ML15222A244

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Enclosure 2 - Attachment 2 - Atkins-NS-DAC-SHN-15-04, Revision 0
ML15222A244
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Site: SHINE Medical Technologies, PROJ0792
Issue date: 07/23/2015
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SHINE Medical Technologies
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Office of Nuclear Reactor Regulation
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SMT-2015-036 Atkins-NS-DAC-SHN-15-04, Rev 0
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ENCLOSURE 2 ATTACHMENT 2 SHINE MEDICAL TECHNOLOGIES, INC.

SHINE MEDICAL TECHNOLOGIES, INC. APPLICATION FOR CONSTRUCTION PERMIT RESPONSE TO REQUEST FOR ADDITIONAL INFORMATION 6B.3-30 ATKINS-NS-DAC-SHN-15-04, REVISION 0 SINGLE PARAMETER SUBCRITICAL LIMITS FOR HOMOGENEOUS 21 WT% 235U URANYL SULFATE, URANIUM OXIDE, AND URANIUM METAL 22 pages follow

Design Analyses and Calculation Table of Contents 1 INTRODUCTION .................................................................................................................................. 4

1.1 BACKGROUND

/PURPOSE ......................................................................................................................... 4 1.2 LIMITS OF APPLICABILITY ......................................................................................................................... 4 2 CONCLUSIONS ................................................................................................................................... 4 3 ANALYSIS/PROCESS METHODOLOGY ........................................................................................... 5 4 COMPUTER CODES USED IN DAC ................................................................................................... 5 5 ASSUMPTIONS & OPEN ITEMS......................................................................................................... 5 5.1 ASSUMPTIONS......................................................................................................................................... 5 5.2 OPEN ITEMS ........................................................................................................................................... 6 6 ACCEPTANCE CRITERIA ................................................................................................................... 6 6.1 BIASES AND UNCERTAINTIES.................................................................................................................... 6 6.2 AREA OF APPLICABILITY (AOA) ................................................................................................................ 7 7 CALCULATIONS.................................................................................................................................. 9 7.1 METHOD DISCUSSION.............................................................................................................................. 9 7.2 EVALUATIONS, ANALYSIS, AND DETAILED CALCULATIONS ........................................................................ 12 8 REFERENCES ................................................................................................................................... 21 APPENDIX 1: REPRESENTATIVE INPUT FILES .................................................................................... 22 Page 3 of 24 Atkins-NS-DAC-SHN-15-04

Design Analyses and Calculation 1 INTRODUCTION 1.1 Background/Purpose The SHINE Medical Technologies project will use uranium sulfate solution as a subcritical neutron fission target to produce 99Mo for medical uses. In addition, the facility will handle uranium metal as a feed material and uranium oxide for recycling uranium during the process. It is important that those who are designing process vessels and material handling equipment know the subcritical limits applicable to the material being processed. This report will provide such information.

1.2 Limits of Applicability The results of this report are only applicable to the material types that have been studied at the enrichment limit assumed.

2 CONCLUSIONS Subcritical limits have been determined as follows:

Table 1: Subcritical Limits for 21 wt% 235U Material type Parameter studied Subcritical limit 3.69 kg U Mass (0.7749 kg 235U) 9.14 liters Volume Uranyl Sulfate (2.41 gallons)

Infinite concentration 53.16 g U/l Infinite cylinder 6.65 in diameter (16.891 cm) 3.59 kg U Mass (0.7539 kg 235U)

Uranium Oxide 7.82 liters Volume (UO2) (2.07 gallons)

Infinite cylinder 6.24 in diameter (15.85 cm) 3.57 kg U Mass (0.7497 kg 235U) 6.96 liters Uranium Metal Volume (1.84 gallons)

Infinite cylinder 5.96 in diameter (15.138 cm)

Page 4 of 24 Atkins-NS-DAC-SHN-15-04

Design Analyses and Calculation 3 ANALYSIS/PROCESS METHODOLOGY This DAC does not model a process. See Section 7.1 for description of the models and calculation methodology.

4 COMPUTER CODES USED IN DAC MCNP 6.1 is a general-purpose Monte Carlo N-Particle code that can be used for neutron, photon, electron, or coupled neutron/photon/electron transport, including the capability to calculate eigenvalues for critical systems (Reference 1).

MCNP 6.1 was run on the Atkins Linux computer cluster. All computers have 64-bit hardware and use the 64-bit version of Linux. Distribution of the calculation jobs among the individual CPUs is controlled by the Sun Grid Engine queue software running on the master Linux computer. Additional Linux execution hosts run calculation jobs at the command of the queue master. MCNP 6.1 has been installed in the read only disk area; the installation has been verified with the execution of the sample problems. This disk is shared with the execution hosts.

Hardware and software used with the Atkins Linux computer cluster is managed with the Atkins NS Systems configuration control.

MCNP models a physical system with a three-dimensional configuration of geometric cells bounded by first and second-degree surfaces and fourth-degree elliptical tori. Each geometric cell contains a material or void as specified by the user to model the physical system. Material characteristics (i.e., cross sections) are represented by point-wise continuous cross-section data. For neutrons, all reactions given in a particular cross-section library (such as ENDF/B-VII) are taken into account. Thermal neutrons are described by the free gas and S(, ) models.

The MCNP neutron data library based on Evaluated Neutron Data File B-VII.1 (ENDF/B-VII.1) is the default for continuous energy neutron transport.

The specific elements used in this evaluation are listed here:

235 U 92235.80c 238 U 92238.80c S 16032.80c H 1001.80c O 8016.80c The light water S(,) correction (lwtr.20t) is used for water.

5 ASSUMPTIONS & OPEN ITEMS 5.1 Assumptions

1. Temperature of all cases is assumed to be 20°C. Higher temperatures will result in lower reactivity due to the increase in neutron absorption due to Doppler broadening of the resonance region within 238U.
2. Solute saturation is assumed to be unlimited. Realistic saturation behavior is ignored in favor of showing the peak reactivity for the various materials regardless of concentration.
3. Uranyl sulfate is modeled assuming no excess acid as a conservative simplification, as excess acid reduces reactivity due to increased neutron absorption and decreased moderation within the solution.
4. Uranium is assumed to be enriched to 21 wt% 235U.

Page 5 of 24 Atkins-NS-DAC-SHN-15-04

Design Analyses and Calculation

5. Uranium dioxide theoretical density is 10.96 g/cc.
6. Uranium metal theoretical density is 19.05 g/cc.
7. Water theoretical density is 0.9982 g/cc.
8. The following atom masses are assumed for the modeled isotopes and molecules.

235 U: 235.04392 g/mole 238 U: 238.05079 g/mole U (21 wt%): 237.42 g/mole S: 32.064388 g/mole O: 15.999 g/mole H: 1.0079 g/mole H2O: 18.0148 g/mole H2SO4: 98.076188 g/mole UO2SO4: 365.478 g/mole UO2: 269.418 g/mole

9. Avogadros number is assumed to be 0.6022 atom-cm2/bn.

5.2 Open Items There are no open items.

6 ACCEPTANCE CRITERIA 6.1 Biases and Uncertainties The methodology and results for the MCNP 6.1 code system validation for its use with the SHINE Medical Technologies applications are documented in Reference 2. 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 processes within the SHINE facility. The bias results demonstrate that the calculated values sufficiently matched the reality of the experiments. The final validation is expressed as an Upper Subcritical Limit (USL) calculated using the statistical accumulation of the experiments bias and bias uncertainty.

The Upper Subcritical Limit (USL) is calculated using the following equation:

USL = 1.0 + Bias - Bias Uncertainty - MOS

where, MOS = Margin of Subcriticality = 0.05 k, and Bias = 0.0025 k (positive bias is set to zero in the equation.)

Bias Uncertainty = 0.0109 k Therefore the USL = 0.9391.

For an acceptable result, the MCNP keff + 2

  • must be less than the USL value.

Page 6 of 24 Atkins-NS-DAC-SHN-15-04

Design Analyses and Calculation 6.2 Area of Applicability (AoA)

The AoA derived in Reference 2 is compared to the calculations performed here in Table 2. All parameters are within the AoA of the MCNP 6.1 validation except for the H/235U ratio. The calculations performed with infinite solutions met the USL at very low uranium concentrations resulting in high ratios. However, the Average Neutron Energy Causing Fission (ANECF) parameter is within the AoA and is a good judge of the validity of the USL to the infinite concentration calculation. Additionally, Reference 2 concludes that the H/235U value characterizes the system neutron moderation only as it is affected by the n-H scatter reaction while the MCNP calculated ANECF is a summation of the effect of all n scatter reactions, and is therefore judged to be a more useful parameter when comparing applications to the validation AoA. Therefore, no additional AoA margin is necessary for the infinite concentration cases.

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Design Analyses and Calculation Table 2: Area of Applicability Summary Area of Applicability from Area of Applicability for Parameter Validation Calculations UO2, UH3, Metal, UO2(NO3)2, Fissile Material UF4, U-ZrH, UO2F2, UxOy, UO2, Metal, UO2SO4 UO2SO4 Fissile Material Form Solid and Solution Solid and Solution H/235U ratio 0 H/235U 1400 45 H/235U 23191 Average Neutron Energy Causing 0.0027 < ANECF < 1.46 0.0044 < ANECF < 0.104 Fission (MeV)

Enrichment 10 to 36 wt.% 235U 21 wt.% 235U None, Water, nitric acid, sulfuric Moderating Materials Water, sulfuric acid acid, Hydrocarbon, CF2 None, Water, Concrete, BeO, Reflecting Materials Hydrocarbon Material, Iron, Water Graphite Boron, Cadmium, Aluminium, Absorber Materials Steel, Stainless Steel, None Hydrocarbon Material Homogeneous and Heterogeneous Geometry Spheres, Hemispheres, Homogeneous Spheres, Cylinders, Cuboids Cylinders Single Units and Arrays 1 The H/235U value of 2319 corresponds to the infinite concentration calculations. The highest ratio for all other systems is 1233 which is well within the Area of Applicability.

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Design Analyses and Calculation 7 CALCULATIONS 7.1 Method Discussion 7.1.1 Geometry Models For determination of subcritical mass and subcritical volume, a simple sphere model was used.

The uranium layer is followed by 12 inches of close-fitting water reflection.

Uranium Reflector For the infinite fissile solution concentration calculation, a cuboid with a dimension of 200 cm on each side was modeled with a reflective boundary condition on all sides to simulate an infinite amount of material.

For the infinite cylinder, the height of the cylinder was modeled as 200 cm with a reflective boundary condition top and bottom.

7.1.2 Material Specification Uranyl sulfate, uranium oxide mixed with water, and uranium metal mixed with water were all modeled in this report. The following equations were used to determine the MCNP number density input. MCNP inputs are noted with italics.

Uranyl Sulfate Uranyl sulfate density is based on an empirical correlation which is specified in Reference 3. No excess acid (molarity = 0, normality = 0) is assumed for conservatism. The temperature is set at 20°C. The following equation was used to determine the uranyl sulfate density:

( + )

= + . ( )

x .

Where:

= ,

= ,

= ,

= ( +/)

Page 9 of 24 Atkins-NS-DAC-SHN-15-04

Design Analyses and Calculation The uranium concentration is specified which allows the uranyl sulfate solution density to be calculated. Then the number densities for all isotopes can be determined using the following equations:

235 U atom density (atoms/bn-cm) = uran_conc/1000

  • 235U_wo / 235U_amu
  • avog 238 U atom density (atoms/bn-cm) = uran_conc/1000
  • 238U_wo / 238U_amu
  • avog U atom density (atoms/bn-cm) = 235U atom density + 238U atom density UO2SO4 density (g/cc) = U atom density/avog
  • UO2SO4_amu H2O density in mix (g/cc) = solution_dens - UO2SO4 density S atom density (atoms/bn-cm) = U atom density O atom density (atoms/bn-cm) = 6 * (U atom density) + (H2O density in mix/H2O_amu)
  • avog H atom density (atoms/bn-cm) = 2 * (H2O density in mix/H2O_amu)
  • avog
where, uran_conc = uranium concentration in g/liter, 235U_wo = mass fraction of 235U in uranium, 238U_wo = mass fraction of 238U in uranium, 235U_amu = atomic mass of 235U, 238U_amu = atomic mass of 238U, UO2SO4_amu = atomic mass of UO2SO4, H2O_amu = atomic mass of H2O.

solution_dens = uranyl sulfate density based on uranium concentration, and avog = Avogadros number.

Uranium Oxide and Water Uranium oxide was modeled as UO2. This molecule has the least number of oxygen atoms per uranium atoms which will result in the highest reactivity when compared to other oxide compounds (ie. UO3, U3O8, etc.). A simple volume additive relation is used to derive the constituent element atom densities assuming a given uranium density within the mixture. The following equations were used to derive the number densities:

Page 10 of 24 Atkins-NS-DAC-SHN-15-04

Design Analyses and Calculation 235 U atom density (atoms/bn-cm) = uran_dens

  • 235U_wo / 235U_amu
  • avog 238 U atom density (atoms/bn-cm) = uran_dens
  • 238U_wo / 238U_amu
  • avog UO2 density in mixture (g/cc) = uran_dens/U_amu
  • UO2_amu H2O density in mixture (g/cc) = (1 - UO2 density in mixture/10.96)
  • 0.9982 O atom density (atoms/bn-cm) = (H2O density in mixture/H2O_amu)
  • avog + (2
  • UO2 density in mixture/UO2_amu)
  • avog H atom density (atoms/bn-cm) = 2 * (H2O density in mixture/H2O_amu)
  • avog
where, uran_dens = uranium density in g/cc, 235U_wo = mass fraction of 235U in uranium, 238U_wo = mass fraction of 238U in uranium, 235U_amu = atomic mass of 235U, 238U_amu = atomic mass of 238U, U_amu = atomic mass of U, UO2_amu = atomic mass of UO2, H2O_amu = atomic mass of H2O.

UO2 density in mixture = uranium dioxide mass density in mixture, H2O density in mixture = water mass density in mixture, and avog = Avogadros number.

Uranium Metal and Water A simple volume additive relation is used to derive the constituent element atom densities assuming a uranium metal density within the mixture. The following equations were used to derive the number densities:

235 U atom density (atoms/bn-cm) = uran_dens

  • 235U_wo / 235U_amu
  • avog 238 U atom density (atoms/bn-cm) = uran_dens
  • 238U_wo / 238U_amu
  • avog H2O density in mixture (g/cc) = (1 - uran_dens/19.05)
  • 0.9982 O atom density (atoms/bn-cm) = (H2O density in mixture/H2O_amu)
  • avog H atom density (atoms/bn-cm) = 2 * (H2O density in mixture/H2O_amu)
  • avog
where, uran_dens = uranium density in g/cc, 235U_wo = mass fraction of 235U in uranium, 238U_wo = mass fraction of 238U in uranium, 235U_amu = atomic mass of 235U, 238U_amu = atomic mass of 238U, H2O_amu = atomic mass of H2O.

H2O density in mixture = water mass density in mixture, and avog = Avogadros number.

Page 11 of 24 Atkins-NS-DAC-SHN-15-04

Design Analyses and Calculation 7.1.3 Optimum Value Methodology For each parameter, a search was performed to find the optimum uranium concentration or density that yields the lowest value. For each uranium concentration, the value at the USL was determined. These values were then compared over the optimum concentration or density range to find the minimum value.

7.2 Evaluations, Analysis, and Detailed Calculations The results of the single parameter calculations are listed in the following sections.

7.2.1 Uranyl Sulfate Subcritical Mass Calculations were performed with uranyl sulfate spheres with a uranium concentration ranging from 150 to 300 gU/l. Two data points were calculated at each concentration; one above and one below the USL. Linear interpolation was used to estimate the uranium mass value for the USL of 0.9391. Table 3 presents the MCNP results and Table 4 shows the minimum subcritical uranium mass for each uranium concentration.

Table 3: Uranyl Sulfate Sphere MCNP Results for Minimum Subcritical Mass Uranium Sphere Sphere Uranium Case Concentration Diameter keff keff+2 Volume Mass (gU/l) (cm) (l) (kg) sphere_sulfate_150_37.2 150 37.2 0.93437 0.00076 0.93589 26.95 4.04 sphere_sulfate_150_37.4 150 37.4 0.93779 0.00070 0.93919 27.39 4.11 sphere_sulfate_200_32.8 200 32.8 0.93691 0.00079 0.93849 18.48 3.70 sphere_sulfate_200_33 200 33 0.93881 0.00072 0.94025 18.82 3.76 sphere_sulfate_225_31.4 225 31.4 0.93494 0.00075 0.93644 16.21 3.65 sphere_sulfate_225_31.6 225 31.6 0.93855 0.00094 0.94043 16.52 3.72 sphere_sulfate_250_30.4 250 30.4 0.93541 0.00077 0.93695 14.71 3.68 sphere_sulfate_250_30.6 250 30.6 0.94087 0.00082 0.94251 15.00 3.75 sphere_sulfate_300_29 300 29 0.93687 0.00078 0.93843 12.77 3.83 sphere_sulfate_300_29.2 300 29.2 0.93912 0.00080 0.94072 13.04 3.91 Table 4: Minimum Subcritical Mass for each Uranyl Sulfate Uranium Concentration Uranium Subcritical Concentration Uranium (gU/l) Mass (kg) 150 4.11 200 3.72 225 3.69 250 3.71 300 3.85 Examination of the Table 4 results shows a subcritical uranium mass limit of 3.69 kg U for uranyl sulfate.

7.2.2 Uranyl Sulfate Subcritical Volume Calculations were performed with uranyl sulfate spheres with a uranium concentration ranging from 600 to 1200 gU/l. Two data points were calculated at each concentration; one above and one below the USL. Linear interpolation was used to estimate the uranium volume value for the Page 12 of 24 Atkins-NS-DAC-SHN-15-04

Design Analyses and Calculation USL of 0.9391. Table 5 presents the MCNP results and Table 6 shows the minimum subcritical uranium volume for each uranium concentration.

Table 5: Uranyl Sulfate Sphere MCNP Results for Minimum Subcritical Volume Uranium Sphere Sphere Case Concentration Diameter keff keff+2 Volume (gU/l) (cm) (l) sphere_sulfate_600_26.2 600 26.2 0.93691 0.00095 0.93881 9.42 sphere_sulfate_600_26.3 600 26.3 0.93931 0.00097 0.94125 9.53 sphere_sulfate_700_25.9 700 25.9 0.93471 0.00089 0.93649 9.10 sphere_sulfate_700_26 700 26 0.93730 0.00092 0.93914 9.20 sphere_sulfate_800_25.9 800 25.9 0.93549 0.00088 0.93725 9.10 sphere_sulfate_800_26 800 26 0.94017 0.00091 0.94199 9.20 sphere_sulfate_900_25.9 900 25.9 0.93343 0.00096 0.93535 9.10 sphere_sulfate_900_26 900 26 0.93831 0.00085 0.94001 9.20 sphere_sulfate_1000_26.1 1000 26.1 0.93720 0.00089 0.93898 9.31 sphere_sulfate_1000_26.2 1000 26.2 0.94093 0.00093 0.94279 9.42 sphere_sulfate_1100_26.4 1100 26.4 0.93711 0.00095 0.93901 9.63 sphere_sulfate_1100_26.5 1100 26.5 0.94104 0.00097 0.94298 9.74 sphere_sulfate_1200_26.5 1200 26.5 0.93548 0.00097 0.93742 9.74 sphere_sulfate_1200_26.6 1200 26.6 0.93740 0.00092 0.93924 9.85 Table 6: Minimum Subcritical Volume for each Uranyl Sulfate Uranium Concentration Uranium Subcritical Concentration Volume (l)

(gU/l) 600 9.43 700 9.20 800 9.14 900 9.18 1000 9.31 1100 9.64 1200 9.85 Examination of the Table 6 results shows a subcritical uranium volume limit of 9.14 liters for uranyl sulfate.

7.2.3 Uranyl Sulfate Infinite Subcritical Concentration Calculations were performed with an infinite amount of uranyl sulfate with a uranium concentration of 53.0 and 53.2 gU/l. Table 7 presents the MCNP results.

Page 13 of 24 Atkins-NS-DAC-SHN-15-04

Design Analyses and Calculation Table 7: Infinite Subcritical Concentration MCNP Results for Uranyl Sulfate Uranium Case Concentration keff keff+2 (gU/l) inf_sulfate_53 53.0 0.93730 0.00020 0.93770 inf_sulfate_53.2 53.2 0.93906 0.00019 0.93944 Linear interpolation of the Table 7 results shows an infinite subcritical uranium concentration limit of 53.16 gU/l for uranyl sulfate.

7.2.4 Uranyl Sulfate Subcritical Cylinder Diameter Calculations were performed with uranyl sulfate cylinders of infinite height with a uranium concentration ranging from 600 to 1100 gU/l. Two data points were calculated at each concentration; one above and one below the USL. Linear interpolation was used to estimate the cylinder diameter value for the USL of 0.9391. Table 8 presents the MCNP results and Table 9 shows the minimum subcritical cylinder diameter for each uranium concentration.

Table 8: Uranyl Sulfate Cylinder MCNP Results for Minimum Cylinder Diameter Uranium Cylinder Case Concentration Diameter keff keff+2 (gU/l) (in) cyl_sulfate_600_6.75 600 6.75 0.93662 0.00085 0.93832 cyl_sulfate_600_6.8 600 6.8 0.94178 0.00087 0.94352 cyl_sulfate_700_6.65 700 6.65 0.93542 0.00086 0.93714 cyl_sulfate_700_6.7 700 6.7 0.93828 0.00079 0.93986 cyl_sulfate_800_6.64 800 6.64 0.93523 0.00080 0.93683 cyl_sulfate_800_6.65 800 6.65 0.93784 0.00097 0.93978 cyl_sulfate_850_6.65 850 6.65 0.93584 0.00090 0.93764 cyl_sulfate_850_6.66 850 6.66 0.93837 0.00088 0.94013 cyl_sulfate_900_6.64 900 6.64 0.93706 0.00084 0.93874 cyl_sulfate_900_6.66 900 6.66 0.93781 0.00081 0.93943 cyl_sulfate_1000_6.65 1000 6.65 0.93466 0.00072 0.93610 cyl_sulfate_1000_6.7 1000 6.7 0.93978 0.00101 0.94180 cyl_sulfate_1100_6.7 1100 6.7 0.93492 0.00083 0.93658 cyl_sulfate_1100_6.75 1100 6.75 0.94029 0.00081 0.94191 Table 9: Minimum Subcritical Cylinder Diameter for each Uranyl Sulfate Uranium Concentration Uranium Cylinder Concentration Diameter (gU/l) (in) 600 6.76 700 6.69 800 6.65 850 6.66 900 6.65 1000 6.68 1100 6.72 Examination of the Table 9 results shows a subcritical cylinder diameter limit of 6.65 inches for uranyl sulfate.

Page 14 of 24 Atkins-NS-DAC-SHN-15-04

Design Analyses and Calculation 7.2.5 Uranium Oxide Subcritical Mass Calculations were performed with uranium dioxide spheres with a uranium density ranging from 0.15 to 0.35 gU/cc. Two data points were calculated at each density; one below and one above the USL. Linear interpolation was used to estimate the uranium mass value for the USL of 0.9391. Table 10 presents the MCNP results and Table 11 shows the minimum subcritical uranium mass for each uranium density.

Table 10: Uranium Dioxide Sphere MCNP Results for Minimum Subcritical Mass Uranium Sphere Uranium Case Density Diameter keff keff+2 Mass (gU/cc) (cm) (kg) sphere_oxide_0.15_37 0.15 37 0.93333 0.00062 0.93457 3.98 sphere_oxide_0.15_37.5 0.15 37.5 0.94027 0.00073 0.94173 4.14 sphere_oxide_0.2_32.6 0.2 32.6 0.93531 0.00084 0.93699 3.63 sphere_oxide_0.2_32.7 0.2 32.7 0.93828 0.00080 0.93988 3.66 sphere_oxide_0.225_31.2 0.225 31.2 0.93680 0.00077 0.93834 3.58 sphere_oxide_0.225_31.3 0.225 31.3 0.93800 0.00076 0.93952 3.61 sphere_oxide_0.25_30.1 0.25 30.1 0.93458 0.00084 0.93626 3.57 sphere_oxide_0.25_30.2 0.25 30.2 0.93872 0.00089 0.94050 3.61 sphere_oxide_0.3_28.6 0.3 28.6 0.93457 0.00080 0.93617 3.67 sphere_oxide_0.3_28.7 0.3 28.7 0.93759 0.00086 0.93931 3.71 sphere_oxide_0.35_27.6 0.35 27.6 0.93652 0.00077 0.93806 3.85 sphere_oxide_0.35_27.7 0.35 27.7 0.93830 0.00069 0.93968 3.89 Table 11: Minimum Subcritical Mass for each Uranium Dioxide Uranium Density Uranium Subcritical Density Uranium (gU/cc) Mass (kg) 0.15 4.08 0.2 3.65 0.225 3.60 0.25 3.59 0.3 3.71 0.35 3.88 Examination of the Table 11 results shows a subcritical uranium mass limit of 3.59 kg U for uranium dioxide.

7.2.6 Uranium Oxide Subcritical Volume Calculations were performed with uranium dioxide spheres with a uranium density ranging from 0.8 to 1.4 gU/cc. Seven data points were calculated at each density. Linear interpolation was used to estimate the uranium volume value for the USL of 0.9391. Table 12 presents the MCNP results and Table 13 shows the minimum subcritical volume for each uranium density.

Page 15 of 24 Atkins-NS-DAC-SHN-15-04

Design Analyses and Calculation Table 12: Uranium Dioxide Sphere MCNP Results for Minimum Subcritical Volume Uranium Sphere Sphere Case Density Diameter keff keff+2 Volume (gU/cc) (cm) (l) sphere_oxide_0.8_24.8 0.8 24.8 0.93579 0.00088 0.93755 7.99 sphere_oxide_0.8_24.85 0.8 24.85 0.93798 0.00083 0.93964 8.03 sphere_oxide_0.85_24.75 0.85 24.75 0.93594 0.00075 0.93744 7.94 sphere_oxide_0.85_24.8 0.85 24.8 0.93742 0.00093 0.93928 7.99 sphere_oxide_0.9_24.65 0.9 24.65 0.93366 0.00095 0.93556 7.84 sphere_oxide_0.9_24.7 0.9 24.7 0.93783 0.00099 0.93981 7.89 sphere_oxide_1_24.65 1 24.65 0.93696 0.00094 0.93884 7.84 sphere_oxide_1_24.7 1 24.7 0.93802 0.00094 0.93990 7.89 sphere_oxide_1.05_24.6 1.05 24.6 0.93467 0.00096 0.93659 7.79 sphere_oxide_1.05_24.65 1.05 24.65 0.93796 0.00080 0.93956 7.84 sphere_oxide_1.1_24.6 1.1 24.6 0.93646 0.00091 0.93828 7.79 sphere_oxide_1.1_24.65 1.1 24.65 0.93812 0.00090 0.93992 7.84 sphere_oxide_1.2_24.6 1.2 24.6 0.93676 0.00081 0.93838 7.79 sphere_oxide_1.2_24.65 1.2 24.65 0.93778 0.00097 0.93972 7.84 sphere_oxide_1.3_24.7 1.3 24.7 0.93564 0.00088 0.93740 7.89 sphere_oxide_1.3_24.75 1.3 24.75 0.93735 0.00097 0.93929 7.94 sphere_oxide_1.4_24.75 1.4 24.75 0.93342 0.00092 0.93526 7.94 sphere_oxide_1.4_24.8 1.4 24.8 0.93749 0.00095 0.93939 7.99 Table 13: Minimum Subcritical Volume for each Uranium Dioxide Uranium Density Uranium Subcritical Density Volume (l)

(gU/cc) 0.8 8.02 0.9 7.98 1 7.88 1.05 7.84 1.1 7.82 1.2 7.82 1.3 7.93 1.4 7.98 Examination of the Table 13 results shows a subcritical uranium volume limit of 7.82 liters for uranium oxide.

7.2.7 Uranium Oxide Subcritical Cylinder Diameter Calculations were performed with uranium dioxide cylinders of infinite height with a uranium density ranging from 0.8 to 1.5 gU/cc. Two data points were calculated at each density; one below and one above the USL. Linear interpolation was used to estimate the cylinder diameter Page 16 of 24 Atkins-NS-DAC-SHN-15-04

Design Analyses and Calculation value for the USL of 0.9391. Table 14 presents the MCNP results and Table 15 shows the minimum subcritical cylinder diameter for each uranium density.

Table 14: Uranium Dioxide Cylinder MCNP Results for Minimum Cylinder Diameter Uranium Cylinder Case Density Diameter keff keff+2 (gU/cc) (in) cyl_oxide_0.8_6.3 0.8 6.3 0.93422 0.00094 0.93610 cyl_oxide_0.8_6.35 0.8 6.35 0.93815 0.00092 0.93999 cyl_oxide_0.9_6.25 0.9 6.25 0.93414 0.00086 0.93586 cyl_oxide_0.9_6.3 0.9 6.3 0.93946 0.00080 0.94106 cyl_oxide_1_6.25 1 6.25 0.93583 0.00078 0.93739 cyl_oxide_1_6.3 1 6.3 0.94183 0.00077 0.94337 cyl_oxide_1.1_6.2 1.1 6.2 0.93412 0.00088 0.93588 cyl_oxide_1.1_6.25 1.1 6.25 0.93790 0.00085 0.93960 cyl_oxide_1.2_6.2 1.2 6.2 0.93341 0.00077 0.93495 cyl_oxide_1.2_6.25 1.2 6.25 0.93847 0.00091 0.94029 cyl_oxide_1.3_6.2 1.3 6.2 0.93296 0.00096 0.93488 cyl_oxide_1.3_6.25 1.3 6.25 0.93837 0.00087 0.94011 cyl_oxide_1.4_6.25 1.4 6.25 0.93624 0.00091 0.93806 cyl_oxide_1.4_6.3 1.4 6.3 0.94098 0.00086 0.94270 cyl_oxide_1.5_6.25 1.5 6.25 0.93575 0.00094 0.93763 cyl_oxide_1.5_6.3 1.5 6.3 0.93930 0.00080 0.94090 Table 15: Minimum Subcritical Cylinder Diameter for each Uranium Dioxide Density Uranium Cylinder Density Diameter (gU/cc) (in) 0.8 6.34 0.9 6.28 1.0 6.26 1.1 6.24 1.2 6.24 1.3 6.24 1.4 6.26 1.5 6.27 Examination of the Table 15 results shows a subcritical cylinder diameter limit of 6.24 inches for uranium oxide.

7.2.8 Uranium Metal Subcritical Mass Calculations were performed with uranium metal spheres with a uranium density ranging from 0.10 to 0.30 gU/cc. Two data points were calculated at each density; one below and one above the USL. Linear interpolation was used to estimate the uranium mass value for the USL of Page 17 of 24 Atkins-NS-DAC-SHN-15-04

Design Analyses and Calculation 0.9391. Table 16 presents the MCNP results and Table 17 shows the minimum subcritical uranium mass for each uranium density.

Table 16: Uranium Metal Sphere MCNP Results for Minimum Subcritical Mass Uranium Sphere Uranium Case Density Diameter keff keff+2 Mass (gU/cc) (cm) (kg) sphere_metal_0.1_49 0.1 49 0.93316 0.00064 0.93444 6.16 sphere_metal_0.1_50 0.1 50 0.94189 0.00061 0.94311 6.54 sphere_metal_0.15_37.3 0.15 37.3 0.93700 0.00064 0.93828 4.08 sphere_metal_0.15_37.4 0.15 37.4 0.93850 0.00067 0.93984 4.11 sphere_metal_0.2_32.6 0.2 32.6 0.93682 0.00070 0.93822 3.63 sphere_metal_0.2_32.7 0.2 32.7 0.93876 0.00074 0.94024 3.66 sphere_metal_0.225_31.2 0.225 31.2 0.93557 0.00080 0.93717 3.58 sphere_metal_0.225_31.3 0.225 31.3 0.94079 0.00079 0.94237 3.61 sphere_metal_0.25_30 0.25 30 0.93379 0.00080 0.93539 3.53 sphere_metal_0.25_30.1 0.25 30.1 0.93775 0.00082 0.93939 3.57 sphere_metal_0.3_28.5 0.3 28.5 0.93648 0.00086 0.93820 3.64 sphere_metal_0.3_28.6 0.3 28.6 0.93835 0.00086 0.94007 3.67 Table 17: Minimum Subcritical Mass for each Uranium Metal Density Uranium Subcritical Density Uranium (gU/cc) Mass (kg) 0.10 6.37 0.15 4.09 0.20 3.64 0.225 3.59 0.25 3.57 0.30 3.65 Examination of the Table 17 results shows a subcritical uranium mass limit of 3.57 kg U for uranium metal.

7.2.9 Uranium Metal Subcritical Volume Calculations were performed with uranium metal spheres with a uranium density ranging from 0.8 to 2.0 gU/cc. Two data points were calculated at each density; one below and one above the USL. Linear interpolation was used to estimate the volume for the USL of 0.9391. Table 18 presents the MCNP results and Table 19 shows the minimum subcritical volume for each uranium density.

Page 18 of 24 Atkins-NS-DAC-SHN-15-04

Design Analyses and Calculation Table 18: Uranium Metal Sphere MCNP Results for Minimum Subcritical Volume Uranium Sphere Sphere Case Density Diameter keff keff+2 Volume (gU/cc) (cm) (l) sphere_metal_0.8_24.2 0.8 24.2 0.93353 0.00087 0.93527 7.42 sphere_metal_0.8_24.3 0.8 24.3 0.93849 0.00094 0.94037 7.51 sphere_metal_0.9_24.1 0.9 24.1 0.93718 0.00085 0.93888 7.33 sphere_metal_0.9_24.2 0.9 24.2 0.93958 0.00097 0.94152 7.42 sphere_metal_1_23.9 1 23.9 0.93542 0.00091 0.93724 7.15 sphere_metal_1_24 1 24 0.93791 0.00090 0.93971 7.24 sphere_metal_1.1_23.9 1.1 23.9 0.93673 0.00097 0.93867 7.15 sphere_metal_1.1_24 1.1 24 0.94201 0.00082 0.94365 7.24 sphere_metal_1.2_23.7 1.2 23.7 0.93450 0.00097 0.93644 6.97 sphere_metal_1.2_23.8 1.2 23.8 0.93861 0.00081 0.94023 7.06 sphere_metal_1.3_23.7 1.3 23.7 0.93462 0.00090 0.93642 6.97 sphere_metal_1.3_23.8 1.3 23.8 0.94058 0.00093 0.94244 7.06 sphere_metal_1.4_23.7 1.4 23.7 0.93557 0.00090 0.93737 6.97 sphere_metal_1.4_23.8 1.4 23.8 0.93978 0.00102 0.94182 7.06 sphere_metal_1.5_23.7 1.5 23.7 0.93603 0.00084 0.93771 6.97 sphere_metal_1.5_23.72 1.5 23.72 0.93744 0.00093 0.93930 6.99 sphere_metal_1.6_23.6 1.6 23.6 0.93419 0.00090 0.93599 6.88 sphere_metal_1.6_23.7 1.6 23.7 0.93749 0.00094 0.93937 6.97 sphere_metal_1.7_23.7 1.7 23.7 0.93651 0.00090 0.93831 6.97 sphere_metal_1.7_23.8 1.7 23.8 0.94007 0.00100 0.94207 7.06 sphere_metal_1.8_23.7 1.8 23.7 0.93597 0.00097 0.93791 6.97 sphere_metal_1.8_23.8 1.8 23.8 0.93924 0.00097 0.94118 7.06 sphere_metal_1.9_23.8 1.9 23.8 0.93706 0.00087 0.93880 7.06 sphere_metal_1.9_23.9 1.9 23.9 0.94004 0.00101 0.94206 7.15 sphere_metal_2_23.7 2 23.7 0.93426 0.00093 0.93612 6.97 sphere_metal_2_23.8 2 23.8 0.93827 0.00091 0.94009 7.06 Table 19: Minimum Subcritical Volume for each Uranium Metal Uranium Density Uranium Subcritical Density Volume (l)

(gU/cc) 0.8 7.49 0.9 7.34 1 7.22 1.1 7.16 Page 19 of 24 Atkins-NS-DAC-SHN-15-04

Design Analyses and Calculation Uranium Subcritical Density Volume (l)

(gU/cc) 1.2 7.03 1.3 7.01 1.4 7.00 1.5 6.99 1.6 6.96 1.7 6.99 1.8 7.00 1.9 7.07 2 7.04 Examination of the Table 19 results shows a subcritical uranium volume limit of 6.96 liters for uranium metal.

7.2.10 Uranium Metal Subcritical Cylinder Diameter Calculations were performed with uranium metal cylinders of infinite height with a uranium density ranging from 1.2 to 2.4 gU/cc. Two data points were calculated at each density; one below and one above the USL. Linear interpolation was used to estimate the cylinder diameter value for the USL of 0.9391. Table 20 presents the MCNP results and Table 21 shows the minimum subcritical cylinder diameter for each uranium density.

Table 20: Uranium Metal Cylinder MCNP Results for Minimum Cylinder Diameter Uranium Cylinder Case Density Diameter keff keff+2 (gU/cc) (in) cyl_metal_1.2_6 1.2 6 0.93724 0.00090 0.93904 cyl_metal_1.2_6.02 1.2 6.02 0.93918 0.00082 0.94082 cyl_metal_1.4_5.96 1.4 5.96 0.93624 0.00090 0.93804 cyl_metal_1.4_5.98 1.4 5.98 0.93865 0.00094 0.94053 cyl_metal_1.6_5.94 1.6 5.94 0.93684 0.00093 0.93870 cyl_metal_1.6_5.96 1.6 5.96 0.93821 0.00090 0.94001 cyl_metal_1.8_5.96 1.8 5.96 0.93747 0.00071 0.93889 cyl_metal_1.8_5.98 1.8 5.98 0.94005 0.00089 0.94183 cyl_metal_2_5.94 2 5.94 0.93390 0.00090 0.93570 cyl_metal_2_5.96 2 5.96 0.93813 0.00090 0.93993 cyl_metal_2.2_5.96 2.2 5.96 0.93610 0.00070 0.93750 cyl_metal_2.2_5.98 2.2 5.98 0.93820 0.00090 0.94000 cyl_metal_2.4_5.98 2.4 5.98 0.93643 0.00072 0.93787 cyl_metal_2.4_6 2.4 6 0.93821 0.00084 0.93989 Page 20 of 24 Atkins-NS-DAC-SHN-15-04

Design Analyses and Calculation Table 21: Minimum Subcritical Cylinder Diameter for each Uranium Metal Density Uranium Cylinder Density Diameter (gU/cc) (in) 1.2 6.00 1.4 5.97 1.6 5.95 1.8 5.96 2.0 5.96 2.2 5.97 2.4 5.99 Examination of the Table 21 results shows a subcritical cylinder diameter limit of 5.96 in. for uranium metal.

8 REFERENCES

1. MCNP6 USER MANUAL, LA-CP-13-00634, Rev. 0, Los Alamos National Laboratory, May 2013.
2. Revolinski, S., MCNP 6.1 Validation with Continuous Energy ENDF/B-VII.1 Cross Sections for SHINE Medical Technologies, Atkins-NS-DAC-SHN-15-03, Rev. 1, June 2015.
3. Glunz, H., V and V Report: Uranyl Sulfate Solution Densities, NSA-TR-SHN-12-03, Rev. 1, February 2012.

Page 21 of 24 Atkins-NS-DAC-SHN-15-04

Design Analyses and Calculation APPENDIX 1: REPRESENTATIVE INPUT FILES Sphere Model All sphere model inputs are a variation of the model described in this input file, with case descriptive information, sphere radii and material #1 changed as appropriate.

Uranyl Sulfate Sphere at 150 g/l, 37.2 cm dia c

c Uranium Concentration = 150 c Acid molarity = 0 c Soln temperautre = 20 c Sphere diameter = 37.2 c Sphere volume = 26954 c Sphere mass = 4043.1 c

c cells 1 1 -1.2022 -10 imp:n=1 2 15 -0.9982 -20 10 imp:n=1 3 0 20 imp:n=0 c surfaces 10 so 18.6 20 so 49.08 c Data kcode 5000 1.0 100 300 ksrc 0 0 0 c materials c 150 g/L U c Density (g/cm3): 1.2022 m1 92235.80c 8.0705e-05 92238.80c 2.9977e-04 16032.80c 3.6153e-04 16033.80c 2.8536e-06 16034.80c 1.6018e-05 16036.80c 7.6095e-08 8016.80c 3.4751e-02 1001.80c 6.4937e-02 mt1 lwtr.20t c Water (0.9982 g/cc) m15 1001.80c 2 8016.80c 1 mt15 lwtr.20t Page 22 of 24 Atkins-NS-DAC-SHN-15-04

Design Analyses and Calculation Infinite Concentration Model All infinite concentration inputs are a variation of the model described in this input file, with case descriptive information and material #1 changed as appropriate.

Uranyl Sulfate Sphere at 53 g/l, 0 cm dia c

c Uranium Concentration = 53 c Acid molarity = 0 c Soln temperature = 20 c

c cells 1 1 -1.0707 -10 11 -12 13 -14 15 imp:n=1 3 0 #1 imp:n=0 c surfaces

  • 10 px 100
  • 11 px -100
  • 12 py 100
  • 13 py -100
  • 14 pz 100
  • 15 pz -100 c Data kcode 5000 1.0 100 300 ksrc 0 0 0 c materials c 53 g/L U c Density (g/cm3): 1.0707 m1 92235.80c 2.8516e-05 92238.80c 1.0592e-04 16032.80c 1.2774e-04 16033.80c 1.0083e-06 16034.80c 5.6597e-06 16036.80c 2.6887e-08 8016.80c 3.3869e-02 1001.80c 6.6126e-02 mt1 lwtr.20t Page 23 of 24 Atkins-NS-DAC-SHN-15-04

Design Analyses and Calculation Infinite Cylinder Model All infinite cylinder inputs are a variation of the model described in this input file, with case descriptive information, cylinder radii and material #1 changed as appropriate.

Uranyl Sulfate Cylinder at 1000 g/l, 6.7 in dia c

c Uranium Concentration = 1000 c Soltn Dens = 2.3408 c Excess acid (M) = 0 c Temperature (C) = 20 c Cylinder diameter (in) = 6.7 c

c cells 1 1 -2.3408 12 14 imp:n=1 2 15 -0.9982 -20 10 -12 14 imp:n=1 3 0 (20:12:-14) imp:n=0 c surfaces 10 cz 8.509

  • 12 pz 100
  • 14 pz -100 20 cz 38.989 c Data kcode 5000 1.0 100 300 ksrc 0 0 0 c materials c 1000 g/L U c Density (g/cm3): 2.3408 m1 92235.80c 5.3804e-04 92238.80c 1.9985e-03 16032.80c 2.4102e-03 16033.80c 1.9024e-05 16034.80c 1.0679e-04 16036.80c 5.0730e-07 8016.80c 4.2008e-02 1001.80c 5.3578e-02 mt1 lwtr.20t c Water (0.9982 g/cc) m15 1001.80c 2 8016.80c 1 mt15 lwtr.20t Page 24 of 24 Atkins-NS-DAC-SHN-15-04
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