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NWMl-2014-RPT-006, Northwest Medical Isotopes, LLC - MCNP 6.1 Validations with Continuous Energy ENDF/B-VII.1 Cross-Sections (Rev. 0) (Public Version)
	ML16344A054
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Site:	Northwest Medical Isotopes
Issue date:	11/28/2016
From:	Revolinski S; Atkins - Nuclear Solutions, Northwest Medical Isotopes
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NORTHW£SfM£DICALISOTOPES Report Cover Sheet Report No: NWMl-2014-RPT-006 Revision No: 0 Report Title: MCNP 6.1 Validations with Continuous Energy ENDF/B-Vll.1 Cross-Sections Project Title: NWMI Radioisotope Production Facility Status: D In Process ~Final Contains assumptions and/or inputs that require verification? 0Yes ~No Approvals

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Northwest Medical Isotopes, LLC Notice This document and its contents have been prepared and are intended solely for Northwest Medical Isotopes, LLC information and use in relati<;>n to Nuclear Criticality Safety evaluations.

Atkins NS assumes no responsibility to any other party in respect of or arising out of or in connection with this document and/or its contents.

This document has 66 pages including the cover.

Document History

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MCNP 6.1 Validation with Continuous Energy ENDF/B-Vll.1 Cross-Sections

.DoturYJ~nt r,eferenc¢ .* Atkins-NS-NMl-14-01 2

Northwest Medical Isotopes, LLC Table of Contents Chapter Pages Executive Summary............................................................................*.................................................. 5

1. Introduction ..................*....*.............*......*......................*.*......................................................... 6 1.1 . Limits of Applicability ................................................................................................................... 6

2. MCNP 6.1 Code .............................................................*..........................*................................. 7 2.1. MCNP Summary .......................................................................................................................... 7 2.2. ENDF/B-Vll.1 Cross Section Library ............................................................................................. 7

3. Validation Methodology ....................................................................*.............................*......*. 11 3.1. Establishment of an Upper Subcritical Limit (USL) ..................................................................... 12 3.2. Margin of Subcriticality ............................................................................................................... 13 3.3. Determination of the Area of Applicability ................................................................................... 13 3.4. Discussion of Statistical Analysis ............................................................................................... 13

4. Benchmark Experiment Descriptions ..................................................................................... 18 4.1. [Proprietary Information] ............................................................................................................ 18 4.2. [Proprietary Information] ............................................................................................................ 19 4.3. [Proprietary Information] ............................................................................................................ 22

5. .Evaluation Results ................................................................................................................... 25 5.1. Trend Evaluation ....................................................................................................................... 30 5.2. Normalcy Evaluation .................................................................................................................. 37 5.3. Bias and Bias Uncertainty Evaluation ......................................................................................... 43

6. Area of Applicability ............................................*.*......*.**......*.*.*......*....*.........*.....*.*.........**... 54

7. References ...................................................................................*........................................... 55 Appendices 57 Appendix A. Combined Data Normalcy Test Calculations ........................................................... 58 Appendix B. Electronic Copy of Input I Output Files .................................................................... 71 Tables Table 1 - Library Definitions for Various Elements .................................................................................... 7 Table 2 - Critical Benchmark Experiments Summary .............................................................................. 23 Table 3 - MCNP 6.1 Results Summary................................................................................................... 26 Table 4 - Normalcy Results Summary .................................................................................................... 37 Table 5 - LEU Results ............................................................................................................................ 38 Table 6 - IEU Normalcy ......................................................................................................................... 39 Table 7 - HEU Normalcy ........................................................................................................................ 41 Table 8 - USL Results Summary ............................................................................................................ 43 Table 9 - LEU USL ................................................................................................................................ 43 Table 10 - IEU USL ............................................................................................................................... 45 Table 11 - HEU USL .............................................................................................................................. 48 Table 12 - Combined USL ..................................................................................................................... 49 Table 13 - Area of Applicability Summary ............................................................................................... 54 3

Northwest Medical Isotopes, LLC Figures Figure 1 - ANECF Trend ........................................................................................................................ 31 Figure 2 - Hl235 U Trend .......................................................................................................................... 32 Figure 3 - ANECF vs. Hl235 U 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 - Combined Group Distribution ................................................................................................. 42 List of Terms ANECF Averaae Neutron Enerav Causina Fission rMeVl Ao A Area of Aoolicabilitv cm centimeter ENDF Evaluated Nuclear Data File Hf235U Ratio of hydroaen to 235 U number densities in a material HIX Ratio of hydrogen to fissile nuclide number densities in a material HEU Hiah Enrichment Uranium IEU Intermediate Enrichment Uranium in inch LANL Los Alamos National Laboratory LEU Low Enrichment Uranium LTL Lower Tolerance Limit MeV Million Electron Volt Mos Margin of Subcriticality NPM Non-Parametric Margin NWMI Northwest Medical Isotopes, LLC pcm per cent mille USL Uooer Subcritical Limit VNllEF All Russian Research Institute of Experimental Physics (Russian)

ZAID Nuclide identifier 4

Northwest Medical Isotopes, LLC Executive Summary This report documents the methodology and results for the MCNP 6.1 code system validation for its use with the Northwest Medical Isotopes, LLC (NWMI) applications. Criticality safety experiments were selected from the International Handbook of Evaluated Criticality Safety Benchmark Experiments that adequately match the uranium enrichment, geometry, moderator, reflector, and neutron energy relevant to the NWMI applications. The bias results demonstrate that the calculated values matched the reality of the experiments. The final validation is expressed as an Upper Subcritical Limit (USL) calculated using the statistical accumulation of the experiment's bias and bias uncertainty. MCNP 6.1 calculations of NWMI applications should result in values less than [Proprietary Information] to ensure criticality safety of the application.

The primary focus of this validation is to determine the bias and bias uncertainty for intermediate enriched uranium (IEU) systems (about 20%), however sufficient experiments for low enriched uranium (LEU) and high enriched uranium (HEU) are included to demonstrate that there is no variation in the USL with varying enrichment. Similarly, the primary focus of this validation is upon thermal neutron energy systems, however sufficient experiments for intermediate and fast energy experiments are included to demonstrate that there is no variation in the USL with increasing neutron energy.

The recommended USL for the NWMI applications with approximately 20% wt. % 235 U material is

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The physical parameters of the NWMI applications bounded by this validation are shown below.

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A1Kln5 1v1v1~r u. 1 va11aation with Continuous Energy ENDF/B-Vll.1 Cross Sections Atkins-NS-NMl-14-01 5

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1. Introduction Nuclear criticality safety analysis is performed for fissile material systems for the Northwest Medical Isotopes, LLC 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 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.

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 Northwest Medical Isotopes, LLC operations, statistical evaluation of the calculation results, and the code bias and bias uncertainty. The validation is conducted using the ENDF/B-Vll.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 I 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 operations. Applications using the bias and bias uncertainty established for this experiment data set must use the modeling conventions described in Table 1 or have the Upper Subcritical Limit (USL) reduced. The benchmark calculations were performed on the Atkin's Linux computer cluster (Reference 3), therefore the validation conclusions herein are applicable to this computer.

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Atkins MCNP 6.1 Validation with Continuous Energy ENDF/B-Vll.1 Cross Sections Atkins-NS-NMl-14-01 6

Northwest Medical Isotopes, LLC

2. MCNP 6.1 Code The verification of MCNP 6.1 has been completed on the Atkins' system. The Atkins' system is a computer cluster composed of several servers that use Intel processors running the Fedora Linux operating system.

MCNP 6.1 has been installed in the read only disk area; the installation has been verified with the execution of the sample problems (Reference 2).

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. 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-Vll.1) are accounted for. Thermal neutrons are described by both the free gas and S(a,j3) models. For photons, the code accounts for incoherent and coherent scattering, the possibility of fluorescent emission after photoelectric absorption, absorption in pair production with local emission of annihilation radiation, and bremsstrahlung. A continuous-slowing-down model is used for electron transport that includes positrons, k x-rays, and bremsstrahlung, but does not include external or self-induced fields.

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-Vll.1 Cross Section Library The ENDF/B-Vll.1 cross-section library is used for the critical experiment calculations in this validation analysis. This library contains data for all nuclides (more than 300). 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 poly (poly.20t) S(a,j3) correction are used for graphite, water and hydrocarbon materials respectively.

Table 1 - Library Definitions for Various Elements

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Hydrogen 1001 Boron 5010 0.199 5011 0.801 Carbon 6000 Nitrogen 7014 0.9963 7015 0.0037 Oxygen 8016

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Atkins MCNP 6.1 Validation with Continuous Energy ENDF/B-Vll.1 Cross Sections Atkins-NS-NMl-14-01 7

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Sodium 11023 Magnesium 12024 0.78990 12025 0.10000 12026 0.11010 Aluminum 13027 Silicon 14028 0.92223 14029 0.04685 14030 0.03092 Phosphorus 15031 Sulfur 16032 0.9502 16033 0.0075 16034 0.0421 Chlorine 17035 0.7576 17037 0.2424 Potassium 19039 0.92223 19040 0.04685 19041 0.03092 Calcium 20040 0.96940 20042 0.00647 20043 0.00135 20044 0.02087 20046 0.00004 20048 0.00187 Titanium 22046 0.08250 22047 0.07440 Atkins MCNP 6.1 Validation with Continuous Energy ENDF/B-Vll.1 Cross Sections Atkins-NS-NMl-14-01 8

Northwest Medical Isotopes, LLC

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22048 0.73720 22049 0.05410 22050 0.05400 Chromium 24050 0.04345 24052 0.83789 24053 0.09501 24054 0.02365 Manganese 25055 Iron 26054 0.05845 26056 0.91754 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 I ***--- ---- ~- -

Atkins MCNP 6.1 Validation with Continuous Energy ENDF/B-Vll.1 Cross Sections Atkins-NS-NMl-14-01 9

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Zirconium 40090 0.51450 40091 0.11220 40092 0.17150 40094 0.17380 40096 0.02800 Niobium 41093 Molybdenum 42092 0.14530 42094 0.09150 42095 0.15840 42096 0.16670 42097 0.09600 42098 0.24390 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

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Gadolinium 64152 0.002 64154 0.0218 64155 0.1480 64156 0.2047 64157 0.1565 64158 0.2484 64160 0.2186 Tantalum 73181 Tungsten 74180 0.0012 74182 0.265 74183 0.1431 74184 0.3064 74185 0.2843 Gold 79197 Uranium 92234 92235 Specified by individual experiments.

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3. Validation Methodology ANSl/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

- -

Atkins MCNP 6.1 Validation with Continuous Energy ENDF/B-Vll.1 Cross Sections Atkins-NS-NMl-14-01 11

Northwest Medical Isotopes, LLC either a positive or negative bias. A positive bias occurs when the computations tend to report a higher keff 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).

ANSl/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 perfonning 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 detennined by statistical analysis of the calculated keffs from the benchmark critical experiments.

3.1. Establishment of an Upper Subcritical Limit (USL)

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

-keff =1.0 - Bias and K*St =Bias Uncertainty gives:

USL = keff - K.St - MoS where: USL = Maximum subcritical value of keff

-keff = 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 S2 = variance about the mean Mos = margin of subcriticality (0.05 for NWMI)

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

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

As defined, the USL explicitly incorporates a Margin of Subcriticality, which is required per ANSl/ANS-8.1.

The Margin of Subcriticality is an additional safety factor which is applied to the statistically calculated limit (e.g., a lower tolerance limit).

Atkins MCNP 6.1 Validation with Continuous Energy ENDF/B-Vll.1 Cross Sections Atkins-NS-NMl-14-01 12

Northwest Medical Isotopes, LLC 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.

3.2. Margin of Subcriticality The margin of subcriticality is an administrative addition in Ak applied to nuclear criticality safety calculations. The Margin of Subcriticality (MoS) is site specific and usually contained in the fuel facility license or other regulatory authorization basis. The Mos value for NWMI applications is 0.05.

For systems which are outside the validation area of applicability, an increased margin of subcriticality 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 insures 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, with a proscribed 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, the modified Chi Square test, Kolmogorov-Smirnov test, Lillifores test or the Shapiro-Wilk test may be utilized. The modified Chi Square and Kolmogorov-Smirnov tests may be used to test for normality regardless of the number of data points. The Lilliefors test for normality is performed for cases with greater than 50 data points, while the Shapiro-Wilk test for normality is performed for cases with less than or equal to 50 data points. The methodology for these tests can be found in NUREG/CR-4604 (Reference 8) and Natrella (Reference 9).

For the modified Chi Square test, the critical experiment data are ordered and grouped into classes. For each class, the data range midpoint (mi) and data point frequency (Oi) are recorded. The method of moments is used to estimate the mean(µ) and the variance (a 2):

Atkins MCNP 6.1 Validation with Continuous Energy ENDF/B-Vll.1 Cross Sections Atkins-NS-NMl-14-01 13

Northwest Medical Isotopes, LLC

-2 _. [ ""'Ojmj c

a - L . i - - -µ 2] -2 j=l n Where c is the number of classes in which the experimental data are grouped. The expected values Ei are then computed for a normal distribution with mean µ and variance a 2. The test statistic is computed using the following:

x*= [ L~ c o~

j=l EJ l -n x* is compared to xf-a (c-k-I) obtained from Table A4 of Reference 8; k is the number of unspecified parameters and a is 0.05. If x* is less than xl-a(c-k-I), the hypothesis that the data is from a normal distribution is supported.

For the Kolmogorov-Smirnov test, the empirical cumulative distribution function (cdf) G(x) from the random sample is compared with the hypothesized cdf F*(x). The empirical cdf is a function of x, which equals the fractions of the observations Xi that are less than or equal to x for each x, - 00 <x< 00

The test statistic is calculated as follows:

r* = suplF* (x) - G(x)I x

The supremum requires comparing F*(x) to G(x) both just before and just after each step in G(x). Both f *(x; )- G(x; )I and f *(x;) -G(x;_ )I1 are calculated and T* is the largest of the absolute differences over all i. If T* is less than W1-a. (determined from Table A 17 in Reference 8), the hypothesis that the data are from a normal distribution is supported.

For the Lilliefors test, the standardized sample values are calculated:

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1 s where: x = sample mean s = sample standard deviation The test consists of letting F*(z) be the standard normal cumulative distribution function (cdf) and then comparing it to the empirical cdf of the ZiS, denoted by G(z). The Lilliefors test statistic is the greatest difference between F*(z) and G(z), i.e.

Atkins MCNP 6.1 Validation with Continuous Energy ENDF/B-Vll.1 Cross Sections Atkins-NS-NMl-14-01 14

Northwest Medical Isotopes, LLC T* = suplF*(=)-G(=)I z

T* is the largest of all values IF*(zi) - G(Zi)I or IF*(zi) - G(Zi-1)1. Values of F*(zi) are obtained from Table A3 in Reference 8. The table consists of values for the cumulative standard normal distribution. T* is compared to w1-c., obtained from Table A 18 of Reference 8. The variable w1-c. is dependent on the sample size as well as the desired level of significance. If T* is less than W1-<<, the data are probably from a normal distribution.

For the Shapiro-Wilk test, the sample observations are ordered from smallest to largest. The test statistic is given by:

W*= b2 (n-l)s 2 k

where: b = Lai(x<n-i+l) -x!

i=l s = the sample standard deviation k = n/2 if n is even or (n-1 )/2 if n is odd ai =coefficients (which depend on n) obtained from Table A19 of Reference 8 W* is compared to w,., obtained from Table A20 of Reference 8. The variable w,. is dependent on the number of sample observations and the desired level of significance. If W* is greater than w,., the data are probably from a normal 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 is taken from NUREG/CR-6698.

It should be noted that this approach is more conservative than other methods for dealing with non-normal data distribution, for example calculating a distribution-free confidence interval based on the sign test (Thompson, Savur) as presented in Hollander and Wolfe (Reference 7).

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 an Upper Subcritical Limit (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 margin of subcriticality to define the USL. The USL is defined by the following:

USL = keir - K*St - MoS where: USL= Maximum subcritical value of keir

-

keir = weighted mean keir 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)

-Atkins MCNP-6.1 Validation with Continuous Energy ENDF/B-Vll.1 Cross Sections Atkins-NS-NMl-14-01 15

Northwest Medical Isotopes, LLC 1

L.2keff;

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uJ where: Os= Monte Carlo statistical uncertainty associated with the calculation, Oe = experimental uncertainty associated with the benchmark experiment, cr2 = average uncertainty The statistical uncertainty, Os, is the standard deviation calculated by the code and reported in the output for each benchmark experiment. If available, the experimental uncertainty, Oe, 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:

Zp +~z; -ab K*=------

a where z2 a=l--~r-2(N-l)

Atkins MCNP 6.1 Validation with Continuous Energy ENDF/8-Vll.1 Cross Sections Atkins-NS-NM 1-14-01 16

Northwest Medical Isotopes, LLC 2

z zr b=z - -

P N And z P and z r values are the critical values from the normal distribution that is exceeded with specified probability (P = 95% and y = 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 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:

m-1 I

/3 = 1-" L.J n.

"I(n - }")I*

(1-q

)j q

n-j j=O ).

where:

13 = level of confidence, q= the desired population fraction (0.95 for this validation),

n= the number of data in one data sample, m= the rank order indexing from the smallest sample to the largest (m=1 for the smallest sample). Non-parametric techniques do not require reliance upon distributions, but are rather an analysis of ranks, j= the ranked sample in the sample population being evaluated.

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:

13 = 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: Si = standard deviation corresponding to the smallest keff value in the data set NPM = non-parametric margin, determined from j3 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.

I Atkins MCNP 6: fValidation with Continuous Energy ENDF/B-Vll.1 Cross Sections Atkins-NS-NMl-14-01 17

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4. Benchmark Experiment Descriptions The input files are specifically developed for MCNP 6.1 and the continuous energy ENDF/B-Vll.1 cross section library. Ninety-two benchmark cases are modeled. The majority are in the thermal neutron energy range, however some bridge into intermediate and fast energy ranges. The ANECF ranges from 0.0043 to 1.46 MeV. The majority of the experiments are intermediate 235 U enrichment; however sufficient low and high enriched experiments are included to allow these to be included in the AoA. A broad range of chemical forms and metal are included to evaluate potential bias from the physical form. Additionally, the cases are fairly evenly split between homogeneous and heterogeneous physical forms. Hydrogen identified in water is modeled with the water lwtr.20t S(a,j3) while hydrogen in hydrocarbon materials is modeled with the poly.20t S(a,j3). Graphite is modeled with the grph.20t S(a,j3).

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[Proprietary Information]

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4.2. [Proprietary Information]

4.2.1. [Proprietary Information]

[Proprietary Information]

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[Proprietary Information]

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[Proprietary Information]

4.2.2. [Proprietary Information]

[Proprietary Information]

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4.3.3. Input Summary Tabulation The characteristics of the benchmark experiments from Reference 1 are tabulated in Table 2. The H/2 35 U 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 cr.

Table 2 - Critical Benchmark Experiments Summary

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Northwest Medical Isotopes, LLC

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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 kett results divided by the Reference 1 experimental results shown in Table 3.

Atkins MCNP 6.1 Validation with Continuous Energy ENDF/B-Vll.1 Cross Sections Atkins-NS-NMl-14-01 25

Northwest Medical Isotopes, LLC Table 3 - MCNP 6.1 Results Summary

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Northwest Medical Isotopes, LLC

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Atkins MCNP 6.1 Validation with Continuous Energy ENDF/B-Vll.1 Cross Sections Atkins-NS-NMl-14-01 27

Northwest Medical Isotopes, LLC

- *. MCNP 6.1 Calculation

Benchmark. Values NormaUzed Results

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Atkins MCNP 6.1 Validation with Continuous Energy ENDF/B-Vll.1 Cross Sections Atkins-NS-NMl-14-01 29

Northwest Medical Isotopes, LLC

~enchmark Values. :Nqrrnalized Results :

* ' .. ANECF . '.

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[Proprietary Information] [Proprietary [Proprietary [Proprietary [Proprietary [Proprietary [Proprietary [Proprietary Information] Information] Information] Information] Information] Information] Information]

The results of each enrichment group are examined for normality. The Shapiro-Wilk test (Section 3.4.1) is used to test the k-normalized values for normality within each subgroup of experiments. 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 of the pooled data are shown in Section 5.2.4.

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 (HIX), the Average Neutron Energy Causing Fission (ANECF), the 235 U enrichment, the moderator material, the reflector material and the chemical form of the fissile material. Graphs of the validation results for 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 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.

AtKms Ml,;NI-' 0.1 validation with Continuous Energy ENDF/B-Vll.1 Cross Sections Atkins-NS-NMl-14-01 30

Northwest Medical Isotopes, LLC 5.1.1. Average Neutron Energy Causing Fission (ANECF)

The ANECF value is a 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 [Proprietary Information]. However, sufficient higher energy experiments are included with ANECF values up to [Proprietary Information] to demonstrate that there is no trend in the kett values relative to the ANECF value. Figure 1 presents the MCNP 6.1 data. The very slight negative slope to the data's 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.

[Proprietary Information]

Figure 1 -ANECF Trend Atkins MCNP 6.1 Validation with Continuous Energy ENDF/B-Vll.1 Cross Sections Atkins-NS-NMl-14-01 31

Northwest Medical Isotopes, LLC 5.1.2. Hl2 35 U Values The Hf235U 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 Hf235 U values from [Proprietary Information] are well represented. However, sufficient higher energy experiments are included with Hf235 U values as low as 3.1 to demonstrate that there is no trend in the kerr values relative to the Hf235 U value. Figure 2 presents the MCNP 6.1 data.

[Proprietary Information]

Figure 2 - Hl235 U Trend

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Atkins MCNP 6.1 Validation with Continuous Energy ENDF/B-Vll.1 Cross Sections Atkins-NS-NMl-14-01 32

Northwest Medical Isotopes, LLC 5.1.3. ANECF vs. H/235 U Both the ANECF and the Hl235 U values are measures of the system neutron energy. Note that the H!235 U value characterizes the system neutron moderation only as it is affected by the n-H scatter reaction while the ANECF is a summation of the effect of all n scatter reactions. Therefore, the MCNP calculated ANECF is judged to be a more useful parameter when comparing applications to the validation AoA. However, the Hl235U value is a physical property of the experiments. Thus, it is useful to observe the relationship between the two parameters.

Figure 3 shows this relationship for the MCNP data. Note that the high thermal neutron capture in HEU solution systems produces the only significant aberration in the relationship. From this relationship it is judged that the ANECF value accurately characterizes the system neutron energy in the absence of accurate Hl235 U values and in the presence of other neutron scattering isotopes (e.g., carbon).

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Figure 3 - ANECF vs. H/235 U Evaluation

' with Continuous Energy ENDF/B-Vll.1 Cross Sections Atkins MCNP 6.1 Validation Atkins-NS-NMl-14-01 33

Northwest Medical Isotopes, LLC 5.1.4. Enrichment The system enrichment (wt. % 235 U) is a physical system parameter used to characterize the system.

Consistent with the purpose of this validation, the majority of the experiments evaluated are [Proprietary Information] to demonstrate that there is no trend in the keff values relative to enrichment. Figure 4 presents the MCNP 6.1 data. The very slight positive slope to the data's linear fit is judged to be insignificant as its change in value over the entire data range is much less than the average total uncertainty.

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Figure 4 - Enrichment Trend Atkins MCNP 6.1 Validation with Continuous Energy ENDF/B-Vll.1 Cross Sections Atkins-NS-NMl-14-01 34

Northwest Medical Isotopes, LLC 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. As shown, there is no significant bias with the various moderator materials

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Figure 5 - Moderator Evaluation

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Atkins MCNP 6.1 Validation with Continuous Energy ENDF/B-Vll.1 Cross Sections Atkins-NS-NMl-14-01 35

Northwest Medical Isotopes, LLC 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. As shown, there is no significant bias in the calculated keff values relative to the system reflector material.

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Figure 6 - Reflector Evaluation Atkins MCNP 6.1 Validation with Continuous Energy ENDF/B-Vll.1 Cross Sections Atkins-NS-NMl-14-01 36

Northwest Medical Isotopes, LLC 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. As shown, there is no significant bias in the calculated keff values relative to the chemical form of the system fissile material.

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Figure 7 - Chemical Form Evaluation 5.2. Normalcy Evaluation The summary of the normalcy results is show in Table 4.

Table 4 - Normalcy Results Summary

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Northwest Medical Isotopes, LLC 5.2.1. Low Enriched Uranium The examination of these data includes 22 cases as shown in Table 5. As the number of cases (22) is less than the range of coefficients (50) for the Shapiro-Wilk test, this test was used to evaluate the distribution of the results. As shown in the data are normally distributed.

Table 5 - LEU Results

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Atkins MCNP 6.1 Validation with Continuous Energy ENDF/B-Vll.1 Cross Sections Atkins-NS-NMl-14-01 38

Northwest Medical Isotopes, LLC 5.2.2. Intermediate Enriched Uranium The examination of these data includes 50 cases as shown in Table 6 below. The Shapiro-Wilk test was used to evaluate the distribution of the results and the results are shown in Table 6. Therefore, the data are judged to be from a normal distribution.

Table 6 - IEU Normalcy

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Atkins MCNP 6.1 Validation with Continuous Energy ENDF/B-Vll.1 Cross Sections Atkins-NS-NMl-14-01 39

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Atkins MCNP 6.1 va11aat1on with Continuous Energy ENDF/B-Vll.1 Cross Sections Atkins-NS-NMl-14-01 40

Northwest Medical Isotopes, LLC

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5.2.3. High Enriched Uranium The examination of these data includes 20 cases as shown below. The Shapiro-Wilk test was used to evaluate the distribution of the results and the results are shown in Table 7. Therefore, the data are judged to be from a normal distribution.

Table 7 - HEU Normalcy

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