogen Hydrogen Hydrogen Moderator Physical Form Water; ZrH rods Water Water Water Atomic Density 6.67e-02 (H2O) 6.67e-02 6.67e-02 6.68e-02 (atoms/b-cm) 5.34e-02 (ZrH) For solution: 6.65e-02 to 6.68e-02 Ratio to Fissile 60 to 91 25 36 to 302 170 Material (In Region Containing Fissile Material) Temperature Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Reflector Material/ Physical Form Reflected by water and stainless steel Reflected by water and stainless steel Reflected by water Reflected by water Materials/ Element None Boron B as Boric Acid None Neutron (few cases) Absorber Physical Form N/A B4C rods In solution N/A Atomic Density (atoms/b-cm) N/A B10: 3.92e-03 to 1.12e-03 B-10: 4.32E-07-3.49E-06 N/A Geometry Heterogeneity Cylindrical hexagonally pitched double lattice of cross-shaped fuel rods and ZrH rods Cylindrical hexagonally double lattice of fuel rods and B4C rod Square or cylindrical assemblies with square or hexagonal pitched lattices Square clusters of cylindrical fuel rods arranged in square geometry Shape Cylinder Cylinder Cylinder Cylinder Neutron AENCF 0.034 to 0.088 to 0.092 MeV 0.023 to 0.080 MeV 0.047 to Energy 0.048 MeV 0.053 MeV EALF 0.257 to 0.445 eV 2.50 to 2.90 eV 0.080 to 0.880 eV 0.430 to 0.720 eV Neutron Energy Spectraa T: 8.0 to 11.9% I: 36.9 to 38.0% F: 51.2 to 54.0% T: 2.5 to 3.0% I: 38.9 to 39.1% F: 57.9 to 58.6% T: 6.1 to 28.2% I: 25.4 to 36.7% F: 46.4 to 57.2% T: 6.6 to 10.0% I: 37.6 to 40.1% F: 52.4 to 53.5% Fission Rate vs. T: 73.8 to 80.9% T: 53.6 to 55.2% T: 67.7 to 92.5% T: 68.4 to 74.2% Neutron I: 17.1 to 23.3% I: 39.2 to 40.6% I: 6.3 to 27.8% I: 22.8 to 28.2% Energya F: 2 to 2.9% F: 5.6 to 5.8% F: 1.2 to 4.5% F: 3.0 to 3.4% Source: BSC 2002 and NEA 2001, Spectra NOTE: a Spectral range defined as follows: thermal (T) [0 to 1 eV], intermediate (I) [1eV to 100 keV], fast (F) [100 keV to 20 MeV]. CAL-DS0-NU-000003 REV 00A XI-7 September2004 Criticality Model Table XI-6. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with Heterogeneous Moderated Configurations of Shippingport PWR SNF (Set 3) Experiment HEU-COMP- Experiment HEU-COMP- Experiment HEU-COMP- Category/ THERM-012 THERM-013 THERM-014 Description Parameter (2 cases) (2 cases) (2 cases) Materials/ Fissionable Material Fissionable Element Uranium Uranium Uranium Physical Form UO2 + Al alloy UO2 + Al alloy UO2 + Al alloy Isotopic Composition 80 wt. % 235U 80 wt. % 235U 80 wt. % 235U Atomic Density (atoms/b-cm) 235U: 2.66e-03 238U: 6.47e-03 235U: 2.66e-03 238U: 6.47e-03 235U: 2.66e-03 238U: 6.47e-03 Temperature Room Temp. Room Temp. Room Temp. Materials/ Moderator Element Hydrogen Hydrogen Hydrogen Physical Form Water Water Water Atomic Density (atoms/b-cm) 6.68e-02 6.68e-02 6.68e-02 Ratio to Fissile Material 35 40 170 (In Region Containing Fissile Material) Temperature Room Temp. Room Temp. Room Temp. Materials/ Reflector Material/Physical Form Reflected by water Reflected by water Reflected by water Materials/ Neutron Absorber Element None None None Physical Form N/A N/A N/A Atomic Density (atoms/b-cm) N/A N/A N/A Geometry Heterogeneity Square clusters of cylindrical fuel rods arranged in Square clusters of cylindrical fuel rods arranged in Square clusters of cylindrical fuel rods arranged in square geometry square geometry square geometry Shape Cylinder Cylinder Cylinder Neutron AENCF 0.051 to 0.043 to 0.023 to Energy 0.055 MeV 0.048 MeV 0.026 MeV EALF 0.43 to 0.56 eV 0.32 to 0.45 eV 0.10 to 0.12 eV Neutron Energy Spectraa T: 7.3 to 9.4% T: 8.6 to 12.1% T: 17.0 to 20.6% I: 37.1 to 38.4% I: 36 to 37.9% I: 31.4 to 33.1% F: 53.5 to 54.3% F: 51.9 to 53.5% F: 48.0 to 49.9% Fission Rate vs. Neutron Energya T: 71.8 to 74.7% T: 73.7 to 77.6% T: 87.9 to 89.8% I: 22.2 to 24.8% I: 19.7 to 23.2% I: 8.9 to 10.6% F: 3.1 to 3.4% F: 2.7 to 3.1% F: 1.3 to 1.5% Source BSC 2002 and NEA 2001, Spectra NOTE: a Spectral range defined as follows: thermal (T) [0 to 1 eV], intermediate (I) [1eV to 100 keV], fast (F) [100 keV to 20 MeV]. XI.3 CALCULATION OF LOWER-BOUND TOLERANCE LIMIT The following results are excerpted from Analysis of Critical Benchmark Experiments and Critical Limit Calculation for DOE SNF (BSC 2003b) which present in detail the methodology and calculations performed for evaluating the LBTL for each set of configurations of the waste package containing Shippingport PWR SNF. The calculated keff values for the critical CAL-DS0-NU-000003 REV 00A XI-8 September2004 Criticality Model benchmarks are taken from Analysis of Critical Benchmark Experiments and Critical Limit Calculation for DOE SNF (BSC 2003b, Attachment II). The results of the trending parameter analysis for the critical benchmark subset representative for moderated intact (heterogeneous) configurations of the waste package containing Shippingport PWR SNF are presented in Table XI-7. The parameters in the following tables describe the regression statistics for the linear trend evaluations (see Attachment III for definitions). The P-value parameter gives a direct estimation of the probability of having a linear trending due to chance only. Table XI-7. Trending Parameter Results for the Critical Benchmark Subset Representative for Moderated Intact (Heterogeneous) Configurations of the Waste Package Containing Shippingport PWR SNF Trend Parameter n Intercept Slope r2 T t0.025,n-2 P-Value Goodness-of-Fit Tests Valid Trend AENCF 77 1.0064 -0.2336 0.3500 -6.3542 1.960 1.5E-8 Passed Yes keff Source: BSC 2003b, p. 26 Figure XI-4 presents the keff values and the calculated LBTL. Details for the calculation of the LBTL function are provided in Analysis of Critical Benchmark Experiments and Critical Limit Calculation for DOE SNF (BSC 2003b, Attachment I) with results as follows: Lower-bound tolerance limit = 0.969 for 0 MeV < AENCF < 0.0278 MeV Lower-bound tolerance limit = -0.2336 × AENCF + 0.9755 for 0.0278 MeV < AENCF < 0.0922 MeV 1.04 1.03 1.02 1.01 1.00 0.99 0.98 0.97 0.96 0.95 0.94 litLower Bound Toerance Lim 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 AENCF (MeV) NOTE: AENCF = average energy of a neutron causing fission. Figure XI-4. Lower-Bound Tolerance Limit Applicable for Shippingport PWR SNF for Intact (Heterogeneous) Moderated Configurations CAL-DS0-NU-000003 REV 00A XI-9 September2004 Criticality Model INTENTIONALLY LEFT BLANK CAL-DS0-NU-000003 REV 00A XI-10 September2004 Criticality Model ATTACHMENT XII LBTL CALCULATION AND ROA DETERMINATION FOR CONFIGURATIONS EXTERNAL TO THE WASTE PACKAGE CAL-DS0-NU-000003 REV 00A September 2004 Criticality Model CAL-DS0-NU-000003 REV 00A September 2004 Criticality Model ATTACHMENT XII LBTL CALCULATION AND ROA DETERMINATION FOR CONFIGURATIONS EXTERNAL TO THE WASTE PACKAGE XII.1 INTRODUCTION This attachment presents the calculations of the LBTL and the determination of ROA for benchmarks that could potentially be applicable to configurations external to the waste package. The calculations includes experiments applicable to highly enriched uranium (HEU), intermediate enriched uranium (IEU), low enriched uranium (LEU), mixture of uranium and plutonium, and 233U systems presented in Sections XII.2 through XII.6, respectively. A listing of corroborating and supporting data, models, or information used for the calculation is provided in Table XII-1. Table XII-1. Supporting Information and Sources Description Source Guidance for benchmarking a calculational method Dean and Tayloe 2001 Benchmark Experiments NEA 2003, BSC 2002 and Moscalu 2004 External accumulation of fissile material can occur in the near-field or the far-field. The near-field is defined as the invert, which is the part of the drift that is directly underneath the waste package. The invert is made up of crushed tuff with a high porosity. The far-field is defined as several meters of tuff underneath the drift, which has a distribution of fractures and lithophysae (cavities in rock). XII.2 HEU SYSTEMS Selection of the criticality benchmark experiments for HEU systems, determination of the range of applicability of the selected benchmarks, and the calculation of the LBTL are discussed in the following three sections. XII.2.1 Selection of the Criticality Benchmark Experiments The criticality experiments selected for inclusion in the benchmarking of the criticality computational method must be representative of the types of materials, conditions, and parameters to be represented. A sufficient number of experiments with varying experimental parameters should be selected for inclusion in the benchmarking to ensure as wide an area of applicability as feasible and statistically significant results. While there is no absolute guideline for the minimum number of critical experiments necessary to benchmark a computational method, the use of only a few (i.e., less than 10) experiments should be accompanied by a suitable technical basis supporting the rationale for acceptability of the results (Dean and Tayloe 2001, p. 5). For the present application (configurations with mixtures of IEU fissile material external to the waste package), the criticality benchmark experiments have been selected based on their fissile content, moderator and geometry. The benchmark experiments are from the International CAL-DS0-NU-000003 REV 00A XII-1 September 2004 Criticality Model Handbook of Evaluated Criticality Safety Benchmark Experiments (NEA 2003) unless otherwise noted. The set of criticality benchmark experiments has been constructed to accommodate large variations in the range of parameters of the configurations and also to provide adequate statistics for the LBTL calculations. The selected benchmark experiments containing a total of 187 individual cases are presented in Table XII-2 along with the results of the MCNP code calculations. All cases have been run using the isotopic libraries described in Table 2 (Section 4.2.2). Table XII-2. Critical Benchmarks Selected for Validation of the Criticality Model for External Configurations Containing Mixture Highly Enriched in 235U Experiment Case Name Benchmark Values Calculated Values (MCNP) keff sexp keff scalc AENCF Experiment hmm5_1 1.0007 0.0027 1.01308 0.00057 0.307 HEU-MET -MIXED-005 (5 cases) hmm5_2 1.0003 0.0028 1.0217 0.00055 0.247 hmm5_3 1.0012 0.0029 1.01904 0.00052 0.212 hmm5_4 1.0016 0.003 1.0145 0.0006 0.3175 hmm5_5 1.0005 0.004 1.00682 0.00052 0.377 Experiment hmt001 1.0010 0.0060 1.0097 0.0010 0.0215 HEU-MET-THERM-001 (1 case) Experiment hmt14 0.9939 0.0015 1.0125 0.0004 0.0233 HEU-MET-THERM-014 (1 case) Experiment hcm-1 1.0000 0.0059 1.0027 0.001 0.1045 HEU-COMP-MIXED-001 (26 cases) hcm-2 1.0012 0.0059 1.0059 0.0011 0.1053 hcm-5 0.9985 0.0056 0.9963 0.001 0.7833 hcm-6 0.9953 0.0056 0.9899 0.001 0.7962 hcm-7 0.9997 0.0038 0.9949 0.001 0.8015 hcm-8 0.9984 0.0052 0.9915 0.0011 0.6872 hcm-9 0.9983 0.0052 0.9931 0.0011 0.6536 hcm-10 0.9979 0.0052 0.9941 0.001 0.6494 hcm-11 0.9983 0.0052 0.9934 0.0011 0.6385 hcm-12 0.9972 0.0052 0.9960 0.0011 0.6358 hcm-13 1.0032 0.0053 0.9977 0.0011 0.6309 hcm-15 1.0083 0.005 0.9949 0.0011 0.4671 hcm-16 1.0001 0.0046 0.9926 0.0011 0.4692 hcm-17 0.9997 0.0046 1.0012 0.0011 0.4647 hcm-18 1.0075 0.0046 1.0000 0.001 0.4625 hcm-19 1.0039 0.0047 1.0000 0.0011 0.5191 hcm-20 1.006 0.0065 1.0051 0.0015 0.5357 hcm-21 1.0026 0.0064 1.0046 0.0016 0.5378 hcm-22 1.0013 0.0064 0.9995 0.0016 0.5371 hcm-23 0.9995 0.0053 1.0056 0.0015 0.535 hcm-24 1.002 0.0053 1.0003 0.0016 0.5352 hcm-25 0.9983 0.0053 0.9970 0.0014 0.5333 hcm-26 0.9998 0.0053 1.0001 0.0015 0.5283 hcm-27 0.9991 0.0053 0.9978 0.0016 0.5302 hcm-28 1.0037 0.0053 1.0033 0.0015 0.541 hcm-29 0.9992 0.0052 0.9998 0.0014 0.5401 CAL-DS0-NU-000003 REV 00A XII-2 September 2004 Criticality Model Table XII-2. Critical Benchmarks Selected for Validation of the Criticality Model for External Configurations Containing Mixture Highly Enriched in 235U (Continued) Experiment Case Name Benchmark Values Calculated Values (MCNP) keff sexp keff scalc AENCF Experiment hcm02_1 1.0000 0.0085 0.9866 0.0017 0.868 HEU-COMP-MIXED-002 (23 cases) hcm02_10 1.0000 0.0081 0.9856 0.0019 0.57 hcm02_11 1.0000 0.0088 0.9829 0.0019 0.568 hcm02_12 1.0000 0.0078 0.9900 0.0019 0.556 hcm02_13 1.0000 0.0083 0.9874 0.0017 0.559 hcm02_14 1.0000 0.0112 0.9880 0.0017 0.735 hcm02_15 1.0000 0.0111 0.9850 0.0017 0.73 hcm02_16 1.0000 0.0108 0.9861 0.0017 0.735 hcm02_17 1.0000 0.0112 0.9861 0.0016 0.732 hcm02_18 1.0000 0.0111 0.9902 0.0017 0.727 hcm02_19 1.0000 0.0107 0.9910 0.0017 0.712 hcm02_2 1.0000 0.0088 0.9907 0.0017 0.865 hcm02_20 1.0000 0.0108 0.9824 0.0018 0.735 hcm02_21 1.0000 0.0092 0.9843 0.0016 0.902 hcm02_22 1.0000 0.009 0.9879 0.0019 0.899 hcm02_23 1.0000 0.0093 0.9866 0.0016 0.896 hcm02_3 1.0000 0.0093 0.9914 0.0016 0.724 hcm02_4 1.0000 0.0087 0.9923 0.0017 0.716 hcm02_5 1.0000 0.0089 0.9933 0.0017 0.722 hcm02_6 1.0000 0.0093 0.9852 0.0018 0.574 hcm02_7 1.0000 0.0086 0.9813 0.0019 0.578 hcm02_8 1.0000 0.0068 0.9943 0.0018 0.537 hcm02_9 1.0000 0.0076 0.9913 0.0018 0.541 Experiment hest1-1 1.0000 0.0025 1.00241 0.00131 0.01582 HEU-SOL-THERM-001 (10 cases) hest1-2 1.0000 0.0025 0.99816 0.00209 0.03873 hest1-3 1.0000 0.0025 1.00453 0.00199 0.01546 hest1-4 1.0000 0.0025 1.0013 0.00203 0.0405 hest1-5 1.0000 0.0025 1.00361 0.00166 0.00651 hest1-6 1.0000 0.0025 1.01038 0.00187 0.00678 hest1-7 1.0000 0.0025 1.0023 0.00201 0.01501 hest1-8 1.0000 0.0025 1.00505 0.00213 0.0161 hest1-9 1.0000 0.0025 0.99973 0.00212 0.04099 hest110 1.0000 0.0025 0.99468 0.00178 0.00757 Experiment hest2-1 1.0000 0.002 1.00548 0.00148 0.01558 HEU-SOL-THERM-002 (14 cases) hest2-2 1.0000 0.002 1.00773 0.00235 0.01516 hest2-3 1.0000 0.002 1.00219 0.0022 0.0374 hest2-4 1.0000 0.002 1.00809 0.00242 0.03541 hest2-5 1.0000 0.002 1.01049 0.0023 0.01622 hest2-6 1.0000 0.002 1.00968 0.00215 0.01496 hest2-7 1.0000 0.002 1.00691 0.00224 0.03747 hest2-8 1.0000 0.002 1.01131 0.00206 0.03511 hest2-9 1.0000 0.002 1.00348 0.00209 0.00654 hest2-10 1.0000 0.002 1.00937 0.00202 0.00663 CAL-DS0-NU-000003 REV 00A XII-3 September 2004 Criticality Model Table XII-2. Critical Benchmarks Selected for Validation of the Criticality Model for External Configurations Containing Mixture Highly Enriched in 235U (Continued) Experiment Case Name Benchmark Values Calculated Values (MCNP) keff sexp keff scalc AENCF Experiment HEU-SOL-THERM-002 (14 cases) (continued) hest2-11 1.0000 0.002 1.00875 0.00211 0.01595 hest2-12 1.0000 0.002 1.0127 0.00209 0.01487 hest2-13 1.0000 0.002 0.99869 0.00232 0.03676 hest2-14 1.0000 0.002 1.01062 0.00238 0.03377 Experiment HEU-SOL-THERM-007 (17 cases) CASE_1 1.0000 0.0035 1.0164 0.0019 0.0071 CASE_2 1.0000 0.005 1.0178 0.0025 0.0361 CASE_3 1.0000 0.0035 1.0084 0.0019 0.0071 CASE_4 1.0000 0.0035 1.0144 0.0019 0.0357 CASE_5 1.0000 0.0035 1.0112 0.0019 0.0835 CASE_6 1.0000 0.0035 1.0045 0.0023 0.0376 CASE_7 1.0000 0.0035 1.0067 0.0019 0.0085 CASE_8 1.0000 0.0035 1.0026 0.0025 0.0390 CASE_9 1.0000 0.0035 1.0087 0.0021 0.0088 CASE_10 1.0000 0.0035 1.0144 0.0018 0.0087 CASE_11 1.0000 0.0035 1.0097 0.0020 0.0356 CASE_12 1.0000 0.0035 1.0091 0.0019 0.0088 CASE_13 1.0000 0.0035 1.0095 0.0023 0.0345 CASE_14 1.0000 0.0035 1.0097 0.0021 0.0363 CASE_15 1.0000 0.0035 1.0046 0.0021 0.0369 CASE_16 1.0000 0.0035 1.0043 0.0022 0.0368 CASE_17 1.0000 0.0035 1.0120 0.0023 0.0368 Experiment HEU-SOL-THERM-008 (5 cases evaluated) heust81 1.0000 0.003 1.00316 0.00134 0.00661 heust83 1.0000 0.003 0.9973 0.0019 0.00644 heust86 1.0000 0.003 1.00969 0.0023 0.03669 heust89 1.0000 0.003 1.00373 0.00116 0.0066 hest813 1.0000 0.003 1.00331 0.002 0.03616 Experiment HEU-SOL-THERM-009 (4 cases) heust9c1 1.0000 0.0057 1.0051 0.0006 0.058 heust9c2 1.0000 0.0057 1.0045 0.0006 0.045 heust9c3 1.0000 0.0057 1.0047 0.0007 0.029 heust9c4 1.0000 0.0057 0.9994 0.0007 0.018 Experiment HEU-SOL-THERM-033 (26 cases) hst33d_02a 1.0000 0.0111 1.00007 0.00128 0.036 hst33d_02b 1.0000 0.0108 0.99792 0.00113 0.036 hst33d_02c 1.0000 0.0065 0.99796 0.00119 0.036 hst33d_03a 1.0000 0.0114 1.00634 0.00108 0.033 hst33d_03b 1.0000 0.0111 1.00608 0.00115 0.034 hst33d_03c 1.0000 0.007 1.01079 0.00118 0.032 hst33d_04a 1.0000 0.0114 1.0057 0.00109 0.035 hst33d_04b 1.0000 0.0111 1.0116 0.00117 0.035 hst33d_05a 1.0000 0.0111 1.01126 0.00114 0.035 hst33d_05b 1.0000 0.0108 1.00608 0.00128 0.035 hst33d_06a 1.0000 0.0111 1.00936 0.00112 0.035 hst33d_06b 1.0000 0.0108 1.00915 0.00114 0.034 hst33d_07a 1.0000 0.0111 1.00453 0.00107 0.035 hst33d_07b 1.0000 0.0108 1.00406 0.00109 0.035 CAL-DS0-NU-000003 REV 00A XII-4 September 2004 Criticality Model Table XII-2. Critical Benchmarks Selected for Validation of the Criticality Model for External Configurations Containing Mixture Highly Enriched in 235U (Continued) Experiment Case Name Benchmark Values Calculated Values (MCNP) keff sexp keff scalc AENCF Experiment hst33d_08a 1.0000 0.0111 1.00558 0.00113 0.034 HEU-SOL-THERM-033 (26 cases) (continued) hst33d_08b 1.0000 0.0108 1.00213 0.00111 0.035 hst33d_09a 1.0000 0.0111 1.00228 0.00115 0.036 hst33d_09b 1.0000 0.0108 0.99359 0.00113 0.035 hst33d_09c 1.0000 0.0104 0.99619 0.00116 0.036 hst33d_10a 1.0000 0.0114 1.00267 0.00113 0.034 hst33d_10c 1.0000 0.007 1.00333 0.00103 0.032 hst33d_10d 1.0000 0.0104 0.99286 0.00111 0.033 hst33d_11a 1.0000 0.0111 1.00669 0.0011 0.035 hst33d_11b 1.0000 0.0108 1.00176 0.00097 0.034 hst33d_12a 1.0000 0.0111 1.00386 0.00112 0.036 hst33d_12b 1.0000 0.0108 1.00165 0.00107 0.035 Experiment CASE_1 1.0000 0.0025 0.9995 0.0004 0.0437 HEU-SOL-THERM-038 (28 cases evaluated) CASE_2 1.0000 0.0025 0.9989 0.0004 0.0405 CASE_3 1.0000 0.0025 1.0022 0.0004 0.0421 CASE_4 1.0000 0.0025 1.0007 0.0004 0.0438 CASE_5 1.0000 0.0025 1.0011 0.0004 0.0434 CASE_6 1.0000 0.0025 0.9985 0.0004 0.0405 CASE_7 1.0000 0.0032 1.0013 0.0004 0.0420 CASE_8 1.0000 0.0026 1.0016 0.0004 0.0416 CASE_9 1.0000 0.0033 1.0009 0.0004 0.0412 CASE_10 1.0000 0.0026 1.0007 0.0004 0.0425 CASE_11 1.0000 0.0025 1.0017 0.0004 0.0434 CASE_12 1.0000 0.0025 1.0006 0.0004 0.0434 CASE_13 1.0000 0.0050 1.0066 0.0004 0.0440 CASE_14 1.0000 0.0050 1.0060 0.0004 0.0443 CASE_15 1.0000 0.0050 1.0065 0.0004 0.0442 CASE_16 1.0000 0.0050 1.0065 0.0004 0.0442 CASE_17 1.0000 0.0026 1.0013 0.0004 0.0432 CASE_18 1.0000 0.0032 1.0017 0.0004 0.0431 CASE_19 1.0000 0.0032 1.0011 0.0004 0.0430 CASE_20 1.0000 0.0032 1.0021 0.0004 0.0430 CASE_21 1.0000 0.0025 0.9994 0.0004 0.0412 CASE_22 1.0000 0.0027 0.9998 0.0004 0.0407 CASE_23 1.0000 0.0027 0.9997 0.0004 0.0408 CASE_24 1.0000 0.0026 1.0027 0.0004 0.0438 CASE_25 1.0000 0.0032 1.0025 0.0004 0.0429 CASE_26 1.0000 0.0032 1.0018 0.0004 0.0429 CASE_27 1.0000 0.0032 1.0012 0.0004 0.0483 CASE_28 1.0000 0.0025 1.0013 0.0004 0.0425 Experiment CASE_1 0.9957 0.0045 0.9982 0.0003 0.0024 HEU-SOL-THERM-042 (8 cases) CASE_2 0.9965 0.0040 0.9983 0.0003 0.0024 CASE_3 0.9994 0.0028 1.0011 0.0002 0.0022 CASE_4 1.0000 0.0034 1.0025 0.0002 0.0021 CAL-DS0-NU-000003 REV 00A XII-5 September 2004 Criticality Model Table XII-2. Critical Benchmarks Selected for Validation of the Criticality Model for External Configurations Containing Mixture Highly Enriched in 235U (Continued) Experiment Case Name Benchmark Values Calculated Values (MCNP) keff sexp keff scalc AENCF Experiment CASE_5 1.0000 0.0034 0.9997 0.0002 0.0020 HEU-SOL-THERM-042 (8 cases) (continued) CASE_6 1.0000 0.0037 1.0005 0.0002 0.0021 CASE_7 1.0000 0.0036 1.0011 0.0002 0.0021 CASE_8 1.0000 0.0035 1.0013 0.0001 0.0021 Experiment heust43c1 0.9986 0.0017 0.9995 0.0007 0.014 HEU-SOL-THERM-043 (3 cases) heust43c2 0.9995 0.0041 1.0082 0.0004 0.003 heust43c3 0.999 0.0044 1.0033 0.0004 0.003 Experiment hst4410 0.9944 0.0077 0.9909 0.0018 0.039 HEU-SOL-THERM-044 (16 cases) hst4411 0.9944 0.0078 0.9847 0.002 0.041 hst4412 0.9944 0.0078 0.9872 0.0017 0.040 hst4413 0.9964 0.0067 1.0000 0.0018 0.042 hst4416 0.9974 0.0062 1.0178 0.0018 0.043 hst4417 0.9964 0.0057 0.9987 0.0017 0.044 hst4419 0.9974 0.0063 1.0079 0.0018 0.045 hst4444 0.9984 0.0057 1.0004 0.0017 0.045 hst4449 0.9964 0.0047 1.0116 0.0017 0.034 hst4450 0.9946 0.0047 0.9881 0.0018 0.038 hst4451 0.9984 0.0057 1.0047 0.0017 0.046 hst4453 0.9984 0.0064 1.0189 0.0018 0.047 hst4454 0.9984 0.0065 1.0142 0.0015 0.046 hst4455 0.9984 0.0065 1.0196 0.0017 0.046 hst447 0.9944 0.0097 0.9948 0.0018 0.037 hst448 0.9946 0.0083 0.9955 0.0021 0.042 Source: Moscalu 2004, Section 5.1 The experiments listed in Table XII-2 cover configuration classes NF-1 through NF-5 and FF-1 through FF-3 for configurations containing mixtures of highly enriched uranium external to the waste package. XII.2.2 Range of Applicability of Selected Critical Benchmark Experiments Tables XII-3 through XII-5 summarize the range of applicability of the experiments listed in Table XII-2. The information is excerpted from Moscalu (2004, Section 5.1). CAL-DS0-NU-000003 REV 00A XII-6 September 2004 Criticality Model Table XII-3. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with External Configurations Containing Mixtures Highly Enriched in 235U (Set 1) Experiment Experiment Experiment Experiment Experiment HEU-MET-HEU-MET-HEU-MET HEU-COMP-HEU-COMP- Category/ MIXED-005 THERM-001 THERM-014 MIXED-001 MIXED-002 Description Parameter (5 cases) (1 case) (1case) (26 cases) (23 cases) Materials/ Fissionable Fissionable Element Uranium Uranium Uranium Uranium Uranium Material Physical Form Uranium metal pellets Uranium metal foils Uranium metal foils UO2 UO2 Isotopic Composition 89.39 wt% 235U 93.23 wt% 235U 93.23 wt% 235U 93.15 wt% 235U 89.42 and 89.6 wt% 235U Atomic Density (atoms/b-cm) 235U: 4.24e-02 235U: 3.84e-02 to 4.28e-02 235U: 3.84e-02 to 4.38e-02 235U: 4.48e-03 to 1.39e-02 235U: 1.26e-02 and 1.32e-02 Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Moderator Element Si as scatterer H in sand H, C Si as scatterer H, C Si as scatterer H H and Deuterium (D) Physical Form SiO2 pellets interspersed with Plates of polyethylene and Plates of polyethylene and Water, alcohol- water solution, Mixture water with heavy water U pellets silicon glass silicon glass Plexiglas Atomic Density (atoms/b-cm) Si: 1.99e-02 H: 2.65e-05 H: 8.23e-02 to 8.28e-02 C: 4.11e-02 to 4.14e-02 H: 8.19e-02 to 8.34e-02 C: 4.10e-02 to 4.17e-02 Fuel Region: 2.16e-2 (7 cases) 5.68e-2 H: 7.36e-03 to 6.67e-02 D: 0 to 5.91e-02 Si: 2.17 to 2.24e- 02 Si: 2.20 to 2.28e- 02 (Plexiglas) 6.24e-2 (alcoholwater) Ratio to Not available Not available H/X: Not 0 - 49 Not available Fissile available Material Si/235U = 42 Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Reflector Material/ Physical Form Reflected by polyethylene, SiO2 sand and Reflected by polyethylene Reflected by polyethylene Reflected by polyethylene Reflected by water stainless steel and concrete walls concrete Materials/ Neutron Absorber Element Boron None None None None Physical Form Impurity in SiO2 N/A N/A N/A N/A Atomic Density (atoms/b-cm) 10B: 4.40e-08 N/A N/A N/A N/A Geometry Heterogeneity Complex hexagonal Rectangular column of plates Rectangular column of plates Complex arrays of cans in Hexagonal array of tubes containing geometry of pellets in Al tubes and foils and foils rectangular geometry UO2 in a cylindrical tank Shape Cylinder Parallelepiped Parallelepiped Cylinder Cylinder Neutron Energy AENCF b 0.212 to 0.377 MeV 0.0212 MeV 0.0234 MeV 0.1045 to 0.8015 MeV 0.537 to 0.899 MeV EALF b 1.48 to 5150 eV 0.0865 eV Not Available 0.438 to 2.14e- 03 237 to 4.61e04 eV Neutron Energy Spectraa T: 0.3 to 25.0 % I: 28.1 to 50.5 % F: 46.8 to 54.2 % T: 22.7 % I: 27.7 % F: 49.7 % Not Available T: 4.3 to 26.1 % I: 14.2 to 25.9 % F: 48.3 to 81.4 % T: 0.4 to 8.0 % I: 16.0 to 33.8 % F:65.1 to 82.9 % Fission Rate T: 4.4 to 68.4 % T: 91.2 % Not Available T: 25.4 to 78.0 % T: 3.8 to 34.5 % vs. Neutron I: 20.5 to 68.4 % I: 7.7 % I: 16.4 to 43.1 % I: 26.8 to 54.6 % Energya F: 11.1 to 27.2 % F: 1.2 % F: 5.6 to 49.3 % F: 31.9 to 63.6 % Source: Moscalu 2004, Section 5.1 NOTES: a Spectral range defined as follows: thermal (T) [0 to 1 eV], intermediate (I) [1eV to 100 keV], fast (F) [100 keV to 20 MeV]. b AENCF = average energy of a neutron causing fission, EALF = energy of average lethargy causing fission. CAL-DS0-NU-000003 REV 00A XII-7 September 2004 Criticality Model Table XII-4. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with External Configurations Mixtures Highly Enriched in 235U (Set 2) Experiment HEU-SOL- Experiment HEU-SOL- Experiment HEU-SOL- Experiment HEU-SOL- Experiment HEU-SOL- Category/ THERM-001 THERM-002 THERM-007 THERM-008 THERM-009 Description Parameter (10 cases) (14 cases) (17 cases) (5 cases) (4 cases) Materials/ Fissionable Fissionable Element Uranium Uranium Uranium Uranium Uranium Material Physical Form Aqueous solution of uranyl nitrate Aqueous solution of uranyl nitrate Aqueous solution of uranyl nitrate Aqueous solution of uranyl nitrate Aqueous solution of uranium oxyfluoride Isotopic 93.17 wt% 235U 93.17 wt% 235U 93.17 wt% 235U 93.17 wt% 235U 93.18 wt% 235U Composition Atomic Density (atoms/b-cm) 235U: 1.31e-04 to 8.54E-04 238U: 7.46e-06 to 4.86e-05 235U: 1.42e-04 to 7.99e-04 238U: 8.11e-06 to 4.55e-05 235U: 1.60e-04 to 8.69e-04 238U: 9.14e-6 to 1.03e-05 235U: 1.44e-04 to 8.50e-04 238U: 8.20e-6 to 4.84e-05 235U: 5.09e-04 to 1.66e-03 238U: 2.88e-5 to 9.41e-05 Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Element H H H H H Moderator Physical Form Solution Solution Solution Solution Solution Atomic Density (atoms/b-cm) 5.82e-02 to 6.54e- 02 5.88e-02 to 6.53e- 02 5.78e-02 to 6.48e- 02 5.84e-02 to 6.53e- 02 5.96e-02 to 6.44e- 02 Ratio to Fissile Material 86 to 499 74 to 460 65 to 405 69 to 454 35.8 to 126.5 Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Reflector Material/ Physical Form Unreflected (concrete walls) Reflected by concrete walls Concrete Plexiglas Water Materials/ Element None None None None None Neutron Absorber Physical Form N/A N/A N/A N/A N/A Atomic Density (atoms/b-cm) N/A N/A N/A N/A N/A Geometry Heterogeneity Homogeneous solution contained in a cylindrical Homogeneous solution contained in a cylindrical tank Arrays of cylindrical tanks placed in a Arrays of cylindrical tanks placed in a Homogeneous solution contained tank rectangular rectangular in a spherical geometry geometry vessel made of Al. Shape Cylinder Cylinder Cylinder Cylinder Sphere Neutron Energy AENCFb 0.0065 to 0.0410 MeV 0.0066 to 0.0375 MeV 0.0071 to 0.0369 MeV 0.0064 to 0.0367 MeV 0.0180 to 0.0450 MeV EALFb 0.04 to 0.29 eV 0.04 to 0.25 eV 0.046 to 0.27 eV 0.04 to 0.25 eV 0.09 to 0.52 eV Neutron Energy Spectraa T:8.1 to 31.1 % I: 29.1 to 36.5% F:39.8 to 55.6% T:8.7 to 30.4 % I: 29.6 to 36.7% F:39.9-55.2% T:8.3 to 28.7 % I: 30.5 to 37.0 % F:40.8 to 55.0 % T:8.5 to 30.8 % I: 29.1 to 36.3% F:40.0 to 55.5% T:5.8 to 15.4 % I: 34 to 35.7% F:50.6 to 58.5% Fission Rate vs. Neutron Energya T: 77.5 to 95.5% I: 4.1 to 20.3% F: 0.4 to 2.2% T: 79.2 to 90.3% I: 4.2 to 18.8% F: 0.4 to 2.0% T: 78.2 to 95.0% I: 4.6 to 19.7% F: 0.4 to 2.1% T: 78.9 to 95.5% I: 4.1 to 19.0% F: 0.4 to 2.1% T: 71.8 to 89.1% I: 9.9 to 25.0 % F: 1.0 to 3.2% Source: Moscalu 2004, Section 5.1 NOTES: aSpectral range defined as follows: thermal (T) [0 to 1 eV], intermediate (I) [1eV to 100 keV], fast (F) [100 keV to 20 MeV]. bAENCF = average energy of a neutron causing fission, EALF = energy of average lethargy causing fission. CAL-DS0-NU-000003 REV 00A XII-8 September 2004 Criticality Model Table XII-5. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with External Configurations Mixtures Highly Enriched in 235U (Set 3) Category/ Description Parameter Experiment HEU-SOL- THERM-033 (26 cases) Experiment HEU-SOL- THERM-038 (28 cases)b Experiment HEU-SOL- THERM-042 (8 cases) Experiment HEU-SOL- THERM-043 (3 case) Experiment HEU-SOL- THERM-044 (16 cases) Materials/ Fissionable Fissionable Element Uranium Uranium Uranium Uranium Uranium Material Physical Form Aqueous solution of uranyl nitrate Aqueous solution of uranyl nitrate Aqueous solution of uranyl nitrate Aqueous solution of uranium oxyfluoride Aqueous solution of uranyl nitrate Isotopic Composition 93.2 wt% 235U 93.1 wt% 235U 92.78 to 93.22 wt% 235U 93.2 wt% 235U 93.17 wt% 235U Atomic Density (atoms/b-cm) 235U: 8.54e-4 238U: 4.85e-5 235U: 9.64e-04 238U: 5.90e-05 235U: 3.24e-05 to 4.13e-05 238U: 1.89e-6 to 2.34e-06 235U: 4.77e-05 to 3.20e-04 238U: 2.86e-06 to 1.79e-05 235U: 8.65e-4 238U: 4.95e-5 Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp Materials/ Element H H H H H Moderator Physical Form Solution Solution Solution Solution Solution Atomic Density (atoms/b-cm) 5.81e-02 5.78e-02 6.62e-02 to 6.648e-02 6.53e to 2 to 6.67e-2 5.81e-02 Ratio to Fissile Material 68.1 60.0 1602 to 2050 204 to 1392 67.2 Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. Materials/ Reflector Material/ Physical Form Concrete Reflected by various plates (Pb, U, Be, Cd, Polyethylene, Stainless steel, Unreflected Unreflected Concrete Boraflex, etc) and concrete walls Materials/ Neutron Absorber Element B and Cd B, Cd, Pb, U, Fe, etc None None B, Cl, Cd and Gd Physical Form B and Cd in solution Absorbers were inserted as plates N/A N/A Absorbers are in various forms (pyrex glass, boraflex rubber,Cd sleeves etc.) Atomic Density (atoms/b-cm) B-10:1.74e-8 Cd: 1.49e-8 Not available N/A N/A B-10:6.99e-03 to 9.57e-4 Cd: 5.19e-03 to 4.63e-02 Geometry Heterogeneity Homogeneous solution contained in Homogeneous solution Homogeneous solution contained Homogeneous solution contained Homogeneous solution contained in a nested structure of cylindrical tanks made of stainless steel. contained in two cylindrical tanks in a cylindrical tank in a spherical vessel made of Al. a nested structure of cylindrical tanks made of stainless steel. Shape Cylinder Cylinder Cylinder Sphere Cylinder Neutron Energy AENCF c 0.032 to 0.036 MeV 0.041 to 0.048 MeV 0.0020 to 0.0024 MeV 0.003 to 0.014 MeV 0.0340 to 0.0470 MeV EALF c 0.269 to 0.316 eV 0.31 to 0.41 eV 0.031 to 0.032 eV 0.033 to 0.075 eV Not available Neutron Energy Spectraa T:8.1 to 8.8 % I: 38.2 to 39 % F:52.6 to 53.4 % T:5.0 to 26.0 % I: 31.7 to 40.4 % F: 41.5 to 57.7% T:52.1 to 56.4 % I: 19.6 to 21.3 % F: 24.0 to 26.6 % T:18.0 to 49.8 % I: 22.2 to 33.7 % F:28.0 to 48.3 % Not available Fission Rate vs. Neutron Energya T: 76.2 to 78.0 % I: 20.1 to 21.7 % F: 1.9 to 2.1 % T: 73.8 to 76.9 % I: 20.8 to 23.6 % F: 2.3 to 2.6 % T: 98.1 to 98.4% I: 1.5 to 1.8% F: 0.1% T: 90.8 to 97.9 % I: 1.9 to 8.4 % F: 0.1 to 0.8 % Not available Source: Moscalu 2004, Section 5.1 a NOTES: Spectral range defined as follows: thermal (T) [0 to 1 eV], intermediate (I) [1eV to 100 keV], fast (F) [100 ke to 20 MeV]. b Spectral data include only selected cases for HEU-SOL-THERM-038 (cases 1 to 28). c AENCF = average energy of a neutron causing fission, EALF = energy of average lethargy causing fission. CAL-DS0-NU-000003 REV 00A XII-9 September2004 Criticality Model XII.2.3 Calculation of Lower-Bound Tolerance Limit The results of the trending parameter analysis for the criticality benchmark subset representative for external configurations containing HEU are presented in Table XII-6. Some of the trending parameters for AENCF (r2, T, P-value) from Table XII-6, indicate a slight trend of keff with AENCF (Moscalu 2004, Section 5.1). Table XII-6. Trending Parameter Results for the Criticality Benchmark Subset Representative for Configurations Containing HEU External to the Waste Package Trend Parameter n Intercept Slope r2 T t0.025,n-2 P-value Goodness-of-Fit Tests Valid Trend AENCF 187 1.0055 -0.019 0.4264 -11.73 1.980a 4.2E-24 Passed Yes k eff Source: Moscalu 2004, Section 5.1 NOTES: aTable A-4 from Natrella (1963) has a limited number of entries for n (t=1.98 for n=120 and t=1.96 for n close to infinity); using t=1.98 is conservative for the current application where n=187. b AENCF = average energy of a neutron causing fission, EALF = energy of average lethargy causing fission. Figure XII-1 presents the keff values and the calculated lower bound tolerance limit for this set of benchmark experiments. The lower bound tolerance limit can be also written as (Moscalu 2004, Section 5.1): Lower Bound Tolerance Limit = 0.970611 for 0 MeV