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 
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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 Projects 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 configurations 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 formwaste 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, , is defined as 
 = kC - 1 (Eq. 5) 
and thus the uncertainty in the bias is identical to the uncertainty in kC (i.e., .kC = .). 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. 
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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. 
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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). 
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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 configurations 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 <AENCF < 0.247 MeV) 
ks + .ks < -1.7411e-02*AENCF + 0.97491 (0.247 = AENCF 
< 0.902 MeV) 
233U External Homogeneous (Solution) None ks + .ks < 0.9748 
Mixture of U and Homogeneous (Solution) None ks + .ks < 0.9644 
Pu External 
NOTES: AENCF = average energy of a neutron causing fission, CRCs = commercial reactor critical, BWR = boiling water 
reactor, FFTF = Fast flux Test Facility, LCEs = laboratory critical experiments, LWBR = light water breeder reactor, 
PWR = pressurized water reactor, SNF = spent nuclear fuel, TRIGA = Training Research Isotopes General Atomic 
LEU = Low Enriched Uranium, IEU = Intermediate Eriched Uranium, HEU = Highly Enriched Uranium, P = Pitch, 
BU = Burnup. 
CAL-DS0-NU-000003 REV 00A 42 September2004 

Criticality Model 
8. CONCLUSIONS 
This analysis documents the criticality potential evaluation process together with a number of 
representative analyses for a variety of LWR and DOE-EM SNF fuel types. The analyses use 
current data for pressurized and boiling water reactor and DOE-owned SNF and provides results 
that may be updated as additional data becomes available. The computational method discussed 
in Section 6 illustrates how criticality potential for configurations of fissionable materials is 
determined. 
The MCNP code was selected to perform the Monte Carlo method along with the material cross 
section data identified in Tables 1 and 2 as implemented by MCNP for representing neutron 
transport. Sets of benchmark experiments were presented to cover the range of various waste 
form/waste package and external configuration classes in Attachments III through XII. The 
major parameters covered by the benchmark experiments were burnup (where applicable), initial 
enrichment, spectrum, and geometry. Example criticality benchmark experiment trending 
parameter analyses were performed and results presented in Attachment III. The selected 
benchmark experiments were separated into subset applicability from which LBTL were 
statistically derived, and a specified ROA was provided. Criticality potential criteria were 
established for the experiment subsets over the given ROA in Table 5. 
Three open items (13, 15, and 17) from Safety Evaluation Report for Disposal Criticality 
Analysis Methodology Topical Report, Revision 0 (Reamer 2000) are addressed in analysis. Open 
Items 13, 15 and 17 are addressed in Section 6.3. Uncertainties based on .kEROA and .kISO 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. 
9. INPUTS AND REFERENCES 
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B00000000-01717-0210-00018 REV 01. Las Vegas, Nevada: CRWMS M&O. 
ACC: MOL.19990526.0294. 
CRWMS M&O 1999e. LCE for Research Reactor Benchmark Calculations.
B00000000-01717-0210-00034 REV 00. Las Vegas, Nevada: CRWMS M&O. 
ACC: MOL.19990329.0394. 
CRWMS M&O 1999f. Evaluation of Codisposal Viability for MOX (FFTF) DOE-Owned Fuel 
BBA000000-01717-5705-00023 REV 00. Las Vegas, Nevada: CRWMS M&O. 
ACC: MOL.19991014.0235. 
CRWMS M&O 2000a. Evaluation of Codisposal Viability for HEU Oxide (Shippingport PWR)
DOE EM-Owned Fuel. TDR-EDC-NU-000003 REV 00. Las Vegas, Nevada: CRWMS M&O. 
ACC: MOL.20000227.0240. 
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CRWMS M&O 2000b. Evaluation of Codisposal Viability for UZrH (TRIGA) DOE EM-Owned 
Fuel. TDR-EDC-NU-000001 REV 00. Las Vegas, Nevada: CRWMS M&O. 
ACC: MOL.20000207.0689. 
CRWMS M&O 2000c. Evaluation of Codisposal Viability for U-Zr/U-Mo Alloy (Enrico Fermi)
DOE EM-Owned Fuel. TDR-EDC-NU-000002 REV 00. Las Vegas, Nevada: CRWMS M&O. 
ACC: MOL.20000815.0317. 
CRWMS M&O 2000d. Users Manual for SCALE-4.4A. 10129-UM-4.4A-00. Las Vegas, 
Nevada: CRWMS M&O. ACC: MOL.20001130.0136; MOL.20010822.0084; 
MOL.20010822.0085; MOL.20010822.0086; MOL.20010822.0087. 
CRWMS M&O 2000e. Evaluation of Codisposal Viability for Th/U Oxide (Shippingport 
LWBR) DOE EM-Owned Fuel. TDR-EDC-NU-000005 REV 00. Las Vegas, Nevada: CRWMS 
M&O. ACC: MOL.20001023.0055. 
CRWMS M&O 2001. Evaluation of Codisposal Viability for U-Metal (N Reactor) DOE EM-
Owned Fuel. TDR-EDC-NU-000004 REV 00. Las Vegas, Nevada: CRWMS M&O. 
ACC: MOL.20010314.0004. 
D'Agostino, R.B. and Stephens, M.A., eds. 1986. Goodness-Of-Fit Techniques. Statistics, 
Textbooks and Monographs Volume 68. New York, New York: Marcel Dekker. TIC: 253256. 
Dean, J.C. and Tayloe, R.W., Jr. 2001. Guide for Validation of Nuclear Criticality Safety 
Calculational Methodology. NUREG/CR-6698. Washington, D.C.: U.S. Nuclear Regulatory 
Commission. TIC: 254004. 
DOE (U.S. Department of Energy) 2002. DOE Spent Nuclear Fuel Information in Support of 
TSPA-SR. DOE/SNF/REP-047, Rev. 2. Idaho Falls, Idaho: U.S. Department of Energy, Idaho 
Operations Office. TIC: 252089. 
Duderstadt, J.J. and Hamilton L.J. 1976. Nuclear Reactor Analysis. New York, New York: 
John Wiley & Sons. TIC: 245454. 
Durst, B.M.; Bierman, S.R.; and Clayton, E.D. 1982. Critical Experiments with 4.31 Wt% 235U 
Enriched UO2 Rods in Highly Borated Water Lattices. NUREG/CR-2709. Washington, D.C.: 
U.S. Nuclear Regulatory Commission. TIC: 232755. 
Harwell, J. W. 2003. Commercial Reactor Reactivity Analysis for Grand Gulf, Unit 1. 
32-5029393-00. Lynchburg, Virginia: Framatome ANP. ACC: DOC.20040109.0003. 
Lichtenwalter, J.J.; Bowman, S.M.; DeHart, M.D.; and Hopper, C.M. 1997. Criticality 
Benchmark Guide for Light-Water-Reactor Fuel in Transportation and Storage Packages. 
NUREG/CR-6361. Washington, D.C.: U.S. Nuclear Regulatory Commission. TIC: 233099. 
Massie, H. 2003. Critical Limit Development for PWR and BWR SNF Waste Package. 32-
5037984-01. Lynchburg, Viginia: Framatome ANP. ACC: DOC.20040709.0001. 
CAL-DS0-NU-000003 REV 00A 46 September2004 

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Miyoshi, Y.; Umano, T.; Tonoike, K.; Izawa, N.; Sugikawa, S.; and Okazaki, S. 1997. Critical 
Experiments on 10% Enriched Uranyl Nitrate Solution Using a 60-cm-Diameter Cylindrical 
Core. Nuclear Technology, 118, (1), 69-82. La Grange Park, Illinois: American Nuclear 
Society. TIC: 244153. 
Moscalu, D.R. 2004. Analysis of Critical Benchmark Experiments for Configurations External to 
WP. 32-5045840-00. Las Vegas, Nevada: Areva. ACC: DOC.20040701.0003. 
Natrella, M.G. 1963. Experimental Statistics. National Bureau of Standards Handbook 91. 
Washington, D.C.: U.S. Department of Commerce, National Bureau of Standards. 
TIC: 245911. 
NEA (Nuclear Energy Agency) 1998. International Handbook of Evaluated Criticality Safety 
Benchmark Experiments. NEA/NSC/DOC(95)03. Paris, France: Nuclear Energy Agency. 
TIC: 243013. 
NEA 2001. International Handbook of Evaluated Criticality Safety Benchmark Experiments. 
2001 Edition. NEA/NSC/DOC(95)03. Paris, France: Nuclear Energy Agency, Organization for 
Economic Co-operation and Development. TIC: 251945. 
NEA (Nuclear Energy Agency) 2003. International Handbook of Evaluated Criticality Safety 
Benchmark Experiments. 2003 Edition. NEA/NSC/DOC(95)03. [Paris, France]: Nuclear Energy 
Agency, Organization for Economic Co-Operation and Development. TIC: 256092. 
Newman, L.W. 1984. Urania-Gadolinia: Nuclear Model Development and Critical Experiment 
Benchmark. DOE/ET/34212-41. Lynchburg, Virginia: Babcock & Wilcox. TIC: 233536. 
ORNL (Oak Ridge National Laboratory) 1995. Analysis of Fresh Fuel Critical Experiments 
Appropriate for Burnup Credit Validation. ORNL/TM-12959. Oak Ridge, Tennessee: Oak 
Ridge National Laboratory. ACC: HQO.19951023.0010. 
Punatar, M.K. 2001a. Summary Report of Commercial Reactor Criticality Data for Crystal 
River Unit 3. TDR-UDC-NU-000001 REV 02. Las Vegas, Nevada: Bechtel SAIC Company. 
ACC: MOL.20010702.0087. 
Punatar, M.K. 2001b. Summary Report of Commercial Reactor Criticality Data for Grand Gulf 
Unit 1. TDR-UDC-NU-000002 REV 00. Las Vegas, Nevada: Bechtel SAIC Company. 
ACC: MOL.20011008.0008. 
Putman, V.L. 2003. Criticality Safety Code Validation with LWBR's SB Cores. INEEL/EXT-02-
00304. Idaho Falls, Idaho: Idaho National Engineering and Environmental Laboratory. 
TIC: 253902. 
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. ACC: MOL.20000919.0157. 
CAL-DS0-NU-000003 REV 00A 47 September2004 

Criticality Model 
Scheaffer, R.L. and McClave, J.T. 1990. Probability and Statistics for Engineers. 3rd Edition. 
Boston, Massachusetts: PWS-Kent. TIC: 249631. 
Taylor, E.G. 1965. Saxton Plutonium Program, Critical Experiments for the Saxton Partial 
Plutonium Core. EURAEC-1493, WCAP-3385-54. Pittsburgh, Pennsylvania: Westinghouse 
Electric Corporation, Atomic Power Division. TIC: 223286. 
Walpole, R.E.; Myers, R.H.; and Myers, S.L. 1998. Probability and Statistics for Engineers and 
Scientists. 6th Edition. Upper Saddle River, New Jersey: Prentice Hall. TIC: 242020. 
Wimmer, L.B. 2001. Summary Report of Commercial Reactor Criticality Data for Three Mile 
Island Unit 1. TDR-UDC-NU-000004 REV 01. Las Vegas, Nevada: Bechtel SAIC Company. 
ACC: MOL.20010921.0047. 
Wittekind, W.D. 1992. K Basin Criticality Evaluation for Irradiated Fuel Canisters in Sludge.
WHC-SD-NR-CSER-001, Rev. 0. Richland, Washington: Westinghouse Hanford. 
TIC: 240971. 
YMP (Yucca Mountain Site Characterization Project) 2003. Disposal Criticality Analysis 
Methodology Topical Report. YMP/TR-004Q, Rev. 02. Las Vegas, Nevada: Yucca Mountain 
Site Characterization Office. ACC: DOC.20031110.0005. 
9.2 CODES, STANDARDS, REGULATIONS, AND PROCEDURES 
ANSI/ANS-8.1-1998. Nuclear Criticality Safety in Operations with Fissionable Material 
Outside Reactors. La Grange Park, Illinois: American Nuclear Society. TIC: 242363. 
ANSI/ANS-8.17-1984. Criticality Safety Criteria for the Handling, Storage, and Transportation 
of LWR Fuel Outside Reactors. La Grange Park, Illinois: American Nuclear Society. 
TIC: 231625. 
9.3 SOFTWARE CODES 
Software Code: CLREG. V1.0. PC - Windows 2000. 10528-1.0-01. 
Software Code: MCNP. V4B2LV. HP, HPUX 9.07 and 10.20; PC, Windows 95; Sun, 
Solaris 2.6. 30033 V4B2LV. 
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10. ATTACHMENTS 
The description of the attachments is provided in Table 6. 
Table 6. Attachment Listing 
Attachment Description 
I Listing of LUTB and MCNP Spectral Characteristic Input and Output Files Contained in Attachment II 
II Compact Disc 
III LBTL Calculation and ROA Determination for LWR SNF 
IV LBTL Calculation and ROA Determination for Shippingport LWBR 
V LBTL Calculation and ROA Determination for Enrico Fermi 
VI LBTL Calculation and ROA Determination for N-Reactor 
VII LBTL Calculation and ROA Determination for FFTF 
VIII LBTL Calculation and ROA Determination for Melt and Dilute Ingots 
IX LBTL Calculation and ROA Determination for TRIGA SNF 
X LBTL Calculation and ROA Determination for Fort St. Vrain SNF 
XI LBTL Calculation and ROA Determination for Shippingport PWR 
XII LBTL Calculation and ROA Determination for Configurations External to the Waste Package 
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INTENTIONALLY LEFT BLANK 
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ATTACHMENT I 
LISTING OF LUTB AND MCNP SPECTRAL CHARACTERISTIC INPUT AND 
OUTPUT FILES CONTAINED IN ATTACHMENT II 
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ATTACHMENT I 
LISTING OF LUTB AND MCNP SPECTRAL CHARACTERISTIC INPUT AND 
OUTPUT FILES CONTAINED IN ATTACHMENT II 
This attachment contains a listing and description of the zip file contained on the attachment CD 
of this model report. The zip archive was created using WinZip 8.1. The zip file attributes are: 
Archive File Name File Size (bytes) FileDate File Time 
CM-R00A.zip 8,086,179 09/09/2004 10:16 AM 
There are 31 total files contained in a unique directory structure. Upon file extraction, the 
following directory and files structure will be found: 
Zip File Directories Subdirectories Files 
CM-R00A.zip CLREG Files CLREG input and output files for Attachment III, 
lower bound tolerance limit calculations 
PWR MCNP input and output files for Attachment III 
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INTENTIONALLY LEFT BLANK 
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ATTACHMENT II 
COMPACT DISC 
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ATTACHMENT II 
COMPACT DISC 
This CD contains a listing of LUTB and MCNP spectral characteristic input and output files. 
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INTENTIONALLY LEFT BLANK 
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ATTACHMENT III 
LBTL CALCULATION AND ROA DETERMINATION FOR LWR SNF 
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ATTACHMENT III 
LBTL CALCULATION AND ROA DETERMINATION FOR LWR SNF 
III.1 INTRODUCTION 
This attachment presents the calculations of the lower-bound tolerance limit (LBTL) and the 
determination of range of applicability (ROA) for benchmarks that could potentially be 
applicable to waste package configurations containing pressurized water reactor (PWR) and 
boiling water reactor (BWR) spent nuclear fuel (SNF). A listing of corroborating and supporting 
data, models, or information used for the calculation is provided in Table III-1. 
Table III-1. Supporting Information and Sources 
Description Source 
Criticality benchmark experiments Durst et al. 1982; Miyoshi et al. 1997; Newman 1984; NEA 1998; ORNL 
1995; Taylor 1965; Wittekind 1992; Bierman et al. 1984; Bierman et al. 
1981; Bierman et al. 1977; Bierman and Clayton 1981; Bierman 1990; 
Baldwin et al. 1979; CRWMS M&O 1999a 
Measured critical systems CRWMS M&O 1998d 
Trending parameters CRWMS M&O 1999b, CRWMS M&O 1999c CRWMS M&O 1999d, 
CRWMS M&O 1999e 
Fuel characteristics Punatar 2001a, Punatar 2001b , Wimmer 2001, CRWMS M&O 1998f, 
CRWMS M&O 1998e 
Benchmark selection guidance Lichtenwater et al. 1997 
III.2 SELECTION OF CRITICALITY BENCHMARK EXPERIMENTS 
The calculation method used to establish the criticality potential for a waste package must be 
benchmarked against measured data (criticality benchmark experiments). The criticality 
benchmark experiments must be applicable to the package under consideration. This section 
provides brief descriptions of the criticality benchmark experiments selected for benchmarking 
the computational method for commercial light water reactor (LWR) SNF. 
Two types of experimental data are used: laboratory critical experiments (LCEs) and 
commercial reactor critical (CRCs). Various parameters are trended with the keff values from the 
LCEs and the CRCs. These trends are used to establish biases and uncertainties of the criticality 
computational method. 
Guidelines for experiment selection come from Lichtenwalter et al. (1997), which states, There 
are three fundamental parameters that should be considered in the selection of suitable 
experiments for use in the evaluation of transportation and storage package designs. They are as 
follows: (1) geometry of construction; (2) materials of construction (including fissionable 
material); and (3) the inherent neutron energy spectrum affecting the fissionable material. 
With these fundamental parameters in mind, CRCs fulfill each to a degree. The geometry of the 
waste package configuration and the CRC configuration are similar. Both approximate 
cylindrical systems and the fuel assembly geometric arrangement is identical when it comes 
down to lattice, pin pitch, structural materials, cladding, and guide tube positions. Differences 
arise in the assembly-to-assembly pitch, interstitial materials between assemblies, and moderator 
CAL-DS0-NU-000003 REV 00A III-1 September 2004 

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and fuel cross section temperature differences. Also, due to the size differences between a 
reactor pressure vessel and a waste package, a CRC has less neutron leakage than in a waste 
package. 
The fuel assembly material compositions used in the CRC representations are sufficiently similar 
to the fuel assemblies used in the waste package representations. Both systems contain burned 
fuel isotopics. Since the waste package is designed to remain subcritical, the materials between 
assemblies (i.e., borated steel plates in waste package) are different between the waste package 
and the CRC. These materials cause a reduction in the neutron multiplication factor for the 
waste package environment. 
The reflector and moderator materials are similar for both the CRC and the waste package. PWR 
CRCs contain borated moderator, which is used for additional neutron population control. The 
moderator-to-fuel ratio is greater in the waste package due to the presence of full-density water. 
The temperature in the CRC environment is greater than in the waste package environment, 
which has an effect on Doppler broadening of the resonances and an increase in resonance 
absorption. Doppler broadening refers to a change in cross section resulting from thermal 
motion of nuclei in a target material. The end result of these minor differences in the moderator 
and reflector material compositions produces a small difference in the hydrogen-to-fissile atom 
(H/X) ratio between the two systems and causes a slight spectral shift. 
The CRCs represent intact commercial SNF in known critical configurations. The keff values 
obtained from analysis of the CRCs do not include any bias from SNF isotopic concentrations of 
the individual isotopes. Isotopic bias will be addressed as part of the isotopic model 
(BSC 2004b) and incorporated in the critical limit (CL). 
LCEs benchmark the criticality computational method for a range of fissionable materials, 
enrichments of fissile isotopes, moderator materials, and absorber materials. The homogeneous 
LCEs are used to calculate bias and uncertainties for degraded waste forms and configurations 
where the fuel assembly geometry has been lost. 
Criticality benchmark experiments were selected from a group of experiments that include LCEs 
and CRCs. Numerous references were used along with descriptions of pertinent information 
regarding each of the experiments. LCEs are used to benchmark the criticality computational 
method for un-irradiated, fresh fuel in various configurations representative of the range of 
potential configurations anticipated in the repository. CRCs are used to benchmark the criticality 
computational method for irradiated, burned SNF in intact lattice geometry. The criticality 
benchmark experiments that were selected provide a range of enrichments, lattice geometries, 
and fuel rod spacings typical of commercial LWR fuel in an intact configuration. The LCEs also 
contain homogeneous solution criticality benchmark experiments that are representative of 
degraded waste form configurations. These criticality benchmark experiment configurations 
cover the span of potential configurations possible over time in the repository. The CRCs 
provide a range of fuel enrichments in actual reactor geometries and conditions. CRCs are 
described in Section III.2.1 and LCEs are described in Section III.2.2. The criticality benchmark 
experiment sources are used for descriptions of experiment parameters. The rationale for their 
use in this attachment for commercial LWR SNF is provided in Table III-2. 
The following sources were used to demonstrate applicability as part of the benchmarking 
process. They were used to take previously evaluated benchmark experiment MCNP input cases 
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Criticality Model 
and add a tally output edit that illustrates the neutron spectral characteristics. The results of these 
tallies are illustrated in Section III.3.5. The MCNP input and output files for the tally 
calculations are documented in Attachment I (Attachment I provides a listing of the files 
contained on compact disc [Attachment II]) such that an independent repetition of the software 
use could be performed. 
 Waste Package, LCE, CRC, and Radiochemical Assay Comparison Evaluation 
(CRWMS M&O 1999c) (cases crc2 and wp2 referred to as crc and wp) 
 Laboratory Critical Experiment Reactivity Calculations (CRWMS M&O 1999d) 
(case exp22e5 referred to as exp22) 
 LCE for Research Reactor Benchmark Calculations (CRWMS M&O 1999e) 
(cases ssr48.i and ssr53.i referred to as ssr48 and ssr53). 
Table III-2. Rationale for Use of Experiment Sources 
Source Rationale for Use 
Critical Experiments with 4.31 wt. % 235U-Enriched UO2 Rods Applicable to LWR SNF in waste package configurations 
in Highly Borated Water Lattices (Durst et al. 1982) 
Critical Experiments on 10% Enriched Uranyl Nitrate Solution Applicable to LWR SNF in waste package configurations 
Using a 60-cm-Diameter Cylindrical Core (Miyoshi et al. 1997) 
Urania-Gadolinia: Nuclear Model Development and Critical Applicable to LWR SNF in waste package configurations 
Experiment Benchmark (Newman 1984) 
International Handbook of Evaluated Criticality Safety Applicable to LWR SNF in waste package configurations 
Benchmark Experiments (NEA 1998) 
Analysis of Fresh Fuel Critical Experiments Appropriate for Applicable to LWR SNF in waste package configurations 
Burnup Credit Validation (ORNL 1995) 
Saxton Plutonium Program, Critical Experiments for the Applicable to LWR SNF in waste package configurations 
Saxton Partial Plutonium Core (Taylor 1965) 
K Basin Criticality Evaluation for Irradiated Fuel Canisters in Applicable to LWR SNF in waste package configurations 
Sludge (Wittekind 1992) 
Criticality Experiments with Low Enriched UO2 Fuel Rods in Applicable to LWR SNF in waste package configurations 
Water Containing Dissolved Gadolinium (Bierman et al. 1984) 
Criticality Experiments with Subcritical Clusters of 2.35 wt. % 
and 4.31 wt. % 235U-Enriched UO2 Rods in Water with 
Applicable to LWR SNF in waste package configurations 
Uranium or Lead Reflecting Walls; Undermoderated 
Water-to-Fuel Volume Ration of 1.6 (Bierman et al. 1981) 
Critical Separation Between Subcritical Clusters of 2.35 wt. % 
235U-Enriched UO2 Rods in Water with Fixed Neutron Poisons 
Applicable to LWR SNF in waste package configurations 
(Bierman et al. 1977) 
Criticality Experiments with Subcritical Clusters of 2.35 wt. % 
and 4.31 wt.% 235U-Enriched UO2 Rods in Water with Steel 
Applicable to LWR SNF in waste package configurations 
Reflecting Walls (Bierman and Clayton 1981) 
Criticality Experiments with Neutron Flux Traps Containing Applicable to LWR SNF in waste package configurations 
Voids (Bierman 1990) 
Critical Experiments Supporting Close Proximity Water Applicable to LWR SNF in waste package configurations 
Storage of Power Reactor Fuel (Baldwin et al. 1979) 
Summary Report of Commercial Reactor Critical Analyses Monitored PWR critical systems 
Performed for the Disposal Criticality Analysis Methodology 
(CRWMS M&O 1998d) 
Summary Report of Laboratory Critical Experiment Analyses 
Performed for the Disposal Criticality Analysis Methodology 
(CRWMS M&O 1999a) 
Applicable to LWR SNF in waste package configurations 
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III.2.1 CRC Experiments 
The CRC keff values were calculated using the best-estimate isotope set corresponding to those 
listed in Table 4. Each of the CRC benchmark cases used water scattering kernels corresponding 
to a temperature of 500 K. 
III.2.1.1 Crystal River Unit 3 
The Crystal River Unit 3 plant operated by Progress Energy is a Babcock & Wilcox (B&W) 
PWR with 177 fuel assemblies. The fuel assemblies are the B&W 1515 design type. A total of 
33 CRC experiments have been evaluated for Crystal River Unit 3 where the core thermal power 
varied between 2452 MW and 2544 MW (Punatar 2001a, pp. 2-5 and 4-238 to 4-246). 
Table III-3 provides some general information about the Crystal River Unit 3 CRC experiments. 
The information includes the statepoint cycle length in effective full power days (EFPD,) the 
core average burnup, the initial weight percent enrichments of the fuel batches in the core during 
the CRC experiment (fresh fuel is identified by [] around the enrichment values), the down 
time in days since the core was last at power before restarting, along with the calculated keff 
values, sigma (s), and average energy of a neutron causing fission (AENCF). The pin pitch for 
the assemblies from this reactor was 1.44272 cm, which results in a moderator-to-fuel volume 
ratio of 1.7 (Punatar 2001a, p. 2-3). 
Table III-3. General Crystal River Unit 3 CRC Statepoint Information 
Case 
Cycle Length 
to Statepoint 
(EFPD, Cycle)a 
Initial 
Enrichments 
(wt. % 235U)a 
Core Average 
Burnup 
(GWd/MTU)b 
Downtime 
(d)a keff 
a sa 
AENCFc 
(MeV) CCd 
CR1 0.0 (Cy 1A) [1.93, 2.54, 2.83] 0.00 0.0 0.99601 0.00043 0.2344 3a, 3b, 
3c, 3dCR2 268.8 (Cy 1B) 1.93, 2.54, 2.83, 
2.00 
8.09 195.3 0.99285 0.0004 0.2504 
CR3 411.0 (Cy 1B) 1.93, 2.54, 2.83, 
2.00 
12.34 14.8 0.99502 0.00046 0.2518 
CR4 0.0 (Cy 2) 2.54, [2.64], 2.83 8.67 97.0 0.99282 0.00044 0.2498 
CR5 0.0 (Cy 3) 2.54, [2.62], 2.64, 
2.83 
7.50 164.0 0.99408 0.00045 0.2489 
CR6 168.5 (Cy 3) 2.54, 2.62, 2.64, 
2.83 
12.54 16.8 0.99304 0.00045 0.2536 
CR7 250.0 (Cy 3) 2.54, 2.62, 2.64, 
2.83 
14.98 12.3 0.99073 0.00045 0.2547 
CR8 0.0 (Cy 4) 2.62, [2.62], 2.64, 
[2.95] 
6.92 73.0 0.99134 0.00047 0.2499 
CR9 228.1 (Cy 4) 2.62, 2.64, 2.95 14.00 15.2 0.99152 0.00046 0.2576 
CR10 253.0 (Cy 4) 2.62, 2.64, 2.95 14.77 24.0 0.99603 0.00047 0.2568 
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Table III-3. General Crystal River Unit 3 CRC Statepoint Information (Continued) 
Case 
Cycle Length 
to Statepoint 
(EFPD, Cycle)a 
Initial 
Enrichments 
(wt. % 235U)a 
Core Average 
Burnup 
(GWd/MTU)b 
Downtime 
(d)a keff 
a sa 
AENCFc 
(MeV) CCd 
CR11 0.0 (Cy 5) 2.62, 2.64, 2.95, 
[2.95, 3.29] 
7.08 127.0 0.99479 0.00047 0.2475 
CR12 388.5 (Cy 5) 2.62, 2.64, 2.95, 
3.29 
19.12 5.0 0.99805 0.00045 0.2605 
CR13 0.0 (Cy 6) 2.62, 2.64, 2.95, 
3.29, [3.49] 
12.01 163.0 0.99561 0.00043 0.2513 
CR14 96.0 (Cy 6) 2.62, 2.64, 2.95, 
3.29, 3.49 
14.99 168.9 0.99579 0.00047 0.2557 
CR15 400.0 (Cy 6) 2.62, 2.64, 2.95, 
3.29, 3.49 
24.41 10.4 0.99273 0.00044 0.2612 
CR16 0.0 (Cy 7) 2.54, 2.62, 2.64, 
3.29, 3.49, [3.84] 
10.02 113.0 0.99324 0.00052 0.2504 
CR17 260.3 (Cy 7) 2.54, 2.62, 2.64, 
3.29, 3.49, 3.84 
18.09 18.9 0.99083 0.00045 0.2583 
CR18 291.0 (Cy 7) 2.54, 2.62, 2.64, 
3.29, 3.49, 3.84 
19.04 39.5 0.99222 0.00049 0.2598 
CR19 319.0 (Cy 7) 2.54, 2.62, 2.64, 
3.29, 3.49, 3.84 
19.91 109.5 0.98993 0.00047 0.2587 
CR20 462.3 (Cy 7) 2.54, 2.62, 2.64, 
3.29, 3.49, 3.84 
24.35 2.2 0.99321 0.00042 0.2582 
CR21 479.0 (Cy 7) 2.54, 2.62, 2.64, 
3.29, 3.49, 3.84 
24.87 7.2 0.99247 0.00046 0.2616 3a, 3b, 
3c, 3d 
CR22 0.0 (Cy 8) 1.93, 2.62, 3.29, 
3.49, 3.84, [3.94] 
12.26 99.0 0.99039 0.00043 0.2532 
CR23 97.6 (Cy 8) 1.93, 2.62, 3.29, 
3.49, 3.84, 3.94 
15.27 15.5 0.99021 0.00046 0.2572 
CR24 139.8 (Cy 8) 1.93, 2.62, 3.29, 
3.49, 3.84, 3.94 
16.58 6.2 0.99063 0.00049 0.2582 
CR25 404.0 (Cy 8) 1.93, 2.62, 3.29, 
3.49, 3.84, 3.94 
24.74 44.4 0.99054 0.00042 0.2615 
CR26 409.6 (Cy 8) 1.93, 2.62, 3.29, 
3.49, 3.84, 3.94 
24.91 4.9 0.99067 0.00047 0.2610 
CR27 515.5 (Cy 8) 1.93, 2.62, 3.29, 
3.49, 3.84, 3.94 
28.19 7.6 0.98772 0.00044 0.2643 
CR28 0.0 (Cy 9) 1.93, 3.84, [3.90], 
3.94 
14.18 75.0 0.99208 0.00044 0.2546 
CR29 158.8 (Cy 9) 1.93, 3.84, 3.90, 
3.94 
19.10 2.1 0.99311 0.0005 0.2584 
CR30 219.0 (Cy 9) 1.93, 3.84, 3.90, 
3.94 
20.96 53.1 0.99078 0.00048 0.2597 
CR31 363.1 (Cy 9) 1.93, 3.84, 3.90, 
3.94 
25.42 1.6 0.98837 0.00048 0.2635 
CR32 0.0 (Cy 10) 3.84, 3.90, 3.94, 
[4.167] 
15.24 55.0 0.99164 0.00052 0.2558 
CR33 573.7 (Cy 10) 3.84, 3.90, 3.94, 
4.167 
33.00 16.4 0.98725 0.00048 0.2660 
a
NOTES: Values are from CRWMS M&O 1998d, pp. 40 and 41. 
b 
Simple average of statepoint assemblies nodal height weighted averages from Punatar 2001a, Sections 3 and 4. 
c 
Values are from CRWMS M&O 1999b, pp. 60, 61, and 64 to 66. 
d 
CC = configuration class applicability (IP-). 
CAL-DS0-NU-000003 REV 00A III-5 September 2004 

Criticality Model 
III.2.1.2 Three Mile Island Unit 1 
The Three Mile Island Unit 1 plant operated by Exelon Nuclear Corporation is a B&W PWR 
with 177 fuel assemblies. The fuel assemblies are the B&W 1515 design type. A total of three 
CRC experiments have been evaluated for Three Mile Island Unit 1 where the core thermal 
power was 2535 MW (Wimmer 2001, pp. 2-5 and 3-2). 
Table III-4 provides some general information about the Three Mile Island Unit 1 CRC 
experiments. The information includes the statepoint cycle length in EFPD, the core average 
burnup, the initial weight percent enrichments of the fuel batches in the core during the CRC 
experiment (fresh fuel is identified by [] around the enrichment values), the down time in days 
since the core was last at power before restarting, along with the calculated keff values, sigma, 
and AENCF. The pin pitch for the assemblies from this reactor was 1.44272 cm, which results 
in a moderator-to-fuel volume ratio of 1.7 (Wimmer 2001, p. 2-3). 
Table III-4. General Three Mile Island Unit 1 CRC Statepoint Information 
Case 
Cycle Length 
to Statepoint 
(EFPD, Cycle)a 
Initial 
Enrichments 
(wt. % 235U)a 
Core 
Average 
Burnup 
(GWd/MTU)b 
Downtime 
(d)a keff 
a sa 
AENCFc 
(MeV) CCd 
TMI1 0.0 (Cy 1) [2.06, 2.75, 0.00 0.0 1.00141 0.00042 0.2353 3a, 3b, 
3.05] 3c, 3d 
TMI2 0.0 (Cy 5) 2.64, 2.85, 10.33 2,420.0 0.99088 0.00046 0.2476 
[2.85] 
TMI3 114.4 (Cy 5) 2.64, 2.85 13.87 32.2 0.99162 0.00048 0.2498 
NOTES: a Values are from CRWMS M&O 1998d, p. 41. 
bSimple average of statepoint assemblies nodal height weighted averages from Wimmer 2001, Sections 3 
and 4. 
c Values are from CRWMS M&O 1999b, pp. 60, 61, and 64 to 66. 
dCC = configuration class applicability (IP-). 
III.2.1.3 Sequoyah Unit 2 
The Sequoyah Unit 2 plant operated by Tennessee Valley Authority Nuclear is a 1148 MWe 
Westinghouse PWR with 193 fuel assemblies. The fuel assemblies are the Westinghouse 1717 
design type. A total of three CRC experiments have been evaluated for Sequoyah Unit 2 
(CRWMS M&O 1998d, p. 29). 
Table III-5 provides some general information about the Sequoyah Unit 2 CRC experiments. 
The information includes the statepoint cycle length in EFPD, the core average burnup, the initial 
weight percent enrichments of the fuel batches in the core during the CRC experiment (fresh fuel 
is identified by [] around the enrichment values), the down time in days since the core was last 
at power before restarting, along with the calculated keff values, sigma, and AENCF. The pin 
pitch for the assemblies from this reactor was 1.25984 cm, which results in a moderator-to-fuel 
volume ratio of 1.6 (CRWMS M&O 1998f, p. 7). 
CAL-DS0-NU-000003 REV 00A III-6 September 2004 

Criticality Model 
Table III-5. General Sequoyah Unit 2 CRC Statepoint Information 
Case 
Cycle Length 
to Statepoint 
(EFPD, Cycle)a 
Initial 
Enrichments 
(wt. % 235U)a 
Core Average 
Burnup 
(GWd/MTU)b 
Downtime 
(d)a keff 
a sa 
AENCFc 
(MeV) CCd 
SQ1 0.0 (Cy 1) [2.10, 2.60, 0.00 0.0 0.99631 0.00043 0.2374 3a, 3b, 
3.10] 3c, 3d 
SQ2 0.0 (Cy 3) 2.60, 3.10, 
3.50, [3.60, 
3.80] 
11.11 81.0 0.99158 0.00044 0.2518 
SQ3 210.9 (Cy 3) 2.60, 3.10, 
3.50, 3.60, 
19.20 995.7 0.99180 0.00050 0.2555 
3.80 
NOTES: aValues are from CRWMS M&O 1998d, p. 41. 
bSimple average of statepoint assemblies nodal height weighted averages from CRWMS M&O 1998f, 
Sections 3 and 4. 
c Values are from CRWMS M&O 1999b, pp. 60, 61, and 64 to 66. 
dCC = configuration class applicability (IP-). 
III.2.1.4 McGuire Unit 1 
The McGuire Unit 1 plant operated by Duke Power Company is a 1129 MWe Westinghouse 
PWR with 193 fuel assemblies. The fuel assemblies are the Westinghouse 17  17 design type. 
A total of six CRC experiments have been evaluated for McGuire Unit 1 (CRWMS M&O 1998d, 
p. 25). 
Table III-6 provides some general information about the McGuire Unit 1 CRC experiments. The 
information includes the statepoint cycle length in EFPD, the core average burnup, the initial 
weight percent enrichments of the fuel batches in the core during the CRC experiment (fresh fuel 
is identified by [] around the enrichment values), the down time in days since the core was last 
at power before restarting, along with the calculated keff values, sigma, and AENCF. The pin 
pitch for the assemblies from this reactor was 1.25984 cm, which results in a moderator-to-fuel 
volume ratio between 1.7 and 1.9 (CRWMS M&O 1998e, p. 7). 
Table III-6. General McGuire Unit 1 CRC Statepoint Information 
Case 
Cycle Length 
to Statepoint 
(EFPD, Cycle)a 
Initial 
Enrichments 
(wt. % 235U)a 
Core 
Average 
Burnup 
(GWd/MTU)b 
Downtime 
(d)a keff 
a sa 
AENCFc 
(MeV) CCd 
MG1 0.0 (Cy 1) [2.108, 2.601, 0.00 0.0 0.99946 0.00045 0.2390 3a, 3b, 
3.106] 3c, 3d 
MG2 0.0 (Cy 6) 2.92, 3.204, 11.67 78.0 0.98541 0.00050 0.2351 
3.40, [3.60] 
MG3 62.4 (Cy 6) 2.92, 3.204, 14.34 62.7 0.98771 0.00049 0.2375 
3.40, 3.60 
MG4 0.0 (Cy 7) 2.92, 3.204, 10.76 130.0 0.98954 0.00047 0.2362 
3.40, 3.60, 
[3.75] 
CAL-DS0-NU-000003 REV 00A III-7 September 2004 

Criticality Model 
Table III-6. General McGuire Unit 1 CRC Statepoint Information (Continued) 
Case 
Cycle Length 
to Statepoint 
(EFPD, Cycle)a 
Initial 
Enrichments 
(wt. % 235U)a 
Core 
Average 
Burnup 
(GWd/MTU)b 
Downtime 
(d)a keff 
a sa 
AENCFc 
(MeV) CCd 
MG5 129.0 (Cy 7) 2.92, 3.204, 
3.40, 3.60, 
16.14 29.6 0.99175 0.00046 0.2388 
3.75 
MG6 282.3 (Cy 7) 2.92, 3.204, 22.54 18.8 0.98723 0.00049 0.2426 
3.40, 3.60, 
3.75 
NOTES: aValues are from CRWMS M&O 1998d, p. 41. 
b 
Simple average of statepoint assemblies nodal height weighted averages from CRWMS M&O 1998e, 
Sections 3 and 4. 
c 
Values are from CRWMS M&O 1999b, pp. 60, 61, and 64 to 66. 
d 
CC = configuration class applicability (IP-). 
III.2.1.5 Grand Gulf Unit 1 
The Grand Gulf Unit 1 plant operated by Entergy Operations Inc is a 3833 MWt General Electric 
BWR with 800 8x8 and 9x9 fuel assemblies. A total of 16 CRC statepoints have been evaluated 
for Grand Gulf Unit 1 (Harwell 2003, p. 78). 
Table III-7 provides some general information about the Grand Gulf Unit 1 CRC experiments. 
The information includes the statepoint cycle length in EFPD, the core average burnup, the initial 
weight percent enrichments of the fuel batches in the core during the CRC experiment (fresh fuel 
is identified by [] around the enrichment values), the down time in days since the core was last 
at power before restarting, along with the calculated keff values, sigma, and AENCF. 
Table III-7. General Grand Gulf Unit 1 CRC Statepoint Information 
Case 
Cycle Length 
to Statepoint 
(EFPD, Cycle)a 
Initial 
Enrichments 
(Wt. % 235U)a 
Core 
Average 
Burnup 
(MWd/MTU)c 
Downtime 
(d)b keff s 
AENCF 
(MeV) CCd 
SP5 0.0 (Cy 4) 2.81, 3.01, 
[3.25, 3.37] 11 41.4 0.99554 0.0001 0.1737 
SP6 4.01 (Cy 4) 2.81, 3.01, 
3.25, 3.37 11 17.7 0.99324 0.0001 0.1762 
SP7 73.49 (Cy 4) 2.81, 3.01, 
3.25, 3.37 13 8.5 0.99296 0.0001 0.1785 
SP10 0.0 (Cy 5) 3.01, 3.25, 
3.37, [3.42] 13 55.8 0.99461 0.0001 0.1733 
SP11 16.54 (Cy 5) 3.01, 3.25, 
3.37, 3.42 13 11.4 0.99810 0.0001 0.1763 
CAL-DS0-NU-000003 REV 00A III-8 September 2004 

Criticality Model 
Table III-7. General Grand Gulf Unit 1 CRC Statepoint Information (Continued) 
Case 
Cycle Length 
to Statepoint 
(EFPD, Cycle)a 
Initial 
Enrichments 
(Wt. % 235U)a 
Core 
Average 
Burnup 
(MWd/MTU)c 
Downtime 
(d)b keff s 
AENCF 
(MeV) CCd 
SP12 148.27 (Cy 5) 3.01, 3.25, 17 4.8 0.98685 0.0001 0.1813 3a, 3b, 
3.37, 3.42 3c, 3d 
SP13 165.29 (Cy 5) 3.01, 3.25, 
3.37, 3.42 
17 3.5 0.98551 0.0001 0.1812 
SP14 203.58 (Cy 5) 3.01, 3.25, 
3.37, 3.42 
18 7.7 0.98295 0.0001 0.1807 
SP15 340.41 (Cy 5) 3.01, 3.25, 
3.37, 3.42 
22 10.3 0.98309 0.0001 0.1811 
SP16 0.0 (Cy 6) 3.25, 3.37, 13 48.3 0.99875 0.0001 0.1727 
3.42, [2.94, 
3.38] 
SP18 0.0 (Cy 7) 2.94, 3.38, 
3.42, [3.20, 
3.42] 
14 60.0 0.98993 0.0001 0.1733 
SP19 108.81 (Cy 7) 2.94, 3.20, 17 5.8 0.98249 0.0001 0.1915 
3.38, 3.42 
SP20 245.05 (Cy 7) 2.94, 3.20, 
3.38, 3.42 
20 3.9 0.96644 0.0001 0.1900 
SP21 0.0 (Cy 8) 2.94, 3.20, 13 56.2 0.99211 0.0001 0.1740 
3.38, 3.42, 
[3.07, 3.56] 
SP22 0.0 (Cy 8) 2.94, 3.20, 
3.38, 3.42, 
13 3.8 0.99380 0.0001 0.1748 
[3.07, 3.56] 
SP23 17.59 (Cy 8) 2.94, 3.07, 
3.20, 3.38, 
14 4.4 0.98986 0.0001 0.1783 
3.42, 3.56 
a
NOTES: Values are from Punatar (2001b, pp. 3-1 and 3-2). 
bValues are from Harwell (2003, p. 10). 
c Values are from Massie (2003, Table 2). 
dCC = configuration class applicability (IP-). 
III.2.2 Lattice Laboratory Critical Experiments 
The fresh fuel LCEs presented in this section represent moderated lattice configurations 
containing fissile oxide fuel. Each of the LCE configurations described in this section has been 
analyzed with the MCNP code system and used a water-scattering kernel corresponding to a 
temperature of 300 K. An experiment identifier for each benchmark configuration is provided 
for subsequent reference. The keff, s, and AENCF values for each of the LCEs described in the 
following sections were taken from Section 4 of Summary Report of Laboratory Critical 
Experiment Analyses Performed for the Disposal Criticality Analysis Methodology (CRWMS 
M&O 1999a). 
In the subsequent tables the P/D term represents the pin pitch to pin outer diameter ratio and CC 
indicates configuration class applicability (IP-). 
CAL-DS0-NU-000003 REV 00A III-9 September 2004 

Criticality Model 
III.2.2.1 Critical Configurations of Subcritical Clusters of 2.35 Weight Percent Enriched 
UO2 Rods in Water with Fixed Neutron Absorber Plates 
Experiments with subcritical clusters of low-enrichment UO2 fuel rods were performed at the 
Pacific Northwest Laboratory (PNL) and documented by Bierman et al. (1977). The four 
experiments represented with MCNP consisted of three rectangular arrays of aluminum-clad fuel 
rods. The fuel rods comprising the arrays had a uniform enrichment of 2.35 weight percent 235U 
with a 2.032 cm pitch and pellet and cladding outer diameters of 1.12 and 1.27 cm, respectively 
(Bierman et al. 1977, p. 7). The three arrays of fuel were arranged in a row and, in three of the 
experiments, sheets of neutron poison were interposed between adjacent arrays. The pertinent 
differences among these four experiments are shown in Table III-8F. These critical experiments 
help demonstrate the ability of MCNP to accurately predict the critical multiplication factor for 
configurations containing light-water reactor fuel separated by absorber plates. 
Table III-8. Clusters of 2.35 Weight Percent 235U-Enriched UO2 Fuel Rods with Different Absorber 
Plates 
Exp ID Interposed plate P/D keff s AENCF (MeV) CC 
exp1 None 1.81 1.00084 0.00088 0.12095 2a, 3a, 3b, 
3c, 3d, 4a 
exp2 BoralTM 1.81 0.99842 0.00088 0.12469 1a, 1b, 2a, 
3a, 3b, 3c, 
3dexp3 Aluminum Type 6061 1.81 0.99898 0.00089 0.12172 
exp4 Stainless Steel Type 304 1.81 1.00104 0.00087 0.12003 
III.2.2.2 Water-Reflected Fuel Rod Clusters in Square Pitched Arrays 
A series of critical experiments with clusters of aluminum clad UO2 fuel rods in a large 
water-filled tank was performed over a period of several years at the Critical Mass Laboratory at 
PNL. Eight cases were analyzed under this category that correspond to water-reflected clusters 
at 2.032 cm square pitch with no absorber plates, reflecting walls, dissolved poison, or 
gadolinium impurity. Table III-9 provides a brief description of the experiments that come from 
International Handbook of Evaluated Criticality Safety Benchmark Experiments (NEA 1998, 
Volume IV, LEU-COMP-THERM-001, p. 10). Each of the experiments used 2.35 weight 
percent 235U-enriched UO2 fuel with an average loading of 17.08 g of 235U per rod, with pellet 
and cladding outer diameters of 1.12 and 1.27 cm, respectively (NEA 1998, 
LEU-COMP-THERM-001, Volume IV, pp. 7 and 21). 
Table III-9. Water-Reflected Fuel Rod Cluster Critical Experiments 
Description 
Number of Rodsa (XY),Number of AENCF 
Exp ID Clusters, Cluster Separation P/D keff s (MeV) CC 
Case 1 2018.08, 1 cluster 1.81 0.99436 0.00167 0.1229 1a, 2a, 
3a, 3b, 
3c, 3d, 4aCase 2 2017, 3 clusters, 11.92  0.04 cm 
separation 
1.81 0.99445 0.00158 0.1223 
Case 3b 2016, 3 clusters, 8.41  0.05 cm 1.81 0.99982 0.00159 0.1200 
separation 
Case 4 2016 (center), 2216 (two outer), 3 1.81 0.99313 0.00161 0.1222 
clusters, 10.05  0.05 cm separation 
CAL-DS0-NU-000003 REV 00A III-10 September 2004 

Criticality Model 
Table III-9. Water-Reflected Fuel Rod Cluster Critical Experiments (Continued) 
Description 
Number of Rodsa (XY),Number of AENCF 
Exp ID Clusters, Cluster Separation P/D keff s (MeV) CC 
Case 5 2015, 3 clusters, 6.39  0.05 cm 1.81 0.99310 0.00169 0.1204 
separation 
Case 6 2015 (center), 2415 (two outer), 1.81 0.99831 0.00158 0.1221 
3 clusters, 8.01  0.06 cm separation 
Case 7 2014, 3 clusters, 4.46  0.10 cm 1.81 0.99261 0.00138 0.1211 
separation 
Case 8c 196, 3 clusters, 7.57  0.04 cm 1.81 0.99888 0.00151 0.1209 
separation 
NOTES: aFor three-cluster configurations, the first dimension is along the direction of the cluster placement. The 
second dimension is the width of facing sides, as shown in Figure 5 of NEA 1998, Volume IV, p. 11 
LEU-COMP-THERM-001. 
b 
The cluster separation referenced was 8.41 cm, but footnote (d) in NEA 1998, Volume IV, 
LEU-COMP-THERM-001, p. 10, states that the cluster separation should be 0.762 cm less. Thus, 7.648 
cm was represented in the MCNP case for the cluster separation. 
c 
The cluster separation referenced was 7.57 cm, but footnote (d) in NEA 1998, Volume IV, 
LEU-COMP-THERM-001, p. 10, states that the cluster separation should be 0.762 cm less. Thus, 6.808 
cm was represented in the MCNP case for the cluster separation. 
III.2.2.3 Critical Configurations with Subcritical Clusters of 4.31 Weight Percent 
Enriched UO2 Rods in Water with Reflecting Walls 
Three experiments were performed at PNL and are documented in Bierman et al. (1981) and 
Bierman and Clayton (1981). In these experiments three similar fuel assemblies were laterally 
surrounded by reflectors of different compositions. The fuel lattices in each critical experiment 
contained 4.31 weight percent 235U-enriched UO2 fuel rods on a square pitch of 1.892 cm. The 
distinguishing characteristics of each experiment are given in Table III-10. 
Table III-10. Clusters of 4.31 Weight Percent 235U-Enriched UO2 Fuel Rods with Different Reflectors 
Exp ID Reflector P/D keff s AENCF (MeV) CC 
exp5 uranium 1.50 1.00037 0.00107 0.27968 1a, 1b, 2a, 3a, 
3b, 3c, 3d, 4aexp6 lead 1.50 0.99675 0.00103 0.17662 
exp7 stainless steel 1.50 0.99724 0.00111 0.1784 
III.2.2.4 Critical Configurations with 4.31 Weight Percent 235U-Enriched UO2 Rods in 
Highly Borated Water Lattices 
A set of four experiments was performed at PNL and documented by Durst et al. (1982). These 
experiments used 4.31 weight percent 235U-enriched UO2 fuel rods arranged in square-pitch, 
water-moderated lattices of different size with various amounts of boric acid in the moderator. 
The characteristics of each of these experiments is provided in Table III-11. 
CAL-DS0-NU-000003 REV 00A III-11 September 2004 

Criticality Model 
Table III-11. Configurations with 4.31 Weight Percent 235U-Enriched UO2 Fuel Rods in Highly Borated 
Water Lattices 
Exp ID 
Description 
Pitch, # of Fuel Rods, Moderator P/D keff s 
AENCF 
(MeV) CC 
exp8 1.89 cm, 357, nonborated water 1.50 1.00719 0.00110 0.17735 1a, 1b, 3a, 
3b, 3c, 3d, 
4a, 4b, 5a, 
6a 
exp9 1.89 cm, 1237, water with 2.55 g/l of boron 1.50 1.00827 0.00099 0.22171 
exp10 1.715 cm, 509, nonborated water 1.36 1.00660 0.00174 0.2239 
exp11 1.715 cm, 1192, water with 2.55 g/l of boron 1.36 1.00358 0.00157 0.26643 
III.2.2.5 Critical Configurations with Neutron Flux Traps 
PNL performed experiments studying the effect of neutron flux traps on criticality. These 
experiments were documented by Bierman (1990) and served as the source for 
two configurations represented with MCNP. These two critical experiments were each 
composed of four fuel rod arrays arranged in a square and separated by a neutron flux trap 
region. Each fuel lattice in a given configuration was nearly equal in size. The fuel rods were 
composed of aluminum-clad 4.31 weight percent 235U-enriched UO2 fuel rods with a 1.891 cm 
pitch. The neutron flux traps were created by positioning two plates of BoralTM between 
interacting faces of each fuel lattice. The experimental configurations were moderated and 
closely reflected by full-density water. A brief description of these experiments is provided in 
Table III-12. 
Table III-12. Configurations with Neutron Flux Traps 
Exp ID Configuration Description P/D keff s 
AENCF 
(MeV) CC 
exp12 952 rods arranged in three 1516 arrays, 
one 1515 array, and a 1515 array with a 
partial row of 7 rods 
1.49 1.00546 0.00108 0.19461 1a, 2a, 3a, 
3b, 3c, 3d, 
4a, 4b, 5a, 
6aexp13 862 rods arranged in two 1415 arrays, one 1.49 1.00371 0.00113 0.19421 
1515 array, and a 1415 array with a 
partial fifteenth row of 7 fuel rods 
III.2.2.6 Electric Power Research Institute 2.35 Weight Percent 235U-Enriched Light 
Water Reactor Fuel Critical Configurations 
Criticality experiments were sponsored by Electric Power Research Institute (EPRI) for light 
water reactor fuel configurations. These were documented by EPRI and subsequently described 
in Analysis of Fresh Fuel Critical Experiments Appropriate for Burnup Credit Validation 
(ORNL 1995, p. 52). Two critical experiment configurations composed of water-moderated 
lattices of 2.35 weight percent 235U-enriched UO2 fuel rods were represented with MCNP. The 
fuel rods were supported in a core structure composed of "eggcrate" type lattice plates with an 
upper lead shield. The configuration was closely reflected by full-density water laterally and 
below the fuel. These experiments are shown in Table III-13. 
CAL-DS0-NU-000003 REV 00A III-12 September 2004 

Criticality Model 
Table III-13. EPRI 2.35 Weight Percent 235U-Enriched UO2 Critical Configurations 
Exp ID 
Description 
Pitch, # of Fuel Rods P/D keff s 
AENCF 
(MeV) CC 
exp14 1.562 cm, 708a 1.40 0.99593 0.00099 0.20945 1a, 2a, 3a, 
3b, 3c, 3d, 4aexp15 2.210 cm, 342 1.98 1.00074 0.00087 0.10984 
a
NOTE: The MCNP representation used 709 rods due to symmetry used in the input specifications. 
III.2.2.7 Water-Moderated, Lead-Reflected Uranium Dioxide Rod Array 
This case is documented in International Handbook of Evaluated Criticality Safety Benchmark 
Experiments (NEA 1998, Volume IV, LEU-COMP-THERM-027, Sections 1, 2, and 3), and 
consisted of a 1414 array of 4.74 weight percent 235U-enriched UO2 fuel rods reflected on 
four sides by 30 cm-thick lead reflectors with no water gap between the array and the lead 
reflectors. This experiment was denoted as lct27-1 with relevant information listed in 
Table III-14. The experiment was a subcritical approach extrapolated to critical; the neutron 
multiplication factor reached is within 0.1 percent of 1.000. The experiments were tests of the 
lead reflector effect. 
Table III-14. Lead-Reflected UO2 Rod Array Critical Experiment 
Exp ID Pitch P/D keff s 
AENCF 
(MeV) CC 
lct27-1 1.6 cm 2.03 1.0157 0.0005 0.1025 1a, 1b, 2a, 3a, 
3b, 3c, 3d, 4a 
III.2.2.8 Laboratory Critical Experiments from the Urania-Gadolinia: Nuclear Model 
Development and Critical Experiment Benchmark Report 
A number of critical experiments were performed by B&W for urania fuel incorporating 
gadolinia as an integral burnable absorber. These experiments were documented in Newman 
(1984). The configurations represented with MCNP included critical configurations containing 
arrangements of 2.46 weight percent 235U-enriched UO2 fuel rods, 4.02 weight percent 
235U-enriched UO2 fuel rods, combination 4 weight percent Gd2O3 and 96 weight percent 
(1.944 weight percent 235U-enriched) UO2 fuel rods, Ag-In-Cd absorber rods, and B4C absorber 
rods. The central 45  45 array of rod lattice cells was separated into nine 15  15 arrays of rod 
lattice cells with a square pitch of 1.636 cm (0.644 in. [Newman 1984, p. 3-1]). The 
moderator-to-fuel volume ratio was between 2.7 and 3.2 depending on the fuel rod enrichment, 
which was calculated based on pitch and pellet dimensions from Newman (1984, pp. 3-6 
and 3-7). These arrays were intended to simulate pressurized water reactor fuel assembly 
lattices. 
Descriptions of the experimental configurations are provided in Table III-15. 
CAL-DS0-NU-000003 REV 00A III-13 September 2004 

Criticality Model 
Table III-15. Urania-Gadolinia Critical Experiments 
Mod. 
Boron 
Exp 
ID Descriptiona 
Conc. 
(ppm) P/D keff s 
AENCF 
(MeV) CC 
A B C D E F G 
ugd1 4808 0 0 0 0 0 153 1337.9 1.59 1.00033 0.00143 0.20132 2a, 3a, 
3b, 3c, 
3d, 4augd2 4808 0 0 0 16 0 137 1250.0 1.59 0.99945 0.00145 0.19828 
ugd3 4788 0 20 0 0 0 153 1239.3 1.59 1.00054 0.00147 0.19948 
ugd4 4788 0 20 0 16 0 137 1171.7 1.59 1.00193 0.0015 0.19985 
ugd5 4780 0 28 0 0 0 153 1208.0 1.59 0.99955 0.00154 0.19752 
ugd6 4780 0 28 0 16 0 137 1155.8 1.59 0.99996 0.00152 0.19775 
ugd7 4780 0 28b 0 0 0 153 1208.8 1.59 1.0041 0.00148 0.19675 
ugd8 4772 0 36 0 0 0 153 1170.7 1.59 0.99929 0.00154 0.19756 
ugd9 4772 0 36 0 16 0 137 1130.5 1.59 1.00135 0.00156 0.19873 
ugd10 4772 0 36 0 0 16 137 1177.1 1.59 0.9979 0.00144 0.2011 
ugd12 3920 888 0 0 0 0 153 1899.3 1.56 0.9994 0.00161 0.20965 
ugd13 3920 888 0 16 0 0 137 1635.4 1.56 1.00049 0.00155 0.20841 
ugd14 3920 860 28 0 0 0 153 1653.8 1.56 1.00066 0.00156 0.20416 
ugd15 3920 860 28 16 0 0 137 1479.7 1.56 1.00158 0.00151 0.2056 
ugd16 3920 852 36 0 0 0 153 1579.4 1.56 1.00335 0.00151 0.20648 
ugd17 3920 852 36 16 0 0 137 1432.1 1.56 0.99912 0.00151 0.20341 
ugd18 3676 944 0 0 0 0 180 1776.8 1.56 0.99876 0.0015 0.20851 
ugd19 3676 928 16 0 0 0 180 1628.3 1.56 1.00133 0.00153 0.21011 
ugd20 3676 912 32 0 0 0 180 1499.0 1.56 1.00322 0.00153 0.20698 
NOTES: aDescription column designations are as follows: 
A - Number of 2.46 weight percent 235U fuel rods. 
B - Number of 4.02 weight percent 235U fuel rods. 
C - Number of Gd2O3 fuel rods. 
D - Number of B4C rods. 
E - Number of Ag-In-Cd rods. 
F - Number of void rods. 
G - Number of water holes. 
bAnnular Gd2O3 fuel rods. 
III.2.2.9 Saxton UO2 and PuO2-UO2 Critical Configurations 
Single-and multi-region uranium and plutonium oxide fueled cores, water moderated, clean, and 
borated, have been used in a series of critical experiments at the Westinghouse Reactor 
Evaluation Center in support of the Saxton Plutonium Program. In this series of experiments, 
criticality was achieved entirely by varying the water level inside the core tank. The fuel used in 
the experiments was UO2 fuel with 5.74 weight percent 235U enrichment and mixed oxide 
(MOX) fuel containing 6.6 weight percent PuO2 and natural enriched UO2 (Taylor 1965, p. A-1). 
This work was documented by Taylor (1965) and subsequently described in Analysis of Fresh 
Fuel Critical Experiments Appropriate for Burnup Credit Validation (ORNL 1995, pp. 52 
and 60). This section includes eight single-region configurations and six multiregion 
configurations. The fuel rod type, pitch, array size, moderator height, and boron concentration 
CAL-DS0-NU-000003 REV 00A III-14 September 2004 

Criticality Model 
were adjusted in each LCE. Table III-16 presents a description of the various single-region 
experiments, and Table III-17 presents a description of the multiregion experiments. 
Table III-16. Saxton Single-Region Critical Configurations 
Exp ID Description P/D keff s 
AENCF 
(MeV) CC 
ssr83 Fuel: UO2; Pitch: 1.3208 cm; 
Configuration: 449 cylindrical; Critical 
water height: 95.25 cm 
1.46 0.99299 0.00074 0.18197 1a, 2a, 
3a, 3b, 
3c, 3d, 4a 
ssr48 Fuel: UO2; Pitch: 1.4224 cm; 
Configuration: 1919 square; Critical 
water height: 83.71 cm 
1.57 0.9939 0.00071 0.15568 
ssr70 Fuel: MOX; Pitch: 1.3208 cm; 
Configuration: 2223 square; Critical 
water height: 84.56 cm 
1.54 0.99543 0.00072 0.2295 
ssr57 Fuel: MOX; Pitch: 1.4224 cm; 
Configuration: 1919 square; Critical 
water height: 82.46 cm 
1.66 0.99807 0.00075 0.1938 
ssr27 Fuel: MOX; Pitch: 1.4224 cm; 
Configuration: 2121 square; Critical 
water height: 89.70 cm 
1.66 0.99881 0.00082 0.2015 
ssr66 Fuel: MOX; Pitch: 1.8669 cm; 
Configuration: 1313 square; Critical 
water height: 70.11 cm 
2.18 1.00308 0.00073 0.1183 
ssr53 Fuel: MOX; Pitch: 2.0117 cm; 
Configuration: 1212 square; Critical 
water height: 78.43 cm 
2.35 1.00454 0.00066 0.1065 
ssr74 Fuel: MOX; Pitch: 2.6416 cm; 
Configuration: 1111 square; Critical 
water height: 81.17 cm 
3.08 1.00505 0.00068 0.079 
CAL-DS0-NU-000003 REV 00A III-15 September 2004 

Criticality Model 
Table III-17. Saxton Multiregion Critical Configurations 
Exp ID Description P/D keff s 
AENCF 
(MeV) CC 
smr1 Configuration: 1919 square - 1111 
MOX center region, UO2 outer region; 
Critical water height: 91.07 cm 
1.60 0.99783 0.00073 0.1715 1a, 2a, 
3a, 3b, 
3c, 3d, 4a 
smr9 Configuration: 1919 square  1111 
MOX center region, UO2 outer region 
with Al plate at the fuel interface; 
Critical water height: 92.07 cm 
1.60 0.99683 0.00078 0.1673 
smr5 Configuration: 2727 square - 1919 
UO2 center region, MOX outer region; 
Critical water height: 86.70 cm 
1.61 0.99349 0.00073 0.1919 
smr11 Configuration: 2727 square  1919 
MOX center region, UO2 outer region 
with water slot at the region boundary; 
Critical water height: 99.80 cm 
1.61 0.99783 0.00078 0.0205 
smr12 Configuration: 2727 square - 1919 
MOX center region, UO2 outer region 
with Al slab at the interface; 
1.61 0.99992 0.0008 0.2049 
Critical water height: 106.35 cm 
smr8 Configuration: 2727 square - 1919 
MOX center region, UO2 outer region 
with L shaped UO2 insert in MOX 
region; Critical water height: 92.19 cm 
1.61 0.99956 0.00068 0.2051 
III.2.2.10 Critical Configurations Simulating Light Water Reactor Fuel in Close Proximity 
Pool Storage 
B&W performed experiments simulating neutron multiplication in pool storage racks. These 
were documented in Baldwin et al. (1979). Nineteen such critical configurations, each 
containing a 33 array of 1414 fuel rod assemblies with a square pin pitch of 1.636 cm 
(0.644 in. [Baldwin et al. 1979, p. 3-3]), were represented with MCNP. The gaps between 
assemblies contained a number of B4C rods and water, stainless steel sheets and water, borated 
aluminum sheets and water, or only water. The fuel rods were composed of 2.46 weight percent 
235U-enriched UO2 clad in Aluminum Type 6061 with a diameter of 1.03 cm (Baldwin et al. 
1979, p. 8-2). The B4C rods were aluminum tubes filled with B4C powder. Six sets of borated 
aluminum sheets were used in the critical experiments. The soluble boron concentration and 
moderator heights were adjusted to obtain a critical configuration. The key parameters that 
distinguish the twenty critical configurations are shown in Table III-18. 
CAL-DS0-NU-000003 REV 00A III-16 September 2004 

Criticality Model 
Table III-18. Close Proximity Critical Benchmarks 
Exp ID Description P/D keff s 
AENCF 
(MeV) CC 
core2 Assembly spacing (pin pitch): 0; # B4C rods: 0; Metal 
between unit assemblies: N/A 
1.59 1.00058 0.00159 0.19988 1a, 2a, 
3a, 3b, 
3c, 3d, 
4acore3 Assembly spacing (pin pitch): 1; # B4C rods: 0; Metal 
between unit assemblies: N/A 
1.59 1.00019 0.00148 0.18078 
core4 Assembly spacing (pin pitch): 1; # B4C rods: 84; 
Metal between unit assemblies: N/A 
1.59 0.9948 0.0015 0.17908 
core5 Assembly spacing (pin pitch): 2; # B4C rods: 64; 
Metal between unit assemblies: N/A 
1.59 0.99445 0.00153 0.16919 
core6 Assembly spacing (pin pitch): 2; # B4C rods: 64; 
Metal between unit assemblies: N/A 
1.59 0.99556 0.00152 0.17216 
core7 Assembly spacing (pin pitch): 3; # B4C rods: 34; 
Metal between unit assemblies: N/A 
1.59 0.99463 0.00151 0.15963 
core8 Assembly spacing (pin pitch): 3; # B4C rods: 34; 
Metal between unit assemblies: N/A 
1.59 0.98895 0.00149 0.16496 
core9 Assembly spacing (pin pitch): 4; # B4C rods: 0; Metal 
between unit assemblies: N/A 
1.59 0.99298 0.00144 0.15528 
core10 Assembly spacing (pin pitch): 3; # B4C rods: N/A; 
Metal between unit assemblies: None 
1.59 0.99511 0.00148 0.16036 
core11 Assembly spacing (pin pitch): 1; # B4C rods: N/A; 
Metal between unit assemblies: SS 
1.59 0.99699 0.00148 0.17893 
core12 Assembly spacing (pin pitch): 2; # B4C rods: N/A; 
Metal between unit assemblies: SS 
1.59 0.99549 0.00151 0.16671 
core13 Assembly spacing (pin pitch): 1; # B4C rods: N/A; 
Metal between unit assemblies: B/Al set 5 
1.59 0.99933 0.00151 0.18075 
core15 Assembly spacing (pin pitch): 1; # B4C rods: N/A; 
Metal between unit assemblies: B/Al set 3 
1.59 0.99107 0.00157 0.18348 
core16 Assembly spacing (pin pitch): 2; # B4C rods: N/A; 
Metal between unit assemblies: B/Al set 3 
1.59 0.99041 0.0015 0.16952 
core17 Assembly spacing (pin pitch): 1; # B4C rods: N/A; 
Metal between unit assemblies: B/Al set 2 
1.59 0.99365 0.00151 0.18187 
core18 Assembly spacing (pin pitch): 2; # B4C rods: N/A; 
Metal between unit assemblies: B/Al set 2 
1.59 0.9947 0.0015 0.16855 
core19 Assembly spacing (pin pitch): 1; # B4C rods: N/A; 
Metal between unit assemblies: B/Al set 1 
1.59 0.99383 0.00153 0.18354 
core20 Assembly spacing (pin pitch): 2; # B4C rods: N/A; 
Metal between unit assemblies: B/Al set 1 
1.59 0.99392 0.00151 0.16933 
core21 Assembly spacing (pin pitch): 3; # B4C rods: N/A; 
Metal between unit assemblies: B/Al set 1 
1.59 0.9916 0.0014 0.16225 
III.2.2.11 Electric Power Research Institute Mixed Oxide Critical Configurations 
Analysis of Fresh Fuel Critical Experiments Appropriate for Burnup Credit Validation 
(ORNL 1995, p. 60) describes criticality tests with MOX fuel performed for EPRI. Six critical 
experiment configurations composed of unborated and borated water moderated lattices of 
2 weight percent PuO2 (8 weight percent plutonium-240) and 98 weight percent natural UO2 fuel 
rods were represented with MCNP. Although the relative distribution of the plutonium isotopes 
differs from that found in burned light water reactor fuel, the ratio of plutonium/235U (2.79) 
bounds that calculated for such fuel (1.01) (ORNL 1995, p. 60). The fuel rods were 1.283 cm in 
CAL-DS0-NU-000003 REV 00A III-17 September 2004 

Criticality Model 
diameter (ORNL 1995, p. 65), clad with aluminum, and supported in a core structure composed 
of "eggcrate" type lattice plates with an upper lead shield. The configurations were closely 
reflected with full-density water laterally and below the core. These experiments are denoted as 
exp22 through exp27 and brief descriptions of the variations are provided in Table III-19. 
Table III-19. EPRI Mixed Oxide Critical Configurations 
Exp ID Description P/D keff s AENCF (MeV) CC 
exp22 Pitch =1.778 cm, 469 fuel rods, 
unborated water moderator 
1.39 0.99624 0.00174 0.25557 1a, 2a, 
3a, 3b, 
3c, 3d, 4aexp23 Pitch =1.778 cm, 761 fuel rods, 680.9 
ppm borated water moderator 
1.39 1.0005 0.00169 0.27397 
exp24 Pitch =2.210 cm, 197 fuel rods, 
unborated water moderator 
1.72 1.00302 0.00171 0.16128 
exp25 Pitch =2.210 cm, 761 fuel rods, 1090.4 
ppm borated water moderator 
1.72 1.00835 0.00161 0.18944 
exp26 Pitch =2.515 cm, 160 fuel rods, 
unborated water moderator 
1.96 1.00709 0.0016 0.13192 
exp27 Pitch =2.515 cm, 689 fuel rods, 767.2 
ppm borated water moderator 
1.96 1.00752 0.00155 0.15372 
III.2.2.12 Critical Triangular Lattice of MOX and UO2 Fuel Rods 
Bierman et al. (1984) documented critical experiments performed at PNL incorporating both 
urania and MOX fuel rods in a triangular lattice. One such experiment, designated exp34, 
contained a triangular lattice of uniformly distributed PuO2-UO2 and UO2 fuel rods. The fuel 
rods were placed in a uniform distribution with a plutonium/235U ratio approximating that of a 
20,000 MWd/MTU burnup. Each PuO2-UO2 fuel rod was surrounded by six UO2 fuel rods with 
a triangular lattice pitch. The UO2 rods were 4.31 weight percent 235U-enriched, and the MOX 
fuel was 2 weight percent PuO2 and 98 weight percent natural UO2. Information for this 
experiment is provided in Table III-20. 
Table III-20. Critical Configuration of MOX and UO2 Fuel Rods in a Triangular Lattice 
Exp ID Description P/Db keff s AENCF (MeV) CC 
exp34 583 MOX fuel rods with 1174 UO2 
fuel rods with a 1.598 cm pitcha 
1.26 0.9875 0.00168 0.37762 2a, 3a, 3b, 
3c, 3d, 4a 
a
NOTES: Configuration evaluated corresponds to lattice 32 in Bierman et al. 1984, p. F.66. 
b 
Fuel pellet dimensions from Bierman et al. 1984, pp. 2.9 and 2.10. 
III.2.3 Homogeneous Solution Experiments 
The LCEs presented in this section represent solutions containing uranium, plutonium, or both 
uranium and plutonium. Each of the LCE configurations described in this section have been 
analyzed with the MCNP code system. An experiment identifier for each configuration is 
provided for subsequent reference in this document. With a few exceptions that are noted in the 
text, the assessed benchmarks come from International Handbook of Evaluated Criticality Safety 
Benchmark Experiments (NEA 1998). 
CAL-DS0-NU-000003 REV 00A III-18 September 2004 

Criticality Model 
The following sections briefly describe the LCEs according to the grouping in which the results 
are presented. 
III.2.3.1 Mixed Plutonium and Natural Uranium Nitrate Solutions 
The experiments involving plutonium and uranium with naturally occurring isotopic ratios are 
from International Handbook of Evaluated Criticality Safety Benchmark Experiments 
(NEA 1998, Volume VI) and are listed in Table III-21. 
Table III-21. Configurations Incorporating Mixed Plutonium and Natural Uranium Nitrate Solutions 
Exp ID Description keff s 
AENCF 
(MeV) CC 
Water Reflected Annular Cylindrical Tank with Central Bottle and Annular Inserts (NEA 1998, Volume VI, 
MIX-SOL-THERM-001, Sections 1, 2, and 3) 
PNL3187 102.19 g Pu/l, 365.20 g U/l, 2% B4C Concrete 
Annulus, No Bottle, CH: 48.55 cm, H/239Pu 
(annular tank) = 234, 91.118 wt. % 239Pu in Pu 
0.99821 0.00116 0.04158 1a, 1b, 
2a, 4a, 
4b, 5a, 
6aPNL3391 103.37 g Pu/l, 363.66 g U/l, 0% B4C Concrete 
Annulus, Bottle 2, CH: 27.67 cm, H/239Pu (annular 
tank) = 231, H/239Pu (bottle) = 231, 91.118 wt. % 
239Pu in Pu 
0.99318 0.00112 0.04075 
PNL3492 103.37 g Pu/l, 363.66 g U/l, 1% B4C Concrete 
Annulus, Bottle 2, CH: 37.19 cm, H/239Pu (annular 
tank) = 225, H/239Pu (bottle) = 231, 91.117 wt. % 
239Pu in Pu 
0.99619 0.00113 0.04386 
PNL3593 107.91 g Pu/l, 379.55 g U/l, 6% B4C Concrete 
Annulus, Bottle 2, CH: 51.10 cm, H/239Pu (annular 
tank) = 220, H/239Pu (bottle) = 231, 91.117 wt. % 
239Pu in Pu 
0.99694 0.00121 0.04614 
PNL3694 108.27 g Pu/l, 380.41 g U/l, No Concrete Annulus, 
Bottle 2, CH: 32.86 cm, H/239Pu (annular tank) = 
219, H/239Pu (bottle) = 231, 91.117 wt. % 239Pu in 
Pu 
1.00275 0.00113 0.04483 
PNL3795 195.61 g Pu/l, 6.5 g U/l, 2% B4C Concrete 
Annulus, Bottle 3, CH: 27.51 cm, H/239Pu (annular 
tank) = 125, H/239Pu (bottle) = 126, 91.572 wt. % 
239Pu in Pu 
1.00302 0.00117 0.03965 
PNL3896 110.13 g Pu/l, 3.8 g U/l, 2% B4C Concrete 
Annulus, Bottle 3, CH: 25.69 cm, H/239Pu (annular 
tank) = 242, H/239Pu (bottle) = 126, 91.572 wt. % 
239Pu in Pu 
1.00263 0.0011 0.02357 
PNL3897 58.30 g Pu/l, 2.3 g U/l, 2% B4C Concrete Annulus, 
Bottle 3, CH: 28.94 cm, H/239Pu (annular tank) 
= 477, H/239Pu (bottle) = 126, 91.572 wt. % 239Pu 
in Pu 
1.00323 0.00125 0.01447 
PNL3898 72.74 g Pu/l, 247.33 g U/l, 2% B4C Concrete 
Annulus, Bottle 2, CH: 39.58 cm, H/239Pu (annular 
tank) = 354, H/239Pu (bottle) = 231, 91.117 wt 
239Pu in Pu 
1.00297 0.00118 0.02973 
CAL-DS0-NU-000003 REV 00A III-19 September 2004 

Criticality Model 
Table III-21. Configurations Incorporating Mixed Plutonium and Natural Uranium Nitrate Solutions 
(Continued) 
Exp ID Description keff s 
AENCF 
(MeV) CC 
PNL3808 47.08 g Pu/l, 161.72 g U/l, 2% B4C Concrete 
Annulus, Bottle 2, CH: 45.09 cm, H/239Pu (annular 
tank) = 569, H/239Pu (bottle) = 231, 91.117 wt. % 
239Pu in Pu 
1.00178 0.00095 0.02059 1a, 1b, 
2a, 4a, 
4b, 5a, 
6a 
PNL3999 73.64 g Pu/l, 250.30 g U/l, Polyethylene with Cd 
Cover Annulus, Bottle 2, CH: 79.18 cm, H/239Pu 
(annular tank) = 349, H/239Pu (bottle) = 349, 
91.117 wt. % 239Pu in Pu 
1.00707 0.00108 0.02933 
PNL5300 74.25 g Pu/l, 251.64 g U/l, Solid Polyethylene with 
Cd Cover Center, CH: 104.62 cm, H/239Pu 
(annular tank) = 346, 91.117 wt. % 239Pu in Pu 
1.0067 0.00105 0.02917 
Water Reflected Cylindrical Tank With a 68.68 cm Inner Diameter (ID), 91.102 wt. % 239Pu in Pu (NEA 1998, 
Volume VI, MIX-SOL-THERM-002, Sections 1, 2, and 3) 
PNL1158 11.83 g Pu/l, 11.05 g U/l, 
CH: 76.80 cm, H/239Pu = 2,403 
1.00686 0.00067 0.00393 1a, 1b, 
2a, 4a, 
4b, 5a, 
6aPNL1159 11.73 g Pu/l, 10.78 g U/l, 
CH: 83.14 cm, H/239Pu = 2,435 
1.00558 0.00064 0.0038 
PNL1161 12.19 g Pu/l, 41.04 g U/l, 
CH: 81.72 cm, H/239Pu = 2,317 
1.00751 0.00066 0.00597 
Water/Polyethylene Reflected Cylindrical Tank With Various Diameters, 93.95 wt. % 239Pu in Pu (NEA 1998, 
Volume VI, MIX-SOL-THERM-003, Sections 1, 2, and 3) 
awre1 101.3 g Pu/l, 228.5 g U/l, ID = 25.425 cm, 
CH: 56.31 cm, H/239Pu = 239 
1.01511 0.0012 0.03133 1a, 1b, 
2a, 4a, 
4b, 5a, 
6aawre2 101.3 g Pu/l, 228.5 g U/l, ID = 30.62 cm, 
CH: 29.89 cm, H/239Pu = 239 
1.01167 0.00117 0.03206 
awre3 101.3 g Pu/l, 228.5 g U/l, ID = 37.99 cm, 
CH: 21.17 cm, H/239Pu = 239 
1.01028 0.00114 0.03183 
awre4 101.3 g Pu/l, 228.5 g U/l, ID = 50.72 cm, 
CH: 16.05 cm, H/239Pu = 239 
1.00486 0.00111 0.03228 
awre5 31.58 g Pu/l, 71.3 g U/l, ID = 30.62 cm, 
CH: 46.18 cm, H/239Pu = 847 
1.00875 0.00101 0.01062 
awre6 31.58 g Pu/l, 71.3 g U/l, ID = 37.99 cm, 
CH: 28.24 cm, H/239Pu = 847 
1.01337 0.00108 0.01053 
awre7 31.58 g Pu/l, 71.3 g U/l, ID = 50.72 cm, 
CH: 20.39 cm, H/239Pu = 847 
1.0064 0.00102 0.01089 
awre8 18.61 g Pu/l, 42.2 g U/l, ID = 37.99 cm, 
CH: 72.86 cm, H/239Pu = 1461 
1.01255 0.00091 0.00684 
awre9 18.61 g Pu/l, 42.2 g U/l, ID = 50.72 cm, 
CH: 33.59 cm, H/239Pu = 1461 
1.00977 0.00088 0.00684 
awre10 17.50 g Pu/l, 39.6 g U/l, ID = 50.72 cm, 
CH: 37.16 cm, H/239Pu = 1556 
1.00839 0.00081 0.00648 
Cylindrical Tank With a 35.39 cm ID and either Water Reflector, Concrete Reflector, or No Reflector, 91.118 
wt. % 239Pu in Pu (NEA 1998, Volume VI, MIX-SOL-THERM-004, Sections 1, 2, and 3) 
PNL1577 172.56 g Pu/l, 262.79 g U/l, No Reflector, 
CH: 57.97 cm, H/239Pu = 137 
0.99645 0.00128 0.05956 1a, 1b, 
2a, 4a, 
4b, 5a, 
6aPNL1678 172.82 g Pu/l, 262.55 g U/l, Water Reflector, 
CH: 28.93 cm, H/239Pu = 136 
0.99976 0.00115 0.05069 
PNL1783 173.22 g Pu/l, 262.88 g U/l, Concrete Reflector, 
CH: 30.60 cm, H/239Pu = 136 
0.99976 0.00115 0.05386 
CAL-DS0-NU-000003 REV 00A III-20 September 2004 

Criticality Model 
Table III-21. Configurations Incorporating Mixed Plutonium and Natural Uranium Nitrate Solutions 
(Continued) 
Exp ID Description keff s 
AENCF 
(MeV) CC 
PNL1868 118.71 g Pu/l, 173.98 g U/l, Concrete Reflector, 
CH: 27.03 cm, H/239Pu = 214 
1.00247 0.00119 0.03416 1a, 1b, 
2a, 4a, 
4b, 5a, 
6a 
PNL1969 119.04 g Pu/l, 174.67 g U/l, Water Reflector, 
CH: 25.26 cm, H/239Pu = 213 
0.99967 0.00111 0.0336 
PNL2070 118.90 g Pu/l, 174.53 g U/l, No Reflector, 
CH: 41.08 cm, H/239Pu = 214 
0.99925 0.00115 0.03743 
PNL2565 41.69 g Pu/l, 63.38 g U/l, No Reflector, 
CH: 44.46 cm, H/239Pu = 664 
1.00363 0.00112 0.01295 
PNL2666 41.89 g Pu/l, 63.65 g U/l, Water Reflector, 
CH: 28.11 cm, H/239Pu = 660 
1.00337 0.00105 0.0116 
PNL2767 41.83 g Pu/l, 63.55 g U/l, Concrete Reflector, 
CH: 29.36 cm, H/239Pu = 661 
1.00629 0.00113 0.01197 
NOTE: CH = Critical Height. 
III.2.3.2 Plutonium Nitrate Solutions 
The experiments involving plutonium are from International Handbook of Evaluated Criticality 
Safety Benchmark Experiments (NEA 1998, Volume I) and are listed in Table III-22. 
Table III-22. Configurations Incorporating Plutonium Nitrate Solutions 
Exp ID Description keff 
a s 
AENCF 
(MeV) CC 
Water Reflected 11.5-Inch Diameter Spheres, 0.049-in. thick shell of Stainless Steel Type 304L, 4.57 wt. % 
240Pu in Pu, 95.12 wt. % 239Pu in Pu (NEA 1998, Volume I, PU-SOL-THERM-001, Sections 1, 2, and 3) 
pust1t1 73.0 g Pu/liter, CM: 945 gm, 
H/239Pu = 371 
1.00995 0.00102 0.01252 1a, 1b, 
2a, 4a, 
4b, 5a, 
6apust1t2 96.0 g Pu/liter, CM: 1243 gm, 
H/239Pu = 272 
1.01109 0.001 0.01702 
pust1t3 119.0 g Pu/liter, CM: 1541 gm, 
H/239Pu = 216 
1.01396 0.00094 0.02159 
pust1t4 132.0 g Pu/liter, CM: 1709 gm, 
H/239Pu = 190 
1.00643 0.00104 0.02397 
pust1t5 140.0 g Pu/liter, CM: 1813 gm, 
H/239Pu = 180 
1.01014 0.00101 0.02479 
pust1t6 268.7 g Pu/liter, CM: 3480 gm, 
H/239Pu = 91 
1.00831 0.00104 0.04809 
Water Reflected 13-Inch Diameter Spheres, 0.050-in. thick shell of Stainless Steel Type 347 Unless Otherwise 
Indicated (NEA 1998, Volume I, PU-SOL-THERM-003, Sections 1, 2, and 3) 
pu003-1 33.32 g Pu/liter, CM: 631 gm, 
H/239Pu = 788, 1.76 wt. % 240Pu 
1.00962 0.00091 0.00623 1a, 1b, 
2a, 4a, 
4b, 5a, 
6apu003-2 34.32 g Pu/liter, CM: 650 gm, 
H/239Pu = 756, 1.76 wt. % 240Pu 
1.00885 0.00091 0.00651 
pu003-3 37.43 g Pu/liter, CM: 709 gm, 
H/239Pu = 699, 3.12 wt. % 240Pu 
1.01228 0.00092 0.00693 
pu003-4 38.12 g Pu/liter, CM: 722 gm, 
H/239Pu = 682, 3.12 wt. % 240Pu 
1.00965 0.00094 0.0072 
CAL-DS0-NU-000003 REV 00A III-21 September 2004 

Criticality Model 
Table III-22. Configurations Incorporating Plutonium Nitrate Solutions (Continued) 
Exp ID Description keff 
a s 
AENCF 
(MeV) CC 
pu003-5 40.65 g Pu/liter, CM: 770 gm, 
H/239Pu = 627, 3.12 wt. % 240Pu 
1.01393 0.00092 0.00785 
pu003-6 44.09 g Pu/liter, CM: 835 gm, 
H/239Pu = 563, 3.12 wt. % 240Pu 
1.01214 0.00091 0.00845 
pu003-7 35.98 g Pu/liter, CM: 649 gm, H/239Pu = 738, 
3.12 wt. % 240Pu, 20 Gauge 2S Al Shell 
1.01369 0.00093 0.00678 
pu003-8 36.81 g Pu/liter, CM: 664 gm, H/239Pu = 714, 
3.12 wt. % 240Pu, 20 Gauge 2S Al Shell 
1.01175 0.00095 0.00703 
Water Reflected 14-Inch Diameter Spheres, 0.050-in. thick shell of Stainless Steel Type 347 (NEA 1998, 
Volume I, PU-SOL-THERM-004, Sections 1, 2, and 3) 
pu004-1 26.27 g Pu/liter, CM: 621 gm, 
H/239Pu = 987, 0.54 wt. % 240Pu 
1.01134 0.00088 0.00524 1a, 1b, 
2a, 4a, 
4b, 5a, 
6apu004-2 26.31 g Pu/liter, CM: 622 gm, 
H/239Pu = 977, 0.54 wt. % 240Pu 
1.00448 0.00082 0.00541 
pu004-3 27.20 g Pu/liter, CM: 643 gm, 
H/239Pu = 935, 0.54 wt. % 240Pu 
1.00916 0.00087 0.00538 
pu004-4 28.09 g Pu/liter, CM: 664 gm, 
H/239Pu = 889, 0.54 wt. % 240Pu 
1.00712 0.00086 0.00561 
pu004-5 27.58 g Pu/liter, CM: 652 gm, 
H/239Pu = 942, 1.76 wt. % 240Pu 
1.00753 0.00091 0.00543 
pu004-6 28.60 g Pu/liter, CM: 676 gm, 
H/239Pu = 927, 3.12 wt. % 240Pu 
1.00862 0.00087 0.00564 
pu004-7 29.57 g Pu/liter, CM: 699 gm, 
H/239Pu = 892, 3.12 wt. % 240Pu 
1.01248 0.0009 0.0056 
pu004-8 29.95 g Pu/liter, CM: 708 gm, 
H/239Pu = 869, 3.12 wt. % 240Pu 
1.00778 0.00086 0.0062 
pu004-9 31.60 g Pu/liter, CM: 747 gm, 
H/239Pu = 805, 3.12 wt. % 240Pu 
1.00965 0.00089 0.00619 
pu04-10 35.36 g Pu/liter, CM: 836 gm, 
H/239Pu = 689, 3.12 wt. % 240Pu 
1.00987 0.00092 0.00715 
pu04-11 39.38 g Pu/liter, CM: 931 gm, 
H/239Pu = 592, 3.12 wt. % 240Pu 
1.0095 0.00092 0.00805 
pu04-12 29.44 g Pu/liter, CM: 696 gm, 
H/239Pu = 893, 3.12 wt. % 240Pu 
1.01108 0.00087 0.00594 
pu04-13 29.27 g Pu/liter, CM: 692 gm, 
H/239Pu = 903, 3.43 wt. % 240Pu 
1.00856 0.00091 0.00579 
Water Reflected 14-Inch Diameter Spheres, 0.050-in. thick shell of Stainless Steel Type 347 (NEA 1998, 
Volume I, PU-SOL-THERM-005, Sections 1, 2, and 3) 
pu005-1 29.65 g Pu/liter, CM: 701 gm, 
H/239Pu = 903, 4.05 wt. % 240Pu 
1.0086 0.00088 0.00571 1a, 1b, 
2a, 4a, 
4b, 5a, 
6apu005-2 30.54 g Pu/liter, CM: 722 gm, 
H/239Pu = 868, 4.05 wt. % 240Pu 
1.00908 0.00088 0.00589 
pu005-3 31.43 g Pu/liter, CM: 743 gm, 
H/239Pu = 834, 4.05 wt. % 240Pu 
1.01116 0.00091 0.0062 
pu005-4 33.54 g Pu/liter, CM: 793 gm, 
H/239Pu = 765, 4.05 wt. % 240Pu 
1.01197 0.00093 0.00664 
pu005-5 36.04 g Pu/liter, CM: 852 gm, 
H/239Pu = 694, 4.05 wt. % 240Pu 
1.01367 0.0009 0.00723 
CAL-DS0-NU-000003 REV 00A III-22 September 2004 

Criticality Model 
Table III-22. Configurations Incorporating Plutonium Nitrate Solutions (Continued) 
Exp ID Description keff 
a s 
AENCF 
(MeV) CC 
pu005-6 38.49 g Pu/liter, CM: 910 gm, 
H/239Pu = 633, 4.05 wt. % 240Pu 
1.0102 0.00095 0.00766 
pu005-7 40.91 g Pu/liter, CM: 967 gm, 
H/239Pu = 581, 4.05 wt. % 240Pu 
1.01073 0.00094 0.00838 
pu005-8 30.58 g Pu/liter, CM: 723 gm, 
H/239Pu = 869, 4.40 wt. % 240Pu 
1.00799 0.00091 0.00593 
pu005-9 31.85 g Pu/liter, CM: 753 gm, 
H/239Pu = 825, 4.40 wt. % 240Pu 
1.01023 0.00089 0.00631 
Water Reflected Partly Filled 11.5-Inch Diameter Spheres, 0.049-in. thick shell of Stainless Steel Type 304L, 
4.67 wt. % 240Pu, 95.059 wt. % 239Pu in Pu (NEA 1998, Volume I, PU-SOL-THERM-007, Sections 1, 2, and 3) 
pu007-2 232 g Pu/liter, Critical Volume: 12.35 liters, 
Height Above Sphere Center: 10.8373 cm, 
H/239Pu = 110 
1.01024 0.00102 0.04021 1a, 1b, 
2a, 4a, 
4b, 5a, 
6apu007-3 221 g Pu/liter, Critical Volume: 12.35 liters, 
Height Above Sphere Center: 10.8373 cm, 
H/239Pu = 114 
1.00591 0.00111 0.03928 
pu007-5 100.2 g Pu/liter, Critical Volume: 12.39 liters, 
Height Above Sphere Center: 10.9741 cm, 
H/239Pu = 268 
1.01502 0.00106 0.01764 
pu007-6 101.5 g Pu/liter, Critical Volume: 12.30 liters, 
Height Above Sphere Center: 10.6720 cm, 
H/239Pu = 262 
1.00873 0.00101 0.01799 
pu007-7 100.1 g Pu/liter, Critical Volume: 12.39 liters, 
Height Above Sphere Center: 10.9741 cm, 
H/239Pu = 266 
1.01053 0.00103 0.01783 
pu007-8 101.6 g Pu/liter, Critical Volume: 12.37 liters, 
Height Above Sphere Center: 10.9051 cm, 
H/239Pu = 258 
1.00254 0.00103 0.0181 
pu007-9 101.6 g Pu/liter, Critical Volume: 12.23 liters, 
Height Above Sphere Center: 10.4503 cm, 
H/239Pu = 260 
1.00327 0.00106 0.01815 
pu07-10 93.5 g Pu/liter, Critical Volume: 12.35 liters, 
Height Above Sphere Center: 10.8373 cm, 
H/239Pu = 285 
1.00706 0.00104 0.01653 
Unreflected 48-Inch Diameter Sphere, 0.303-inch thick shell of Type 1100 Aluminum, 97.386 wt. % 239Pu and 
2.521 wt. % 240Pu in Pu (NEA 1998, Volume I, PU-SOL-THERM-009, Sections 1, 2, and 3) 
pust9-1 10.02 g Pu/liter, Critical Volume: 656.6 liters, 
Height Above Sphere Center: 15.9558 cm, 
H/239Pu = 2648 
1.01886 0.00088 0.00257 1a, 1b, 
2a, 4a, 
4b, 5a, 
6apust9-2 9.539 g Pu/liter, Critical Volume: 906.5 liters, 
Height Above Sphere Center: 45.3705 cm, 
H/239Pu = 2779 
1.0239 0.00089 0.00266 
pust9-3 9.457 g Pu/liter, Critical Volume: 949.1 liters, 
Full Sphere, H/239Pu = 2803 
1.02176 0.00089 0.00246 
CAL-DS0-NU-000003 REV 00A III-23 September 2004 

Criticality Model 
Table III-22. Configurations Incorporating Plutonium Nitrate Solutions (Continued) 
Exp ID Description keff 
a s 
AENCF 
(MeV) CC 
Water Reflected Cylinders, 0.062-inch thick shell of Stainless Steel Type 347, 2.9 wt. % 240Pu in Pu (NEA 1998, 
Volume I, PU-SOL-THERM-010, Sections 1, 2, and 3) 
pu10091 99.09 g Pu/liter, IR = 11.4264 cm, 
CH: 30.7086 cm, CM: 1249 g, H/239Pu = 267 
1.02337 0.00101 0.01675 1a, 1b, 
2a, 4a, 
4b, 5a, 
6apu10092 73.92 g Pu/liter, IR = 11.4264 cm, 
CH: 35.4076 cm, CM: 1073 g, H/239Pu = 357 
1.02091 0.00097 0.01299 
pu10093 54.53 g Pu/liter, IR = 11.4264 cm, 
CH: 44.5770 cm, CM: 997 g, H/239Pu = 484 
1.01316 0.00097 0.00994 
pu10111 54.53 g Pu/liter, IR = 13.9684 cm, 
CH: 25.6032 cm, CM: 856 g, H/239Pu = 485, Extra 
0.065 inch layer of stainless steel placed around 
cylinder 
1.01879 0.00099 0.01001 
pu10112 47.21 g Pu/liter, IR = 13.9684 cm, 
CH: 28.1686 cm, CM: 815 g, H/239Pu = 558, Extra 
0.065 inch layer of stainless steel placed around 
cylinder 
1.01543 0.00098 0.00873 
pu10113 47.21 g Pu/liter, IR = 13.9684 cm, 
CH: 27.0764 cm, CM: 784 g, H/239Pu = 558 
1.01615 0.00092 0.00852 
pu10114 41.73 g Pu/liter, IR = 13.9684 cm, 
CH: 32.6390 cm, CM: 835 g, H/239Pu = 606 
1.00903 0.00091 0.0079 
pu10115 36.90 g Pu/liter, IR = 13.9684 cm, 
CH: 43.0022 cm, CM: 973 g, H/239Pu = 665 
1.01069 0.00093 0.00755 
pu10116 63.99 g Pu/liter, IR = 13.9684 cm, 
CH: 22.8092 cm, CM: 895 g, H/239Pu = 414 
1.01992 0.00101 0.01114 
pu10117 48.98 g Pu/liter, IR = 13.9684 cm, 
CH: 25.9588 cm, CM: 780 g, H/239Pu = 535 
1.01146 0.00092 0.00879 
pu10121 48.75 g Pu/liter, IR = 15.2390 cm, 
CH: 22.3520 cm, CM: 799 g, H/239Pu = 543 
1.0156 0.00097 0.00896 
pu10122 42.29 g Pu/liter, IR = 15.2390 cm, 
CH: 25.2476 cm, CM: 779 g, H/239Pu = 618 
1.01616 0.00095 0.00776 
pu10123 36.52 g Pu/liter, IR = 15.2390 cm, 
CH: 28.4734 cm, CM: 758 g, H/239Pu = 728 
1.02352 0.00094 0.00691 
pu10124 31.14 g Pu/liter, IR = 15.2390 cm, 
CH: 33.4264 cm, CM: 759 g, H/239Pu = 850 
1.01642 0.00087 0.0061 
Unreflected 16- & 18-Inch Diameter Spheres, 0.050-in. thick shell of Stainless Steel Type 347, 
0.020-in. thick Cd Cover on the 18-inch sphere, 4.2 wt. % 240Pu in Pu (NEA 1998, 
Volume I, PU-SOL-THERM-011, Sections 1, 2, and 3) 
pu11161 34.96 g Pu/liter, IR = 20.1206 cm, 
CM: 1194 g, H/239Pu = 765 
1.01661 0.00103 0.00738 1a, 1b, 
2a, 4a, 
4b, 5a, 
6apu11162 36.22 g Pu/liter, IR = 20.1206 cm, 
CM: 1237 g, H/239Pu = 736 
1.02377 0.00101 0.00777 
pu11163 38.13 g Pu/liter, IR = 20.1206 cm, 
CM: 1302 g, H/239Pu = 691 
1.02224 0.00101 0.00827 
pu11164 38.16 g Pu/liter, IR = 20.1206 cm, 
CM: 1303 g, H/239Pu = 682 
1.01688 0.00105 0.00845 
pu11165 43.43 g Pu/liter, IR = 20.1206 cm, 
CM: 1483 g, H/239Pu = 575 
1.01338 0.00104 0.00973 
pu11181 22.35 g Pu/liter, IR = 22.6974 cm, 
CM: 1095 g, H/239Pu = 1208 
1.00169 0.00089 0.00505 
CAL-DS0-NU-000003 REV 00A III-24 September 2004 

Criticality Model 
Table III-22. Configurations Incorporating Plutonium Nitrate Solutions (Continued) 
Exp ID Description keff 
a s 
AENCF 
(MeV) CC 
pu11182 23.27 g Pu/liter, IR = 22.6974 cm, 
CM: 1140 g, H/239Pu = 1151 
1.0068 0.00088 0.00549 
pu11183 23.10 g Pu/liter, IR = 22.6974 cm, 
CM: 1132 g, H/239Pu = 1158 
1.00336 0.00097 0.00514 
pu11184 23.82 g Pu/liter, IR = 22.6974 cm, 
CM: 1167 g, H/239Pu = 1100 
1.00285 0.00088 0.00547 
pu11185 25.20 g Pu/liter, IR = 22.6974 cm, 
CM: 1235 g, H/239Pu = 1039 
1.01131 0.00093 0.00593 
pu11186 27.49 g Pu/liter, IR = 22.6974 cm, 
CM: 1347 g, H/239Pu = 908 
1.00796 0.00097 0.00633 
pu11187 23.94 g Pu/liter, IR = 22.6974 cm, 
CM: 1173 g, H/239Pu = 1103 
1.00792 0.00088 0.00548 
NOTES: a Calculated keff values for the Pu solution experiments which significantly exceed a value of 1.01 are often 
found when using the ENDF/B-V libraries. The most likely reason is that the Pu cross sections have a 
tendency to over-predict keff, but since the calculated values are over-predictions of a critical system, this 
is considered conservative with respect to criticality safety applications. 
bCH = Critical Height; CM = Critical Mass; IR = Internal Radius. 
III.2.3.3 Low-Enrichment Uranium Solutions 
The first set of experiments involving low-enrichment uranium is from International Handbook 
of Evaluated Criticality Safety Benchmark Experiments (NEA 1998, Volume IV); the second set 
(case prefix LEUJ) is from work at the Japan Atomic Energy Research Institute (Miyoshi et al. 
1997), and the third set (case prefix SPHU9) is cases that look at UO3-H2O critical solutions 
(Wittekind 1992). These experiments are listed in Table III-23. 
Table III-23. Configurations Incorporating Low-Enrichment Uranium Solutions 
Exp ID Description keff s 
AENCF 
(MeV) CC 
174 Liter Spherical Tank of 4.9% Enriched UO2F2 Solutions, 34.399 cm Radius, 0.1588 cm thick 1100 
Aluminum Shell (NEA 1998, Volume IV, LEU-SOL-THERM-002, Sections 1, 2, and 3) 
LEUST21 452.2 g U/liter, 22.11 g 235U/liter, Water Reflector, 
Critical Volume: 170.5 Liters Critical Mass = 
3769.8 g 235U, H/235U: 1098 
0.99892 0.00053 0.02487 1a, 1b, 
2a, 4a, 
4b, 5a, 
6aLEUST22 491.7 g U/liter, 24.04 g 235U/liter, No Reflector, 
Critical Volume: 172 Liters, Critical Mass = 4134.9 
g 235U, H/235U: 1001 
0.99469 0.00061 0.02832 
LEUST23 491.7 g U/liter, 24.04 g 235U/liter, Water Reflector, 
Critical Volume = 145.6 Liters, Critical Mass = 
3500.2 g 235U, H/235U: 1001 
1.00078 0.00057 0.02665 
CAL-DS0-NU-000003 REV 00A III-25 September 2004 

Criticality Model 
Table III-23. Configurations Incorporating Low-Enrichment Uranium Solutions (Continued) 
Exp ID Description keff s 
AENCF 
(MeV) CC 
Cylindrical Tank With a 59.0 cm ID, 0.3 cm thick Stainless Steel SS 304, 235U Enrichment of 9.97 wt. % 
(Miyohsi et al. 1997) 
LEUJA01 310.1 g U/liter, 30.9 g 235U/liter, Water Reflector, 
Critical Height: 41.53 cm, Critical Mass = 3508.4 g 
235U, H/235U: 719.0, H/U: 72.5 
1.00425 0.00085 0.01896 1a, 1b, 
2a, 4a, 
4b, 5a, 
6aLEUJA29 290.4 g U/liter, 29.0 g 235U/liter, Water Reflector, 
Critical Height: 46.70 cm, Critical Mass = 3702.6 g 
235U, H/235U: 771.3, H/U: 77.8 
1.00377 0.00082 0.01806 
LEUJA33 270.0 g U/liter, 26.9 g 235U/liter, Water Reflector, 
Critical Height: 52.93 cm, Critical Mass = 3892.7 g 
235U, H/235U: 842.2, H/U: 84.9 
0.99961 0.0009 0.01662 
LEUJA34 253.6 g U/liter, 25.3 g 235U/liter, Water Reflector, 
Critical Height: 64.85 cm, Critical Mass = 4485.6 g 
235U, H/235U: 895.8, H/U: 90.3 
1.0029 0.00079 0.0159 
LEUJA46 241.9 g U/liter, 24.1 g 235U/liter, Water Reflector, 
Critical Height: 78.56 cm, Critical Mass = 5176.2 g 
235U, H/235U: 941.7, H/U: 95.0 
1.00311 0.0008 0.01535 
LEUJA51 233.2 g U/liter, 23.3 g 235U/liter, Water Reflector, 
Critical Height: 95.50 cm, Critical Mass = 6083.5 g 
235U, H/235U: 982.5, H/U: 99.1 
1.00279 0.0007 0.01479 
LEUJA54 225.3 g U/liter, 22.5 g 235U/liter, Water Reflector, 
Critical Height: 130.33 cm, Critical Mass = 
8017.2 g 235U, H/235U: 1017.5, H/U: 102.6 
1.00246 0.00072 0.0144 
LEUJA14 313.0 g U/liter, 31.2 g 235U/liter, No Reflector, 
Critical Height: 46.83 cm, Critical Mass = 3994.6 g 
235U, H/235U: 709.2, H/U: 71.5 
0.99755 0.00094 0.02001 
LEUJA30 290.7 g U/liter, 29.0 g 235U/liter, No Reflector, 
Critical Height: 54.20 cm, Critical Mass = 4297.3 g 
235U, H/235U: 770.0, H/U: 77.7 
0.99885 0.00086 0.01881 
LEUJA32 270.0 g U/liter, 26.9 g 235U/liter, No Reflector, 
Critical Height: 63.55 cm, Critical Mass = 4673.7 g 
235U, H/235U: 842.2, H/U: 84.9 
1.00143 0.00086 0.01757 
LEUJA36 253.9 g U/liter, 25.3 g 235U/liter, No Reflector, 
Critical Height: 83.55 cm, Critical Mass = 5779.1 g 
235U, H/235U: 896.0, H/U: 90.4 
1.00185 0.00084 0.01665 
LEUJA49 241.9 g U/liter, 24.1 g 235U/liter, No Reflector, 
Critical Height: 112.27 cm, Critical Mass = 7397.3 
g 235U, H/235U: 942.2, H/U: 95.0 
0.99875 0.00078 0.01593 
UO3-H2O Solution Experiments (Wittekind 1992, p. 43) 
SPHU9A 1.0059 wt. % enriched 235U, 
H/235U: 370.3, H/U: 3.772 
0.9920a/ 
0.99004b 
0.0060c/ 
0.00249d 
0.2541 1a, 1b, 
2a, 4a, 
4b, 5a, 
6a 
SPHU9B 1.0059 wt. % enriched 235U, 
H/235U: 490.8, H/U: 4.999 
0.9925/ 
0.99269 
0.0050/ 
0.00249 
0.2163 
SPHU9C 1.0059 wt. % enriched 235U, 
H/235U: 605.1, H/U: 6.164 
0.9875/ 
0.97871 
0.0058/ 
0.00256 
0.1883 
SPHU9D 1.0059 wt. % enriched 235U, 
H/235U: 675.5, H/U: 6.881 
0.9821/ 
0.97914 
0.0054/ 
0.00242 
0.1737 
SPHU9E 1.0059 wt. % enriched 235U, 
H/235U: 731.2, H/U: 7.449 
0.9702/ 
0.96607 
0.0070/ 
0.00163 
0.1591 
SPHU9F 1.0704 wt. % enriched 235U, 
H/235U: 343.9, H/U: 3.728 
1.0063/ 
1.00952 
0.0073/ 
0.00261 
0.2511 
CAL-DS0-NU-000003 REV 00A III-26 September 2004 

Criticality Model 
Table III-23. Configurations Incorporating Low-Enrichment Uranium Solutions (Continued) 
Exp ID Description keff s 
AENCF 
(MeV) CC 
SPHU9G 1.0704 wt. % enriched 235U, 
H/235U: 533.1, H/U: 5.778 
1.0064/ 
1.0136 
0.0078/ 
0.00246 
0.1839 
SPHU9H 1.0704 wt. % enriched 235U, 
H/235U: 652.7, H/U: 7.075 
0.9957/ 
0.99713 
0.0061/ 
0.00198 
0.1651 
SPHU9I 1.1586 wt. % enriched 235U, 
H/235U: 317.7, H/U: 3.728 
1.0298/ 
1.03372 
0.0056/ 
0.00274 
0.2495 
SPHU9J 1.1586 wt. % enriched 235U, 
H/235U: 475.6, H/U: 5.926 
1.0330/ 
1.04207 
0.0051/ 
0.00224 
0.1783 
SPHU9K 1.1586 wt. % enriched 235U, 
H/235U: 582.8, H/U: 6.838 
1.0313/ 
1.02951 
0.0032/ 
0.00216 
0.1661 
SPHU9L 1.1586 wt. % enriched 235U, 
H/235U: 634.9, H/U: 7.449 
1.0209/ 
1.02281 
0.0051/ 
0.0021 
0.1549 
NOTES: a For the UO3-H2O solution experiments the experimental determinations are the top numbers and were 
stated as k8 although the experiment was on a reflected sample (Wittekind 1992, p. 40). 
bFor the UO3-H2O solution experiments the calculated k8 value is the bottom number. 
c For the UO3-H2O solution experiments the top number represents experimental uncertainty. 
dFor the UO3-H2O solution experiments the bottom number represents calculation uncertainty. 
III.2.3.4 Low Enriched Uranyl Fluoride Solutions 
This experiment involved an aqueous solution of about 5 weight percent enriched uranyl fluoride 
and is taken from International Handbook of Evaluated Criticality Safety Benchmark 
Experiments (NEA 1998, Volume IV, LEU-SOL-THERM-001, Sections 1, 2, and 3). This 
experiment used the Solution High Energy Burst Assembly-II, which is a critical assembly 
experiment that was operated at the Los Alamos Critical Experiments Facility. This experiment 
is listed in Table III-24. 
Table III-24. Configurations Incorporating Uranyl Fluoride Solutions 
Exp ID Description keff s 
AENCF 
(MeV) CC 
lst1-1 
Average solution density: 2.1092 g/cm3, Average 
uranium density: 0.9783 g/cm3, Average 235U 1.01069 0.00085 0.0523 
1a, 1b, 2a, 
4a, 4b, 5a, 
enrichment: 4.9977 atom percent, H/X: 453.9 6a 
III.3 CRITICAL LIMIT COMPUTATION 
The CL is derived from 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 III-27 September 2004 

Criticality Model 
III.3.1 Statistical Analyses 
Evaluation of benchmark experiments that cover a wide range of parameters and configurations 
requires the determination of which groups of experiments can be statistically analyzed together 
and which should be analyzed separately. The benchmark experiments were grouped based on 
experimental similarity and are as follows: 
 CRC Experiments 
 Lattice LCEs (UO2 and MOX based fuel) 
 Uranium Solution LCEs 
 Plutonium Solution LCEs. 
The Student t-distribution (Walpole et al. 1998, pp. 228 to 232) is used to test the benchmark 
group results to determine if they can be analyzed together or not. 
With the Student t-test for two groups it can be determined, with 95 percent confidence, whether 
subsets have different mean values and thus should not be analyzed together. The equality test 
requires computing the statistic T in Equation III-1. 
Y1 - Y2
T = 
(Eq. III-1) 
2
(n - 1)Sy1 + (m - 1)Sy 
221 1
+ 
n + m - 2 nm 
where 
Y1= the calculated multiplication factor averages for subset 1 
Y2 = the calculated multiplication factor averages for subset 2 
n = the number of observations for subset 1 
m = the number of observations for subset 2 
Sy1 
2 
Sy2 
2 
= 
= 
the estimated variances for subset 1 (as shown in Equation III-2) 
the estimated variances for subset 2 (as shown in Equation III-3) 
(. Yi )2 
1- Y 
2 
1S y= ,1 = ni 
1-n 
(Eq. III-2) 
(. Yi )2 
2- Y 
2 
2S y= ,1 = mi 
1-m 
(Eq. III-3) 
The T statistic is compared to the Student t-distribution with 95 percent confidence and n+m-2 
degrees of freedom. The null hypothesis the two subsets of data can be statistically combined 
(the mean values are approximately equal) would be accepted if |T|<ta/2,n+m-2 and rejected 
otherwise where a is defined below. Table III-25 presents the test results. 
CAL-DS0-NU-000003 REV 00A III-28 September 2004 

Criticality Model 
Table III-25. Equality Test Statistic Results 
Subsets UO2 and MOX LCEs 
Sample Size Average keff Variance T statistic ta/2,n+m-2a Combine? 
UO2 LCEs 64 0.9985 2.282E-05 -1.2143 1.9897 Y 
MOX LCEs 19 1.0000 2.777E-05 
CRCs and LCEs 
CRCs 60 0.9918 1.510E-05 -9.3984 1.9769 N 
LCEs 83 0.9988 2.237E-05 
Uranium and Plutonium Solutions 
Uranium 
Solutions 
28 1.0028 2.512E-04 -3.4257 1.9780 N 
Plutonium 
Solutions 
107 1.0094 3.942E-05 
NOTE: a a = 1-confidence level (i.e., 0.95). 
III.3.2 Regression Analyses 
The calculated multiplication factors for the benchmark experiments were trended against 
several parameters from each subset using a linear regression fit in order to determine whether a 
trend does exist and which parameters exhibit the strongest trends. A variation of the Student 
t-test along with the slope test was used to determine if a particular trend is considered 
statistically significant. 
The linear regression fitted equation is in the form y(x) = a + bx. The slope test requires 
calculating the test statistic T as follows in Equation III-4 along with the statistical parameters 
in Equations III-5 and III-6. 
xx
T =b (n - 2)S 
(Eq. III-4) 
SSR 
where b comes from the fitted linear regression equation 
2
Sxx = .(x - x) (Eq. III-5) 
i 
i=,1 n 
and 
SSR = .(y - a - bxi )2 (Eq. III-6) 
i 
i=,1 n 
The test statistic is compared to the Student t-distribution (ta/2,n-2) with 95 percent confidence and 
n-2 degrees of freedom. Given a null hypothesis of no statistically significant trend exists 
(slope is zero), the hypothesis would be accepted if |T| < ta/2,n-2 and rejected otherwise. Unless 
the data is exceptional, the linear regression results will have a nonzero slope. By only accepting 
trends that the data supports with 95 percent confidence, trends due to the randomness of the data 
are eliminated. 
CAL-DS0-NU-000003 REV 00A III-29 September 2004 

Criticality Model 
III.3.3 Trending Evaluation 
Trending against various parameters was performed in order to determine correlations between 
characteristics and the calculated multiplication factors for each subset. Depending on the type 
of benchmark, different trending parameters were evaluated in order to determine which exhibit 
the strongest trends. The regression statistics for the trend evaluations are presented in 
Tables III-26 to III-29 for each of the subsets and illustrated in Figures III-1 to III-12. The W/F 
term represents the unit cell moderator-to-fuel volume ratio. The P-value parameter gives a 
direct estimation of the probability of having linear trending due to chance only. 
Table III-26. CRC Trending Parameter Results 
Trend 
Parameter N Intercept Slope r2a T ta/2,n-2 P-Value 
Goodness-of-Fit 
Tests 
Valid 
Trend 
Core Avg. 60 0.9963 -0.0003 2.665 4.59 2.016 2.42E-05 Passed Yes 
BU 
AENCF 60 0.9892 0.0113 0.0095 0.74 2.016 0.4595 Failed No 
Source: Massie 2003, Section 6 
a
NOTE: r2 is the correlation coefficient. 
Table III-27. UO2 and MOX LCE Trending Parameter Results 
Trend 
Parameter N Slope Intercept Sxx SSR ra T ta/2,n-2 Trend? 
AENCF 83 -6.336E-03 1.000E+00 1.941E-01 1.965E-03 0.063 -0.57 1.99 No 
P/D 83 5.966E-03 9.890E-01 4.534E+00 1.811E-03 0.286 2.69 1.99 Yes 
Pitch 83 6.723E-03 9.871E-01 5.687E+00 1.716E-03 0.361 3.48 1.99 Yes 
W/F 83 1.156E-03 9.963E-01 1.238E+02 1.807E-03 0.290 2.72 1.99 Yes 
NOTE: ar represents the r-value correlation coefficient (positive square root of squared correlation coefficient). 
Table III-28. Uranium Solution Trending Parameter Results 
Trend 
Parameter N Slope Intercept Sxx SSR r T ta/2,n-2 Trend? 
AENCF 28 2.184E-02 1.001E+00 2.247E-01 6.676E-03 0.126 0.65 2.06 No 
H/X 28 -2.199E-05 1.019E+00 1.343E+06 6.134E-03 0.309 -1.66 2.06 No 
ALFa 28 -1.566E-03 1.011E+00 3.758E+01 6.691E-03 0.117 -0.60 2.06 No 
a
NOTE: ALF is the average lethargy of a neutron causing fission. 
Table III-29. Plutonium Solution Trending Parameter Results 
Trend 
Parameter N Slope Intercept Sxx SSR r T ta/2,n-2 Trend? 
AENCF 107 -2.545E-01 1.013E+00 1.976E-02 2.898E-03 0.554 -6.81 1.98 Yes 
H/X 107 3.221E-06 1.007E+00 3.338E+07 3.832E-03 0.288 3.08 1.98 Yes 
ALF 107 4.072E-03 9.817E-01 6.412E+01 3.115E-03 0.504 5.99 1.98 Yes 
CAL-DS0-NU-000003 REV 00A III-30 September 2004 

Criticality Model 
1.004 
keff 
keff 
1.002 
1
0.998
0.996 
0.994 
0.992 
0.99 
0.988 
0.986 
0.984 
R2y = -0.0824x + 1.013 
= 0.0511 
0.23 0.235 0.24 0.245 0.25 0.255 0.26 0.265 0.27 
AENCF (MeV) 
Figure III-1. CRC Subset with AENCF as Trending Parameter 
1.004
1.002
1
0.998
0.996
0.994
0.992
0.99
0.988
0.986
0.984
R2y = -0.0002x + 0.9958 
= 0.3273 
0.000 5.000 10.000 15.000 20.000 25.000 30.000 35.000 
Core Average Burnup (GWd/MTU) 
Figure III-2. CRC Subset with Core Average Burnup as Trending Parameter 
CAL-DS0-NU-000003 REV 00A III-31 September 2004 

Criticality Model 
R20.985 
0.99 
0.995 
1 
1.005 
1.01 
1.015 
1.02 
keff 
y = -0.0063x + 1 
= 0.0039 
keff 
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 
AENCF (MeV) 
Figure III-3. UO2 and MOX LCE Subset with AENCF as Trending Parameter 
1.02 
1.015 
1.01
1.005
1
0.995
0.99 
0.985 
R2y = 0.006x + 0.989 
= 0.0818 
1.00 1.50 2.00 2.50 3.00 3.50 
P/D 
Figure III-4. UO2 and MOX LCE Subset with P/D as Trending Parameter 
CAL-DS0-NU-000003 REV 00A III-32 September 2004 

Criticality Model 
keff keff 
1.02 
1.015 
1.01
1.005
1
0.995
0.99 
0.985 
R2y = 0.0067x + 0.9871 
= 0.1303 
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 
Pin Pitch (cm) 
Figure III-5. UO2 and MOX LCE Subset with Pin Pitch as Trending Parameter 
1.02 
1.015 
1.01
1.005
1
0.995
0.99 
0.985 
R2y = 0.0012x + 0.9963 
= 0.0839 
0.00 2.00 4.00 6.00 8.00 10.00 12.00 
Water to Fuel Volume Ratio 
Figure III-6. UO2 and MOX LCE Subset with Moderator-to-Fuel Volume Ratio as Trending Parameter 
CAL-DS0-NU-000003 REV 00A III-33 September 2004 

Criticality Model 
1.05 
keff keff 
1.04 
1.03 
1.02 
1.01
1
0.99 
0.98 
0.97 
0.96 
R2y = 0.0218x + 1.0007 
= 0.0158 
0 0.05 0.1 0.15 0.2 0.25 
AENCF (MeV) 
Figure III-7. Uranium Solution Subset with AENCF as Trending Parameter 
1.05 
1.04 
1.03 
1.02 
1.01
1
0.99 
0.98 
0.97 
0.96 
200 300 400 500 600 700 800 900 1000 1100 1200 
R2y = -2E-05x + 1.0187 
= 0.0957 
H/X 
Figure III-8. Uranium Solution Subset with H/X as Trending Parameter 
CAL-DS0-NU-000003 REV 00A III-34 September 2004 

Criticality Model 
1.05 
keff 
keff 
1.04 
1.03 
1.02 
1.01
1
0.99 
0.98 
0.97 
0.96 
R2y = -0.0016x + 1.011 
= 0.0136 
33.5 44.5 55.566.57 
ALF 
Figure III-9. Uranium Solution Subset with ALF as Trending Parameter 
1.03 
1.025 
1.02 
1.015 
1.01 
1.005 
1 
0.995 
0.99 
R2y = -0.2545x + 1.0133 
= 0.3064 
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 
AENCF (MeV) 
Figure III-10. Plutonium Solution Subset with AENCF as Trending Parameter 
CAL-DS0-NU-000003 REV 00A III-35 September 2004 

Criticality Model 
R21 
ky = 3E-06x + 1.0071 
= 0.0829 
0.99 
0.995 
1.005 
1.01 
1.015 
1.02 
1.025 
1.03 
eff 
keff 
0 500 1000 1500 2000 2500 3000 
H/X 
Figure III-11. Plutonium Solution Subset with H/X as Trending Parameter 
1.03 
1.025 
1.02 
1.015 
1.01
1.005
1
0.995
0.99 
R2y = 0.0041x + 0.9817 
= 0.2545 
44.5 55.5 66.5 77.5 88.5 
ALF 
Figure III-12. Plutonium Solution Subset with ALF as Trending Parameter 
CAL-DS0-NU-000003 REV 00A III-36 September 2004 

Criticality Model 
III.3.4 Lower-Bound Tolerance Limit Determination 
The LBTL is characterized by statistical tolerance limits that account for biases and uncertainties 
associated with the criticality code trending process. The LBTL is calculated by CLREG only 
when a trending regression is identified as statistically significant. If no trend is identified, the 
normal distribution tolerance limit (NDTL) or the distribution-free tolerance limit method is used 
as previously discussed in Section 6.1.1.3. 
CLREG is a computer program that calculates sets of LBTL functions based on benchmark 
experiment results. Each LBTL represents the value of keff at which a configuration is 
considered potentially critical. This method accounts for the criticality analysis method bias and 
uncertainty of the calculated critical keff values for a set of critical experiments that represent the 
waste package, as explained by linear regression trending. A complete discussion of the 
statistical methodology for CLREG is provided in the CLREG documentation (BSC 2001c). 
LBTLs were calculated for each subset of experiments for the parameter that had the most 
statistically significant trend. This is determined by which parameter has a correlation 
coefficient closest to one. 
The selected LBTL values are presented in Table III-30 for each of the subsets. The CLREG 
results, as a function of the most statistically significant trending parameters, are provided in 
Tables III-31 for Lattice LCEs, Table III-32 for plutonium solutions, and in Massie (2003, 
Section 6.1) for CRCs. The CLREG results are illustrated in Figures III-13 to III-15. The results 
presented in Table III-30 were generated for a 95 percent confidence level covering 99.5 percent 
of the population. For the UO2 solution experiments, Figures III-16 and III-17 show that the data 
set appears to be normally distributed therefore the NDTL method was used for calculating the 
LBTL. 
Table III-30. Lower-Bound Tolerance Limits for Experiment Subsets 
Subset Trend Parameter Lower-Bound Tolerance Limt 
CRCsa Core Average Burnup (BU) f(BU) = -0.0003  BU + 0.9866 (0 < BU < 33 GWd/MTU)c 
Lattice LCEsb Pin Pitch (P) f(P) = 7.0175E-03  P + 0.9677 (1.32 cm = P = 1.89 cm); f(P) 
= 0.982 (1.89 cm < P = 2.64 cm)c 
UO2 Solutionsb None f(x) = 0.952d 
Plutonium 
Solutionsb 
AENCF f(AENCF) = 0.980 (2.46E-03 MeV = AENCF = 5.96E-02 MeV) 
Source: a Massie 2003, Section 6.1 
b Calculated in current analysis 
NOTES: c Upper limit set at 0.982 since no positive bias credit is taken. 
dCalculated using the NDTL method with 95 percent confidence level covering 99.5 percent of the 
population. 
CAL-DS0-NU-000003 REV 00A III-37 September 2004 

Criticality Model 
keff 
1.005 
1.000 
0.995 
0.990 
0.985 
0.980 
0.975 
kef f - Regression 
Lower Bound Tolerance Limit 
kef f - CRC 
keff 
0 5 101520253035 
Burnup (GWd/MTU) 
Figure III-13. Lower-Bound Tolerance Limit Plot for CRC Experiment Subset 
1.02 
1.015 
1.01
1.005
1
0.995
0.99 
0.985 
0.98 
0.975 
keff 
keffLii-Lat LCE 
- Regression 
Lower Bound Tolerance mit 
Lower Bound Tolerance 
Limit wth positive bias 
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 
Pin Pitch (cm) 
Figure III-14. Lower-Bound Tolerance Limit Plot for Lattice LCE Subset 
CAL-DS0-NU-000003 REV 00A III-38 September 2004 

Criticality Model 
1keff 
keff 
kLi0.975 
0.98 
0.985 
0.99 
0.995 
1.005 
1.01 
1.015 
1.02 
1.025 
1.03 
-Pu soln LCE 
eff - Regression 
Lower Bound Tolerance mit 
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 
AENCF (MeV) 
Figure III-15. Lower-Bound Tolerance Limit Plot for Plutonium Solution LCE Subset 
0 
2 
4 
6 
8 
10 
12 
14 
16 
Frequency 
0.96 0.98 1 1.02 1.04 
UO2 Solution LCE keff 
Figure III-16. Histogram Plot for UO2 Solution LCE keff Values 
CAL-DS0-NU-000003 REV 00A III-39 September 2004 

Criticality Model 
-3 
-2 
-1 
0 
1 
2 
3 
Normal Quantile 
0.96 0.98 1 1.02 1.04 1.06 
UO2 Solution LCE keff 
Figure III-17. Normal Quantile Plot for UO2 Solution LCE keff Values 
Table III-31. Lattice LCEs with Pitch as Trend Parametera 
Ind Var Keff(cc) Pred Keff PreClos CL LUTB CL Bonf LTL 
1.32E+00 0.993 0.996 0.987 0.977 0.977 
1.32E+00 0.995 0.996 0.987 0.977 0.977 
1.42E+00 0.994 0.997 0.988 0.978 0.977 
1.42E+00 0.998 0.997 0.988 0.978 0.977 
1.42E+00 0.998 0.997 0.988 0.978 0.977 
1.42E+00 0.999 0.997 0.988 0.978 0.977 
1.42E+00 1.000 0.997 0.988 0.978 0.977 
1.42E+00 0.997 0.997 0.988 0.978 0.977 
1.42E+00 0.993 0.997 0.988 0.978 0.977 
1.42E+00 0.998 0.997 0.988 0.978 0.977 
1.42E+00 1.000 0.997 0.988 0.978 0.977 
1.53E+00 0.996 0.997 0.989 0.979 0.978 
1.60E+00 0.988 0.998 0.989 0.979 0.978 
1.60E+00 1.016 0.998 0.989 0.979 0.978 
1.64E+00 0.995 0.998 0.990 0.980 0.979 
1.64E+00 0.996 0.998 0.990 0.980 0.979 
1.64E+00 0.994 0.998 0.990 0.980 0.979 
1.64E+00 0.995 0.998 0.990 0.980 0.979 
1.64E+00 1.000 0.998 0.990 0.980 0.979 
1.64E+00 1.001 0.998 0.990 0.980 0.979 
1.64E+00 0.989 0.998 0.990 0.980 0.979 
1.64E+00 0.993 0.998 0.990 0.980 0.979 
1.64E+00 0.995 0.998 0.990 0.980 0.979 
CAL-DS0-NU-000003 REV 00A III-40 September 2004 

Criticality Model 
Table III-31. Lattice LCEs with Pitch as Trend Parametera (Continued) 
Ind Var Keff(cc) Pred Keff PreClos CL LUTB CL Bonf LTL 
1.64E+00 0.997 0.998 0.990 0.980 0.979 
1.64E+00 0.995 0.998 0.990 0.980 0.979 
1.64E+00 0.999 0.998 0.990 0.980 0.979 
1.64E+00 0.991 0.998 0.990 0.980 0.979 
1.64E+00 0.990 0.998 0.990 0.980 0.979 
1.64E+00 0.994 0.998 0.990 0.980 0.979 
1.64E+00 0.995 0.998 0.990 0.980 0.979 
1.64E+00 0.994 0.998 0.990 0.980 0.979 
1.64E+00 0.994 0.998 0.990 0.980 0.979 
1.64E+00 0.992 0.998 0.990 0.980 0.979 
1.64E+00 0.998 0.998 0.990 0.980 0.979 
1.64E+00 0.999 0.998 0.990 0.980 0.979 
1.64E+00 1.000 0.998 0.990 0.980 0.979 
1.64E+00 1.001 0.998 0.990 0.980 0.979 
1.64E+00 1.002 0.998 0.990 0.980 0.979 
1.64E+00 1.003 0.998 0.990 0.980 0.979 
1.64E+00 0.999 0.998 0.990 0.980 0.979 
1.64E+00 0.999 0.998 0.990 0.980 0.979 
1.64E+00 1.001 0.998 0.990 0.980 0.979 
1.64E+00 1.003 0.998 0.990 0.980 0.979 
1.64E+00 1.001 0.998 0.990 0.980 0.979 
1.64E+00 0.999 0.998 0.990 0.980 0.979 
1.64E+00 1.004 0.998 0.990 0.980 0.979 
1.64E+00 1.000 0.998 0.990 0.980 0.979 
1.64E+00 1.000 0.998 0.990 0.980 0.979 
1.64E+00 1.000 0.998 0.990 0.980 0.979 
1.64E+00 1.002 0.998 0.990 0.980 0.979 
1.64E+00 1.001 0.998 0.990 0.980 0.979 
1.64E+00 0.999 0.998 0.990 0.980 0.979 
1.72E+00 1.007 0.999 0.990 0.980 0.979 
1.72E+00 1.004 0.999 0.990 0.980 0.979 
1.78E+00 1.001 0.999 0.990 0.981 0.980 
1.78E+00 0.996 0.999 0.990 0.981 0.980 
1.87E+00 1.003 1.000 0.991 0.981 0.980 
1.89E+00 1.008 1.000 0.991 0.981 0.980 
1.89E+00 1.007 1.000 0.991 0.981 0.980 
1.89E+00 1.005 1.000 0.991 0.981 0.980 
1.89E+00 1.004 1.000 0.991 0.981 0.980 
1.89E+00 0.997 1.000 0.991 0.981 0.980 
1.89E+00 0.997 1.000 0.991 0.981 0.980 
1.89E+00 1.000 1.000 0.991 0.981 0.980 
2.01E+00 1.005 1.001 0.991 0.982 0.981 
CAL-DS0-NU-000003 REV 00A III-41 September 2004 

Criticality Model 
Table III-31. Lattice LCEs with Pitch as Trend Parametera (Continued) 
Ind Var Keff(cc) Pred Keff PreClos CL LUTB CL Bonf LTL 
2.03E+00 0.998 1.001 0.991 0.982 0.981 
2.03E+00 0.993 1.001 0.991 0.982 0.981 
2.03E+00 1.001 1.001 0.991 0.982 0.981 
2.03E+00 0.993 1.001 0.991 0.982 0.981 
2.03E+00 0.993 1.001 0.991 0.982 0.981 
2.03E+00 1.000 1.001 0.991 0.982 0.981 
2.03E+00 0.994 1.001 0.991 0.982 0.981 
2.03E+00 0.994 1.001 0.991 0.982 0.981 
2.03E+00 1.001 1.001 0.991 0.982 0.981 
2.03E+00 0.999 1.001 0.991 0.982 0.981 
2.03E+00 0.998 1.001 0.991 0.982 0.981 
2.03E+00 0.999 1.001 0.991 0.982 0.981 
2.21E+00 1.001 1.002 0.991 0.982 0.981 
2.21E+00 1.003 1.002 0.991 0.982 0.981 
2.21E+00 1.008 1.002 0.991 0.982 0.981 
2.52E+00 1.007 1.004 0.991 0.982 0.981 
2.52E+00 1.008 1.004 0.991 0.982 0.981 
2.64E+00 1.005 1.005 0.991 0.982 0.981 
a
NOTES: Descriptions of the meanings of the values in each column can be obtained from CLREG Documentation 
(BSC 2001c). 
Table III-32. Plutonium Solution Experiments with AENCF as Trend Parametera 
Ind Var Keff(cc) Pred Keff PreClos CL LUTB CL Bonf LTL 
2.46E-03 1.022 1.013 0.991 0.980 0.980 
2.57E-03 1.019 1.013 0.991 0.980 0.980 
2.66E-03 1.024 1.013 0.991 0.980 0.980 
3.80E-03 1.006 1.012 0.991 0.980 0.980 
3.93E-03 1.007 1.012 0.991 0.980 0.980 
5.05E-03 1.002 1.012 0.991 0.980 0.980 
5.14E-03 1.003 1.012 0.991 0.980 0.980 
5.24E-03 1.011 1.012 0.991 0.980 0.980 
5.38E-03 1.009 1.012 0.991 0.980 0.980 
5.41E-03 1.004 1.012 0.991 0.980 0.980 
5.43E-03 1.008 1.012 0.991 0.980 0.980 
5.47E-03 1.003 1.012 0.991 0.980 0.980 
5.48E-03 1.008 1.012 0.991 0.980 0.980 
5.49E-03 1.007 1.012 0.991 0.980 0.980 
5.60E-03 1.012 1.012 0.991 0.980 0.980 
5.61E-03 1.007 1.012 0.991 0.980 0.980 
5.64E-03 1.009 1.012 0.991 0.980 0.980 
5.71E-03 1.009 1.012 0.991 0.980 0.980 
5.79E-03 1.009 1.012 0.991 0.980 0.980 
5.89E-03 1.009 1.012 0.991 0.980 0.980 
CAL-DS0-NU-000003 REV 00A III-42 September 2004 

Criticality Model 
Table III-32. Plutonium Solution Experiments with AENCF as Trend Parametera (Continued) 
Ind Var Keff(cc) Pred Keff PreClos CL LUTB CL Bonf LTL 
5.93E-03 1.011 1.012 0.991 0.980 0.980 
5.93E-03 1.008 1.012 0.991 0.980 0.980 
5.94E-03 1.011 1.012 0.991 0.980 0.980 
5.97E-03 1.008 1.012 0.991 0.980 0.980 
6.10E-03 1.016 1.012 0.991 0.980 0.980 
6.19E-03 1.010 1.012 0.991 0.980 0.980 
6.20E-03 1.011 1.012 0.991 0.980 0.980 
6.20E-03 1.008 1.012 0.991 0.980 0.980 
6.23E-03 1.010 1.012 0.991 0.980 0.980 
6.31E-03 1.010 1.012 0.991 0.980 0.980 
6.33E-03 1.008 1.012 0.991 0.980 0.980 
6.48E-03 1.008 1.012 0.991 0.980 0.980 
6.51E-03 1.009 1.012 0.991 0.980 0.980 
6.64E-03 1.012 1.012 0.991 0.980 0.980 
6.78E-03 1.014 1.012 0.991 0.980 0.980 
6.84E-03 1.010 1.012 0.991 0.980 0.980 
6.84E-03 1.013 1.012 0.991 0.980 0.980 
6.91E-03 1.024 1.012 0.991 0.980 0.980 
6.93E-03 1.012 1.012 0.991 0.980 0.980 
7.03E-03 1.012 1.012 0.991 0.980 0.980 
7.15E-03 1.010 1.011 0.991 0.980 0.980 
7.20E-03 1.010 1.011 0.991 0.980 0.980 
7.23E-03 1.014 1.011 0.991 0.980 0.980 
7.38E-03 1.017 1.011 0.991 0.980 0.980 
7.55E-03 1.011 1.011 0.991 0.980 0.980 
7.66E-03 1.010 1.011 0.991 0.980 0.980 
7.76E-03 1.016 1.011 0.991 0.980 0.980 
7.77E-03 1.024 1.011 0.991 0.980 0.980 
7.85E-03 1.014 1.011 0.991 0.980 0.980 
7.90E-03 1.009 1.011 0.991 0.980 0.980 
8.05E-03 1.010 1.011 0.991 0.980 0.980 
8.27E-03 1.022 1.011 0.991 0.980 0.980 
8.38E-03 1.011 1.011 0.991 0.980 0.980 
8.45E-03 1.017 1.011 0.991 0.980 0.980 
8.45E-03 1.012 1.011 0.991 0.980 0.980 
8.52E-03 1.016 1.011 0.991 0.980 0.980 
8.73E-03 1.015 1.011 0.991 0.980 0.980 
8.79E-03 1.011 1.011 0.991 0.980 0.980 
8.96E-03 1.016 1.011 0.991 0.980 0.980 
9.73E-03 1.013 1.011 0.991 0.980 0.980 
9.94E-03 1.013 1.011 0.991 0.980 0.980 
1.00E-02 1.019 1.011 0.991 0.980 0.980 
1.05E-02 1.013 1.011 0.991 0.980 0.980 
1.06E-02 1.009 1.011 0.991 0.980 0.980 
CAL-DS0-NU-000003 REV 00A III-43 September 2004 

Criticality Model 
Table III-32. Plutonium Solution Experiments with AENCF as Trend Parametera (Continued) 
Ind Var Keff(cc) Pred Keff PreClos CL LUTB CL Bonf LTL 
1.09E-02 1.006 1.011 0.991 0.980 0.980 
1.11E-02 1.020 1.010 0.991 0.980 0.980 
1.16E-02 1.003 1.010 0.991 0.980 0.980 
1.20E-02 1.006 1.010 0.991 0.980 0.980 
1.25E-02 1.010 1.010 0.991 0.980 0.980 
1.30E-02 1.004 1.010 0.991 0.980 0.980 
1.30E-02 1.021 1.010 0.991 0.980 0.980 
1.45E-02 1.003 1.010 0.991 0.980 0.980 
1.65E-02 1.007 1.009 0.991 0.980 0.980 
1.68E-02 1.023 1.009 0.991 0.980 0.980 
1.70E-02 1.011 1.009 0.991 0.980 0.980 
1.76E-02 1.015 1.009 0.991 0.980 0.980 
1.78E-02 1.011 1.009 0.991 0.980 0.980 
1.80E-02 1.009 1.009 0.991 0.980 0.980 
1.81E-02 1.003 1.009 0.991 0.980 0.980 
1.82E-02 1.003 1.009 0.991 0.980 0.980 
2.06E-02 1.002 1.008 0.991 0.980 0.980 
2.16E-02 1.014 1.008 0.991 0.980 0.980 
2.36E-02 1.003 1.007 0.991 0.980 0.980 
2.40E-02 1.006 1.007 0.991 0.980 0.980 
2.48E-02 1.010 1.007 0.991 0.980 0.980 
2.92E-02 1.007 1.006 0.991 0.980 0.980 
2.93E-02 1.007 1.006 0.991 0.980 0.980 
2.97E-02 1.003 1.006 0.991 0.980 0.980 
3.13E-02 1.015 1.005 0.991 0.980 0.980 
3.18E-02 1.010 1.005 0.991 0.980 0.980 
3.21E-02 1.012 1.005 0.991 0.980 0.980 
3.23E-02 1.005 1.005 0.991 0.980 0.980 
3.36E-02 1.000 1.005 0.991 0.980 0.980 
3.42E-02 1.002 1.005 0.991 0.980 0.980 
3.74E-02 0.999 1.004 0.991 0.980 0.980 
3.93E-02 1.006 1.003 0.991 0.980 0.980 
3.97E-02 1.003 1.003 0.991 0.980 0.980 
4.02E-02 1.010 1.003 0.991 0.980 0.980 
4.08E-02 0.993 1.003 0.991 0.980 0.980 
4.16E-02 0.998 1.003 0.991 0.980 0.980 
4.39E-02 0.996 1.002 0.991 0.980 0.980 
4.48E-02 1.003 1.002 0.991 0.980 0.980 
4.61E-02 0.997 1.002 0.991 0.980 0.980 
4.81E-02 1.008 1.001 0.991 0.980 0.980 
5.07E-02 1.000 1.000 0.991 0.980 0.980 
5.39E-02 1.000 1.000 0.990 0.980 0.979 
5.96E-02 0.996 0.998 0.989 0.979 0.978 
NOTES: a Descriptions of the meanings of the values in each column can be obtained from CLREG Documentation 
(BSC 2001c). 
CAL-DS0-NU-000003 REV 00A III-44 September 2004 

Criticality Model 
III.3.5 Range of Applicability 
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. The geometry of the waste package and waste forms 
3. The inherent neutron energy spectrum affecting the fissionable materials. 
In this case, the application is for four experiment subsets representative of a waste package in 
various forms of degradation as defined by the Master Scenarios (YMP 2003, Figures 3-2a 
and -2b). 
Important areas for evaluating criticality are the geometry of the configuration, the concentration 
of important materials (reflecting materials, moderating materials, fissionable materials, and 
significant neutron absorbing materials), and the nuclear cross sections that characterize the 
nuclear reaction rates that will occur in a system containing fissionable and absorbing materials. 
In a light-water moderated and reflected environment with fuel rods arranged in a lattice 
configuration, the neutronic behavior (spectra) is expected to be fairly constant in terms of 
relative distribution regardless of the surrounding environment. Differences in neutron spectra 
between the various configurations are expected to occur as a result of factors including 
H/X ratio, material differences, and moderator temperature differences. 
Figure III-18 illustrates the neutron flux spectral characteristics that were compared for a 
representative 21 PWR waste package (WP in Figure III-20), a PWR CRC statepoint, two MOX 
LCEsSSR53 (1212 PuO2 lattice) and EXP22 (1212 PuO2 Lattice), and one fresh fuel LCE 
(SSR48 UO2 lattice). The MCNP input and output files used to generate the spectral tallies are 
listed in Attachment I but contained in Attachment II. 
CAL-DS0-NU-000003 REV 00A III-45 September 2004 

Criticality Model 
WP 
1.00E-04 
1.00E-03 
1.00E-02 
1.00E-01 
1.00E+00 
Flux FractionCRC 
EXP 22 
SSR 48 
SSR 53 
1.00E-09 
1.00E-08 
1.00E-07 
1.00E-06 
1.00E-05 
1.00E-04 
1.00E-03 
1.00E-02 
1.00E-01 
1.00E+00 
1.00E+01 
Energy (MeV) 
Figure III-18. Neutron Energy Spectra of Waste Package and Critical Benchmarks 
The commercial reactor used for the CRC data was the Crystal River Unit 3 PWR with statepoint 
data corresponding to a mid-cycle restart, performed 400 EFPD into Cycle 6. A fuel assembly 
arrangement in the CRC was represented as shown in Figure III-19. A 21-assembly area of the 
core was represented in a fully flooded, intact waste package configuration as shown in 
Figure III-19. The waste package representation was loaded with a grouping of 21 assemblies 
out of the CRC statepoint to remove material composition differences from the comparison. The 
burned fuel assemblies represented in the waste package varied in average assembly burnup from 
16.4 through 34.4 GWd/MTU and initial enrichments of 2.64 through 3.49 weight percent 235U. 
Each of the irradiated fuel assemblies was represented explicitly with 18 axial nodes in both the 
CRC and in the waste package and was depleted through each of their own unique operating 
history profiles. 
CAL-DS0-NU-000003 REV 00A III-46 September 2004 

Criticality Model 
i) 
2.64 
28.3 
3.29 
30.1 
2.64 
29.6 
3.29 
26.7 
2.95 
34.4 
3.49 
16.4 
2.62 
31.6 
3.29 
25.8 
3.29 
33.2 
3.49 
17.0 
2.95 
32.8 
3.49 
17.1 
3.29 
34.2 
3.29 
24.9 
3.49 
14.2 
2.95 
32.0 
3.49 
17.3 
3.29 
34.3 
3.49 
16.1 
2.62 
23.4 
3.29 
23.4 
2.62 
34.7 
3.49 
16.6 
3.29 
30.9 
3.29 
23.3 
3.29 
30.8 
3.49 
13.2 
2.62 
23.6 
2.95 
23.6 
3.29 
33.2 
3.49 
17.0 
2.95 
32.8 
3.49 
17.1 
3.29 
34.2 
3.29 
24.9 
3.49 
14.2 
2.95 
32.0 
3.49 
17.3 
3.29 
34.3 
3.49 
16.1 
2.62 
23.4 
3.29 
23.4 
2.62 
34.7 
3.49 
16.6 
3.29 
30.9 
3.29 
23.3 
3.29 
30.8 
3.49 
13.2 
2.62 
23.6 
2.95 
23.6 
y placed nto 
Initial Enrichment 
Avg. Burnup (GWd/MTU
XXX 
XXX 
Represents 
assemblwaste package 
Figure III-19. Radial Profile for CRC and Waste Package Spectral Comparison 
A basic understanding of the effect of the spectral variations on reactivity can be achieved by 
evaluating the fission and absorption reaction rates between the systems. The energy dependent 
reaction rates are the product of the neutron flux spectrum and the energy dependent total 
macroscopic cross section. The probability of a fission reaction occurring in the fuel material 
when a neutron is absorbed in the fuel can be expressed in terms of cross sections. It is the ratio 
of the fission cross section to that of the total absorption cross section in the fuel material. A plot 
of reaction rate ratios for a fresh fuel waste package configuration is also provided for 
comparison against the LCEs in order to exhibit that the fuel material composition is what is 
governing the reaction rates. With the total macroscopic cross sections for the fuel region in the 
CRCs and waste package being composed of nearly the same isotopics, the fission probability in 
the fuel material for these two systems will be very nearly the same as shown in Figure III-20. 
The magnitude of the fission to absorption ratio for the CRCs and waste package will vary based 
on burnup, but the shape and area under the curve are expected to remain similar between the 
two systems. 
In the spectral characteristic comparisons, the average flux fraction versus energy was calculated 
across the system as well as the fission and reaction rates. Although spectral shifts of the type 
CAL-DS0-NU-000003 REV 00A III-47 September 2004 

Criticality Model 
seen in the LCEs are the result of several effects (e.g., material, H/X ratio, etc.), when compared 
to the waste package (WP in Figure III-20), the results indicate that CRCs are just as adequate 
for benchmarks and more closely represents the reaction rates for burned fuel in a waste package 
configuration. 
8.50E-01 
8.00E-01 
Fission to Absorption Ratio
7.50E-01 
7.00E-01 
6.50E-01 
6.00E-01 
5.50E-01 
5.00E-01 
4.50E-01 
4.00E-01 
/a 
/a 
/a 
/a 
CRC fWP f/a 
SSR48 fSSR53 fFresh WP f/a 
EXP22 f
0.00E+00
1.00E-07
2.00E-07
3.00E-07
4.00E-07
5.00E-07
6.00E-07
7.00E-07
Energy (MeV) 
Figure III-20. Thermal Region Reaction Ratio Comparison 
The ROA covered by the current set of benchmark experiments are summarized in Table III-33. 
Table III-33. Experiment Parameter Summary 
Number of 
Subset Experiments Range of Applicability 
CRCs 60 Initial enrichment (wt. % 235U): 1.93 through 4.17; System average burnup 
(GWd/MTU): 0.0 through 33; Applicable to intact lattice geometry; Pin pitch 
(cm): 1.26 through 1.62, AENCF (MeV): 0.235 through 0.265 
Lattice LCEs 83 Initial enrichment (wt. % 235U): 2.35 through 5.74; mixture of uranium and MOX 
fuel; Pin Pitch (cm): 1.32 through 2.64 Applicable to intact lattice geometry 
UO2 Solutions 28 Initial enrichment (wt. % 235U): 1.01 through 9.97; H/X: 318 through 1098; 
Applicable to homogeneous mixtures 
Plutonium 107 Initial enrichment (wt. % 239Pu): 91.1 through 99.5; H/X: 91 through 2803; 
Solutions AENCF (eV): 2.46E-03 through 5.96E-02; Applicable to homogeneous mixtures 
CAL-DS0-NU-000003 REV 00A III-48 September 2004 

Criticality Model 
ATTACHMENT IV 
LBTL CALCULATION AND ROA DETERMINATION FOR SHIPPINGPORT LWBR 
CAL-DS0-NU-000003 REV 00A September 2004 

Criticality Model 
CAL-DS0-NU-000003 REV 00A September 2004 

Criticality Model 
ATTACHMENT IV 
LBTL CALCULATION AND ROA DETERMINATION FOR SHIPPINGPORT LWBR 
IV.1 INTRODUCTION 
This attachment presents the calculations of LBTL and the determination of ROA for 
benchmarks that could potentially be applicable to waste package configurations containing 
Shippingport LWBR SNF. A listing of corroborating and supporting data, models, or 
information used for the calculation is provided in Table IV-1. 
Table IV-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 
Shippingport LWBR summary report CRWMS M&O 2000e 
The SNF from the Shippingport LWBR is representative of the thorium-uranium oxide 
(Th/U oxide) SNF group, which is a mixture of thorium and uranium oxides clad with 
Zircaloy-4. The natural uranium concentration in the mixture is a maximum of 5.2 wt. %, 
whereas the 233U content is 5.11 wt. %. 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 LWBR SNF is collected from Evaluation of 
Codisposal Viability for Th/U Oxide (Shippingport LWBR) DOE-Owned Fuel (CRWMS M&O 
2000e, Section 2.1.4). The LWBR core was fueled with fertile 232Th and fissile 233U, the relative 
concentrations of which varied axially and radially across the core to promote high neutron 
economy. The uranium that was used in fabricating the fuel was mostly (greater than 98 wt. %) 
233U, but some isotopic impurities were also present. The design called for vertical fuel rods on a 
triangular pitch with the space between taken up by circulating cooling water. The fuel rods 
featured cladding tubes loaded with cylindrical fuel pellets of thoria (ThO2) or a binary mixture 
of thoria and UO2, and backfilled with helium at 1 atmosphere. The binary fuel is a solid 
solution fabricated from the two oxides in powder form. Processing of the well-mixed powder 
preparation achieved a nearly homogeneous structure due to diffusion at elevated temperature 
during sintering. Axial variations in fissile material concentration was achieved by loading 
individual fuel rods such that part of the length bore a binary mixture of fissile and fertile 
material and the rest bore only fertile material. Radial variation was achieved by the 
arrangement of fuel rods that differed in their axial loading and by using binary pellets of 
different binary mixtures, depending on the radial location of the rod. Details on the fuel rod 
characteristics per each fuel zone in the core are available in Evaluation of Codisposal Viability 
for Th/U Oxide (Shippingport LWBR) DOE-Owned Fuel (CRWMS M&O 2000e, p. 13). 
The standardized 18-in. diameter DOE SNF canister (15-ft-long) placed with five high-level 
radioactive waste (HLW) pour canisters in the waste package is used for disposal of 
Shippingport LWBR fuels, and holds a single Shippingport LWBR SNF seed assembly in a 
CAL-DS0-NU-000003 REV 00A IV-1 September2004 

Criticality Model 
specially designed basket (CRWMS M&O 2000e, Section 2.1.3). A cross section of the DOE 
SNF canister containing one Shippingport LWBR assembly and the waste package containing 
one Shippingport LWBR canister are shown in Figures IV-1 and IV-2, respectively. The basket 
consists of a 295 mm by 257 mm rectangular grid. The basket plate is stainless steel 
(Type 316L) with a 9.5-mm thickness. Inside the basket is placed a spacer to limit the length of 
space available for the Shippingport LWBR seed assembly to 3,350 mm, slightly greater than the 
maximum length of the intact assemblies, including the shipping plates (3,327.4 mm). The 
purpose of this limitation is to avoid significant movements of the assembly within the space 
available during the handling of the DOE SNF canister, with the potential of damaging the 
assembly and the DOE SNF canister components. The spacer consists of a 293 mm by 255 mm 
rectangular tube made of 9.5-mm-thick plates that has a 19.1-mm-thick plate attached at the end 
closer to the assembly location. The spacer plates are made of Stainless Steel Type 316L. 
The void inside the DOE SNF canister will be filled with shot consisting of a mixture of Al and 
GdPO4. This mixture has the role of a neutron absorber intended to prevent criticality inside the 
waste package. 
295 mm 
B-Plate 
257 mm 
DOE SNF Canister 
A-Plate 
Basket Assembly 
9.5-mm-Thick 
Stainless Steel 
(Type 316L) 
Figure IV-1. Cross Section of the DOE SNF Canister Containing an Assembly of Shippingport LWBR 
SNF 
Figure IV-2 presents a simplified cross section of the waste package containing one DOE SNF 
canister placed with 5 HLW canisters in a waste package. 
CAL-DS0-NU-000003 REV 00A IV-2 September2004 

Criticality Model 
lOuter Barrier 
Inner Barrier 
Waste Package 
Basket 
Support Tube 
HLW Gass 
DOE SNF 
Canister 
Figure IV-2. Cross Section of the Waste Package Containing Shippingport LWBR SNF 
IV.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 (of Shippingport LWBR SNF), the selected benchmark experiments 
have been grouped in two subsets (BSC 2002, Section 6.1.7) that include moderated 
heterogeneous and homogeneous experiments. The benchmark experiments come 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 2000e, 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) with MCNP cases constructed and the calculation results. 
The cases, keff results, and their uncertainties for all benchmark experiments are also summarized 
in Analysis of Critical Benchmark Experiments and Critical Limit Calculation for DOE SNF 
(BSC 2003b, Attachment II). Table IV-2 presents the list of the benchmark experiments and the 
number of cases for each subset selected for Shippingport LWBR SNF. 
CAL-DS0-NU-000003 REV 00A IV-3 September2004 

Criticality Model 
Table IV-2. Critical Benchmarks Selected for Shippingport LWBR SNF 
Subset Benchmark Experiment Identificationb No. of Cases Included 
Heterogeneous moderatedc Experiment with SB coresa 8 
HEU-COMP-MIXED-001 26 
U233-SOL-THERM-006 12 
HEU-COMP-THERM-003 15 
HEU-COMP-THERM-005 1 
HEU-COMP-THERM-006 3 
HEU-COMP-THERM-007 3 
HEU-COMP-THERM-011 3 
HEU-COMP-THERM-012 2 
HEU-COMP-THERM-013 2 
Homogeneous moderatedc U233-SOL-THERM-001 5 
U233-SOL-THERM-002 17 
U233-SOL-THERM-003 10 
U233-SOL-THERM-004 8 
U233-SOL-THERM-005 2 
U233-SOL-THERM-006 12 
U233-SOL-THERM-008 1 
HEU-COMP-MIXED-001 26 
Source: Subsets defined and evaluated in BSC 2002 except SB cores experiments that are evaluated in 
BSC 2003b 
NOTES: aThese experiments were evaluated in BSC 2003b, Section 6.1. 
bThe convention for naming the benchmark experiments is from NEA 2001. 
c Identification of each subset from BSC 2002 has been modified to better reflect the subsets 
main characteristics. The benchmark experiments in each subset have not been affected. 
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 Shippingport LWBR DOE SNF as described in 
Section 6.6.1. 
IV.2.1 Range of Applicability of Selected Critical Benchmark Experiments 
This section summarizes in a set of tables (Tables IV-3 to IV-6) the range of applicability of the 
experiments listed in Table IV-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 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 IV-4 September2004 

Criticality Model 
Table IV-3. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with 
Heterogeneous Moderated Configurations of Shippingport LWBR SNF (Set 1) 
Category/ 
Description Parameter 
Experiment 
SB-Coresa 
(8 cases) 
Experiment 
HEU-COMP-
MIXED-001 
(26 cases) 
Experiment 
U233-SOL-
THERM-006 
(6 cases) 
Experiment 
HEU-COMP-
THERM-003 
(15 cases) 
Experiment 
HEU-COMP-
THERM-005 
(1 case) 
Materials/ 
Fissionable 
Fissionable 
Element 
Uranium Uranium Uranium Uranium Uranium 
Material 
Physical 
Form 
235UO2- ZrO2 
(3 cases) or233UO2-ZrO2 
(5 cases) 
UO2 Uranyl nitrate UO2 + Cu UO2 + Cu 
Isotopic 
Composition 
92.73 wt. % 
235U (3 cases) 
97.19 wt. % 
233U (3 cases) 
97.29 wt. % 
233U (5 cases) 
93.15 wt. % 
235U 
97.56 or 
97.54 wt. % 
233U 
79.66 wt. % 
235U 
79.66 wt. % 
235U 
Atomic 
Density 
(atoms/b-cm) 
235U: 
3.8791e-03 (3 
cases)
233U: 2.23e-4 
235U: 4.48e-03 
to 1.39e-02 
233U: 5.14e-04 
to 8.64e-04 
235U: 3.63e-03 
238U: 8.72e-04 
235U: 
4.42e-03 
238U: 1.06 
e-03 
to 3.84e-3 (5 
cases) 
Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. 
Materials/ Element H H H H H 
Moderator Physical 
Form 
Water Water, 
Alcohol-water 
Water in 
aqueous 
Water Water 
solution, solution of 
Plexiglas uranyl nitrate 
Atomic 
Density 
(atoms/b-cm) 
6.67e-2 Fuel Region: 
2.16e-2 
(7 cases) 
5.68e-2 
5.89e-02 to 
6.15e-02 
6.67e-02 6.67e-02 
(Plexiglas) 
6.24e-2 
(alcohol-water) 
Ratio to 37 to 110 0 to 49 69 to 121 51 to 349 23 
Fissile 
Material 
(In Region 
Containing 
Fissile 
Material) 
Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. 
Materials/ 
Reflector 
Material/ 
Physical 
Reflected by 
water 
Reflected by 
polyethylene 
Unreflected Reflected by 
water and 
Reflected by 
water and 
Form stainless steel stainless steel 
Materials/ 
Neutron 
Element None None None None None 
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 IV-5 September2004 

Criticality Model 
Table IV-3. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with 
Heterogeneous Moderated Configurations of Shippingport LWBR SNF (Set 1) (Continued) 
Category/ 
Description Parameter 
Experiment 
SB-Coresa 
(8 cases) 
Experiment 
HEU-COMP-
MIXED-001 
(26 cases) 
ExperimentU233-SOL-
THERM-006 
(6 cases) 
Experiment 
HEU-COMP-
THERM-003 
(15 cases) 
Experiment 
HEU-COMP-
THERM-005 
(1 case) 
Geometry Heterogeneity Various 
arrays 
(triangular- or 
square-
pitched 
lattices) of 
fuel rods 
surrounded 
Complex 
arrays of cans 
in rectangular 
geometry 
Complex 
arrays of cans 
containing 
uranyl nitrate 
solution in 
rectangular 
geometry 
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 
by a blanket 
region and 
cross-shaped 
fuel rods) 
water 
Shape Rectangular, 
hexagonal 
Cylinder Cylinder Cylinder Cylinder 
Neutron AENCF 0.057 to 0.1045 to 0.0344 to 0.0139 to 0.0764 MeV 
Energy 0.095 MeV 0.8015 MeV 0.0599 MeV 0.0467 MeV 
EALF Not available Not available Not available 0.06 to 0.38 1.46 eV 
eV 
Neutron Not available Not available Not available T: 9.9 to T: 6.5% 
Energy 
Spectraa 
37.7% 
I: 26.4 to 37% 
I: 38.4% 
F: 55.1% 
F: 35.9 to 
53.1% 
Fission Rate Not available Not available Not available T: 75.3 to T: 61.3% 
vs. Neutron 94.1% I: 33.8% 
Energya I: 5.2 to F: 4.9% 
21.9% 
F: 0.7 to 2.8% 
Source: BSC 2002, NEA 2001, and BSC 2003b, Section 6.1 
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 IV-6 September2004 

Criticality Model 
Table IV-4. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with 
Heterogeneous Moderated Configurations of Shippingport LWBR SNF (Set 2) 
Experiment 
HEU-COMP-
Experiment 
HEU-COMP-
Experiment 
HEU-COMP-
Experiment 
HEU-COMP-
Experiment 
HEU-COMP-
Category/ 
Description Parameter 
THERM-006 
(3 cases) 
THERM-007 
(3 cases) 
THERM-011 
(3 cases) 
THERM-012 
(2 cases) 
THERM-013 
(2 cases) 
Materials/ Fissionable Uranium Uranium Uranium Uranium Uranium 
Fissionable Element 
Material Physical Form UO2 + Cu UO2 + Cu UO2 + Al alloy UO2 + Al alloy UO2 + Al alloy 
Isotopic 
Composition 
79.66 wt. % 
235U 
79.66 wt. % 235U 79.4 wt. % 235U 79.4 wt. % 235U 79.4 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: 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. Room Temp. 
Materials/ Element Hydrogen Hydrogen Hydrogen Hydrogen Hydrogen 
Moderator Physical Form Water Water; ZrH rods Water Water Water 
Atomic 6.67e-02 6.67e-02 (H2O) 6.68e-02 6.68e-02 6.68e-02 
Density 5.34e-02 (ZrH) 
(atoms/b-cm) 
Ratio to 30 to 716 60 to 91 170 35 40 
Fissile 
Material 
(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 Reflected by water 
Reflector Physical Form water and water and water water 
stainless steel stainless steel 
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 Cylindrical 
hexagonally 
Cylindrical 
hexagonally 
Square clusters of 
cylindrical fuel 
Square clusters of 
cylindrical fuel 
Square clusters of 
cylindrical fuel rods 
pitched lattice pitched double rods arranged in rods arranged in arranged in square 
of cross-lattice of square geometry square geometry geometry 
shaped fuel cross-shaped fuel 
rods rods and ZrH rods 
Shape Cylinder Cylinder Cylinder Cylinder Cylinder 
Neutron AENCF 0.0104 to 0.0339 to 0.047 to 0.051 to 0.043 to 
Energy 0.0720 MeV 0.0475 MeV 0.053 MeV 0.055 MeV 0.048 MeV 
EALF 0.05 to 1.12 0.257 to 0.445 eV 0.43 to 0.72 eV 0.43 to 0.56 eV 0.32 to 0.45 eV 
eV 
Neutron T: 4.9 to 47% T: 8.0 to 11.9% T: 6.6 to 10.0% T: 7.3 to 9.4% T: 8.6 to 12.1% 
Energy 
Spectraa 
I: 23.2 to 
37.7% 
F: 29.8 to 
I: 36.9 to 38.0% 
F: 51.2 to 54.0% 
I: 37.6 to 40.1% 
F: 52.4 to 53.5% 
I: 37.1 to 38.4% 
F: 53.5 to 54.3% 
I: 36 to 37.9% 
F: 51.9 to 53.5% 
57.4% 
Fission Rate T: 64.1 to T: 73.8 to 80.9% T: 68.4 to 74.2% T: 71.8 to 74.7% T: 73.7 to 77.6% 
vs. Neutron 96.1% I: 17.1 to 23.3% I: 22.8 to 28.2% I: 22.2 to 24.8% I: 19.7 to 23.2% 
Energya I: 3.4 to 31.5% 
F: 0.5 to 4.4% 
F: 2 to 2.9% F: 3.0 to 3.4% F: 3.1 to 3.4% F: 2.7 to 3.1% 
Source: BSC 2002 and NEA 2001 
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 IV-7 September2004 

Criticality Model 
Table IV-5. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with 
Homogeneous Moderated Configurations of Shippingport LWBR SNF (Set 1) 
Experiment 
U233-SOL-
Experiment 
U233-SOL-
Experiment 
U233-SOL-
Experiment 
U233-SOL-
Experiment 
U233-SOL-
Category/ 
Description Parameter 
THERM-001 
(5 cases) 
THERM-002 
(17 cases) 
THERM-003 
(10 cases) 
THERM-004 
(8 cases) 
THERM-005 
(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 to 233U: 8.56e-05 to 233U: 4.15e-04 to 233U: 1.27e-04 
Density to 5.00e-05 9.84e-04 1.55e-03 9.84e-04 and 1.60e-04 
(atoms/b-cm) 
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 
Reflector Physical Form paraffin paraffin paraffin water 
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-07 
to 1.01e-6 
N/A N/A N/A N/A 
Geometry Heterogeneity Solution 
contained in an 
Al sphere 
Solution 
contained in an 
Al sphere 
Solution 
contained in 
single Al 
cylindrical vessel 
Solution 
contained in 
single Al 
cylindrical vessel 
2 
configurations: 
first has 
solution 
contained in a 
spherical Al 
vessel,second 
has solution 
contained in 
single Al 
cylindrical 
vessel 
Shape Sphere Sphere Cylindrical Cylindrical Cylindrical/ 
Spherical 
Neutron AENCF 0.0038 to 0.0056 to 0.0490 0.0056 to 0.0693 0.0208 to 0.0493 0.0078 to 
Energy 0.0043 MeV MeV MeV MeV 0.0094 MeV 
EALF 0.0392 to 0.0464 to 0.046 -1.03 eV 0.138 -0.486 eV Not available 
0.0417 eV 0.471 eV 
Neutron 
Energy 
Spectraa 
T: 48.9 to 
52.5% 
I: 21.0 to 
22.6% 
F: 26.5 to 
28.5% 
T: 7.7 to 42.2% 
I: 24.8 to 33.9% 
F: 33.0 to 58.3% 
T: 5.2 to 42.6% 
I: 24.6 to 34.2% 
F: 32.7 to 60.6% 
T: 7.8 to 17.2% 
I: 32.4 to 34.0% 
F: 50.4 to 58.3% 
Not available 
Fission Rate T: 94.0 to T: 76.0 to 92.5% T: 54.5 to 92.7% T: 63.8 to 79.5% Not available 
vs. Neutron 94.8% I: 7.1 to 33.5% I: 7.0 to 41.5% I: 19.3 to 33.4% 
Energya I: 5.0 to 5.8% F: 0.3 to 2.8% F: 0.3 to 4.0% F: 1.2 to 2.8% 
F: 0.2% 
Source: BSC 2002 and NEA 2001 
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 IV-8 September2004 

Criticality Model 
Table IV-6. Range of Applicability of Critical Benchmark Experiments Selected for 
Comparison with Homogeneous Moderated Configurations of Shippingport 
LWBR SNF (Set 2) 
Experiment 
U233-SOL-
Experiment 
U233-SOL-
Experiment 
HEU-COMP-
Category/ THERM-006 THERM-008 MIXED-001 
Description Parameter (6 cases) (1 case) (26 cases) 
Materials/ Fissionable Element Uranium Uranium Uranium 
Fissionable Material Physical Form Uranyl nitrate Uranyl nitrate UO2 
Isotopic Composition 97.56 or 97.54 wt. % 
233U 
97.67 wt. % 
233U 
93.15 wt. % 235U 
Atomic Density 
(atoms/b-cm) 
233U: 5.14e-04 to 
8.64e-04 
233U: 3.34e-05 235U: 4.48e-03 to 
1.39e-02 
Temperature Room Temp. Room Temp. Room Temp. 
Materials/ Element H H H 
Moderator Physical Form Water in aqueous Solution Water, 
solution of uranyl Alcohol-water 
nitrate solution, plexiglas 
Atomic Density 
(atoms/b-cm) 
5.89e-02 to 6.15e-02 6.64e-02 Fuel Region: 
2.16e-2 (few 
cases) 
5.68e-2 
(Plexiglas) 
6.24e-2 
(alcohol-water) 
Ratio to Fissile Material H/X=69 to 121 1324 to 1533 H/X=0 to 49 
Temperature Room Temp. Room Temp. Room Temp. 
Materials/ Material/Physical Form Unreflected Unreflected Reflected by 
Reflector polyethylene 
Materials/ Element None None None 
Neutron Absorber Physical Form N/A N/A N/A 
Atomic Density N/A N/A N/A 
(atoms/b-cm) 
Geometry Heterogeneity Complex arrays of 
cans containing 
uranyl nitrate solution 
in rectangular 
Solution 
contained in an 
Al sphere 
Complex arrays of 
cans in 
rectangular 
geometry 
geometry 
Shape Parallel-piped Sphere Cylinder 
Neutron Energy AENCF 0.0344 to 0.0030 MeV 0.1045 to 
0.0599 MeV 0.8015 MeV 
EALF Not available 0.037 eV Not available 
Neutron Energy Spectraa Not available T: 57.0% 
I: 19.3% 
F: 23.7% 
Not available 
Fission Rate vs. Neutron Not available T: 95.5% Not available 
Energya I: 4.3% 
F: 0.2% 
Source: BSC 2002 and NEA 2001 
NOTE: aSpectral 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 IV-9 September2004 

Criticality Model 
IV.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 Shippingport LWBR 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 Shippingport LWBR SNF are presented in 
Table IV-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 IV-7. Trending Parameter Results for the Critical Benchmark Subset Representative for 
Moderated Intact Fuel (Heterogeneous) Configurations of the Waste Package Containing 
Shippingport LWBR SNF 
Trend 
Parameter n Intercept Slope r2 T t0.025,n-2 P-Value 
Goodness-of-Fit 
Tests 
Valid 
Trend 
AENCF 75 0.9998 -4.87E-03 0.0237 -1.3309 1.960 0.1874 Failed No 
H/X 64 0.9984 1.07E-05 0.0185 1.0821 1.960 0.2834 Failed No 
Source: BSC 2003b, p. 53 
Figure IV-3 presents the keff values and the calculated lower-bound tolerance limit. The LBTL 
value calculated with the distribution-free tolerance limit (DFTL) method for this subset 
(normality test failed) is calculated in Analysis of Critical Benchmark Experiments and Critical 
Limit Calculation for DOE SNF (BSC 2003b, Attachment I) as 0.9751. 
1 
() 
klit 
0.97 
0.98 
0.99 
1.01 
1.02 
1.03 
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
Figure IV-3. Lower-Bound Tolerance Limit Applicable for Shippingport LWBR SNF for Intact 
(Heterogeneous) Moderated Configurations 
CAL-DS0-NU-000003 REV 00A IV-10 September2004 

Criticality Model 
The results of the trending parameter analysis for the critical benchmark subset representative for 
moderated degraded configurations of the waste package containing Shippingport LWBR SNF 
are presented in Table IV-8. 
Table IV-8. Trending Parameter Results for the Critical Benchmark Subset Representative for 
Moderated Degraded Configurations of the Waste Package Containing Shippingport LWBR 
SNF 
Trend 
Parameter n Intercept Slope r2 T t0.025,n-2 P-Value 
Goodness-of-Fit 
Tests 
Valid 
Trend 
AENCF 81 1.0042 -0.0115 0.1205 -3.2902 1.960 1.497E-03 Failed No 
H/X 78 1.0024 -1.02E-06 2.304E-03 -0.4189 1.960 0.6765 Failed No 
Source: BSC 2003b, p. 55 
Figure IV-4 presents the keff values and the calculated LBTL. The LBTL value calculated with 
the DFTL method for this subset (normality test failed) is 0.9748 (BSC 2003b, Attachment I). 
1 
) 
keff 
limit 
0.97 
0.98 
0.99 
1.01 
1.02 
1.03 
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 
AENCF (MeVLower Bound Toerance L
Figure IV-4. Lower-Bound Tolerance Limit Applicable for Shippingport LWBR SNF for Degraded 
(Homogeneous) Moderated Configurations 
Table IV-9 presents a summary of the results of the analyses performed on the subsets of critical 
benchmark experiments applicable to the waste package containing Shippingport LWBR SNF 
and the calculated LBTL values. 
Table IV-9. Lower-Bound Tolerance Limits for Benchmark Subsets Representative for the 
Configurations of the l Waste Packages Containing Shippingport LWBR SNF 
Subset 
Trend 
Parameter 
Test for 
Normality 
Applied 
Calculational 
Method 
Lower-Bound Tolerance Limit or 
Lower-Bound Tolerance Limit Function 
Intact (heterogeneous) Moderated None Failed DFTL Lower-bound tolerance limit = 0.9751 
Degraded (homogeneous) Moderated None Failed DFTL Lower-bound tolerance limit = 0.9748 
Source: BSC 2003b, p. 57 
CAL-DS0-NU-000003 REV 00A IV-11 September2004 

Criticality Model 
INTENTIONALLY LEFT BLANK 
CAL-DS0-NU-000003 REV 00A IV-12 September2004 

Criticality Model 
ATTACHMENT V 
LBTL CALCULATION AND ROA DETERMINATION FOR ENRICO FERMI 
CAL-DS0-NU-000003 REV 00A September 2004 

Criticality Model 
CAL-DS0-NU-000003 REV 00A September 2004 

Criticality Model 
ATTACHMENT V 
LBTL CALCULATION AND ROA DETERMINATION FOR ENRICO FERMI 
V.1 INTRODUCTION 
This attachment presents the calculations of LBTL and the determination of ROA for 
benchmarks that could potentially be applicable to waste package configurations containing 
Enrico Fermi SNF. A listing of corroborating and supporting data, models, or information used 
for the calculation is provided in Table V-1. 
Table V-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 
Enrico Fermi summary report CRWMS M&O 2000c 
The Enrico Fermi uranium-molybdenum (U-Mo) alloy SNF is representative of the U-Zr and 
U-Mo highly enriched uranium (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 Enrico Fermi SNF is collected from Evaluation of 
Codisposal Viability for U-Zr/U-Mo Alloy (Enrico Fermi) DOE-Owned Fuel (CRWMS M&O 
2000c, Section 2.1.4) except where indicated otherwise. The Enrico Fermi SNF pin is made of a 
solid uranium-molybdenum alloy, 3.7592 mm (0.148 in.) in diameter, and is bonded 
metallurgically to a zirconium cladding with an outer diameter of 4.0132 mm (0.158 in.). There 
is no gap between the fuel and the clad. The U-Mo fuel alloy contains 84.6 wt. % U with an 
enrichment of 25.69 wt. % 235U. The length of the SNF pins is 774.70 mm (30.5 in.) and the 
ends of the pins have been cold swaged to a point to provide mechanical seal for the U-Mo alloy. 
Currently, all the Enrico Fermi fuel assemblies are disassembled (derodded), and the fuel pins 
are stored under water in aluminum canisters. Fuel sections of 140 pins are stored loose-packed 
without any supporting/spacing mechanism in aluminum canisters (referred to as -04 canisters) 
that were placed inside aluminum shipping canisters (referred to as -01 canisters) (CRWMS 
M&O 2000c, Section 2.1.3). 
The current conceptual design for disposing Enrico Fermi SNF in the repository is the use of the 
standardized 18-in. diameter DOE SNF codisposal canister (CRWMS M&O 2000c, 
Section 2.1.3) placed with five HLW pour canisters in the waste package. The DOE SNF 
canister is placed in a carbon-steel support basket that holds the canister in the center of the 
waste package. The five HLW canisters are evenly spaced around the support that holds the 
DOE SNF canister. 
The disposal configuration for the Enrico Fermi SNF comprises a stack of two baskets 
containing SNF placed inside a DOE SNF canister. Twelve 4-in. diameter stainless steel pipes 
CAL-DS0-NU-000003 REV 00A V-1 September2004 

Criticality Model 
(316L) are welded to a base plate to form a basket. An aluminum shipping canister 
(-01 canister) containing the -04 canister with 140 fuel pins is placed in each fuel pipe. The 
space between all the 4-in.-diameter pipes in each basket and between each -01 canister and 
the stainless steel pipe is filled with a mixture of iron shot (moderator displacer) and gadolinium 
phosphate (neutron absorber). The iron shot contains 3 percent by volume gadolinium phosphate 
(GdPO4), i.e., 14.5 kg of gadolinium phosphate per 737.9 kg of iron (CRWMS M&O 2000c, 
pp. vii and viii). 
Figure V-1 presents a cross section of the DOE SNF canister containing Enrico Fermi SNF 
placed in a waste package. The rest of the waste package is not represented in order to show the 
constituents inside the DOE SNF canister. 
Diiing 
Alumiith 
l Pins 
4 
MiInner 
Supporti18-inch 
ameter DOE 
SNF Canister 
4-inch Dameter 
Pipe Containnum 
Canisters w140 FueIron shotGdPOxture 
HLW Canister 
Waste 
Package 
ng 
Structure 
Figure V-1. Cross Section of the DOE SNF Canister Containing Enrico Fermi SNF Placed Inside Waste 
Package 
V.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 Enrico Fermi SNF), the selected benchmark 
experiments have been grouped in four subsets (BSC 2002, Section 6.1.4), that include 
heterogeneous and homogeneous experiments, each divided into subsets of moderated (thermal 
spectrum) and nonmoderated experiments (fast spectrum). The benchmark experiments come 
from International Handbook of Evaluated Criticality Safety Benchmark Experiments 
CAL-DS0-NU-000003 REV 00A V-2 September2004 

Criticality Model 
(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 
2000c, 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) 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 V-2 presents the list of the benchmark experiments and the 
number of cases for each subset selected for Enrico Fermi SNF. 
The experiments cover configuration classes IP-1a, IP-2a, IP-3a, IP-3b, IP-3c, and IP-3d for the 
degraded waste package containing Enrico Fermi SNF as described in Section 7. 
Table V-2. Critical Benchmarks Selected for Enrico Fermi SNF 
Subset Benchmark Experiment Identificationa No. of Cases Included 
Heterogeneous Moderatedb IEU-COMP-THERM-002 6 
IEU-COMP-THERM-003 2 
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 
IEU-COMP-THERM-001 29 
Heterogeneous Nonmoderatedb IEU-MET-FAST-001 4 
IEU-MET-FAST-002 1 
IEU-MET-FAST-003 1 
IEU-MET-FAST-004 1 
IEU-MET-FAST-005 1 
IEU-MET-FAST-006 1 
IEU-MET-FAST-007 1 
IEU-MET-FAST-008 1 
IEU-MET-FAST-009 1 
IEU-MET-FAST-010 1 
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: Subsets defined in BSC 2002 
NOTES: a 
bThe convention for naming the benchmark experiments is from NEA 2001. 
Identification of each subset from BSC 2002 has been modified to better reflect the subsets main 
characteristics. The benchmark experiments in each subset have not been affected. 
CAL-DS0-NU-000003 REV 00A V-3 September2004 

Criticality Model 
V.2.1 RANGE OF APPLICABILITY OF SELECTED CRITICAL BENCHMARK 
EXPERIMENTS 
This section summarizes in a set of tables (Tables V-3 to V-9) the range of applicability of the 
experiments listed in Table V-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. 
Table V-3. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with 
Heterogeneous Moderated Configurations of Enrico Fermi SNF (Set 1) 
Category/ 
Description 
Parameter Experiment 
IEU-COMP-
THERM-001 
Experiment 
IEU-COMP-
THERM-002 
Experiment 
IEU-COMP-
THERM-003 
Experiment 
HEU-COMP-
THERM-003 
(29 cases) (6 cases) (2 cases) (15 cases) 
Materials/ Fissionable Uranium Uranium Uranium Uranium 
Fissionable Element 
Material Physical Form UF4 compound UO2 U-ZrH UO2 + Cu 
with polytetrafluoroethylene 
Isotopic 
Composition 
29.83 wt. % 235U 17 wt. % 235U 19.9 wt. % 235U 79.66 wt. % 235U 
Atomic 235U: 2.37e-03 235U: 1.89e-03 235U: 3.68e-04 235U: 3.63e-03 
Density 238U: 5.50e-03 238U: 9.06e-03 238U: 1.46e-03 238U: 8.72e-04 
(atoms/b-cm) 
Temperature Room Temp. 288 K to 492 K Room Temp. Room Temp. 
Materials/ 
Moderator 
Element H; C H H H 
Physical Form Polyethylene Water ZrH; Water Water 
Atomic H:7.5224e-02 5.64e-02 to 5.63e-02 (in 6.67e-02 
Density 
(atoms/b-cm) 
C:3.9232e-02 6.67e-02 ZrH) 
6.67e-02 (H2O) 
Ratio to 
Fissile 
Range: 
H/235U = 4 to 222 
Not available 150.1 51 to 349 
Material 
(In Region 
Containing 
Fissile 
Material) 
Temperature Room Temp. 288 K to 492 K Room Temp. Room Temp. 
Materials/ 
Reflector 
Material/ 
Physical Form 
Unreflected or 
reflected by 
paraffin, Cd 
Reflected by water Reflected 
radially by 
graphite and 
Reflected by water 
and stainless steel 
axially by water 
Materials/ 
Neutron 
Element B or Cd for some 
experiments 
Gd, Cd for some 
experiments 
B None 
Absorber Physical Form Metallic sheets Gd2O3 or CdO B4C absorber Not needed for 
placed in rods rods ROA and ROP 
comparison 
CAL-DS0-NU-000003 REV 00A V-4 September2004 

Criticality Model 
Table V-3. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with 
Heterogeneous Moderated Configurations of Enrico Fermi SNF (Set 1) (Continued) 
Experiment 
IEU-COMP-
Experiment 
IEU-COMP-
Experiment 
IEU-COMP-
Experiment 
HEU-COMP-
Category/ THERM-001 THERM-002 THERM-003 THERM-003 
Description Parameter (29 cases) (6 cases) (2 cases) (15 cases) 
Atomic 
Density 
(atoms/b-cm) 
N/A Gd-2.16e-3 Not needed for 
ROA and ROP 
comparison 
Not needed for 
ROA and ROP 
comparison 
Geometry Heterogeneity Heterogeneous 
small cubes of 
fissile compound 
interspersed with 
moderator cubes 
Cylindrical 
hexagonally 
pitched lattice of 
pins (pitch=6.8 cm) 
Complex 
cylindrical 
arrays of pins 
Cylindrical two 
zones hexagonally 
pitched lattice of 
cross-shaped fuel 
rods 
Shape Cuboid Cylinder Cylinder Cylinder 
Neutron AENCF 0.0455 to 0.2168 0.0440 to 0.0240 MeV 0.0139 to 0.0467 
Energy MeV 0.0490 MeV MeV 
EALF 0.11 to 9.09 eV Not available Not available 0.06 to 0.38 eV 
Neutron T: 1.8 to 22.8% Not available Not available T: 9.9 to 37.7% 
Energy 
Spectraa 
I: 24.9 to 40.2% 
F: 49.6 to 63% 
I: 27.4 to 37% 
F: 35.9 to 53.1% 
Fission Rate T: 47.5 to 90.9% Not available Not available T: 75.3 to 94.1% 
vs. Neutron I: 7.1 to 42.8% I: 5.2 to 21.9% 
Energya F: 2.0 to 11.1% F: 0.7 to 2.8% 
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 V-5 September2004 

Criticality Model 
Table V-4. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with 
Heterogeneous Moderated Configurations of Enrico Fermi SNF (Set 2) 
Experiment 
HEU-COMP-
Experiment 
HEU-COMP-
Experiment 
HEU-COMP-
Experiment 
HEU-COMP-
Category/ THERM-004 THERM-005 THERM-006 THERM-007 
Description Parameter (4 cases) (1 case) (3 cases) (3 cases) 
Materials/ 
Fissionable 
Fissionable 
Element 
Uranium Uranium Uranium Uranium 
Material Physical Form UO2 + Cu UO2 + Cu UO2 + Cu UO2 + Cu 
Isotopic 
Composition 
88.87 wt. % 235U 79.66 wt. % 235U 79.66 wt. % 235U 79.66 wt. % 235U 
Atomic Density 
(atoms/b-cm) 
235U: 5.13e-03 
238U: 5.77e-04 
235U: 4.42e-03 
238U: 1.06 e-03 
235U: 4.42e-03 
238U: 1.06 e-03 
235U: 3.63e-03 
238U: 8.72e-04 
Temperature Room Temp. Room Temp. Room Temp. Room Temp. 
Materials/ Element Hydrogen Hydrogen Hydrogen Hydrogen 
Moderator Physical Form Water Water Water Water; ZrH rods 
Atomic Density 
(atoms/b-cm) 
6.67e-02 6.67e-02 6.67e-02 6.67e-02 (H2O) 
5.34e-02 (ZrH) 
Ratio to Fissile 35 23 30 to 716 60 to 91 
Material 
(In Region 
Containing 
Fissile 
Material) 
Temperature Room Temp. Room Temp. Room Temp. Room Temp. 
Materials/ Material/ Reflected by Reflected by Reflected by Reflected by 
Reflector Physical Form water and water and water and water and 
stainless steel stainless steel stainless steel stainless steel 
Materials/ 
Neutron 
Absorber 
Element Gd; Sm None None None 
Physical Form Gd2O3 or Sm2O3 
Rods 
N/A N/A N/A 
Atomic Density 
(atoms/b-cm) 
Gd: 3.11e-04 N/A N/A N/A 
Geometry Heterogeneity Cylindrical 
hexagonally 
Hexagonally 
pitched array of 
Cylindrical 
hexagonally 
Cylindrical 
hexagonally 
pitched double fuel rod clusters pitched lattice of pitched double 
lattice of cross-(each containing cross-shaped fuel lattice of cross-
shaped fuel rods a hexagonally rods shaped fuel rods 
and absorber pitched lattice of and ZrH rods 
rods cross-shaped fuel 
rods) 
Shape Cylinder Cylinder Cylinder Cylinder 
Neutron AENCF 0.0736 to 0.0764 MeV 0.0104 to 0.0339 to 
Energy 0.0756 MeV 0.0720 MeV 0.0475 MeV 
EALF 1.35 to 1.52 eV 1.46 eV 0.05 to 1.12 eV 0.257 to 0.445 eV 
Neutron T: 3.6 to 4.1% T: 6.5% T: 4.9 to 47% T: 8.0 to 11.9% 
Energy 
Spectraa 
I: 38.2 to 38.5% 
F: 57.6 to 58.1% 
I: 38.4% 
F: 55.1% 
I: 23.2 to 37.7% 
F: 29.8 to 57.4% 
I: 36.9 to 38.0% 
F: 51.2 to 54.0% 
Fission Rate T: 60.6 to 62.6% T: 61.3% T: 64.1 to 96.1% T: 73.8 to 80.9% 
vs. Neutron I: 32.9 to 34.7% I: 33.8% I: 3.4 to 31.5% I: 17.1 to 23.3% 
Energya F: 4.5 to 4.7% F: 4.9% F: 0.5 to 4.4% F: 2 to 2.9% 
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 V-6 September2004 

Criticality Model 
Table V-5. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with 
Heterogeneous Nonmoderated Configurations of Enrico Fermi SNF (Set 3) 
Experiment 
IEU-MET-
Experiment 
IEU-MET-
Experiment 
IEU-MET-
Experiment 
IEU-MET-
Experiment 
IEU-MET-
Category/ FAST-001 FAST-002 FAST-003 FAST-004 FAST-005 
Description Parameter (4 cases) (1 case) (1 case) (1 case) (1 case) 
Materials/ 
Fissionable 
Fissionable 
Element 
Uranium Uranium Uranium Uranium Uranium 
Material Physical Form Metal discs 
(highly 
enriched 
Metal discs 
(highly 
enriched 
U metal U metal U metal 
interspersed 
with natural 
interspersed 
with natural U 
U 
Isotopic 
Composition 
93.4 wt. % 
235U (for 
highly 
enriched 
16.19 wt. % 
235U 
(average) 
36.5 wt. % 235U 
(average) 
36.5 wt. % 235U 
(average) 
36.5 wt. % 235U 
(average) 
discs[HEU]) 
Atomic Density 
(atoms/b-cm) 
For HEU 
disks 
235U: 
235U: 
7.78e-03 
238U: 
235U: 1.71e-02 
238U: 2.92e-02 
235U: 1.74e-02 
238U: 2.97e-02 
235U: 1.72e-02 
238U: 2.93e-03 
4.50e-02 
238U: 
3.97e-01 
2.65e-03 
Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. 
Materials/ 
Moderator 
Element None None None None None 
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 
Ratio to Fissile N/A N/A N/A N/A N/A 
material 
Temperature N/A N/A N/A N/A N/A 
Materials/ 
Reflector 
Material/ 
Physical Form 
Unreflected Reflected by 
natural U 
Unreflected Reflected by 
graphite 
Reflected by 
steel 
Materials/ Element None None None None None 
Neutron 
Absorber Physical Form N/A N/A N/A N/A N/A 
Atomic Density N/A N/A N/A N/A N/A 
(atoms/b-cm) 
Geometry Heterogeneity Complex 
cylindrical 
geometry 
comprising 
interspersed 
U discs 
Complex 
cylindrical 
geometry 
comprising 
interspersed 
U discs 
Spherical core 
with multiple 
layers 
Spherical core 
with multiple 
layers 
Spherical core 
with multiple 
layers 
(highly 
enriched and 
(highly 
enriched and 
natural U) natural U) 
Shape Cylinder Cylinder Sphere Sphere Sphere 
CAL-DS0-NU-000003 REV 00A V-7 September2004 

Criticality Model 
Table V-5. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with 
Heterogeneous Nonmoderated Configurations of Enrico Fermi SNF (Set 3) (Continued) 
Category/ 
Description Parameter 
Experiment 
IEU-MET-
FAST-001 
(4 cases) 
Experiment 
IEU-MET-
FAST-002 
(1 case) 
Experiment 
IEU-MET-
FAST-003 
(1 case) 
Experiment 
IEU-MET-
FAST-004 
(1 case) 
Experiment 
IEU-MET-
FAST-005 
(1 case) 
Neutron 
Energy 
AENCF 1.3859 to 
1.4398 MeV 
1.2784 MeV 1.3502 MeV 1.3071 MeV 1.2852 MeV 
EALF from 7.18e5 
to 7.74 e5 eV 
5.64e05 eV 6.87e05 eV 6.46e05 eV 6.47e05 eV 
Neutron 
Energy 
Spectraa 
T: 0% 
I: 5.4 to 6.8% 
F: 93.2 to 
94.6% 
T: 0% 
I: 14% 
F: 86 
T: 0% 
I: 7.2% 
F: 92.8 
T: 0% 
I: 8.2% 
F: 91.8% 
T: 0% 
I: 7.8% 
F: 92.2% 
Fission Rate 
vs. Neutron 
Energya 
T: 0% 
I: 7 to 8.3% 
F: 91.7 to 
93% 
T: 0% 
I: 15.4% 
F: 84.6% 
T: 0% 
I: 8.8% 
F: 91.2% 
T: 0% 
I: 10.1% 
F: 89.9% 
T: 0% 
I: 9.6% 
F: 90.4% 
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]. 
Table V-6. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with 
Heterogeneous Nonmoderated Configurations of Enrico Fermi SNF (Set 4)
Experiment 
IEU-MET-
Experiment 
IEU-MET-
Experiment 
IEU-MET-
Experiment 
IEU-MET-
Experiment 
IEU-MET-
Category/ 
Description Parameter 
FAST-006 
(1 case) 
FAST-007 
(1 case) 
FAST-008 
(1 case) 
FAST-009 
(1 case) 
FAST-010 
(1 case) 
Materials/ Fissionable Uranium Uranium Uranium Uranium Uranium 
Fissionable Element 
Material Physical U metal U metal U metal U metal U metal 
Form 
Isotopic 
Composition 
36.5 wt. % 235U 
(average) 
10 wt. % 235U 
(average) 
36.5 wt. % 
235U (average) 
36.5 wt. % 
235U (average) 
9 wt. % 235U 
(average) 
Atomic 235U: 1.72e-02 235U: 4.82e-03 235U: 1.72e-02 235U: 1.74e-02 235U: 
Density 
(atoms/b-cm) 
238U: 2.93e-02 238U: 4.32e-02 238U: 2.95e-02 238U: 2.99e-02 3.48e-03 
238U: 
3.52e-02 
Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. 
Materials/ 
Moderator 
Element None None None None None 
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 
Ratio to N/A N/A N/A N/A N/A 
Fissile 
Material 
Temperature N/A N/A N/A N/A N/A 
CAL-DS0-NU-000003 REV 00A V-8 September2004 

Criticality Model 
Table V-6. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with 
Heterogeneous Nonmoderated Configurations of Enrico Fermi SNF (Set 4) (Continued) 
Experiment 
IEU-MET-
Experiment 
IEU-MET-
Experiment 
IEU-MET-
Experiment 
IEU-MET-
Experiment 
IEU-MET-
Category/ FAST-006 FAST-007 FAST-008 FAST-009 FAST-010 
Description Parameter (1 case) (1 case) (1 case) (1 case) (1 case) 
Materials/ 
Reflector 
Material/ 
Physical 
Form 
Reflected by 
duralumin 
Reflected by 
depleted U 
Reflected by 
depleted U 
Reflected by 
polyethylene 
Reflected by 
depleted U 
Materials/ 
Neutron 
Absorber 
Element None None None None None 
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 Spherical core 
with multiple 
layers 
Complex 
cylindrical 
geometry 
Spherical core 
with multiple 
layers 
Spherical core 
with multiple 
layers 
Spherical 
core with 
multiple 
layers 
Shape Sphere Cylinder Sphere Sphere Sphere 
Neutron AENCF 1.2892 MeV 1.2530 MeV 1.3650 MeV 1.0140 MeV 1.1490 MeV 
Energy EALF 6.39e05 eV 4.97e05 eV 6.85e05 eV 1.68e04 eV 4.25e05 eV 
Neutron T: 0% T: 0% T: 0% T: 0.1% T: 0% 
Energy 
Spectraa 
I: 8% 
F: 92% 
I: 19.0% 
F: 81% 
I: 7.9% 
F: 92.1% 
I: 9.6% 
F: 90.3% 
I: 22% 
F: 78% 
Fission Rate T: 0% T: 0% T: 0% T: 17.5% T: 0% 
vs. Neutron I: 9.8% I: 19.6% I: 9.8% I: 19.3% I: 22.7% 
Energya F: 90.2% F: 80.4% F: 90.2% F: 63.2% F: 77.3% 
Source: BSC 2002 and NEA 2001, Spectra 
NOTE: aSpectral 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 V-9 September2004 

Criticality Model 
Table V-7. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with 
Homogeneous Moderated Configurations of Enrico Fermi SNF (Set 1) 
Experiment 
IEU-SOL-
Experiment 
IEU-COMP-
Experiment 
LEU-SOL-
Experiment 
LEU-SOL-
Experiment 
LEU-SOL-
Category/ 
Description Parameter 
THERM-001 
(4 cases) 
THERM-001 
(29 cases) 
THERM-003 
(9 cases) 
THERM-004 
(7 cases) 
THERM-006 
(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 
7.90e-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 1438 719 to 1018 532 
Material 
Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. 
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 
Heterogeneous 
small cubes of 
Homogeneous 
solution in a 
Homogeneous 
solution in a 
Homogeneous 
solution in a 
contained in a 
cylindrical tank 
fissile compound 
interspersed with 
moderator cubes 
spherical tank cylindrical tank cylindrical tank 
Shape Cylinder Cuboid Sphere Cylinder Cylinder 
Neutron AENCF 0.0149 to 0.0455 to 0.0114 to 0.0142 to 0.0245 to 0.0257 
Energy 0.0275 MeV 0.2168 MeV 0.0186 MeV 0.0188 MeV MeV 
EALF 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 to 27.3% 
F: 28.2 to 35.1% 
I: 25.3 to 27.8% 
F: 31.6 to 35.4% 
I: 30 to 30.5% 
F: 38.8 to 43.5% 
Fission Rate T: 90.7 to 94.6% T: 47.5 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: 2.0 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 
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 V-10 September2004 

Criticality Model 
Table V-8. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with 
Homogeneous Moderated Configurations of Enrico Fermi SNF (Set 2) 
Experiment 
LEU-SOL-
Experiment 
LEU-SOL-
Experiment 
LEU-SOL-
Experiment 
LEU-SOL-
Experiment 
LEU-SOL-
Category/ 
Description Parameter 
THERM-007 
(5 cases) 
THERM-008 
(4 cases) 
THERM-009 
(3 cases) 
THERM-010 
(4 cases) 
THERM-016 
(7 cases) 
Materials/ Fissionable Uranium Uranium Uranium Uranium Uranium 
Fissionable Material Element 
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: 6.18e-05 235U: 6.14e-05 235U: 6.26e-05 235U: 6.18e-05 to 235U: 7.65e-5 to 
Density 
(atoms/b-cm) 
to 8.00e-05 
238U:5.5e-04 
to 6.13e-05 
238U: 5.47e-04 
to 6.25e-06 
238U: 5.57e-04 
6.21e-05 
238U: 5.51e-04 to 
1.19e-04 
238U: 6.82e-04 to 
to 7.12e-04 to 5.49e-04 to 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 polyethylene water 
concrete 
Materials/ 
Neutron Absorber 
Element None None None None None 
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 
Homogeneous 
solution 
Homogeneous 
solution 
Homogeneous 
solution in a 
Homogeneous 
solution in a 
contained 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 Energy AENCF 0.0159 to 0.0152 to 0.0155 to 0.0153 to 0.0180 to 
0.0200 MeV 0.0154 MeV 0.0158 MeV 0.0154 MeV 0.0267 MeV 
EALF 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 T: 41.5 to T: 40.8 to 4 T: 41.6% T: 29.1 to 37.7% 
Energy 
Spectraa 
41.1% 
I: 26 to 28.1% 
F: 32.9 to 36% 
41.7% 
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 to 
39.7% 
Fission Rate T: 95.9 to T: 96.8% T: 96.7% T: 96.8% T: 94.3 to 96.2% 
vs. Neutron 96.7% I: 2.6% to 2.8% I: 2.7% I: 2.6% I: 3.2 to 4.6% 
Energya I: 2.7 to 3.4% 
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 
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 V-11 September2004 

Criticality Model 
Table V-9. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with 
Homogeneous Moderated Configurations of Enrico Fermi SNF (Set 3) 
Category/ 
Description 
Parameter Experiment 
LEU-SOL-
THERM-017 
Experiment 
LEU-SOL-
THERM-018 
Experiment 
LEU-SOL-
THERM-019 
Experiment 
LEU-SOL-
THERM-020 
Experiment 
LEU-SOL-
THERM-021 
(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 
Density 
(atoms/b-cm) 
235U: 8.05e-05 to 
1.19e-04 
238U:7.17e-04 to 
1.06e-03 
235U: 7.87e-5 to 
8.04e-05 
238U: 7.01e-04 
7.16e-04 
235U: 8.07e-05 
to 8.13e-05 
238U: 7.19e-04 
to 7.24e-04 
235U: 4.95e-05 to 
6.21e-05 
238U: 4.41e-04 to 
5.53e-04 
235U: 4.95e-5 to 
6.21e-05 
238U: 4.41e-04 
to 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 to 729 731 to 751 721 to 728 971 to 1239 971 to 1239 
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 AENCF 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 
EALF 4.24e-02 to 0.042-0.0425 Not available Not available Not available 
5.23e-02 eV eV 
Neutron T: 28.9 to 36.5% T: 36.5 - 37.0 Not available Not available Not available 
Energy 
Spectraa 
I: 28 to 31.1% 
F: 35.5 to 40.0% 
% 
I: 28.0 - 28.3 % 
F: 34.9 - 35.2 
% 
Fission Rate T: 94.3 to 96.0% T: 96.0% Not available Not available Not available 
vs. Neutron I: 3.3 to 4.6% I: 3.3% 
Energya F: 0.7 to 1.0% F: 0.7 
Source: BSC 2002 and NEA 2001, Spectra 
NOTE: aSpectral 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 V-12 September2004 

Criticality Model 
V.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 Enrico Fermi 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 configurations of the waste package 
containing Enrico Fermi SNF are presented in Table V-10. 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 V-10. Trending Parameter Results for the Critical Benchmark Subset Representative for 
Moderated Intact (Heterogeneous) Configurations of the Waste Package Containing Enrico 
Fermi SNF 
Trend 
Parameter n Intercept Slope r2 T t0.025,n-2 P-Value 
Goodness-of-Fit 
Tests 
Valid 
Trend 
AENCF 63 1.0005 -0.0214 0.0376 -1.5430 1.960 0.1280 Failed No 
Enrichment 
(235U/U) 
63 0.9990 -3.4E-06 2.24E-04 -0.1169 1.960 0.9073 Failed No 
H/235U 57 0.9976 1.51E-05 0.0697 2.0295 1.960 0.0473 Failed No 
keff 
Source: BSC 2003b, p. 39 
Figure V-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 0.9751 (BSC 2003b, Attachment I). 
1.020
1.015
1.010
1.005
1.000
0.995
0.990
0.985
0.980
0.975
0.970
0.00 0.05 0.10 0.15 0.20 0.25 
litLower Bound Toerance Lim
AENCF (MeV) 
Figure V-2. Lower-Bound Tolerance Limit Applicable for Enrico Fermi SNF Intact (Heterogeneous) 
Moderated Configurations 
CAL-DS0-NU-000003 REV 00A V-13 September2004 

Criticality Model 
The results of the trending parameter analysis for the critical benchmark subset representative for 
nonmoderated intact configurations of the waste package containing Enrico Fermi SNF are 
presented in Table V-11. 
Table V-11. Trending Parameter Results for the Critical Benchmark Subset Representative for 
Nonmoderated Intact Fuel (Heterogeneous) Configurations of the Waste Package 
Containing Enrico Fermi SNF 
Trend 
Parameter n Intercept Slope r2 T t0.025,n-2 P-Value 
Goodness-of-Fit 
Tests 
Valid 
Trend 
AENCF 13 1.0132 -6.26E-03 0.0325 -0.6082 2.201 0.5554 Failed No 
keff 
Source: BSC 2003b, p. 40 
Figure V-3 presents the keff values and the calculated LBTL. The LBTL value calculated with 
NDTL method for this subset (the normality test passed) is 0.9872 (BSC 2003b, Attachment I). 
1.015 
1.010 
1.005 
1.000 
0.995 
0.990 
0.985 
litLower Bound Toerance Lim
0.90 1.00 1.10 1.20 1.30 1.40 1.50 
AENCF (MeV) 
Figure V-3. Lower-Bound Tolerance Limit Applicable for Enrico Fermi SNF for Intact (Heterogeneous) 
Nonmoderated Configurations 
The results of the trending parameter analysis for the critical benchmark subset representative for 
moderated degraded configurations of the waste package containing Enrico Fermi SNF are 
presented in Table V-12. 
CAL-DS0-NU-000003 REV 00A V-14 September2004 

Criticality Model 
Table V-12. Trending Parameter Results for the Critical Benchmark Subset Representative for Moderated 
Degraded (Homogeneous) Configurations of the Waste Package Containing Enrico Fermi SNF 
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 
(235U/U) 
103 1.0048 -2.5E-04 0.1300 -3.8842 1.960 1.84E-04 Failed No 
H/235U 103 0.9984 3.93E-06 0.0664 2.6792 1.960 8.618E-03 Failed No 
Source: BSC 2003b, p. 41 
Figure V-4 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). 
) 
k 
it 
0.960 
0.965 
0.970 
0.975 
0.980 
0.985 
0.990 
0.995 
1.000 
1.005 
1.010 
1.015 
0.00 0.05 0.10 0.15 0.20 0.25 
AENCF (MeVeff 
Lower Bound Tolerance Lim
Figure V-4. Lower-Bound Tolerance Limit Applicable for Enrico Fermi SNF for Degraded 
(Homogeneous) Moderated Configurations 
Table V-13 presents a summary of the results of the analyses performed on the subsets of critical 
benchmark experiments applicable to the waste package containing Enrico Fermi SNF and the 
calculated LBTL values. 
Table V-13. Lower-Bound Tolerance Limits for Benchmark Subsets Representative for the 
Configurations of the Waste Package Containing Enrico Fermi SNF 
Subset 
Trend 
Parameter 
Test for 
Normality 
Applied 
Calculational 
Method 
Lower-Bound Tolerance 
Limit or Lower-Bound 
Tolerance Limit Function 
Intact (Heterogeneous) Moderated None Failed DFTL CL = 0.9751 
Intact (Heterogeneous) Nonmoderated None Passed NDTL CL = 0.9872 
Degraded (Homogeneous) Moderated None Failed DFTL CL = 0.9659 
Source: BSC 2003b, p. 43 
CAL-DS0-NU-000003 REV 00A V-15 September2004 

Criticality Model 
INTENTIONALLY LEFT BLANK 
CAL-DS0-NU-000003 REV 00A V-16 September2004 

Criticality Model 
ATTACHMENT VI 
LBTL CALCULATION AND ROA DETERMINATION FOR N-REACTOR 
CAL-DS0-NU-000003 REV 00A September 2004 

Criticality Model 
CAL-DS0-NU-000003 REV 00A September 2004 

Criticality Model 
ATTACHMENT VI 
LBTL CALCULATION AND ROA DETERMINATION FOR N-REACTOR 
VI.1 INTRODUCTION 
This attachment presents the calculations of LBTL and the determination of ROA for 
benchmarks that could potentially be applicable to waste package configurations containing 
N-Reactor SNF. A listing of corroborating and supporting data, models, or information used for 
the calculation is provided in Table VI-1. 
Table VI-1. Supporting Information and Sources 
Description Source 
Guidance for benchmarking of a calculational method Dean and Tayloe 2001 
Criticality benchmark experiments, tending parameters, BSC 2002; BSC 2003b; NEA 2001, and 
and CL calculations CRWMS M&O 1999a 
N-Reactor summary report CRWMS M&O 2001 
The N-Reactor SNF is representative of the uranium metal (U-metal) 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 N-Reactor SNF is collected from Evaluation of Codisposal 
Viability for U-Metal (N Reactor) DOE-Owned Fuel (CRWMS M&O 2001, Section 2.1.3). The 
N-Reactor fuels are composed of zirconium cladding and a low-enriched uranium metal fuel 
matrix. The N-Reactor fuel elements consist of the two basic design variants, both of which use 
two concentric tubes of uranium metal co-extruded with Zircaloy-2 cladding. The N-Reactor 
core was fueled with low enriched (0.947 wt. %, and 0.947 to 1.25 wt. % 235U in Mark IV and 
Mark IA fuels, respectively) uranium metal. Differences in the enrichment were selected based 
on the intended mode of reactor operation (i.e., plutonium or power production). Table VI-2 
presents the main characteristics of the N-Reactor fuel elements. 
CAL-DS0-NU-000003 REV 00A VI-1 September2004 

Criticality Model 
Table VI-2. N-Reactor Fresh Fuel Elements Description 
Fuel type Mark IV Mark IA 
Preirradiation enrichment of 235U 0.947% enriched 0.947% and 1.25% enriched for the 
inner and outer cylinders of the fuel 
element, respectively 
Type-length codea E S A C M T FF 
Length, cm (in.) 66 62 59 44 53b 50 38 
(26.1) (24.6) (23.2) (17.4) (20.9) (19.6) (14.9) 
Element Diameter, mm (in.) 
1. Outer of outer fuel element 61.47 (2.42) 60.96 (2.40) 
2. Inner of outer fuel element 43.18 (1.70) 44.96 (1.77) 
3. Outer of inner fuel element 32.51 (1.28) 31.75 (1.25) 
4. Inner of inner fuel element 12.19 (0.48) 11.18 (0.44) 
Cladding weight, kg (lb.) 
1. Outer element 1.094 1.041 0.991 0.791 0.882 0.832 0.659 
(2.41) (2.29) (2.18) (1.74) (1.94) (1.83) (1.45) 
2. Inner element 0.550 0.523 0.500 0.400 0.536 0.509 0.405 
(1.21) (1.15) (1.10) (0.88) (1.18) (1.12) (0.89) 
Weight of uranium in outer fuel element 
1. 0.947% 235U, kg 16.0 15.0 14.2 10.5 N/A 
(lb.) (35.2) (33.1) (31.2) (23.1) 
2. 1.25% 235U, kg N/A 11.1 10.4 7.9 
(lb.) (24.4) (22.9) (17.3) 
Uranium isotopics (0.947 wt. %) (1.25 wt. %) 
235U 0.9470 1.2500 
236U 0.0392 0.0392 
238U 99.0138 98.7108 
Weight of uranium in inner fuel element 
kg 7.5 7.0 6.6 5.0 5.5 5.1 3.9 
@ 0.947% 235U, (lb.) (16.5) (15.5) (14.6) (10.9) (12.1) (11.3) (8.6) 
Maximum weight of a fuel element, kg 
(lb.) 25.15 23.65 22.31 16.65 18.01 16.89 12.84 
(55.32) (52.04) (49.08) (36.62) (39.62) (37.15) (28.24) 
Weighted average of uranium in a fuel 22.73 (50.0) 16.32 (35.9) 
element, kg (lb.) 
Ratio of Zircaloy-2 to uranium, kg/MT 140 141.6 143.2 154.1 171.0 172.5 180.7 
Source: CRWMS M&O 2001, p. 2-6 
NOTES: aLetter code differentiates the various lengths of Mark IV or Mark IA fuel elements (i.e., a type E 
element is 26.1 inches long). 
bThere are 12 Mark IA elements with an overall length of 66.3 cm; they will be considered as a special 
case fuel loading in a Mark IV fuel basket. 
The current conceptual design for disposing of N-Reactor SNF (CRWMS M&O 2001, 
Section 2.1.4) in the repository contains two defense high-level radioactive waste canisters and 
two multicanister overpacks (MCO) loaded with N-Reactor spent nuclear fuel. It should be 
noted that this waste package configuration differs from the other DOE spent nuclear fuel types, 
CAL-DS0-NU-000003 REV 00A VI-2 September2004 

Criticality Model 
which have five defense high-level radioactive waste canisters surrounding a single DOE SNF 
canister. 
The canister design (CRWMS M&O 2001, p. 2-9) includes a nominal length of 4198.37 mm 
(165.29 in.) and a maximum outer diameter of 642.9 mm (25.31 in.) Beyond these basic 
dimensions, fuel-specific internals have been designed for each canister based on the known 
maximum lengths of the fuels (Mark IV or IA) contained therein. In addition, a central process 
post constructed out of Stainless Steel Type 304L is present in the MCOs. This central post is 
associated with the stacked baskets, and each post is drilled to facilitate water removal from the 
bottom of the MCO after underwater loading. In the case of the Mark IV fuel and scrap baskets, 
the post outer diameter is 7.20 cm (2.835 in.) with a 1.37 cm (0.54 in.) thick wall. The Mark IA 
fuel and scrap baskets use a 16.83 cm (6.625 in.) post diameter and a 4.458 cm (1.755 in.[max.]) 
drilled hole in the center for a 6.18 cm (2.435 in.) wall thickness. 
Five baskets containing Mark IV spent nuclear fuel are placed in the MCO. The two top and 
bottom baskets may be scrap baskets (baskets containing various-sized pieces of SNF). A 
similar arrangement but with six baskets is possible for the MCO containing Mark IA SNF 
(CRWMS M&O 2001, Sections 2.1.4.2 and 2.1.4.3). Based on the preliminary criticality 
analyses no neutron absorber is necessary to be added for the current design configuration 
(CRWMS M&O 2001, Section 8.7). 
Figure VI-1 presents a simplified cross section of the waste package containing 2 MCOs placed 
in a waste package (CRWMS M&O 2001, p. 2-3). 
l 
r 
MCO 
iWaste package outer shelWaste package inner shell 
DHLW canisteWaste separaton plates 
Figure VI-1. Cross Section of the Waste Package Containing N-Reactor SNF 
CAL-DS0-NU-000003 REV 00A VI-3 September2004 

Criticality Model 
VI.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 N-Reactor SNF), the selected benchmark experiments 
have been grouped in two subsets (BSC 2002, Section 6.1.8) that include moderated 
heterogeneous and homogeneous experiments. The benchmark experiments come 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 packages (CRWMS M&O 2001, 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) 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 VI-3 presents the list of the benchmark experiments and the number of 
cases for each subset selected for N-Reactor SNF. 
Table VI-3. Critical Benchmarks Selected for N-Reactor SNF 
Subset Benchmark Experiment Identificationb No. of Cases Included 
Heterogeneous moderatedc Experiment with N-reactor Mark IA Fuel Elements 3 
LEU-COMP-THERM-001 8 
LEU-COMP-THERM-016a 4 
LEU-COMP-THERM-010a 3 
LEU-COMP-THERM-042 7 
Homogeneous moderatedc Experiment with LEU UO3-H2O solutions 12 
LEU-SOL-THERM-001 1 
LEU-SOL-THERM-002 3 
LEU-SOL-THERM-005 3 
LEU-COMP-THERM-049 18 
Source: Subsets defined and evaluated in BSC 2002 
a
NOTES: Only the cases evaluated in CRWMS M&O 1999a have been used. 
bThe convention for naming the benchmark experiments is from NEA 2001. 
cIdentification of each subset from BSC 2002 has been modified to better reflect the subsets main 
characteristics. The benchmark experiments in each subset have not been affected. 
The experiments cover configuration classes IP-1a, IP-1b, IP-2a, IP-3a, IP-3b, IP-3c, and IP-3b 
for the degraded waste package containing N-Reactor SNF as described in Section 7. 
CAL-DS0-NU-000003 REV 00A VI-4 September2004 

Criticality Model 
VI.2.1 Range of Applicability of Selected Critical Benchmark Experiments 
This section summarizes in a set of tables (Tables VI-4 and VI-5) the range of applicability of 
the experiments listed in Table VI-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 VI-4. Range of Applicability of Critical Benchmark Experiments Selected for Comparison With 
Heterogeneous Moderated Configurations of N-Reactor SNF 
Experiment 
with N-reactor Experiment Experiment Experiment Experiment 
MkIA fuel LEU-COMP- LEU-COMP- LEU-COMP- LEU-COMP- 
Category/ elements THERM-001 THERM-016 THERM-010 THERM-042 
Description Parameter (3 cases) (8 cases) (4 cases) (3 cases) (7 cases) 
Materials/ Fissionable Uranium Uranium Uranium Uranium Uranium 
Fissionable Element 
Material 
Physical Form U metal UO2 UO2 UO2 UO2 
Isotopic 0.947 wt. % 235U 2.35 wt. % 235U 2.35 wt. % 235U 4.31 wt. % 235U 2.35 wt. % 235U 
Composition (inner cylinder) 
1.25 wt. % 235U 
(outer cylinder) 
Atomic Density 
(atoms/b-cm) 
235U:4.56e-04 
(inner cylinder)
235U:6.04e-04 
235U: 4.88e-04 235U: 4.88e-04 235U: 1.01e-03 235U: 4.88e-04 
(outer cylinder) 
Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. 
Materials/ 
Moderator 
Element H H H H H 
Physical Form Water Water Water Water Water 
Atomic Density 6.67e-02 6.67e-02 6.67e-02 6.67e-02 6.67e-02 
(atoms/b-cm) 
Ratio to Fissile 994 to 1876 449 to 487 449 to 487 Not available Not available 
Material 
(In Region 
Containing 
Fissile Material) 
Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. 
Materials/ 
Reflector 
Material/ 
Physical Form 
Reflected by 
water 
Reflected by 
water 
Reflected by 
water 
Reflected by 
water, lead, 
uranium, and 
Reflected by 
water and steel 
steel 
Materials/ 
Neutron 
Absorber 
Element None None B None B, Cd 
Physical Form N/A N/A B, C (boral) N/A Plates 
Atomic Density 
(atoms/b-cm) 
N/A N/A Not needed for 
ROA and ROP 
N/A Not needed for 
ROA and ROP 
comparison comparison 
CAL-DS0-NU-000003 REV 00A VI-5 September2004 

Criticality Model 
Table VI-4. Range of Applicability of Critical Benchmark Experiments Selected for Comparison With 
Heterogeneous Moderated Configurations of N-Reactor SNF (Continued) 
Experiment 
with N-reactor Experiment Experiment Experiment Experiment 
MkIA fuel LEU-COMP- LEU-COMP- LEU-COMP- LEU-COMP- 
Category/ elements THERM-001 THERM-016 THERM-010 THERM-042 
Description Parameter (3 cases) (8 cases) (4 cases) (3 cases) (7 cases) 
Geometry Heterogeneity Heterogeneous 
complex lattice 
Square pitched 
clusters in a 
rectangular 
Square pitched 
clusters in a 
rectangular 
Square pitched 
clusters in a 
rectangular 
Square pitched 
clusters in a 
rectangular 
geometry geometry geometry geometry 
Shape Parallel-piped Parallel-piped Parallel-piped Parallel-piped 
Neutron AENCF 0.3145 MeV to 0.11186 to 0.1201 to 0.1778 to 0.1690 to 
Energy 0.4085 MeV 0.1239 MeV 0.1229 MeV 0.2839 MeV 0.1750 MeV 
EALF Not available 0.109 to 0.01 to 0.114 eV 0.325 to Not available 
0.113 eV 0.821 eV 
Neutron Energy 
Spectraa 
Not available T: 29.3 to 31.6% 
I: 28.8 to 29.9% 
T: 26.6 to 40.3% 
I: 27.6 to 31.2% 
T: 19.6 to 20.7% 
I: 31.7 to 33.9% 
Not available 
F: 39.6 to 40.8% F: 33.9 to 42.6% F: 44.2 to 46.8% 
Fission Rate Not available T: 91.3 to 91.6% T: 91.2 to 91.5% T: 79.2 to 82.9% Not available 
vs. Neutron I: 4.4 to 4.6% I: 4.5 to 4.7% I: 10.9 to 12.1% 
Energya F: 4.0 to 4.1% F: 4.0 to 4.1% F: 6.2 to 10.4% 
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]. 
Table VI-5. Range of Applicability of Critical Benchmark Experiments Selected for Comparison With 
Homogeneous Moderated Configurations of N-Reactor SNF
Experiments Experiment Experiment Experiment Experiment 
with LEU-UO3 -LEU-SOL-LEU-SOL-LEU-SOL-LEU-COMP- 
Category/ H2O solutions THERM-001 THERM-002 THERM-005 THERM-049 
Description Parameter (12 cases) (1 case) (3 cases) (3 cases) (18 cases) 
Materials/ 
Fissionable 
Fissionable 
Element 
Uranium Uranium Uranium Uranium Uranium 
Material Physical Form Aqueous 
solution of UO3 
Aqueous 
solution of 
Aqueous solution 
of uranium 
Aqueous solution 
of uranyl nitrate 
UO2 
uranyl oxy-fluoride 
fluoride 
Isotopic 
Composition 
1.0059 to 
1.1586 wt. % 
235U 
5 wt. % 235U 4.9 wt. % 235U 5.64 wt. % 235U 5 wt. % 235U 
Atomic Density 
(atoms/b-cm) 
235U: 2.99e-05 
to 3.97e-05 
238U: 2.91e-03 
to 3.72e-03 
235U: 1.24e-4 
238U: 2.35e-3 
235U: 5.67e-05 
to 6.16e-05 
238U: 1.09e-03 
to 1.18e-03 
235U: 5.783e-05 
238U: 9.55e-04 
235U: 3.69e-4 
238U: 6.94e-03 
Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. 
Materials/ 
Moderator 
Element H H H H H 
Physical Form Solution Solution Solution Solution Solution 
Atomic Density 1.26e-02 5.62e-02 6.17e-0 5.62e-02 1.47e-0 
(atoms/b-cm) to 2.19e-02 to 6.22e-02 to 2.20e-02 
Ratio to Fissile 370 to 731 454 1,001 to 10,098 972 2 to 3 
Material 
Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. 
CAL-DS0-NU-000003 REV 00A VI-6 September2004 

Criticality Model 
Table VI-5. Range of Applicability of Critical Benchmark Experiments Selected for Comparison With 
Homogeneous Moderated Configurations of N-Reactor SNF (Continued) 
Category/ 
Description Parameter 
Experiments 
with LEU-UO3 -
H2O solutions 
(12 cases) 
Experiment 
LEU-SOL-
THERM-001 
(1 case) 
Experiment 
LEU-SOL-
THERM-002 
(3 cases) 
Experiment 
LEU-SOL-
THERM-005 
(3 cases) 
Experiment 
LEU-COMP- 
THERM-049 
(18 cases) 
Materials/ 
Reflector 
Material/ 
Physical Form 
Unreflected Unreflected Unreflected or 
reflected by water 
Reflected by 
water 
Reflected by 
polyethylene 
Materials/ 
Neutron 
Absorber 
Element None None None B None 
Physical Form N/A N/A N/A B4C rods N/A 
Atomic Density 
(atoms/b-cm) 
N/A N/A N/A Not needed for 
ROA and ROP 
comparison 
N/A 
Geometry Heterogeneity Homogeneous 
solution in a 
single spherical 
vessel 
Homogeneous 
solution in a 
cylindrical 
vessel 
Homogeneous 
solution in a 
spherical vessel 
Homogeneous 
solution in a 
cylindrical tank 
Array of boxes in 
rectangular 
geometry 
Shape Sphere Cylinder Sphere Cylinder Parallel-piped 
Neutron 
Energy 
AENCF 0.1549 to 
0.2541 MeV 
0.0519 MeV 0.0251 to 
0.0283 MeV 
0.0254 to 
0.0260 MeV 
0.2270 to 
0.3000 MeV 
EALF Not available 0.0629 eV 0.0395 to 
0.0416 eV 
0.0412 to 
0.0415 eV 
0.899 to 2.78 eV 
Neutron Energy 
Spectraa 
Not available T: 28.6% 
I: 31.2% 
F: 40.2% 
T: 43.9 to 45.5% 
I: 24.1 to 25.3% 
F: 30.4 to 32.1% 
T: 30.2 to 41.2% 
I: 26.2 to 27.7% 
F: 32.6 to 42.1% 
T: 7.1 to 15.0 % 
I: 38.6 to 41.0 % 
F: 46.2 to 51.9 % 
Fission Rate 
vs. Neutron 
Energya 
Not available T: 93.6% 
I: 4.6% 
F: 1.8% 
T: 96.6 to 96.9% 
I: 2.3 to 2.5% 
F: 0.8 to 1.1% 
T: 96.4% 
I: 2.7% 
F: 0.9% 
T: 63.2 to 72.9 % 
I: 19.0 to 25.9 % 
F: 8.1 to 10.9 % 
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]. 
VI.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 N-Reactor 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 N-Reactor SNF are presented in Table VI-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. 
CAL-DS0-NU-000003 REV 00A VI-7 September2004 

Criticality Model 
Table VI-6. Trending Parameter Results for the Critical Benchmark Subset Representative for 
Moderated Intact (Heterogeneous) 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 25 0.9866 0.0765 0.3775 3.7349 2.069 0.0011 Passed Yes 
Enrichment 
(235U/U) 
25 1.0140 -0.0057 0.2062 -2.4441 2.069 0.0226 Failed No 
keff 
Source: BSC 2003b, p. 57 
Figure VI-2 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 = 0.0765  AENCF + 0.9434 for 0 MeV < AENCF < 0.175 MeV 
Lower-bound tolerance limit = 0.9568 for AENCF > 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 
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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. 
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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 
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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. 
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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). 
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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 subsets 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. 
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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. 
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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 
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Criticality Model 
INTENTIONALLY LEFT BLANK 
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Criticality Model 
ATTACHMENT VIII 
LBTL CALCULATION AND ROA DETERMINATION 
FOR MELT AND DILUTE INGOTS 
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Criticality Model 
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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 
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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 subsets 
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. 
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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 
subsets 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 m 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 subsets 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. 
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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. 
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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 subsets 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<AENCF < 0.247 MeV 
Lower Bound Tolerance Limit = -1.7411e-02*AENCF +0.97491 for 0.247 MeV =AENCF 
< 0.902 MeV 
1.03 
1.02 
1.01
1
0.99 
0.98 
0.97 
0.96 
0.95 
litLow er Bound Toerance Lim
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 
AENCF (MeV) 
NOTE: AENCF = average energy of a neutron causing fission. 
Figure XII-1. Lower-Bound Tolerance Limit Applicable for Configurations Containing HEU External to the 
Waste Package 
CAL-DS0-NU-000003 REV 00A XII-10 September2004 

Criticality Model 
XII.3 IEU SYSTEMS 
Selection of the criticality benchmark experiments for IEU 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.3.1 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 
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 109 individual cases are presented in 
Table XII-7 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-7. keff Values for Benchmarks Applicable to Intact Moderated Configurations Containing 
Intermediate Enrichment Uranium Mixtures 
Experiment Case Name 
Benchmark Values Calculated Values (MCNP) 
keff sexp keff scalc AENCF 
Experiment iect101 1.0000 0.004 0.9974 0.0009 0.21679 
IEU-COMP-THERM-001 
(29 cases) 
iect102 1.0000 0.004 0.9960 0.0009 0.15817 
iect103 1.0000 0.004 0.9931 0.0010 0.10412 
iect104 1.0000 0.004 0.9974 0.0011 0.07405 
iect105 1.0000 0.004 1.0085 0.0009 0.04552 
iect106 1.0000 0.004 1.0003 0.0010 0.10793 
iect107 1.0000 0.004 0.9980 0.0010 0.11064 
iect108 1.0000 0.004 0.9960 0.0010 0.11867 
iect109 1.0000 0.004 1.0004 0.0008 0.1679 
iect110 1.0000 0.004 0.9967 0.0010 0.15756 
iect111 1.0000 0.004 0.9958 0.0010 0.15732 
iect112 1.0000 0.004 0.9964 0.0010 0.15568 
iect113 1.0000 0.004 0.9967 0.0010 0.0743 
CAL-DS0-NU-000003 REV 00A XII-11 September2004 

Criticality Model 
Table XII-7. keff Values for Benchmarks Applicable to Intact Moderated Configurations Containing 
Intermediate Enrichment Uranium Mixtures (Continued) 
Experiment Case Name 
Benchmark Values Calculated Values (MCNP) 
keff sexp keff scalc AENCF 
Experiment iect114 1.0000 0.004 0.9979 0.0009 0.07375 
IEU-COMP-THERM-001 
(29 cases) 
(continued) 
iect115 1.0000 0.004 0.9981 0.0010 0.074 
iect116 1.0000 0.004 1.0021 0.0009 0.05547 
iect117 1.0000 0.004 0.9965 0.0010 0.20814 
iect118 1.0000 0.004 0.9976 0.0011 0.13428 
iect119 1.0000 0.004 1.0045 0.0010 0.06114 
iect120 1.0000 0.004 1.0005 0.0009 0.15539 
iect121 1.0000 0.004 0.9988 0.0009 0.21334 
iect122 1.0000 0.004 0.9990 0.0011 0.19772 
iect123 1.0000 0.004 0.9952 0.0011 0.12826 
iect124a 1.0000 0.004 1.0004 0.0011 0.13305 
iect125 1.0000 0.004 0.9987 0.0009 0.05992 
iect126 1.0000 0.004 1.0044 0.0010 0.05663 
iect127 1.0000 0.004 1.0032 0.0009 0.05633 
iect128 1.0000 0.004 1.0051 0.0009 0.15824 
iect129 1.0000 0.004 1.0012 0.0010 0.15184 
Experiment case2 0.980 0.003 0.9807 0.0004 0.48226 
IEU-COMP-THERM-005 
(2 cases) 
case3 1.014 0.006 1.0158 0.0005 0.25976 
Experiment lst3-1 0.9997 0.0039 0.9993 0.0004 0.0186 
LEU-SOL-THERM-003 
(9 cases) 
lst3-2 0.9993 0.0042 0.9971 0.00038 0.0166 
lst3-3 0.9995 0.0042 1.0015 0.00037 0.0164 
lst3-4 0.9995 0.0042 0.9954 0.00038 0.0162 
lst3-5 0.9997 0.0048 0.9990 0.00031 0.0133 
lst3-6 0.9999 0.0049 0.9992 0.0003 0.0129 
lst3-7 0.9994 0.0049 0.9972 0.0003 0.0127 
lst3-8 0.9993 0.0052 1.0008 0.00025 0.0114 
lst3-9 0.9996 0.0052 0.9973 0.00025 0.0114 
Experiment lst4_1 0.9994 0.0008 1.0029 0.0007 0.0188 
LEU-SOL-THERM-004 
(7 cases) 
lst4_29 0.9999 0.0009 1.0034 0.0006 0.0179 
lst4_33 0.9999 0.0009 1.0013 0.0007 0.017 
lst4_34 0.9999 0.001 1.0037 0.0006 0.0157 
lst4_46 0.9999 0.001 1.0032 0.0006 0.0154 
lst4_51 0.9994 0.0011 1.0023 0.0005 0.0148 
lst4_54 0.9996 0.0011 1.0026 0.0005 0.0142 
Experiment leust7_1 0.9961 0.0009 0.9966 0.0002 0.02 
LEU-SOL-THERM-007 
(5 cases) 
leust7_2 0.9973 0.0009 0.9995 0.0002 0.0187 
leust7_3 0.9985 0.001 0.9979 0.0002 0.0173 
leust7_4 0.9988 0.0011 1.0005 0.0002 0.0166 
leust7_5 0.9983 0.0011 0.9989 0.0002 0.0159 
Experiment lst8_72 0.9999 0.0014 1.0038 0.0002 0.0152 
LEU-SOL-THERM-008 
(4 cases) 
lst8_74 1.0002 0.0015 1.0023 0.0002 0.0154 
lst8_76 0.9999 0.0014 1.0028 0.0002 0.0153 
lst8_78 0.9999 0.0014 1.0040 0.0002 0.0153 
CAL-DS0-NU-000003 REV 00A XII-12 September2004 

Criticality Model 
Table XII-7. keff Values for Benchmarks Applicable to Intact Moderated Configurations Containing 
Intermediate Enrichment Uranium Mixtures (Continued) 
Experiment Case Name 
Benchmark Values Calculated Values (MCNP) 
keff sexp keff scalc AENCF 
Experiment lst9_92 0.9998 0.0014 1.0018 0.0005 0.0155 
LEU-SOL-THERM-009 
(3 cases) 
lst9_93 0.9999 0.0014 1.0021 0.0002 0.0157 
lst9_94 0.9999 0.0014 1.0022 0.0002 0.0158 
Experiment lst10_83 0.9999 0.0153 1.0023 0.0003 0.0153 
LEU-SOL-THERM-010 
(4 cases) 
lst10_85 0.9999 0.0154 1.0019 0.0003 0.0154 
lst10_86 1.0000 0.0153 1.0032 0.0003 0.0153 
lst10_88 1.0001 0.0154 1.0026 0.0003 0.0154 
Experiment lst16_05 0.9996 0.0013 1.0093 0.0007 0.0267 
LEU-SOL-THERM-016 
(7 cases) 
lst16_13 0.9999 0.0013 1.0080 0.0006 0.0248 
lst16_25 0.9994 0.0014 1.0075 0.0006 0.0216 
lst16_29 0.9996 0.0014 1.0068 0.0006 0.0209 
lst16_31 0.9995 0.0014 1.0059 0.0005 0.0195 
lst16_40 0.9992 0.0015 1.0043 0.0005 0.0186 
lst16_96 0.9994 0.0015 1.0047 0.0005 0.018 
Experiment lst17_04 0.9981 0.0013 1.0051 0.0007 0.0275 
LEU-SOL-THERM-017 
(6 cases) 
lst17_22 0.9986 0.0013 1.0049 0.0006 0.0258 
lst17_23 0.9989 0.0014 1.0052 0.0006 0.0224 
lst17_26 0.9992 0.0014 1.0043 0.0006 0.0212 
lst17_30 0.9987 0.0015 1.0043 0.0005 0.02 
lst17_47 0.9996 0.0015 1.0042 0.0006 0.0192 
Experiment RUN133 0.9992 0.001 1.0033 0.0002 0.0183 
LEU-SOL-THERM-018 
(6 cases) 
RUN142 0.9996 0.001 1.0042 0.0003 0.0187 
RUN143 0.9996 0.001 1.0045 0.0003 0.0188 
RUN144 0.9997 0.001 1.0033 0.0003 0.0187 
RUN145 0.9992 0.001 1.0038 0.0003 0.0187 
RUN146 0.9996 0.001 1.0037 0.0003 0.0186 
Experiment RUN149 0.9997 0.0009 1.0043 0.0003 0.019 
LEU-SOL-THERM-019 
(6 cases) 
RUN150 0.9995 0.0009 1.0043 0.0003 0.019 
RUN151 0.9999 0.0009 1.0049 0.0002 0.0191 
RUN152 0.9996 0.0009 1.0054 0.0003 0.0191 
RUN153 0.9998 0.0009 1.0050 0.0003 0.0191 
RUN183 0.9994 0.0009 1.0036 0.0003 0.0189 
Experiment LST20C1 0.9995 0.001 1.0014 0.0003 0.015 
LEU-SOL-THERM-020 
(4 cases) 
LST20C2 0.9996 0.001 1.0000 0.0003 0.0143 
LST20C3 0.9997 0.0012 0.9993 0.0003 0.0131 
LST20C4 0.9998 0.0012 1.0004 0.0003 0.0125 
Experiment LST21C1 0.9983 0.0009 0.9991 0.0003 0.0154 
LEU-SOL-THERM-021 
(4 cases) 
LST21C2 0.9985 0.001 0.9996 0.0003 0.0144 
LST21C3 0.9989 0.0011 0.9976 0.0003 0.0135 
LST21C4 0.9993 0.0012 0.9999 0.0003 0.0127 
Experiment case1 0.9999 0.0010 1.0049 0.0002 0.0185 
LEU-SOL-THERM-022 
(4 cases) 
case2 0.9994 0.0010 1.0058 0.0002 0.0184 
case3 0.9993 0.0010 1.0055 0.0002 0.0185 
case4 0.9994 0.0010 1.0050 0.0002 0.0186 
CAL-DS0-NU-000003 REV 00A XII-13 September2004 

Criticality Model 
Table XII-7. keff Values for Benchmarks Applicable to Intact Moderated Configurations Containing 
Intermediate Enrichment Uranium Mixtures (Continued) 
Experiment Case Name 
Benchmark Values Calculated Values (MCNP) 
keff sexp keff scalc AENCF 
Experiment 261 0.9963 0.0009 1.0000 0.0005 0.0175 
LEU-SOL-THERM-023 
(9 cases) 
274 0.9967 0.0009 0.9950 0.0005 0.0177 
273 0.9967 0.0009 1.0000 0.0005 0.0179 
262 0.9960 0.0009 0.9986 0.0005 0.0177 
263 0.9959 0.0009 0.9990 0.0005 0.0176 
264 0.9959 0.0009 0.9992 0.0005 0.0175 
267 0.9966 0.0009 0.9993 0.0005 0.0177 
268 0.9970 0.0009 0.9996 0.0005 0.0177 
269 0.9977 0.0009 0.9997 0.0005 0.0178 
Source: Moscalu 2004, Section 5.2 
The experiments listed in Table XII-6 cover configuration classes NF-1 through NF-5 and FF-1 
through FF-3 for configurations containing mixtures of intermediate enriched uranium external 
to the waste package. 
XII.3.2 Range of Applicability of Selected Critical Benchmark Experiments 
Tables XII-8 through XII-11 summarize the range of applicability of the experiments listed in 
Table XII-7. The information is excerpted from Moscalu (2004, Section 5.2). 
CAL-DS0-NU-000003 REV 00A XII-14 September2004 

Criticality Model 
Table XII-8. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with 
External Configurations Containing IEU Mixtures (Set 1) 
Experiment 
IEU-COMP-
Experiment 
IEU-COMP-
Experiment 
LEU-SOL-
Experiment 
LEU-SOL-
Category/ THERM-001 THERM-005 THERM-003 THERM-004 
Description Parameter (29 cases) (2 cases) (9 cases) (7 cases) 
Materials/ 
Fissionable 
Fissionable 
Element 
Uranium Uranium Uranium Uranium 
Material Physical Form UF4 compound 
with polytetrafluoroethylene 
Mixture of UO2 and 
Th metal 
Aqueous solution of 
uranyl nitrate 
Aqueous solution of 
uranyl nitrate 
Isotopic 
Composition 
29.83 wt% 235U 90 wt% and 36 wt% 
235U 
10 wt% 235U 9.97 wt% 235U 
Atomic 
Density 
(atoms/b-cm) 
235U: 2.37e-03 
238U: 5.50e-03 
235U: 5.39e-03 and 
1.35E-02 
238U: 1.47e-03 and 
9.53e-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 
Temperature Room temp. Room temp. Room temp. Room temp. 
Materials/ Element H; C H; C H H 
Moderator Physical Form Polyethylene Polyethylene Solution Solution 
Atomic H:7.52e-02 H: 7.2588-e02 5.89e-02 to 6.23e-5.70e-02 to 5.86e-
Density C:3.92e-02 C: 3.6294e-02 02 02 
(atoms/b-cm) 
Ratio to H/235U = 4 to 222 H/235U = 0 to 10 770 to 1437 719 to 1018 
Fissile 
Material 
Temperature Room temp. Room temp. Room temp. Room temp. 
Materials/ 
Reflector 
Material/ 
Physical Form 
Unreflected or 
reflected by 
paraffin 
Kinf experimental 
set-up 
Unreflected Reflected by water 
Materials/ 
Neutron 
Absorber 
Element B or Cd for some 
experiments 
None None None 
Physical Form Metallic sheets N/A N/A N/A 
Atomic 
Density 
(atoms/b-cm) 
Cd: 4.64e-02 
10B: 3.21e-03 
N/A N/A N/A 
Geometry Heterogeneity Heterogeneous 
small cubes of 
Heterogeneous 
set of stainless 
Homogeneous 
solution in a 
Homogeneous 
solution in a 
fissile compound 
interspersed with 
moderator cubes 
steel tubes forming 
a hexagonal infinite 
lattice 
spherical tank cylindrical tank 
Shape Cuboid Cylinder Sphere Cylinder 
Neutron 
Energy 
AENCFb 0.0455 to 0.2168 
MeV 
0.260 and 0.483 
MeV 
0.0114 to 0.0186 
MeV 
0.0142 to 0.0188 
MeV 
EALF b 0.11 to 9.09 eV 1e+02 and 
2.97e+04 eV 
3.46e-02 to 4.14e-
02 eV 
3.75e-02 to 4.21e-
02 eV 
Neutron 
Energy 
Spectraa 
T: 1.8 to 22.8% 
I: 24.9 to 40.2% 
F: 49.6 to 63% 
T: 0 and 1.0% 
I: 35.0 and 43.0% 
F: 56.0 and 65.0% 
T: 37.6 to 49.1 % 
I: 22.7 to 27.3% 
F: 28.2 to 35.1% 
T: 36.8 to 43.1 % 
I: 25.3 to 27.8% 
F: 31.6 to 35.4% 
Fission Rate 
vs. Neutron 
Energya 
T: 49.9 to 90.9% 
I: 7.1 to 42.8% 
F: 2.0 to 11.1% 
T: 0.2 and 21.4% 
I: 56.5 and 63.6% 
F: 15 and 43.2% 
T: 96.2 to 97.6% 
I: 2 to 3.1% 
F: 0.4 to 0.7% 
T: 96.1 to 97.0% 
I: 2.5 to 3.2% 
F: 0.5 to 0.7% 
Source: Moscalu 2004, Section 5.2 
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 XII-15 September2004 

Criticality Model 
Table XII-9. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with 
External Configurations Containing IEU Mixtures (Set 2) 
Experiment Experiment Experiment Experiment 
LEU-SOL-LEU-SOL-LEU-SOL-LEU-SOL-
Category/ THERM-007 THERM-008 THERM-009 THERM-010 
Description Parameter (5 cases) (4 cases) (3 cases) (4 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 
uranyl nitrate 
Aqueous solution of 
uranyl nitrate 
Isotopic 9.97 wt% 235U 9.97 wt% 235U 9.97 wt% 235U 9.97 wt% 235U 
Composition 
Atomic Density 235U: 6.18e-05 to 235U: 6.14e-05 235U: 6.26e-05 235U: 6.18e-05 to 
(atoms/b-cm) 8.00e-05 238U:5.47e-04 238U:5.57e-04 6.21e-05 
238U:5.5e-04 to 238U: 5.51e-04 to 
7.12e-04 5.53e-04 
Temperature Room temp. Room temp. Room temp. Room temp. 
Materials/ Element H H H H 
Moderator Physical Form Solution Solution Solution Solution 
Atomic Density 
(atoms/b-cm) 
5.67e-02 to 5.82e-
02 
5.86e-02 5.85e-02 5.85e-02 
Ratio to Fissile 
Material 
709 to 942 951 to 956 934 to 936 942 to 946 
Temperature Room temp. Room temp. Room temp. Room temp. 
Materials/ 
Reflector 
Material/ 
Physical Form 
Unreflected Reflected by 
concrete 
Reflected by borated 
concrete 
Reflected by 
polyethylene 
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 Homogeneous 
solution contained 
Homogeneous 
solution contained in 
Homogeneous 
solution contained in 
Homogeneous 
solution contained 
in a cylindrical tank a cylindrical tank a cylindrical tank in a cylindrical tank 
Shape Cylinder Cylinder Cylinder Cylinder 
Neutron AENCFb 0.0159 to 0.0200 0.0152 to 0.0154 0.0155 to 0.0158 0.0153 to 0.0154 
Energy MeV MeV MeV MeV 
EALF b 3.87e-02 to 4.28e-
02 eV 
3.84e-02 eV 3.89e-02 eV 3.84e-02 V 
Neutron Energy 
Spectraa T:35.9 to 41.1 % 
I: 26 to 28.1% 
F:32.9 to 36% 
T: 41.5 to 41.7% 
I: 25.9 to 26% 
F: 32.4 to 35% 
T: 40.8 to 41 % 
I: 26.2 to 26.3% 
F: 32.8 to 32.9% 
T: 41.6 % 
I: 25.8 to 25.9% 
F: 32.5 to 32.6% 
Fission Rate vs. T: 95.9 to 96.7% T: 96.8% T: 96.7% T: 96.8% 
Neutron 
Energya I: 2.7 to 3.4% 
F: 0.6 to 0.7% 
I: 2.6% 
F: 0.6% 
I: 2.7% 
F: 0.6% 
I: 2.6% 
F: 0.6% 
Source: Moscalu 2004, Section 5.2 
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 XII-16 September2004 

Criticality Model 
Table XII-10. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with 
Homogeneous Moderated Configurations of IEU (Set 3) 
Experiment Experiment Experiment Experiment 
Category/ LEU-SOL-THERM-016 LEU-SOL-THERM-017 LEU-SOL-THERM-018 LEU-SOL-THERM-019 
Description Parameter (7 cases) (6 cases) (6 cases) (6 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 
uranyl nitrate 
Aqueous solution of 
uranyl nitrate 
Isotopic 9.97 wt% 235U 9.97 wt% 235U 9.97 wt% 235U 9.97 wt% 235U 
Composition 
Atomic 235U: 7.65e-5 to 235U: 8.05e-05 to 235U: 7.87e-5 to 235U: 8.07e-05 to 
Density 
(atoms/b-cm) 
1.19e-04 
238U: 6.82e-04 to 
1.19e-04 
238U:7.17e-04 to 
8.04e-05 
238U:7.01e-04 to 
8.13e-05 
238U:7.19e-04 to 
1.06e-03 1.06e-03 7.16e-04 7.24e-04 
Temperature Room temp. Room temp. Room temp. Room temp. 
Materials/ Element H H H H 
Moderator Physical Form Solution Solution Solution Solution 
Atomic 5.56e-02 to 5.91e-02 5.56e-02 to 5.87e-02 5.87e-02 to 5.91e-02 5.87e-02 
Density 
(atoms/b-cm) 
Ratio to 469 to 772 469 to 729 731 to 751 721 to 728 
Fissile 
Material 
Temperature Room temp. Room temp. Room temp. Room temp. 
Materials/ 
Reflector 
Material/ 
Physical Form 
Reflected by water Unreflected Reflected by 
concrete 
Reflected by 
polyethylene 
Materials/ Element None None None None 
Neutron 
Absorber Physical Form N/A N/A N/A N/A 
Atomic 
Density 
N/A N/A N/A N/A 
(atoms/b-cm) 
Geometry Heterogeneity Homogeneous Homogeneous Homogeneous Homogeneous 
solution in a solution in a solution in a solution in a 
rectangular slab tank rectangular slab tank rectangular slab tank rectangular slab tank 
Shape Rectangular slab Rectangular slab Rectangular slab Rectangular slab 
Neutron AENCFb 0.0180 to 0.0267 0.0192 to 0.0275 0.0183 to 0.0188 0.0189 to 0.0191 
Energy MeV MeV MeV MeV 
EALFb 4.15e-02 to 5.22e-02 
eV 
4.24e-02 to 5.23e-02 
eV 
0.042 to 0.0425 eV 0.0425 to 0.0426 eV 
Neutron 
Energy 
Spectraa 
T: 29.1 to 37.7 % 
I: 27.7 to 31.2% 
F: 34.7 to 39.7% 
T: 28.9 to 36.5 % 
I: 28 to 31.1% 
F:35.5 to 40.0% 
T: 36.5 to 37 % 
I: 28 to 28.3 % 
F: 34.9 to 35.2% 
T: 36.4 to 36.5 % 
I: 28.1 to 28.2 % 
F: 35.4 % 
Fission Rate T: 94.3 to 96.2% T: 94.3 to 96.0% T: 96 to 96.1% T: 95.9 to 96.0% 
vs. Neutron 
Energya I: 3.2 to 4.6% 
F: 0.7 to 1.0% 
I: 3.3 to 4.6% 
F: 0.7 to 1.0% 
I: 3.3 % 
F: 0.7 % 
I: 3.3 % 
F: 0.7 % 
Source: Moscalu 2004, Section 5.2 
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 XII-17 September2004 

Criticality Model 
Table XII-11. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with 
Homogeneous Moderated Configurations of IEU (Set 4) 
Experiment Experiment Experiment Experiment 
Category/ LEU-SOL-THERM-020 LEU-SOL-THERM-021 LEU-SOL-THERM-022 LEU-SOL-THERM-023 
Description Parameter (4 cases) (4 cases) (4 cases) (9 cases) 
Materials/ 
Fissionable 
Fissionable 
Element 
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 
Isotopic 9.97 wt% 235U 9.97 wt%235U 9.97 wt% 235U 9.97 wt% 235U 
Composition 
Atomic 
Density 
(atoms/b-cm) 
235U: 4.95e-05 to 
6.21e-05 
238U: 4.41e-04 to 
5.53e-04 
235U: 4.95e-5 to 6.21e-
05 
238U: 4.41e-04 to 
5.53e-04 
235U: 7.88e-05 to 
7.93e-05 
238U:7.03e-04 to 7.07e-
04 
235U: 7.42e-5 to 7.56e-05 
238U:6.61e-04 to 6.73e-04 
Temperature Room Temp. Room Temp. Room Temp. Room Temp. 
Materials/ Element H H H H 
Moderator Physical Form Solution Solution Solution Solution 
Atomic 6.03e-02 to 6.13e-02 6.03e-02 to 6.13e-02 5.90e-02 to 5.91e-02 5.93e-02 to 5.95e-02 
Density 
(atoms/b-cm) 
Ratio to 971 to 1239 971 to 1239 744 to 750 785 to 803 
Fissile 
Material 
Temperature Room Temp. Room Temp. Room Temp. Room Temp. 
Materials/ Material/ Reflected by water Unreflected Reflected by borated Unreflected 
Reflector Physical Form concrete 
Materials/ Element None None None None 
Neutron 
Absorber Physical Form N/A N/A N/A N/A 
Atomic N/A N/A N/A N/A 
Density 
(atoms/b-cm) 
Geometry Heterogeneity Homogeneous solution Homogeneous solution Homogeneous solution Homogeneous solution in 
in a cylindrical tank in a cylindrical tank in a rectangular slab a rectangular slab tank 
tank 
Shape Cylinder Cylinder Rectangular slab Rectangular slab 
Neutron AENCFb 0.0125 to 0.0150 MeV 0.0127 to 0.0154 MeV 0.0184 to 0.0186 MeV 0.0175 to 0.0179 MeV 
Energy EALFb 3.57e-02 to 3.81e-02 3.58e-02 to 3.83e-02 4.21e-02 to 4.22e-02 Not available 
Neutron 
Energy 
Spectraa 
T: 42.2 to 46.6 % 
I: 23.8 to 25.6 % 
F: 29.6 to 32.2 % 
T: 41.8 to 46.3 % 
I: 23.9 to 25.7 % 
F: 29.8 to 32.5 % 
T:36.8 to 36.9 % 
I: 28.1% 
F:35.0 to 35.1 % 
Not available 
Fission Rate 
vs. Neutron 
Energya 
T: 96.8 to 97.3 % 
I: 2.2 to 2.6 % 
F: 0.5 to 0.6 % 
T: 96.8 to 97.3 % 
I: 2.2 to 2.6 % 
F: 0.5 to 0.6 % 
T: 96.0 to 96.1% 
I: 3.3% 
F: 0.7% 
Not available 
Source: Moscalu 2004, Section 5.2 
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. 
XII.3.3 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 XIII-6 (Moscalu 2004, 
Section 5.2.3). 
CAL-DS0-NU-000003 REV 00A XII-18 September2004 

Criticality Model 
Table XII-12. Trending Parameter Results for the Criticality Benchmark Experiments Representative for 
Configurations Containing IEU External to the Waste Package 
Trend 
Parameter n Intercept Slope r2 T t0.025,n-2 P-value 
Goodness-of-Fit 
Tests 
Valid 
Trend 
AENCFb 109 1.0030 -0.0194 0.1708 -4.6939 1.984a 7.98e-06 Passed Yes 
Source: Moscalu 2004, Attachment II 
NOTES: aValue interpolated from Table A-4 of Natrella 1963. 
b 
AENCF = average energy of a neutron causing fission. 
The trending parameters for AENCF (r2, T, P-value) from Table XII-11 indicate a trend of keff 
with AENCF.(Moscalu 2004, Section 5.2). The LBTL is calculated for this situation using the 
CLREG code (BSC 2001c). 
Figure XII-2 presents the keff values and the LBTL calculated with CLREG code. The LBTL can 
be also written as (Moscalu 2004, Section 5.2): 
Lower Bound Tolerance Limit = 0.97841 for 0 MeV < AENCF < 0.1518 MeV 
Lower Bound Tolerance Limit = -1.9322e-02*AENCF +0.981339 for 0.1518 MeV = AENCF 
< 0.482 MeV 
1 
klit 
0.97 
0.98 
0.99 
1.01 
1.02 
eff 
Lower Bound Toerance Lim 
0.00 0.10 0.20 0.30 0.40 0.50 0.60 
AENCF (MeV) 
NOTE: AENCF = average energy of a neutron causing fission. 
Figure XII-2. Lower Bound Tolerance Limit Applicable for Configurations Containing IEU Mixtures 
External to the Waste Package 
XII.4 LEU SYSTEMS 
Selection of the criticality benchmark experiments for LEU systems, determination of the range 
of applicability of the selected benchmarks, and the calculation of the LBTL are discussed in the 
following three sections. 
CAL-DS0-NU-000003 REV 00A XII-19 September2004 

Criticality Model 
XII.4.1 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 LEU 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 
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 96 individual cases are presented in 
Table XII-13 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-13. Critical Benchmarks Selected for Validation of the Criticality Model for External 
Configurations Containing Mixtures with Low Enriched Uranium 
Experiment Case Name 
Benchmark Values Calculated Values (MCNP) 
keff sexp keff scalc AENCF 
Experiment case1 1.0000 0.0038 0.9945 0.0007 0.1791 
LEU-COMP-THERM-033 
(52 cases) 
case2 1.0000 0.0038 0.9959 0.0006 0.1792 
case3 1.0000 0.0038 0.9965 0.0007 0.1789 
case4 1.0000 0.0038 0.9957 0.0006 0.1793 
case5 1.0000 0.0039 0.9993 0.0006 0.1379 
case6 1.0000 0.0039 1.0002 0.0007 0.1376 
case7 1.0000 0.0039 0.9983 0.0006 0.1371 
case8 1.0000 0.0040 0.9971 0.0006 0.1114 
case9 1.0000 0.0040 0.9957 0.0006 0.1119 
case10 1.0000 0.0039 0.9970 0.0007 0.0973 
case11 1.0000 0.0039 0.9963 0.0006 0.0972 
case12 1.0000 0.0039 0.9963 0.0006 0.0973 
case13 1.0000 0.0041 0.9973 0.0006 0.0840 
case14 1.0000 0.0051 0.9905 0.0005 0.0619 
case15 1.0000 0.0051 0.9915 0.0005 0.0623 
case16 1.0000 0.0051 0.9917 0.0005 0.0617 
case17 1.0000 0.0038 1.0048 0.0007 0.1657 
case18 1.0000 0.0038 1.0052 0.0007 0.1665 
CAL-DS0-NU-000003 REV 00A XII-20 September2004 

Criticality Model 
Table XII-13. Critical Benchmarks Selected for Validation of the Criticality Model for External 
Configurations Containing Mixtures with Low Enriched Uranium (Continued) 
Experiment Case Name 
Benchmark Values Calculated Values (MCNP) 
keff sexp keff scalc AENCF 
Experiment case19 1.0000 0.0038 1.0058 0.0007 0.1657 
LEU-COMP-THERM-033 
(52 cases) 
(continued) 
case20 1.0000 0.0038 1.0041 0.0007 0.1657 
case21 1.0000 0.0038 1.0061 0.0007 0.1650 
case22 1.0000 0.0039 1.0078 0.0007 0.1015 
case23 1.0000 0.0040 0.9946 0.0007 0.1952 
case24 1.0000 0.0040 0.9949 0.0007 0.1945 
case25 1.0000 0.0040 0.9950 0.0007 0.1953 
case26 1.0000 0.0039 0.9985 0.0007 0.1503 
case27 1.0000 0.0039 0.9992 0.0007 0.1503 
case28 1.0000 0.0039 0.9973 0.0007 0.1502 
case29 1.0000 0.0039 0.9993 0.0007 0.1503 
case30 1.0000 0.0039 0.9970 0.0007 0.1204 
case31 1.0000 0.0039 0.9981 0.0007 0.1199 
case32 1.0000 0.0039 0.9973 0.0006 0.1208 
case33 1.0000 0.0039 0.9955 0.0007 0.1209 
case34 1.0000 0.0039 0.9960 0.0007 0.1205 
case35 1.0000 0.0040 0.9965 0.0006 0.1047 
case36 1.0000 0.0040 0.9963 0.0006 0.1049 
case37 1.0000 0.0040 0.9950 0.0007 0.1047 
case38 1.0000 0.0040 0.9964 0.0006 0.1044 
case39 1.0000 0.0040 0.9964 0.0006 0.1047 
case40 1.0000 0.0040 0.9954 0.0006 0.1049 
case41 1.0000 0.0041 0.9965 0.0006 0.0901 
case42 1.0000 0.0041 0.9955 0.0006 0.0896 
case43 1.0000 0.0041 0.9946 0.0006 0.0890 
case44 1.0000 0.0050 0.9913 0.0005 0.0645 
case45 1.0000 0.0050 0.9908 0.0005 0.0637 
case46 1.0000 0.0050 0.9893 0.0005 0.0645 
case47 1.0000 0.0042 1.0110 0.0007 0.1880 
case48 1.0000 0.0042 1.0065 0.0007 0.1878 
case49 1.0000 0.0042 1.0063 0.0008 0.1889 
case50 1.0000 0.0041 1.0095 0.0007 0.1140 
case51 1.0000 0.0041 1.0127 0.0007 0.1146 
case52 1.0000 0.0041 1.0076 0.0007 0.1148 
Experiment lct49-01 1.0000 0.0034 0.9923 0.0006 0.294 
LEU-COMP-THERM-049 
(18 cases) 
lct49-02 1.0000 0.0034 0.9937 0.0006 0.293 
lct49-03 1.0000 0.0034 0.9929 0.0006 0.297 
lct49-04 1.0000 0.0034 0.9931 0.0006 0.300 
lct49-05 1.0000 0.0042 0.9944 0.0007 0.255 
lct49-06 1.0000 0.0042 0.9946 0.0007 0.256 
lct49-07 1.0000 0.0042 0.9932 0.0007 0.253 
CAL-DS0-NU-000003 REV 00A XII-21 September2004 

Criticality Model 
Table XII-13. Critical Benchmarks Selected for Validation of the Criticality Model for External 
Configurations Containing Mixtures with Low Enriched Uranium (Continued) 
Experiment Case Name 
Benchmark Values Calculated Values (MCNP) 
keff sexp keff scalc AENCF 
Experiment lct49-08 1.0000 0.0042 0.9921 0.0007 0.258 
LEU-COMP-THERM-049 
(18 cases) 
(continued) 
lct49-09 1.0000 0.0037 0.9933 0.0006 0.227 
lct49-10 1.0000 0.0037 0.9946 0.0007 0.227 
lct49-11 1.0000 0.0037 0.9933 0.0006 0.227 
lct49-12 1.0000 0.0037 0.9924 0.0007 0.231 
lct49-13 1.0000 0.0036 0.9935 0.0006 0.271 
lct49-14 1.0000 0.0036 0.9941 0.0006 0.272 
lct49-15 1.0000 0.0036 0.9937 0.0006 0.271 
lct49-16 1.0000 0.0036 0.9938 0.0007 0.254 
lct49-17 1.0000 0.0036 0.9929 0.0007 0.258 
lct49-18 1.0000 0.003 0.997 0.0006 0.251 
Experiment leust1 0.9991 0.0029 1.01182 0.00101 0.05186 
LEU-SOL-THERM-001 
(1 case) 
Experiment leust21 1.0038 0.004 0.99855 0.00058 0.02513 
LEU-SOL-THERM-002 
(3 cases) 
leust22 1.0024 0.0037 0.99659 0.00064 0.0283 
leust23 1.0024 0.0044 1.0009 0.0006 0.02684 
Experiment lst3-1 0.9997 0.0039 0.9993 0.0004 0.0186 
LEU-SOL-THERM-003 
(9 cases) 
lst3-2 0.9993 0.0042 0.9971 0.00038 0.0166 
lst3-3 0.9995 0.0042 1.0015 0.00037 0.0164 
lst3-4 0.9995 0.0042 0.9954 0.00038 0.0162 
lst3-5 0.9997 0.0048 0.9990 0.00031 0.0133 
lst3-6 0.9999 0.0049 0.9992 0.0003 0.0129 
lst3-7 0.9994 0.0049 0.9972 0.0003 0.0127 
lst3-8 0.9993 0.0052 1.0008 0.00025 0.0114 
lst3-9 0.9996 0.0052 0.9973 0.00025 0.0114 
Experiment lst8_72 0.9999 0.0014 1.0038 0.0002 0.0152 
LEU-SOL-THERM-008 
(4 cases) 
lst8_74 1.0002 0.0015 1.0023 0.0002 0.0154 
lst8_76 0.9999 0.0014 1.0028 0.0002 0.0153 
lst8_78 0.9999 0.0014 1.0040 0.0002 0.0153 
Experiment lst9_92 0.9998 0.0014 1.0018 0.0005 0.0155 
LEU-SOL-THERM-009 
(3 cases 
lst9_93 0.9999 0.0014 1.0021 0.0002 0.0157 
lst9_94 0.9999 0.0014 1.0022 0.0002 0.0158 
Experiment RUN133 0.9992 0.001 1.0033 0.0002 0.0183 
LEU-SOL-THERM-018 
(6 cases) 
RUN142 0.9996 0.001 1.0042 0.0003 0.0187 
RUN143 0.9996 0.001 1.0045 0.0003 0.0188 
RUN144 0.9997 0.001 1.0033 0.0003 0.0187 
RUN145 0.9992 0.001 1.0038 0.0003 0.0187 
RUN146 0.9996 0.001 1.0037 0.0003 0.0186 
Source: Moscalu 2004, Section 5.3 
CAL-DS0-NU-000003 REV 00A XII-22 September2004 

Criticality Model 
The experiments listed in Table XII-12 cover configuration classes NF-1 through NF-5 and FF-1 
through FF-3 for configurations containing mixtures of low enriched uranium external to the 
waste package. 
XII.4.2 Range of Applicability of Selected Critical Benchmark Experiments 
Tables XII-13 and XII-14 summarize the range of applicability of the experiments listed in 
Table XII-12. The information is excerpted from Moscalu (2004, Section 5.3). 
Table XII-14. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with 
External Configurations Containing Mixtures with Low Enriched Uranium (Set 1) 
Experiment Experiment Experiment Experiment Experiment 
LEU-COMP- LEU-COMP- LEU-SOL-LEU-SOL-LEU-SOL-
Category/ THERM-033 THERM-049 THERM-001 THERM-002 THERM-003 
Description Parameter (52 cases) (18 cases) (1 case) (3 cases) (9 cases) 
Materials/ Fissionable Uranium Uranium Uranium Uranium Uranium 
Fissionable Element 
Material Physical Form Uranium fluoride UO2 Aqueous Aqueous solution Aqueous solution 
solution of of uranium oxy-of uranyl nitrate 
uranyl fluoride fluoride 
Isotopic 2 to 3 wt% 235U 2.35 wt% 235U 5 wt% 235U 4.9 wt% 235U 10 wt% 235U 
Composition 
Atomic 235U: 6.23e-05 to 235U: 3.69e-4 235U: 1.24e-4 235U: 5.67e-05  235U: 4.34e-05  
Density 
(atoms/b-cm) 
2.35e-04 238U: 6.94e-03 238U: 2.35e-3 6.16e-05 
238U:1.09e-03  
7.64e-05 
238U:3.82e-04  
1.18e-03 6.73e-04 
Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. 
Materials/ 
Moderator 
Element H, C H H H H 
Physical 
Form 
Paraffin Solution Solution Solution Solution 
Atomic H: 3.09e-02 to 1.47e-02 to 2.20e-5.62e-02 6.17e-02 to 6.22e-5.89e-02 to 
Density 
(atoms/b-cm) 
6.06e-02 
C: 1.49e-02 to 
02 02 6.23e-02 
2.91e-02 
Ratio to H/235U = 133.4 to 2 to 3 454 1001 to 10098 770 to 1437 
Fissile 973 
Material 
Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. 
Materials/ 
Reflector 
Material/ 
Physical 
Form 
Reflected by 
paraffin, 
polyethylene or 
Reflected by 
polyethylene 
Unreflected Unreflected or 
reflected by water 
Unreflected 
Plexiglas 
Materials/ 
Neutron 
Element None None None None None 
Absorber Physical 
Dorm 
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 XII-23 September2004 

Criticality Model 
Table XII-14. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with External 
Configurations Containing Mixtures with Low Enriched Uranium (Set 1) (Continued) 
Experiment Experiment Experiment Experiment Experiment 
LEU-COMP-LEU-COMP-LEU-SOL-LEU-SOL-LEU-SOL-
Category/ THERM-033 THERM-049 THERM-001 THERM-002 THERM-003 
Description Parameter (52 cases) (18 cases) (1 case) (3 cases) (9 cases) 
Geometry Heterogeneity Rectangular stacks 
of UF2 or UF4  
paraffin cubes 
Array of boxes in 
rectangular 
geometry 
Homogeneou 
s solution in a 
cylindrical 
vessel 
Homogeneous 
solution in a 
spherical vessel 
Homogeneous 
solution in a 
spherical tank 
Shape Parallelepiped Parallelepiped Cylinder Sphere Sphere 
Neutron AENCFb 0.0617 to 0.1953 0.2270 to 0.3000 0.0519 MeV 0.0251 to 0.0283 0.0114 to 0.0186 
Energy MeV MeV MeV MeV 
EALFb 0.0541 to 0.393 eV 0.899 to 27.8 eV 0.0629 eV 0.0395 to 0.0416 
eV 
3.46e-02 to 
4.14e-02 eV 
Neutron Energy 
Spectraa 
T: 13.4 to 42.4 % 
I: 26.2 to 41.3 % 
F: 31.5 to 45.3 % 
T: 7.1 to 15.0 % 
I: 38.6 to 41.0 % 
F: 46.2 to 51.9 % 
T: 28.6% 
I: 31.2% 
F: 40.2% 
T: 43.9 to 45.5% 
I: 24.1 to 25.3% 
F: 30.4 to 32.1% 
T: 37.6 to 49.1 % 
I: 22.7 to 27.3% 
F: 28.2 to 35.1% 
T: 80.6 to 95.4 % T: 63.2 to 72.9 % T: 93.6% T: 96.6 to 96.9% T: 96.2 to 97.6% 
Fission Rate vs. 
Neutron Energya I: 2.6 to 12.9 % 
F: 2.0 to 6.6 % 
I: 19.0 to 25.6 % 
F: 8.1 to 10.9 % 
I: 4.6% 
F: 1.8% 
I: 2.3 to 2.5% 
F: 0.8 to 1.1% 
I: 2 to 3.1% 
F: 0.4 to 0.7% 
Source: Moscalu 2004, Section 5.3 
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. 
Table XII-15. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with 
External Configurations Containing Mixtures with Low Enriched Uranium (Set 2) 
Experiment Experiment Experimen 
Category/ 
Description Parameter 
LEU-SOL-THERM-008 
(4 cases) 
LEU-SOL-THERM-009 
(3 cases) 
LEU-SOL-THERM-018 
(6 cases) 
Materials/ 
Fissionable 
Fissionable 
Element 
Uranium Uranium Uranium 
Material Physical Form Aqueous solution of 
uranyl nitrate 
Aqueous solution of 
uranyl nitrate 
Aqueous solution of uranyl 
nitrate 
Isotopic 9.97 wt% 235U 9.97 wt% 235U 9.97 wt% 235U 
Composition 
Atomic Density 
(atoms/b-cm) 
235U: 6.14e-05 
238U: 5.47e-04 
235U: 6.26e-05 
238U: 5.57e-04 
235U: 7.87e-5 to 8.04e-05 
238U: 7.01e-04 to 7.16e-04 
Temperature Room Temp. Room Temp. Room Temp. 
Materials Element H H H 
Moderator Physical Form Solution Solution Solution 
Atomic Density 
(atoms/b-cm) 
5.86e-02 5.85e-02 5.87e-02 to 5.91e-02 
Ratio to Fissile 951 to 956 934 to 936 731 to 751 
Material 
Temperature Room Temp. Room Temp. Room Temp. 
Materials/ 
Reflector 
Material/ 
Physical Form 
Reflected by concrete Reflected by borated 
concrete 
Reflected by concrete 
CAL-DS0-NU-000003 REV 00A XII-24 September2004 

Criticality Model 
Table XII-15. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with External 
Configurations Containing Mixtures with Low Enriched Uranium (Set 2) (Continued) 
Category/ 
Description Parameter 
Experiment 
LEU-SOL-THERM-008 
(4 cases) 
Experiment 
LEU-SOL-THERM-009 
(3 cases) 
Experimen 
LEU-SOL-THERM-018 
(6 cases) 
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 Homogeneous solution 
contained in a 
cylindrical tank 
Homogeneous solution 
contained in a 
cylindrical tank 
Homogeneous solution in 
a rectangular slab tank 
Shape Cylinder Cylinder Rectangular slab 
Neutron Energy AENCF 0.0152 to 0.0154 MeV 0.0155 to 0.0158 MeV 0.0183 to 0.0188 MeV 
EALF 3.84e-02 eV 3.89e-02 eV 0.042 to 0.0425 eV 
Neutron Energy 
Spectraa 
T: 41.5 to 41.7% 
I: 25.9 to 26% 
F: 32.4 to 35% 
T: 40.8 to 41 % 
I: 26.2 to 26.3% 
F: 32.8 to 32.9% 
T: 36.5 to 37.0 % 
I: 28.0 to 28.3 % 
F: 34.9 to 35.2 % 
Fission Rate vs 
Neutron Energya 
T: 96.8% 
I: 2.6% 
F: 0.6% 
T: 96.7% 
I: 2.7% 
F: 0.6% 
T: 96.0% 
I: 3.3% 
F: 0.7 
Source: Moscalu 2004, Section 5.3 
NOTE: aSpectral range defined as follows: thermal (T) [0 to 1 eV], intermediate (I) [1eV to 100 keV], fast (F) [100 keV to 
20 MeV]. 
XII.4.3 Calculation of Lower-Bound Tolerance Limit 
The calculated LBTL value using DFTL method for the current set is f(x) = 0.9842 (Moscalu 
2004, Section 5.3). Figure XII-3 presents the keff values and the calculated LBTL for this set of 
benchmark experiments. 
1 
k 
lit 
0.96 
0.97 
0.98 
0.99 
1.01 
1.02 
1.03 
eff 
Low er Bound Toerance Lim
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 
AENCF (MeV) 
NOTE: AENCF = average energy of a neutron causing fission. 
Figure XII-3. Lower-Bound Tolerance Limit Applicable for Configurations Containing LEU External to 
the Waste Package 
CAL-DS0-NU-000003 REV 00A XII-25 September2004 

Criticality Model 
XII.5 MIXTURE OF URANIUM AND PLUTONIUM SYSTEMS 
Selection of the criticality benchmark experiments for mixture of uranium and plutonium 
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.5.1 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 
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 120 individual cases are presented in 
Table XII-16 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-16. Critical Benchmarks Selected for Validation of the Criticality Model for External 
Configurations Containing Mixtures of Uranium and Plutonium Isotopes 
Experiment Case Name 
Benchmark Values Calculated Values (MCNP) 
keff sexp keff scalc AENCF 
Experiment pnl3187 1.0000 0.0016 0.9976 0.0012 0.0417 
MIX-SOL-THERM-001 
(12 cases) 
pnl3391 1.0000 0.0016 0.9943 0.0012 0.0411 
pnl3492 1.0000 0.0016 0.9975 0.0012 0.0431 
pnl3593 1.0000 0.0016 0.9973 0.0011 0.0459 
pnl3694 1.0000 0.0016 1.0026 0.0012 0.0445 
pnl3795 1.0000 0.0016 1.0017 0.0012 0.0400 
pnl3896 1.0000 0.0016 1.0024 0.0012 0.0232 
pnl3897 1.0000 0.0016 1.0045 0.0011 0.0142 
pnl3898 1.0000 0.0016 1.0029 0.0010 0.0299 
pnl3808 1.0000 0.0016 1.0020 0.0011 0.0213 
pnl3999 1.0000 0.0052 1.0092 0.0011 0.0296 
pnl5300 1.0000 0.0052 1.0080 0.0011 0.0288 
CAL-DS0-NU-000003 REV 00A XII-26 September2004 

Criticality Model 
Table XII-16. Critical Benchmarks Selected for Validation of the Criticality Model for External 
Configurations Containing Mixtures of Uranium and Plutonium Isotopes (Continued) 
Experiment Case Name 
Benchmark Values Calculated Values (MCNP) 
keff sexp keff scalc AENCF 
Experiment pnl1158 1.0000 0.0024 1.0069 0.0007 0.0038 
MIX-SOL-THERM-002 
(3 cases) 
pnl1159 1.0000 0.0024 1.0074 0.0006 0.0037 
pnl1161 1.0000 0.0024 1.0079 0.0007 0.0061 
Experiment awre1 0.9985 0.0020 1.0147 0.0010 0.0315 
MIX-SOL-THERM-003 
(10 cases) 
awre2 0.9960 0.0020 1.0157 0.0012 0.0315 
awre3 0.9935 0.0020 1.012 0.0012 0.0320 
awre4 0.9909 0.0020 1.0051 0.0012 0.0319 
awre5 0.9981 0.0022 1.0085 0.0010 0.0104 
awre6 0.9959 0.0022 1.0107 0.0010 0.0104 
awre7 0.9935 0.0022 1.0080 0.0010 0.0105 
awre8 0.9988 0.0025 1.0128 0.0008 0.0069 
awre9 0.9958 0.0025 1.0094 0.0009 0.0066 
awre10 0.9964 0.0025 1.0102 0.0008 0.0066 
Experiment pnl1577 1.0000 0.0033 0.9958 0.0012 0.0589 
MIX-SOL-THERM-004 
(9 cases) 
pnl1678 1.0000 0.0033 0.9974 0.0012 0.0504 
pnl1783 1.0000 0.0078 0.9992 0.0012 0.0534 
pnl1868 1.0000 0.0078 1.0039 0.0013 0.0343 
pnl1969 1.0000 0.0033 1.0000 0.0012 0.0334 
pnl2070 1.0000 0.0033 0.9996 0.0014 0.0377 
pnl2565 1.0000 0.0033 1.0015 0.0012 0.0129 
pnl2666 1.0000 0.0033 1.0018 0.0011 0.0117 
pnl2767 1.0000 0.0078 1.0061 0.0011 0.0123 
Experiment msl5-63 1.0000 0.0037 0.9877 0.0008 0.013 
MIX-SOL-THERM-005 
(7 cases) 
msl5-64 1.0000 0.0037 1.0045 0.0007 0.012 
msl5-71 1.0000 0.0037 1.0032 0.0008 0.033 
msl5-72 1.0000 0.0037 1.0001 0.0008 0.032 
msl5-74 1.0000 0.0037 0.9922 0.0009 0.037 
msl5-75 1.0000 0.0037 0.9898 0.0009 0.059 
msl5-76 1.0000 0.0037 0.9974 0.0007 0.049 
Experiment C1 1.0000 0.0011 0.9992 0.0006 0.0352 
MIX-SOL-THERM-006 
(6 cases) 
C2 1.0000 0.0010 1.0018 0.0006 0.0375 
C3 1.0000 0.0012 1.0025 0.0005 0.0380 
C4 1.0000 0.0016 1.0041 0.0005 0.0396 
C5 1.0000 0.0011 1.0039 0.0005 0.0405 
C6 1.0000 0.0014 1.0021 0.0005 0.0404 
Experiment c1_mc50 1.0042 0.0058 0.9764 0.0007 0.0709 
MIX-COMP-THERM-012 
(33 cases) 
c2_mc50 1.0042 0.0058 0.9770 0.0007 0.0712 
c3_mc50 1.0042 0.0058 0.9743 0.0007 0.0708 
c4_mc50 1.0042 0.0058 0.9804 0.0007 0.0709 
c5_mc50 1.0042 0.0058 0.9756 0.0007 0.0710 
c6_mc50 1.0042 0.0058 0.9805 0.0007 0.0714 
CAL-DS0-NU-000003 REV 00A XII-27 September2004 

Criticality Model 
Table XII-16. Critical Benchmarks Selected for Validation of the Criticality Model for External 
Configurations Containing Mixtures of Uranium and Plutonium Isotopes (Continued) 
Experiment Case Name 
Benchmark Values Calculated Values (MCNP) 
keff sexp keff scalc AENCF 
Experiment c7_mc50 1.0023 0.0036 1.0353 0.0006 0.0268 
MIX-COMP-THERM-012 
(33 cases) 
(continued) 
c8_mc50 1.0023 0.0036 1.0309 0.0006 0.0264 
c9_mc50 1.0023 0.0036 1.0281 0.0006 0.0267 
c10_mc50 1.0023 0.0036 1.0277 0.0006 0.0268 
c11_mc50 1.0023 0.0036 1.0264 0.0006 0.0265 
c12_mc50 1.0023 0.0036 1.0287 0.0007 0.0266 
c13_mc50 1.0023 0.0036 1.0372 0.0007 0.0266 
c14_mc50 1.0002 0.0027 1.0231 0.0007 0.0464 
c15_mc50 1.0002 0.0027 1.0234 0.0008 0.0464 
c16_mc50 1.0002 0.0027 1.0194 0.0007 0.0463 
c17_mc50 1.0002 0.0027 1.0188 0.0007 0.0457 
c18_mc50 1.0002 0.0027 1.0172 0.0007 0.0459 
c19_mc50 1.0002 0.0027 1.0167 0.0007 0.0456 
c20_mc50 1.0004 0.0037 1.0173 0.0008 0.0571 
c21_mc50 1.0004 0.0037 1.0160 0.0008 0.0581 
c22_mc50 1.0004 0.0037 1.0129 0.0008 0.0571 
c23_mc50 0.9997 0.0049 1.0108 0.0007 0.0388 
c24_mc50 0.9997 0.0049 1.0122 0.0008 0.0386 
c25_mc50 0.9997 0.0049 1.0112 0.0007 0.0384 
c26_mc50 0.9997 0.0049 1.0092 0.0007 0.0382 
c27_mc50 0.9997 0.0049 1.0089 0.0007 0.0380 
c28_mc50 0.9997 0.0049 1.0104 0.0007 0.0381 
c29_mc50 0.9997 0.0049 1.0113 0.0007 0.0376 
c30_mc50 0.9997 0.0049 1.0090 0.0007 0.0379 
c31_mc50 1.0007 0.0052 0.9963 0.0009 0.0493 
c32_mc50 1.0007 0.0052 0.9970 0.0008 0.0490 
c33_mc50 1.0007 0.0052 0.9935 0.0008 0.0498 
Experiment 81-1-B5 1.0002 0.0037 1.0003 0.0017 0.4567 
PU-MET-MIXED-001 
(6 cases) 
81-1AB5 1.0002 0.0032 0.9991 0.0019 0.4505 
81-2-B5 1.0005 0.0025 1.0040 0.0019 0.3800 
81-3-b5 1.0000 0.0025 1.0094 0.0019 0.3405 
81-4-b5 1.0001 0.0025 1.0165 0.0017 0.2178 
81-5-b5 1.0003 0.0025 1.0163 0.0017 0.2145 
Experiment case1 0.9986 0.0041 1.0286 0.0009 1.7019 
PU-COMP-MIXED-001 
(5 cases) 
case2 1.0000 0.0068 1.0188 0.0013 0.6331 
case3 0.9990 0.0067 1.0150 0.0013 0.2753 
case4 1.0000 0.0066 0.9853 0.0014 0.2878 
case5 0.9989 0.0072 1.0084 0.0013 0.0999 
Experiment case1 0.9990 0.0046 1.0318 0.0009 1.0458 
PU-COMP-MIXED-002 
(29 cases) 
case2 0.9990 0.0046 1.0309 0.0009 1.0303 
case3 0.9990 0.0046 1.0253 0.0008 1.0089 
CAL-DS0-NU-000003 REV 00A XII-28 September2004 

Criticality Model 
Table XII-16. Critical Benchmarks Selected for Validation of the Criticality Model for External 
Configurations Containing Mixtures of Uranium and Plutonium Isotopes (Continued) 
Experiment Case Name 
Benchmark Values Calculated Values (MCNP) 
keff sexp keff scalc AENCF 
Experiment case4 0.9990 0.0046 1.0199 0.0009 0.9807 
PU-COMP-MIXED-002 
(29 cases) 
(continued) 
case5 0.9990 0.0046 1.0139 0.0008 0.9433 
case6 1.0000 0.0075 1.0168 0.0009 0.4377 
case7 1.0000 0.0075 1.0183 0.0008 0.4334 
case8 1.0000 0.0075 1.0177 0.0008 0.4234 
case9 1.0000 0.0075 1.0189 0.0009 0.4137 
case10 1.0000 0.0073 1.0282 0.0009 0.1836 
case11 1.0000 0.0073 1.0248 0.0009 0.1872 
case12 1.0000 0.0073 1.0250 0.0008 0.1919 
case13 1.0000 0.0073 1.0220 0.0010 0.1932 
case14 1.0000 0.0073 1.0268 0.0009 0.1933 
case15 1.0000 0.0073 1.0224 0.0009 0.1938 
case16 1.0000 0.0073 1.0188 0.0009 0.1917 
case17 0.9988 0.0055 1.0062 0.0009 0.1963 
case18 0.9988 0.0055 1.0071 0.0008 0.2040 
case19 0.9988 0.0055 1.0068 0.0009 0.2040 
case20 0.9988 0.0055 1.0078 0.0009 0.2060 
case21 0.9988 0.0055 1.0075 0.0009 0.2063 
case22 0.9988 0.0055 1.0118 0.0009 0.2038 
case23 1.0000 0.0068 1.0058 0.0009 0.0770 
case24 1.0000 0.0068 1.0090 0.0009 0.0770 
case25 1.0000 0.0068 1.0081 0.0009 0.0777 
case26 1.0000 0.0068 1.0103 0.0010 0.0774 
case27 1.0000 0.0068 1.0090 0.0009 0.0776 
case28 1.0000 0.0068 1.0095 0.0009 0.0777 
case29 1.0000 0.0068 1.0104 0.0009 0.0785 
Source: Moscalu 2004, Section 5.4 
NOTE: AENCF = average energy of a neutron causing fission. 
The experiments listed in Table XII-15 cover configuration classes NF-1 through NF-5 and FF-1 
through FF-3 for configurations containing mixtures of low enriched uranium external to the 
waste package. 
XII.5.2 Range of Applicability of Selected Critical Benchmark Experiments 
Tables XII-17 and XII-18 summarize the range of applicability of the experiments listed in 
Table XII-16. The information is excerpted from Moscalu (2004, Section 5.4). 
CAL-DS0-NU-000003 REV 00A XII-29 September2004 

Criticality Model 
Table XII-17. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with 
External Configurations Containing Mixtures with Plutonium and Uranium (Set 1) 
Experiment Experiment Experiment Experiment Experiment 
MIX-SOL-MIX-SOL-MIX-SOL-MIX-SOL-MIX-SOL-
Category/ THERM-001 THERM-002 THERM-003 THERM-004 THERM-005 
Description Parameter (12 cases) (3 cases) (10 cases) (9 cases) (7 cases) 
Materials/ 
Fissionable 
Fissionable 
Element 
Plutonium + 
Uranium 
Plutonium + Uranium Plutonium + 
Uranium 
Plutonium + 
Uranium 
Plutonium + 
Uranium 
Material Physical Form Pu-U nitrate 
solution 
Pu-U nitrate solution Pu-U nitrate 
solution 
Pu-U nitrate solution Pu-U nitrate 
solution 
Isotopic 
Composition 
91.1 to 91.57 wt% 
239Pu in Pu 
0.44 to 0.71 wt % 
235U in U 
91.1 wt% 239Pu in Pu 
0.7 to 2.29 wt % 235U 
in U 
94 wt% 239Pu in Pu 
0.72 wt % 235U in U 
91.1 wt% 239Pu in 
Pu 
0.56 wt % 235U in U 
91.1 wt% 239Pu in 
Pu 
0.56 wt % 235U in U 
Atomic 
Density 
(atoms/b-cm) 
239Pu: 1.08e-04 to 
4.51e-04 
235U: 1.35e-06 to 
6.86e-06 
239Pu: 2.69e-05 to 
2.80e-04 
235U: 1.94e-06 to 
4.6e-06 
239Pu: 7.47e-05 to 
2.40e-04 
235U: 7.6e-07 to 
4.2e-06 
239Pu: 9.60e-05 to 
3.98e-04 
235U: 9.16e-07 to 
3.8e-06 
239Pu: 9.42e-05 to 
3.97e-04 
235U: 9.09e-07 to 
3.8e-06 
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 H: 5.45e-02 to H: 6.48e-02 to 6.55e-H: 5.73e-02 to H: 5.41e-02 to H: 5.40e-02 to 
Density 6.71e-02 02 6.44e-02 6.35e-02 6.35e-02 
(atoms/b-cm) 
Ratio to 
Fissile 
H/239Pu = 125 to 
569 (annular tank) 
H/239Pu = 2317 to 
2434 
H/239Pu = 239 to 
1556 
H/239Pu = 126 to 
664 
H/239Pu = 136 to 
674 
Material 
Temperature Room Temp. Room Temp. Room Temp Room Temp Room Temp 
Materials/ 
Reflector 
Material/ 
Physical Form 
Reflected by water Reflected by water Reflected by water 
and polyethylene 
Reflected by water 
or concrete 
Reflected by water 
or concrete 
Materials/ Element B, Cd None None None None 
Neutron 
Absorber Physical Form B in concrete, Cd in 
inserts 
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 in annular 
Homogeneous 
solution in a 
Homogeneous 
solution in a 
Homogeneous 
solution in a 
Homogeneous 
solution in slab 
cylinder; Center 
contained solution 
cylindrical vessel cylindrical vessel cylindrical vessel tank 
and/or inserts 
Shape Cylinder Cylinder Cylinder Cylinder Parallelepiped 
Neutron 
Energy 
AENCF 0.0142 to 0.0459 
MeV 
0.0039 to 0.0061 MeV 0.0065 to 0.0320 
MeV 
0.0117 to 0.0589 
MeV 
0.012 to 0.059 MeV 
EALF 0.0541 to 0.393 eV 0.0423 to 0.0433 eV 0.0477 to 0.144 eV 0.06669 to 0.302 eV 0.0667 to 0.361 eV 
Neutron 
Energy 
Spectraa 
T: 5.1 to 27.5 % 
I: 32.1 to 40.1 % 
F: 40.4 to 54.8 % 
T: 47.4 to 48.5 % 
I: 22.6 to 23.1 % 
F: 28.7 to 29.5 % 
T: 11.2 to 39.2 % 
I: 26.0 to 36.9 % 
F: 33.8 to 51.9 % 
T: 6.1 to 24.6 % 
I: 31.8 to 39.0 % 
F: 43.6 to 55.7 % 
T: 5.6 to 24.9 % 
I: 31.7 to 38.8 % 
F: 43.4 to 55.6 % 
Fission Rate 
vs. Neutron 
Energya 
T: 84.1 to 93.5 % 
I: 5.7 to 13.8 % 
F: 0.8 to 2.1 % 
T: 98.3 to 98.5 % 
I: 1.3 to 1.4 % 
F: 0.1 to 0.3 % 
T: 90.6 to 97.9% 
I: 1.8 to 7.9% 
F: 0.3 to 1.4% 
T: 82.8 to 96.1% 
I: 3.4 to 14.5 % 
F: 0.5 to 2.7% 
T: 82.7 to 96.1% 
I: 3.4 to 14.6 % 
F: 0.6 to 2.7% 
Source: Moscalu 2004, Section 5.4 
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-30 September2004 

Criticality Model 
Table XII-18. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with 
External Configurations Containing Mixtures with Plutonium and Uranium (Set 2) 
Experiment Experiment Experiment Experiment Experiment 
MIX-SOL-MIX-COMP- PU-MET-PU-COMP- PU-COMP- 
Category/ THERM-006 THERM-012 MIXED-001 MIXED-001 MIXED-002 
Description Parameter (6 cases) (33 cases) (6 cases) (5 cases) (29 cases) 
Materials/ 
Fissionable 
Fissionable 
Element 
Plutonium + Uranium Plutonium + uranium Plutonium Plutonium Plutonium 
Material Physical Form Pu-U nitrate solution Pu-U oxide (MOX) Pu metal pellets Pu oxide Pu oxide 
Isotopic 
Composition 
Pu: 75.4 wt % 239Pu ; 
20.4 wt % 240Pu ; 2.9 
wt % 241Pu 
0.56 wt % 235U in U 
Pu: 8 and 23 wt% 
240Pu in Pu 
0.151 wt% 235U in U 
95.17 wt% 239Pu 75.2 to 97.7 wt% 
239Pu in Pu 
75.2 to 97.7 wt% 
239Pu in Pu 
Atomic Density 
(atoms/b-cm) 
239Pu: 1.72e-04 to 
1.73e-04 
235U: 2.66e-06 to 
2.7e-06 
239Pu: 6.51e-05 to 
1.09e-04 
235U: 1.01e-06 to 
2.9e-06 
239Pu: 3.67e-02 239Pu: 7.00e-04 to 
1.09e-02 
239Pu: 7.00e-04 to 
1.09e-02 
Temperature Room temp. Room temp. Room temp. Room temp. Room temp. 
Materials/ 
Moderator 
Element H H, C H, C, Si as 
scatterer 
H, C H, C 
Physical Form Solution Polystyrene Polyethylene, 
sand 
Polystyrene Polystyrene 
Atomic Density 
(atoms/b-cm) 
H: 5.48e-02 to 5.52e-
02 
H: 4.15e-02 to 
5.66e-02 
C: 3.56e-02 to 
In Polythylene 
pellets: 
H: 7.83e-02 
H: 5.51e-04 to 
4.57e-02 
C: 0 to 4.50e-02 
H: 5.51e-04 to 
4.57e-02 
C: 0 to 4.50e-02 
4.54e-02 C: 3.91e-02 
Silicone dioxide: 
Si:1.57e-02 and 
1.98e-02 
Ratio to Fissile 
Material 
H/X = 297 to 303 H/239Pu = 174 to 724 Not available H/239Pu = 0.05 to 
65.37 
H/239Pu = 0.05 to 
65.37 
Temperature Room temp. Room temp. Room temp. Room temp. Room temp. 
Materials/ 
Reflector 
Material/ 
Physical Form 
Reflected by water Unreflected or 
reflected by 
Plexiglas 
Reflected by 
sand and 
depleted uranium 
Unreflected Reflected by 
Plexiglas 
Materials/ 
Neutron 
Absorber 
Element Gd None B None None 
Physical Form Solution N/A B4C N/A N/A 
Atomic Density 
(atoms/b-cm) 
Gd: 1.15e-07 to 
2.67e-06 
N/A 10B: 1.10e-02 
11B: 4.46e-02 
N/A N/A 
Geometry Heterogeneity Homogeneous 
solution in cylindrical 
Arrays of 
MOX/polystyrene 
Complex 
heterogeneous 
Arrays of Pu-
oxide/polystyrene 
Arrays of Pu-
oxide/polystyrene 
tank compact blocks in 
rectangular 
arrangements of 
Pu and silicon 
compact blocks in 
rectangular 
compact blocks in 
rectangular 
configurations dioxide pellets configurations configurations 
placed in array of 
rods 
Shape Cylinder Slab, parallelepiped Cylindrical array 
of rods 
Rectangular slab Rectangular slab 
Neutron 
Energy 
AENCF 0.035 to 0.040 MeV 0.026 to 0.071 MeV 0.214 to 0.457 
MeV 
0.100 to 1.702 MeV 0.077 to 1.046 MeV 
EALF Not available 0.070 to 0.264 eV 1.29 to 5540 eV 1.67 to 1.02e6 eV 0.749 to 6800 eV 
Neutron 
Energy 
Spectraa 
Not available T: 7.2 to 27.9% 
I: 31.2 to 38.8% 
F: 40.9 to 54.0% 
T: 0.2 to 18.5% 
I: 31.9 to 52.3% 
F: 47.5 to 54.6% 
T: 0 to 2.3 % 
I: 5.9 to 39.7 % 
F: 58. to 94.1 % 
T: 0.1 to 3.2 % 
I: 13.9 to 39.2 % 
F: 57.6 to 86.0 % 
Fission Rate 
vs Neutron 
Energya 
Not available T: 86.0 to 96% 
I: 3.0 to 11.8% 
F: 1.0 to 2.6% 
T: 4.1 to 70.6% 
I: 18.1 to 63.7% 
F: 11.4 to 32.2% 
T: 0.2 to 65.2% 
I: 5.3 to 57.7% 
F: 5.2 to 94.5 % 
T: 23 to 72.4% 
I: 19.8 to 44.9% 
F: 4.0 to 57.2 % 
Source: Moscalu 2004, Section 5.4 
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]. 
AENCF = average energy of a neutron causing fission, EALF = energy of average lethargy causing fission. 
CAL-DS0-NU-000003 REV 00A XII-31 September2004 

Criticality Model 
XII.5.3 Calculation of Lower-Bound Tolerance Limit 
The calculated lower bound tolerance limit value using DFTL method for this set of benchmark 
experiments is 0.9644. Figure XII-4 presents the keff values and the calculated LBTL 
k 
eff 
(Moscal 2004, Section 5.4). 
1.05 
1.04 
1.03 
1.02 
1.01 
1 
0.99 
0.98 
0.97 
0.96 
limitLow er Bound Toerance L
0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 
AENCF (MeV) 
NOTE: AENCF = average energy of a neutron causing fission. 
Figure XII-4. Lower Bound Tolerance Limit Applicable for Configurations Containing Mixtures of 
Plutonium and Uranium External to the Waste Package 
XII.6 233U SYSTEMS 
Selection of the criticality benchmark experiments for 233U 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.6.1 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 233U 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 Handbook of 
Evaluated Criticality Safety Benchmark Experiments (NEA 2003) unless otherwise noted. The 
CAL-DS0-NU-000003 REV 00A XII-32 September2004 

Criticality Model 
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 83 individual cases are presented in 
Table XII-19 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-19. Critical Benchmarks Selected for Validation of the Criticality Model for External 
Configurations Containing 233U 
Experiment Case Name 
Benchmark Values Calculated Values (MCNP) 
keff sexp keff scalc AENCF 
Experiment ust001-1 1 0.0031 1.0018 0.0005 0.0038 
U-233-SOL-THERM-001 
(5 cases) 
ust001-2 1.0005 0.0033 1.0004 0.0006 0.0041 
ust001-3 1.0006 0.0033 0.9994 0.0006 0.0043 
ust001-4 0.9998 0.0033 0.9989 0.0006 0.0043 
ust001-5 0.9999 0.0033 0.9987 0.0006 0.0043 
Experiment ust02-04 1.004 0.0087 1.0103 0.0011 0.026 
U-233-SOL-THERM-002 
(17 cases) 
ust02-05 1.004 0.0087 0.9973 0.0011 0.0214 
ust02-08 1.004 0.0087 1.0113 0.001 0.0173 
ust02-10 1.004 0.0087 1.0096 0.0011 0.0138 
ust02-11 1.004 0.0087 1.0126 0.001 0.0115 
ust02-12 1.004 0.0087 1.0006 0.001 0.01 
ust02-14 1.004 0.0087 0.9875 0.0009 0.0098 
ust02-15 1.004 0.0087 1.0026 0.001 0.0083 
ust02-17 1.004 0.0087 0.9897 0.0009 0.0072 
ust02-18 1.004 0.0087 1.0029 0.0008 0.0066 
ust02-19 1.004 0.0087 1.0102 0.0008 0.0056 
ust02-22 1.004 0.0087 0.9967 0.0011 0.0356 
ust02-24 1.004 0.0087 0.9976 0.0012 0.049 
ust02-34 1.004 0.0087 1.0038 0.0011 0.0223 
ust02-35 1.004 0.0087 1.0103 0.0009 0.0155 
ust02-36 1.004 0.0087 1.0115 0.0009 0.0096 
ust02-38 1.004 0.0087 1.0097 0.0008 0.0075 
Experiment ust03-40 0.9995 0.0087 1.008 0.001 0.0387 
U-233-SOL-THERM-003 
(10 cases) 
ust03-41 0.9991 0.0151 1.026 0.0011 0.0397 
ust03-42 1.0007 0.0087 1.0044 0.0011 0.04 
ust03-45 1.0015 0.0126 1.014 0.0011 0.061 
ust03-55 1.0006 0.0122 1.0197 0.0011 0.0693 
ust03-57 1.0012 0.0087 1.0244 0.001 0.0209 
ust03-58 1.0016 0.0087 1.0167 0.001 0.0138 
ust03-61 1.0016 0.0087 1.0133 0.001 0.0108 
ust03-62 1.0018 0.0087 1.0107 0.001 0.0095 
ust03-65 1.0008 0.0087 1.0073 0.0008 0.0056 
CAL-DS0-NU-000003 REV 00A XII-33 September2004 

Criticality Model 
Table XII-19. Critical Benchmarks Selected for Validation of the Criticality Model for External 
Configurations Containing 233U (Continued) 
Experiment Case Name 
Benchmark Values Calculated Values (MCNP) 
keff sexp keff scalc AENCF 
Experiment ust04-03 1.0039 0.0088 1.0086 0.0011 0.0257 
U-233-SOL-THERM-004 
(10 cases) 
ust04-06 1.0034 0.0086 1.0113 0.001 0.0208 
ust04-20 1.0041 0.0089 1.0006 0.0011 0.0353 
ust04-25 1.0051 0.0089 0.9936 0.0011 0.0493 
ust04-27 1.002 0.0105 1.0119 0.0011 0.0479 
ust04-28 1.002 0.0104 1.0063 0.0011 0.0425 
ust04-30 1.0037 0.009 0.9988 0.0011 0.043 
ust04-33 1.002 0.0102 1.0087 0.0011 0.0215 
Experiment ust05-01 1.000 0.004 1.0054 0.0009 0.0094 
U-233-SOL-THERM-005 
(2 cases) 
ust05-02 1000 0.0049 1.0075 0.0009 0.0078 
Experiment ust008 1.0006 0.0029 0.9986 0.0004 0.003 
U-233-SOL-THERM-008 
(1 case) 
Experiment m35 1.000 0.0035 1.023 0.0008 0.0576 
U-233-SOL-THERM-006 
(12 cases) 
m36 1.000 0.0035 1.0113 0.0008 0.0583 
m37 1.000 0.0035 0.9996 0.0008 0.0588 
m38 1.000 0.0035 1.0011 0.0008 0.0584 
m45 1.000 0.0035 1.0186 0.0011 0.059 
m61 1.000 0.0035 1.0228 0.0008 0.0345 
m62 1.000 0.0035 1.0132 0.0008 0.0346 
m63 1.000 0.0035 0.9988 0.0008 0.0352 
m65 1.000 0.0035 0.9939 0.0008 0.0350 
m77 1.000 0.0035 0.9939 0.0011 0.0358 
m78 1.000 0.0035 0.9932 0.0011 0.0358 
m79 1.000 0.0035 0.9929 0.0011 0.0355 
Experiment hcm-1 1.000 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 0.996 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 0.001 0.4625 
hcm-19 1.0039 0.0047 1 0.0011 0.5191 
CAL-DS0-NU-000003 REV 00A XII-34 September2004 

Criticality Model 
Table XII-19. Critical Benchmarks Selected for Validation of the Criticality Model for External 
Configurations Containing 233U (Continued) 
Experiment Case Name 
Benchmark Values Calculated Values (MCNP) 
keff sexp keff scalc AENCF 
Experiment hcm-20 1.006 0.0065 1.0051 0.0015 0.5357 
HEU-COMP-MIXED-001 
(26 cases) 
(continued) 
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 0.997 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 
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) 
Source: Moscalu 2004, Section 5.5 
XII.6.2 Range of Applicability of Selected Critical Benchmark Experiments 
Tables XII-19 and XII-20 summarize the range of applicability of the experiments listed in 
Table XII-18. The information is excerpted from Moscalu (2004, Section 5.5). 
Table XII-20. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with 
External Configurations Containing 233U (Set 1) 
Category/ 
Description Parameter 
Experiment 
U-233-SOL- 
THERM-001 
(5 cases) 
Experiment 
U-233-SOL- 
THERM-002 
(17 cases) 
Experiment 
U-233-SOL- 
THERM-003 
(10 cases) 
Experiment 
U-233-SOL- 
THERM-004 
(8 cases) 
Experiment 
U-233-SOL- 
THERM-005 
(2 cases) 
Materials/ 
Fissionable 
Fissionable 
Element 
Uranium Uranium Uranium Uranium Uranium 
Material Physical Form Uranyl nitrate Uranyl nitrate Uranyl fluoride Uranyl nitrate Uranyl nitrate 
Isotopic 
Composition 
97.7 wt% U-233 98.7 wt% U-233 98.7 wt% U-233 98.7 wt% U-233 98.7 wt% U-233 
Atomic 
Density 
(atoms/b-cm) 
U-233: 4.33e-05 
to 5.00e-05 
U-233: 8.71e-05 
to 9.84e-04 
U-233: 8.56e-05 
to 1.55e-03 
U-233: 4.15e-04 
to 9.84e-04 
U-233: 1.27e-04 
and 1.60e-04 
Temperature Room Temp. Room Temp. Room Temp. Room Temp. Room Temp. 
CAL-DS0-NU-000003 REV 00A XII-35 September2004 

Criticality Model 
Table XII-20. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with 
External Configurations Containing 233U (Set 1) (Continued) 
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/ 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/ 
Reflector 
Material/ 
Physical Form 
Unreflected Reflected by 
paraffin 
Reflected by 
paraffin 
Reflected by 
paraffin 
Reflected by 
water 
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-07 to 
1.01e-6 
N/A N/A N/A N/A 
Geometry Heterogeneity Solution 
contained in an 
Al sphere 
Solution 
contained in an 
Al sphere 
Solution 
contained in 
single Al 
cylindrical vessel 
Solution 
contained in 
single Al 
cylindrical vessel 
Solution in 
spherical or 
cylindrical Al 
vessel 
Shape Sphere Sphere Cylindrical Cylindrical Cylindrical/ 
Spherical 
Neutron 
Energy 
AENCFb 0.0038 to 0.0043 
MeV 
0.0056 to 0.0490 
MeV 
0.0056 to 0.0693 
MeV 
0.0208 to 0.0493 
MeV 
0.0078 to 0.0094 
MeV 
EALFb 0.0392 to 0.0417 
eV 
0.0464 to 0.471 
eV 
0.046 to 1.03 eV 0.138 to 0.486 
eV 
0.055 to 0.062 
eV 
Neutron 
Energy 
Spectraa 
T: 48.9 to 52.5 % 
I: 21.0 to 22.6% 
F: 26.5 to 28.5% 
T: 7.7 to 42.2 % 
I: 24.8 to 33.9% 
F: 33.0 to 58.3% 
T: 5.2 to 42.6 % 
I: 24.6 to 34.2 % 
F: 32.7 to 60.6 % 
T: 7.8 to 17.2 % 
I: 32.4 to 34.0 % 
F: 50.4 to 58.3 % 
T: 31.3 to 35.5 % 
I: 27.1 to 28.5 % 
F: 37.4 to 40.1 % 
Fission Rate 
vs. Neutron 
Energya 
T: 94.0 to 94.8% 
I: 5.0 to 5.8% 
F: 0.2 % 
T: 76.0 to 92.5% 
I: 7.1 to 33.5% 
F: 0.2 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 % 
T: 88.9 to 90.5% 
I: 9.0 to 10.6 % 
F: 0.4 to 0.5 % 
Source: Moscalu 2004, Section 5.5 
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 XII-36 September2004 

Criticality Model 
Table XII-21. Range of Applicability of Critical Benchmark Experiments Selected for Comparison with 
External Configurations Containing 233U (Set 2) 
Experiment Experiment Experiment Experiment Experiment 
U-233-SOL- U-233-SOL- HEU-COMP- HEU-MET-HEU-MET-
Category/ THERM-006 THERM-008 MIXED-001 THERM-001 THERM-014 
Description Parameter (6 cases) (1 case) (26 cases) (1 case) (1 case) 
Materials/ 
Fissionable 
Fissionable 
Element 
Uranium Uranium Uranium Uranium Uranium 
Material Physical Form Uranyl nitrate Uranyl nitrate UO2 Uranium metal 
foils 
Uranium metal 
foils 
Isotopic 
Composition 
97.56 or 97.54 wt% 
U-233; 
97.67 wt% U-233 93.15 wt% U-235 93.23 wt% U235 
93.23 wt% U235 
Atomic Density 
(atoms/b-cm) 
U-233:5.14e-04 to 
8.64e-04 
U-233: 3.34e-05 U-235: 4.48e-03 to 
1.39e-02 
U-235: 3.84e-02 
to 4.28e-02 
U-235: 3.84e-02 
to 4.38e-02 
Temperature Room temp. Room temp. Room temp. Room temp. Room temp. 
Materials/ 
Moderator 
Element H H H H, C 
Si as scatterer 
H, C 
Si as scatterer 
Physical Form Water in aqueous 
solution of uranyl 
nitrate 
Solution Water, Alcohol-water 
solution, Plexiglas 
Plates of 
polyethylene and 
silicon glass 
Plates of 
polyethylene and 
silicon glass 
Atomic Density 
(atoms/b-cm) 
5.89e-02 to 6.15e-02 6.64e-02 Fuel Region: 2.16e-
2 (few cases) 
5.68e-2 (plexiglas) 
6.24e-2 (alcohol-
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 
water) Si: 2.17 to 2.24e-Si: 2.20 to 2.28e-
02 02 
Ratio to Fissile 
Material 
H/X = 69 to 121 H/X = 1324 to 1533 H/X = 0 to 49 Not available H/X: Not 
available 
Si/U235 = 42 
Temperature Room temp. Room temp. Room temp. Room Temp. Room Temp. 
Materials/ 
Reflector 
Material/ 
Physical Form 
Unreflected Unreflected Reflected by 
polyethylene 
Reflected by 
polyethylene 
Reflected by 
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 
Geometry Heterogeneity Arrays of cans 
containing uranyl 
nitrate solution in 
rectangular 
Solution contained 
in an Al sphere 
Complex arrays of 
cans in rectangular 
geometry 
Rectangular 
column of plates 
and foils 
Rectangular 
column of plates 
and foils 
geometry 
Shape Parallelepiped Sphere Cylinder Parallelepiped Parallelepiped 
Neutron 
Energy 
AENCFb 0.0344 to 0.0599 
MeV 
0.0030 MeV 0.1045 to 0.8015 
MeV 
0.0212 MeV 0.0234 MeV 
EALFb 0.303 to 0.896 eV 0.0037 eV 0.438 to 2070 eV 0.0865 eV Not Available 
Neutron Energy 
Spectraa 
T: 6.1 to 10.7 % 
I: 34.8 to 35.4 % 
F: 54.4 to 58.4 % 
T: 57.0 % 
I: 19.3 % 
F: 23.7 % 
T: 4.3 to 25.3 % 
I: 14.2 to 25.9 % 
F: 56.0 to 81.4 % 
T: 22.7 % 
I: 27.7 % 
F: 49.7 % 
Not Available 
Fission Rate vs. 
Neutron Energya 
T: 55.0 to 68.4 % 
I: 29.7 to 41.7 % 
F: 2.0 to 3.3 % 
T: 95.5 % 
I: 4.3 % 
F: 0.2 % 
T: 25.4 to 78.0 % 
I: 16.4 to 43.1 % 
F: 5.6 to 49.9 % 
T: 91.2 % 
I: 7.7 % 
F: 1.2 % 
Not Available 
Source: Moscalu 2004, Section 5.5 
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 XII-37 September2004 

Criticality Model 
XII.6.3 Calculation of Lower-Bound Tolerance Limit 
The calculated lower bound tolerance limit value using DFTL method for the current set is 
f(x) = 0.9748 (Moscalu 2004, Section 5.5.3). Figure XII-5 presents the keff values and the
keff 
calculated LBTL for this set of benchmark experiments. 
1.03 
1.02 
1.01
1
0.99 
0.98 
0.97 
itLower Bound Tolerance Lim
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 
AENCF (MeV) 
NOTE: AENCF = average energy of a neutron causing fission. 
Figure XII-5. Lower-Bound Tolerance Limit Applicable for Configurations Containing 233U External to the 
Waste Package 
CAL-DS0-NU-000003 REV 00A XII-38 September2004