ML22010A068
| ML22010A068 | |
| Person / Time | |
|---|---|
| Site: | Three Mile Island  |
| Issue date: | 01/05/2022 |
| From: | EnergySolutions |
| To: | Office of Nuclear Reactor Regulation |
| References | |
| TMI2-DPL-N-00-0001, Rev 1, TMl2-RA-COR-2022-0001 TMI2-EN-RPT-0002, Rev 1 | |
| Download: ML22010A068 (37) | |
Text
Attachment 3 to TMl2-RA-COR-2022-0001 Supplemental Information to License Amendment Request Three Mile Island Nuclear Station, Unit 2 NRC Possession Only License No. DPR-73 Revision to TMl2-EN-RPT-0002 "MCNP Version 6.2 Bias Determination for Low Enrichment Uranium Using the ENDF/B-VIII.0 Cross Section Library"
~ Calculation Doc. No.: TMI2-EN-RPT-0002 ENERGYSOLUTIONS Package Rev.: 1
Title:
MCNP Version 6.2 Bias Determination for Low Enrichment Uranium Using the ENDF/B-VIII.0 Cross Section Library Design Plan No.: TMI2-DPL-N-00-0001 DP Rev.: 1 Signatures (printed name, signature, date)
Preparer Derrick Faunce Approval (Responsible Engineer) Guy Rhoden Record of Verification Item Verified Acceptable N/A - Explain a) Design Verification by Independent Checking Method 0 b) Computer Software approved per CG-EN-PR-204 0 c) Calculation Package complete and per CG-EN-PR-203 0 Signature (printed name, signature, date)
Verifier Guy Rhoden Record of Revisions Affected Affected (Print or Type)
Rev. Description Pages Media Preparer Verifier 0 All All Initial Issue Derrick Faunce Guy Rhoden Revision to address 1 4, 12-15 None Derrick Faunce Guy Rhoden comments received Page 1 of36
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ENERGYSOLUTIONS Table of Contents
- 1. Introduction ............................................................................................................................. 4
- 1. 1. Purpose and Objectives .................................................................................................... 4 1.2. Scope ................................................................................................................................ 4 1.3. Hardware and Software Description ................................................................................ 5
- 2. Requirements ........................................................................................................................... 5 2.1. Design Inputs .................................................................................................................... 5 2.1.1. LEU-COMP-THERM-002 .................................................................................................... 5 2.1.2. LEU-COMP-THERM-009 .................................................................................................... 5 2.1.3. LEU-COMP-THERM-013 .................................................................................................... 6 2.1.4. LEU-COMP-THERM-033 .................................................................................................... 6 2.1.5. LEU-COMP-THERM-042 .................................................................................................... 6 2.1.6. LEU-COMP-THERM-049 .................................................................................................... 6 2.1.7. LEU-COMP-THERM-092 .................................................................................................... 6 2.1.8. LEU-SOL-THERM-001 ....................................................................................................... 6 2.1.9. LEU-SOL-THERM-002 ....................................................................................................... 6
- 3. References ............................................................................................................................... 7
- 4. Assumptions ............................................................................................................................ 7
- 5. Calculation Methodology ........................................................................................................ 7 5.1. Benchmark Data Preparation ........................................................................................... 7 5.2. Normality Testing Methodology ...................................................................................... 8 5.2.1. Lilliefors Test ........................................................................................................................ 8 5.2.2. Normal Probability Plot ............................................................................ ;........................... 9 5.3. Trend Analysis Methodology ........................................................................................... 9 5.4. Bias Determination Methodology .................................................................................. 10 5.4.1. Bias Determination for Non-Normal Distributions ............................................................. 10 5.4.2. Bias Determination for Normal Distributions ..................................................................... 10
- 6. Calculations ........................................................................................................................... 12 6.1. Bias Determination ......................................................................................................... 12 6.2. Area of Applicability Review ........................................................................................ 13 6.3. Margin of Subcriticality ................................................................................................. 14
- 7. Conclusions ........................................................................................................................... 15
- 8. Electronic Files ...................................................................................................................... 16 8.1. Computer Runs ............................................................................................................... 16 8.2. Other Electronic Files ..................................................................................................... 21
- 9. Attachment A- Sample Computer Input/Output.. ................................................................ 22
- 10. Attachment B - Benchmark Data Set.. .............................................................................. 24 Calculation Package No. TMI2-EN-RPT-0002, Revision 1 Page 2 of 36
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- 11. Attachment C -Tables ofkactj Values ................................................................................ 27
- 12. Attachment D - Lilliefors Testing Tables ......................................................................... 30
- 13. Attachment E- Normal Plot Figures ................................................................................. 33
- 14. Attachment F -Trend Analysis Figures ............................................................................ 34 List of Figures Figure 1: N01mal Probability Plot for LEU kactj Results ............................................................... 33 Figure 2: ANECF Trend Analysis Plots for LEU ......................................................................... 35 Figure 3: Enrichment Trend Analysis Plots for LEU ................................................................... 36 List of Tables Table 1. Summary of Lilliefors Test Results and Initial Bias Determination .............................. 12 Table 2. Basic Properties of the MCNP6 Benchmark Models for LEU ....................................... 14 Table 3. Summary of Bias Determination .................................................................................... 15 Table 4: Benchmark Results for MCNP6 ..................................................................................... 24 Table 5: Ordered kactj Values for LEU .......................................................................................... 27 Table 6: Lilliefors Normality Test Determination for MCNP6 Benchmark Results for LEU ..... 30 Calculation Package No. TMI2-EN-RPT-0002, Revision 1 Page 3 of 36
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ENERGYSOLUTIONS
- 1. INTRODUCTION
- 1. 1. Purpose and Objectives The following calculation consists of two parts. The first involves the determination of the MCNP Version 6.2 (MCNP6) computer code bias and bias uncertainty. The second part examines the area of applicability (AOA) of the benchmark cases used to determine the bias.
This determination was performed in accordance with ANSI/ANS-8.24-2017, Validation of Neutron Transport Methods for Nuclear Criticality Safety Calculations (Ref. [l]). The methodology used in this determination is taken from NUREG/CR-4604, Statistical Methods for Nuclear Material Management, (Ref. [2]) and NUREG/CR-6698, Guide for Validation ofNuclear Criticality Safety Methodology, (Ref. [3]) which are both listed in Appendix C of ANSI/ANS-8.24.
1.2. Scope The MCNP6 computer code is validated as appropriate for use in estimating keff values. This validation report determines the calculational margin and the Margin of Subcriticality (MoS) to establish the maximum Upper Subcritical Limit (USL) for the AOA. Additional margin may be needed for extension of the AOA and is determined in the applicable evaluation, as necessaiy. The USL is defined as follows:
USL =1 - Moc - MoA - Mos> kcalc + 2CTcazc
- Where, MoC is the calculational margin and includes the bias and bias uncertainty (see Section 5.4) in addition to any uncertainties related to trending (see Section 5.3)
MoA is the Margin of Applicability, which is an allowance for any uncertainties related to extenstion of the AOA (see Section 6.2)
MoS is the Margin of Subcriticality, which is an administratve allowance beyond the MoC to ensure subcriticality (see Section 6.3) kcalc is the calculated neutron multiplication factor using this validated method CTcalc is the standard deviation associated with kcalc Within this validation report the value 1 - MoC is collectively refeITed to as the "bias".
The bias determinations were performed based on the use of the ENDF/B-VIII.0 based continuous energy data libraries as prepared by the Los Alamos National Laboratory (LANL). The bias determination was performed for low enrichment uranium (LEU) benchmark models based on the range of process parameters (e.g., enrichment, fissile form) used in this report.
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ENERGYSOLUTIONS 1.3. Hardware and Software Description The software used herein is Version 6.2 of the MCNP code system. MCNP6 was developed at LANL and acquired from the Radiation Safety Infmmation Computational Center (RSICC). The cross-section library used in this calculation report is the ENDF/B-VIII.0 based library that is processed and distributed by LANL [including the1mal scattering S(a,~) libraries]. The specific material libraries used are listed in Section 6.2.
The MCNP6 code system is installed on the NSTS computational platforms NSTS-LS0l and NSTS-LS2. The installation and verification of MCNP6 performance on each NSTS computer is documented in accordance with the Software Qualification and Validation Plan, ESCD-000038, MCNP6.2 (NSTS) Software Qualification and Validation Plan (Ref. [4]).
NSTS-LS0I consists of an AMD Ryzen Threadripper 3970x 32-core processor configured with 32 GB RAM, and the CentOS 8 Linux 64-bit operating system with GNOME desktop environment. NSTS-LS0l is configured for Remote Desktop Access via a secured, encrypted internet connection with enabled firewall.
NSTS-LS2 consists of an AMD Ryzen Threadripper 3990x 64-core processor configured with 64 GB RAM, and the Fedora 32 Linux 64-bit operating system with the XFCE window manager.
NSTS-LS2 is configured to allow authorized access via X2GO software which uses an encrypted secure shell to connect to X2GO client software with the X2GO server on NSTS-LS2.
- 2. REQUIREMENTS 2.1. Design Inputs The following present a brief description for each benchmark used. These descriptions are meant only to give the simplest of indication as to the critical configurations represented by the benchmarks. Complete descriptions of the benchmarks can be found in NEA/NSC/DOC(95)03, International Handbook of Evaluated Criticality Safety Benchmark Experiments, (Ref. [5]) and should be referred to regarding any detail of the benchmark models discussed herein. A total of 125 benchmark cases are chosen.
2.1.1. LEU-COMP-THERM-002 This benchmark included five configurations that consisted of various arrangements of UO2 fuel rods. The arrangements are water moderated and reflected.
2.1.2. LEU-COMP-THERM-009 This benchmark included twenty-seven configurations that consisted of various arrangements of UO2 fuel rods. The fuel rods are arranged in three clusters that are arranged in a single row.
Between the clusters are placed plates made of steel, Boral, copper, cadmium, aluminum, or Zircalloy-4. The fuel rods are water moderated and reflected.
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ENERGYSOLUTIONS 2.1.3. LEU-COMP-THERM-013 This benchmark included seven configurations that consisted of three water moderated rectangular cluster of UO2 fuel rods. The three clusters were separated by plates made of steel, Boral B, Boroflex, cadmium, copper, or copper-cadmium. Two sides of the arrangement of three clusters were reflected by steel walls.
2.1.4. LEU-COMP-THERM-033 This benchmark included fifty-two configurations that consisted rectangular parallelepipeds created from cube blocks of finely divided UF4 dispersed in paraffin. The configurations were either unreflected or reflected by paraffin or polyethylene.
2.1.5. LEU-COMP-THERM-042 This benchmark included seven configurations that consisted of three water moderated rectangular cluster of UO2 fuel rods. The three clusters were separated by plates made of steel, Boral B, Boroflex, cadmium, copper, or copper-cadmium. Two sides of the arrangement of three clusters were reflected by steel walls.
2.1.6. LEU-COMP-THERM-049 This benchmark included eighteen configurations that consisted of a stacked array of small boxes filled with UO2. These were moderated and reflected by polyethylene.
2.1.7. LEU-COMP-THERM-092 This benchmark included six configurations that consisted of an array of stainless-steel-clad cylindrical UO2 fuel rods. The fuel rods are water moderated and reflected. Control rods consist of Ag-In-Cd: Varying concentrations of soluble boron are in the moderator water.
2.1.8. LEU-SOL-THERM-001 This benchmark included a single configuration that consisted of a cylindrical tank filled with UO2F2 solution. The tank was not reflected.
2.1.9. LEU-SOL-THERM-002 This benchmark included three configurations that consisted of spherical geometries of UO2F2 solutions with no reflection.
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- 3. REFERENCES
[1] ANSI/ANS-8.24-2017, Validation ofNeutron Transport Methods for Nuclear Criticality Safety Calculations, American Nuclear Society, 2017.
[2] NUREG/CR-4604, Statistical Methods for Nuclear Material Management, Pacific Northwest Laboratory, 1988.
[3] NUREG/CR-6698, Guide for Validation ofNuclear Criticality Safety Methodology, Science Applications International Corporation, 2001.
[4] ESCD-000038, Rev. 0, MCNP6.2 (NSTS) Software Qual(fication and Validation Plan, Energy Solutions, 2020.
[5] NEA/NSC/DOC(95)03, International Handbook of Evaluated Criticality Safety Benchmark Experiments, National Energy Agency, 2019.
[6] "NIST/SEMATECH e-Handbook of Statistical Methods," October 2013. [Online].
Available: http://www.itl.nist.gov/div898/handbook/.
- 4. ASSUMPTIONS None.
- 5. CALCULATION METHODOLOGY The following sections present the methods for determination of the bias for MCNP6 based on a selection of experimental benchmarks. The benchmarks represent a selection of .uranium based critical experiments that were chosen as being representative of the configurations modeled as part of this report. The description of each experiment may be found in NEA/NSC/DOC(95)03 (Ref.
[5]).
For each set of benchmark cases the MCNP6 run parameters were 10,000 neutrons/cycle, 100 skipped cycles, and 5,000 active cycles to minimize the code bias in keff. All results showed convergence of fission-source entropy (within 1 standard deviation of the average) in less than 40 cycles. Each set of cases were run on the NSTS-LS0l and NSTS-LS2 computers and produced identical results.
5 .1. Benchmark Data Preparation The benchmark data consists ofresults from MCNP6 calculations and experimental data. Not all the benchmarks resulted in an experimental keff of exactly 1.0. The benchmarks also have experimental uncertainties that need to be accounted for along with MCNP6 calculation uncertainty. As a result, some preparation of the data must be performed before conducting any statistical analyses.
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ENERGYSOLUTIONS The first thing that needs to be done is to normalize the keff values to 1.0 and to combine the MCNP6 and experimental uncertainties. Normalization of the keffvalues is needed in those cases where the benchmark experiments have a keff other than 1.0. This is done using the following formula:
_ kcalc k adj - - -
kexp Where, kadJ = Adjusted calculated keff value nonnalized to 1. 0 kcalc = The MCNP6 calculated keff value for a benchmark case kexp = The experimental keff value for a benchmark case The combined uncertainty is determined by:
Clcom = Clcalc 2 + Clexp 2 Where, a-com = Combined uncertainty a-calc = The MCNP6 uncertainty for the calculated keff value for a benchmark case a-exp = The experimental uncertainty for the keff value for a benchmark case 5.2. Normality Testing Methodology 5 .2 .1. Lilliefors Test The kaaj values are examined to determine if they are from a nonnal distribution. The Lilliefors test as presented in Section 9.6.3.1 of NUREG/CR-4604 (Ref. [2]) was selected given that there are more than 50 values. The first step in this test is to rank the kaaj values from smallest to largest and then determine the standardized sample values. As applied to the kaaj values, the standardized sample values are determined by the following equation:
ki-k zi=--
s Where, Zi = Standardized sample value for the ith keff benchmark value k = The kaaj value of the ith benchmark case k = The mean of the kaaj values s = Sample standard deviation The values of Zi are used to determine values of the normal cumulative distribution function (cdf) denoted as F*(z) based on Table A3 in Reference [2]. It is noted that for negati:ve values of Zi, the value of F*(z) is one minus the value from Table A3 in Reference [2] based on the absolute value of Zi- Also note that these values may be readily attained using the 'NORMSDIST()' function in Excel. Next, empirical cumulative distribution function values (denoted as G(z)) are determined for the ordered kaaj values. This is simply the ranked value divided by the total number of cases.
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ENERGYSOLUTIONS The Lilliefors test statistic (T*) is the largest of all values of IF*(zi)-G(zi)I or IF*(z;)-G(z;-1)1. T* is compared to WI-a obtained from Table A18 of Reference [2]. For a 95% confidence level and a 0 6 sample size over 30, WJ-a is given by : where n is the number of cases. If T* is less than WJ-a the data is probably from a normal distribution.
5.2.2. Normal Probability Plot The basic description and technique for the normal probability plot are taken from the Section 1.3.3.21 of NISTISEMATECH e-Handbook of Statistical Methods (Ref. [6]). The normal probability plot is formed by:
- Vertical axis: Ordered response values
- Horizontal axis: N01mal order statistic medians The response values are the kactj values ordered from smallest to largest.
The normal order statistic medians are defined by the following function:
Ni =G(Ui)
Where U; are the uniform order statistic medians and G is the percent point function of the normal distribution. The percent point function is the inverse of the cumulative distribution function. This provided by the Excel spreadsheet function NORM.S.INV(). The uniform order statistic medians are defined as:
Ui = 1 - Un for i= 1 U; = (i- 0.3175)/(n+0.365) for i=2,3,4, ... , n-1 U; = 0.5(1/n) for i=n A straight line is fitted to the data. The further the data departs from the straight line, the greater the indication of departures from normality.
5.3. Trend Analysis Methodology The benchmark data is examined for potential trends in the kactj data versus the Average Energy of Neutron Energy Causing Fission (AENCF) and also versus the enrichment (wt. % 235 U). This is used to determine the proper bias determination method for data that has been determined to come from a normal distribution.
The kactj versus AENCF or enrichment data will be fitted to a number of simple functions along with a determination of the coefficient of determination (R2). Should the value of R 2 be 0.8 or greater, this would indicate correlation between the data and the fitted function. Depending on the exact nature of the correlated fitted function, a trend in the data that may impact the USL determination is possible. An R2 value less than 0.8 would indicate either a poor or no correlation between the data and the fitted function.
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ENERGYSOLVTIONS 5.4. Bias Determination Methodology The methods for determining the bias are presented in this section. Depending on the result of the normality testing one of three methods will be used to determine the bias. The following presents the methods used herein.
5.4.1. Bias Determination for Non-N01mal Distributions For data that is demonstrated to likely not come from a normal distribution, the bias is determined based on the nonparametric statistical treatment presented in NUREG/CR-6698 (Ref. [3]). 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 is determined with the following equation:
m-1
/3 = 1 - '\"' ., ( n~ ")1 (1 - q)j qn-j
~J- n J.
J=O Where, q = the desired population fraction (e.g., 0.95) n = the number of data in one data sample (e.g., number of benchmark cases) m = the indexed rank from the smallest to the largest.
This equation can be simplified for a desired population fraction of 0.95 and a rank of 1 (smallest data sample) to:
/3 = 1 - qn =l - 0.95n The bias may then be determined by the following:
Bias= k1 - cr1 - NPM Where, k1 = Smallest kaaj value from the benchmark cases a-1 = Standard deviation for smallest kaaj value from the benchmark cases NPM = Nonparametric margin to account for small sample sizes based on the value of /3 5.4.2. Bias Determination for Normal Distributions For data that is demonstrated to likely come from a normal distribution, the bias is determined based one of two methods as described in NUREG/CR-6698 (Ref. [3]). For data that show no trend in kaaj versus the AENCF or enrichment the single-sided tolerance limit method is used to determine the bias. For data that show a trend in kactj versus the AENCF or enrichment the one-sided lower tolerance band method is used. For the benchmark data examined herein, the trend information presented in Attachment F - Trend Analysis Figures demonstrates that no trends were present in the data. Therefore, only the single-sided tolerance limit method is presented here.
The bias determined by the single-sided tolerance limit method is defined by the following set equations:
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ENERGYSOLUTIONS Bias= kadj - USP u = zp + -vlzp -
2 ab a
2 2 1-a a= 1 - - - -
Z(n - 1) 2
- 2 Z1-a b -Zp - - -
n 1
I;-k*.2 l (J
- l kadj = 1 I (J.2 l
Where, kadj = Weighted mean kactj value U = One-sided lower tolerance factor z 1 _a = z value for the cumulative standard normal dist1ibution for a confidence value of 1-a, Zp = z value for the cumulative standard normal distribution for a confidence value ofp n = Number of data points (kactj values) in data set ki = The ith kactj value
<Ji = Uncertainty of the ith kactj value Sp = Square root of the pooled variance u2 = Average total variance Calculation Package No. TMI2-EN-RPT-0002, Revision 1 Page 11 of 36
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ENERGYSOLUTJONS
- 6. CALCULATIONS 6.1. Bias Determination Table 4 in Attachment B - Benchmark Data Set contains the results of the 125 cases used to detennine the MCNP6 computer code bias for use with low enrichment 235 U fissile materials.
Table 4 also contains the experimental result and uncertainty as provided in the benchmark experiments handbook (Ref. [5]), the adjusted keff (l<actj), and combined uncertainty (cr com) for each benchmark. The values for kactj and <Jcom were determined based on the formulas from Section 5.1.
The next step was to order the kactj values from smallest to largest. These ordered values are presented in Attachment C -Tables ofkactj Values.
The data was checked to determine if the data come from a normal distribution based on the Lilliefors test discussed in Section 5.2.1. The results of the test are used to help determine which of the bias dete1mination methods from Section 5.4 is used. The Lilliefors test detenninations and the bias results are presented in detail in Attachment D - Lilliefors Testing Tables and summarized in Table 1. The normal probability plots are created based on the discussion in Section 5.2.2 as a visual aid. These are shown in Attachment E - Normal Plot Figures.
Table 1. Summary of Lilliefors Test Results and Initial Bias Determination Normal Observations W1-a MaxT* Bias 1 Distribution 125 0.07925 0.19559 No 0.9798 1 Bias determination details at the bottom of the Lilliefors test table in Attachment D - Lilliefors Testing Tables and includes the bias uncertainty of 0.0006.
The results of the trend analysis presented in Attachment F - Trend Analysis Figures demonstrate that there is no notable trend within the data that needs to be compensated for in the determination of the bias. The AOA review presented in Section 6.2 should be consulted before using any of the bias results presented in Table 1.
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ENERGYSOLUTIONS 6.2. Area of Applicability Review The AOA consists of the range or values of various parameters important to the reactivity of the benchmark models. These define the range or values for a system parameter or parameter(s) over which the bias presented above is considered valid without modification. These parameters include such things as fissile material(s), moderators, reflectors, geometry, other significant non-fissile materials (e.g., poisons such as boron or other materials such as steel), and energy characteristics of the experimental system (e.g., fast or thermal). These parameter ranges of the benchmark models are compared to the models of the system being evaluated. If the system parameter ranges fall within the AOA then no additional margin is needed beyond the MoS when determining the USL.
If one or more of the system parameters are found to fall outside of the AOA, then an additional margin of applicability (MoA) may be needed on the USL to extend the applicability of the bias determination. It should be noted that it is anticipated that there will be limited (e.g., one) supporting analyses for TMI-2 decommissioning relying upon this validation report, and that all evaluations are intended to be within this AOA. Nevertheless, the need for an any additional margin based on AOA considerations is addressed in the applicable evaluation, with the following methodology.
If the extension of the system parameter is substantial (e.g., more than 10% outside of the AOA),
then this validation report should be revised to include additional critical expermiment benchmarks to enhance the validated AOA. Extension of the AOA to a lesser extent may be made within the analysis with supporting technical justification. This may include sensitivity studies on the effect of changes in the parameter to be extended on keff of the modeled system, extension of any bias trends noted in this validation report, or other detailed technical justification supporting whether extension of the AOA requires a MoA on the USL.
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ENERGYSOLUTIONS Table 2. Basic Properties of the MCNP6 Benchmark Models for LEU Property LEU AOA 235 U (2 -10 wt.% U) in the form of compounds (U02, LJF4) and solution Fissile Materials (U02F2)
Array of fuel rods, array of rectangular parallelepipeds, cubes in cubic Fissile Geometry array, finely divided particles in cubes, cylinders, spheres, slabs Moderator Materials Water, Paraffin, Polyethylene Reflector Materials None, Water, Acrylic, Steel, Plexiglas, Paraffin, Polyethylene, Concrete Al alloys, steel, borated steel, Bora!, boroflex, Ag-In-Cd, Cu, Cu with Cd, Other Significant absorbers, Cd, Zircaloy-4, rubber poisons, or structural materials present Soluble Boron: 0 - 96 ppm 1001.00c 17035.00c 26054.00c 42092.00c 50112.00c h-h2o.40t 501 0.00c 17037.00c 26056.00c 42094.00c 50114.00c h-poly.40t 5011.00c 19039.00c 26057.00c 42095.00c 50115.00c 6012.00c 19040.00c 26058.00c 42096.00c 50116.00c 6013.00c 19041.00c 27059.00c 42097.00c 50117.00c 7014.00c 20040.00c 28058.00c 42098.00c 50118.00c 8016.00c 20042.00c 28060.00c 42100.00c 50119.00c 8017.00c 20044.00c 28061.00c 47107.00c 50120.00c 9019.00c 20046.00c 28062.00c 47109.00c 50122.00c 11023.00c 20048.00c 28064.00c 48106.00c 50124.00c Specific Cross Sections and 12024.00c 22046.00c 29063.00c 48108.00c 92234.00c S(a,J3) used 12025.00c 22047.00c 29065.00c 48110.00c 92235.00c (MCNP6 identifiers) 12026.00c 22048.00c 30064.00c 48111.00c 92236.00c 13027.00c 22049.00c 30066.00c 48112.00c 92238.00c 14028.00c 22050.00c 30067.00c 48113.00c 14029.00c 24050.00c 30068.00c 48114.00c 14030.00c 24052.00c 30070.00c 48116.00c 15031.00c 24053.00c 40090.00c 49113.00c 16032.00c 24054.00c 40091.00c 49115.00c 16033.00c 25055.00c 40092.00c 16034.00c 40094.00c 16036.00c 40096.00c Average Energy of Neutrons Range (MeV): 2.43E 2.88E-01 Causing Fission Average (MeV): 1.40E-01 6.3. Margin of Subcriticality The MoS is a subcritical margin to ensure that calculational results below the USL are adequately subcritical, and is sometimes referred to as an administrative margin. This value typically ranges from 0.02 (at a minimum) to 0.05, and depends on factors such as the systems to be modeled, the reliability of the calculational method, and knowledge of physical and chemical aspects of the sytems to be modeled. A USL of 0.95 has been typically used for facilities with LEU, and is widely recognized as being adequately subcritical with sufficient subcritical margin. Therefore, assuming a USL of 0.95 (for both normal and credible abnormal conditions), and the bias (including bias uncertainties) of 0.9798, then the implied MoS would be:
Mos= USL - Bias= 0.9798 - 0.95 = 0.0298 A MoS of 0.0298, that results in a USL of 0.95, is adequate for this AOA as discussed below.
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ENERGYSOLUTIONS There are a large number of experimental benchmarks utilized in this validation (125 cases cove1ing 9 benchmarks). This provides a large set of cases for the statistical evaluation of the bias and bias uncertainty. Based on the statistical evaluation of the data, the non-parametric (i.e.,
distribution free) method is used, with sufficient number cases to provide a 95% degree of confidence that 95% of the population lies above the smallest observed value (which requires a minimum of 59 cases). Due to this, there is high confidence that the calculational margin is sufficiently and conservatively quantified for the AOA. The TMI-2 decommissioning operations are for the handling of low enriched uranium (LEU) fuel within a water-moderated system, which is well documented in the benchmark experiments of LEU fuel (as clusters of rods, blocks ofUO2, finely divided UF4, and solutions of UO2F2). These experiments have a high degree of similarity to the anticipated calculations. The anticipated calculations are also simple systems (e.g., spherical, repeating lattice of fuel) with significant conservativisms in the modeling practices such as optimum conditions in moderation, reflection, fuel density, pellet size, and geometry. Additionally, conservative assumptions are made for non-optimized system parameters. For the LEU systems anticipated to be modeled under these conditions, small changes in reactivity (~keff) require large changes to the system parameters (e.g., fissile mass). The combination of these factors contribute to the conclusion that there is a high degree of confidence in the calculated keff values; therefore, a MoS of 0.0298 is determined to be adequate for the resulting USL of 0.95.
- 7. CONCLUSIONS This calculation report has determined the bias (including bias uncertainty) for the use of the MCNP Version 6.2 code system and ENDF/B-VIII.0 library installed on the NSTS computers for use in performing calculations that estimate keff values. The bias values determined herein are applicable to problems that involve low enrichment 235 U fissile materials with various moderator and reflector materials. The AOA has been detailed in Section 6.2. The determined bias value is summarized in the following table.
Table 3. Summary of Bias Determination AOA Bias LEU 0.9798 Additionally, this validation report has determined the MoS associated with the anticipated calculations within this AOA to be 0.0298. Therefore, the USL for this AOA is:
USL = Bias - MoS - MoA = 0.9798 - 0.0298 - 0 = 0.95 Any additional subcritical margin for applications outside the AOA provided in Table 2 (MoA) are to be justified within the applicable evaluation.
Calculations using this method are considered safely subcritical when the following inequality is fulfilled:
kcalc + 2CTcazc < USL(0.95)
- Where, kcalc is the calculated neutron multiplication factor
<J'calc is the standard deviation associated with kcalc Calculation Package No. TMI2-EN-RPT-0002, Revision 1 Page 15 of 36
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ENERGYSOLUTIONS
- 8. ELECTRONIC FILES 8.1. Computer Runs Computer Computer Filename File Date Ver. Computer Filename File Date Ver. Computer Code Code LCT002_01 .in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT002_01 .in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT002_01 .ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT002_01 .ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT002_02.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT002 02 .in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT002 02.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT002_02 .ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT002_03.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT002_03.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT002_03.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT002_03.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT002 04.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT002 04.in 11 /12/2020 MCNP 6.2 NSTS-LS2 LCT002_04.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT002_04.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT002_05.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT002_05.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT002_05.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT002_05.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009_01 .in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT009_01 .in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009 01.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT009 01 .ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009_02 .i n 11/12/2020 MCNP 6.2 NSTS-LS0 1 LCT009_02 .in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009_02 .ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT009_02 .ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009 03.in 11/12/2020 MCNP 6.2 NSTS-LS0 1 LCT009 03.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009 _ 03.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT009_03.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009_04.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT009_ 04.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009_04.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT009_ 04.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009 05.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT009 05.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009_05.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT009_05.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009 06.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT009_06.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009_06.ino 11 /1 8/2020 MCNP 6.2 NSTS-LS01 LCT009_06.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009_07.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT009_07.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009_07.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT009_07.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009 08.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT009 08.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009_08.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT009 _ 08.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009_09.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT009_09.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009_09.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT009 09.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009_ 1O.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT009_ 1O.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009_ 1O.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT009_ 1O.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009_ 11 .in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT009_ 11.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009 11 .ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT009_ 11.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009_12.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT009 12.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009_12 .ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT009 12.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009_13.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT009_13.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009_ 13.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT009_ 13.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009_ 14.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT009_ 14.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009_14.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT009_ 14.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009_ 15.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT009_ 15.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009_ 15.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT009_ 15.ino 11/12/2020 MCNP 6.2 NSTS-LS2 Calculation Package No. TMI2-EN-RPT-0002, Revision 1 Page 16 of 36
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ENERGYSOLUTIONS Computer Computer Filename File Date Ver. Computer Filename File Date Ver. Computer Code Code LCT009 16.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT009 16.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009 16.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT009 16.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009 17.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT009 17.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009 17.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT009_ 17.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009 18.i n 11/12/2020 MCNP 6.2 NSTS-LS01 LCT009_18.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009 18.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT009_18.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009 19.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT009_19.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009 19.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT009 19.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009 20.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT009 20.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009 20.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT009 20.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009_21 .in 11 /12/2020 MCNP 6.2 NSTS-LS01 LCT009_21 .in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009 21 .ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT009 21 .ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009_22 .in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT009 22 .in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009 22 .ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT009_22.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009 23.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT009_23.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009 23.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT009_23.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009 24.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT009 24.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009 24.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT009 24.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009 25.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT009 25.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009 25.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT009 25.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009 26.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT009 26.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT009 26.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT009 26.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT013 01 .in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT013 01.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT013 01 .ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT013 01 .ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT013_02 .in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT013_02 .in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT013_02 .ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT013 02 .ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT013 03.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT013_03.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT013 03.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT013_03.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT013 04.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT013_04.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT013 04.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT013 04.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT013 05.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT013 05.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT013_05.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT013_05.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT013_06.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT013_06.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT013_06.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT013 06.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT013_07.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT013 07.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT013_07.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT013_07 .ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_01 .in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_01 .in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_01 .ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_01 .ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_02.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_02 .in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033 02.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033 02 .ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033 03.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033 03.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033 03.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_03.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_04.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_04.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033 04.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033 04.ino 11/12/2020 MCNP 6.2 NSTS-LS2 Calculation Package No. TMI2-EN-RPT-0002, Revision 1 Page 17 of 36
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ENERGYSOLUTIONS Computer Computer Filename File Date Ver. Computer Filename File Date Ver. Computer Code Code LCT033 05.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_05.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_05.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_05.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_06.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_06.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_06.i no 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033 06.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_07.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_07 .in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_07.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_07 .ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_08.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033 08.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_08.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033 08.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033 09.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_09.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_09.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_09.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_ 10.i n 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_ 10.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_ 10.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033 10.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_ 11 .i n 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_ 11.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_ 11 .ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_ 11 .ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_ 12.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_12 .in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_ 12.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_ 12.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_13.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_13.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033 13.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_ 13.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033 14.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033 14.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033 14.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_ 14.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_ 15.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_15.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_ 15.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_ 15.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033 16.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033 16.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_ 16.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_ 16.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_ 17.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_ 17.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033 17.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_ 17.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033 18.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_18.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033 18.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_18.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_ 19.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_19.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_ 19.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_19.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_20 .i n 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_20.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_20.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033 _ 20 .ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_21 .in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033 21 .in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_21 .ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_21 .ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_22.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_22 .in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_22 .ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_22.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_23.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_23.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_23.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033 23.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_24.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033 24.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_24.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_24.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033 25.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_25.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_25.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_25.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_26.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_26.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_26.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033 26.ino 11/12/2020 MCNP 6.2 NSTS-LS2 Calculation Package No. TMI2-EN-RPT-0002, Revision 1 Page 18 of36
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ENERGYSOLUTIONS Computer Computer Filename File Date Ver. Computer Filename File Date Ver. Computer Code Code LCT033_27.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_27.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_27.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_27.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_28.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_28.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_28.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033 28.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_29.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_29.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_29.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_29.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_30.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033 30 .in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_30 .ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033 30 .ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_31 .in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_31.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_31 .ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_31.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_32 .in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033 32.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_ 32 .ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_32 .ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_33 .in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_33.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_33.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_33.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033 34.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_34.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_34.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_34.ino 11 /12/2020 MCNP 6.2 NSTS-LS2 LCT033_35.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_35.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_35.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_35.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_36.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_36.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_36.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_36.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_37.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_37.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_37.i no 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_37.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_38.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_38.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_38.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033 38.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_39.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_39.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_39.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_39.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_40 .in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_40.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_40.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_40.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033 41 .in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_41 .in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_41.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_41.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_42.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_ 42 .in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_42 .ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_42.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_ 43.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_ 43.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_43.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_43.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_44.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_44.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_44.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_44.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_45.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_45.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_45.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_ 45.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_46.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_ 46.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_46.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_ 46.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_ 47.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_ 47.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_47.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_ 47.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_48.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_48.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_48.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_48.ino 11/12/2020 MCNP 6.2 NSTS-LS2 Calculation Package No. TMI2-EN-RPT-0002, Revision 1 Page 19 of 36
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ENERGYSOLUTIONS Computer Computer Filename File Date Ver. Computer Filename File Date Ver. Computer Code Code LCT033_49.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_49.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_ 49.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033 49 .ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_50 .in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_50.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_ 50 .ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_50.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_51 .in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033 51 .in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_51 .ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_51.ino 11 /12/2020 MCNP 6.2 NSTS-LS2 LCT033_ 52 .i n 11/12/2020 MCNP 6.2 NSTS-LS01 LCT033_52 .i n 11/12/2020 MCNP 6.2 NSTS-LS2 LCT033_52 .ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT033_52 .ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT042_01 .in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT042_0 1.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT042_01 .ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT042_01 .ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT042_02 .in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT042_02 .in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT042 02 .ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT042_02.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT042_03.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT042_03.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT042_03.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT042 03.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT042 04.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT042_04.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT042_04.ino 11 /18/2020 MCNP 6.2 NSTS-LS01 LCT042_04.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT042_05.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT042_05.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT042_05.i no 11/18/2020 MCNP 6.2 NSTS-LS01 LCT042_05.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT042_06.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT042 06.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT042_06.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT042_06.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT042_07.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT042_07.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT042_07.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT042_07.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049_01 .i n 11/12/2020 MCNP 6.2 NSTS-LS01 LCT049 01 .in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049 01 .ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT049_01 .ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049_02 .in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT049_02.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049_02.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT049_02 .ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049_03.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT049_03.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049_03.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT049 03.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049_04.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT049_04.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049_04.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT049_04.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049_05.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT049 05.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049_05.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT049 05.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049_06.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT049_06.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049 _ 06.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT049_06.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049_07.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT049_07.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049_07.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT049_07.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049_08.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT049_08.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049 08.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT049 _ 08.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049 09.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT049_09.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049_09.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT049_09.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049_ 10.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT049_ 10.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049_ 10.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT049_ 1O.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049_ 11 .in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT049_ 11.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049 11 .ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT049_ 11.ino 11/12/2020 MCNP 6.2 NSTS-LS2 Calculation Package No. TMI2-EN-RPT-0002, Revision 1 Page 20 of36
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ENERGYSOLUTIONS Computer Computer Filename File Date Ver. Computer Filename File Date Ver. Computer Code Code LCT049_12 .in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT049 12.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049_12 .ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT049_12.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049_13.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT049_13.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049_ 13.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT049_ 13.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049_14.in 11 /12/2020 MCNP 6.2 NSTS-LS01 LCT049_14.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049_14.i no 11/18/2020 MCNP 6.2 NSTS-LS01 LCT049_ 14.i no 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049_ 15.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT049_ 15.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049_ 15.ino 11 /18/2020 MCNP 6.2 NSTS-LS01 LCT049_ 15.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049_ 16.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT049_16.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049_ 16.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT049_ 16.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049_ 17.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT049 17.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049 17.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT049_ 17.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049_ 18.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT049_18.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT049_ 18.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LCT049_18.ino 11/12/2020 MCNP 6.2 NSTS-LS2 LCT092 01.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT092_01 .in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT092_01 .ino 11/19/2020 MCNP 6.2 NSTS-LS01 LCT092_01 .ino 11/17/2020 MCNP 6.2 NSTS-LS2 LCT092_02 .in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT092 02 .in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT092_02.ino 11/19/2020 MCNP 6.2 NSTS-LS01 LCT092_02 .ino 11/17/2020 MCNP 6.2 NSTS-LS2 LCT092_03.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT092_03.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT092_03.ino 11 /19/2020 MCNP 6.2 NSTS-LS01 LCT092 03.ino 11/17/2020 MCNP 6.2 NSTS-LS2 LCT092_04.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT092_04.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT092_04.ino 11/19/2020 MCNP 6.2 NSTS-LS01 LCT092_04.ino 11/17/2020 MCNP 6.2 NSTS-LS2 LCT092_05.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT092_05.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT092 05.ino 11/19/2020 MCNP 6.2 NSTS-LS01 LCT092_05.ino 11/17/2020 MCNP 6.2 NSTS-LS2 LCT092_06.in 11/12/2020 MCNP 6.2 NSTS-LS01 LCT092 06.in 11/12/2020 MCNP 6.2 NSTS-LS2 LCT092_06.i no 11/19/2020 MCNP 6.2 NSTS-LS01 LCT092_06.ino 11/17/2020 MCNP 6.2 NSTS-LS2 LST001_01 .in 11/12/2020 MCNP 6.2 NSTS-LS01 LST001_01 .in 11/12/2020 MCNP 6.2 NSTS-LS2 LST001_01 .ino 11/18/2020 MCNP 6.2 NSTS-LS01 LST001_01 .ino 11/12/2020 MCNP 6.2 NSTS-LS2 LST002_01 .in 11/12/2020 MCNP 6.2 NSTS-LS01 LST002 01.in 11/12/2020 MCNP 6.2 NSTS-LS2 LST002_01 .ino 11/18/2020 MCNP 6.2 NSTS-LS01 LST002_01 .ino 11/12/2020 MCNP 6.2 NSTS-LS2 LST002_02 .in 11/12/2020 MCNP 6.2 NSTS-LS01 LST002_02 .in 11/12/2020 MCNP 6.2 NSTS-LS2 LST002_02.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LST002_02 .ino 11/12/2020 MCNP 6.2 NSTS-LS2 LST002_03.in 11/12/2020 MCNP 6.2 NSTS-LS01 LST002_03.in 11/12/2020 MCNP 6.2 NSTS-LS2 LST002_03.ino 11/18/2020 MCNP 6.2 NSTS-LS01 LST002_03.ino 11/12/2020 MCNP 6.2 NSTS-LS2 8.2. Other Electronic Files Filename File Date Description TMl2-EN-RPT-0002 Data .xlsm 12/10/2020 Data preparation , normality testing , trend analysis, and bias determination Calculation Package No. TMI2-EN-RPT-0002, Revision 1 Page21 of36
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ENERGYSOLUTIONS
- 9. ATTACHMENT A - SAMPLE COMPUTER INPUT/OUTPUT LCT002 0 I .in M401 l0Xll +5 CLUSTER OF U(4.31 )O2 RODS, 2.54 CM PITCH 1 1 .069930523 -1 7 -8 u=l imp : n=l $ uo2 fuel 2 0 -2 1 7 -8 u=l i mp :n=l $ gap 3 3 .059751598 -12 2 u=l imp:n=l $ c l ad 4 4 .11734156 -2 8 u=l imp:n=l $ rubber end plug (top) 5 4 . 11 73 415 6 7 u=l imp:n=l $ rubber end plug (bottom) 6 2 .100059 1 2 u=l imp:n=l $ water 7 0 -4 3 -6 5 imp:n=l lat=l u=2 fill=l $ lattice of fuel rods 8 0 -10 11 -20 2 1 -9 23 fill=2 imp:n=l $ rod cluster 9 0 -1 3 11 -21 19 -9 23 imp:n=l fill=2 $ p art ial r ow o f fu e l rods 10 2 .100059 13 21 1 9 -9 23 imp:n=l $ water of partial row 11 5 .106563 19 - 20 11 23 29 imp : n=l $ acrylic support plate 12 2 .1 000 59 ( - 11:10:20 :- 19:9 : -29) -24 25 -26 27 -28 30 imp:n=l $ water 13 0 24: - 25 : 26 :- 27 : 28 :- 30 i mp :n= 0 1 c/ z 1.27 1.27 .6 32 5 $ fuel cylinder 2 c/ z 1.2 7 1.27 .6415 $ clad inner surface 3 px 0.0 $ fuel rod cell boundary 4 px 2.54 $ fuel rod cell boundary 5 py 0.0 $ fu e l rod cell b oundary 6 py 2 .54 $ fuel rod cell boundary 7 pz 0 . 0 $ bottom of fuel 8 pz 92.075 $ top of fuel 9 pz 94 . 2975 $ top of clad 10 px 25 . 399 $ farthest edge of closest cluster ***
11 px .0001 $ c l osest edge of closest cluster 12 c/ z 1.27 1.27 . 7075 $ clad outer surface 13 px 12.699 $ edge of part i al row ***
19 py 0.000 1 $ c l ose edge o f c l uster+ partial row 20 py 30.479 $ sides of clusters ***
21 py 2 .541 $ side of partial row and full cluster 23 pz -2.2225 $ bottom of fuel rod 24 px 55 .4 $ side of water reflector ***
25 px -30 $ side of water reflector 26 py 60. 48 $ side of water reflecto r ***
27 py -30 $ side of water reflector 28 pz 107.075 $ top of water 29 pz -4.7625 $ bottom of acry l ic support plate 30 pz -20 .0625 $ bottom of water kcode 1000 0 1 100 5100 50000 sdef x=dl y =d2 z=d3 c el=d4 sil 0 41 spl 0 1 si2 0 37 sp2 0 1 si3 0 93 sp3 0 1 si4 1 8 sp4 V print C
c MATERIALS FOR U (4.31 )O2 RODS C
C ml is UO2 fuel ml 92234 5.1835e-6 92235 l . 0102e-3 92236 5 .1395e-6 92238 2.2157e-2 8016 4 .67 53e-2 C m2 is water m2 8016 3.3353e-2 1001 6.6706e-2 mt2 h-h2 O.40 t c m3 is 6061 Al (c lad )
m3 13027 5.8433e-2 C Cr To tal: 6.2310E-05 24050 2.7074E-06 Calculation Package N o. TMI2-EN -RPT-0002, Revision 1 Page 22 of 36
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ENERGYSOLUTIONS 24052 5.2209E-05 24053 5.9201E-06 24054 l.4736E-06 c Cu Total: 6.3731E-05 29063 4.4083E-05 29065 l.9648E-05 c Mg Total: 6.6651E-04 12024 5.2648E-04 12025 6.6651 E -05 12026 7.3383 E- 05 c Ti Total: 2.5375 E-05 22046 2.0934E-06 22047 l.8879E-06 22048 l.8706E-05 22049 l.3728E-06 22050 l.3144E-06 25055 2.2115e-s c Si Total : 3.4607E-04 14028 3 .1 918E-04 14029 l.6161E-05 14030 l.0728E-05 3006 4 l.5236E-05 30066 8.5779E-06 30067 l.2387E-06 30068 5.7289E - 06 30070 l.8580E-07 c Fe Total: 1. 0152E-04 26054 5.9338E-06 26056 9.3149E-05 26057 2.1512E-06 26058 2.8629E-07 c m4 is rubber (end plugs )
m4 6012 4.3083E-02 6013 4.7918E-04 100 1 5.8178e-2 c Ca Total: 2.5660E-03 20040 2.4875E-03 20042 l . 6602E-05 20043 3.4641E-06 20044 5.3527E-05 20046 l.0264E-07 20048 4.7984E-06 16032 4.7820e-4 c Si Total : 9.6360E-05 14028 8 . 8873E-05 14029 4.S000E-06 14030 2 . 9872E-06 8016 l.246le-2 mt4 h-poly.40t c m5 is acry lic (support plate) ms 1001 5 .6642e-2 6012 3 . 5256E-02 6013 3.9213 E-04 8016 1. 4273e-2 mtS h-pol y. 40t Calculation Package No. TMI2-EN -RPT-0002, Revision 1 Page 23 of 36
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ENERGYSOLVTIONS
- 10. ATTACHMENT B - BENCHMARK DATA SET The following table provides all the results for all the benchmark cases run. The results are identical for all cases run on NSTS-LS0l and NSTS-LS2 .
Table 4: Benchmark Results for MCNP6 Benchmark ID from Ref. [5] Case# kexp CY exp kcalc CY ca le kadj CYcom LEU-COMP-THERM-002 1 0.9997 0.0020 0.99854 0.00010 0.9988 0.0020 LEU-COMP-THERM-002 2 0.9997 0.0020 0.99964 0.00010 0.9999 0.0020 LEU-COMP-THERM-002 3 0.9997 0.0020 0.99937 0.00010 0.9997 0.0020 LEU-COMP-THERM-002 4 0.9997 0.0018 0.99884 0.00010 0.9991 0.0018 LEU-COMP-THERM-002 5 0.9997 0.0019 0.99777 0.00010 0.9981 0.0019 LEU-COMP-THERM-009 1 1.0000 0.0021 0.99928 0.00010 0.9993 0.0021 LEU-COMP-THERM-009 2 1.0000 0.0021 0.99890 0.00010 0.9989 0.0021 LEU-COMP-TH ERM-009 3 1.0000 0.0021 0.99854 0.00010 0.9985 0.0021 LEU-COMP-TH ERM-009 4 1.0000 0.0021 0.99928 0.00010 0.9993 0.0021 LEU-COMP-TH ERM-009 5 1.0000 0.0021 0.99962 0.00010 0.9996 0.0021 LEU-COMP-TH ERM-009 6 1.0000 0.0021 0.99904 0.00010 0.9990 0.0021 LEU-COMP-TH ERM-009 7 1.0000 0.0021 0.99971 0.00010 0.9997 0.0021 LEU-COMP-THERM-009 8 1.0000 0.0021 0.99884 0.00011 0.9988 0.0021 LEU-COMP-THERM-009 9 1.0000 0.0021 0.99929 0.00011 0.9993 0.0021 LEU-COMP-THERM-009 10 1.0000 0.0021 0.99910 0.00010 0.9991 0.0021 LEU-COMP-THERM-009 11 1.0000 0.0021 0.99916 0.00010 0.9992 0.0021 LEU-COMP-THERM-009 12 1.0000 0.0021 0.99965 0.00010 0.9997 0.0021 LEU-COMP-TH ERM-009 13 1.0000 0.0021 0.99971 0.00010 0.9997 0.0021 LEU-COMP-TH ERM-009 14 1.0000 0.0021 0.99786 0.00010 0.9979 0.0021 LEU-COMP-TH ERM-009 15 1.0000 0.0021 0.99967 0.00010 0.9997 0.0021 LEU-COMP-TH ERM-009 16 1.0000 0.0021 0.99877 0.00011 0.9988 0.0021 LEU-COMP-THERM-009 17 1.0000 0.0021 0.99971 0.00010 0.9997 0.0021 LEU-COMP-TH ERM-009 18 1.0000 0.0021 0.99857 0.00010 0.9986 0.0021 LEU-COMP-THERM-009 19 1.0000 0.0021 0.99957 0.00011 0.9996 0.0021 LEU-COMP-THERM-009 20 1.0000 0.0021 0.99886 0.00011 0.9989 0.0021 LEU-COMP-THERM-009 21 1.0000 0.0021 0.99951 0.00010 0.9995 0.0021 LEU-COMP-THERM-009 22 1.0000 0.0021 0.99903 0.00011 0.9990 0.0021 LEU-COMP-TH ERM-009 23 1.0000 0.0021 0.99971 0.00010 0.9997 0.0021 LEU-COMP-TH ERM-009 24 1.0000 0.0021 0.99893 0.00010 0.9989 0.0021 LEU-COMP-TH ERM-009 25 1.0000 0.0021 0.99913 0.00010 0.9991 0.0021 LEU-COMP-THERM-009 26 1.0000 0.0021 0.99938 0.00010 0.9994 0.0021 LEU-COMP-THERM-013 1 1.0000 0.0018 1.00047 0.00011 1.0005 0.0018 LEU-COMP-THERM-013 2 1.0000 0.0018 1.00009 0.00011 1.0001 0.0018 LEU-COMP-THERM-013 3 1.0000 0.0018 0.99992 0.00011 0.9999 0.0018 LEU-COMP-THERM-013 4 1.0000 0.0018 1.00047 0.00011 1.0005 0.0018 LEU-COMP-TH ERM-013 5 1.0000 0.0032 0.98707 0.00011 0.9871 0.0032 LEU-COMP-THERM-013 6 1.0000 0.0018 0.99967 0.00011 0.9997 0.0018 LEU-COMP-THERM-013 7 1.0000 0.0018 0.99944 0.00011 0.9994 0.0018 LEU-COMP-THERM-033 1 1.0000 0.0038 1.00297 0.00010 1.0030 0.0038 LEU -COMP-THERM-033 2 1.0000 0.0038 1.00360 0.00010 1.0036 0.0038 LEU-COMP-TH ERM-033 3 1.0000 0.0038 1.00455 0.00010 1.0046 0.0038 LEU-COMP-THERM-033 4 1.0000 0.0038 1.00360 0.00010 1.0036 0.0038 Calculation Package No. TMI2-EN-RPT-0002, Revision 1 Page 24 of36
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ENERGYSOLUTIONS Benchmark ID from Ref. rs1 Case# kexp CYexp kcalc CYcalc kadj CY com LEU-COMP-THERM-033 5 1.0000 0.0039 1.00603 0.00010 1.0060 0.0039 LEU-COMP-THERM-033 6 1.0000 0.0039 0.99752 0.00010 0.9975 0.0039 LEU-COMP-THERM-033 7 1.0000 0.0039 0.99756 0.00010 0.9976 0.0039 LEU-COMP-THERM-033 8 1.0000 0.0040 0.99893 0.00010 0.9989 0.0040 LEU-COMP-THERM-033 9 1.0000 0.0040 0.99943 0.00010 0.9994 0.0040 LEU-COMP-THERM-033 10 1.0000 0.0039 0.99141 0.00010 0.9914 0.0039 LEU-COMP-THERM-033 11 1.0000 0.0039 0.99306 0.00009 0.9931 0.0039 LEU-COMP-THERM-033 12 1.0000 0.0039 0.99439 0.00009 0.9944 0.0039 LEU-COMP-THERM-033 13 1.0000 0.0041 1.00164 0.00009 1.0016 0.0041 LEU-COMP-THERM-033 14 1.0000 0.0051 0.99448 0.00007 0.9945 0.0051 LEU-COMP-THERM-033 15 1.0000 0.0051 0.99472 0.00007 0.9947 0.0051 LEU-COMP-THERM-033 16 1.0000 0.0051 0.99499 0.00007 0.9950 0.0051 LEU-COMP-THERM-033 17 1.0000 0.0038 0.99374 0.00011 0.9937 0.0038 LEU-COMP-TH ERM-033 18 1.0000 0.0038 0.99537 0.00011 0.9954 0.0038 LEU-COMP-THERM-033 19 1.0000 0.0038 0.99765 0.00011 0.9977 0.0038 LEU-COMP-TH ERM-033 20 1.0000 0.0038 0.99885 0.00011 0.9989 0.0038 LEU-COMP-TH ERM-033 21 1.0000 0.0038 0.99947 0.00011 0.9995 0.0038 LEU-COMP-THERM-033 22 1.0000 0.0039 1.01380 0.00011 1.0138 0.0039 LEU-COMP-THERM-033 23 1.0000 0.0040 1.00458 0.00011 1.0046 0.0040 LEU-COMP-THERM-033 24 1.0000 0.0040 1.00418 0.00010 1.0042 0.0040 LEU-COMP-THERM-033 25 1.0000 0.0040 1.00342 0.00011 1.0034 0.0040 LEU-COMP-THE RM-033 26 1.0000 0.0039 1.00688 0.00010 1.0069 0.0039 LEU-COMP-THE RM-033 27 1.0000 0.0039 1.00720 0.00010 1.0072 0.0039 LEU-COMP-THERM-033 28 1.0000 0.0039 1.00735 0.00010 1.0074 0.0039 LEU-COMP-TH ERM-033 29 1.0000 0.0039 1.00677 0.00011 1.0068 0.0039 LEU-COMP-TH ERM-033 30 1.0000 0.0039 1.00481 0.00010 1.0048 0.0039 LEU-COMP-THERM-033 31 1.0000 0.0039 1.00436 0.00010 1.0044 0.0039 LEU-COMP-THERM-033 32 1.0000 0.0039 1.00455 0.00010 1.0046 0.0039 LEU-COMP-THERM-033 33 1.0000 0.0039 1.00435 0.00010 1.0044 0.0039 LEU-COMP-THERM-033 34 1.0000 0.0039 1.00446 0.00010 1.0045 0.0039 LEU-COMP-THERM-033 35 1.0000 0.0040 1.00307 0.00010 1.0031 0.0040 LEU-COMP-THE RM-033 36 1.0000 0.0040 1.00316 0.00010 1.0032 0.0040 LEU-COMP-TH ERM-033 37 1.0000 0.0040 1.00254 0.00010 1.0025 0.0040 LEU-COMP-THERM-033 38 1.0000 0.0040 1.00261 0.00010 1.0026 0.0040 LEU-COMP-TH ERM-033 39 1.0000 0.0040 1.00268 0.00010 1.0027 0.0040 LEU-COMP-THERM-033 40 1.0000 0.0040 1.00219 0.00010 1.0022 0.0040 LEU-COMP-THERM-033 41 1.0000 0.0041 1.00293 0.00009 1.0029 0.0041 LEU-COMP-THERM-033 42 1.0000 0.0041 1.00169 0.00009 1.0017 0.0041 LEU-COMP-THERM-033 43 1.0000 0.0050 1.00079 0.00009 1.0008 0.0050 LEU-COMP-THERM-033 44 1.0000 0.0050 0.99503 0.00007 0.9950 0.0050 LEU-COMP-THERM-033 45 1.0000 0.0050 0.99467 0.00008 0.9947 0.0050 LEU-COMP-TH ERM-033 46 1.0000 0.0050 0.99409 0.00008 0.9941 0.0050 LEU-COMP-THERM-033 47 1.0000 0.0042 1.01824 0.00012 1.0182 0.0042 LEU-COMP-THERM-033 48 1.0000 0.0042 1.01685 0.00012 1.0169 0.0042 LEU-COMP-THERM-033 49 1.0000 0.0042 1.01700 0.00011 1.0170 0.0042 LEU-COMP-THERM-033 50 1.0000 0.0041 1.01851 0.00012 1.0185 0.0041 LEU-COMP-TH ERM-033 51 1.0000 0.0041 1.01966 0.00012 1.0197 0.0041 LEU-COMP-TH ERM-033 52 1.0000 0.0041 1.01572 0.00011 1.0157 0.0041 Calculation Package No. TMI2-EN-RPT-0002, Revision 1 Page 25 of36
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ENERGYSOLUTJONS Benchmark ID from Ref. £51 Case# kexp <Yexp k ca lc <Ycalc kadj <Ycom LEU-COMP-THERM-042 1 1.0000 0.0016 0.99770 0.00010 0.9977 0.0016 LEU-COMP-THERM-042 2 1.0000 0.0016 0.99756 0.00010 0.9976 0.0016 LEU-COMP-TH ERM-042 3 1.0000 0.0016 0.99831 0.00010 0.9983 0.0016 LEU-COMP-THERM-042 4 1.0000 0.0017 0.99876 0.00010 0.9988 0.0017 LEU-COMP-THERM-042 5 1.0000 0.0033 0.99871 0.00010 0.9987 0.0033 LEU-COMP-THERM-042 6 1.0000 0.0016 0.99886 0.00010 0.9989 0.0016 LEU-COMP-THERM-042 7 1.0000 0.0018 0.99722 0.00010 0.9972 0.0018 LEU-COMP-THERM-049 1 1.0000 0.0034 0.99564 0.00011 0.9956 0.0034 LEU-COMP-THERM -049 2 1.0000 0.0034 0.99618 0.00011 0.9962 0.0034 LEU-COMP-THERM-049 3 1.0000 0.0034 0.99617 0.00011 0.9962 0.0034 LEU-COMP-THERM-049 4 1.0000 0.0034 0.99655 0.00011 0.9966 0.0034 LEU-COMP-THERM -049 5 1.0000 0.0042 0.99580 0.00011 0.9958 0.0042 LEU-COMP-THERM-049 6 1.0000 0.0042 0.99738 0.00011 0.9974 0.0042 LEU-COMP-THERM-049 7 1.0000 0.0042 0.99650 0.00011 0.9965 0.0042 LEU-COMP-THERM-049 8 1.0000 0.0042 0.99591 0.00011 0.9959 0.0042 LEU -COMP-THERM-049 9 1.0000 0.0037 0.99564 0.00011 0.9956 0.0037 LEU-COMP-THERM-049 10 1.0000 0.0037 0.99784 0.00011 0.9978 0.0037 LEU-COMP-THERM-049 11 1.0000 0.0037 0.99615 0.0001 1 0.9962 0.0037 LEU-COMP-THERM-049 12 1.0000 0.0037 0.99610 0.00011 0.9961 0.0037 LEU-COMP-THERM-049 13 1.0000 0.0036 0.99562 0.00011 0.9956 0.0036 LEU-COMP-THERM-049 14 1.0000 0.0036 0.99608 0.00011 0.9961 0.0036 LEU-COMP-THERM-049 15 1.0000 0.0036 0.99736 0.00011 0.9974 0.0036 LEU-COMP-THERM-049 16 1.0000 0.0036 0.99667 0.00011 0.9967 0.0036 LEU-COMP-THERM-049 17 1.0000 0.0036 0.99671 0.00011 0.9967 0.0036 LEU-COMP-TH ERM-049 18 1.0000 0.0030 0.99951 0.00011 0.9995 0.0030 LEU-COMP-THERM-092 1 1.00033 0.00044 1.00089 0.00010 1.0006 0.0005 LEU-COMP-THERM-092 2 1.00033 0.00044 0.99967 0.00010 0.9993 0.0005 LEU-COMP-TH ERM-092 3 1.00032 0.00044 0.99860 0.00010 0.9983 0.0005 LEU-COMP-THERM-092 4 1.00033 0.00044 0.99632 0.00010 0.9960 0.0005 LEU-COMP-THERM-092 5 1.00033 0.00046 0.99168 0.00010 0.9914 0.0005 LEU-COMP-THERM-092 6 1.00033 0.00055 0.98076 0.00010 0.9804 0.0006 LEU-SOL-THERM-001 1 0.9991 0.0029 1.01215 0.00011 1.0131 0.0029 LEU-SOL-THERM-002 1 1.0038 0.0040 1.00016 0.00008 0.9964 0.0040 LEU-SOL-THERM-002 2 1.0024 0.0037 0.99591 0.00009 0.9935 0.0037 LEU-SOL-THERM-002 3 1.0024 0.0044 1.00101 0.00008 0.9986 0.0044 Calculation Package No. TMI2-EN-RPT-0002, Revision 1 Page 26 of 36
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ENERGYSOLUTIONS
- 11. ATTACHMENT C- TABLES OF K ADJ VALUES The following table contains the ordered kactj values. The MCNP6 output fi lename is also provided to aid in traceability .
Table 5: Ord ered kactj Va lu es for LEU Filename Observation k adi Ocom LCT092 06.ino 1 0.9804 0.0006 LCT01 3 05.ino 2 0.9871 0.00 32 LCT092 05.ino 3 0.9914 0.0005 LCT033 10.ino 4 0.9914 0.0039 LCT033 11.ino 5 0.9931 0.0039 LST002 02 .ino 6 0.9935 0.0037 LCT033 17.ino 7 0.9937 0.0038 LCT033 46.ino 8 0.9941 0.0050 LCT033 12.ino 9 0.9944 0.0039 LCT033 14.ino 10 0.9945 0.0051 LCT033 45.ino 11 0.9947 0.0050 LCT033 15.ino 12 0.9947 0.0051 LCT033 16.ino 13 0.9950 0.0051 LCT033 44.ino 14 0.9950 0.0050 LCT033 18.ino 15 0.9954 0.0038 LCT049 13.ino 16 0.9956 0.0036 LCT049 01 .ino 17 0.9956 0.0034 LCT049 09.ino 18 0.9956 0.0037 LCT049 05.ino 19 0.9958 0.0042 LCT049 08.ino 20 0.9959 0.0042 LCT092 04.ino 21 0.9960 0.0005 LCT049 14.ino 22 0.9961 0.0036 LCT049 12.ino 23 0.9961 0.0037 LCT049 11.ino 24 0.9962 0.0037 LCT049 03.ino 25 0.9962 0.0034 LCT049 02.ino 26 0.9962 0.0034 LST002 01 .ino 27 0.9964 0.0040 LCT049 07.ino 28 0.9965 0.0042 LCT049 04.ino 29 0.9966 0.0034 LCT049 16.ino 30 0.9967 0.0036 LCT049 17.ino 31 0.9967 0.0036 LCT042 07.ino 32 0.9972 0.0018 LCT049 15.ino 33 0.9974 0.0036 LCT049 06.ino 34 0.9974 0.0042 LCT033 06.ino 35 0.9975 0.0039 LCT033 07.ino 36 0.9976 0.0039 LCT042 02 .ino 37 0.9976 0.0016 LCT033 19.ino 38 0.9977 0.0038 LCT042 01.ino 39 0.9977 0.0016 LCT049 10.ino 40 0.9978 0.0037 LCT009 14.ino 41 0.9979 0.0021 LCT002 05.ino 42 0.998 1 0.0019 LCT092 03.ino 43 0.9983 0.0005 LCT042 03 .ino 44 0.9983 0.0016 LCT009 03.ino 45 0.9985 0.0021 Calculation Package No. TMI2-EN-RPT-0002, Revision 1 Page 27 of 36
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ENERGYSOLVTIONS Filename Observation kadi O com LCT009 18.ino 46 0.9986 0.0021 LST002 03.ino 47 0.9986 0.0044 LCT042 05.ino 48 0.9987 0.0033 LCT042 04.ino 49 0.9988 0.0017 LCT009 16.ino 50 0.9988 0.0021 LCT002 01 .ino 51 0.9988 0.0020 LCT009 08.ino 52 0.9988 0.0021 LCT033 20 .ino 53 0.9989 0.0038 LCT009 20 .ino 54 0.9989 0.0021 LCT042 06.ino 55 0.9989 0.0016 LCT009 02 .ino 56 0.9989 0.0021 LCT009 24.ino 57 0.9989 0.0021 LCT033 08.ino 58 0.9989 0.0040 LCT009 22 .ino 59 0.9990 0.0021 LCT009 06.ino 60 0.9990 0.0021 LCT009 10.ino 61 0.9991 0.0021 LCT009 25.ino 62 0.9991 0.0021 LCT002 04.ino 63 0.9991 0.0018 LCT009 11 .ino 64 0.9992 0.0021 LCT009 01.ino 65 0.9993 0.0021 LCT009 04.ino 66 0.9993 0.0021 LCT009 09.ino 67 0.9993 0.0021 LCT092 02 .ino 68 0.9993 0.0005 LCT009 26.ino 69 0.9994 0.0021 LCT033 09.ino 70 0.9994 0.0040 LCT013 07.ino 71 0.9994 0.0018 LCT033 21 .ino 72 0.9995 0.0038 LCT009 21 .ino 73 0.9995 0.0021 LCT049 18.ino 74 0.9995 0.0030 LCT009 19.ino 75 0.9996 0.0021 LCT009 05.ino 76 0.9996 0.0021 LCT009 12.ino 77 0.9997 0.0021 LCT002 03.ino 78 0.9997 0.0020 LCT009 15.ino 79 0.9997 0.0021 LCT013 06.ino 80 0.9997 0.0018 LCT009 07.ino 81 0.9997 0.0021 LCT009 13.ino 82 0.9997 0.0021 LCT009 17.ino 83 0.9997 0.0021 LCT009 23.ino 84 0.9997 0.0021 LCT013 03.ino 85 0.9999 0.0018 LCT002 02 .ino 86 0.9999 0.0020 LCT013 02.ino 87 1.0001 0.0018 LCT013 01 .ino 88 1.0005 0.0018 LCT013 04.ino 89 1.0005 0.0018 LCT092 01 .ino 90 1.0006 0.0005 LCT033 43.ino 91 1.0008 0.0050 LCT033 13.ino 92 1.0016 0.0041 LCT033 42 .ino 93 1.0017 0.0041 LCT033 40.ino 94 1.0022 0.0040 LCT033 37.ino 95 1.0025 0.0040 LCT033 38.ino 96 1.0026 0.0040 LCT033 39.ino 97 1.0027 0.0040 Calculation Package No. TMI2-EN-RPT-0002, Revision 1 Page 28 of36
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ENERGYSOLUTIONS Filename Observation kadi O com LCT033 41.ino 98 1.0029 0.0041 LCT033 01.ino 99 1.0030 0.0038 LCT033 35.ino 100 1.0031 0.0040 LCT033 36.ino 101 1.0032 0.0040 LCT033 25.ino 102 1.0034 0.0040 LCT033 02.ino 103 1.0036 0.0038 LCT033 04.ino 104 1.0036 0.0038 LCT033 24.ino 105 1.0042 0.0040 LCT033 33.ino 106 1.0044 0.0039 LCT033 31.ino 107 1.0044 0.0039 LCT033 34.ino 108 1.0045 0.0039 LCT033 03.ino 109 1.0046 0.0038 LCT033 32.ino 110 1.0046 0.0039 LCT033 23.ino 111 1.0046 0.0040 LCT033 30.ino 112 1.0048 0.0039 LCT033 05.ino 113 1.0060 0.0039 LCT033 29.ino 114 1.0068 0.0039 LCT033 26.ino 115 1.0069 0.0039 LCT033 27.ino 116 1.0072 0.0039 LCT033 28.ino 117 1.0074 0.0039 LST001 01.ino 118 1.0131 0.0029 LCT033 22.ino 119 1.0138 0.0039 LCT033 52 .ino 120 1.0157 0.0041 LCT033 48.ino 121 1.0169 0.0042 LCT033 49.ino 122 1.0170 0.0042 LCT033 47.ino 123 1.0182 0.0042 LCT033 50.ino 124 1.0185 0.0041 LCT033 51.ino 125 1.0197 0.0041 Calculation Package No . TMI2-EN-RPT-0002, Revision 1 Page 29 of36
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ENERGYSOLUTIONS
- 12. ATTACHMENT D-LILLIEFORS TESTING TABLES Table 6: Lilliefors Normality Test Determination for MCNP6 Benchmark Results for LEU Case# kadj O"com Z; F(z) G(z) IF*(z;)-G(z;)I IF*(z;)-G(z;-1)1 1 0.9804 0.0006 -3.40840 0.00033 0.00800 0.00767 0.00033 2 0.9871 0.0032 -2 .25560 0.01205 0.01600 0.00395 0.00405 3 0.9914 0.0005 -1 .51131 0.06535 0.02400 0.04135 0.04935 4 0.9914 0.0039 -1 .50138 0.06663 0.03200 0.03463 0.04263 5 0.9931 0.0039 -1.21464 0.11225 0.04000 0.07225 0.08025 6 0.9935 0.0037 -1.13374 0.12845 0.04800 0.08045 0.08845 7 0.9937 0.0038 -1.09647 0.13644 0.05600 0.08044 0.08844 8 0.9941 0.0050 -1.03564 0.15018 0.06400 0.08618 0.09418 9 0.9944 0.0039 -0.98351 0.16268 0.07200 0.09068 0.09868 10 0.9945 0.0051 -0.96787 0.16656 0.08000 0.08656 0.09456 11 0.9947 0.0050 -0.93485 0.17493 0.08800 0.08693 0.09493 12 0.9947 0.0051 -0 .92616 0.17718 0.09600 0.08118 0.08918 13 0.9950 0.0051 -0 .87924 0.18964 0.10400 0.08564 0.09364 14 0.9950 0.0050 -0.87229 0.19153 0.11200 0.07953 0.08753 15 0.9954 0.0038 -0.81320 0.20805 0.12000 0.08805 0.09605 16 0.9956 0.0036 -0.76975 0.22072 0.12800 0.09272 0.10072 17 0.9956 0.0034 -0.76628 0.22176 0.13600 0.08576 0.09376 18 0.9956 0.0037 -0.76628 0.22176 0.14400 0.07776 0.08576 19 0.9958 0.0042 -0.73847 0.23011 0.15200 0.07811 0.08611 20 0.9959 0.0042 -0.71936 0.23596 0.16000 0.07596 0.08396 21 0.9960 0.0005 -0 .70522 0.24034 0.16800 0.07234 0.08034 22 0.9961 0.0036 -0 .68981 0.24516 0.17600 0.06916 0.07716 23 0.9961 0.0037 -0.68634 0.24625 0.18400 0.06225 0.07025 24 0.9962 0.0037 -0.67765 0.24900 0.19200 0.05700 0.06500 25 0.9962 0.0034 -0 .67417 0.25010 0.20000 0.05010 0.05810 26 0.9962 0.0034 -0.67244 0.25065 0.20800 0.04265 0.05065 27 0.9964 0.0040 -0.63876 0.26149 0.21600 0.04549 0.05349 28 0.9965 0.0042 -0.61682 0.26868 0.22400 0.04468 0.05268 29 0.9966 0.0034 -0.60814 0.27155 0.23200 0.03955 0.04755 30 0.9967 0.0036 -0.58728 0.27851 0.24000 0.03851 0.04651 31 0.9967 0.0036 -0.58033 0.28085 0.24800 0.03285 0.04085 32 0.9972 0.0018 -0.49170 0.31147 0.25600 0.05547 0.06347 33 0.9974 0.0036 -0.46737 0.32012 0.26400 0.05612 0.06412 34 0.9974 0.0042 -0.46390 0.32136 0.27200 0.04936 0.05736 35 0.9975 0.0039 -0.43957 0.33013 0.28000 0.05013 0.05813 36 0.9976 0.0039 -0.43261 0.33265 0.28800 0.04465 0.05265 37 0.9976 0.0016 -0.43261 0.33265 0.29600 0.03665 0.04465 38 0.9977 0.0038 -0.41697 0.33835 0.30400 0.03435 0.04235 39 0.9977 0.0016 -0.40829 0.34153 0.31200 0.02953 0.03753 40 0.9978 0.0037 -0.38396 0.35051 0.32000 0.03051 0.03851 41 0.9979 0.0021 -0.38048 0.35179 0.32800 0.02379 0.03179 42 0.9981 0.0019 -0.34409 0.36539 0.33600 0.02939 0.03739 43 0.9983 0.0005 -0 .30740 0.37927 0.34400 0.03527 0.04327 44 0.9983 0.0016 -0.30228 0.38122 0.35200 0.02922 0.03722 45 0.9985 0.0021 -0 .26231 0.39654 0.36000 0.03654 0.04454 46 0.9986 0.0021 -0.25709 0.39855 0.36800 0.03055 0.03855 47 0.9986 0.0044 -0.24956 0.40146 0.37600 0.02546 0.03346 48 0.9987 0.0033 -0.23276 0.40797 0.38400 0.02397 0.03197 Calculation Package No. TMI2-EN-RPT-0002, Revision 1 Page 30 of36
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ENERGYSOLUTIONS Case# kadj CYcom Z; F(z) G(z) IF*(z;)-G(z;)I I F*(z;)-G(z;-1) I 49 0.9988 0.0017 -0 .22407 0.41135 0.39200 0.01935 0.02735 50 0.9988 0.0021 -0.22234 0.41203 0.40000 0.01203 0.02003 51 0.9988 0.0020 -0 .21023 0.41674 0.40800 0.00874 0.01674 52 0.9988 0.0021 -0 .21017 0.41677 0.41600 0.00077 0.00877 53 0.9989 0.0038 -0.20843 0.41744 0.42400 0.00656 0.00144 54 0.9989 0.0021 -0 .20670 0.41812 0.43200 0.01388 0.00588 55 0.9989 0.0016 -0 .20670 0.41812 0.44000 0.02188 0.01388 56 0.9989 0.0021 -0 .19975 0.42084 0.44800 0.02716 0.01916 57 0.9989 0.0021 -0 .19453 0.42288 0.45600 0.03312 0.02512 58 0.9989 0.0040 -0 .1 9453 0.42288 0.46400 0.04112 0.03312 59 0.9990 0.0021 -0 .17715 0.42969 0.47200 0.04231 0.03431 60 0.9990 0.0021 -0 .1 7542 0.43038 0.48000 0.04962 0.04162 61 0.9991 0.0021 -0.16499 0.43448 0.48800 0.05352 0.04552 62 0.9991 0.0021 -0 .15978 0.43653 0.49600 0.05947 0.05147 63 0.9991 0.0018 -0.15808 0.43720 0.50400 0.06680 0.05880 64 0.9992 0.0021 -0.15456 0.43858 0.51200 0.07342 0.06542 65 0.9993 0.0021 -0.13371 0.44682 0.52000 0.07318 0.06518 66 0.9993 0.0021 -0.13371 0.44682 0.52800 0.08118 0.07318 67 0.9993 0.0021 -0.13197 0.44750 0.53600 0.08850 0.08050 68 0.9993 0.0005 -0.12324 0.45096 0.54400 0.09304 0.08504 69 0.9994 0.0021 -0.11633 0.45370 0.55200 0.09830 0.09030 70 0.9994 0.0040 -0.10764 0.45714 0.56000 0.10286 0.09486 71 0.9994 0.0018 -0.10590 0.45783 0.56800 0.11017 0.10217 72 0.9995 0.0038 -0.10069 0.45990 0.57600 0.11610 0.10810 73 0.9995 0.0021 -0.09374 0.46266 0.58400 0.12134 0.11334 74 0.9995 0.0030 -0 .09374 0.46266 0.59200 0.12934 0.12134 75 0.9996 0.0021 -0.08331 0.46680 0.60000 0.13320 0.12520 76 0.9996 0.0021 -0.07462 0.47026 0.60800 0.13774 0.12974 77 0.9997 0.0021 -0.06941 0.47233 0.61600 0.14367 0.13567 78 0.9997 0.0020 -0.06595 0.47371 0.62400 0.15029 0.14229 79 0.9997 0.0021 -0.06593 0.47372 0.63200 0.15828 0.15028 80 0.9997 0.0018 -0.06593 0.47372 0.64000 0.16628 0.1 5828 81 0.9997 0.0021 -0.05898 0.47648 0.64800 0.17152 0.16352 82 0.9997 0.0021 -0.05898 0.47648 0.65600 0.17952 0.17152 83 0.9997 0.0021 -0.05898 0.47648 0.66400 0.18752 0.17952 84 0.9997 0.0021 -0.05898 0.47648 0.67200 0.19552 0.18752 85 0.9999 0.0018 -0.02249 0.49103 0.68000 0.18897 0.18097 86 0.9999 0.0020 -0.01901 0.49241 0.68800 0.19559 0.18759 87 1.0001 0.0018 0.00706 0.50282 0.69600 0.19318 0.18518 88 1.0005 0.0018 0.07309 0.52913 0.70400 0.17487 0.16687 89 1.0005 0.0018 0.07309 0.52913 0.71200 0.1 8287 0.17487 90 1.0006 0.0005 0.08870 0.53534 0.72000 0.18466 0.17666 91 1.0008 0.0050 0.1 2870 0.55120 0.72800 0.17680 0.16880 92 1.0016 0.0041 0.27642 0.60889 0.73600 0.1 2711 0.11911 93 1.0017 0.0041 0.28511 0.61222 0.74400 0.13178 0.12378 94 1.0022 0.0040 0.37200 0.64505 0.75200 0.10695 0.09895 95 1.0025 0.0040 0.43283 0.66743 0.76000 0.09257 0.08457 96 1.0026 0.0040 0.44499 0.67184 0.76800 0.09616 0.08816 97 1.0027 0.0040 0.45715 0.67622 0.77600 0.09978 0.09178 98 1.0029 0.0041 0.50060 0.69167 0.78400 0.09233 0.08433 99 1.0030 0.0038 0.50755 0.69412 0.79200 0.09788 0.08988 100 1.0031 0.0040 0.52493 0.70018 0.80000 0.09982 0.09182 Calculation Package No. TMI2-EN-RPT-0002, Revision 1 Page31 of36
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ENERGYSOLUTIONS Case# kadj Ocom Z; F(z) G(z) IF*(z;)-G(z;)I IF*(z;)-G(z;.1) I 101 1.0032 0.0040 0.54057 0.70560 0.80800 0.10240 0.09440 102 1.0034 0.0040 0.58575 0.72098 0.81600 0.09502 0.08702 103 1.0036 0.0038 0.61704 0.73139 0.82400 0.09261 0.08461 104 1.0036 0.0038 0.61704 0.73139 0.83200 0.10061 0.09261 105 1.0042 0.0040 0.71783 0.76357 0.84000 0.07643 0.06843 106 1.0044 0.0039 0.74737 0.77258 0.84800 0.07542 0.06742 107 1.0044 0.0039 0.74911 0.77310 0.85600 0.08290 0.07490 108 1.0045 0.0039 0.76649 0.77831 0.86400 0.08569 0.07769 109 1.0046 0.0038 0.78213 0.78293 0.87200 0.08907 0.08107 110 1.0046 0.0039 0.78213 0.78293 0.88000 0.09707 0.08907 111 1.0046 0.0040 0.78734 0.78446 0.88800 0.10354 0.09554 112 1.0048 0.0039 0.82731 0.79597 0.89600 0.10003 0.09203 113 1.0060 0.0039 1.03933 0.85067 0.90400 0.05333 0.04533 114 1.0068 0.0039 1.16793 0.87858 0.91200 0.03342 0.02542 115 1.0069 0.0039 1.18704 0.88239 0.92000 0.03761 0.02961 116 1.0072 0.0039 1.24265 0.89300 0.92800 0.03500 0.02700 117 1.0074 0.0039 1.26872 0.89773 0.93600 0.03827 0.03027 118 1.0131 0.0029 2.26133 0.98813 0.94400 0.04413 0.05213 119 1.0138 0.0039 2.38962 0.99157 0.95200 0.03957 0.04757 120 1.0157 0.0041 2.72329 0.99677 0.96000 0.03677 0.04477 121 1.0169 0.0042 2.91966 0.99825 0.96800 0.03025 0.03825 122 1.0170 0.0042 2.94573 0.99839 0.97600 0.02239 0.03039 123 1.0182 0.0042 3.16122 0.99921 0.98400 0.01521 0.02321 124 1.0185 0.0041 3.20814 0.99933 0.99200 0.00733 0.01533 125 1.0197 0.0041 3.40799 0.99967 1.00000 0.00033 0.00767 Lilliefors Test Results k = 1.0000 I s = 0.0058 n=125 W1-a=0.07925 Max T*=0.19559 k1=0.9804 ; 01=0.0006 T* > W1 -a therefore these cases are probably not 13 = 99.99% ; NPM (125) = 0 from a normal distribution . As such the (Table 2.2, NUREG/CR-6698, Ref. [3])
nonparametric method is used to define the bias as Bias= 0.9804 - 0.0006 described in Section 5.4.1.
Bias= 0.9798 Calculation Package No. TMI2-EN-RPT-0002, Revision 1 Page 32 of36
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ENERG\'SOWT/ONS
- 13. ATTACHMENT E- NORMAL PLOT FIGURES The following figure is the normal probability plot of results identified in Section 6.1.
1.025 1.020 1.015 1.010
.,, 1.005 cu
- I iii
'ij'
~* 1.000
-0 cu cu
-0 O 0.995 0 .990 0.985 0 .980 0 .975
-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 Normal Order Statistic Medians Figure 1: Normal Probability Plot for LEU kadj Results Calculation Package No. TMI2-EN-RPT-0002, Revision 1 Page 33 of36
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ENERGYSOLUTIONS
- 14. ATTACHMENT F-TREND ANALYSIS FIGURES The following figures present the results of the trend analysis performed on the kadj values over the range of ANECF and enrichment. The data is fitted to a linear, a 3rd order polynomial, and a power function . The best fit of these functions is shown in the figures along with the determined value ofR2 .
The largest R2 value was 0.2 for the kadj vs. enrichment data fitted to a 3rd order polynomial. None of the data resulted in a R 2 value greater than 0.8 which indicates that none of the data demonstrated a good correlation with the various assumed functions. Therefore, none of the data is considered to demonstrate any significant or relevant trend that would need to be compensated for in the bias.
Calculation Package No. TMI2-EN-RPT-0002, Revision 1 Page 34 of36
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ENERGYSOLVTIONS y = -8 .32E-03x + 1.00E+OO Fitted line formula R2 = 6.91E-03 1.025 1.02 1.015 1.01
~
1.005
-9' IV 1
~
- .!">~
~~ 11111 lf:995 0.99
- 0.985 0.98 0.975 1.0000E-02 1.0000E-01 1.0000E+OO AENCF(MeV) y =-1.31E-Olx1 - 2:95E-Ol x1 + 9.83E-02x 9 .94E-01 Fitted line formula R2 = 7.37E-02 1.025 1.02 1.0 15
-~
1.0 1
~
1.005 l
~
i L ~
", ltlllirt 0.995 0.99 * "' 1 0.985 0.98 0 .975 1.0000E-02 UJOOOE-01 1.0000E+OO AENCF(MeV)
Fitted line formula v= l.OOE+OOx UBE-115 R2 ='6-54E-06 1.025 1.02 ~
1.015
~
-~r--
1.01 1.005 -~
l,... , "
'5'" 1
!II (P.g95 0 .99*
0.985
~
- . . ~
0.98 ....
~
0.975 1.0000E-02 l .OOOOf-01 l.OOOOE+OO AENCF (MeV)
Figure 2: ANECF Trend Analysis Plots for LEU Calculation Package No. TMI2-EN-RPT-0002, Revision 1 Page 35 of 36
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ENERG\'SOLUTIONS Fitted line formula y =-1.44E-o3x + 1.0 lE+OO R' = 8.97E-02 1.025 1.02 1.015 l 1.01 I
1.005
'ti 1 IQ
~.995 0.99 J
rn 0 ..985 0.98 ....
0.975 1.0 10.0 Enrichment *(wt%. 235U)
- r. =2.13E-03x 3
- 2.47E-02x 2 + 8.84E-02x + 9.0SE-01 Fitted line formu a IR' = 2.17f-01 1.025 1.02 1
1.015 <
1.01 1.005 i:) 1 Ill
(¥.995 0.99 V
- " l
.A
~
0.985 0.98 ....
0.975 1.00 10.00 Enrichment (wt% 235U)
Fmed rine formula .lSE-113 yo: 1.00E+OO
- R 2
=7.42E-02 1.025 1.02 1.015 1.01 1.005
'1)
~
1
~
f 0:-995 0.99 0.985 0.98 ...
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0.975 1.00 10.00 Enrichment (wt% 235UI Figure 3: Enrichment Trend Analysis Plots for LEU Calculation Package No. TMI2-EN-RPT-0002, Revision 1 Page 36 of36