ML15222A245

Enclosure 2 - Attachment 4 - Atkins-NS-DAC-SHN-15-03, Revision 2

ML15222A245
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Site:	SHINE Medical Technologies, PROJ0792
Issue date:	07/23/2015
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SMT-2015-036 Atkins-NS-DAC-SHN-15-03, Rev 2
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81 pages follow ENCLOSURE 2 ATTACHMENT 4 SHINE MEDICAL TECHNOLOGIES, INC.

SHINE MEDICAL TECHNOLOGIES, INC. APPLICATION FOR CONSTRUCTION PERMIT RESPONSE TO REQUEST FOR ADDITIONAL INFORMATION 6B.3-30 ATKINS-NS-DAC-SHN-15-03, REVISION 2 MCNP 6.1 VALIDATION WITH CONTINUOUS ENERGY ENDF/B-VII.1 CROSS SECTIONS FOR SHINE MEDICAL TECHNOLOGIES

Design Analyses and Calculation Page 2 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 Table of Contents

1.

Introduction 4

1.1.

Limits of Applicability 4

2.

MCNP 6.1 Code 4

2.1.

MCNP Summary 4

2.2.

ENDF/B-VII.1 Cross Section Library 5

3.

Validation Methodology 8

3.1.

Establishment of an Upper Subcritical Limit 9

3.2.

Margin of Subcriticality 10 3.3.

Determination of the Area of Applicability 10 3.4.

Discussion of Statistical Analysis 10

4.

Benchmark Experiment Descriptions 14 4.1.

Low Enriched Uranium 15 4.2.

Intermediate Enriched Uranium 16 4.3.

High Enriched Uranium 19

5.

Evaluation Results 25 5.1.

Trend Evaluation 29 5.2.

Normalcy Evaluation 38 5.3.

Bias and Bias Uncertainty Evaluation 41

6.

Area of Applicability 50 6.1.

AoA Sensitivity - H/235U Ratio 51 6.2.

AoA Sensitivity - 235U Enrichment 51 6.3.

AoA Sensitivity - U:O Ratio 51 6.4.

AoA Sensitivity - Sulfate Solution 51 6.5.

AoA Sensitivity - Boron 51

7.

References 55 Appendix A.

Combined Data Normalcy Test Calculations 56 Appendix B.

Electronic Copy of Input / Output Files 82

Design Analyses and Calculation Page 3 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 Tables Table 1 - Library Definitions for Various Elements 5

Table 2 - Critical Benchmark Experiments Summary 22 Table 3 - MCNP 6.1 Results Summary 26 Table 4 - Normalcy Results Summary 38 Table 5 - USL Results Summary 41 Table 6 - Intermediate Enriched USL 41 Table 7 - Low and Intermediate Enriched USL 43 Table 8 - Combined USL 46 Table 9 - Area of Applicability Summary 50 Table 10 - Boron Sensitivity 52 Figures Figure 1 - ANECF Trend 30 Figure 2 - H/235U Trend 32 Figure 3 - ANECF vs. H/235U Evaluation 33 Figure 4 - Enrichment Trend 34 Figure 5 - Moderator Evaluation 35 Figure 6 - Reflector Evaluation 36 Figure 7 - Chemical Form Evaluation 37 Figure 8 - Intermediate Enriched Distribution 38 Figure 9 - Intermediate Enriched Distribution 39 Figure 10 - Combined Group Distribution 40

Design Analyses and Calculation Page 4 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2

1.

Introduction Nuclear criticality safety analysis is performed for fissile material systems for the SHINE Medical Technologies facility. The nuclear criticality safety analysis establishes the nuclear safety operating limits for the systems and operations. Calculation methods are used to provide an estimate of criticality conditions and the margin of subcriticality (MoS) for the systems and operations under evaluation. The computational methods predict the neutronic behavior of the system and operation. However, certain approximations are inherent in the computer code used including inexact neutron cross section data and statistical uncertainty.

Validation compares the computational method with documented critical experiments to determine any bias that might exist between the calculated reactivity of a given system and the actual conditions. Validation is a process that determines and establishes computational method applicability, adequacy, and uncertainty.

Following the guidance in Reference 10, this report documents the MCNP 6.1 validation. This report includes discussions of input files that model the critical experiments chosen for validation of the MCNP 6.1 computer code system for SHINE Medical Technologies operations, statistical evaluation of the calculation results, and the code bias and bias uncertainty. The validation is conducted using the ENDF/B-VII.1 continuous energy group cross section library. The validation is for use by nuclear criticality safety personnel in performing analysis and evaluation of various facility / site activities involving enriched uranium. Through the selection and validation of appropriate benchmark critical experiments and analysis, this report will validate the computational methods for an entire range of normal and off-normal operating conditions involving heterogeneous and homogeneous fissile material. Toward that end, critical experiments are modeled as reported in NEA/NCS/DOC (95)03 (Reference 1).

1.1.

Limits of Applicability The parameters associated with the critical experiments documented in this report will be used to set the Area of Applicability (AoA) for applications modeling fissile material systems and operations. Applications using the bias and bias uncertainty established for this experiment data set must use the modeling conventions described in Table 1 and the AoA listed in Table 9, or have the Upper Subcritical Limit (USL) reduced. The benchmark calculations were performed on the Atkins Linux computer cluster (Reference 3); therefore the validation conclusions herein are applicable to this computer cluster. This is a cluster of similar computers utilizing Intel processors that have been demonstrated to accurately reproduce the LANL supplied MCNP 6.1 verification test cases; this is recorded in Reference 10. The configuration control of this cluster is maintained by Reference 11; any hardware or operating system modification to the cluster requires a repeat of the verification tests.

2.

MCNP 6.1 Code The verification of MCNP 6.1 has been completed on the Atkins Linux computer cluster (Reference 3). All computers have 64-bit hardware and use the 64-bit version of Linux. Distribution of the calculation jobs among the individual CPUs is controlled by the Sun Grid Engine queue software running on the master Linux computer. Additional Linux execution hosts run calculation jobs at the command of the queue master. MCNP 6.1 has been installed in the read only disk area; the installation has been verified with the execution of the sample problems from Reference 2. This disk is shared with the execution hosts. Hardware and software used with the Atkins Linux computer cluster is managed with the Atkins NS Systems configuration control.

2.1.

MCNP Summary MCNP is a general-purpose Monte Carlo N-Particle code that can be used for neutron, photon, electron, or coupled neutron/photon/electron transport, including the capability to calculate eigenvalues for critical systems (Reference 2). 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.

Pointwise cross-section data are used. For neutrons, all reactions given in a particular cross-section evaluation (such as ENDF/B-VII.1) are accounted for. Thermal neutrons are described by both the free gas and S(,)

models.

Design Analyses and Calculation Page 5 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 Important standard features that make MCNP very versatile and easy to use include a powerful general source, criticality source, and surface source; both geometry and output tally plotters; a rich collection of variance reduction techniques; a flexible tally structure; and an extensive collection of cross-section data.

2.2.

ENDF/B-VII.1 Cross Section Library The ENDF/B-VII.1 cross-section library is used for the critical experiment calculations in this validation analysis. This library contains data for over 300 nuclides. A list of the elements used in this evaluation is provided in Table 1. Where the library does not contain a natural mixture of isotopes, the isotopic fractions are included. All of these isotopes were identified with the.80c extension in the cases executed for the validation. The graphite (grph.20t) light water (lwtr.20t) and polyethylene (poly.20t) S(,) correction are used for graphite, water and hydrocarbon materials respectively. The lwtr.20t correction is used for water that is found in concrete as well. Both the be-o.20t and o-be.20t corrections are used with the cases containing BeO.

Note that experiment HEU-SOL-THERM-046 included 2H and 17O in an attempt to improve the accuracy of the model. However, the USL calculated with this validation is for applications modeling all oxygen as 16O and all hydrogen as 1H. While this introduced some small bias, it is exactly this bias that is measured herein.

Table 1 - Library Definitions for Various Elements Element ZAID Isotopic Fraction*

Hydrogen 1001 Boron 5010 0.199 5011 0.801 Carbon 6000 Nitrogen 7014 0.99636 7015 0.00364 Oxygen 8016 Sodium 11023 Magnesium 12024 0.7899 12025 0.100 12026 0.1101 Aluminum 13027 Silicon 14028 0.92223 14029 0.04685 14030 0.03092 Phosphorus 15031 Sulfur 16032 0.9499

Design Analyses and Calculation Page 6 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 Element ZAID Isotopic Fraction*

16033 0.0075 16034 0.0425 16036 0.0001 Chlorine 17035 0.7576 17037 0.2424 Potassium 19039 0.932581 19040 0.000117 19041 0.067302 Calcium 20040 0.96941 20042 0.00647 20043 0.00135 20044 0.02086 20046 0.00004 20048 0.00187 Titanium 22046 0.0825 22047 0.0744 22048 0.7372 22049 0.0541 22050 0.0518 Chromium 24050 0.04345 24052 0.83789 24053 0.09501 24054 0.02365 Manganese 25055 Iron 26054 0.05845 26056 0.91754

Design Analyses and Calculation Page 7 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 Element ZAID Isotopic Fraction*

26057 0.02119 26058 0.00282 Cobalt 27059 Nickel 28058 0.68077 28060 0.26223 28061 0.011399 28062 0.036346 28064 0.009255 Copper 29063 0.6915 29065 0.3085 Zinc 30064 0.4917 30066 0.2773 30067 0.0404 30068 0.1845 30070 0.0061 Zirconium 40090 0.5145 40091 0.1122 40092 0.1715 40094 0.1738 40096 0.0280 Niobium 41093 Molybdenum 42092 0.1453 42094 0.0915 42095 0.1584 42096 0.1667 42097 0.0960

Design Analyses and Calculation Page 8 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 Element ZAID Isotopic Fraction*

42098 0.2439 42100 0.09820 Silver 47107 0.51839 47109 0.48161 Cadmium 48106 0.0125 48108 0.0089 48110 0.1249 48111 0.1280 48112 0.2413 48113 0.1222 48114 0.2873 48116 0.0749 Indium 49113 0.0429 49115 0.9571 Tantalum 73181 Uranium 92234 Specified by individual experiments.

92235 92236 92238

• From Reference 12.

3.

Validation Methodology ANSI/ANS-8.1 (Reference 4) requires that calculational methods used for nuclear criticality safety (e.g.,

determining keff of a system or deriving subcritical limits) be validated to determine the appropriate biases and uncertainties for the areas of applicability. The bias and uncertainty represent the numerical difference between the results of modeling critical benchmark experiments with a computer code and the experimental keff. These biases may result in either under-or over-predictions of criticality. The bias may be reported as either a positive or negative bias. A positive bias occurs when the computations tend to report a higher keff

Design Analyses and Calculation Page 9 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 than the benchmark experiments (i.e., keff > 1.0). A negative bias occurs when the calculated results tend to report a lower keff than the benchmark experiments (i.e., keff < 1.0).

ANSI/ANS-8.24 (Reference 6) outlines the validation methodology and documentation used herein while NUREG/CR-6698 (Reference 10) details the calculation algorithms. Biases (and their associated uncertainties) are determined through statistical treatment of the calculated results from criticality benchmark experiments. Weighted single sided lower tolerance limits are used for statistical calculations in this validation report when the calculated results data are normally distributed. A non-parametric method is used when the calculated results data are not from a normal statistical distribution.

When performing calculations to assess the subcriticality of a system or operation, a limit must be established on the calculated keff to ensure that subcriticality is achieved. This limit is defined for the purposes of this validation as the Upper Subcritical Limit (USL). In this validation, the USL is determined by statistical analysis of the calculated keffs from the benchmark critical experiments.

3.1.

Establishment of an Upper Subcritical Limit The purpose of a computer code validation is to determine values of keff that are demonstrated to be subcritical (at or below the USL) for areas of applicability similar to systems or operations being analyzed. The USL is defined as follows:

USL = 1.0 + Bias - Bias Uncertainty - Margin of Subcriticality (MoS) setting eff k

= 1.0 + Bias and K*St = Bias Uncertainty gives:

USL = eff k

- K*St - MoS where: USL

= Maximum subcritical value of keff eff k

= weighted mean keff value of the benchmark experiments K*

= tolerance factor for 95% confidence that 95% of the population is bound St

= square root of the pooled variance MoS

= margin of subcriticality From this, a keff calculated by the analysis is required to meet the following condition:

calculated keff + 2 USL where is the Monte Carlo statistical uncertainty associated with the analysis.

As defined, the USL explicitly incorporates a MoS, which is required per ANSI/ANS-8.1. The MoS is an additional safety factor which is applied to the statistically calculated limit (e.g., a lower tolerance limit).

The bias and its associated uncertainty may be represented by one of several statistical methods:

a weighted, single sided, lower tolerance limit, a weighted confidence interval, or a non-parametric statistical analysis.

[Proprietary Information - Withheld from Public Disclosure Under 10 CFR 2.390(a)(4)]

Design Analyses and Calculation Page 10 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 3.2.

Margin of Subcriticality The MoS is an administrative addition in k applied to nuclear criticality safety calculations. The MoS is site specific and usually contained in the fuel facility license or other regulatory authorization basis. The MoS value for SHINE applications is 0.05. This value is typical of uranium processing facilities. All materials and processes within the SHINE facility are established technology and benchmarking against experiments using sufficiently similar materials and enrichments as expected to be used in the SHINE facility is performed herein.

This report documents the ability to predict keff accurately for the SHINE processes. Therefore, it is judged that the proposed margin of subcriticality is acceptable and greater margin is not needed.

For systems which are outside the validation area of applicability, an increased MoS may be warranted, depending on the specific problem being analyzed. The analyst must document any extrapolation beyond the validation area of applicability and justification must be made for no adjustments to the MoS when extrapolations are made.

3.3.

Determination of the Area of Applicability The area of applicability determination quantifies parameters potentially important to the computational calculation of keff. An area of applicability determination should be performed as a part of every calculation done and compared to the area of applicability of the benchmark experiments used for the code validation.

This comparison ensures that appropriate benchmark experiments have been selected to determine the USL for the calculation. The area of applicability determination for the benchmark experiments used in this validation has been performed using guidelines consistent with LA-12683 (Reference 5), specifically Appendix E of that report.

3.4.

Discussion of Statistical Analysis A weighted, single sided lower tolerance limit is a single lower limit above which a defined fraction of the true population of keff is expected to lie, within a prescribed confidence and with the defined area of applicability. A lower tolerance limit should be used when there are no apparent trends in the benchmark results. Use of this limit requires the benchmark results to have a normal statistical distribution. If the data does not have a normal statistical distribution, a non-parametric statistical treatment must be used. The method used for analysis of data with a non-normal distribution in this validation is taken from NUREG/CR-6698 (Reference 10).

3.4.1.

Normality Testing of Data There are several tests which can be performed to determine if data follows a normal distribution. Depending on the size of the data sets used in establishing the areas of applicability, [Proprietary Information ]. The methodology for these tests can be found in NUREG/CR-4604 (Reference 8) and Natrella (Reference 9).

Proprietary Information

[Proprietary Information - Withheld from Public Disclosure Under 10 CFR 2.390(a)(4)]

Design Analyses and Calculation Page 11 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 Proprietary Information

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Design Analyses and Calculation Page 12 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 Proprietary Information 3.4.2.

Weighted Single Sided Lower Tolerance Limits If the benchmark experiment results are verified to be part of a normal distribution, a weighted, single sided lower tolerance limit technique may be used to construct a USL for criticality. The weighted, single sided lower tolerance limit is calculated with a 95% confidence that 95% of the benchmark data lies above it. Thus, a calculation involving a subcritical system would have a 95% confidence that 95% of all calculations performed on it would yield a result less than the tolerance limit. The weighted, single sided lower tolerance limit is calculated using the method presented in NUREG/CR-6698 (Reference 10). The weighted, single sided lower tolerance limit is adjusted by applying a MoS to define the USL. The USL is defined by the following:

USL = eff k

- K*St - MoS where: USL= Maximum subcritical value of keff eff k

= weighted mean keff value of the benchmark experiments K*= tolerance factor St = square root of the pooled variance S2 = variance about the mean MoS

= margin of subcriticality (0.05) i 2

1 k eff i i

2 1

=

eff k

and

Design Analyses and Calculation Page 13 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 i

2 1

n 1

2 eff eff i

2 1

1 n

1

)

k (k

)

(

=

2 S

)

+

s

(

=

S

=

)

e 2

+

s 2

(

=

2 2

t n

2 i

i 2

1

where:

s = Monte Carlo statistical uncertainty associated with the calculation, e = experimental uncertainty associated with the benchmark experiment, 2 = average uncertainty The statistical uncertainty, s, is the standard deviation calculated by the code and reported in the output for each benchmark experiment. If available, the experimental uncertainty, e, is determined through rigorous evaluation of each benchmark experiment. NEA/NCS/DOC (95)03 documents such evaluations and thus reports an experimental uncertainty.

The tabulated lower tolerance factors (Reference 10) are listed for a maximum of 50 data items, however the evaluation herein uses more data points. Therefore, the lower tolerance factors (K*) for data collections greater than 50 items are derived from Reference 9:

a ab z

z P

P

+

=

2 K*

where

)1

(

2 1

2

=

N z

a

N z

z b

P 2

2

=

And Pz and z values are the critical values from the normal distribution that is exceeded with specified probability (P = 95% and = 95%) and are both 1.645.

3.4.3.

Non-Parametric Analysis Data that do not follow a normal distribution curve can be analyzed using non-parametric techniques. The method used for this validation is taken from NUREG/CR-6698. As stated previously, this approach is more conservative than other non-parametric techniques available to determine distribution-free confidence

[Proprietary Information - Withheld from Public Disclosure Under 10 CFR 2.390(a)(4)]

Design Analyses and Calculation Page 14 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 interval (e.g., one based on the sign test as presented in Hollander and Wolfe, Reference 7). This method results in a determination of the degree of confidence that a fraction of the true population of data lies above the smallest observed value. This determination is calculated as follows:

Proprietary Information As stated in NUREG/CR-6698, for a desired population fraction of 95% and a rank order of 1 (the smallest data sample) the equation simplifies to:

= 1 -0.95n For a non-parametric set of data, the USL is determined as follows:

USL = Smallest keff value in the data set - St - NPM - MoS Where: St

= standard deviation corresponding to the smallest keff value in the data set NPM

= non-parametric margin, determined from MoS

= margin of subcriticality (0.05)

The non-parametric margin is an additional amount subtracted from the lowest data point to account for the small sample size and non-normal distribution of the data. Recommended values for the non-parametric margin are established in NUREG/CR-6698.

4.

Benchmark Experiment Descriptions Reference 10 provides guidance for selecting critical experiment data. This guidance is utilized as follows: the desired range of operating conditions for SHINE is nominally 19.75 wt. % 235U (metal, oxide and solution),

thermal neutron energies, sulfate solution, nitrate solution, borated-polyethylene absorber, and concrete reflector. All critical benchmark experiments are taken from Reference 1. One-hundred-forty (140) experiments were selected that include the materials, conditions, and operating parameters to be considered in the SHINE applications. Of these, 30 have 10 wt. % 235U, 54 have between 14.7 and 36 wt. % 235U, and 56 have between 89 and 94 wt. % 235U. Included in these are 9 metal, 66 oxide, and 59 solution experiments.

One-hundred-thirty-one (131) experiments have thermal neutron energies. Of the solution experiments, 45 are uranyl nitrate and 14 are uranyl sulfate. Twenty-nine (29) experiments have boron absorbers with 8 of these having borated-polyethylene absorber. Twelve (12) experiments have a concrete reflector. Many additional materials and configurations are also included. Reference 10 provides no minimum number of experiments to produce a rational validation. The guide only states that less than 10 should be accompanied by a technical basis supporting the rationale for acceptability of the validation results. It is judged that the data set herein provides a sufficient number of experiments with varying experimental parameters to ensure a wide area of applicability (AoA) and statistically significant results with no additional justification.

The input files are specifically developed for MCNP 6.1 and the continuous energy ENDF/B-VII.1 cross section library. One-hundred-forty benchmark cases are modeled. The majority are in the thermal neutron

[Proprietary Information - Withheld from Public Disclosure Under 10 CFR 2.390(a)(4)]

Design Analyses and Calculation Page 15 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 energy range, however some bridge into intermediate and fast energy ranges. The MCNP 6.1 calculated ANECF values range from 0.0027 to 1.46 MeV. The largest group of the experiments have intermediate 235U enrichment; however sufficient low and high enriched experiments are included to evaluate for trends in the bias. The USL is evaluated with and without the LEU and HEU cases, and the more conservative value is chosen. A broad range of chemical forms and metal are included to evaluate potential bias from the chemical form and to encompass the range of expected and potential forms of material at the SHINE facility.

Additionally, the cases are fairly evenly split between homogeneous and heterogeneous physical forms.

Hydrogen identified in water (including water found in concrete) is modeled with the water lwtr.20t S(,) while hydrogen in hydrocarbon materials is modeled with the poly.20t S(,). Graphite is modeled with the grph.20t S(,). BeO is modeled with both the be-o.20t and o-be.20t.

The descriptions below are taken from Reference 1.

4.1.

Low Enriched Uranium 4.1.1.

LEU Homogeneous Uranyl Nitrate Solution with Boron Absorber Rods (LEU-SOL-THERM-006)

A large number of critical experiments with absorber elements of different types in uranyl nitrate solution of different enrichments and concentrations were performed in 1961 - 1963 at the Solution Physical Facility of the Institute of Physics and Power Engineering (IPPE), Obninsk, Russia. The five experiments included in this evaluation were performed with uranium enriched to 10 wt.% 235U. Uranyl nitrate solution with uranium concentration of 420.5 g/l was pumped into the core or inner tank, a stainless steel cylindrical tank with inner diameter 110 cm. One experiment was performed without absorber rods. In each of four experiments a different number of boron carbide absorber rods was inserted in the core tank. The absorber rods were arranged in a hexagonal lattice with different pitches. There was a thick side and bottom water reflector in these experiments.

All five experiments are included in this evaluation. Note that these experiments use the same tank and absorber rods as those used in HEU-SOL-THERM-035, thus the only significant difference is the 235U enrichment. [ Proprietary Information ]

Uranyl Nitrate Solution with Concrete Reflector (LEU-SOL-THERM-008)

Four critical configurations included in this data set are part of the Static Experiment Critical Facility (STACY) series of experiments. Utilizing the 60-cm diameter cylindrical stainless-steel core tank, a 10% enriched uranyl nitrate solution (UO2(NO3)2) was used in these experiments. The uranium concentration and the free nitric-acid concentration were adjusted to approximately 240 g/l and 2.1 mol/l, respectively. Four concrete reflectors of different thicknesses, packed in annular tube-shaped containers, were prepared and arranged against the outer wall of the core tank.

All four experiments are included in this evaluation. This data set is included herein to evaluate uranyl nitrate and concrete reflection.

Uranyl Nitrate Solution with Borated-Concrete Reflector (LEU-SOL-THERM-009)

Three critical configurations included in this data set are part of the Static Experiment Critical Facility (STACY) series of experiments. Utilizing the 60-cm diameter cylindrical stainless-steel core tank, a 10% enriched uranyl nitrate solution (UO2(NO3)2) was used in these experiments. The uranium concentration and the free nitric-acid concentration were adjusted to approximately 240 g/l and 2.1 mol/l, respectively. Three borated-concrete reflectors of different boron content, packed in annular tube-shaped containers, were prepared and arranged against the outer wall of the core tank.

All three experiments are included in this evaluation. Note that these experiments differ from those in LEU-SOL-THERM-008 only in the addition of the boron. This data set is included herein to evaluate uranyl nitrate, concrete reflection, and, in conjunction with LEU-SOL-THERM-008, potential sensitivity to boron addition.

Design Analyses and Calculation Page 16 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 4.1.2.

LEU Heterogeneous UO2 Fuel Rods (LEU-COMP-THERM-022, -023, -024 & -032)

A series of critical experiments with water moderated and reflected lattices of UO2 fuel rods, (enriched to 10%

235U), was performed over the course of several years (1965-1967) in RRC Kurchatov Institute. These data sets are included herein to evaluate potential heterogeneous effects, uranium oxide, and to provide a spectrum of H/235U values.

These highly correlated experiments are detailed below.

LEU-COMP-THERM-022 This evaluation describes seven critical experiments for uniform fully flooded hexagonal lattices with pitch values of 0.7, 0.8, 1.0, 1.22, 1.4, 1.83, and 1.852 cm. These configurations have H/235U values between 50 and 629. All seven configurations are included in this validation.

LEU-COMP-THERM-023 This evaluation describes six critical experiments for different levels of water in the active core, which was a hexagonally pitched lattice of fuel rods. The pitch value of the lattice was 1.4 cm. All six configurations are included in this validation.

Note that the submerged portion of these lattices had an H/235U value of 340, but their ANECF values are slightly higher than the near identical configuration of LEU-COMP-THERM-022 because of the contribution of more energetic neutron in the dry portion of the lattice.

LEU-COMP-THERM-024 This evaluation describes critical experiments for two square-pitched lattices of fuel rods. The two studied configurations are arrays of nearly rectangular cross section containing fuel rods with pitches of 0.62 cm and 0.62x2 cm.

LEU-COMP-THERM-032 This evaluation describes nine critical experiments for uniform fully flooded hexagonal lattices with pitch values of 0.7, 1.4, and 1.852 cm at three different temperatures (ranging from 20°C to 274°C) for each lattice. Only the three 20°C configurations are used in this validation. The critical numbers of rods for these configurations differ from those reported in LEU-COMP-THERM-022 because of different assembly support structure and application of steel tubes for safety rods in the present experiments.

4.2.

Intermediate Enriched Uranium 4.2.1.

IEU Homogeneous Bare Sphere Enriched Uranium (IEU-MET-FAST-003)

Criticality measurements of bare metal 235U(36%) assemblies were conducted at the Russian federation Nuclear Center VNIIEFs criticality test facility in 1994. The assembly had a core of 235U(36%) incorporating 10 spherical layers of fissile material.

This experiment is modeled using the simple model as homogeneous.

Reflected Sphere Enriched Uranium (IEU-MET-FAST-004)

Criticality measurements of a graphite-reflected assembly of 235U(36%) were performed by VNIIEF in September 1977 at its criticality test facility. The assembly core had a central cavity of 2-cm radius and

Design Analyses and Calculation Page 17 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 incorporated 7 spherical layers of fissile material. The graphite reflector was a single spherical layer with an outer radius of 17.2 cm. The value of the uncertainty in reflector radius was 0.2%. Each core and reflector layer consisted of two hemispherical pieces.

This experiment is modeled using the simple model as homogeneous.

Reflected Sphere Enriched Uranium (IEU-MET-FAST-006)

Criticality measurements of a Duralumin-reflected assembly of 235U(36%) were conducted by VNIIEF in 1994 at its criticality test facility. The core pieces were manufactured in 1977. As a result of these experiments, two benchmark models, one detailed and one simplified, of a single experiment were developed. The simplified configuration is used herein.

Reflected Sphere Enriched Uranium (IEU-MET-FAST-009)

Criticality measurements of a polyethylene-reflected assembly of 235U(36%) were conducted by VNIIEF in 1977 at its criticality test facility (CTF).

The above metal experiments are included herein to evaluate uranium metal and fast neutron effects.

Hydrocarbon Moderated and Reflected UO2 (IEU-COMP-THERM-015)

During the late 1950s and 1960s an experimental survey was carried out jointly at Aldermaston and Dounreay of the critical parameters of uranium / hydrogen systems at ~30% 235U enrichment. The Aldermaston phase made use of the solid UO2/wax compacts had H/235U values between about 8 and 80. This information was obtained primarily as an experimental base for safety calculations in the intermediate enrichment range. The cores were constructed in rectangular geometry from small blocks (mostly 1 in. cubes) to facilitate stacking changes. The proportions of oxide and wax were changed at intervals during the experiment to provide a range of H/235U values.

Experiment nos. 4 - 12 were selected for this evaluation; these are the first nine experiments with the polyethylene reflector and cover the range of H/235U values. However, only eight of these experiments are included in this validation (see note below). While the experiments contained heterogeneous elements, they are modeled as homogeneous.

Note that experiment number 6 has been rejected. While this case calculates low (0.9923) the reason for the rejection is the very high bias in the benchmark keff (1.0008). Examination of Tables 27 and 28 of the IEU-COMP-THERM-015 section of Reference 1 displays conflicting information for the determination of the experimental bias. In Table 27 a positive bias of 0.0006 is added to the raw experiment value of 1.0000 due to the model simplification of ignoring block/wax impurities and homogenizing the cube lacquer coating.

However, this value is not assigned to experiments nos. 1 and 23 using this same material (#16); these are inconsistently assigned bias values of 0.0003 and -0.0001, respectively. Alternately, the bias value of 0.0006 is consistently assigned to experiments nos. 2, 8 & 25 which use material #40. Therefore, it is judged that the experimental bias for experiment nos. 1, 6 & 23 are incorrect, and that the correct values cannot be determined from the information in Reference 1.

This data set is included herein to evaluate uranium oxide, hydrocarbon moderator / reflectors, and to add low H/235U values.

Bare and Water Reflected UO2F2 (IEU-SOL-THERM-002)

During the late 1950s and early 1960s an experimental survey was carried out jointly at Aldermaston and Dounreay of the critical parameters of uranium/hydrogen systems at ~ 30% 235U enrichment. The Dounreay phase of this survey was concerned with the criticality of UO2F2 aqueous solutions (in cylindrical, slab, and spherical and hemispherical geometries) and covered the H/235U values from about 50 and higher.

[Proprietary Information - Withheld from Public Disclosure Under 10 CFR 2.390(a)(4)]

Design Analyses and Calculation Page 18 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 Five aluminium spheres of nominal internal diameters 12 in. (30.48 cm), 13.75 in. (34.925 cm), 16 in. (40.64 cm), 22 in. (55.88 cm) and 38 in. (96.52 cm) were used in these experiments with the key objective being to determine the solution concentration necessary for criticality when a sphere was completely filled. This was achieved by measuring critical conditions for a partly filled sphere over a range of fractional volumes and extrapolation to the full spherical volume. Three types of reflection conditions were examined: bare, partial water-reflected (i.e. with water reflector up to the level of the fuel solution), and fully water-reflected. Critical parameters of full spheres were determined for the following configurations: 12 in. sphere - fully water-reflected; 13.75 in. sphere - bare (at two concentrations) and fully water-reflected; 16 in. sphere - bare, part water-reflected, and fully water reflected; 22 in. sphere - bare, part water-reflected, and fully water-reflected; and 38 in. sphere - bare.

Twelve of the thirteen experimental configurations are evaluated herein; case 6 has been rejected from consideration as its experimental uncertainty is unacceptably high (0.0109) for a criticality safety validation.

This data set is included herein to add high H/235U values and unreflected solutions.

BeO Reflected UO2SO4 (IEU-SOL-THERM-004)

The experiment was performed at Los Alamos Scientific Laboratory on May 9, 1944. This experiment was to determine the critical mass of 235U in homogenous solutions at various concentrations and moderating media.

The experiment was a simple configuration of a hollow sphere containing fissile solution within a beryllium oxide reflector.

The critical configuration involved approximately 14.7% enriched uranyl sulfate (UO2SO4) solution in a 1-foot (30.48 cm) diameter stainless steel sphere centered in a beryllium oxide pseudo-sphere approximately 3 feet (91.44 cm) in diameter. The H/235U value was 646.

Note that this benchmark model keff applies to the temperature of 39oC. However, Reference 1 specifies that a temperature bias of keff =+0.0072 should be applied to the benchmark model keff when the benchmark is compared with calculational models whose cross sections are at room temperature (21oC). As this is the case herein, this temperature bias has been applied.

[ Proprietary Information ]

4.2.2.

IEU Heterogeneous Reflected Sphere Enriched Uranium (IEU-MET-FAST-005)

Criticality measurements of steel-reflected 235U(36%) assemblies were conducted by VNIIEF in 1994 at its CTF. The assembly core had a central cavity of 2-cm radius and included 6 spherical layers of fissile material.

The steel reflector was represented by 5 spherical layers that differed slightly in density. The outermost layer had an outer radius of 21.5 cm. Each of the 5 layers consisted of two hemispherical pieces; the outer 3 steel layers were modeled as one layer and the inner 2 steel layers were modeled as one layer. The value of the uncertainty in the reflector radius, averaged over 5 layers, was 0.15%.

This experiment is modeled using the simple model; the hemispherical pieces of the reflector layers were each modeled as continuous spheres. This experiment is included herein to evaluate uranium metal and heterogeneous effects.

Polyethylene-Moderated UF4-Polyetrafluoroethylene Cubes (IEU-COMP-THERM-001)

One-inch cubes of U(30)F4 -polytetrafluoroethylene [(CF2)n ] ("U-cubes") were stacked with one-inch cubes and half-cubes of polyethylene ("H-cubes") into cuboid shapes on aluminium platforms. Most critical cores were reflected by paraffin. Twenty-nine ratios and patterns of "U-cubes" and "H-cubes" are included in this benchmark.

Design Analyses and Calculation Page 19 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 Twenty-five experiments are modeled (3 cadmium reflected cases and 1 boron reflected case are not included). This data set is included herein to add a range of H/235U values and to evaluate hydrocarbon moderator / reflectors.

UO2 Fuel Rods (IEU-COMP-THERM-002)

Critical approach experiments with stainless steel clad UO2 fuel rods (17 wt. % 235U) in a water filled tank were performed in 1970 - 1973 in the MATR facility at the Institute of Physics and Power Engineering, Obninsk, Russia. The fuel rods were arranged in hexagonal lattices with a pitch of 6.8 cm. Each lattice comprised one of three forms of the fuel rod: without absorber element, with gadolinium absorber element, or with cadmium absorber element in the center of each fuel rod. The lattices were fully reflected on all sides with water. Note that due to the complex geometry of this experiment only case 1 was used and no H/235U value was determined.

This experiment is included herein to evaluate uranium oxide and heterogeneous effects.

U-ZrH Fuel Rods (IEU-COMP-THERM-003)

The benchmark experiments were performed as a part of startup test of the TRIGA Mark II reactor in Ljubljana, Slovenia, after reconstruction and upgrading in 1991, during which all core components (top and bottom grid plates, fuel, control rods, irradiation channels), with the exception of the graphite reflector around the core, were replaced with new ones. The experiments in steady-state operation were performed with completely fresh fuel (including instrumented elements and fuel followers of control rods) in a compact and uniform core (i.e., all elements including the fuel followers of control rods were of the same type with no nonfuel components in the critical core configuration) at well-controlled operating conditions. Standard commercial TRIGA fuel elements of 20 wt.% enrichment and 12 wt.% uranium concentration were used.

This evaluation describes two critical experiments. The core configurations differed only in the position of 7 outermost fuel elements and so are closely correlated. Both cores were critical within 300 pcm (0.3%). The two experiments are included herein to evaluate heterogeneous effects.

4.3.

High Enriched Uranium 4.3.1.

HEU Homogeneous Concrete Reflected Arrays of Uranyl Nitrate (HEU-SOL-THERM-007)

Seventeen of the experiments utilized concrete-reflected arrays of uranyl nitrate cylinders. Uranium was enriched to 93.2 wt% 235U and the cylinders were constructed of aluminium with stainless steel sleeves. Arrays of various sizes were placed with a ~10 inch-thick concrete box that was used for the experiments. The inside dimensions of this box formed a rough cube (~122 cm per side).

Experiments nos. 1, 3, 7, 11 & 14 were selected for inclusion in this evaluation. This data set is included herein to evaluate concrete reflectors and potential bias with increasing enrichment.

Water Reflected Oxyfluoride Solution (HEU-SOL-THERM-012)

This water-reflected sphere is part of a series of experiments performed in the 1950s at the Oak Ridge National Laboratory with highly enriched uranium (93.2 wt.% 235U). This measurement was made with a uranium oxyfluoride (UO2F2) solution in a 27.9-cm inner radius (91 liters) water-reflected sphere. The sphere was fabricated of 0.20-cm-thick 1100 aluminium and surrounded by an effectively infinite water reflector.

This experiment is included herein to add its high H/235U value (1272).

Design Analyses and Calculation Page 20 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 Uranyl Nitrate Solution with Boron Absorber (HEU-SOL-THERM-027)

A large number of critical experiments with absorber elements of different types in uranyl nitrate solution of different enrichments and concentrations were performed in 1961 - 1963 at the Solution Physical Facility of the IPPE, Obninsk, Russia. The nine experiments included in this evaluation were performed with uranium enriched to 89 wt.% 235U. Uranyl nitrate solution was pumped into the core or inner tank, a stainless steel cylindrical tank with inner diameter 40.07 cm. In eight of the nine experiments, an absorber rod of various diameters with boron or cadmium was inserted in the center of the core tank. There was no outer reflector in these experiments.

Experiment nos. 1 - 5 were selected for inclusion in this evaluation. The first case has no absorber while the next 4 have a boron carbide absorber. This data set is included herein to evaluate uranyl nitrate, boron effects and potential bias with increasing enrichment.

Uranyl Nitrate Solution with Boron Absorber Rods (HEU-SOL-THERM-031)

A large number of critical experiments with absorber elements of different types in uranyl nitrate solution of different enrichments and concentrations were performed in 1961 - 1963 at the Solution Physical Facility of the IPPE, Obninsk, Russia. The four experiments included in this evaluation were performed with uranium enriched to 89 wt.% 235U. Uranyl nitrate solution with uranium concentration of 289 g/l was pumped into the core or inner tank, a stainless steel cylindrical tank with inner diameter 40.07 cm. Eighteen or thirty-six boron carbide absorber rods were inserted in the center of the core tank. The rods were arranged in hexagonal lattices with pitches of 4.0 and 6.0 cm. There was a thick side and bottom water reflector in these experiments.

All four experiments are included herein to evaluate uranyl nitrate, boron effects and potential bias with increasing enrichment.

Uranyl Nitrate Solution with Boron Absorber Rods (HEU-SOL-THERM-035)

A large number of critical experiments with absorber elements of different types in uranyl nitrate solution of different enrichments and concentrations were performed in 1961 - 1963 at the Solution Physical Facility of the Institute of Physics and Power Engineering (IPPE), Obninsk, Russia. The nine experiments included in this evaluation were performed with uranium enriched to 89 wt.% 235U. Uranyl nitrate solution with uranium concentration of 37.51 g/l, 74.87 g/l, or 152.3 g/l was pumped into the core or inner tank, a stainless steel cylindrical tank with inner diameter 110 cm. Three experiments were performed without absorber rods. In six experiments different numbers of boron carbide absorber rods were inserted in the core tank. The absorber rods were arranged in a hexagonal lattice with different pitches. There was a thick side and bottom water reflector in these experiments.

All nine experiments are included in this evaluation. Note that these experiments use the same tank and absorber rods as those used in LEU-SOL-THERM-006, thus the only significant difference is the 235U enrichment. This data set is included herein to evaluate uranyl nitrate, boron effects and potential bias with increasing enrichment.

Uranyl Nitrate Solution with Borated Polyethylene Absorber (HEU-SOL-THERM-038)

Thirty critical experiments involving 93.1%-enriched uranyl nitrate solution were performed in 1988 at the Los Alamos National Laboratory (LANL). The experiments consisted of two thin coaxial slab tanks with various neutron absorber and reflector plates positioned on top of one or both tanks. The reactivity worth (keff ) of the neutron absorber and reflector plates was as much as 7.5 %. Three different types of borated polyethylene plates, BP-2, BP-6, and BP-7, were used in the experiments. BP-2 and BP-6 are 5 wt.% borated polyethylene and BP-7 is 30 wt.% borated polyethylene.

Ten experiments (one with no absorber and nine with the borated polyethylene) are included in this evaluation.

Design Analyses and Calculation Page 21 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 Note that the BP-7 borated polyethylene material used in experiments 10, 11 & 17 is nearly identical to the PPC-B material used in the SHINE applications. This data set is included herein to evaluate uranyl nitrate, boron effects and potential bias with increasing enrichment.

Beryllium and Graphite Reflected Uranyl Sulfate Solutions (HEU-SOL-THERM-046)

This evaluation considers thirteen subcritical approaches performed in the early sixtys (1960-1961) at Saclay, France, with homogeneous aqueous solution of uranium (89.84 wt.% 235U) sulfate, containing 0.5 N and 0.1 N excess sulfuric acid respectively. The range of the 235U concentration was 36.588 to 56.51 g/liter. All thirteen experiments are acceptable for use as benchmarks. The estimated experimental uncertainty (1) obtained is about 0.3%, mostly due to the outer tank: its thickness, its gap with the inner tank and its gap with the beryllium oxide reflector.

The core was comprised of the fissile solution inside a cylindrical tank, of Zircaloy-2. This inner tank was 25 cm in diameter and 30 cm in height, with a conical bottom, surrounded by an outer aluminum-alloy tank, and reflected by a minimum of 27.5 cm of beryllium oxide followed by a layer of at least 50 cm of graphite. The reflectors contained structural plates of aluminum alloy, as well as several penetrations throughout to accommodate the fill tube, experimental channels, control rods, safety rods, etc.

This data set is included herein to evaluate uranyl sulfate and potential bias with increasing enrichment.

This set of experiments overestimated the experimental keff values by ~1.5% using the APOLLO-MORET code (Reference 1). During the development of the MCNP models, several simplifications in the previous models were identified and corrected. For the MCNP models used herein, material compositions are calculated following the approach used in the benchmark specification. Isotopic number densities are calculated from the supplied weight fraction data using MCNP6 molecular weight data and natural abundance data. For hydrogen and oxygen, 1H is substituted atom-for-atom for 2H, as is common practice.

Similarly 16O is substituted for 18O since MCNP6 lacks cross section data for 18O. While the cases still overestimate, the accuracy of the model has been improved.

4.3.2.

HEU Heterogeneous Graphite Reflected UO2 Rods (HEU-COMP-FAST-002)

A series of small, compact critical assembly (SCCA) experiments were completed in 1962-1965 at Oak Ridge National Laboratorys Critical Experiments Facility. This evaluation had the 253 fuel tubes at a 1.506-cm triangular lattice in a 25.96 cm OD core tank and graphite reflectors on all sides. Note that this fast neutron experiment was modeled with the o2/u.20t, u/02.20t, and al27.20t s(,) corrections.

This experiment is included herein to evaluate uranium oxide, heterogeneous effects, and potential biases with fast neutron energies and increasing uranium enrichment.

Reflected Cylinder (HEU-COMP-INTER-003)

The COMET universal critical assembly machine was used to perform a series of seven uranium hydride critical experiments in 1987-88 at Los Alamos National Laboratory. The cylindrical assemblies were disks of canned UH3 powder, reflected by depleted uranium, beryllium, and iron. Two 2-cm and two 3-cm-thick disks of canned UH3 compressed powder (6-in. diameter) were used in four of the experiments. These experiments had outer reflectors of depleted uranium and inner reflectors of D38, Be, and Fe. The difference in the next two experiments with Be inner reflectors was that in one experiment one of the 2-cm cans of UH3 was inverted.

The total mass of the UH3 for each of these experiments was 17.7 kg. Four 3-cm disks were used for two of the three experiments with the outer reflector removed. The total UH3 mass for the Be and one D38 experiment was 21.3 kg. The total mass for the third D38 experiment was 23.1 kg. This was achieved by using two 2-cm disks and three 3-cm disks.

Design Analyses and Calculation Page 22 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 Only cases 2, 3, 4 and 5, without the depleted uranium inner reflector, are included in this evaluation. Note that cases 2, 3 and 4 have an outer depleted uranium reflector. This data set is included herein to evaluate heterogeneous effects, potential biases with fast neutron energies and increasing uranium enrichment, and potential bias with beryllium reflector.

Bare Sphere (HEU-MET-FAST-001)

One of the experiments performed at Los Alamos in the 1950's to determine the critical mass of a bare, 94 wt.% 235U, sphere of highly enriched uranium (HEU) consisted of two identical sets of nested oralloy hemispheres. This experiment is widely known as Godiva.

This experiment is included herein to evaluate uranium metal, potential biases with fast neutron energies, increasing uranium enrichment, and potential bias with beryllium reflector.

Graphite Moderated Cylinder (HEU-MET-INTER-006)

The Zeus experiments are a series of on-going critical assemblies at the Los Alamos Critical Experiments Facility (LACEF) at LANL designed to test the adequacy of 235U cross sections in the intermediate-energy range. The three experiments included herein used plates of highly enriched uranium (HEU) metal interspersed with graphite plates in a cylindrical stack that was completely surrounded by copper reflectors.

This data set is included herein to evaluate uranium metal, potential biases with fast neutron energies and increasing uranium enrichment.

4.3.3.

Input Summary Tabulation The characteristics of the benchmark experiments from Reference 1 are tabulated in Table 2. The H/235U values are included in some Reference 1 experiment descriptions. Where these values are not provided they were calculated by the author. Some experiment configurations were too complex to allow this determination.

The benchmark keff and uncertainty are included as kexp and.

Table 2 - Critical Benchmark Experiments Summary Case wt%235U Chem Form Geometry Moderator/Reflector H/235U Other Materials k-meas sigma HEU-COMP-FAST-02 02 93.2 UO2 Fuel Pin Array None/Graphite n/a steel, Al 0.9985 0.0006 HEU-COMP-INTER-03 02 90.5 UH3 Homogeneous Stack of Disks Hydrogen/Be 3

steel, Al 1.0000 0.0061 03 90.5 UH3 Hydrogen/Be 3

steel, Al 1.0000 0.0056 04 90.5 UH3 Hydrogen/Fe 3

steel, Al 1.0000 0.0055 05 90.5 UH3 Hydrogen/Be 3

steel, Al 1.0000 0.0047 HEU-MET-FAST-001 01 94.0 Metal Sphere None/Bare n/a None 1.0000 0.0010 HEU-MET-INTER-006 01 93.2 Metal Heterogeneous Cylinder Graphite/Copper n/a Al 0.9977 0.0008 02 93.2 Metal Graphite/Copper n/a Al 1.0001 0.0008 03 93.2 Metal Graphite/Copper n/a Al 1.0015 0.0009 HEU-SOL-THERM-007 01 93.2 UO2(NO3)2 Homogeneous Cylinders Water/Concrete 405 SS, Al 1.0000 0.0035 03 93.2 UO2(NO3)2 Water/Concrete 405 SS, Al 1.0000 0.0035 07 93.2 UO2(NO3)2 Water/Concrete 357 SS, Al 1.0000 0.0035 11 93.2 UO2(NO3)2 Water/Concrete 67 SS, Al 1.0000 0.0035 14 93.2 UO2(NO3)2 Water/Concrete 68 SS, Al 1.0000 0.0035 HEU-SOL-THERM-012 01 93.2 UO2F2 Homogeneous Sphere Water/Water 1272 Al 0.9999 0.0058 HEU-SOL-THERM-027

Design Analyses and Calculation Page 23 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 Case wt%235U Chem Form Geometry Moderator/Reflector H/235U Other Materials k-meas sigma 01 89 UO2(NO3)2 Homogeneous Cylinders w/

Heterogeneous Absorber Rods Water/Bare 204 SS 1.0000 0.0046 02 89 UO2(NO3)2 204 SS, B 1.0000 0.0043 03 89 UO2(NO3)2 204 SS, B 1.0000 0.0037 04 89 UO2(NO3)2 204 SS, B 1.0000 0.0037 05 89 UO2(NO3)2 204 SS, B 1.0000 0.0044 HEU-SOL-THERM-031 01 89 UO2(NO3)2 Homogeneous Cylinders w/

Heterogeneous Absorber Rods Water/Water 91 SS, B 1.0000 0.0046 02 89 UO2(NO3)2 91 SS, B 1.0000 0.0058 03 89 UO2(NO3)2 91 SS, B 1.0000 0.0058 04 89 UO2(NO3)2 91 SS, B 1.0000 0.0068 HEU-SOL-THERM-035 01 89 UO2(NO3)2 Homogeneous Cylinders w/

Heterogeneous Absorber Rods Water/Water 767 SS 1.0000 0.0031 02 89 UO2(NO3)2 767 SS, B, C 1.0000 0.0032 03 89 UO2(NO3)2 767 SS, B, C 1.0000 0.0030 04 89 UO2(NO3)2 767 SS, B, C 1.0000 0.0030 05 89 UO2(NO3)2 379 SS 1.0000 0.0033 06 89 UO2(NO3)2 379 SS, B, C 1.0000 0.0029 07 89 UO2(NO3)2 181 SS 1.0000 0.0035 08 89 UO2(NO3)2 181 SS, B, C 1.0000 0.0038 09 89 UO2(NO3)2 181 SS, B, C 1.0000 0.0041 HEU-SOL-THERM-038 01 93.1 UO2(NO3)2 Homogeneous Coaxial Slab Tanks Water/Bare 60 SS, Al 1.0000 0.0025 02 93.1 UO2(NO3)2 Water/Poly 60 SS, Al 1.0000 0.0025 07 93.1 UO2(NO3)2 Water/B-Poly 60 SS, Al, B 1.0000 0.0032 08 93.1 UO2(NO3)2 Water/B-Poly 60 SS, Al, B 1.0000 0.0026 09 93.1 UO2(NO3)2 Water/B-Poly 60 SS, Al, B 1.0000 0.0033 10 93.1 UO2(NO3)2 Water/B-Poly 60 SS, Al, B 1.0000 0.0026 11 93.1 UO2(NO3)2 Water/B-Poly 60 SS, Al, B 1.0000 0.0025 12 93.1 UO2(NO3)2 Water/B-Poly 60 SS, Al, B 1.0000 0.0025 17 93.1 UO2(NO3)2 Water/B-Poly 60 SS, Al, B 1.0000 0.0026 18 93.1 UO2(NO3)2 Water/B-Poly 60 SS, Al, B 1.0000 0.0032 HEU-SOL-THERM-046 01 89.9 UO2SO4 Homogeneous Cylinders H2SO4-H2O / BEO &

Graphite 708 Al, Zr 1.0011 0.0029 02 89.9 UO2SO4 689 Al, Zr 1.0011 0.0029 03 89.9 UO2SO4 678 Al, Zr 1.0011 0.0029 04 89.9 UO2SO4 661 Al, Zr 1.0011 0.0029 05 89.9 UO2SO4 653 Al, Zr 1.0011 0.0030 06 89.9 UO2SO4 641 Al, Zr 1.0011 0.0029 07 89.9 UO2SO4 622 Al, Zr 1.0011 0.0031 08 89.9 UO2SO4 601 Al, Zr 1.0011 0.0032 09 89.9 UO2SO4 593 Al, Zr 1.0011 0.0037 10 89.9 UO2SO4 561 Al, Zr 1.0011 0.0029 11 89.9 UO2SO4 531 Al, Zr 1.0011 0.0028 12 89.9 UO2SO4 488 Al, Zr 1.0011 0.0029 13 89.9 UO2SO4 457 Al, Zr 1.0011 0.0030 IEU-COMP-THERM-001 01 30.0 UF4 Heterogeneous Arrays of Cubes Poly-CF2/Paraffin 8

Al 1.0000 0.0040 02 30.0 UF4 Poly-CF2/Paraffin 16 Al 1.0000 0.0040 03 30.0 UF4 Poly-CF2/Paraffin 32 Al 1.0000 0.0040 04 30.0 UF4 Poly-CF2/Paraffin 64 Al 1.0000 0.0040 05 30.0 UF4 Poly-CF2/Paraffin 222 Al 1.0000 0.0040 06 30.0 UF4 Poly-CF2/Paraffin 32 Al 1.0000 0.0040 07 30.0 UF4 Poly-CF2/Paraffin 32 Al 1.0000 0.0040 08 30.0 UF4 Poly-CF2/Paraffin 32 Al 1.0000 0.0040

Design Analyses and Calculation Page 24 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 Case wt%235U Chem Form Geometry Moderator/Reflector H/235U Other Materials k-meas sigma 09 30.0 UF4 Poly-CF2/Paraffin 16 Al 1.0000 0.0040 10 30.0 UF4 Poly-CF2/Paraffin 16 Al 1.0000 0.0040 11 30.0 UF4 Poly-CF2/Paraffin 16 Al 1.0000 0.0040 12 30.0 UF4 Poly-CF2/Paraffin 16 Al 1.0000 0.0040 13 30.0 UF4 Poly-CF2/Paraffin 64 Al 1.0000 0.0040 14 30.0 UF4 Poly-CF2/Paraffin 64 Al 1.0000 0.0040 15 30.0 UF4 Poly-CF2/Paraffin 64 Al 1.0000 0.0040 16 30.0 UF4 Poly -CF2/Paraffin 127 Al 1.0000 0.0040 17 30.0 UF4 Poly -CF2/Bare 16 Al 1.0000 0.0040 18 30.0 UF4 Poly -CF2/Bare 32 Al 1.0000 0.0040 19 30.0 UF4 Poly -CF2/Bare 127 Al 1.0000 0.0040 20 30.0 UF4 Poly -CF2/Paraffin 16 Al 1.0000 0.0040 21 30.0 UF4 Poly-CF2/Paraffin 8

Al 1.0000 0.0040 26 30.0 UF4 Poly-CF2/Paraffin 127 Al 1.0000 0.0040 27 30.0 UF4 Poly-CF2/Paraffin 127 Al 1.0000 0.0040 28 30.0 UF4 Poly-CF2/Paraffin 16 Al 1.0000 0.0040 29 30.0 UF4 Poly-CF2/Paraffin 16 Al 1.0000 0.0040 IEU-COMP-THERM-002 01 17.0 UO2 Heterogeneous Hexagonally Pitched Water/Water n/a SS, Al 1.0014 0.0039 IEU-COMP-THERM-003 01 20.0 U-ZrH Annular Fuel Pin Arrays Water/Graphite 150 Al, Zr 1.0006 0.0056 02 20.0 U-ZrH Water/Graphite 150 Al, Zr 1.0046 0.0056 IEU-COMP-THERM-015 04 30.1 UO2 Homogeneous Cube Wax/Wax 8

None 0.9982 0.0032 05 30.1 UO2 Wax/Wax 8

None 0.9982 0.0031 07 30.1 UO2 Wax/Wax 16 None 0.9981 0.0036 08 30.1 UO2 Wax/Wax 39 None 0.9990 0.0044 09 30.1 UO2 Wax/Wax 39 None 0.9991 0.0047 10 30.1 UO2 Wax/Wax 39 None 0.9995 0.0045 11 30.1 UO2 Wax/Wax 81 None 0.9985 0.0050 12 30.1 UO2 Wax/Wax 81 None 0.9985 0.0051 IEU-MET-FAST-003 01 36.0 Metal Homogeneous Stack of Disks None/Bare n/a None 1.0000 0.0019 IEU-MET-FAST-004 01 36.0 Metal Homogeneous Stack of Disks None/Graphite n/a None 1.0000 0.0032 IEU-MET-FAST-005 01 36.0 Metal Heterogeneous Stack of Disks None/Steel n/a None 1.0000 0.0023 IEU-MET-FAST-006 01 36.0 Metal Sphere None/Aluminium n/a Fe, Cu 1.0000 0.0025 IEU-MET-FAST-009 01 36.0 Metal Sphere None/Polyethylene n/a None 1.0000 0.0053 IEU-SOL-THERM-002 01 30.5 UO2F2 Spheres and Hemispheres Water/Water 352 Al 1.0004 0.0026 02 30.5 UO2F2 Water/Water 574 Al 1.0003 0.0032 03 30.5 UO2F2 Water/Water 788 Al 1.0003 0.0038 04 30.5 UO2F2 Water/Water 1194 Al 1.0003 0.0046 05 30.5 UO2F2 Water/Bare 218 Al 0.9989 0.0042 07 30.5 UO2F2 Water/Bare 534 Al 0.9991 0.0032 08 30.5 UO2F2 Water/Bare 1039 Al 0.9996 0.0042 09 30.5 UO2F2 Water/Bare 1611 Al 1.0001 0.0054 10 30.5 UO2F2 Water/Water 765 Al 1.0005 0.0038

Design Analyses and Calculation Page 25 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 Case wt%235U Chem Form Geometry Moderator/Reflector H/235U Other Materials k-meas sigma 11 30.5 UO2F2 Water/Water 1178 Al 1.0004 0.0048 12 30.5 UO2F2 Water/Water 729 Al 1.0004 0.0042 13 30.5 UO2F2 Water/Bare 489 Al 0.9984 0.0042 IEU-SOL-THERM-004 01 14.7 UO2SO4 Sphere Water/BeO 646 SS 1.0091 0.0041 LEU-COMP-THERM-022 01 10.0 UO2 Fuel Pin Array Water/Water 50 SS 1.0000 0.0046 02 10.0 UO2 Water/Water 80 SS 1.0000 0.0046 03 10.0 UO2 Water/Water 151 SS 1.0000 0.0036 04 10.0 UO2 Water/Water 247 SS 1.0000 0.0037 05 10.0 UO2 Water/Water 340 SS 1.0000 0.0038 06 10.0 UO2 Water/Water 613 SS 1.0000 0.0046 07 10.0 UO2 Water/Water 629 SS 1.0000 0.0046 LEU-COMP-THERM-023 01 10.0 UO2 Fuel Pin Array Water/Water 340 SS, Al 1.0000 0.0044 02 10.0 UO2 Water/Water 340 SS, Al 1.0000 0.0044 03 10.0 UO2 Water/Water 340 SS, Al 1.0000 0.0044 04 10.0 UO2 Water/Water 340 SS, Al 1.0000 0.0044 05 10.0 UO2 Water/Water 340 SS, Al 1.0000 0.0044 06 10.0 UO2 Water/Water 340 SS, Al 1.0000 0.0044 LEU-COMP-THERM-024 01 10.0 UO2 Fuel Pin Array Water/Water 41 SS, Al 1.0000 0.0054 02 10.0 UO2 Water/Water 128 SS, Al 1.0000 0.0040 LEU-COMP-THERM-032 01 10.0 UO2 Fuel Pin Array Water/Water 50 SS 1.0000 0.0045 04 10.0 UO2 Water/Water 340 SS 1.0000 0.0037 07 10.0 UO2 Water/Water 629 SS 1.0000 0.0045 LEU-SOL-THERM-06 01 10.0 UO2(NO3)2 Homogeneous Cylinders w/

Heterogeneous Absorber Rods Water/Water 532 SS 1.0000 0.0037 02 10.0 UO2(NO3)2 Water/Water 532 SS, B 1.0000 0.0038 03 10.0 UO2(NO3)2 Water/Water 532 SS, B 1.0000 0.0041 04 10.0 UO2(NO3)2 Water/Water 532 SS, B 1.0000 0.0041 05 10.0 UO2(NO3)2 Water/Water 532 SS, B 1.0000 0.0047 LEU-SOL-THERM-08 72 10.0 UO2(NO3)2 Homogeneous Array of Cylinders Water/Concrete 956 SS, Al 0.9999 0.0014 74 10.0 UO2(NO3)2 Water/Concrete 955 SS, Al 1.0002 0.0015 76 10.0 UO2(NO3)2 Water/Concrete 952 SS, Al 0.9999 0.0014 78 10.0 UO2(NO3)2 Water/Concrete 951 SS, Al 0.9999 0.0014 LEU-SOL-THERM-09 92 10.0 UO2(NO3)2 Homogeneous Array of Cylinders Water/ B-Concrete 936 SS, Al 0.9998 0.0014 93 10.0 UO2(NO3)2 Water/ B-Concrete 934 SS, Al 0.9999 0.0014 94 10.0 UO2(NO3)2 Water/ B-Concrete 933 SS, Al 0.9999 0.0014

5.

Evaluation Results The results for the individual Reference 1 experiment groups are shown in the sections below. The k-normalized values are the MCNP 6.1 calculation keff results divided by the Reference 1 experimental results shown in Table 3. From this point forward, all references to keff will reference the normalized value.

Design Analyses and Calculation Page 26 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 Table 3 - MCNP 6.1 Results Summary MCNP 6.1 Calculation Benchmark Values Normalized Results Exp Name k-calc

-calc ANECF MeV k-meas

-exp k-norm

-tot Maximum 1.0139 0.0008 1.4585 1.0091 0.0068 1.0128 0.0068 Minimum 0.9934 0.0001 0.0027 0.9977 0.0006 0.9952 0.0007 Average 1.0027 0.0003 0.1318 1.0001 0.0037 1.0026 0.0037 HEU-COMP-FAST-002 1.0001 0.0003 0.771 0.9985 0.0006 1.0016 0.0007 HEU-COMP-INTER-003-02 1.0051 0.0003 0.649 1.0000 0.0061 1.0051 0.0061 HEU-COMP-INTER-003-03 1.0048 0.0003 0.652 1.0000 0.0056 1.0048 0.0056 HEU-COMP-INTER-003-04 1.0028 0.0003 0.677 1.0000 0.0055 1.0028 0.0055 HEU-COMP-INTER-003-05 0.9979 0.0003 0.542 1.0000 0.0047 0.9979 0.0047 HEU-MET-FAST-001-01 0.9996 0.0002 1.459 1.0000 0.0010 0.9996 0.0010 HEU-MET-INTER-006-01 0.9934 0.0003 0.334 0.9977 0.0008 0.9956 0.0009 HEU-MET-INTER-006-02 0.9965 0.0003 0.377 1.0001 0.0008 0.9964 0.0009 HEU-MET-INTER-006-03 1.0000 0.0004 0.447 1.0015 0.0009 0.9985 0.0010 HEU-SOL-THERM-007-01 1.0110 0.0005 0.007 1.0000 0.0035 1.0110 0.0035 HEU-SOL-THERM-007-03 1.0060 0.0005 0.007 1.0000 0.0035 1.0060 0.0035 HEU-SOL-THERM-007-07 1.0031 0.0005 0.008 1.0000 0.0035 1.0031 0.0035 HEU-SOL-THERM-007-11 1.0072 0.0006 0.035 1.0000 0.0035 1.0072 0.0035 HEU-SOL-THERM-007-14 1.0069 0.0006 0.035 1.0000 0.0035 1.0069 0.0035 HEU-SOL-THERM-012-01 1.0009 0.0004 0.003 0.9999 0.0058 1.0010 0.0058 HEU-SOL-THERM-027-01 0.9968 0.0004 0.015 1.0000 0.0046 0.9968 0.0046 HEU-SOL-THERM-027-02 0.9967 0.0004 0.015 1.0000 0.0043 0.9967 0.0043 HEU-SOL-THERM-027-03 0.9975 0.0004 0.015 1.0000 0.0037 0.9975 0.0037 HEU-SOL-THERM-027-04 0.9983 0.0004 0.015 1.0000 0.0037 0.9983 0.0037 HEU-SOL-THERM-027-05 0.9962 0.0004 0.015 1.0000 0.0044 0.9962 0.0044 HEU-SOL-THERM-031-01 0.9970 0.0004 0.028 1.0000 0.0046 0.9970 0.0046 HEU-SOL-THERM-031-02 1.0080 0.0004 0.029 1.0000 0.0058 1.0080 0.0058 HEU-SOL-THERM-031-03 0.9970 0.0004 0.029 1.0000 0.0058 0.9970 0.0058 HEU-SOL-THERM-031-04 1.0015 0.0004 0.030 1.0000 0.0068 1.0015 0.0068 HEU-SOL-THERM-035-01 1.0005 0.0004 0.004 1.0000 0.0031 1.0005 0.0031 HEU-SOL-THERM-035-02 1.0034 0.0004 0.004 1.0000 0.0032 1.0034 0.0032 HEU-SOL-THERM-035-03 1.0043 0.0004 0.004 1.0000 0.0030 1.0043 0.0030 HEU-SOL-THERM-035-04 1.0037 0.0004 0.004 1.0000 0.0030 1.0037 0.0030 HEU-SOL-THERM-035-05 1.0023 0.0004 0.008 1.0000 0.0033 1.0023 0.0033 HEU-SOL-THERM-035-06 1.0037 0.0004 0.008 1.0000 0.0029 1.0037 0.0029 HEU-SOL-THERM-035-07 1.0051 0.0005 0.015 1.0000 0.0035 1.0051 0.0035 HEU-SOL-THERM-035-08 0.9987 0.0005 0.016 1.0000 0.0038 0.9987 0.0038 HEU-SOL-THERM-035-09 0.9997 0.0005 0.016 1.0000 0.0041 0.9997 0.0041

Design Analyses and Calculation Page 27 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 MCNP 6.1 Calculation Benchmark Values Normalized Results Exp Name k-calc

-calc ANECF MeV k-meas

-exp k-norm

-tot HEU-SOL-THERM-038-01 0.9955 0.0002 0.043 1.0000 0.0025 0.9955 0.0025 HEU-SOL-THERM-038-02 0.9970 0.0002 0.040 1.0000 0.0025 0.9970 0.0025 HEU-SOL-THERM-038-07 0.9979 0.0002 0.042 1.0000 0.0032 0.9979 0.0032 HEU-SOL-THERM-038-08 0.9986 0.0002 0.041 1.0000 0.0026 0.9986 0.0026 HEU-SOL-THERM-038-09 0.9985 0.0002 0.041 1.0000 0.0033 0.9985 0.0033 HEU-SOL-THERM-038-10 0.9970 0.0002 0.042 1.0000 0.0026 0.9970 0.0026 HEU-SOL-THERM-038-11 0.9966 0.0002 0.043 1.0000 0.0025 0.9966 0.0026 HEU-SOL-THERM-038-12 0.9963 0.0002 0.043 1.0000 0.0025 0.9963 0.0025 HEU-SOL-THERM-038-17 0.9969 0.0002 0.043 1.0000 0.0026 0.9969 0.0026 HEU-SOL-THERM-038-18 0.9974 0.0002 0.043 1.0000 0.0032 0.9974 0.0032 HEU-SOL-THERM-046-01 1.0139 0.0003 0.004 1.0011 0.0029 1.0128 0.0029 HEU-SOL-THERM-046-02 1.0105 0.0003 0.004 1.0011 0.0029 1.0094 0.0029 HEU-SOL-THERM-046-03 1.0110 0.0003 0.004 1.0011 0.0029 1.0099 0.0029 HEU-SOL-THERM-046-04 1.0119 0.0003 0.004 1.0011 0.0029 1.0108 0.0029 HEU-SOL-THERM-046-05 1.0098 0.0003 0.004 1.0011 0.0030 1.0087 0.0030 HEU-SOL-THERM-046-06 1.0111 0.0003 0.004 1.0011 0.0029 1.0100 0.0029 HEU-SOL-THERM-046-07 1.0120 0.0003 0.004 1.0011 0.0031 1.0109 0.0031 HEU-SOL-THERM-046-08 1.0113 0.0003 0.004 1.0011 0.0032 1.0102 0.0032 HEU-SOL-THERM-046-09 1.0107 0.0003 0.004 1.0011 0.0037 1.0096 0.0037 HEU-SOL-THERM-046-10 1.0086 0.0003 0.004 1.0011 0.0029 1.0075 0.0029 HEU-SOL-THERM-046-11 1.0114 0.0003 0.005 1.0011 0.0028 1.0103 0.0028 HEU-SOL-THERM-046-12 1.0105 0.0003 0.005 1.0011 0.0029 1.0094 0.0029 HEU-SOL-THERM-046-13 1.0100 0.0003 0.005 1.0011 0.0030 1.0089 0.0030 IEU-COMP-THERM-001-01 1.0021 0.0007 0.210 1.0000 0.0040 1.0021 0.0041 IEU-COMP-THERM-001-02 1.0047 0.0007 0.155 1.0000 0.0040 1.0047 0.0041 IEU-COMP-THERM-001-03 0.9987 0.0007 0.103 1.0000 0.0040 0.9987 0.0041 IEU-COMP-THERM-001-04 1.0000 0.0007 0.073 1.0000 0.0040 1.0000 0.0041 IEU-COMP-THERM-001-05 1.0053 0.0006 0.045 1.0000 0.0040 1.0053 0.0040 IEU-COMP-THERM-001-06 1.0034 0.0007 0.105 1.0000 0.0040 1.0034 0.0041 IEU-COMP-THERM-001-07 1.0015 0.0007 0.109 1.0000 0.0040 1.0015 0.0041 IEU-COMP-THERM-001-08 0.9998 0.0007 0.117 1.0000 0.0040 0.9998 0.0041 IEU-COMP-THERM-001-09 1.0084 0.0007 0.164 1.0000 0.0040 1.0084 0.0041 IEU-COMP-THERM-001-10 1.0014 0.0007 0.154 1.0000 0.0040 1.0014 0.0041 IEU-COMP-THERM-001-11 1.0006 0.0007 0.154 1.0000 0.0040 1.0006 0.0041 IEU-COMP-THERM-001-12 1.0011 0.0006 0.153 1.0000 0.0040 1.0011 0.0040 IEU-COMP-THERM-001-13 0.9999 0.0007 0.073 1.0000 0.0040 0.9999 0.0041 IEU-COMP-THERM-001-14 0.9998 0.0007 0.073 1.0000 0.0040 0.9998 0.0041 IEU-COMP-THERM-001-15 1.0023 0.0007 0.073 1.0000 0.0040 1.0023 0.0041 IEU-COMP-THERM-001-16 1.0033 0.0007 0.054 1.0000 0.0040 1.0033 0.0041 IEU-COMP-THERM-001-17 1.0042 0.0008 0.202 1.0000 0.0040 1.0042 0.0041

Design Analyses and Calculation Page 28 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 MCNP 6.1 Calculation Benchmark Values Normalized Results Exp Name k-calc

-calc ANECF MeV k-meas

-exp k-norm

-tot IEU-COMP-THERM-001-18 1.0053 0.0008 0.131 1.0000 0.0040 1.0053 0.0041 IEU-COMP-THERM-001-19 1.0051 0.0007 0.060 1.0000 0.0040 1.0051 0.0041 IEU-COMP-THERM-001-20 1.0088 0.0007 0.151 1.0000 0.0040 1.0088 0.0041 IEU-COMP-THERM-001-21 1.0031 0.0007 0.207 1.0000 0.0040 1.0031 0.0041 IEU-COMP-THERM-001-26 1.0077 0.0006 0.055 1.0000 0.0040 1.0077 0.0041 IEU-COMP-THERM-001-27 1.0021 0.0007 0.056 1.0000 0.0040 1.0021 0.0041 IEU-COMP-THERM-001-28 1.0111 0.0007 0.154 1.0000 0.0040 1.0111 0.0041 IEU-COMP-THERM-001-29 1.0077 0.0007 0.148 1.0000 0.0040 1.0077 0.0041 IEU-COMP-THERM-002-01 1.0001 0.0005 0.044 1.0014 0.0039 0.9987 0.0039 IEU-COMP-THERM-003-01 1.0043 0.0003 0.023 1.0006 0.0056 1.0037 0.0056 IEU-COMP-THERM-003-02 1.0087 0.0003 0.023 1.0046 0.0056 1.0040 0.0056 IEU-COMP-THERM-015-04 0.9954 0.0001 0.283 0.9982 0.0032 0.9972 0.0032 IEU-COMP-THERM-015-05 0.9947 0.0001 0.283 0.9982 0.0031 0.9964 0.0031 IEU-COMP-THERM-015-07 0.9941 0.0001 0.179 0.9981 0.0036 0.9960 0.0036 IEU-COMP-THERM-015-08 0.9980 0.0001 0.089 0.9990 0.0044 0.9990 0.0044 IEU-COMP-THERM-015-09 0.9976 0.0001 0.090 0.9991 0.0047 0.9985 0.0047 IEU-COMP-THERM-015-10 0.9977 0.0001 0.089 0.9995 0.0045 0.9982 0.0045 IEU-COMP-THERM-015-11 1.0005 0.0001 0.047 0.9985 0.0050 1.0020 0.0050 IEU-COMP-THERM-015-12 1.0010 0.0001 0.047 0.9985 0.0051 1.0025 0.0051 IEU-MET-FAST-003-01 1.0031 0.0003 1.262 1.0000 0.0019 1.0031 0.0019 IEU-MET-FAST-004-01 1.0076 0.0003 1.222 1.0000 0.0032 1.0076 0.0032 IEU-MET-FAST-005-01 1.0016 0.0003 1.208 1.0000 0.0023 1.0016 0.0023 IEU-MET-FAST-006-01 0.9965 0.0003 1.205 1.0000 0.0025 0.9965 0.0025 IEU-MET-FAST-009-01 1.0110 0.0003 0.946 1.0000 0.0053 1.0110 0.0053 IEU-SOL-THERM-002-01 1.0095 0.0001 0.013 1.0004 0.0026 1.0091 0.0026 IEU-SOL-THERM-002-02 1.0000 0.0001 0.009 1.0003 0.0032 0.9997 0.0032 IEU-SOL-THERM-002-03 1.0005 0.0001 0.007 1.0003 0.0038 1.0002 0.0038 IEU-SOL-THERM-002-04 1.0020 0.0001 0.005 1.0003 0.0046 1.0016 0.0046 IEU-SOL-THERM-002-05 1.0045 0.0002 0.024 0.9989 0.0042 1.0056 0.0042 IEU-SOL-THERM-002-07 1.0005 0.0001 0.011 0.9991 0.0032 1.0014 0.0032 IEU-SOL-THERM-002-08 1.0039 0.0001 0.006 0.9996 0.0042 1.0043 0.0042 IEU-SOL-THERM-002-09 1.0085 0.0001 0.004 1.0001 0.0054 1.0084 0.0054 IEU-SOL-THERM-002-10 1.0024 0.0001 0.007 1.0005 0.0038 1.0019 0.0038 IEU-SOL-THERM-002-11 1.0050 0.0001 0.005 1.0004 0.0048 1.0046 0.0048 IEU-SOL-THERM-002-12 1.0043 0.0001 0.007 1.0004 0.0042 1.0039 0.0042 IEU-SOL-THERM-002-13 1.0051 0.0001 0.012 0.9984 0.0042 1.0068 0.0042 IEU-SOL-THERM-004-01 1.0094 0.0002 0.013 1.0091 0.0041 1.0003 0.0041 LEU-COMP-THERM-022-01 1.0032 0.0001 0.157 1.0000 0.0046 1.0032 0.0046 LEU-COMP-THERM-022-02 1.0065 0.0003 0.115 1.0000 0.0046 1.0065 0.0046 LEU-COMP-THERM-022-03 1.0069 0.0003 0.074 1.0000 0.0036 1.0069 0.0036

Design Analyses and Calculation Page 29 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 MCNP 6.1 Calculation Benchmark Values Normalized Results Exp Name k-calc

-calc ANECF MeV k-meas

-exp k-norm

-tot LEU-COMP-THERM-022-04 1.0081 0.0003 0.054 1.0000 0.0037 1.0081 0.0037 LEU-COMP-THERM-022-05 1.0031 0.0003 0.045 1.0000 0.0038 1.0031 0.0038 LEU-COMP-THERM-022-06 1.0015 0.0002 0.035 1.0000 0.0046 1.0015 0.0046 LEU-COMP-THERM-022-07 1.0046 0.0003 0.034 1.0000 0.0046 1.0046 0.0046 LEU-COMP-THERM-023-01 0.9952 0.0003 0.059 1.0000 0.0044 0.9952 0.0044 LEU-COMP-THERM-023-02 0.9980 0.0003 0.053 1.0000 0.0044 0.9980 0.0044 LEU-COMP-THERM-023-03 0.9995 0.0003 0.051 1.0000 0.0044 0.9995 0.0044 LEU-COMP-THERM-023-04 1.0012 0.0003 0.050 1.0000 0.0044 1.0012 0.0044 LEU-COMP-THERM-023-05 1.0024 0.0003 0.048 1.0000 0.0044 1.0024 0.0044 LEU-COMP-THERM-023-06 1.0024 0.0003 0.047 1.0000 0.0044 1.0024 0.0044 LEU-COMP-THERM-024-01 1.0007 0.0003 0.178 1.0000 0.0054 1.0007 0.0054 LEU-COMP-THERM-024-02 1.0081 0.0003 0.081 1.0000 0.0040 1.0081 0.0040 LEU-COMP-THERM-032-01 1.0016 0.0003 0.158 1.0000 0.0045 1.0016 0.0045 LEU-COMP-THERM-032-04 1.0029 0.0003 0.046 1.0000 0.0037 1.0029 0.0037 LEU-COMP-THERM-032-07 1.0045 0.0002 0.034 1.0000 0.0045 1.0045 0.0045 LEU-SOL-THERM-006-01 0.9978 0.0003 0.025 1.0000 0.0037 0.9978 0.0037 LEU-SOL-THERM-006-02 1.0034 0.0003 0.025 1.0000 0.0038 1.0034 0.0038 LEU-SOL-THERM-006-03 0.9978 0.0003 0.025 1.0000 0.0041 0.9978 0.0041 LEU-SOL-THERM-006-04 0.9992 0.0003 0.025 1.0000 0.0041 0.9992 0.0041 LEU-SOL-THERM-006-05 1.0008 0.0003 0.026 1.0000 0.0047 1.0008 0.0047 LEU-SOL-THERM-008-72 1.0021 0.0002 0.015 0.9999 0.0014 1.0022 0.0014 LEU-SOL-THERM-008-74 1.0011 0.0002 0.015 1.0002 0.0015 1.0009 0.0015 LEU-SOL-THERM-008-76 1.0014 0.0002 0.015 0.9999 0.0014 1.0015 0.0014 LEU-SOL-THERM-008-78 1.0021 0.0002 0.015 0.9999 0.0014 1.0022 0.0014 LEU-SOL-THERM-009-92 0.9998 0.0002 0.016 0.9998 0.0014 1.0000 0.0014 LEU-SOL-THERM-009-93 1.0008 0.0002 0.016 0.9999 0.0014 1.0009 0.0014 LEU-SOL-THERM-009-94 1.0013 0.0002 0.016 0.9999 0.0014 1.0014 0.0014 The results of each enrichment group are examined for normality. The null hypothesis is that the data are normally distributed, and 95% confidence is required to reject this assumption herein. The hypothesis of normality is accepted for all subgroups. The results of the normality testing are shown in Section 5.2.

5.1.

Trend Evaluation The keff results are also analyzed to determine if a trend exists with important validation parameters. A calculational methodology should have a bias that neither has dependence on a characteristic nor is a smooth function of a parameter. If a trend exists, the bias will vary as a function of that trend over the parameter range. If no trend exists, then the bias will be constant over the area of applicability. Critical experiment parameters examined include the hydrogen to fissile material ratio (H/X), the Average Neutron Energy Causing Fission (ANECF), the 235U enrichment, the moderator material, the reflector material and the chemical form of the fissile material. Graphs of the validation results versus these parameters are shown.

Where appropriate, the graphs of the results and the trending parameters also include a plotted trend line and the coefficient of determination value (R2) for the trend line. Note, an R2 value less than 0.3 is

Design Analyses and Calculation Page 30 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 considered to indicate no data correlation, while an R2 value of 0.8 or greater is indicative of data correlation.

It is concluded that no trend in the bias is observed.

5.1.1.

Average Neutron Energy Causing Fission (ANECF)

The ANECF value is a MCNP calculated value used to characterize the system neutron energy. Consistent with the purpose of this validation, the majority of the experiments evaluated are in the thermal neutron range with ANECF values between 0.005 and 0.10 MeV. However, sufficient higher energy experiments are included with ANECF values up to 1.46 MeV to demonstrate that there is no trend in the keff values relative to the ANECF value. Figure 1 presents the MCNP 6.1 data.

Complete Data Set HEU, IEU & LEU Shown Individually Figure 1 - ANECF Trend y = -0.0008x + 1.0027 R² = 0.0028 0.995 1.000 1.005 1.010 1.015 1.0E-03 1.0E-02 1.0E-01 1.0E+00 1.0E+01 k-normalized ANECF MeV y = -0.0034x + 1.003 R² = 0.0288 y = 0.0003x + 1.0027 R² = 0.0009 0.995 1.000 1.005 1.010 1.015 1.0E-03 1.0E-02 1.0E-01 1.0E+00 1.0E+01 k-normalized ANECF MeV HEU IEU LEU HEU-SOL-THERM-046

Design Analyses and Calculation Page 31 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 In the complete data set, the very slight negative slope to the datas linear fit is judged to be insignificant as its change in value over the entire data range is on the order of the average total uncertainty (-tot) and the R2 value is much less than the minimally acceptable value of 0.3.

Also included are the individual HEU, IEU and LEU data sets. As shown, the HEU and IEU data sets span the entire ANECF range while the LEU set is concentrated in the center. This is a consequence of the difficulty in creating a LEU critical configuration that is either excessively over or under moderated. The lower trendline displayed is a linear fit for only the HEU data. As indicated, the overestimation of keff with the HEU-SOL-THERM-046 experiments (as stated in Section 4.3.1) results in the apparent negative slope for this line and the linear fit for the combined data set in the chart above. This overestimation is evaluated below and is judged to be the consequence of a systematic error in the Reference 1 Benchmark description.

The second, upper trendline shown displays a linear fit for only the IEU data, and has no indication of a variable bias with respect to ANECF.

In order to evaluate the overestimation of HEU-SOL-THERM-046, it is compared with other, similar data sets.

The HEU-SOL-THERM-007, -012, and -035 sets are very similar and have identical ANECF values, yet do not exhibit this overestimate. Additionally, the IEU-SOL-THERM-002 experiments have similar geometry and identical ANECF values without exhibiting an overestimate. Therefore, it is judged that the overestimate cannot result from a MCNP 6.1 calculation error related to the geometry or cross sections of the shared materials. The materials exclusive to HEU-SOL-THERM-046 are the sulfate solution and the beryllium-graphite reflector.

The following data sets also include beryllium or graphite reflectors without exhibiting an overestimate in their keff values: HEU-COMP-FAST-002, HEU-COMP-INTER-003, IEU-COMP-THERM-003, IEU-MET-FAST-004 and IEU-SOL-THERM-004. These are shown graphically in Section 5.1.6. Note that only IEU-COMP-THERM-003 and IEU-SOL-THERM-004 have an ANECF values in the thermal range (albeit, slightly more energetic than HEU-SOL-THERM-0046). From this it is judged to be unlikely that an error in the cross sections for the reflector materials is the cause of the overestimate.

The sulfate solution (H2SO4-H2O) is essential to the SHINE applications and this validation; however, it is very rare within the Reference 1 Benchmarks. The IEU-SOL-THERM-004 experiment (included herein) also contains this solution and does not exhibit an overestimate, but this is only one experiment. The sulfur solution was selected for SHINE applications because, among other features, of sulfurs very small neutron absorption cross section (~0.5 barns). This is much lower than most other solution materials usually included in the Benchmark experiments. For example, nitrogen (used in the common nitric acid) has an absorption cross section of about 1.9 barns. Given that the sulfur cross section is so small, it is judged to be very unlikely that an error in the cross section could be the cause of the overestimate.

To further test this notion, the experiments HEU-SOL-THERM-046-01 and IEU-SOL-THERM-004 were recalculated with the sulfur replaced (atom for atom) by sodium. Sodium has a similar atomic mass and virtually identical neutron absorption cross section. The result of this computational experiment was an increase in the keff values of 0.0012 and 0.0016, respectively.

Additionally, it is noted in Reference 1 that the benchmark calculation results show a 1.5% overestimate when using the APOLLO2-MORET4 code without explanation.

Therefore, it is judged that the overestimate does not result from an error in the MCNP 6.1 calculation or the cross sections. Rather, it is most likely due to a systematic error in the Reference 1 Benchmark description.

However, the overestimate is not so large as to make the experiments unusable. These are retained within this validation, with the understanding that they are the cause of the apparent bias with respect to ANECF, H/235U (see Section 5.1.2), moderator (see Section 5.1.5), reflector (see Section 5.1.6), and chemical form (see Section 5.1.7).

Design Analyses and Calculation Page 32 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 5.1.2.

H/235U Values The H/235U value is a physical system parameter used to characterize the system neutron energy. Consistent with the purpose of this validation, the majority of the experiments evaluated are in the thermal neutron range and H/235U values from 20 to 1200 are well represented. However, sufficient higher energy experiments are included with H/235U values as low as 3.1 to demonstrate that there is no trend in the keff values relative to the H/235U value. Figure 2 presents the MCNP 6.1 data.

The positive slope of the datas linear fit is about 2 times the average total uncertainty (-tot) for the collection of experiments. However, it is judged that this does not represent a valid trend because:

The R2 value is much less than the minimally acceptable value of 0.3, thus this trendline does not represent an acceptable fit to the data.

The upward slope of the trendline is largely an artifact of the overestimation of the HEU-SOL-THERM-046 experiments (as stated in Section 4.3.1). This overestimation is evaluated in Section 5.1.1 and is judged to be the consequence of a systematic error in the Reference 1 Benchmark description. While not shown herein, removal of this data set eliminates the apparent upward slope of the trendline.

Figure 2 - H/235U Trend y = 3E-06x + 1.0017 R² = 0.0577 0.995 1.000 1.005 1.010 1.015 0

200 400 600 800 1000 1200 1400 1600 1800 k-normalized H/U-235 HEU-SOL-THERM-046

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Design Analyses and Calculation Page 33 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 5.1.3.

ANECF vs. H/235U

[ Proprietary Information ]

Proprietary Information Figure 3 - ANECF vs. H/235U Evaluation

Design Analyses and Calculation Page 34 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 Note that there is a strong relationship between the two parameters. However, the exact relationship varies as the 238U concentration decreases; i.e., the variation from LEU to IEU to HEU. From this relationship it is judged that the ANECF value accurately characterizes the system neutron energy in the absence of accurate H/235U values and in the presence of other neutron scattering isotopes (e.g., carbon, sulfur).

5.1.4.

Enrichment The system enrichment (wt. % 235U) is a physical system parameter used to characterize the system.

Consistent with the purpose of this validation, the majority of the experiments evaluated are intermediate uranium enrichment with wt. % 235U values between 10 and 30%. However, sufficient higher enrichment experiments are included with wt. % 235U values as high as 94% to demonstrate that there is no trend in the keff values relative to enrichment. Figure 4 presents the MCNP 6.1 data. There is no discernible slope to the datas linear fit over the entire data range and that the R2 value is much less than the minimally acceptable value of 0.3.

Figure 4 - Enrichment Trend y = 4E-06x + 1.0024 R² = 0.0009 0.995 1.000 1.005 1.010 1.015 0

20 40 60 80 100 k-normalized wt % U-235

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Design Analyses and Calculation Page 35 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 5.1.5.

Moderator The system neutron moderator material is a physical system parameter used to characterize the system.

Figure 5 displays the normalized keff values for the various moderator materials used herein. Also shown are average bias values for the various moderator materials. Note that the complete data set average keff and -

tot values are 1.0026 and 0.0037, respectively. The only significant biases are those related to the sulfate solution (see Section 5.1.1) and graphite. Graphite will not be included as a moderator in the AoA for this evaluation.

Proprietary Information Figure 5 - Moderator Evaluation

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Design Analyses and Calculation Page 36 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 5.1.6.

Reflector The system reflector material is a physical system parameter used to characterize the system. Figure 6 displays the normalized keff values for the various reflector materials used herein. Also shown are average bias values for the various reflector materials. Note that the complete data set average keff and -tot values are 1.0026 and 0.0037, respectively. The only significant biases are those related to the beryllium oxide /

graphite (see Section 5.1.1) and miscellaneous metals. Only iron (and stainless steel), which are structural materials found in many of the experiments included herein, will be included as a metal reflector in the AoA for this evaluation.

Proprietary Information Figure 6 - Reflector Evaluation

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Design Analyses and Calculation Page 37 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 5.1.7.

Chemical Form The chemical form of the system fissile material is a physical system parameter used to characterize the system. Figure 7 displays the normalized keff values for the various chemical forms of uranium materials used herein. Also shown are average bias values for the various materials. Note that the complete data set average keff and -tot values are 1.0026 and 0.0037, respectively. The only significant bias is that related to the sulfate solution (see Section 5.1.1).

Proprietary Information Figure 7 - Chemical Form Evaluation 5.1.8.

Homogeneous Vs. Heterogeneous Eighty-four (84) of the experiments are homogeneous with an average keff value of 1.0025 and an average -

tot value of 0.0035. Comparing this with the 56 heterogeneous experiments, with an average keff value of 1.0026 and an average -tot value of 0.0040, indicates that there is no bias between homogeneous and heterogeneous MCNP 6.1 models.

[Proprietary Information - Withheld from Public Disclosure Under 10 CFR 2.390(a)(4)]

Design Analyses and Calculation Page 38 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 5.2.

Normalcy Evaluation Since 20 wt. % 235U is the target of this evaluation, the IEU data set is evaluated individually. However, the 10 wt. % 235U LEU experiments have been added to the IEU data set to bound the 20% target value.

Additionally, the combined LEU, IEU and HEU data set is included for completeness. The summary of the normalcy results is show in Table 4.

Table 4 - Normalcy Results Summary Intermediate Enriched Uranium Normal Low and Intermediate Enriched Uranium Normal Combined LEU, IEU and HEU Data Set Normal 5.2.1.

Intermediate Enriched Uranium The examination of these data includes 54 cases as shown in Appendix 1. [ Proprietary Information ]

Proprietary Information These calculations are shown in Appendix A and the comparison of the observed distribution vs. the expected distribution of a normal system is shown in Figure 8. The data are judged to be from a normal population because all three normality tests indicate that the data are normal.

Figure 8 - Intermediate Enriched Distribution 0

2 4

6 8

10 12 14 Frequency Bins Observed Expected

[Proprietary Information - Withheld from Public Disclosure Under 10 CFR 2.390(a)(4)]

Design Analyses and Calculation Page 39 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 5.2.2.

Low and Intermediate Enriched Uranium The examination of these data includes 84 cases as shown in Appendix 1. [ Proprietary Information ]

Proprietary Information These calculations are shown in Appendix A and the comparison of the observed distribution vs. the expected distribution of a normal system is shown in Figure 9. The data are judged to be from a normal population because all three normality tests indicate that the data are normal.

Figure 9 - Low and Intermediate Enriched Distribution 5.2.3.

Combined Data Set As there is no trend associated with combined data set, it can also be evaluated. The examination of these data includes 140 cases as shown in Appendix 1. [ Proprietary Information ]

Proprietary Information 0

5 10 15 20 25 Frequency Bins Observed Expected

[Proprietary Information - Withheld from Public Disclosure Under 10 CFR 2.390(a)(4)]

Design Analyses and Calculation Page 40 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 Proprietary Information These calculations are shown in Appendix A and the comparison of the observed distribution vs. the expected distribution of a normal system is shown in Figure 10. The data are judged to be from a normal population because:

Two of the three normality tests indicate the data are normal, and

[ Proprietary Information ]

Figure 10 - Combined Group Distribution 0

5 10 15 20 25 30 Frequency Bins Observed Expected

Design Analyses and Calculation Page 41 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 5.3.

Bias and Bias Uncertainty Evaluation While the SHINE applications will use nominally 19.75 wt. % 235U materials, three sets of the data are evaluated for bias and bias uncertainty. First, the set including only the 54 IEU experiments with 14.7 to 36 wt. % 235U is considered as this most accurately brackets the SHINE applications. However, as there are only four experiments with less than 30 wt. % 235U in the IEU data set, a second evaluation considers the 84 experiments in the combined LEU and IEU data sets (10 to 36 wt. % 235U). This is judged to better encompass the SHINE application value of approximately 20 wt. % 235U. Lastly, all three LEU, IEU and HEU data sets are combined to evaluate the complete 140 experiment data set.

A summary of the weighted bias and USL calculations is shown in Table 5. Per Reference 10, positive bias values are not used and the bias is set to zero for the USL calculation. The SHINE specific MoS value of 0.05 is included in the USL. The USL value of 0.9391 is recommended for use with the SHINE 20 wt. % 235U materials, which was selected from Table 5 as the most conservative value.

Table 5 - USL Results Summary Bias Bias Uncertainty USL Intermediate Enriched Uranium 0.0025 0.0109 0.9391 Low and Intermediate Enriched Uranium 0.0020 0.0078 0.9422 Combined Enrichments 0.0011 0.0091 0.9409 5.3.1.

Intermediate Enriched Uranium As the data are judged to be from a normal distribution the bias and bias uncertainty is represented with a Lower Tolerance Limit (LTL). The USL calculation for MCNP 6.1 (0.9391) is developed in Table 6. Note that the positive bias of 0.0025 is set to zero.

Table 6 - Intermediate Enriched USL File Name keff 1/()2 Weighted keff Weighted Variance IEU-COMP-THERM-001-01 1.00207 0.00406 60744.4844 6.0870E+04 0.0120 IEU-COMP-THERM-001-02 1.00466 0.00406 60744.4844 6.1028E+04 0.2796 IEU-COMP-THERM-001-03 0.99872 0.00406 60744.4844 6.0667E+04 0.8747 IEU-COMP-THERM-001-04 1.00003 0.00407 60485.4563 6.0487E+04 0.3734 IEU-COMP-THERM-001-05 1.00528 0.00405 61079.5194 6.1402E+04 0.4671 IEU-COMP-THERM-001-06 1.00341 0.00406 60693.9749 6.0901E+04 0.0486 IEU-COMP-THERM-001-07 1.00152 0.00407 60485.4563 6.0577E+04 0.0598 IEU-COMP-THERM-001-08 0.99984 0.00406 60794.3388 6.0785E+04 0.4349 IEU-COMP-THERM-001-09 1.00841 0.00406 60693.9749 6.1204E+04 2.1094 IEU-COMP-THERM-001-10 1.00144 0.00406 60591.0047 6.0678E+04 0.0700 IEU-COMP-THERM-001-11 1.00061 0.00406 60744.4844 6.0782E+04 0.2204 IEU-COMP-THERM-001-12 1.00109 0.00405 61033.6662 6.1100E+04 0.1239 IEU-COMP-THERM-001-13 0.99990 0.00406 60744.4844 6.0738E+04 0.4153

Design Analyses and Calculation Page 42 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 File Name keff 1/()2 Weighted keff Weighted Variance IEU-COMP-THERM-001-14 0.99976 0.00406 60693.9749 6.0679E+04 0.4606 IEU-COMP-THERM-001-15 1.00229 0.00406 60744.4844 6.0884E+04 0.0031 IEU-COMP-THERM-001-16 1.00334 0.00406 60794.3388 6.0997E+04 0.0414 IEU-COMP-THERM-001-17 1.00417 0.00407 60322.3627 6.0574E+04 0.1653 IEU-COMP-THERM-001-18 1.00526 0.00407 60322.3627 6.0640E+04 0.4546 IEU-COMP-THERM-001-19 1.00510 0.00406 60538.5509 6.0847E+04 0.4046 IEU-COMP-THERM-001-20 1.00879 0.00406 60794.3388 6.1329E+04 2.3940 IEU-COMP-THERM-001-21 1.00313 0.00405 60843.5348 6.1034E+04 0.0230 IEU-COMP-THERM-001-26 1.00772 0.00405 60939.9376 6.1410E+04 1.6512 IEU-COMP-THERM-001-27 1.00213 0.00406 60744.4844 6.0874E+04 0.0090 IEU-COMP-THERM-001-28 1.01109 0.00405 60843.5348 6.1518E+04 4.4742 IEU-COMP-THERM-001-29 1.00773 0.00406 60744.4844 6.1214E+04 1.6522 IEU-COMP-THERM-002-01 0.99866 0.00393 64882.4006 6.4796E+04 0.9631 IEU-COMP-THERM-003-01 1.00371 0.00561 31808.2345 3.1926E+04 0.0453 IEU-COMP-THERM-003-02 1.00403 0.00561 31802.4685 3.1931E+04 0.0732 IEU-COMP-THERM-015-04 0.99721 0.00320 97519.1137 9.7248E+04 2.7390 IEU-COMP-THERM-015-05 0.99644 0.00310 103927.4171 1.0356E+05 3.8306 IEU-COMP-THERM-015-07 0.99597 0.00360 77060.0066 7.6750E+04 3.2984 IEU-COMP-THERM-015-08 0.99899 0.00440 51607.8423 5.1556E+04 0.6415 IEU-COMP-THERM-015-09 0.99848 0.00470 45234.7457 4.5166E+04 0.7369 IEU-COMP-THERM-015-10 0.99817 0.00450 49334.9647 4.9245E+04 0.9317 IEU-COMP-THERM-015-11 1.00201 0.00500 39968.6646 4.0049E+04 0.0101 IEU-COMP-THERM-015-12 1.00253 0.00510 38417.8013 3.8515E+04 0.0000 IEU-MET-FAST-003-01 1.00305 0.00192 271525.1568 2.7235E+05 0.0778 IEU-MET-FAST-004-01 1.00762 0.00321 96965.9359 9.7705E+04 2.5273 IEU-MET-FAST-005-01 1.00163 0.00232 186466.2776 1.8677E+05 0.1459 IEU-MET-FAST-006-01 0.99647 0.00252 158017.8244 1.5746E+05 5.7737 IEU-MET-FAST-009-01 1.01098 0.00531 35507.7069 3.5898E+04 2.5445 IEU-SOL-THERM-002-01 1.00911 0.00260 147501.3275 1.4884E+05 6.4089 IEU-SOL-THERM-002-02 0.99971 0.00320 97495.3446 9.7467E+04 0.7669 IEU-SOL-THERM-002-03 1.00018 0.00380 69204.1522 6.9217E+04 0.3772 IEU-SOL-THERM-002-04 1.00165 0.00460 47240.8955 4.7319E+04 0.0354 IEU-SOL-THERM-002-05 1.00562 0.00420 56607.1914 5.6925E+04 0.5445 IEU-SOL-THERM-002-07 1.00136 0.00320 97469.6869 9.7602E+04 0.1297 IEU-SOL-THERM-002-08 1.00434 0.00420 56657.2238 5.6903E+04 0.1891 IEU-SOL-THERM-002-09 1.00840 0.00540 34286.0278 3.4574E+04 1.1872 IEU-SOL-THERM-002-10 1.00186 0.00380 69194.0964 6.9323E+04 0.0297

Design Analyses and Calculation Page 43 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 File Name keff 1/()2 Weighted keff Weighted Variance IEU-SOL-THERM-002-11 1.00456 0.00480 43387.5244 4.3585E+04 0.1812 IEU-SOL-THERM-002-12 1.00393 0.00420 56650.4835 5.6873E+04 0.1132 IEU-SOL-THERM-002-13 1.00675 0.00420 56626.4242 5.7009E+04 1.0161 IEU-SOL-THERM-004-01 1.00030 0.00410 59408.8816 5.9427E+04 0.2921 kmean 1.0025 1/()2 1/()2keff 1.0000 3.7897E+06 3.7992E+06 (mean)2 S2 St K*

USL 1.4249E-05 1.3765E-05 5.2929E-03 2.065 0.9391 5.3.2.

Low and Intermediate Enriched Uranium As the data are judged to be from a normal distribution the bias and bias uncertainty is represented with a Lower Tolerance Limit (LTL). The USL calculation for MCNP 6.1 (0.9422) is developed in Table 7. Note that the positive bias of 0.0020 is set to zero.

Table 7 - Low and Intermediate Enriched USL File Name keff 1/()2 Weighted keff Weighted Variance IEU-COMP-THERM-001-01 1.00207 0.00406 60744.4844 6.0870E+04 0.0003 IEU-COMP-THERM-001-02 1.00466 0.00406 60744.4844 6.1028E+04 0.4293 IEU-COMP-THERM-001-03 0.99872 0.00406 60744.4844 6.0667E+04 0.6541 IEU-COMP-THERM-001-04 1.00003 0.00407 60485.4563 6.0487E+04 0.2351 IEU-COMP-THERM-001-05 1.00528 0.00405 61079.5194 6.1402E+04 0.6565 IEU-COMP-THERM-001-06 1.00341 0.00406 60693.9749 6.0901E+04 0.1204 IEU-COMP-THERM-001-07 1.00152 0.00407 60485.4563 6.0577E+04 0.0140 IEU-COMP-THERM-001-08 0.99984 0.00406 60794.3388 6.0785E+04 0.2840 IEU-COMP-THERM-001-09 1.00841 0.00406 60693.9749 6.1204E+04 2.4926 IEU-COMP-THERM-001-10 1.00144 0.00406 60591.0047 6.0678E+04 0.0191 IEU-COMP-THERM-001-11 1.00061 0.00406 60744.4844 6.0782E+04 0.1176 IEU-COMP-THERM-001-12 1.00109 0.00405 61033.6662 6.1100E+04 0.0507 IEU-COMP-THERM-001-13 0.99990 0.00406 60744.4844 6.0738E+04 0.2683 IEU-COMP-THERM-001-14 0.99976 0.00406 60693.9749 6.0679E+04 0.3050 IEU-COMP-THERM-001-15 1.00229 0.00406 60744.4844 6.0884E+04 0.0051 IEU-COMP-THERM-001-16 1.00334 0.00406 60794.3388 6.0997E+04 0.1089 IEU-COMP-THERM-001-17 1.00417 0.00407 60322.3627 6.0574E+04 0.2837

Design Analyses and Calculation Page 44 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 File Name keff 1/()2 Weighted keff Weighted Variance IEU-COMP-THERM-001-18 1.00526 0.00407 60322.3627 6.0640E+04 0.6405 IEU-COMP-THERM-001-19 1.00510 0.00406 60538.5509 6.0847E+04 0.5812 IEU-COMP-THERM-001-20 1.00879 0.00406 60794.3388 6.1329E+04 2.8016 IEU-COMP-THERM-001-21 1.00313 0.00405 60843.5348 6.1034E+04 0.0775 IEU-COMP-THERM-001-26 1.00772 0.00405 60939.9376 6.1410E+04 1.9928 IEU-COMP-THERM-001-27 1.00213 0.00406 60744.4844 6.0874E+04 0.0010 IEU-COMP-THERM-001-28 1.01109 0.00405 60843.5348 6.1518E+04 5.0257 IEU-COMP-THERM-001-29 1.00773 0.00406 60744.4844 6.1214E+04 1.9934 IEU-COMP-THERM-002-01 0.99866 0.00393 64882.4006 6.4796E+04 0.7236 IEU-COMP-THERM-003-01 1.00371 0.00561 31808.2345 3.1926E+04 0.0926 IEU-COMP-THERM-003-02 1.00403 0.00561 31802.4685 3.1931E+04 0.1310 IEU-COMP-THERM-15-04 0.99721 0.00320 97519.1137 9.7248E+04 2.2342 IEU-COMP-THERM-15-05 0.99644 0.00310 103927.4171 1.0356E+05 3.2104 IEU-COMP-THERM-15-07 0.99597 0.00360 77060.0066 7.6750E+04 2.8012 IEU-COMP-THERM-15-08 0.99899 0.00440 51607.8423 5.1556E+04 0.4684 IEU-COMP-THERM-15-09 0.99848 0.00470 45234.7457 4.5166E+04 0.5614 IEU-COMP-THERM-15-10 0.99817 0.00450 49334.9647 4.9245E+04 0.7246 IEU-COMP-THERM-15-11 1.00201 0.00500 39968.6646 4.0049E+04 0.0000 IEU-COMP-THERM-15-12 1.00253 0.00510 38417.8013 3.8515E+04 0.0109 IEU-MET-FAST-003-01 1.00305 0.00192 271525.1568 2.7235E+05 0.2985 IEU-MET-FAST-004-01 1.00762 0.00321 96965.9359 9.7705E+04 3.0610 IEU-MET-FAST-005-01 1.00163 0.00232 186466.2776 1.8677E+05 0.0257 IEU-MET-FAST-006-01 0.99647 0.00252 158017.8244 1.5746E+05 4.8350 IEU-MET-FAST-009-01 1.01098 0.00531 35507.7069 3.5898E+04 2.8624 IEU-SOL-THERM-002-01 1.00911 0.00260 147501.3275 1.4884E+05 7.4457 IEU-SOL-THERM-002-02 0.99971 0.00320 97495.3446 9.7467E+04 0.5119 IEU-SOL-THERM-002-03 1.00018 0.00380 69204.1522 6.9217E+04 0.2296 IEU-SOL-THERM-002-04 1.00165 0.00460 47240.8955 4.7319E+04 0.0059 IEU-SOL-THERM-002-05 1.00562 0.00420 56607.1914 5.6925E+04 0.7396 IEU-SOL-THERM-002-07 1.00136 0.00320 97469.6869 9.7602E+04 0.0400 IEU-SOL-THERM-002-08 1.00434 0.00420 56657.2238 5.6903E+04 0.3103 IEU-SOL-THERM-002-09 1.00840 0.00540 34286.0278 3.4574E+04 1.4033 IEU-SOL-THERM-002-10 1.00186 0.00380 69194.0964 6.9323E+04 0.0014 IEU-SOL-THERM-002-11 1.00456 0.00480 43387.5244 4.3585E+04 0.2836 IEU-SOL-THERM-002-12 1.00393 0.00420 56650.4835 5.6873E+04 0.2103 IEU-SOL-THERM-002-13 1.00675 0.00420 56626.4242 5.7009E+04 1.2772 IEU-SOL-THERM-004-01 1.00030 0.00410 59408.8816 5.9427E+04 0.1725

Design Analyses and Calculation Page 45 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 File Name keff 1/()2 Weighted keff Weighted Variance LEU-COMP-THERM-022-01 1.00318 0.00461 47058.8235 4.7208E+04 0.0654 LEU-COMP-THERM-022-02 1.00647 0.00461 47058.8235 4.7363E+04 0.9396 LEU-COMP-THERM-022-03 1.00688 0.00361 76663.0124 7.7190E+04 1.8245 LEU-COMP-THERM-022-04 1.00808 0.00371 72536.8306 7.3123E+04 2.6801 LEU-COMP-THERM-022-05 1.00308 0.00381 68851.0820 6.9063E+04 0.0801 LEU-COMP-THERM-022-06 1.00154 0.00461 47130.6840 4.7203E+04 0.0100 LEU-COMP-THERM-022-07 1.00455 0.00461 47108.4814 4.7323E+04 0.3060 LEU-COMP-THERM-023-01 0.99522 0.00441 51444.5633 5.1199E+04 2.3659 LEU-COMP-THERM-023-02 0.99798 0.00441 51429.4825 5.1326E+04 0.8317 LEU-COMP-THERM-023-03 0.99952 0.00441 51444.5633 5.1420E+04 0.3168 LEU-COMP-THERM-023-04 1.00116 0.00441 51444.5633 5.1504E+04 0.0364 LEU-COMP-THERM-023-05 1.00235 0.00441 51429.4825 5.1550E+04 0.0062 LEU-COMP-THERM-023-06 1.00244 0.00441 51486.6778 5.1612E+04 0.0099 LEU-COMP-THERM-024-01 1.00068 0.00541 34194.9316 3.4218E+04 0.0597 LEU-COMP-THERM-024-02 1.00805 0.00401 62195.2433 6.2696E+04 2.2754 LEU-COMP-THERM-032-01 1.00163 0.00451 49149.4684 4.9230E+04 0.0068 LEU-COMP-THERM-032-04 1.00288 0.00371 72659.1053 7.2868E+04 0.0561 LEU-COMP-THERM-032-07 1.00448 0.00451 49242.6481 4.9463E+04 0.3025 LEU-SOL-THERM-06-01 0.99783 0.00371 72536.8306 7.2379E+04 1.2623 LEU-SOL-THERM-06-02 1.00341 0.00381 68823.1246 6.9058E+04 0.1365 LEU-SOL-THERM-06-03 0.99780 0.00411 59150.2475 5.9020E+04 1.0442 LEU-SOL-THERM-06-04 0.99920 0.00411 59192.2624 5.9145E+04 0.4646 LEU-SOL-THERM-06-05 1.00078 0.00471 45097.6590 4.5133E+04 0.0673 LEU-SOL-THERM-08-72 1.00221 0.00142 498977.0970 5.0008E+05 0.0217 LEU-SOL-THERM-08-74 1.00092 0.00151 436681.2227 4.3708E+05 0.5110 LEU-SOL-THERM-08-76 1.00149 0.00142 498977.0970 4.9972E+05 0.1305 LEU-SOL-THERM-08-78 1.00221 0.00142 498977.0970 5.0008E+05 0.0217 LEU-SOL-THERM-09-92 1.00004 0.00142 497908.7831 4.9793E+05 1.9157 LEU-SOL-THERM-09-93 1.00093 0.00142 498977.0970 4.9944E+05 0.5728 LEU-SOL-THERM-09-94 1.00139 0.00142 498977.0970 4.9967E+05 0.1865 kmean 1.0020 1/()2 1/()2keff 1.0000 8.5065E+06 8.5235E+06 (mean)2 S2 St K*

USL 9.8748E-06 6.1730E-06 4.0060E-03 1.952 0.9422

Design Analyses and Calculation Page 46 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 5.3.3.

Combined LEU, IEU and HEU Enrichments As the data are judged to be from a normal distribution the bias and bias uncertainty is represented with a Lower Tolerance Limit (LTL). The USL calculation for MCNP 6.1 (0.9409) is developed in Table 8. Note that the positive bias of 0.0011 is set to zero.

Table 8 - Combined USL File Name keff 1/()2 Weighted keff Weighted Variance HEU-COMP-FAST-02 1.0016 0.0007 2102607.2330 2.1060E+06 0.4936 HEU-COMP-INTER-03-02 1.0051 0.0061 26817.9917 2.6955E+04 0.4274 HEU-COMP-INTER-03-03 1.0048 0.0056 31802.4685 3.1954E+04 0.4265 HEU-COMP-INTER-03-04 1.0028 0.0055 32972.3955 3.3065E+04 0.0933 HEU-COMP-INTER-03-05 0.9979 0.0047 45085.6628 4.4991E+04 0.4698 HEU-MET-FAST-001 0.9996 0.0010 949757.8118 9.4939E+05 2.1595 HEU-MET-INTER-006-01 0.9956 0.0009 1358511.0719 1.3526E+06 40.6166 HEU-MET-INTER-006-02 0.9964 0.0009 1346982.7586 1.3422E+06 29.5972 HEU-MET-INTER-006-03 0.9985 0.0010 1072386.0590 1.0707E+06 7.6196 HEU-SOL-THERM-007-01 1.0110 0.0035 79935.4122 8.0811E+04 7.7274 HEU-SOL-THERM-007-03 1.0060 0.0035 79935.4122 8.0418E+04 1.9366 HEU-SOL-THERM-007-07 1.0031 0.0035 79935.4122 8.0182E+04 0.3109 HEU-SOL-THERM-007-11 1.0072 0.0035 79595.0205 8.0165E+04 2.9058 HEU-SOL-THERM-007-14 1.0069 0.0035 79595.0205 8.0147E+04 2.6888 HEU-SOL-THERM-012-01 1.0010 0.0058 29606.0325 2.9635E+04 0.0006 HEU-SOL-THERM-27-01 0.9968 0.0046 46849.5987 4.6701E+04 0.8654 HEU-SOL-THERM-27-02 0.9967 0.0043 53572.1939 5.3397E+04 1.0315 HEU-SOL-THERM-27-03 0.9975 0.0037 72116.7715 7.1938E+04 0.9335 HEU-SOL-THERM-27-04 0.9983 0.0037 72202.1661 7.2079E+04 0.5774 HEU-SOL-THERM-27-05 0.9962 0.0044 51208.2589 5.1014E+04 1.2335 HEU-SOL-THERM-31-01 0.9970 0.0046 46938.6606 4.6796E+04 0.8115 HEU-SOL-THERM-31-02 1.0080 0.0058 29592.7155 2.9829E+04 1.3935 HEU-SOL-THERM-31-03 0.9970 0.0058 29592.7155 2.9503E+04 0.5116 HEU-SOL-THERM-31-04 1.0015 0.0068 21551.7241 2.1585E+04 0.0037 HEU-SOL-THERM-35-01 1.0005 0.0031 102596.7231 1.0265E+05 0.0343 HEU-SOL-THERM-35-02 1.0034 0.0032 96435.7352 9.6761E+04 0.4891 HEU-SOL-THERM-35-03 1.0043 0.0030 109619.0737 1.1008E+05 1.0754 HEU-SOL-THERM-35-04 1.0037 0.0030 109533.8240 1.0994E+05 0.7360 HEU-SOL-THERM-35-05 1.0023 0.0033 90223.3931 9.0428E+04 0.1198 HEU-SOL-THERM-35-06 1.0037 0.0029 116230.4152 1.1666E+05 0.7570 HEU-SOL-THERM-35-07 1.0051 0.0035 80186.6746 8.0594E+04 1.2588 HEU-SOL-THERM-35-08 0.9987 0.0038 68208.6366 6.8121E+04 0.3955

Design Analyses and Calculation Page 47 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 File Name keff 1/()2 Weighted keff Weighted Variance HEU-SOL-THERM-35-09 0.9997 0.0041 58716.8030 5.8702E+04 0.1115 HEU-SOL-THERM-38-01 0.9955 0.0025 159081.1473 1.5837E+05 5.0029 HEU-SOL-THERM-38-02 0.9970 0.0025 159081.1473 1.5860E+05 2.7238 HEU-SOL-THERM-38-07 0.9979 0.0032 97276.2646 9.7070E+04 1.0198 HEU-SOL-THERM-38-08 0.9986 0.0026 147058.8235 1.4685E+05 0.9697 HEU-SOL-THERM-38-09 0.9985 0.0033 91491.3083 9.1358E+04 0.6080 HEU-SOL-THERM-38-10 0.9970 0.0026 147058.8235 1.4662E+05 2.4455 HEU-SOL-THERM-38-11 0.9966 0.0025 158982.5119 1.5844E+05 3.2738 HEU-SOL-THERM-38-12 0.9963 0.0025 158982.5119 1.5840E+05 3.6597 HEU-SOL-THERM-38-17 0.9969 0.0026 147058.8235 1.4661E+05 2.5669 HEU-SOL-THERM-38-18 0.9974 0.0032 97276.2646 9.7025E+04 1.3302 HEU-SOL-THERM-46-01 1.0128 0.0029 117807.8319 1.1931E+05 16.0113 HEU-SOL-THERM-46-02 1.0094 0.0029 117884.2141 1.1899E+05 8.0270 HEU-SOL-THERM-46-03 1.0099 0.0029 117728.7764 1.1889E+05 9.0574 HEU-SOL-THERM-46-04 1.0108 0.0029 117807.8319 1.1908E+05 11.0166 HEU-SOL-THERM-46-05 1.0087 0.0030 110082.4518 1.1104E+05 6.2627 HEU-SOL-THERM-46-06 1.0100 0.0029 117647.0588 1.1883E+05 9.3420 HEU-SOL-THERM-46-07 1.0109 0.0031 103216.2173 1.0434E+05 9.8123 HEU-SOL-THERM-46-08 1.0102 0.0032 96748.2900 9.7737E+04 8.0133 HEU-SOL-THERM-46-09 1.0096 0.0037 72568.9405 7.3265E+04 5.2081 HEU-SOL-THERM-46-10 1.0075 0.0029 117562.6903 1.1844E+05 4.7911 HEU-SOL-THERM-46-11 1.0103 0.0028 125906.5270 1.2720E+05 10.5431 HEU-SOL-THERM-46-12 1.0094 0.0029 117562.6903 1.1867E+05 8.0439 HEU-SOL-THERM-46-13 1.0089 0.0030 109861.1355 1.1083E+05 6.5855 IEU-COMP-THERM-001-01 1.0021 0.0041 60744.4844 6.0870E+04 0.0551 IEU-COMP-THERM-001-02 1.0047 0.0041 60744.4844 6.1028E+04 0.7621 IEU-COMP-THERM-001-03 0.9987 0.0041 60744.4844 6.0667E+04 0.3493 IEU-COMP-THERM-001-04 1.0000 0.0041 60485.4563 6.0487E+04 0.0716 IEU-COMP-THERM-001-05 1.0053 0.0040 61079.5194 6.1402E+04 1.0581 IEU-COMP-THERM-001-06 1.0034 0.0041 60693.9749 6.0901E+04 0.3189 IEU-COMP-THERM-001-07 1.0015 0.0041 60485.4563 6.0577E+04 0.0098 IEU-COMP-THERM-001-08 0.9998 0.0041 60794.3388 6.0785E+04 0.0993 IEU-COMP-THERM-001-09 1.0084 0.0041 60693.9749 6.1204E+04 3.2274 IEU-COMP-THERM-001-10 1.0014 0.0041 60591.0047 6.0678E+04 0.0063 IEU-COMP-THERM-001-11 1.0006 0.0041 60744.4844 6.0782E+04 0.0157 IEU-COMP-THERM-001-12 1.0011 0.0040 61033.6662 6.1100E+04 0.0000 IEU-COMP-THERM-001-13 0.9999 0.0041 60744.4844 6.0738E+04 0.0901

Design Analyses and Calculation Page 48 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 File Name keff 1/()2 Weighted keff Weighted Variance IEU-COMP-THERM-001-14 0.9998 0.0041 60693.9749 6.0679E+04 0.1119 IEU-COMP-THERM-001-15 1.0023 0.0041 60744.4844 6.0884E+04 0.0835 IEU-COMP-THERM-001-16 1.0033 0.0041 60794.3388 6.0997E+04 0.3002 IEU-COMP-THERM-001-17 1.0042 0.0041 60322.3627 6.0574E+04 0.5619 IEU-COMP-THERM-001-18 1.0053 0.0041 60322.3627 6.0640E+04 1.0350 IEU-COMP-THERM-001-19 1.0051 0.0041 60538.5509 6.0847E+04 0.9600 IEU-COMP-THERM-001-20 1.0088 0.0041 60794.3388 6.1329E+04 3.5784 IEU-COMP-THERM-001-21 1.0031 0.0041 60843.5348 6.1034E+04 0.2463 IEU-COMP-THERM-001-26 1.0077 0.0041 60939.9376 6.1410E+04 2.6562 IEU-COMP-THERM-001-27 1.0021 0.0041 60744.4844 6.0874E+04 0.0622 IEU-COMP-THERM-001-28 1.0111 0.0041 60843.5348 6.1518E+04 6.0505 IEU-COMP-THERM-001-29 1.0077 0.0041 60744.4844 6.1214E+04 2.6557 IEU-COMP-THERM-002-01 0.9987 0.0039 64882.4006 6.4796E+04 0.3914 IEU-COMP-THERM-003-01 1.0037 0.0056 31808.2345 3.1926E+04 0.2134 IEU-COMP-THERM-003-02 1.0040 0.0056 31802.4685 3.1931E+04 0.2700 IEU-COMP-THERM-15-04 0.9972 0.0032 97519.1137 9.7248E+04 1.4855 IEU-COMP-THERM-15-05 0.9964 0.0031 103927.4171 1.0356E+05 2.2707 IEU-COMP-THERM-15-07 0.9960 0.0036 77060.0066 7.6750E+04 2.0403 IEU-COMP-THERM-15-08 0.9990 0.0044 51607.8423 5.1556E+04 0.2339 IEU-COMP-THERM-15-09 0.9985 0.0047 45234.7457 4.5166E+04 0.3151 IEU-COMP-THERM-15-10 0.9982 0.0045 49334.9647 4.9245E+04 0.4290 IEU-COMP-THERM-15-11 1.0020 0.0050 39968.6646 4.0049E+04 0.0320 IEU-COMP-THERM-15-12 1.0025 0.0051 38417.8013 3.8515E+04 0.0770 IEU-MET-FAST-003-01 1.0031 0.0019 271525.1568 2.7235E+05 1.0136 IEU-MET-FAST-004-01 1.0076 0.0032 96965.9359 9.7705E+04 4.0995 IEU-MET-FAST-005-01 1.0016 0.0023 186466.2776 1.8677E+05 0.0489 IEU-MET-FAST-006-01 0.9965 0.0025 158017.8244 1.5746E+05 3.4136 IEU-MET-FAST-009-01 1.0110 0.0053 35507.7069 3.5898E+04 3.4535 IEU-SOL-THERM-002-01 1.0091 0.0026 147501.3275 1.4884E+05 9.4129 IEU-SOL-THERM-002-02 0.9997 0.0032 97495.3446 9.7467E+04 0.1932 IEU-SOL-THERM-002-03 1.0002 0.0038 69204.1522 6.9217E+04 0.0609 IEU-SOL-THERM-002-04 1.0016 0.0046 47240.8955 4.7319E+04 0.0134 IEU-SOL-THERM-002-05 1.0056 0.0042 56607.1914 5.6925E+04 1.1454 IEU-SOL-THERM-002-07 1.0014 0.0032 97469.6869 9.7602E+04 0.0058 IEU-SOL-THERM-002-08 1.0043 0.0042 56657.2238 5.6903E+04 0.5888 IEU-SOL-THERM-002-09 1.0084 0.0054 34286.0278 3.4574E+04 1.8177 IEU-SOL-THERM-002-10 1.0019 0.0038 69194.0964 6.9323E+04 0.0380

Design Analyses and Calculation Page 49 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 File Name keff 1/()2 Weighted keff Weighted Variance IEU-SOL-THERM-002-11 1.0046 0.0048 43387.5244 4.3585E+04 0.5135 IEU-SOL-THERM-002-12 1.0039 0.0042 56650.4835 5.6873E+04 0.4475 IEU-SOL-THERM-002-13 1.0068 0.0042 56626.4242 5.7009E+04 1.7967 IEU-SOL-THERM-004-01 1.0003 0.0041 59408.8816 5.9427E+04 0.0400 LEU-COMP-THERM-022-01 1.0032 0.0046 47058.8235 4.7208E+04 0.2001 LEU-COMP-THERM-022-02 1.0065 0.0046 47058.8235 4.7363E+04 1.3480 LEU-COMP-THERM-022-03 1.0069 0.0036 76663.0124 7.7190E+04 2.5454 LEU-COMP-THERM-022-04 1.0081 0.0037 72536.8306 7.3123E+04 3.5159 LEU-COMP-THERM-022-05 1.0031 0.0038 68851.0820 6.9063E+04 0.2651 LEU-COMP-THERM-022-06 1.0015 0.0046 47130.6840 4.7203E+04 0.0084 LEU-COMP-THERM-022-07 1.0046 0.0046 47108.4814 4.7323E+04 0.5549 LEU-COMP-THERM-023-01 0.9952 0.0044 51444.5633 5.1199E+04 1.7895 LEU-COMP-THERM-023-02 0.9980 0.0044 51429.4825 5.1326E+04 0.5064 LEU-COMP-THERM-023-03 0.9995 0.0044 51444.5633 5.1420E+04 0.1314 LEU-COMP-THERM-023-04 1.0012 0.0044 51444.5633 5.1504E+04 0.0001 LEU-COMP-THERM-023-05 1.0024 0.0044 51429.4825 5.1550E+04 0.0781 LEU-COMP-THERM-023-06 1.0024 0.0044 51486.6778 5.1612E+04 0.0900 LEU-COMP-THERM-024-01 1.0007 0.0054 34194.9316 3.4218E+04 0.0066 LEU-COMP-THERM-024-02 1.0081 0.0040 62195.2433 6.2696E+04 2.9887 LEU-COMP-THERM-032-01 1.0016 0.0045 49149.4684 4.9230E+04 0.0129 LEU-COMP-THERM-032-04 1.0029 0.0037 72659.1053 7.2868E+04 0.2256 LEU-COMP-THERM-032-07 1.0045 0.0045 49242.6481 4.9463E+04 0.5566 LEU-SOL-THERM-06-01 0.9978 0.0037 72536.8306 7.2379E+04 0.7841 LEU-SOL-THERM-06-02 1.0034 0.0038 68823.1246 6.9058E+04 0.3616 LEU-SOL-THERM-06-03 0.9978 0.0041 59150.2475 5.9020E+04 0.6511 LEU-SOL-THERM-06-04 0.9992 0.0041 59192.2624 5.9145E+04 0.2177 LEU-SOL-THERM-06-05 1.0008 0.0047 45097.6590 4.5133E+04 0.0051 LEU-SOL-THERM-08-72 1.0022 0.0014 498977.0970 5.0008E+05 0.5954 LEU-SOL-THERM-08-74 1.0009 0.0015 436681.2227 4.3708E+05 0.0171 LEU-SOL-THERM-08-76 1.0015 0.0014 498977.0970 4.9972E+05 0.0691 LEU-SOL-THERM-08-78 1.0022 0.0014 498977.0970 5.0008E+05 0.5954 LEU-SOL-THERM-09-92 1.0000 0.0014 497908.7831 4.9793E+05 0.5785 LEU-SOL-THERM-09-93 1.0009 0.0014 498977.0970 4.9944E+05 0.0176 LEU-SOL-THERM-09-94 1.0014 0.0014 498977.0970 4.9967E+05 0.0370 kmean 1.0011 1/()2 1/()2keff 1.0000 1.9963E+07 1.9985E+07

Design Analyses and Calculation Page 50 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 File Name keff 1/()2 Weighted keff Weighted Variance (mean)2 S2 St K*

USL 7.0129E-06 1.6403E-05 4.8390E-03 1.8765 0.9409

6.

Area of Applicability With the use of the minimum USL for the IEU data set and with the observation that no trends exist in the combined LEU, IEU and HEU data set, it is judged that this validation may be conservatively used with the AoA of the combined data set. An exception is made in that the uranium enrichment is constrained to the values bracketed by the LEU-IEU data set.

This validation is appropriate for homogeneous and heterogeneous intermediate enriched uranium systems.

A summary of the area of applicability for these experiments is provided in Table 9. For systems outside the validation area of applicability, an increased MoS value may be warranted, depending on the specific problem being analyzed. The analyst must document any extrapolation beyond the validation area of applicability and justification must be made for any adjustments to the MoS when extrapolating.

Table 9 - Area of Applicability Summary Parameter Area of Applicability Fissile Material*

UO2, UH3, Metal, UO2(NO3)2, UF4, U-ZrH, UO2F2, UxOy, UO2SO4 Fissile Material Form Solid and Solution H/235U ratio*

0 H/235U 1400 Average Neutron Energy Causing Fission (MeV) 0.0027 < ANECF < 1.46 Enrichment*

10 to 36 wt.% 235U Moderating Materials*

None, Water, nitric acid, sulfuric acid, Hydrocarbon, CF2 Reflecting Materials None, Water, Concrete, BeO, Hydrocarbon Material, Iron, Graphite Absorber Materials*

Boron, Cadmium, Aluminium, Steel, Stainless Steel, Hydrocarbon Material Geometry Homogeneous and Heterogeneous Spheres, Hemispheres, Cylinders, Cuboids Single Units and Arrays

• See following text.

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Design Analyses and Calculation Page 51 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 6.1.

AoA Sensitivity - H/235U Ratio The H/235U ratio of the experiments has values ranging from 0 to 1611 and Figure 2 of Section 5.1.2 demonstrates that ratios up to an H/235U ratio of 1200 are well covered. However, above 1272 there is only one value. However, as described in Reference 5, a +/- 20% interpolation is considered acceptable for the ratio of moderator to fissile material in an AoA. Adding 20% to the 1200 value yields 1440. Therefore, given that Section 5.1.2 demonstrates that there is no trend between H/235U values and bias, it is judged herein that this validation can be conservatively used for the H/235U value range listed in Table 9.

6.2.

AoA Sensitivity - 235U Enrichment The enrichment range for the data set experiments ranges from 10 to 94 wt.% 235U, while the enrichment of greatest interest in SHINE criticality applications is approximately 20 wt.% 235U. Figure 4 of Section 5.1.4 shows the distribution of the bias as a function of enrichment and indicates that there is no trend and that values around 20% enrichment are well covered. Therefore, this validation is conservatively adjusted to use only the enrichment range listed in Table 9.

6.3.

AoA Sensitivity - U:O Ratio While the chemical form U3O8 is not utilized in any of the experiments herein, UO2 and other chemical forms containing a variety of U:O ratios are included. Additionally, Section 5.1.7 found no bias variability with chemical form. Therefore, this validation can be conservatively used for applications utilizing U3O8 or any other U:O ratio material.

6.4.

AoA Sensitivity - Sulfate Solution SHINE applications contain uranium in the chemical form of UO2SO4 and sulfate solution moderator (H2SO4-H2O). However, these are contained in only one IEU experiment, IEU-SOL-TERM-004.

Additional sulfate solution experiments are included with the HEU-SOL-THERM-046 data set. Since no trends in the parameters of interest were observed (see Section 5.1) it is judged that this validation (with the IEU USL) can be conservatively used with IEU and sulfate solutions.

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AoA Sensitivity - Boron Proprietary Information

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7.

References

1. International Handbook of Evaluated Criticality Safety Benchmark Experiments, NEA/NCS/DOC (95)03, Organization for Economic Cooperation and Development, September 2014.

2. MCNP6 USER MANUAL, LA-CP-13-00634. Rev.0, Los Alamos National Laboratory, May 2013.

3. Revolinski, S. M., Installation of MCNP6 on the Linux Computers, NSA-SMR-13-04, Rev. 0, September 2013.

4. Nuclear Criticality Safety in Operations with Fissionable Material Outside of Reactors, ANSI/ANS-8.1(2014), American Nuclear Society.

5. Forecast of Criticality Benchmark Experiments and Experimental Programs Needed to Support Nuclear Operations in the United States of America: 1994-1999, LA-12683 (Appendix E), Los Alamos, March, 1994.

6. Validation of Neutron Transport Methods for Nuclear Criticality Safety Calculations, ANSI/ANS-8.24-2007, American Nuclear Society.

7. Hollander, M., and D. A. Wolfe, Nonparametric Statistical Methods, John Wiley & Sons, 1973.

8. Statistical Methods for Nuclear Material Management, NUREG/CR-4604, PNL, December, 1988.

9. Natrella, M. G., Experimental Statistics, National Bureau of Standards Handbook 91, August, 1963.

10. J. C. Dean, R. W. Tayloe, NUREG/CR-6698, Guide for Validation of Nuclear Criticality Safety Calculational Methodology, January 2001.

11. Software Quality, Atkins-NS-QA-12, Rev. 7.

12. Berglund, M. And Wieser, M., Isotopic Compositions of the Elements 2009 (IUPAC Technical Report), Pure Appl. Chem. Vol. 83, No. 2, pp. 397-410, 2011.

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Design Analyses and Calculation Page 56 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 Appendix A.

Combined Data Normalcy Test Calculations Tables A1 through Table A3 present the calculations for the IEU data set normality tests for MCNP data from Section 5.2.1. Tables A4 through Table A6 present the calculations for the LEU-IEU data set normality tests for MCNP data from Section 5.2.2. Tables A7 through Table A9 present the calculations for the combined data set normality tests for MCNP data from Section 5.2.3.

Table A1 - IEU Data Set Modified Chi Square Normality Test Proprietary Information

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Design Analyses and Calculation Page 58 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 Proprietary Information Table A2 - IEU Data Set [ Propreitary Information ]

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Design Analyses and Calculation Page 64 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 Proprietary Information Table A5 - LEU-IEU Data Set [ Proprietary Information ]

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Design Analyses and Calculation Page 67 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 Table A6 - LEU - IEU Data Set [ Proprietary Information ]

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Design Analyses and Calculation Page 78 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 Table A9 - Combined Data Set [ Proprietary Information ]

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Design Analyses and Calculation Page 81 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 Proprietary Information

Design Analyses and Calculation Page 82 of 82 Atkins-NS-DAC-SHN-15-03 Rev. 2 Appendix B.

Electronic Copy of Input / Output Files A CD with all Input and output files is included with the original copy